CAMBRIDGE IGCSE™ ADDITIONAL MATHEMATICS: TEACHER’S RESOURCE

Misconception/issue How to identify How to avoid or overcome

When considering whether a quadratic equation has real roots, students sometimes only consider either real and equal or real and different, but not both.

As with chapter 1, thinking that, for y = | f (x) |, the values of x cannot be negative.

Starter ideas

1 Alpha beta starter

Students will form a quadratic equation or use an incorrect inequality sign when forming an inequality.

This can be checked using PowerPoint 2.6.

This is very common when solving equations. Should a value of x be negative, students often think it should be rejected and will indicate this in their working.

Make sure you model the correct language when considering the nature of roots and ensure that students are experienced in using b2 − 4ac > 0 when real roots are specifically required.

This can be resolved by working on the graphs of absolute value functions so that students can clearly see that x can have negative values but that y cannot and then linking the graphs back to the equations they are solving.

Description and purpose: This is a good starter for any lesson involving the use of factorising quadratic expressions. It makes students think about products and sums of numbers, the need for which is relatively clear.

Resources:

• PowerPoint 2 starter: Alpha beta

• Pens and paper

Activity:

There are five questions.

Each question asks for a pair of numbers, alpha and beta, that have a given sum and product. A timer appears on the screen and runs for 1 minute (30 seconds green and 30 seconds blue). Students have this time to write down their answers. As soon as they have done this, they put up their hand.

If all hands are up before the timer runs out, click to reveal the answer. If not, the answer will appear once the time is up. Click to move to the next question.

This activity could possibly lead into: any activity that was dependent on factorising quadratics as a tool. This activity could be adapted: The numbers in each question can be changed if you wish to use the starter as a review as well as a starter – or if you wish to use it again with the same group for a different lesson.

2 What’s my equation?

Description and purpose: This activity can be used to recap the work on modulus functions when f(x) is linear, covered in Chapter 1, in readiness for extending to quadratic functions.

Resources:

• Geogebra or Desmos or other free graphing software.

Activity:

Present the class with the graph of a modulus function and ask them for the possible equations. To keep this as a short starter, limit the number of functions to one or two (or at the very most, three).