MATHEMATICS PAPER 2 - 2019 KCSE KASSU JOINT MOCK EXAMS (QUESTIONS AND ANSWERS)

SECTION I (50 MARKS)
ANSWER ALL QUESTIONS IN THE SPACES PROVIDED

1. Without using logarithm tables or a calculator, solve the equation
   log (5x – 4) = log (x+ 2) + ¹/₃ log 27           (3mks)                                                            

2. Make y the subject of the formula. (3mks)
    
3. A rectangular block has a square base whose side is exactly 8cm. Its height measured to the nearest millimetre is 3.1cm. find in cubic centimetres the greatest possible error in calculating its volume        (3mks)

4. Evaluate without using mathematical tables. (3mks)
   

5. Find the value of x in the equation. (3mks)
   16^(x+2) x 8^(x+3) =2^x

6. Njau, Juma and Kimindiri invested some money in the ratio 5:4:3 respectively. The business realized a profit of Sh 48,000. They shared 50% of the profit equally and the remainder in the ratio of their contributions. Calculate the total amount of money received by Kimindiri. (3mks) 

7. A triangle PQR is such that PQ is 6CM and QR =8cm and < PQR =60 Calculate :
   1. The length of PR (2mks)
   2. The diameter of the circumcircle. (2mks)

8. Simplify  (3mks)
   

9. Find the area bounded by the curve y= x³ + 5, the x axis and lines x=1 and x = 3 (3mks)

10.  
    1. Expand (1 + 2x)⁷ up to the term in x³.                                                       (2mks)                                                                                                                       
    2. Hence use the expansion to estimate the value of (1.02)⁷ correct to four decimal places. (2 mks)

11. A bag contains 2 green balls, 3 red balls and one blue ball. Another bag contains 4 green balls, 5 red balls and 3 blue balls. A ball is chosen at random from a bag. Find the probability that the chosen ball is blue. (3mks)

12. P varies partly as the square of V and partly as the cube of V. When V= 2, P = -20 and when V = -3, P = 135. Find the relationship between P and V. (3mks)

13. The second term of a G.P is 6, and the fifth term is 48, find the common ratio and the 3^rd term of the G.P. (3mks)                         

14. The diagram below represents a field ABC.  
    
    
    1. Draw the locus of points equidistant from sides AB and AC (1mk)
    2. Draw the locus of points equidistant from points A and C.            (1mk)
    3. A coin is lost within a region which is nearer to point A than to point C and closer to side AC than to side AB. Shade the region where the coin can be located. (1mk)

15. Nancy pays for a car on hire purchase in 15 monthly instalments. The cash price of the car is Ksh. 300,000 and the interest rate is 15% p.a. A deposit of Ksh 75,000 is made. Calculate her monthly repayments. (4mks)

16. Solve for q in the equation 2 sin (2q + 10) = -1 for 0 < q < 360⁰. (3mks)

SECTION II (50 MARKS)
ANSWER ANY FIVE QUESTIONS IN THIS SECTION

17. The table below shows Kenya Tax Rates in a certain year.
    Income                             Tax Rate
    (k£ per annum)               (Sh. Per £)
         1 – 1800                            2
    1801 – 3600                            3
    3601 – 5400                            5
    5401 – 7200                            7
    A married man earns sh. 6600 per month and is housed by the employer. The man is given benefits amounting to K£1200p.a for a car, school fees and medical fee. He is allowed a relief of K£ 48 p.a. for insurance and claims K£ 120 family relief p.a. Calculate:                                            
    1. The man’s annual taxable income in K£         (4mks)
    2. The monthly tax paid by the man in KSh.      (6mks) 

18.  
    1. Complete the table below to 2 decimal places. (2mks)
       

       X	00	300	600	900	1200	1500	1800	2100	2400	2700	3000	3300	3600
       Cos x	-1		-0.5		0.5	0.87		0.87			-0.5	0.87
       Sin (x-300)		0.0	0.5			0.87	0.5		–0.5			-0.87	-0.5

    2. Draw the graphs of y = sin (x – 30⁰) and y = – Cos x on the same axes, for 0⁰ < x < 360⁰.    (5mks)
    3. Use your graph to solve the equation sin (x - 30⁰) + Cos x = 0. (3mks) 

19. Figure below is a pyramid on a rectangular base. PQ=16cm, QR = 12cm and VP = 13cm.
    
    Find
    1. The length of QS.               (2mks)
    2. The height of the pyramid to 1 decimal place.    (2mks)
    3. The angle between VQ and the base.                                                                   (2mks)
    4. The angle between plane VQR and the base.                                                      (2mks)
    5. The angle between planes VQR and VPS                                                           (2mks) 

20. The following table shows the distribution of marks obtained by 50 students in a test.
    

    Marks	45-49	50 – 54	55 – 59	60 – 64	65 – 69	70 – 74	75 – 79
    No. of students	3	9	13	15	5	4	1

    
    By using an assumed mean of 62, calculate
    1. the mean    (5mks)
    2. the variance    (3mks)
    3. the standard deviation    (2mks)

21. The velocity of a particle is given as V = 12t – 2t².
    1. Determine the distance travelled by the particle in terms of t if the distance is 6 meters when t = 1.  (3mks)                                                                           
    2. Determine the distance moved by the particle between t = 2 and t =3. (2mks)                        
    3. Calculate the maximum distance moved by the particle. (3mks)
    4. Determine the acceleration after 2 seconds. (2mks)

22. Triangle ABC has vertices A(1,1) ,B(3,1) and C (3,3).
    1. On the grid provide draw triangle ABC. (1mk)
    2. A'B'C' is the image of ΔABC under positive quarter burn about the origin. On the same grid. Draw the image of triangle A'B'C'. (2mks)                                           
    3. A''B''C'' is the image of A'B'C' under transformation given by the matrix 
    4. Determine the co-orrdination of A''B''C''. (2mks)
    5. On the same grid draw the triangle A''B''C''. (1mk)
    6. Find the object area hence determine the area of the final image. (2mks)                 

23. In the figure below OA is a and OB is b M is the mid point OA and AN :AB 3:1
    
    
    1. Express in terms of a and b
       1. AB (1mk)
       2. AN (1mk)
       3. ON (1mk)
    2. Given that  BX= hBM  and OX=kON determine the values of h and k. (6mks) 

24. A manager wishes to hire two types of machine. He considers the following facts.
                                                                    Machine A                 Machine B
    Floor space                                                   2m²                             3m²
    Number of men required to operate                4                                  3         
    He has a maximum of 24m² of floor space and a maximum of 36 men available. In addition he is not allowed to hire more machines of type B than of type A.
    1. If he hires x machines of type A and y machines of type B, write down all the inequalities that satisfy the above conditions.   (4mks)
    2. Represent the inequalities on the grid and shade the unwanted region. (4mks)
    3. If the profit from machine A is Ksh. 4 per hour and that from using B is Ksh. 8 per hour. What number of machines of each type should the manager choose to give the maximum profit? Calculate the maximum profit obtained. (2mks)       

 MARKING SCHEME