Math Review

Question 1

Order of operations

Answer 1

PEMDAS

Question 2

Is zero positive or negative?

Answer 2

Neither

Question 3

How to find a remainder

Answer 3

If m and n are positive integers and if r is the remainder when n is divided by m, then n is r more than a multiple of m.

That is, n = mq + r where q is an integer and 0 < m

Question 4

Is 1 prime?

Answer 4

No

Question 5

First ten prime numbers

Answer 5

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Question 6

Relationship between GCF and LCM

Answer 6

The product of the GCF and LCM of two numbers is equal to the product of the two numbers.

GCF x LCM = ab

Question 7

Laws of exponents

Answer 7

For any numbers b and c and positive integers m and n:

```
b^m)(b^n) = b^(m+n
(b^m)/(b^n) = b^(m-n)
(b^m)^n = b^mn
(b^m)(c^m) = (bc)^m
~~~

Question 8

Laws of radicals

Answer 8

For any positive numbers a and b:

√(ab) = √a x √b
√(a/b) = √a/√b

Question 9

Distributive Property

Answer 9

a(b + c) = ab + ac
a(b - c) = ab - ac

(b + c)/a = b/a + c/a
(b - c)/a = b/a - c/a

Question 10

Fractions and inequalities

Answer 10

If 0 < x < 1, and a is positive, then xa < a
If 0 < x < 1, and m and n are positive integers with m > n, then x^m < x^n < x
If 0 < x x
If 0 < x x and (1/x) > 1

Question 11

Is 0 even or odd?

Answer 11

Even

Question 12

Comparing fractions

Answer 12

Cross-multiply:

To compary (1/3) and (3/8), multiply 3 x 3 and 8 x 1.

3 x 3 > 8 x 1, so (3/8) > (1/3)

Question 13

Dividing by fractions

Answer 13

To divide any number by a fraction, multiply that number by the reciprocal of the fraction.

Question 14

Convert a fraction to a percent

Answer 14

Convert the fraction to a decimal, then convert the decimal to a percent.

Question 15

Which is greater: a% of b or b% of a?

Answer 15

a% of b = b% of a

Question 16

Percent increase and percent decrease

Answer 16

If a < b, the percent increase in going from a to b is always greater than the percent decrease going from b to a.

An increase of k% followed by a decrease of k% is equal to a decrease of k% followed by an increase of k%, and is always less than the original value.

Question 17

(x + y)(x - y)

Answer 17

x^2 - y^2

Question 18

(x - y)^2

Answer 18

x^2 - 2xy + y^2

Question 19

(x + y)^2

Answer 19

x^2 + 2xy + y^2

Question 20

How to solve a system of equations

Answer 20

Add or subtract them

Question 21

Distance

Answer 21

rate x time

Question 22

Vertical angles

Answer 22

Have equal measure.

Question 23

Transversal

Answer 23

A line that transects two lines. If those lines are parallel, the four acute angles are equal and the four obtuse angles are equal.

Question 24

The measure of an exterior angle

Answer 24

Is equal to the sum of the measures of the two opposite interior angles.

Question 25

Measures of the sides of triangles

Answer 25

a^2 + b^2 = c^2 for a right triangle
a^2 + b^2 < c^2 if angle C is obtuse
a^2 + b^2 > c^2 if angle C is acute

Question 26

Common right triangles

Answer 26

3-4-5 and 5-12-13

Question 27

Sides of a 45-45-90 triangle

Answer 27

x - x - x√2 (hypotenuse)

Question 28

Sides of a 30-60-90 triangle

Answer 28

x - x√3 - 2x (hypotenuse)

Question 29

Sum of the sides of a triangle

Answer 29

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

The difference of the lengths of any two sides of a triangle is less than the length of the third side

Question 30

Area of a triangle

Answer 30

A = (1/2)bh

Question 31

Area of an equilateral triangle

Answer 31

A = (s^2√3)/4

Question 32

Sum of the angles in a quadrilateral

Answer 32

360

Question 33

Sum of the angles in a polygon with n sides

Answer 33

(n - 2) x 180

Question 34

Sum of exterior angles in a polygon

Answer 34

360

Question 35

Area of a square

Answer 35

A = s^2 OR A = (1/2)d^2

Question 36

Relationship between circumference and diameter of a circle

Answer 36

C = πd

Question 37

Area of a circle

Answer 37

A = πr^2

Question 38

Surface area of a rectangular solid

Answer 38

A = 2(l + w + h)

Question 39

Surface area of a cube

Answer 39

A = 6e^2

Question 40

Diagonal of a box

Answer 40

d^2 = l^2 + w^2 + h^2

Question 41

Volume of a cylinder

Answer 41

V = π(r^2)h

Question 42

Surface area of a cylinder

Answer 42

A = 2πrh

Question 43

Total area of a cylinder

Answer 43

T = 2πrh + 2π(r^2)

Question 44

Finding the distance between two points

Answer 44

d = √((x2-x1) + (y2 - y1))

Essentially the Pythagorean Theorem

Question 45

Midpoint of any two points

Answer 45

The average of the x coordinates and the average of the y coordinates

(x1 + x2)/2, (y1 + y2)/2

Question 46

Slope

Answer 46

(y2 - y1)/(x2 - x1)

Question 47

The counting principle

Answer 47

If two jobs need to be completed and there are m ways to do the first job and n ways to do the second job, then there are m x n ways to do one followed by the other.

Question 48

Probability

Answer 48

If an experiment is done two or more times, the probability that the first one event will occur and then a second event will occur is the product of the probabilities.