**NAME……………………………………………………...... INDEX NO……...... ……………………..**

**121/2 CANDIDATE’S SIGNATURE…………………**

**MATHEMATICS ALT A**

**PAPER 2 DATE…………………………………………….**

May/June, 2016

TIME: 2½hours

**LAINAKU I JOINT EXAM YEAR 2016**

**Kenya Certificate of Secondary Education**

**MATHEMATICS ALT A**

PAPER 2

TIME: 2½hours

**INSTRUCTIONS TO CANDIDATES:**

*(a) Write your name, admission and class in the spaces provided at the top of this page.*

(b) *Sign and Write the date of examination in the spaces provided above.*

(c) This paper consists of TWO Sections; Section I and Section II.

(d) Answer ALL the questions in Section I and only five questions from Section II.

**(e) Show all the steps in your calculation, giving your answer at each stage in the spaces provided**

**below each question.**

*(f) Marks may be given for correct working even if the answer is wrong.*

(g) **Non-programmable** silent electronic calculators and *KNEC Mathematical tables may be used except *

where stated otherwise.

(h) **This paper consists of 14 printed pages**.

**(i) Candidates should check the question paper to ascertain that all the pages are printed as indicated and that no questions are missing**

(j) **Candidates should answer the questions in English.**

**FOR EXAMINER’S USE ONLY:**

SECTION I

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / TOTAL**SECTION II GRAND TOTAL**

SECTION 1 (50 marks)

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

1. Using logarithm tables evaluate. (4 Mks)

2. The diagram below (not drawn to scale), shows the respective positions of three football players Samuel Paul and John. If Samuel had the ball possession and wanted to make a pass to the nearest player, by how many meters was this player nearer to Samuel than the other? (3 Mks)

3. (i) Expand and Simplify (2mks)

(ii) Hence use your first four terms in your expansion above to estimate ( 0.98)5 (2mks)

4. Find, without using mathematical tables or calculators the values of x which satisfy the equation (3 mks)

5. Solve the following simultaneous inequality and list down the integral values. (3 mks)

6. Sketch the net of the triangular prism shown below. Show the trend of a tight string which was tied from vertex A to vertex E as shown on the diagram and determines its length. (3 mks)

7. Identify the transformation illustrated below and define it fully. (3 mks)

8. Evaluate leaving your answer in the form (3 mks)

9. A circle which passes through the point (-1, 7) has its center out at (3, -3). Determine the equation of the circle in the form. Where a, b and c are constants. (3 mks)

10. Find the inverse of . (1 mks)

Hence solve for (2 mks)

11. Construct two tangents from point T to the circle drawn below with Centre O and measure their length.

(3 mks)

12. A triangle ABC has measurement such that AB=32cm BC=24cm and AC=40cm. to the nearest centimeter. Calculate the percentage error in working out the area of this triangle. (3 mks)

13. Make of the formulae in the following equation (3 Mks)

14. A value Given that and that , then find the value of (4 mks)

15. Mr. Njoroge, a trader bought an item and gave it a marked price such that it would give him a profit of 50%. A buyer visited his shop and bargained for the same item. Mr Njoroge gave him a discount of 20%. The buyer paid Ksh. 600 for the item. Determine how much profit Mr. Njoroge made on this item.

(3 mks)

16. There are two grades of the, grade A and Grade B. Grade A costs Sh 100 per Kg while Grade B costs Sh 60 per Kg. **In what ratio must** the two be mixed in order to produce a blend costing Sh 75 per Kg. (2 marks)

SECTION 11(50 marks)

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

17. The diagram below shows a special dart board made of three concentric circles whose radius is 14cm, 28cm and 42cm respectively. The inner circle forms the bull’s eye.

Taking dermine:

- The probability that a dart player hits the bull’s eye. (2 Mks)

- The probability that a dart player hits the middle ring of the dart board. (3 Mks)

- The probability that a dart player hits the middle ring or the bull’s eye of the dart board. (2 Mks)

- The probability that a dart player hits the shaded part of the dart board. (3 Mks)

18. In the figure below and. AE:BC=7:3. D divides AE in the ratio 4:3. DC and BE intersect at N. Find in terms of and

- AC (1 marks)

- DC (2 marks)

- BD (1 marks)

- BE (1 marks)

- Given that and that , determine the value of and and hence find the ratio BE:EN (5 marks)

19. a) Complete the table below of y = -x2 +2x+3 (2 marks)

x / -3 / -2 / -1 / 0 / 1 / 2 / 3 / 4 / 5-x2 / -9 / -1 / 0 / -4 / -9

2x / -4 / 0 / 2 / 8 / 10

3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3

y / 3

b) Draw the graph of y = y = -x2 +2x+3 on the grind provided. (3 marks)

c) What is the turning point of the curve y=3+2x-x2 (1 marks)

d) What is the equation of the line of symmetry of the curve? (1 marks)

e) Use your curve to solve 0 = 8 + 6x -2x2 (3 marks)

20. Two circles with center R and M intersect at points A and B as shown in the diagram below. Their radii are RA=70cm and MA=52.5cm. Their common chord AB=84cm. RM and AB intersect at Q.

Determine:

a) The ratio RQ:QM (3 marks)

b) The angle AMB (2 marks)

c) The angle ARB (2 marks)

d) The area of the shaded part to the nearest one decimal place taking (3 marks)

21. The heights of 50 plants at a research station were measured and the results tabulated as in the table below.

Height in cm / 1-5 / 6-10 / 11-15 / 16-20 / 21-25 / 26-30 / 31-35 / 36-40 / 41-45 / 46-50Number of plants / 1 / 3 / 5 / 6 / 7 / 7 / 7 / 7 / 5 / 2

Draw a cumulative frequency curve on the grid provided. (4 Mks)

Hence determine

a) The median height (1mks)

b) The quartile deviation (2mks)

c) The range of the height of the middle 50% of the plants. (2 mks)

d) If 28 plants were doing well, what was the heath required to determine if the plants were doing well.

(1mks)

22. The first third and the fourth term of a geometric progression form the first, the fifth and the fourteenth term of an arithmetic progression. If the first term of the geometric progression is 2, determine.

a) The common difference of the arithmetic progression. (4 mks)

b) The common ratio of the geometric progression (2 mks)

c) The sum of the first ten terms of the arithmetic progression. (2 mks)

d) The sum of the first ten terms of the geometric progression. (2 mks)

23. Given that AB is 5cm find the locus of K such that AK=AB. On the same diagram, find the locus of H such that angle and that the area of triangle (10 mks)

24. a) Complete the table below of (1 marks)

/ 0 / 15 / 30 / 45 / 60 / 75 / 90 / 105 / 120 / 135 / 150 / 165 / 180 / 195 / 210 / 225 / 240 / 255 / 270/ 0 / 0.71 / 0.97 / 0.5 / 0 / -0.5 / -1

/ 1 / 0.87 / 0.5 / -0.5 / -1 / -0.5 / 0

/ 0 / 0.58 / 1.73 / -1 / 0 / 0.27 / 1 / 3.73

b) Taking a scale of and , draw the graph of on the grind provided. (7 marks)

c) Hence solve

(1 mks)

(1 mks)

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