# Extending GCSE mathematics in readiness for AS level

This collection features resources produced by Shirley Fall designed to enable high ability GCSE students to explore further mathematical topics beyond the scope of the syllabus thus bridging the gap between GCSE and AS level. The resources could also be used as introductory work at AS level in preparation for more in depth study. The resources have been written so they can be used as teacher-led resources or a supported self-study units.

The resources in this collection are:
Exploring gradient functions – starting with the gradient of a straight line, activities progress to finding the gradient of a chord between two points on a curve as one point tends to the other. Generalisation produces the gradient function
Exploring transformations of graphs – used function notation to explore translations, stretches and combinations of the two. Extension work challenges students to explore reflections
Graphs Mystery- in which students use the clues provided to draw nine graphs in appropriate places

## Resources

In this resource from Shirley Fall, students are presented with a general straight line y=mx+c and are shown that the gradient of the line between any two points that lie on the line is always equal to m. Students should be encouraged to explain the proof to check understanding.

Students then move on to...

Publication date:
2010 to date

2 files

0

### Exploring transformations of graphs

This activity, from Shirley Fall, requires students to use and interpret function notation, sketch graphs using key points, explore the common transformations of translate parallel to the y axis, translate parallel to the x axis, stretch parallel to the y axis from the x axis and stretch parallel to the x axis from...

Publication date:
2010 to date

2 files

0

### Graphs mystery

This Durham Maths Mystery is designed to extend high achieving GCSE students and for use with students studying mathematics post-16.

Task 1A: students are presented with a blank three by three grid and twenty fact cards. Students have to use the clues on the fact cards to help them sketch...

Publication date:
2010 to date

1 file

1

### Exploring area linked to graphs

This activity, from Shirley Fall, contains ten linked problems which are intended to lead to students developing a rule for integrating functions of the form y=ax n where n not equal to -1. Problem 1 begins by exploring the area enclosed under a straight line y=2x+3 from x=0 to x=a for varying values of a, leading...

Publication date:
2010 to date

1 file

0

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