Instructions to Candidates

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1 DIRECTORTE FOR QULITY ND STNDRDS IN EDUCTION Department for Curriculum Management and elearning Educational ssessment Unit nnual Examinations for Secondary Schools 2012 FORM 4 MTHEMTICS SCHEME TIME: 20 minutes Non Calculator Paper Name: Class: Mark Instructions to Candidates nswer LL questions. This paper carries a total of 20 marks. Calculators and protractors are NOT LLOWED.

2 No. QUESTION Space for Working if Required 1. Write forty two thousand as a number in standard form. ns: 2. Find the value of: ns: 3. X = and Y = Find the least common factor of X and Y. ns: 4. Francesca scored 36 out of 40 in a test. Express her mark as a percentage. ns: % 5. Expand 2a 2 b(3a 4b 2 ). ns: 6. Make x subject of the equation: y = 5x 2 ns: 7. y Make y subject of the formula given that x 1. x ns: 8. Chris wants to draw this parallelogram using Logo. Fill in the missing command. PD RT 30 FD 50 RT 60 FD 100 FD 50 RT 60 FD 100 RT 90 PU Page 2 of 4 Mathematics Non Calculator Paper Form 4 Secondary Scheme 2012

3 No. QUESTION Space for Working if Required 9. tank has a volume of 0.25 m 3. Express the volume of the tank in cm 3. ns: cm Simplify: 4x 6 25y 4 ns: 11. point (3, 4) is reflected in the y axis. Find the coordinates of, the image of point. ns: (, ) 12. Factorise: x 2 + x 12 ns: 13. Work out: Give your answer in standard form. ns: 14. prism has a volume of 128 cm 3. It is 8 cm long. Find the cross-sectional area. 8cm ns: cm If tan x = 4 3, find sin x. x ns: Mathematics Non Calculator Paper Form 4 Secondary Scheme 2012 Page 3 of 4

4 depth depth depth No. QUESTION Space for Working if Required 16. Find the gradient of the line joining the points P(4, 5) and Q(2, 3). ns: 17. The figure shows the position of three villages, B and C. Find the bearing of C from B. N 20 N B C ns: 18. Water is poured in a hemispherical bowl at a steady rate. Which graph best describes how the depth of the water varies over time? B C time time time ns: 19. Five drinks and a sandwich cost sandwich costs as much as a drink. Find the cost of one sandwich. ns: 20. fan opens up to an angle of 120 and has a radius of 15 cm. Find the length of lace needed to decorate the fan at the edge. lace cm Give your answer in terms of. ns: Page 4 of 4 Mathematics Non Calculator Paper Form 4 Secondary Scheme 2012

5 DIRECTORTE FOR QULITY ND STNDRDS IN EDUCTION Department for Curriculum Management and elearning Educational ssessment Unit nnual Examinations for Secondary Schools 2012 FORM 4 MTHEMTICS SCHEME TIME: 1h 40 min Main paper Question Total Main Non Calc Global Mark Mark Name: Class: CLCULTORS RE LLOWED BUT LL NECESSRY WORKING MUST BE SHOWN. NSWER LL QUESTIONS. 1. Rachel invested 2500 at r % compound interest. fter 2 years the invested sum amounted to Calculate the rate of investment, r. Give your answer correct to the nearest whole number. r P n ns. (4 marks) Mathematics Main Paper Form 4 Secondary Scheme 2012 Page 1 of 11

6 2. a) Solve the equation: 2x 9 = 5x 3(3x + 2) ns. x 1 3x 1 b) Solve the equation: ns. (6 marks) 3. The figure below represents a container consisting of a cylinder attached to a hemisphere. The hemisphere has a radius 2 cm. The height of the container is 12 cm. Calculate the volume of the container. Give your answer correct to 1 decimal place. 2 cm 12 cm Volume of sphere = 4 r 3 3 ns. cm 3 (5 marks) Page 2 of 11 Mathematics Main Paper Form 4 Secondary Scheme 2012

7 Name: Class: b b 2 4ac 4. Use the formula x to solve the equation 2x 2 7x + 4 = 0. Give your 2a answer correct to 2 decimal places. x = x = (3 marks) 5. y Line L y = 2x 7 x B a) Find the coordinates of the points and B shown on the graph above. b) Line L is parallel to the line y = 2x 7 and passes through the point (0, 3). Find the equation of Line L. (, ) B(, ) (5 marks) Mathematics Main Paper Form 4 Secondary Scheme 2012 Page 3 of 11

8 6. The shapes below represent the first four terms of a sequence. Shape 1 Shape 2 Shape 3 Shape 4 a) Fill in the following table: Shape Number of Dots 2 18 b) Find the number of dots in shape 10. c) Choose the expression which gives the number of dots in shape n. ns.. 3n + 2 B. 5n + 3 C. 2n 2 D. n ns. d) Is there a shape in the sequence having 154 dots? Give a reason for your answer. (6 marks) Page 4 of 11 Mathematics Main Paper Form 4 Secondary Scheme 2012

9 Name: Class: 7. On the grid below: a) 6 Translate triangle by column vector. Label the image B. 9 b) Rotate triangle 90 clockwise about point P. Label the image C. P (4 marks) Mathematics Main Paper Form 4 Secondary Scheme 2012 Page 5 of 11

10 8. Trevor checked 20 boxes of nails of the brand Nailit and recorded the number of nails in each box in the frequency table shown below. Number of nails, x Frequency, f a) Complete the table below for the nail boxes of the brand Nailit. Nailit Mean Median Mode Trevor also checked a sample of nail boxes of the brand Fixall and obtained the following results. Fixall Mean Median Mode b) Which brand is likely to contain more nails? Give a reason for your answer by comparing the results of both brands. Brand Reason (6 marks) Page 6 of 11 Mathematics Main Paper Form 4 Secondary Scheme 2012

11 9. The diagram shows a tower BCGH, next to a building CDEF. The angle of elevation of H from is 47 and H = 22 m. The angle of elevation of G from E is 43. BC = 10.5 m and D = 37 m., B, C and D lie on level ground. H G 22 m F 43 E 47 B 10.5 m C D 37 m Giving your answer correct to 1 decimal place, find: a) BH, the height of the tower BCGH. BH = m b) B. B = m c) CD. CD = m d) GF. GF = m e) ED, the height of the building CDEF. ED = m (11 marks) Mathematics Main Paper Form 4 Secondary Scheme 2012 Page 7 of 11

12 10., B, C, D and E are five points on the circumference of a circle centre O. CF is a tangent to the circle. a E O 68 c B D d C b F Find the value of angles a, b, c and d. Give reasons for your answers. ngle a = Reason ngle b = Reason ngle c = Reason ngle d = Reason (8 marks) Page 8 of 11 Mathematics Main Paper Form 4 Secondary Scheme 2012

13 11. In the diagram below the lines B and BC meet at point B. B C On the above diagram: a) draw the locus of points equidistant from B and C. b) draw the locus of points equidistant from B and BC. c) shade the region consisting of all points that are nearer to B than to C and nearer to B than to BC. (3 marks) Mathematics Main Paper Form 4 Secondary Scheme 2012 Page 9 of 11

14 12. a) Complete the table for y = 4x 2 8x 5. x x x y b) Complete the table for y = 8x +11. x x y 5 c) Plot the graphs of y = 4x 2 8x 5 and y = 8x +11 on the grid below. 30 y x 10 d) Use your graph: 20 i) to find the minimum value of y = 4x 2 8x 5. ns. ii) to solve the simultaneous equations y = 4x 2 8x 5 and y = 8x +11. x =, y = and x =, y = (11 marks) Page 10 of 11 Mathematics Main Paper Form 4 Secondary Scheme 2012

15 13. a) box contains 45 chocolates. There are three varieties of chocolate: white, dark and mint chocolates. The probability of picking a white chocolate is 3 1, and the probability of picking a dark chocolate is 5 2. How many mint chocolates are there inside the box? ns. chocolates b) The probability that Lina waters her plant is 7 4. If she waters her plant, the probability that flowers grow is 5 3. If she does not water her plant, the probability that flowers grow is 5 1. i) Complete the tree diagram below: 3 5 flowers grow waters plant 4 7 flowers do not grow flowers grow does not water plant flowers do not grow ii) Calculate the probability that flowers grow. ns. END OF PPER (8 marks) Mathematics Main Paper Form 4 Secondary Scheme 2012 Page 11 of 11

MATHEMATICS (SYLLABUS D) 4024/02

CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level MATHEMATICS (SYLLABUS D) 4024/02 Paper 2 Additional Materials: Answer Booklet/Paper Electronic calculator Geometrical