Core Mathematics Mock 2023

Question 1 of 50

If f(x) = 4x − 3, find f(−2).

Question 2 of 50

What is the gradient of the line y = −3x + 7?

Question 3 of 50

When a transversal cuts two parallel lines, alternate angles are

Question 4 of 50

What is the exact value of sin 30°?

Question 5 of 50

Factorise x² − 7x + 12.

Question 6 of 50

What is the nth term of the sequence 4, 7, 10, 13, …?

Question 7 of 50

Solve 5(y − 2) = 3y + 4.

Question 8 of 50

Solve the inequality 3x − 5 > 7.

Question 9 of 50

What is the sum of the interior angles of a hexagon?

Question 10 of 50

A ladder 13 m long reaches 12 m up a wall. How far is its foot from the wall?

Question 11 of 50

Find the magnitude of the vector (6, −8).

Question 12 of 50

A vector starts at (1, 2) and ends at (4, 6). How long is it?

Question 13 of 50

In a right-angled triangle, the side opposite θ is 3 and the hypotenuse is 5. What is cos θ?

Question 14 of 50

From a point 50 m from the foot of a tower on level ground, the angle of elevation of the top is 45°. How tall is the tower?

Question 15 of 50

Find the area of a trapezium with parallel sides of 8 cm and 12 cm and a height of 5 cm.

Question 16 of 50

A statement that is always true, whatever the truth values of its parts, is a

Question 17 of 50

What is the converse of "If x = 2, then x² = 4"?

Question 18 of 50

The cost of a party varies partly as the number of guests. With 20 guests it costs GH¢700 and with 30 guests GH¢900. What is the fixed part of the cost?

Question 19 of 50

Form a quadratic equation whose roots are 2 and −3.

Question 20 of 50

For which value of k does x² + kx + 9 = 0 have equal roots (k > 0)?

Question 21 of 50

The angle between a tangent and a chord at the point of contact equals

Question 22 of 50

A chord of length 16 cm is in a circle of radius 10 cm. How far is the chord from the centre?

Question 23 of 50

What is the period of y = sin 2x?

Question 24 of 50

What is the minimum value of y = 3 + sin x?

Question 25 of 50

By De Morgan's law, (A ∪ B)′ is equal to

Question 26 of 50

Which set of numbers is NOT closed under subtraction?

Question 27 of 50

Find the compound interest on GH¢2,000 for 2 years at 5% per annum.

Question 28 of 50

A phone bought for GH¢2,000 loses 10% of its value each year. What is it worth after 2 years?

Question 29 of 50

Solve −3 < 2x + 1 ≤ 7.

Question 30 of 50

Make h the subject of V = (1/3)πr²h.

Question 31 of 50

Convert 1010 (base two) to base five.

Question 32 of 50

If log 2 = 0.3010, find log 8.

Question 33 of 50

Factorise ab + ac − 2b − 2c.

Question 34 of 50

Find the value of k if x = 2 is a root of x² + kx − 10 = 0.

Question 35 of 50

A cylinder has a volume of 308 cm³ and radius 7 cm. Find its height. (Take π = 22/7.)

Question 36 of 50

The interior angles of a pentagon are x, 2x, 3x, 4x and 5x. Find x.

Question 37 of 50

A rectangle has a diagonal of 25 cm and width 7 cm. Find its perimeter.

Question 38 of 50

If OA = (3, 4) and OB = (7, 1), find |AB|.

Question 39 of 50

If tan θ = 8/15 and θ is acute, find sin θ + cos θ.

Question 40 of 50

The vectors (2, k) and (6, 9) are parallel. Find k.

Question 41 of 50

The mean of a grouped distribution uses the

Question 42 of 50

A fair coin is tossed three times. The probability of exactly two heads is

Question 43 of 50

P(A) = 1/3, P(B) = 1/4, independent. Find P(neither A nor B).

Question 44 of 50

Find the base y if 23 in base y equals 17 in base ten.

Question 45 of 50

Simplify (√18 + √8)/√2.

Question 46 of 50

Each interior angle of a regular polygon exceeds its exterior angle by 132°. How many sides has it?

Question 47 of 50

A circular path 2 m wide surrounds a circular pond of radius 10 m. The area of the path is (π = 22/7)

Question 48 of 50

The radius of a cylinder is doubled and its height halved. Its volume becomes

Question 49 of 50

A histogram with unequal class widths should plot

Question 50 of 50

Express 3/(2 + √3) in the form a + b√3.