MEI online resources for mathematics
Mathematics in Education and Industry

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Core 1 (MEI) - Sample TAM resources

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Chapters:
  Core 1 (MEI): Chapter 1: Basic algebra Manipulating algebraic expressions, Equations, Quadratic equations, Solving quadratic equations, Simultaneous equations
  Core 1 (MEI): Chapter 2: Co-ordinate geometry Co-ordinates, The gradient of a line, Parallel and perpendicular lines, The distance between two points, The midpoint of a line joining two points, The equation of a straight line, Drawing a line given its equation, Finding the equation of a line, The intersection of two lines, The circle
Sections

A chapter devoted to lines and circles

Our women are Straight Lines. Our Soldiers and Lowest Classes of Workmen are Triangles...they form at their vertices a very sharp and formidable angle....Finally when the number of sides becomes so numerous, and the sides themselves so small, that the figure cannot be distinguished from a circle, he is included in the Circular or Priestly order; and this is the highest class of all.

If our highly pointed Triangles of the soldier class are formidable, it may be readily inferred that far more formidable are our Women. For if a soldier is like a wedge, a Woman is a needle; being, so to speak, all point, at least at the two extremities. Add to this the power of making herself practically invisible at will, and you will perceive that a Female, in Flatland, is a creature by no means to be trifled with.

From "Flatland" by Edwin A. Abbott

Things to think about when reading this chapter for the first time.
Chapter Overview
Typical student misconceptions and errors and how to avoid them.
Common errors
The first lesson on coordinate geometry building on ideas from GCSE.
Coordinate Geometry lesson plan
Thinking about the equation of a circle.
Introducing circles lesson plan
Activities to introduce and explore straight lines and circles.
Coordinate geometry activities
Including suggestions how you might use this with your students.
Introducing y-y1=m(x-x1)
With suggestions for use in the classroom.
Points of intersection of curves and lines
With suggestions for use in a revision lesson.
Points of intersection of a circle and a line
Circles and lines spreadsheet
Other resources you might find useful when teaching this chapter.
Additional resources
Thinking about pairs of lines and their points of intersection
Coordinate geometry arithmogons
What is the distance between the parallel lines y=2x+7 and y=2x-1?
Parallel lines
Categorising simultaneous equations
Intersecting lines and Venn diagrams
Categorising circles
Circles and Venn diagrams
Finding the point on a line which divides it in a given ratio.
Ratio Theorem
Given two intersecting circles finding an infinite number of others passing through the points of intersection.
Intersecting circles
How we can tell from the equations of two circles whether they touch each other, intersect in two points or have no common points.
Circles
Using the formula for the distance between a point and a line allows us to easily find the equation of the circle centred on a given point touching a given line.
Distance of a point from a line

Click the links in the menu to access multiple choice tests with fully worked solutions.

Group/pair activities for learning about straight line graphs
Linear functions: Activities
Sheets to accompany the activities
Linear functions: Activity sheets
Group/pair activities for learning about circles
Circles: Activities
Sheets to accompany the circle activities
Circles: Activity sheets

Points and straight lines

Before you start...
  • You will have been introduced to these ideas at GCSE.
  • You will need to be fluent with simultaneous equations work from chapter 1.
When you have finished you should...
  • Be able to find the gradient of a straight line (pages 35-36).
  • Know the relationships between the gradients of parallel and perpendicular lines (pages 37-38).
  • Be able to calculate the distance between two points (pages 37-38).
  • Be able to find the mid-point of a line joining two points (page 38).
  • Be familiar with the various forms of the equation for a straight line and fluent in their use (pages 42-44).
  • Be able to find the equation of a straight line from two points on it, or from one point and the gradient of the line (pages 46-47).
  • Be able to solve problems involving straight lines (pages 48-49).
  • Be able to establish whether straight lines intersect and, if they do, to find their point of intersection (pages 55-56).
TestTest Questions
Submit answers Co-ordinate geometry 1

Curves and circles

Before you start...
  • You will have been introduced to these ideas at GCSE.
  • You will need to be fluent with simultaneous equations work from chapter 1.
When you have finished you should...
  • Be familiar with the curves produced when graphing odd and even powers of x and the reciprocals of odd and even powers of x (pages 60-61).
  • Be familiar with the equations of a circle (pages 62-63).
  • Know the the angle in a semicircle is a right-angle (page 63).
  • Know that the perpendicular from the centre of a circle to a chord bisects the chord (page 63).
  • Know that the tangent to a circle at a point is perpendicular to the radius at that point (page 64).
  • Be able to find the point(s) of intersection between a line and a curve or between two curves (pages 68-72).
TestTest Questions
Submit answers Co-ordinate geometry 2
Please complete this once you have finished all four sections. Give it to your teacher / tutor for marking.
Co-ordinate geometry chapter assessment
This glossary covers all of this chapter.
Glossary
  Core 1 (MEI): Chapter 3: Polynomials Operations with polynomials, Polynomial curves, The graphs of quadratic functions, Using transformations to sketch the curves of functions, Binomial expansions
  Core 1 (MEI): Chapter 4: Uncertainty Errors and inequalities, The algebra of inequalities
  Core 1 (MEI): Chapter 5: Indices Working with square roots, Negative and fractional indices,
  Core 1 (MEI): Chapter 6: The language of mathematics Problem solving, Types of numbers, Writing mathematics, The converse of a theorem, Proof