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ISEE Algebra Questions
Practise algebra (mathematics) for the Independent School Entrance Exam: 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 19 terms of the AP 16, 23, 30, …
Show answer & explanation
Answer: D — 1501
Sₙ = n/2 × [2a + (n − 1)d] = 19/2 × [32 + 126] = 1,501.
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Q2.Solve: x² − x − 6 = 0
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Answer: C — -2, 3
Find two roots with sum 1 and product -6: 3 and -2. So x² − x − 6 = (x − 3)(x + 2) = 0.
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Q3.Solve: x + 4y = -20 and 3x + 4y = -28
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Answer: A — x = -4, y = -4
Elimination/substitution gives x = -4, y = -4. Check: 1(-4) + 4(-4) = -20 ✓ and 3(-4) + 4(-4) = -28 ✓.
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Q4.Solve: x² + 12x + 36 = 0
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Answer: B — -6, -6
Find two roots with sum -12 and product 36: -6 and -6. So x² + 12x + 36 = (x + 6)(x + 6) = 0.
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Q5.Find the sum of the first 21 terms of the AP 20, 28, 36, …
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Answer: B — 2100
Sₙ = n/2 × [2a + (n − 1)d] = 21/2 × [40 + 160] = 2,100.
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Q6.Solve: 2x + 5y = 50 and 3x + 3y = 30
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Answer: A — x = 0, y = 10
Elimination/substitution gives x = 0, y = 10. Check: 2(0) + 5(10) = 50 ✓ and 3(0) + 3(10) = 30 ✓.
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Q7.Solve: x² − 3x − 28 = 0
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Answer: C — -4, 7
Find two roots with sum 3 and product -28: 7 and -4. So x² − 3x − 28 = (x − 7)(x + 4) = 0.
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Q8.Solve: x² − 6x − 7 = 0
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Answer: B — -1, 7
Find two roots with sum 6 and product -7: -1 and 7. So x² − 6x − 7 = (x + 1)(x − 7) = 0.
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Q9.Find the sum of the first 29 terms of the AP 16, 18, 20, …
Show answer & explanation
Answer: B — 1276
Sₙ = n/2 × [2a + (n − 1)d] = 29/2 × [32 + 56] = 1,276.
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Q10.Solve: x² + 6x − 16 = 0
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Answer: D — -8, 2
Find two roots with sum -6 and product -16: 2 and -8. So x² + 6x − 16 = (x − 2)(x + 8) = 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 ISEE
Independent School Entrance Exam — conducted by Educational Records Bureau (ERB). Admission test for independent schools with verbal and quantitative reasoning sections.
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.
ISEE practice topics
| Topic | Section | Question source |
|---|---|---|
| Vocabulary & Idioms | English | Question bank |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |