Level 7 Pack 1 Info

Pages 3/4.Probability 1. 

Revision of Level 5 and 6 single event probability, including the probability of events not happening. 

Pages 5/6. Probability 2. 

Mutually exclusive and exhaustive events. Pupils have to be familiar with fractional addition and subtraction as well as with decimal addition and subtraction. The addition (OR) rule. 

Pages 7/8. Experimental Probabilities 1.

Assigning probabilities. Finding the expectation of a probability. 

Page 9. Experimental Probabilities 2. 

Experiments to compare theory and experiment. Pupils will use the experimental probability diagrams (p 10) to find out experimental probabilities and compare them with theoretical probabilities. 

Page 10. Experimental Probability Diagram. 

A grid for recording experimental probability for an event. After 50 trials read off the experimental probability. This could be used for some of the level 5 probability. Photocopy this sheet back to back so pupils will only need one sheet to complete Experimental Probabilities 2. 

Pages 11/12. Experimental Probabilities 3. 

Relative frequency and relative frequency graphs. A pictorial way to show relative frequency "settling down" to theoretical probability with the greater the number of trials. "140 trials" has been chosen so as to fit on 1 piece of A4 graph paper landscape (long ways). 

Pages 13/14. Lists and Possibility Spaces. 

Revision of the Level 6 descriptors. 

Pages 15/16. Tree Diagrams (Independent Events). 

Complete the tree diagram by adding the appropriate probabilities and then solve the questions. Drawing tree diagrams from worded questions. 

Pages 17/18. 'AND' and 'OR' Rules.. 

The multiplication rule (AND rule). Questions that involve the AND and Or rules. 

Pages 19/20. Substitution (Negative numbers and fractions). 

Before pupils can plot linear functions they must be comfortable with this type of substitution, with and without a calculator. The formulae chosen are typical of the formulae they will meet around the school. 

Pages 21/22. Plotting Linear Functions. 

Revision of all the level 6 skills. Finding the gradient and y intercept of a line. Rearranging linnear equations. Finding the coordinate of the mid-point of a line segment. 

Page 23. Finding the Equation of a Straight Line. 

Given two coordinates, pupils have to find the equation of the line. Scales are changed on the axes so that pupils realise they have to read off axes and not count squares. 

Page 24. Finding Equations of Straight Line Graphs 1. 

The lines are drawn already, pupils have to find the equations. 

Pages 25/26. Finding Equations of Straight Line Graphs 2. 

As above. 

Pages 27-30. Linear Function Snap Cards. 

These cards can be used in a variety of ways. They may be used as a simple pairing exercise to stick in the book. They may be used in a game of "pairs",- cards are turned upside down, two are turned over. If they match you win them. Use 2 sets of each sheet and play "snap!" The list is as endless as your imagination! 

Pages 31/32. Scatter Graphs 1. 

Plotting scatter graphs and finding the line of best fit by inspection. The line of best fit is then used to find some estimations. 

Pages 33/34. Scatter Graphs 2. 

Scatter graphs are extended by finding the mean of the scores which is plotted to aid positioning the line of best fit. Then the equation of lines of best fit have to be found. This equation is then used to find further estimates of values. 

Pages 35/36. Direct Proportion. 

Finding the constant of proportionality to solve direct proportion questions. 

Pages 37/38. Quadratic Sequences. 

Revision of finding the nth term of linear sequences. Simple and more difficult quadratic sequences. 

Pages 39/40. Finding Quadratic Functions (Difference Method). 

Only required for coursework. This is a useful sheet to do the week before attempting coursework with a class. It shows pupils how to derive the formula for a quadratic using the difference method. This enables them to score higher marks in strand iii at AT 1. 

Note: this is not a justification of a formula. 

Pages 41/42. Practical Quadratic Number Patterns. 

Looking at practical patterns that derive quadratic functions. These are in the style of "Matchsticks" investigations pupils may meet through coursework. 

Pages 43/44. Investigations (Quadratic Patterns).

Some investigations that again derive quadratic functions. The first set is grouped together through a football theme, each one is an investigation so all don't have to be completed. The onions investigation is a very good one to stretch the more able and keep the rest going! It is also quite simple to justify the quadratic (see above). Regroup the onions into squares, each diagram will make 2 squares n² and (n + 1) ² in dimension. By working out the bracket and adding them all together it is fairly simple to derive 2n2 + 2n + 1. 

For the very able, the first pattern can be extended into 3 dimensions leading to the cubic 4/3 n ³ + 2n ² + 8/3n + 1 !!! 

Level 7 Pack 2 Info