Core Mathematics — 2005

Correct 0.04945 to two significant figures

Simplify \(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}\)

Evaluate, correct to the nearest whole number \(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div\frac{33}{2}\)

Simplify the expression \(log_{10}18 - log_{10}2.88+log_{10}16\)

Find the equation whose roots are 2 and \(-3\frac{1}{2}\)

A man bought 220 mangoes at N5x. He sold each for 3x kobo and made a gain of N8. Find the value of x

From a point P, R is 5km due west and 12km due south. Find the distance between P and R

A fair die is tossed once, what is the probability of obtaining neither 5 or 2

In the diagram, KL//MN, ∠LKP = 30 o and ∠NMP = 45 o . Find the size of the reflex ∠KPM.

In the diagram, PR is a diameter, ∠PRQ = (3x-8) o and ∠RPQ = (2y-7) o . s x in terms of y

Convert 101101 two to a number in base ten

Solve the equation 2\(^7\) = 8\(^{5-x}\)

expand (2x-3y)(x-5y)

Make f the subject of the relation \(v = u + ft\)

The lengths of the adjacent sides of a right - angled triangle are xcm, (x-1)cm. If the length of the hypotenuse is \(\sqrt{13}cm\), find the value of x

The probability that John and James pass an examination are 3/4 and 3/5 respectively, find the probability of both boys failing the examination

In the diagram PQ and MN are straight lines. Find the value of x

In the diagram, PQRS is a parallelogram and ∠QRT = 30 o . Find x

From a point R, 300m north of P, man walks eastward to a place Q which is 600m from P. Find the bearing of P from Q, correct to the nearest degreeee

What is the diameter of a circle of area 77cm 2 [Take \(\pi = \frac{22}{7}\)]

Solve the equation 2x - 3y = 22; 3x + 2y = 7

Solve the equation \(\frac{2y-1}{3} - \frac{3y-1}{4} = 1\)

If \(log_9x= 1.5\),find x

A sequence is given by \(2\frac{1}{2}, 5, 7\frac{1}{2}, .....\) if the nth term is 25, find n

Given that the root of an the equation \(2x^2 + (k+2)x+k=0\) is 2, find the value of k

Find the mean of the numbers 1, 3, 4, 8, 8, 4 and 7

What is the total surface area of a closed cylinder of height 10cm and diameter 7cm? [Take \(\pi = \frac{22}{7}\)]

An arc of a circle of radius 14cm subtends angle 300 o at the center. Find the perimeter of the sector formed by the arc

which of the following statements describes the locus of a point R which moves in a plane such that its equidistant from two intersecting lines?

P = {3, 9, 11, 13} and Q = {3, 7, 9, 15} are subset of the universal set ξ = {1, 3, 7, 9, 11, 13, 15} find P I ∩ Q I

A train moving at a uniform speed covers 36km in 21 minutes. How long does it take to cover 60km?

The salary of a man was increased in the ratio 40:47. calculate the percentage increase in the salary

A regular polygon has 9 sides. What is the size of one of its exterior angles?

Simplify: \(\frac{2}{3xy} - \frac{3}{4yz}\)

The total surface area of the walls of a room 7m long, 5m wide and xm high is 96m2. Find the value of x

For what values of y is the expression \(\frac{6y-1}{y^2 - y-6}\) not defined?

What are the roots of the equation?

What is the equation of the curve?

In the diagram PQRS is a circle, |PT| = |QT| and ∠QPT = 70 o what is the size of ∠PRS?

The angle of elevation of the top of a cliff 15 meters high from a landmark is 60º. How far is the landmark from the foot of the cliff? Leave your answer in surd form

XOY is a real sector of a circle center O of radius 3.5cm which subtends an angle of 144o at the center. Calculate, in term of \(\pi\), the area of the sector

A rectangular packet has inner dimension 16cm by 12cm by 6cm. How many cubes of sugar of side 2cm can be neatly packed into the packet?

If y  \(\alpha\)  x\(^2\) and y = 1\(\frac{1}{4}\) when x = 4, find the value of y when x = \(\frac{1}{2}\)

Ladi sold a car for N84,000 at a loss of 4%. How much did ladi buy the car?

The monthly salary of a man increased from N2,700 to N3,200. Find the percentage increase

In the diagram, O is the center of the circle, ∠MON = 80 o , ∠LMO = 10 o and ∠LNO = 15 o . Calculate the value of x

The figure shows a quadrilateral PQRS having equal sides and opposite sides parallel. The diagonals PR and QS intersect perpendicularly at O, Which of the following statements cannot be correct