# Edexcel GCE Core Maths C3 Advanced January 2013

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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 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 sin2θ – sinθ = 0, stating the value of k.

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

cos 2θ + sinθ = 1 6 (b) Solving Trig. Equations

C3 Edexcel Core Mathematics January 2013 Question 7

Simplifying Algebraic Fractions

7 (a) Show that h(x) = 2x/(x2 + 5)

(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 7 (b) 7 (c) C3 Edexcel Core Mathematics January 2013 Question 8

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.

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