1. Tell me everything you can about this relationship:
Polynomials 1
Tell me everything you can about this relationship:
State where crosses x axis
Expand & complete the square
State where crosses y axis
Find expression for gradient
Find coordinates where gradient is zero
State x value for which graph is a maximum
Draw a good sketch of the graph
Polynomials 2
Tell me everything you can about this relationship:
State where crosses y axis
Factorise (using factor theorem?)
State where crosses x axis
Find expression for gradient
Find coordinates where gradient is zero
Draw a good sketch of the graph

2. Problem Solving 1 Problem Solving 2
A rectangular pen is formed from 40m of fencing with a long wall forming one side of the pen, as shown in the diagram;
Wall
Cattle pen x x
The two opposite sides of the pen which touch the wall and each have length x metres.
What is the maximum area that can be enclosed?
Find, in terms of x, an expression for the length of the other two sides
Find an expression, in terms of x, for the area of the pen
Differentiate the expression for the area of the pen
Find the x value for which the area of the pen is a maximum (ie gradient = 0)
Use the x value of the max area of the pen to answer the question
Problem Solving 2
An open cubiodal tank of height h metres is to be made with a square base of length x metres and breadth x metres, as shown in the diagram;
The external surface area of the tank is to be 48m2.
What is the maximum volume that can be held?
Find, in terms of x, an expression for the height, h, of the tank
Find an expression, in terms of x, for the volume of the tank
Differentiate the expression for the volume of the tank
Find the x value for which the volume of the tank is a maximum (ie gradient = 0)
Use the x value of the max volume of the tank to answer the question

3. (+3, -6) and (5, +4) (-14, +1) and (-2, -4) Coordinates 1
Tell me everything that you can about the line segment that joins this pair of coordinates;
(+3, -6) and (5, +4)
Find the length of the line segment (distance between the two points)
Find the gradient of line segment
Find the equation of line
Find the midpoint of line segment
Coordinates 2
Tell me everything that you can about the line segment that joins this pair of coordinates;
(-14, +1) and (-2, -4)
Find the length of the line segment (distance between the two points)
Find the gradient of line segment
Find the equation of line
Find the midpoint of line segment