Question

(a) Write down and simplify, in ascending powers of x, the first three terms of the
following expansions.
i) (1 + 2x)
7

[2]

ii) (2 – x)
7

[2]

(b) Hence, find the coefficient of x
2
in the expansion of (2 + 3x − 2x
2
)
7
. [4]
(8 marks)

2. (a) Find, in descending powers of x, the first three terms in the expansion of (x −
2
x
)
6
. [3]

(b) Hence, find the coefficient of x
4
in the expansion of (2 + 3x
2
)
2
(x −
2
x
)
6
. [3]
(6 marks)

3. The line y = 2x + 3 does not cut the curve y = x(1 + 2k − x) + 2 at real points.
(a) Find the range of values of k. [5]
(b) Hence, state the value of k for which line will be a tangent to the curve. [1]
(6 marks)

Answer 1

Answer:

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