Math
What is a milligram?
.001
1g= ___ pounds
.002 pounds
How many kilograms are in a pound?
0.454 kg
How many meters are in a yard?
0.914 meters
How many angles have measurements greater than 90° in an obtuse triangle?
1
What is 10^0?
1
What is a gram?
1
x^0
1 Ex: 3^0= 1 10^0= 1 6^0= 1
Convert 12 feet to inches
1 foot= 12 inches 144 inches
In 1/2, 1 is the _____ and 2 is the ____
1 is the numerator and 2 is the denominator
Convert 4.25 kilometers to meters
1 km= 1,000 meters 4,250 meters
1 cm^3 = ____ mL
1 mL
Solve: 1) -18 + 12 2) -3.64 + (-2.18) 3) 9.37 - 4.25 4) 86-(-20)
1) -6 2) -5.82 3) 5.12 4) 106
Using PEMDAS solve: 1) 2 (21-14) + 6 / (-2) x 3 - 10 2) -3^2 + 4(5) + (5-6)^2 -8 3) (7-9)^3 + 8(10-12) _______________________________ 4^2 - 5^2
1) 2(7) + 6 / (-2) X 3 - 10 14 + 6 / (-2) X 3 - 10 14 + (-3) x 3 - 10 14 + (-9) - 10 5 - 10 = -5 2) -3^2 + 4(5) + (-1)^2 -8 -9 + 4(5) + 1 -8 -9 + 20 + 1 - 8 11 - 7 = 4 3) (7-9)^3 + 8(10-12) (-2)^3 + 8(-2) -8 + (-16) -24 8 ________________________ = ________________ = __________ = _____ = ____ 4^2 - 5^2 4^2 - 5^2 16 - 25 -9 3 (simplify sep. using PEMDAS)
Tera (t)
1,000,000,000,000
Multiplying fractions
1. Multiply the numerators 2. Multiply the denominators
How would you set this up: The patient's weight has dropped by 1.5 pounds over the last 3 days. If the rate of weight loss remains the same, how much more weight will be lost in the next 10 days? ? ? ____ = ____ ? ?
1.5 x ____ = ____ 3 10 So, x= 5
1 mile/ hour= ____ kilometers/ hour
1.61
Deca (da)
10
What is a kilogram?
1000
How many grams are in a kilogram?
1000 grams
How many mL in a L?
1000 mL
How many meters are in a kilometer?
1000 meters
How many milligrams are in a gram?
1000 milligrams
How many mm are in a meter?
1000 mm
Erica is visiting Rome for vacation. She sees an old building with "MCCLIII" written on it. What number is this?
1000+100+100+50+1+1+1=1253 is the number on the building
What is 50.125 / .05?
1002.5 (In this problem, be sure to move both decimal points two places to the right before dividin) so its 5012.5/5
There are 10 boys and 12 girls in a class. Whats the ratio of boys to the total number of students? Ratio of girls to boys?
10:22 (5:11) and 12:10 (6:5)
The populations of 5 towns are 12,341 , 8,975 , 9,431 , 10,521 , and 11, 427. Estimate the population to the nearest 1,000 people.
12,341= 12,000 8,975= 9,000 9,431= 9,000 10,521= 11,000 11, 427= 11,000 so add all them up and you get 52,000
What is 0.125 as a percent?
12.5%
Jason has 174 pounds of apples for sale at his farmer's market stall. He sells 48 pounds by the end of the day. How many pounds of apples does he have left for sale the next day? Without calculator
126
_____ form is when a fraction can't be reduced anymore
Simplified
72 is a ____ number
Whole, natural, integer, and rational (can be written as 72/1)
Convert 13.86g to kg
.01386kg
How many miles are in a kilometer?
0.62 miles
What is 3/5 as a percent?
0.6= 60%
Kilo (k)
1,000
Mega (m)
1,000,000
Giga (g)
1,000,000,000
1m = ___ yd
1.094 yd
What is 12.56 - 2.24?
10.32
Solve: (10.4)(18.2)
10.4 x 18.2 (2 places after the decimal) 104 x 182 18928 so 189.28 (2 places after the decimal)
A percentage is simply a ratio of a:b where b is always ____
100
Simplify: (8.1 X 10^-5) (1.4 X 10^7)
11.34 X 10^2 but the a has to be btw 1 and 10 so adjust it to 1.134 X 10^3
The track team are buying new uniforms. T shirts cost $12, pants cost $15, and shoes cost $45. If they have a budget of $2,500. How much can they buy?
12t + 15p + 45s < $2,500
What is 18% as a fraction?
18/100 or 9/50
What is the mode of this set: 16, 19, 19, 25, 27, 29, 75
19 because it occurs the most
How many grams are in an ounce?
28 grams
In 53.264, whats the ones place?
3
How many grams in a pound?
454 grams
What is the outlier: 16, 19, 19, 25, 27, 29, 75
75
Unimodal distribution
A distribution with one peak
Point
A location in space that is represented by a dot and has no dimension like length or area
Lines, rays, and line segments can intersect to create _____ which are measure in degrees or radians
Angles
Ratio example: Samuel has 20 pencils and Maria has 10. Whats the ratio?
By dividing each quantity by 10, we get a ratio of 2:1 describing Samuel's pencils in comparison to Maria's
Box Plot (Box and Whisker Plot)
Divides data into four quartiles
When rounding, if the value of the underlined digit is ____ than 5, increase the underlined value by one and replace all digits to the right of the underlined with zero
Greater
Solve: 5/6 / 2/3
Keep it change it flip it 5/6 x 3/2 15/12 = 5/4
Negative numbers are ___ ____ zero
Less than
Adding is easiest when you align the numbers by ____ _____
Place values
What is the median of a data set?
The number in the middle of the set
What is a numerator?
The number on the top of a fraction
Long divison and the numerator
The numerator always goes under the house for divison
Y intercept
The point where the graph crosses the y-axis and where x equals zero Ex: (0,-4)
What is 10^1?
10
What is a dekagram?
10
Order from greatest to least: -2/3, 1.2, 0, -2.1, 5/4, -1, 1/8
5/4, 1.2, 1/8, 0, -2/3, -1, -2.1
Solve: 5/6 x 2/3
5/6 x 2/3 10/18 = 5/9
Line
A collection of an infinite number of points in a straight pathway with unlimited length and having no width
Ratios
A comparison of two quantities using division; can be represented as a/b where b doesn't equal 0; represents a constant relationship not a specific value
Improper fraction
A fraction whose numerator is larger than the denominator
What is a prime number?
A number greater than 1 that is divisible only by 1 and itself. Ex: 1, 2, 3, 5, 7, 11, 13 e.g. 7 is a prime number as it's factors are 1 and 7. 9 is not a prime number as it's factors are 1, 3 and 9.
How do you find the area of a sector?
A= x degree/ 360 degree (πr^2)
How do you find the perimeter of a square?
Add all 4 sides
Real numbers are all ________ and ______ numbers
All rational and irrational numbers
Regular polygons
All sides are the same length
Proportions
An equation stating that two ratios are equal
How do you find the perimeter of a circle?
C= 2πr
7,200
Can be called 72 hundreds or 7 thousands and 2 hundreds
Every natural number (except one) is either a prime or ____ number
Composite
How to convert fractions to decimals without a calculator?
Convert the denominator to 10, 100, 1000, etc. Whichever number you multiplied the denominator by to get to 10, 100, 1000 needs to also be multiplied to the numerator. Then, use the numerator as the value and put the decimal in the correct position. Ex: 4⁄5 = 8⁄10 = .8
How do you solve proportions? a/b=c/d
Cross multiplication a/b=c/d turns into ad=bc 4/6=10/15 4(15)=6(10) 60=60
Solve this proportion for x: 3-5x/2 = -8/3
Cross multiply 3(3-5x) = 2(-8) 9-15x = -16 -15x = -25 x= 5/3
How is a decimal converted to a fraction? How is a fraction converted to a decimal?
Decimal to fraction: Take note of the smallest place value of the number. This will be the denominator. The numbers to the right of the decimal will be the numerator. Reduce if possible. Fraction to decimal: divide the numerator by the denominator. Decimal to fraction: 0.758, read as 758 thousandths, convert to 758/1000 Fraction to decimal: 758/1000→758÷1000=0.758 .
Direction of the skew
Describes the side of the graph with fewer data points
An equation states that two expressions are ____ to each other
Equal
100(x+5) Solve: 20 ---------- = 1 20
Get rid of the denominator by multiplying my 20 on both sides 100(x+5) = 20 Distribute the 100: 100x + 500= 20 100x= -480 x= -4.8
How do you find a percentage of a number?
In word problems, these equations are often useful: is/of= percent/100 or part/whole= percent/100 Plug in the known values and solve for the unknown.
Inequalities are similar to equations but not the same because what?
Inequalities are when both sides of the problem are not equal; use <, >, < or equal to, and > or equal to
Dividing fractions
Keep change flip then multiply across like normal
Mertic system
Kilogram: 10000 Hectogram: 100 Dekagram: 10 Gram: 1 Decigram: 0.1 Centigram: .01 Milligram: .001
What 4 things does a box and whisker plot highlight?
Median, range, and the two outliers
For length, ____ are used
Meters
Scientific Notation
Method of writing very small or very large numbers in the form a X 10^n where a is a value btw 1 and 10, and n is an integer
What values do the prefixes: milli-, centi-, and kilo- indicate?
Milli- = one thousandth Centi- = one hundredth Kilo- = one thousand 1millimeter=1/1000meter or a =0.001meter or a thousandth meter 4centigrams=4/100gram=0.04gram or 4 hundredth gram 25kilometers=25⋅1000meters=25,000meters or 25 thousand meters
How is a decimal converted to a percent?
Multiply the decimal by 100 Ex: 0.37 x 100= 37%
Composite number
Natural number greater than 1 that can be evenly divided by at least one other number besides 1 and itself Ex: 6 because it can be divided by 1, 2, 3, and 6
Both positive and negative numbers can be shown on a _____ ____
Number line
Bar graphs have categories on the x axis and histograms have ___ ____
Number ranges
Real Numbers
Number that can be represented by a point on a number line
Outliers
Numbers that are much greater or much less than the other numbers in the set
Lines, rays, and line segments are ____ objects because they can only be measured in one dimension (length)
One dimensional
54.32 What place is the 4 in?
Ones
1.234567 place values
Ones: 1 Decimal: . Tens: 2 Hundreds: 3 Thousandths: 4 Ten Thousandths: 5 Hundred Thousandths: 6 Millionths: 7
Will an outlier have the biggest effect on the value of the mean, median, or mode?
Outliers affect mean by shifting it away from the median. Outliers do not affect mode.
Lines that do not intersect?
Parallel lines
Percent equation
Percent= Part / Whole Part= Whole X Percent Whole= Part / Percent
Rounding
Performed for a specific place value and the result will be a less precise value
Two lines that form right angles are ________
Perpendicular
Two lines that intersect to form right angles are ______
Perpendicular
In a pie chart, the _____ is the whole and each _____ represents a percentage or part of the whole
Pie; slice
Uniform data set
Points are distributed evenly along the graph
Positive divided by positive
Positive Ex: 8/4= 2
Double line graphs
Present two sets of data on the same set of axes
Slope is rise over run, rise is the ___ values and run is the ____ values
Rise= Y's Run= X's
Line graphs
Show changes in data by connecting points on a scatter graph using a line
What information is shown in a pie chart?
Show the percentages of each element of a set
How do you find the area of a square?
Side squared
Range
The difference between the highest and lowest scores in a distribution
How do you find the perimeter of a triangle?
The sum of all three sides
What is the fundamental counting principle?
The total number of possible outcomes is the product of the total possible number of outcomes in each trial
____ is three places after the decimal point
Thousandths
Line graphs will often measure ____ on the x axis and are used to show trends in the data such as temp change over a day
Time
How do you reduce fractions? What are equivalent fractions?
To reduce fractions: Divide both the numerator and denominator by their greatest common factor. Equivalent fractions are those that have the same value when reduced to their simplest form.
Bimodal distribution
Two peaks
A normal bell shaped distribution is usually symmetrical and _____modal with a specific distribution of data points
Unimodal
Percentage
Way to express a number out of 100
Skewed distribution
Weighted more heavily towards the left or right
Dot plots have a value or category on the ___ axis
X
Proportions set up
a/b = c/d a and d are extremes b and c are the means
"Skewed to the Left"
mean < median The mean of a data set that is skewed to left is less than the median
Solve: 1) 10/3 (-9/5) 2) -64/-10 3) (2.2)(3.3) 4) -52/13
1) -90/15 or -6 2) 6.4 3) 7.26 4) -4
10^6 is what? 10^2 is what?
1,000,000 100
What is 360x21? Without calculator
126
A bag of saline solution originally containing 975 mL has delivered 190 mL to the patient. How much saline is left in the bag? Without calculator
785
For multiplying in scientific notation multiply the a factors, and _____ the exponents
Add
Natural numbers?
Are counting numbers; greater than 0; no decimals or fractions; 1, 2, 3, 4, 5
Negative minus a negative
Keep the sign of the number with larger value Ex: -7 - (-8)= 1 or -7 + 8= 1
A negative minus a positive
Negative Ex: -7 -8= -15 or -7 + (-8)= -15
Positive minus positive
Positive if the 1st number is larger and negative if the 2nd number is larger Ex: 8-4= 4 4-8= -4
What is the slope of a vertical line?
Undefined
Mili (m)
0.001
A smart TV that originally costs $1,500 is on sale for 45% off. What is the sale price of that item?
Amount of change= original amount x percent change Amount of change= 1,500 x .45 $675 1,500-675= the final price is $825
Percent Change Formula
Amount of change= original amount x percent change Percent change= amount of change/ original amount Original amount= amount of change/ percent change
What is 10^-2?
1/100, or 0.01 which is hundredths
How do you find the area of a trapezoid?
1/2h(b1+b2)
Expand: 5x(x^2 - 2c + 10)
5x(x^2 - 2c + 10) 5x^3 - 10xc + 50x
In 53.264, whats the hundredths place?
6
What is the area of a window that is 3 feet long and 2 feet wide?
6 feet^2
What is the median in this set: 75, 80, 82, 100
80+82/ 2 81 is the median
What's 5,800 + 3,500?
9,300
What is 927,000,000 in SN?
9.27 X 10^8
1 degree Fahrenheit equation
9/5 C + 32 C
Complementary angles add to _____ degrees
90
Perimeter
The distance around a 2D figure, which can be found by adding the lengths of all the sides
Harriet and Samantha are sisters. In the spring, their father tells them they can each have 1/3 of the garden to grow whatever they want during the summer, but they have to plan it out first. Harriet decides she wants to grow 3/4 of her land with corn. How much of the total garden will have her corn growing on it?
1/4
How many cups are in a pint?
2 cups
How many pints are in a quart?
2 pints
Polygon
A two-dimensional shape that has three or more straight sides and angles
Composite Numbers
A whole number greater than 1 that has more than two factors; not 1; can be divided by a least one another number besides 1 and itself Ex: 6 because it can be divided by 1, 2, 3, and 6
Symmetric distribution
Data that are evenly distributed; two mirrored halves
Composite numbers can be broken down into prime numbers using ____ ____
Factor trees
Given that 1m = .000621 mile, how many miles are in 45km?
First, solve that 1km = .621 mile by moving the decimal 3 places to the right (you may think of this as multiplying by 1000) as you move from meter to km. Next, multiply 45 x .621 to solve the equation = 27.945mi
Subtract and simplify 2 14/15-3/5
First, we'll convert 2 14/15 to an improper fraction; answer is 2 and 1/3
______ are parts of numbers, or portions of a whole
Fraction
Bars of a bar graph show actual data, but bins or bars of a histogram show the _____ of the data in various ranges
Frequency
What is the exponent of a polynomial equation?
Highest power of the variables they contain
What is the mode of a data set?
It occurs most often in the set
For volume, ____ are used
Liters
Compound shape area example
Look in photos in file on computer for more
Manuel is a dispensary technician in a hospital. He is sorting 872 smocks from a new shipment into 16 groups evenly for each department's use. How many smocks will each department receive and how many will be left over? Use long divison
Manuel will have sixteen groups of 54 smocks evenly, but 8 smocks will be left over
Skewed Left Distribution
Mean < median
Skewed Right Distribution
Mean > median Skewed right because there are fewer data points on the right half
Median
Middle number
What is the process for writing a number in scientific notation?
Place a decimal after the first digit and count the number of places the original decimal needs to be moved. The number of places will be the positive exponent for large numbers, and it will be the negative exponent for numbers less than 1. 58,300,000 = 5.83 x 107 0.00000124 = 1.24 x 10-6
If m=4, solve this 5 (m-2)^3 + 3m^2 - m/4 -1
Plug in and then use PEMDAS 5 (4-2)^3 + 3(4)^2 - 4/4 -1 5 (2)^3 + 3(4)^2 - 4/4 -1 5 (8) + 3 (16) - 4/4 - 1 40 + 48 - 2 Answer= 86
Negative divided by a negative is a ____
Positive Ex: -8 / (-4)= 2
Multiplying a negative number by a negative number results in a ____ number
Positive Ex: -8 X (-4)= 32
Adding a positive and positive gives you a ____
Positive Ex: 7 + 8= 15
In a Venn diagram with two circles representing the probability of A and the probability of B, what is represented by the area outside the circles?
The area outside of both circles is the probability of neither A nor B.
Integers
The set of whole numbers and their opposites; positive and negative natural numbers and zero; (-1, -2, 0, 1, 2)
Surface area
The sum of all the areas of all the faces or surfaces that enclose a solid
Rewrite x^a X x^b as a single term
x^a+b
For temp, ____ is used
Celcius
The distance around a circle is referred to as _____
Circumference
Coeficient's are ______
Constant
How do you convert a fraction to a decimal?
Divide numerator by denominator
Solve for x: 2(x+2)^2 -2x^2 +10= 20
Do exponents first 2(x+2)^2 -2x^2 +10= 20 2(x+2)(x+2) -2x^2 +10= 20 FOIL: 2 (x^2+4x+4)-2x^2+10= 20 Distribute the 2: 2x^2+8x+8-2x^2+10= 20 Combine like terms: 8x+18= 20 8x= 2 x= 2/8 or 1/4
Bar graphs have gaps and histograms ___ have gaps
Don't
In a _____ ______ the number of times that value appears in the data set is represented by a line of vertical dots
Dot plot
How do you turn a mixed number into an improper fraction?
Determine the numerator of the improper fraction by multiplying the denominator by the whole number then adding the numerator Ex: a m/n = n x a + m/n 2 7/9= 25/9
Adding and subtracting fractions with like denominators
If the denominators are the same, add or subtract the numerators and the denominator stays the same
If a real number is a _____ number then it is also an integer, whole number, and a rational number
Natural
Multiplying a negative number by a positive number results in a ____ number
Negative Ex: -8 X 4= -32
Irrational Numbers
Numbers that cannot be expressed as a fraction. Their decimal expansions are nonending and nonrepeating. Ex: Pi, .345688280, and the neg square root of 7
What are the irrational numbers?
Numbers that cannot be written as a fraction Ex: e, pi, and the square root of 3
In a fraction, the top number is the ____ and bottom is the ____
Numerator; denominator
Angles between 90 and 180 are _____ angles
Obtuse
What kind of angle is larger than 90 degrees?
Obtuse
Shawna received a container, which measures 250 fluid ounces, to store chemicals. However, her lab uses the metric system, liters, to measure everything. How many liters should she label the container as, rounded to three decimal places?
approximately 7.393L
Cameron has $8,726,904 in his bank account. At the end of the next week, his paycheck is $791 after taxes. How much money is in his bank account after he deposits the check? Without calculator
$8,727,695
Scientific Notation Example
(3.8 X 10^3) + (4.7 X 10^2) 38 X 10^2 + 4.7 X 10^2 Answer: 42.7 X 10^2 but the a has to be btw 1 and 10 so adjust it to 4.27 X. 10^3
What is a centigram?
.01
What is a decigram?
.1
Positive numbers are always greater than...
0
What is the slope of a horizontal line?
0
Pico (p)
0.000000000001 (10^-12)
Nano (n)
0.000000001 (10^-9)
Micro (u)
0.000001 (10^-6)
Centi C)
0.01
Deci (d)
0.1
Rewrite X^-a with a positive exponent
1 ___ x^a
Sebastian invites his friend to meet for coffee at 2:20 p.m. "What time is that in military time?
1420
How many liters in a gallon?
3.785 L
How many liters in a gallon?
3.79L = 1 gallon
1L= ____ oz
33.81oz
What is sum of the exterior angles for any polygon?
360 degrees
What is 0.125 as a fraction and a percent?
1/8 place the numbers to the right of the decimal in the numerator and there are three numbers so 1000 goes in the denominator 125/1000 = 1/8
Hecto (h)
100
What is a hectogram?
100
How many cm are in a meter?
100 cm
1g = ___ mg
1000
Abby needs $395 to buy a new bike. She borrow $150 from her dad, and plans to earn the rest working. If she makes $10 per hour, how many hours will she need to work?
150 + 10x = 395 10x = 245 x= 24.5 hours
How many ounces are in 19.02 pints?
16 X 19.02= 304.32
How many kilometers are in a mile?
16 km
How many ounces are in a pint?
16 ounces
How many tablespoons are in a cup?
16 tablespoons
Jordan takes a measurement of a patient's height as 5 feet and 8 inches. However, when he goes to mark the chart, he realizes the measurement should have been in centimeters. Convert the patient's height to centimeters.
172.72cm
Xavier and his friend go out for lunch together. At the end of the meal, Xavier offers to pay. If he leaves a $6.16 tip and the food bill was $34.24, what percentage of the food bill was Xavier's tip (round to the nearest whole number of the percent)?
18%
In 53.264, whats the tenths place?
2
What is the exponent of a quadratic equation?
2
Solve: 2 3/5 + 3 1/4 - 1 1/2
2 3/5 + 3 1/4 - 1 1/2 Change all to have the same LCD LCD: 20 2 12/20 + 3 5/20 - 1 10/20 add whole numbers and fractions WN: 4 F: 7/20 so = 4 7/20
What is the improper fraction 25/9 as a mixed number?
2 and 7/9 because 9 goes into 25 two times with a remainder of 7 (25-18)
A map is drawn such that 2.5 inches on the map equates to an actual distance of 40 miles. If the distance between two cities measured on the map is 17.25 inches, what is the actual distance between them in miles?
2.5/ 40 = 17.25/ x 2.5x= 690 x= 276 miles apart
How many cm in an inch?
2.54 cm
40% is ___ / ____
40⁄100
A percentage such as 42% means ___ out of 100
42 or 42/100
HPV was contracted at a 42.5% rate among adults 18-59 years of age. How many students in a university of 40,000 are expected to have had HPV? ? ? ____ = ____ ? ?
42.5 x ____ = ____ 100 40,000 so, x= 17,000 people
What is 42% as a decimal?
42/100= 0.42
Solve: 4x + 10 > 58
4x + 10 > 58 4x > 48 x > 12
Jordan received a bouquet of two-dozen pink and yellow roses for her birthday. The ratio of pink to yellow roses was 3:1. How many pink and how many yellow roses did she receive?
First, we must add the terms: 3 + 1 = 4. Then we divide the total number of flowers by that: 24 ÷ 4 = 6. Then we multiply each term by that. Pink: 3 x 6 = 18. Yellow: 1 x 6 = 6
10^5, 5 means it should have ___ zeros
Five
What is the procedure for adding or subtracting fractions?
For fractions with a common denominator: Add or subtract the numerators as usual while keeping the denominator. For fractions with unlike denominators: Determine the least common denominator (LCD). Convert the first fraction to an equivalent fraction with the LCD as its denominator. Do the same with the second fraction. Add the two fractions as you would with fractions with a common denominator. Subtraction will follow the same procedures except that you use subtraction or "minus." 2/3+5/7 The LCD of the 2 fractions is 21. Converting to equivalent fractions: 2/3=14/21 and 5/7=15/21 Proceeding to addition: 14/21+15/21=29/21
What is the SI for mass? length? volume? force? pressure? work and energy? temp? charge?
Grams; meter; liter; newton; pascal; joule; kelvin; coulomb
54.32 What place is the 2 in?
Hundredths
In the number 12,408.57, what place is the number 7 in?
Hundredths
____ is two places after the decimal point
Hundredths
Roman numerals
I - 1 V - 5 X - 10 L - 50 C - 100 D - 500 M - 1000
What do the Roman Numerals I, V, X, L, C, D, and M represent?
I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000
A decimal have have an ____ in front of it Ex: 1.2
Integer; integer of 1 and a decimal of .2
Square root of 5 is a ____ number
Irrational (cannot be written as a fraction and the decimal is 2.2360679 which is non terminating or repeating)
What is the distributive property?
Is used to multiply a single term by two or more terms inside a set of parentheses Ex: a(b+c+d)=ab+ac+ad
Another way of writing a mixed number is as an improper fraction, where the numerator is ______ than the denominator
Larger
The steps Multiply, Divide, Add, Subtract in PEMDAS go from _____ to ______
Left to right
2D objects can be measured in two dimensions- _____ and ______
Length and width
How do you find the area of a rectangle?
Length x Width
3D objects can be measured in three dimensions- _______, _____, and ______
Length, width, and height
What is 12x + 7xy - 9y + 8x - 9xz + 7z
Only like terms are 12x and 8x 20x + 7xy - 9y - 9xz + 7z
What is the American for mass? length? volume? force? pressure? work and energy? temp? charge?
Ounce/pound/ton; inch/foot/yard/mile; cup/pint/quart/gallon; pound-force; pound-force per square inch; cal; fahrenheit; faraday
Fraction
Part of a whole
PEDMAS
Please Excuse My Dear Aunt Sally Order of operations: parentheses, exponents, multiplication, division, addition, subtraction
PEMDAS "Order of Operations"
Please Excuse My Dear Aunt Sally (Parenthesis, Exponents, Multiply, Divide, Add, Subtract); order in which an equation is worked out - multiplication and division as well as adding and subtracting can be interchanged, depending on which comes first (from left to right) in the equation
A positive minus a negative
Positive Ex: 7-(-8) = 15
Multiplying a positive number by a positive number results in a ____ number
Positive Ex: 8 X 4= 32
Dependent variables on bar graphs are _______ and the independent variable is grouped into categories such as months or flowers
Quantities
In division problems, the answer is called the _____
Quotient; dividend ÷ divisor = quotient.
A ____ is a relationship between two numbers that compares their quantities
Ratio
-2/3 is a ____ number
Rational
Angles that are exactly 90 degrees are ____ angles
Right
How to convert a decimal to a fraction?
Separate the integer and decimal into their positions, and then find the common denominator Ex: 1.25 Ones: 1 Tenths: 2 Hundredths: 5 Rewrite as 1 + 2⁄10 + 5⁄100 Rewrite with common denominator: 100⁄100 + 20⁄100 + 5⁄100 = 125⁄100
7,654,321 in words
Seven million, six hundred fifty-four thousand, three hundred and twenty-one
How is standard time converted to military time? How is military time converted to standard time?
Standard and military time formats are the same from 1:00 (in the morning) to 12:59 (in the afternoon), except that standard time indicates a.m. for the morning and p.m. starting from 12 noon. Military time uses no other notation. Starting at 1:00 pm (standard time), add 12 to convert from standard to military. To convert military time (applicable for the time from 13:00 to 24:00), simply subtract 12 and you get the equivalent standard time. Standard time uses the 12-hour format, making distinction between a.m. and p.m. Military time uses the 24-hour format, where a day starts at 00:01 and ends at 24:00. Military time from 00:01-12:59 matches up with 12:01 a.m.-12:59 p.m., and from 13:00-24:00 matches up with 1:00 p.m.-12:00 a.m. 21:40 is the same as 9:40 p.m. (21:40 - 12 = 9:40)
For dividing in scientific notation divide the a factors, and _____ the exponents
Subtract
A decimal, like a fraction, represents part of a whole (T/F)
TRUE
54.32 What place is the 5 in?
Tens
54.32 What place is the 3 in?
Tenths
____ is one place after the decimal point
Tenths
What is the sum of all probabilities in any probability distribution?
The sum of all probabilities is always 1.
Mixed and Improper Fractions
To add or subtract mixed fractions, first convert them to improper Then if they are like, you may simply add the numerators. If they are unlike, you will need to convert to equivalent like fractions and then add or subtract. Ex: 2 1⁄8 + 3 1⁄6 = 17⁄8 + 19⁄6 = 102⁄48 + 152⁄48 = 254⁄48 which is simplified to 127⁄24 or 5 7⁄24
Box is 4 feet long, 3 feet wide, and 1 foot deep. What is the surface area?
Top: 4ft x 3ft= 12ft^2 Back: 4ft x 1ft= 4ft^2 Front: 4ft x 1ft= 4ft^2 Bottom: 4ft x 3ft= 12ft^2 Left: 1ft x 3ft= 3ft^2 Right: 1ft x 3ft= 3ft^2 Surface area: 38 ft^2
Write 84% as a decimal
Two places to the left so 0.84
Write 1.125 as a percent
Two places to the right so 112.5%
Any measurement of an object will be taken in a certain ___
Unit
Variables are the foundation of algebra and they are ______
Unknown
Histograms
Use bars to compare data, but the independent variable is a continuous variable that has been binned or divided into categories
Scatter plots
Use points to show relationships between two variables which can be plotted as coordinate points suggest relationships between points
What is the procedure for adding or subtracting numbers with decimals?
Vertically align the numbers so that the decimal points are on top of each other, add zeroes as placeholders where necessary, and add or subtract as usual 1.1 minus 3.02 becomes 1.10−3.02 The added 0 in 1.1 acts as a placeholder and does not change the number's value.
When graphing the inequality y > 4x -1, which side of the line will be shaded?
What is the y-intercept form of a linear equation? y-intercept form: y = mx + b
Adding and subtracting decimals
When adding or subtracting decimals, it is the same as adding or subtracting with whole numbers. Just remember to align the ones position or the decimal point. When working down, the decimal point must be carried down into the answer. Ex: 12.35 + 03.63 __________ 15.98
A football field is 100 yards, while a basketball court is 50 ft. Whats the ratio?
When both are converted to feet, we can see that the ratio is 300ft:50ft which is simplified to a size of 6:1
Mixed number
Whole number added to the fraction Ex: 4/4 + 1/4= 1 and 1/4
An improper fraction can be written as a ___ ___ or a _____ ____
Whole number or a mixed number
The denominator of a fraction cannot be _____
Zero
How do you find the perimeter of a rectangle?
l+w+l+w l= length w= width; add all sides
"Skewed to the Right"
mean > median The mean of a data set that is skewed to the right is greater than the median.
What are the place values from largest to smallest for seven places to the left of the decimal? What are the place values from largest to smallest for six places to the right of the decimal?
millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths
Expand: x(5 + z) - z(4x - z^2)
x(5 + z) - z(4x - z^2) 5x + xz - 4zx + z^3 xz and zx are the commutative property so they can be combined; change order also with highest exponent in the front z^3 - 3xz + 5x
Terms are quantities that can be added or subtracted. Whats an example?
x^2 - 3x + 5 are all three terms
Formula for slope
y2-y1 m= __________ x2-x1
Formula to find slope
y2-y1/x2-x1
What is the y-intercept form of a linear equation?
y= mx+b
What is slope intercept form?
y=mx+b
1/4 and 2/4 are like (T/F)
TRUE
2/4 and 4/2 are unlike (T/F)
TRUE
In a circle, what is the relationship between the diameter and the radius?
The diameter is twice the length of the radius. d= 2r
Solve: 80 / 2.5
The divisor is 2.5 so move the . one place to the right so it is a whole number, have to do the same for numerator so its 800 / 25= 32
Whole Numbers?
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
How do you find the area of a triangle?
A = ½ bh
Proper fraction
A fraction with a numerator smaller than the denominator
Box Plot
A graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a box, and the median
What is a histogram?
A histogram plots the frequency of quantitative data with number ranges grouped together.
What is a line graph?
A line graph is typically used to show data that is changing continuously over time. The graph looks like a scatterplot with line segments connecting each point.
Mixed number
A number made up of a whole number that is not zero and a fraction
Line segment
A part of a line with two endpoints
Percent
A ratio that compares a number to 100
Percent Change
A ratio that compares the change in a quantity to the original amount
What is the definition of a function?
A realtionship where each input value has only one output value
Plane
A two-dimensional flat surface that extends indefinitely in all directions
What is the formula for area of a circle?
A= πr²
Angles between 0 and 90 degrees are _____ angles
Acute
How to find the whole of ratios?
Add the values of the ratio Ex: if a ratio of boys to girls in a class is 2:3, the whole is 5
A house was purchased in 2000 for $100,000 and sold in 2015 for $120,000. What was the percent growth in the value of the house from 2000-2015?
Amount of change= original amount x percent change 20,000= 100,000 x percent change 20,000/100,000= percent change 0.20 so the answer is 20%
How do you find the perimeter of a sector?
Arc length= x degree/ 360 degree (2πr)
____ is the size of the surface of a 2D object
Area
How do you find the area of a circle?
Area = πr2
What are domain and range?
Domain refers to acceptable inputs, or x-values, for a given function. Range refers to the outputs, or y-values, of a given function.
Adding and subtracting in scientific notation
Exponents must be the same for the power 10, then add the a terms, leave the 10^n unchanged for answer
Polynomial
Expression where all the exponents on the variables are whole numbers
_____ is the opposite of distribution
Factoring
Find the slope: (2,-1) and (3,-3)
(-3) - (-1) / 3 - 2 -2/1= -2 So, y= -2x + b
What is the formula for calculating an average?
(sumofthedata)/(numberofdata)=average Average of 3, 5, 6: Average = 3+5+6/3=4.67
Factor x^2-y^2
(x+y)(x-y)
Dot plots
Display the frequency of a value or event graphically using dots and thus can be used to observe the distribution of a set of data; make it easy to see which values occur the most often
Order the following from least to greatest: 1/3, -5/6, 1 1/8, 7/12, -3/4, -3/2
-3/2, -5/6, -3/4 1/3, 7/12, 1 1/8
Which terms in the expression 3xy^2+6xy -3y^2-xy^2 can be added?
3xy2 and - xy2 Only terms with the same variables can be added.
In 53.264, whats the thousandths place?
4
What's is the coefficient in 4x?
4
Solve: 4 1/2 / 2/3
4 1/2 becomes 9/2 9/2 / 2/3 KCF 9/2 x 3/2 27/4 or 6 3/4
Which of the following numbers satisfies the inequality 0 < 8 ? 0, 4, 8, 12
4 and 8
How many quarts are in a gallon?
4 quarts
How many joules are in a calorie?
4.19 J
At a factory, every 4 out of 1,000 parts made will be defective. If in a month there are 125,000 parts made how many will be defective?
4/1,000 = x/125,000 1,000x = 500,000 x= 500
In 53.264, whats the tens places?
5
How many feet in a mile?
5,280 feet
54.32, broken down?
50 + 4 + .30 + .02
How many weeks are in a year?
52 weeks
____ means 54 out of every 100
54%
Sharon is selling tickets for her college's theater production. There are 540 seats in the theater. If she sells tickets for 66.7% of the seats, how many seats is that? Round to the nearest whole number.
540 x .667= about 360 seats
Lliana is planning her day. She marks down "Workout―0545 to 0630." In civilian time, when is Iliana working out?"
5:45am to 6:30am
If there is a $3 entry fee, each ticket costs $5. If a student paid $28. How many tickets did he buy? Set up an equation.
5x + 3 = 28 5x = 25 x= 5 tickets
Jada works at a popular mobile phone and technology store. She receives 245 boxes each filled with 27 brand-new phones to be released for sale the next week. How many phones do they have in stock total? Without calculator
6,615
How many minutes are in an hour?
60
How many seconds are in a minute?
60 seconds
A family spends $600 a month on rent, $400 on utilities, $750 on groceries, and $550 on others. What is the ratio of the family's rent to the total of all their expenses?
600/2,300 (6:23)
Using long divison, what is 7/8 and 5/11 as decimals?
7/8= 0.875 5/11= 0.4545 repeating
What is the range: 16, 19, 19, 25, 27, 29, 75
75-16 59 is the range
Simplify 75/100
75/100 find a CD 25/25 or 3/4
Tiana has to report for work at 1945 hours. What time is this in civilian time?
7:45pm
Round 138,472 to the nearest thousandth
8 is in the thousandths place and the number so the right is 4 which is less than 5 so the 8 remains and the rest becomes zeros, so it becomes 138,000
How many ounces in a cup?
8 ounces
Converting Fractions to Percentages
Divide the numerator(dividend) by the denominator (divisor).
How many points are needed to draw a line?
2 points
How many pounds is one kilogram?
2.2 pounds
Whats the conversion factor for cm and inches?
2.54 cm ____________ 1 inch
What is the mean of this set: 16, 19, 19, 25, 27, 29, 75
210/7= 30 30 is the mean
How many hours are in a day?
24
Solve: 24.38 + 16.51 - 29.87
24.38 + 16.51 - 29.87 40.89 - 29.87= 11.02 Solve left to right
How many grams are in an ounce?
28.35 grams
Denali owns a party space that hosts rentals for birthdays, weddings, and other celebrations. One day, while cleaning up after two birthday parties, he finds leftover pizzas, which are served as 8 slices to one pie. One party left behind 2 3/8 pizzas. The other party left behind 9/8 pizzas. How much pizza was left behind in total?
28/8 or 3 and 1/2
2^4
2x2x2x2
What is the exponent of a cubic equation?
3
Change 3 and 1/3 to an improper fraction
3 1/3 so you multiply the whole number 3 by the denom 3 and add the num 1 so its 9+1 so 10 and the denom is the same so 10/3
Solve: 7/8 (3 1/3)
3 and 1/3 becomes 10/3 7/8 (10/3) so = 70/ 24 or 35/12 which is 2 11/12
Repeated factors can be written using exponents; ex: 3^4 means what?
3 x 3 x 3 x 3
1m = ___ ft
3.281 ft
What is 15.3 x 0.25?
3.825
1 degree Celsius= _____ degrees Frahreneit
33.8F
How many degrees are in a quadrilateral?
360 degrees
How many seconds are in an hour?
3600 seconds
How many days are in a year?
365 days
The ratio 3:5 can mean
3:5, 30:50, or 36:60
Cubes are ____D
3D
What are the like terms? 2x + 3xy - 2z + 6y + 2xy? Simplify?
3xy and 2xy; simplified it is 2x + 5xy - 2z + 6y
Mean
Average; add all of the values then divide by how many there are in the set
A polynomial with 2 terms is a ____ and one with three terms is a _____
Binomial and trinomial
Rational Numbers can be represented by?
By *fractions* Includes: Whole Numbers, Positives/Negatives, Zero, and all decimals that either terminate or resolve into a repeating pattern Ex: -12, 7.777777, 0.35, and 4/5
How do you convert improper fractions to mixed numbers?
By dividing the numerator by the denominator which gives the whole number part and the remainder becomes the numerator of the proper fraction part
How do you convert a decimal to a fraction?
By multiplying the numerator and denominator by the of digits to the right of the decimal point. Example: 0.625 * 1000 = 625/1000 divide by 125 = 5/8
What is dimensional analysis and how is it used?
Dimensional analysis is also known as conversion factor method or factor-label method. It involves expressing numbers and dimensions of a thing in one unit of measurement to another without changing the value of that thing. It is useful for performing unit conversions, especially complex unit conversions (such as converting from the English System to the International or metric system). Convert 23 days to seconds: 23days⋅(24hours)/(1day)⋅(60minutes)/(1hour)⋅(60seconds)/(1minute)=1987200seconds . Notice that a measurement unit occurring on top of a fraction cancels out the same unit at the bottom of the fraction. All other units are cancelled in this manner, leaving the unit we want the original value converted to.
Dividing decimals
For division, you must move the decimal place to the right in the divisor until it is a whole number. However many places you moved it, the decimal place in the dividend must also be moved to the right. You may have to add zeros to the dividend during this process. Ex: 12.35/ 3.63 1235/363= 3.4
For mass, ____ are used
Grams
What is the exponent of a linear equation?
Highest power is 1
When multiplying or dividing mixed numbers always change them to ____ ____ first
Improper fractions
Metric system mnemonic device?
KHDDCM
If the answer to an inequality is x < or equal to 3, every number ____ than three would also be correct answers
Less
When rounding, if the value of the underlined digit is ____ than 5, keep the underlined value and replace all digits to the right of the underlined with zero
Less
To add or subtract ____ fractions, simply add or subtract the numerators and keep the denominator the same Ex: 1/4 + 1/4= 2/4
Like
To multiply simple fractions, you do not need to have _____ denominators. You simply multiply the numerators and multiply the denominators. Ex: 1⁄2 x 1⁄4 = 1⁄8
Like
Add and subtract expressions by combining what?
Like terms
Ray
Line that extends infinitely in only one direction
What is the mean of a data set?
Mean is the average value, or the sum of the values divided by the number of values in the set.
Which of the 3 does an outlier mostly effect?
Mean, it raises it
What are the 3 measures of central tendency?
Mean, median, mode
The _____ _____ is a standardized method of measuring length, weight, mass and time
Metric system
Military time
Military time starts at midnight with 0000 and continues up to 2400 (midnight again)
7,654,321 place values
Millions: 7 Hundred Thousands: 6 Ten Thousands: 5 Thousands: 4 Hundreds: 3 Tens: 2 Ones: 1
How do you convert mixed numbers to improper fractions and improper fractions to mixed numbers?
Mixed number to improper fraction: Multiply the whole number and the denominator. Add this product to the numerator. The result becomes the new numerator which you put over the denominator. Improper fraction to mixed number: Divide the numerator by the denominator to find the whole number. If there is a remainder, this becomes the numerator of the fraction which you place above the denominator. An example of a mixed number converted to improper faction: 3 2/3=9+2/3=11/3 An example of an improper fraction converted to mixed number: 29/3=9 2/3
Mode
Most frequently occurring score; if every appears the same amount of time then there is no mode; mOde and Often both have O's
How do you convert a decimal to a percent?
Move decimal 2 places to RIGHT and add the % or X by 100
What is the procedure for dividing numbers with decimals?
Move the decimal to the right in both the divisor and the dividend, making both whole numbers. The number of places moved for the dividend must be the same number of places for the divisor. Add zeroes where necessary to do this. Divide as usual, putting the decimal point directly above its place in the dividend. 0.0023÷2.32 becomes 23÷23200
What is the procedure for dividing a fraction by another fraction?
Multiply the first fraction by the reciprocal of the second fraction 2/3÷5/4=2/3⋅4/5 2⋅4/3⋅5=8/15
What is the procedure for multiplying numbers with decimals?
Multiply the numbers as usual. Count the number of digits to the right of the decimal point in the numbers being multiplied. The final answer must contain the same number of digits to the right of the decimal place as in the numbers being multiplied 0.2345⋅1.1 There are 5 numbers to the right of the decimal point, so the answer will contain 5 numbers to the right of the decimal point. 0.2345⋅1.1=0.25795
How can miles per hour be converted to feet per second?
Multiply the original value by the appropriate conversion factors. The original units should cancel, leaving only the new units. xmile 5280ft 1hr (x)(5280) ______ X _______ X _____ = ____ hour 1mile 60sec 60 sec
Multiplying decimals
Multiplying is similar, but you may ignore the decimal point until the very end. Then, the total number of decimal places present between the two numbers you multiplied should also be the number of places present in your answer. Ex: 12.35 x 3.63 (4 places behind the DP) 1235 x 363= 448305 = 44.8305 (4 places behind the DP)
Adding and subtracting fractions withOUT like denominators
Must find the LCD Ex: 2/3 - 1/2 6 is the smallest multiple of 2 and 3 so it would be 4/6 - 3/6 =1/6
Adding a negative and a negative gives you a ____
Negative Ex: -7 + (-8)= -15
Positive divided by a negative; vice versa is a ____
Negative Ex: 8 / (-4)= -2 -8 / 4= -2
How is percent difference calculated?
New Amt - Orig Amt PD= _________________________ X 100 Orig Amt
Two lines that lie in the same plane but never intersect are ______
Parallel
Fraction means _____ over _____
Part over whole
In a school of 650 students, 54% of the students are boys. How many students are girls?
Part= Whole X Percent x= 650 x .46 x= 351 boys and 299 girls
In scatter plots one variable describes a position on the x axis and the other a ____ on the y axis
Point
Adding a positive and negative gives you a ____
Sign of number with larger value Ex: 7 + (-8) = -1
How do you convert a percent to a decimal?
Remove the % and move the decimal place two places to the left
____ ____ can suggest relationships between variables
Scatter plots Ex: both variables might increase together, or one may increase when the other decreases
Double bar graph
Show more than one data set on the same set of axes
1/2 and 2/4 are equivalent (T/F)
TRUE
What is the most common way to write a linear equation?
Slope intercept form
If you are not sure which way to move the decimal point after multiplying, remember it should be making the final answer _____
Smaller
What determines whether the graph of an inequality is a solid or dashed line?
Solid: the inequality is > or < Dashed: the inequality is either < or >
What is the slope of this line: 6x - 2y - 8= 0
Solve for y -2y = -6x + 8 Divide by 2 y= 3x - 4 Slope: 3
_____ is the study of data
Statistics
What is the formula for finding the probability of a single event?
Success Outcomes Prob= _____________________________ Possible Outcomes
What is the acronym FOIL used for?
To multiply two binomials (First, Outer, Inner, Last) Ex: (x+3)(2x-5)= 2x^2-15x+6x-15=2x^2-9x-15
Which quadrilateral has exactly one pair of parallel sides?
Trapezoid
Compound shape
Two or more paths that are combined
To add or subtract ______ fractions, convert the fractions to equivalent fractions of the same denominator, and then simply add or subtract the numerators while keeping the same denominator Ex: 1⁄2 + 1⁄3 = 3⁄6 + 2⁄6 = 5⁄6
Unlike
Bar graph
Use bars of different lengths to compare data
Circle graph (pie chart)
Used to show parts of a whole
Writing a percent as a fraction
Write the percent as a fraction with 100 as the denominator
What is the value of x for the equation 3(x-5)=3?
X= 6
Is -75 smaller than -25?
Yes
Denominator can never be what?
Zero (0)
In SN, your answer should be written in the form __________
a X 10^n
What is the Pythagorean Theorem?
a^2+b^2=c^2
How do you find the perimeter of a trapezoid?
b+l+b+l
In y=mx+b, m is the ____ and b is the _____
m= slope b= y intercept
What are the sides of a 45 - 45 - 90 right triangle?
x, x, and x squared root 2