Edexcel Core Mathematics C1 June 2011

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Core 1 Mathematics Edexcel June 2011 Question 1
Indices

1. 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 = 2x⁵ + 7 + 1/x³, x ≠ 0, find, in their simplest form,
(a) dy/dx
(b) ∫ y dx.

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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.

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Core 1 Mathematics Edexcel June 2011 Question 4 4. Solve the simultaneous equations
x + y = 2
4y² - x² = 11

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Core 1 Mathematics Edexcel June 2011 Question 5
Sequences 5. A sequence a₁, a₂, a₃, … is defined by
a₁ = k
a_n+1 = 5a_n + 3, n ≥ 1
where k is a positive integer.
(a) Write down an expression for a₂ in terms of k.
(b) Show that a₃ = 25k + 18
(c) (i) Find in terms of k, in its simplest form.
(ii) Show that is divisible by 6.

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5. (c)

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