| Date | None Specimen | Marks available | 3 | Reference code | SPNone.1.sl.TZ0.3 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
A toy car travels with velocity v ms−1 for six seconds. This is shown in the graph below.
The following diagram shows the graph of \(y = f(x)\), for \( - 4 \le x \le 5\).
Write down the car’s velocity at \(t = 3\) .
Write down the value of \(f( - 3)\);
Find the car’s acceleration at \(t = 1.5\) .
Find the total distance travelled.
Markscheme
\(4{\text{ (m}}{{\text{s}}^{ - 1}}{\text{)}}\) A1 N1
[1 mark]
\(f( - 3) = - 1\) A1 N1
[1 mark]
recognizing that acceleration is the gradient M1
e.g. \(a(1.5) = \frac{{4 - 0}}{{2 - 0}}\)
\(a = 2\) \({\text{(m}}{{\text{s}}^{ - 2}}{\text{)}}\) A1 N1
[2 marks]
recognizing area under curve M1
e.g. trapezium, triangles, integration
correct substitution A1
e.g. \(\frac{1}{2}(3 + 6)4\) , \(\int_0^6 {\left| {v(t)} \right|} {\rm{d}}t\)
distance 18 (m) A1 N2
[3 marks]
