Edexcel Core Mathematics C1 January 2012

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

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Edexcel Core Mathematics C1 January 2012 Past Paper

Core 1 Mathematics Edexcel January 2012 Question 1
Differentiation, Integration
Given that y = x⁴ + 6x^1/2 find in their simplest form

(a) dy/dx

(b) ∫y dx Core 1 Mathematics Edexcel January 2012 Question 2
Surds, Rationalising Surds
2. (a) Simplify √32 + √18 giving your answer in the form a√2 , where a is an integer. (b) Simplify (√32 + √18)/(3 + √2) giving your answer in the form b√2 + c, where b and c are integers.

Core 1 Mathematics Edexcel January 2012 Question 3
Linear Inequality, Quadratic Inequality
3. Find the set of values of x for which
(a) 4x - 5 > 15 - x (b) x(x - 4) > 12

Core 1 Mathematics Edexcel January 2012 Question 4
Sequences
4. A sequence x₁, x₂, x₃,,... is defined by
x₁ = 1
x_n+1 = ax_n + 5, n ≥ 1 where a is a constant.

(a) Write down an expression for x₂ in terms of a.

(b) Show that x₃ = a² + 5a + 5

Given that x₃ = 41
(c) find the possible values of a.

Core 1 Mathematics Edexcel January 2012 Question 5
Intersecting Curves, Curve Sketching
The curve C has equation y = x(5 -x) and the line L has equation 2y = 5x + 4
(a) Use algebra to show that C and L do not intersect.

(b) In the space on page 11, sketch C and L on the same diagram, showing the coordinates of the points at which C and L meet the axes. Core 1 Mathematics Edexcel January 2012 Question 6
Gradient of a Straight Line, Equation of a Perpendicular Line

The line l₁ has equation 2x - 3y + 12 = 0
(a) Find the gradient of l₁ The line l₁ crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure 1.
The line l₂ is perpendicular to l₁ and passes through B.
(b) Find an equation of l2. The line l₂ crosses the x-axis at the point C.
(c) Find the area of triangle ABC. More Questions