A2-Level Mathematics Edexcel: Complete Revision & Practice by CGP Books

By CGP Books

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This publication is filled with transparent revision notes and examination perform questions for A2 Maths scholars. It covers the C3, C4, S2 and M2 modules for the Edexcel examination, and it’s effortless to learn and revise from - everything’s defined easily and carefully. each few pages there are speedy warm-up questions, a few exam-style questions and on the finish of every module there are perform examination papers (answers on the back). There’s additionally a sprinkling of jokes to lighten the temper. It’s precisely what you must organize on your assessments!

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Additional resources for A2-Level Mathematics Edexcel: Complete Revision & Practice

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2 The graph below shows the function y = f(x), x d R , with turning points A(−1, −2) and B(3, 2). f(x) = 3 ln x − ln 3x, x>0 the exact value of x when f(x) = 0. (2 marks) −1 (2 marks) the exact value of x when f (x) = 1. −1 (2 marks) (2 marks) y y = f (x) B (3, 2) 0 A (–1, –2) a) On separate axes, sketch the graphs of the following, clearly showing the coordinates of A and B where possible. (i) y = f(|x|). (ii) y = 3f(x + 2). 5 and h(x) = 2 6 , x > 2, find: x -4 (i) gh(4) (ii) hg(3) (iii) hg(x) (3 marks) (3 marks) (2 marks) (2 marks) (3 marks) 41 3 Part of the curve is shown below.

3 -1 -2 Look at the graph above at the root x = 1. For x-values just before the root, f(x) is negative, and just after the root, f(x) is positive. It’s the other way around for the other two roots, but either way: f(x) changes sign as it passes through a root. This is only true for continuous functions — ones that are joined up all the way along with no ‘jumps’ or gaps. To show that a root lies in the interval between two values ‘a’ and ‘b’: 1) Find f(a) and f(b). 2) If the two answers have different signs, and the function is continuous, there’s a root somewhere between ’em.

Sadly no magic here, but all the right kinds of questions to prepare you for the exam. Which may not be what you want, but it’s definitely what you need. Exam Questions 1 The sketch below shows part of the graph of the function f(x) = 2xex − 3. The curve crosses the x-axis at the point P (p, 0), as shown, so p is a root of the equation f(x) = 0. 8. p. p. C3 Section 5 — Numerical Methods (3 marks) x = 3 e−x. 2 (2 marks) xn+1 = 3 e−x 2 n (3 marks) (3 marks) 39 C3 SectionMain 5 — Practice Heading Questions 2 The graph of the function: y = sin 3x + 3x, 0 < x < p, meets the line y = 1 when x = a.

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