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DAT Algebra Questions
Practise algebra (mathematics) for the Dental Admission 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.Solve: 2x + 2y = 6 and 3x + y = 3
Show answer & explanation
Answer: C — x = 0, y = 3
Elimination/substitution gives x = 0, y = 3. Check: 2(0) + 2(3) = 6 ✓ and 3(0) + 1(3) = 3 ✓.
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Q2.Solve: x + 4y = 27 and x + 5y = 33
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Answer: D — x = 3, y = 6
Elimination/substitution gives x = 3, y = 6. Check: 1(3) + 4(6) = 27 ✓ and 1(3) + 5(6) = 33 ✓.
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Q3.Find log₅ 25.
Show answer & explanation
Answer: B — 2
log_5(25) asks “5 to what power gives 25?” → 5^2 = 25, so the answer is 2.
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Q4.Find the sum of the first 13 terms of the AP 7, 13, 19, …
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Answer: D — 559
Sₙ = n/2 × [2a + (n − 1)d] = 13/2 × [14 + 72] = 559.
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Q5.Find the sum of the first 10 terms of the AP 19, 22, 25, …
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Answer: C — 325
Sₙ = n/2 × [2a + (n − 1)d] = 10/2 × [38 + 27] = 325.
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Q6.Find log₂ 8.
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Answer: C — 3
log_2(8) asks “2 to what power gives 8?” → 2^3 = 8, so the answer is 3.
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Q7.Solve: x² + 14x + 45 = 0
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Answer: D — -9, -5
Find two roots with sum -14 and product 45: -9 and -5. So x² + 14x + 45 = (x + 9)(x + 5) = 0.
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Q8.Solve: x² + x − 42 = 0
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Answer: D — -7, 6
Find two roots with sum -1 and product -42: 6 and -7. So x² + x − 42 = (x − 6)(x + 7) = 0.
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Q9.Find the sum of the first 17 terms of the AP 3, 6, 9, …
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Answer: B — 459
Sₙ = n/2 × [2a + (n − 1)d] = 17/2 × [6 + 48] = 459.
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Q10.Solve: x² − 16 = 0
Show answer & explanation
Answer: A — -4, 4
Find two roots with sum 0 and product -16: 4 and -4. So x² − 16 = (x − 4)(x + 4) = 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 DAT
Dental Admission Test — conducted by American Dental Association (ADA). Dental school admission test covering natural sciences, perceptual ability, reading and quantitative reasoning.
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.
DAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Biology | Science | Question bank |
| Chemistry | Science | Calculated + question bank |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |