Graph gradients and areas

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 3 marks
(a) A vehicle has speeds 1, 5, 8 and 6 m/s at times 0, 2, 4 and 6 seconds respectively. Use three trapezia, each 2 seconds wide, to estimate the distance travelled from 0 to 6 seconds. (3)
Question 2Non-calculator · 4 marks
A tangent to a distance-time curve at t = 4 passes through $(1,4)$ and $(7,28)$ . Time is in seconds and distance in metres.
(a) Estimate the instantaneous speed at t = 4. (2)
(b) At t = 4 the distance is 18 m. Find the average speed over the first 4 seconds if the distance at t = 0 was 2 m. (2)
Question 3Non-calculator · 4 marks
A car starts from rest and accelerates steadily to 15 m/s in $T$ seconds. It then travels at 15 m/s for 40 seconds, and then slows steadily to rest in 10 seconds. The total distance travelled is 750 m.
(a) Find the value of $T$ . (4)

Answers and marks

(a) $33$ m

P1 Establishing $(1+5)\times 2/2$ or an equivalent valid method.
P1 Establishing $(5+8)\times 2/2+(8+6)\times 2/2$ or an equivalent valid method.
A1 Correct answer: $33$ m

(a) $4$ m/s

(b) $4$ m/s

(a) $T = 10$

Graph gradients and areas

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