Questions and Worked Solutions for C1 Edexcel Core Mathematics June 2011.

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Core 1 Mathematics Edexcel June 2011 Question 1

Indices

- Find the value of

(a) 25^{1/2}

(b) 25^{-3/2}

Core 1 Mathematics Edexcel June 2011 Question 2

Differentiation, Integration
2. Given that

y = 2x^{5} + 7 + 1/x^{3}, x ≠ 0, find, in their simplest form,

(a) dy/dx

(b) ∫ y dx.

Core 1 Mathematics Edexcel June 2011 Question 3

Coordinate Geometry
3. The points P and Q have coordinates (–1, 6) and (9, 0) respectively.

The line l is perpendicular to PQ and passes through the mid-point of PQ.

Find an equation for l, giving your answer in the form ax + by + c = 0, where a, b and c

are integers.

Core 1 Mathematics Edexcel June 2011 Question 4
4. Solve the simultaneous equations

x + y = 2

4y^{2} - x^{2} = 11

Core 1 Mathematics Edexcel June 2011 Question 5

Sequences
5. A sequence a_{1}, a_{2}, a_{3}, … is defined by

a_{1} = k

a_{n+1} = 5a_{n} + 3, n ≥ 1

where k is a positive integer.

(a) Write down an expression for a_{2} in terms of k.

(b) Show that a_{3} = 25k + 18

(c) (i) Find in terms of k, in its simplest form.

(ii) Show that is divisible by 6.

- (c)

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