SECTION A
1. Simplify
(i) 
(ii) 
2. Solve for x in 
3. An examination is marked out of 130 marks. If Rita obtained 60% in the examination, how many marks did she get out of 130?
4. Given that P = { (x, y): 2x - 3y ≤ 6} and Q = { (x, y): x + y < 0}, show by shading the unwanted region, the region representing P∩Q.
5. Use logarithm tables to evaluate 
correct to 2 decimal places.
6. Evaluate 5600 + 80,000, leaving your answer in the form a x 10n where 1 ≤ a < 10 and n is an integer.
7. In a homework marked out of 20, a group of pupils obtained the following marks: 15, 20, 18, 17, 8, 18, 16, 20, 18, 17, 12 and 19. Find the mode and median marks.
8. Under an enlargement of scale factor 3, the image of the point P (0, 3) is P' (4, 5). Find the coordinates of the centre of enlargement.
9. Express 
as a fraction in its simplest form.
10. A fair die is tossed only once and the number which appears on its top face noted. what is the probability of a top face showing
(i) A number greater than 4?
(ii) An odd number or prime number?
SECTION B
11. Draw graphs y = 2x2 + 3x - 3 and y - 7x + 3 = 0 for -3 ≤ x ≤ 3 using a scale of 1cm: 2 units for the vertical axis and 1 cm: 0.5 units for the horizontal axis. Using your graph find the:
a) Point of intersection of the line and the curve,
b) Gradient of the curve between the points of intersection of the line and the curve.
12. a) At a certain point on the level ground the angle of elevation of the top of a tower, T is 280. At another point 100 meters away from the first point, the angle of elevation is 350. Find the two expressions for the height of the tower hence find the height of the tower and give your answer to the nearest meter.
b) If cos x = -0.634 for 900 < x < 2700, find the two possible values of x.
13. A helicopter left Kampala at 0600hours and flew on a bearing of 0900, at a velocity of 300 km per hour. It landed at Nairobi airport at 0830 hours. At exactly 0900 hours, it left Nairobi airport and flew on a bearing of 3400, at the same original velocity. It then landed at Kitgum Airstrip at 1200 hours. Using graphical construction and a scale of 1cm: 100km, find the:
a) distance of kitgum from Kampala,
b) bearing of Kampala from kitgum.
14. Two cars A and B start off from rest at the same time moving in the same direction on a straight road. The speeds of the two cars in ms-1 are shown in the table below:
| t (s) | 0 | 2 | 4 | 6 | 8 | 10 | 12 |
| speed of car A (ms-1) | 0 | 4.5 | 9.0 | 13.5 | 18.0 | 22.5 | 27.0 |
| speed of car B (ms-1) | 0 | 2.0 | 5.0 | 10.5 | 23.0 | 27.0 | 28.5 |
Using a suitable scale, draw on the same axes the velocity time graphs of cars A and B.
From your graph find the:
a) Time when the two cars have equal speed and the magnitude of that speed.
b) Difference in speed after a period of 9 seconds,
c) Distance covered by car A by way of estimating the area under the curve described by car A for the 12 seconds.
15. OAB is a triangle, OA = a, and OB = b. points C and E are points on lines
and 
such that they divide the lines and in the ratios 1:2 and respectively. Point D lies on OE such that 
TRIANGLE
a) Find the vectors AB, OE and CB in terms of vectors a and b.
b) Show that the points B, D and C lie on a straight line.
16. A man earns a gross annual income of shs10,500,000. He is entitled to the following monthly allowances:
| Children | shs15,000 for each child aged 12 and below. shs12,000 for each child between age 13 and 18 inclusive |
| Lunc | shs60,000 |
| Transport | shs110,000 |
| Medical | 1/10th of gross monthly income |
| Marriage | 1/25th of gross monthly income. |
| Housing | 1/100thof gross annual income |
The man is married with five children of whom two are aged 12 and below, the other two aged 21 and 24 and the other aged 17.
The following tax structure is applicable on the taxable income in excess of shs30,000.
| Taxable income (shs) | Rate (% ages) |
| 00001 - 30,000 | Free |
| 30,001 - 130,000 | 8.0 |
| 130,001 - 260,000 | 14.5 |
| 260,001 - 380,000 | 23.0 |
| 380,001 - 490,000 | 28.5 |
| 490,001 - 590,000 | 35.0 |
| 590,001 and above | 42.5 |
(NB: A month has 30 days and a year 360 days)
Calculate:
a) The man's
(i) Total monthly allowances,
(ii) Monthly taxable income,
(iii) Monthly income tax.
b) The percentage of his gross annual that goes to tax.
17. FIGURE
The figure above (in thick, heavy lines) shows a lamp shed ABCD bounded by circles of radii 15 cm and 25cm. the slanting side AB is 30 cm.
If the lamp shed was cut from an original figure OABCD, of a complete cone, calculate the:
a) (i) slanting length of the cone OAB,
(ii)the angle formed by producing CD and BA to O.
b) (i) vertical height of the lamp shed,
(ii) volume of the lamp shed.