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 + log3 3-1 -log3 62 + 1 as a single logarithm log3 Q.

4. Given that P = mathe_2008_1 , 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: mathe_2008_2

7. Solve for w: mathe_2008_3

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 = 1640

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 = mathe_2008_4 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 = mathe_2008_5 and M = mathe_2008_6 , 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 = 2x2 - 3x - 7,

x -11/2 -1 -1/2 0 1/2 1 11/2 2 21/2 3
2x2 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 = 2x2 - 3x - 7.

c) Use your graph to solve the equation: 2x2 - 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 cm3 and a surface area of 8000 cm2. Find the surface area of a similar container which has a volume of 2700cm3.

PAPER 2

SECTION A

1. simplify: mathe_2008_7

2. Factorize completely: 2p2q3 - pq3 + pq - 2p2q.

3. Simplify. mathe_2008_8Give your answer in standard form.

4. Given the vectors QR = mathe_2008_9, ST = mathe_2008_10 and SR = mathe_2008_11, find the vector QT.

5. If mathe_2008_12, 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 5.6km2. What would be the area of this farm in cm2 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 mathe_2008_13. 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 mathe_2008_14, 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 = 400.

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 4BC 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.