Get premium membership and access revision papers, questions with answers as well as video lessons.
Keiyo District Maths Paper 1 Question Paper
Keiyo District Maths Paper 1
Course:Secondary Level
Institution: Mock question papers
Exam Year:2006
121/1
Paper 1
SECTION I ( 50 marks)
(Answer all questions in this section)
1. Use mathematical tables to evaluate. 4mks *Kyo*
1
(0.02374)2 - 0.02374
2. Simplify completely 4mks *Kyo*
(a + 2b)2 - ( 2 a – b)2
9b2 - a2
3. Find the number such that ¼ of it is added to 4 1/3, the result is the same as when 1/3 of it is subtracted from 20 2/3. 2mks *Kyo*
4. Expand and simplify without using tables and calculator. 3mks *Kyo*
3 + ? 2 2 - 3 - ?2 2
?2 ?2
5. The points P,Q and R have co-ordinates (2,4), (7,-2) and (6,2) respectively. Find the equation of the line L, which is perpendicular to the line PQ and passes through the mid-point of PR. 3mks *Kyo*
6. Find the range of x if x + 21 > 15 – 2x > x + 12. 3mks *Kyo*
7. Two sides of a triangle have column vectors:AB = 4 and BC = 3
3 3
Write down the column vector of CA, hence find its length, giving your answer in 4 significant figures. 3mks *Kyo*
8. The cost of the car outside Kenya is US $ 4,800. You intend to buy one such car through an agent who deals in Japanese yen. The agent will charge 15% commission on the price of the car and further 72,220 Japanese for shipment of the car. How many Kenya shillings will you need to send to the agent to obtain the car, given that;
1 US $ = 117.20 Japanese yen
1 US $ = Ksh. 72.34 3mks *Kyo*
9. A container of height 90cm has a capacity of 4.5litres. What is the height of a similar container of volume 9m3. 3mks *Kyo*
10. Junior paid shs.320 for a video tape after getting a discount of 13.5%. How much should a shopkeeper have sold the tape to enable him make a profit of 5%. 3mks *Kyo*
11. Three towns J, K and L are such that K is 40km on a bearing 2900 from J. Town L is directly to the south of J. The distance between K and L is 60km. By scale drawing, find the distance of L from J. Using scale of 1:1000 000. 4mks *Kyo*
12. Express 0.73 as fraction. 2mks *Kyo*
13. The figure below shows a hemispherical bowl of thickness 1.5cm. Given that the external surface area is 509cm2. Find the volume of the bowl. (Take ?= 3.142) 3mks *Kyo*
14. In the figure below ? MNO = 540, and ?PLM = 500, PN = NM and PO is parallel to LM. Find the value of ?LPM. 3mks *Kyo*
15. In the figure below, AB is a diameter of the circle and AB = 8cm, BC=xcm and AC= 2xcm. Calculate the length of AC to 2 significant figures. 3mks *Kyo*
16. The angle of elevation of the top of a storey building from point P is 23.610. From another point Q, six metres nearer to the base of the building, the angle of depression from the top of the building is 350. Calculate to 1 decimal place the height of the building. 4mks *Kyo*
SECTION II ( 50 MARKS)
Answer any five questions from this question.
17. A sector of angle 1080 is cut from a circle of radius 20cm. It is folded and fixed to form a cone. Taking ? as 22/7, calculate:-
a) The curved area of the cone. 2mks *Kyo*
b) The base radius of the cone. 3mks *Kyo*
c) The vertical height of the cone. 2mks *Kyo*
d) If 12cm of the cone is chopped off to form a frustrum as shown below
Calculate the volume of the frustrum formed. 3mks *Kyo*
18. A car travels a long a road and at various intervals, the following reading were taken from a specially constructed speedometer.
Time (s) 0 5 10 15 20 25 30 35 40 45
Speed m/s 0 7.2 17.2 23 25 26 25 20 12 2.5
a) Using the data above
(i) Plot the graph of speed against time on the grid provided. 3mks *Kyo*
(ii) Estimate the acceleration of the car after 17 seconds. 3mks *Kyo*
b) Use the trapezoidal rule to estimate the distance traveled in the first 40 seconds, using 8 trapezia. 4mks *Kyo*
19. Use a ruler and a pair of compass only in this question. A treasure T, is hidden within the upper side of path AB, and that angle ATB = 300. It is also located 4km from point B and 3.5km from the path AB. Path AB is drawn to scale of 1:100,000.
a) Determine the actual length of path AB in km 2mks *Kyo*
b) Locate the possible position where the treasure is hidden. 6mks *Kyo*
c) Find the distance from the treasure to the path. 2mks *Kyo*
20. A cold water tap can fill a bath in 3 minutes while a hot water tap can fill in 5 minutes. The drain pipe can empty the full bath in 3 ¾ minutes. The two taps and the drain pipe are fully open for 2 minutes, after which the drain pipe is closed.
a) What fraction of the tank is filled after the first two minutes. 3mks *Kyo*
b) How many more seconds are required for the bath to be completely filled. 3mks *Kyo*
c) Given that, the cold water tap delivers water at the rate of 200cm3/s determine:-
(i) Capacity of the bath in litres. 2mks *Kyo*
(ii) Rate of flow of hot water tap. 2mks *Kyo*
21. Eldoret and Nairobi are 350km apart. Two buses A and B started from Nairobi at the same time traveling towards Eldoret. Bus B, traveling at an average speed of 12km/hr greater than that of A reaches Eldoret 1 1/5 hours earlier.
a) Find the average speed of A. 6mks *Kyo*
b) How far was A from Nairobi when B was 20 minutes to reach Eldoret. 4mks *Kyo*
22. The figure below shows a triangle OAB. Point Y divides line OA in the ratio 1:2 and point x divides OB in the ratio 1:2
AX anfd YB intersect at z.
a) Given that OA = 12a and OB= 12b, express in terms of a and b.
7. (i) AB. 1mk *Kyo*
8. (ii) YX 1mk *Kyo*
Given that YZ= ¼ YB, express in terms of a and b
9. (i) YB 2mks *Kyo*
10. (ii) AZ. 2mks *Kyo*
11. (iii) ZX 2mks *Kyo*
c) Show that points A, Z and X are collinear. 2mks
23. The following are masses of 25 students in form 4 class.
49, 51, 50, 60, 55, 45, 56, 51, 58, 59
44, 59, 42, 50, 62, 46, 43, 57, 56, 52
43, 41, 40, 54, 44.
a) Draw a frequency distribution table with the lower class as 40-43. 4mks
b) Estimate the median mass.
c) Draw a histogram for the data. 4mks
24. The figure below shows two circles that intersect at points A and B. Point E is the centre of the smaller circle and lies on the circumference of the larger one. FAC and FBD are straight lines. ?AFB = 650 and ? FCD = 700.
Calculate:
(a) The obtuse angle AEB. 2mks
(b) Angle ACB. 2mks
(c ) Angle BAD. 3mks
(d ) Angle EBF. 3mks
More Question Papers