Derivative as a Rate of Change (Kinematics and Related Rates) · CSEC Additional Mathematics

15 past-paper questions on Derivative as a Rate of Change (Kinematics and Related Rates), part of Differentiation, from every CSEC Additional Mathematics paper on Quelpr.

1. 5(c)5 marks· Additional Mathematics Q5 5(c)Determine the rate of increase of the volume of water in the container in terms of π.
2. 5(c)5 marks· Additional Mathematics Q5 5(c)Calculate, in terms of π, the rate at which the radius is increasing when the radius of the balloon is 10 cm.
3. 5(c)5 marks· Additional Mathematics Q5 5(c)Find the rate of increase of the area when the length of the side is 5 cm.
4. 5(ii)3 marks· Additional Mathematics Q5 5(ii)Use your expression to find the approximate change in the value of y when x increases from 2 to 2.04.
5. 8(a)(i)3 marks· Additional Mathematics Q8 8(a)(i)Determine the velocity of the particle at t = 3.5 s, clearly stating the correct unit.
6. 8(a)(i)2 marks· Additional Mathematics Q8 8(a)(i)Determine its velocity when t = 2.
7. 8(a)(ii)3 marks· Additional Mathematics Q8 8(a)(ii)Calculate the average speed for the whole journey.
8. 8(a)(iii)3 marks· Additional Mathematics Q8 8(a)(iii)Determine the distance between the rest points.
9. 8(a)(iii)3 marks· Additional Mathematics Q8 8(a)(iii)Calculate the average velocity of the whole journey.
10. 8(b)(i)5 marks· Additional Mathematics Q8 8(b)(i)Determine the values of t for which the particle is stationary.
11. 8(b)(iii)a)2 marks· Additional Mathematics Q8 8(b)(iii)a)Calculate the value of dv/dt when t = 2 seconds.
12. 8(b)(iii)b)1 mark· Additional Mathematics Q8 8(b)(iii)b)Calculate the value of dv/dt when t = 3 seconds.
13. 8(b)(iv)a)1 mark· Additional Mathematics Q8 8(b)(iv)a)Give an interpretation for the value in 8(b)(iii)a).
14. 8(b)(iv)b)1 mark· Additional Mathematics Q8 8(b)(iv)b)Give an interpretation for the value in 8(b)(iii)b).
15. 11(i)4 marks· Additional Mathematics Q11 11(i)Find the acceleration of the particle at A and at B.