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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.

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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