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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced January 2013. The questions are given here.

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C3 Edexcel Core Mathematics January 2013 Question 1

Chain Rule Application

1. The curve C has equation y = (2x -3

The point P lies on C and has coordinates (w, – 32).

Find

(a) the value of w,

(b) the equation of the tangent to C at the point P in the form y mx c = + , where m and c are constants.

Iteration

2. g(x) = e^{x-1} + x - 6

(a) Show that the equation g(x) = 0 can be written as

x = ln(6 -x) + 1, x < 6

The root of g(x) = 0 is α.

The iterative formula

x_{n + 1} = ln(6 -x_{n}) + 1, x_{0} = 2

is used to find an approximate value for α.

(b) Calculate the values of x_{1} , x_{2} and x_{3} to 4 decimal places.

(c) By choosing a suitable interval, show that α = 2.307 correct to 3 decimal places.

Functions - Transformation of Graphs

Figure 1 shows part of the curve with equation y = f(x), x ∈ ℜ.

The curve passes through the points Q(0, 2) and P(−3, 0) as shown.

(a) Find the value of ff(−3) .

On separate diagrams, sketch the curve with equation

(b) y = f^{-1}(x)

(c) y = f(|x|) - 2

(d) y = 2 f(½ x)

Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.

Rcos(x-alpha) method

4. (a) Express 6 cos θ +8 sin θ in the form Rcos(θ - α), where R > 0 and 0 < α < π/2

Give the value of α to 3 decimal places.

(b) p(θ) = 4/(12 + 6cosθ + 8 sinθ, 0 ≤ θ ≤ 2π

Calculate

(i) the maximum value of p(θ),

(ii) the value of θ at which the maximum occurs.

Differentiation - Product and Chain Rule

5. (i) Differentiate with respect to x

(a) y = x^{3}ln2x

(b) y = (x + sin2x)^{3}

Given that x = cot y ,

(ii) show that dy/dx = -1/(1 + x^{2})

5(ii) Differentiation

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