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ACT Algebra Questions
Practise algebra (mathematics) for the ACT: 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: 3x + 3y = 3 and 3x + 4y = 9
Show answer & explanation
Answer: A — x = -5, y = 6
Elimination/substitution gives x = -5, y = 6. Check: 3(-5) + 3(6) = 3 ✓ and 3(-5) + 4(6) = 9 ✓.
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Q2.Solve: x² + 5x + 4 = 0
Show answer & explanation
Answer: D — -4, -1
Find two roots with sum -5 and product 4: -4 and -1. So x² + 5x + 4 = (x + 4)(x + 1) = 0.
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Q3.Find the sum of the first 25 terms of the AP 16, 23, 30, …
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Answer: D — 2500
Sₙ = n/2 × [2a + (n − 1)d] = 25/2 × [32 + 168] = 2,500.
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Q4.Solve: x² − 5x − 14 = 0
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Answer: C — -2, 7
Find two roots with sum 5 and product -14: 7 and -2. So x² − 5x − 14 = (x − 7)(x + 2) = 0.
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Q5.Find the sum of the first 26 terms of the AP 6, 9, 12, …
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Answer: C — 1131
Sₙ = n/2 × [2a + (n − 1)d] = 26/2 × [12 + 75] = 1,131.
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Q6.Solve: x² − x − 12 = 0
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Answer: B — -3, 4
Find two roots with sum 1 and product -12: -3 and 4. So x² − x − 12 = (x + 3)(x − 4) = 0.
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Q7.Solve: x + y = 2 and 3x + 4y = 9
Show answer & explanation
Answer: C — x = -1, y = 3
Elimination/substitution gives x = -1, y = 3. Check: 1(-1) + 1(3) = 2 ✓ and 3(-1) + 4(3) = 9 ✓.
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Q8.Solve: x² + x − 72 = 0
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Answer: A — -9, 8
Find two roots with sum -1 and product -72: -9 and 8. So x² + x − 72 = (x + 9)(x − 8) = 0.
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Q9.Find the sum of the first 20 terms of the AP 7, 16, 25, …
Show answer & explanation
Answer: B — 1850
Sₙ = n/2 × [2a + (n − 1)d] = 20/2 × [14 + 171] = 1,850.
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Q10.Solve: x² + 5x + 6 = 0
Show answer & explanation
Answer: B — -3, -2
Find two roots with sum -5 and product 6: -2 and -3. So x² + 5x + 6 = (x + 2)(x + 3) = 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 ACT
ACT — conducted by ACT, Inc.. US college admission test with English, Math and Reading, plus an optional Science section.
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.
ACT practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| English Grammar | English | Question bank |
| Physics | Science | Calculated + question bank |
| Chemistry | Science | Calculated + question bank |