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MBOGO MIXED SECONDARY SCHOOL
END OF TERM I EXAMS APRIL-2007
S.4
MATHEMATICS PAPER 456/2
TIME: 2 ½ HRS.
INSTRUCTIONS:
- Attempt all questions in section A and any five from section B.
- Show clearly all the necessary working.
- No marks will be awarded for dubious work.
SECTION A (40 MARKS)
1. Solve for x in the equation 23x-1 x 8x-1 = 256. (4 mks)
2. Express r in terms of g,t,m and a where
t = g – ar
r+m (4 mks)
3. The line passing through the points A(-1, 3k) and B(k,3) is parallel to the line whose
equation is 2y + 3x = 9. Write down the co-ordinates of A and B. (4 mks)
4. If the point P(-1,2) undergoes translations T1 = 5 followed by T2 = -4 . Find the
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image of P under those translations.
5. The length of a rectangle is increased by 25% while the width is decreased by 10%.
Determine the percentage increase in the area of the rectangle. (4 mks)
6. A large estate is represented by a rectangle 8cm long and 6cm wide on a map whose
scale is 1:200,000. Determine the actual area of the estate in km2. (4 mks)
7. The average height of forty boys in a class is 145cm. The average height of the first
ten boys in the class is 130cm. Determine the average height of the remaining thirty
boys. (4 mks)
8. Use mathematical tables to evaluate (0.483)3/5 (4 mks)
9. A two digit number is such that the sum of its digits is 11. The number formed when
the digits are interchanged exceeds the original number by 27. Determine the original
number.
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10. The figure below shows a circle with centre O lines OB and AC meet at X.
Given that angle ACB =25o and angle BOC =70o. Determine the size of
(i) angle ABC (ii) angle OCX (iii) angle OBA
SECTION B: (60 MKS)
11. (a) Use the matrix method to solve the following a pair of simultaneous
equations.
3x – 2y + 1 =0
x + y –3 = 0
(b) Given that the transformation matrices
T1 = 2 1 followed by T2 = 3 1 can be
-1 -2 1 3
replaced by a single transformation T. Write down the matrix for T.
(c) The points A (7, -11), B (-7, -13) and C (-8,16) are the images of points A,B
and C respectively under transformation T1 followed by T2. Write down the co-
ordinates of A,B and C. (12 mks)
12.
R = 28cm
r = 21cm
The diagram above shows a hollow frustrum used in constructing a musical drum.
The top and bottom radii of the frustrum are 28cm and 21cm respectively as shown.
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The frustrum is 90cm high. All the outside surface of the frustrum is covered with
leather. Calculate to three significant figures;
(i) The volume of the drum in litres
(ii) The total surface area covered with leather in square metres. (12 mks)
13. Using a ruler, pencil and pair of compasses only,
(i) Construct a triangle ABC such that AB = 8.7cm AC=10.6cm and angle
BAC = 60o.
(ii) Inscribe a circle in the triangle ABC.
(iii) Construct a perpendicular from onto AC to meet it at point D.
(iv) Measure length BC and the radius of the circle.
(v) Measure length BD and calculate the area of triangle ABC. (12 mks)
14. (a) Express x2 – x – 12 in the form (x –p)2 + q, and state the values of p and q .
Hence solve the equation x2-x-12 =0.
(a) Given the functions f(x) = 1 – 2x and g(x) = x+ 3 determine the values of x
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for which gf(x) = 8x2 + 24x + 9 (12 mks)
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15. In a village of 75 families, 45 families have Tvs, 30 families have computers, 15
families have Tvs and Radios, 10 families have computers and Radios while 3
families have none of these items. If the number of families having Tvs and
computers only is equal to the families having radios only, and the number of
those families having Tvs only is equal to twice those having radios only.
(a) Draw a venn diagram representing the data.
(b) Use your venn diagram to find the number of families having
(i) radios only
(ii) all the 3 items
(c) Find the probability that a family selected at random has a T.V. (12 mks)
16. (a) Given that 3 a is singular, find the value of a.
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(b) Mrs Opolot bought 3kg of sugar, 2 loaves of broad and 3 litres of milk.
Mrs.Musoke bought 4kg of sugar, 3 loaves of bread and 2 litres of milk.
Mrs. Mwebe bought 2kg of sugar, 4 loaves of bread and 5 litres of milk.
The prices at the local shop for sugar, bread and milk are shs.1500, shs.1400 and
shs.800 respectively, while at the super market the corresponding prices are shs.
1300, shs.1000 and shs.700 respectively.
The return journey costs shs. 1400 for each lady.
(i) Write down a 3 x 3 matrix for the commodities bought.
(ii) Write down a 3 x 2 matrix for the prices of the commodities.
(iii) Determine by matrix multiplication the total expenditure for each
person from each of the shops.
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(iv) How much does Mrs. Musoke save by buying the commodities at a
super market? (12 mks)
17. Town B is 100km away from town A on bearing of 135o. Town D is on a
bearing of 090o from town B, 124km a part. Town C to 160km away from town
D is on bearing 030o from D.
(a) Using a scale of 1cm to represent 20km 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 A.
(ii) Distance and bearing of town B from town C. (12 mks)
END
Carseem.
