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Questions and Solutions for C4 Edexcel Core Mathematics January 2010### C4 Mathematics Edexcel January 2010 Question 1

### C4 Mathematics Edexcel January 2010 Question 2

### C4 Mathematics Edexcel January 2010 Question 3

### C4 Mathematics Edexcel January 2010 Question 4

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Questions and Solutions for C4 Edexcel Core Mathematics January 2010

Edexcel Core Mathematics C4 January 2010 Past Paper

1. (a) Find the binomial expansion of

√(1 - 8x), |x| < 1/8

in ascending powers of x up to and including the term in x^{3}

(b) Show that, when x = 1/100, the exact value of √(1 - 8x) is √23/5

(c) Substitute x = 1/100 into the binomial expansion in part (a) and hence obtain an
approximation to √23. Give your answer to 5 decimal places.

Figure 1 shows a sketch of the curve with equation y = x 1n x, x ≥ 1. The finite region R,
shown shaded in Figure 1, is bounded by the curve, the x-axis and the line x = 4.

The table shows corresponding values of x and y for y = x 1n x.

(a) Complete the table with the values of y corresponding to x = 2 and x = 2.5, giving your
answers to 3 decimal places.

(b) Use the trapezium rule, with all the values of y in the completed table, to obtain an
estimate for the area of R, giving your answer to 2 decimal places.

(c) (i) Use integration by parts to find ∫ x lnx dx

(ii) Hence find the exact area of R, giving your answer in the form ¼(a ln2 + b)
where a and b are integers.

3. The curve C has the equation

cos 2x + cos 3y = 1, -π/4 ≤ x ≤ π/4, 0 ≤ y ≤ π/6

(a) Find dy/dx in terms of x and y.

The point P lies on C where x = π/6

(b) Find the value of y at P.

(c) Find the equation of the tangent to C at P, giving your answer in the form

ax + by + cπ = 0, where a, b and c are integers.

The lines l_{l} and l_{2} intersect at the point A and the acute angle between l_{l} and l_{2}
intersect at the point A and the acute angle between l_{l} and l_{2} is θ

(a) Write down the coordinates of A.

(b) Find the value of cos θ.

The point X lies on l_{l} where λ = 4.

(c) Find the coordinates of X.

(d) Find the vector AX.

(e) Hence, or otherwise, show that |AX| = 4√26.

The point Y lies on l_{2}. Given that the vector YX is perpendicular to l_{l}

(f) find the length of AY, giving your answer to 3 significant figures.

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