1. A standard die is rolled 36 times. The results are shown in the following table.
(a) Write down the standard deviation.
(b) Write down the median score.
(c) Find the interquartile range.
The velocity v ms−1 of an object after t seconds is given by v (t) =15√t − 3t , for 0 ≤ t ≤ 25 .
(a) On the grid below, sketch the graph of v , clearly indicating the maximum point.
Let d be the distance travelled in the first nine seconds.
(b) (i) Write down an expression for d .
(ii) Hence, write down the value of d .
3. The nth term of an arithmetic sequence is given by un = 5 + 2n .
(a) Write down the common difference.
(b) (i) Given that the nth term of this sequence is 115, find the value of n .
(ii) For this value of n , find the sum of the sequence.
5.Consider the function f (x) = px3 + qx2 + rx . Part of the graph of f is shown below.
The graph passes through the origin O and the points A(−2, −8) , B(1, − 2) and C(2, 0) .
(a) Find three linear equations in p , q and r .
(b) Hence find the value of p , of q and of r .