Number

Chapter 1: Number

• Square numbers & cube numbers
• Multiples of whole numbers
• Factors of whole numbers
• Prime numbers
• More about HCF & LCM
• Real Numbers

Chapter 2: Fractions & Percentages

• Equivalent fractions
• Fractions and decimals
• Recurring decimals
• Percentages, fractions & decimals
• Calculating percentages
• Increasing or decreasing quantities by a percentage

Chapter 3: The four rules

• Order of operations
• Choosing the correct operation
• Finding a fraction of a quantity
• Multiplying & dividing fractions

Chapter 4: Directed numbers

• Introduction to directed numbers
• Everyday use of directed numbers
• The number line
• Adding & subtracting directed numbers
• Multiplying and dividing directed numbers

Chapter 5: Powers & roots

• Squares & square roots
• Cubes & Cube roots
• More powers and roots
• Exponential growth – Extended syllabus

Chapter 6: Ordering & set notation

• Inequalities
• Sets & Venn Diagrams
• More about Venn Diagrams – Extended syllabus

Chapter 7: Ratio, proportion & rate

• Ratio
• Increases & decreases using ratios
• Speed
• Rates
• Direct proportion
• Inverse proportion

Chapter 8: Estimation & limits of accuracy

• Rounding whole numbers
• Rounding decimals
• Rounding to significant figures
• Upper & lower bounds
• Upper & lower bounds for calculations – Extended

Chapter 9: Standard Form

• Standard form
• Calculating with standards form

Chapter 10: Applying numbers & using calculators

• Units of measurements
• Converting between metric units
• Time
• Currency conversions

Algebra

Chapter 11: Algebraic representation & Formulae

• The language of algebra
• Substitution into formulae
• Rearranging formulae
• More complicated formula – Extended

Chapter 12: Algebraic manipulation

• Simplifying expressions
• Expanding brackets
• Factorisation
• Multiplying two brackets – using single brackets
• Multiplying two brackets – using double brackets
• Expanding three brackets – Extended
• Algebraic fractions – Extended

Chapter 13: Solutions of equations & Inequalities

• Solving linear equations
• Setting up equations
• Solving quadratic equations by factorisation – Extended
• Solving quadratic equations by completing the square – Extended
• Simultaneous equations
• Linear & Non-linear simultaneous equations – Extended
• Solving inequalities  – Extended

Chapter 14: Graphs in practical situations

• Conversion graphs
• Travel graphs
• Speed-time graphs – Extended
• Curved graphs – Extended

Chapter 15: Straight-line graphs

• Drawing straight-line graphs
• The equation y = mx + c
• Solving equations graphically
• Parallel lines
• Points & lines
• Perpendicular lines

Chapter 16: Graphs of functions

• Turning points on a quadratic graph
• Reciprocal graphs
• More graphs
• Exponential graphs

Chapter 17: Number sequences

• Patterns in number sequences
• The nth term of a sequence
• General rules from pattern
• Further sequences

Chapter 18: Indices

• Using indices
• Negative indices
• Multiplying & dividing with indices
• Fractional indices – Extended

Chapter 19: Variation

• Direct Variation – Extended
• Inverse Variation – Extended

Chapter 20: Linear programming

• Graphical inequalities – Extended
• More than one inequality – Extended
• Linear programming – Extended

Chapter 21: Functions

• Function notation
• Inverse functions
• Composite functions

Chapter 22: Differentiation

• The gradient of a curve
• More complex curves
• Turning points

Geometry & trigonometry

Chapter 23: Angle properties

• Angle facts
• Parallel lines
• Angles in a triangle
• Regular polygons
• Irregular polygons – Extended
• Tangents & Diameters
• Angles in a circle  – Extended
• Alternate segment theorem – Extended

Chapter 24: Geometrical terms & relationships

• Measuring & drawing angles
• Bearings
• Nets
• Congruent shapes
• Congruent triangles – Extended
• Similar shapes
• Areas of similar triangles – Extended
• Areas & volumes of similar shapes – Extended

Chapter 25: Geometrical constructions

• Constructing shapes
• Scale Drawings

Chapter 26: Trigonometry

• Pythagoras theorem
• Trigonometric ratios
• Calculating angles
• Using sine, cosine & tangent functions
• Which ratio to use
• Applications of trigonometric ratios – Extended
• Problems in three dimensions – Extended
• Sine & cosine of obtuse angles – Extended
• Using sine rule and the cosine rule – Extended
• Using sine to find an area of a triangle – Extended
• Sine, cosine and tangent of any angle – Extended

Chapter 27: Mensuration

• Perimeter & aera of a rectangle
• Area of a triangle
• Area of a parallelogram
• Area of a trapezium
• Circumference & area of a circle
• Surface area & volume of a cuboid
• Volume & surface area of a prism
• Volume & surface area of a cylinder
• Sectors & arcs: 1
• Sectors & arcs: 2 – Extended
• Volume of a pyramid
• Volume & surface area of a cone
• Volume & surface area of a sphere

Chapter 28: Symmetry

• Lines of symmetry
• Rotational symmetry
• Symmetry of special two-dimensional shapes
• Symmetry of three-dimensional shapes
• Symmetry in circles

Chapter 29: Vectors

• Introduction to vectors
• Using vectors
• The magnitude of a vector

Chapter 30: Transformations

• Translations
• Reflections
• Rotations
• Enlargements

Statistics & Probability

Chapter 31: Statistical representation

• Frequency tables
• Pictograms
• Bar charts
• Pie charts
• Scatter diagrams
• Histograms
• Histograms with bars of unequal width

Chapter 32: Statistical measures

• The mode
• The median
• The mean
• The range
• Stem-and-leaf diagrams
• Using frequency tables
• Grouped data
• Cumulative frequency diagrams
• Box-and-whisker plots

Chapter 33: Probability

• The probability scale
• Calculating probabilities
• Probability that an event will not happen
• Probability in practise
• Using Venn diagrams
• Possibility diagrams
• Tree diagrams
• Conditional probabilities