 # Edexcel Core Mathematics C4 January 2011

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Edexcel Core Mathematics C4 January 2011 Past Paper

C4 Mathematics Edexcel January 2011 Question 1

1. Use integration to find the exact value of

1. Integration by parts
C4 Mathematics Edexcel January 2011 Question 2

2. The current, I amps, in an electric circuit at time t seconds is given by

I = 16 –16(0.5)t , t ≥ 0

Use differentiation to find the value of dI/dt when t = 3.

Give your answer in the form ln a , where a is a constant.

2. Differentiation

C4 Mathematics Edexcel January 2011 Question 3

3. (a) Express 5/[(x + 1)(3x + 2)] in partial fractions.

(b) Hence find ∫ 5/[(x + 1)(3x + 2)] dx, where x > 1.

(c) Find the particular solution of the differential equation

(x - 1)(3x + 2) dy/dx = 5y, x > 1

for which y = 8 at x = 2 . Give your answer in the form y = f(x).

3(a) Partial Fractions
3(b) Integration (Partial Fractions)

3(c) Differential Equation
C4 Mathematics Edexcel January 2011 Question 4

4. Relative to a fixed origin O, the point A has position vector i - 3j + 2k and the point B has position vector -2i + 2j - k. The points A and B lie on a straight line l.

(a) Find AB.

(b) Find a vector equation of l.

The point C has position vector 2i + pj - 4k with respect to O, where p is a constant.

Given that AC is perpendicular to l, find

(c) the value of p,

(d) the distance AC.
4 (a)

4 (b)
4 (c)

4 (d)
C4 Mathematics Edexcel January 2011 Question 5

5. (a) Use the binomial theorem to expand

(2 - 3x)-2, |x| < 2/3

in ascending powers of x, up to and including the term in x3. Give each coefficient as a simplified fraction.

f(x) = (a + bx)/(2 -3x)2, |x| < 2/3 , where a and b are constants.

In the binomial expansion of f ( ) x , in ascending powers of x, the coefficient of x is 0 and the coefficient of x2 is 9/16. Find

(b) the value of a and the value of b,

(c) the coefficient of x3 , giving your answer as a simplified fraction.

5(a)Binomial Expansion

5 (b)
5 (c)

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