Merryn Horrocks

Exercises for HELM Book 2.7.1

For the graphs in HELM Book 2 Figure 30, identify which are one-to-one, and which are many-to-one.

Identify whether or not an expression is a polynomial. From HELM Book 2.7.1.

Unmarked question, with advice.

Write down an example of a polynomial of given degree and given variable.

Write down a non-polynomial function.

Explain why a polynomial with a fractional index is not a polynomial.

Given an arbitrary polynomial, identify its degree.

Given one or two circles centre (0,0) describe the region given by the circle inequality ( or inequalitites). e.g. x^2+y^2 < 4

Given a circle equation in the form (x-a)^2+(y-b)^2=r^2, write down the radius and centre coordinates.

Write down the equation of a circle centre C and radius R.

Given a circle with radius between 2 and 6 units, students are given a set of 8 points and asked to identify whether they are on, inside or outside the circle locus.

Given that the circle touches the x-axis at a given point and given a point on the circumference, find the equation of the circle.

Given a circle centre and radius, write an appropriate inequality for the region either inside or outside the circle.

Draw the annulus given by a double inequality. The user moves circles on an interactive jsxgraph.

Fixed question: Given two points at opposite ends of a diameter, write down the equation of the circle.

Given a circle centre and a point on the circumference, write down the circle equation.

Determine the radius and centre coordinates of a circle with equation expressed in expanded form.

Given the radius and centre coordinates of a circle write down its equation.

Rearrange a homogeneous circle equation into the form (x-xc)^2+(y-yc)^2=r^2 to find the centre and radius.

Given a graph of a circle, write down its equation.

Exercises for HELM Book 2.5.3.

Find the gradient and y-axis intercept of a line through 2 points. The line is not vertical.

Find the equation of a line through 2 points. The line is not vertical.

Find the equation of a line passing through two points in the form y=mx+b. The question is set up so that m and b will be integers.

Find the gradient of a line through 2 given points. Part of HELM Book 2.5.2.

Find the gradient of a line through 2 points. The line is not vertical.

Exercises for HELM Book 2.5.1

Identify the gradient and y-axis intercept of a random non-vertical line.

Given one of ax+b, a/x, x^(1/a), a, is it a straight line.  a is a randomised integer.

State the general form of the equation of a straight line explaining the role of each of the terms in your answer.

Compare the gradients of 3 lines and choose the steepest. Part of HELM Book 2.5.1.

Find the gradients of 3 lines. Part of HELM Book 2.5.1.