**PAPER 1**

**SECTION A**

1. Write down the next term of each of the given sequences;

(i) 2, 3, 1, 4, 0, ...........

(ii) 1, 4, 20, 120, .......

2. Without using tables or calculator find the value of

(i) Cos 780^{0},

(ii) Sin 390^{0}.

3. Without using tables or calculator, simplify

4. At lunch time a certain hotel received 80 customers. Of these 45 had a posho (**P**) meal and 50 had Matoke **(M).**

(i) Represent this information in a Venn diagram

(ii) Find the number of people who had a meal of both P and M.

5. If the point **P**(2, -1) undergoes a translation represented by the matrix find the image of P.

6. Calculate the simple interest on shs96,000 for 10 months at a rate of 8^{1/}_{3}% per annum.

7. Use mathematical tables to evaluate (0.48)^{3/5} correct to 2 decimal places.

8. A stretch of land on a map of scale 1:15,000 has an area of 300 cm^{2}. Determine the actual area of the land in km^{2}.

9. A floor measuring 6m x 4m is to be covered with square tiles measuring 50 cm each. Find the cost of covering the floor. If the price of a dozen of the tiles is shs15,000.

10. Show that the points (3x, -2y), (2x, y) and (0, 7y) lie on a straight line.

**SECTION B**

*Attempt any five questions from this section. All questions carry equal marks.*

11. a) Express x^{2} + x - 12 in the form (x+a)^{2}+ b. hence solve the equation x^{2 }+ x - 12 = 0.

b) Given the functions **f(x**) = and **g(x)** = . Determine the values of **x** for which **fg(x)** =

12. a) use matrix methods to solve the following pair of simultaneous equations:

x + y = 3,

3x - 2y + 1 = 0.

b) A transformation maps (1, 2) onto (-1, 4) and (2, 3) onto (-1, 7).

(i) Find the matrix of this transformation.

(ii) Determine the image of (3, 0) under this transformation.

13. Using a ruler, pencil and pair of compasses only,

(i) Construct a triangle **ABC** such that =8.7 cm, = 10.6 cm and angle **BAC** = 60^{0},

(ii) Inscribe a circle on the triangle **ABC,**

(iii) Construct a perpendicular from **B** onto to meet it at point **D**.

(iv) Measure length and the radius of the circle

(v) Measure and calculate the area of triangle **ABC**.

14. The figure below shows a hollow pipe of external diameter 16mm, internal diameter 10 mm and length 50cm.

FIGURE

(i) Calculate the surface area (in cm^{2}) of the pipe correct to decimals places.

(ii) What would be the surface area of a similar pipe of length 150 cm, external diameter 48 mm and internal diameter 30 mm?

15. The table below shows the marks obtained in a chemistry test by S4 student in a certain school.

54 | 49 | 60 | 58 | 54 |

60 | 51 | 57 | 56 | 54 |

53 | 59 | 56 | 52 | 55 |

57 | 62 | 54 | 54 | 56 |

48 | 51 | 52 | 55 | 58 |

65 | 55 | 54 | 57 | 61 |

a) Using class widths of 3 marks and starting with the 48-50 class, make a frequency distribution table.

b) Use your table to

(i) Draw a histogram

(ii) Determine the median and mean marks.

16. a) Okello bought 3 pens and 2 rulers from a book shop at shs3.150. Mukasa bought 2 pens and 3 rulers from the same bookshop at shs2,850.

(i) Find the cost of each pen and ruler.

(ii) If Mugisha spends shs6,000 to buy n pens and n rulers, find n.

b)a pick up van can be bought by cash at shs8,750,000 or can be bought on hire purchase by paying a 25% deposit of the cash price and 12 monthly installment of shs600,000 per month.

Calculate the:

(i) Cost of the pick up by hire purchase.

(ii) Extra money paid for the pick up by hire purchase than by cash.

17. A transport company has 8 Lorries of 8 tones carrying capacity each, and 5 Lorries of 10 tones capacity each. There are 12 drivers available. The company was contracted to transport 480 tones of cement from the factory to a town on a given day. The 8 tone Lorries can make 6 journeys in a day and the 10 tone Lorries 4 journeys a day. The costs of using an 8 tone lorry and a 10 tone lorry are shs40,000 and shs60,000 respectively.

(i) Write down four inequalities to represent the above information.

(ii) Plot a graph for the inequalities, shading out the unwanted regions.

(iii) From your graph find the numbers of 10 tone and 8 tone Lorries the company used, keeping its costs as minimal as possible.

**PAPER 2**

**SECTION A**

1. Find the highest common factor (**HCF**) of 18, 45 and 42.

2. When thirty times a number is increased by 32, the result in equal to twice the square of the number. Find the number.

3. If the exchange rate for a French France to a pound sterling is **£**1 = 9.00 francs and **£**1 - $1.53 (American dollars), find how many American dollars one would get in exchange for 1,000 francs.

4. In the diagram below, **O** is the centre of the circle. and are tangents to the circle. Angle **ABC** = 54^{0}.

CIRCLE

Find angle **ADC**.

5. The representative fraction of a amp is

Find the area of a lake in (km^{2}) which is represented on the map by an area of 4.6cm^{2}.

6. If 135_{n} = 75_{ten}, find the value of n.

7. Use matrix method to solve the pair of simultaneous equations:

2x - y = 8,

4x - 3y = 14.

8. In the figure below, =6cm, = 2cm, = 4cm and =5cm.

FIGURE

If is parallel to , find length

9. A far coin with one side showing court of arms (**A**) and other side showing a cow (**C)** is tossed twice. Find the probability that at least a cow (**C**) will show up in the two tosses.

10. The angle of elevation of the top of a flag pole to a policeman of height 1.7 m is 20^{0}. If the policeman is standing at a distance of 16m from the pole on level ground, find the approximate height of the flag pole, correct to 2 significant figures.

**SECTION B**

11. Mr. Lwanga and Mr. Okot were each given Uganda shillings 980,000 at the beginning of 1999. Mr. Lwanga exchanged his money to united states dollars and then banked it on his foreign currency account at a compound interest rate of 2% per annum, while Mr. Okot banked his money without exchanging it, at a compound interest rate of 12% per annum. The exchange rates in 1999 and 2000 were ug.shs1, 250 and ug.shs1, 500 to a dollar respectively. If Mr. Okot withdrew shs120, 000 at the end of 2000.

(i) Calculate the amount of money (in ug.shs) each man had in the bank at the end of 2000.

(ii) Who had more money and by how much?

12. Two cyclists **C _{1}** and

**C**begin traveling at the same time from town

_{2}**A**to town

**B,**18km apart.

**C**travels at a steady speed of 15km h

_{1}^{-1}faster than that of cyclist

**C**who also travels at a steady speed. When

_{2}**C**has covered half the distance, he delays for half an hour, after which he travels at a speed 20% less his original speed. He arrives in town

_{1}**B**is minutes earlier than cyclist

**C**.

_{2}(i) Determine the speeds of the two cyclists, **C _{1}** and

**C**

_{2}.(ii) If cyclist **C _{2}** started from town B while

**C**at the same time started from town A and all the two travel non-stop, determine the distance from town A where the two cyclists will meet. After how long will they meet?

_{1}13. Using suitable scales, plot on the same axes the graphs of y = 2x^{2} and for -2≤ x ≤ 3. Use your graphs to estimate the solutions of the equations:

(i) 4x^{2} - 5x - 10 = 0,

(ii) 6x^{2} + 10x - 30 = 0.

Correct to 2 decimal places.

14. Town **B** is 100km away from town **A** on bearing of 135^{0}. Town **D** is on a bearing of 090^{0} from town **B**, 124 km apart. Town **C** 160km away from town **D** is on bearing 030^{0} from **D**.

a) Using a scale of 1 cm to represent 20 km, make an accurate drawing to show the relative positions and distances of towns **A, B, C** and **D**.

b) Determine The

(i) Shortest distance and bearing of town **C** from town **A**.

(ii) Distance and bearing of town **B** from town **C.**

15. a)(i) Find the images of the points **A**(1, 4), **B**(1, 1) and **C**(2, 1) of a triangle **ABC** under a transformation *l* whose matrix is

(ii)Plot triangle **ABC **and its image **A' B' C' **on the same graph. Describe the matrix transformation *l*. hence deduce the matrix transformation which would map triangle **A' B' C'** onto triangle **ABC**.

b) triangle **A' B' C'** is mapped onto triangle **A'' B'' C''** by matrix transformation **M** =

(i) Find the coordinates of **A'' B'' C''**.

(ii) Plot **A'' B'' C''** on the same graph in (a)(ii) above. Use your graph to describe a single transformation that will map triangle **ABC** onto triangle **A'' B'' C''**. Hence find the single matrix transformation which maps triangle **ABC** onto **A'' B'' C''**.

16. in a triangle **OAB**, **OA **= **a, OB = b**. a point **L **is on the side **AB** and **M** on the side **OB**. **OL** and **AM** meet at **S**. and **OS** = ^{3/}_{4} **OL**.

Given that **OM** = **xOB** and **AL** = **yAB**, express the vectors,

(i) **AM** and **OS** in terms of **a, b** and **x**.

(ii) **OL** and **OS** in terms of **a, b** and **y**.

Hence find **x **and **y.**

17. The figure below shows part of a solid right circular cone whose original height was 20 cm before part of its top was cut off. The radius of the bas is 12 cm and that of the top is 8 cm. a circular hole of radius 8 cm was drilled through the centre of the solid as shown:

CONE

Calculate the volume of the remaining solid.