This lesson

• shows how 3 digit numbers are formed
• compares 1, 2 and 3 digit numbers

This lesson

• how addition is done
• develops addition combinations
• uses the combinations in longer problems

This lesson

• shows subtraction to be the opposite of addition
• introduces the combinations used in subtraction

This lesson

• shows multiplication to be compounded addition
• introduces the tables to assist in multiplication

This lesson

• shows division to be the reverse of multiplication
• introduces the notion of a 'remainder'

This lesson

• shows what a fraction is
• introduces the terms numerator and denominator
• explains equivalent fractions

This lesson

• introduces 4-sided figures, the square and the rectangle
• introduces the 3-sided figure, the triangle
• introduces the circle
• illustrates the basic properties of the square (adjacent sides equal) and the rectangle

This lesson

• explains mans' 3 ways of finding time - the sundial, the mechanical watch and the digital display
• teaches the mechanical 24 hour as the basis for time-telling
• outlines the South African money system

This lesson

• introduces the gram and litre as the SI units of mass and capacity
• shows that kilo-, milli- and centi- are abbreviations that indicate multiples of the basic units

This lesson -

• hundreds
• tens
• units

This lesson

• addition as the summation of parts
• addition using 10 combinations

This lesson

• subtraction as removal of elements
• subtraction using combinations

This lesson

• multiplication as an addition short cut
• multiplication using tables
• problems using table look - up

This lesson

• multiplication as an addition short cut
• multiplication using tables
• problems using table look - up

This lesson

• what is a fraction
• definitions of numerator, denominator
• equal fractions

This lesson

• the concept of a fraction
• decimals as fractions in denominator 10
• the correct way of writing decimals

This lesson

• what is a quadrilateral
• the definitions and properties of
• a square
• a rhombus
• a rectangle
• parallelogram

This lesson

• pictogram
• bar chart
• broken line graph
• Cartesian plane

This lesson

• introduces the BODMAS concept
• gives examples of all the BODMAS combinations

This lesson

• shows what factors are
• introduces factor-based shortcuts such as multiplication by 25,
• division by 100
• teaches two-digit division

This lesson

• revises addition of fractions
• revises subtraction of fractions
• introduces BODMAS into fractions

This lesson

• introduces multiplication of fractions that are mixed fractions
• shows division to be the reverse of multiplication

This lesson

• introduces decimals as 10 - based fraction
• shows how to add and subtract decimals

This lesson

• introduces proportion
• introduces ratio
• shows representation on rectangular axes
• uses pictograms, straight-line graphs and bar graphs to represent data
  

This lesson

• introduces four sided figures
• square
• rectangle
• parallelogram
• rhombus
• trapezium
  

This lesson

• revises the digital and rotary clocks
• introduces time loss and time gain in travel

This lesson

• extends BODMAS to two types of brackets
• introduces the division of a fraction by a fraction
• consolidates the use of 'of ' as a multiplier

This lesson

• reinforces the short-cuts in multiplication and division
• shows how to bind the factors of a number
  

This lesson

• revises adding and subtracting fractions
• introduces more difficult problems which contain brackets
  

This lesson

• revises multiplication and division of fractions
• introduces the division of a fraction by a fraction
  
  

This lesson

• reinforces the formation of a decimal fraction
• addition and subtracting decimals
  

This lesson

• revises the pictogram, bar graph, straight line graph and pie chart
  

This lesson

• revises the theorem that the sum of the angles of a triangle is 180 degrees
• introduces acute, obtuse and reflex angles
• shows the parts of a circle and the acute, obtuse and reflex angles within a circle
  
  

This lesson

• introduces the percentage as a fraction with a denominator of 100
• introduces loss and gain
• introduces percentage of a total

This lesson

• revises multiplication and division of decimals
• introduces more difficult problems which contain brackets

This lesson

• revises the concepts of perimeter and area

This lesson

• the difference between a base and an exponent
• the use of exponents as a short-cut to multiplication
• why exponents are added when bases are multiplied
• the use of exponents with number bases as well as unknown bases
  

This lesson

• when a base to a power is raised to a power
• why the exponents are multiplied
• how this affects integer bases
• that the base can be any number (including fractions)
  
  

This lesson

• adding and subtracting like terms that contain exponents
• shows that only like terms may be added
  

This lesson

• shows the replacement of unknowns in an expression by integer values
  
  

This lesson

• division of a monomial by a monomial and division of a polynomial by a monomial
• demonstration of 'long' method of base division
• why exponents can be subtracted when dividing

This lesson

• using the intuitive method of finding the root term
• using fractional exponents to express the square & cube root
• applying this Power to Power to integers and unknown
• showing how prime base are reducible in this way
  

This lesson

• the equation is such because it is balanced
• an operation on one side must be repeated on the other
• that brackets need to be removed before simplifying
  
  

This lesson

• the different numbers systems
• how the number systems are related
• the meaning of OPEN and CLOSED operationsl

This lesson

• the HCF of integers
• the HCF of expressions containing unknowns
• the LCM of expressions
• how to use the LCM to find the common denominators

This lesson

• sum and difference
• product and quotient
• consecutive natural numbers
• consecutive odd and even numbers
  

This lesson

• problems finding the total cost
• problems finding the number bought
• problems finding the unit price
• the 'buy and sell' of trade is repeated again and again

This lesson

• finding the perimeter using integers
• finding perimeter using unknowns
• finding 'area' from 'perimeter' and visa versa
• using word problems with one unknown

this lesson

• let today's age be 'x' years
• then last years is (x - 1) and the next year's is (x + 1)
• let the younger person always be 'x' years
  

This lesson

• the definition of a circle
• the definition of the terms associated with the circle
• basic properties e.g. radius perpendicular to tangent
  

This lesson

• vertically opposite angles
• adjacent angles
• right angles
• complementary angles
• supplementary angles

This lesson

• alternate angles
• adjacent angles
• co-interior angles
• corresponding angles
• supplementary angles
  

This lesson

• the definition of a triangle
• that the sum of its angle is always 180 degrees
• that the exterior angles equals the interior opposite angle
• the differences between : - scalene
• isosceles
• equilateral
• right-angle triangles
  

This lesson

• the square
• the rhombus
• the parallelogram
• the rectangle
• the trapezium
• the kite

This lesson

• the replacement of variables by constant values
  

This lesson

• revises and extends the multiplication of like bases the addition of their exponents
  
  

This lesson

• revises how to find the square root of constant terms that have rational square roots
• shows how to find square roots by raising the term to a of 1/2
  

This lesson

• shows that the negative exponent is the reciprocal term
• multiplies and divides bases which have negative exponents
  
  

This lesson

• introduces scientific notation
• shows conversion of numbers into and out of scientific notation
  

This lesson

• shows how to remove a common factor from two or more terms
  
  

This lesson

• introduces the compound factor
• shows the change of sign outside a compound factor bracket
  
  

This lesson

• introduces the Difference of two squares as a factorisation pattern
• introduces a common factor as preliminary step to the difference of two squares
  

This lesson

• introduces the use of the ' cross method ' as mnemonic for trinomial factorisation
• uses the perfect square trinomial as a starting point

This lesson

• uses the ' cross method ' multiplication to factorise trinomials where both brackets contain negative signs
  

This lesson

• introduces the trinomial which has a (+) sign in one bracket and a (-) sign in the other
• uses only trinomials whose first coefficient is ultimately one

This lesson

• reinforces the trinomial with (+) sign in one bracket and (-) sign in the other
• introduces coefficients other than one

this lesson

• reinforces the notion of an equation having sides that are balanced
• introduces the use of brackets in equations

This lesson

• shows how fractions in equations can be removed by use of common denominators
  

This lesson

• shows how to factorise before simplifying an expression that has no exposed (+) or (-) signs

This lesson

• shows how to find algebraic common denominators
  
  

This lesson

• revises the Cartesian plane
• introduces the straight line graph
  

This lesson

• revises the angles on two lines and three lines
• introduces congruent triangles
• illustrates the Theorem of Pythagorean
  

This lesson

(Proportion, Mean, Median, Mode & Range)

• introduces each of these concepts
• gives illustrations of their usage

This lesson
(Removing a common factor that is a single term)

• to identify a common factor
• to remove the factor
• to then factorise
  
  

This lesson
(Removing a common factor that is composite)

• how to isolate a composite common factor
• how to factorise by removing the this factor
  
  

This lesson
(The difference of two squares)

• to identify the difference of two squares
• to factorise the difference of two squares
  
  

This lesson
(Trinomials - All (+) signs)

• what a trinomial is
• how a trinomial is factorised

This lesson
(Trinomials - Middle term (-) )

• introduces trinomials with the middle term negative and final term positive

This lesson
(Trinomials - 'A' term '1')

• finding which is the larger ((+) or (-)) based on analysis of the middle term sign
• how to use the cross-multiplication in the cross-method to confirm this
  

This lesson
(Trinomials - mixed 'A' terms)

• expands the cross method to include to coefficients of x to the power 2 other than 1

This lesson
(Multiplying and Dividing)

• how fractions can be simplified once they have been factorised
• how parts of fractions can be removed by cancellation of like terms

This lesson
(Adding and Subtracting)

• shows how to find an algebraic L.C.D.
• how to convert all terms to this L.C.D.
• how to factorise if possible

This lesson
(Linear)

• explains the mathematical logic of an equation
• shows students how to isolate terms in an equation
• introduces brackets and fractions into equations
  

This lesson
(Quadratic)

• explains the logic of (a) (b) = 0
• shows that finding values for the unknown is the logical development of factorisation

This lesson
(Inequalities - Linear only)

• explains the number set which can act as definition sets for inequalities
• introduces the Box Method for finding the solution set to an inequality

this lesson
(Simultaneous)

• substitution of a value from one into the other
• adding/subtracting of like coefficients
• multiplication/division of one equation by a constant to make coefficients like

This lesson
(Number Type)

• several number combinations, such as 'even numbers' or 'consecutive numbers'
• the key words, such as 'sum', 'difference' that recur in these problems
  

This lesson
(Commercial Type)

• the basic equation of (Unit Price)(Number)= Total cost
• how to find values for each one of these unknowns and how to find profit
  

This lesson
(Distance, Speed and Time)

• introduces the basic equation Distance = (Speed)(Time)
• shows how to extricate time for ETA and ETD data

This lesson
(Age Type)

• teaches that present age is always 'x' years
• shows that all our ages can then be related to this age

This lesson
(Quadratic Equations)

• shows the difference between functions and relations
• gives three definitions of functions
• shows how relations may be tested as being functions or non-functions
  
  

This lesson
Tutorial

• shows that the circle graph is the union of two functions(the semi-circle functions)plots the full circle, semi-circle and quarter circles in each of 0<x<0
  

This lesson
Parabola

• shows how to draw the function f (x) = ax 2 + b
• explains the effect of changing the values and signs of 'a' and 'b'

• This lesson : - shows how to draw the hyperbola
• draws the function under quadrant restrictions
  

This lesson
(Straight Line)

• teaches the straight line function by substitution of values method, i.e. the Table Method
• then shows the Gradient Intercept Method
• then uses the Dual Intercept Method

This lesson
(Simplifying expressions one)

• simplification of single term exponential expressions. The lesson is structured around the following five rules : - remove surd signs, decimals and mixed numbers
• factorise to prime bases
• use power to power law
• multiply and divide bases
• remove negative exponents

This lesson
(Simplifying expressions two)

• simplification of exponential expressions with (+) and (-) signs between the bases.
• give each exponents its own base
• the term containing an unknown is replaced by 'k'
• simplifying - replace 'k' if the answer still contains a 'k'

This lesson
(Linear Equations)

• exponential equations of the linear type, i.e. the unknown has only one solution
• writing exponential equations in the form of expressing one term as a power to another base

This lesson
(Quadratic Equations)

• exponential equations of the quadratic and polynomial type, i.e. where the unknown has more than one root
• simultaneous exponential equations
  

This lesson
(Quadrilaterals)

• highlights the difference between the definition and properties of a figure
• lists and explains the properties of all the quadrilaterals

This lesson
(Mid-point Theorem)

• revises the other triangle theorems
• explains the mid-point theorem
  
  

This lesson
(Definitions)

• introduces the circle in quadrant 1
• explains the basic trigonometric ratios
• applies the ratios in right angled triangles in 2-dimentional and 3- dimensional sketches

This lesson

• explains why a quadratic has determinable values (as opposed to factorisation without solving)
• shows how quadratics can be solved using the following steps :
  1. Make equation standard form as x ² (a) + x(b) + c = 0
  2. Factorise so that (a)(b) = 0
  3. Now find values for a, b
  

This lesson

• completion of the square using the following steps :
  
• Make equation standard
  Isolate the 'x' terms on the left-hand side of the equation
• Isolate x ² term - divide each term by 'a'
  Add {1/2 coefficient of x}², to both sides
• Factorise the left-hand side of the equation as
  [x.....the sign of the middle term .....3rd term]²
• Simplifying the right-hand side
  Square root both sides
• Solve for x
  
  

This lesson

• derives the quadratic formula and applies the formula for the solution of Quadratic Equations
  
  

This lesson

• shows how to remove fractions from within an equation by using a denominator applicable to all terms in the equation
  
• uses the simple and complex fractions including the use of brackets

This lesson

• Division of a monomial by a monomial and division of a polynomial by a monomial
• demonstration of 'long' method of base division
• uses a quadratic of the same form as a polynomial to solve for the polynomial
  

This lesson

• equations containing a single surd sign can be solved by :
  
• writing the equation in standard form
• isolating the surd sign
• squaring both sides of the equation
• checking values in the original equation

This lesson

• Simultaneous Equations of the Linear-Quadratic type :
  
• using the substitution of one value for another
• using addition, subtraction when coefficients are similar
• using graphical solutions
  

This lesson

• shows how linear inequalities are solved
  
• shows how quadratic inequalities can be solved by one of two methods
• explains why denominatorial unknowns cannot be used as denominators for every term

This lesson

• show the origin of the discriminant
  
• explains the significance of the discriminants
• outlines the conditions for the discriminants
• solves for a second unknown, based on data about the nature of the roots for the first unknown

This lesson

• uses the discriminant to prove the roots to be of a certain type
• revises the solution of a second unknown using the nature of the roots of the first equation

This lesson

• -y = a (x-t)² + P, used to find the equation for a function whose Turning Point and 1 other point are given on a sketch
• -y = a (x-1st root)(x-2nd root ), used to find the equation for a function whose roots and one other point are given on a sketch
• - y = ax² + bx + c, used to find the equation for a function where any 3 points on the function are given

This lesson

• a linear program is merely the solution set of two or more linear inequalities
• that the formation of the inequalities is no different from the formation of equations in applied quadratic and calculus questions
• what is meant by ' feasible region'; 'optimisation point'; optimisation area, and; profit line and equation

this lesson

• what 'absolute value' or 'modulus' is
• how it is remove from an equation by :
  
• squaring both sides of the equation
• replacing the modulus by + and - values
• why roots for the unknown in a modulus equation will not always satisfy the original equation

This lesson

• sketching of the Absolute Value Function
• the function combinations of :
  
• quadratic and absolute value
• straight line and absolute value
• hyperbola and absolute value
• circle and absolute value
  
  

This lesson

• remove surd signs, decimals and mixed numbers
• factorise to prime bases
• use power to power law
• multiply and divide bases
• remove negative exponents
  
  

This lesson

• give each exponents its own base
• the term containing an unknown is replaced by 'k'
• simplify - replace 'k' if the answer still contains a 'k'
  

This lesson

• exponential equations of the linear type, i.e. the unknown has only one solution
• writing exponential equations in the form of expressing one term as a power to another base
  

This lesson

• exponential equations of the quadratic and polynomial type, i.e. where the unknown has more than one root
• simultaneous exponential equations
  
  

This lesson

• explains what the Remainder Theorem is
• shows how it is applied
• explains the Factor Theorem
• shows how the latter can be used to solve polynomials
  
  

This lesson

• introduces the student to the six trigonometric ratios
• shows how the circle is divided into 4 quadrants
• explains the rules for each quadrant
• gives examples in each quadrant
  

• derives the special angles from a circle radius 2
• applies the special angles to all quadrants
• remove negative angles by adding 360 degrees (or its multiplies) to any given negative angle
• shows that the co-ratios are just inverse functions and the exchange of 'x' for 'y' thus makes them relatively straight forward
  

This lesson

• shows that all trigonometric expressions can be expressed as sines or cosines
• teaches the student to reduce all ratios in an expressions to a sine / cosine / number combination
• also introduces the conventional ratios e.g.;
  sin²q+ cos²q = 1
  sec²q = 1 + tan² q
  cosec²q = 1 + cot² q

This lesson

• solves trigonometric equations which contain a single ratio
• solves in the range of - 360° to + 360°
• introduces the general solution to an equation without given restrictions

This lesson

• test the student knowledge of ratio usage
• expand the use of co-ratios
• introduces heights and distances

This lesson

• introduces the Sine Rule
• outlines the two cases when the rule should be used
• explains why the ambiguous case arises
  

This lesson

• introduces the Cosine Rule
• outlines the two cases when the rule should be used
• gives alternative formulations of the rule
  
  

This lesson

• introduces the rule that area of the triangle is 1/2 (base)(height)
• derives the Area Rule (1/2 ab Sin C) from the first formulation
• uses the Area Rule in 2 dimensional problems

This lesson

• uses colours to indicate the horizontal plane intersecting other planes
• introduces the Link side Method
• introduces the Substitution Method
  

This lesson

• uses colour (green) to indicate horizontal planes
• introduces Link Side method
• introduces the Substitution method
  

This lesson

• introduces the sine, cosine, tangent graphs
• explains the amplitude, period, horizontal axis shift
• uses interpretation of two or more functions
  

This lesson

• that the line from the centre of the circle to the mid-point
  of a chord is perpendicular to the chord
• that the angle at the centre of the circle is twice the angle at the circumference
• that the angle in a semi-circle is 90°
  

This lesson

• explains what a cyclic quadrilateral
• illustrates each of the three theorems which makes a quadrilateral cyclic

This lesson

• explains what an alternate segment is
• shows that the angle created there is equal to the angle between the chord that makes the segment and the tangent at that point

This lesson

• explains what concurrency is
• introduces all the terms used in concurrency

This lesson

• explains what a mathematical progression is
• isolates Arithmetic & Geometric progressions
• introduces the subtraction and division of tests
• introduces the Term Formulae for Arithmetic & Geometric Progressions

This lesson

• introduces the Arithmetic & Geometric means
• introduces concepts from other sections into AP and GP problems
  
  
  

This lesson

• introduces logarithmic expressions as another form of an exponential equation
• shows the relationship between the log laws and the laws of exponents
• uses change of base law to simplify most logarithmic expressions
  
  

This lesson

• solve logarithmic equations :
  
• with a single on each side
• which simplify to Quadratic expressions
• which require change of base applications
• that contain inequalities

This lesson

• teaches the exponential function y = a(to the power x)
• teaches the logarithmic function as the inverse of the exponential function
• shown how the mappings around the horizontal and vertical axes take place
  

This lesson

• teaches differentiation
• shows how differentiation changes with fractions, denominators and surd signs
• explains the theory behind the finding of the discriminant
• teaches first principles

This lesson

• shows the five steps in sketching any polynomial function
• analyses sketches of functions into the five steps
• analyses sketches of more than one function

This lesson

• uses language-based questions to :
  
• solve maxima and minima problems
• solve distance, speed, and time problems
• introduce related rates

This lesson

• shows simple interest versus compound interest
• uses the formulae each
• manipulates the formulae

This lesson

• the distance between two points
• the mid-point of two points
• proportion division of the line joining two points
• gradient of a straight line
• equation of a straight line
• the equation of a circle
• tangents and secants to a circle
• locus

This lesson

• extends identities to include co-ratios and compound angles

This lesson

• single ratio
• multiple ratio
• the tangent type
• the difference of two squares
• the trinomial type
• the four term type
• the pythagorus type

this lesson

• derives the formulae Cos (A+B) geometrically
• derives the formulae for the 10 derivations based on Cos(A+B)
• applies compound angles to each of the derivations

This lesson

• explains what geometric similarity is
• how to analyse sketches containing similar figures
• the I method
  
  

This lesson

• sets out the conditions for geometric proportion
• shows how triangles can be found from given proportionalities