(a) In a class of 50 students, 30 offered History, 15 offered History and Geography while 3 did not offer any of the two subjects.
(i)Represent the information on a Venn diagram.
(ii)Find the number of candidates that offered:
(A) History only;
(B) Geography only.
(b) A trader sold an article at a discount of 8% for N 828.00. If the article was initially marked to gain 25%, find the
(i)cost price of the article;
(ii)discount allowed.
Question 2
(a) (i) Solve the inequality: 1/2x - 5/6( ex + 2) ≤ 1 + x.
(ii) Illustrate the solution on a number line.
(b) When the price of an apple increased by N 5.00f18 apples cost N 60.00 more than 20 apples cost before the increase. Find the new price of an apple.
Question 3
(a) Two children shared an amount of money in the ratio 3/4 : 2/5. If the smaller share was GH¢25.00, how much was shared between them?
(b) A box contains 5 red, 3 green and 4 blue balls of the same size. If a boy picks two balls from the box one after the other without replacement, what is the probability that both balls are red?
Question 3
(a) In a right angled triangle, sin x = 3/5. Evaluate 5(cos x)³ - 3.
(b) The angle of elevation of the top of a vertical pole from a point 63m east of the base of the pole is 30°. From another point due west of the pole, the angle of elevation of the top is 60°
(i)Draw a sketch diagram to illustrate the information.
(ii)Calculate, correct to three significant figures, the distance of the second point from the base of the pole.
Question 4
(a) The diagonals of a rhombus are 14em and gem. Calculate, correct to the nearest centimetre, the perimeter of the rhombus.
(b) The cross section of a rectangular tank measures l.2m by 0.9m. It contains water to a depth of O.4m. If a cubical block of side 50em is lowered into the tank, calculate, correct to 2 significant figures, the rise in the water level (in metres).
Question 5
(a) Copy and complete the following table for the relation y = ½x(x - 6) for -2 ≤ x ≤ 8.
(b) Using scales of 2cm to 1 unit on the x - axis, and 2cm to 2 units on the y-axis, draw the graph of the relation y = ½x(x - 6) for -2 ≤ x ≤ 8.
(c) Use the graph to find the:
(i)range of values of x for which y is negative;
(ii)minimum value of y;
(iii)roots of the equation ~x(x - 6) = 5
Question 6
Using ruler and a pair of compasses only:
(a) construct a triangle PQRwith /PQ/ = lOcm, ∠QPR = 90° and ∠PQR = 30°;
(b) (i) construct I, the locus of all points equidistant from PR and QR;
(ii) locate M, the point where / intersects with po,
(c) (i) with M as centre and radius MP, draw a circle;
(ii) calculate the area of the circler correct to one decimal place.
[Take Π= 22/7].
Question 7
The table gives the distribution of marks for 360 candidates who sat for an examination.
Marks (%)
0-9
10 - 19
20 - 29
30 -39
40 - 49
50 - 59
60 - 69
70 -79
80 -89
Number of
20
48
60
72
80
40
25
10
5
candidates
Question 8
(a) Draw a cumulative frequency curve for the distribution.
(b) Use your graph to estimate the semi-interquartile range.
(c) If the minimum mark for distinction is 75%, how many candidates passed with distinction?
Question 9
(a) A ship Pis 3km due east of a harbour. Another ship Q is also 3 km from the harbour but on a bearing of 042° from the harbour.
(i)Find the distance between the two ships.
(ilFind the bearing of ship Q from ship P.
(b) A motorist travelled 300 km at an average speed of 75 km/h and returned at an average speed of v km/b. If his average speed for the whole journey is 60 km/h, find v.
Question 10
P(lat 400N, long 18°W) and Q(lat 400N, long 78OW) are two cities on the surface of the earth. Calculate, the:
(a) radius of the parallel of latitude on which P and Q lie, correct to the nearest 10km;
(b) length of the minor arc PQ, correct to the nearest 100 km;
(c) vertical distance between the centre of the earth and the centre of the small circle on which P and Q lie, correct to the nearest km.
[Take π = 22/7 and radius of the earth= 6400 km]