أسئلة تدريبية في الرياضيات – الصف العاشر – المنهج اللبناني

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Question 1

A = {7, 9} and B = {u, x}. Which set is A × B?

Accepted Answer

{(7 ; u), (7 ; x), (9 ; u), (9 ; x)}. A × B contains every pair (a ; b) with a ∈ A first and b ∈ B second: 2 × 2 = 4 pairs.

Question 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?

Accepted Answer

12. The set of meals is S × J: card(S × J) = 6 × 2 = 12.

Question 3

On an axis, A has abscissa −5 and B has abscissa 7. Find the distance AB.

Accepted Answer

12. AB = |7 − (−5)| = |12| = 12.

Question 4

Write the set of real numbers x such that −6 ≤ x < 0 as an interval.

Accepted Answer

[−6 ; 0[. −6 ≤ x < 0 gives [−6 ; 0[: the bracket turns towards a number when it is included.

Question 5

Write √216 in simplest form.

Accepted Answer

6√6. √216 = √(36 × 6) = √36 × √6 = 6√6.

Question 6

Write √405 in simplest form.

Accepted Answer

9√5. √405 = √(81 × 5) = √81 × √5 = 9√5.

Question 7

x < y. Which statement is true?

Accepted Answer

x − 4 < y − 4. Adding the same number to both sides keeps the order.

Question 8

Given 6 ≤ x ≤ 9, a framing of x² is:

Accepted Answer

36 ≤ x² ≤ 81. All values are positive, so squaring keeps the order: 6² = 36 and 9² = 81.

Question 9

For any points H, F, E: HF→ − HE→ = ?

Accepted Answer

EF→. HF→ − HE→ = HF→ + EH→ = EH→ + HF→ = EF→.

Question 10

DABC is a parallelogram. DA→ + BC→ = ?

Accepted Answer

0→. In the parallelogram DABC, BC→ = AD→, so the sum is DA→ + AD→ = 0→.

Question 11

R is defined by PR→ = (2/5)PO→. Then RP→ = ?

Accepted Answer

−(2/5)PO→. RP→ = −PR→ = −(2/5)PO→.

Question 12

C is the midpoint of [BD]. BD→ = ?

Accepted Answer

2CD→. BD→ = BC→ + CD→ and BC→ = CD→.

Question 13

For every real x, (a + 1)x² + (b − 4)x + c = −5x² − 3x − 8. Find a, b and c.

Accepted Answer

a = −6, b = 1, c = −8. Identify the coefficients: a + 1 = −5, b − 4 = −3 and c = −8, so a = −6, b = 1, c = −8.

Question 14

For every real x, (a − 2)x² + (b + 2)x + c = 2x² + 4x − 2. Find a, b and c.

Accepted Answer

a = 4, b = 2, c = −2. Identify the coefficients: a − 2 = 2, b + 2 = 4 and c = −2, so a = 4, b = 2, c = −2.

Question 15

p is the projection on (d) parallel to (Δ), with p(u→) = a→ and p(v→) = b→. Then p(2u→ + 2v→) = ?

Accepted Answer

2a→ + 2b→. A projection keeps sums and multiples: p(2u→ + 2v→) = 2p(u→) + 2p(v→) = 2a→ + 2b→.

أسئلة الرياضيات الصف العاشر مع الحل

15 سؤالاً تدريبياً في الرياضيات – الصف العاشر

1. A = {7, 9} and B = {u, x}. Which set is A × B?

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?

3. On an axis, A has abscissa −5 and B has abscissa 7. Find the distance AB.

4. Write the set of real numbers x such that −6 ≤ x < 0 as an interval.

5. Write √216 in simplest form.

6. Write √405 in simplest form.

7. x < y. Which statement is true?

8. Given 6 ≤ x ≤ 9, a framing of x² is:

9. For any points H, F, E: HF→ − HE→ = ?

10. DABC is a parallelogram. DA→ + BC→ = ?

11. R is defined by PR→ = (2/5)PO→. Then RP→ = ?

12. C is the midpoint of [BD]. BD→ = ?

13. For every real x, (a + 1)x² + (b − 4)x + c = −5x² − 3x − 8. Find a, b and c.

14. For every real x, (a − 2)x² + (b + 2)x + c = 2x² + 4x − 2. Find a, b and c.

15. p is the projection on (d) parallel to (Δ), with p(u→) = a→ and p(v→) = b→. Then p(2u→ + 2v→) = ?

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