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

Past Paper (pdf)

**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) = 12x^{2} - 8x + 1

find f(x).**Core 1 Mathematics Edexcel January 2011 Question 8 - Roots of a Quadratic**

8. The equation x^{2} + (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real

roots.

(a) Show that k satisfies

k^{2} + 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 L_{1} has equation 2y -3x - k = 0 where k is a constant.

Given that the point A (1, 4) lies on L_{1} , find

(a) the value of k,

(b) the gradient of L_{1} .

The line L_{2} passes through A and is perpendicular to L_{1} .

(c) Find an equation of L_{2} giving your answer in the form ax + by + c = 0, where a, b and

c are integers.

The line L_{2} 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 x^{3} - 9 x^{2/3} + 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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for A Level Maths

Math Worksheets

Solutions, examples, videos, activities, and worksheets that are suitable for A Level Maths

Past Paper (pdf)

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.

7. The curve with equation y = f(x) passes through the point (-1,0).

Given that

f'(x) = 12x

find f(x).

8. The equation x

roots.

(a) Show that k satisfies

k

(b) Find the set of possible values of k.

9. The line L

Given that the point A (1, 4) lies on L

(a) the value of k,

(b) the gradient of L

The line L

(c) Find an equation of L

c are integers.

The line L

(d) Find the coordinates of B.

(e) Find the exact length of AB.

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

11. The curve C has equation

y = 1/2 x

(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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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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