Elective Mathematics Mock 2022

Question 1 of 50

What is the equation of the circle with centre (0, 0) and radius 3?

Question 2 of 50

The locus of points 4 cm from a fixed point is

Question 3 of 50

A rank correlation coefficient of +1 means

Question 4 of 50

A correlation coefficient of −0.9 shows

Question 5 of 50

Differentiate sin x with respect to x.

Question 6 of 50

Find ∫3x² dx.

Question 7 of 50

The disjunction p ∨ q is false only when

Question 8 of 50

Find ∫cos x dx.

Question 9 of 50

Find the remainder when x³ − 2x + 5 is divided by (x − 2).

Question 10 of 50

Which is a factor of x³ − 6x² + 11x − 6?

Question 11 of 50

For 2x² − 8x + 3 = 0, what is the sum of the roots?

Question 12 of 50

For 2x² − 8x + 3 = 0, what is the product of the roots?

Question 13 of 50

The locus of points equidistant from two fixed points A and B is

Question 14 of 50

A is (2, 4) and B is (6, 0). What is the position vector of the midpoint of AB?

Question 15 of 50

The matrix (1 0; 0 −1) represents

Question 16 of 50

Solve log₃ x = 4.

Question 17 of 50

Which identity is always true?

Question 18 of 50

sin 2θ is equal to

Question 19 of 50

cos²θ − sin²θ is equal to

Question 20 of 50

Evaluate the integral of 2x from x = 0 to x = 2.

Question 21 of 50

Find ∫(4x³ − 2) dx.

Question 22 of 50

At what value of x does y = x² − 6x + 5 have a stationary point?

Question 23 of 50

The stationary point of y = x² − 6x + 5 is

Question 24 of 50

A particle moves so that s = t³ − 2t. Find its velocity at t = 2.

Question 25 of 50

P(A ∩ B) = 0.2 and P(B) = 0.5. Find P(A | B).

Question 26 of 50

The implication "if p then q" (p → q) is false only when

Question 27 of 50

The converse of p → q is

Question 28 of 50

Find the determinant of the 3 × 3 diagonal matrix with diagonal entries 1, 2 and 3.

Question 29 of 50

To solve the system AX = B when A is invertible, you calculate

Question 30 of 50

What is the vertex of the parabola y = (x − 1)² + 3?

Question 31 of 50

sin(A + B) is equal to

Question 32 of 50

Find ∫eˣ dx.

Question 33 of 50

Find ∫(1/x) dx for x ≠ 0.

Question 34 of 50

Find the area under y = x² from x = 0 to x = 3.

Question 35 of 50

A particle starts at the origin with velocity v = 2t m/s. How far does it travel in the first 3 s?

Question 36 of 50

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

Question 37 of 50

The parabola y² = 16x has focus

Question 38 of 50

∫₀^(π/2) sin x dx =

Question 39 of 50

If tan A = 1/2 and tan B = 1/3, find A + B.

Question 40 of 50

An open box is made from a 12 cm square sheet by cutting squares of side x from each corner. The value of x that maximises volume is

Question 41 of 50

The radius of a circle increases at 2 cm/s. How fast is its area increasing when r = 5 cm?

Question 42 of 50

A bag has 3 red and 2 white balls. Two are drawn at random without replacement. P(at least one red) is

Question 43 of 50

The statement p → q is logically equivalent to

Question 44 of 50

Find the determinant of [[1, 2, 3], [0, 1, 4], [5, 6, 0]].

Question 45 of 50

The length of the latus rectum of y² = 8x is

Question 46 of 50

Find the general solution of sin x = 0.

Question 47 of 50

∫ 1/(2x + 1) dx =

Question 48 of 50

Find the volume generated when y = x² from x = 0 to x = 1 is rotated about the x-axis.

Question 49 of 50

A particle has velocity v = 4 − 2t. Find the distance travelled in the first 3 s.

Question 50 of 50

X ~ N(50, 16). Find P(X > 58) given P(Z < 2) = 0.9772.