MATHEMATICS PAPER 1 - 2019 KCSE CEKENA MOCK EXAMINATION (QUESTIONS AND ANSWERS)

SECTION 1   (50 Marks)

Answer all Questions from this Section

1. Evaluate  [3 Marks]
   

2. Owino spends ¹/₄ his salary on school fees. He spends ²/₃ of the remainder on food and a fifth of what is left on transport. He saves the balance. In certain month he saved Sh. 3400. What was his salary?      (3 marks)

3. Simplify:    3mks
   

4. Find the integral values of x that satisfy the inequalities below  [3 Marks]
   3x+1≤4+7x≤3x+11

5. A salesman gets a commission of 2.4% on sales up to Sh. 100,000. He gets additional commission of 1.5% on sales above this. Calculate the commission he gets for sales worth Sh. 280,000. (3 Marks)

6. A minor arc of a circle subtends an angle of 105⁰ at the centre of the circle. If the radius of the circle is 8.4cm, find the length of the major arc (take π=²²/₇ ) (3mks)

7. Given that the matrix is singular find the value of (35x+2x) [3Marks]                                                                                        

8. State the amplitude, period and the phase angle of the curve  y=2 sin sin (³/₂x-30⁰) [3 marks]

9. Without using logarithm table or calculator evaluate  [4marks]
   

10. A tourist arrived in the country with Us $ 2000 which he changed in Kenya shillings. He spent Kshs. 75,000 on hotel accommodation and Kshs. 40,000 on travel and other expenses. He changed the remaining money into sterling pounds. If he did all his transactions based on the bank rate shown below. How many £ did he remain with? Give your answer correct to 2 d.p. [3 Marks]
                                       US$                                £
    Buying (Kshs)             78.45                          112.27
    Selling (Kshs)              79.50                         121.04

11. Evaluate without using tables or calculators [2 Marks]
    

12. Three men working 8hrs daily can complete a piece of work in 5 days. Find how long it will take 10 men working 6hrs a day can complete the same work. [3 Marks]

13. An electric pole is supported to stand vertically on a level ground by a tight wire. The wire is pegged at a distance of 6 metres from the foot of the pole as shown. 
    
    The angle which the wire makes with the ground is three times the angle it makes with the pole. Calculate the length of the wire to the nearest centimeter.  (3 Marks)

14.  
    1. Using line AB given below , construct the locus of point P such that angle APB =90^o .       (1 marks)
       
    2. On the same diagram locate two possible positions of point C such that point C is on the locus of P and is equidistant from A and B.

15. A watch which loses a half minutes every hour was setto reach the correct time at 05 45h on Monday. Determine the time in the 12 hour system, the   watch will show on the watch will show on the following Friday at 1945h.     (3 marks)                                                                                    

16. Given that OA= 2i + 3j and OB=3i- 2j. Find the magnitude of AB to one decimal   (3 Marks) 

SECTION II  (50 Marks)
Answer any 5 questions from this section

17. Complete the table below for the function y=3x²-2x-1 for -3≤×≤4 [2 Marks]
    1. Draw the graph of y=3x² - 2x-1 on the grid provided.                                    [4 Marks]
    2. Draw the line y=3x+1  on the same axis hence find the values of x for which y=3x+1 and y=3x² - 2x-1    [4 Marks]

18. A group of people agreed to raise Ksh. 7 200,000 to start a business. They were to share the amount equally. However 20 members were unable to contribute and withdrew from the group. The remaining members therefore had to contribute Kshs 6000 more each in order to raise the agreed target.
    1. Write down the expression of the amount each member would contribute originally [1 Mark]
    2. Write down an expression of the amount each member would contribute after the withdrawal of some members.    [1 Mark]
    3. Calculate the original number of members of the group.                                [6 marks]
    4. Calculate the percentage increase in the amount of contribution per each number. [2 Marks]

19. Mtwapa Primary School is 30km on a bearing of 015⁰ from a tourist hotel. The nearest town is 45km from the school on a bearing of 120⁰.
    1. Using a scale of 1cm to represent 6km, make a scale drawing of the positions of the school, the tourist hotel and the town. [4 Marks]
    2. How far is the tourist hotel from the town? [2 Marks]
    3. What is the bearing of
    4. The town from the tourist hotel. [2 Marks]
    5. The school from the town [2 Marks]

20. A line L passes through (-2, 3) and (-1, 6) and is perpendicular to a line P at (-1, 6).
    1. Find the equation of L (2mks)
    2. Find the equation of P in the form ax + by = c,where a, b and c are constants. (2mks)
    3. Given that another line Q is parallel to L and passes through point (1, 2) find the x and y intercepts of Q       (3mks)
    4. Find the point of the intersection of lines P and Q (3mks)

21. The diagram below represents a conical vessel which stands vertically which stands vertically. The vessels contains water to a depth of 30cm. The radius of the surface in the vessel is 21cm. (Take π =22/7). 
                
    1. Calculate the volume of the water in the vessels in cm³ (2 Marks)
    2. When a metal sphere is completely submerged in the water, the level of the water in the vessels rises by 6cm.
       Calculate:
       1. The radius of the new water surface in the vessel;   (2 marks)
       2. The volume of the metal sphere in cm³         (3 marks)  
       3. The radius of the sphere.      (3 marks)

22. On The vertices of quadrilateral OPQR are O (0, 0), P (2, 0), Q (4, 2) and R (0, 3). The vertices of its image under a rotation are O’ (1, -1), P'(1, -3) Q'(3, -5) an R'(4, -1).
    1.  
       1. On the grid provided, draw OPQR and its image O'P'Q'R' (2marks)
       2. By construction, determine the centre and angle of rotation.     (3marks)
    2. On the same grid as (a) (i) above, draw O''P''Q''R'', the image of O'P'Q'R' under a reflection in the line y = x     (2marks)
    3. From the quadrilaterals drawn, state the pairs that are:
       1. Directly congruent;                (2marks)
       2. Oppositely congruent         (2marks)

23. The table below shows marks obtained by 100 candidates at East side high school in biology examination.
    

    Marks	15-24	25-34	35-44	45-54	55-64	65-74	75-84	85-94
    Frequency	6	14	24	14	x	10	6	4

    
    
    1. Determine the value of x. (2marks)
    2. State the modal class (1 mark)
    3. Calculate the median mark. (3marks)
    4. Calculate the mean mark. (4marks)

24. The figure below represents a speed time graph for a cheetah which covered 825m in 40 seconds.
    
    
    1. State the speed of the cheetah when recording of its motion started (1 mk)
    2. Calculate the maximum speed attained by the cheetah (3mks)
    3. Calculate the acceleration of the cheetah in:
       1. The first 10 seconds (2mks)
       2. The last 20 seconds      (1mk)
       3. Calculate the average speed of the cheetah in first 20 seconds (3mks)

MARKING SCHEME