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EJU Mathematics Practice Questions
Original practice questions for the Examination for Japanese University Admission — Mathematics (Japan Student Services Organization (JASSO)), mixed across 3 topics with instant answers and explanations. Practise by topic below or take the timed mock test.
EJU Mathematics mixed practice
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Q1.AlgebraSolve: x² − 4x − 21 = 0
Show answer & explanation
Answer: C — -3, 7
Find two roots with sum 4 and product -21: -3 and 7. So x² − 4x − 21 = (x + 3)(x − 7) = 0.
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Q2.Probability & CombinatoricsIn how many ways can a committee of 3 be chosen from 12 people?
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Answer: A — 220
Order does not matter → combinations: 12C3 = 12! / (3!·9!) = 220.
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Q3.Geometry & MensurationA right triangle has legs 7 cm and 24 cm. Find the hypotenuse.
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Answer: C — 25 cm
By Pythagoras, hypotenuse = √(7² + 24²) = √625 = 25.
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Q4.AlgebraSolve: 5x + 4y = 108 and 5x + 3y = 96
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Answer: D — x = 12, y = 12
Elimination/substitution gives x = 12, y = 12. Check: 5(12) + 4(12) = 108 ✓ and 5(12) + 3(12) = 96 ✓.
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Q5.Probability & Combinatorics2 fair coins are tossed. What is the probability of at least one head?
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Answer: D — 3/4
P(no head) = (1/2)^2 = 1/4; P(at least one head) = 1 − 1/4 = 3/4.
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Q6.Geometry & MensurationA right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
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Answer: C — 10 cm
By Pythagoras, hypotenuse = √(6² + 8²) = √100 = 10.
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Q7.AlgebraFind the sum of the first 13 terms of the AP 19, 24, 29, …
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Answer: A — 637
Sₙ = n/2 × [2a + (n − 1)d] = 13/2 × [38 + 60] = 637.
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Q8.Probability & CombinatoricsIn how many ways can a committee of 2 be chosen from 10 people?
Show answer & explanation
Answer: C — 45
Order does not matter → combinations: 10C2 = 10! / (2!·8!) = 45.
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Q9.Geometry & MensurationFind the area of a right triangle with legs 6 cm and 8 cm.
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Answer: C — 24 cm²
Area = ½ × base × height = ½ × 6 × 8 = 24 cm².
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Q10.AlgebraSolve: x + 3y = 16 and 5x + 5y = 40
Show answer & explanation
Answer: D — x = 4, y = 4
Elimination/substitution gives x = 4, y = 4. Check: 1(4) + 3(4) = 16 ✓ and 5(4) + 5(4) = 40 ✓.
About EJU Mathematics
Examination for Japanese University Admission — Mathematics — conducted by Japan Student Services Organization (JASSO). Taken by international students applying to Japanese universities.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
Practise by topic
- Algebra questions — Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution.
- Probability & Combinatorics questions — Probability = favourable ÷ total outcomes.
- Geometry & Mensuration questions — Memorise core formulas (circle πr², triangle ½bh, Pythagoras, distance √((x₂−x₁)² + (y₂−y₁)²)).
- EJU Mathematics mock test — 25 timed questions.
EJU Mathematics practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |