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SAT Algebra Questions
Practise algebra (mathematics) for the SAT (Digital): 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 the sum of the first 25 terms of the AP 4, 12, 20, …
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Answer: D — 2500
Sₙ = n/2 × [2a + (n − 1)d] = 25/2 × [8 + 192] = 2,500.
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Q2.Find the sum of the first 23 terms of the AP 8, 17, 26, …
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Answer: A — 2461
Sₙ = n/2 × [2a + (n − 1)d] = 23/2 × [16 + 198] = 2,461.
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Q3.Solve: 5x + 3y = 40 and 4x + 2y = 34
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Answer: B — x = 11, y = -5
Elimination/substitution gives x = 11, y = -5. Check: 5(11) + 3(-5) = 40 ✓ and 4(11) + 2(-5) = 34 ✓.
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Q4.Find the sum of the first 22 terms of the AP 20, 26, 32, …
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Answer: C — 1826
Sₙ = n/2 × [2a + (n − 1)d] = 22/2 × [40 + 126] = 1,826.
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Q5.Solve: x² + 2x − 8 = 0
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Answer: B — -4, 2
Find two roots with sum -2 and product -8: 2 and -4. So x² + 2x − 8 = (x − 2)(x + 4) = 0.
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Q6.Find log₃ 81.
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Answer: B — 4
log_3(81) asks “3 to what power gives 81?” → 3^4 = 81, so the answer is 4.
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Q7.Find the sum of the first 27 terms of the AP 12, 16, 20, …
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Answer: D — 1728
Sₙ = n/2 × [2a + (n − 1)d] = 27/2 × [24 + 104] = 1,728.
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Q8.Solve: 2x + 4y = 42 and x + y = 9
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Answer: D — x = -3, y = 12
Elimination/substitution gives x = -3, y = 12. Check: 2(-3) + 4(12) = 42 ✓ and 1(-3) + 1(12) = 9 ✓.
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Q9.Find log₅ 3,125.
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Answer: A — 5
log_5(3125) asks “5 to what power gives 3125?” → 5^5 = 3125, so the answer is 5.
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Q10.Find the sum of the first 24 terms of the AP 5, 10, 15, …
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Answer: A — 1500
Sₙ = n/2 × [2a + (n − 1)d] = 24/2 × [10 + 115] = 1,500.
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 SAT
SAT (Digital) — conducted by College Board. The US college admission test with Reading & Writing and Math sections, now delivered digitally.
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.
SAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Averages & Statistics | Quantitative aptitude | Calculated (new numbers every set) |
| English Grammar | English | Question bank |
| Vocabulary & Idioms | English | Question bank |