Edexcel Mathematics Specimen paper · Paper 1 · Question 1 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

Specimen paper · Paper 1 · Question 1 · 6 marks

1. y DO NOT WRITE IN THIS AREA x 1 1.5 2 2.5 3 y 0.5 0.6742 0.8284 0.9686 1.0981 R O 1 3 x Figure 1 x Figure 1 shows a sketch of the curve with equation y = The finite region R, shown shaded in Figure 1, is bounded by the curve, the line with equation x = 1, the x‑axis and the line with equation x = 3 The table below shows corresponding values of x and y for y = area of R. exemplar DRAFT 1 + √, x x  0 x 1 + √ x (a) Use the trapezium rule, with all the values of y in the table, to find an estimate for the area of R, giving your answer to 3 decimal places. (3) (b) Explain how the trapezium rule can be used to give a better approximation for the (1) (c) Giving your answer to 3 decimal places in each case, use your answer to part (a) to deduce an estimate for 3 x 5 (i) ∫ √ d x 1 + x 1 3  (ii) 6 ∫x 1    + 1 + √ d x   x

Lesson: Locating Roots by Change of Sign