Elective Mathematics Mock 2018

Question 1 of 50

If y = x³, find the rate of change of y when x = 2.

Question 2 of 50

Events A and B are independent with P(A) = 0.5 and P(B) = 0.4. P(A and B) is

Question 3 of 50

Mutually exclusive events cannot

Question 4 of 50

If P(A) = 0.6, P(B) = 0.3 and A and B are mutually exclusive, find P(A or B).

Question 5 of 50

The probability of an impossible event is

Question 6 of 50

The negation of "It is raining" is

Question 7 of 50

p ∧ q is true only when

Question 8 of 50

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

Question 9 of 50

A matrix has no inverse if its determinant is

Question 10 of 50

Using the sine rule, a/sin A =

Question 11 of 50

∫ 4x³ dx =

Question 12 of 50

A normal distribution curve is

Question 13 of 50

The sum of all probabilities in a probability distribution is

Question 14 of 50

Solve log₃ (x + 1) = 2.

Question 15 of 50

P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2. Find P(A ∪ B).

Question 16 of 50

p → q is false only when

Question 17 of 50

The contrapositive of p → q is

Question 18 of 50

A statement that is always true is a

Question 19 of 50

Find x if [[x, 2], [3, 4]] is singular.

Question 20 of 50

The determinant of [[1, 0, 0], [0, 2, 0], [0, 0, 3]] is

Question 21 of 50

The vertex of y = (x − 3)² + 2 is

Question 22 of 50

The axis of symmetry of y = x² − 6x + 1 is

Question 23 of 50

Solve sin x = 0.5 for 0° ≤ x ≤ 360°.

Question 24 of 50

The area of a triangle with sides 6 and 8 and included angle 30° is

Question 25 of 50

∫ cos x dx =

Question 26 of 50

Evaluate ∫₁³ 2x dx.

Question 27 of 50

∫ (1/x) dx =

Question 28 of 50

The area under y = x² from x = 0 to x = 3 is

Question 29 of 50

If the velocity is v = 6t, the displacement from t = 0 to t = 2 is

Question 30 of 50

In a normal distribution, about 68% of values lie within

Question 31 of 50

If X ~ N(50, 25), the standard deviation of X is

Question 32 of 50

The z-score of a value 60 when μ = 50 and σ = 5 is

Question 33 of 50

For a binomial distribution B(n, p), the mean is

Question 34 of 50

For X ~ B(10, 0.3), the variance is

Question 35 of 50

If f(x) = 3x − 2 and g(x) = x², find g(f(1)).

Question 36 of 50

The determinant of [[3, 2], [5, 4]] is

Question 37 of 50

If a = 3i + 4j, |a| is

Question 38 of 50

If α and β are roots of 2x² − 3x − 5 = 0, find 1/α + 1/β.

Question 39 of 50

Find the range of f(x) = x² + 4x + 7.

Question 40 of 50

Express 3/((x − 1)(x + 2)) in partial fractions.

Question 41 of 50

The inverse of f(x) = (2x + 1)/(x − 3), x ≠ 3, is

Question 42 of 50

The sum of the coefficients in the expansion of (2x − 1)⁵ is

Question 43 of 50

The coefficient of x² in (1 + 2x)⁵ is

Question 44 of 50

The dot product of (2i + 3j) and (4i − j) is

Question 45 of 50

The equation of the line with intercepts 3 on the x-axis and −2 on the y-axis is

Question 46 of 50

If tan A = 3/4 (A acute), find sin 2A.

Question 47 of 50

Solve 2 sin x = 1 for 0° ≤ x ≤ 360°.

Question 48 of 50

The centre and radius of x² + y² − 4x + 6y − 3 = 0 are

Question 49 of 50

cos 75° expressed exactly is

Question 50 of 50

The perpendicular distance from (1, 2) to the line 3x + 4y − 1 = 0 is