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Bondo District Maths Paper 1 Question Paper
Bondo District Maths Paper 1
Course:Secondary Level
Institution: Mock question papers
Exam Year:2006
121/1
PAPER 1
SECTION 1 ( 50 MARKS)
Answer all the questions
1. Show that 8260439 is exactly divisible by 11, using test of divisibility. (2mks) *BND*
2. Use logarithms tables to evaluate
3 (4.562 x 0.038) ( 0.3 + 0.52)-1
Giving your answer to 3 significant figures. (4mks) *BND*
3. Without using a calculator, evaluate
36 – 8 x –4 - 15 ? - 3
3 x –3 + -8 ( 6 – (-2)) (3mks) *BND*
4.
The above figure (not drawn to scale) shows the cross-section of a metal bar of length 3 meters. The ends are equal semi-circles. Determine the mass of the metal bar in kilograms if the density of the metal is 8.87 g/cm3 . (3mks) *BND*
5. In the figure below, O is the center of the circle. AOD and BCD are straight lines. Angle AOC = 1380 and angle OAB=350. Determine the size of angle ADB. (2mks) *BND*
6. At 10.30am, a boy starts out from town A and cycles at an average speed of 15km/h towards B which is 65km away. Some 20 minutes later a motorist leaves town B and travels towards A at an average speed of 75km/h. At what time did the two meet. (4mks) *BND*
7. Find the integral values of X which satisfy the following inequality.
2x + 3 > 5x – 3 > - 8 (3mks) *BND*
8. a) Sketch the net of a wedge in the following figure.
b) Calculate the surface area of the net drawn above. (3mks) *BND*
9. The G.C.D of two numbers is 12 and their L.C.M is 240. If one of the numbers is 60, find the other number. (2mks) *BND*
10. ABCD is a Rhombus with three of its vertices A(2,5), B (1, -2), C (-5,1). Determine the equation of line BD in the form of y = mc + c. (3mks) *BND*
11. A surveyor recorded the information about a tea farm in his field book as in the table below.
Q
600 90 to C
To A 180 420
300 90 to D
To B 50 50
P
a) Given that PQ = 650m, make a sketch of the field. (2mks) *BND*
b) Hence find the area of the field in hectares. (2mks) *BND*
12. Factorise completely the expression,
3x2y2 – 8xy – 51 (3mks) *BND*
. On the grid below, draw a histogram to represent the following distribution. (3mks) *BND*
Length (cm) 1 – 5 6 – 15 16 – 30 31 – 40
Frequency 2 9 10 8
14. An observer stationed 20m away from a tall building finds that the angle of elevation of the top of the building is 680 and the angle of depression of its foot is 500. Calculate the height of the building. (3mks) *BND*
15. Find by construction, the center and the angle of rotation if A1B1 is the image of AB.
(3mks) *BND*
16. Solve without using tables.
9x + 1 + 3 2x+1 = 108 (3mks) *BND*
SECTION II ( 50 MARKS)
Answer any 5 questions in this section
17. The table below shows marks scored by 120 candidates in an examination.
Marks 1 – 10 11-20 21-30 31-40 41-50 51- 60 61-70 71-80 81-90 91-100
Frequency 2 6 10 a 24 21 19 12 8 1
a) Determine the value of a. 1mk*BND*
b) Taking 1cm to represent 10 marks on the horizontal axis and 1cm to represent 10 pupils on the vertical axis, draw an ogive. (3mks) *BND*
From your graph
(i) deterine the median. (2mks) *BND*
(ii) determine the range of marks of the middle 60% of the students. (2mks) *BND*
(iii) If 63% is the pass mark for grade B+, how many students will get B+ and above? (1mk) *BND*
c) State the median class (1mk) *BND*
18. The position vectors of points A and B with respect to the origin are a and b respectively. P is
? ?
a point on OA such that OA = 3OP. Q divides OB externally in the ratio 5:2. PQ intersect AB
? ? ? ?
at N.
a) Express the vectors AB, AP, OQ and PQ in terms of a and b. (3mks) *BND*
? ? ? ? ? ?
b) Express AN in two different ways. (5mks) *BND*
c) (i) In which ratio does N divide AB (1mk) *BND*
(ii) Express PN in terms of PQ. (1 mk) *BND*
19. A commuter train moves from station A to station D via B and C in that order, the distance from A to C via B is 70km and that from B to D via C is 88km. Between the stations A and B, the train travels at an average speed of 48km/h, and takes 15 minutes between C and D. The average speed of the train is 45km/h. Find
(a) The distance from B to C. (2mks) *BND*
(b) Time taken between C and D. (2mks) *BND*
c) If the train halts at B for 3 minutes and at C for 4 minutes and the average speed for the whole journey is 50km/h. Find its average speed between B and C. (4mks) *BND*
(d) If the return journey was at 54km/h, how long did he take for the journey. (2mks) *BND*
20. a) Construct a triangle PQR, such that PQ = 7.5cm, the ratio of <QPR = <PQR = 5:3, and <QRP is 600. (4mks) *BND*
b) Construct the locus of a point S, on the same side as R which moves such that < PSQ = 750. (3mks) *BND*
c) Construct the locus of a point T which moves such that it is always equidistant from lines PQ and PR and produce it to intersect the locus of S at M. (1mk) *BND*
d) By dropping a perpendicular from point M on to PQ at N, measure MN hence calculate the area of triangle PMQ. (2mks) *BND*
21. The marked price of a pick-up is Kshs.1,087,500. A financial company bought this car at a discount of 20%, for a company employee, who was then to give a down payment of Kshs.180,000 and 36 monthly instalments of Ksh.35,600.
(a) Calculate the cash price (2mks) *BND*
(b) How much will the employee have paid for the pick-up after 3 years? (2mks) *BND*
(c) What percentage profit did the financial company get from the employee on the pick up?
(2mks) *BND*
(d) If the car was depreciating at the rate of 12% p.a, calculate the value of the car after 3 years. (2mks) *BND*
(e) If the employee is to buy a new car at the same initial cost, at what percentage profit, on the value of the car after the third year, must he sell it? (2mks) *BND*
22. Three planes P,Q and R left Jomo Kenyatta International Airport at 8.10a.m, 8:40a.m and 9.20a.m respectively. Plane P traveled at 300km/h along N700W, plane Q traveled at 240km/h along ENE and R traveled at 400km/h along 2100.
a) Using a scale of 1cm to represent 100km, locate the position of the planes at 10.50a.m. (6mks) *BND*
b) Find the distance of plane Q and R at 10.50a.m. (2mks) *BND*
c) Find the bearing of plane Q from plane P (1mk) *BND*
d) Find the bearing of plane R from plane Q. (1mk*BND*
23. a) Complete the following table for the function, y = x3 – 2x2 + 5.
X -3 -2 -1 0 1 2 3 4
x3 -8 -1 0 1 27 64
-2x2 -18 -2 0 -2 -8 -18
5 5 5 5 5 5 5 5
y -40 2 5 4 5 14
b) By using the scale of 2cm to represent one unit on the horizontal scale and 1cm to represent 5 units on the vertical scale, Draw the graph of y= x3 – 2x2 + 5 (3mks) *BND*
c) Using your graph estimate the roots of x3 – 2x2 – 7x – 4 = 0.
d) Use integration to find the area bounded by the curve y = x3 – 2x2 + 5, the y-axis and line y = 7x + 9.
24. Water flows through a pipe of internal radius of 3.5cm at 9 metres per second into a storage tank of rectangular base of 12m by 8m.
Calculate
a) the volume of water delivered into the tank in one minute in litres. (2mks) *BND*
b) the capacity of water in litres that is consumed by a village of 435 families that depend on this water, in one week, if each family consumes an average of six jericans of 20 litres each per day. (2mks) *BND*
c) the minimum height of the water level in the storage tank that will ensure that the village doesn’t suffer from water shortage within the week. (2mks) *BND*
d) how long will it take the pipe to fill the tank to that level giving your answer in hours.
(2mks) *BND*
e) Calculate the monthly bill of the village if the cost of water is Kshs.1.50 per jerry can (take a month of 30 days) (2mks) *
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