TeasV Math, TEAS Math
Order of Operations - Rules - What to do first?
"PEMDAS" Parentheses, Exponents, Multiplication and Division (Left to Right) and Addition and Subtraction (Left to Right)
When solving an application problem involving percentages, refer to the statement
"What percent of a whole is the part
Written statements read for percents
"What percent of a whole is the part"
subtraction
"decreased by", "less than," or "less"
addition
"increased by", "more than" & "total"
irrational #'s
#'s that cannot be written as fractions (square roots, cube roots)
Alfred wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he receive?
$1,200
Mrs. Simpson is picking up an order of drug "T" #100 tablets which costs her $122.00. While you're ringing up her order, she asks "How much does each tablet cost?"
$1.22
The selling price for a particular prescription is $12.35 and the patient qualifies for a 10% discount. How much will the patient pay for this prescription after the discount?
$11.12
The cost of 100 tablets of a particular drug is $320.00. The percent mark up on prescriptions is 15%. What would be the retail price of 30 tablets of the drug?
$110.40
In a writing competition, the first place winner receives ½ of the prize money. The second runner up receives ¼ of what the winner won. What was the total amount of prize money distributed if the winner receives $6,000?
$12,000
The sales price of a car is $12,590, which is 20% off the original price. What is the original price?
$12,590 = Original Price - 0.2*Original Price = 0.8*Original Price, Original Price = $12,590/0.8 = $15,737.50
A discount store takes 50% off of the retail price of a desk. For the store's holiday sale, it takes an additional 20% off of all furniture. The desk's retail price was $320. How much is the desk on sale for during the holiday sale?
$128
You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back?
$13.40
you need to purchase a textbook for nursing school. the book costs $80.00, and the sales tax is 8.25%. you have $100. how much change will you receive back?
$13.40
Your supervisor instructs you to purchase 240 pens and 6 staplers for the nurse's station. Pens are purchased in sets of 6 for $2.35 per pack. Staplers are sold in sets of 2 for 12.95. How much will purchasing these products cost?
$132.85
you are throwing a huge surprise birthday party for your best friend. you need to purchase 240 cans of soda and 6 veggie platters for your guests. soda cans are purchased in sets of 6 for $2.35 per pack. veggie platters are sold in sets of 2 for $12.95. how much will purchasing these products cost?
$132.85
A prescription costs $65.28 and the patient pays with $80.00. How much money do you give the patient back?
$14.72
what will it cost to carpet a room with indoor/outdoor carpet if the room is 10 ft wide and 12 ft long? the carpet costs $12.51 per sq yard.
$166.80
Jimmy made a 15% profit on the sale of a custom designed boat, and the original cost of the boat was $15,000. The boat sold for how much?
$17,250.00
Simon arrived at work at 8:15 A.M. and left work at 10: 30 P.M. If Simon gets paid by the hour at a rate of $10 and time and ½ for any hours worked over 8 in a day. How much did Simon get paid?
$173.75
the sales price of a truck is $14,590, which is 20% off the original price. What is the original price?
$18,247.50
If a discount of 25% off the retail price of a desk saves Mark $45, how much did he pay for the desk? A. $145 B. $160 C. $180 D. $210 E. $215
$180
if a discount of 25% off the retail price of a desk saves Mark $45, what was desk's original price?
$180
If edging cost $2.32 per 12-inch stone, and you want a double layer of edging around your flower bed that is 6 yards by 1 yard. How much will edging you flower bed cost?
$194.88
A computer is on sale for $1600, which is a 20% discount off the regular price. What is the regular price?
$2000
Jill earns $120 for 8 hours of work. At the same pay rate, how much will she earn for 15 hours of work?
$225
What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile cost $8.91 per square yard?
$237.60
A lamp is marked with a sale price of $23.80, which is 15% off of the regular price. What is the regular price?
$28
A car dealer sells a SUV for $39,000, which represents a 25% profit over the cost. What was the cost of the SUV to the dealer?
$31,200
a car dealer sells an SUV for $39,000, which represents a 25% profit over the cost. what was the actual cost of the SUV to the dealer?
$31,200
After having to pay increased income taxes this year, Edmond has to sell his BMW. Edmond bought the car for $49,000, but he sold it for a 20% loss. What did Edmond sell the car for?
$39,200
Over the course of a week, Fred spent $28.49 on lunch. What was the average cost per day?
$4.07
Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $5.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $7.89 on lunch. What was her average daily cost?
$4.08
An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost?
$400
You purchase a car making a down payment of $3,000 and 6 monthly payments of $225. How much have you paid so far for the car?
$4350
Sue receives a base salary of $90 weekly plus a 12% commission on all sales. Sue had $3,000 in sales this week. How much did she make total?
$450
If fifty tablets of Biaxin 500 mg cost $25.00, how much would ten tablets of Biaxin 500 mg cost?
$5.00
Sarah has a 20 dollar bill and a 5 dollar bill. If she purchases two items, one for $11.23 and the other for $8.32, then how much money does she have left over?
$5.45
John pays $650 in property tax. What is the assessed value of his property if property taxes are 1.2% of assessed value?
$54,166.67
A mattress store sells their stock for 15% off of retail. If someone pays cash, they take an additional 10% off of the discounted price. If a mattress's retail price is $750, what is the price after the store discount and the cash discount?
$573.75
Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him?
$670 = Cost + 0.35*Cost = 1.35*Cost, Cost = $670/1.35 = $496.30
After purchasing a flat screen television for $750, John realizes that he got a great deal on it and wishes to sell it for a 15% profit. What should his asking price be for the television?
$862.50
The retail prices for two prescriptions are $26.70 and $65.35. After receiving a 5% discount, the patient pays?
$87.45
Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make?
$90
The electric company charges 3 cents per kilowatt-hour. George used 2800 kilowatt-hours in April, 3200 kilowatt-hours in May, and 3600 kilowatt-hours in June. What was his average cost of electricity for the 3 months?
$96
Find what percentage of some number another number is....(what percent of 40 is 8?)
%=P/W
if [2k +4]/8 = 2, which of the following values of k satisfies this equation?
(-10, 6)
[2r + 1] - 10 = 13, which of the following values of r satisfies the given equation?
(-12, 11)
2 - 3 [4n] = 26. which of the following correctly gives us the value of n?
(-2, 2)
Steps for solving percent problems
(1) Change the written statement into a mathematical equation -"of" translate into multiply -"is" translates into equal -decimal form of the percent should be used in the equation (2) Solve for the unknown quantity (3) Rewrite the statement
2 Different methods that convert Fractions to Percents
(1) Convert the fraction to a decimal (2) Convert the decimal to a percent
2 Different methods that convert Fractions to Decimals
(1) Divide the numerator by the denominator (works for all fractions) (2) Works only for fractions whose denominators are power of 10 -the numerators of the fractions expressed become the digits in the decimal forms of the numbers and the numbers of zeros in the denominators determine the placement of the decimal points *if fraction had a denominator of, the decimal form would be 1 decimal place
Word problems can be solved using the following steps
(1) Read the Problem carefully (2) Determine what is being asked (3) Underline important words, numbers, and keywords (4) Set up the problem (5) Solve the problem
Word Problems can be solved using the following steps
(1) Read the problem carefully (2) Determine what is being asked (3)Read the problem & underline important things (4) Set up the problem (5) Solve the problem (6) Check your answer
Convert Percents to Fractions
(1) Remove the percent symbols (2) Write the number from step in the numerator of the fraction and write 100 in the denominator (3) Simplify the fraction
Process for multiplying decimals is as follows:
(1) Set up the problem as if the numbers are whole numbers (2) Multiply the numbers (3) Once multiplication is done, count the total number of decimals in the factors (4) Start from the far right end of the product, count back (to the left) the number of decimal places (5) Put the decimal point in the spot
An equation can be solved by
(1) Use the distributive property to remove parentheses (2) If there are fraction present, remove them by multiplying each term by the LCD (3) Use the addition principle to move like terms together on both sides of equation (4) Use the multiplication principle to isolate the variable by multiplying both sides of the equation by the reciprocal of the coefficient of the variable (5) Check the solution
To change Roman Numerals to Arabic
(1) Write from Left to Right as a sum (2) Begin with the largest Possible Value (3) When I, X, or C, is used to the left of a larger value, subtract its value from the larger value
To change Arabic Numerals to Roman Numerals
(1) Write from left to right (2) Take each place value & change to a Roman numeral (3) I,X,C may be written 2 or 3 times in a row as long as they are not followed by a larger value (4) Use I,X & C to the left of larger values to indicate subtraction from larger values (5) V,L, D are never used to the left of a larger value (6) V, L, D are never used more than one time
Process for dividing decimals is as follows:
(1) set up the problem to be an equivalent problem in which the divisor (b in a/b) is a whole number by moving the decimal point in the dividend (a in a/b) the same number of places that the decimal point is moved in the divisor (2) Performing long division, place the decimal point in the quotient directly above the decimal point in the dividend (3) Divide the Equation
if [3x +2] = 5, which of the following options give us the correct values of x?
(1, -7/3)
simplify binomials by FOIL
(3x+5)(x-1)= 3x^2-3x+5x-5= 3x^2 +2x - 5
Michelle wants to expand her flowerbed by increasing the length and width each by 2 ft. What will the new area of the flowerbed be, if L and W represent the original dimensions of the flowerbed's length and width?
(L+2) (W+2)
Calculate Percent Increase
(New Value - Original Value) / Original Value * 100
Calculate Percent Decrease
(Original Value - New Value) / Original Value * 100
area of a trapezoid
(average of parallel sides)xheight=area
area of a parallelogram
(base)(height)=area
Using scaling, very long distances can be scaled down to very small lengths that will fit on paper, such as a map
(ex) 1 inch may represent 10 miles
Not all roots are irrational
(ex) square root of nine = 3
area of a rectangle
(length)x(width)=area
Interest equals
(principle * rate * time) / 100%
Convert from Celsius to Fahrenheit
(°C × 9/5) + 32 = °F
Convert from Fahrenheit to Celsius
(°F - 32) x 5/9 = °C
Income and expenses and profit
+ income -expenses=profit
+3m + 7 = 5
- 2/3
[x-n] < a
- a < [x-n] < a
Statements and sentences contain verbs such as
- is, was, or because -symbols such as =, >, <, >, <
subtracting integers
- subtracting a positive is the same as adding a negative - subtracting a negative is the same as adding a positive
In order to solve an absolute value equation, |x-n| equals
- x-n when x-n is positive - - (x-n) when x-n is negative
Solve the following equation for A : 2A/3 = 8 + 4A
-2.4
-32 + 7 equals:
-25
what is the result of the following expression? (3/4 + 1/5) - (2/3 + 3/2) =
-73/60
-37 + -47 equals:
-84
To determine whether one decimal is greater than another decimal
-Compare the digits in each of the place values -Beginning with the digit in the greatest place value -Determine which number has the greatest value -If the two values are the same, then look at the digit in the the next greatest value and compare
To compare Fraction & Decimals together, either
-Convert all fraction to decimals -Or Convert all decimals to fractions
Convert Percent to Decimals
-Converting a percent to a decimal is a process of dividing by 100 -Converting a percent to a decimal is to remove the % symbol and move the decimal point left two places
To Divide Fractions
-First convert any mixed numbers into improper fractions -Keep the first fraction as it is written, but change the division sign to a multiplication sign, & flip the second fraction (put the numerator in the denominator & the original denominator in the numerator) -Simplify the factors in the numerator with factors in the denominator -Finally, multiply the numerators together & the denominators together
Ratios can be written as
-Fractions -Colons (4:5) -Words (ration 4 to 5)
To balance, or reconcile, a checking or saving account, first
-Group the deposits & add them together, then group the checks, & add them together -Next, add the deposits to the previous balance & subtract the checks from the result -Finally, subtract the service charge & add the interest
3 Common types of Graphs
-Line graph -Bar graphs -Circle graphs
Convert Decimals to Percents
-Multiply the decimal by 100 and add the % symbol -Move the decimal point right two place and add the % symbol
When setting up a proportion, the
-Numerators of both ratios must be in the same units -Denominators of both ratios must be in the same units
To convert from Decimal to Fractions
-The decimal number expressed becomes the numerator of the fraction -The number of decimal places to the right of the decimal determines the value of the denominator -If the decimal form of a number only had one decimal place, then the number would be divided by 10
Use the method called finding cross products to solve the equation; this means
-The numerator of the ratio on the left side of the proportion is multiplied by the denominator of the ratio on the right side of the proportion -Same with the other side
|x-n| < a
-a < x - n < a
|x-n| < a
-a < x - n <a
[x-n] is less than or equal to a
-a is less than or equal to [x-n] which is less than or equal to a
/x-n/<or equal to a
-a< or equal to x-n < or equal to a
/x-n/<a
-a<x-n<a
Measurement tools for Volume
-beakers -graduated cylinder -measuring cups -pipettes -measuring spoons
To multiply fractions
-first convert any mixed numbers into improper fractions -then, simplify or reduce factors in the numerator with factors in the denominator -finally, multiply the numerators together & the denominators together
Steps for PEDMAS
-first, perform operation in parentheses -work on the innermost set of parentheses first; then work outwards -second, simplify any exponents -third, complete the multiplication & division from left to right -fourth, complete addition & subtraction left to right
Length/ Height units of measurements
-inches -feet -yards -miles -meters
FOIL means to
-multiply the first term within each set of parentheses first -Then multiply the outer terms -Then multiply the inner terms -Finally, multiply the last terms *once everything is multiplied, combine like-terms
|n| equals
-n when n is a positive number - -(n) when n is a negative number
There are 3 types of percent problems
-part -whole -percent
Weight Units of measurement
-pounds -ounces -grams
Volume Units of Measurement
-teaspoon -tablespoon -pints -quarts -galloons -liters
If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?
. 500 miles
to be continued...
...pg 71
1/10
.1
1/9
.1111
Find 0.12 ÷ 1
.12
find 0.12 divide by 1
.12
1/8
.125
1/8
.125 or 12.5% half of 1/4
1/7
.142857(142857)
1/6
.165 or 16.5%
1/6
.16666
1/5
.2
1/5
.2 or 20%
2/10
.2 or 20%
1/4
.25
1/4
.25 or 25%
2/8
.25 or 25%
1/3
.33 or 33.5%
1/3
.3333
3/8
.375 or 37.5% half of 3/4
2/5
.4 or 40%
4/10
.4 or 40%
41% equals:
.41
convert decimal to fraction
.45 = 45/100 = 9/20 .657 = 657/1000
1 lb.
.454 kg
2/4
.50 or 50%
4/8
.50 or 50%
3/5
.6 or 60%
6/10
.6 or 60%
5/8
.625 or 62.5%
2/3
.67 or 67%
3/4
.75 or 75%
6/8
.75 or 75%
4/5
.8 or 80%
8/10
.8 or 80%
7/8
.875 or 87.5%
6 x 0 x 5
0
6 x 0 x 5 equals
0
If 3x + 5x = -8, then x + 1 =
0
0!=
0!=1
Whole numbers
0, 1, 2, 3, etc.
1 Milligram
0.001 Grams
1 milliliter equals what in liters
0.001 L
1 milligram equals what in grams
0.001 grams
1 mm equals what in meters
0.001 m
1 millimeter/liter/gram = ? meters
0.001 meters
Find 0.12 ÷12
0.01
1 centiliter equals what in liters
0.01 L
1 centigram equals what in grams
0.01 grams
1 cm equals what in meters
0.01 m
1 centimeter/liter/gram = ? meters
0.01 meters
Convert 50 ml to L.
0.05 L
Multiply 2.345 x 0.023
0.053935
Which of the following is equal to 5.93 x 10 w/ exp.-2?
0.0593
1 deciliter equals what in liters
0.1 L
1 decigram equals what in grams
0.1 grams
1 decimeter/liter/gram = ? meters
0.1 meters
1 dm equals what in meters
0.1m
convert 5/20 into a decimal form
0.25
You have a stock bottle of 1% viscous lidocaine oral solution. How many grams of lidocaine are in each 30 ml bottle?
0.3 g
1 cm equals what in inches
0.394 inches
How many kilograms are in a pound?
0.45
1 pound equals what in kilograms (kg)
0.45 kg
solve 0.48 divided by 1.2
0.48/1.2=4.8/12 =.4
1/2
0.5
A finger tip unit (ftu) is equal to?
0.5 g
How many meters are in a yard?
0.914
1 yard equals what in meters
0.914 m
1 yd.
0.914m
How many liters are in a quart?
0.95
1 quart equals what in Liters
0.95 L
What is the cost in dollars to steam clean a room W yards wide and L yards long it the steam cleaners charge 10 cents per square foot?
0.9WL
celsius freezing point
0°
1 squared
1
3/4 x 4/5 x 5/3
1
I
1
I is
1
Squares: 1²
1
What is 1/9 of 9?
1
Which of the following numbers could be described in the following way: an integer that is a natural, rational and whole number?
1
10^0 Prefix
1 No prefix
Simplify 3 3/4 divided by 2 1/2
1 1/2
The largest tomato in a farmer's garden last year was 5 3/4 inches in diameter. The largest tomato in the garden this year is 4 1/16 inches in diameter. Which of the following is the difference in diameter between last year's largest tomato and this year's?
1 11/16
1 L = ___ quarts
1 L = 1.06 quart
fluids in the metric system
1 LITER= •1000 ML •100 CL •10 DECILETERS •1/10 DECALITER (1DECA=10L) •1/100 HECTOLITER (1 HECT= 100 L) •1/1000 KL (1 KG= 1000 L)
metric to US conversions
1 M = 1.09 YARDS 2.54 CM = 1 INCH 28 GRAMS = 1 OZ 1 KG = 2.2 LBS 1L= 1.06 QUARTS
lengths in the metric system
1 METER= •1000 MM •100 CM •10 DECIMETERS •1/10 DECAMETERS (1DECA=10M) •1/100 HECTOMETERS (1 HECT= 100 M) •1/1000 KMETERS (1 KG= 1000 M)
0.01 grams
1 centigram equals how many grams?
0.01 liters
1 centiliter equals how many liters?
0.01 meters
1 centimeter equals how many meters?
1 cm = ___inches
1 cm = .394 inches
1 millimeter is ____ cubic centimeters
1 cubic centimeter
8 oz.
1 cup is equal to how many ounces?
0.1 grams
1 decigram equals how many grams?
0.1 liters
1 deciliter equals how many liters?
0.1 meters
1 decimeter equals how many meters?
10 grams
1 dekagram equals how many grams?
10 liters
1 dekaliter equals how many liters?
10 meters
1 dekameter equals how many meters?
12 inches
1 foot is equal to how many inches?
1 gallon = ___liters
1 gallon = 3.785 L
4 quarts
1 gallon is equal to how many quarts?
4 quarts
1 gallon is how many quarts?
1 gram
1 gram equals how many grams?
1 gram equals what in grams
1 grams
100 grams
1 hectogram equals how many grams?
100 liters
1 hectoliter equals how many liters?
100 meters
1 hectometer equals how many meters?
how many inches are in 12.75 cm?
1 inch = .394 inches so 1.75 cm *.394 cm =5.02
1 inch = ___cm
1 inch = 2.54 cm
2.54 cm
1 inch equals how many centimeters?
2.54 cm
1 inch is how many cm?
English VS Metric Units
1 inch= 2.54 centimeters 1.09 yards= 1 meter 1.06 quarts= 1 liter 2.2 pounds= 1 kilogram 1 ounce= 28 grams
1 kg = __lb
1 kg = 2.2 lb
2.2 pounds equals what in kilograms
1 kilogram
1000 grams
1 kilogram equals how many grams?
2.2 pounds
1 kilogram equals how many pounds?
2.2 pounds
1 kilogram is how many pounds?
1000 liters
1 kiloliter equals how many liters?
1,000 meters
1 kilometer equals how many meters?
1 km = ___miles
1 km = .62 miles
1 liter equals what in liters
1 liter
1 quart equals what in liters
1 liter
1 liter
1 liter equals how many liters?
1 m = ___inches
1 m = 39.37 inches
1cm3 (cubed)
1 mL
1 meter equals what in meters
1 meter
1 meter
1 meter equals how many meters?
5280 feet
1 mile is equal to how many feet?
1 miles = ___km
1 miles = 1.6 km
0.001 grams
1 milligram equals how many grams?
0.001 liters
1 milliliter equals how many liters?
0.001 meters
1 millimeter equals how many meters?
10^0
1 no prefix
4/4
1 or 100%
1 ounce = ___grams
1 ounce = 28 grams
1 ounce = ___ml
1 ounce = 30 mL
28 grams
1 ounce equals how many grams?
2 cups
1 pint is equal to how many cups?
16 ounces
1 pound (lb) is equal to how many ounces?
1 pound = ___kg
1 pound = .45 kg
1 quart = ___ L
1 quart = 0.95 L
1 liter
1 quart equals how many liters?
2 pints
1 quart is equal to how many pints?
1 teaspoon = ___ml
1 teaspoon = 5 ml
2,000 pounds
1 ton is equal to how many pounds?
1 yard = ___m
1 yard = .914 m
1 meter to yard
1 yard and 3 inches
1 meter
1 yard is approximately how many meters?
3 feet
1 yard is equal to how many feet?
3 feet
1 yard is how many feet?
James invested $4,000 at 5% interest per year; how long will it take him to earn $200 in simple interest?
1 year
Roman numeral M stand for.....
1,000
The number of milliliters in 1 liter is
1,000
millimeters in a meter
1,000
1 Kilometer = _________ meters
1,000 meters
1 kilometer/liter/gram = ? meter
1,000 meters
solve 1,000-99
1,000-99=901
1 miles equals what in meters
1,609 meters
yards in a mile
1,760
Roman numeral I
1- can be used to the left to subtract
convert 0.025 to a fraction in simplest form
1-25/? 2-25/1,000 3-25 divided by 25/1,000 divided by 25=1/40
convert 35% to a fraction
1-35 2-35/100 3-35divided by 5/100divided by 5 =7/20
to change arabic numerals to Roman numerals
1-L to R 2-take each value and change to Roman 3-I, X, and C may be written 2/3 times in a row 4-use I, X, and C to the L of larger values indicate subtraction from the larger values 5-V, L, and D are never used to the L of a larger value 6-V, L, and D are never used more than one time
converting from fractions to decimals
1-divide the numerator by the denominator; long division i.e. 3.000 divided by 125=0.025 (add as needed 0s to the dividend 2-works only for denominators who are powers of 10 i.e. 1/5=2/10=0.2
3 common types of graphs
1-line 2-circle or pie 3-histogram and bar
classify each as rational, irrational, or real 1-square root of 36 2-negative square root of 36 3-square root of 37 4-1/3 5-0.6 6-0.66666666666 7-0.7070007007...
1-rational 2-rational 3-irrational 4-rational 5-rational 6-rational 7-irrational
converting from percents to fractions
1-remove % 2-write the number from step 1 in the numerator of the fraction and 100 in the denominator 3-simplify
multiplying decimals
1-set up problem as whole numbers 2-multiply 3-count total number of decimal places 4-start from R to L the number of decimal places
dividing decimals
1-set up the problem in which the divisor is a whole number moving the decimal point in the dividend the same number of places that the decimal point is moved in the divisor 2-place decimal in the quotient directly above the decimal point in the dividend 3-divide
converting decimals to fractions
1-write the digits of the decimal number in the numerator of the fraction 2-write a number that is a power of 10 as the denominator 3-write the decimal fraction in simplest form
Convert Percent to Fraction Ex: 35%
1. 35 2. 35/100 3. simplify - > 7/20
Calculation of Take Home Pay
1. Add all of the deductions together, and subtract that total from the beginning salary.
Subtracting Whole Numbers
1. Arrange the whole numbers in rows with like place values in like columns. 2. Subtract in the ones place, regrouping if needed. 3. Subtract in the tens place, regrouping if needed. 4. Subtract in the hundreds place, regrouping if needed. 5. Keep moving through each place, regrouping if needed. "Regrouping" also known as borrowing is necessary to subtract a larger number from a smaller number.
Word Problems involving Percents
1. Change the written statement into a mathematical equation. Keep in mind the word OF translates into MULTIPLY, the word IS translates into EQUALS, and the decimal form of the percent should be used in the equation. 2. Solve for unknown quantity 3. Rewrite the statement and make sure that the answer is reasonable.
Steps for Solving Percent Problems
1. Change the written statement into a mathematical equations, keep in mind: the word OF equals multiply, the word IS translates into equals, and the decimal form of the percent should be used in the equation. 2. Solve for the unknown quantity 3. Rewrite the statement and make sure that the answer is reasonable.
Dividing Fractions
1. Convert any mixed numbers into improper fractions 2. Keep the first fraction as it is written, but change the division sign to a multiplication sign, and flip the second fraction( put its numerator in the denominator and the original denominator in the numerator) 3. Simplify or reduce factors in the numerator with factors in the denominator. 4. Multiply numerators and denominators together. 5. Check to make sure the fraction is a simplified fraction.
Multiplying Fractions
1. Convert any mixed numbers into improper fractions 2. Simplify or reduce factors in the numerator with factors in the denominator 3. Multiply the numerators and denominators together 4. Check to make sure the fraction is a simplified fraction
Addition & Subtraction of Fractions or Mixed numbers with UNLIKE DENOMINATORS
1. Convert any mixed numbers to fractions. 2. Determine the Least Common Denominator. 3. Rewrite each fraction as an equivalent fraction with the LCD. 4. Add or Subtract the numerators, while keeping the common denominator the same. 5. Make sure end fraction is a simplified fraction.
Addition and Subtraction of Fractions with Unlike Denominators - Summary of Steps
1. Convert mixed numbers to improper fractions 2. Simplify if possible 3. Find Least Common Denominator (LCD) - will be new denominator for both fractions 4. Make fractions equivalent - multiply numerator and denominator by same number to get LCD 5. Add or subtract numerators, leave Den. unchanged 6. Always Simplify! Never leave improper fractions
Balance/ Reconcile a Checking or Savings Account
1. Group deposits and add them together 2. Group checks and add them together 3. Add the deposits to the previous balance and subtract checks from that result 4. Subtract service charge and add interest
Converting Decimals to Percents
1. Move the decimal point right two places 2. Add % symbol
Multiplying Decimals
1. Multiple numbers as if whole numbers. 2. Then count total number of decimal places in the factors and add them (Ex: 2.2 and 2.33 has three total decimal places) 3. Add the total number of Decimal places to product, counting left to right (Ex: 22*233 = 5126 --> 5.126 final answer)
Steps to Solving a Word Problem
1. Read the problem carefully 2. Determine what is being asked 3. Read the problem again and underline important words, numbers, and keywords based on what is being asked 4. Set up the problem 5. Solve the problem 6. Check your answer. Is it reasonable?
Converting Percent to Decimals
1. Remove % symbol 2. Move decimal left two places
Converting Percents to Fractions
1. Remove the % symbol 2. Write the number from step one in the numerator of the fraction and write 100 in the denominator. 3. Simplify the fraction
Finding the Estimation
1. Round the numbers so there is only one nonzero digit in each number. 2. This means that the first digit in the number will not be a zero, but all the other digits will be zeros. 3. Perform the indicated calculation of Addition, Subtraction, Multiplication or Division.
Solving Rate of Change
1. Set up proportions for ratio #1 2. Set up proportions for ratio #2 3. Subtract ratio #2 from ratio #1 ( or vice verse) to get the rate of Change
Multiplying Decimals
1. Set up the problem as if the numbers are whole numbers, without paying specific attention to the decimal points. 2. Multiply the numbers without paying specific attention to the decimal points. 3. Once the multiplication is complete, count the total number of decimal places in the factors. 4. Starting from the far right end of the product, count back (to the left) the number of decimal places. 5. Put the decimal point in this spot!
Dividing Decimals
1. Set up the problem to be an equivalent problem in which the divisor (b in a/b) is a whole number by moving the decimal point in the dividend (a in a/b) the same number of places that the decimal point is moved in the divisor. 2. When performing long division, place the decimal point in the quotient directly above the decimal point in the dividend. 3. Divide the quotient as if it were a whole number.
Equations with One Unknown
1. Use the distributive property to remove any parentheses. 2. If there are fractions present, remove them by multiplying each term by the least common denominator. 3. Use the addition principle to move like terms together on both sides of the equation. 4. Use the multiplication principle to isolate the variable by multiplying both sides of the equation by the reciprocal of the coefficient of the variable. 5. Check the solution. Substitute the answer into the original equation to make sure both expressions result in the same value.
Change Arabic Numerals to Roman Numerals
1. Write from left to right 2.Take each place value and change to a Roman numeral. 3.I,X,C may be written two or three times in a row as long as they are not followed by a larger value 4. Use I,X,C to the left of larger values to indicate subtraction from the larger values. 5. V,L and D are never used to the left of a larger value. 6. V,L, and D are never used more than one time. Example: 825 DCCC+XX+V DCCCXXV
Pg 85 Convert Roman Numeral To arabic
1. Write from left to right as a sum 2. Start with largest, M = 1000, D = 500, C = 100, L = 50, X = 10, I = 1 3. When I, X, or C is used to left of larger, it is subtracted MCCXXXIV = 1234
Change Roman Numerals to Arabic Numerals
1. Write from let to right as a sum 2. Begin with the largest possible value M=1,000, D=500, C=100, L=50, X=10, V=5, I=1 3. When I,X,or C is used to the left of a larger value, subtract its value from the larger value. Example: MCCXXXIV 1000+200+30+4=1234.
Convert Arabic to Roman Numeral
1. Write left to write 2. Convert each place value 3. I, X, C may be written two or three times in a row as long as they NOT followed by a larger value 4. Use I, X, C to left of larger values to indicate subtraction from larger values 5. V, L, D never used to left of larger values 6. V, L, and D never used more than on time
Convert from Decimals to Fractions
1. Write the digits of the decimal in numerator 2. Denominator should be the power of ten equal to number of decimal places right of decimal (.025 = 25/1000) 3. Simplify fraction
Converting Decimals to Fractions
1. Write the digits of the decimal number in the numerator of the fraction. 2. Write a number that is a power of 10 as denominator. The number should have as many zeros as there are decimal places to the right of the decimal. 3. Write the decimal fraction in simplest form.
10/10
1. or 100%
exponent rules
1. when multiplying similar bases, add the exponents 2. when dividing similar bases, subtract the exponents 3. when raising a power to another power, multiply the exponents (ex:(s^2)^3 = s^ 6 4. when the exponent is negative, move its base to the denominator & make the exponent positive 5. any base (except zero) to the 0 power equals 1
to change roman numerals to arabic numerals
1. write from left to right as a sum 2. being with largest possible value 3. when I, X, or C is used to the left of a larger value, subtract its value from the larger value
5/5
1.0 or 100%
Which of the following is 2/5% of 42?
1.05
How many quarts are in a liter?
1.06
1 liter (L) equals what in quarts
1.06 quarts
1 liter to quart
1.06 quarts
1L = ? quarts
1.06 quarts
If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?
1.09 days
An ointment contains 5% hydrocortisone. How many grams of hydrocortisone are in a 30 gram tube of ointment?
1.5 g
If a prescription reads: Amoxicillin 250mg/5ml, dispense 150ml, 375mg tid x 5d, what is one dose in household units?
1.5 tsp
How many kilometers are in a mile?
1.609
1 mile = ? km
1.609 km
1 mile = ______ km = ______ ft = ______ yards
1.609 km 5280 ft 1760 yards
1 mile to kilometers
1.61 kilometers
1 mi.
1.61km
Square root of 3
1.7
Converting Fractions to Percents
1.Convert the fraction into a decimal. 2.Convert the decimal to a percent.
100%
1/1 or 1 1 or 1.0 or 1.00
10%
1/10 0.10 or 0.1
10^-1 Prefix
1/10 deci (d)
10^-2 Prefix
1/100 centi (c)
10^-3 Prefix
1/1000 milli (m)
What is the next number in the following pattern? 1, 1/2, 1/4, 1/8, ___
1/16
50%
1/2 0.50 or 0.5
Finding total area for a triangle (formula)
1/2 x base x height
5%
1/20 0.05
Which of the following fractions is the equivalent of 0.5%?
1/200
How many yards in one foot?
1/3yard in one foot.
25%
1/4 0.25
Which of the following fractions are correctly placed from the least in value to the greatest in value?
1/4, 17/25, 11/16, 3/4
20%
1/5 0.2 or 0.20
Which fraction is equal to 0.20%?
1/500
what is the result when we multiply these given fractions? 2/9 x 3/25 x 125/6 x 3/10
1/6
3/8 - 1/4 =
1/8
The reciprocal of 8 is?
1/8
12.5%
1/8 0.125
combined work problem
1/personA + 1/personB= 1/time it takes
If 6 is 24% of a number, what is 40% of the same number?
10
If 8x + 5 = 21, then 3 x + 4 =
10
Roman numeral X
10
Roman numeral X stand for....
10
X
10
X is
10
sides in a decagon
10
10^1 Prefix
10 deka (da)
Kilo
10 cubed =1,000
For the prescription: Bactrim DS #20, 1 bid NR, how many days should the prescription last?
10 days
1 dekagram equals what in grams
10 grams
1 dekaliter equals what in liters
10 liters
A patient has an order for 20 meq of potassium chloride (KCL) and the pharmacy has a vial in stock of 2 meq/ml. How much volume is needed to fill this order?
10 mL
If a medication is available as a 20mg/5ml suspension, how many milliliters would be needed to give a dose of 40mg?
10 mL
1 decameter/liter/gram = ? meter
10 meters
1 dekameter equals what in meters
10 meters
1 Centimeter= _______ milliliters
10 millimeters
Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
10 minutes
Milli
10 negative cubed = 1/1000
Centi
10 negative squared = 1/100
Multiply 10 w/ exp.4 by 10 w/ exp.2
10 w/ exp.6
years in a decade
10 years
10 squared
100
C
100
C is
100
Roman numeral C (century)
100
Roman numeral C stand for.....
100
Squares: 10²
100
what number is 5% of 2000?
100
10^2 Prefix
100 hecto (h)
1 Meter = _______ centimeters
100 centimeters
centimeters in a meter
100 cm
How many cm in one meter?
100 cm in one meter
1 hectogram equals what in grams
100 grams
1 hectoliter equals what in liters
100 liters
A 20% solution has been diluted to 400 ml and is now a 5% solution. What was the beginning volume of the 20% solution?
100 mL
1 hectometer equals what in meters
100 meters
1 hectometer/liter/gram = ? meter
100 meters
years in a century
100 years
(Exponent Practice Questions) 10 w/exp.4 is not equal to which of the following?
100,000
M
1000
M is
1000
Roman numeral M (milli)
1000
10^3 Prefix
1000 Kilo (K)
How many meters are in a kilometer?
1000 = 0.62 mile
1 kilogram equals what in grams
1000 grams
1 kilogram = _______ grams _______ pounds
1000 grams 2.2 pounds
1 kiloliter equals what in liters
1000 liters
1 km equal what in meters and miles
1000 m = 0.62 miles
How many mL in a L?
1000 mL
1 kilometer equals what in meters
1000 meters
1 gram = _______ milligrams
1000 mg
A doctor writes a prescription that reads: Biaxin 250 mg: 2 tabs po q 12h x 10d. How many mg of Biaxin will the patient receive in a day?
1000 mg
1 liter = ________ milliliters
1000 milliliters
celsius boiling point
100°
Add 0.98 + 45.102 + 32.3333 + 31 + 0.00009
109.41539
add 0.98 + 45.102 + 32.3333 + 31 + 0.00009.
109.41539
common prefixes in the metric system
10^3=1000; kilo (k) 10^2=100; hecto (h) 10^1=10; deka (da) 10^0=1; no prefix 10^-1=1/10; deci (d) 10^-2=1/100; centi (c) 10^-3=1/1000; milli (m)
Which of the following has the least value?
11%
Which of the following is not a whole number followed by its square?
11, 144
55%
11/20 0.55
What are the steps of changing an improper fraction to a mixed fraction? 11/4
11/4 = 2¾ Divide the mixed fraction. 11/4 is 2 with a remainder of of 3. *please note we kept the same denominator when applying the remainder.
11 squared
11=121
How many inches are in a foot?
12
US measurement in lengths
12 INCHES = 1 FOOT 3 FEET = 1 YARD 5280 FEET = 1 MILE
How many fl oz are in 360 mL?
12 fl oz
1 foot = ? inches
12 inches
1 foot = _______ inches
12 inches
1 ft equals what in inches
12 inches
a jogger on a treadmill is jogging at 5 miles per hour. Which of the following is the time it will take him to jog 1 mile?
12 minutes
3, 6, 9, ?, ?, 18, 21
12, 15
How much hydrocortisone powder is needed to compound 60g of hydrocortisone cream 2%?
1200 mg
11 squared
121
Squares: 11²
121
What is 1230.932567 rounded to the nearest hundredths place?
1230.93
what is 1230.932567 rounded to the nearest hundredths place?
1230.93
On a Map, 1 inch represents 20 miles. The distance between 2 towns is 6 1/5 inches. How many miles are actually between the two towns?
124 miles
There are 8 ounces in a ½ pound. How many ounces are in 7 3/4 lbs?
124 ounces
1 gallon ________ ounces ________ quarts
128 ounces 4 quarts
Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
13
If 3x=6x-15 then x + 8=
13
65%
13/20 0.65
You are lying 120 ft away from a tree that is 50 feet tall. You look up at the top of the tree. Approximately how far is your hear from the top of the tree in a straight line?
130 feet
What is the mathematical average of the number of days in a typical year, the number of days in a week, and the number of hours in a day?
132
12 squared
144
Squares: 12²
144
How many square inches in a square foot
144 (12x12)
A building that is 150 ft tall casts a shadow of 20 feet long. At the same time a tree casts a shadow of 2 ft. How tall is the tree?
15
Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother?
15
The fine for a driver riding in the carpool lane without any passengers is $133. A driver is issued a bench warrant for $2,294.25, which includes a 15% fee for late charges and court costs. How many tickets has the driver not paid?
15
How many mL in a tbsp?
15 mL
Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?
15 minutes
How to calculate percents academically
15% of 500 is what? 15 percent is always out of 100, OF is multiplication, IS is equals, WHAT is X! 15/100 x 500 = X Or the question can be worded what is 60% of 5? *this can be tricky, but you always put the percent over 100 Ex: 60/100 = X/5
Which of the following choices is equivalent to 5/6?
15/18
A doctor writes a prescription that reads: Rx:Tylenol® suspension 160mg/5ml Take 5 ml every 4 hours if needed for fever Dispense a 5-day supply How much Tylenol® will you dispense?
150 mL
If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?
150/x
which of the following is the roman numeral CLVII equal?
157
4 squared
16
How many ounces are in a pound?
16
Squares: 4²
16
if the area of a square quilt is 16 square feet, then how many feet is the quilt's perimeter?
16
ounces in a pound
16
what is the result when we multiply these given fractions? 4/5 x 14/25 x 125/7 x 4/2
16
US Measurement weights
16 OZ = 1 POUND 2000 LBS = 1 TON
If the perimeter of a rectangular house is 25 1/3 yards, and the length is 22 feet. What is the width?
16 feet
1 pound = ? ounces
16 ounces
1 pound = ______ ounces = _______kg
16 ounces .45 kg
How many ounces in one pound?
16 ounces in one pound
1 pound equals what in ounces (oz)
16 oz.
At a company fish fry, 1/2 in attendance are employees. Employees' spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not employees or employee spouses?
16.7%
85% of what number is 136?
160
A patient is ordered to take 4 ml of medication that is stocked as 200 mg/ 5 ml. How may milligrams are contained in one dose?
160 mg
On a map, 1/3 inch equals 15 miles. The distance between two towns on a map is 3 2/3 inches. How many miles are actually between the two towns?
165
13 squared
169
Squares: 13²
169
1 pound is how many ounces?
16oz
The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs $55 before taxes, how much will the city receive in taxes from him?
17 cents
85%
17/20 0.85
a vitamins expiration date has passed. it was supposed to contain 500 mg of calcium, but it has lost 325 mg of calcium. how many mg of calcium are left?
175 mg
1.75 x 10 w/ exp.5=
175,000
Degrees in a triangle
180
the sum of the measures of the interior angles of a triangle always equal what?
180 degrees
a straight angle
180°
What is 6:30 pm in military time?
18:30
95%
19/20 0.95
14 squared
196
Squares: 14²
196
Must know squares! 1-10
1=1 2=4 3=9 4=16 5=25 6=36 7=49 8=64 9=81 10=100
to balance a checking or savings
1st group the deposits & add them together -then group the checks & add them together- next add the deposits to the previous balance & subtract the checks from the result- then subtract the service charge & add interest
converting from fractions to percents
1st, convert the fraction to a decimal - convert the decimal to a percent by multiplying by 100 & adding the % symbol 5/8= 0.625 = 62.5%
How many cups are in a pint?
2
How many pints are in a quart?
2
In the number 743.25 which digit represents the tenths space?
2
cups in a pint
2
sqrt(4)
2
Finding an approximate decimal for a cube root: Cube root of 8: Cube root of 27: Cube root of 64: so to find the cube root of 10? Cube root of 15?
2 3 4 You would know it's somewhere between 8 and 27 or 2 & 3 = 2.15 Estimate by multiplying 2.5 x 2.5 x 2.5 = 15.625
how to find the surface area of a rectangular solid
2 (LxW) + 2 (WxH) + 2 (LxH)
molly's headband broke and her hair is falling in her face. she has 4 pieces of ribbon to choose from. she needs to choose the piece that will be able to go around her 22 in head. the piece must be at least 4 in longer than her head so that she can tie a knot, but it cannot be more than 6 in so that the ends will show through her hair. which of the following pieces of ribbon will work best?
2 1/3
solve 2and 5/8 x 3 and 1/7
2 and 5/8=21/8; 3 and 1/3=22/7 21/8x22/7; can be simplified by diving by 7 and 2 =3x11/4x1 =33/4 =8and 1/4
1 pint = ? cups
2 cups
1 pint = _______ cups
2 cups
1 pint equals what in cups
2 cups
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
2 hours and 24 minutes
Ampicillin is available in 2g vials and when reconstituted with 9.6mL the total volume is 10mL. How many mL are required for a 400mg dose?
2 mL
converting from fractions to percents
2 methods 1-convert fraction to a decimal 2-convert decimal to percent
If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?
2 minutes and 44 seconds
1 quart = ? pints
2 pints
1 quart = _____ pints
2 pints
1 quart equals what in pints
2 pints
pints in a quart
2 pints
1 ounce = ______ tablespoons = ______ grams
2 tablespoons 28 g
The doctor orders Diuril 0.5 g po. Your pharmacy only stocks Diuril 250 mg po. How many tablets do you dispense?
2 tablets
Circumference of a circle formula:
2 x Pi x radius (Pi is always 3.14)
perimeter of a rectangle
2(length+width)=perimeter
The 10 smallest prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
pounds in a ton
2,000
How many pounds in a ton?
2,000 pounds in one ton
How many pounds are in a kilogram?
2.2
Square root of 5
2.2
1 kg = ? lbs
2.2 lbs
1 kg equals what in pounds
2.2 lbs
1 kilogram to pounds
2.2 pounds
1 inch to Centimeter
2.5 centimeters
How many centimeters are in an inch?
2.54
1 inch = _______ centimeters
2.54 centimeters
1 inch equals what in centimeters
2.54 centimeters
1 inch = ? cm
2.54 cm
1 inch equal what in centimeters
2.54 cm
How many cm in one inch?
2.54 cm in one inch.
1 in.
2.54cm
1/7 x 2/3 =
2/21
1/7 x 2/5 =
2/35
40%
2/5 0.40
What is the fractional equivalent of 12.5%?
2/7
(5 x 3) x 1 + 5 =
20
You have to draw up an 11ml dose. Which syringe is the most appropriate to use? 20 ml 10 ml 60 ml 30 ml
20 mL
35% of what number is 70?
200
How many pounds are in a ton?
2000
1 ton = ? lbs
2000 lbs
1 ton equals what in pounds
2000 lbs
1 ton = _______ pounds
2000 pounds
Subtract the following numbers rounded to the nearest tenths place. 134.679 -45.548 -67.8807
21.3
subtract the following numbers and round to the nearest tenths place: 134.679 -45.548 -67.8807
21.3
fahrenheit boiling point
212°
15 squared
225
Squares: 15²
225
What is 10:45 pm in military time?
22:45
Change 4 3/5 to an improper fraction.
23/5
3x8
24
6x4
24
8x3
24
How many cubed pieces of fudge that are 3 inches on an edge can be packed into a Christmas tin that is 9 inches deep by 12 inches wide by 8 inches high with the lid still being able to be closed?
24
There are 12 more apples than oranges in a basket of 36 apples and oranges. How many apples are in the basket?
24
If a ¼ of a teaspoon is 1 ml, then how many milliliters are in 6 teaspoons?
24 ml
5 squared
25
If one side of a square is 5 units, what is the area of the square?
25
Squares: 5²
25
How many days supply would a ProAir HFA, which has 200 metered inhalations, last if the sig code is 2 puffs q6h?
25 days
you have orders to give a patient 20 mg of a certain medication. the medication is sotred as 4 mg per 5-mL dose. how many milliliters will need to be given?
25 mL
In order to prepare 100 ml of a 2.5% solution from a 10% solution, you would need?
25 ml of the 10% solution
25% of what number is 8?
25/100 x X = 8
Which of the following fractions is equal to 5/6?
25/30
16 squared
256
(5 raised to 3 + 7) x 2 =
264
3x9
27
9x3
27
7x4
28
How many grams are in an ounce?
28
What is 35% of a number if 12 is 15% of a number?
28
1 ounce = ? g
28 g
1 ounces equals what in grams
28 g
1 ounce equals what in grams
28 grams
1 ounce to grams (weight)
28 grams
A roast was cooked at 325° F in the oven for 4 hours. The internal temperature rose from 32° F to 145° F. What was the average rise in temperature per hour?
28.25° F/hr
1oz.
28.35 g
A scale on a map states that every ¼ of an inch represents 20 miles. If two cities are 3 ½ inches apart, how many miles are actually between the two cities?
280 miles
What is the mathematical average of the number of weeks in a year, seasons in a year, and the number of days in January?
29
What are the steps of changing a mixed fraction to an improper fraction? 2¾
2¾ = 11/4 Multiply 4 x 2 = 8 Add the sum of 8 to numerator thus 8+3= 11 Keep the same denominator
At your pharmacy, the minimum/ maximum inventory level for drug A is 10/12. You have 9 bottles on hand. What is the re-order quantity?
3
How many feet are in a yard?
3
simplify the following expression: 5 1/3 - 2 1/3
3
sqrt(9)
3
teaspoons in a tablespoon
3
Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best?
3 3/8 feet
ratio
3 apples & 4 oranges = 3/7 & 4/7 rewrite a ratio 3 minutes to 7 seconds = 180 seconds to 7 seconds
1 yard equals what in feet
3 feet
how many feet in one yard?
3 feet in one yard
1 yard = ? ft
3 ft
If a patient is to receive 15,000 units of heparin and the pharmacy stocks 5000 units/ml, how many milliliters are needed for the dose?
3 mL
1 Yard = ______ meters ______ feet
3 meters 3 feet
A physician orders a 150 mg dose of a medication. The pharmacy stocks 50 mg tablets. How many tablets should be administered?
3 tablets
Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best?
3 ½ feet
A student receives his grade report from a local community college, but the GPA is smudged. He took the following classes: a 2 hour credit art, a 3 hour credit history, a 4 hour credit science course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a "B" in the art class, an "A" in the history class, a "C" in the science class, a "B" in the mathematics class, and an "A" in the science lab. What was his GPA if the letter grades are based on a 4 point scale?
3.0
In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; History is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology?
3.08
In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; history is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a "C" in Trigonometry, a "B" in American History, an "A" in Botany, and a "B" in Microbiology?
3.08
How many liters are in a gallon?
3.785
1 gal.
3.785 L
1 galloon equals what in Liters
3.785 L
1 gallon to liter
3.785 liters (estimate 4 liters)
30%
3/10 0.3 or 0.30
15%
3/20 0.15
A recent study showed that an increase in body weight by 10 kilograms resulted in a 0.15% increase in heart disease. What fraction is equal to 0.15%?
3/2000
75%
3/4 0.75
60%
3/5 0.6 or 0.60
A hockey team won 6 games and lost 8. What is the ratio of wins to number of games?
3/7
37.5%
3/8 0.375
5x6
30
How many milliliters are in a ounce?
30
if a rectangular field has a perimeter of 44 yards, and a length of 36 feet, what is the field's width?
30 feet
1 ounces equals what in mL
30 mL
1 ounce (volume) to millimeter
30 millimeter
1 ounce = _______ ml
30 ml
Express 30 minutes to 4 hours as a ratio I'm fraction
30/240 (make the hours to minutes) then simplify. Don't forget to get rid of the zeros to make it easier! 3/24= 1/8
Percent to fraction Ex: 319%
319/100 then turn into a proper fraction = 3 19/100 Basically put it over 100 and simplify..
8x4
32
fahrenheit freezing point
32°
Art realized that he had 2 more quarters than he had originally thought in his pocket. If all of the change in his pocket is quarters and it totals to $8.75, how many quarters did he originally think were in his pocket?
33
If 8x + 5x + 2x + 4x = 114, the 5x + 3 =
33
5x7
35
A couple isplanning a wedding and has $500 to spend on candles. Large candles cost $6 and small candles cost $4. After spending $360 on large canclde, which of the following is the number of small candles the couple can purchase witht he remaining money?
35
If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then what is x?
35
If a physician orders 25% dextrose,1000ml and all you have is 70% dextrose 1000 ml, how much 70% dextrose and how much sterile water will be used to make 1000ml of 25% dextrose?
357 ml 70% Dextrose and 643 ml SW
6 squared
36
6x6
36
9x4
36
Squares: 6²
36
inches in a yard
36
Degrees in a circle
360
Degrees in a quadrilateral
360
1 hr
3600 s
A nurse has to record her temperatures in Celsius but her thermometer reads Fahrenheit. A patient's temperature is 100.7° F. What is the temperature in °C?
38.2° C
Find the missing term in the following sequence: 4, 9, 19, __, 79
39
1 meter to inches
39 inches
How many inches are in a meter?
39.37
1 m equals what in inches
39.37 inches
special right triangles
3:4:5------30-60-90 degrees 5:12:13------45-45-90 degrees
If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number?
3V- Z - Y
2 squared
4
Find the mode of the following list of numbers: 2, 4, 6, 4, 8, 2, 9, 4, 3, 8
4
How many quarts are in a cup?
4
How many quarts are in a gallon?
4
IV (roman numeral)
4
Squares: 2²
4
The cost to ride on a ferry is $5.00 per vehicle and driver with an additional cost of 50 cents per passenger. If the charge to get on the ferry is $6.50, how many people were in the vehicle?
4
sides in a quadrilateral
4
sqrt(16)
4
If a match box is 0.17 feet long, what is its length in inches the most closely comparable to the following?
4 1/2 inch calculator
Gallon ---> Cups
4 Q = 1 G 2 P = 1 Q 8 P = 1 G 2 C = 1 P 4 C = 1 Q 16 C = 1 G
1 quart is how many cups
4 cups
1 gallon = ? quarts
4 quarts
1 gallon equals what in quarts
4 quarts
quarts in a gallon
4 quarts
A patient comes to your pharmacy needing help. She received a prescription from a pharmacy across town. Her prescription label reads, "metoclopramide 5 mg/5 ml solution- take 20 ml every 8 hours." She does not know how to measure out 20 ml. How many teaspoons should you tell her to take per dose?
4 tsp
How long will Lucy have to wait before for her $2,500 invested at 6% earns $600 in simple interest?
4 years
Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?
4 ½ hours
A newly constructed convention center has a floor space of 307,463 square feet that will be covered in carpeting. The carpet comes in rolls of 67 square feet. Which of the following is the number of rolls required to carpet the floor space?
4,589
1 cal
4.19 J
convert 0.045 to a percent
4.5 percent
jim works for $15.50 per hour at a health care facility. he is supposed to get a $0.75 per hour raise after one year of service. what will be his percent increase in hourly pay?
4.8%
80%
4/5 0.8 or 0.80
XL (roman numeral)
40
A doctor writes a prescription that reads: Biaxin 250 mg: 2 tabs po q 12h x 10d. How many tablets do you dispense?
40 tablets
20 squared
400
A study reported that in a random sampling of 100 women over the age of 35 showed that 8 of the women were married 2 or more times. Based on the study results, how many women in a group of 5,000 women over the age of 35 would likely be married 2 or more times?
400
CD (roman numeral)
400
Squares: 20²
400
Two angles of a triangle each measure 70°. What is the measure of the third angle in degrees?
40°
What is 5ºC in ºF?
41ºF
6x7
42
7x6
42
(72-23-6) =
43
(43+2-1) =
44
5x9
45
How many grams are in a pound?
454 g
8x6
48
7 squared
49
Squares: 7²
49
A men's basketball team won 24 games and lost 32. What is the ratio of games lost to the number of games played?
4:7
How many milliliters are in a teaspoon?
5
Roman numeral V
5
Roman numeral V stand for....
5
V
5
V is
5
sides in a pentagon
5
Calculate the day supply: Z-PAK #6: 500 mg PO on the first day and then 250 mg PO once daily for 4 days.
5 days
If a prescription calls for 2 TBSP TID, dispense 450 ml, how long will the bottle last the patient?
5 days
Famotidine is available in 200 mg/20 ml injectable solution. How many 40 mg doses are contained in one 20 ml vial?
5 doses
1 teaspoon = ? mL
5 mL
1 teaspoon equals what in mL
5 mL
1 teaspoon = _____ ml
5 ml
What simple interest rate will Susan need to secure to make $2,500 in interest on a $10,000 principal over 5 years?
5%
feet in a mile
5,280
1 mile = ? ft
5,280 ft
7.95 divide 1.5
5.3
7.95 ÷ 1.5
5.3
Of the following fractions, which is less than 2/3?
5/7
alan bought a pizza which had 8 slices. he ate 3 slices of pizza for lunch, and left the remaining pizza for jenny. what fraction of pizza did alan leave for jenny?
5/8
62.5%
5/8 0.625
convert 5/8 to a percent
5/8=0.625 (long division) 0.625=62.5%
what is the result of following expression? 2/9 + (5/6 - 1/2) =
5/9
1°F
5/9 (°F - 32°C)
If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes?
5/p
L
50
L is
50
Roman numeral L
50
Roman numeral L stand for....
50
A patient is using a 100 unit/ml insulin. If a patient uses 20 units of insulin daily, how many days will one vial of insulin last? A typical vial of insulin is 10 ml.
50 days
Vancomycin is supplied as a sterile product for reconstitution. The vial of vancomycin 1 gm reads "add 20 ml sterile water for injection." What is the resulting concentration of the dilution?
50 mg/ml
An amount of 50 decreases by 5, what is the percent decrease?
50-45 ------- X 100 = 10% 50 Or if we're Keshwani =) we don't do all that work, we just know that 5 of 50 is 10%
D
500
D is
500
Roman numeral D (Demi)
500
Roman numeral D stand for......
500
If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?
500 miles
In triangle ABC, AB=BC and (C's measure is 65°.) What is the measure of angle B?
50°
How many feet are in a mile?
5280
1 mile equals what in feet
5280 feet
6x9
54
9x6
54
A patient weighs 121 pounds. What is her weight in kilograms?
55 kg
A professor puts together a 98 page handout to distribute at a seminar. The registration list indicates there will be 568 participants. Which of the following is the number of pages the professor will print?
55,664
7x8
56
8x7
56
John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
56 mph
The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?
58%
Which of the following values is NOT equal to 34(58+9)?
58(34+9)
7x + 5xy + 3y - 9x
5xy + 3y - 2x
(9 divide 3) x (8 divide 4)
6
(9 ÷ 3) x (8 ÷ 4) =
6
sides in a hexagon
6
convert the following into a fraction: 5.25 + 1.5
6 3/4
Brett started a race at 6:30 A.M., and he did not cross the finish line until 1:05 P.M. How long did it take for Brett to finish the race?
6 hours and 35 minutes
A patient needs a 300 mg dose of amikacin. How many milliliters do you need to draw from a vial containing 100mg/2ml of amikacin?
6 mL
what is the least common multiple of 2, 3, 4, and 5?
60
What quantity is required for a 30 day supply of the following prescription: Phenytoin suspension (Phenytoin is supplied as 125mg/5mL) 125mg bid at 0800, 1200 and 250mg hs.
600 mL
How many milligrams of clindamycin are in a 60 gram tube of 1% clindamycin topical gel?
600 mg
Two angle in a triangle equal 120°. What is the measure of the third angle?
60°
25 squared
625
Squares: 25²
625
7x9
63
9x7
63
6.334 x 10 w/ exp.4 =
63340
8 squared
64
8x8
64
Squares: 8²
64
what is the volume of a cube whose width is 5 inches?
64 cubic inches
1 grain is the same as?
64.8 mg
If y = 3, then y3(y3-y)=
648
if y=3, then what is y raised to 3 (y raised to 3 - y)?
648
4p + 7d - 6p - 3d + 8p
6p + 4d
sides in a heptagon
7
If Jack needs 2 ½ pints of cream to make a dessert. How many pints will he need to make 3 desserts?
7 ½
70%
7/10 0.7 or 0.70
convert 7/10 to a percent
7/10=7x10/10x10=70/100 70/100=70%
35%
7/20 0.35
convert 0.28 into a fraction
7/25
1/2 ÷ 3/7 =
7/6
87.5%
7/8 0.875
round 707.456 to the nearest tens place
710
8x9
72
9x8
72
A suspension of naladixic acid contains 250mg/5ml. The syringe contains 15 ml. What is the dose (in milligrams) contained in the syringe?
750 mg
convert 78% to a decimal
78%=0.78
solve quotient of 3/4 and 7
7=7/1; reciprocal is 1/7 =3/4x1/7 =3/28
3b + 3a + 4b - 5a =
7b - 2a
1/2 gallon = ___ cups
8
How many ounces are in a cup?
8
If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?
8
What is the median of the following list of numbers? 4, 5, 7, 9, 10, 12
8
sides in an octagon
8
what is the median of the following list of numbers: 4, 5, 7, 9, 10 and 12?
8
US measurement chart fluid
8 OUNCE = 1 CUP 2 CUPS = 1 PINT 2 PINTS = 1 QUART 4 QUARTS = 1 GALLON
1 cup = ? ounces
8 ounces
1 cup = _______ ounces
8 ounces
1 cup equals what in ounces (oz)
8 oz.
83,000 equals:
8.3 x 10 w/ exp.4
.00875 equals:
8.75 x 10 w/ exp.-3
A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
8.9
1/5 + 1/3 =
8/15
Convert 825 to roman number
800= 500 +100+100+100 DCCC 20 = 10 + 10 = XX 5 = 5 = V DCCXXV
Al Khwarizmi wrote the first book of algebra in 825 C. E. Write this date in Roman numerals
800=500+100+100+100, so DCCC 20=10+10, so XX 5=5, so V DCCCXXV
Two angles of a triangle measure 15° and 85 °. What is the measure for the third angle?
80°
9 squared
81
Squares: 9
81
Find 8.23 x 10 w/ exp.9
8230000000
At a certain high school, the respective weights for the following subjects are: Mathematics 3, English 3, History 2, Science 2 and Art 1. What is a student's average whose marks were the following: Geometry 89, American Literature 92, American History 94, Biology 81, and Sculpture 85?
88.2
If 5 ounces is equal to 140 grams, then 2 pounds of ground meat is equal to how many grams?
896
3 squared
9
IX (roman numeral)
9
In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
9
Melinda's lights went out. She has 3 pairs of red socks in her drawer, 2 pairs of black socks, and 5 pairs of white socks. What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color?
9
Squares: 3²
9
What is the absolute value of -9?
9
sides in a nonagon
9
what is the absolute value of -9?
9
How many square feet in a square yard
9 (3x3)
Which of the following correctly identifies 4 consecutive odd integers where the sum of the middle two integers is equal to 24?
9, 11, 13, 15
During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday?
9,315
during a 5-day convention, the number of visitors tripled each day. if the convention started on a Tuesday with 345 visitors, what was the attendance on that Friday?
9,315
90%
9/10 0.9 or 0.90
1 yard to meters
9/10 meters
45%
9/20 0.45
what is the result when we add these given fractions? 1/5 + 4/25 =
9/25
*Tricky with percents* 9 is what percent of 25?
9/25 =X/100
XC (roman numeral)
90
CM (roman numeral)
900
degrees in a right angle
90°
Round 907.457 to the nearest tens place
910
3 x (2 x 4 raised to 3) divided by 4
96
What is the next number in the sequence? 6, 12, 24, 48, ___
96
2x + 2y + 7x - 7y
9x - 5y
1 Milliliter
= 0.001 Liters
1 Millimeter
= 0.001 Meters
1 Centigram
= 0.01 Grams
1 Centiliter
= 0.01 Liters
1 Centimeter
= 0.01 Meters
12 Inches
= 1 Foot
1 Gram
= 1 Gram
1 Liter
= 1 Liter
1 Meter
= 1 Meter
1 Kilogram
= 1,000 Grams
1 Kiloliter
= 1,000 Liters
1 Kilometer
= 1,000 Meters
1 Dekagram
= 10 Grams
1 Dekaliter
= 10 Liters
1 Dekameter
= 10 Meters
1 Hectogram
= 100 Grams
1 Hectoliter
= 100 Liters
1 Pound
= 16 Ounces
1 Pint
= 2 Cups
1 Quart
= 2 Pints
1 Yard
= 3 Feet
1 Gallon
= 4 Quarts
1 Mile
= 5,250 Feet
1 Cup
= 8 Ounces
percent change
= amount of change / original amount
original amount
= amount of change / percent change
probability
= desired outcomes / total possible outcomes
amount of change
= original amount X percent change
whole
= part / percent
percent
= part / whole
work
= rate * time
d distance
= rt rate * time
part
= whole X percent
Fraction to decimal ex: 60/100
=.60 move the decimal place to the left 2 spaces because it's over 100 (2 zeros=2 spaces left). Ex: 18/10 = 1.8 (one space left because it's over 10. One zero=one space) Ex: 800/1000 = .800 (1000 on bottom, 3 zeros = 3 spaces left) *basically however many zeros on bottom (1000, 100, 10) is how many spaces to the left.
Percent to decimal Ex: 68.1%
=.681 Two spaces to the left
1 Decigram
=0.1 Grams
1 Deciliter
=0.1 Liters
1 Decimeter
=0.1 Meters
1 Hectometer
=100 Meters
1 Ton
=2,000 Pounds
Decimal to percent Ex: 0.681
=68.1% Always 2 spaces to the right
simplify |5| + |-3|
=8 Ignore the negative sign!
13.) The graph provided shows the population of three American cities. Between which two years did the population of all three cities decline? A) 1960 and 1980 B) 1920 and 1940 C) 1940 and 1960 D) It never declined in all three cities at once
A
15 is 20 % of what number? A) 75 B) 300 C) 45 D) 3
A
15.) What is the product of 0.52x 0.04? A) 0.0208 B) 2.08 C) 0.00208 D) 0.208
A
19.) Order this list of numbers from least to greatest. -2, 2.3, -1.5, 11/5 A) -2, -1.5, 11/5, 2.3 B) -1.5, -2, 2.3, 11/5 C) -2, -1.5, 2.3, 11/5 D) -1.5, -2, 11/5, 2.3
A
22.) For a species count, a scientist is measuring the length of a clearing in the forest. Which would be an appropriate unit of measure? A) Meter B) Centimeter C) Kilometer D) Mile
A
26.) How many miles are there in 8 kilometers? (Note 1 mile= 1.6 kilometers) A) 5 miles B) 4.6 miles C) 10 miles D) 12.8 miles
A
Angela's scores on five science tests were 85, 82, 94, 96, 88. What was the average of her test scores? A) 89 B) 90 C) 88 D) 87
A
How many pounds are there in 8 kilograms? (note: 1 kg= 2.2 lbs.) A) 17.6 pounds B) 16.6 pounds C) 3.6 pounds D) 16 pounds
A
area of a triangle
A = 1/2 bh A = area, b = base, h = height
the formula for area
A = 1/2 bh A = area, b = base, h = height
area of a square
A = s^2 A = area, s = side
area of a circle
A = πr
Histogram
A bar graph that shows how many data values fall into a certain interval. The number of data items in an interval is a frequency. The width of the bar represents the interval, while the height indicates the number of data items, or frequency, in that interval. Bars on a histogram MUST TOUCH.
Terminating Decimal
A decimal number that ends or terminates
Repeating Decimal
A decimal with a sequence of digits that repeats itself indefinitely
Graph
A diagram showing the relation between variable quantities, typically of two variables measured along a pair of lines at right angles.
Improper Fraction
A fraction in which the numerator is greater than or equal to the denominator
Line Graphs
A graph that shows changes over a period of time or compares the relationship between two quantities, created on a coordinate axes. The horizontal axis it typically referred to as the x-axes and the vertical axes is typically referred to as the y-axes. To denote any given point write the x and y coordinates as an ordered pair (x,y).
Bar Graph
A graph that uses horizontal or vertical bars to represent data.
Equation
A mathematical sentence that contains an equals sign.
Inequality
A mathematical sentence that contains less than, greater than, less than or equal to, greater than or equal to, or not equal
Mixed Number
A number made up of a whole number and a fraction
Decimal Number
A number taft uses a decimal point to show the part of the number that is less than 1. Ex. 1.234
Real Number
A number that appears on the number line as either a rational number or irrational number.
Fraction
A number that names part of a whole
Constant
A quantity that does not change
Comparison of Rational Numbers
A rational number can be a fraction or a decimal. Ordering d by size is useful in solving problems.
Multiplication Principle
A rule that makes it possible to isolate the variable in an equation by multiplying both expressions by the reciprocal of the variables coefficient.
Addition Principle
A rule that makes it possible to move terms from one side of an equation to the other by adding opposites to each expression.
Table
A set of rows and columns used to organize information.
Composite Number
A whole number greater than 1 that has more than two factor, that is any whole number that is not a prime number. For example composite number 8 has the factors of 1,2,4,8.
Prime Numbers
A whole number greater than 1 that has only two factors, that is a number that can be divided evenly ONLY by one and itself.
What will it cost to carpet a room with indoor/outdoor carpet if the room is 10 feet wide and 12 feet long? The carpet costs 12.51 per square yard. A. $166.80 B. $175.90 C. $184.30 D. $189.90 E. $192.20
A. $166.80
What is the cost in dollars to steam clean a room W yards wide and L yards long it the steam cleaners charge 10 cents per square foot? A. 0.9WL B. 0.3WL C. 0.1WL D. 9WL E. 3WL
A. 0.9WL
How many years does Steven need to invest his $3,000 at 7% to earn $210 in simple interest? A. 1 year B. 2 years C. 3 years D. 4 years E. 5 years
A. 1 year
If the perimeter of a rectangular house is 44 yards, and the length is 36 feet, what is the width of the house? A. 10 yards B. 18 yards C. 28 feet D. 32 feet E. 36 yards
A. 10 yards
25% of 400 = A. 100 B. 200 C. 800 D. 10,000 E. 12,000
A. 100
A room measures 11 ft x 12 ft x 9 ft. What is the volume? A. 1188 ft3 B. 32 ft3 C. 120 ft3 D. 1300 ft3 E. 1350 ft3
A. 1188 ft3
If 45 is 120% of a number, what is 80% of the same number? A. 30 B. 32 C. 36 D. 38 E. 41
A. 30
Triangle: Area
A= 1/2BH (base times height)
area of a rectangle
A= lw A = area, l = length, w = width
Circle: Area
A= πR²
temperature
AMERICAN Fahrenheit SI kelvin
work and energy
AMERICAN cal / British thermal unit SI joule
volume
AMERICAN cup - pint - quart - gallon SI liter
charge
AMERICAN faraday SI coulomb
length
AMERICAN inch - foot - yard - mile SI meter
mass
AMERICAN ounce - pound - ton SI gram
force
AMERICAN pound - force SI newton
pressure
AMERICAN pound - force per square inch SI pascal
Of number n, written in |n|, is the distance between the number n and zero on the number line
Absolute Value
Celsius to kelvin
Add 273
To determine the amount of take-home pay for a given time period
Add all of the deductions together and then subtract that total from the beginning salary
Addition and Subtraction
Add and Subtract from left to right.
Exponent: When bases are the same and multiplied
Add the exponents 3²x3⁵= 3⁷
What is the value of X if the average is 6? 5cm, 7cm, 7cm, 6cm, and X?
Add them all up and divide by # of places. 25/5=5
Square Feet Review - Finding Total Square Feet
Add up all four sides to find total square feet A fence that is 25 feet by 30 feet means Total SqFt = 25+25+30+30 = 110 square feet
Adding/Subtracting Like Terms in Polynomials
Add/Subtract the coefficients and keep the variables the same.
A rule that makes it possible to move terms from one side of an equation to the other by adding opposites to each expression
Addition Principle
If |x-n| > negative #, then the solution is
All Real Numbers
If |x-n| > 0, then the solution is
All real numbers
Prime factor
Also a prime number. Prime factors of 12 are 3 and 5. Prime factor for 15 are 3, and 5
When estimating
Always make sure your estimating low or high! Ex: 6.3 x 7.6, you know 6x7=42 then add .5 of 7 so that's 3.5, =45.5 But I know that's an under estimation cause the answer is 47.88
When multiplying/dividing fractions
Always simplify before! Any number that will go into the both other numbers.
Variable
An unknown quantity in an expression, usually in the form of a letter such as x,y, or z.
Variable
An unkown quantity in an expression, usually in the form of a letter such as x,y, or z
Rational number
Any real number that can be written as a fraction
Rational Number
Any real number that can be written as a fraction, terminating decimal, or repeating decimal.
Square root of 2 ✔️
Approx 1.4
A system of writing numbers using a combination of 0,1,2,3,4,5,6,7,8,9
Arabic Numeral System
Mean
Average Add up the numbers then divide by the number of numbers
Calculating Hypotenuse and Diagonals: Pythagorean Theorem
A²+B²= C² Ex. 4²+6²= ²C => 16+36= C² => 50= C² => √50= C² => 5√2= C => C= 5√2
14.) How many millimeters are there in 4 liters? A) 40 millimeters B) 4000 millimeters C) 40000 millimeters D) 400 millimeters
B
17.) Which of these dates is represented by the Roman numeral MDXVI? A) 1506 B) 1516 C) 1106 D) 1116
B
21.) l x+2 l = 8 Which of the following is the solution set for the equation above? A) {-6, 10} B) {6, -6} C) {6, -10} D) {6, 6}
B
27.) (2 3/5 x 1 1/8) Simplify the expression. Which of the following is correct? A) 2 5/8 B) 2 37/40 C) 3 1/20 D) 2 3/40
B
28.) Colleen's textbook purchases for the semester come to $55, $69, $74, $40, and $34. Which of the following is an accurate estimate of her textbook expenses? A) $320 B) $270 C) $370 D) $300
B
3 ¼ x 1/16 Simplify the expression above. Which of the following is correct? A) 5/8 B) 13/64 C) 13/16 D) 3 3/16
B
If a train travels 270 miles in three hours, how far will it travel in 4.5 hours? A) 425 miles B) 405 miles C) 300 miles D) 350 miles
B
The person wants to take a bath. The GRAPH represents the water level in the bathtub over time. At which of the following points in time does the person get into the tub?
B
A car dealer sells a SUV for $39,000, which represents a 25% markup over the dealer's cost. What was the cost of the SUV to the dealer? A. $29,250 B. $31,200 C. $32,500 D. $33,800 E. $33,999
B. $31,200
If 6 is 24% of a number, what is 40% of the same number A. 8 B. 10 C. 15 D. 20 E. 25
B. 10
What number is 5% of 2000? A. 50 B. 100 C. 150 D. 200 E. 250
B. 100
At a company fish fry, ½ in attendance are employees. Employees' spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not employees or employee spouses? A. 10.5% B. 16.7% C. 25% D. 32.3% E. 38%
B. 16.7%
Sabrina's boss states that she will increase Sabrina's salary from $12,000 to $14,000 per year if she enrolls in business courses at a local community college. What percent increase in salary will result from Sabrina taking the business courses? A. 15% B. 16.7% C. 17.2% D. 85% E. 117%
B. 16.7%
A vitamin's expiration date has passed. It was supposed to contain 500 mg of Calcium, but it has lost 325 mg of Calcium. How many mg of Calcium are left? A. 135 mg B. 175 mg C. 185 mg D. 200 mg E. 220 mg
B. 175 mg
22% of $900 = A. 90 B. 198 C. 250 D. 325 E. 375
B. 198
One slice of bread is 80 calorie. Approximately how many calories are in 2 ½ slices of bread? A. 140 calories B. 200 calories C. 220 calories D. 240 calories E. 260 calories
B. 200 calories
A can's diameter is 3 inches, and its height is 8 inches. What is the volume of the can? A. 50.30 B. 56.55 C. 75.68 D. 113.04 E. 226.08
B. 56.55
Of the following units which would be more likely used to measure the amount of water in a bathtub? A. kilograms B. liters C. milliliters D. centigrams E. volts
B. liters
Exponent 5²
Base= 5 Exponent= 2
Measuring tsp
Beaker
Volume
Beakers, Graduated cylinders, Measuring Cups, Pipettes, Measuring Spoons.
A polynomial with two terms
Binomial
11.) 4 1/8 ÷1 ½ Simplify the expression above. Which of the following is correct? A) 2 1/4 B) 4 1/4 C) 2 3/4 D) 4 ½
C
12.) Soda $ 1.75 Chips and Salsa $ 2.25 Subs $ 3.15 French Fries $ 1.25 The concession stand menu above shows the costs of several items. A customer bought 2 subs, an order of French fries, and 2 sodas. How much did he pay in all? A) $ 7.55 B) $ 13.25 C) $ 11.05 D) $ 9.30
C
20.) A number is 10 less than double a given number. Translate this phrase into a mathematical expression A) n-10 x2 B) 2 (n-10) C) 2n-10 D) (n+2)-10
C
23.) A plan for a house is drawn in a 1:40 scale. The length of the living room in the plan measures 4.5 inches, what is the actual length of the built living room? A) 12 feet B) 25 feet C) 15 feet D) 45 feet
C
25.) Find the volume of a box 6 inches high, 6 inches wide and 6 inches deep. A) 18 cubic inches B) 36 cubic inches C) 216 cubic inches D) 128 cubic inches
C
At the bake sale, Josie bought three brownies for $1.35 a piece. She paid with a $5 bill. What change should she receive? A) $ 1.15 B) $ 1.05 C) $ 0.95 D) $ 0.85
C
Population Graph City Population, 2009 Population, 1999 Detroit, MI 910,921 965,074 Jacksonville, FL 813,518 965,877 Memphis, TN 676,640 606,109 San Francisco, CA 815,358 747,777 Please use this passage to answer question 2 The chart above shows the populations of four cities in two different years. Which city had the greatest growth between 1999 and 2009? A) Detroit B) San Francisco C) Jacksonville D) Memphis
C
A customer pays $1,100 in state taxes on a newly purchased car. What is the value of the car if state taxes are 8.9% of the value? A. $9.765.45 B. $10,876.90 C. $12,359.55 D. $14,345.48 E. $15,745.45
C. $12,359.55
A computer is on sale for $1600, which is a 20% discount off the regular price. What is the regular price? A. $1800 B. $1900 C. $2000 D. $2100 E. $2200
C. $2000
Which of these percentages equals 1.25? A. 0.125% B. 12.5% C. 125% D. 1250% E. 1250.5%
C. 125%
You need exactly a 1680 ft3 aquarium for your fish. At the pet store you see four choices of aquariums, but the volume is not listed. The length, width, and height are listed on the box. Which of the following aquariums would fit your needs? A. 12 ft x 12 ft x 12 ft B. 13 ft x 15 ft x 16 ft C. 14 ft x 20 ft x 6 ft D. 15 ft x 16 ft x 12 ft E. 15 ft x 12 ft x 12 ft
C. 14 ft x 20 ft x 6 ft
If the area of a square flowerbed is 16 square feet, then how many feet is the perimeter of the flowerbed? A. 4 B. 12 C. 16 D. 20 E. 24
C. 16
One inch equals 2.54 cm, How many centimeters tall is a 76 inch man? A. 20 cm B. 29.92 cm C. 193.04 cm D. 300.04 cm E. 593.04 cm
C. 193.04 cm
You have orders to give a patient 20 mg of a certain medication. The medication is stored 4 mg per 5-mL dose. How many milliliters will need to be given? A. 15 mL B. 20 mL C. 25 mL D. 30 mL E. 35 mL
C. 25 mL
What is 35% of a number if 12 is 15% of a number? A. 5 B. 12 C. 28 D. 33 E. 62
C. 28
What percent of 90 is 27? A. 15% B. 20% C. 30% D. 33% E. 41%
C. 30%
How long will Lucy have to wait before her $2,500 invested at 6% earns $600 in simple interest? A. 2 years B. 3 years C. 4 years D. 5 years E. 6 years
C. 4 years
Circle: Circumference
C= 2πR
Fahrenheit to Celsius
C=(F-32)/1.8
Perimeter of Circle
C=2(pi)r
Used to measure very small lengths, usually 6 inches or fewer
Calipers
Measuring Length or Height
Calipers, Rulers, Yard Sticks, Meter Sticks, Tape Measures,
Irrational number
Can't be written as a fraction, terminating decimal, repeating decimal A square root number ✔️ or a decimal that never ends = 3.1415927......forever and ever or square root ✔️37= 6.082762.......
Irrational Number - Define
Cannot be written as fractions. Common ones are some square roots, cube roots, and pie
10^-2 = 1/100
Centi
Dependent variable
Change as a consequence of changes in other values in the equation. Cannot be manipulated!
A circular graph divided into sectors representing the frequency of an event
Circle (or pie) Graphs
Circle (pie) Graphs
Circular graph divided into sectors representing the frequency of an event.
The numerical part of a term; the number that is being multiplied to the variable
Coefficient
A quantity that does not change
Constant
Calculating Percent
Convert written statements into mathematical equations and solve for an unknown. i.e. What PERCENT of the WHOLE is the PART?
Line graphs are created on
Coordinate Axis
Decimal to fraction
Count how many decimal places then put it over either 100, 1000, etc Ex: .7723 = 4 decimal spaces so it's 7723/10000 (4 zeros) Ex: 12.28 = 12 28/100 Ex: 12.289 = 12 289/1000
(2x-1) (x +5) Simplify the expression. Which of the following is correct? A) 2X2- 5X - 5 B) 2X2-4 C) 2X2-5 D) 2X2 + 9X-5
D
16.) The daily average temperatures during one week in July were 70F. 72F, 76F, 69F, 76F, 75F, and 73F. What was true of the median temperatures during that week? A) It was greater than the mode B) It was less than the average temperature C) It was the same as the mode D) It equaled the average temperature
D
18.) Which type of graph would best indicate the percentage of a hospital budget spent on various items? A) Histogram B) Line Graph C) Scatter Graph D) Circle Graph
D
24.) Grayson left a $ 2.43 tip for a lunch that cost $ 13.50. What percentage tip did he leave? A) 22% B) 20% C) 16% D) 18%
D
29.) Which of the following decimal numbers are approximately equal to √10? A) 3.26 B) 3.2 C) 3.1 D) 3.16
D
30.) 3n+ 3> 9 Solve the inequality A) N>6 B) N>3 C) N>1 D) N>2
D
31) Professor Simpson's class has 75 students in all. Thirty of them are women. Which of the following is the ratio of women to the total number of students in the class? A) 2/3 B) 1/4 C) 3/5 D) 2/5
D
Express 20 % as a fraction in lowest terms A) 1/ 20 B) 1/10 C) 1/2 D) 1/5
D
What is the product of the numbers 0.35x 0.25? A) 0.00875 B) 0.875 C) 8.75 D) 0.0875
D
If a match box is 0.17 feet long, what is its length in inches the most closely comparable to the following? A. 5 1/16 inch highlighter B. 3 1/8 inch jewelry box C. 2 3/4 inch lipstick D. 2 3/16 inch staple remover E. 4 1/2 inch calculator
D. 2 3/16 inch staple remover
Jim works for $15.50 per hour for a health care facility. He is supposed to get a 75 cent per hour raise at one year of service. What will his percent increase in hourly pay be? A. 2.7% B. 3.3% C. 133% D. 4.8% E. 105%
D. 4.8%
Which of the following percentages is equal to 0.45? A. 0.045% B. 0.45% C. 4.5% D. 45% E. 0.0045%
D. 45%
Sally has three pieces of material. The first piece is 1 yd. 2 ft. 6 in. long, the second piece is 2 yd. 1 ft. 5 in long, and the third piece is 4 yd. 2ft. 8in long. How much material does Sally have? A. 7 yd. 1 ft. 8 in. B. 8 yd. 4 ft. 4 in. C. 8 yd. 11 in. D. 9 yd. 7 in. E. 10 yd.
D. 9 yd. 7 in.
Circles: Diameter
D= 2R
What irrational number can be approximated by 3.3166?
DONT multiply the whole decimal cause it will take too long. Take it and round up or down, so take 3.32 and multiply it by 3.32 = 11.0224 So the answer is the irrational number is approximately 11.
10^-1 = 1/10
Deci
Farenheight to Celsius
Deduct 32, multiply by 5 then divide by nine
The exponent or sum of exponents of the variable(s) of a term
Degree
10^1 = 10
Deka
The output based on the input
Dependent Variable
(Estimation Sequence Practice Questions) Describe the following sequence in mathematical terms. 144, 72, 36, 18, 9
Descending geometric sequence
Proportions
Dis-similar (unlike things) Miles/gallon Books/dollars Proportions have to have units
A property that usually removes parentheses in an expression, such as a(x + y) = ax + ay
Distributive Property
From fractions to decimals
Divide
To change a percent to a fraction
Divide the number by 100
Fraction to decimal
Divide the numerator by the denominator
Expressing an improper fraction as a mixed fraction
Divide the numerator by the denominator Top number is the number on left, remainder is numerator and divisor is denominator. Ex: 7/3 = 2 1/3
Converting Fractions to Decimals
Divide the numerator(dividend) by the denominator (divisor).
From fractions to percents
Divide then move the decimal place two places to the right
The numerator in a division problem; example 14/2, 14 is the
Dividend
What is the quotient of
Division! And just multiply it by the reciprocal. Ex: 5/3 divided by 4/15 becomes = 5/3 x 15/4
The denominator in a division problem; example 14/2, 2 is the
Divisor
15% of 500?
Don't make this complicated. What is 10% of 500? Well that's easy, it's 50, so half of that would be 25! So 50+25 is 75% yay
After having to pay increased income taxes this year, Edmond has to sell his BMW. Edmond bought the car for $49,000, but he sold it for a 20% loss. What did Edmond sell the car for? A. $24,200 B. $28,900 C. $35,600 D. $37,300 E. $39,200
E. $39,200
What is the volume of a cube whose width is 5 inches? A. 15 cubic inches B. 25 cubic inches C. 64 cubic inches D. 100 cubic inches E. 125 cubic inches
E. 125 cubic inches
35% of what number is 70? A. 100 B. 110 C. 150 D. 175 E. 200
E. 200
Comparing Fractions to Decimals
Either turn all decimals into fractions or all fractions into decimals.
A statement or sentence can be translated into an
Equation or inequality
Data Interpretation
Every set of data has a dependent and independent variable
Adding algebraic expressions
Ex: (8xsquared -7 +3) + (3xsquared -2x -1) Easy just drop the parenthesis and add the like terms together = 11xsquared -9x +2
Subtracting algebraic expressions
Ex: (8xsquared -7 +3) - (3xsquared -2x -1) Subtracting must put a 1 before the second parenthesis and multiply it in, basically reversing the numbers signs. Then can drop the parenthesis and add the like squares together.. = 5xsquared -5x + 4
Multiplying algebraic expressions
Ex: -5y (7y-squared -4y -2) Distribute the -5y into the parenthesis. *important to not forget to and or change the squares, -5y x 7y-squared = -35y-cubed And -5y x -4y = 20y-squared **take your time on these** it's easy to make a mistake
Fraction addition
Ex: 3 + 3/5= 3 3/5 Ex: 8 + 1/5 = 8 1/5
A number written as a superscript that is used to denote the number of times a number should be multiplied by itself
Exponent
One or more terms consisting of an combination of constants and/or variables
Expression
Celsius to Fahrenheit
F= 1.8 (C) +32
The pharmacist has asked you to compound a 50% Dextrose solution. Before beginning, you want to double-check the pharmacist's calculations. He has asked you to make a 500 ml bag of dextrose solution by adding 250 g of dextrose to 500 ml sterile water. According to your calculations, this will make a 50% Dextrose solution. So the pharmacist calculated the solution correctly. True or False
False
How do you find which fraction is greater?
Find least common denominator and compare numerators
When multiplying two binomials, what does Foil mean?
First Outer Inner Last
Ex: 70 ---- X 7 = x 100
First step is make the problem easier for you! If the top number has a zero/zeros, take away one or two and then take away one or two on the bottom! Ex: 7/10 X 7 = X Then continue to make it easier by simplifying! 7/2 X 7 cause 2 fives go into 10 and 7 fives go into 35! Then solve from there, so much easier! Don't forget needs to be divided! 7 X 7 49 ------ = ---- = 24.5 2
FOIL
First, outer, inner, last
A rational number can be either a
Fraction or a Decimal
giga
G billion 1,000,000,000
highest factor that 2 numbers have in common
GCF
Easy fraction to percentage problem
Get the denominator as close to 100 as possible. Multiply the bottom by a number to get it as close to 100, then multiply the top by that same number. Ex: 8/11 = multiply both by 9 = 72/99 answer is = 72%
Measuring tbsp
Graduated cylinder
Metric: Weight
Gram
Metric measure: Weight
Gram (g)
Weight in Unit of Metric Measure
Gram (g)
Mathmatical symbols: >
Greater than
Word phrases to expressions-ratio of the square h to 6 increased by 8 is=
H-squared/6 + 8
10^2
Hcto (h) = 100
10^2 = 100
Heckto
A graph used to compare the frequencies of an event
Histogram or Bar Graphs
then is there no solution to absolute prob
If [x-n] = negative number if [x-n] < 0 if [x-n]< negative number If [x-n] is less than or equal to negative number
When will the solution be all real numbers
If [x-n] > 0 If [x-n] > negative number
To determine the cost of an event, multiply the number of people attending by each item they will receive & add those results together
If everyone attending is receiving the same items, add all the items first, then multiply by the number of people attending
What irrational number can be approximated by the number 3.3166?
If the square root of 9 is 3 and the square root of 16 is 4 then it must be between those two square roots. Square Root of 11 is a good estimate be 3.3166 is closer to 3 than 16
Calculating Median/Middle value
If there is an even number of values, average the two in the middle (make sure there in order first) Ex: 3, 4, 5, 6, = (4+5) divided by 2 = 4.5 Odd number: the median is the middle number
Which fraction is greater and arrange fractions in order
If you know the decimal for the fraction it's the easiest way to decipher which is greater and arrange them in order If you don't know the decimal for the fraction you want to get the LCD fast! Ex: which is greater 4/7 or 5/9? multiply 4/7 by 9/9 and 5/9 by 7/7. But don't waste time doing the bottom numbers! Only do the top, and then you will know which is greater! So simple!
How is volumed measured?
In cubic units
How is area measured?
In square units
How is perimeter measured?
In units
The variable that is put into the set of data, or the input
Independent Variable
Independent variable
Input into a system that may take on values freely. It can be manipulated doesn't depend on anything.
Most square roots are
Irrational
Number that cannot be written as fractions; square roots, cube roots & pi are the most common
Irrational numbers
Pi
Is 3.14, a number that goes on forever..........
Term
Is a constant, a variable or a product of a constant and a variable.
Polynomial
Is a term or combination of terms.
Rational number
Is any number that can be written as a fraction = 3/8, 3/4 A terminating decimal = .375, .75 Repeating decimal = .33333333, .54545454 (has a pattern) It can be a square root number, ex: square root of ✔️36 is 6 so that's a rational number, or negative square root of ✔️36 is -6 so it's still rational.
_>_
Is greater than or equal to, is at least
>
Is greater than, is more than
When translating word phrase to expressions Factor of is?
Is like saying divisor of Ex: 29 minus K decreased by the factor of six are three = 29-k/6 = 3
Square root
Is the inverse operation of squaring a number Ex: 10 squared is =100 , square root ✔️100
Reciprocal of a Number
Is the multiplicative inverse of the number. i.e. the reciprocal of 1/2 is 2.
Mathmatical symbols: =
Is, was, becomes, measures
If a number is divisible by 10...?
It ends in 0
If a number is divisible by 5...?
It ends in 0 or 5
If a number is divisible by 3...?
It has digits that add up to 3
If a number is divisible by 6...?
It is both even and divisible by 3
If a number is divisible by 2...?
It's even
Independent variable
It's independent, it doesn't change by other variables. Ex: what effect is the treatment having on two groups= the two groups are the independent variable, cause it doesn't change. A person exercises to lose weight = exercising is the independent variable and losing weight "depends" on the exercise
Kelvin
K=Celsius + 273.15
10^3 = 1,000
Kilo
What is the metric measurements? hint. Kangaroos Hop Down Mountains During Cold Months
Kilo Hecto Deka Meter Deci Centi Milli
10^3
Kilo (k) = 1,000
Square: Area
L x W
solve 1/4=1/6
LCD of denominators is 12 1x3/4x3+1x2/6x2=3/12+2/12 3/12+2/12 =5/12
smallest multiple that 2 numbers have in common
LCM
Which of the following is the roman number equivalent of 80?
LXXX
Greatest common factor (GCF)
Largest number that is a factor of two or more numbers. For example for 15 factors are (1,3,5,15) and for 35 factors are 91,5,7,35) SO the GCF is 5.
The smallest common multiple of the denominators or the least number that both denominators divide into evenly
Least Common Denominator
Types of Measurement
Length Volume Weight
English Units
Length: Inches, Foot, Yard, Mile Volume: Ounces, Cup, Pint, Quart, Gallon Weight: Ounces, Pounds
Metric Units
Length:Millimeter, Centimeter, Decimeter, Meter, Dekameter , Hectometer, Kilometer. Volume: Milliliter, Centiliter, Deciliter, Liter, Dekaliter, Hectoliter, Kiloliter. Weight: Milligram, Centigram, Decigram, Gram, Dekagram, Hectogram, Kilogram.
-
Less than
Mathmatical symbols: -
Less than
Mathmatical symbols: <
Less than
Terms that have the same variable and with the same exponent
Like Terms
A graph that shows changes over a period of time or compares the relationship between two quantities
Line graphs
Solving addition/subtraction problems involving decimals
Line up the decimal points
Metric: Volume
Liter
Metric measure: Volume
Liter (L)
Volume in Unit of Metric Measure
Liter (L)
Cube root
Little 3 ✔️of a number..what number multiplied by 3 is the cube root Ex: Little 3 ✔️8 = ✔️2x2x2 answer: 2 is the cube root of 8!
mega
M million 1,000,000
roman numerals
M, D, C, L, X, V & I
an antique gold coin is stamped with the date MCCXXXIV; what is this date in arabic numerals
M=1,000 CC=100+100=200 XXX=10+10+10=30 IV=5-1=4 1234
Operations must be performed in the correct order when performing calculations with numbers
Mathematical
A phrase in words can be translated into a
Mathematical Expression
Absolute value
Measures distance away from zero on a number line Removing all negative signs and to think of all numbers as positive If you have a negative number on the opposite side, this is no solution.
Measuring a pint
Measuring cups
Measuring spoons for
Medication
Metric: Length
Meter
Length in Unit of Metric Measure
Meter (m)
Metric measure: Length
Meter (m)
Used for measurements no longer than 1 meter
Meter Sticks
10^-3 = 1/1,000
Milli
A polynomial with one term
Monomial
Dividing polynomials, the divisor can be a
Monomial or Binomial
Mathmatical symbols: +
More than
From decimals to percents
Move the decimal place two places to the right and add a percent sign
To change a decimal to a percent
Move the decimal place two places to the right and add a percent sign
From decimals to fractions
Move the decimal two places to the right and make the number the numerator and a put 100 as the denominator, then reduce
What is the product of
Multiplication
A rule that makes it possible to isolate the variable in an equation by multiplying both expression by the reciprocal of the variable's coefficient
Multiplication Principle
Division and Multiplication of Fractions or Mixed Numbers - Summary of Steps
Multiplication: 1. Convert Mixed Number to Improper Fraction 2. Simplify 3.Multiple numerators and denominators together 4. Simplify and convert any improper fractions Division: Simplify, flip second fraction and multiply as above
Multiplication and Division
Multiply and divide from let to right.
Celsius to farenheight
Multiply by 9, divide by 5, then add 32
Finding a total area/square footage of a square/rectangle
Multiply one side by the other Ex: rectangle is 6ft by 8ft = 48ft
Multiplying Polynomials
Multiply the coefficients and multiply the variables. When multiplying common variables (such as x by x) add the exponents on the common variables.
Exponents: When an exponent is raised to another exponent
Multiply the exponents (3²)⁴= 3⁸
To change a fraction to percent
Multiply the fraction by 100 Reduce if necessary.
Do mathematical expression have equal signs?
NO!!!
Do exponents have to be integers?
NO!!! Fractional or decimal exponent follow the same rules
Whole Numbers
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
Percent Increase Formula
New Value - Original Value/ Original Value * 100
Percent increase
New value - old value over old value X 100
10^0 = 1
No prefix
If |x-n| < 0, then there is
No solution
If |x-n| < negative #, then there is
No solution
If |x-n|= negative #, then there is
No solution
Are all roots irrational numbers?
No, roots can be rational numbers.
Real number
Number that appears as a rational and irrational number
Irrational numbers
Numbers that cannot be written as fractions
Irrational Number
Numbers that cannot be written as fractions. I.E. Square roots, cube roots, and pi.
Dividend and Divisor - which is which
Numerator = Dividend Denominator = Divisor (divisor goes on outside of fraction bar)
Setting up Proportions
Numerators of both ratios have to be same unit. Denominators of both ratios have to be same unit.
Any number raised to the power of 0 is equal...
ONE! for example, 12^0=1
The number 1 raised to any power is equal to...
ONE! for example, 1^25=1
RATIO
Of/to ex. "the ratio of 20 oranges to 12 apples is 20/12"
Percent decrease
Old value - new value over original value X 100
Word phrases to expressions-one half of the cube of K=
One half means division = k-cubed/2
Expression
One or more terms consisting of any combination of constants and/ or variables.
Expression
One or more terms consisting of any combination of constants and/or variables
To denote any point given, either on one of the axes or in on of the quadrants created by the two axes, writ the X-coordinate and then the Y-coordinate as an
Ordered Pair (X,Y)
Percent Decrease Formula
Original Value - New Value/ Original Value * 100
perimeter of a rectangle
P = 2l + 2w
perimeter of square
P = 4s
perimeter of a triangle
P = s + s + s
Square: Perimeter
P= 2L + 2W
Triangle: Perimeter
P= S₁+S₂+S₃ (just add up all the sides)
Perimeter Formula for Rectangle
P=2L+2W or P= 2(L+W)
Perimeter Formula for Parallelogram
P=2a+2b or P= 2 (a+b)
Perimeter Formula Square
P=4s
Find what number is some percentage of a given number......(what number is 20% of 40?)
P=W x % (p=part) (w=whole) (%=percentage)
Perimeter Formula Triangle
P=a+b+c (sum of all sides) For equilateral triangle P=3s
Perimeter Formula for Trapezoid
P=a+b1+c+b2
order of operations
PEMDAS: parentheses exponents multiplication/division (L to R) addition/subtraction (L to R)
"Please Excuse My Dear Aunt Sally"
Parentheses, Exponent, Multiplication & Division, Addition & Subtraction.
PEMDAS
Parenthesis Exponents Multiplication and Division (from left to right) Addition and Subtraction (from left to right)
PEMDAS
Parenthesis, Exponents, Multiplication, Division, Addison, Subtraction
what is the Percent Formula
Part= Percent x Whole
What does percent mean
Per 100 or over 100
Remember to think logically in percents!
Percents are always per 100! So if they give you a problem like: what percent of 25 is 5? Well obviously 5 goes into 25, 5 times. So if you think money $, $20 out of 100 is 20%!
Measuring a quart
Pipettes
A term or combination of terms
Polynomial
Monomial
Polynomial with one term
Binomial
Polynomial with two terms
Types of measurments: Weight
Pounds, ounces, grams,
The metric system is a system of measurement based on
Prefixes and every prefix corresponds to a power of 10
Probability
Probability= Number of desired outcomes/number of total possible outcomes
States that two ratios are equal
Proportion
The answer to the division problem, example 14/2; 7 is the
Quotient
1 ML = 1CM CUBED
REMEMBER THAT!!!
Problems use proportion to determine the difference in completion times for a given task
Rate of Change
Used to express a relationship between 2 quantities
Ratio
Any real number that can be written as a fraction, terminating decimal or repeating decimal
Rational Number
A number that appears on the number line as either a rational or an irrational number
Real Number
Rational Number
Real number that can be a fraction, terminating decimal or repeating decimal
Of a number is the multiplicative inverse of the number; ex 1/2 is 2; multiplicative inverse of -4 is -1/4
Reciprocal
Addition/Subtraction Problems with Decimals
Remember to line up the decimal points.
Addition/Subtraction Problems with Fractions
Remember to use a Common Denominator
A system of writing numbers using a combination of M, D, C, L, X , V & I
Roman Numeral System
Used for measurements no longer than 12 inches
Rulers
Surface area of a circle
SA=4(pi)r^2
Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?
Sale Price = $450 - 0.15*$450 = $382.50, Employee Price = $382.50 - 0.2*$382.50 = $306
Measurement tools for Weight
Scales
Weight
Scales
Due to the fact that the world and the universe are very large, there must be methods that will allow measurement of these very long distances
Scaling
To determine the given cost of a set of items
Select the items to be purchased and add their prices together
Cost of a Given Set of Items
Select the items to be purchased and add their prices together.
Adding a bunch of fractions together
Separate the fractions and add them first then combine Ex: 3 1/2 + 5 1/3 + 1 3/4 Take the fraction part first and add them together 1/2 + 1/3 + 3/4 = 19/12 simplify this by making making it 1 7/12 Then add up the whole numbers 3+5+1= 9 9 + 1 7/12= 10 7/12
Chart
Serves as a visual picture of information from a table.
1250 college students enrolled in 50 sections of beginning algebra, and 1550 in advanced algebra. How many sections offered?
Set it up as a proportion: 1250/50 = 1550 Remember that when there is an equals sign between you have to cross multiply! 1550 X 50 ----------- (get rid of one zero up top and on bottom, and simplify) 1250 155 X 2 310 -------- = ----- 62 sections of beginning algebra needed 5 5
Sarah needs to make a cake and some cookies. The cake requires 3/8 cup of sugar and the cookies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need?
She needs 3/80 of a cup of sugar
the only common facto between the numerator and the denominator is 1
Simplified Fraction
Exponents
Simplify the exponents
The addition principle and the multiplication principle may be applied when
Solving an equation with one unknown
Dependent variable
Something that depends on other factors Ex:test score is dependent variable cause it depends on how much someone studies, a worker gets paid by the hour = gets paid is the dependent variable cause it depends on how many hours are worked
Scaling
Specifying a percentage of the original size to enlarge or reduce an object.
Proportion
States that the two ratios are equal.
Kelvin to Celsius
Subtract 273
Exponent: When bases are the same and divided
Subtract the exponent 4⁷÷4⁵= 4²
Perimeter
Sum of all sides Ex: garden is a rectangle that's 25 feet but 30 feet, add it all together. 25+25+30+30=110
how to find the SUM OF CONSECUTIVE NUMBERS
Sum=(Average)x(number of terms)
how to use the AVERAGE to find the SUM
Sum=(average)x(number of terms)
Arabic Numeral System
System of writing numbers using a combination of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Roman Numeral System
System of writing numbers using a combination of M, D, C, L, X, V, I
tera
T trillion 1,000,000,000,000
If a number is divisible by 4...?
THe last two digits (if there are that many) are divisible by 8
From percents to decimals
Take off the percent sign and move the decimal two places to the left
To change a percent to decimal
Take off the percent sign and move the decimal two places to the left
Used for larger measurements that are usually no more than 50 feet long
Tape Measures
Types of measurments: Volume
Teaspoons, tablespoons, pints, quarts, gallons, liters
A constant, a variable, or a product of a constant and a variable; an expression separated by a plus or minus sign
Term
Like Terms
Terms that have the same variable and with the same exponent.
Like terms
Terms that have the same variable within the same exponent
Quotient
The answer to the division problem
Quotient
The answer to the division problem; for example 14/2 7 is the quotient.
Estimation
The approximate value of the solution to a problem.
Denominator
The bottom number in a fraction
Divisor
The denominator in a division problem
Divisor
The denominator in a division problem; for example 14/2 2 is the divisor.
Determining the range in a set
The difference between the highest and lowest value in the set
If a number is divisible by 9...?
The digits add up to 9 or multiples of 9
Absolute Value
The distance a number is from zero on a number line. ALWAYS POSITIVE! Absolute Value of number n, written InI means: InI = n when n is a positive number InI = -(n) when n is a negative number.
Dividing Polynomials
The divisor can be a monomial or binomial. When divisor is monomial: 1.create fractions by dividing each term in the dividend by the divisor. 2. reduce each fraction that was created 3. Make sure that nothing else will simplify
Degree
The exponent or sum of exponents of the variable(s) of a term
Degree
The exponent or sum of exponents of the variables of a term.
If a number is divisible by 8...?
The last three digits (if there are that many) are divisible by 8
Calculating the mode
The most frequent score Ex: 87, 92, 87, 88, 91. = 87 would be the mode cause it's most frequent
Median
The number in the middle
Mode
The number that appears most frequently
Dividend
The numerator in a division problem; for example 14/2 14 is the dividend.
Dividend
The numerator of a division problem
Coefficient
The numerical part of a term The number that is being multiplied to the variable
Coefficient
The numerical part of a term; the number that is being multiplied to the variable.
Dependent variable
The output based on the input
Dependent Variable
The output based on the input. On an xy plane, y values are usually the dependent variable.
Decimal Place
The position of a number to the right of the decimal point. For example, 0.123 1=tenths 2=hundreds 3=thousands place
Integers
The set of whole (+ or -) numbers, including zero. Integers do not include fractions, decimals, or mixed numbers.
What do you do if roman numeral are written in order of value from smallest to greatest?
The smaller number is subtracted from the larger number. For example, LIV represent 50+ (5-1)=54 Subtact since I (which equals 1 is before V which equals 5)
Least Common Denominator
The smallest common multiple of the denominators or the least number both denominators divide into evenly.
Independent variable
The variable that is put into the set of data, or the input
Independent Variable
The variable that is put into the set of data, or the input. On an xy plane, x values are usually the independent variable.
Calculation of Percents
The word "of" = multiply. 15 of 500 = % --- > 15*500 =25% What percent of 250 is 10? ---> set up equation and solve 250X = 10 -->X = 4%
Roman numerals important to remember
They are additive! 10+5+1+1 = XVII Left to right - **do each place value at a time** like Keshwani 😁 If a smaller number is to the left, your subtracting it from the next letter.
Ratios
Things that are similar (like things) Boys vs girls Blue cars vs red cars Radios don't have units
Materials and Cost of Planning an Event
To determine the cost of an event multiply the number of people attending by each of the items they will receive and add those results together. If everyone attending is receiving the same items, add all the items first, then multiply by the number of people attending.
Comparing Fractions
To determine whether one fraction is greater than another, find a common denominator for the fractions, the fraction with the greatest numerator is the greater fraction.
Comparing Decimals
To determine which decimal is greater than the other compare the digits in each of the place values, beginning with the greatest place value.
Calculating Mean/Average
Total the values, then divide by the number of values Ex: mean of 3, 4, 5 = 12/3 = 4
Penicillin 400,000 units/5 ml means there are 80,000 units of drug in 1 ml of solution. True or False
True
If an IV drip was started on a patient at 9 am on Monday and changed 16 hours later, what days and time was the IV drip changed?
Tuesday at 01:00
Can a fraction have a denominator of zero?
Typically no! if it does it is considered undefined
No expressions between to 2 sets of parenthesis
Use FOIL **And don't forget to change the squares**
Solving addition/ subtraction problems involving fractions,
Use a common denominator
Measuring weight ex: grams, pounds, oz
Use a scale
Rate of Change
Use proportions to determine the difference in completion times for a given task.
FOIL
Used to determine the product of two binomials. FOIL: First, Outer, Inner, Last 1.Multiply the first term within each set of parentheses 2.Multiply the outer terms within each set of parentheses 3. Multiply the inner term within each set of parentheses 4. Multiply the last terms within each set of parentheses. 5. Combine like terms.
Ratio
Used to express a relationship between two quantities. Can be written as fractions, with colons, or with words. Ratios are always written in simplest form.
An unknown quantity in an expression, usually in the form of a letter such as X,Y, & Z
Variable
Find what number another number is a given percentage of.... (what number is 8 20% of?)
W=P/%
Dividing algebraic expressions
Watch out this can get tricky Ex: (24x-squared y + 14xy) Divided by (-4xy) Put a line under the first parenthesis and divide -4xy into it **when your dividing the squares are dropped, and if there's an xy into xy then they cancel out..
What is the factors of 12? Is the same as saying what is the divisors of 12?
What can go into 12? =1, 2, 3, 4, 6, 12 *make sure you put 1, it's always a divisor, and the actual number 12.
Changing a mixed fraction 2 1/3 to a improper fraction
Whole number multiplied by denominator then added to numerator = 7/3 bottom number stays the same!
Parentheses
Work on inner most set of parentheses first then work outward.
To Solve a proportion use this formula
Write Formula
The horizontal axis is referred to as the
X-axis
The vertical axis is referred to as the
Y-axis
Slop-Intercept Formula
Y= MX+B M= Slope X=0 B= Where the line crosses the y axis
Used for measurements no longer than a yard, 3 ft., or 36 inches
Yard Sticks
What do you do if roman numeral are written in order of value from greatest to smallest?
You add them together For example, LVI represents 50+5+1=56
Simplify Fractions while Multiplying - Saving time!
You can Cross Simplify fractions by dividing opposite numerators and denominators with a common factor before multiplying.
Approximating Decimals of Irrational Numbers - What is the cube root of 10?
You know cube root of 8 and the cube root of 27 is 3 so it must be between 2 and 3 and closer to 2 - estimation: 2.15
area of a trapezoid
[(base + base)÷2] × height
[x-n] = a
[x-n] = a OR [x-n]= -a
[x-n]> a
[x-n] > a OR [x-n]< - a
[x-n] is greater or equal to a
[x-n] is great than or equal to a OR [x-n] is less than or equal to -a
2a + 5 = 14
a = 4.5
pie (circle) graphs
a circular graph divided into sectors representing the frequency of an event- percentage of a whole, where the whole circle or pie equals 100%- shows how much of the whole each part represents
ratio
a comparison of 2 #'s, usually by division (ex: in a class of 15 people, there are 7 boys & 8 girls. The ratio pf boys to girls is 7 to 8 or 7:8 or 7/8)
term
a constant, a variable, or a product of a constant and a variable
Percent Decrease
a decrease given as a percent of the original amount: ((Original Value - New value) / Original Value) x 100 Remember: The whole is the original value, or the value that existed first.
improper fraction
a fraction that has a numerator larger than its denominator
Proper fraction
a fraction whose denominator is greater than its numerator.
Improper fraction
a fraction whose numerator is greater than its denominator
histograms
a graph used to compare the frequencies of an event; displayed on vertical touching bars; continuous data
negative powers
a number raised to the exponent -x is the reciprocal of that number raised to the exponent x ex. 2^-3= 1/2^3 =1/8
real number
a number that appears on the number line as either a rational number/irrational number
A graphical representation requires the reader to use
a paper or ruler marked with the length to measure the desired distance
binomial
a polynomial with 2 terms
monomial
a polynomial with one term
distributive property
a property that usually removes parentheses in an experssion
constant
a quantity that does not change
rate
a ratio made up of 2 different units of measurement or amounts (ex: I can drive my car 250 mi on 10 gal of gas. This relationship can be expressed as a ratio of miles to gallons: 250 to 10, 250:10, or 250 mi/ 10 gal = 25/ 1 or 25 miles per gal)
multiplication principle
a rule that makes it possible to isolate the variable in an equation by multiplying both expressions by the reciprocal of the variable's coefficient
addition principle
a rule that makes it possible to move terms from one side of an equation to the other by adding opposites to each expression
Decimal Point
a symbol used to separate the ones place from the tenths place in decimal or dollars from cents in currency.
roman numeral system
a system in writing numbers using a combination of M, D, C, L, X, V, and I M=1,000 D=500 C=100 L=50 X=10 V=5 I=1
polynomial
a term or combination of terms
Distributive Property
a(b + c) = ab + ac
A student decides to have lunch at the school deli. The special for the day is a hamburger basket including fries for $6.95. the student adds a side salad for $ 2.45, a medium drink for $1.49, and a browniefor $1.19. Which of the following is the cost of this lunch?
a) $10.89 b) $11.99 c) $12.08 d) $12.20 Correct answer is c= $12.08
A couple is buying living-room furniture. The sofa retails for $ 899, the chair with ottoman for $695,the coffee table for $ 379, end tables for $ 229, and a set of lamps for $149, which of the following is an estimate of the cost of the living room?
a) $2,200 b) $2,300 c) $2,600 d) $2,900 Correct answer is b=$2,300
Reconcile this checking account for the month of April 2009. The previous balance is $2,355.14. Deposits were made for $1,527.28. Checks were written for $ 1,203.97. Interest earned is $ 1.56 and there is a service charge of $5.00. Which of the following is the balance after reconciling this account?
a) $2,675.01 b) $2,671.89 c) $2,678.45 d) $2,685.01 Correct answer is A = $ 2,675.01
A legal assistant works at a local law firm and earns $1,278.00 per pay period. The assistant's deductions each pay period are: Federal tax $125.78, Federal Insurance $63.28, State Tax $93.68, Retirement Plan $50.00, and Health Insurance $ 89.51. Which of the following is the assistant's take- home pay per pay period?
a) $216.75 b) $422.25 c) $855.75 d) $997.75 Correct answer is c= $855.75
A School nurses' association is having its annual conference in september. Nurses' elegant events is catering the closing luncheon. Reservations have been recieved for 315 nurses and 53 guests. The luncheon cost for each nurse is $18.00 and for each guest $25.00. which of the following is the cost of the luncheon?
a) $3,755.00 b) $6,545.00 c) $6,995.00 d) $8,829.00 Correct answer is c= $6,995.00
A fence being built to enclose a backyard. They yard is 150 Feet (ft) wide by 325 ft long. The back of the house (325 ft) will act as one side of the fence. Fencing sells for $13.00 per ft. Which of the following will be the cost of the fence?
a) $6,175 b) $8,125 c) $10,400 d) $12,350 Correct answer is b=$8,125
Order the following list of numbers from least to greatest. -3, 4, 11/3, 3.8
a) -3,3.8,11/3,4 b) 4,3.8,11/3,-3 c)-3,3.8,4,11/3 d)-3,11/3,3.8,4 Correct answer is d= -3, 11/3, 3.8, 4
6x(5+7)/4-7x2+3x3 Simplify the expression above. Which of the following is correct? ( / means divide)
a) -72 b) -5 c) 13 d) 75 Correct answer is c= 13
Which of the following percents is equivalent to 0.003?
a) 0.03% b) 0.3% c) 3% d) 30% Correct answer is b=0.3%
which of the following is the number of centimeters in 4 meters?
a) 0.04 b) 0.4 c) 40 d) 400 Correct answer is d=400
5.13 x 0.02 Simplify the expression above
a) 0.1026 b) 1.026 c) 10.26 d) 1026 Correct answer is a=0.1026
The scale on a map indicates that every 1 centimeter (cm) on the map equals 10miles (mi) on the ground. The desired distance on the map meausures 8cm. Which of the following numbers represents the distance in miles?
a) 0.8 b) 8 c) 80 d) 800 Correct answer is c=80
7/8 -5/12 Simplify
a) 1/12 b) 11/24 c) 1/2 d) 3/5 Correct answer is b=11/24
215.4% of 55=_________________ which of the following completes the equation above?
a) 11.847 b) 118.47 c) 1184.7 d) 11847 Correct answer is b=118.47
Many builders have a cornerstone that gives the date the building was completed. In Arabic numerals, Which of the following dates is represented by MDCCCLIV?
a) 1845 b) 1846 c) 1854 d) 1855 Correct answer is c= 1854
which of the following decimal numbers is appoximaterly equal to (squar root symbol) 27?
a) 2.56 b) 3.14 c) 4.2 d) 5.2 Correct answer is d=5.2
A symphony has 125 musicians. Seventy-Five of them are women. Which of the following is the ratio of the men to the total musicians in the symphony?
a) 2/5 b) 3/5 c) 2/3 d) 5/2 Correct answer is a= 2/5
(x^2 + 3x -2) - ( x^2 -2x -5) Simplify the expression above, which of the following is correct?
a) 5x+7 b) x^2+5x c) x-7 d) 5x+3 Correct answer is d= 5x+3
2 1/3x 4 1/2 simplify the expression above. Which of the following is correct?
a) 6 1/6 b) 8 1/6 c)10 1/2 d) 20 1/2 Correct answer is c= 10 1/2
783-45 Solve
a) 732 b) 737 c) 738 d) 742 Correct answer is c=738
the enrollment at a college went from 625 to 710 students over a period of 1 year. Which of the following is the percent of increase to the nearest tenth of a percent?
a) 8.8% b) 11.4% c) 12.0% d) 13.6% Correct answer is D=13.6%
An average person grows taller with age. Which of the following is the independent variable in the event described above?
a) Age b) Height c) Hair Color d) Weight Correct answer is a= Age
which of the following metric units of measurement is most reasonable to measure the amount of liquid oral medication?
a) Milliliters (ml) b) Liter ( L) c) Deciliter (dL) d) Kiloliter (kL) Correct answer is a= MIllileters ( ml)
a chemist must measure exactly 2.3 millileters of a chemical to add to his experiment. Which of the following measurement tools is appropriate for this task?
a) beaker b) pipette c) Measuring Cup d) Graduated cylinder Correct answer is B= Pipette
a nurse is collecting catergorial data on the different ethinicities of her clients. Which of the following graphs should the nurse use to present the date in terms of percents totaling 100?
a) pie chart b) Line graph c) histogram d) scatterplot Correct answer is A= pie chart
x/2 +5=9 solve the equation above. which of the following is correct?
a) x=4 b) x=8 c) x=13 d) x=14 Correct answer is B= x=8
A father's age, y, is 4 less than three times his daughter's age, x. Which of the following algebraic equations best represents the statement above?
a) y=3x-4 b) y=3x+4 c) x=3y-4 d) x=3y+4 Correct answer is a= y=3x-4
/x+2/=5 what is the solution set for the following equation
a) {-7,3} b) {-3,7} c) {3,7} d) {-7,-3} Correct answer is a= { -7,3}
A man is putting a fence around his rectangular yard. His lot measures 13.5feet(ft) long and 47.75ft wide. The fencing comes in rolls that are 50 ft long. Which of the following is the number of rolls of fencing the man will need to buy?
a)1 b)2 c)3 d)4 Correct answer is c=3 rolls
(a / b)^2
a^2 / b^2
(a x b)^2
a^2 x b^2
(a^n)^m
a^n(x)m
a^n x a^m (Multiplication)
a^n+m
a^n / a^m (division)
a^n-m
angle less than 90°
acute
perimeter
add all sides
take-home pay
add deductions together and then subtract that total from beginning salary
When multiplying common variable (such as X times X),
add the exponents on the common variables
How to find the AVERAGE of CONSECUTIVE NUMBERS
add the lowest and highest number and divide by 2
how do you find perimeter?
add up all the sides
how to find the original whole before percent increase/decrease
after decreasing by 5 percent, the population is now 57,000. what was the original population? setup: .95x(original population)=57,000 original popluation=60,000
scaling
allow measurement of very long distances; long distances can be scaled down to very small lengths that will fit on a paper, such as map.
Way to remember x,y
always alphabetical, x,y
When doing absolute value problems, always remember to ____before doing problem
always remember to isolate absolute value if possible
proportion
an equation of 2 equal ratios. All proportions equations have have a special property: cross products are equal. When you multiply the numerator on the left side of the equation by the denominator on the other side & then multiply the left-side denominator by the right-side numerator, the are products equal to each other (ex: if a car gets 25 miles to the gallon, then how many gallons do I need to drive 125 miles? set up a proportion to solve this problem. Make sure you align your units correctly on both sides of the equation: in this case, miles across from miles & gallons across from gallons 25 mi / 1 gal = 125 mi / x gal now cross multiply: 25x = 125 now divide both sides by 25 to solve for x. x = 5 this is your answer- you need 5 gal to go 125 mi
Percent Increase
an increase given as a percent of the original amount: ((New Value - Original Value)/ Original Value) x 100 Remember: The whole is the original value, or the value that existed first.
variable
an unknown quantity in an expression
rational #'s
any # that can be written as a fraction, terminating (ending) decimal (0.25), or repeating decimal (0.212121....)
Even number
any integer that can be divided by two without leaving a remainder.
Odd Number
any integer that cannot be divided evenly by 2.
Factors
any numbers that are multiplied together to obtain a product. For example, 2 x 3=6 (2 and 3 are factors)
mixed numbers
any numbers that represents the sum of a whole number and a proper fraction
rational number
any real number that can be written as a fraction, terminating (ending) decimal or repeating decimal
estimation
approximate value; round digits so that there is only one nonzero digt
how to find the area of the double shaded area?
area of the big circle minus the area of the little circle. pie x ? squared minus pie x ? squared
how to calculate the volume of a prism?
area x height
how to find the AREA of a TRIANGLE
area= 1/2(base)(height)
area of a square
area=side squared
isosceles triangles
at least two equal sides, and two equal angles
how to find average rate
average A per B= Total A/Total B
average speed
average speed=total distance/time
area of a parallelogram?
base x height
area of a triangle?
base x height divided by 2
areas of a parallelogram
base × height
what measures columes
beakers, graduated cylinders, cups, pipettes, measuring spoons
appropriate unites of measure and measurement tools (volume)
beakers, graduated cylinders, measuring cups, pipettes, measuring spoons
denominator
bottom part of fraction
how do you find COMMON FACTOR of two numbers
break both numbers to their prime factors, then see which numbers they have in common, then multiply the shared prime factors in all ways possible
centi
c hundredth .01 (decimal = 2)
3c - 78 = 12
c = 30
Irrational number
cannot be written as fractions or decimals because the number of decimal places is infinite and there is no recurring pattern of digits within a number.
0.01
centi
10^-2
centi (c) = 1/100
Line graph shows
changes over a period of time or compares relationship between two quantities
When multiplying polynomials, multiply the
coefficients and multiply the variables
figures with the same size and shape
congruent
similar triangles
corresponding angles are equal, corresponding sides are proportional
what is it measured in?
cubic cm or m
Of the following units, which would be most likely to measure the amount of sugar needed in a recipe for 2 dozen cookies
cups
Of the following units, which would be most likely to measure the amount of sugar needed in a recipe for 2 dozen cookies?
cups
Which of the following would be an appropriate unit to measure sugar for a cookie recipe?
cups
deci
d tenth .1 (decimal = 1)
deca
da 10
0.1
deci
10^-1
deci (d) = 1/10
10
deka
10^1
deka (da) = 10
Every set of data has a
dependent and an independent variable
area of a trapezium?
diagonal 1 x diagonal 2 divided by 2
distance across the middle of a circle
diameter
answer in subtraction
difference
To convert centimeters into inches
divide 2.54 cm
MM to CM
divide by 10
measurement for area (mfa) MM to CM
divide by 10 squared
CM to M
divide by 100
mfa CM to MM
divide by 100 squared
M to KM
divide by 1000
capacity: L to KL
divide by 1000
capacity: ML to L
divide by 1000
mfa M to KM
divide by 1000 squared
converting from percents to decimals
divide by 100; remove % and move the decimal point left two places
converting from fractions to decimals
divide the numerator by the denominator
measurement of volume (mov): MM to CM
divided by 10 cubed (3)
CM to M
divided by 100 cubed
M to KM
divided by 1000 cubed
circle (or pie) graphs
divided into sectors representing the frequency of an event
how to calculate the area of a quarter of a circle?
do one quarter x pie x radius squared
constant
does not change
circumference of a circle
dπ
Real Number - Define
either rational or irrational
any non zero number raised to the exponent 0
equals 1
zero raised to any non zero exponent
equals zero
triangle with 3 equal sides
equilateral
multiplied together get a product
factor
determining which fraction is greatest
find a common denominator for the fractions- the fraction with the greater numerator is the greater fraction
comparison of rational numbers (fractions/decimals)
find a common denominator to compare convert all fractions to decimals or all decimals to fractions
how to simplify a radical
find perfect squares
permutation problem
five runners come in first second and third how many possible outcomes? 5 x 4 x 3 =60 possible outcomes
how to find the HYPOTENUSE or a LEG of a RIGHT TRIANGLE
for all right triangles, the Pythagorean theorem is a2 + b2 = c2 where a and b are the legs and c is the hypotenuse
proper fraction
fraction whose numerator is less than the denominator
once LCD is determined, rewrite each fraction as an equivalent
fraction with the least common denominator
radius
from centre to edge
diameter
from edge to edge
bar graph
graph used to compare the frequencies of an event; the frequencies are displayed as non-touching, horizontal/ vertical bars; noncontinuous data
how to find the RANGE
greatest value minus the least value
Both/Neither problems
group 1 + group 2 + neither - both = total
hecto
h 100
volume of a triangle?
half x base x width x height
100
hecto
whole numbers
i.e. 0,1,2,3, etc.
solutions and all real numbers as a solution for equations involving absolute values
if /x-n/... =negative number-no solution <0-no solution <negative number-no solution < or equal to negative number-no solution >0-all real numbers >negative number-all real numbers
Types of measurments: Length or height
inches, feet, yards, miles, meters
appropriate unites of measure and measurement tools (length or height)
inches, feet, yards, miles, meters calipers- small lenghts; usually 6 inches or less rulers-no longer than 12 inches yard sticks-no longer than 1 yard, 3 feet, or 36 inches meter sticks-no longer than 1 meter tape measure-larger measurements; no more than 50 ft long
Rational number
includes all interferes, decimals, and fractions. Any terminating or repeating decimal number is a rational number.
Dependent versus independent
independent = input, unaffected by other dependent - output, dependent on the other "the amount of studying she did for the TEAS impacted her score" The score is dependent on the studying
pipettes
instrument used for measuring small volumes of fluid
simple interest
interest= amount or principal x (interest rate)(number of payment periods)
Any number to the power of 1.....
is equal to itself. Ex 2^1=2
>, Read as
is greater than or equal to, is at least
>, Read as
is greater than, is more than
<, Read as
is less than or equal to, is at most
_<_
is less than or equal to, is at most
<
is less than, is no greater than
<, Read as
is less than, is no greater than
dependent variable
is the output based on the input, (statistics) a variable in a logical or mathematical expression whose value depends in the independent variable
=
is, was, measures, becomes
=, Read as
is, was, measures, becomes
triangle with 2 equal sides
isosceles
kilo
k 1,000
Add or subtract the numerators, while
keeping the common denominators the same
1000
kilo
LCD
least common denominator; the smallest common multiple of the denominators or the least number that both denominators divide into evenly
volume equals
length * width * height
area of a rectangle?
length x width
how to calculate volume of a rectangular prism?
length x width x height
area
length × width
volume
length × width × height
common units of measure in the metric system
length-meter-m volume-lite-L weight-gram-g
conversion from one measurement scale to another ( English versus metric measurement system)
length: 1 inch is about 2.54 cm 1 yard (1.09 yards) is about 1 meter volume: 1 quart (1.06 quarts)= 1 L weight: 2.2 pounds is about 1 kilogram 1 ounce is about 28 grams
conversion from one measurement scale to another ( English measurement system)
length: 1 foot = 12 inches 1 yard= 3 feet 1 mile=5280 feet volume: 1 cup=8 ounces 1 pint=2 cups 1 quart = 2 pints 1 gallon= 4 quarts weight: 1 pound= 16 ounces 1 ton= 2000 pounds
conversions between English and metric measurement
length: 1 inch=2.54 cm 1 km=1000 m =0.62 mile 1 m=39.37 inch 1 cm =0.394 inch 1 mile=1609 m 1 yard=0.914 m weight: 1 kg=2.2 pounds 1 ounce = 28g 1 pound=0.45 kg volume: 1 L = 1.06 quarts 1 ounce=30 mL 1 teaspoon= 5 mL 1 quart=0.95 L 1 gallon=3.785 L
conversion from one measurement scale to another ( metric measurement system)
length: 1 mm=0.001 meters 1 cm=0.01 meters 1 decimeter=0.1 meters 1 meter=1 meter 1 dekameter=10 meters 1 hectometer= 100 meters 1 kilometer=1000 meters volume: 1 mL= 0.001 L 1 centiliter=0.01 L 1 deciliter=0.1 L 1L= 1L 1 dekaliter=10 liters 1 hectoliter= 100 liters 1 kiloliter=1000 liters weight: 1 milligram= 0.001 grams 1 centigram=0.01 grams 1 decigram=0.1 grams 1 gram=1 gram 1 dekagram=10 grams 1 hectogram=100 grams 1 kilogram= 1000 grams
-, Read as
less than
When subtracting whole numbers it is important to arrange the numbers in columns with
like place values in each column
The scale may also be represented graphically; with a graphical representation, there would be a
line on the map indicating the length of the line
Of the following units which would be more likely used to measure the amount of water in a bathtub?
liters
how to find the dimensions or area of an inscribed or circumscribed figure
look for the connection, is the diameter the same as a side or a diagonal?
milli
m thousandth .001 (decimal = 3)
equation
mathematical sentence in which 2 expressions are set equal to each other
inequality
mathematical sentence in which one expression may not be equal to another expression
"is"
means "="
evaluate
means to find the value of something
meter stick
measures no longer than 1 meter
yard stick
measures no longer than 1 yard, 3 feet, or 36 inches
middle number
median
What is the standard measurement system for medical professions?
metric
0.001
milli
10^-3
milli (m) = 1/1000
dividing fractions
mixed number? -yes-convert mixed number to improper fraction (then proceed) -no-change division to multiplication, flip the second fraction, and continue. -simplify -multiply numerators and denominators together -simplify -done
multiplying fractions
mixed number? -yes-convert mixed number to improper fraction (then proceed) -no-simplify -multiply the numerators together and the denominators together -simplify -done
adding/subtraction fractions
mixed number? -yes-convert the mixed number into an improper fraction (then proceed to next listed steps) -no-find LCD -LCD is new denominator -write equivalent fractions by multiplying both the denominator and numerator by the same number -add/subtract the numerators; denominators remain -unchanged -simplify -done
To add or subtract fractions, first convert any
mixed numbers into improper fractions
+
more than
+, Read as
more than
To convert from a percent to a decimal?
move the decimal point two places to the left. For example, 700%=7.00 or 86%=.86 or 00.15%=.0015
To convert from a decimal to percent?
move the decimal point two places to the right. For example 0.23=23% or 5.34=534%
can be easily divided by a number
multiple
reciprocal
multiplicative inverse of the number
CM to MM
multiply by 10
CM to MM
multiply by 10 cubed
mfa CM to MM
multiply by 10 squared
M to CM
multiply by 100
M to CM
multiply by 100 cubed
mfa M to CM
multiply by 100 squared
KM to M
multiply by 1000
capacity: KL to L
multiply by 1000
capacity: L to ML
multiply by 1000
KM to M
multiply by 1000 cubed
mfa KM to M
multiply by 1000 squared
converting decimals to percents
multiply the decimal by 100 and add the %; move the decimal point right 2 places and add the %
how to find the volume of a prism without knowing the area of the base?
multiply the length x width then multiply by the height.
nano
n billionth .0000000001 (decimal = 10)
By what percentage does 3/4 exceed 1/3?
new fraction-original fraction/original fraction x 100%=percent increase
The part (%) is the
new value
coefficient
number being multiplied by variable
Common factor
number that divides exactly into two or more other numbers. For example factors of 12 are (1,2,3,4,6,12) and for 15 are (1,3,5,15) The common factor between 12 and 15 is 3.
irrational number
numbers that cannot be written as fractions (square roots, cube roots, and pi)
Convert any number that represents the sum of a whole number and a proper fraction into a fraction whose
numerator is greater than the denominator
coefficient
numerical part of a term; the number that is being multiplied to the variable
angle greater than 90°
obtuse
percentage increase & decrease
often the problem asks you to determine the percentage of increase or decrease. This type of problem is easily solved by making a fraction out of the information provided 1. write the amount of increase or decrease as the numerator 2. write the original amount as the denominator 3. change fraction to percent
Roman numeral I stand for...
one
expression
one or more terms consisting of any combination of constants and/or variables
When solving a percent decrease or increase problem, the "whole" is the
original value, or the value that existed first
The whole (%) is the
original value, or value that existed first
pico
p trillionth .0000000000001 (decimal = 13)
3p - 17 = 19
p = 12
What does the word "percent" mean?
per hundred
solving for percent decrease
percent decrease = original value minus new value divided by original value then multiply by 100
percent decrease
percent decrease= (Amount of decrease/original whole)x100%
calculating percents
percent decrease=original value-new value/original value x 100 percent increase=new value-original value/original value x 100
solving for percent increase
percent increase = new value minus original value divided by original value then multiply by 100
percent increase formula
percent increase= (Amount of increase/ original whole)x100%
how do you find the perimeter of a circle?
pie x diameter
volume of a cylinder?
pie x radius squared multiplied by height
area of a circle
pie x radius squared. WE MUST ALWAYS USE THE RADIUS.
adding integers
positive + positive = positive negative + negative = negative when signs are different = subtract the smaller # from larger & give the sign of the larger #
multiplying integers
positive x positive = positive negative x negative = positive positive x negative = negative
number with only 2 factors
prime
answer in multiplication
product
divisor
quantity by which another is divided (b in a/b)
divident
quantity to be divided (a in a/b)
answer in division
quotient
half of the diameter
radius
percents
ratios whose denominators are 100
A new product has arrived to your pharmacy. The storage requirements on the label read: Store at 1.7ºC- 3.3ºC. Where would you store it?
refrigerator
If the value of x and y in the fraction XZ/Y are both tripled, how does the value of the fraction change?
remains the same
converting from percents to decimals
remove the % symbol & move the decimal point left 2 places (example: 0.045= 4.5 %)
100
roman numeral C=
500
roman numeral D=
1
roman numeral I=
50
roman numeral L=
1000
roman numeral M=
5
roman numeral V=
10
roman numeral X=
triangle with no equal sides
scalene
appropriate unites of measure and measurement tools (weight)
scales
Real Numbers
set of all rational and irrational number
how many centiliters are in 10 liters?
set up as proportion, 1 Liter / 100 centiliters = 10 liters / X centiliters , so x = 1,000 centiliters
leslie needs to make a pie and some cupcakes. the pie requires 3/8 cup of sugar, and the cupcakes require 3/5 cup of sugar. leslie has 15/16 cups of sugar. does she have enough sugar, or how much more does she need?
she needs 3/80 of a cup of sugar
line graph
shows changes over a period of time or compares the relationship between 2 quantities; created on coordinate axes; x/y-axis
Circle or pie graph
shows percentage or frequency - whole pie = 100%
Histogram
shows/compares frequency of continuous data, bars have to touch
Bar graph
shows/compares frequency of non-continuous data bars don't always touch
30-60-90 triangle
side lengths are multiples of 1, _/3, and 2
figures with same shape different size
similar
simplified fraction
simplest form
slope of a line
slope=Rise/Run or Change in Y/Change in X
Least common multiple (LCM)
smallest number that is a multiple of two or more numbers. For example, for 3 multiples are (3,6,9,12,15) and of 5 are (5,10,15,20) the LCM is 15.
Which of the following is not a rational number? a)-4 b)1/5 c)0.833.. d) square root of 2
square root of 2
x^1/2
square root of x
proportion
states that two ratios are equal unites of an item/units of a diff item=units of an item/units of a diff item; cross products (numerator times denominator)
calculation of percents
step 1. change the written statement into a mathematical equation. Keep in mind: - the word of translates into multiply - the word is translates into equals - the decimal form of the percent should be used in the equation step 2. solve for the unknown quantity step 3. rewrite the statement & make sure that the answer is reasonable (example: 15% of 500 is what #?= 0.15 x 500= 75 )
converting from percents to fractions
step 1. remove the % sign step 2. write the number from step 1 in the numerator of the fraction & write 100 in the denominator step 3. simplify the fraction
answer in addition
sum
how to find the sum of all the anlges of a polygon and one angle measure of a regular polygon
sum of thee interior angles in a polygon with n sides: (n-2)x180 degree measure of one angle in a regular polygon with n sides: (n-2)x180/n
Mary is reviewing her algebra quiz. She has determined that one of her solutions is incorrect. Which one is it?
t - 2t - 3t = 32, t = 8
like terms
terms that have the same variable and with the same exponent
what is volume?
the amount of space taken up.
quotient
the answer to the division problem
estimation
the approximate value= the 1st digit in the # will not be zero but all the other digits will be zeros
converting from decimals to fractions
the decimal # expressed becomes the numerator of the fraction & the # of decimal places to the right of the decimal determines the value of the denominator
divisor
the denominator in a division problem
absolute value
the distance between the number n and zero on the number line
degree
the exponent or sum of exponents
how to COUNT CONSECUTIVE NUMBERS
the number of integers from A to B inclusive is B-A+1
dividend
the numerator in a division problem
which way is the height?
the opposite way of the base
Order of Operations
the order in which operations in an expression to be evaluated are carried out. 1. parentheses 2. exponets 3. multiplication and divison 4. addition and subtraction
dependent variable
the output based on the input
Numerator
the top number in a fraction
subtraction from the larger values
the use of I, X, & C to the left of larger values indicates what
independent variable
the variable that input into the set of data
independent variable
the variable that is put into the set of data, or the input, (statistics) a variable whose values are independent of changes in the values of other variables
tables
these are helpful for organizing raw data
measuring cups
these are used for measurements in pints
graduated cylinders
these are used for measurements in tablespoons
beakers
these are used for measurements in teaspoons
scales
these are used to measure weight
line graphs
these graphs show changes over a period of time or compares the relationship between 2 quantities (compare time of day to temperature)
bar graphs
this graph is used to compare the frequencies of an event (the number of inches of rain that fell in a certain city in the each month)
yard sticks
this is used for measurements no longer than 1 yard, 3 feet, or 36 inches
rulers
this is used for measurements no longer than 12 inches
ratio
this is used to express a relationship between 2 quantities
calipers
this is used to measure very small lengths, usually 6 inches or fewer with greater precision than a ruler
Beware of absolute value equation and inequalities in which one of the expression, or sides, contains zero or a negative number
this results in infinite solutions or no solution
proportion
this states that 2 ratios are equal- when setting up this, the numerators must be in the same units & the denominators of both ratios must be in the same units- use this formula to solve for this: units of an item = units of an item divided by units of a different # Divided by units of a different #
equilateral triangles
three equal sides, and three 60 degree angles
percentage discount & tax increase
to find the amount of discount or increase when the % is known 1. change the percentage to a decimal (or fraction) 2. multiply by the original cost 3. add or subtract accordingly
multiply/divide roots
to multiply/divide roots, deal with what's inside the root and outside the root separately
numerator
top part of fraction
The bars on histograms must
touch each other
When dividing a positive number by a negative number, the results are negative.
true
2
twice
2, Read as
twice
0 raised to the 0 power
undefined
Solving Proportions
units of an item/units of a different item = units of an item/units of a different item. Use finding cross products to solve equations. a/b = c/d solve to ad=bc
Variable
unknown quantity, x,y, or z
When should you use a chart over table?
use chart when visual presentation is important
rate of change
use proportions to determine the difference in completion times for a given task
rate of change problems
use proportions to determine the difference in completion times for a given task example: 10 pages / 1 hour = 288 pages / A hours use the method of cross products to solve: 10 x A= 288 x 1 - 10A / 10 = 288 / 10 A= 28.8 hrs
how to find the diagonal of a rectangular solid
use the pythagorean theorem twice
caliper
used t measure very small lengths
ration
used to express a relationship between 2 quantities; fractions, with colons, or with words
Rulers
used to measure no longer than 12 inches
tape measures
used to measure something no longer than 50 feet long
Intersecting Lines
vertical angles are equal, angles along a line add up to 180 degrees
how to find the volume of a rectangular solid
volume=length x width x height
how to find an angle formed by a transversal across parallel lines
when a transversal crosses parallel lines, all the acute angles formed are equal and all the obtuse angles formed are equal, any acute angle plus any obtuse angle equals 180 degrees e=g, p=r, f=h, q=s, add to 180 to make straight lines
arabic numeral system
writing numbers in a combination of 0,1,2,3,4,5,6,7,8, and 9
Calculating percents is done by
written statements into mathematical equations & solving for an unknown
x - 3 = -2
x = 1
201 - x = 54
x = 147
34x = 102
x = 3
3x + 4x = 21
x = 3
if 3x + 2 less than 5, which of the following options is correct?
x is greater than 1
if 2x + 7/9 less than 2, which of the following options is correct?
x is less than 11/2
Divide x w/ exp.5 by x w/ exp.2
x w/ exp.3
Divide x w/ exp.5 by x w/exp.2
x w/ exp.3
|x-n| > a
x-n > a or x-n < -a
|x-n|= a
x-n= a or x-n= -a
/x-n/=a
x-n=a or z-n=-a
/x-n/>a
x-n>a or x-n<-a
/x-n/>or equal to a
x-n>or equal to a or x-n< or equal to -a
2x = 10
x=5
If r = 5 z then 15 z = 3 y, then r =
y
y x y = 9
y = 3
a tire company manufactures 50 tires an hour with its current staff. The company can make 10 extra tires per hour for every extra worker it hires. Which of the following equations represents this relationship mathematically, with x being the number of extra workers hired and y being the number of tires produced?
y = 50 + 10x
add/subtract roots
you can add/subtract roots only when the parts inside the root are identical
If y(x-1)=z then x=
z/y + 1
In the fraction 3/x, x may not be substituted by which of the following sets?
{0, 10, 20}
To solve an absolute value inequality such as |x-n| <a
|x-n| < a |x-n| > a |x-n| > a
micro
µ millionth .0000001 (decimal = 7)
area of a triangle
½ base × height
area of a circle
πr²
