SSAT Math Mastery — Official Practice Test

20 Questions · All Core Topics · Exam Style · Time Allowed: 40 Minutes

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SSAT Upper Level · Official Style

Master SSAT Math
in One Session

20 real-exam-style questions spanning every core topic. Instant feedback, detailed solutions, and a final score to track your readiness.

20Questions
7Topics
40minTimer

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Core Concepts & Formulas
Review each topic — tap to expand. Key formulas, memory aids, and worked examples.
🔢

Arithmetic & Number Properties

Integers, primes, factors, multiples, order of operations

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Key Concepts to Memorize

  • Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (2 is the only even prime)
  • Even × Even = Even · Odd × Odd = Odd · Even × Odd = Even
  • Divisibility: ÷2 → last digit even; ÷3 → digit sum ÷3; ÷9 → digit sum ÷9
  • GCF × LCM = Product of the two numbers
  • Order of operations: Parentheses → Exponents → ×÷ → +−

Formulas

GCF/LCM: GCF(a,b) × LCM(a,b) = a × b
Remainder: a = q × d + r (0 ≤ r < d)
Absolute: |−n| = n, |n| = n (n ≥ 0)

Worked Example

Q: What is the least common multiple of 12 and 18?
12 = 2² × 3 · 18 = 2 × 3² · LCM = 2² × 3² = 36 ✓
½

Fractions, Decimals & Percentages

Conversions, percent change, ratios, proportions

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Key Concepts to Memorize

  • Percent change = (New − Old) / Old × 100%
  • % increase then % decrease ≠ back to original (e.g., +50% then −50% = −25%)
  • a/b ÷ c/d = a/b × d/c (flip and multiply)
  • Cross-multiplication: a/b = c/d → ad = bc

Formulas

% of: Part = (Percent/100) × Whole
% change: (New−Old)/Old × 100
Ratio: a:b = a/(a+b) of total

Worked Example

Q: A price increased from $40 to $50. What is the percent increase?
(50−40)/40 × 100 = 10/40 × 100 = 25% ✓
𝑥

Algebra & Expressions

Equations, inequalities, systems, word problems

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Key Concepts to Memorize

  • FOIL: (a+b)(c+d) = ac + ad + bc + bd
  • Difference of squares: a² − b² = (a+b)(a−b)
  • Perfect square: (a+b)² = a² + 2ab + b²
  • Quadratic formula: x = (−b ± √(b²−4ac)) / 2a
  • If a system has no solution → parallel lines (same slope, different y-intercept)

Formulas

Linear: y = mx + b (slope-intercept)
Slope: m = (y₂−y₁)/(x₂−x₁)
Quadratic: ax² + bx + c = 0

Worked Example

Q: Solve: 3x + 7 = 22
3x = 15 → x = 5 ✓
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Geometry

Angles, triangles, circles, area, volume, coordinate geometry

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Key Concepts to Memorize

  • Triangle angle sum = 180°; quadrilateral = 360°
  • Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25
  • Similar triangles: corresponding sides are proportional
  • Parallel lines cut by transversal: alternate interior angles are equal
  • Inscribed angle = ½ × central angle (same arc)

Formulas

Circle A: A = πr² C = 2πr
Triangle: A = ½bh
Rectangle: A = lw P = 2(l+w)
Cylinder: V = πr²h
Pythagorean: a² + b² = c²

Worked Example

Q: A circle has radius 5. What is its area?
A = π × 5² = 25π ≈ 78.5 ✓
📊

Data Analysis & Statistics

Mean, median, mode, range, probability, graphs

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Key Concepts to Memorize

  • Mean = sum ÷ count (sensitive to outliers)
  • Median = middle value when sorted (not affected by outliers)
  • Mode = most frequent value
  • Range = max − min
  • Probability = favorable outcomes / total outcomes
  • P(A or B) = P(A) + P(B) − P(A and B)

Formulas

Mean: x̄ = Σx / n
Prob: P(E) = n(E) / n(S)
Compound: P(A∩B) = P(A)×P(B) [independent]

Worked Example

Q: The mean of {4, 7, 9, x} is 7. Find x.
(4+7+9+x)/4 = 7 → 20+x = 28 → x = 8 ✓
x²

Exponents & Roots

Laws of exponents, square roots, scientific notation

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Key Concepts to Memorize

  • aᵐ × aⁿ = aᵐ⁺ⁿ · aᵐ ÷ aⁿ = aᵐ⁻ⁿ · (aᵐ)ⁿ = aᵐⁿ
  • a⁰ = 1 (a ≠ 0) · a⁻ⁿ = 1/aⁿ
  • √(ab) = √a × √b · √(a/b) = √a / √b
  • Perfect squares: 1,4,9,16,25,36,49,64,81,100,121,144,169

Formulas

Product: aᵐ × aⁿ = aᵐ⁺ⁿ
Power: (aᵐ)ⁿ = aᵐⁿ
Negative: a⁻ⁿ = 1/aⁿ

Worked Example

Q: Simplify: (2³)² ÷ 2²
2⁶ ÷ 2² = 2⁴ = 16 ✓
⚡

Word Problems & Rates

Distance-rate-time, work problems, mixtures, sequences

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Key Concepts to Memorize

  • Distance = Rate × Time (D = RT)
  • Work: 1/A + 1/B = 1/T (time working together)
  • Mixture: c₁v₁ + c₂v₂ = c_f(v₁+v₂)
  • Arithmetic sequence: aₙ = a₁ + (n−1)d
  • Geometric sequence: aₙ = a₁ × rⁿ⁻¹

Formulas

D=RT: Distance = Rate × Time
Work: Time = AB/(A+B)
Arith: aₙ = a₁ + (n−1)d

Worked Example

Q: A train travels 240 km in 3 hours. What is its speed?
Speed = D/T = 240/3 = 80 km/h ✓
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