SSAT Math Master | 20 Essential Practice Questions

🔢 Numbers & Operations

The foundation of all SSAT math. You must master integer operations, factors, multiples, prime numbers, and the order of operations (PEMDAS).

PEMDAS: Parentheses → Exponents → Multiply/Divide → Add/Subtract GCF(a,b): Greatest number that divides both a and b LCM(a,b): Smallest number divisible by both a and b GCF × LCM = a × b

★ Even × Even = Even★ Odd × Odd = Odd★ Even × Odd = Even★ Prime: exactly 2 factors★ 1 is NOT prime

Quick Example

Find GCF(36, 48)

36 = 2² × 3² ; 48 = 2⁴ × 3 → GCF = 2² × 3 = 12 ✓

½ Fractions, Decimals & Ratios

Converting between fractions, decimals, and percents is essential. Ratios compare quantities; proportions set two ratios equal.

a/b ÷ c/d = a/b × d/c (Flip & multiply) Proportion: a/b = c/d → a × d = b × c (Cross-multiply) Unit Rate: Total ÷ Number of units

★ Simplify before multiplying★ Common denominator for +/−★ Cross-multiply to solve proportions

Quick Example

If 3/5 = x/25, find x.

Cross-multiply: 3 × 25 = 5 × x → x = 75/5 = 15 ✓

% Percents & Percent Change

Percents appear constantly on the SSAT — discounts, tax, increase/decrease. Know the three forms of percent equations and percent change.

Part = Percent × Whole (P = % × W) Percent = Part / Whole × 100 Percent Change = (New − Old) / Old × 100% Discount Price = Original × (1 − rate) Tax/Tip Price = Original × (1 + rate)

★ IS / OF = % / 100★ % change: always divide by ORIGINAL★ 1% of N = N/100

Quick Example

A jacket costs $80, 25% off. Final price?

$80 × 0.75 = $60 ✓

x Algebra & Equations

Solving linear equations, inequalities, and interpreting expressions is core SSAT algebra. Also know slope and basic quadratic factoring.

Linear: ax + b = c → x = (c − b)/a Slope: m = (y₂ − y₁)/(x₂ − x₁) Slope-intercept: y = mx + b Quadratic: ax² + bx + c = 0 x = [−b ± √(b²−4ac)] / 2a FOIL: (a+b)(c+d) = ac + ad + bc + bd

★ Do same operation to both sides★ Flip inequality when ×/÷ by negative★ Slope = rise/run

Quick Example

Solve: 3x − 7 = 11

3x = 18 → x = 6 ✓

△ Geometry

Know all area and perimeter formulas, angle rules, Pythagorean theorem, and properties of special triangles.

Rectangle: A = l × w ; P = 2(l + w) Triangle: A = ½ × b × h Circle: A = π r² ; C = 2πr Pythagorean: a² + b² = c² Special triangles: 30-60-90 → sides: x, x√3, 2x 45-45-90 → sides: x, x, x√2 Angles in triangle: sum = 180°

★ Sum of angles in triangle = 180°★ Vertical angles are equal★ 3-4-5, 5-12-13 Pythagorean triples

Quick Example

Right triangle: legs 6 and 8. Hypotenuse?

c = √(36 + 64) = √100 = 10 ✓

📊 Data & Statistics

Mean, median, mode, and range are the four core measures. Know how each changes when data is added or removed.

Mean = Sum of all values ÷ Number of values Median = Middle value (data sorted in order) Mode = Most frequently occurring value Range = Maximum − Minimum Probability = Favorable outcomes / Total outcomes

★ Mean affected by outliers★ Median NOT affected by outliers★ P(A and B) = P(A) × P(B) if independent

Quick Example

Data: 3, 7, 7, 9, 14. Find mean, median, mode.

Mean = 40/5 = 8 ; Median = 7 ; Mode = 7 ✓

📝 Word Problems

Define variables first. Use the D = R × T formula for motion, and set up equations matching the relationships described.

Distance = Rate × Time (D = R × T) Work: W = Rate × Time ; combined rate = 1/t₁ + 1/t₂ Age problems: set up variable for current age Mixture: amount₁ × conc₁ + amount₂ × conc₂ = total × conc

★ Underline key numbers★ Let x = unknown quantity★ Check answer back in problem

Quick Example

Train travels 120 miles in 2 hours. Speed?

R = D/T = 120/2 = 60 mph ✓

🔗 Sequences & Patterns

Arithmetic sequences add a constant; geometric sequences multiply by a constant. Know how to find the nth term.

Arithmetic: aₙ = a₁ + (n−1)d Sum = n/2 × (a₁ + aₙ) d = common difference Geometric: aₙ = a₁ × r^(n−1) r = common ratio Pattern: find the rule → apply to find the nth term

★ Arithmetic: constant DIFFERENCE★ Geometric: constant RATIO★ n starts at 1

Quick Example

Sequence: 3, 7, 11, 15, … Find the 10th term.

d = 4 ; a₁₀ = 3 + 9×4 = 39 ✓

SSAT Math
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SSAT Math Master — Practice Exam

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SSAT MathMaster

Core Concepts & Key Formulas

Answer all 20 questions

Your Results

Answer Key & Explanations

SSAT Math Master — Practice Exam

Answer Key & Explanations

SSAT Math
Master