Edexcel GCE Core Mathematics C2 Advanced January 2012

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C2 Edexcel Core Mathematics January 2012 Question 1

Geometric Series

1. A geometric series has first term a = 360 and common ratio r = 7/8
   Giving your answers to 3 significant figures where appropriate, find
   (a) the 20th term of the series,
   (b) the sum of the first 20 terms of the series,
   (c) the sum to infinity of the series.

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C2 Edexcel Core Mathematics January 2012 Question 2
Circle Coordinate Geometry
2. A circle C has centre (−1, 7) and passes through the point (0, 0). Find an equation for C.

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C2 Edexcel Core Mathematics January 2012 Question 3
Binomial Expansion
3. (a) Find the first 4 terms of the binomial expansion, in ascending powers of x, of
(1 + x/4⁾⁸
giving each term in its simplest form.
(b) Use your expansion to estimate the value of (1.025)⁸ giving your answer to 4 decimal places.

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C2 Edexcel Core Mathematics January 2012 Question 4
Logarithms
4. Given that y = 3x²
(a) show that log₃ y = 1 + 2 log₃x
(b) Hence, or otherwise, solve the equation 1 + 2 log₃x = log₃ (28x -9)

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C2 Edexcel Core Mathematics January 2012 Question 5
Remainder Theorem
f(x) = x³ + ax² + bx + 3, where a and b are constants.
Given that when f(x) is divided by (x + 2) the remainder is 7,
(a) show that 2a - b = 6
Given also that when f(x) is divided by (x −1) the remainder is 4,
(b) find the value of a and the value of b.

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