Questions and Video Solutions for C2 Edexcel Core Mathematics June 2009Related Topics:
1. Use calculus to find the value of ∫(2x + 3√x) dx
2. (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of
(2 + kx)7 where k is a constant. Give each term in its simplest form.
Given that the coefficient of x2 is 6 times the coefficient of x,
(b) find the value of k.
3. f(x) = (3x - 2)(x - k) - 8
where k is a constant.
(a) Write down the value of f (k).
When f(x) is divided by (x − 2) the remainder is 4
(b) Find the value of k.
(c) Factorise f(x) completely.
4. (a) Complete the table below, giving values of √(2x + 1) decimal places.
Figure 1 shows the region R which is bounded by the curve with equation y = √(2x + 1) , the x-axis and the lines x = 0 and x = 3
(b) Use the trapezium rule, with all the values from your table, to find an approximation for the area of R.
(c) By reference to the curve in Figure 1 state, giving a reason, whether your approximation in part (b) is an overestimate or an underestimate for the area of R.
5. The third term of a geometric sequence is 324 and the sixth term is 96
(a) Show that the common ratio of the sequence is 2/3
(b) Find the first term of the sequence.
(c) Find the sum of the first 15 terms of the sequence.
(d) Find the sum to infinity of the sequence.