Maths resources

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Course: Research Help for High School
Book: Maths resources
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Date: Friday, 19 August 2022, 11:58 AM

Arithmetic

Print based resources

More than just numbers (Level A):

  • Our number system (including whole numbers, place value & estimation)
  • Working with numbers (including power notation and the square root)
  • Calculations involving negative numbers
  • Order of calculations
  • Fractions (including equivalent fractions, mixed numbers and improper fractions, calculating with fractions, addition and subtraction of fractions, multiplication of fractions and division of fractions)
  • Decimals (including converting between decimals and fractions)

The Power of numbers (Level A):

  • Power notation
  • Calculating with powers including multiplying powers, dividing powers, negative indices, the zero index, adding and subtracting powers, special powers, fractional indices, finding a power of a power and finding a power of a product)
  • Common applications of powers (including scientific notation, the metric system, converting between units)

Comparing numbers (Level A)

  • Comparing quantities of subtraction
  • Comparing quantities by division (including percentages)
  • Ratios (including ratios in squares, rectangles, circles & triangles) 
  • Rates
Quicktips

Video based resources

  • Calculating with negative numbers (printable handout)
    This 10 minute video covers how to calculate with negative numbers.
  • Order of operations (printable handout)
    This 6 minute video covers the importance of the order of operations with examples.
  • Fractions (printable handout)
    This 16 minute video covers:
    • Equivalent fractions 
    • Mixed number and improper fractions 
    • Addition, subtraction, multiplication and division.
  • Decimals: Fractions in other forms (printable handout)
    This 11 minute video covers:
    • the link between fractions and decimals
    • converting between fractions and decimals
    • percentages, including percentage increase and decrease
    • rates.

      Algebra, functions and graphing

      Representing relationships (Level A)

      • Writing relationships in words
      • Writing relationships as formulas
      • Representing relationships as graphs 
      • Describing relationships

      Generalising numbers - Algebra (Level A)

      • Simplifying expressions
      • Rearranging equations
      • Solving equations Equations involving powers and roots including Pythagoras' Theorem
      • Simultaneous equations

      Generalising numbers - Graphs (Level A)

      • Gradients of line graphs (including finding the gradient of a given line, and drawing a line given the gradient)
      • Linear equations (including special lines, and what if two lines cross) Introduction to curve
      • Parabolic equations (including the axis of symmetry)
      • Exponential equations (including a special number)
      • When two graphs meet

      Algebra: Tools for change (Level B)

      • Describing relationships
      • Manipulating relationships (including grouping like terms, factors and factorization, algebraic fractions and working with powers)
      • Special relationships (including equations, solving equations, rearranging formulas, inequations, absolute value, quadratic equations, factorisation of quadratic equations, the quadratic formula, quadratic equations in the real world, solving simultaneous equations using substitution and elimination)
      Relations and functions (Level B)

      • What are relations and functions (including domain and range of relations and functions and function notation)
      • The linear function (including rate of change of a linear function, the inverse – undoing a function and when two linear functions meet)
      • The quadratic function (including sketching parabolas and rate of change of a quadratic function)
      • Other functions

      Relations and functions (Level C)

      • What are functions Function toolbox (including functional notation, zero conditions of a function, average rate of change of a function, continuity and the inverse of a function)
      • Families of functions (including polynomial functions (which include the constant function, the linear function, the quadratic function, and other polynomial functions), exponential and logarithmic functions, rational functions and functions over an integral domain (including arithmetic and geometric sequences)

      Algebra, functions and geometry (Level D)

      • Inequalities and the real number line (including operations on inequalities, and linear inequalities of two variables)
      • Quadratic Equations and Completing the Square
      • Functions (including polynomials, rational functions, other important non-linear functions, solving simultaneous equations algebraically and graphically inverse functions and continuity)

      Video based resources (Algebra)

      • Introduction to Algebra: relationships as words (printable handouts)
        This 12 minute video covers:
        • translating from words to symbols (relationships)
        • variables and expressions
        • collecting like terms.
      • Substituting and rearranging equations (printable handouts)
        This 12 minute video covers:
        • substituting values into equations
        • rearranging equations.
      • Expanding Brackets (printable handout)
        This 19 minute video covers:
        • the distributive law
        • expanding brackets (single, double and triple)
        • common expressions to get to know.
      • Algebra: factorising quadratic expressions (printable handout)
        This 13 minute video covers:
        • simple factorisations (adding one set of brackets)
        • factoring quadratic expressions (two brackets).
      • Solving quadratic equations using factorisation (printable handout)
        This 7 minute video covers:
        • quadratic equations
        • solving quadratic equations using factorisation.
      • Solving quadratic equations using the quadratic formula (printable handout)
        This 12 minute video covers:
        • quadratic equations
        • the quadratic equation
        • using the quadratic equation
        • finding the number of solutions a quadratic equation will have.
      • Solving simultaneous equations (using the substitution method) (printable handout)
        This 15 minute video covers the use of substitution method to solve simultaneous equations (two unknown variables and two equations).
      • Solving simultaneous equations (using the elimination method) (printable handout). 
        This 16 minute video covers the use of the elimination method to solve simultaneous equations (two unknown variables and two equations).
      • Inequalities (printable handout)

        This 12 minute video covers graphing inequalities and rearranging inequalities.

      • Cancelling with algebraic fractions (printable handout)
        This 12 minute video covers graphing inequalities and rearranging inequalities.

      Video based resources (Graphing)

      • Geometry (printable handout)
        This 7 minute video covers common shapes and their characteristics.
      • Pythagoras' Theorem (printable handout)
        This 4 minute video covers using Pythagoras' Theorem.
      • Relationships as graphs (printable handout)
        This 8 minute video covers the Cartesian co-ordinate system and drawing graphs.
      • Gradient (printable handout)
        This 7 minute video covers how to
        • find the gradient (or slope) of a straight (linear) line
        • drawing a line using a point and the gradient.
      • Exponential graphs (printable handout)
        This 3 minute video introduces the exponential equation for growth and decay along with with the corresponding graphs.

      Exponentials and logarithms

      Generalising Numbers (part of module)

      • Gradients of line graphs (including finding the gradient of a given line, and drawing a line given the gradient)
      • Linear equations (including special lines, and what if two lines cross)
      • Introduction to curve
      • Parabolic equations (including the axis of symmetry)
      • Exponential equations (including a special number)
      • When two graphs meet

      Exponential and logarithmic functions

      • Exponential functions (including the function and its graph, case studies, average rate of change and the inverse of the exponential function)
      • Logarithmic functions (including the function and its graph, case studies, average rate of change and properties of logarithms)
      • Putting it all together – solving equations and real world applications

      Relations and functions (part of module)

      • What are functions
      • Function toolbox (including functional notation, zero conditions of a function, average rate of change of a function, continuity and the inverse of a function)
      • Families of functions (including polynomial functions (which include the constant function, the linear function, the quadratic function, and other polynomial functions), exponential and logarithmic functions, rational functions and functions over an integral domain (including arithmetic and geometric sequences)

      Algebra, functions and geometry

      • Inequalities and the real number line (including operations on inequalities, and linear inequalities of two variables)
      • Quadratic Equations and Completing the Square
      • Functions (including polynomials, rational functions, other important non-linear functions, solving simultaneous equations algebraically and graphically inverse Functions and continuity)    

      Video based resources

      • An introduction to logarithms (printable handout)
        This 12 minute video shows an introduction to logarithms.  It has examples of using different bases and applying the different logarithms laws.
      • Solving equations using logarithms (printable handout)
        This 7 minute video works through some examples of using logarithms to solve equations.
      • Introduction to exponential and their graphs (printable handout)
        This 3 minute video shows examples of using exponential to solve equations and the interpretations of exponential growth and decay curve. 



      Trigonometry

      Print based materials

      Comparing numbers (part of module only)

      • Comparing quantities of subtraction
      • Comparing quantities by division (including percentages)
      • Ratios (including ratios in squares, rectangles, circles & triangles)
      • Rates

      Trigonometry (Level B)

      • Sine (including the sine ratio, the sine function, the inverse of the sine function, degrees, minutes and seconds, amplitude and period)
      • Cosine (including the cosine ratio, the cosine function, the inverse of the cosine function, amplitude and period)
      • Tangent (including the tangent ratio, the tangent function, the inverse of the tangent function, amplitude and period)

      Trigonometric functions (Level C)

      • Radian measure (including what are radians, converting from degrees to radians, converting from radians to degrees, using radians measure in real world applications)
      • Graphs of sine, cosine, and tangent functions
      • Modelling using trigonometric functions (including amplitude, vertical shift, the period of trigonometric functions, the phase of trigonometric functions)
      • Inverse functions
      • Solving trigonometric equations

      Trigonometry (Level D) 

      • Radian Measure
      • Polar Co-Ordinates
      • Trigonometric Identities and Multiple Angle Formulae
      • Solving Trigonometric Equation
      • Periodicity
      • Amplitude
      • Triangle Solution
      • Compound Angles
      • Solving Equations Involving Trigonometric Functions

      Video based resources

      • Introduction to trigonometry (printable handout)

        This 20 minute video introduces:

        • labeling triangles for trigonometry
        • Pythagoras' Theorem
        • trigonometric ratios
        • worked examples using trigonometric ratios


      Matrices, vectors and discrete maths

      Matrices (Level B)

      • What are matrices (including: tables to matrices, defining a matrix, and matrix equality)
      • Calculating with matrices (including: addition, subtraction and multiplication)
      • Some special matrices (including: the identity matrix and the inverse matrix)
      • Solving matrix equations
      • Real world problems

      Analytical geometry (Level C)

      • Describing points in space (including: rectangular coordinates, polar coordinates, and vectors)
      • Describing straight lines (including: equations of a straight line, distance between points and mid-point of a line)
      • Describing other curves (including circles)
      • Transformations (including: transforming points, straight lines, parabolas, circles and other curves)

      Matrices (Level D)

      • Matrix representation of data
      • Addition and subtraction of matrices
      • Multiplication of a matrix by a scalar
      • Multiplication of a matrix by a vector
      • Multiplication of two matrices
      • Special matrices
      • Linear equations in matrix form
      • Solution of a system of linear equations by row reduction
      • Solution of linear equations using the inverse of the coefficient matrix
      • Inverse matrices
      • Determinant of a square matrix

      Discrete Mathematics (Level D)

      • Factorials
      • Binomial theorem
      • Sequence and series
      • Mathematical induction




      Calculus

      Differentiation – looking at change (Level C)

      • Rate of change – the problem of the curve
      • Instantaneous rate of change and the derivative function
      • Shortcuts for differentiation (including: polynomial and other power functions, exponential functions, logarithmic functions, trigonometric functions, and where the derivative cannot be found)
      • Some applications of differential calculus (including: displacement-velocity-acceleration: when derivatives are meaningful in their own right, twists and turns, and optimization)

      Integration – looking at change (Level C)

      • Area under the curve
      • The definite integral
      • The antiderivative
      • Steps in integration (including: using standard rules of integration, integrals of functions with constant multiples, and integrals of sum and difference functions)
      • More areas
      • Applications of integral calculus

      Differentiation

      • Derivatives
      • Gradient functions
      • Differentiability
      • Derivatives of simple functions
      • Practical interpretations of the derivative
      • Simple applications of the derivative
      • The product rule
      • The quotient rule
      • The chain rule
      • Stationary points
      • Curve sketching
      • Maximum / minimum problems
      • Newton-Raphson method for finding roots
      • Solutions to exercise sets

      Integration

      • Integration of basic functions
      • Integration by guess and check
      • Integration by substitution
      • Definite integration
      • Trapezoidal Rule
      • Simpson’s Rule



      Statistics

      Dealing with data (Level A)

      • Collecting data
      • Organising and displaying data from tables
      • Organising and displaying raw data (including: frequency distribution tables and grouped frequency distribution tables, frequency histograms, and stem-and-leaf plots)
      • Analysing data (including: measuring the centre and spread of data)
      • Data with two variables.

      Statistics and probability (Level B)

      • Collecting data (including: how data are displayed and exploring single variable data sets)
      • Take your chances – probability (including: experimental probabilities, theoretical probabilities, and probability in practice)
      • Describing single data sets (including: the centre and spread of a data set)
      • Describing bivariate data sets