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Questions and Video Solutions for C3 Edexcel Core Mathematics June 2009

Edexcel Core Mathematics C3 June 2009 Past Paper

### C3 Mathematics Edexcel June 2009 Question 1

Figure 1 shows part of the curve with equation y = -x^{3} + 2x^{2} + 2, which intersects the
x-axis at the point A where x = α.

To find an approximation to α, the iterative formula

x_{n+1} = 2/(x_{n})^{2} + 2

is used.

(a) Taking x_{0}= 2.5, find the values of x_{1}, x_{2}, x_{3} and x_{4}

Give your answers to 3 decimal places where appropriate.

(b) Show that α = 2.359 correct to 3 decimal places.### C3 Mathematics Edexcel June 2009 Question 2

### C3 Mathematics Edexcel June 2009 Question 3

### C3 Mathematics Edexcel June 2009 Question 4

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

Questions and Video Solutions for C3 Edexcel Core Mathematics June 2009

Edexcel Core Mathematics C3 June 2009 Past Paper

To find an approximation to α, the iterative formula

x

is used.

(a) Taking x

Give your answers to 3 decimal places where appropriate.

(b) Show that α = 2.359 correct to 3 decimal places.

2. (a) Use the identity cos^{2} θ + sin^{2} θ = 1 to prove that tan^{2} θ = sec^{2} θ – 1.

(b) Solve, for 0 ≤ θ < 360°, the equation

2 tan^{2} θ + 4 sec θ + sec^{2} θ = 2

3. Rabbits were introduced onto an island. The number of rabbits, P, t years after they were
introduced is modelled by the equation

P = 80e^{1/3t}, t ∈ ℝ, t ≥ 0

(a) Write down the number of rabbits that were introduced to the island.

(b) Find the number of years it would take for the number of rabbits to first exceed
1000.

(c) Find dP/dt

(d) Find P when dP/dt 50.

4. (i) Differentiate with respect to x

(a) x^{2} cos 3x

(b) ln(x^{2} + 1)/(x^{2} + 1)

(ii) A curve C has the equation

y = √(4x + 1), x > -¼ , y > 0

The point P on the curve has x-coordinate 2. Find an equation of the tangent to C at
P in the form ax + by + c = 0, where a, b and c are integers.

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