UNIT 29 Using Graphs to Solve Equations: CSEC Revision Test
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1 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve 1. Shell bus 3 litres of oil and 40 litres of gasoline for $30. The cost of one litre of oil is $ and the cost of one litre of gasoline is $. (a) Eplain wh the cost of Shell's purchases is given b the equation: = 30 (1 mark) Craig bus litres of oil and 10 litres of gasoline for his motorbike for $10. (b) Write down the equation for Craig's purchases. (1 mark) (c) Plot these two equations on graph paper like that shown on the net page. (3 marks) (d) B using our graph, or otherwise, find: (i) the cost of one litre of oil, (1 mark) (ii) the cost of one litre of gasoline. (1 mark). The dotted lines on the diagram below show part of the graph of = 3. A B (a) On a cop of diagram A, sketch the graph of = ( marks) (b) On a cop of diagram B, sketch the graph of = 3. ( marks) CIMT and e-learning Jamaica 1
2 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve Graph paper for Question CIMT and e-learning Jamaica
3 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve 3. The four sketch graphs below each represent one of the following functions. = = + = 0 = Graph A Graph B Graph C Graph D (a) Cop and complete the table to show which graph represents which function. GRAPH A B C D FUNCTION The line = will intersect three of the four graphs in two places. (4 marks) (b) State which graph does not intersect the line =. (1 mark) (c) State the coordinates of the points of intersection of = with each of the other graphs. (6 marks) CIMT and e-learning Jamaica 3
4 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve = 14 1 = = (a) The graphs of the lines =, = and = have been drawn. What is the gradient of the line =? (1 mark) (b) A rectangle has dimensions cm b cm. It has an area of 8 cm. (i) Complete the table to show some possible values of and, where = ( marks) (ii) Plot these points on a cop of the aes above and draw the graph of CIMT and e-learning Jamaica 4 = 8. (3 marks)
5 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve (iii) (iv) A rectangle has an area of 8 cm. The length of the rectangle is twice the width. Mark a point on the graph where the dimensions of the rectangle can be found. Label it A. A square has an area of 8 cm. Mark a point on the graph where the length of the side of the square can be found. Label it B. (1 mark) (1 mark) 5. Graph paper must be used for this question. h cm cm cm A rectangular block has a square base of side cm and a height of h cm. The total surface area of the block is 7 cm. (a) Epress h in terms of. ( marks) (b) Show that the volume, V cm 3, of the block is given b V = ( marks) (c) Cop and complete the following table to show corresponding values of and V (d) V Using a scale of cm to represent 1 unit on the -ais and cm to represent 10 units on the V-ais, draw the graph of V = for values of from 0 to 6 inclusive. ( marks) (3 marks) (e) A block of this tpe has a volume of 30 cm 3. Given that h >, find the dimensions of the block. ( marks) CIMT and e-learning Jamaica 5
6 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve 6. (a) The grid shows the line, l, which passes through the points A ( 1, ) and B (, 4). (i) Determine the gradient of the line, l. ( marks) (ii) Write down the equation of the line, l. (1 mark) (b) (i) Given that f( ) = 3, cop and complete the table below for f( ) 6 1 ( marks) (ii) On a cop of the following grid, draw the graph of f 3 for 3. (3 marks) ( ) = (iii) Write down the coordinates of the points where the line, l, and the graph f ( ) = 3 intersect. ( marks) CIMT and e-learning Jamaica 6
7 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve 6. (continued) 4 B A - -3 l (CXC) CIMT and e-learning Jamaica 7
8 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve ( ) = 7. The figure provided shows the graph of f of the graph of g ( ) = 7 9 for 3 3 and (a) State the elements in the domain of f( ) for which f( ) = 5. ( marks) (b) Given that f g ( ) = ( ), show that + = 0. ( marks) (c) Solve the equation + = 0. (3 marks) 1 f () f( ) = g ( ) = 7 (CXC) CIMT and e-learning Jamaica 8
9 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve 8. An athlete runs on a track so that his distance, d metres, from the starting point after t seconds is as shown in the table below. Time (seconds), t Distance (metres), d (a) (i) Using a horizontal scale of 1 cm to represent 1 second and a vertical scale of 1 cm to represent 10 metres, construct a distance-time graph to show the motion of the athlete. (ii) Draw a smooth curve through all the plotted points. (b) Use our graph to estimate (i) (ii) the distance travelled b the athlete after 3 seconds the average speed of the athlete during the interval t = 6 seconds to t = 8 seconds. (iii) the speed of the athlete 6 seconds after leaving the starting point. (10 marks) (CXC) TOTAL MARKS: 68 CIMT and e-learning Jamaica 9
10 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve ANSWERS 1. (a) Eplanation (b) + 10 = 10 B1 B1 (c) Graph B3 (d) (i) $ (ii) 60 cents B1 B1 (7 marks). (a) (b) A B B B (4 marks) 3. (a) Graph Function A = B1 B = B1 C = B1 D + = 0 B1 (b) D B1 (c) A : (0, 0), ( 1, 1 ) B1 B1 B : (0, 0), ( 1, 1) B1 B1 C : (, ), (, ) B1 B1 (11 marks) 4. (a) 1 B1 (b) (i) (ii) B B3 5 A(iii) B(iv) B1 B1 (8 marks) CIMT and e-learning Jamaica 101
11 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve ANSWERS (a) h = 18 = (b) V = h M1 A1 B (c) B V (d) Graph B3 (e) 1.85 B (11 marks) ( ) 6. (a) (i) 4 Gradient = ( 1) M1 A1 (ii) = B1 ( ) = ( ) = ( ) = (b) (i) f 1, f 0 3, f 1 ( 1 for each mistake) B (ii) 4 B A - -3 l ( ) (iiii) 3, 6 and 1, CIMT and e-learning Jamaica 11 ( ) B1 B1 (10 marks) B3
12 UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve ANSWERS 7. (a) = and = B1 B1 (b) 9 = 7 + = 0 M1 A1 (c) From graph, = and = 1 M1 A1 A1 (7 marks) 8. d (m) t (s) (a) (i) Ais B1 Points B (ii) Curve B (b) (i) 5 m B1 distance travelled (ii) Average speed = = time taken = 10 m/s M1 A1 8 6 increase in distance (iii) Speed = increase in time m/s M1 A1 (10 marks) TOTAL MARKS: 68 CIMT and e-learning Jamaica 1 3
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