 # Edexcel Core Mathematics C1 June 2013

Questions and Worked Solutions for C1 Edexcel Core Mathematics June 2013.

Core 1 Mathematics Edexcel June 2013 Question 1
Surds
1. Simplify (7 + √5)/(√5 - 1)
giving your answer in the form a + b√5 , where a and b are integers.
Core 1 Mathematics Edexcel June 2013 Question 2
Integration
2. Find
∫(10x4 - 4x -3/√x) dx
giving each term in its simplest form.

Core 1 Mathematics Edexcel June 2013 Question 3
Indices (Exponents)
3. (a) Find the value of 85/3
(b) Simplify fully (2x1/2)3/4x2
Core 1 Mathematics Edexcel June 2013 Question 4
Sequences and Sigma Notation
4. A sequence a1, a2, a3, ... is defined by
a1 = 4
an +1 = k (an + 2), for n ≥ 1

where k is a constant.
(a) Find an expression for a2 in terms of k.

Given that
(b) find the two possible values of k.

Core 1 Mathematics Edexcel June 2013 Question 5
5. Find the set of values of x for which

(a) 2(3x + 4) > 1 – x
(b) 3x2 + 8x – 3 < 0

Core 1 Mathematics Edexcel June 2013 Question 6
Coordinate Geometry
6. The straight line L1 passes through the points (–1, 3) and (11, 12).
(a) Find an equation for L1 in the form ax + by + c = 0,
where a, b and c are integers.

The line L2 has equation 3y + 4x – 30 = 0.
(b) Find the coordinates of the point of intersection of L1 and L2.

Core 1 Mathematics Edexcel June 2013 Question 7
Arithmetic Progressions

7. A company, which is making 200 mobile phones each week, plans to increase its production. The number of mobile phones produced is to be increased by 20 each week from 200 in week 1 to 220 in week 2, to 240 in week 3 and so on, until it is producing 600 in week N.
(a) Find the value of N.

The company then plans to continue to make 600 mobile phones each week.
(b) Find the total number of mobile phones that will be made in the first 52 weeks starting from and including week 1.

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