Praxis Math

Which expression is equivalent to dividing 400 by 16? A. 2(200-8) B. (400/4) /12 C. (216/8) + (184 / 8) D. (216 / 16) + (184 / 16)

D. Solve in the parentheses first. Equals 25.

Which of the following is a solution to the inequality 2x + y <- -10? A. (0,0) B. (10,2) C. (10,10) D. (-10,-10)

D. plug in each set of values and determine if the inequality is true. 2(-10) + (-10) <- -10 TRUE!!

How do you multiply binomials?

FOIL. First - Outer - Inner - Last.

In the theater, there are 4,500 lower-level seats and 2,000 upper-level seats. What is the ratio of lower-level seats to total seats?

Find the total number of seats and set up a proportion. total seats = 4,500 + 2,000. Lower seats/total seats = 4,500/6,500 = 9/13

Absolute value

(| |) of a number is the positive value of a number or its opposite; example: |-3| = 3 and |3| = 3

Cross Multiply

.(v.) multiply the numerator of each ratio by the denominator of the other ration. a/b = c/d ---> ad = bc

Whole numbers

0,1,2,3. (Includes 0)

Pico

0.000000000001

Nano

0.000000001

Micro

0.0000001

Milli

0.001

Centi

0.01

Deci

0.1

What is 20% of 50?

0.2 x 50 = 10.

321. Which is in the ones place?

1

Negative exponents

1 / x^b = x^(-b). They take the reciprocal of the base and then make the exponent positive.

10^0

1 no prefix

Kilo

1,000

10^6

1,000,000

Mega

1,000,000

Giga

1,000,000,000

Tera

1,000,000,000,000

Natural numbers

1,2,3

10^-2

1/100

Deca

10

321. Which is in the tens place?

2

How to perform this equation: 2/3 - 1/2?

2/3 (2/2) - 1/2 (3/3) = 4/6 - 3/6 = 1/6. 6 was the least common multiple to make the common denominator.

200 is 40% of what number?

200=40% x ? 200=0.4 x ? 200/0.4 = 500 ?=500

321. Which is the hundreds place?

3

Which is the divisor? 12 / 3 = 4

3

Which is the correct scientific notation for the number 34,500,000?

3.45 X 10^7. Move the decimal unit between the 3 and 4, making a number between 1 and 10. Count the number of spots the decimal moved and make this the value the exponent on the 10.

Allison used 2 1/2 cups of flour to make a cake, and 3/4 of a cup of flour to make a pie. If she started with 4 cups of flour, how many cups of flour does she have left?

3/4. 2 1/2 + 3/4 = 5/2 +3/4 = 10/4 + 3/4 = 13/4. next 4 - 13/4 = 16/4 - 13/4 = 3/4!!

Which of the following could be the perimeter of a triangle with two sides that measure 13 and 5? A. 24.5 B. 26.5 C. 36 D. 37

36. Use the third-side rule to find the possible values for the third side, then calculate the possible perimeters. 13 - 5 < s < 13 + 5 8 < s < 18 13 + 5 +8 < P < 13 +5 +18 26 < P < 36!!

Convert this decimal to a percentage 0.375

37.5%

Convert this decimal to a fraction 0.375

375/1,000=3/8

Which is the quotient? 12 / 3 = 4

4

Associative property

(a+b)+c=a+(b+c) (ab)c=a(bc)

Hecto

100

Which is the dividend? 12 / 3 = 4

12

120 is what percentage of 80?

120 = ?% x 80 ?%=120/80 = 1.5 = 150%.

Cone A is similar to cone B with a scale factor of 3:4. If the volume of cone A is 54pi, what is the volume of cone B? A. 72pi B. 128 pi C. 162 pi D. 216 pi

128 pi. Set up a proportion. Cube the scale factor when calculating volume. 54pi/x = 3^3/4^3 x = 128 pi

W, X, Y, and Z lie on a circle with center A. If the diameter of the circle is 75, what is the sum of AW, AX, AY, AND AZ?

150. All the points lie on the circle, so each line segment is a radius. The sum of the 4 lines will be 4 times the radius. r=75/2 = 37.5 4r = 150

What is 498,235 rounded to the nearest thousands?

498,000. The 8 is in the thousands place. Because the value to the right of the 8 is less than 5, the 8 remains the same and all values to its right become zero.

Perimeter of a square?

4s

How to perform this equation: 5/6 / 2/3 =

5/6 / 2/3 = 5/6 x 3/2<--(switch numerator and denominator) = 15/12 = 5/4.

How to perform this equation: 5/6 x 2/3 =

5/6 x 2/3 = 10/18 = 5/9. Multiply across.

Ken has 6 grades in English class. Each grade is worth 100 points. Ken has a 92% average in English. If Ken's first five grades are 90, 100, 95, 83, and 87, what did Ken earn for the sixth grade?

97. If Ken has six scores that average 92%, his total number of points earned is found by multiplying the average by the number of scores. 96 x 6 = 552 To find how many points he earned on the sixth test, subtract the sum of the other scores from 552: 90 + 100 + 95 +83 + 87 = 455 552 - 455 = 97

Area of a triangle equation?

A = 1/2 bh

Area of a rectangle?

A = L x W or bh

Area of a square equation?

A = s^2

common denominator

A denominator that is the same in two or more fractions.

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

Bar graph

A graph that uses horizontal or vertical bars to display data

Tangent?

A line in the plane of a circle that intersects the circle in exactly one point.

Exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself. The number 54 can be written as 2 x 3 x 3 x 3 or 2 x 3^3

scientific notation

A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10.

Binomial

A polynomial with two terms. 3x +16y

Skewed left

A skewed distribution with a tail that stretches left, toward the smaller values.

Isosceles triangle

A triangle that has 2 equal sides.

Scalene triangle

A triangle with no equal sides

Equilateral triangle

A triangle with three congruent sides

Outlier

A value much greater or much less than the others in a data set

Prime number

A whole number that has exactly two factors, 1 and itself. 7 can be only divided by itself and 1.

Convert the following measurements: A. 4.25 kilometers to meters B. 8 m^2 to mm^2 C. 12 Feet to inches D. 23 meters to feet

A. 4.25 km (100m/1km) = 4250 B. 8m^2/BOX x 1000mm/1m = 8,000,000 mm^2 C. 12 ft (12 inch/1 ft) = 144 ft D. 23 m (3.28 ft/1m) = 75.44 ft

The pie graph below shows how a state's government plans to spend its annual budget of $ 3 billion. How much more money does the state plan to spend on infrastructure than education? Pension:32% Education: 18% Infrastructure: 20% Employees: 8% Healthcare: 22% A. $60,000,000 B. $ 120,000,000 C. $300,000,000 D. $600,000,000

A. 60,000,000 Find the amount the state will spend on infrastructure and education, and then find the difference. infrastructure: 0.2 (3,000,000,000) = 600,000,000 education: 0.18 (3,000,000,000) = 540,000,000 600,000,000 - 540,000,000 = $60,000,000

What number is equal to (5^2 + 1)^2 +3^3? A. 703 B. 694 C. 30 D. 53

A. 703

What is the relationship between the mean and the median in a data set that is skewed right? A. The mean is greater than the median B. The mean is less than the median C. The mean and median are equal D. The mean may be greater than, less than, or equal to the median.

A. If the data is skewed right, the set includes extreme values that are to the right or high. The median is unaffected by these high values, but the mean includes these high values and would therefore be greater.

What is the measure of each exterior angle of a regular 300-gon? A. 1.2 degrees B. 2.4 degrees C. 178.8 degrees D. 360 degrees

A. The sum of all the exterior angles of a regular n-gon always 360 degrees. Because there are 300 vertices in a 30-gon, the exterior angle at each vertex is 360/300 = 1.2 degrees

Valerie receives a base salary of $740 a week for working 40 hours. For every extra hour she works, she is paid at a rate of $27.75 per hour. If Valerie works t hours in a week, which of the following equations represents the amount of money, A, she will receive? A. A=740 + 27.75 (t-40) B. A=740 + 27.75 (40 - t) C. A = 27.75t - 740 D. A= 27.75t + 740

A. Valerie will receive her base pay plus 27.75 for every hour she worked in addition to her 40 hours. A=base pay + 27.75 x extra hours A = 740 + 27.75 (t - 40)

To which of the following number sets does 3 NOT belong? A. irrational B. rational C. whole D. integer

A. the number 3 is not irrational because it can be written as the fraction 3/1

Area of a circle?

A=πr²

Proportion

An equation stating that two ratios are equal

Rational numbers

Any number that can be expressed as a fraction

What is the square root of 169? A. 9 B. 13 C. 16 D. 19

B. 13

Simplify (1 1/2) (2 2/3) / 1 1/4 A. 3 1/12 B. 3 1/5 C. 4 D. 5

B. Convert each item to an improper fraction and multiple.divide left to right. 1 1/2 = 3/2. 2 2/3 = 8/3. 1 1/4 = 5/4. So then, (3/2) (8/3) / 5/4. next 24/6 / 5/4. Next, 4/1 x 4/5 = 16/5 = 3 1/5.

What is the remainder when 397 is divided by 4? A. 0 B. 1 C. 2 D. 4

B. Find the highest possible multiple of 4 that is less than or equal to 397 and then subtract to find the remainder. 99 x 4 = 397. 397 - 396 = 1

Perimeter of a circle?

C = 2(pi)r (circumference)

Whats the surface area of this regular polygon? (2inches is on one side of the 5 sided polygon) A. 4 in B. 8 in C. 10 in D. 32 in

C. 10 inches. Add the length of each side to find the perimeter: 2 in + 2 in + 2 in + 2 in + 2 in = 10 in

Classify the number 13/14 A. irrational B. imaginary C. rational D. integer

C. 13/14 is a rational number because it can be written as a fraction but not as a whole number (without the fraction). It is not imaginary because it does not have an i component.

Which of the following has the greatest value? A. -4(3)(-2) B. -16-17+31 C. 18-15+27 D. -20+10+10

C. 18 - 15 +27 = 30!!

Some of a hotel's 400 rooms have an ocean view and the rest of the rooms do not. If the probability of getting a room with an ocean view is 35%, how many rooms do NOT have an ocean view? A. 140 B. 299 C. 260 D. 300

C. 260 The probability of getting a room without an ocean view is equal to 1 minus the probability of getting a room with an ocean view. P(view) = 1 - P(noview) P(view) = 1 - 0.35 = 0.65 Use the equation for percentages to find the number of rooms without a view. part = percentage x whole = (0.65)400 = 260 rooms

Which digit is in the hundredths place when 1.3208 is divided by 5.2? A. 0 B. 4 C. 5 D. 8

C. 5 (1.3208 / 5.2 = .254)

A teacher has 50 notebooks to hand out to students. If she has 16 students in her class, and each student receives 2 notebooks, how many notebooks will she have left over? A. 2 B. 16 C. 18 D. 32

C. If each student receives 2 notebooks, the teacher will need 16 x 2 = 32 notebooks. After handing out the notebooks, she will have 50 - 32 = 18 notebooks left

What is the least common multiple of the numbers 10 and 12? A. 2 B. 24 C. 60 D. 120

C. Write out the multiples for each number until reaching a number in both lists. 10: 10,20,30,40,50,60. 12. 12, 24, 36, 48, 60. 60!

What base -10 system is this? 2x10^-2 2x1/100 0.02

Hundredths

Solve for x: 5x - 4 = 3(8+3x)

Isolate the variable x on one side of the equation. 5x - 4 = 3(8 + 3x) 5x - 4 = 24 + 9x -4 - 24 = 9x - 5x -28 = 4x -28/4 = 4x/4 x=-7

Composite number

Natural number greater than 1 that can be evenly divided by at least one other number besides 1 and itself. 6 can be divided by 123 and 6.

Factors

Numbers that are multiplied together to get a product

What base - 10 system is this? 4x10^0 = 4x1= 4

Ones

Perimeter of a rectangle?

P = 2L + 2W

Perimeter of a triangle equation?

P = s1 + s2 + s3

Order of operation?

PEMDAS = Parentheses, Exponents, Multiplication, and/or Division, Addition, and/or Subtraction in this order

Surface area of a sphere?

SA = 4πr^2

Surface area of a cube?

SA = 6s^2

Surface area of a right rectangular prism?

SA = LA + 2B

Surface area of a cylinder?

SA = LA + 2B = 2(pi)rh+2(pi)r^2

If a car uses 8 gallons of gas to travel 650 miles, how many miles can it travel using 12 gallons of gas?

Set up a proportion and solve. 8/650 = 12/x. 12(650) = 8x. x=975 miles

40% of what number is equal to 17?

Solve using ratios. part/whole = 40/100 = 17/? 40? = 100(17) ?=42.5

If x = 5, what is the value of the algebraic expression 2x - x?

Substitute 5 for x. 2(5) - 5 = 10 - 5 = 5!!

What base - 10 system is this? 5x10^1= 5x10= 50

Tens

What base -10 system is this? 3x10^-1 3x1/10= 0.3

Tenths

The greatest common factor (GCF)

The largest factor that two or more numbers have in common. Set of numbers is the greatest number (other than 1) that each number in the set is divisible by without any remainders. For the numbers 4 and 8, the GCF is 4, since 4 goes into both 4 and 8.

Least common multiple (LCM)

The least number that is a common multiple of two or more numbers. Find the smallest common multiple of those numbers, which is the smallest number that can be divided by both numbers without a remainder. The LCM of 6 and 8 is 24, since 24 is the smallest n umber that is divisible by both 6 and 8. Write out all the multiples and look for the smallest number that is in both lists. 6: 6, 12, 18, 24, 30. 8: 8, 16, 24, 32. 24!

Divisor

The number by which another number is divided.

Dividend

The number that is being divided into groups

Remainder

The number that is left over when a number does not divide evenly into another number

Radical

The opposite of an exponent and is an expression that has a square root, cube root, or a higher root. For example: The (squareroot) of 16 = 4 since 4^2 = 16. and the (squareroot) of 8 = 2 since 2^3 = 8.

least common multiple

The smallest multiple (other than zero) that two or more numbers have in common.

(3x + 2)^2

Use foil to solve. (3x +2)(3x+2)= 9x^2 + 6x + 6x + 4 = !!!9x^2 + 12x + 4!!!

What is the percent increase in an employee's salary if it is raised from $57,000 to $60,000?

Use the formula for percent increase. Percent increase=new amount - original amount/original amount x 100. 60,000-57,000/57,000 x 100 = 5%

Histograms

Used when data is continuous The bars touch each other

Volume of a sphere?

V = 4/3πr^3

Volume of a right rectangular prism

V = bh

Volume of a cylinder?

V = πr^2h

Volume of a cube?

V=s³

Are integers rational numbers?

Yes. They can be written as a fraction with a denominator of 1.

Zero property

a * 0 = 0

Double bar graph

a bar graph that compares two related sets of data

Unit fraction

a fraction with a numerator of 1

Dot plots

a graph where dots that represent the value of data are plotted above a number line

Scatterplot

a graphed cluster of dots, each of which represents the values of two variables

Secant?

a line that intersects a circle at 2 points

Distributive Property

a(b + c) = ab + ac

Identity property

a+0=a or a*1=a

Commutative Property

a+b=b+a and ab=ba

What is the percent change equation?

amount of change/original x 100

What is the percent increase equation?

new-old/old x 100

Inverse operations

operations that undo each other. 2 + 3 = 5, and so is the inverse 5-3 = 2

unit rates

rates in which the second quantity is 1

Quotient

the answer to a division problem

Product

the answer to a multiplication problem

The mean

the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores

Range

the difference between the highest and lowest scores in a distribution

The median

the middle score in a distribution; half the scores are above it and half are below it

Mode

the most frequently occurring score(s) in a distribution

Scale factor

the ratio of the lengths of two corresponding sides of two similar polygons

Skewed right

the tail to the right of the peak is longer than the tail to the left of the peak

Integers

whole numbers and their opposites

Which of the following is an equation of the line that passes through the points, (4, -3) and (-2, 9) in the xy plane? A. y=-2x +5 B. y=-1/2x-1 C. y=1/2x-5 D. y=2x - 11

y=-2x+5 Use the points to find the slope. m= y2-y1/x2-x1 = -3-9/4-(-2) = -2 Use the point-slope equation to find the equation of the line. (y-y1) = m(x-x1) y-(-3) = -2(x-4) =y=-2x+5