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