Edexcel GCE Core Mathematics C3 Advanced January 2012

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C3 Edexcel Core Mathematics January 2012 Question 1

1. Differentiate with respect to x, giving your answer in its simplest form,

(a) x²ln(3x)

(b) sin 4x/x³ 1 (a) Differentiation - Product Rule.

1 (b) Differentiation - Quotient Rule.

C3 Edexcel Core Mathematics January 2012 Question 2

Figure 1 shows the graph of equation y = f(x).

The points P (– 3, 0) and Q (2, – 4) are stationary points on the graph.

Sketch, on separate diagrams, the graphs of

(a) y = 3f(x + 2)

(b) y = |f (x)|

On each diagram, show the coordinates of any stationary points.

2 (a) Transformations of graphs.

2 (b) Exponential functions.



C3 Edexcel Core Mathematics January 2012 Question 3

3. The area, A mm², of a bacterial culture growing in milk, t hours after midday, is given by

A = 20e^1.5t, t ≥ 0

(a) Write down the area of the culture at midday.

(b) Find the time at which the area of the culture is twice its area at midday. Give your answer to the nearest minute.

3) Exponential functions.

C3 Edexcel Core Mathematics January 2012 Question 4

4. The point P is the point on the curve x = 2 tan (y + π/12) with y-coordinate π/4

Find an equation of the normal to the curve at P.

4) Normal to a curve.



C3 Edexcel Core Mathematics January 2012 Question 5

5. Solve, for 0° ≤ θ ≤ 180°,

2cot² 3θ = 7 cosec 3θ - 5

Give your answers in degrees to 1 decimal place.

5) Trig. equations

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