**KCSE Past Papers 2017 Mathematics Alt B Paper 2**

**SECTION I (50 marks)**

Answer all the questions in this section in the spaces provided.

**1. Evaluate 190.1 x 30, correct to 3 signiﬁcant ﬁgures. (2 marks)**

l90.lx30=5703

= 5700

**2. Find the sum of the ﬁrst 10 terms in the Geometric Progression 3, 6, 12, (3 marks)**

Common Ratio? = 6/3=2 3(2^{10}/2-1)/2 -1)

3(1024_1)/1= 3069

**3. Given that 5, x, 35 and 84 are in proportion, ﬁnd the value of x. (3 marks)**

5/x=5/34

x=5×84/35

=12

**4. The base of a triangle is 3 cm longer than its height and its area is 35 cm. Determine the height and base of the triangle. (4 marks)**

1/2(x+3)x=35

x^{2}+3x-70=0

(x+10)(x-7)=0

x=7

0r x=-10

**5. The ﬁgure below is a map of a piece of land on a grid of l cm squares.**

**Estimate the area of the map in square centimetres. (3 marks)**

Full square =11

Fractional square = 26

Area estimate = 11+26/2

=24cm^{2}

**6. A chord of a circle, radius 5 cm, subtends an angle of 30° at the centre of the circle. Determine the length of the chord, correct to 2 decimal places. (3 marks)**

**7. The extension (E), in cm, of a rubber band when pulled by a force (F) was found experimentally and recorded as shown in the table below:**

**(a) On the grid provided, draw a graph of extension(E) against force(F). (2 marks)**

**(b) Use the graph to determine the extension when the force is 7 units. (1 mark)**

– Extensions when forces is 7 units 10.5cm

**8. The position of towns M and N are M(0 °, 5 l °W) and N(0 °, 37 °E). Find the distance between the two towns in kilometres, correct to one decimal place.**

**(Take the radius of the earth as 6370km and π = 22/7) (3 marks)**

**9. The table below shows the values of y = 2sin(6 + 30°) for 0° S 95 360°.**

**(a) On the grid provided below, draw the graph of y = 2sin(0+ 30°) for 0° S 6 5 360 Use l cm for 30° on the x-axis and 2cm for one unit on the y-axis. (3 marks)**

**(b) Use the graph to detemine the value of y when 0 = 162°. (1 mark)**

When θ = 162°,y=0.4

**10. The ﬁgure below represents the distance covered by a car within a given period of time**

**Find the average speed of the car in kilometres per hour. (3 marks)**

**11. Kitonga deposited Ksh50000 in a bank which paid compound interest at the rate of 10% per annum. Find the compound interest accrued by the end of the fourth year. (3 marks)**

**12. The number of different vehicles allowed through a road block was recorded as follows:**

**Represent the above data in a pie chart. (3 marks)**

**14. (a) Find a matrix which, when multiplied by matrix M =**

**gives the identity matrix. (2 marks)**

(b) Given that N =is a singular matrix, ﬁnd the value of x. (2 marks)

**15. A square QRST with vertices Q(l,1), R(3,1), S(3,3) and T(l,3) is transformed by the matrix**

** Find: (a) the area of square QRST; (2 marks)**

(b) the area of image Q’R’S’T’. (2 marks)

**16. Given that p = 6i + Zj, determine the magnitude of p, correct to 2 decimal places. (2 marks)**

**SECTION II (50 marks)**

Answer any ﬁve questions from this section in the spaces provided.

17. The second term of an arithmetic progressi0n(AP) and fourth tenn of a geometric progression(GP) are each 80. The sixth terms of the AP and GP are each 320.

(a) Find:

(i) the ﬁrst term and the common differences of the AP. (2 marks)

**(ii) the ﬁrst teirn and the common ratio of the GP. (2 marks)**

**(b) Determine the 20*“ term of the AP. (2 marks)**

A.P.T_{20}=20+19X60

=1160

**(c) Determine the difference between the sum of the ﬁrst 12 terms of the GP and the sum of the ﬁrst l2 terms of the AP. (4 marks)**

G.P.S_{12}=12(12^{12}-1)/2-1

=49149

A.P.S_{12}=12/2{2×12+(12-1)60}

=4104

Difference=49140-4104

=45036

**18. (a) (i) Complete the table below for the values of y = x2 ex — 6 for -3 5 x S 4. (2 marks)**

**(ii) Find y when x is 1/2= (l mark)**

**(b) On the grid provided, draw a graph of y = xi —x ~ 6 for —3 5 x 5 4. (3 marks)**

**(c) On the same grid, draw line y = 3- x + l and hence solve the equation x2—x~6= ;3x+l. (4marks)**

Line y = -3/2x+1

=2.4

=-2.8

**19. The marked price of a wall unit was Ksh 50 000. The price on hire purchase (HP) terms was 175% of the marked price.**

**(a) A customer bought the wall unit in cash and was offered 10% discount. Find the amount of money the customer paid for the wall unit. (2 marks)**

50,000×0.9

=ksh 45000

**(b) A second customer decided to purchase a similar wall unit on HP terms.**

**(i) Determine the HP price. (2 marks)**

50000×1.75

=87,500

**(ii) The customer paid 20% of the HP price as deposit and was to pay the balance in 28 equal monthly instalments. Find the amount of each monthly instalment. (3 marks)**

Amount to pay in instalments;

87500×0.8

ksh 70,000

Monthley instalments =70000/28

ksh2500

**(c) A third customer bought a similar wall unit in cash by taking a loan equal to the marked price. The loan was to be repaid in 15 months and the bank charged interest at the rate of 4% compounded monthly.**

**(i) Find, correct to the nearest shilling, the amount of money the third customer paid the bank. (2 marks)**

50,000×1.04^{15}

90047.17528

90047

**(ii) Find the amount of money the third customer spent more than the marked price. (l mark)**

90047-50000=ksh4007

**20. The figure below shows triangle ABC IN which AB=6cm,BC=8cm,BD=4.2cm and AD=5.3cm.Angle CBD=45°**

**Calculate to one decimal place**

**the length of CD; (3 marks**)

**size of angle ABD; (3 marks)**

**size of angle BCD; (2 marks)**

**area of triangle ABD. (2 marks)**

1/2x6x4.2sin59.5

=10.9cm

**21. Mawira, a poultry farmer carried out the following transactions during the month of February 2017:**

February l: Had Ksh 10000 carried forward from January 2017

3:Bought 2 bags poultry feed @Ksh 1250

7:Paid Ksh 750 for water

11:Bought materials for construction for Ksh 1 900

13:Received Ksh 12 000 from sale of broilers

17:Sold 500 eggs at Ksh 8 each

21:Paid Wages to 2 casuals at Ksh 1 750 each

24:Sold chicks for Ksh 5 000

25:Paid Ksh l 300 for electricity

26:Sold 30 layers at Ksh 500 each

28:Bought incubator for Ksh l2 500

**Prepare a single column cash book for Mawira’s transactions and balance it as at ls‘ March 2017. (10 marks)**

22. The table below shows the marks of 50 candidates in a test.

**(a) Draw a cumulative frequency curve for the data. (5 marks)**

**(b) Use the graph to determine:**

**(i) the median mark; (2 marks)**

Median=46

**(ii) the percentage of students who scored above 64%. (3 marks)**

50-41

=9

=9/50×100

=18%

**23. Two boxes B and C contain identical balls except for the colour. Box B contains 5 violet balls and 3 green balls. Box C contains 3 violet balls and 4 green balls.**

**(a) A ball is drawn at random from each box. Find the probability that both balls are of the same colour. (4 marks)**

**(b) Two balls were drawn at random from each box, one ball at a time without replacement. Find the probability that:**

**(i) the two balls drawn from box B or box C are violet; (4 marks)**

**ii) all the four balls drawn are violet. (2 marks)**

5/14×1/7

=5/98

**24. The vertices of a triangle ABC are A(2, 2), B(5, 3) and C(3, 5)**

**. (a) Find the vertices of A A’B’C’ the image of A ABC under the transformation represented by the matrix**

**(2 marks)**

**(b) Triangle ABC is mapped onto A A”B”C” whose vertices are A”(—2, 2), B”(-5, 3) and C”(-3, 5) Find the matrix of this transformation. (4 marks)**

**(c) Triangle ABC undergoes two successive transformations PQ =**

**Determine the vertices of A A”’B”’C”‘, the image of AABC, under the combined transformation. (4 marks)**