| 10Ticks.co.uk - Level 9/10 Information |
Here you see the contents of the VLE Level 9/10 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 9/10 Pack 1 Info| Level 9/10 Pack 1 Content/Teacher Notes |
Pages 3/4. Accuracy of Measurement Notes.
Notes about accuracy of measurement and the lower and upper bound.
This includes four rules calculations with rounded numbers and finding the range in which the answers are valid.
Pages 5/6. Accuracy of Measurement 1.
Four rules calculations with rounded numbers, calculating the answer and then the lower and upper bounds of the answers.
Pages 7/8. Accuracy of Measurement 2.
Calculating the percentage error and the maximum percentage error for four rules calculations with rounded numbers.
Pages 9/10. Accuracy of Measurement 3.
Typical examination questions covering accuracy of measurement.
Pages 11/12. Variation 1.
The worksheets revise direct proportion and concepts which pupils should already be familiar with. This is then extended to direct proportion including squares, cubes and square roots.
Pages 13/14. Variation 2.
The first page deals with basic inverse proportion. This is then extended to indirect proportion including squares, cubes and square roots.
Pages 15/16. Direct and Indirect Proportion.
Typical examination questions covering direct and indirect proportion.
Pages 17/18. Indices (Powers).
Introducing negative indices by pattern and then evaluating numbers involving negative indices. Indices that represent roots. Whole numbers and fractions that have negative and fraction indices.
Pages 19/20. Indices 1/2.
Patterns using indices.
Pages 21/22. Compound Growth and Decay 1. (Exponential Functions).
Questions that show compound growth and graphs. Investigation to highlight the difference between uniform and compound growth. Compound decay.
Pages 23/24. Compound Growth and Decay 2. (Exponential Functions).
Typical examination questions covering exponential functions.
Pages 25/26. Exponential Functions.
Carbon dating and radioactivity. Notes on radiometric dating.
Pages 27/28. Surds.
Multiplying and dividing surds. Rationalising expressions that contain surds.
Pages 29/30. Rational and Irrational Numbers 1.
Showing numbers to be rational. Converting decimals and recurring decimal to simple fractions.
Pages 31/32. Rational and Irrational Numbers 2.
Irrational numbers. Which are rational numbers and which are irrational numbers? Typical examination questions covering rational and irrational numbers.
Page 33. Using Surds in Trigonometry.
Using the trigonometrical ratios and Pythagoras' Theorem to find lengths of sides of right angled triangles.
Page 34. Trigonometric Ratios for 45°, 30° and 60° in Surd Form.
Finding these values.
Page 35. Using Trigonometric Ratios for 45°, 30° and 60° in Surd Form.
Finding missing values in diagrams using the trigonometric ratios for 45°, 30° and 60° in surd form.
Pages 36/37. Investigations with Irrational and Prime Numbers.
Seven investigations, four of which are enjoyable paper folding problems.
Page 38. Proving Irrationality.
Proof by contradiction.
Pages 39/40. Calculating .
Using spreadsheets to calculate . Pierre de Fermat's Prime Numbers and more on rationalising.
Page 41. Approximating 2 by Iteration.
As it says.
Page 42. Powers of 10/Logarithms.
Investigating decimal powers of 10 in a spreadsheet. Logarithms.
| Level 9/10 Pack 2 Content/Teacher Notes |
Pages 3/4. Trigonometry in Three Dimensions.
Questions involving solids and trigonometry.
Pages 5/6. Trigonometry 3-d Models.
Cut outs to help visualise angles in 3-d solids. Stick in pupils books as an aid to support the questions in the previous 2 pages.
Pages 7/8. The Sine and Cosine Rules 1.
Labelling diagrams correctly. Finding missing lengths in triangles using the sine rule and the cosine rule.
Pages 9/10. The Sine and Cosine Rules 2.
Using the two rules together to find missing lengths in triangles. Worded questions involving the sine and cosine rules.
Pages 11/12. Areas and the Sine Rule.
Finding areas of triangles using the sine rule. More worded questions.
Pages 13/14. Trigonometry, Sine and Cosine Rule. Exam Style Questions 1.
Typical examination style questions involving the sine and cosine rule.
Pages 15/16. Trigonometry, Sine and Cosine Rule. Exam Style Questions 2.
Typical examination style questions involving the sine and cosine rule.
Pages 17/18. Trigonometric Graphs 1.
Plotting the basic trigonometric graphs. Discovering amplitude and wavelength and the effect they have on the shape of trigonometric graphs. Using graphs to solve problems. Sketching trigonometric graphs.
Pages 19/20. Trigonometric Graphs 2.
Finding the equation of a trigonometric graph.
Pages 21/22. Trigonometric Graphs 3.
Using trigonometric graphs to find solutions to equations. Finding maximum and minimum values of functions. Typical examination style questions.
Pages 23/24. Making and using a Sundial.
An activity for maths clubs or activity days. Sun dials are rich in mathematical content. The maths contained here barely scratches the surface of all that is possible from the topic. Make a sundial, set it up and check its accuracy!
Pages 25/26. Probability 1. Revision.
A revision exercise to cover the style of questions that pupils should be familiar with. Pupils should revise the level 7/8 work if they do not successfully complete these exercises.
Pages 27/28. Probability 2. Revision.
As above.
Pages 29/30. Conditional Probability.
Introducing dependent events through worded questions. This leads eventually into tree diagrams.
Pages 31/32. Tree Diagrams (Dependent Events).
Typical questions involving tree diagram and dependent events.
Pages 33/34. Probability. Exam Style Questions 1.
Typical examination style questions involving all aspects of probability.
Pages 35/36. Probability. Exam Style Questions 2.
Typical examination style questions involving all aspects of probability.
Page 37. Probability Investigations.
Four investigations to stretch the more able mathematician. "Birthdays" looks at the probability of 2 people having the same birth date in a class. Geometrical probability looks at an old experiment first performed by le Comte de Buffon. "Odds" and "National Lottery" explore horse racing and lottery odds respectively.
Page 38. Schichi-fuku-jin
A probability game/investigation adapted to a Japanese theme.
Page 39. Solving Quadratics by Factorising.
Solving quadratics by factorising, progressing to rearranging equations then factorising to solve equations.
Page 40. The nth term of a Quadratic.
Another method to find the nth term of a quadratic sequence. This method uses solving simultaneous equations.
Pages 41/42. Completing the Square.
Solving quadratics by completing the square. This leads to demonstrating how the equation is derived for solving quadratics.
Pages 43/44. Solving Quadratics by Formula.
Using the equation to solve quadratic equations. Worded questions involving solving quadratics.
| 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.
| Level 9/10 Pack 4 Content/Teacher Notes |
Pages 3/4. Using Graphs to Solve Equations.
The questions have graphs drawn out. Pupils have to use the graphs to solve equations. This will be an approximate answer and pupils should leave the this to an appropriate degree of accuracy
Page 5. Finding Lines to be Drawn
An exercise in rearranging equations to find a line to plot to solve a given equation. There is no actual plotting in this exercise.
Pages 6/7. Drawing Graphs.
Plotting graphs. Solving equations using the graphs by rearranging and plotting further lines.
Page 8. Solving Equations Involving Circles.
Plotting circles based on the equation of a circle. Using the graphs to solve further equations.
Page 9. Arcs and Sectors.
Questions finding arc lengths and sector areas.
Page 10. Volume of a Cone.
Questions involving the volume of a cone.
Page 11. Curved Surface area of a Cone.
Questions involving the curved surface area of a cone.
Page 12. Total Surface Area of a Cone.
Questions involving the total surface area of a cone.
Page 13. The Frustrum.
Questions involving a frustrum.
Page 14. General Pyramids and Cones.
Generalising the formula to fit all pyramids.
Page 15. The Sphere
The volume and total surface area of a sphere.
Page 16. The Annulus.
Finding the area of an annulus and then applying this to questions on pipes.
Page 17. Density, Mass and Volume.
Finding and using densities in complex solids.
Pages 18/19. Mixed Areas and Volumes 1.
Applying all the skills taught in the previous worksheets into worded questions.
Pages 20/21. Mixed Areas and Volumes 2.
As above.
Pages 22/23. More Areas and Volumes 1.
Examination style questions.
Pages 24/25. More Areas and Volumes 2.
More examination style questions.
Pages 26/27. Factorising.
Factorising trinomials and other expressions. Factorising by grouping into pairs. Using the difference of two squares to factorise.
Pages 28/29. Simplifying Algebraic Fractions.
The complexity of the problems increases until questions involve dividing, factorizing and then cancelling down lgebraic fractions.
Page 30. Combining Algebraic Fractions.
Making terms into one single algebraic fraction.
Pages 31/32. Equations involving Algebraic Fractions.
The worksheets starts with basic equations involving algebraic fractions and finishes with quite complex equations involving algebraic fractions.
Pages 33/34. Transformation of Formulae.
Typical `Make x the Subject' style questions. Starting simply but ending with quite complex rearrangement.
Page 35. Transformation of Formulae. Mixture.
As above, but rearranging some familiar equations.
Page 36. Problems Leading to Algebraic Fractions.
Worded questions which lead to algebraic fractions.
Page 37. Simultaneous Equations.
Solving simultaneous equations where one equation is linear and the other isn't.
Pages 38/39. Maximum and Minimum Values Within Regions
Using inequalities to define regions. Finding maximum and minimum values within these regions.
Pages 40/41. Linear Programming.
Linear programming is not needed at GCSE. This worksheet extends the last one introducing simple linear programming.
Pages 42/43. Translations.
Translating the graph of y = f(x).
Page 44. Reflections.
Reflecting the graph of y = f(x).
Pages 45/46. Stretches.
Stretching the graph of y = f(x).
Pages 47/48. Mixed Transformations.
Transformations of the graph of y = f(x).
| Level 9/10 Pack 5 Content/Teacher Notes |
Page 3. Vectors.
Using column vectors. Drawing a vector given the column vector, finding a column vector.
Pages 4/5. Adding Column Vectors.
Drawing vectors to discover the addition properties.
Pages 6/7. Scalar Multiples.
Drawing scalar multiples of a vector. Subtracting column vectors.
Pages 8/9. Magnitude of a Vector.
Finding the magnitude of a vector using Pythagoras' theorem. Proving vectors are perpendicular.
Page 10. Vector Equations.
Finding missing column vectors in equations. Finding missing column vectors in simultaneous equations.
Pages 11/12. Components.
Using trigonometry to find the component form of vectors i.e. the x and y distances.
Pages 13/14. General Vector Addition.
Vector addition and subtraction using scale drawing and the cosine rule.
Pages 15/16/17. Adding Forces
Finding the magnitude of the resultant of forces. Worded questions.
Pages 18/19. Position Vectors 1.
Writing position vectors as column vectors. Position vectors involving triangles. Note the notation with the arrow above letters is used here. Make sure a post script printer driver is selected before printing, as your printer may not recognise this notation.
Pages 20/21. Position Vectors 2.
Questions involving position vectors in polygons.
Pages 22/23. Some Proofs.
Some proofs. The mid-point rule and proofs using the mid-point rule.
Pages 24/25. Linear Independence.
Questions involving linear independence.
Pages 26/27. Miscellaneous Vector Questions.
A mixture of questions that cover the vector topic.
Pages 28/29. Trapezium Rule 1/2.
Find the area under a curve by splitting the area into strips and finding the area of each individual strip, ie. the trapezium rule.
Page 30. Distance Time Graphs.
Distance Time graphs involving straight lines and curves.
Pages 31/32/33. Velocity Time Graphs 1/2/3.
Velocity Time graphs that involve drawing gradients to find the acceleration and calculating the area under the graph to find the distance travelled.
Page 34. Drawing Velocity Time Graphs.
Drawing and sketching Velocity Time graphs.
Page 35. Stopping Distances Investigations.
An investigation into stopping distances using information from the Highway Code.
Pages 36/37. Plotting Motion Graphs.
Plotting graphs and using the graph to solve problems.
Pages 38/39. Perpendicular Lines 1/2.
Inverses of gradients. Perpendiculars to lines.
Pages 40/41. Gradients of Curves 1/2.
Extension material for those that need it. Introducing differentiation.
Pages 42/43. Integration 1/2.
Extension material for those that need it. Introducing integration.
| Level 9/10 Pack 6 Content/Teacher Notes |
The material contained in this workpack is specifically aimed at those attempting `O' levels and not the GCSE course.
Pages 3-10. Matrices 1/2/3/4.
These worksheets cover the basics of matrices, including the notation used to describe the size of a matrix, and addition, subtraction and multiples of matrices. Worded questions are also included.
Pages 11-16. Matrix Multiplication 1/2/3.
The complexity of multiplying matrices is built up from a simple row matrix x column matrix to varying sizes of matrices. Pupils are encouraged to work out the resulting size of the end matrix, before calculating the individual cells. Worded questions are also included.
Pages 17/18. Commutative Matrices.
Matrix order when multiplying.
Pages 19/20. Identity and Zero Matrices.
As it says.
Pages 21/22. Multiple Matrix Multiplication.
Multiplying more than 2 matrices together.
Pages 23/24. Inverses of Square Matrices of Order 2 (1).
Inverses linked to the Identity Matrix. Finding Determinants.
Pages 25/26. Inverses of Square Matrices of Order 2 (2).
Finding determinants and solving equations with matrices.
Pages 27-30. Miscellaneous Matrix Questions (1)/(2).
A mixture of questions covering work attempted with the previous worksheets.
Pages 31/32. Matrices and Transformations (Introduction).
The link between matrices and transformations.
Pages 33/34. Single Matrix Multiplication.
Multiplying coordinates by a single matrix.
Pages 35-38. Multiple Matrix Transformations (1)/(2).
Describing the effect of multiple matrix transformations in terms of reflections, rotations and enlargements.
Pages 39/40. Inverse Transformations and Inverse Matrices.
Discovering the link between inverse transformations and inverse matrices.
Pages 41/42. Further Questions on Matrix Transformations.
A mixture of questions covering work attempted with matrix transformations.
Pages 43/44. Finding a Transformation Matrix.
Given the transformation, find the matrix under which the transformation took place.
Page 45. Shape Orientation and Determinants.
Looking at object and image direction and finding the link to the determinant.
Page 46. Transformations involving Singular Matrices.
Transformations that show a matrix is singular.
Pages 47/48. Area Scale Factors and Determinants.
Finding the link between the area scale factor and the determinant
Pages 49/50. Sets. Basic Ideas (1).
Simple set notation and applying this new notation in question form.
Pages 51/52. Sets. Basic Ideas (2).
More simple set notation and applying this new notation in question form.
Pages 53/54. Venn Diagrams.
Using Venn Diagrams to solve simple set problems.
Pages 55/56. The Intersection of Sets.
The intersection of sets in Venn Diagrams and worded questions.
Pages 57/58. The Union of Sets.
The union of sets in Venn Diagrams and worded questions.
Pages 59/60. Regions in Venn Diagrams.
Using set notation to describe areas in Venn Diagrams.
Pages 61/62. Miscellaneous Set Notation Questions.
A mixture of questions covering work attempted with the previous set and Venn Diagram worksheets.
Pages 63/64. Numerical Questions involving Venn Diagrams.
As it says.
Pages 65/66. Miscellaneous Set Venn Diagram Questions.
A mixture of questions covering work attempted using set theory.