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# Math(F5) Gradient And Area Under A Graph

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### Math(F5) Gradient And Area Under A Graph

1. 3. GRADIENT AND AREA UNDER A GRAPH
2. 4. Distance-Time Graph <ul><li>How to draw a graph? </li></ul><ul><li>Recall previous knowledge </li></ul><ul><li>x axis represent time </li></ul><ul><li>y axis represent distance </li></ul><ul><li>Note : </li></ul><ul><li>When a distance-time graph is drawn, the gradient of the graph gives the speed. </li></ul>
3. 5. Example <ul><li>The following table shows the distance travelled and time taken by Amin to his office. Draw the distance-time graph made by Amin </li></ul>15 10 5 Distance (km) 0.3 0.2 0.1 Time (hours)
4. 6. The Gradient of a Distance-Time Graph <ul><li>What is gradient? </li></ul><ul><li>- Is the change of the quantity on the vertical axis with respect to the change of the quantity on the horizontal axis </li></ul>
5. 7. How to find gradient? <ul><li>Recall the formula of gradient : </li></ul><ul><li>m = </li></ul><ul><li>Example :………….. </li></ul><ul><li>What is the general equation of straight line? </li></ul><ul><li>The gradient of distance-time graph represent speed </li></ul>
6. 8. <ul><li>Please do worksheet 1…Exercise 6.1 B and 6.1 C with your partner </li></ul>Exercise
7. 10. How to find speed for a period of time from a distance-time graph <ul><li>Notes: </li></ul>
8. 11. The distance-time graph shows the distance covered by a boy from the starting point to another point and back. Example:
9. 12. <ul><li>a) Find the speed for the first 15 seconds. </li></ul><ul><li>b) How long did he rest? </li></ul><ul><li>c) Find the speed where the boy back to starting point. </li></ul><ul><li>d) Find the average speed for the whole journey. </li></ul>From the graph,
10. 13. a) Find the speed for the first 15 seconds. Answers: <ul><li>a) Speed for the first 15 seconds: </li></ul>
11. 14. Answers: <ul><li>b) How long did he rest? </li></ul><ul><li>Time taken = 30 s – 15 s </li></ul><ul><li> = 15 seconds </li></ul>-He takes 15 seconds to rest
12. 15. Answers: <ul><li>c) The speed where the boy back to the starting point: </li></ul>Negative sign indicates the direction of the journey is reversed