3. Introduction - slide 3 Temasek Secondary School Preliminary Examination 1999 Paper 1 8, 11 Paper 2 5ai, 5bii, 6ci, 6ciii,7a Thanks for viewing our presentation!

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5. The figure is a sketch of the graph y=x(x-2)(3-x). Find the equation of the tangents at x=2 and x=3.

6. y=-x 3 +5x 2 -6x when x=2, y=0, when x=3, y=0 y=x(x-2)(3-x) Equation of the tangent at (2,0) is y=2x-4 Equation of the tangent at (3,0) is y=-3x+9

7. Find the area of the region enclosed by the curve and the two tangents at x=2 and x=3.

8. To find the intersecting point of the two tangents, 2x-4=-3x+9 The intersecting point of the two tangents is (2.6,1.2).

9. Area of the triangle Area under the curve

10. Area of the triangle Area under the curve The area of the region enclosed by the curve and the two tangents at x=2 and x=3

11. A particle P travels in a straight line so that its distance, S m, from a fixed a point O is given by Where t is the time in seconds measured from the start of the motion. Calculate the velocity of P when it is next at its starting point. 11

12. When t=0, S=18 When S=18, t 2 -8t=0  t=0 or t=8 When t=8, the velocity of P when it is next at its starting point is

13. Cos(2x-30 o )=sin2x

14.  Cos(2x-30 o )=cos(90 o- 2x)  2x-30 o = 90 o- 2x or 360 o +90 o- 2x or 720 o +90 o -2x or 1080 o +90 o- 2x  4x=120 o or 480 o or 840 o or 1200 o  x= 30 o or 120 o or 210 o or 300 o

15. Given that find in terms of p, for

17. Given that V=12-12sin6t Find the range of values of V.

19. Graph of V=12-12sin6t Range of v is 0  v  24 V=12-12sin 6t

20. The distance travelled by the particle from O to the first instance at which it is at rest. V=12-12sin6t

21. Sin6t=1 The distance travelled= When V=0, 12-12sin6t=0

22. Find

23. Where c is a constant