Core Mathematics Mock 2018

Question 1 of 50

A relation in which every input has exactly one output is a

Question 2 of 50

For f(x) = 3x + 2, find x when f(x) = 17.

Question 3 of 50

The rule for the mapping 1 → 3, 2 → 5, 3 → 7 is

Question 4 of 50

The two shorter sides of a right-angled triangle are 8 cm and 15 cm. Find the hypotenuse.

Question 5 of 50

Find the sum of the interior angles of an octagon.

Question 6 of 50

Vertically opposite angles are

Question 7 of 50

Co-interior (allied) angles between parallel lines add up to

Question 8 of 50

If tan θ = 1 and θ is acute, find θ.

Question 9 of 50

What is the exact value of cos 60°?

Question 10 of 50

Find the area of a circle of diameter 14 cm. (Take π = 22/7.)

Question 11 of 50

Find the circumference of a circle of radius 21 cm. (Take π = 22/7.)

Question 12 of 50

The marks 4, 7, 7, 8, 9, 9, 9, 10 were scored. What is the mode?

Question 13 of 50

The ages 12, 15, 13, 17 and 18 are listed. What is the median?

Question 14 of 50

Data collected by a researcher through his own interviews is

Question 15 of 50

The running total of frequencies in a table is the

Question 16 of 50

In a pie chart, a sector of 72° represents what fraction of the data?

Question 17 of 50

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

Question 18 of 50

A die is thrown twice. What is the probability of getting a 6 both times?

Question 19 of 50

The sum of four consecutive even numbers is 36. What is the smallest?

Question 20 of 50

Two interior angles of a triangle are 50° and 65°. What is the exterior angle at the third vertex?

Question 21 of 50

Which set of sides forms a right-angled triangle?

Question 22 of 50

Find the size of an angle whose supplement is four times the angle.

Question 23 of 50

Each exterior angle of a regular polygon is 24°. How many sides does it have?

Question 24 of 50

A 10 m ladder makes an angle of 60° with the ground. How high up the wall does it reach?

Question 25 of 50

From the top of an 80 m cliff, a boat is seen at an angle of depression of 45°. How far is the boat from the foot of the cliff?

Question 26 of 50

In a right-angled triangle, sin θ = 5/13. Find cos θ.

Question 27 of 50

If a = (3, −2) and b = (−1, 5), find 2a − b.

Question 28 of 50

What is the exact value of tan 60°?

Question 29 of 50

A triangular prism has a cross-section of base 6 cm and height 4 cm and a length of 10 cm. Find its volume.

Question 30 of 50

Find the volume of a cylinder of radius 3 cm and height 7 cm. (Take π = 22/7.)

Question 31 of 50

A rectangular tank is 2 m long, 1.5 m wide and 1 m deep. How many litres does it hold when full?

Question 32 of 50

The area of a rectangle is 48 cm² and its length is 8 cm. Find its perimeter.

Question 33 of 50

In a frequency table, the scores 1, 2, 3 have frequencies 4, 5, 1. What is the mean score?

Question 34 of 50

A coin is tossed and a die is thrown. What is the probability of a tail and an even number?

Question 35 of 50

The probability that it rains on a day is 1/3. What is the probability that it does not rain on two particular days, independently?

Question 36 of 50

The weights of 5 students are 50, 55, x, 62 and 68 kg. If the mean is 58 kg, find x.

Question 37 of 50

A box has 10 bulbs, 3 of which are faulty. If 2 are picked at random, find P(both faulty).

Question 38 of 50

Solve 2/(x − 1) − 3/(x + 1) = 0.

Question 39 of 50

The nth term of a GP is 3 × 2ⁿ⁻¹. Find the sum of the first 6 terms.

Question 40 of 50

The first term of an AP is 4 and the 10th term is 31. Find the sum of the first 10 terms.

Question 41 of 50

Find the largest integer x such that 3(x − 2) < 2x + 4.

Question 42 of 50

If 3^(2x − 1) = 1/27, find x.

Question 43 of 50

Express 1,350 as a product of prime factors.

Question 44 of 50

Given cos A = −0.5 and 180° ≤ A ≤ 270°, find A.

Question 45 of 50

The probability of event E is 0.35. Find the odds in favour of E.

Question 46 of 50

A solid cylinder of radius 3 cm and height 8 cm is melted and recast into spheres of radius 1 cm. How many spheres are made?

Question 47 of 50

R varies directly as S and inversely as √T. If R = 6 when S = 3 and T = 16, find R when S = 5 and T = 25.

Question 48 of 50

Make x the subject of y = (2x + 1)/(x − 3).

Question 49 of 50

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

Question 50 of 50

Find the value of (0.04)^(−3/2).