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

Related Topics:

More videos, activities and worksheets that are suitable for A Level Maths

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)

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

data-ad-region="y21">