**PAPER 1**

**SECTION A**

1. Find the lowest common multiple (**LCM**) and the highest common factor (**HCF**) of 54 and 84.

2. The pie chart below represents yields of beans from three fields **A, B** and **C**.

PIE

If the total yield of beans was 300 sacks, calculate the number of sacks got from field **C.**

3. Express 2log _{3} 18 + log_{3} 3^{-1} -log_{3} 6^{2} + 1 as a single logarithm log_{3} **Q.**

4. Given that **P** = , find a matrix P^{-1} such that PP-1 = I where I is the identity matrix of order 2.

5. Study the graph below:

GRAPH

Find the inequality representing the shaded region.

6. Evaluate:

7. Solve for w:

8. Given that f(x) = 2x - 5, find:

a) F(-2)

b) F^{-1}(x)

9. In triangle **BCD, AD** = 15cm, **BD** = 25cm, **AB** = **AC** and **AB** is perpendicular to **CD**.

TRIANGLE

Find the length of **CB** correct to one decimal place.

10. In the diagram below, **O** is the centre of the circle and angle **BOD** = 164^{0}

CIRCLE

Find:

a) Angle **BAD**,

b) Angle **BCD**.

**SECTION B**

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

11. a) The points (-1, 9) and (r, 2) lie on the line y = 2 - x. find the values of q and r.

b) In the figure below, **P** is 4 units from **O**. the equation of the line **MN** is 4y + x = 12.

FIGURE

Find the area of **OPMN.**

12. a) Adikini bought a television set for which the cash price was shs 599,000. She bought the television set on a hire purchase scheme and had to pay an extra shs71, 000. If she made eight equal monthly installments, how much did she pay per month?

b) Mukasa wants to buy a house which is priced at shs56, 000,000. A deposit of 25% of the value of the house is required. A bank will lend him the rest of the money at a compound interest of 15% per annum and payable after two years.

Calculate the:

(i) Deposit Mukasa must make.

(ii) Amount of money Mukasa will have to pay the bank after two years.

(iii) Total money which Mukasa will spend to buy the house.

13. A club held swimming tests in Crawl (**C**), Backstroke (**B**) and Diving (**D**) for 72 members. Those who passed crawl were 49, 30 passed backstroke and 30 passed diving. 5 passed crawl and backstroke but not diving, 4 passed backstroke and diving but not crawl. 6 passed crawl and diving but not backstroke. 14 passed all the three tests.

a) Draw a Venn diagram to represent the given information.

b) Use the Venn diagram to find the number of members who:

(i) Passed the crawl test only.

(ii) Did not pass any test.

c) If a member is picked at random, what is the probability that the member passed two tests only?

14. Given that the point **A** has co-ordinates (-8, 6), vector **AB** = and **M** is the mid point of **AB**;

a) Find the:

(i) Column vector AM.

(ii) Co-ordinates of **M**.

(iii) Magnitude of **OM**.

b) (i) Draw the vector **AB** on a graph paper.

(ii) From your graph, state the co-ordinates of **B**.

15. a) A unit square whose vertices are **O**(0, 0), **I** (1, 0),** j**(0, 1) and **k**(1, 1) is transformed by rotating through a positive quarter turn about the origin. Find the matrix for this transformation.

b) Give **T** = and **M** = , find the:

(i) Image of the points **A** (0, 3) and **B **(5, 3) under the transformation **TM**.

(ii) Matrix of transformation which will map the images of A and B back to their original positions.

16. a) copy and complete the table below for the equation y = 2x^{2} - 3x - 7,

x | -1^{1/2} |
-1 | ^{-1/2} |
0 | ^{1/2} |
1 | 1^{1/2} |
2 | 2^{1/2} |
3 |

2x^{2} |
2 | 0 | ||||||||

-3x | 3 | 0 | ||||||||

-7 | -7 | -7 | ||||||||

y | -2 | -7 |

b)plot the points (**x, y**) obtained from the completed table on a graph paper using 2 cm to represent 1 unit on the **x** - axis and 1 cm to represent 1 unit on the **y** - axis.

Hence draw a graph for y = 2x^{2} - 3x - 7.

c) Use your graph to solve the equation: 2x^{2} - 3x - 8 = 0.

17. a) The dimensions of a rectangle are 60 cm by 45 cm. if the length and width are each reduced by 10%, calculate the percentage decrease in area.

b) A container has a volume of 6400 cm^{3} and a surface area of 8000 cm^{2}. Find the surface area of a similar container which has a volume of 2700cm^{3}.

**PAPER 2**

**SECTION A**

1. simplify:

2. Factorize completely: 2p^{2}q^{3} - pq^{3} + pq - 2p^{2}q.

3. Simplify. Give your answer in standard form.

4. Given the vectors **QR **= , **ST** = and **SR** = , find the vector **QT**.

5. If , express p in terms of **x **and **y**.

**6. **Given that **D** = {All odd numbers less than 20} and **M** = {All multiplies of three less than 20}, find **n(D****∩M).**

7. Find the equation of the line of gradient ^{-3/}_{5} and passing through the point (3, 4).

8. A farm is on a piece of land whose area is 5.6km^{2}. What would be the area of this farm in cm^{2} on a map whose scale is 1:40,000?

9. A forex bureau buys one US dollar at UG.shs1, 900 and sells one pound sterling at ug.shs3, 450. Atim wants to exchange 3,000 US dollars to pound sterlings. How many pound sterlings will she get?

10. Two points A (5, 1) and B (6, 0) are given a transformation defined by the matrix . Find the co-ordinates of their images.

**SECTION B**

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

11. a) A man gave half of his welfare allowance to his wife. ^{1/}_{5} to each of his two sons and the rest to his daughter.

Find:

(i) The fraction given to the daughter.

(ii) His welfare allowances if each son was given shs16, 000.

b)The difference between the values of **y **when x = 6 and when x = 10 is 16. Given that **y** is inversely proportional to the square of **x**, find the equation relating **x **and **y**.

12. The table below shows the weights in kilogrammes of thirty pupils.

48 | 44 | 33 | 52 | 54 | 44 |

53 | 38 | 37 | 35 | 53 | 46 |

59 | 51 | 32 | 37 | 49 | 42 |

48 | 59 | 52 | 40 | 54 | 46 |

45 | 62 | 35 | 54 | 48 | 35 |

a) Construct a frequency table with a class width of 5 starting from the class of 30-34.

b) Use your table in (a) to:

(i) Estimate the mean weight of the pupils.

(ii) Draw a histogram and use it to estimate the modal weight of the pupils.

13. Four students; Kale, Linda, Musa and Nana went to a stationery shop.

Kale bought 4 pens, 6 counter books and 1 graph book.

Linda bought 10 pens and 5 counter books.

Musa bought 3 pens and 3 graph books.

Nana bought 5 pens, 2 counter books and 8 graph books.

The costs of a pen, a counter book and a graph book were shs400.

Shs1,200 and shs1,000 respectively.

a) (i) Write a 4x3 matrix for the items bought by the four students.

(ii) Write a 3x1 matrix for the costs of each item.

b) Use the matrices in (a) to calculate the amount of money spent by each student.

c) If each student was to buy 4 pens, 10 counter books and 6 graph books, how much money would be spent by all the four students?

14. a) The lines ax + 2y = 3 and ax - by = 5 intersect at (1, 2). Find **a** and **b**.

b) If , determine the values of **x** and **y**.

15. In the figure below, **QXRYP** is a semi circle with centre **O** and radius 10 cm. **MN** is parallel to the diameter **QP**. Angle **XOQ** = 40^{0}.

SEMI CIRCLE

Find the

a) length of:

(i) the are **XRY**.

**(ii) ****MQ**

**(iii) ****MX**

b) Perimeter of the given figure.

16. In the figure below, **ABCDH** is a right pyramid on a square base 4**BC** of side 5m. Each of the slanting edges is 5m.

SQUARE BASE

Calculate the:

a) Height of the pyramid, correct to two decimal places.

b) Angle between the plane **HBC** and the base.

c) Volume of the pyramid, correct to one decimal place.