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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
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.
Core 2 Mathematics Edexcel May 2015 Question 3
f(x) = 6x3 + 3x3 + Ax2 + 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.
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.
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.
(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.
Core 2 Mathematics Edexcel May 2015 Question 6
Core 2 Mathematics Edexcel May 2015 Question 7
(i) Use logarithms to solve the equation 82x + 1 = 24, giving your answer to 3 decimal places.
(ii) Find the values of y such that
log2(11y - 3) - log23 - 2 log2y = 1, y > 3/11
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
4sin2x + 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°
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 cm3.
The cost of polishing the surface area of this glass cylinder is £2 per cm3 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 = 6πr2 + (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.
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