XMS Integration and Kinematics practice

Xinmin Secondary School Math Department Additional Mathematics: Calculus Practice Name: ______________________________ ( ) Date: ___________ Differentiation and Integration 1 XMS 2020 AM P2, Q4 (a) Find 21e d1e x x x− − . [2] (b) It is given that 3 2 1 d7ax x = , where a is a constant. Find the value of 6 2 2 dax x . [3] 2 XMS 2020 AM P2, Q6 (a) Differentiate 4 (cos sin )xe x x− + with respect to x . [3] (b) Hence evaluate π 2 0 sin dxe x x−  . [2] 3 XMS 2022 AM P1, Q12

4 MFSS 2022 AM P2, Q7 5 FMSS 2022 AM P2, Q2 Integration to find equation of a graph 1 XMS 2022 AM P1, Q3 2 MFSS 2022 AM P1 Q8 3 FMSS 2022 AM P2, Q4

Integration: Area under Curve 1 XMS 2020 AM P1, Q1 2 XMS 2022 AM P2, Q11

3 4 FMSS 2022 AM P2, Q9b

Kinematics 1 XMS 2020 AM P2, Q8 A particle moves in a straight line, so that t seconds after leaving a fixed point O, its velocity, v m/s, is given by 2 24v t kt= − + . The particle passes O with an acceleration of 10− m/s2. (i) Show that 10k = . (ii) Find the time when the particle reaches minimum velocity. (iii) Find the distance travelled by the particle in the tenth second. (iv) Explain with workings, whether the particle will return to O for 9t . [2] [3] [4] [2] 2 XMS 2022 AM P1, Q13 3 MFSS 2022 AM P1, Q12

4 FMSS 2022 AM P1, Q11