Questions and Worked Solutions for C3 Edexcel Core Mathematics June 2010.

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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 = x^{2}

(c) Find f(x).

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

6 (a)

7. (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.

7(a)

7 (b)

7 (d)

8. (a) Simplify fully (2x

Given that

ln(2x^{2} + 9x - 5) = 1 + ln (x^{2} + 2x - 15), x ≠ -05

(b) find x in terms of e.

8 (a)

8 (b)

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