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Questions and Worked Solutions for C2 Edexcel Core Mathematics May 2015.

Edexcel Core Mathematics C2 May 2015 Past Paper (PDF)

Core 2 Mathematics Edexcel May 2015 Question 1

Step by Step Solutions for Question 1

Core 2 Mathematics Edexcel May 2015 Question 2

A circle C with centre at the point (2, -1) passes through the point A at (4, -5).

(a) Find an equation for the circle C.

(b) Find an equation of the tangent to the the circle at point A, giving your answer in the form ax + by + c = 0, where a, b and c are integers.

Step by Step Solutions for Question 2

Core 2 Mathematics Edexcel May 2015 Question 3

f(x) = 6x^{3} + 3x^{3} + Ax^{2} + B, where A and B are constants.

Given that when f(x) is divided by (x + 1) the remainder is 45.

(a) show that B - A = 48

Given also that (2x + 1) is a factor of f(x).

(b) find the value of A and the value of B.

(c) Factorise f(x) fully.

Step by Step Solutions for Question 3

Core 2 Mathematics Edexcel May 2015 Question 4

Figure 1 shows a sketch of a design for a scraper blade. The blade AOBCDA consists of an isosceles triangle COD joined along its equal sides to sectors OBC and ODA of a circle with centre O and radius 8 cm. Angles AOD and BOC are equal. AOB is a straight line and is parallel to the line DC. DC has length 7 cm.

(a) Show that the angle COD is 0.906 radians, correct to 3 significant figures.

(b) Find the perimeter of AOBCDA, giving your answer to 3 significant figures.

(c) Find the area of AOBCDA, giving your answer to 3 significant figures.

Step by Step Solutions for Question 4

Core 2 Mathematics Edexcel May 2015 Question 5

(i) All the terms of a geometric series are positive. The sum of the first two terms is 34 and the sum to infinity is 162.

Find

(a) the common ratio.

(b) the first term.

(ii) A different geometric series has a first term of 42 and a common ratio of 6/7.

Find the smallest value of n for which the sum of the first n terms of the series exceeds 290.

Step by Step Solutions for Question 5

Core 2 Mathematics Edexcel May 2015 Question 6

Step by Step Solutions for Question 6

Core 2 Mathematics Edexcel May 2015 Question 7
(i) Use logarithms to solve the equation 8^{2x + 1} = 24, giving your answer to 3 decimal places.

(ii) Find the values of y such that

log_{2}(11y - 3) - log_{2}3 - 2 log_{2}y = 1, y > 3/11

Step by Step Solutions for Question 7

Core 2 Mathematics Edexcel May 2015 Question 8

(i)Solve, for 0 ≤ θ < π, the equation

sin3θ - √3cos3θ = 0

giving your answers in terms of π

(ii) Given that

4sin^{2}x + cos x = 4 - k, 0 ≤ k ≤ 3

(a) find cos x in terms of k.

(b) When k = 3, find the values of x in the range 0 ≤ x < 360°

Step by Step Solutions for Question 8

Core 2 Mathematics Edexcel May 2015 Question 9

A solid glass cylinder, which is used in an expensive laser amplifier, has a volume of 75π cm^{3}.

The cost of polishing the surface area of this glass cylinder is £2 per cm^{3} for the circular top and base areas.

Given that the radius of the cylinder is r cm.

(a) show that the cost of the polishing, £C, is given by

C = 6πr^{2} + (300π)/r

(b) Use calculus to find the minimum cost of the polishing, giving you answer to the nearest pound.

(c) Justify that the answer that you have obtained in part (b) is a minimum.

Step by Step Solutions for Question 9

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