Math Formulas

Question 1

Order of Operations

Answer 1

PEMDAS

1. Parentheses
2. Exponentiation
3. Multiplication/Division
4. Addition/Subtraction

Question 2

Commutative Property

Answer 2

a + b = b + a
a * b = b * a
&laquo_space;does not work with division or subtraction&raquo_space;

Question 3

Associative Property

Answer 3

(a + b) + c = a + (b + c)
(a * b) * c = a * (b * c)
&laquo_space;does not work with division or subtraction&raquo_space;

Question 4

Distributive Property

Answer 4

a * (b + c) = ab + ac

a * (b - c) = ab - ac

Question 5

1 [is / is not] prime

Answer 5

1 is not prime

Question 6

2 [is / is not] prime

Answer 6

2 is prime; it is the smallest prime number and the only even prime

Question 7

Prime Numbers < 60

Answer 7

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59

Question 8

Prime Factorization

Answer 8

dividing a number up into its constituent primes
Ex: 21 = 3 x 7
60 = 2 x 2 x 3 x 5

Question 9

How many factors does 720 have?

Answer 9

prime factorization: (24) x (32) x (5)
all factors can be written as: (2a) x (3b) x (5c)
for 720: a = 0, 1, 2, 3, or 4 &raquo_space; 5 options
b = 0, 1, or 2 &raquo_space; 3 options
c = 0 or 1 &raquo_space; 2 possibilities
number of factors = 532 = 30

Question 10

What is the GCF of 12 and 30

Answer 10

6

explanation: factors of 12 are 1, 2, 3, 4, 6. factors of 30 are 1, 2, 3, 5, 6, 10, 15&raquo_space; GCF

Question 11

Fractions:

(1/x) + (1/y) = ?

Answer 11

(1/x) + (1/y) = (x + y)/(xy)

Question 12

%change = ?

Answer 12

(final - original)
% change = —————————
(original)

Question 13

(ya) x (yb) = ?

Answer 13

(ya) x (yb) = y**(a+b)

Question 14

(xa) / (xb) = ?

Answer 14

(xa) / (xb) = x**(a - b)

Question 15

(xa)b = ?

Answer 15

(xa)b = x**(a*b)

Question 16

x**(1/2) = ?

Answer 16

x**(1/2) = sqrt(x)

Question 17

x**(2/3) = ?

Answer 17

x(2/3) = cuberoot(x2)

Question 18

x**(-1) = ?

Answer 18

x**(-1) = (1/x)

Question 19

x**(-2) = ?

Answer 19

x(-2) = 1/(x2)

Question 20

2sqrt(7) + 9sqrt(7) = ?

Answer 20

2sqrt(7) + 9sqrt(7) = 11*sqrt(7)

&laquo_space;roots can be added like variables&raquo_space;

Question 21

(x + 2)(x + 7) = ?

Answer 21

Using FOIL:

(x**2) + 9x + 14

Question 22

(a + b)**2

Answer 22

a2 + 2ab + b2

Question 23

(a - b)**2

Answer 23

a2 - 2ab + b2

Question 24

(a + b)(a - b)

Answer 24

(a2) - (b2)

Question 25

factor using quadratic polynomials:

(x**2) + ax + b = ?

Answer 25

(x**2) + ax + b = (x + m)(x + n)
where a = m+n;
where b = m*n

Question 26

Eliminate fractions by multiplying by _________

Answer 26

the Least Common Denominator (LCD)

Question 27

cross-multiplication:

a/b = c/d&raquo_space; ?

Answer 27

cross-multiplication:

a/b = c/d&raquo_space; ad = bc

Question 28

quadratic equation

Answer 28

b +/- sqrt( (b**2) - 4ac)
x = ————————————— ;
2a
where a != 0

Question 29

2 methods to solve equations in two variables / systems of equations:

Answer 29

1. Substitution
   (solve for one variable in terms of the other &raquo_space; substitute &raquo_space; solve)
2. Elimination
   (add the equations together &raquo_space; if one variable cancels out, then solve for the remaining variable)

Question 30

if given f(x) and asked what f(something else) is, _____________________________

Answer 30

simply replace every instance of x in the “…” expression with whatever is now in the parentheses
(same rule applies for functions with strange symbols)