Grade 11 Mathematics practice questions – Lebanese curriculum

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Question 1

Calculate the determinant D of the system { −5x − 2y = 9 ; −2x + y = 4 }.

Accepted Answer

−9. D = ab′ − a′b = (−5) × 1 − (−2) × (−2) = −5 − 4 = −9.

Question 2

(6 ; 1) is a solution of { x − 6y = 0 ; 2x + y = 12 }.

Accepted Answer

False. x − 6y = 0 holds, but 2 × 6 + 1 = 13 ≠ 12.

Question 3

The product of the roots of 2x² + x − 14 = 0 is −7.

Accepted Answer

True. P = c/a = −14/2 = −7.

Question 4

x² − 4x + 4 = 0 has a double root.

Accepted Answer

True. Δ′ = 4 − 4 = 0: double root x₀ = 2; x² − 4x + 4 = (x − 2)².

Question 5

The trinomial 2x² − 3x + 2 is:

Accepted Answer

strictly positive for every real x. Δ = (−3)² − 4 × 2 × 2 = −7 < 0: no root, the trinomial has the sign of a = 2.

Question 6

The solution set of (x − 8)² ≤ 0 is { 8 }.

Accepted Answer

True. A square is never negative, and it is zero only at x = 8.

Question 7

What is the remainder of the division of P(x) = x³ − x² + x + 6 by x + 2?

Accepted Answer

−8. The remainder of the division by x + 2 is P(−2) = −8.

Question 8

A is a polynomial of degree 2. What is the degree of A² × (x⁵ + 1)?

Accepted Answer

9. deg A² = 2 × 2 = 4; deg(x⁵ + 1) = 5; the degrees of a product add up: 9.

Question 9

The circle (C): (x − 5)² + (y − 2)² = 9 has:

Accepted Answer

centre (5 ; 2), radius 3. (x − a)² + (y − b)² = r² gives a = 5, b = 2 and r² = 9, so r = 3.

Question 10

The circle (C): (x + 3)² + (y − 5)² = 25 has:

Accepted Answer

centre (−3 ; 5), radius 5. (x − a)² + (y − b)² = r² gives a = −3, b = 5 and r² = 25, so r = 5.

Question 11

f(x) = x² + 2x − 3. The image of 2 by f is:

Accepted Answer

5. f(2) = 2² + 2 × 2 − 3 = 5.

Question 12

The curve of an even function is symmetric about the origin O.

Accepted Answer

False. An even function is symmetric about the y-axis; an odd function is symmetric about O.

Question 13

The line y = 3 is an asymptote to the curve of f(x) = (3x + 1)/(x − 2).

Accepted Answer

True. At ±∞, f(x) → 3x/x = 3.

Question 14

Calculate lim(x→−∞) (−x⁴ + 5x³ − 4).

Accepted Answer

−∞. A polynomial behaves at −∞ like its highest-degree term: lim(x→−∞) −x⁴ = −∞.

Question 15

If f(x) = 9x², then f′(3) = 81.

Accepted Answer

False. f′(x) = 18x, so f′(3) = 54.

Grade 11 Mathematics Questions and Answers

15 Grade 11 Mathematics practice questions

1. Calculate the determinant D of the system { −5x − 2y = 9 ; −2x + y = 4 }.

2. (6 ; 1) is a solution of { x − 6y = 0 ; 2x + y = 12 }.

3. The product of the roots of 2x² + x − 14 = 0 is −7.

4. x² − 4x + 4 = 0 has a double root.

5. The trinomial 2x² − 3x + 2 is:

6. The solution set of (x − 8)² ≤ 0 is { 8 }.

7. What is the remainder of the division of P(x) = x³ − x² + x + 6 by x + 2?

8. A is a polynomial of degree 2. What is the degree of A² × (x⁵ + 1)?

9. The circle (C): (x − 5)² + (y − 2)² = 9 has:

10. The circle (C): (x + 3)² + (y − 5)² = 25 has:

11. f(x) = x² + 2x − 3. The image of 2 by f is:

12. The curve of an even function is symmetric about the origin O.

13. The line y = 3 is an asymptote to the curve of f(x) = (3x + 1)/(x − 2).

14. Calculate lim(x→−∞) (−x⁴ + 5x³ − 4).

15. If f(x) = 9x², then f′(3) = 81.

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