Core Mathematics Mock 2017

Question 1 of 50

Evaluate (2√3)².

Question 2 of 50

Solve x² − 9 = 0.

Question 3 of 50

Enlarge (3, −1) by scale factor 2 about the origin.

Question 4 of 50

Reflect (−3, 4) in the y-axis.

Question 5 of 50

A transformation that keeps the shape and size but changes position without turning is a

Question 6 of 50

A car travels 150 km in 2½ hours. What is its average speed?

Question 7 of 50

If 3 kg of rice cost GH¢54, how much do 5 kg cost?

Question 8 of 50

The ratio of boys to girls in a class is 3 : 5. There are 40 pupils. How many are girls?

Question 9 of 50

Find the sum 2 + 6 + 18 + 54.

Question 10 of 50

Which sequence is geometric?

Question 11 of 50

A spinner lands on red 30 times in 120 spins. What is the relative frequency of red?

Question 12 of 50

A ship sails 6 km due east, then 8 km due north. How far is it from its start?

Question 13 of 50

What is the bearing of due west?

Question 14 of 50

Simplify √12 + √27.

Question 15 of 50

Which of these is a rational number?

Question 16 of 50

Solve 2x + y = 7 and x − y = 2.

Question 17 of 50

Solve x² + 2x − 15 = 0.

Question 18 of 50

Solve (x − 1)/3 = (x + 3)/5.

Question 19 of 50

Reflect the point (2, 5) in the line y = x.

Question 20 of 50

Rotate (4, −3) through 180° about the origin.

Question 21 of 50

Increase GH¢40 in the ratio 5 : 4.

Question 22 of 50

Convert 72 km/h to metres per second.

Question 23 of 50

Find the 20th term of the sequence 5, 8, 11, …

Question 24 of 50

Find the 8th term of the geometric sequence 3, 6, 12, …

Question 25 of 50

The 3rd term of an arithmetic sequence is 10 and the 7th term is 22. Find the common difference.

Question 26 of 50

Find the volume of a pyramid with a square base of side 6 cm and height 10 cm.

Question 27 of 50

A cone has base radius 6 cm and height 8 cm. Find its slant height.

Question 28 of 50

Find the curved surface area of a cone with radius 6 cm and slant height 10 cm, in terms of π.

Question 29 of 50

A cube has a volume of 64 cm³. Find its total surface area.

Question 30 of 50

Which average is most affected by an extreme value?

Question 31 of 50

B is 5 km north and 5 km east of A. What is the bearing of B from A?

Question 32 of 50

Find the sum of the roots of 3x² − 6x + 1 = 0.

Question 33 of 50

Solve x² = 5x.

Question 34 of 50

Two tangents are drawn to a circle from an external point. The two tangent lengths are

Question 35 of 50

To bisect an angle with ruler and compasses, you draw arcs from the vertex and then

Question 36 of 50

Find two consecutive odd numbers whose product is 143.

Question 37 of 50

If 2x + 3y = 12 and x − y = 1, find x + y.

Question 38 of 50

A cuboid tank 2 m × 1.5 m × 1 m is half full. How many litres must be added to fill it?

Question 39 of 50

A cone and a cylinder have the same base and height. The ratio of their volumes is

Question 40 of 50

Two angles of a triangle are in the ratio 2 : 3 and the third is 80°. The largest of the other two angles is

Question 41 of 50

Simplify log₃ 81 − log₂ 0.25.

Question 42 of 50

Evaluate (101₂)² in base two.

Question 43 of 50

Solve x² − 4x − 1 = 0, correct to 2 decimal places.

Question 44 of 50

The expression ax² + bx + c has a factor (x − 1) when

Question 45 of 50

Simplify (x³ − 8)/(x − 2).

Question 46 of 50

A wire 88 cm long is bent into a circle. The area enclosed is (π = 22/7)

Question 47 of 50

Find the coordinates of the point dividing (2, 3) and (8, 9) internally in the ratio 1 : 2.

Question 48 of 50

The line kx + 2y = 5 is perpendicular to 2x − y = 3. Find k.

Question 49 of 50

If sin θ = 0.6 and 90° < θ < 180°, find tan θ.

Question 50 of 50

From a point on level ground, the angle of elevation of a tower is 30°. Moving 20 m closer, it becomes 60°. The height of the tower is (√3 ≈ 1.732)