Cxc Mathematics Past Papers And Answers 2009

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1. 1. v rESr coDE 01234020 FORM TP 2009492 MAY/JUNE 2OO9 CARIBBEAN EXAMINATIONS COUNCIL SECONDARY EDUCATION CERTIFICATE EXAMINATION MATHEMATICS Paper 02 - General Proficiency 2 hours 40 minutes 20 MAY 2ID9 (a.m.) INSTRUCTIONS TO CANDIDATES . 1. Answer ALL questions in Section I, and ANY TWO in Section II. 2. Write your answers in the booklet provided. 3. All working must be shown clearly. 4. A list of formulae is provided on page 2 of this booklet. Examination Materials Electronic calculator (non-programmable) Geometry set Mathematical tables Graph paper (provided) I I I - DO NOT TURN TIIIS PAGE I.INTIL YOU ARE, TOLD TO DO SO. - I Copyright @ 2OO7 Caribbean Examinations Council@. I I All rights reserved. I 012340208 2009
2. 2. U Page 3 SECTION I Answer ALL the questions in this section. All working must be clearly shown. 1. (a) Using a calculator, or otherwise, calculate the EXACT value of 2t 2- + 1- (i)35 2 6- 5 giving your answer as a common fraction ( 3 marks) T) ) o.o2s6 (ii) giving your answer in standard form. ( 3 marks) (b) The basic wage earned by a truck driver for a 4O-hour week is $560.00. (i) Calculate his hourly rate. ( L mark ) For overtime work, the driver is paid one and a half times the basic hourly rate. (ii) Calculate his overtime wage for 10 hours of overtime. ( 2 marks) (iii) Calculate the TOTAL wages earned by the truck driver for a 55-hour week. ( 3 marks) Total 12 marks n (a) Factorise completely: (i) 2ax +.3oy - 2bx - 3by ( 2 marks) (ii) sf - 20 ( 2 marks) (iiD 3* + 4x- 15 ( 2 marks) (b) One packet of biscuits costs $x and one cup of ice cream costs $y. One packet of biscuits and two cups of ice cream cost $8.00, while three packets of biscuits and one cup of ice cream cost $9.00. (i) Write a pair of simultaneous equations in -r and y to represent the given informationabove. ( 2marks) (ii) Solve the equations obtained in (b) (i) above to find the cost of one packet of biscuits and the cost of one cup of ice cream. ( 4 marks) Total 12 marks GO ON TO THE NEXT PAGE ot234020tF 2009
3. 3. v Page 4 3. (a) In a survey of 50 students, 23 owned cellular phones 18 owned digital cameras x owned cellular phones and digital cameras 2x owned neither. Let C represent the set of students in the survey who owned cellular phones, and D the set of students who owned digital cameras. (i) Copy and complete the Venn diagram below to represent the information obtained from the survey. ( 2 marks) (ii) Write an expression in x for the TOTAL number of students in the survey. ( Lmark) (iii) Calculate the value of x. ( 2 marks) (b) The diagram below, not drawn to scale, shows a rhombus, PQRS, with the diagonal PR = 6 cm, and the angle RPQ - 60". (i) Using a ruler, a pencil, and a pair of compasses, construct the rhombus PpRS accurately. ( 4 marks) (ii) Join O,S. Measure and state, in centimetres, the length of QS. ( 2 marks) Total ll marks GO ON TO TI{E NEXT PAGE ot2340208 2009
4. 4. t- , Page 5 4. (a) The table below shows two readings taken from an aircraft's flight record. Time Distance Travelled (km) 08:55 957 09:O7 1083 For the period of time between the two readings, calculate (i) the distance travelled in kilometres ( l mark ) (iD the average speed of the aircraft in km/h. ( 3 marks) (b) The map shown below is drawn to a scale of 1:50 000. (D Measure and state, in centimetres, the distance on the map from Lto M along a straight line. ( 2 marks) (ii) Calculate the actual distance, in kilometres, from Lto M. ( 2 marks) (iiD The actual distance between two points is 4.5 km. Calculate the number of centimetres that should be used to represent this distance on the map. ( 3 marks) Total LL marks GO ON TO TIIE NEXT PAGE ot2340208 2009
5. 5. b. Page 6 (a) Given thatflx) =2x- 5 and g(-r) - * - 31, calculate the value of (i) fl-2) ( lmark) (ii) s(1) ( 2 marks) (iii) f-l3). ( 2 marks) (b) Giventhaty= *+2x-3 (i) Copy and complete the table below. .| x -4 -3 -1 0 1 2 v 5 -3 -4 --t 5 ( 2 marks) (iD Using a scale of 2 cm to represent 1 unit on the x-axis and I cm to represent l unit on they-axis, draw the graph of y = * +?-x- 3 for -4<x<2. ( 5 marks) Total 12 marks GO ON TO THE NEXT PAGE 0t2340208 2AO9
6. 6. tt Page 7 6. The diagram below shows triangles A, B andD. The line y = x is also shown. (a) Describe, FllLLY, the single transformation which maps triangle A onto (i) tnangleD (3marks) (ii) triangle B. ( 3 marks) (b) State the coordinates of the vertices of triangle C, the image of triangle A after a reflection in the line y = 1. ( 4 marks) Total 10 marks GO ON TO THE NEXT PAGE 0r234020/F 2009
7. 7. b.. Page 8 7. An answer sheet is provided for this question. The table below shows the time, to the nearest minute, that 80 students waited to be served at a school's canteen. Waiting Time Cumulative (minutes) No. of Students Frequency 1-5 4 4 6- 10 7 11 11-15 11 22 t6 -20 18 2t -25 22 26-30 10 31-3s 5 36-40 3 (a) Copy and complete the table, showing the cumulative frequency. ( 2 marks) (b) On the answer sheet provided, use the values from your table to complete the cumulative frequency curve. ( 4 marks) (c) Use your graph from (b) above to estimate (i) the median for the data ( 2 marks) (ii) the number of students who waited for no more than29 minutes ( 2 marks) (iii) the probability that a student, chosen at random from the group, waited for no more than 17 minutes. ( 2 marks) Total 12 marks GO ON TO THE NEXT PAGE o1234020tF 2009
8. 8. - 'b Page 9 8. An answer sheet is provided for this question. The drawings below show the first three diagrams in a sequence. Each diagram in the sequence is obtained by drawing a l-unit square on each side that forms the perimeter of the previous diagram. For example, Diagram 2 is obtained by drawing a l-unit square on each of the four sides of Diagram 1. On the answer sheet provided: (a) Draw Diagram 4 in the sequence. ( 2 marks) (b) Complete the table by inserting the appropriate values at the rows marked (i), (ii) and (iii). ( 8 marks) Total l0 marks GO ON TO THE NEXT PAGE 012340208 2009
9. 9. b Page 10 SECTION II Answer TWO questions in this section. RELATIONS, FUNCTIONS AID GRAPHS 9. (a) Solve the pair of simultaneous equations Y=4 - _3x 2x ( 4marks) _,_.>rz y-L + 1.. (b) Express * - 3x +l intheforma(x+h)2+k,where a,handftarerealnumbers. ( 3 marks) (c) Using your answer from (b) above, or otherwise, calculate (D theminimumvalueof 2*-3x+l ( lmark) (ii) the value of .x for which the minimum occurs. ( L mark ) (d) Sketch the graph of y = Z* -Zx + 1, clearly showing the coordinates of the minimum point the value of the y-intercePt the values of x where the graph cuts the r-axis. ( 4 marks) (e) Sketch on your graph of y = Zi - Zx + 1, the line which intersects the curve at the values of x and y calculated in (a) above. ( 2 marks) Total L5 marks GO ON TO THE NEXT PAGE 01234020tp 2009
10. 10. 'b Page 11 10. (a) The owner of a shop wishes to buy x guitars and y violins. To satisfy the demands of his customers, the number of violins must be less than or equal to the number of guitars. (i) Write an inequality to represent this information. ( lmark) The cost of one guitar is $150 and the cost of one violin is $300. He has $4 500 to spend on the purchase of these instrurnents. (ii) Write an inequality to represent this information. ( 2 marks) To get a good bargain, the owner of the shop must buy at least 5 violins. (iii) Write an inequality to represent this information. ( lmark) (b) (i) Using a scale of 2 cm on the horizontal axis to represent 5 guitars, and 2 cm on the vertical axis to represent 5 violins, draw the graphs of the lines associated with the THREE inequalities written in (a) (i), (ii) and (iii) above. ( 4 marks) (ii) shade the region on your graph that satisfies all rHREE inequalities. ( lmark) (iii) State the coordinates of the vertices of the shaded region. ( 2 marks) (c) The owner of the shop sells the instruments to make a profit of $60 on each guitar and $100 on each violin. (D Express the TOTAL profit in terms of x and y. ( lmark) (iD Calculate the maximum profit. ( 3 marks) Total L5 marks GO ON TO THE NEXT PAGE o1234020tF 2009
11. 11. ! Page 12 GEOMETRY AND TRIGONOMETRY 11. (a) The diagram below, not drawn to scale, shows a circle, centre O. The line DCE is a tangent to the circle. Angle ACE = 48" and angle OCB = 26". D Calculate: (i) ZABC l mark ) (ii) zAoc L mark ) (iii) LBCD l mark ) (iv) ZBAC L mark ) (v) ZOAC l mark ) (vi) IOAB l mark ) GO ON TO THE NEXT PAGE or234020tF 2009
12. 12. b Page 13 (b) The diagram below, not drawn to scale, shows the positions of two hurricane tracking stations, P andQ,relative to apoint o. p is on abearingof oZ5" fromo, and OP = 400 krn. Qis on a bearing of 080" from p and pe= 700 km. (i) Copy the diagram above. On your diagram label the angles that show the bearings of 025" and 080". ( 2 marks) (ii) Calculate a) <OPQ b) the length, to the nearest kilometre, of OQ c) the bearing of Qfrom O. ( 7 marks) Total 15 marks GO ON TO THE NEXT PAGE 0I234A20E 2009
13. 13. Page 15 VECTORS AND MATRICES (a) A =(-: -'- in= f o.] where o is the I s,i -- z)""-^ The points A and B have position vecrors una origin (0, 0). The point G lies on rhe rine AB such thatAG = !en. Express in the "*t []) ) (i) the vectors AB and AG ( 4marks) (ii) -) the position vector OG . ( 2marks) (b) In the diagram below, not drawn to scale, B is the midpoint of OX, C is the midpoint of AB, and D is such that OD = 2DA. The vectors a and b are such that -+ -+ OA =3a and OB =b. (i) Write in terms of a and b: -+ A) AB -+ b) AC -+ C) DC -+ d) DX ( 6 marks) (ii) State TWO geometrical relationships between DX DC. ( and, 2 marks) (iii) State ONE geometrical relationship between the points D, C, and X. ( lmark) Total L5 marks GO ON TO THE NEXT PAGE ot2340.20tr. 2009
14. 14. .V Page 16 o) 14. (a) The value of the determinan tot M =(: x) ,, ,r. 3 Calculate the values of x. ( 4 marks) (-t o 1b) The transformation R is represented by tne matrix I O t) (o1 The transformation S is represenred by tne matrix [_t O) (o b (D Write a single matrix, in the form | - ".1 to represent the combined [c d) transformation .S followed by R. ( 2 marks) (ii) Calculate the image of the point (5, -2) under the combined transformation in @) (i) above. ( 3 marks) (z -1 (c) rhe matrix = " [, s) (i) Determine the inverse mafrix of N. ( 2 marks) (iD Hence, calculate the value of x and the value of y for which 3x - y -5 2x + 5y =). ( 4marks) | Total 15 marks I END OF TEST 012340201F 2009

Cxc Mathematics Past Papers And Answers 2009

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