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.
Parentheses
Evaluate everything inside parentheses (and brackets) first.
Exponents
Next, compute all powers and roots (e.g., 3² = 9).
Multiply & Divide
Work left-to-right for all multiplication and division.
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
Median
Middle value when data is sorted. Average the two middles if even count.
{1, 3, 7, 9, 11} → Median = 7
Mode
The value(s) that appear most often. A set can have 0, 1, or many modes.
{2, 4, 4, 7} → Mode = 4
Standard Deviation
Average distance of each value from the mean. Low σ = tightly clustered.
σ = √(Σ(xᵢ−x̄)² / n)
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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