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GED Algebra Questions
Practise algebra (mathematics) for the GED Test: 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 log₂ 32.
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Answer: A — 5
log_2(32) asks “2 to what power gives 32?” → 2^5 = 32, so the answer is 5.
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Q2.Solve: x + 3y = 45 and 5x + 5y = 105
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Answer: C — x = 9, y = 12
Elimination/substitution gives x = 9, y = 12. Check: 1(9) + 3(12) = 45 ✓ and 5(9) + 5(12) = 105 ✓.
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Q3.Find the sum of the first 11 terms of the AP 3, 4, 5, …
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Answer: C — 88
Sₙ = n/2 × [2a + (n − 1)d] = 11/2 × [6 + 10] = 88.
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Q4.Find log₅ 3,125.
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Answer: D — 5
log_5(3125) asks “5 to what power gives 3125?” → 5^5 = 3125, so the answer is 5.
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Q5.Find log₂ 4.
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Answer: C — 2
log_2(4) asks “2 to what power gives 4?” → 2^2 = 4, so the answer is 2.
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Q6.Find log₂ 16.
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Answer: C — 4
log_2(16) asks “2 to what power gives 16?” → 2^4 = 16, so the answer is 4.
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Q7.Find the sum of the first 26 terms of the AP 6, 12, 18, …
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Answer: C — 2106
Sₙ = n/2 × [2a + (n − 1)d] = 26/2 × [12 + 150] = 2,106.
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Q8.Solve: 5x + 5y = 90 and x + 3y = 30
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Answer: A — x = 12, y = 6
Elimination/substitution gives x = 12, y = 6. Check: 5(12) + 5(6) = 90 ✓ and 1(12) + 3(6) = 30 ✓.
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Q9.Solve: 4x + y = -5 and 3x + 5y = 9
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Answer: D — x = -2, y = 3
Elimination/substitution gives x = -2, y = 3. Check: 4(-2) + 1(3) = -5 ✓ and 3(-2) + 5(3) = 9 ✓.
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Q10.Solve: 3x + 4y = -13 and 5x + 3y = -18
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Answer: A — x = -3, y = -1
Elimination/substitution gives x = -3, y = -1. Check: 3(-3) + 4(-1) = -13 ✓ and 5(-3) + 3(-1) = -18 ✓.
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 GED
GED Test — conducted by GED Testing Service. A high-school equivalency credential covering math, language arts, science and social studies.
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.
GED practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| English Grammar | English | Question bank |
| World General Knowledge | General awareness | Question bank |