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Edexcel Core Mathematics C1 January 2012




 

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


Edexcel Core Mathematics C1 January 2012 Past Paper

Core 1 Mathematics Edexcel January 2012 Question 1
Differentiation, Integration
Given that y = x4 + 6x1/2 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
xn+1 = axn + 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.
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