| Level 9/10 Pack 3 Content/Teacher Notes |
Pages 3/4. Enlargements.
Looking at the effect a negative enlargement has on varying shapes.
Page 5. Constructing Enlargements.
Given the centre of enlargement and the scale factor, including negative scale factors, pupils have to construct the enlargement.
Page 6. Similar Triangles (Revision).
Recapping earlier work on similar triangles in preparation for work on scale factors.
Pages 7/8. Ratios, Scale Factors and Similar Triangles 1.
Discovering the link between linear scale factors and area scale factors of similar shapes.
Pages 9/10. Ratios, Scale Factors and Similar Triangles 2.
Calculations using the link between linear scale factors and area scale factors of similar shapes.
Pages 11/12. Similar Solids.
Discovering the link between linear scale factors, area scale factors and volume scale factors of similar solids. Using these facts to calculate missing dimensions in similar solids.
Pages 13/14. Similar Shapes.
Examination style questions covering similar shapes.
Page 15. Ratio Questions.
Again, examination style questions covering ratio.
Pages 16/17. Congruent Triangles and Proofs.
Some simple proofs based on congruent triangles. Other angle property proofs.
Pages 18/19. Constructions and Proofs.
Some proofs based on constructions. Construction of the a circumcircle and an inscribed circle.
Pages 20/21. Circle Theory.
Revision of the circle theories incorporating their proofs.
Pages 22/23. Alternate Segment Theorem.
The proof of the Alternate Segment Theorem. Questions based on the Alternate Segment Theorem.
Page 24. Proving Pythagoras and Ptolemy's Theorems
Using angle properties to prove Pythagoras' Theorem and Ptolemy's Theorem.
Pages 25/26. Circle Properties. Examination Style Questions.
Examination style questions pupils will need to attempt.
Pages 27/28. Measures of Spread. Standard Deviation.
Standard deviation is currently not on the GCSE syllabus and hence will not be tested in the examination. The syllabus states that comparisons are based on a measure of an average and a spread. Hence at A/ A* level this could be a useful tool in a coursework assignment to endorse a pupils A/A* rating.
Pages 29/30. Standard Deviation 1.
Two methods of finding standard deviation by laying out the information in a table.
Pages 31/32. Standard Deviation 2.
Calculating the mean and standard deviation from frequency tables.
Pages 33/34. Normal Distributions
Experiments to produce normal and skewed distributions. Notes of the normal
and skewed distributions.
Pages 35/36. Plotting Histograms of Unequal Intervals.
Completing a table to include frequency density then plotting the histograms of unequal intervals. Finding estimates of means. We have also included finding estimates of standard deviation for those pupils who you may wish to challenge.
Pages 37/38. Histograms of Unequal Intervals.
Questions taking information from histograms of unequal intervals. Again this also includes estimates of means and standard deviations.
Pages 39/40. Statistical Investigations 1.
Notes on carrying out an investigation.
Page 41. Statistical Investigations 2.
Notes on sampling.
Page 42. GCSE Statistical Investigations .
Five possible investigations students may wish to undertake.