Core Mathematics — 2003

Simplify \(\left(\frac{3}{4} - \frac{1}{3}\right)\times 4\frac{1}{3}\div 3\frac{1}{4}\)

The table below gives the distribution of marks obtained by a number of pupils in a class test. The mode of the distribution is

The table below gives the distribution of marks obtained by a number of pupils in a class test. Find the median of the distribution

The table below gives the distribution of marks obtained by a number of pupils in a class test. How many pupils scored at least 2 marks?

Interprete the inequality represented on the number line

A student bought 3 notebooks and 1 pen for N35. After misplacing these items, she again bought 2 notebooks and 2 pens, all of the same type for N30. What is the cost of a pen?

Simplify \(\frac{4}{a-3}-\frac{1}{a+2}\)

Simplify \(\frac{4\sqrt{18}}{\sqrt{8}}\)

In the diagram, PQ/RT /RS/ =/QS/, ∠QST= 70 o and ∠PQW = 55 o Find the size of reflex ∠WQS

Three men, Bedu, Bakre and Kofi shared' N500 in the ratio 3:2: x respectively. If Bedu’s share is N150, find the value of x.

Simplify \(\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2\)

Find the value of x which satisfies the equation 5(x-7)=7-2x

Evaluate \(\frac{log8}{log\left(\frac{1}{4}\right)}\)

A pyramid of volume 120cm3 has a rectangular base which measures 5cm by 6cm. Calculate the height of the pyramid

PQRS is a cyclic quadrilateral. If ∠QPS = 75°, what is the size of ∠QRS?

In the diagram, ZM is a straight line. Calculate the value of x.

Find the value of x in the equation 3x\(^2\) - 8x - 3 = 0

In\( ∆ PQR, P\hat{Q}P = 84^°, |Q\hat{P}R |= 43^°\) and |PQ| = 5cm. Find /QR/ in cm, correct to 1 decimal place.

Given, that \(4P4_5 = 119_{10}\), find the value of P

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

What is the size of angle x in the diagram

The four interior angles of a quadrilateral are (x + 20) o , (x+ 10) o (2x - 45) o and (x - 25) o . Find the value of x

Calculate the value of y in the diagram

Out of 60 members of an Association, 15 are Doctors and 9 are Lawyers. If a member is selected at random from the Association, what is the probability that the member is neither a Doctor Nor a Lawyer

Find the values of x for which \( \frac{1}{2x^2 - 13x +15} \) is not defined,

In the diagram, \(P\hat{Q}S = 65^o, R\hat{P}S = 40^o\hspace{1mm}and\hspace{1mm}Q\hat{S}R=20^o\hspace{1mm} Find    P\hat{S}Q\)

Evaluate \((111_{two})^2 - (101_{two})^2\)

Given that x ≅ 0.0102 correct to 3 significant figures, which of the following cannot be the actual value of x?

If \(\frac{3^{(1-n)}}{9^{-2n}}\) = \(\frac{1}{9}\) find n

Which of the following is/are not the interior angle(s) of a regular polygon? I.108° II. 116° III. 120°

In a ∆ XYZ, /YZ/ = 6cm YXZ = 60o and XYZ is a right angle. Calculate /XZ/in cm, leaving your answer in surd form

If \(P = \sqrt{QR\left(1+\frac{3t}{R}\right)}\), make R the subject of the formula.

From the Venn diagram below, how many elements are in P∩Q?

From the Venn Diagram below, find Q' ∩ R.

The square root of a number is 2k. What is half of the number

Given that p varies as the square of q and q varies inversely as the square root of r. How does p vary with r?

The probabilities of a boy passing English and Mathematics test are x and y respectively. Find the probability of the boy failing both tests

The locus of points equidistant from two intersecting straight lines PQ and PR is

Find the equation whose roots are \(-\frac{2}{3}\) and 3

Evaluate Cos 45o Cos 30o - Sin 45o Sin 30o leaving the answer in surd form

In constructing an angle, Olu draws line OX. With centre O and a convenient radius, he draws an arc intersecting OX at P. With centre P and the same radius, he draws an arc intersecting the first arc at Q and finally joins OQ. What is the size of angle POQ so constructed?

In the diagram /PS/ = 9 cm, /OR/ = 5cm, \(P\hat{S}R = 63^o\) and \(S\hat{P}Q = P\hat{Q}R = 90^o\). Find, correct to the nearest whole number, the area of the trapezium,

A right circular cone is such that its radius r is twice its height h. Find its volume in terms of h

A man made a loss of 15% by selling an article for N595. Find the cost price of the article

The bearing of P from Q is x, where 270o < x < 360o. Find the bearing of Q from P

Which of the following is not a measure of dispersion?