Mathematics Paper 1 Questions - Alliance Boys High School Post Mock KCSE 2020

INSTRUCTIONS TO CANDIDATES

• Write your name, class and school number, signature in the spaces provided
• The paper contains two sections Section / and section //
• Answer ALL questions in section / and any five questions in section ll
• Answers and working must be written on the question paper in the spaces provided below each question
• Show all steps in your calculation below each question
• Marks may be given for correct working even if the answer is wrong
• Non programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise

Section I (50 marks)
Attempt all the questions in the spaces provided.

1. Without using a mathematical table or a calculator, evaluation.
   -24 ÷ 8 - 9x 3 - 2 x 5
         -56 ÷1 of 5¼
   (3 marks)
2. Simplify the expression
   3x² - 4xy + y²
        9x² - y²
3. The exterior angles of an irregular pentagon are xº, (x+10)º. (x - 10)º,(2x - 90)º and (2x - 40)º. Determine the value of x (3 marks)
4. The figure below shows a circle ABCDE centre O. The line FEG is a tangent to the circle at point E. Line DE is
   parallel to CG, angle DEC -28° and angle AGE - 32°
   
   Calculate
   1. Angle AEG (2 marks)
   2. Angle ABC (2 marks)
5. Line Ll passes through point (1, 2) and has a gradient of 5. Line L2 is perpendicular to LI and the two lines meet at a point where x=4, find the equation of L2 in the form ymx+c (3 marks)
6. A kilo of robusta coffee costs Kshs 80 and a kilo of Arabica costs kshs 50. The two are mixed in the ratio of 1:3. At what price should the mixture be sold to make a 40% profit? (3 marks)
7.  
   1. In the space below, construct a rhombus PQRS of side 4.4 cm and one angle 45° using a tuler and a pair of compasses only. (2 marks)
   2. Calculate the area of the rhombus.(2 marks)
8. Find all the integral, values of x which satisfy the inequalities 2(2-x) < 4x-9<x+11(3 marks)
9. Barongo uses of her income on her mandatory expenses and saves a quarter of it. The difference between his expenditure and savings is Kshs 14,000. If she uses the rest for leisure, determine
   1. her income  (2 marks)
   2. the amount she uses for leisure. (2 marks)
10. Find the value of which satisfies the equation.
    5^2x - 6 x 5^x + 5 = 0 (3 marks)
11. In the figure below IN = 5cm, KM =2cm, LM-4cm and NM = x cm.
    
    Determine the value of x to 2 significant figures. (3 marks)
12. A clothes dealer sold three shirts and two trousers for shs 840 and four shirts and five trousers for shs 1680. Form equations to represent the above information and solve them to find the cost of one shirt and one trouser. (3 marks)
13. Given that log 3 =0.4771 and log 5=0.6990, determine the value of log (0.045) without the use of mathematical tables or a calculator(3 marks)
14. Juma walks directly from point X towards the foot of a building 300m away. After covering 160m, he observes that the angle of elevation of the top of the building is 50o. Determine the angle of elevation of the top of the building from X. (3marks)
15. John and Peter working together candig a piece of land in 4.8 days. John working alone takes 4 days less than Peter. How many days does peter take to dig the piece of land alone? (3marks)
16. The figure below shows a histogram.(3marks)
    
    Complete the frequency distribution table below.
    

    length x cm	class width	frequency density	frequency
    8-9		1.2	24
    12-15			48
    		2.0

    
    Section II (50 marks)
    Answer only five questions in this section in the spaces provided.
17. The figure below shows a trough used to hold water for bathing
    
    
    1. Calculate the capacity of the trough in litres. (4 marks)
    2. Agnes used a small rectangular container below to fill the trough with water
       
       How many times did she pour water to fill the trough? (3 marks)
    3. Calculate the surface area of the trough(3 marks)
18.  
    1. Coast Bus left Nairobi at 8.00a.m. and traveled towards Mombasa at an average speed of 80km/hr. At 8.30am, City Bus left Mombasa towards Nairobi at an average speed of 120km/hr. Given that the distance between Nairobi and Mombasa is 400km, calculate:
       1. The time the two vehicles met. (4mks)
       2. The distance from Nairobi to the meeting point. (2mks)
    2. A car accelerated from rest to a velocity of 10m/s in 10 seconds. It travelled at this velocity for 20 seconds and then came to a stop in 5 seconds.
       1. Draw a velocity time graph (2marks)
       2. Find the distance travelled. (2marks)
19.  
    1. Three towns A, B and Care situated so that AB - 65 km and AC = 115 km. The bearing of B from A is 062° and the bearing of C from A is 278°.
       1. Draw a sketch to show the relative positions of A,B and C (Imark)
       2. Calculate the distance BC (2 marks)
       3. Calculate the bearing of B from C (2 marks
    2. Two ships R and S left port A at 7.00 am. R sails on a bearing of S60°W at 90km/h and S sails eastwards at a speed of 75km/h.
       1. Using a scale drawing of Icm represents 10 km, show the relative positions of the ships at 7.40 am. (4 marks)
       2. State the bearing of S from R. (1 mark)
20.  
    1. The angles of elevation of the top of a building 24m high is observed from the top and from the bottom of a vertical ladder and found to bc 450 and 60° respectively. Find the height of the ladder. (4 marks)
    2. A square is drawn in a semi-circle of diameter 12cm as in the figure below
       
       O being the centre of the circle, calculate
       1. the length of the side of the square leaving your answer in surd form. (2 marks)
       2. angle YAO (2 marks)
       3. the length YA (2 marks)
21. Three partners Mutua, Muthoka and Mwikali contributed Sh. 600,000, Sh. 400,000 and Sh. 800,000 respectively to start a business of a matatu plying Mbumbuni - Machakos route. The matatu carries 14 passengers with each paying Sh. 250. The matatu makes two round trips each day and ever full. Each day Sh.
    6000 is used to cover running costs and wages.
    1. Calculate their net profit per day. (2 marks)
    2. The matatu works for 25 days per month and is serviced every month at a cost of KSh.10,000. Calculate their monthly profit in June.(1 mark)
    3. The three partners agreed to save 40% of the profit, 24% to be shared in the ratio of their contribution, Calculate Muthoka's share in the month of July (4 marks)
    4. The matatu developed mechanical problems and they decided to sell it through an agent who charged a commission of 5% on selling price. Each partner received K Sh. 475.000 from the agent after he had taken his commission. Determine the price at which the agent sold the matatu. (3 marks)
22. In the figure below BA a and BC - E divides AC in the ratio 1:2, D is the midpoint of AB and F is the intersection of BÉ and CD. Given that DF =hDC and BF - (1 - K) BE where h and k are scalars.
    
    1. Find in terms of a and b
       1. AC (1 mark)
       2. BE (1 mark)
       3. DC (1 mark)
    2. Determine the values of h and k. (6 marks)
    3. Hence state the ratio in which D divides CF. (mark)
23.  
    1. Find the equation of a function whose solutions are obtained from points P and Q as shown in the diagram below (2marks)
       
    2. The table below shows values of x and some values of y for the curve y = x³ + 2x² -3x - 4 for -3 ≤ x ≤ 2. 
       

       x	-3	-2.5	-2	-1.5	-1	-0.5	0	0.5	1	1.5	2
       y	-4.0	0.4		1.6	0		-4.0	-4.9			6.0

       1. Complete the table correct to 1 decimal place.(2marks)
       2. On the grid provided, draw the graph of y= x³ + 2x² -3x - 4. Using the scale 1cm represents 0.5 units on x-axis and 1 cm represent 1 unit on y-axis. (3marks)
       3. Use the graph to solve, x³ + 2x² -3x - 4 = 0 (1mark)
       4. By drawing a suitable line on the graph to solve the equation x³ + 2x² - 3x = ²/₃x + 3¹/₃  (2marks)
          
24. The displacement s metres of a moving particle after t seconds is given by:- s= 2t² - 5t² + 4t + 2
    Determine:
    1. The velocity of the particle when t = 2 (2marks)
    2. The value of t when the particle is momentarily at rest.(2marks)
    3. The displacement when the particle is momentarily at rest.(2 marks)
    4. The acceleration of the particle when t = 5. (2marks)
    5. The maximum velocity attained (2marks)