Official SSAT Math Practice

SSAT Math
Master

20 essential problems across all core topics — concept review, timed practice, and detailed explanations.

20Problems
40Min Timer
10Topics
5Choices
Number Theory
Fractions & Ratios
Percents
Algebra
Geometry
Data & Statistics
Word Problems
Sequences & Patterns
Probability
Functions & Graphs
Step 1 of 2 — Concept Review

Core Concepts & Key Formulas

01 Number Theory — Factors, Multiples & Primes ▶
Key Concepts
A factor of n divides n with no remainder. A multiple of n equals n × k for integer k.
A prime has exactly 2 factors: 1 and itself. 1 is NOT prime.
LCM = least common multiple; GCF = greatest common factor.
Even numbers are divisible by 2. Odd numbers are not.
Must-Memorize Primes
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Quick Formula
LCM(a,b) = (a × b) ÷ GCF(a,b)
Example
Find the LCM of 12 and 18.
GCF(12,18) = 6 → LCM = (12×18)÷6 = 36
02 Fractions, Decimals & Ratios ▶
Key Concepts
To compare fractions, cross-multiply: a/b vs c/d → compare ad vs bc.
Ratio a:b means a parts to b parts; total parts = a + b.
Part ÷ Whole = Fraction; convert to decimal by dividing.
Must-Know Conversions
1/2 = 0.5 = 50% 1/3 ≈ 0.333 1/4 = 0.25 = 25% 1/5 = 0.2 = 20% 3/4 = 0.75 = 75% 1/8 = 0.125
Example
In a class, ratio of boys to girls is 3:5. If there are 40 students, how many are girls?
Girls = 5/(3+5) × 40 = 5/8 × 40 = 25
03 Percents & Percent Change ▶
Key Formulas
Percent = (Part ÷ Whole) × 100 Part = Percent × Whole ÷ 100 Percent Change = (New − Old) ÷ Old × 100
Increase by x% → multiply by (1 + x/100).
Decrease by x% → multiply by (1 − x/100).
Two successive changes: 10% increase then 10% decrease ≠ original (it's 99% of original).
A shirt costs $40. It goes up 25% then down 20%. Final price?
$40 × 1.25 = $50 → $50 × 0.80 = $40
04 Algebra — Equations & Inequalities ▶
Key Rules
Solve by isolating the variable: do the same operation to both sides.
Inequality: when multiplying/dividing by a NEGATIVE number, flip the sign.
FOIL for binomials: (a+b)(c+d) = ac + ad + bc + bd.
Distributive: a(b+c) = ab + ac FOIL: (a+b)(a−b) = a² − b² Perfect Square: (a+b)² = a² + 2ab + b²
Solve: 3x − 7 = 14
3x = 21 → x = 7
05 Geometry — Angles, Area & Volume ▶
Area Formulas
Rectangle: A = l × w Triangle: A = ½ × b × h Circle: A = π × r² Trapezoid: A = ½(b₁+b₂) × h Parallelogram: A = b × h
Perimeter & Volume
Circumference = 2πr Cube Volume = s³ Rectangular Prism = l × w × h Pythagorean Theorem: a² + b² = c²
Angles in a triangle sum to 180°.
Supplementary angles sum to 180°; complementary to 90°.
Common right-triangle triples: 3-4-5, 5-12-13, 8-15-17.
A right triangle has legs 6 and 8. What is the hypotenuse?
c = √(6² + 8²) = √(36+64) = √100 = 10
06 Data & Statistics — Mean, Median, Mode, Range ▶
Mean = Sum ÷ Number of values Median = Middle value (sorted list) Mode = Most frequent value Range = Maximum − Minimum
For even number of values, median = average of the two middle values.
A dataset can have more than one mode, or no mode.
Outliers affect the mean more than the median.
Find mean and median of: 3, 7, 7, 10, 13.
Mean = 40 ÷ 5 = 8 | Median = 7 (middle of sorted list)
07 Word Problems — Rate, Work & Distance ▶
Distance = Rate × Time (D = R × T) Work: 1/A + 1/B = 1/T (combined rate) Average Speed = Total Distance ÷ Total Time
Two workers together: T = AB ÷ (A+B).
If A goes at speed r₁ and B at r₂, time to meet = d ÷ (r₁ + r₂) (towards) or (r₁ − r₂) (same direction).
A and B can paint a wall in 6 and 3 hours respectively. How long together?
T = (6×3)÷(6+3) = 18÷9 = 2 hours
08 Sequences & Patterns ▶
Arithmetic: aₙ = a₁ + (n−1)d Sum = n(a₁+aₙ)/2 Geometric: aₙ = a₁ × r^(n−1)
Arithmetic sequence: constant difference d between terms.
Geometric sequence: constant ratio r between terms.
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
What is the 10th term of: 3, 7, 11, 15, …?
d=4, a₁₀ = 3 + 9×4 = 3 + 36 = 39
09 Probability & Counting ▶
P(event) = Favorable outcomes ÷ Total outcomes P(A and B) = P(A) × P(B) [independent] P(A or B) = P(A) + P(B) − P(A and B)
Probability always between 0 (impossible) and 1 (certain).
Counting Principle: if A has m ways and B has n ways, both = m × n.
Combinations: choosing r from n = C(n,r) = n! ÷ [r!(n−r)!].
Bag has 4 red, 3 blue, 3 green marbles. P(not red)?
P(not red) = 6 ÷ 10 = 3/5 = 0.6
10 Functions, Graphs & Coordinate Plane ▶
Slope m = (y₂−y₁) ÷ (x₂−x₁) Slope-intercept: y = mx + b Point-slope: y−y₁ = m(x−x₁) Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2) Distance: √[(x₂−x₁)² + (y₂−y₁)²]
Positive slope: line rises left to right. Negative: falls.
Parallel lines have equal slopes. Perpendicular lines: slopes are negative reciprocals.
y-intercept is where the line crosses the y-axis (x = 0).
Find the slope between (2, 5) and (6, 13).
m = (13−5)÷(6−2) = 8÷4 = 2
Q 1 / 20
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SSAT Math Master — Answer Key & Explanations
20 Essential Practice Problems
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Answer Key & Detailed Explanations