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ACCUPLACER Algebra Questions
Practise algebra (mathematics) for the ACCUPLACER placement tests: 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: 4x + 4y = 24 and 3x + 4y = 25
Show answer & explanation
Answer: B — x = -1, y = 7
Elimination/substitution gives x = -1, y = 7. Check: 4(-1) + 4(7) = 24 ✓ and 3(-1) + 4(7) = 25 ✓.
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Q2.Find log₅ 3,125.
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Answer: B — 5
log_5(3125) asks “5 to what power gives 3125?” → 5^5 = 3125, so the answer is 5.
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Q3.Solve: x² − 10x + 16 = 0
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Answer: D — 2, 8
Find two roots with sum 10 and product 16: 2 and 8. So x² − 10x + 16 = (x − 2)(x − 8) = 0.
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Q4.Find the sum of the first 17 terms of the AP 18, 25, 32, …
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Answer: D — 1258
Sₙ = n/2 × [2a + (n − 1)d] = 17/2 × [36 + 112] = 1,258.
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Q5.Solve: 2x + 4y = -16 and 4x + 5y = -26
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Answer: C — x = -4, y = -2
Elimination/substitution gives x = -4, y = -2. Check: 2(-4) + 4(-2) = -16 ✓ and 4(-4) + 5(-2) = -26 ✓.
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Q6.Solve: x² − 6x − 16 = 0
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Answer: A — -2, 8
Find two roots with sum 6 and product -16: 8 and -2. So x² − 6x − 16 = (x − 8)(x + 2) = 0.
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Q7.Find the sum of the first 20 terms of the AP 3, 6, 9, …
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Answer: B — 630
Sₙ = n/2 × [2a + (n − 1)d] = 20/2 × [6 + 57] = 630.
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Q8.Find log 10,000 (base 10).
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Answer: A — 4
log_10(10000) asks “10 to what power gives 10000?” → 10^4 = 10000, so the answer is 4.
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Q9.Find the sum of the first 10 terms of the AP 10, 15, 20, …
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Answer: D — 325
Sₙ = n/2 × [2a + (n − 1)d] = 10/2 × [20 + 45] = 325.
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Q10.Solve: 4x + 5y = -5 and 3x + 3y = 0
Show answer & explanation
Answer: D — x = 5, y = -5
Elimination/substitution gives x = 5, y = -5. Check: 4(5) + 5(-5) = -5 ✓ and 3(5) + 3(-5) = 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 ACCUPLACER
ACCUPLACER placement tests — conducted by College Board. College placement tests in reading, writing and math used by community colleges.
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.
ACCUPLACER practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| English Grammar | English | Question bank |