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**Section II [Theory]
Answer ALL questions in Part I**

1. 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].

**Answer any FIVE questions in Part II.**

**Write your answers on the answer booklet provided.**

1. (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?

2. 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.

3.

In the diagram above, the points A, B, C and D lie on the circle, centre O. TA and TB are tangents touching the circle at A and B respectively.

AÔB = 132°, AĈD = 59° and AOC is a straight line.

(i) Find A*T*B.

(ii) Find B*D*A.

(iii) Find B*D*C.

(iv) Find O*B*D.

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).

5. (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.

6. (a) The second, fourth and sixth terms of an Arithmetic Progression (A.P.) are x – 1, x + 1 and 7 respectively. Find the:

(i)common difference;

(ii)first term;

(iii)value of x.

(b) A spherical bowl of radius r *em *is one-quarter full when 6 litres of water is poured into it. Calculate, correct to three significant figures, its diameter. [Take *π *=22/7]

7. 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]

8. The table below 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 |

(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?

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