Grade 10 Mathematics Questions and Answers
A free sample of Grade 10 Mathematics practice questions with the correct answer and an explanation, following the Lebanese curriculum. Useful for revision before school tests.
أسئلة الرياضيات للصف 10 مع الأجوبة والشرح وفق المنهج اللبناني.
How to use this page: read each question, try to answer it yourself, then open the answer to check your reasoning. Questions are grouped by the chapter they belong to on EduRise, in the order of the Lebanese Grade 10 Mathematics programme.
15 Grade 10 Mathematics practice questions
Chapter: Sets and Cartesian Product · easy
1. A = {7, 9} and B = {u, x}. Which set is A × B?
- A. {(u ; 7), (u ; 9), (x ; 7), (x ; 9)}
- B. {(7 ; u), (9 ; x)}
- C. {(7 ; u), (7 ; x), (9 ; u), (9 ; x)}
- D. {(7 ; u), (9 ; u)}
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Answer: {(7 ; u), (7 ; x), (9 ; u), (9 ; x)}
Explanation: A × B contains every pair (a ; b) with a ∈ A first and b ∈ B second: 2 × 2 = 4 pairs.
Chapter: Sets and Cartesian Product · easy
2. A school canteen in Zahle offers 6 sandwiches and 2 juices. A meal is an ordered pair (sandwich ; juice). How many meals are possible?
- A. 8
- B. 4
- C. 36
- D. 12
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Answer: 12
Explanation: The set of meals is S × J: card(S × J) = 6 × 2 = 12.
Chapter: Absolute Value and Intervals · easy
3. On an axis, A has abscissa −5 and B has abscissa 7. Find the distance AB.
- A. 12
- B. −12
- C. 2
- D. 10
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Answer: 12
Explanation: AB = |7 − (−5)| = |12| = 12.
Chapter: Absolute Value and Intervals · easy
4. Write the set of real numbers x such that −6 ≤ x < 0 as an interval.
- A. [−6 ; 0]
- B. [−6 ; 0[
- C. ]−6 ; 0[
- D. ]−6 ; 0]
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Answer: [−6 ; 0[
Explanation: −6 ≤ x < 0 gives [−6 ; 0[: the bracket turns towards a number when it is included.
Chapter: Powers and Radicals · easy
5. Write √216 in simplest form.
- A. 7√6
- B. 6√6
- C. 6√7
- D. 36√6
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Answer: 6√6
Explanation: √216 = √(36 × 6) = √36 × √6 = 6√6.
Chapter: Powers and Radicals · easy
6. Write √405 in simplest form.
- A. 5√9
- B. 10√5
- C. 81√5
- D. 9√5
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Answer: 9√5
Explanation: √405 = √(81 × 5) = √81 × √5 = 9√5.
Chapter: Order on ℝ – Framing and Approximation · easy
7. x < y. Which statement is true?
- A. x − 4 < y − 4
- B. x − 4 = y − 4
- C. x − 4 > y − 4
- D. x − 4 ≥ y − 4
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Answer: x − 4 < y − 4
Explanation: Adding the same number to both sides keeps the order.
Chapter: Order on ℝ – Framing and Approximation · easy
8. Given 6 ≤ x ≤ 9, a framing of x² is:
- A. −81 ≤ x² ≤ −36
- B. 36 ≤ x² ≤ 81
- C. 12 ≤ x² ≤ 18
- D. 54 ≤ x² ≤ 81
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Answer: 36 ≤ x² ≤ 81
Explanation: All values are positive, so squaring keeps the order: 6² = 36 and 9² = 81.
Chapter: Addition of Vectors · easy
9. For any points H, F, E: HF→ − HE→ = ?
- A. FH→
- B. EF→
- C. FE→
- D. HE→
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Answer: EF→
Explanation: HF→ − HE→ = HF→ + EH→ = EH→ + HF→ = EF→.
Chapter: Addition of Vectors · easy
10. DABC is a parallelogram. DA→ + BC→ = ?
- A. 0→
- B. AC→
- C. DB→
- D. DC→
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Answer: 0→
Explanation: In the parallelogram DABC, BC→ = AD→, so the sum is DA→ + AD→ = 0→.
Chapter: Multiplication of a Vector by a Real Number · easy
11. R is defined by PR→ = (2/5)PO→. Then RP→ = ?
- A. −(3/5)PO→
- B. (2/5)PO→
- C. −(2/5)PO→
- D. (3/5)PO→
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Answer: −(2/5)PO→
Explanation: RP→ = −PR→ = −(2/5)PO→.
Chapter: Multiplication of a Vector by a Real Number · easy
12. C is the midpoint of [BD]. BD→ = ?
- A. 2DC→
- B. CD→
- C. (1/2)CD→
- D. 2CD→
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Answer: 2CD→
Explanation: BD→ = BC→ + CD→ and BC→ = CD→.
Chapter: The Polynomials · easy
13. For every real x, (a + 1)x² + (b − 4)x + c = −5x² − 3x − 8. Find a, b and c.
- A. a = −5, b = −3, c = −8
- B. a = −6, b = 1, c = −8
- C. a = −6, b = −7, c = −8
- D. a = −4, b = 1, c = −8
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Answer: a = −6, b = 1, c = −8
Explanation: Identify the coefficients: a + 1 = −5, b − 4 = −3 and c = −8, so a = −6, b = 1, c = −8.
Chapter: The Polynomials · easy
14. For every real x, (a − 2)x² + (b + 2)x + c = 2x² + 4x − 2. Find a, b and c.
- A. a = 0, b = 2, c = −2
- B. a = 4, b = 6, c = −2
- C. a = 4, b = 2, c = −2
- D. a = 2, b = 4, c = −2
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Answer: a = 4, b = 2, c = −2
Explanation: Identify the coefficients: a − 2 = 2, b + 2 = 4 and c = −2, so a = 4, b = 2, c = −2.
Chapter: Projection in the Plane · easy
15. p is the projection on (d) parallel to (Δ), with p(u→) = a→ and p(v→) = b→. Then p(2u→ + 2v→) = ?
- A. −2a→ + 2b→
- B. a→ + b→
- C. 2a→ + 2b→
- D. 2a→ − 2b→
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Answer: 2a→ + 2b→
Explanation: A projection keeps sums and multiples: p(2u→ + 2v→) = 2p(u→) + 2p(v→) = 2a→ + 2b→.
More practice
These are sample questions only. The full Grade 10 Mathematics course on EduRise includes every chapter, lessons, 2,392 questions and timed exams.
Mathematics questions in other grades
Other Grade 10 subjects
See also: Grade 10 Mathematics chapters · All question pages · Study guides
About these questions
Where do these Grade 10 Mathematics questions come from?
They are a sample from EduRise's Grade 10 Mathematics question bank (2,392 questions across 23 chapters), written to follow the Lebanese curriculum. Each chapter on EduRise has its own practice set and a timed exam.
Are the answers explained?
Yes. Every question on EduRise shows the correct answer and an explanation after you answer, in practice mode and in the exam review.
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