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ASVAB Algebra Questions
Practise algebra (mathematics) for the Armed Services Vocational Aptitude Battery: 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.Find log 1,000 (base 10).
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Answer: A — 3
log_10(1000) asks “10 to what power gives 1000?” → 10^3 = 1000, so the answer is 3.
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Q2.Find the sum of the first 8 terms of the AP 13, 14, 15, …
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Answer: D — 132
Sₙ = n/2 × [2a + (n − 1)d] = 8/2 × [26 + 7] = 132.
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Q3.Find log 100 (base 10).
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Answer: B — 2
log_10(100) asks “10 to what power gives 100?” → 10^2 = 100, so the answer is 2.
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Q4.Solve: 2x + 2y = 22 and 3x + 2y = 24
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Answer: B — x = 2, y = 9
Elimination/substitution gives x = 2, y = 9. Check: 2(2) + 2(9) = 22 ✓ and 3(2) + 2(9) = 24 ✓.
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Q5.Solve: x + 4y = 26 and 3x + 4y = 38
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Answer: C — x = 6, y = 5
Elimination/substitution gives x = 6, y = 5. Check: 1(6) + 4(5) = 26 ✓ and 3(6) + 4(5) = 38 ✓.
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Q6.Solve: 4x + 2y = 20 and x + 3y = 25
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Answer: C — x = 1, y = 8
Elimination/substitution gives x = 1, y = 8. Check: 4(1) + 2(8) = 20 ✓ and 1(1) + 3(8) = 25 ✓.
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Q7.Solve: x² − 36 = 0
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Answer: C — -6, 6
Find two roots with sum 0 and product -36: 6 and -6. So x² − 36 = (x − 6)(x + 6) = 0.
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Q8.Find log₃ 81.
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Answer: C — 4
log_3(81) asks “3 to what power gives 81?” → 3^4 = 81, so the answer is 4.
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Q9.Solve: 5x + 5y = 65 and x + 4y = 49
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Answer: D — x = 1, y = 12
Elimination/substitution gives x = 1, y = 12. Check: 5(1) + 5(12) = 65 ✓ and 1(1) + 4(12) = 49 ✓.
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Q10.Solve: x² − 12x + 32 = 0
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Answer: B — 4, 8
Find two roots with sum 12 and product 32: 8 and 4. So x² − 12x + 32 = (x − 8)(x − 4) = 0.
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 ASVAB
Armed Services Vocational Aptitude Battery — conducted by US Department of Defense. Determines eligibility and job placement in the US military.
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.
ASVAB practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Physics | Science | Calculated + question bank |
| Vocabulary & Idioms | English | Question bank |
| English Grammar | English | Question bank |