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Mike’s pulse rate was measured at 72 beats per minute.

1. Mike’s pulse rate was measured at 72 beats per minute. Explain exactly what this means. ( i ). Every minute, Mick’s heart beats 72 times. (ii). How many heartbeats would Mike expect to have in a two-hour period?. = 72  60  2. = 8640 heart beats in two hours. 2.

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Mike’s pulse rate was measured at 72 beats per minute.

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  1. 1. Mike’s pulse rate was measured at 72 beats per minute. Explain exactly what this means. (i) Every minute, Mick’s heart beats 72 times. (ii) How many heartbeats would Mike expect to have in a two-hour period? = 72  60  2 = 8640 heart beats in two hours.

  2. 2. Alex worked 12 hours for €111, whereas Ryan worked 14 hours for €136·50. Who worked for the better hourly rate of pay? (i) Alex: 12 hours = €111 = €9·25 Ryan: 14 hours = €136·50 = €9·75 Therefore, Ryan works for the better hourly rate of pay.

  3. 2. Alex worked 12 hours for €111, whereas Ryan worked 14 hours for €136·50. If they both worked for 20 hours, who would get paid more? And by how much? (ii) Alex = 20  €9·25 = €185 Ryan = 20  €9·75 = €195 Difference: €195 − €185 = €10 Ryan gets paid €10 more than Alex.

  4. 3. A plane left Dublin at 13 : 52 and travelled to Rome, Italy, a distance of 2,475 km. The plane arrived in Rome at 17 : 07. Find, correct to one decimal place, the average speed of the plane in: Find the time taken for the journey: (i) kilometres per hour

  5. 3. A plane left Dublin at 13 : 52 and travelled to Rome, Italy, a distance of 2,475 km. The plane arrived in Rome at 17 : 07. Find, correct to one decimal place, the average speed of the plane in: Find the time taken for the journey: (ii) metres per second. Alternatively: 761·5 km = 1 hour 761,500 m = 60 min 761,500 m = 3600 seconds 211·52 m = 1 second = 211·5 m/second

  6. 4. By studying the following graphs, find: (a) (i) The rate of change of the graph

  7. 4. By studying the following graphs, find: (a) (ii) the equation of the graph, in the form f (x) = mx + c, where m, c. c = y-intercept = +3 and m =Rate of change=2 f (x) = mx + c f (x) = 2x + 3

  8. 4. By studying the following graphs, find: (b) (i) The rate of change of the graph

  9. 4. By studying the following graphs, find: (b) (ii) the equation of the graph, in the form f (x) = mx + c, where m, c. c = y-intercept = +4 and f (x) = mx + c

  10. 5. The graphs below show y = x2with tangents drawn at various points. Use the shaded triangles to find the rate of change (slope) of the tangents to the curve at the indicated point. (i)

  11. 5. The graphs below show y = x2with tangents drawn at various points. Use the shaded triangles to find the rate of change (slope) of the tangents to the curve at the indicated point. (ii)

  12. 5. The graphs below show y = x2with tangents drawn at various points. Use the shaded triangles to find the rate of change (slope) of the tangents to the curve at the indicated point. (iii)

  13. 5. The graphs below show y = x2with tangents drawn at various points. Use the shaded triangles to find the rate of change (slope) of the tangents to the curve at the indicated point. (iv)

  14. 6. For each of the following graphs, use the grid to estimate the rate of change at the point indicated.Make sure to include the correct units in your answer. (i) t = 1 Acceptable answer is 1 ± 0·1 m/s

  15. 6. For each of the following graphs, use the grid to estimate the rate of change at the point indicated.Make sure to include the correct units in your answer. (ii) Acceptable answer is €50 ± €5 profit/item

  16. 6. For each of the following graphs, use the grid to estimate the rate of change at the point indicated.Make sure to include the correct units in your answer. (iii) t = 3 Acceptable answer is 3 ± 0·3 km/h

  17. 6. For each of the following graphs, use the grid to estimate the rate of change at the point indicated.Make sure to include the correct units in your answer. (iv) t Acceptable answer is ̶ 4 ± 0·4 bat colonies/week

  18. 7. (a) The diagram shows the graph of a quadratic function. Use the grid to estimate the rate of change of the function, at the following values of :

  19. 7. (a) The diagram shows the graph of a quadratic function. Use the grid to estimate the rate of change of the function, at the following values of : 2 (i) Acceptable answer is1·5 ± 0·1

  20. 7. (a) The diagram shows the graph of a quadratic function. Use the grid to estimate the rate of change of the function, at the following values of : − 2 (ii) Acceptable answer is ̶ 2·5 ± 0·2

  21. 7. (a) The diagram shows the graph of a quadratic function. Use the grid to estimate the rate of change of the function, at the following values of : 4 (iii) Acceptable answer is 3·5 ± 0·3

  22. 7. (a) The diagram shows the graph of a quadratic function. Use the grid to estimate the rate of change of the function, at the following values of : 0 (iv) Acceptable answer is ̶0·5 ± 0·1

  23. 7. (a) The diagram shows the graph of a quadratic function. Use the grid to estimate the rate of change of the function, at the following values of : 0∙5 (v) Acceptable answer is 0 ± 0·1

  24. 7. (b) Write down the range of values of , for which the graph is decreasing. The graph is decreasing when it is moving downwards, reading from left to right. Therefore, the graph is decreasing when

  25. 8. (i) Graph the function g(x) = x2 + 3x − 4 in the domain − 5 ≤ x ≤ 2.

  26. 8. (ii) Use your graph to find the rate of change of g(x) at the points: (a) (− 4, 0) Acceptable answer is − 5 ± 0·5

  27. 8. (ii) Use your graph to find the rate of change of g(x) at the points: (b) (− 1, − 6) Acceptable answer is 1 ± 0·1

  28. 8. (ii) Use your graph to find the rate of change of g(x) at the points: (c) (2, 6) Acceptable answer is 7 ± 0·5

  29. 9. (a) The diagram shows part of the graph of a cubic function. Use the grid to estimate the rate of change of the function, at the following values of x: − 2 (i) Acceptable answer is 4·6 ± 0·25

  30. 9. (a) The diagram shows part of the graph of a cubic function. Use the grid to estimate the rate of change of the function, at the following values of x: 0 (ii) Acceptable answer is – 1·8 ± 0·1

  31. 9. (a) The diagram shows part of the graph of a cubic function. Use the grid to estimate the rate of change of the function, at the following values of x: 2 (iii) Acceptable answer is – 3·4 ± 0·3

  32. 9. (a) The diagram shows part of the graph of a cubic function. Use the grid to estimate the rate of change of the function, at the following values of x: 4 (iv) Acceptable answer is – 0·2 ± 0·05

  33. 9. (b) Write down the range of values of for which the graph is increasing. The graph is increasing when it is moving upwards, reading from left to right. Therefore, the graph is increasing when x < − 0·75 and x > 4·1.

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