Mathematics Practice

Mathematics Practice

Build confidence across algebra, geometry, statistics, calculus basics, and problem-solving with 44 questions in 5 categories. Every answer comes with a clear explanation that reinforces the underlying concept.

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Visual Study Guides

Quick-reference cards for the formulas and rules that come up on every exam.

Order of Operations (PEMDAS)

Always evaluate expressions in this order to get the correct answer.

P

Parentheses

Evaluate everything inside parentheses (and brackets) first.

E

Exponents

Next, compute all powers and roots (e.g., 3² = 9).

MD

Multiply & Divide

Work left-to-right for all multiplication and division.

AS

Add & Subtract

Finally, work left-to-right for all addition and subtraction.

Worked example: 2 + 3 × (4² − 6)

P: 4² − 6 inside parentheses → compute next

E: 4² = 16 → expression becomes 2 + 3 × (16 − 6)

P: 16 − 6 = 10 → expression becomes 2 + 3 × 10

M: 3 × 10 = 30 → expression becomes 2 + 30

A: 2 + 30 = 32

Geometry Formulas

Essential formulas for area, volume, and the relationships between sides.

Circle Area

A = πr²

r = radius

Triangle Area

A = ½bh

b = base, h = height

Pythagorean Theorem

a² + b² = c²

c = hypotenuse

Rectangle Area

A = l × w

l = length, w = width

Cylinder Volume

V = πr²h

h = height

Sphere Surface Area

SA = 4πr²

r = radius

Algebra Rules & Formulas

The most commonly tested algebra rules — know these cold.

Slope Formula

m = (y₂ − y₁) / (x₂ − x₁)

Rise over run between two points

Quadratic Formula

x = (−b ± √(b²−4ac)) / 2a

Solves ax² + bx + c = 0

Exponent Rules

xᵃ · xᵇ = xᵃ⁺ᵇ

Also: (xᵃ)ᵇ = xᵃᵇ, xᵃ/xᵇ = xᵃ⁻ᵇ

FOIL Method

(a+b)(c+d) = ac+ad+bc+bd

First · Outer · Inner · Last

Slope-Intercept Form

y = mx + b

m = slope, b = y-intercept

Distributive Property

a(b + c) = ab + ac

Multiply across the parentheses

Stats Quick Reference

Core descriptive statistics — what each measure tells you and when to use it.

Mean

Sum of all values divided by the count.

{2, 4, 6} → (2+4+6)/3 = 4

M

Median

Middle value when data is sorted. Average the two middles if even count.

{1, 3, 7, 9, 11} → Median = 7

Mo

Mode

The value(s) that appear most often. A set can have 0, 1, or many modes.

{2, 4, 4, 7} → Mode = 4

σ

Standard Deviation

Average distance of each value from the mean. Low σ = tightly clustered.

σ = √(Σ(xᵢ−x̄)² / n)

When to use median over mean: Use median when data is skewed or has outliers (e.g., income, house prices). The mean is pulled toward extreme values; the median is not.

Math Study Tips

Do problems, don't just read

Watching someone solve math feels like understanding but isn't. Work every example yourself before checking the solution.

Show all steps

Writing out every step slows you down just enough to catch errors and builds the habits exams reward.

Understand, don't memorize

Derive the quadratic formula once. Understanding where it comes from makes it unforgettable and lets you reconstruct it under pressure.

Check with estimation

After computing, ask: is this answer reasonable? If you get 1,400 when the answer should be around 14, you'll catch the error immediately.

Space your practice

20 minutes a day beats a 3-hour cram. Spaced repetition is the most proven technique for retaining math skills long-term.

Learn error patterns

Keep a log of mistakes. Most people repeat the same 3-4 errors. Identifying your patterns is the fastest path to improvement.

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