1. The first three terms of an arithmetic sequence are 5 , 6.7 , 8.4 .
(a) Find the common difference.
(b) Find the 28th term of the sequence.
(c) Find the sum of the first 28 terms.
3.Let f (x) = x3 − 2x − 4 . The following diagram shows part of the curve of f .
The curve crosses the x-axis at the point P.
(a) Write down the x-coordinate of P.
(b) Write down the gradient of the curve at P.
(c) Find the equation of the normal to the curve at P, giving your equation in the form y = ax + b .
4.The third term in the expansion of (2x + p)6 is 60x4 . Find the possible values of p .
5.Let f (x) = acos(b(x − c)) . The diagram below shows part of the graph of f ,for 0 ≤ x ≤10 .
The graph has a local maximum at P(3, 5) , a local minimum at Q(7, − 5) , and crosses the x-axis at R.
(a) Write down the value of
(i) a ;
(ii) c .
(b) Find the value of b .
(c) Find the x-coordinate of R.
6.In a large city, the time taken to travel to work is normally distributed with mean μ and standard deviation σ . It is found that 4 % of the population take less than 5 minutes to get to work, and 70 % take less than 25 minutes. Find the value of μ and of σ .