Core Mathematics — 2022

Evaluate, correct to four significant figures, 573.06 × 184.25.

Change 432five to a number in base three.

Given that A and B are sets such that n(A) = 8, n(B) = 12 and n(A ∩ B) = 3, find n(A ∪ B).

If √24 + √96 − √600 = y√6, find the value of y.

Evaluate 23 × 54(mod7).

If 43x = 16x+1, find the value of x.

A weaver bought a bundle of grass for $50.00 from which he made 8 mats. If each mat was sold for $15.00, find the percentage profit.

Find the 17th term of the arithmetic progression, given that first three terms are −6, −1, 4.

M varies directly as n and inversely as the square of p. If M = 3 when n = 2 and p = 1, find M in terms of n and p.

If a = 3 and b = −7, find the value of 5b+(a+b)2 (a−b)2 .

Three boys shared D 10, 500.00 in the ratio 6 : 7 : 8. Find the largest share.

The length of a piece of stick is 1.75 m. A boy measured it as 1.80 m. Find the percentage error.

If 5x + 3y = 4 and 5x − 3y = 2, what is the value of (25x2 − 9y2)?

Mary has $3.00 more than Ben but $5.00 less than Jane. If Mary has $x, how much does Jane and Ben have altogether?

Consider the statements: p: Stephen is intelligent q : Stephen is good at Mathematics If p ⇒ q, which of the following is a valid conclusion?

What value of p will make (x2 − 4x + p) a perfect square?

Find the value of x such that 1 x + 4 3x − 5 6x + 1 = 0.

Make t the subject of k = m √ t−p r .

An exterior angle of a regular polygon is 22.5◦. Find the number of sides.

In the diagram, ∠P OQ = 150◦ and the radius of the circle P SQR is 4.2 cm. What is the length of the minor arc? [Take π = 22 7 ]

Find the area of the sector OPSQ.

A ladder 6 m long leans against a vertical wall at an angle 53◦ to the horizontal. How high up the wall does the ladder reach?

A cylinder, opened at one end, has a radius of 3.5 cm and height 8 cm. Calculate the total surface area.

In the diagram below ∠W ZY and ∠W Y X are right angles. Find the perimeter of W XY Z.

The length of a rectangle is 10 cm. If its perimeter is 28 cm, find the area.

A boy 1.4 m tall, stood 10 m away from a tree of height 12 m. Calculate, correct to the nearest degree, the angle of elevation of the top of the tree from the boy’s eyes.

Given that sin(5x − 28)◦ = cos(3x − 50)′′, 0◦ ≤ x ≤ 90◦, find the value of x.

In the diagram, M N R is a tangent to the circle at N and ∠N OS = 108◦. Find ∠OSN .

Mrs Gabriel is pregnant. The probability that she will give birth to a girl is 1 2 and with blue eyes is 1 4 . What is the probability that she will give birth to a girl with blue eyes?

The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find the 10th number.

Simplify 2−18m2 1+3m .

In the diagram, triangle M N R is inscribed in the circle, and line P Q is a straight line; ∠M RN = 41◦ and ∠RM P = 141◦, find ∠QN R.

Solve y+2 4 − y−1 3 > 1.

The age in years of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36. Find the lower quartile.

The age in years of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36. Find the mean.

Find, correct to two decimal places, the volume of a sphere whose radius is 3 cm. [Take π = 22 7 ]

The lengths of the parallel sides of a trapezium are 9 cm and 12 cm. If the area of the trapezium is 105 cm2, find the perpendicular distance between the parallel sides.

Find the volume of a cone of radius 3.5 cm and vertical height 12 cm. [Take pi = 22 7 ]

A local community has two newspapers: the morning tomes and the evening dispatch. The morning times is read by 45% of the households. The Evening Dispatch is read by 60% of the households. Twenty percent of the households read both papers. What is the probability that a particular household reads at least one paper?

A rectangle with width 3 4 cm and area 3 3 8 cm2. Find the length of the rectangle.

The mean of two numbers x and y is 4. Find the mean of four numbers x, 2x, y and 2y.

The straight line y = mx − 4 passes through the point (−4, 16). Calculate the gradient of the line.

If the equations x2 − 5x + 6 = 0 and x2 + px + 6 = 0 have the same roots, find the value of p.

A trader made a loss of 15% when an article was sold. Find the ratio (selling price):(cost price).

Given that log3 27 = 2x + 1, find the value of x.

Solve 6x2 = 5x − 1.