CAMBRIDGE

IGCSE™ ADDITIONAL MATHEMATICS: TEACHER’S RESOURCE

Differentiation:

Support: In the problem after worked example 5, some students may struggle to see why the number of intersections of the line and curve is the same as the number of solutions of the given equation. PowerPoint 2.3b looks at this very point. A statement is made regarding the roots of an equation and the points of intersection of two lines as being the same and the question ‘Why?’ is asked. This could be used as a class investigation. Many students will find it intuitively obvious, but some will not. Those to whom it is obvious may not find it easy to put their case in a watertight argument. There is more work on this point later with non-horizontal lines.

Challenge: Worked example 9 is solved using the discriminant. This is the most straightforward approach. There is an alternative calculus method which some students may prefer. You may wish to set this as an investigation for your students once you have covered simple differentiation.

Assessment for Learning: As part of assessment for learning for this topic, be careful to check that students understand the language used and are able to devise a method of solution based on that language. You can check this by marking written work or through general discussion, for example.

Review activities

1 Order review

Description and purpose: This review requires students to order the six steps needed to rearrange and solve a quadratic inequality. They then have to decide whether the solution that has been given is correct. The purpose of this review is to consolidate the logical steps practised in the lesson and also to remind students of the importance of sketching the graphs!

Resources:

• PowerPoint 2 review: Quadratics order order

Activity:

Students are given this scenario:

Disaster! Neena’s pet bookworm has shredded her homework! She cannot tell which part of her answer comes first…. help Neena by sorting her work into the correct order! Now tell her if she was correct!

Allow students to discuss and write down what they think the correct order is. They can use the A, B, C…. marked alongside.

Answer: The correct order on the PowerPoint is CEFBDA.

When everyone is ready, click to move the statements to the correct place. Click again to move to a second slide where the sketch graph of the quadratic is revealed for students to judge the solution. This activity could possibly lead from: a lesson focused on solving quadratic inequalities. This activity could be adapted: The six statements that need to be ordered could be written on large pieces of paper in exactly the same way as in the PowerPoint and pinned onto a board. Labelling them A, B, C etc. will give students an easy way to describe which order is the correct order. As another alternative, the statements could be printed or written in regular sized font/print and the class split into pairs or groups and given a set each which they can then move around to form the correct order.

2 Check my graph review

Description and purpose: This task is designed to make students think about the shape of the graphs they draw and how accuracy and attention to detail can improve a solution. It can be used as an assessment for learning exercise. It should be a useful tool in assessing whether they have fully understood what they have learned.

CAMBRIDGE IGCSE™ ADDITIONAL MATHEMATICS: TEACHER’S RESOURCE

Resources:

• Check my graph

• Check my graph teacher notes

Activity:

The Check my graph file can either be printed as a handout or displayed on a flip chart or interactive whiteboard.

It has two graphs for your students to check for accuracy and award marks. They should identify and be able to explain how to correct any errors. They then have to find two good comments about the work and set one target for improvement. Suggested comments and marks are made in the Check my graph teacher notes file. Your students may think of others!

This activity could possibly lead from: a lesson on sketching the graphs of the modulus of a quadratic function.

This activity could be adapted: The graphs could be updated or added to, and this could also be used with other types of modulus function.

Homework ideas

1 Coursebook: Quadratic equations and the parabola, Exercise 2.2

Completion of this exercise should give students a good amount of practice of finding roots, sketching graphs and completing the square.

2 PowerPoint 2.6

Completion of the questions in this PowerPoint should measure the ability of students when solving problems involving the nature of the roots of a quadratic equation. It will also check whether they can solve quadratic inequalities successfully and whether they can make the connections between points of intersection and roots. This PowerPoint has two versions. The first version has no model answers included, but does have some hints in the teacher notes for each slide. These can be removed if you do not want to give any hints at all. The second version includes animated answers and is very supportive of those who need greater modelling of what is needed. Again, hints, and also details of what each animation will reveal, are included in the Teacher notes for each slide. As well as a useful homework tool, this PowerPoint can be used as a revision exercise, for self-study, further practice in class or as part of a bank of resources students can access at any point throughout the course when needed. This practice material is also available as a PDF file in case technology is not available to your students.