SSAT Prep Β· All Levels

SSAT
Math
Master

20 authentic exam-style problems across every topic β€” with instant feedback & detailed solutions

20 Questions
5 Topics
25 Minutes
πŸ”’
Number Operations
Q1–Q4
πŸ“
Algebra
Q5–Q8
πŸ“
Geometry
Q9–Q12
πŸ“Š
Data & Probability
Q13–Q16
πŸ“
Word Problems
Q17–Q20
Review Mode

Concepts & Key Formulas

Tap each topic to expand β€” memorize before the exam

πŸ”’ Topic 1 β€” Number Operations
1
Fractions, Decimals & Percentages
NUMBER OPS
β–Ό
Core Conversions
Fraction β†’ Decimal: divide numerator Γ· denominator
Decimal β†’ %: multiply by 100
% of N = (% Γ· 100) Γ— N
β˜… Must Memorize
  • 1/4 = 0.25 = 25%
  • 1/3 β‰ˆ 0.333 = 33.3%
  • 3/8 = 0.375 = 37.5%
  • % increase = (newβˆ’old)/old Γ— 100
Quick Example
What is 35% of 140?
βœ“ 0.35 Γ— 140 = 49
2
Prime Numbers & Factoring
NUMBER OPS
β–Ό
Key Rules
LCM(a,b) = (a Γ— b) Γ· GCF(a,b)
GCF: largest factor shared by both
Prime: divisible only by 1 and itself
β˜… Must Memorize
  • Primes under 30: 2,3,5,7,11,13,17,19,23,29
  • 1 is NOT prime
  • 2 is the only even prime
  • All primes >2 are odd
Quick Example
Find LCM(12, 18).
βœ“ GCF = 6, LCM = (12Γ—18)/6 = 36
πŸ“ Topic 2 β€” Algebra
3
Linear Equations & Inequalities
ALGEBRA
β–Ό
Rules
Solve: isolate the variable
Inequality: flip sign when Γ· or Γ— by negative
Two equations β†’ substitution or elimination
β˜… Must Memorize
  • Multiply both sides β†’ same operation on each side
  • Flip inequality: βˆ’2x > 6 β†’ x < βˆ’3
  • Distributive: a(b+c) = ab + ac
Quick Example
Solve: 3x βˆ’ 7 = 14
βœ“ 3x = 21, x = 7
4
Exponents & Roots
ALGEBRA
β–Ό
Exponent Laws
aᡐ Γ— aⁿ = aᡐ⁺ⁿ
aᡐ ÷ aⁿ = aᡐ⁻ⁿ
(aᡐ)ⁿ = aᡐⁿ
a⁰ = 1 (a β‰  0)
a⁻ⁿ = 1/aⁿ
β˜… Must Memorize
  • √(aΓ—b) = √a Γ— √b
  • Perfect squares: 1,4,9,16,25,36,49,64,81,100,121,144,169
  • Cube of 2 = 8, 3 = 27, 4 = 64
Quick Example
Simplify: 2Β³ Γ— 2⁴
βœ“ 2³⁺⁴ = 2⁷ = 128
πŸ“ Topic 3 β€” Geometry
5
Perimeter, Area & Volume
GEOMETRY
β–Ό
Essential Formulas
Rectangle: A = lΓ—w, P = 2(l+w)
Triangle: A = Β½bh
Circle: A = Ο€rΒ², C = 2Ο€r
Trapezoid: A = Β½(b₁+bβ‚‚)h
Box Vol: V = lΓ—wΓ—h
Cylinder: V = Ο€rΒ²h
β˜… Must Memorize
  • Pythagorean theorem: aΒ² + bΒ² = cΒ²
  • Common triples: 3-4-5, 5-12-13, 8-15-17
  • Ο€ β‰ˆ 3.14 (use unless told otherwise)
Quick Example
A circle has radius 5. Find its area.
βœ“ A = Ο€(5Β²) = 25Ο€ β‰ˆ 78.5
6
Angles & Triangle Properties
GEOMETRY
β–Ό
Angle Rules
Triangle sum: 180Β°
Straight line: 180Β°
Quadrilateral: 360Β°
Exterior angle = sum of two remote interior angles
β˜… Must Memorize
  • Isosceles: 2 equal sides β†’ 2 equal base angles
  • Equilateral: all angles = 60Β°
  • Vertical angles are equal
  • Parallel lines cut by transversal: alternate interior angles equal
Quick Example
Triangle has angles 55Β° and 72Β°. Find the third.
βœ“ 180 βˆ’ 55 βˆ’ 72 = 53Β°
πŸ“Š Topic 4 β€” Data & Probability
7
Mean, Median, Mode & Range
DATA
β–Ό
Statistics
Mean = sum Γ· count
Median = middle value (when sorted)
Mode = most frequent value
Range = max βˆ’ min
β˜… Must Memorize
  • Even count: median = avg of middle two
  • Adding equal value shifts mean by that amount
  • Outlier affects mean more than median
Quick Example
Data: {3, 7, 7, 9, 14}. Find mean, median, mode.
βœ“ Mean = 8, Median = 7, Mode = 7
8
Probability & Counting
DATA
β–Ό
Probability Rules
P(event) = favorable Γ· total
P(A and B) = P(A) Γ— P(B) [independent]
P(A or B) = P(A) + P(B) βˆ’ P(A and B)
Complement: P(not A) = 1 βˆ’ P(A)
β˜… Must Memorize
  • 0 ≀ P(event) ≀ 1 always
  • Counting principle: multiply choices at each step
  • Permutation (order matters) vs Combination (order doesn't)
Quick Example
A bag has 4 red, 6 blue marbles. P(red)?
βœ“ 4/10 = 2/5 = 0.4
πŸ“ Topic 5 β€” Word Problems
9
Rate, Time & Distance
WORD PROBLEMS
β–Ό
RTD Triangle
Distance = Rate Γ— Time
Rate = Distance Γ· Time
Time = Distance Γ· Rate
Work = Rate Γ— Time
β˜… Must Memorize
  • Average speed = total distance Γ· total time
  • Combined work: 1/t = 1/a + 1/b
  • Same direction catch-up: relative speed = difference
Quick Example
Car travels 240 miles in 4 hours. What is its speed?
βœ“ Rate = 240/4 = 60 mph
10
Ratios, Proportions & Mixtures
WORD PROBLEMS
β–Ό
Key Formulas
Ratio a:b means a/(a+b) and b/(a+b)
Proportion: a/b = c/d β†’ ad = bc
Scale: map distance Γ— scale factor = real distance
β˜… Must Memorize
  • If ratio is 3:5, total parts = 8
  • Cross-multiply to solve proportions
  • Mixture: weighted average formula
Quick Example
Boys to girls ratio is 3:4. There are 28 girls. How many boys?
βœ“ 3/4 = x/28, x = 21 boys
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SSAT Math Master β€” Answer Key & Solutions

20 Questions | All Topics | Detailed Explanations