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More Lessons for A Level Maths

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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.

C3 Edexcel Core Mathematics January 2013 Question 1

Chain Rule Application

1. The curve C has equation y = (2x -3^{)5}

Iteration

C3 Edexcel Core Mathematics January 2013 Question 3

Functions - Transformation of Graphs

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

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

C3 Edexcel Core Mathematics January 2013 Question 5

Differentiation - Product and Chain Rule

More Lessons for A Level Maths

Math Worksheets

Are you looking for A-level Maths help?

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.

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.

C3 Edexcel Core Mathematics January 2013 Question 2Iteration

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.

C3 Edexcel Core Mathematics January 2013 Question 4Rcos(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.

C3 Edexcel Core Mathematics January 2013 Question 5

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})

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