1. If {x : 2 ≤ x ≤18; x ∈ integer} and 7 + x = 4 (mod 9), find the highest value of x.

The sum of 11011₂, 11111₂ and 10000₂ is 10m10n0₂. Find the values of m and n.

A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to #1.00, how much did the engine cost in naira?

If (27ˣ × 3¹⁻ˣ) / 9²ˣ = 1, find the value of x.

Find the 7th term of the sequence: 2, 5, 10, 17, 26,..........

Given that logₓ 64 = 3, evaluate x log₂ 8.

If 2ⁿ = y, find 2⁽² ⁺ ⁿ⁄³⁾.

Factorize completely: 6ax - 12by - 9ay + 8bx.

Find the equation whose roots are 3/4 and -4.

If m = 4, n = 9 and r = 16, evaluate m/n - 1(7/9) + n/r.

Adding 42 to a given positive number gives the same result as squaring the number. Find the number.

Ada draws the graphs of x² - x - 2  and y= 2x - 1 on the same axes. Which of these equations is she solving?

The volume of a cone of height 3cm is 38(1/2)cm³. Find the radius of its base. [Take π= 22/7].

A sector of a circle with radius 6cm subtends an angle of 60º at the centre. Calculate its perimeter in terms of π.

The dimensions of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4m, calculate the base radius of the cylindrical tank. [Takeπ = 22/7]

In the diagram above, O  is the centre of the circle. if  PQ||RS and  <ONS = 140º. find the size of <POM

In the diagram, PTR is a tangent to the circle centre O. If angle TON = 108 º, calculate the size of <PTN.

In the diagram PQ||RT, QR||SU, <PQR = 48º and <RTS= xº. find the value of xº.

In the diagram above, O is the centre of the circle, line RT is a diameter, <PQT = 33º and <TOS = 76º .Use the diagram to answer questions 19 and 20.

Calculate the value of angle PTR

In the diagram above, O is the centre of the circle, line RT is a diameter, <PQT = 33º and <TOS = 76º .Use the diagram to answer questions 19 and 20.

Find the size of <PRS

the table below shows the value of a linear graph

use it to answer question 21 and 22.

Find the gradient of the line

the table below shows the value of a linear graph

use it to answer question 21 and 22.

What is the value of y when x = 2?

Given that tan x = 2/3, where 0º ≤ x ≤ 90º, find the value of 2sin x.

PQRS is a square. If X is the midpoint of PQ, calculate correct to the nearest degree, < PXS

The angle of elevation of an aircraft from point K on the horizontal ground is 30º. If the aircraft is 800m above the ground, how far is it from K?

The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 72 students.

The scores of twenty students in a test are as follows: *(Note: text cuts off at the bottom, numbers are partially visible: 48, 49, 50, 51, 52, 53, 53, 54, 58, 60, 61, 63, 65, 67, 70, 73, 75... Find the third quartile.

Scores:     0–4 5–9 10–14
Frequency: 2     1       2

The table above shows the distribution of the scores of some students in a test. Calculate the mean score.

The probabilities that Kenna, Ebou and Omar will hit a target are 2/3, 3/4 and 4/5 respectively. Find the probability that only Kebba will hit the target.

In the diagram, VW \\ ZY, |WX| = 6cm, |XY| = 16cm, |YZ| = 20cm and |ZX| = 12cm. Calculate |VX|.

Tom will be 25 years old in n year's time. If he is 5 years younger than Bade, find Bade's present age.

If (√2 + √3)/√3 is simplified as  m + n√6, find the value of (m +n)

In the diagram, line QT and line PR are straight lines,<ROS = (3nº - 20º), <POT = 2mº, <SOT = nº, <POL = mº and <QOL is a right angle. Find the value of nº

Make k the subject of the relation T = √[(Tk − H) / (k − H)].

Which of the following is used to determine the mode of a grouped data?

The area of a rhombus is 110cm². If the diagonals are 20 and (2x + 1)cm long, find the value of x.

Simplify: {3x - y}/xy - {2x + 3y}/2xy + 1/2

Illustrate graphically, the solution of y/2 + 1/8 > 5y/8

A farmer uses 2/5 of his land to grow cassava, 1/3 of the remainder for yam and the rest for maize. Find the part of the land used for maize.

The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15 km, how far would the vehicle go on 9 litres of petrol?

A trader bought 100 oranges at 5 for #40.00 and sold them at 20 for #120.00. Find the profit or loss percent.

Describe the shaded portion in the diagram above.

Find the value of p if 1/4p + 3q = 10 and 2p -1/3q = 7

Calculate the mean deviation of 5, 3, 0, 7, 2, 1

In the diagram above, the shaded part is a carpet laid in a room with dimensions 3.5m by 2.2m leaving a margin of 0.5m round it. Find the area of the margin.

Two angles of a pentagon are in the ratio 2:3. The others are 60° each. Calculate the smaller of the two angles.

A letter is selected from the letters of the English alphabet. What is the probability that the letter selected is from the word MATHEMATICS?

In a circle radius rcm, a chord is 16√3cm long is 10cm from the centre of the circle. Find, correct to the nearest cm, the value of rcm.

Consider the following statements:

X: Locally manufactured tyres are attractive

Y: Many locally manufactured tyres do not last long.

Denoting locally manufactured tyres by M, attractive tyres by R and long lasting tyres by L, which of these Venn diagrams illustrates the statements?

In the diagram above, line OX bi-sects <XYZ and line OZ bisects <YZX$. If <XYZ = 68º, calculate the value of <XOZ.