Core Mathematics — 2008

If x% of 240 equals 12, find x

Evaluate \(\frac{(3.2)^2 - (4.8)^2}{3.2 + 4.8}\)

Simplify \(\sqrt{50} + \frac{10}{\sqrt{2}}\)

P naira invested for 4 years invested for 4 years at r% simple interest per annum yields 0.36 p naira interest. Find the value of r

A trader bought 100 tubers at 5 for N350.00. She sold them in sets of 4 for N290.00. Find her gain percent.

If p-2g + 1 = g + 3p and p - 2 = 0, find g

Simplify \(\frac{\frac{1}{x} + \frac{1}{y}}{x + y}\)

Simplify 3\(\sqrt{27x^3y^9}\)

Given that x = 2 and y = -\(\frac{1}{4}\), evaluate \(\frac{x^2y - 2xy}{5}\)

Factorize 5y2 + 2ay - 3a2

If 4y is 9 greater than the sum of y and 3x, by how much is y greater than x?

If p = \(\frac{3}{5} \sqrt{\frac{q}{r}}\), express q in terms of p and r

Simplify: \(\frac{2x^2 - 5x - 12}{4x^2 - 9}\)

PQR is a sector of a circle centre O, radius 4cm. If PQR = 30 o , find, correct to 3 significant figures, the area of sector PQR. [Take \(\pi = \frac{22}{7}\)]

If the volume of a cube is 343cm 3 , find the length of its side

The angles of a quadrilateral are (x + 10) o , 2y o , 90 o and (100 - y) o , Find y in terms of x

If x o is obtuse, which of the following is true?

If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form

If cos (x + 25) o = sin 45 o , find the value of x

If \(2^n = 128\), find the value of \(2^{n - 1})(5^{n - 2})\)

If x \(\alpha\) (45 + \(\frac{1}{2}y\)), which of the following is true>?

Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\)

A train travels 60km in M minutes. If its average speed is 400km per hour, find the value of M

An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree, the angle which the arc subtends at the centre of the circle. [T = \(\frac{22}{7}\)]

What is the length of an edge of a cube whose total surface area is X cm\(^2\) and whose volume is \(\frac{X}{2}\)cm\(^3\)?

XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120 o at the centre of the circle. Calculate the perimeter of the minor segment. [Take \(\pi = \frac{22}{7}\)]

If p = \(\frac{1}{2}\) and \(\frac{1}{p - 1} = \frac{2}{p + x}\), find the value of x

Find the quadratic equation whose roots are c and -c

Solve the inequality 1 - 2x < - \(\frac{1}{3}\)

Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is selected at random from set B, what is the probability that the number is prime?

Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is picked at random from each of the two sets, what is the probability that their product is odd?

Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is picked at random from each of the two sets, what is the probability that their difference is 6 or 7?

Find the mean deviation of these numbers 10, 12, 14, 15, 17, 19.

In the diagram, < QPR = 90 o . If q 2 = 25 - r 2 . Find the value of p

In the diagram, /PQ/ = /QR/ and /PR/ = /RS/ = /SP/, calculate the side of < QRS

In the diagram above, PQRS is a rhombus. /PR/ = 10cm and /QS/ = 24cm. Calculate the perimeter of the rhombus.

In the figure shown, PQs is a straight line. What is the value of < PRQ?

In the diagram, PQ//RS, QU//PT, and < PSR = 42º. Find angle x.

In the figure /PX/ = /XQ/, PQ//YZ and XV//QR. What is the ratio of the area of XYZQ to the area of \(\bigtriangleup\)YZR?

In the diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral. Find the value of x.

If the perimeter of \(\bigtriangleup\)PQR in thr diagram is 24cm, what is the area of \(\bigtriangleup\)PRS?

In the diagram, PX is a tangent to the circle and RST is an equilateral triangle. Calculate < PTS

In the diagram, < QPR = 60 o < PQR = 50 o < QRS = 2x o < SRP = 3x o < UQP = y o and RS//TU calculate y

In the diagram, find the size of the angle marked a°

Every staff in an office owns either a Mercedes and/or a Toyota car. 20 own Mercedes, 15 own Toyota and 5 own both. How many staff are there in the office?