Mathematics Enhancement Programme- Key Stage 4 Resources

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1 Indices

1.1 Multiplication and division

1.2 Squares, cubes, square roots and cube roots

1.3 Index notation

1.4 Factors

1.5 Prime factors

1.6 Further index notation

1.7 Standard form

1.8 Calculations with standard form

2 Formulae

2.1 Using formulae

2.2 Construct and use simple formulae

2.3 Revision of negative numbers

2.4 Substitution in formulae

2.5 More complex formulae

2.6 Changing the subject (of a formula)

2.7 Further change of the subject (of a formula)

2.8 Expansion of brackets

2.9 Factorisation

2.10 Algebraic manipulation

2.11 Algebraic fractions

3 Angle geometry

3.1 Measuring angles

3.2 Line and rotational symmetry

3.3 Angle geometry

3.4 Angles with parallel and intersecting lines

3.5 Angle symmetry in polygons

3.6 Symmetry properties of 3D shapes

3.7 Compass bearings

3.8 Angles and circles 1

3.9 Angles and circles 2

3.10 Circles and tangents

4 Trigonometry

4.1 Squares and triangles

4.2 Pythagoras’ theorem

4.3 Further work with Pythagoras’ theorem

4.4 Sine, cosine and tangent

4.5 Finding lengths in right angled triangles

4.6 Finding angles in right angles triangles

4.7 Mixed problems with trigonometry

4.8 Sine and cosine rules

4.9 Angles larger than 90 degrees

5 Probability

5.1 Probabilities

5.2 Simple probabilities

5.3 Outcome of two events

5.4 Finding probabilities using relative frequency

5.5 Determining probabilities

5.6 Probability of two events

5.7 Use of tree diagrams

5.8 Multiplication for independent events

5.9 Mutually exclusive events

5.10 Tree diagrams and conditional probability

5.11 Using Venn diagrams to find probabilities

6 Number system

6.1 Decimals

6.2 Multiplying and dividing with decimals

6.3 Fractions and decimals

6.4 Long multiplication and division

6.6 Using brackets and memory on a calculator

6.7 Upper and lower bounds

6.8 Number system

6.9 Surds

7 Mensuration

7.1 Units and measuring

7.2 Estimating areas

7.3 Making solids using nets

7.4 Constructing nets

7.5 Conversion of units

7.6 Squares, rectangles and triangles

7.7 Area and circumference of circles

7.8 Volumes of cubes, cuboids, cylinders and prisms

7.9 Plans and elevations

7.10 Using isometric paper

7.11 Discrete and continuous measures

7.12 Areas of parallelograms, trapeziums, kites and rhombuses

7.13 Surface area

7.14 Mass, volume and density

7.15 Volumes, areas and lengths

7.16 Dimensions

7.17 Areas of triangles

8 Data handling

8.1 Tables and timetables

8.2 Pictograms and bar charts

8.3 Pie charts

8.4 Line graphs

8.5 Questionnaires and surveys

8.6 Frequency graphs

8.7 Histograms with unequal class intervals

8.8 Sampling

9 Data analysis

9.1 Mean, median, mode and range

9.2 Finding the mean from tables and tally charts

9.3 Calculations with the mean

9.4 Mean, median and mode for grouped data

9.5 Cumulative frequency

9.6 Standard deviation

10 Equations

10.1 Negative numbers

10.2 Arithmetic with negative numbers

10.3 Simplifying expressions

10.4 Simple equations

10.5 Solving equations

10.6 Trial and improvement method

10.7 Expanding brackets

10.8 Simultaneous linear equations

10.9 Factorisation 1

10.10 Factorisation 2

10.11 Solving quadratic equations by factorisation

10.12 Solving quadratic equations using the formula

10.13 Algebraic fractions

10.14 Completing the square

10.15 Algebraic fractions and quadratic equations

11 Fractions and percentages

11.1 Fractions, decimals and percentages

11.2 Fractions and percentages of quantities

11.3 Quantities as percentages

11.4 More complex percentages

11.5 Percentage increase and decrease

11.6 Addition and subtraction of fractions

11.7 Multiplication an division of fractions

11.8 Compound interest and depreciation

11.9 Reverse percentage problems

12 Number patterns

12.1 Simple number patterns

12.2 Recognising number patterns

12.3 Extending number patterns

12.4 Formulae and number patterns

12.5 General laws

13 Graphs

13.1 Positive coordinates

13.2 Coordinates

13.3 Plotting straight lines

13.4 Plotting curves

13.6 Applications of graphs

13.7 Scatter plots and lines of best fit

13.8 The equation of a straight line

13.9 Horizontal and vertical lines

13.10 Solution of simultaneous equations by graphs

13.11 Graphs of common functions

13.12 Graphical solutions of equations

14 Loci and transformations

14.1 Drawing and symmetry

14.2 Scale drawings

14.3 Constructing triangles and other shapes

14.4 Enlargements

14.5 Reflections

14.6 Construction of loci

14.7 Enlargements which reduce

14.8 Further reflections

14.9 Rotations

14.10 Translations

14.11 Combined transformations

14.12 Congruence

14.13 Similarity

14.14 Enlargements with negative scale factors

15 Variation

15.1 Simple ratios

15.2 Proportion and ratio

15.3 Map scales and ratio

15.4 Proportional division

15.5 Direct proportion

15.6 Inverse proportion

15.7 Functional and graphical representations

15.8 Further functional representations

16 Inequalities

16.1 Inequalities on a number line

16.2 Solution of linear inequalities

16.4 Graphical approach to inequalities

16.5 Dealing with more than one inequality

17 Using Graphs

17.1 Transformations of graphs

17.2 Areas under graphs

17.3 Tangents to curves

17.4 Finding coefficients

18 3D geometry

18.1 Using Pythagoras’ theorem and trigonometry in three dimensions

18.2 Angles and planes

19 Vectors

19.1 Vectors and scalars

19.2 Applications of vectors

19.3 Vectors and geometry

19.4 Further work with vectors

19.5 Commutative and associative properties

20 Statistics

20.1 Data collection

20.2 Presentation of data

20.3 Measures of location and spread

20.4 Weighted averages: index numbers

20.5 Birth and death rates

20.6 Time series analysis: moving averages

20.7 Correlation and regression

20.8 Distributions