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
- Adding and subtracting fractions
- 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
- Quadratic Factorisation – 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 the quadratic formula – 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
- More about straight-line graphs
- Solving equations graphically
- Parallel lines
- Points & lines
- Perpendicular lines
Chapter 16: Graphs of functions
- Quadratic graphs
- Turning points on a quadratic graph
- Reciprocal graphs
- More graphs
- Exponential graphs
- Estimating gradients
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
- More about 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
- Angles in a quadrilateral
- Regular polygons
- Irregular polygons – Extended
- Tangents & Diameters
- Angles in a circle – Extended
- Cyclic quadrilaterals – 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