Edexcel Core Maths C1 January 2011

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

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Core 1 Mathematics Edexcel January 2011 Question 6 - Arithmetic Sequence

6. An arithmetic sequence has first term a and common difference d. The sum of the first 10 terms of the sequence is 162.
(a) Show that 10a + 45d = 162

Given also that the sixth term of the sequence is 17,
(b) write down a second equation in a and d,

(c) find the value of a and the value of d. Core 1 Mathematics Edexcel January 2011 Question 7 - Equation of a curve given f'(x)

7. The curve with equation y = f(x) passes through the point (-1,0).
Given that
f'(x) = 12x2 - 8x + 1
find f(x). Core 1 Mathematics Edexcel January 2011 Question 8 - Roots of a Quadratic

8. The equation x2 + (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real
roots.
(a) Show that k satisfies
k2 + 2k - 3 > 0
(b) Find the set of possible values of k.

Core 1 Mathematics Edexcel January 2011 Question 9 - Coordinate geometry (straight lines)

9. The line L1 has equation 2y -3x - k = 0 where k is a constant.
Given that the point A (1, 4) lies on L1 , find
(a) the value of k,

(b) the gradient of L1 .

The line L2 passes through A and is perpendicular to L1 .
(c) Find an equation of L2 giving your answer in the form ax + by + c = 0, where a, b and
c are integers.

The line L2 crosses the x-axis at the point B.
(d) Find the coordinates of B.

(e) Find the exact length of AB. Core 1 Mathematics Edexcel January 2011 Question 10 - Curve sketching

10. (a) On the axes below, sketch the graphs of
(i) y = x(x + 2)(3 - x)
(ii) y = -2/x
showing clearly the coordinates of all the points where the curves cross the coordinate
axes.
(6)
(b) Using your sketch state, giving a reason, the number of real solutions to the equation
x(x + 2)(3 - x) + 2/x = 0 Core 1 Mathematics Edexcel January 2011 Question 11: Differentiation - normals

11. The curve C has equation
y = 1/2 x3 - 9 x2/3 + 8/x + 30
(a) Find dy/dx

(b) Show that the point P(4, 8) − lies on C.
(2)
(c) Find an equation of the normal to C at the point P, giving your answer in the form
ax + by + c = 0, where a, b and c are integers.

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