# Edexcel Core Mathematics C3 June 2010

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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 June 2010.

Edexcel Core Mathematics C3 June 2010 Past Paper

C3 Mathematics Edexcel June 2010 Question 6

Figure 2 shows a sketch of the curve with the equation y = f(x), x ∈ ℝ

The curve has a turning point at A(3, 4) − and also passes through the point (0, 5).

(a) Write down the coordinates of the point to which A is transformed on the curve with equation

(i) y = |f(x)| ,

(ii) y = 2f(1/2x)

(b) Sketch the curve with equation y = f(|x|)

On your sketch show the coordinates of all turning points and the coordinates of the point at which the curve cuts the y-axis.

The curve with equation y = f(x) is a translation of the curve with equation y = x2

(c) Find f(x).

(d) Explain why the function f does not have an inverse.

1. (a)

6 (b)

6 (c)(d)

C3 Mathematics Edexcel June 2010 Question 7

1. (a) Express 2 sin θ – 1.5 cos θ in the form R sin (θ – α), where R > 0 and 0 < α < π/2

Give the value of α to 4 decimal places.

(b) (i) Find the maximum value of 2 sin θ – 1.5 cos θ.

(ii) Find the value of θ, for 0 ≤ θ < π, at which this maximum occurs.

Tom models the height of sea water, H metres, on a particular day by the equation

H = 6 + 2 sin (4πt/25) - 1.5 cos (4πt/25), 0 ≤ t < 12

where t hours is the number of hours after midday.

(c) Calculate the maximum value of H predicted by this model and the value of t, to 2 decimal places, when this maximum occurs.

(d) Calculate, to the nearest minute, the times when the height of sea water is predicted, by this model, to be 7 metres.

1. (a)

7 (b)

7 (c)

7 (d)

C3 Mathematics Edexcel June 2010 Question 8

1. (a) Simplify fully (2x2 + 9x - 5)/(x2 + 2x - 15)

Given that

ln(2x2 + 9x - 5) = 1 + ln (x2 + 2x - 15), x ≠ -05

(b) find x in terms of e.

8 (a)

8 (b)

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