MATHEMATICS PAPER 1 - 2019 KCSE STAREHE MOCK EXAMS (QUESTIONS AND ANSWERS)

INSTRUCTIONS TO CANDIDATES

• This paper consists of TWO sections: Section I and Section II
• Answer ALL the questions in Section I and only five questions form Section II
• All answers and working must be written on the question paper in the spaces provided below each question.
• Show all the steps in your calculations, giving your answers at each stage in the spaces below each question
• Marks may be given for correct working even if the answer is wrong
• Non-programmable silent electronic calculator and KNEC Mathematical tables may be used except where stated otherwise.

SECTION A   (50 Marks)
Attempt all questions in the spaces provided

1. Show that 8260439 is exactly divisible by 11, using test of divisibility.   (2 marks)                                                                                                                          

2. Use logarithms tables to evaluate ∛(4.562×0.0380)(0.3+0.52)^-1
   Give your answer to 3 significant figures.    (4 marks)                                                                                                                            

3. Without using a calculator, evaluate                                          
   36 – 8x – 4 – 15 ÷ -3    (3 marks)                                      
   3x – 3 + -8(6 – (-2))        
4. The figure below (not drawn to scale) shows the cross-section of a metal bar of length 3 metres. The ends are equal semicircles. Determine the mass of the metal bar in kilograms if the density of the metal is 8.87 g/cm³  (3 marks) 
                                                           

5. A solid metal cone has a diameter of 14cm and a height of 24cm. If the cone is melted and recast into a cylinder of the same diameter, what is the height of the cylinder?        (3 marks) 
6. Find the integral values of x which satisfy the following inequality.
   2x+3 > 5x-3 > -8   (3 marks)                                                                                                                                                         

7. 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 = mx+c     (3 marks)                                                       

8. If sinα=5t and cosα=6t, find t. (3 marks)

9. Factorise completely the expression,3x²y²-8xy-51    (3 marks)

10. On the grid below, draw a histogram to represent the following distribution.   (4 marks)
    

    Length (cm)	1 – 5	6 – 9	16 – 30	31 – 40
    Frequency	2	4.5	3.33	4

                

11. An observer stationed 20m away from a tall building finds that the angle of elevation of the top of the building is 68^° and the angle of depression of its foot is 50^°. Calculate the height of the building.    (3 marks)

12. Solve without using tables. 
    9^x+1 + 3^2x+1 = 108   (3 marks)                                                                                                    

13. In the figure below MNO = 54^°, and PLM = 50⁰, PN = NM and PO is parallel to LM. Find the value of LPM  (3 marks)
    

14. A container of height 90cm has a capacity of 4.5litres. What is the height of a similar container of volume 9m³. (3 marks)                                                                                             

15. Express 0.45  as fraction in its simplest form           (3 marks)

16.  
    1. Find by calculation the sum of all the interior angles in the figure ABCDEFGHI below   (2 marks)
       
    2. Find the number of sides of a regular polygon whose interior angle is 162⁰    (2 marks)

SECTION B   (50 Marks)
Attempt five questions only from this section

17. The table below shows marks scored by 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

    
    
    1. Determine the value of a.         (1 mark)                                                                                    
    2. Taking 1cm to represent 10 marks on the horizontal axis and 1cm to represent 10 pupils on the vertical axis draw an ogive.  (3 marks) 
    3. From your graph
       1. Determine the median.                                                            (2 marks)                                                                                                                                        
       2. Determine the range of marks of the middle  of the students.                    (2 marks)                                   
    4. If 63% is the pass mark for grade B+, how many students will get B+ and above?(1 mark)         
    5. State the median class     (1 mark)

18. The position vectors of points A and B with respect to the origin are a and b P is a point on OA such that OA=3OP. Qdivides OB externally in the ratio 5:2. PQ intersects AB at N
    
    1. Express the vectors AB, AP, OQ and PQ in terms of a and b.                         (3 marks) 
                             
    2. Express AN in two different ways.                   (5 marks)                  
    3. In which ratio doesN divide AB                (1 mark)
    4. Express PN in terms of PQ.                 (1 mark)

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:-
    1. The distance from B to C.      (2 marks)
    2. Time taken between C and D.  (2 marks)                                                                                                            
    3. If the train halts at B for 3 minutes and at C for 4minutes and the average speed for the whole journey is 50km/h. Find its average speed between B and (4 marks)           
    4. If the return journey was at 54km/h, how long did he take for the journey?     (2 marks)      

20. On the upper part of a line RQ construct locus of points    (10 marks)
    1. T₁ such that angle RTQ = 45⁰
    2. M on RQ which is equidistant from R and Q.
    3. S which is equidistant from R and Q and lies on T.
    4. Calculate area bounded by loci T₁ and line RQ.

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/= each.
    1. Calculate the cash price.       (2 marks)                                                                                                         
    2. How much will the employee have paid for the pick-up after 3 years?         (2 marks)       
    3. What percentage profit did the financial company get from the employee on the pick up? (2 marks)  
    4. If the car was depreciating at the rate of 12% p.a, calculate the value of the car after 3years.  (2 marks)                                               
    5. 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? (2 marks)                                   

22. Three planes P, Q and R departed Jomo Kenyatta International Airport at 0810 Hrs, 0840 Hrs and 0920 Hrs respectively. Plane P traveled at 300km/h along N70^°W, plane Q traveled at 240 km/h along ENE and R traveled at 400 km/h along 210^°. Using a scale of 1cm to represent100 km, locate the position of the planes at 1050 Hrs. (6 marks)
    1. Find the distance of plane Q and R at 1050 Hrs.  (2 marks)                      
    2. Find the bearing of plane Q from plane P    (1 mark)                                                                                          
    3. Find the bearing of plane R from plane Q.    (1 mark)                                                                                                                

23.  
    1. Complete the following table for the function:y = x³ – 2x²+ 5.  (2 marks)
       

       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

                               
    2. 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.          (3 marks)    
    3. Using your graph estimate the roots of x³ – 2x² – 7x – 4 = 0.                           (2 marks)                                                  
    4. Use integration to find the area bounded by the curve y = x³ – 2x² + 5, the y-axis and line y = 7x + 9.   (3 marks)                                

24. Water flows through a pipe of internal radius of 3.5cmat 9 metresper second into a storage tank of rectangular base of 12m by 8m Calculate:
    1. the volume of water delivered into the tank in one minute in litres.  (2 marks)          
    2. 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 jerrycan of 20 litres each per day.  (2 marks)   
    3. 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. (2 marks)       
    4. how long will it take the pipe to fill the tank to that level giving your answer in hours.(2 marks)
    5. Calculate the monthly bill of the village if the cost of water is Kshs.1.50 per jerrycan (take a month of 30 days)     (2 marks)         

MARKING SCHEME