Core Mathematics Mock 2019

Question 1 of 50

Express 0.000 62 in standard form.

Question 2 of 50

Simplify (3x²y)(4xy³).

Question 3 of 50

Factorise 6ab − 9b.

Question 4 of 50

If f(x) = x² − 3x, find f(−2).

Question 5 of 50

A parallelogram has one angle of 70°. What is the angle next to it?

Question 6 of 50

Find the midpoint of (−4, 6) and (8, −2).

Question 7 of 50

What is the equation of the y-axis?

Question 8 of 50

The range of a set of numbers is 15 and the smallest is 8. What is the largest?

Question 9 of 50

A bag holds 5 red, 3 green and 2 blue balls. What is the probability of picking a ball that is not green?

Question 10 of 50

Express 3/8 as a decimal.

Question 11 of 50

What percentage of 80 is 12?

Question 12 of 50

Factorise x² + 7x + 12.

Question 13 of 50

Find the next term and rule: 1, 4, 9, 16, …

Question 14 of 50

Convert 45 (base ten) to base two.

Question 15 of 50

Evaluate 5⁰ + 2⁻¹.

Question 16 of 50

Correct 0.04582 to two significant figures.

Question 17 of 50

Factorise 4x² − 25.

Question 18 of 50

Simplify (x² − 4)/(x − 2).

Question 19 of 50

Solve 3(2x − 1) = 2(x + 5).

Question 20 of 50

Expand (2x − 3)².

Question 21 of 50

A rectangular field is 120 m long and 80 m wide. How many hectares is it? (1 ha = 10,000 m²)

Question 22 of 50

How many cubes of side 2 cm fit exactly into a box 10 cm × 6 cm × 4 cm?

Question 23 of 50

The radius of a circle is doubled. Its area is multiplied by

Question 24 of 50

Find the total surface area of a cuboid 5 cm × 4 cm × 3 cm.

Question 25 of 50

In triangle PQR, PQ = PR and angle P = 40°. Find angle Q.

Question 26 of 50

The angles of a quadrilateral are x, 2x, 3x and 4x. Find x.

Question 27 of 50

The diagonals of a rhombus

Question 28 of 50

Find the gradient of the line joining (−2, 3) and (4, −9).

Question 29 of 50

Find the value of sin 150°.

Question 30 of 50

In which quadrant are both sine and cosine negative?

Question 31 of 50

The mean of 3, x, 7 and 10 is 6. Find x.

Question 32 of 50

In a histogram with equal class widths, the height of each bar represents the

Question 33 of 50

Work out 2⅓ − 1¾.

Question 34 of 50

A school's population rose from 800 to 920. Find the percentage increase.

Question 35 of 50

Arrange 2/3, 3/5 and 5/8 in ascending order.

Question 36 of 50

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

Question 37 of 50

A cylinder of radius 7 cm is filled with water to a depth of 10 cm. A stone is dropped in and the water rises 2 cm. The volume of the stone is (π = 22/7)

Question 38 of 50

The perimeter of a semicircle of radius 7 cm (including the diameter) is (π = 22/7)

Question 39 of 50

ABCD is a parallelogram with ∠A = 3x + 10 and ∠B = 2x + 20. Find x.

Question 40 of 50

The sum of the interior angles of a polygon is 1,440°. How many sides has it?

Question 41 of 50

Triangles ABC and PQR are similar with AB = 6, PQ = 9 and BC = 8. Find QR.

Question 42 of 50

The line through (k, 3) and (5, 7) has gradient 2. Find k.

Question 43 of 50

Find the equation of the line through (−1, 4) parallel to 2x − y + 3 = 0.

Question 44 of 50

The vertices of a triangle are (1, 1), (5, 1) and (3, 5). Its area is

Question 45 of 50

A pole 9 m high casts a shadow 9√3 m long. The angle of elevation of the sun is

Question 46 of 50

Find the minimum value of 2x² − 8x + 11.

Question 47 of 50

The roots of x² + bx + c = 0 are 3 and −5. Find b + c.

Question 48 of 50

The ratio of the volumes of two spheres is 8 : 27. The ratio of their surface areas is

Question 49 of 50

A frustum is cut from a cone of height 12 cm by a plane 6 cm from the apex. The ratio of the small cone's volume to the original cone is

Question 50 of 50

A man 1.8 m tall stands 20 m from a building and sees its top at an elevation of 40°. Find the height of the building (tan 40° ≈ 0.839).