Contents


Numbers and Algebra

  1. Numbers and operations
    Prime, LCM, squares, cubes, roots, rational and real numbers, symbols, number lines, approximation, rounding off, use of calculators
  2. Ratio and Proportion
  3. Percentage
  4. Rate and Speed
    Conversion of units and average and constant and rates and speeds
  5. Algebraic expression and formulae
    Simple algebraic expressions and formulae, translation of real-world situations into algebraic expressions, number patterns, simplification of linear expressions, common factors
  6. Functions and Graphs
    Relationship between two variables, linear functions, gradient concept
  7. Equations and Inequalities
    Solving linear equations, simple fractional equations
  8. Problems in real-world contexts
    Simple interest, taxation, instalments, utilities bills, currency exchange, analysing data from tables and graphs

Geometry and Measurement

  1. Angles, triangles and polygons
    Types of angles, angles in parallel lines, properties of triangles, special quadrilaterals, regular polygons, interior and exterior angles in polygon, bisectors, construction of simple geometrical figures
  2. Mensuration
    Areas of parallelogram, trapezium, area and perimeter of plane figures, volume and surface area of prism and cylinder, conversions of units, area and volume of composite solids  

Statistics and Probability

  1. Data analysis
    Tables, bar graphs, pictograms, line graphs, pie charts, purposes, advantages and disadvantages of different forms of representation, misinterpretations

Numbers and Algebra

  1. Ratio and proportion
    Maps and scales, direct and inverse proportion
  2. Algebraic expressions and formulae
    Expansion of product of algebraic expressions, subject of formula, expansion formulae, factorisation of linear and quadratic expressions, addition, subtraction, multiplication and division of simple algebraic fractions
  3. Functions and graphs
    Quadratic functions and their gradients, turning points and symmetry
  4. Equations and inequalities
    Graphs of linear equations of two variables, solving quadratic equations with one variable using factorisation, solving simultaneous equations with two variables using substitution, elimination and graphical methods,
  5. Problems in real-world contexts
    Simple interest, taxation, instalments, utilities bills, currency exchange, analysing data from tables and graphs

Geometry and Measurement

  1. Congruency and Similarity
    Congruent and similar figures, properties of similar triangles and polygons, enlargement and reduction of plane figures, scale drawing, solving simple congruency and similarity problems
  2. Pythagoras’ theorem and trigonometry
    Use of Pythagoras’ theorem, use of trigonometric ratios (sine, cosine, tangent) of acute angles in right-angled triangles
  3. Mensuration
    Volume and surface area of pyramid, cone and sphere

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    Statistics and Probability

    1. Data analysis
      Dot diagrams, histograms, stem-and-leaf diagrams, purposes, advantages and disadvantages of different forms of representation, misinterpretations, purposes and use of mean, median and mode, calculating mean for grouped data
    2. Probability
      Probability of single events

    Numbers and Algebra

    1. Numbers and Operations
      Use of standard forms, laws of indices
    2. Functions and graphs
      Sketching of quadratic graphs, power functions, exponential functions, estimation of gradient of curves with tangents
    3. Equations and inequalities
      Solving quadratic equations with one variable with formulae, completing square and graphical methods, solving fractional and linear equations with one variable
    4. Problems in real-world contexts
      Simple interest, taxation, instalments, utilities bills, currency exchange, analysing data from tables and graphs, distance-time, speed-time graphs
    5. Set Language and notation
      Use of set language, union and intersection of sets and venn diagrams
    6. Matrices
      Display, interpretation, addition, subtraction, multiplication of matrices

    Geometry and Measurement

    1. Congruency and Similarity
      Justifying congruency and similarity, ratio of areas and volumes of similar figures and solids
    2. Properties of circles
      Symmetry and angle properties of circles
    3. Pythagoras’ theorem and trigonometry
      Sine and cosine of obtuse angles, sine rule for area, sine and cosine rules for any triangle, problems in two and three dimensions, angles of elevation and depression, bearings
    4. Mensuration
      Arc length, sector area and area of segments, use and conversion of degree and radian measure of angle
    5. Coordinate Geometry
      Gradient of straight line, length of line segment,  interpret and find equation of straight line, geometric problems using coordinates
    6. Vectors in two dimensions
      Translation by vector, position vectors, magnitude, scalar multiplication of vectors

    Statistics and Probability

    1. Data analysis
      Quartiles, percentiles, range, interquartile range, standard deviation, cumulative frequency diagrams, box-and-whisker plots, purposes, advantages and disadvantages of different forms of representation, misinterpretations, purposes and use of mean, median and mode, calculating mean for grouped and ungrouped data, comparison of data
    2. Probability
      Probability of simple combined events, possibility and tree diagrams, mutually exclusive and independent events

    Sets

    1. Sets
      Venn Diagrams, Universal Set, Complements, Subsets, Intersection and Union of Sets

    Probability

    1. Probability of Combined Events
      Possibility and Tree Diagrams, Addition and Multiplication Laws, Mutually Exclusive Events and Independent Events

    Statistical Data Analysis

    1. Statistical Data Analysis
      Cumulative Frequency Table and Curve, Median, Quartiles, Percentiles, Range, Interquartile Range, Box-and-Whisker Plots and Standard Deviation

    Matrices

    1. Matrices
      Addition, Subtraction, Multiplication and Application

    Vectors

    1. Vectors
      Addition, Subtraction and Scalar Multiples of Vectors, Position Vectors and Applications


    BONUS MATERIAL

    1. Revision: Numbers and Algebra
      • Numbers, Percentages, Proportion, Ratio, Rate and Speed
      • Algebraic Manipulation, Formulae, Equations and Inequalities
      • Functions and Graphs
      • Sets
      • Matrices
    2. Revision: Geometry and Measurement
      • Angles, Triangles, Polygons
      • Congruence Similarity
      • Pythagoras' Theorem, Trigonometry  and Mensuration
      • Coordinate Geometry
      • Vectors
      • Properties of Circles
    3. Revision: Probability and Statistics


    MORE BONUS MATERIAL

    1. GCSE & IB Model Exam Questions 2018 and 2019
    2. Lecture: Preparation for Exams - It's a State of Mind
    3. Lecture: Mathematics - Why We Study It
    4. Lecture: Math Mad Moses' Study Tips
    5. Lecture: How to be a Successful Seven-Figure Banker with Math
    Math Mad Moses

    Math Mad Moses
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    mathmadmoses@mathmadmoses.com

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