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Questions and Worked Solutions for C34 Edexcel Core Mathematics January 2015.

Edexcel Core Mathematics C34 January 2015 Past Paper

Core 34 Mathematics Edexcel January 2015 Question 1

The curve C has equation

y = (3x - 2)/(x - 2)^{2}, x ≠ 2

The point P on C has x coordinate 3

Find an equation of the normal to C at the point P in the form ax + by + c = 0, where a, b and c are integers.

Core 34 Mathematics Edexcel January 2015 Question 2

Solve, for 0 ≤ θ < 2π,

2cos2θ = 5 – 13sinθ

Give your answers in radians to 3 decimal places.

(Solutions based entirely on graphical or numerical methods are not acceptable.)

Core 34 Mathematics Edexcel January 2015 Question 3

The function g is defined by

g : x ↦ 6|8 – 2x|, x ∈ ℝ , x ≥ 0

(a) Sketch the graph with equation y = g(x), showing the coordinates of the points where the graph cuts or meets the axes.

(b) Solve the equation

|8 – 2x| = x + 5

The function f is defined by

f : x ↦ x^{2} – 3x + 1, x ∈ ℝ , 0 ≤ x ≤ 4

(c) Find fg(5).

(d) Find the range of f. You must make your method clear.

Core 34 Mathematics Edexcel January 2015 Question 4

Use the substitution x = 2sinθ to find the exact value of

Core 34 Mathematics Edexcel January 2015 Question 5

Core 34 Mathematics Edexcel January 2015 Question 6(i)

(i) Given x = tan^{2}4y, 0 < y < π/8, find dy/dx as a function of x.

Write your answer in the form 1/A(x^{p} + x^{q}), where A, p and q are constants to be found.

(ii) The volume V of a cube is increasing at a constant rate of 2 cm^{3} s^{-1}. Find the rate at which the length of the edge of the cube is increasing when the volume of the cube is 64 cm^{3}.

Core 34 Mathematics Edexcel January 2015 Question 7

(a) Given that

2cos(x + 30)° = sin(x - 30)°

without using a calculator, show that

tan x° = 3√3 - 4

(b) Hence or otherwise solve, for 0 ≤ θ < 180,

2cos(2θ + 40)° = sin(2θ - 20)°

Give your answers to one decimal place.

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