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).
f'(x) = 12x2
- 8x + 1
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
(a) Show that k satisfies
+ 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
(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
(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.
(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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