Shopping trolleys are 80 cm long. When two trolleys are pushed together the resulting pair is 100 cm long. When three are pushed together the resulting triple is 120 cm long. 

i) How long will a set of 10 trolleys pushed together be? 

ii) For safety reasons trolley collectors are not allowed to push a set of trolleys more than 4.5metres long. What is the greatest number of trolleys that can be pushed?

If $\mathcal{y}=8{\mathcal{x}}^3-2\mathcal{x}+5$, find $\frac{d\mathcal{y}}{d\mathcal{x}}$ when $\mathcal{x}=2$.

The tangent to a curve at point N has equation $5\mathcal{x}-\mathcal{y}-1=0$.

i) If $\frac{d\mathcal{y}}{d\mathcal{x}}=4\mathcal{x}-3$, for the curve, find the coordinates of N.

ii) Find the equation of the curve.

Mark invests $1000 in a bank account that pays interest compounded quarterly. After four years he has $1219.89 in the bank. What is the annual interest rate?

The curve $\mathcal{y}=a{\mathcal{x}}^2+b\mathcal{x}-1$ has a stationary point at (1 ,-5). Find the values of a and b.

$$\begin{gathered} The first three terms of an arithmetic series are 5, 9 and 13. What is the 15th term of this series? \\ \left(A\right) 61 \\ \left(B\right) 66 \\ \left(C\right) 495 \\ \left(D\right) 585 \end{gathered}$$

$$\begin{gathered} A particle is moving in a straight line. At time t seconds its displacement from a fixed point O on the line is x = t^2 -2t metres. What dis\tan ce is travelled by the particle in the first 3 seconds of its motion? \\ \left(A\right) 3 metres \\ \left(B\right) 4 metres \\ \left(C\right) 5 metres \\ \left(D\right) 6 metres \end{gathered}$$

$$\begin{gathered} The angle of a sector in a circle of radius 18 cm is \frac{\pi }{9} radians. What is the perimeter of the sector? \\ \left(A\right) 2\pi +18 \\ \left(B\right) 2\pi + 36 \\ \left(C\right) \pi +18 \\ \left(D\right) \pi + 36 \end{gathered}$$

The diagram below shows the cross section of a cylindrical hot-water tank, with diameter 2$\mathcal{x}$ meters and height $\mathcal{y}$meters that fits exactly into the roof of a house. The cross section of the roof is an isosceles triangle with base 8 meters and equal sides 5 meters in length.

Use Simpson's Rule with 5 function values to approximate the area enclosed by the curve y =V(t), the t-axis and the lines t =0 and t =4. 

Evaluate $\sum _{n=2}^{4}2n$

Find a primitive function of $5{\mathcal{x}}^4+2{\mathcal{x}}^3-{\mathcal{x}}^2+1$