O NOW I GET IT EXAMINATION

Transcription

1 TEST CODE PRACTICE PAPER 2017 O NOW I GET IT EXAMINATION MATHEMATICS Paper 02 General Proficiency 2 hours 40 minutes INSTRUCTIONS TO CANDIDATES 1. Answer ALL questions in Section I, and any TWO in section II. 2. Begin the answer for EACH question on a NEW page. 3. ALL working must be shown CLEARLY. 4. Mathematical tables and graph paper are provided. A list of formulae is provided on page 2 of this booklet. 5. Mathematical instruments are needed for this paper. 6. Silent electronic calculators may be used for this paper. 7. You are advised to use the first 10 minutes of the examination time to read through this paper. Writing may begin during this 10 minute period. DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

2 Page 2 LIST OF FORMULAE

3 Page 3 Answer all questions in this section All working must be clearly shown. 1. (a) Using a calculator or otherwise, calculate the EXACT value of: x (b) (c) Tickets Sold for a Bus Tour Category Number of Cost per Tickets Total Cost Tickets Sold $ $ Juvenile 5 P Youths Q Adults R Calculate i. the value of P ii. the value of Q iii. An adult ticket is TWICE the cost of a youth ticket. Calculate the value of R. iv. The bus company pays taxes of 15% on each ticket sold. Calculate the taxes paid by the bus company. 2. (a) write as a single fraction 2x 3 x (b) Write the following statement as an algebraic expression. Three times a number less than twenty. (c) Factorize completely (i) x 2 36 (ii) 2x 2 + 5x 12 (e) The formula for the volume of a cylinder is given as V= πr 2 h. i. Make r the subject of the formula ii. Given that x 2 + bx + c = (x + 2) 2 3, work out the values of b and c.

4 Page 4 3. The incomplete Venn diagram below shows the number of students in a class of 28 who play football and tennis. U U = {all students in the class} F = {students who play football} F T = {students who play tennis} Additional information about the class is that 12 students play tennis 15 students play football 8 students play neither cricket nor football x students play BOTH tennis and football x T (i) (ii) Complete the Venn diagram above to represent the information, showing the number of students in each subset. Calculate the value of x 4. Two functions are defined as follows: g(x) = 4x + 3 and f(x) = 2x + 7 x + 1 i. State the value of x for which f(x) is undefined. ii. Calculate the value of gf(5). iii. Find f 1 (x). 5. A line JK has equation 2y = 5x + 6. (a) Determine the gradient of JK. Another line GH is perpendicular to JK and passes through the point (5, 1). (b) State the gradient of line GH. (c) Determine the equation of line GH. (d)

5 Page 5 6. The graph below shows triangle DEF and its image D E F after a transformation. (i) state the coordinates of the point E. (ii) Describe fully the transformation that maps DEF to its image, D E F. (iii) On a graph sheet, draw triangle D E F, the reflection of triangle D E F in the x axis. 7. The table shows how the minutes taken by all the students to complete a science experiment were recorded and grouped. Time (minutes) Number of students who completed (Frequency) Cumulative Frequency a) Complete the cumulative frequency column. b) Using a scale of 2cm to represent 5 minutes on the x axis and 2cm to represent 5 students on the y axis, draw a cumulative frequency curve to represent the information in the table.

6 Page 6 Using the graph, estimate c) (i) the median time taken to complete the experiment. (ii) the probability that a student, chosen at random, took 30 minutes or less to complete the experiment. Show on your graph, using broken lines, how these estimates were obtained. 8. A sequence of figures is made up of unit squares with unit sides. The first three figures in the sequence are shown below (a) Draw figure 4 of the sequence (b) Study the diagram of numbers in each row of the table below. Each row relates to one of the figures in the sequence. Some rows have not been included in the table. Complete the rows numbered (i), (ii), (iii) and (iv). Figure Number of Unit Squares Perimeter of Figure (i) 4 (ii) 45 (iii) 30 (iv) n