: Edexcel past-paper questions pack
Back to the topic page

Trapezium rule

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 24

Questions are numbered; the mark schemes (the answer key) follow on separate pages so the question pages can be handed out alone. www.mathsaleveltutor.com

Edexcel AS and A-level Maths past-paper questions since June 2018 · 10 parts, 24 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2023 · Paper 1 · Q5(a) · 3 marks
5. A continuous curve has equation y = f(x). The table shows corresponding values of x and y for this curve, where a and b are constants. x 3.2 3.4 3.6 3.8 y a 16.8 b 20.2 18.7 13.5 The trapezium rule is used, with all the y values in the table, to find an approximate area under the curve between x = 3 and x = 4 Given that this area is 17.59 (a) show that a + 2b = 51 (3)
2. June 2023 · Paper 1 · Q5(b) · 3 marks
Given also that the sum of all the y values in the table is 97.2 (b) find the value of a and the value of b (3)
3. June 2022 · Paper 2 · Q5(a) · 3 marks
5. The table below shows corresponding values of x and y for y = log3 2x The values of y are given to 2 decimal places as appropriate. x 4.5 7.5 y 1.63 2.26 2.46 2.63 (a) Using the trapezium rule with all the values of y in the table, find an estimate for ∫ 2x x log3 d (3)
4. June 2022 · Paper 2 · Q5(b) · 3 marks
Using your answer to part (a) and making your method clear, estimate ∫ ( ) (b) (i) 2x x log3 d ∫ (ii) 18x x log3 d (3)
5. Oct 2021 · Paper 1 · Q11(a) · 3 marks
11. y R x Figure 2 Figure 2 shows a sketch of part of the curve with equation y = (ln x) 2 x > 0 The finite region R, shown shaded in Figure 2, is bounded by the curve, the line with equation x = 2, the x-axis and the line with equation x = 4 The table below shows corresponding values of x and y, with the values of y given to 4 decimal places. 2.5 3.5 x y 0.4805 0.8396 1.2069 1.5694 1.9218 (a) Use the trapezium rule, with all the values of y in the table, to obtain an estimate for the area of R, giving your answer to 3 significant figures. (3)
6. Oct 2020 · Paper 2 · Q1(a) · 3 marks
x 1 The table below shows corresponding values of x and y for y = 1 + x The values of y are given to 4 significant figures. x 0.5 1.5 2.5 y 0.5774 0.7071 0.7746 0.8165 0.8452 (a) Use the trapezium rule, with all the values of y in the table, to find an estimate for ∫ 2 5 x x d + x 0 5 giving your answer to 3 significant figures. (3)
7. Oct 2020 · Paper 2 · Q1(b) · 1 marks
∫ 2 5 x x (b) Using your answer to part (a), deduce an estimate for d + x 0 5 (1)
8. Oct 2020 · Paper 2 · Q1(c) · 1 marks
Given that ∫ 2 5 x x = 4.535 to 4 significant figures d + x 0 5 (c) comment on the accuracy of your answer to part (b). (1)
9. June 2019 · Paper 2 · Q2(a) · 3 marks
2. The speed of a small jet aircraft was measured every 5 seconds, starting from the time it turned onto a runway, until the time when it left the ground. The results are given in the table below with the time in seconds and the speed in m sí1. Time (s) Speed (m sí1) Using all of this information, (a) estimate the length of runway used by the jet to take off. (3)
10. June 2019 · Paper 2 · Q2(b) · 1 marks
Given that the jet accelerated smoothly in these 25 seconds, (b) explain whether your answer to part (a) is an underestimate or an overestimate of the length of runway used by the jet to take off. (1)

Mark schemes

Each mark scheme shows the whole question; the parts on this topic are the ones listed above.

June 2023 · Paper 1 · Q5
Mark scheme June 2023 Paper 1 Q5(b)
June 2022 · Paper 2 · Q5
Mark scheme June 2022 Paper 2 Q5(b)
Oct 2021 · Paper 1 · Q11
Mark scheme Oct 2021 Paper 1 Q11(a)
Oct 2020 · Paper 2 · Q1
Mark scheme Oct 2020 Paper 2 Q1(c)
June 2019 · Paper 2 · Q2
Mark scheme June 2019 Paper 2 Q2(b)