Elective Mathematics

Question 1

1If the determinant of the coefficient matrix is zero, the system has

Easy

A. only zero solution B. no unique solution C. two solutions D. a unique solution

Question 2

2The inverse of [[a, b], [c, d]] is

Medium

A. (1/(ad − bc)) [[d, −b], [−c, a]] B. (1/(ad − bc)) [[a, b], [c, d]] C. [[−a, −b], [−c, −d]] D. [[d, b], [c, a]]

Question 3

3The matrix [[k, 2], [8, k]] is singular. Find the values of k.

Hard

A. ±4 B. ±2 C. 16 D. 0

Question 4

4The normal distribution curve is

Easy

A. U-shaped B. skewed to the right C. bell-shaped and symmetrical about the mean D. a straight line

Question 5

5Find a·b if a = (3, −3) and b = (−1, 5).

Easy

A. −17 B. 4 C. 12 D. −18

Question 6

6∫ x eˣ dx =

Hard

A. x eˣ + C B. x² eˣ/2 + C C. eˣ(x + 1) + C D. eˣ(x − 1) + C

Question 7

7Find the distance from the point (3, 4) to the line 3x + 4y − 5 = 0.

Medium

A. 4 B. 5 C. 3 D. 25

Question 8

8The area enclosed by y = x² and y = 4 is

Hard

A. 32/3 B. 8 C. 64/3 D. 16/3

Question 9

9For what values of k does x² + kx + 9 = 0 have equal roots?

Medium

A. k = ±9 B. k = 0 C. k = ±3 D. k = ±6

Question 10

10If f(x) = 2x + 2 and g(x) = 4x − 5, find f(g(3)).

Medium

A. 15 B. 16 C. 27 D. 26

Question 11

11The gradient of y = 1x² at x = 4 is ___

Easy

Your answer (fill in the blank)

Question 12

12∫ (2x + 3) dx =

Easy

A. x² + C B. 2x² + 3x + C C. x² + 3x + C D. 2 + C

Question 13

13The radius of the circle x² + y² = 36 is ___

Easy

Your answer (fill in the blank)

Question 14

14A tautology is true for all truth values of its components.

Easy

A. True B. False

Question 15

15Find the sum of the first 4 terms of the GP 3, 9, 27, …

Medium

A. 243 B. 36 C. 61.5 D. 120

Question 16

16log₍4₎ 16 = ___

Easy

Your answer (fill in the blank)

Question 17

17Σ_{r=1}^{n} r =

Easy

A. n(n + 1)/2 B. n(n + 1)(2n + 1)/6 C. n(n − 1) D. n²

Question 18

18Find the area bounded by y = 3x², the x-axis and the lines x = 2 and x = 3.

Medium

A. 22 square units B. 19 square units C. 57 square units D. 15 square units

Question 19

19Express log 75 in terms of log 3 and log 5.

Hard

A. log 3 + 2 log 5 B. 3 log 5 C. log 3 × log 25 D. 2 log 3 + log 5

Question 20

20Find the coefficient of x³ in the expansion of (1 + x)⁴.

Easy

A. 1 B. 12 C. 4 D. 8