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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 6

Working with Trig Identities

6. (i) Without using a calculator, find the exact value of

(sin 22.5° + cos 22.5°)^{2}

You must show each stage of your working.

(ii) (a) Show that cos 2θ + sinθ = 1 may be written in the form

k sin^{2}θ – sinθ = 0, stating the value of k.

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

cos 2θ + sinθ = 1

Simplifying Algebraic Fractions

7 (a) Show that h(x) = 2x/(x

(b) Hence, or otherwise, find h ′(x) in its simplest form.

Figure 2 shows a graph of the curve with equation y x = h( ) .

(c) Calculate the range of h( ) x

Exponential Equation

8. The value of Bob’s car can be calculated from the formula

V = 17000e^{-0.25t} + 2000e^{-0.5t} + 500

where V is the value of the car in pounds (£) and t is the age in years.

(a) Find the value of the car when t = 0

(b) Calculate the exact value of t when V = 9500

(c) Find the rate at which the value of the car is decreasing at the instant when t = 8.

Give your answer in pounds per year to the nearest pound.

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