Core Mathematics — 1993
WASSCE · 48 questions · Answers included
48 questions
S = {1, 2, 3, 4, 5, 6}, T = {2,4,5,7} and R = {1,4, 5}, and (S∩T) ∪ R
Simplify: \(\frac{3}{4} \div 1\frac{1}{4} \times (1\frac{1}{2} - \frac{2}{3})\)
Solve the inequality: 3m + 3 > 9
Convert 89\(_{10}\) to a number in base two.
A stick of length 1.75m was measured by a boy as 1.80m. Find the percentage error in his measurement
The nth term of a sequence is given by (-1)\(^{n-2}\) x 2\(^{n-1}\). Find the sum of the second and third terms.
Simplify: \(\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}\)
Simplify: \(\frac{\log \sqrt{27}}{\log {81}}\)
Factorize the expression 2s\(^2\) - 3st - 2t\(^2\).
Solve the equation x\(^2\) - 2x - 3 = 0
Write as a single fraction: \(\frac{5}{6r} - \frac{3}{4r}\)
Factorize 2x\(^2\) - 21x + 45
Solve the simultaneous equations y = 3x; 4y - 5x =14
A sector of a circle of radius 9cm subtends angle 120° at the centre of the circle. Find the area of the sector to the nearest cm\(^2\) [Take π = 22/7]
Calculate the total surface area of a cone of height 12cm and base radius 5cm. [Take π = 22/7]
A cone is 14cm deep and the base radius is 4\(\frac{1}{2}\)cm. Calculate the volume of water that is exactly half the volume of the cone.[Take π = \(\frac{22}{7}\)]
The area and a diagonal of a rhombus are 60 cm\(^2\) and 12 cm respectively. Calculate the length of the other diagonal.
The angle of a sector of a circle radius 10.5cm is 120°. Find the perimeter of the sector [Take π = 22/7]
In the diagram, PQR is a tangent to the circle QST at Q. If |QT| = |ST| and ∠SQR = 68°, find ∠PQT.
The sum of an interior angles of a regular polygon is 30 right angles. How many sides has the polygon?
In the diagram above, |QR| = 12cm and |QS| = 10cm. If ∠PQR = 90°, ∠RSQ = 90° and PSQ is a straight line, find |PS|
In the diagram above, |PQ| = |QR|, |PS| = |RS|, ∠PSR = 30o and ∠PQR = 80o. Find ∠SPQ.
Two chords PQ and RS of a circle when produced meet at K. If ∠KPS = 31 o and ∠PKR = 42 o , find ∠KQR
In the diagram above, QRS is a straight line, QP//RT, PRQ = 56°, ∠QPR =84° and ∠TRS = x°. Find x
Simplify \(\frac{2.25}{0.015}\) leaving your answer in standard form
State the fifth and seventh terms of the sequence \(-2, -3, -4\frac{1}{2}, ...\)
A plane tiles 90km on a bearing 030° and then flies 150km due east. How far east of the starting point is the plane?
If sin x = cos 50 o , then x equals
From a point on the edge of the sea, one ship is 24km away on a bearing S 50 o E and another ship is 7km away on a bearing S40 o W. How far apart are the ships?
Given that tan x = 5/12, what is the value of sin x + cos x ?
Cos 75 o has the same value as
If sin x = 12/13, where 0° < x < 90°, find the value of 1 - cos\(^2\)x
The angle of elevation of the top of a tower from a point on the horizontal ground, 40m away from the foot of the tower is 30o. Find the height of the tower.
At a point 500m from the base of a water tank the angle of elevation of the top of the tank is 45o. Find the height of the tank,
Find the median of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15, 25
What is A∩B in the diagram above?
The table above shows the scores of a group of 40 students in a physics test. If the mode is m and the median is n, then (m,n) is
Score 1 2 3 4 5 6 7 8 9 Frequency 2 3 6 7 9 6 2 2 3 The table above shows the scores of a group of 40 students in a physics test What is the mean of the distribution?
Find the median of the set of numbers 12, 15, 13, 14, 12, 12.
The distribution by state of 840 students in the Faculty of Science of a Nigerian University in a certain session is as follows: Bendel 45 kwara 410 Ogun 105 Ondo 126 Oyo 154 In a pie chart drawn to represent this distribution, the angle subtended by Ondo is
How many student took the examination
How many students scored less than 7 marks?
What is the probability that an integer selected from the set of integers (20, 21, ...., 30) is a prime number?
A fair die is rolled once. What is the probability of obtaining a number less than 3?
What is the probability of having an even number in a single toss of a fair die?
What is the probability that a total sum of seven would appear in two tosses of a fair die?
A die is rolled 200 times the outcomes obtained are shown in the table below. Find the probability of obtaining 2.
Number 1 2 3 4 5 6 No of times 25 30 45 28 40 32 A die rolled 200 times. The outcome obtained are shown in the table above. What is the probability of obtaining a number less than 3 ?