Elective Mathematics Mock 2017

Question 1 of 50

Find dy/dx if y = eˣ.

Question 2 of 50

The gradient of the curve y = x³ − 2x at x = 1 is

Question 3 of 50

The mean of x, 2x, 3x is 8. Find x.

Question 4 of 50

The impulse of a force of 10 N acting for 0.5 s is

Question 5 of 50

Simplify (√5 + √2)(√5 − √2).

Question 6 of 50

Evaluate log₂ 64.

Question 7 of 50

The 5th term of the AP with first term 7 and common difference −2 is

Question 8 of 50

If A = [[2, 0], [1, 3]] and B = [[1, 1], [0, 2]], find A + B.

Question 9 of 50

If p = 3i − 2j, find |p|.

Question 10 of 50

Find the vector AB if A = (1, 2) and B = (4, 6).

Question 11 of 50

Convert π/3 radians to degrees.

Question 12 of 50

Find the remainder when 2x³ + x − 3 is divided by (x + 1).

Question 13 of 50

Find the 4th term in the expansion of (1 + x)⁶.

Question 14 of 50

The angle between a = i + j and b = i − j is

Question 15 of 50

If |a| = 3, |b| = 4 and the angle between them is 60°, find a · b.

Question 16 of 50

Find the equation of the line perpendicular to y = 2x + 1 through (0, 3).

Question 17 of 50

Solve 2 sin x − 1 = 0 for 0° ≤ x ≤ 180°.

Question 18 of 50

cos(A − B) =

Question 19 of 50

Differentiate y = (2x + 1)³.

Question 20 of 50

Evaluate ∫₀¹ (3x² + 2x) dx.

Question 21 of 50

In how many ways can a committee of 2 boys and 1 girl be chosen from 4 boys and 3 girls?

Question 22 of 50

How many 3-digit numbers can be formed from 1, 2, 3, 4 without repetition?

Question 23 of 50

A bag contains 5 red and 3 blue balls. Two are drawn with replacement. P(both blue) is

Question 24 of 50

A particle moves with velocity v = 3t² m/s. Its acceleration at t = 2 s is

Question 25 of 50

A ball is projected horizontally at 10 m/s from a height of 20 m (g = 10 m/s²). The time to reach the ground is

Question 26 of 50

A ball is projected horizontally at 10 m/s from a height of 20 m (g = 10 m/s²). How far from the foot of the cliff does it land?

Question 27 of 50

The coefficient of x in (2 + x)⁴ is

Question 28 of 50

Simplify 16^(−1/2).

Question 29 of 50

If f(x) = x² − 1, the range for x ∈ {0, 1, 2} is

Question 30 of 50

Find AB if A = [[1, 2], [3, 4]] and B = [[1], [1]].

Question 31 of 50

Find the equation of the line through (1, 1) and (3, 7).

Question 32 of 50

The angle a line of gradient 1 makes with the positive x-axis is

Question 33 of 50

Find cos 150°.

Question 34 of 50

The period of y = sin 2x is

Question 35 of 50

Evaluate lim (x→3) (x² − 9)/(x − 3).

Question 36 of 50

The turning points of y = x³ − 3x are at x =

Question 37 of 50

∫₀^π cos x dx =

Question 38 of 50

Differentiate y = (3x − 1)⁴.

Question 39 of 50

A binomial distribution has n = 10 and p = 0.3. Its mean is

Question 40 of 50

A body thrown up at 30 m/s returns to the thrower after (g = 10 m/s²)

Question 41 of 50

The maximum value of y = x³ − 3x occurs at x = −1 and equals

Question 42 of 50

Find dy/dx if y = x²eˣ.

Question 43 of 50

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

Question 44 of 50

The gradient of y = ln(2x) at x = 1 is

Question 45 of 50

Find the equation of the tangent to y = x² at (2, 4).

Question 46 of 50

How many diagonals does a polygon with 10 sides have?

Question 47 of 50

A fair die is thrown 3 times. P(at least one six) is

Question 48 of 50

A committee of 3 is chosen from 5 men and 4 women. The number of committees with exactly 2 women is

Question 49 of 50

If P(A) = 0.5, P(B) = 0.4 and A, B are independent, P(A ∪ B) is

Question 50 of 50

A particle moves so that s = t³ − 6t² + 9t. It is momentarily at rest when t =