Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

ACT > Math Formulas > Flashcards

Math Formulas Flashcards

1
Q

distance formula

A

d = rt

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

time formula

A

t = d/r

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

rate formula

A

r = d/t

(rate = speed, so this is the same as s = d/t)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

the quadratic formula

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

radical rule of exponents

A

n√x = x1/n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

area of a trapezoid

A

A = ([a+b]/2)h

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

area of a rhombus

A

A = 1/2(D1)(D2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

surface area of a rectangular prism

A

SA = 2LW + 2WH +2LH

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

area of a circle

A

A = πr2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

circumference of a circle

A

C = 2πr = πd

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

a central angle has the same measure as

A

the intercepted angle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

any inscribed angle in a semi-circle is

A

a right angle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

an inscribed angle is ___ the measure of the intercepted arc

A

half

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

what are the most common triangles on the ACT?

A

3-4-5

6-8-10

5-12-13

7-24-25

8-15-17

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

what are the measurements of the 30-60-90 special right triangle?

A
  • the side opposite the right angle is 2x
  • the side opposite the 30˙ is x
  • the side opposite the 60˙ is x√3
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

what are the measurements of the 45-45-90 special right triangle?

A
  • the side opposite the right angle is x√2
  • the two sides opposite 45˙ angles are x
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

sum of interior angles of a polygon

A

sum of interior angles = (N-2)180˙

where N = the number of sides

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

number of diagonals in a polygon

A

number of diagonals = (N[N-3])/2

where N = the number of sides

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

slope-intercept form

A

y = mx + b

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

standard form

A

Ax + By = C

(on the ACT, convert this to slope-intercept form to solve for y)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

slope formula

A
22
Q

midpoint formula

A
23
Q

distance formula

A
24
Q

equation of a circle

A

(x-h)2 + (y-k)2 = r2

25
Q

multiplication principle

A
  • if there are n ways to select one item and m ways to select another, then there are nm ways to select one of each type*
  • ex: if there are 3 shirts, 4 pants, and 5 shoes, 3x4x5 = 60 outfits are possible
26
Q

ordering of objects

A

there are n! ways to order n different objects

  • n! = n(n-1)(n-2)(n-3) . . .
  • ex: 5 different books can be arranged 5! = 120 different ways
  • evaluate on TI-83/84 by typing the number you would like to find the factorial of, then click ‘math’ and go to PRB and select 4. Hit enter on the main screen and it will calculate the factorial.
27
Q

properties of logs

A
  • logbx = y if and only if by = x
  • logb(xy) = logbx + logby
  • logb(x/y) = logbx - logby
  • logbxn = nlogbx
  • logbx = (logx) / (log b)
28
Q

pythagorean identities

A

sin2θ + cos2θ = 1

1 + tan2θ = sec2θ

1 + cot2θ = csc2θ

29
Q

tangent pythagorean identity

A

tan2θ + 1 = sec2θ

30
Q

cotangent pythagorean identity

A

1 + cot2θ = csc2θ

31
Q

for a quadratic equation ax2 + bx + c = 0, the sum of the roots is

A

-b/a

32
Q

for a quadratic equation ax2 + bx + c = 0, the product of the roots is

A

c/a

33
Q

what is the discriminant?

A

b2 - 4ac

  • if it is greater than zero there are 2 real solutions
  • if it is equal to zero there is 1 real solution
  • if it is less than zero there are no real solutions, but 2 complex solutions
34
Q

what is the vertek form of a parabola?

A

y = a(x - h)2 + k

  • vertex = (h,k)
  • if a > 0 the parabola opens up
  • if a < 0 the parabola opens down
35
Q

difference of squares

A

x2 - y2 = (x-y)(x+y)

36
Q

given standard form Ax + By = C, what is the slope and y-intercept?

A

slope = -A/B

y-intercept = C/B

37
Q

the exterior angle of a triangle is equal to

A

the sum of the two opposite internal angles

38
Q

the sum of the exterior angles of a triangle are

A

360˙

39
Q

what is the generic formula for volume?

A

the area of the base times the height

40
Q

arc length formula

A

s = (θ/360˙)(2πr) if θ is in degrees

s = rθ if θ is in radians

41
Q

properties of trig graphs

A

y = Asin(Bx) or y = Acos(Bx)

  • amplitude = |A|
  • period = 2π/|B| or 360˙/|B|
42
Q

degrees to radians

A

multiply by π/180˙

43
Q

radians to degrees

A

multiply by 180˙/π

44
Q

if an is the nth term and d is the common difference, then

A

an = a1 + (n-1)d

45
Q

the sum of the first n terms (Sn) is

A

Sn = (n/2)(a1 + an)

46
Q

mean

A

mean = (sum of the terms) / (number of terms or amount of different terms)

47
Q

probability formula

A

probability of outcome happening = (number of desired outcomes) / (total possible outcomes)

48
Q

probability of two events both happening

A

probability of event = (event A)(event B)

49
Q
A
50
Q

area of an arc

A

area of arc = (πr2)(degree measure of center of arc / 360)

51
Q

circumference of an arc

A

circumference of arc = (2πr)(degree measure of center of arc / 360)

ACT (3 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions