Date | May 2021 | Marks available | 2 | Reference code | 21M.1.SL.TZ2.13 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 2 |
Command term | Justify and Describe | Question number | 13 | Adapted from | N/A |
Question
A company produces and sells electric cars. The company’s profit, , in thousands of dollars, changes based on the number of cars, , they produce per month.
The rate of change of their profit from producing electric cars is modelled by
.
The company makes a profit of (thousand dollars) when they produce electric cars.
Find an expression for in terms of .
The company regularly increases the number of cars it produces.
Describe how their profit changes if they increase production to over cars per month and up to cars per month. Justify your answer.
Markscheme
recognition of need to integrate (eg reverse power rule or integral symbol) (M1)
A1A1
(M1)
Note: Award M1 for correct substitution of and . A constant of integration must be seen (can be implied by a correct answer).
A1
[5 marks]
profit will decrease (with each new car produced) A1
EITHER
because the profit function is decreasing / the gradient is negative / the rate of change of is negative R1
OR
R1
OR
evidence of finding and R1
Note: Award at most R1A0 if or or both have incorrect values.
[2 marks]