Core Mathematics — 1996
WASSCE · 49 questions · Answers included
49 questions
The 6th term of a G.P is \(\frac{-2}{27}\) and its first term is 18. What is the common ratio?
Convert the decimal number 89 to a binary number
Simplify: \((2\frac{1}{6} - 1\frac{2}{3}) \div 2\frac{2}{3}\).
Simplify 56x\(^{-4}\) \(\div\) 14x\(^{-8}\)
Simplify Log\(_{10}\)4 + Log\(_{10}\)25
A boy measured the length and breath of a rectangular lawn as 59.6m and 40.3m respectively instead of 60m and 40m. What is the percentage error in his calculation of the perimeter of the lawn?
Find the 9th term of the arithmetic progression 18, 12, 6, 0, -6 .........
Expand (2x - 5)(x - 3)
Simplify: \(\frac{5}{x - y} - \frac{4}{y - x}\)
If 3p - q = 6 and 2p + 3q = 4, find q
M varies directly as n and inversely as the square of p. If M = 3, when n = 2 and p = 1, find M in terms of n and p.
If x is a real number which of the following is more illustrated on the number line?
Solve the equation 4 / a + 1 / 5a = 3
Make p the subject if formula y = \(\frac{a + p}{a - p}\)
Factorize 32x 3 - 8xy 2
The roots of a quadratic equation are -1/4 and 3. The quadratic equation is
The graph of 2y = 5x 2 - 3x 2 - 2 cuts the y axis at the point
In the diagram above, O is the center of the circle of radius 3.5cm, ∠POQ = 60o Use the information to answer the question below [Take π = 22/7] What is the length of the arc PXQ?
In the diagram above, O is the center of the circle of radius 3.5cm, ∠POQ = 60°. What is the area of the minor sector POQ? [Take π = 22/7].
If the hypotenuse of a right-angle isosceles triangle is 2, what is the length of each of the other side?
Find, correct to 1 decimal place, the volume of cylinder of height 8cm and base radius 3cm. [Take π = 3.142]
One side of a rectangle is 8cm and the diagonal is 10cm. What is the area of the rectangle?
two towns X and Y both on latitude 60 o S have longitude 27 o E and 33 o W respectively. Find to the nearest kilometers, the distance between X and Y measured along the parallel of latitude. [Take 2πR = 4 x 10 4 km, where R is the Radius of the earth]
The angle of a sector of a circle of radius 35cm is 288 o . Find the perimeter of the sector. [Take π = 22/7]
How many sides has a polygon if the sum of its interior angle is 1440 o ?
Each interior angle of a regular nonagon(nine sided polygon) is equal to
In the diagram above, find x correct to the nearest degree
In the diagram above, TRQ is a straight line. Find p, if p = \(\frac{1}{3}\)(a + b + c)
Which of the following is not true? You may construct a
In the diagram above, PQ is parallel to RST. /RS/ = /SQ/ = /TQ/ and ∠PQR = 35o.Calculate ∠SQT
In the diagram above, /PQ/ = /PS/ and /QR/ = /SR/. Which of the following is/are true? i. the line PR bisects ∠QRS ii. The line PR is the perpendicular bisector of the line segment QS iii. Every point on PR is equidistant from SP and QP
In the diagram, ∠PMN = ∠PRQ and ∠PNM = ∠PQR. If /Pm/ = 3cm, /MQ/ = 7cm and /PN/ = 5cm, find /NR/
In the diagram above, PQ is a tangent to the circle MTN at T. What is the size of ∠MTN?
In the diagram above, KLMN is a cyclic quadrilateral. /KL/ = /KN/, ∠NKM = 55 o and ∠KML = 40 o . Find ∠LKM
In the diagram above, ∠SPQ = 79 o . Find ∠SRQ
Two angles (a + 31) and (b - 49 o ) are adjacent angles on a straight line. Which of the following is true
The trapezium PQRS parallel to SR,∠PQS = 34 o and ∠SPQ = 2 ∠SRQ. Find the size of, SQR
In the diagram above, AB, CD and XY are straight lines intersecting at W. Find ∠CWX
If sin\(\theta\) cos\(\theta\), for 0 o \(\leq\) θ \(\leq\) 360 o , find the value of \(\theta\)
If tan x = \(2\frac{2}{5}\), find the value of sin x; 0 \(\leq\) x \(\leq\) 90 o
A town P is 150km from a town Q in the direction 050 o . What is the bearing of Q from P?
The angle of elevation of the top X of a vertical pole from a point P on a level ground is 60 o . The distance from P to the foot of the pole is 55m. Without using tables, find the height of the pole.
The number of goals scored by a football team in 20 matches is shown in the table above What is the mean goal scored?
The number of goals scored by a football team in 20 matches is shown in the table above What is the modal goal scored?
The cumulative frequency curve may be used to find the
The marks obtained by pupils of class are grouped as shown below; 0 - 4, 5 - 9,10 -14, 15 -19. Which of the following is/are not true? l. The mid values of the grouped marks are 2, 7, 12 and 17. II The class interval is 4. III The class boundaries are 0.5, 4.5, 9.5, 14.5 and 19.5
What percentage of observation lie outside interquartile range of any distribution?
A bag contains 3 red, 4 black and 5 green identical balls. Two balls are picked at random, one after the other without replacement. Find the probability that one is red and the other is green
The table gives the distribution of outcomes obtained when a die was rolled 100 times. What is the experimental probability that it shows at most 4 when rolled again?