SSAT Math Exam Prep | TOP EDU PREP

Master every SSAT Math topic. Study each concept, memorize the key rules, then try the worked example before heading to the Exam tab.

Unit 1

Number & Operations

LCM & GCF

Number Ops

LCM(a,b) = (a × b) ÷ GCF(a,b)

🧠 Memorize

GCF = largest number dividing both. LCM = smallest number both divide into. Prime factorization: take highest powers for LCM, lowest for GCF.

Worked Example

Find the LCM of 8 and 12.

8 = 2³ | 12 = 2² × 3
LCM = 2³ × 3 = 24

Answer: 24

Fractions & Mixed Numbers

Number Ops

a/b + c/d = (ad + bc) / bd · a/b × c/d = ac/bd

🧠 Memorize

Add/Subtract: find common denominator first. Multiply: straight across. Divide: flip the second fraction and multiply.

Worked Example

Calculate 1/2 + 2/5.

LCD = 10: 5/10 + 4/10 = 9/10

Answer: 9/10

Percentages

Number Ops

Part = (Percent ÷ 100) × Whole
% Change = (New − Old) / Old × 100

🧠 Memorize

To find X% of N: multiply N × (X/100). Percent increase/decrease always divides by the original value.

Worked Example

Find 20% of 350.

350 × 0.20 = 70

Answer: 70

Ratios & Proportions

Number Ops

If a:b = c:d then ad = bc (cross-multiply)

🧠 Memorize

In a ratio a:b with total T, part A = T × a/(a+b). Always label what each part of the ratio represents.

Worked Example

Ratio 2:3, total 50. Find the smaller part.

Smaller = 50 × 2/(2+3) = 50 × 2/5 = 20

Answer: 20

Unit 2

Algebra

Linear Equations

Algebra

ax + b = c → x = (c − b) / a

🧠 Memorize

Isolate the variable: undo addition/subtraction first, then multiplication/division. Whatever you do to one side, do to both sides.

Worked Example

Solve: 4x − 3 = 13

4x = 16 → x = 4

Answer: x = 4

Inequalities

Algebra

Same rules as equations — EXCEPT:
flip the sign when multiplying/dividing by a negative

🧠 Memorize

−2x < 6 → divide by −2 → x > −3 (sign flips!). Always check with a test value.

Worked Example

Solve: −3x ≥ 12

Divide by −3 (flip sign): x ≤ −4

Answer: x ≤ −4

Arithmetic Sequences

Algebra

aₙ = a₁ + (n − 1)d d = common difference

🧠 Memorize

d = any term minus the previous term. The formula counts (n−1) gaps from the first term. Always check: does the pattern add or subtract a constant?

Worked Example

Sequence: 5, 8, 11, 14 … Find the 10th term.

a₁=5, d=3 → a₁₀ = 5 + 9×3 = 32

Answer: 32

Rate & Unit-Price Problems

Algebra

Unit Rate = Total Cost ÷ Quantity
Total Cost = Unit Rate × Quantity

🧠 Memorize

Always find the unit rate first, then scale up/down. Use proportional reasoning: if 3 items cost $6, then 1 costs $2, so 7 costs $14.

Worked Example

4 pens cost $2.80. How much do 7 pens cost?

Unit = $2.80/4 = $0.70 → 7 × $0.70 = $4.90

Answer: $4.90

Unit 3

Geometry

Area of Triangles

Geometry

Area = ½ × base × height

🧠 Memorize

The height must be perpendicular to the base — it is NOT the slanted side. For right triangles, the two legs are base and height.

Worked Example

Triangle with base 10 cm and height 6 cm. Find the area.

Area = ½ × 10 × 6 = 30 cm²

Answer: 30 cm²

Perimeter of Rectangles

Geometry

P = 2(l + w) · Area = l × w

🧠 Memorize

Perimeter = total distance around the outside. If given area and one side, find the other: w = Area ÷ l, then use P formula.

Worked Example

Rectangle 9 m × 4 m. Find the perimeter.

P = 2(9 + 4) = 2 × 13 = 26 m

Answer: 26 m

Volume of Rectangular Prisms

Geometry

V = length × width × height

🧠 Memorize

Volume is always in cubic units (cm³, m³). Surface area = 2(lw + lh + wh). Doubling all dimensions multiplies volume by 8.

Worked Example

Box: 5 × 3 × 4. Find the volume.

V = 5 × 3 × 4 = 60 units³

Answer: 60 units³

Angles in Triangles

Geometry

∠A + ∠B + ∠C = 180°

🧠 Memorize

All 3 angles in ANY triangle sum to 180°. Exterior angle = sum of the two non-adjacent interior angles. Isosceles: two base angles are equal.

Worked Example

A triangle has angles 55° and 72°. Find the third.

Third = 180 − 55 − 72 = 53°

Answer: 53°

Circles: Circumference & Area

Geometry

C = 2πr = πd · A = πr²

🧠 Memorize

r = radius, d = diameter = 2r. π ≈ 3.14159. SSAT often asks for answers in terms of π — don't multiply out unless asked.

Worked Example

Circle with radius 5. Find circumference in terms of π.

C = 2 × π × 5 = 10π

Answer: 10π

Unit 4

Data & Statistics

Mean (Average)

Statistics

Mean = Sum of all values ÷ Number of values

🧠 Memorize

The mean is sensitive to outliers. If you know the mean and n, you can find the total: Total = Mean × n. Always divide by the count, not the range.

Worked Example

Scores: 70, 85, 90, 60, 95. Find the mean.

Sum = 400 → Mean = 400 / 5 = 80

Answer: 80

Median

Statistics

Sort the data → middle value (odd n)
Average of two middle values (even n)

🧠 Memorize

Always sort first! For even count: median = average of the n/2 and (n/2 +1) values. The median is NOT affected by extreme outliers.

Worked Example

Data: 6, 2, 9, 4, 7. Find the median.

Sorted: 2, 4, 6, 7, 9 → middle = 6

Answer: 6

Probability

Statistics

P(event) = Favorable outcomes / Total outcomes

🧠 Memorize

Probability is always between 0 and 1. P(impossible) = 0, P(certain) = 1. P(A or B) = P(A) + P(B) if mutually exclusive.

Worked Example

A bag has 3 red and 7 blue balls. P(red)?

P(red) = 3 / (3+7) = 3/10

Answer: 3/10

Mode

Statistics

Mode = value that appears most frequently

🧠 Memorize

A dataset can have no mode (all unique), one mode, or be bimodal / multimodal. Mode is the only measure that works for non-numeric data.

Worked Example

Data: 5, 3, 7, 3, 5, 3, 8. Find the mode.

3 appears 3 times (most frequent)

Answer: 3

Unit 5

Advanced & Mixed Reasoning

Geometric Sequences

Advanced

aₙ = a₁ × rⁿ⁻¹ r = common ratio

🧠 Memorize

r = next term ÷ current term. If r > 1, sequence grows. If 0 < r < 1, sequence shrinks. Multiply the previous term by r to find the next.

Worked Example

Sequence: 3, 6, 12, 24 … Find the 6th term.

r = 2 → a₆ = 3 × 2⁵ = 96

Answer: 96

Systems of Linear Equations

Advanced

Add/subtract equations to eliminate one variable

🧠 Memorize

Elimination: add or subtract equations. Substitution: solve one equation for a variable, plug into the other. Always verify the solution in BOTH equations.

Worked Example

x + y = 8 and x − y = 2. Find x and y.

Add: 2x = 10 → x = 5, y = 3

Answer: x = 5, y = 3

Discount & Sale Price

Advanced

Sale Price = Original × (1 − discount rate)
Discount Amount = Original × rate

🧠 Memorize

A 40% discount means you pay 60% of the original. Sequential discounts are NOT additive: 20% then 10% off ≠ 30% off.

Worked Example

A $60 jacket is 25% off. Find the sale price.

$60 × 0.75 = $45

Answer: $45

SSAT Exam

20 Practice Questions

Q1 Number & Operations · LCM

What is the Least Common Multiple (LCM) of 12 and 18?

Q2 Number & Operations · Fractions

What is 3/4 + 2/3? Express your answer as a fraction in the form p/q (e.g., 17/12).

Q3 Number & Operations · Percentages

A school has 240 students. 15% of them are in the math club. How many students are in the math club?

Q4 Number & Operations · Ratios

The ratio of boys to girls in a class is 3 : 5. There are 120 students in total. How many girls are there?

Q5 Algebra · Linear Equations

Solve for x: 2x + 7 = 19

Q6 Algebra · Inequalities

Solve the inequality: 3x − 4 > 11. What is the smallest integer value of x that satisfies this inequality?

Q7 Algebra · Sequences

An arithmetic sequence has a first term of 3 and a common difference of 5. What is the 8th term?

Q8 Algebra · Rate Problems

At a fruit stall, 5 apples cost $3.50. At the same rate, how much would 8 apples cost? (Enter your answer in dollars, e.g. 5.60)

Q9 Geometry · Area of Triangle

A triangle has a base of 14 cm and a height of 9 cm. What is its area in cm²?

Q10 Geometry · Perimeter

A rectangle has a length of 8 m and a width of 5 m. What is its perimeter in meters?

Q11 Geometry · Volume

Find the volume of a rectangular prism with length 6 cm, width 4 cm, and height 3 cm.

Q12 Geometry · Angles

A triangle has two angles measuring 47° and 63°. What is the measure of the third angle in degrees?

Q13 Geometry · Circles

A circle has a radius of 7 cm. What is its circumference in terms of π? (Enter the coefficient only, e.g., if the answer is 14π, enter 14)

Q14 Statistics · Mean

Find the mean of the following data set: 8, 12, 15, 9, 11

Q15 Statistics · Median

Find the median of the following data set: 3, 7, 2, 9, 5

Q16 Statistics · Probability

A bag contains 4 red and 6 blue marbles. A marble is picked at random. What is the probability of picking a red marble? (Enter as a fraction, e.g. 2/5)

Q17 Statistics · Mode

Find the mode of the following data set: 4, 7, 2, 7, 4, 7, 3

Q18 Advanced · Patterns

A sequence follows the pattern: 2, 6, 18, 54, … What is the next term in this sequence?

Q19 Advanced · Systems of Equations

If x + y = 10 and x − y = 4, what is the value of xy?

Q20 Advanced · Discount

A pair of shoes originally costs $85. A store offers a 30% discount. What is the sale price in dollars? (e.g., 59.50)

out of 20

Complete the Exam

Answer all questions to see your result.

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Answer Key

Full Solutions

Q1 — LCMNumber Ops

What is the LCM of 12 and 18?

Answer: 36

12 = 2² × 3 | 18 = 2 × 3²
LCM = take highest powers: 2² × 3² = 4 × 9 = 36

Q2 — FractionsNumber Ops

3/4 + 2/3

Answer: 17/12

LCD of 4 and 3 = 12
3/4 = 9/12 | 2/3 = 8/12
9/12 + 8/12 = 17/12

Q3 — PercentagesNumber Ops

15% of 240 students

Answer: 36

240 × 0.15 = 36 students

Q4 — RatiosNumber Ops

Ratio 3:5, total 120 — how many girls?

Answer: 75

Total parts = 3 + 5 = 8
Girls = 120 × 5/8 = 75

Q5 — Linear EquationAlgebra

2x + 7 = 19

Answer: x = 6

2x = 19 − 7 = 12
x = 12 ÷ 2 = 6

Q6 — InequalityAlgebra

3x − 4 > 11, smallest integer x

Answer: 6

3x > 15 → x > 5
Smallest integer greater than 5 = 6

Q7 — SequenceAlgebra

a₁ = 3, d = 5, find 8th term

Answer: 38

aₙ = a₁ + (n−1)d
a₈ = 3 + 7 × 5 = 3 + 35 = 38

Q8 — Rate ProblemAlgebra

5 apples = $3.50, cost of 8 apples

Answer: $5.60

Unit price = $3.50 ÷ 5 = $0.70 per apple
8 × $0.70 = $5.60

Q9 — Triangle AreaGeometry

Triangle: base 14 cm, height 9 cm

Answer: 63 cm²

Area = ½ × 14 × 9 = ½ × 126 = 63 cm²

Q10 — PerimeterGeometry

Rectangle 8 m × 5 m

Answer: 26 m

P = 2(l + w) = 2(8 + 5) = 2 × 13 = 26 m

Q11 — VolumeGeometry

Prism: 6 × 4 × 3

Answer: 72 cm³

V = 6 × 4 × 3 = 72 cm³

Q12 — AnglesGeometry

Triangle angles: 47° and 63°, find third

Answer: 70°

Sum of angles = 180°
Third = 180 − 47 − 63 = 70°

Q13 — CircumferenceGeometry

Circle radius = 7 cm, circumference in terms of π

Answer: 14π

C = 2πr = 2 × π × 7 = 14π cm

Q14 — MeanStatistics

Data: 8, 12, 15, 9, 11

Answer: 11

Sum = 8+12+15+9+11 = 55
Mean = 55 ÷ 5 = 11

Q15 — MedianStatistics

Data: 3, 7, 2, 9, 5

Answer: 5

Sorted: 2, 3, 5, 7, 9
Middle value (3rd of 5) = 5

Q16 — ProbabilityStatistics

4 red, 6 blue marbles — P(red)?

Answer: 2/5

P(red) = 4 / (4+6) = 4/10 = 2/5

Q17 — ModeStatistics

Data: 4, 7, 2, 7, 4, 7, 3

Answer: 7

Frequency: 4→2, 7→3, 2→1, 3→1
7 appears most often → mode = 7

Q18 — Geometric SequenceAdvanced

Sequence: 2, 6, 18, 54, … next term?

Answer: 162

Common ratio r = 6/2 = 3
Next term = 54 × 3 = 162

Q19 — SystemsAdvanced

x + y = 10 and x − y = 4, find xy

Answer: 21

Add both: 2x = 14 → x = 7
y = 10 − 7 = 3
xy = 7 × 3 = 21

Q20 — DiscountAdvanced

$85 original price, 30% discount

Answer: $59.50

Discount = 85 × 0.30 = $25.50
Sale price = 85 − 25.50 = $59.50
or: 85 × 0.70 = $59.50