MATHEMATICS PAPER 2 - KCSE 2019 STAREHE PRE MOCK EXAMINATION (WITH MARKING SCHEME)

SECTION I (50 MARKS)
Answer all the questions from this section

1. Use logarithm to solve tables to evaluate (4 marks)
   

2. The length and breadth of a rectangular paper were measured to be the nearest centimeter and found to be 20cm and 15 cm respectively. Find the percentage error in its perimeter leaving your answer to 4 significant figures.      (3 marks)

3. Simplify the following surds leaving your answer in the form a+b√c(3 marks)
   

4. In the figure below QT is a tangent to the circle at Q. PXRT and QXS are straight lines. PX = 6cm, RT = 8cm, QX = 4.8cm and XS = 5cm.                                                   
   Find the length of QT       (3 marks)
   

5. Mary and Jane working together can cultivate a piece of land in 6 days. Mary alone can complete the work in 15 days. After the two had worked for 4 days Mary withdrew the services. Find the time taken by Jane to complete the remaining work. (3 marks)

6. The equation of a circle is given by   3x² + 3y² – 18x + 12y – 9=0. Determine the radius and the center of the circle.       (3 marks)

7. Make Q the subject of the formula   (3 marks)
   

8. Solve for x in the equation
   2sin² x – 1 = cos² x + sin x for 0⁰ ≤   x ≤ 360    (3 marks)

9. Solve for x in  (3 marks)
   

10. In a transformation, an object with area 4cm² is mapped onto an image whose area is 48cm² by a transformation matrix Find the value of y (3 marks)

11.  
    1. Expand (2 + 2y)⁵. (2 marks)
    2. Hence find the value of (2.02)⁵, correct to 4 decimal places when substitution for y is up to y⁴.            (2 marks)

12. A coffee blender mixes 6 parts of type A with 4 parts of type B. If type A costs sh 72 and type B costs him sh 66 per Kg respectively, at what price should he sell the mixture in order to make 5% profit? Give your answer to the nearest ten cents.                         (3 marks)

13. The data below represents the ages in months at which 11 babies started walking: 9,15 , 12, 9, 8, 13, 7, 11, 13, 14 and 10.
    Calculate the interquartile range of the above data       (3 marks)

14. Karimi deposited sh 45000 in a bank which paid compound interest of 12% per annum. Calculate the amount after 2 years to the nearest whole number.        (3marks)

15. Use tables of reciprocals only to work out (3 marks)
    

16. PQR is a triangle of area 9cm² . If PQ is the fixed base of the traingle and 6cm long draw it and describe the locus of point R. (3marks)

SECTION II (50 MARKS)
Answer FIVE questions ONLY from this section

17. Income tax is charged on annual income at the rates shown below.
    Taxable annual income (K£)            Rate sh per   k £
    1 - 2300                                                        2
    2301 - 4600                                                   3
    4601 - 6900                                                   5
    6901 - 9200                                                   7
    9201 - 11, 500                                               9
    11501 and above                                         10
    Personal relief of ksh. 1056 per month
    Insurance relief of ksh. 480 per month
    Mr. Kimathi earns a basic salary sh. 13800 per month. In addition to his salary he get a house allowance of ksh.8000 per month and medical allowance of sh. 5000 per month.
    Calculate;
    1. Kimathi’s taxable income per annum in K£                                                 (2marks)
    2. Kimathi’s net tax per month in Kenya shillings.                 (5marks)
    3. Calculate Mr. Kimathi’s net monthly salary in Kenya shillings. (3marks)                                

18.  
    1. An arithmetic progession is such that the first term is -5, the last is 135 and the sum of the progression is 975. Calculate:
       1. The number of terms in the series (4 marks)
       2. The common difference of the progression (2 marks)
    2. The sum of the first three terms of a geometric progression is 27 and first term is 36. Determine the common ration and the value of the fourth term     (4 marks)

19. The diagram below represents a pyramid standing on rectangular base ABCO. V is the vertex of the pyramid and VA = VC = VD = VE = 26cm. M and N are the midpoints of BC and AC respectively. AB = 24cm and BC = 18cm.
    
    Calculate:-
    1. The length of the line AC             (2marks)
    2. The length of projection of the VA on the plane ABCD.             (1mark)
    3. The angle between line VA and the plane ABCD.             (2marks)
    4. The vertical height of the pyramid.             (2marks)
    5. The size of the angle between the planes VBC and ABCD. (3marks)

20. Three quantities R, S and T are such that R varies directly as S and inversely as the square of T.
    1. Given that R = 480 when S = 150 and T =5, write an equation connecting R, S and T.       (4marks)
       1. Find the value of R when S = 360 and T = 1.5.             (2marks)
       2. Find the percentage change in r if S increases and t decreases by 20%.    (4marks)

21. The water supply in a town depends entirely on two water pumps. A and B. The probability of pump A failing is 0.1 and the probability of pump B failing is 0.2. 
    1. Draw a tree diagram to represent this information                   (2marks)                                 
    2. Calculate the probability that;
       1. Both pumps are working        (2marks)
       2. There is no water in the town     (2marks)
       3. Only one pump is working (2marks)                                                   
       4. There is some water in the town      (2marks)

22. Complete the table below by filling in the blank spaces.                                        (2 marks)
    

    x0	00	300	600	900	1200	1500	1800	2100	240	2700	300	330	3600
    Cos x0	1.00		0.50			-0.87		-0.87
    2 Cos ½ x	2.00	1.93					0.00

    
    
    1. On the grid provided using a scale of 1cm to represent 30⁰ on the horizontal axis and 4 cm to represent 1 unit on the vertical axis draw the graph of y = cos x⁰ and y = 2cos ½ x⁰
       (4 marks)
    2. State the amplitude and period of y = 2cos ½ x (2 marks)
    3. Use your graph to solve the equation (2 marks)
       2 cos ½ x – cos x = 0

23. ABCD is a quadrilateral with coordinates A(2,1) B(3,2) C(3,4) and D(0,3). ABCD is mapped onto A’B’C’D’ under transformation T given by a shear with x – axis invariant such that A’ (4, 1).
    1. Determine the 2×2 transformation matrix representing T and hence determine the coordinates of B’, C’ and D’. (4 marks)
    2. A’B’C’D’ is transformed to A”B”C”D” under a transformation H such that A”(-6,-9) and D”(-12,-15). Determine the 2×2 matrix representing H and hence determine the coordinates of B” and C” (3 marks)
    3. A”B”C”D” mapped onto A”’B”’C”’D”’ under a transformation V representing a reflection in the line y=-x. Determine the  matrix representing V and hence determine the coordinates of A”’B”’C”’D”’  (3 marks)

24. A parallelogram OACB is such that OA = a, OB = D is the mid-point of BC. OE = hOC and AE = kAD.
    
    
    1. Express the following in terms of a, b, h and k.
       1. OC    (1 mark)
       2. OE      (1 mark)
       3. AD    (1 mark)
       4. AE      (1 mark) 
    2. Find the values of h and k. (4 marks)
    3. Determine the ratios:
       1. AE : ED      (1 mark)
       2. OE : OC      (1 mark)

MARKING SCHEME