 # Edexcel Core Mathematics C1 June 2012

Questions and Worked Solutions for C1 Edexcel Core Mathematics June 2012.

Core 1 Mathematics Edexcel June 2012 Question 1
Integration
Find ∫(6x2 + 2/x2 + 5) dx giving each term in its simplest form.
Core 1 Mathematics Edexcel June 2012 Question 2
Indices

(b) Simplify fully (24x4/4)-1/2

Core 1 Mathematics Edexcel June 2012 Question 3
Surds
3. Show 2/(√12 - √8) that can be written in the form √a + √b, where a and b are integers.
Core 1 Mathematics Edexcel June 2012 Question 4
Differentiation
y = 5x3 - 6x4/3 + 2x - 3

(a) Find dy/dx
(b) Find d2y/dx2

Core 1 Mathematics Edexcel June 2012 Question 5
Sequences 5. A sequence of numbers a1, a2, a3 ... is defined by
a1 = 3
an +1 = 2an - c (n ≥ 1)

where c is a constant.

(a) Write down an expression, in terms of c, for a2

(b) Show that a3 = 12 – 3c

Given that

(c) find the range of values of c.

Core 1 Mathematics Edexcel June 2012 Question 6
Arithmetic Sequence
6. A boy saves some money over a period of 60 weeks. He saves 10p in week 1, 15p in week 2, 20p in week 3 and so on until week 60. His weekly savings form an arithmetic sequence.

(a) Find how much he saves in week 15

(b) Calculate the total amount he saves over the 60 week period.

Arithmetic Series
The boy’s sister also saves some money each week over a period of m weeks. She saves 10p in week 1, 20p in week 2, 30p in week 3 and so on so that her weekly savings form an arithmetic sequence. She saves a total of £63 in the m weeks.
(c) Show that m(m + 1) = 35 × 36

(d) Hence write down the value of m.

Core 1 Mathematics Edexcel June 2012 Question 7
Tangents and finding f(x)
7. The point P (4, –1) lies on the curve C with equation y = f(x), x > 0, and
f'(x) = 1/2x - 6/√x + 3

(a) Find the equation of the tangent to C at the point P, giving your answer in the form y = mx + c, where m and c are integers.

(b) Find f(x).

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 