Core Mathematics — 2004

1. Evaluate \( 202^2_{three} - 112^2_{three}\)

If \(y = 23_{five} + 101_{three}\), find y, leaving your answer in base two

Given that sin (5x - 28) o = cos (3x - 50) o ,0 < x < 90 o , find the value of x

Solve for t in the equation \(\frac{3}{4}t+\frac{1}{3}(21-t)\) = 11,

A school girl spends \(\frac{1}{4}\) of her pocket money on books and \(\frac{1}{3}\) on dress. What fraction remains?

In the diagram, R\(\hat{P}\)Q = Q\(\hat{R}\)Y, P\(\hat{Q}\)R = R\(\hat{Y}\)Q, |QP| = 8 cm, |QY| = 4 cm, and |RY| = 5 cm. Find |QR|.

Find the value of x in the diagram

There are m boys and 12 girls in a class. What is the probability of selecting at random a girl from the class?

Simplify \(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2}\)and correct your answer to the nearest whole number

The angle of elevation of the top of a tower from a point on the ground which is 36m away from the foot of the tower is 30 o . Calculate the height of the tower.

Find the area of a rectangle of length 4cm and whose diagonal is 8cm, (Leave your answer in surd form)

Given that x + y = 7 and 3x-y = 5, evaluate \(\frac{y}{2}-3\).

In the diagram, POQ is the diameter of the circle centre O. Calculate ∠QRS

If \(\left(\frac{1}{4}\right)^{(2-y)} = 1\), find y.

Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm

If \(\frac{x}{a+1}+\frac{y}{b}\) 1. Make y the subject of the relation

lf \(log_q p= r\), express p in terms of q and r

Find the next two terms of the sequence 1, 5, 14, 30, 55, ...

Each interior angle of a regular polygon is 108°. How many sides has it?

Solve the equation 10-3x-x 2 = 0

Find, correct to two decimal places, the mean of 9, 13, 16, 17, 19, 23, 24.

In the diagram, ∆XYZ is similar to ∆PRQ, |XY| = 5cm, |XZ| =3.5cm and |PR| = 8cm. Find |PQ|

Factorise 27p 2 x 2 - 48y 2 .

What is the volume of a solid cylinder of diameter 7cm and height 7cm? (Take \(\pi = \frac{22}{7}\))

Find the sum of the roots of the equation 2x 2 + 3x - 9 = 0

Given that ξ = {1, 2, 3, . . . . . . ,10}, P= (x : x is prime) and Q = {y : y is odd}, find P'∩Q

In the diagram, KS is a tangent to the circle centre O at R and ∠ROQ = 80º. Find ∠QRS.

Find the mean deviation of 6, 7, 8, 9, 10

A point X is on the bearing 342 o from a point Y. What is the bearing of Y from X?

In the diagram, O is the centre of the circle where OS//QR and ∠SOR = 35º. Find the value of  ∠QPR.

Find the average of the first four prime numbers greater than10

Given that \(\sqrt{128}+\sqrt{18}-\sqrt{K} = 7\sqrt{2}\), find K,

In the diagram, PQRW is a circle. Line PW and QR are produced to meet at M, where ∠WMR = 30o and |WM| = |MR| Find the value of x

The table above gives the marks scored by a group of students in a test. Use the table to answer the Question below What is the median mark?

The table above gives the marks scored by a group of students in a test Use the table to answer the Question below What is the probability of selecting a student from the group that scored 2 or 3?

Find the range of values of x for which\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\)

A boy walks 800m in 20 minutes. Calculate his average speed in km per hour

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

The diagram is a circle centre O. Find the value of x

Use the graph to answer the Question below What are the roots of the equation x 2 + 3x - 4 = 0?

The values of x when y = 3 are approximately

Which of the following quadratic equations has \(-\frac{1}{2}\) and \(\frac{3}{4}\) as its roots?

The locus of a point which moves in a plane such that it is equidistant from two fixed points X and Y is

Given that \(P\propto \frac{1}{\sqrt{r}}\) and p = 3 when r = 16, find the value of r when p = \(\frac{3}{2}\)

Which of the following is/are true? In a plane, the locus of points I. Equidistant from a straight line is a circle radius d where d is the distance between the point and the straight line. II Equidistant from two given points P and Q is a circle of radius |PQ|. III Equidistant from two points is the perpendicular bisector of the line joining the two points.

The sides of two cubes are in the ratio 2:5. What is the ratio of their volumes?

Given that p = 2, q = -5 and r = - 4, evaluate 3p 2 - q 2 - r 3

A Cooperative Society charges an interest of 5\(\frac{1}{2}\)% per annum on any amount borrowed by its members. If a member borrows N125,000, how much does he pay back after one year?

A bag contains 3 red and 2 white identical balls. lf 2 balls are picked at random from the bag, one after the other and with replacement, find the probability that they are of different colours

A point on the ground is 5m away from the foot of a vertical wall 7 m high, Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall