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Mathematics Paper 1 Question Paper

Mathematics Paper 1

Course:Secondary Level

Exam Year:2011

MATHEMATICS PAPER 1
2011
SECTION 1 (50 marks)
Answer all the questions in this section in the spaces provided.
1. Without using a calculator, evaluate;

(3 marks)

2. The diagonal of a rectangular garden measures 111/4 m while its width measures 63/4 m.
Calculate the perimeter of the garden. (2 marks)

3. A motorist took 2 hours to travel from one town to another town and 1 hour 40 minutes to travel back. Calculate the percentage change in the speed of the motorist. (3 marks)

4 . A square room is covered by a number of whole rectangular slabs of sides 60 cm by 42 cm.
Calculate the least possible area of the room in square rnetres. (3 marks)

(3 marks)
5. Given that sin (x + 60)° = cos (2x)°, find tan (x + 60)°.

(3 marks)
6. Simplify the expression:

7. The external length, width and height of an open rectangular container are 41 cm, 21 cm and 15.5 cm respectively. The thickness of the material making the container is 5 mm. If the container has 8 litres of water, calculate the internal height above the water level.
(4 marks)
8. Factorise 2x2y2 – 5xy - 12 (2 marks)
9. Using a ruler and a pair of compases only:
(a) construct a parallelogram PQRS in which PQ = 6 cm, QR = 4 cm and
angle SPQ= 75°; (3 marks)

(b) determine the perpendicular distance between PQ and SR. (1 mark)

10. The masses of people during a clinic session were recorded as shown in the table below.
Mass (kg)
40-44
45-49
50-54
55-59
60-64
65-69
70-74

No. of people
1
2
12
10
2
2
1

(3 marks)
Calculate the mean mass.

11. A customer paid Ksh. 5 880 for a suit after she was allowed a discount of 2% on the selling price. If the discount had not been allowed, the shopkeeper would have made a profit of 20% on the sale of the suit. Calculate the price at which the shopkeeper bought the suit.
(3 marks)

12 . Three vertices of a parallelogram PQRS are P(-l, 2), Q(8, -5) and R (5,0).
(a) On the grid provided below draw the parallegram PQRS. (1 mark)

(b) Determine the length of the diagonal QS. (2 marks)

13. In January, Mambo donated 1/6th of his salary to a children's home while Simba donated 1/5th of his salary to the same children's home. Their total donation for January was Ksh. 14 820. In February, Mambo donated 1/8th of his salary to the children's home while Simba donated 1/12th of his salary to the children's home. Their total donation for February was Ksh 8 675. Calculate Mambo 's monthly salary. (4 marks)

14. (a) Express 10500 in terms of its prime factors. (1 mark)
(b) Determine the smallest positive number P such that 10500P is a perfect cube.
(2 marks)
15. Three police posts X, Y and Z are such that Y is 50 km on a bearing of 060° from X while Z
is 70 km from Y and on a bearing of 300° from X.

(a) Using a suitable scale, draw a diagram to represent the above situation. (3 marks)
(b) Determine the distance, in km, of Z from X. (1 mark)

16. A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm, if the volume of the smaller cone is 160 cm3, find the volume of the frustum
(3 marks)

(3 marks)
SECTION II (50 marks)
Answer any five questions in this section in the spaces provided.
17. A solid consists of a cone and a hemisphere. The common diameter of the cone and the hemisphere is 12 cm and the slanting height of the cone is 10 cm. (a) Calculate correct to two decimal places:

(i) the surface area of the solid;
(ii) the volume of the solid. (4 marks)

(b) If the density of the material used to make the solid is 1.3 g/cm3, calculate its mass in
kilograms. (3 marks)

18. Makau made a journey of 700 km partly by train and partly by bus. He started his journey at 8.00 a.m. by train which travelled at 50 km/h. After alighting from the train, he took a lunch break of 30 minutes. He then continued his journey by bus which travelled at 75 km/h. The whole journey took 111/2 hours.
(a) Determine:
(i) the distance travelled by bus; (4 marks)
(ii) the time Makau started travelling by bus. , (3 marks)
(b) The bus developed a puncture after travelling 1871/2 km. It took 15 minutes to
replace the wheel.
Find the time taken to complete the remaining part of the journey (3 marks)

19. (a) The product of the matrices
is a singular matrix.

Find the value of p. (3 marks)

(b) A saleswoman earned a fixed salary of Ksh x and a commission of Ksh y for each item sold. In a certain month she sold 30 items and earned a total of Ksh 50 000. The following month she sold 40 items and earned a total of Ksh 56 000.

(2 marks)
(i) Form two equations in x and y.

(ii) Solve the equations in (i) above using matrix method. (3 marks)

(iii) In the third month she earned Ksh 68 000. Find the number of items sold.
(2 marks)

20. In a triangle ABC, BC =8 cm, AC= 12 cm and angle ABC = 120°.
(a) Calculate the length of AB, correct to one decimal place. (4 marks)

(b) If BC is the base of the triangle, calculate, correct to one decimal place:

(i) the perpendicular height of the triangle; (2 marks)

(ii) the area of the triangle; (2 marks)

(iii) the size of angle ACB. (2 marks)

21. (a) Using the trapezium rule with seven ordinates, estimate the area of the region
bounded by the curve y = —x2 +,6x+ 1, the lines x = 0, y = 0 and x = 6.
(5 marks)

(b) Calculate:

(i) the area of the region in (a) above by integration; (3 marks)
(iii) the percentage error of the estimated area to the actual area of the region,correct to two decimal places. (2 marks)

(3 marks)

22. The displacement, s metres, of a moving particle after,t seconds is given by,
s =2t 3- 5t2 + 4t + 2. .
Determine:

(a) the velocity of the particle when t = 3 seconds; (3 marks)

(b) the value of t when the particle is momentarily at rest; (3 marks)

(c) the displacement when the particle is momentarily at rest; (2 marks)

(d) the acceleration of the particle when t = 3 seconds. (2 marks)

23. In the figure below, ABCD is a trapezium, AB is parallel to DC, diagonals AC and DB intersect at X and DC = 2 AB. AB = a, DA = d, AX = k AC and DX = hDB, where h and k are constants.

d

(a) Find in terms of a and d:

(i) BC; (2 marks)

(ii) AX; (2 marks)

(iii) DX; (1 marks)

(b) Determine the values of h and k (5 marks)

24. The frequency table below shows the daily wages paid to casual workers by a certain company.
Wages in shillings
100-150
1.50-200
200-300
300-400
400-600

No: of workers
- 160
120
380
240
100

(a) Draw a histogram to represent the above information.
(5 marks)

(b) (i) State the class in which the median wage lies. (1 mark)
(ii) Draw a vertical line, in the histogram, showing where the median wage lies.
(1 mark)
(c) Using the histogram, determine the number of workers who earn sh 450 or less
per day. (3 marks)

Mathematics Paper 1 Question Paper

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