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

Edexcel Core Mathematics C1 June 2012 Past Paper

Integration

Find ∫(6x

Indices

2. (a) Evaluate (32)

(b) Simplify fully (24x^{4}/4)^{-1/2}

Surds

3. Show 2/(√12 - √8) that can be written in the form √a + √b, where a and b are integers.

Differentiation

y = 5x

(a) Find dy/dx

(b) Find d

Sequences 5. A sequence of numbers a

a

a

where c is a constant.

(a) Write down an expression, in terms of c, for a_{2}

(b) Show that a_{3 = 12 – 3c}

Given that

(c) find the range of values of c.

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.

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).
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