SUBUKIA SUB-COUNTY FORM FOUR 2014 JOINT EXAMINATION

Transcription

1 NAME... INDEX NO /1 CANDIDATE S SIGNATURE MATHEMATICS ALT A PAPER 2 DATE. July/August, 2014 TIME: 2½ hours SUBUKIA SUB-COUNTY FORM FOUR 2014 JOINT EXAMINATION Kenya Certificate of Secondary Education MATHEMATICS ALT A PAPER 2 TIME: 2½ hours 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 consist 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 TOTAL SECTION II GRAND TOTAL TOTAL

2 1 0 Tan Use logarithms tables to evaluate (4mks) 2. Make q the subject of the formula. p q r (3 marks) p pq Given that a b c Find the values of a, b and c. (3mks) 4. a) Expand and simplify ( 1 3x) 5, (2mks) b) Hence use your expansion up to the term x 3 to estimate (0.97) 5 correct to 4 significant figures. (2mks)

3 5. A trader has three grades of tea P,Q and R. Grade P costs sh.140 per kg, grade Q costs sh.160 per kg and grade R costs sh.256 per kg. The trader mixes grade P,Q and R in the ratio 5:3:x to make a brand of tea which he sells at sh per kg hence making a profit of sh Find the value of x. (3mks ) 6. A tailor brought two pair of trousers at sh He marked the price such that after allowing his discount of 20%, he would still make a profit of 30% on the cost price. Determine the price at which a pair of trouser was marked. (3marks) 7. The dimensions of a rectangle are 10cm and 15cm to the nearest cm. Find the percentage error in the area of the rectangle. ( 3mks) 8. The first, the second and sixth terms of an increasing arithmetic progression are three consecutive terms of a geometrical progression. If the first term of the arithmetic progression is 2. Find (i) The common difference of the arithmetic progression. (ii) The common ratio of the geometric progression. (3 marks)

4 9. Mr Kamau and Mr. Njorobe went to buy some similar items. Both of them had Ksh. 700, Meant for this work. Mr Njoroge bargained for these items. The business man accepted to give him a discount of Ksh.20 for every item he bought. As a result he ended up buying four more item more than what Mr. Kamau bought. How many items were bought by Mr. Njoroge? (4 mks) 10. Find the integral values that satisfy the inequality below. X + 21 > 15 2x > x + 12 (3mks) 11. Differentiate. Hence, or otherwise, determine the turning points for the curve (3mks) 12. Without using logarithm tables, solve the equation log (5x 4) = log ( x+ 2) + 1 / 3 log 27. (3mks) 13. A bag contains 10 balls of which 3 are red, 5 are white and 2 green. Another bag contains 12 balls of which 4 are red, 3 are white and 5 are green. A bag is chosen at random and a ball picked at random from the bag. Find the probability that the ball so chosen is red. (3mks).

5 14. Find the inverse of ( ) and hence, Find PQ, hence the point of intersection of the lines 4x + y = 9 and 3y = 2x 1) (3 Mks) 15. The diagram below shows a triangle ABC and it image A 1 B 1 C 1 after a rotation. Find the centre and the angle of tha rotation tha maps ABC onto A 1 B 1 C 1 (3 mks) 16. A camp has enough food to last 12 days. After three days, the daily ration is reduced so that the remaining food can last for another 16 days. In what ratio is the ration reduced? (2mks)

6 17. Quadrilateral WXY with vertices W(5,0), x (2,-3) Y(6, -1) and Z(8,-1) is mapped onto quadrilateral W 1 X 1 Y 1 by reflection on the line y=x. W 2 X 2 Y 2 is the image of W 1 X 1 Y 1 under a reflection on the line y = 0 a) Plot the three quadrilaterals on the grid below. 4mks b) Describe fully the single transformation which maps WXY onto W 2 X 2 Y 2 2mks c) Determine a single matrix which maps W 2 X 2 Y 2 onto WXY. 4mks

7 18. The masses of 50 students in a form 4 class were taken and recorded as in the table below. Mass (kg) Frequency a) Calculate the median mass 4mks b) Calculate the semi-interquartile range 4mks c) If the students are arranged in order from the lightest to the heaviest, find the mass of the 45 th student. 2mks

8 19. The diagram below is a frustrum of a right pyramid of rectangular base ABCD measuring 24cm by 18cm. The frustrum was made by cutting off a small pyramid along the plane EFGH which is parallel to ABCD and exactly two thirds way up the vertical height of the original pyramid. EFGH is a rectangle measuring 8cm by 6cm. The slant length of the original pyramid is 36cm. Calculate a) Vertical height of the original pyramid to 1 decimal place. (3mks) b) The volume of the frustrum to the nearest whole number. (3mks) c) The surface area of the original pyramid to the nearest whole number. (4mks)

9 20. a) Use the trapezium rule to estimate the area under the curve y = x 2 + x - 6 over the interval 0 < x < 8 using 8 trapezia. (5mks) b) Find the exact area under the curve in (a) above. (3mks) c) Find the percentage error in the estimated area in (a) above. (2mks)

10 21. The figure below shows a square ABCD point V is vertically above middle of the base ABCD. AB = 10cm and VC = 13cm. Find; (a) the length of diagonal AC to two decimal places. (1mks) (b) the height of the pyramid to two decimal places. (2mks) (c) the acute angle between VB and base ABCD. (2mks) d) the acute angle between BVA and ABCD. (2mks) e) the angle between AVB and DVC. (3mks)

11 22. a) Complete the table below for y=sin 2x and y=sin ( 2x + 30) giving values to 2d.p 2mks X Sin 2x Sin ( 2x + 30) b) Draw the graphs of y=sin 2x and y = sin (2x + 30) on the axis. 4mks c) Use the graph to solve sin ( 2x + 30)-sin 2x = 0 1mk d) Determine the transformation which maps sin 2x onto sin (2x + 30) 1mk e) State the period and the amplitude of y = sin ( 2x + 30) 2mks

12 23. Use ruler and a pair of compasses only in this question a) Construct triangle ABC such that AB = 6cm, AC=BC and angle ACB = mks b) On one side only construct the locus of P such that: i) < APB = mk ii) area of triangle, APB = 9cm 2 3mks c) i) Locate P 1 and P 2 the two possible positions of P which satisfy the two conditions above1mk ii) Measure the distance between P 1 and P 2. 1mk

13 24. Eldoret Airport is planning to build a fire fighting plant on a space of 250m 2. Two types of machines are to be installed, machine x which occupies a space of 5m 2 and machine Y which occupies 10m 2. The airport can have a maximum of 40 machines at a time. At most 15 machines of type Y are used at any given time. a) write down three inequalities other than x>0, and y>0. 3mks b) On the grid below, show the region satisfying the given conditions. 3mks c) The profit from a type x machine is Ksh 1000 and that of type y is (i) Write down the objective function. 1mk (ii) Use the graph to obtain the number of machines of each type that should be installed to obtain maximum profit. 2mks

14 (iii) Calculate the maximum profit. 1mk

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