By CGP Books
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This publication is stuffed with transparent revision notes and examination perform questions for AS Maths scholars. It covers the C1, C2, S1, M1 and D1 modules for the Edexcel examination, and it’s effortless to learn and revise from - everything’s defined easily and punctiliously. 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 arrange on your assessments!
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Additional resources for AS-Level Mathematics Edexcel: Complete Revision & Practice
4 marks) dx x 5 The curve C is given by the equation y = mx 3 - x 2 + 8x + 2 , for a constant m. a) The point P lies on C, and has the x-value 5. The normal to C at P is parallel to the line given by the equation y + 4x - 3 = 0 . b) Find the gradient of curve C at P. Hence or otherwise, find: c) (i) the value of m. Find dy . dx (2 marks) (3 marks) (3 marks) (ii) the y-value at P. 6 For x ≥ 0 and y ≥ 0, x and y satisfy the equation 2x - y = 6 . a) (2 marks) If W = x 2 y 2 , show that W = 4x 4 - 24x 3 + 36x 2 .
2x 3 - 3x 2 - 3x + 7h - 2x 2 (x - 2) ^2x - 3x - 3x + 7h - 2x + 4x 3 2 3 = x - 3x + 7 2 2 3 2x³ ÷ x = 2x² 2 This is what’s left — so now you have to get rid of the x2 term. Now start again with x² – 3x + 7. ^ x 2 - 3x + 7h - x (x - 2) The highest power of x is the x² term. 2 2 So subtract x lots of (x – 2) to get rid of that. ^ x - 3x + 7h - x + 2x =- x + 7 Now start again with this — and get rid of the x term. ^- x + 7h - ^- 1 (x - 2)h There are no more powers of x to get rid of — so stop here.
Yes, there are fiddly things to remember — but overall, it’s not as bad as all that. And just think of all the lovely marks you’ll get if you can answer questions like these in the exam... Warm-up Questions 1) An easy one to start with. Write down the formula for differentiating any power of x. 2) Differentiate these functions with respect to x: a) y = x 2 + 2, b) y = x 4 + x , c) y = 72 - 3 + 12x 3 x x 3) What’s the connection between the gradient of a curve at a point and the gradient of the tangent to the curve at the same point?
AS-Level Mathematics Edexcel: Complete Revision & Practice by CGP Books