Core Mathematics Mock 2024

Question 1 of 50

Find the value of tan 45°.

Question 2 of 50

Find the range of 12, 7, 15, 3 and 9.

Question 3 of 50

A fair die is thrown once. What is the probability of getting a number greater than 4?

Question 4 of 50

The statement (4 + 9) + 6 = 4 + (9 + 6) shows the

Question 5 of 50

Using the distributive property, 8 × 43 = 8 × 40 + 8 × 3 =

Question 6 of 50

Write 0.85 as a fraction in its lowest terms.

Question 7 of 50

Express 7/8 as a percentage.

Question 8 of 50

Write 0.36 as a fraction in its lowest terms.

Question 9 of 50

Find the mean of the distribution: x = 1, 2, 3 with frequencies 2, 3, 5.

Question 10 of 50

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

Question 11 of 50

Which of these numbers is irrational?

Question 12 of 50

The recurring decimal 0.333… is best described as

Question 13 of 50

A choir has 48 members and 5/8 of them are female. How many members are male?

Question 14 of 50

A phone priced GH¢1,200 is reduced by 15%. What is the sale price?

Question 15 of 50

Expand (x + 6)(x − 2).

Question 16 of 50

Find the length of an arc that subtends 60° at the centre of a circle of radius 21 cm. (Take π = 22/7.)

Question 17 of 50

Two similar triangles have corresponding sides 3 cm and 9 cm. What is the ratio of their areas?

Question 18 of 50

Find the gradient of a line perpendicular to the line joining (1, 2) and (3, 6).

Question 19 of 50

If cos θ = 0.6 and θ is acute, find tan θ.

Question 20 of 50

A pole casts a shadow 12 m long when the sun's elevation is 30°. How tall is the pole?

Question 21 of 50

A trader sold a radio for GH¢360 at a loss of 10%. What was the cost price?

Question 22 of 50

Factorise 2x² + 5x − 3.

Question 23 of 50

Simplify 3/(x + 1) − 2/x.

Question 24 of 50

A square has a diagonal of 10 cm. Find the length of its side.

Question 25 of 50

Find the area of a sector of angle 90° in a circle of radius 14 cm. (Take π = 22/7.)

Question 26 of 50

A card is drawn from a pack of 52, replaced, and a second card drawn. What is the probability that both are aces?

Question 27 of 50

Rationalise 1/(√5 − √3).

Question 28 of 50

Find the value of x if 23ₓ = 13 (base ten).

Question 29 of 50

Complete the square: x² + 6x = (x + 3)² − k. Find k.

Question 30 of 50

Five pens and two books cost GH¢41; one pen and one book cost GH¢13. What does a book cost?

Question 31 of 50

Find the total surface area of a closed cylinder of radius 7 cm and height 10 cm. (Take π = 22/7.)

Question 32 of 50

For the ordered data 2, 4, 5, 7, 8, 10, 12, find the interquartile range.

Question 33 of 50

The mean of 6 numbers is 15. One number, 20, is removed. What is the mean of the rest?

Question 34 of 50

x varies inversely as the square of y, and x = 4 when y = 3. Find x when y = 2.

Question 35 of 50

y = a + bx. When x = 1, y = 5, and when x = 3, y = 9. Find y when x = 5.

Question 36 of 50

Two dice are thrown. Find the probability that the sum is greater than 9.

Question 37 of 50

The operation * is defined on real numbers by a * b = a + b − 3ab. Find 2 * (−1).

Question 38 of 50

If p * q = p² − q, find (2 * 3) * 4.

Question 39 of 50

A trader marks an item 40% above cost and then gives a 10% discount. His percentage profit is

Question 40 of 50

After a 20% increase, a price is GH¢360. The original price was

Question 41 of 50

A man spends 1/4 of his salary on rent and 2/3 of the rest on food. What fraction is left?

Question 42 of 50

Express 0.272727... (recurring) as a fraction in its lowest terms.

Question 43 of 50

Factorise 2x² + 5x − 12.

Question 44 of 50

Simplify (a² − b²)/(a² + ab).

Question 45 of 50

If a + b = 7 and ab = 10, find a² + b².

Question 46 of 50

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

Question 47 of 50

A function f is defined by f(x) = (x + 3)/(x − 2). Find the value of x for which f(x) = 2.

Question 48 of 50

In a frequency table, scores 1, 2, 3, 4 have frequencies 3, 5, x, 2 and the mean is 2.4. Find x.

Question 49 of 50

Which property does the operation a ⊕ b = a + b + 1 satisfy?

Question 50 of 50

Find the inverse of f(x) = (3x − 2)/5.