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Test Best Academy SAT Prep > SAT Math Flashcards > Flashcards

SAT 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

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2
Q

Adding Fractions

What do you need to add fractions?

A

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

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3
Q

Multiplying Fractions

How do you multiply fractions?

A

Multiply straight across the top and straight across the bottom.

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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.

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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

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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…

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7
Q

Least Common Multiple

Definition

A

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

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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

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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

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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)

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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)

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12
Q

Coefficients

Definition

A

A quantity placed before & multiplying the variable in algebraic expressions

Ex: 3x, 4yz

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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

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14
Q

Multiplying & Dividing Exponents

A

Multiplying Like Terms: ADD Exponents

Dividing Like Terms: SUBTRACT Exponents

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15
Q

Percent Definition

A

“Per hundred”

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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

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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

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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

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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)

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20
Q

Median

A

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

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21
Q

Mode

A

The most frequently occurring number in a data set.

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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.

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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.

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24
Q

“With Replacement”

How does this affect your probability fractions?

A

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

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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

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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

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27
Q

Imaginary Numbers (𝑖)

Definition

A

A number that takes the place of √-1

Is not considered a real number.

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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.

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29
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

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30
Q

Logarithm

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

A

Logarithms pull variables out of exponents.

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31
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.

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32
Q

Perimeter

Definition

A

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

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33
Q

Congruent Triangles

Definition

A

Same sides.
Same angles.
Exact same triangle.

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34
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.

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35
Q

Percent Change
(Increase/Decrease From Original)

Formula

A

(Change/Original) x 100

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36
Q

Positive Slope

Imagine an image of a line with a positive slope

A
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37
Q

Negative Slope

Imagine an image of a line with a negative slope

A
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38
Q

Parallel Slopes

Imagine an image of two lines with parallel slopes

A
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39
Q

Perpendicular Slopes

Imagine an image of two lines with perpendicular slopes

A
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40
Q

y = mx + b Variables Explained

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

A
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41
Q

Midpoint Formula

A
42
Q

Distance Formula

A
43
Q

The Quadratic Formula

A
44
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

45
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

46
Q

Power Raised to a Power

What do you do to the exponents?

A

Multiply the Exponents

47
Q

Mean

Formula

A
48
Q

Ratios

What are the three way to write a ratio?

A
49
Q

Imaginary Numbers Chart

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

A
50
Q

Arithmetic Sequences Definition

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

A
51
Q

Area of a Trapezoid

A
52
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.

53
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.

54
Q

Isosceles Triangles

Definition

A
55
Q

Circle Graph Equation

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

A
56
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.
57
Q

Similar Triangles

Definition

A

Same Angles.
Different, Proportional sides.

58
Q

Pythagorean Theorem

What’s the formula?

A
59
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”
60
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.
61
Q

SOH

Sine Equation in SOH | CAH | TOA

A
62
Q

CAH

Cosine Equation in SOH | CAH | TOA

A
63
Q

TOA

Tangent Equation in SOH | CAH | TOA

A
64
Q

Converting Degrees to Radians

A
65
Q

Converting Radians to Degrees

A
66
Q

Inverse Trig Functions

Why do we use these?

A
67
Q

Sine & Cosine Graph Transformations

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

A
68
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

69
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

70
Q

“Real Number”

A

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

71
Q

Integers

Definition

A

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

72
Q

Rational Numbers

Definition

A

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

73
Q

Scientific Notation

Definition

A
74
Q

Irrational Numbers

Definition

A

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

Ex: √3, √7, or 5𝝿

75
Q

Line of Best Fit

Definition

A

A line that averages the data points.

76
Q

Point-Slope Formula

What do we need to use this?

A

If you have the slope of a line (m) and a point on it (X1, Y1), you can create a linear equation using point slope formula:

Y - Y1 = m (X - X1)

77
Q

How To Solve Inequality Equations

(two things)

A

Treat the inequality like an “ = ” sign and solve for x.

If you multiplied or divided by a negative, flip the sign.

78
Q

Inequality Phrasing:

“Greater than”/ “more than” / “exceeds”

Imagine what the inequality sign looks like.

A
79
Q

Inequality Phrasing:
“Greater than or equal to” / “at least” / “meet or exceed”

Imagine what the inequality sign looks like.

A
80
Q

Inequality Phrasing:

“Less than” / “cannot exceed”

Imagine what the inequality sign looks like.

A
81
Q

Inequality Phrasing:

“Less than or equal to” / “no more than” / “at most”

Imagine what the inequality sign looks like.

A
82
Q

Linear Inequality Graph Wording:

“Greater than >”

Where would you shade in? What would the line look like?

A

Shade ABOVE a DASHED line.

83
Q

Linear Inequality Graph Wording:

“Greater than or equal to ≥”

Where would you shade in? What would the line look like?

A

Shade ABOVE a SOLID line.

84
Q

Linear Inequality Graph Wording:

“Less than <”

Where would you shade in? What would the line look like?

A

Shade BELOW a DASHED line.

85
Q

Linear Inequality Graph Wording:

“Less than or equal to ≤”

Where would you shade in? What would the line look like?

A

Shade BELOW a SOLID line.

86
Q

Standard Deviation

Definition

A

The “Spread-out-ness” of the data

More spread out = More variance = Higher standard deviation

87
Q

“Equivalent” Equations
Question Strategy

A

When question asks you for an “equivalent” equation, plug in x=1 to (1) original equation and (2) all the MC answers AND see which answer gives you the same number.

88
Q

“Equating Coefficients”

A
89
Q

Linear Equations vs. Exponential Equations

For each type, what do you do to find the next value?

A

Linear Equations ADD a FIXED NUMBER each time.

Exponential Equations MULTIPLY by a PERCENTAGE/NUMBER each time

90
Q

Exponential Equation
Variables Defined

A
91
Q
A

There are TWO REAL SOLUTIONS
(aka two X-Intercepts)

92
Q
A

There are ONE REAL SOLUTION
(aka one X-Intercept)

93
Q
A

There are ZERO REAL SOLUTIONS
(aka zero X-Intercepts)

(No real solutions = 2 imaginary solutions)

94
Q

All-Variable Question Strategy

A

When given an equation with all variables, roll with it &
consider choosing simple real numbers (like -1, 0, 1) to plug in for each variable.

95
Q

“In Terms Of…”

Phrase Meaning

When told to “solve for x in terms of a, b, and c”….

A

When told to “solve for x in terms of a, b, and c”….
Rearrange the equation so it’s
“x = _____________________”

96
Q

Data Collection Methods

Definition & Strategy (4 Tips)

A

The qualifications for inclusion in the study

When answering data collection questions…
1. Focus on the SPECIFIC GROUP surveyed in the question.
1. Don’t generalize results beyond the SPECIFIC GROUP.
1. Trials must be “random” to be applied to a larger sample.
1. Avoid words like “Exactly” & “Always”

97
Q

Margin of Error

65% with 4% margin of error means…

A

The percentage that the estimate could be off by (add and subtract from the estimated value)

Ex: 65% with 4% margin of error means that real % could be anything between 61% & 69%

98
Q

Grid-In Questions:
“Possible Value” Meaning

A

When an SAT grid-in question asks for a “POSSIBLE VALUE,” there are multiple answers that work - you just need to bubble in one of them.

99
Q

Density = = ??? | (What is the equation for Density?)

A

Density = Mass / Volume (simplified as d=m/v)

100
Q

Speed / Velocity = ??? | (What is the equation for Speed?)

A

Speed/Velocity = Distance / Time (simplified as v=d/t)

101
Q

When SAT asks for “sum of solutions” for a quadratic (x^2) equation, you can solve easily with this formula…

A

Sum of Solutions = -b/a

(Based on quadratic eqn in standard form ax^2 + bx + c)

102
Q
A

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