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EJU Mathematics Algebra Questions
Practise algebra (mathematics) for the Examination for Japanese University Admission — Mathematics: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Algebra practice
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Q1.Solve: x + 3y = 24 and 3x + 3y = 24
Show answer & explanation
Answer: D — x = 0, y = 8
Elimination/substitution gives x = 0, y = 8. Check: 1(0) + 3(8) = 24 ✓ and 3(0) + 3(8) = 24 ✓.
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Q2.Find log₃ 9.
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Answer: B — 2
log_3(9) asks “3 to what power gives 9?” → 3^2 = 9, so the answer is 2.
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Q3.Solve: x + 5y = 36 and 5x + 3y = 4
Show answer & explanation
Answer: D — x = -4, y = 8
Elimination/substitution gives x = -4, y = 8. Check: 1(-4) + 5(8) = 36 ✓ and 5(-4) + 3(8) = 4 ✓.
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Q4.Find the sum of the first 29 terms of the AP 7, 9, 11, …
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Answer: D — 1015
Sₙ = n/2 × [2a + (n − 1)d] = 29/2 × [14 + 56] = 1,015.
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Q5.Solve: 3x + 3y = 33 and x + 5y = 31
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Answer: A — x = 6, y = 5
Elimination/substitution gives x = 6, y = 5. Check: 3(6) + 3(5) = 33 ✓ and 1(6) + 5(5) = 31 ✓.
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Q6.Solve: x² − 12x + 35 = 0
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Answer: C — 5, 7
Find two roots with sum 12 and product 35: 7 and 5. So x² − 12x + 35 = (x − 7)(x − 5) = 0.
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Q7.Solve: 2x + 5y = 4 and 2x + y = 20
Show answer & explanation
Answer: B — x = 12, y = -4
Elimination/substitution gives x = 12, y = -4. Check: 2(12) + 5(-4) = 4 ✓ and 2(12) + 1(-4) = 20 ✓.
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Q8.Solve: x² + 5x + 6 = 0
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Answer: A — -3, -2
Find two roots with sum -5 and product 6: -3 and -2. So x² + 5x + 6 = (x + 3)(x + 2) = 0.
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Q9.Solve: x² − 18x + 81 = 0
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Answer: A — 9, 9
Find two roots with sum 18 and product 81: 9 and 9. So x² − 18x + 81 = (x − 9)(x − 9) = 0.
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Q10.Find log 100,000 (base 10).
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Answer: D — 5
log_10(100000) asks “10 to what power gives 100000?” → 10^5 = 100000, so the answer is 5.
How to approach algebra questions
Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution. For simultaneous equations, elimination is usually faster than substitution under time pressure.
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.
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) |