SSAT Math Mastery — 실전 기출 20문항

📚 Core Concepts & Key Formulas

Numbers & Operations

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Divisibility Rules2: even · 3: digit sum ÷3 · 5: ends 0/5 · 9: digit sum ÷9

LCM / GCFLCM(a,b) = a×b ÷ GCF(a,b)

Order of OperationsPEMDAS: Parentheses → Exponents → ×÷ → +−

Fractionsa/b ÷ c/d = a/b × d/c

Percent% change = (New − Old)/Old × 100

Prime Numbers2, 3, 5, 7, 11, 13, 17, 19, 23, 29 …

📝 Example

What is the LCM of 12 and 18?

Answer: 36 — GCF(12,18) = 6, so LCM = 12 × 18 ÷ 6 = 36

Algebra & Expressions

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Linear Equationax + b = c → x = (c−b)/a

Inequalitiesflip sign when ÷ or × by negative

Slopem = (y₂−y₁)/(x₂−x₁)

Slope-Intercepty = mx + b

Exponent Rulesaᵐ·aⁿ = aᵐ⁺ⁿ · (aᵐ)ⁿ = aᵐⁿ · a⁰ = 1

FOIL(a+b)(c+d) = ac+ad+bc+bd

📝 Example

If 3x − 7 = 14, what is x?

Answer: 7 — 3x = 21, x = 7

Geometry

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Area FormulasRectangle: l×w · Triangle: ½bh · Circle: πr²

PerimeterRectangle: 2(l+w) · Circle: 2πr

Pythagorean Theorema² + b² = c²

Special Triangles3-4-5 · 5-12-13 · 8-15-17

Triangle Anglessum = 180° · exterior = sum of remote interior

VolumeBox: l×w×h · Cylinder: πr²h

📝 Example

A right triangle has legs 6 and 8. What is the hypotenuse?

Answer: 10 — 6² + 8² = 36 + 64 = 100, √100 = 10

Data, Statistics & Probability

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Meansum of values ÷ count

Medianmiddle value (sorted list)

Modemost frequent value

Rangemax − min

ProbabilityP(E) = favorable ÷ total outcomes

Counting Principleevent A × event B = total combinations

📝 Example

Find the mean of: 4, 7, 10, 13, 6

Answer: 8 — (4+7+10+13+6) ÷ 5 = 40 ÷ 5 = 8

Word Problems, Ratios & Proportions

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Ratioa:b = a/b — always reduce

Proportiona/b = c/d → ad = bc

Rate × Time = Distanced = r × t

Work Rate1/t₁ + 1/t₂ = 1/T

Simple InterestI = P × r × t

Mixture Problemsamount × concentration = total substance

📝 Example

A car travels 120 miles in 2 hours. What is its speed in miles per hour?

Answer: 60 — speed = distance ÷ time = 120 ÷ 2 = 60 mph

✏️ Practice Test — 20 Questions

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30-minute timer · Short answer (type your answer) · Immediate feedback after each question

Numbers Medium

What is the greatest common factor (GCF) of 48 and 72?

💡 List the factors of each number and find the largest one they share.

Numbers Medium

A number is divisible by both 4 and 6. What is the smallest positive integer greater than 1 that satisfies this condition?

💡 Find LCM(4, 6).

Numbers Hard

If 40% of a number is 56, what is 75% of that same number?

💡 First find the whole number, then compute 75%.

Numbers Hard

The price of a jacket was $80. After a 15% discount and then a 10% tax applied to the discounted price, what is the final price? (Round to the nearest cent.)

💡 Apply discount first, then apply tax to the result.

Algebra Medium

Solve for x: 5x − 3 = 2x + 12

💡 Collect x terms on one side.

Algebra Medium

If f(x) = 3x² − 2x + 1, what is f(−2)?

💡 Substitute x = −2 carefully, remembering (−2)² = 4.

Algebra Hard

Two lines are given: y = 2x + 5 and y = −x + 11. At what x-coordinate do they intersect?

💡 Set the two equations equal and solve for x.

Algebra Hard

Simplify: (2x³y²)(3x²y⁴). Write your answer in the form ax^m y^n.

💡 Multiply coefficients; add exponents of matching bases.

Geometry Medium

A rectangle has a perimeter of 54 cm. If its length is twice its width, what is the area of the rectangle in cm²?

💡 Write equations: P = 2(l + w) and l = 2w, then solve for w.

Geometry Medium

In triangle ABC, angle A = 47° and angle B = 83°. What is the measure of angle C in degrees?

💡 All angles in a triangle sum to 180°.

Geometry Hard

A circle has an area of 49π cm². What is its circumference? (Express your answer in terms of π.)

💡 Area = πr², so find r, then use C = 2πr.

Geometry Hard

A right triangle has one leg of length 5 and a hypotenuse of length 13. What is the length of the other leg?

💡 Use the Pythagorean theorem: a² + b² = c².

Data & Stats Medium

The ages of 6 students are: 13, 14, 12, 16, 14, 15. What is the median age?

💡 Sort the list, then average the two middle values.

Data & Stats Medium

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is picked at random, what is the probability it is blue? (Express as a simplified fraction.)

💡 P = favorable ÷ total. Simplify your fraction.

Data & Stats Hard

The mean score of 5 tests is 82. If four of the scores are 78, 85, 90, and 76, what is the fifth score?

💡 Mean × count = total sum. Subtract the four known scores.

Ratios & Rates Medium

A recipe calls for flour and sugar in a ratio of 5:2. If you use 350 grams of flour, how many grams of sugar do you need?

💡 Set up a proportion: 5/2 = 350/x, then cross-multiply.

Ratios & Rates Medium

Train A travels 240 miles in 4 hours. Train B travels 300 miles in 5 hours. Which train is faster, and by how many miles per hour?

💡 Calculate speed = distance ÷ time for each train, then compare.

Ratios & Rates Hard

Worker A can complete a job in 6 hours. Worker B can complete the same job in 4 hours. How many hours will it take them to complete the job working together? (Express as a fraction or decimal.)

💡 Combined rate = 1/6 + 1/4. Time = 1 ÷ (combined rate).

Mixed / Hard Hard

A store sells notebooks for $3 each and pens for $1.50 each. Sarah spent exactly $24 buying a total of 10 items. How many notebooks did she buy?

💡 Let n = notebooks, p = pens. Write two equations: n + p = 10 and 3n + 1.5p = 24.

Mixed / Hard Hard

The volume of a rectangular box is 360 cm³. Its length is 10 cm and its width is 6 cm. If the height is doubled while length and width stay the same, what is the new volume in cm³?

💡 Find original height first, then double it and recalculate volume.

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Answer Key & Solutions

Q1: 24 — Factors of 48: 1,2,3,4,6,8,12,16,24,48. Factors of 72: 1,2,3,4,6,8,9,12,18,24,36,72. Greatest common factor = 24.

Q2: 12 — LCM(4,6): multiples of 4: 4,8,12,16… multiples of 6: 6,12,18… First common multiple = 12.

Q3: 105 — 40% of x = 56 → x = 140. Then 75% of 140 = 0.75 × 140 = 105.

Q4: $74.80 — Discounted: 80 × 0.85 = $68. With tax: 68 × 1.10 = $74.80.

Q5: 5 — 5x − 2x = 12 + 3 → 3x = 15 → x = 5.

Q6: 17 — f(−2) = 3(4) − 2(−2) + 1 = 12 + 4 + 1 = 17.

Q7: 2 — 2x + 5 = −x + 11 → 3x = 6 → x = 2.

Q8: 6x⁵y⁶ — Multiply coefficients: 2×3=6. Add exponents: x³⁺²=x⁵, y²⁺⁴=y⁶.

Q9: 162 — 2(2w + w) = 54 → 6w = 54 → w = 9, l = 18. Area = 9 × 18 = 162 cm².

Q10: 50 — C = 180 − 47 − 83 = 50°.

Q11: 14π — πr² = 49π → r² = 49 → r = 7. C = 2π × 7 = 14π cm.

Q12: 12 — a² + 5² = 13² → a² = 169 − 25 = 144 → a = 12.

Q13: 14 — Sorted: 12, 13, 14, 14, 15, 16. Median = (14+14)/2 = 14.

Q14: 3/10 — P(blue) = 3/(5+3+2) = 3/10. Already simplified.

Q15: 81 — Total = 82 × 5 = 410. Sum of 4 scores = 78+85+90+76 = 329. Fifth = 410 − 329 = 81.

Q16: 140 — 5/2 = 350/x → x = (350 × 2)/5 = 140 g.

Q17: Same speed (60 mph) — Train A: 240/4 = 60 mph. Train B: 300/5 = 60 mph. They are equal.

Q18: 12/5 (2.4 hours) — Rate = 1/6 + 1/4 = 2/12 + 3/12 = 5/12. Time = 12/5 = 2.4 hours.

Q19: 6 — n + p = 10, 3n + 1.5p = 24 → multiply first by 1.5: 1.5n + 1.5p = 15 → subtract: 1.5n = 9 → n = 6.

Q20: 720 — Original h = 360/(10×6) = 6 cm. New h = 12. New volume = 10 × 6 × 12 = 720 cm³.

SSAT MathMastery Test

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SSAT Math
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