Quantitative

Question 1

Integers

Answer 1

Any counting number including negative numbers (e.g. -3, -1, 2, 7…but not 2.5)

Question 2

Real Numbers

Answer 2

Numbers that appear on the number line (i.e., one that is not imaginary) including pi, the square root of 2, etc.

Question 3

Order of Operations

Answer 3

PEMDAS: parentheses, exponents, multiplication/division, addition/subtraction

Question 4

Prime Numbers

Answer 4

Number that is divisible only by itself and 1. Examples are 2, 3, 5, 7, 11. 1 is not a prime, 2 is the smallest prime and only even prime.

Question 5

Prime Factorization

Answer 5

The prime factorization of a number is dividing it into its constituent primes. So for 21, this is 3 x 7; for 60, 2 x 2 x 3 x 5. 7644 = 2 x 2 x 3 x 7 x 7 x 13.

Question 6

Greatest Common Factor (aka greatest common divisor)

Answer 6

The biggest factor shared by the two given numbers. The GCF of 12 and 30 is 6 – it is the biggest divisor they both share. If two numbers share no primes, the GCF is 1.

Question 7

Least Common Multiple

Answer 7

The smallest positive integer between two numbers as a factor. The LCM of 4 and 6 is 12 – it is the smallest number that has both 4 and 6 in its divisors.

Question 8

Absolute Values

Answer 8

The absolute value of a number is its distance from a number line (no negatives).
|x| = x, |-x| = x

Question 9

Percentages

Answer 9

Percent is per 100. To find what percent some part of a whole use:
part / whole = percent / 100

Question 10

Percent Change

Answer 10

Percent change: % change = change/original value
If the price of something goes from $40 to $52, the percent change is:
(52-40)/40 = 12/40 = 3/10 = 30/100 = 30%

Question 11

Roots: Perfect Squares

Answer 11

Numbers with integers as their square roots: 4, 9, 16, 25, etc.

Question 12

Roots: Cube roots

Answer 12

3√x is a number that, when cubed, equals x.

Example 3√-8 = -2.

Question 13

Roots: Adding roots

Answer 13

2√7 + 9√7 = 11√7.

Roots can be added like variables.

Question 14

Statistics: Mean, Median, Mode

Answer 14

Mean = average, total sum / n
Median = middlemost value when numbers are arranged in ascending order; for an even amount of numbers, take the average of the middle two
Mode = the number that occurs most frequently

Question 15

Statistics: Standard Deviation and Variance

Answer 15

The standard deviation represents the average distance the data values are away from the mean. Variance = SD^2

Question 16

Counting: Combinations

Answer 16

nCr = n! / r!(n - r)!
Example: 5c3 = 5! / 3!(2!) = 10
When the order does not matter – for example, picking any 3 friends from a group of 5.

Question 17

Counting: Permutations

Answer 17

nPr = n! / (n - r)!

When the order does matter – for example, how many ways you could order 3 letters from the word PARTY?

Question 18

Probability: Formula

Answer 18

Probability that event A will happen:

P(A) = number of outcomes where A occurs / total number of outcomes

Question 19

Formulas: Area of Square

Answer 19

A = s x s
(s = side)

Question 20

Formulas: Perimeter of Square

Answer 20

P = s + s + s + s

Question 21

Formulas: Area of Rectangle

Answer 21

A = L x w

length times width

Question 22

Formulas: Perimeter of Rectangle

Answer 22

P = 2L + 2W

Question 23

Formulas: Area of Triangle

Answer 23

A = 1/2bh

half base times height

Question 24

Formulas: Perimeter of Triangle

Answer 24

P = a + b + c

add all sides

Question 25

Formulas: Area of Trapezoid

Answer 25

A = ((b1+b2)/2)*h

base 1 plus base 2

Question 26

Formulas: Perimeter of Trapezoid

Answer 26

P = s1 + s2 + b1 + b2

add all the sides

Question 27

Formulas: Area of Circle

Answer 27

A = πr^2

Question 28

Formulas: Circumference of Circle

Answer 28

C = 2πr

Question 29

Formulas: Area of Semicircle

Answer 29

A = (πr^2)/2

Question 30

Formulas: Perimeter of Semicircle

Answer 30

P = 1/2πd + d

Question 31

Special Triangles: 45-45-90

Answer 31

An isosceles right triangle, side lengths create a ratio of 1:1:√2. Sides opposite of the 45 angles are x and side opposite of the 90 angle is x√2.

Question 32

Special Triangles: 30-60-90

Answer 32

Angles are 30, 60, 90. Side lengths create a ratio of 1:√3:2. Hypotenuse is twice the length of the side opposite of the 30, the other side is √3 times the side opposite of the 30.

Question 33

x^-2 = _____

Answer 33

1/x^2

Law of negative exponents. N^-a = 1/N^a

Question 34

x^1/3 = _____

Answer 34

3sqrt(x)

Law of fractional exponents. n^1/a = asqrt(n)

Question 35

1^0, 5^0, 10^0, x^0 = _____

Answer 35

1.

Zero exponents.

Question 36

x^-1 = _____

Answer 36

1/x

Negative 1 exponents. n^-1 = 1/n

Question 37

3^4 x 3^6 = _____

Answer 37

3^10

Product of exponents. N^a x N^b = N^(a+b)

Question 38

2^5 x 4 ^5 = _____

Answer 38

(2 x 4)^5

Product of exponents. N^a x M^a = (N x M)^a

Question 39

Formulas: Rates (speed, distance, time)

Answer 39

Distance = s x t
Time = d / s
Speed = d / t

Question 40

Formulas: Average Speed

Answer 40

Average speed = total distance / total time

Question 41

Formulas: Work

Answer 41

Work = xy / x + y
Where x is the time it takes the first worker to complete the job.
Where y is the time it takes the second worker to complete the job.

Question 42

Coordinate Geometry: Slope

Answer 42

M = rise/run = (y2-y1) / (x2-x1)

Question 43

Coordinate Geometry: Slope intercept form

Answer 43

y = mx + b

Question 44

Odd + Odd = _____

Answer 44

Even

-Number Properties

Question 45

Even + Even = _____

Answer 45

Even

-Number Properties

Question 46

Odd + Even = _____

Answer 46

Odd

-Number Properties

Question 47

Odd x Odd = _____

Answer 47

Odd

-Number Properties

Question 48

Even x Even = _____

Answer 48

Even

-Number Properties

Question 49

Odd x Even = _____

Answer 49

Even

-Number Properties