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EJU Mathematics Mock Test
A timed 25-question mock for the Examination for Japanese University Admission — Mathematics covering algebra, probability & combinatorics, geometry & mensuration. Answer, submit and review every question with its explanation; set negative marking to match your exam’s current scheme.
EJU Mathematics mock test
25 questions · 1 mark each · the timer starts with your first answer and the test submits itself when time runs out.
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Q1.AlgebraSolve: 3x + 2y = 22 and 4x + y = 26
Answer: C — x = 6, y = 2
Elimination/substitution gives x = 6, y = 2. Check: 3(6) + 2(2) = 22 ✓ and 4(6) + 1(2) = 26 ✓.
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Q2.Probability & CombinatoricsA card is drawn from a well-shuffled deck of 52. What is the probability that it is a face card (J, Q, K)?
Answer: A — 3/13
There are 12 such cards in 52, so P = 12/52 = 3/13.
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Q3.Geometry & MensurationFind the distance between (0, -2) and (5, 10).
Answer: C — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q4.AlgebraFind the sum of the first 14 terms of the AP 4, 6, 8, …
Answer: C — 238
Sₙ = n/2 × [2a + (n − 1)d] = 14/2 × [8 + 26] = 238.
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Q5.Probability & Combinatorics4 fair coins are tossed. What is the probability of at least one head?
Answer: B — 15/16
P(no head) = (1/2)^4 = 1/16; P(at least one head) = 1 − 1/16 = 15/16.
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Q6.Geometry & MensurationFind the area of a right triangle with legs 20 cm and 21 cm.
Answer: B — 210 cm²
Area = ½ × base × height = ½ × 20 × 21 = 210 cm².
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Q7.AlgebraSolve: x² − 14x + 45 = 0
Answer: D — 5, 9
Find two roots with sum 14 and product 45: 5 and 9. So x² − 14x + 45 = (x − 5)(x − 9) = 0.
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Q8.Probability & CombinatoricsIn how many ways can a committee of 2 be chosen from 10 people?
Answer: A — 45
Order does not matter → combinations: 10C2 = 10! / (2!·8!) = 45.
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Q9.Geometry & MensurationFind the volume of a cone with radius 3 cm and height 12 cm.
Answer: B — 113.1 cm³
Using ⅓πr²h with π = 3.1416: 113.1 cm³.
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Q10.AlgebraSolve: x² − 2x − 63 = 0
Answer: C — -7, 9
Find two roots with sum 2 and product -63: 9 and -7. So x² − 2x − 63 = (x − 9)(x + 7) = 0.
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Q11.Probability & CombinatoricsTwo fair dice are thrown. What is the probability that the sum is 7?
Answer: D — 1/6
6 of the 36 equally likely outcomes give a sum of 7, so P = 6/36 = 1/6.
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Q12.Geometry & MensurationFind the distance between (5, 3) and (11, 11).
Answer: D — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q13.AlgebraSolve: 4x + 3y = 37 and 2x + 2y = 18
Answer: C — x = 10, y = -1
Elimination/substitution gives x = 10, y = -1. Check: 4(10) + 3(-1) = 37 ✓ and 2(10) + 2(-1) = 18 ✓.
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Q14.Geometry & MensurationFind the volume of a sphere of radius 10 cm.
Answer: B — 4,188.79 cm³
Using (4/3)πr³ with π = 3.1416: 4,188.79 cm³.
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Q15.AlgebraFind log 10,000 (base 10).
Answer: C — 4
log_10(10000) asks “10 to what power gives 10000?” → 10^4 = 10000, so the answer is 4.
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Q16.Probability & CombinatoricsIn how many ways can the letters of the word SQUARE be arranged?
Answer: C — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q17.Geometry & MensurationFind the area of a circle of radius 2 cm.
Answer: D — 12.57 cm²
Using πr² with π = 3.1416: 12.57 cm².
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Q18.AlgebraSolve: 4x + 2y = 12 and 5x + y = 3
Answer: D — x = -1, y = 8
Elimination/substitution gives x = -1, y = 8. Check: 4(-1) + 2(8) = 12 ✓ and 5(-1) + 1(8) = 3 ✓.
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Q19.Probability & CombinatoricsIn how many ways can the letters of the word ORANGE be arranged?
Answer: D — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q20.Geometry & MensurationA right triangle has legs 20 cm and 21 cm. Find the hypotenuse.
Answer: B — 29 cm
By Pythagoras, hypotenuse = √(20² + 21²) = √841 = 29.
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Q21.AlgebraSolve: x² + 6x + 8 = 0
Answer: C — -4, -2
Find two roots with sum -6 and product 8: -2 and -4. So x² + 6x + 8 = (x + 2)(x + 4) = 0.
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Q22.Probability & Combinatorics2 fair coins are tossed. What is the probability of at least one head?
Answer: C — 3/4
P(no head) = (1/2)^2 = 1/4; P(at least one head) = 1 − 1/4 = 3/4.
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Q23.Geometry & MensurationFind the volume of a cylinder with radius 5 cm and height 13 cm.
Answer: D — 1,021.02 cm³
Using πr²h with π = 3.1416: 1,021.02 cm³.
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Q24.AlgebraFind log₅ 125.
Answer: D — 3
log_5(125) asks “5 to what power gives 125?” → 5^3 = 125, so the answer is 3.
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Q25.Probability & CombinatoricsIn how many ways can a committee of 3 be chosen from 9 people?
Answer: B — 84
Order does not matter → combinations: 9C3 = 9! / (3!·6!) = 84.
How the mock test works
- The timer starts with your first answer; the test submits itself when time runs out.
- Choose the negative marking that matches your exam (this test has no negative marking by default — check the official notification).
- After submitting you get your score, accuracy, time taken and a topic-wise breakdown, then every explanation.
- “New mock test” builds another paper — calculation questions get new numbers.
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) |