Core Mathematics — 1995
WASSCE · 48 questions · Answers included
48 questions
Find (101\(_2\))\(^2\), expressing the answer in base 2.
If three children shares N10.50 among themselves in ratio 6:7:8, how much is the largest share?
Express 0.000834 in standard form
Given that log 2 a = log 8 4, find a
By selling some crates of soft drinks for N600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?
Find the nth term Un of the A.P., 11, 4, -3,....... .
lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y.
If R = [2, 4, 6, 7] and S = [1, 2, 4, 8], then R∪S equal
Find the value(s) of x for which the expression is undefined: \(\frac{6x - 1}{x^2 + 4x - 5}\)
Which of the following could be the inequality illustrated in the sketch graph above?
Solve the inequality: \(\frac{1}{3}(2x - 1) < 5\)
What is the smaller value of x for which x\(^2\) - 3x + 2= 0?
Factorize the expression x(a - c) + y(c - a)
If \(y \propto \frac{1}{x^2}\) and x = 3 when y = 4, find y when x = 2.
Solve the equation 3x\(^2\) + 25x -18 = 0
Solve the equation (x +2)(x - 7) = 0
Solve the following simultaneous equations: x+ y = 3/2; x - y = 5/2 and use your result to find the value of 2y + x
Use the graph of y = 3x\(^2\) + x - 7 above to answer the question What is the minimum value of y?
Use the graph of y = 3x\(^2\) + x - 7 above to answer the question Find the roots of the equation y=3x\(^2\) + x - 7
In the diagram above. |AB| = 12cm, |AE| = 8cm, |DCl = 9cm and AB||DC. Calculate |EC|
The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.
A water tank of height \(\frac{1}{2}\) m has a square base of side \(1\frac{1}{2}\) m. lf it is filled with water from a water tanker holding 1500 litres, how many litres of water are left in the water tanker? [1000 litres = 1m\(^3\)]
A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7] Find the total surface area of the container
A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7] What is the volume of the container?
Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. [Take π = 22/7]
A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere.
The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.
The positions of two countries P and Q are (15°N, 12°E) and (65°N, 12°E) respectively. What is the difference in latitude?
A 120° sector of a circle of radius 21cm is bent to form a cone. What is the base radius of the cone?
The angle of a sector of a circle is 108°. If the radius of the circle is 3\(\frac{1}{2}\)cm, find the perimeter of the sector
In the diagram above; O is the centre of the circle and |BD| = |DC|. If ∠DCB = 35°, find ∠BAO.
In the diagram above, AO is perpendicular to OB. Find x
In the diagram above, PQ is parallel to TU, ∠PQR = 50°, ∠QRS = 86° and ∠STU = 64°. Calculate the value of x.
If log\(_{10}\) x = \(\bar{2}.3675\) and log\(_{10}\) y = \(\bar{2}.9738\), what is the value of x + y, correct lo three significant figures?
In the diagram above, AB//CD, the bisector of ∠BAC and ∠ACD meet at E. Find the value of ∠AEC
In the diagram above, AB//CD. What is the size of the angle marked x?
The locus of a point which is equidistant from two given fixed points is the
In the diagram above, the value of angles b + c is
Which of the following angles is an exterior angle of a regular polygon?
In ΔABC above, BC is produced to D, /AB/ = /AC/ and ∠BAC = 50 o . Find ∠ACD
Without using tables, find the value of \(\frac{\sin 20°}{\cos 70°} + \frac{\cos 25°}{\sin 65°}\)
In the diagram above, ∠PRQ = 90°, ∠QPR = 30° and /PQ/ = 10 cm. Find y.
The bearing of two points Q and R from a point P are 030° and 120° respectively, lf /PQ/ = 12 m and /PR/ = 5 m, find the distance QR.
What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, 8, 10, 9, 8 and 14?
The mean of 20 observations in an experiment is 4, lf the observed largest value is 23, find the mean of the remaining observations.
Find the median of the following numbers 2.64, 2.50, 2.72, 2.91 and 2.35.
Two fair dice are tossed together once. Find the probability that the sum of the outcome is at least 10.
From a box containing 2 red, 6 white and 5 black balls, a ball is randomly selected. What is the probability that the selected ball is black?