ACT prep

Question 1

area of a circle

Answer 1

πr²

Question 2

area of a rectangle

Answer 2

l•w

Question 3

area of a triangle

Answer 3

½b•h

Question 4

circumference of a circle

Answer 4

2πr

Question 5

area of a trapezoid*

Answer 5

½(b1+b2)•h

*may not be needed

Question 6

volume of a sphere

Answer 6

(4/3)πr²

Question 7

volume of a cone

Answer 7

(h/3)πr²

Question 8

volume of a cube

Answer 8

l•w•h

Question 9

volume of a prism*

Answer 9

area of base • height of prism

*depends what type of prism it is

Question 10

volume of a cylinder

Answer 10

hπr²

Question 11

slope-intercept form

Answer 11

y=mx+b

Question 12

point-slope form

Answer 12

y-y1=m(x-x1)

Question 13

standard form*

Answer 13

Ax+By=C
*A must be a whole, positive number

Question 14

pythagorean theorem (2D and 3D)

Answer 14

2D: a²+b²=c²
3D: a²+b²+c²=d²

Question 15

Parallel lines have ___ ___ slopes

Answer 15

the same

Question 16

Perpendicular lines have ____ ____ slopes

Answer 16

opposite reciprocal

Question 17

first three Pythagorean triples*

Answer 17

3,4,5 - 5,12,13 - 7, 24, 25

*3,4,5 is most common, but these are usually the only three that appear

Question 18

proofs with congruent triangles*

Answer 18

SSS, SAS, ASA, AAS, HL (hypotenuse leg)
*AAA can sometimes be used

Question 19

definition of whole numbers

Answer 19

positive numbers from 0 to ∞

Question 20

definition of integers

Answer 20

posistive and negative whole numbers without any fractions/decimals (includes 0)

Question 21

definition of rational numbers

Answer 21

a number that can be expressed as a fraction or decimal

Question 22

definition of irrational numbers

Answer 22

a number that cannot be expressed as a fraction or decimal (ex. √3)

Question 23

definition of transcendental numbers

Answer 23

a (possibly complex) number that is not an algebraic number of any degree. always irrational. (ex. e, π, gamma)

Question 24

definition of complex numbers

Answer 24

any number of the form (a+bi) where a and b are real numbers and i is the imaginary number (√-1)

Question 25

product of powers

Answer 25

b^m • b^n = b^(m+n)

Question 26

quotient of powers

Answer 26

b^m ÷ b^n = b^(m-n)

Question 27

power of a power

Answer 27

(b^m)^n = b^(m•n)

Question 28

identity rule of exponents

Answer 28

b⁰ = 1

Question 29

log of a product

Answer 29

log,b (mn) = log,b (m) + log,b (n)

Question 30

log of a quotient

Answer 30

log,b (m÷n) = log,b (m) - log,b (n)

Question 31

log of a power

Answer 31

log,b (m^n) = n • log,b (m)

Question 32

identity rule of a log

Answer 32

log,b (1) = 0

Question 33

b^(log,b (a)) =

Answer 33

a

Question 34

e^(ln a) =

Answer 34

a

Question 35

log,b (b^a) =

Answer 35

a

Question 36

ln (e^a) =

Answer 36

a

Question 37

rational exponents

Answer 37

b^(m/n) = (ⁿ√b)^m

Question 38

combination keywords

Answer 38

group, committee, select, sample

Question 39

permutation keywords

Answer 39

arrange, position, schedule, line up, placement, order

Question 40

formulas for permutations

Answer 40

P = P(n, r) = n! ÷ (n-r)! n = total r = # to order

Question 41

formulas for combinations

Answer 41

nCr = C(n, r) = (n r) = n! ÷ r!(n-r)!

Question 45

total sum of angles in a polygon

Answer 45

180•(n-2) n = # of sides of a polygon

Question 46

examples of prime factorization

Answer 46

factors with prime numbers (includes exponents)

Question 47

complimentary angles

Answer 47

two angles whose sum is 90°

Question 48

supplementary angles

Answer 48

two angles whose sum is 180°

Question 49

quadrantal angles

Answer 49

angles whose terminal sides lie on the x- or y-axis

Question 50

coterminal angles

Answer 50

angles whose measures differ by 360°

Question 51

degrees ➡️ minutes ➡️ seconds

Answer 51

1° ➡️ (1/60)° ➡️ (1/3600)°

Question 52

seconds ⬅️ minutes ⬅️ degrees

Answer 52

(1/3600)° ⬅️ (1/60)° ⬅️ 1°

Question 53

range of SOH CAH TOA and inverse signs

Answer 53

sin θ, cos θ = [-1, 1] tan θ, cot θ = (-∞, ∞) sec θ, csc θ = (-∞, -1]U[1, ∞)

Question 54

_² + _² = 1

Answer 54

cos²θ + sin²θ = 1

Question 55

_² + _² = 1 (divided by first term)

Answer 55

1 + tan²θ = sec²θ

Question 56

_² + _² = 1 (divided by second term)

Answer 56

cot²θ + 1 = csc²θ

Question 57

tan θ =

Answer 57

sin θ ÷ cos θ

Question 58

cot θ =

Answer 58

cos θ ÷ sin θ

Question 59

_ = _(90-θ)

Answer 59

sin = cos cos = sin tan = cot csc = sec sec = csc cot = tan

Question 60

cos(A+B) =

Answer 60

cosAcosB - sinAsinB

Question 61

cos(A - B) =

Answer 61

cosAcosB + sinAsinB

Question 62

sin(A + B) =

Answer 62

sinAcosB + cosAsinB

Question 63

sin(A - B) =

Answer 63

sinAcosB - cosAsinB

Question 64

tan(A + B) =

Answer 64

(tanA + tanB) ÷ (1 - tanAtanB)

Question 65

tan(A - B) =

Answer 65

(tan A - tanB) ÷ (1 + tanAtanB)

Question 66

cos2A = _² - _²

Answer 66

cos²A - sin²A

Question 67

cos2A = _² - 1

Answer 67

2cos²A - 1

Question 68

cos2A = 1 - _²

Answer 68

1 - 2sin²A

Question 69

sin2A =

Answer 69

2sinAcosA

Question 70

tan2A =

Answer 70

2tanA ÷ (1 - tan²A)

Question 71

what does y = arccos1 mean? *this goes for all sohcahtoa signs

Answer 71

cos y = 1

Question 72

Law of Sines

Answer 72

a/sinA = b/sinB = c/sinC

Question 73

semi/perimeter for SSS triangle

Answer 73

perimeter = a+b+c semiperimeter = ½(a+b+c)

Question 74

Heron's Area Formula - SSS

Answer 74

√ (s•(s-a)•(s-b)•(s-c))

Question 75

ratios of a right triangle

Answer 75

30° diagonal = x 60° diagonal = x√(3) 90° diagonal = 2x

Question 76

ratios of an isosceles triangle

Answer 76

45° diagonals = x 90° diagonal = x√(2)

Question 77

formula for an arithmetic sequence

Answer 77

a,n = a,1 + d(n+1)

Question 78

sum formula for an arithmetic series

Answer 78

S,n = (n/2)•(a,1 + a,n)

Question 79

formula for a geometric sequence

Answer 79

a,n = a,1•(r)ⁿ‐¹

Question 80

sum formula of finite geometric series

Answer 80

S,n = (a,1•(1-rⁿ)) ÷ (1-r)

Question 81

sum formula of infinite geometric series

Answer 81

S,∞ = a,1÷ (1-r)

Question 82

area formula for non-right triangles

Answer 82

A = ½(a•b•sinθ)

Question 83

Law of Cosines - SSS

Answer 83

a² = b² + c² - 2•b•c•cosA *a can be replaced with the side you're finding