Brainscape's Knowledge GenomeTM

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


See full index

Test Best Academy ACT Prep > ACT Math Flashcards > Flashcards

ACT Math Flashcards

Memorize the key concepts and formulas on the ACT Math section.

1
Q

Like Terms

Definition

A

Terms that have the same variable combination

Ex 1: 3x & 5x
Ex 2: 4xy & 7xy
Ex 3: 6 & 9

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

Adding Fractions

What do you need to add fractions?

A

Requires a common denominator.
(Same number on the bottom of the fraction)

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

Multiplying Fractions

How do you multiply fractions?

A

Multiply straight across the top and straight across the bottom.

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

Variable Denominators

What’s the first step in solving an equation with variable denominators?

A

When there are variables in the denominator, multiply all terms by other denominators.

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

Factors

Definition | What are the factors of 12?

A

(Smaller) numbers that multiply to the “Base Number”

Factors of 12: 1, 2, 3, 4, 6, 12

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

Multiples

Definition | What are the multiples of 12?

A

Bigger Numbers that the “Base Number” can multiply to.

Multiples of 12: 12, 24, 36, 48…

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

Least Common Multiple

Definition

A

The lowest number all terms can multiply up into
(Also used to find common denominator)

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

f(g(x))

What are the two steps to solving these equations?

A

Figure out g(x) value

Plug in g(x) value to f(x) function

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

F.O.I.L.

A

An acronym for how to multiple two factors.

Multiply FIRST terms, OUTSIDE terms, INSIDE terms, and LAST terms

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

The Factor → X-Intercept Relationship

What does the factor (x - 5) tell you?

A

When you have a factor of an equation [ like (x - 5) ], you can set that factor equal to zero & solve for x to find x-intercepts

Ex: factor of (x - 5) means x-intercept at (5,0)

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

The X-Intercept → Factor Relationship

What does the x-intercept (3,0) tell you?

A

When you have an x-intercept of an equation,
Then ( x - [the x intercept] ) is a factor.

Ex: x-intercept at (3,0) means factor of (x - 3)

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

Coefficients

Definition

A

A quantity placed before & multiplying the variable in algebraic expressions

Ex: 3x, 4yz

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

Exponents

Definition | How would you write out (2y)^3

A

A quantity representing the power to which a number or expression is raised.
The value of the exponent is how many times a number is multiplied by itself

Ex: (2y)^3 = 2y × 2y × 2y

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

Multiplying & Dividing Exponents

A

Multiplying Like Terms: ADD Exponents

Dividing Like Terms: SUBTRACT Exponents

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

Percent Definition

A

“Per hundred”

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

“Percent of”

How would you write “40% of x” in an equation?

A

Multiply the percentage (as a decimal) to what’s after the “of”

Ex: “40% of x” means .40x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Increasing by a Percentage

What would you multiply a number by for it to go up by 20%?

A

If increasing by a percentage, add it to 1.00 and multiply

Ex: “up by 20%” means multiply by 1.20

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

Decreasing by a Percentage

What would you multiply a number by for it to go down by 20%?

A

If decreasing by a percentage, subtract it from 1.00 and multiply.

Ex: “down by 20%” means multiply by 0.80

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

Solving Absolute Value Equations

A

Create TWO equations.

One POSITIVE version of absolute value term(s)

One NEGATIVE version of absolute value term(s)

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

Median

A

The middle number in a data set
(When in order of least to greatest)

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

Mode

A

The most frequently occurring number in a data set.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Probability Key Word:
“Or”

What do you do to the two probabilities?

A

If asked what the probability that something OR something else happens, ADD the two probabilities.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Probability Key Word:
“And”

What do you do to the two probabilities?

A

If asked what the probability is that something happens AND then something else happens, MULTIPLY the two probabilities.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

“With Replacement”

How does this affect your probability fractions?

A

If asked to do probability, WITH replacement: total number (denominator) is unchanged

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

“Without Replacement”

How does this affect your probability fractions?

A

If asked to do probability, WITHOUT replacement: reduce the total number (denominator) by 1 after each selection

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Proportions

How do you solve proportions?

A

Setting two ratios equal to each other & cross multiplying.

*Ensure Units of Both Numerators Match & Units of Both Denominators Also Match

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Imaginary Numbers (𝑖)

Definition

A

A number that takes the place of √-1

Is not considered a real number.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Rationalizing The Denominator

What do you do when you have an “𝑖” in the denominator?

A

Random Rule: You’re not supposed to have an “i” in the denominator

Solution: Multiply top & bottom by the “conjugate” of denominator (same numbers, switch +/- Sign)

Ex: if denominator is (3 + 2𝑖), then multiply the top and bottom by (3 - 2𝑖)… and when you solve the “𝑖” will disappear from the denominator.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

Complex Plane

It’s like an x/y coordinate plane, but instead the axes represent…

A

Similar to a normal x/y coordinate plane, but with…
a “real” axis instead of “x” axis | An “imaginary” axis instead of “y” axis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Finding the (Big Number) Term

Ex: Find the 88th term of 0.1͞2͞3͞5͞

A

When asked to find a (big number) term of a sequence,
Use long division of the desired term number by the number of terms in the core repeating sequence, find remainder, and count that far into the core sequence.
(If remainder is equal to zero, then choose the last number in the core sequence.)

Since 88 ÷ 4 has a remainder of zero, the 88th term would be 5.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

Reflection

Where do you put the negative sign for an x-axis or y-axis reflection?

A

f(-x) = y-axis reflection
-f(x) = x-axis reflection

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

Logarithm

Why do we use them? | What are the bases of log & ln?

A

Logarithms pull variables out of exponents.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

Converting Logarithms to Exponential Form

A

When converting from log form to exponential form, keep the “base” in the same spot and switch the other two numbers/variables.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

Term Sequence Notation

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

Perimeter

Definition

A

The total length of all sides of a shape added together.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

Area of a Circle

Formula

A

A = 𝜋r2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

Circumference of a Circle

Formula

A

C = 2𝜋r

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

Congruent Triangles

Definition

A

Same sides.
Same angles.
Exact same triangle.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

How to Factor:

f(x) = ax2 ± bx ± c

A

a. If a ≠ 1, the problem likely requires the Quadratic Formula
b. If a = 1, factor numbers must add to this
c. If a = 1, factor numbers must multiply to this

Find all factor pairs of c.
Select the set that adds to b.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

Percent Change
(Increase/Decrease From Original)

Formula

A

(Change/Original) x 100

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

Positive Slope

Imagine an image of a line with a positive slope

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
42
Q

Negative Slope

Imagine an image of a line with a negative slope

A
43
Q

Parallel Slopes

Imagine an image of two lines with parallel slopes

A
44
Q

Perpendicular Slopes

Imagine an image of two lines with perpendicular slopes

A
45
Q

y = mx + b Variables Explained

What does each variable mean/represent? (4 def’ns of m / 3 def’ns of b)

A
46
Q

Midpoint Formula

A
47
Q

Distance Formula

A
48
Q

The Quadratic Formula

A
49
Q

Negative Exponents

How would you make all exponents positive?

A

Flip term from denominator to numerator (or vise versa) and make the exponent positive

50
Q

Fractional Exponents

What would x^(1/2) convert to?

A

“Top dog in the house”
Top number is in radical, bottom number is the “root” of radical

51
Q

Power Raised to a Power

What do you do to the exponents?

A

Multiply the Exponents

52
Q

Mean

Formula

A
53
Q

Ratios

What are the three way to write a ratio?

A
54
Q

Imaginary Numbers Chart

What are the values of 𝑖 to the powers of 1, 2, 3, & 4?

A
55
Q

Rotation of 90° Clockwise
(Or 270° Counterclockwise)
About the Origin

How would you change the signs of the x and/or y-coordinates?

A
56
Q

Arithmetic Sequences Definition

What is the equation to find the nth term of an arithmetic sequence?

A
57
Q

Geometric Sequences

What is the equation to find the nth term of an arithmetic sequence?

A
58
Q

Area of a Rectangle

A
59
Q

Area of a Square

A
60
Q

Area of a Triangle

A
61
Q

Area of a Trapezoid

A
62
Q

Area of a Rhombus

A
63
Q

Area of Funky Shapes

How would you calculate the total area?

A

When asked to find the area of a large combination of shapes, break the shape up into smaller shapes and add up the areas of each.

64
Q

Finding the Area of a Shaded Region

How would you calculate the total area of the shaded region?

A

When asked to find the “area of the shaded region,” take the area of BIG, OUTSIDE shape MINUS area of SMALL, INSIDE shapes.

65
Q

Volume of a Rectangular Prism

A
66
Q

Volume of a Triangular Prism

A
67
Q

Volume of a Cylinder

A
68
Q

Volume of a Sphere

A
69
Q

Volume of a Cone

A
70
Q

Volume of a Square Pyramid

A
71
Q

Isosceles Triangles

Definition

A
72
Q

Circle Graph Equation

What’s the equation for a circle graph? What does each variable mean?

A
73
Q

Completing the Square

Why do we complete the square? What are the four steps?

A
We complete the square to reorganize the circle/ellipse/hyperbola equations so that we can clearly see the center as constants in the equation.
74
Q

Similar Triangles

Definition

A

Same Angles.
Different, Proportional sides.

75
Q

Pythagorean Theorem

What’s the formula?

A
76
Q

Special Right Triangles

What are the 30-60-90 triangle ratios and the 45-45-90 triangle ratios?

A
76
Q

SOH | CAH | TOA

(“O”, “A”, & “H” Definitions)

A

The acronym for remembering the side ratios for the sine, cosine, and tangent functions.

  • “O” means opposite.
  • “A” means adjacent.
  • “H” means hypotenuse”
77
Q

SOH | CAH | TOA

3 Steps to Solve

A
  1. Draw Out Triangle, Mark Angle of Interest, & Write Out SOH CAH TOA
  2. Label Opposite Side, Then Hypotenuse Side, & LAST Adjacent Side
  3. Write out sine, cosine, or tangent identity & plug in numbers.
78
Q

SOH

Sine Equation in SOH | CAH | TOA

A
79
Q

CAH

Cosine Equation in SOH | CAH | TOA

A
80
Q

TOA

Tangent Equation in SOH | CAH | TOA

A
81
Q

Converting Degrees to Radians

A
82
Q

Converting Radians to Degrees

A
83
Q

Inverse Trig Functions

Why do we use these?

A
84
Q

Sine & Cosine Graph Transformations

What does each variable do in the equation Asin(Bx - C) + D?

A
85
Q

Law of Sines

When do we use this? What is the formula?

A

Used for non-right triangles to find sides/angles
*Typically use when given values for an “angle/opposite side” pair

86
Q

Law of Cosines

When do we use this? What is the formula?

A

Used for non-right triangles to find sides/angles
*Typically use when given a set of consecutive “side/angle/side” values

87
Q

“Real Number”

A

All numbers without an “𝑖” (imaginary) attached to it.

88
Q

Matrix/Matrices

Definition

A

A set of numbers arranged in rows & columns

89
Q

Adding/Subtracting Matrices

How do you do this?

A
  1. Check that the matrices have the same row x column dimensions (if they do not, you cannot add/subtract the matrices)
  2. Add/subtract the numbers in the same spots.
90
Q

Scalar Multiplication of a Matrix

How do you do this?

A

When there’s a number in front of a matrix, distribute it to all numbers in the matrix.

91
Q

Solving a 2x2 Matrix

Formula

A

When asked to solve a 2x2 matrix, use this formula:

“Downhill at first, then uphill”

92
Q

Multiplying Matrices

Three steps

A
  1. Write the row x column dimensions below each matrix.
  2. Confirm that the two middle numbers are the same (if they aren’t, you cannot multiply the matrices)
  3. The resulting matrix will have the dimensions of the outside numbers.
93
Q

Multiplying Matrices
(Using a Calculator)

A

When the ACT asks you to multiply two matrices, use your graphing calculator to solve.

Example in Matrices lesson… or search on YouTube “how to multiply matices on (your calculator name)”

94
Q

Ellipse Graph Equation

What does each variable represent?

A
95
Q

Integers

Definition

A

Any whole number:… -3, -2, -1, 0, 1, 2, 3…

96
Q

Rational Numbers

Definition

A

Any number without a radical (√) or pi (𝝿)

97
Q

Scientific Notation

Definition

A
98
Q

Vector Notation

How do you graph a vector?

A

< x,y >

Draw an arrow from (0,0) to the (x,y) point on a graph

99
Q

Irrational Numbers

Definition

A

Any number with a radical (that doesn’t simplify) or pi (𝝿)

Ex: √3, √7, or 5𝝿

100
Q

Adding/Subtracting Vectors

Ex: < 2 , 1 > + < 5 , 3 > = ?

A

Just add the “x” & “y” terms of the two vectors

Ex: < 2 , 1 > + < 5 , 3 > = < 7 , 4 >

101
Q

“i” & “j” Vector Notation

Ex: 12i + 5j can be written as…

A

“i” notation is for the x-component of vector
“j” notation is for the y-component of vector

Ex: 12i + 5j can be written as < 12 , 5 >

102
Q

Rotation of 180° About the Origin

How would you change the signs of the x and/or y-coordinates?

A
103
Q

Rotation of 90° Counterclockwise
(Or 270° Clockwise) About the Origin

How would you change the signs of the x and/or y-coordinates?

A

Test Best Academy ACT Prep (4 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions