Core Mathematics Mock 2015

Question 1 of 50

Find the value of 2³ + 3² − 4⁰.

Question 2 of 50

Approximate 0.06789 to 3 decimal places.

Question 3 of 50

Solve 4x − 7 = 2x + 5.

Question 4 of 50

If y = 3x² − 2, find y when x = −2.

Question 5 of 50

Simplify (3x − 2) − (x − 5).

Question 6 of 50

The perimeter of a square is 36 cm. Find its area.

Question 7 of 50

The volume of a cuboid is 120 cm³. Its length is 6 cm and width 5 cm. Find its height.

Question 8 of 50

The line y = mx + 3 passes through (2, 7). Find m.

Question 9 of 50

Which point lies on the line y = 2x − 1?

Question 10 of 50

If sin θ = 0.5 and θ is acute, find θ.

Question 11 of 50

In a right-angled triangle, the opposite side is 6 and adjacent side is 8. Find tan θ.

Question 12 of 50

Two coins are tossed. What is the probability of two heads?

Question 13 of 50

The frequencies of scores 1, 2, 3, 4 are 2, 3, 4, 1. What is the modal score?

Question 14 of 50

Which of these is an irrational number?

Question 15 of 50

The property shown by a + b = b + a is the

Question 16 of 50

The additive identity is

Question 17 of 50

The multiplicative inverse of 2/5 is

Question 18 of 50

Express 72 as a product of prime factors.

Question 19 of 50

Solve 2x² = 32.

Question 20 of 50

Simplify (a²b)³.

Question 21 of 50

The sum of two numbers is 20 and their difference is 4. Find the larger number.

Question 22 of 50

If 3/(x − 1) = 2, find x.

Question 23 of 50

Find the area of a trapezium whose parallel sides are 6 cm and 10 cm and height 4 cm.

Question 24 of 50

Find the area of a semicircle of radius 7 cm. (Take π = 22/7.)

Question 25 of 50

A water tank holds 2,400 litres. How many cubic metres is this?

Question 26 of 50

Each interior angle of a regular polygon is 108°. How many sides has it?

Question 27 of 50

In a triangle, two angles are 2x and 3x and the third is 80°. Find x.

Question 28 of 50

The angles of a triangle are in the ratio 1 : 2 : 3. What is the largest angle?

Question 29 of 50

Find the y-intercept of the line 4x − 2y = 8.

Question 30 of 50

Find the distance between (0, 0) and (−5, 12).

Question 31 of 50

A kite string 50 m long makes 30° with the ground. How high is the kite?

Question 32 of 50

Find cos 120°.

Question 33 of 50

The marks 2, 5, 5, 6, 7, 9 have a mean of

Question 34 of 50

The median of 11, 14, 9, 20, 16, 13 is

Question 35 of 50

A number is chosen from 1 to 20. What is the probability that it is a multiple of 5?

Question 36 of 50

The area of a rhombus with diagonals 10 cm and 24 cm is

Question 37 of 50

Arrange √2, 1.5, 7/5 in ascending order.

Question 38 of 50

Simplify (2√3 − √2)(2√3 + √2).

Question 39 of 50

Find x if 32ₓ = 23₁₀.

Question 40 of 50

A shape is translated by (3, −2) then by (−1, 5). The single equivalent translation is

Question 41 of 50

A rhombus with diagonals 10 cm and 24 cm has side length

Question 42 of 50

In an ogive, the interquartile range for 80 students is the difference between the

Question 43 of 50

A box has 4 red and 6 green balls. One is drawn, replaced, then another drawn. P(one of each colour) is

Question 44 of 50

Find the value of 1011₂ × 11₂ in base two.

Question 45 of 50

For what values of k does 2x² + kx + 8 = 0 have real roots?

Question 46 of 50

Solve (x − 2)(x + 3) ≥ 0.

Question 47 of 50

A triangle is reflected in the x-axis and then in the y-axis. The combined transformation is equivalent to

Question 48 of 50

The point (2, 3) is enlarged by scale factor 3 with centre (1, 1). Its image is

Question 49 of 50

A pipe fills a tank in 6 hours and another empties it in 9 hours. With both open, the tank fills in

Question 50 of 50

A 20% solution of salt is mixed with a 50% solution to make 60 litres of 30% solution. How many litres of the 20% solution are used?