McLain ACT Math Power Deck

A collection of flashcards covering ACT Math formulas, geometry rules, algebra concepts, data analysis, and test-taking strategies as outlined in the McLain ACT Math Power Deck.

Slope Formula

$m = \frac{y_2 - y_1}{x_2 - x_1}$. It means change in $y$ divided by change in $x$.

Distance Formula

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Use it to find the length between two points.

Midpoint Formula

$\text{Midpoint} = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$. Average the $x$-values and average the $y$-values.

Slope-Intercept Form

$y = mx + b$, where $m$ is slope and $b$ is the $y$-intercept.

Standard Form of a Linear Equation

$Ax + By = C$. To graph quickly, solve for $y$ or find intercepts.

y-intercept Method

Set $x = 0$ and solve for $y$.

x-intercept Method

Set $y = 0$ and solve for $x$.

Quadratic Formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Use it for $ax^2 + bx + c = 0$.

Vertex Form of a Quadratic

$y = a(x - h)^2 + k$. The vertex is $(h, k)$.

Standard Form of a Quadratic

$y = ax^2 + bx + c$. If $a$ is positive, the parabola opens up. If $a$ is negative, it opens down.

Discriminant

$b^2 - 4ac$ tells how many real solutions: positive = $2$, zero = $1$, negative = $0$.

Equation of a Circle

$(x - h)^2 + (y - k)^2 = r^2$. Center is $(h, k)$, radius is $r$.

Area of a Rectangle

$A = \text{length} \times \text{width}$.

Perimeter of a Rectangle

$P = 2\,\text{length} + 2\,\text{width}$.

Area of a Triangle

$A = \frac{1}{2}bh$. Base and height must be perpendicular.

Area of a Circle

$A = \pi r^2$.

Circumference of a Circle

$C = 2\pi r$ or $C = \pi d$.

Pythagorean Theorem

$a^2 + b^2 = c^2$, where $c$ is the hypotenuse of a right triangle.

Special 45-45-90 Triangle

The sides are $x$, $x$, $x\sqrt{2}$.

Special 30-60-90 Triangle

The sides are $x$, $x\sqrt{3}$, $2x$. The hypotenuse is $2x$.

SOH-CAH-TOA

$\sin = \frac{\text{opposite}}{\text{hypotenuse}}$, $\cos = \frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan = \frac{\text{opposite}}{\text{adjacent}}$.

Degrees in a Triangle

$180$ degrees.

Degrees in a Straight Line

$180$ degrees.

Degrees Around a Point/Circle

$360$ degrees.

Sum of Interior Angles of a Polygon

$(n - 2) \times 180$, where $n$ is the number of sides.

"Of" in Percent Problems

Usually means multiply.

Percent to Decimal Conversion

Move the decimal two places left. Example: $35\% = 0.35$.

Decimal to Percent Conversion

Move the decimal two places right. Example: $0.35 = 35\%$.

Percent Change Formula

$\text{Percent change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%$.

Original Amount (Percent Increase)

Use $\text{original} \times (1 + \text{rate}) = \text{new amount}$.

Original Amount (Percent Decrease)

Use $\text{original} \times (1 - \text{rate}) = \text{new amount}$.

Exponent Rule (Multiplying Same Bases)

$a^m \times a^n = a^{m+n}$. Add exponents.

Exponent Rule (Dividing Same Bases)

$\frac{a^m}{a^n} = a^{m-n}$. Subtract exponents.

Negative Exponent

$a^{-n} = \frac{1}{a^n}$. Move the base to the other side of the fraction.

Zero Exponent Rule

Any nonzero number to the zero power equals $1$.

Distributive Property

$a(b + c) = ab + ac$.

Difference of Squares Pattern

$a^2 - b^2 = (a - b)(a + b)$.

Proportion Strategy

Cross multiply, then solve.

Absolute Value

Distance from zero, so it is usually nonnegative.

System Substitution Method

Solve one equation for one variable, substitute into the other equation, then solve.

System Elimination Method

Add or subtract equations so one variable cancels, then solve.

Probability

$\text{Probability} = \frac{\text{favorable outcomes}}{\text{total possible outcomes}}$.

Mean

$\text{Mean} = \frac{\text{total}}{\text{number of values}}$. It is the average.

Median

The middle value when the numbers are in order.

Mode

The value that appears most often.

Range

$\text{Range} = \text{maximum} - \text{minimum}$.

Positive Correlation

As $x$ increases, $y$ tends to increase.

Negative Correlation

As $x$ increases, $y$ tends to decrease.

Confusing Word Problems

Identify what the question is asking for before calculating.

Backsolving Strategy

When answer choices are numbers, plug in the answer choices to find the one that works.

Picking Numbers Strategy

When answer choices contain variables, pick a simple number for the variable, such as $2$ or $10$.

Graphing Tool Strategy

When a graphing question includes equations, graph the equations in Desmos or the ACT-approved calculator if allowed.

Diagram Labeling

Mark the diagram with the given numbers and relationships.

Guessing Strategy

Eliminate impossible answers first, then choose from what remains.

Mismatch Check

If your answer is not a choice, check whether the question asked for something different, such as perimeter instead of area.

Estimation

Estimation helps eliminate answers that are too large or too small.

Pacing Strategy

If a problem takes too long, circle it, guess if needed, move on, and come back later.

ACT Math Blanks Rule

Never leave blanks. There is no penalty for guessing.