EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Rates of Change
Graphing rates of change · Graphs · Lesson 3 of 8 · 12 marks · 25 minutes
Name Date
Answer all questions. Show your working. The calculator is allowed where the question says so.
Question 1 NON-CALCULATOR [4 marks]
The distance-time graph shows Tom's cycle ride from his home to a lake and back. (a) At what time did Tom arrive at the lake? (b) How long did Tom stay at the lake? (c) Work out Tom's speed on his way home, in km/h.
Question 2 CALCULATOR [2 marks]
For the whole of his ride, including the stop, Tom travelled 60 km in 2 hours 15 minutes. Work out his average speed. Give your answer to 1 decimal place.
Question 3 NON-CALCULATOR [2 marks]
Water is poured into a tank at a constant rate. After 4 minutes the depth is 10 cm. After 10 minutes the depth is 25 cm. Work out the rate at which the depth increases. Give the units of your answer.
Question 4 CALCULATOR · HIGHER [4 marks]
A car accelerates uniformly from rest to 12 m/s in 4 seconds. It travels at 12 m/s for 10 seconds, then slows down uniformly and stops after another 6 seconds. (a) Work out the acceleration in the first 4 seconds. (b) Work out the total distance the car travels.
Answers
Check your answer only once you have written one.
Question 1 [4 marks]
(a) 10:00 (b) 30 minutes (c) 30 km in 45 minutes: 30 ÷ 0.75 = 40 km/h
▸ (a) 10:00 B1
▸ (b) 30 minutes B1
▸ (c) 30 km and 45 minutes, or 30 ÷ 0.75 M1
▸ (c) 40 km/h A1
Question 2 [2 marks]
60 ÷ 2.25 = 26.66…= 26.7 km/h
▸ 60 ÷ 2.25 M1
▸ 26.7 km/h A1
Question 3 [2 marks]
(25 − 10)/(10 − 4) = 15/6 = 2.5 cm per minute
▸ (25 − 10)/(10 − 4) M1
▸ 2.5 cm per minute A1
Question 4 [4 marks]
(a) 12 ÷ 4 = 3 m/s² (b) ½ × 4 × 12 + 10 × 12 + ½ × 6 × 12 = 24 + 120 + 36 = 180 m
▸ (a) 3 m/s² B1
▸ (b) Splitting the area into parts, or using the trapezium rule with parallel sides 20 and 10 M1
▸ (b) One correct part: 24, 120 or 36 M1
▸ (b) 180 m A1