Here you see the contents of the VLE Level 7/8 Licence. Your order will come on CD-Rom or DVD and will contain each of the pages below as a single page pdf stamped to your school name VLE. The pages are not editable. A searchable page of contents also comes on the disc.

Level 7/8 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 !!! 

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Level 7/8 Pack 2 Info

Pages 3/4. Area Revision.
Refreshing all the areas previously studied at level 6 ready for Volume of Prism work later on.

Pages 5/6. Harder Area Revision.
More revision of areas. This time reverse questions. Areas are given and missing dimensions have to be found.

Pages 7/8. More Areas 1.
Working on the mechanics of the calculations involved with area questions.
An important aspect that runs through the topic is rounding errors. Where an answer is used to continue the calculation, the original value, not the rounded answer should be substituted.

Pages 9/10. More Areas 2.
More area calculations. Rounding is central to the circle questions. In some questions the answer given for the diameter is not exactly double the radius due to rounding.

Pages 11/12. Compound Areas.
Questions become progressively more difficult.
Hints: To solve 26). extend the straight lines to form a quarter circle and to solve 27). form a square and four 3/4 circles!

Pages 13/14. Shape Worded Questions.
A worksheet that draws together all the skills needed to solve worded questions. Ideal for Intermediate GCSE revision.

Pages 15/16. Prisms 1.
Naming familiar solids. Faces, Edges and Vertices. Definition of prisms. Finding volumes of a variety of shapes of prisms.

Pages 17/18. Prisms 2.
Volumes of prisms and surface areas. The curved surface area of a cylinder. All the previous work put into context through worded questions. Dimensional Units: looking at expressions and deciding whether it is a length, area, volume or none of these.

Pages 19/20. Shape and Algebra.
Algebra questions using shape properties to form expressions and equations. Algebra should be thoroughly revised before attempting this worksheet.

Pages 21/22. Investigations (Areas and Volumes).
Investigations involving areas and volumes. The main theme throughout is maximising areas and volumes. Notice that the third section of the pig farmer and the start of the guttering question require identical skills. The tower question is a numerical exercise, the generalisations are far too complex for this level.

Pages 23/24. Compound Measures 1 (Speed).
Changing minutes in to fractions of hours and utilising these in Speed/Distance/Time calculations. The units m.p.h., km/h and m/s are used in a series of worded questions.

Pages 25/26. Compound Measures 2 (Speed).
As above, but where the unknown is not the subject of the formula.

Pages 27/28. Compound Measures 3 (Density).
Density calculations using the units g/cmand kg/m. Pressure calculations using the units N/m and a brief visit to population density!

Pages 29/30. Distance/Time Graphs 1.
Taking readings from Distance/Time graphs, calculations involve fractions of hours. Plotting Distance/Time graphs.

Pages 31/32. Distance/Time Graphs 2.
Plotting more advanced Distance/Time graphs. Interpreting velocity/time graphs.

Pages 33/34. Grouped Data. Finding Averages.
Finding the modal class interval, and estimate for the mean, and the class interval where the median lies, from tables of data.

Pages 35/36. Frequency Polygons.
Plotting pairs of frequency polygons and commenting on the distributions relative to each other.

Pages 37/38. Time Series and Moving Averages.
Calculating and plotting moving averages. Using the moving average to make estimates.

Pages 39/40. Interquartile Range and Box Plots.
Finding the IQR from raw data. Drawing Box Plots and comparing two sets of data through Box Plots.

Pages 41/42. Cumulative Frequency and Interquartile Range.
Drawing cumulative frequency graphs and Box Plots. Calculating the IQR and taking readings from cumulative frequency graphs.

Pages 43/44. Statistical Investigations.
Notes on Primary and Secondary data, sampling techniques and bias.

Page 45. GCSE Statistical Investigations.
Notes on breaking down the Statistical Investigation at GCSE level and four investigations that could be attempted.

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Level 7/8 Pack 3 Info

Pages 3/4. Algebra Revision.
Skills that pupils should know from level 6. Multiplication/division of algebra and directed numbers. Collecting like terms. Expanding one bracket.

Pages 5/6. Solving Equations (Revision).
Again skills revisited from level 6. Solving equations involving 2 terms, 3 terms, 3 terms and brackets, 4 terms and 4 terms and brackets.

Pages 7/8. Brackets and Quadratics.
Exercises expanding two brackets. Finding the general equation for two linear equations, multiplying them together to find a quadratic.

Page 9. Factorising.
Factorising into one and two sets of brackets.

Page 10. Solving equations by factorising.
Progressive exercise in solving equations by factorising.

Pages 11/12. Quadratic Multiplication Grid.
Pupils should be familiar with the sheet as it is based on "Multiplication Grids' used at lower levels. It starts with multiplying out brackets and the need to factorise one quadratic. It progresses to the point where pupils have to factorise 7 quadratics to solve the grid.

Pages 13/14. Some Products (Quadratic Algebra).
Again, pupils should be familiar with the sheet as it is based on "Some Products" grids used at lower levels. Once again the progression leads from multiplying out brackets to factorisation skills.

Page 15. Four in a Row (Quadratics).
Four in a row game adapted to quadratics.

Page 16. Four in a Row (Quadratics) Cards.
Cards needed to play Four in a Row (Quadratics).

Pages 17/18. The Quadratic Maze 1/2.
Find your way through the maze by solving quadratic equations. Alternatively known as "Get them to solve another 120 questions"!

Page 19. Algebraic Fractions.
This sheet leads into some higher skills not needed at this level, but it is good to extend the more able.

Page 20. Investigations (Algebra).
Investigations using skills learnt in the previous pages. Some may form the basis of coursework.

Pages 21/22. Transposition of Formulae.
The first exercise deals with substitution into formulae pupils meet in school life. Once the numbers have been substituted in, then the equations are ready to be tidied up and solutions found. The second exercise is traditional algebra, "make x the subject of the formula". Again this leads into some higher skills not needed at this level.

Pages 23/24. Algebra (Worded Questions).
Putting the algebra into context. Converting worded questions into equations ready for solving.

Pages 25/26. Algebra Revision Questions.
Pulling together all aspects of the algebra covered so far. A good revision sheet for GCSE candidates.

Page 27. Trial and Improvement.
Trial and improvement techniques used to solve quadratics, cubics etc..

Page 28. Trial and Improvement (Worded Questions).
Forming equations from the questions, then using trial and improvement to solve the equations.

Pages 29/30. Plotting quadratic Equations.
Substituting into equations, plotting the graph and taking readings from the graph.

Pages 31/32. Shove Penny (Quadratics 1/2).
Shove Penny adapted as a substitution practice game. To start with set the target around 50 and only use x as 1 or 2. As pupils become proficient in the calculations set larger targets/x's, use negative numbers for targets/x's. Give the pupils a range for x from which they can choose before each go. As values change certain areas become less/more desirable. Pupils can then investigate the board for each value of x. See if they can come up with any conclusions as to which areas to aim for as x changes. For a simple game there is a lot of maths. The second board has more complex quadratics.

Pages 33/34. Cubic Functions.
Plotting cubics. Substituting into equations, plotting the graph and taking readings from the graph.

Pages 35/36. Reciprocal Functions.
Plotting reciprocals. Substituting into equations, plotting the graph and taking readings from the graph.

Pages 37/38. Function Shapes.
Pupils have to explore the effects different parts of equations have on the shape of its graph. There are some good software packages about for this, but
computer rooms aren't always available. This sheet is the alternative. Match the graph to the equation, which is the odd one out ?

Pages 39/42. Quadratic Function Snap Cards.
These cards can be used in a variety of ways. They may be used as a simple pairing exercise to stick into 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!" Use them with the linear snap cards in Level 7/8 Pack 1. The list is as endless as your imagination!

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Level 7/8 Pack 4 Info

Pages 3/4. Graphical Intersection.
The worksheet starts solving simultaneous equations through graphical intersection. Pupils can see why there is an x answer and a y answer. This point can be reinforced when solving them algebraically at a later date. The main focus of the sheet is solving quadratics through graphical intersection.

Pages 5/6. Simultaneous Linear Equations (Elimination).
Solving simultaneous equations through elimination. The sections are progressively structured through the required skills.

Pages 7/8. Simultaneous Linear Equations (Other Methods).
Rearranging equations ready for elimination. Substituting one equation into another and some basic trial and improvement solutions.

Pages 9/10. Simultaneous Linear Equations (Worded Questions).
The first section concentrates on the skill of putting a worded question into two simultaneous equations. The second section pulls all the skills of solving simultaneous equations together.

Pages 11/12. Puzzling Algebra (Simultaneous Equations).
Puzzles where objects represent numbers. To solve the puzzle pupils need to be able to form and solve simultaneous equations.

Pages 13/14. Inequalities.
Traditional exercises solving inequalities.

Pages 15/16. Inequalities (Worded Questions).
As with Simultaneous Equations (Worded Questions), the essential skill is to be able to turn the words into an inequality ready for solving. The questions progressively increase in complexity.

Pages 17/18. Graphical Inequalities 1 (without equations).
Suitable for pupils moving on to Higher Level GCSE or for the more able Intermediate pupils. Pupils have to identify the equation of the boundary line then give an inequality for the shaded area. Straight line graphs need to be revisited before attempting the sheet.

Pages 19/20. Graphical Inequalities 2 (without equations).
The complexity of the inequality needed to describe the shaded area increases. Pupils now have to draw required inequalities.

Pages 21/22. Graphical Inequalities 1 (with equations).
This is the previous sheets repeated, except with the boundary equations marked . This eliminates the skill of finding the equation of a line and focuses on inequalities only. Far better for weaker Intermediate GCSE candidates.

Page 23. Graphical Inequalities 2 (with equations).
As above, Page 20 is the reverse of this sheet.

Pages 24-30. Inequality Snap Cards.
The algebra, number line and graphical representations are brought together. Page 24 and 25 are the opposite algebraic ways of writing the equation. It is interesting for pupils to compare the number line to the graphs. One exercise may be to cut out the cards and stick them into books in sets. Another is snap.

Page 31. Translations.
You should be able to fit 4 questions on one side of A4. All you need to know about translations.

Page 32. Reflections.
Reflection questions.

Page 33. Rotations.
Rotation questions.

Pages 34/35. Enlargements.
Enlargements covering fractional and whole number enlargements.

Page 36. Constructing Enlargements.
Practical exercise constructing enlargements using the 'ray' method. The centre of enlargement and scale factor are given, pupils have to construct the
enlargement.

Pages 37/38. Transformations.
An exercise that covers all the transformations needed at this level.

Pages 39/40. Combining Transformations.
The effect two transformations can have upon a given shape. Each transformation is defined by a letter and the notation SV(A) means the shape A is transformed by V then the transformation S.

Pages 41/42. Transformation Investigations.
Some investigations pupils can attempt that involve transformations.

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Level 7/8 Pack 5 Info

Pages 3/4. Constructions.
Revision of perpendicular and angle bisectors. Constructing a perpendicular from a point to a line, constructing a perpendicular from any point on a line, constructing the circumcircle and the inscribed circle of a triangle.

Pages 5/6. Constructing a Protractor.
A practical exercise using all constructions that should be known at this level.
Simple to check- put a protractor on top of the work !

Pages 7/8. Loci 1.
Revision of the constructions pupils need to know at this level. Introduction to practical loci. Some problems may need to be demonstrated. Basic exam type problems using constructions. Pupils will need to work on squared paper for this and the following sheet.

Pages 9/10. Loci 2.
Moving the above worksheet on to more complex exam style questions.

Pages 11/12. Congruency.
Defines congruency. Discovery activity leading to the 4 conditions that need to be met in triangles for congruency.

Pages 13/14. Congruent Triangles.
Spotting congruent triangles with the appropriate reasons. Naming congruent triangles.

Pages 15/16. Circle Properties 1.
Proofs for the circle properties are not required at this level. Therefore the sheet concerns itself with discovery activities rather than the formal proofs. The more able may wish to prove them. This sheet focuses on the angle properties: angle in the semicircle and angle at the centre of a circle.

Pages 17/18. Circle Properties 2.
This sheet focuses on the angle properties: angle in the same segment and angles in a cyclic quadrilateral.

Pages 19/20. Circle Properties 3.
This sheet focuses on the angle properties: tangents and circle constructions.

Pages 21/22. Circle Properties 4.
A variety of questions that revise all the circle properties.

Pages 23/24. Similar Shapes.
Defines similarity. Looking at the link for similar shapes between length and area.

Pages 25/26. Similar Triangles 1.
Looking at rearranging equations and parallel line properties that will be needed in similar triangle questions. Spotting similar triangles and proving triangles are similar.

Pages 27/28. Similar Triangles 2.
Calculations involving similar triangles.

Pages 29/30. Discovering Trigonometry.
Discovering trigonometry through a measuring exercise. Triangles are already drawn, though pupils could draw their own as part of the exercise. The ratios can be shown to work through similar triangles.

Pages 31-34. Trigonometry 1/2.
This approach to trigonometry is not to learn one ratio at a time, but which ratio to use. Once the correct ratio is chosen the mechanics of the calculation are the same regardless. The progressions are therefore within the mechanics of the calculations i.e. "top" missing, "bottom" missing, finding an angle.

Pages 35/36. Trigonometry Worded Questions 1.
Using the skills learnt and applying them to practical situations.

Page 37. Trigonometry Worded Questions 2.
As above. Typical Intermediate GCSE questions.

Page 38. Trigonometry and Circle Properties.
This sheet revises the circle properties that create right angles. This leads to questions that use trigonometry and Pythagoras' Theorem.

Pages 39/40. Trigonometry Activities.
Some "academic" trigonometry activities to try.

Pages 41/42. More Trigonometry Activities.
Some practical applications of trigonometry.

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Level 7/8 Pack 6 Info

Pages 3/4. Area Revision.
Refreshing all the areas previously studied at level 6 ready for Volume of Prism work later on.

Pages 5/6. Harder Area Revision.
More revision of areas. This time reverse questions. Areas are given and missing dimensions have to be found.

Pages 7/8. More Areas 1.
Working on the mechanics of the calculations involved with area questions. An important aspect that runs through the topic is rounding errors. Where an answer is used to continue the calculation, the original value, not the rounded answer should be substituted.

Pages 9/10. More Areas 2.
More area calculations. Rounding is central to the circle questions. In some questions the answer given for the diameter is not exactly double the radius due to rounding.

Pages 11/12. Compound Areas.
Questions become progressively more difficult. Hints: To solve 26). extend the straight lines to form a quarter circle and to solve 27). form a square and four 3/4 circles!

Pages 13/14. Shape Worded Questions.
A worksheet that draws together all the skills needed to solve worded questions. Ideal for Intermediate GCSE revision.

Pages 15/16. Prisms 1.
Naming familiar solids. Faces, Edges and Vertices. Definition of prisms. Finding volumes of a variety of shapes of prisms.

Pages 17/18. Prisms 2.
Volumes of prisms and surface areas. The curved surface area of a cylinder. All the previous work put into context through worded questions. Dimensional Units: looking at expressions and deciding whether it is a length, area, volume or none of these.

Pages 19/20. Shape and Algebra.
Algebra questions using shape properties to form expressions and equations. Algebra should be thoroughly revised before attempting this worksheet.

Pages 21/22. Investigations (Areas and Volumes).
Investigations involving areas and volumes. The main theme throughout is maximising areas and volumes. Notice that the third section of the pig farmer and the start of the guttering question require identical skills. The tower question is a numerical exercise, the generalisations are far too complex for this level.

Pages 23/24. Compound Measures 1 (Speed).
Changing minutes in to fractions of hours and utilising these in Speed/Distance/Time calculations. The units m.p.h., km/h and m/s are used in a series of worded questions.

Pages 25/26. Compound Measures 2 (Speed).
As above, but where the unknown is not the subject of the formula.

Pages 27/28. Compound Measures 3 (Density).
Density calculations using the units g/cmand kg/m. Pressure calculations using the units N/m and a brief visit to population density!

Pages 29/30. Distance/Time Graphs 1.
Taking readings from Distance/Time graphs, calculations involve fractions of hours. Plotting Distance/Time graphs.

Pages 31/32. Distance/Time Graphs 2.
Plotting more advanced Distance/Time graphs. Interpreting velocity/time graphs.

Pages 33/34. Grouped Data.
Finding Averages. Finding the modal class interval, and estimate for the mean, and the class interval where the median lies, from tables of data.

Pages 35/36. Frequency Polygons.
Plotting pairs of frequency polygons and commenting on the distributions relative to each other.

Pages 37/38. Time Series and Moving Averages.
Calculating and plotting moving averages. Using the moving average to make estimates.

Pages 39/40. Interquartile Range and Box Plots.
Finding the IQR from raw data. Drawing Box Plots and comparing two sets of data through Box Plots.

Pages 41/42. Cumulative Frequency and Interquartile Range.
Drawing cumulative frequency graphs and Box Plots. Calculating the IQR and taking readings from cumulative frequency graphs.

Pages 43/44. Statistical Investigations.
Notes on Primary and Secondary data, sampling techniques and bias. Page 45. GCSE Statistical Investigations. Notes on breaking down the Statistical Investigation at GCSE level and four investigations that could be attempted.

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