SAT Math Formulas Practice Flashcards

Comprehensive vocabulary flashcards covering SAT Math formulas, procedures, and concepts from the lecture notes.

Linear Equations (Linear Models)

Always use the equation $5f = 5Z5e + 5O$ for lines.

Parallel Lines Slopes

Slopes that are the SAME.

Perpendicular Lines Slopes

Slopes that are NEGATIVE RECIPROCALS.

Percents over 100

Take $100\%$, add the new percent (e.g. $14\%$), get $114\%$, and convert to decimal $1.14$ by moving the decimal TWO to the LEFT.

Function Notation (finding $f(4)$)

When given an equation like $5S(5e)$, the number in parentheses (4) is the $x$ value; plug 4 in for $x$.

Direct Variation

Usually given as an equation $5f = 5X5e$; solve for $k$ in the first scenario and use it to solve the second scenario.

Absolute Value Expressions/Equations

Always has two answers (unless equal to 0); solve normally and also negate ALL items within the absolute value sign to find the second solution.

Linear Growth

A constantly added or subtracted value, usually identified by the word "constant" in the problem.

Exponential Growth

A constantly multiplied or divided value, usually identified by "$\%$" or words like "doubles".

Ratio

A comparison of "THIS to THAT" written as a fraction: $\frac{\text{this}}{\text{that}}$.

Two Rates

Signals a proportion where you set up like units in two circumstances and cross multiply to solve.

Percent Change

Divide the DIFFERENCE between two values by the ORIGINAL value.

Conversions (Dimensional Analysis)

A method to cancel units by putting them in the next denominator; requires multiplying across and squaring conversion numbers for SQUARE UNITS.

Probability

The ratio of the desired amount (NUMERATOR) over the TOTAL amount (DENOMINATOR).

Standard Deviation (SD)

How much values deviate from the average (Mean); the more values are AWAY from the mean, the HIGHER the SD.

Mean

A simple average found by adding up values and dividing by the FULL number of times.

Median

The physical middle value when values are in order; if using frequency, divide the total number of values in half to find the placeholder.

Density formula

Density equals mass divided by volume, or $D = \frac{m}{v}$.

Range

The highest value in a data set minus the lowest value.

Infinitely Many Solutions (Linear Systems)

The two equations are the SAME or one is a direct multiple of the other, appearing as overlapping lines on DESMOS.

No Solution (Linear Systems)

Equations are the same on the left side but equal different values on the right; appear as parallel lines on DESMOS.

Amplitude (a) in Quadratic Functions

If positive, the graph smiles (minimum); if negative, the graph frowns (maximum).

Exponents: Multiplication Rule

$a^x \times a^y = a^{x+y}$; same base and multiply means add the exponents.

Exponents: Division Rule

$a^x \div a^y = a^{x-y}$; same base and divide means subtract the exponents.

Exponents: Power of a Power Rule

$(a^x)^y = a^{xy}$; power to a power means multiply the exponents.

Zero Exponent

$a^0 = 1$; anything to the zero power is 1.

Fractional Exponent

Follows the "Power over root" model, such as $x^{\frac{1}{2}}$ being the square root of $x$.

Degree of a Polynomial

A value one HIGHER than the number of times a graph turns.

Right Triangle Trigonometry Sine/Cosine Relation

$\sin(x) = \cos(90 - x)$; the sine of an angle equals the cosine of the other acute angle.

Pythagorean Theorem

Default formula for right triangle side lengths: $5N^2 + 5O^2 = 5P^2$.

Degrees to Radians

$\text{degree measure} \times \frac{\pi}{180}$.

Radians to Degrees

$\text{radian measure} \times \frac{180}{\pi}$.

Surface Area of a Box

The sum of the surfaces of a rectangular prism: $25Y5d + 25dh + 25Yh$.

Similar Triangles

Triangles with the same shape but different sizes; angle measures are ALL THE SAME while sides and perimeters are proportionate.

Constant

An actual number disguised as a letter.

y-intercept

Found by plugging in $x=0$; the "b" in $y=mx+b$ or $f(0)$.

x-intercept

Found by setting $y=0$ or $f(x)=0$; these are the solutions to a quadratic equation.

At least

An expression that is greater than or equal to.

At most

An expression that is less than or equal to.

Axis of Symmetry

Cuts a parabola in half; the vertex falls on this vertical line halfway between the x-intercepts.

Equivalent (Graphing method)

Equations where graphs overlap on each other on DESMOS.

Exponential Models

$$f(x) = (\text{initial value})(\text{rate})^{\text{time}}$$

Discriminant

The part under the radical in the Quadratic Formula used to find the number of solutions (0, 1, or 2).

Percent Reduced

Represents what is LEFTOVER from $100\%$; for example, a $30\%$ decline corresponds to $0.7x$.

"Of" and "Product"

Words that always mean MULTIPLY when translating words to math.

Box and Whisker Plot Range

Indicated by the vertical lines on the ENDS of the plot.

Box and Whisker Plot Median

Indicated by the vertical line in the MIDDLE of the box.