Edexcel Core Mathematics C1 June 2013

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

Edexcel Core Mathematics C1 June 2013 Past Paper

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 8^5/3(b) Simplify fully (2x^1/2)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
a_{n +1} = k (a_{n + 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
Linear and Quadratic Inequalities
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.