Edexcel Core Mathematics C2 June 2010

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Edexcel Core Mathematics C2 June 2010 Past Paper

Core 2 Mathematics Edexcel June 2010 Question 1

y = 3^x + 2x

(a) Complete the table below, giving the values of y to 2 decimal places.

(b) Use the trapezium rule, with all the values of y from your table, to find an approximate value for \(\int_0^1 {({3^x} + 2x)\,{\rm{d}}x} \)

Core 2 Mathematics Edexcel June 2010 Question 2

f(x) = 3x³ - 5x² -58x + 40
(a) Find the remainder when f(x) is divided by (x - 3).

Given that (x - 5) is a factor of f(x),
(b) find all the solutions of f(x) = 0.

Core 2 Mathematics Edexcel June 2010 Question 3

y = x² - k√x, where k is a constant.

(a) Find dy/dx

(b) Given that y is decreasing at x = 4 , find the set of possible values of k.

Core 2 Mathematics Edexcel June 2010 Question 4

(a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of (1 + ax)⁷ where a is a constant. Give each term in its simplest form.

Given that the coefficient of x² in this expansion is 525,
(b) find the possible values of a.

Core 2 Mathematics Edexcel June 2010 Question 5

(a) Given that 5 sin θ = 2 cos θ, find the value of tan θ

(b) Solve, for 0° ≤ x < 360°, 5sin 2x = 2cos 2x , giving your answers to 1 decimal place.

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