Math Enrichment (PRIME)

• About
• Ages 10-12
• Ages 11-13
• Ages 12-14
• Ages 13-15
• Ages 14-16

• About
• Ages 10-12
• Ages 11-13
• Ages 12-14
• Ages 13-15
• Ages 14-16

	Whole Numbers We live in the world of numbers, surrounded by numerical facts, data and information. They serve as a foundation for many other branches of mathematics. In this course, we develop the ideas of prime and composite numbers. Finally, we explore some interesting patterns and relationships. Prerequisites: Basic arithmetic Duration: 15 hours     |    Self-paced learning                more Whole Numbers We live in the world of numbers, surrounded by numerical facts, data and information. They serve as a foundation for many other branches of mathematics. In this course, we develop the ideas of prime and composite numbers. Finally, we explore some interesting patterns and relationships. Prerequisites: Basic arithmetic Duration: 15 hours     |    Self-paced learning                less Topics covered: Factors and multiples, LCM and HCF, Squares, Cubes, Square roots, Cube roots, Number patterns, Special numbers (e.g. Triangular numbers, Fibonacci numbers). Students will learn: • To identify prime and composite numbers and list them • The difference between a divisor and a factor • To find the Highest Common Factor and Least Common   Multiple • Divisibility rules to determine divisibility by a number • That geometrical and numerical patterns can be   represented symbolically • About Triangular numbers, Fibonacci sequence, Pascal’s   Triangle etc...		US$ 34.99

Geometry There is a saying 'Where there is matter, there is geometry'. As it suggests geometry is the study of the size, shape and form. You will find their application in art, architecture, robotics, graphics and many more! This course introduces to the basics of geometry, the relationships between points, lines and angles and also to properties of polygons. Prerequisites: Basic arithmetic Duration: 10 hours     |    Self-paced learning                 more Geometry There is a saying 'Where there is matter, there is geometry'. As it suggests geometry is the study of the size, shape and form. You will find their application in art, architecture, robotics, graphics and many more! This course introduces to the basics of geometry, the relationships between points, lines and angles and also to properties of polygons. Prerequisites: Basic arithmetic Duration: 10 hours     |    Self-paced learning                 less Topics covered: Angle Properties, including angles at a point, on a straight line, vertically opposite angles, angles formed by parallel lines, angles formed by triangles. Polygons, sum of interior and exterior angles formed by convex polygons. Students will learn: • That angle is a measure of rotation • That angles can be classified according to their unique   properties • That interior and exterior angles of polygon are dependent   on its number of sides. • To use appropriate angle properties to calculate unknown   angles of regular and irregular polygons.

US$ 34.99

Mensuration I Mensuration is an art of measuring! In this course, you will learn formulas for computing perimeter and areas of plane geometrical figures such as triangles, quadrilaterals and circles based on their known dimensions. Prerequisites: Basic geometry, Arithmetic Skills Duration: 15 hours     |    Self-paced learning                 more Mensuration I Mensuration is an art of measuring! In this course, you will learn formulas for computing perimeter and areas of plane geometrical figures such as triangles, quadrilaterals and circles based on their known dimensions. Prerequisites: Basic geometry, Arithmetic Skills Duration: 15 hours     |    Self-paced learning                 less Topics covered: Area and perimeter of triangles, parallelograms, trapeziums and rectangles, Circumference and Area of circles. Students will learn: • To classify triangles and quadrilaterals • To calculate the perimeter and area of various   quadrilaterals • To calculate the circumference and area of circle • To use the above facts to calculate the perimeter and area   of compound figures

US$ 34.99

Everyday Arithmetic The course explains the concepts of equivalent fractions, simplifying fractions, mixed numbers and improper fractions. Then it explores decimals and percentages and how they relate to fractions. Once you've mastered the basics of fractions, decimals and percentages, you'll be able to apply them to different problems in everyday situations. Prerequisites: Arithmetic skills, Basic algebra Duration: 20 hours     |    Self-paced learning                 more Everyday Arithmetic The course explains the concepts of equivalent fractions, simplifying fractions, mixed numbers and improper fractions. Then it explores decimals and percentages and how they relate to fractions. Once you've mastered the basics of fractions, decimals and percentages, you'll be able to apply them to different problems in everyday situations. Prerequisites: Arithmetic skills, Basic algebra Duration: 20 hours     |    Self-paced learning                 less Topics covered: Fractions, Decimals, Percentages, Conversion from one form to the other, Word problems Students will learn: • What are fractions - proper, improper and mixed numbers? • About equivalent fractions with visual demonstrations. • To represent fractions and mixed numbers on a number   line. • What are decimals and how it relates to fractions? • To order fractions and decimals • The four operations on fractions and decimals • What are percentages and how it relates to fractions and   decimals? • To compare fractions, decimals and percentages and to   convert one form to the another. • How it helps to solve problems in everyday situations.

US$ 44.99

• About
• Ages 10-12
• Ages 11-13
• Ages 12-14
• Ages 13-15
• Ages 14-16

The Real Number System There are different sorts of numbers, with different properties. In this course, you will become fluent in recognising and dealing with prime numbers, irrational numbers, fractions and decimals. Prerequisites: Basic knowledge of whole numbers, Fractions & Decimals, Integers Duration: 15 hours     |    Self-paced learning                 more The Real Number System There are different sorts of numbers, with different properties. In this course, you will become fluent in recognising and dealing with prime numbers, irrational numbers, fractions and decimals. Prerequisites: Basic knowledge of whole numbers, Fractions & Decimals, Integers Duration: 15 hours     |    Self-paced learning                 less Topics covered: Integers, Rational and Irrational numbers, Squares and Square roots, Standard form, Estimation and Approximation, Significant figures, Use of a scientific calculator. Students will learn: • That the real numbers form an extension of the rational   numbers • That real numbers are manifested in real-life situations • How to compare and contrast whole numbers, integers,   rational, and irrational numbers • How to use a calculator to calculate complicated sums with   real numbers • That estimation can be used to judge the reasonableness   of results • How to round off numbers in different ways, to different   degrees of accuracy and for different purposes in real life • How to convert numbers to scientific notation or standard   form and vice versa • How to solve problems of standard form which require the   use of calculator and without a calculator

US$ 34.99

Algebra I Mathematics is sometimes called the science of patterns. In maths, economics, science and art we sometimes need to use algebra to write down what patterns we find and to help us look for others. In this course, you will learn how to use algebra to represent relationships between different quantities and solve problems. Prerequisites: Knowledge of whole numbers and real numbers (fractions, decimals, factors, multiples, HCF, LCM) Duration: 20 hours     |    Self-paced learning                 more Algebra I Mathematics is sometimes called the science of patterns. In maths, economics, science and art we sometimes need to use algebra to write down what patterns we find and to help us look for others. In this course, you will learn how to use algebra to represent relationships between different quantities and solve problems. Prerequisites: Knowledge of whole numbers and real numbers (fractions, decimals, factors, multiples, HCF, LCM) Duration: 20 hours     |    Self-paced learning                 less Topics covered: Algebraic symbols and rules, Manipulate and simplify algebraic expressions, Evaluating expressions, Algebraic fractions, Solving linear equations, Simple linear inequalities. Students will learn: • How mathematical and real-life situations can be   represented and analysed using algebraic symbols and   rules • How to manipulate and simplify algebraic expressions • That algebra is a tool used to solve problems in real life • How to solve linear equations by obtaining equilibrium on   both sides • That real-life situations can be modeled using equations

US$ 44.99

Arithmetic Problems Percentages are often used in newspapers as a quick way to summarise information about politics, science and money, to name a few. In this course, we will look at some of the many ways that maths can be used in real life. Prerequisites: Basic knowledge of real numbers (fractions, decimals) Basic algebra (algebraic terms and expressions) Duration: 10 hours     |    Self-paced learning                 more Arithmetic Problems Percentages are often used in newspapers as a quick way to summarise information about politics, science and money, to name a few. In this course, we will look at some of the many ways that maths can be used in real life. Prerequisites: Basic knowledge of real numbers (fractions, decimals) Basic algebra (algebraic terms and expressions) Duration: 10 hours     |    Self-paced learning                 less Topics covered: Introduction to Percentages, Percentage increase and decrease, Ratios, Average Rate, Direct and Inverse Proportion. Students will learn: • That mathematical problems can be expressed via   symbolic representation. • How to solve problems involving the use of units of mass,   length, time and money. • How to solve problems involving ratio and proportion. • How to recognise and use common measures and rate.

US$ 34.99

Arithmetic in Daily Life Some of the most useful and interesting applications of mathematics concern the real world. They are important in finance, sales and tax. In this course, you will learn how arithmetic helps you in these areas. Prerequisites: Basic knowledge of real numbers, ratio, rate and proportion. Basic algebra (algebraic terms and expressions) Duration: 10 hours     |    Self-paced learning                 more Arithmetic in Daily Life Some of the most useful and interesting applications of mathematics concern the real world. They are important in finance, sales and tax. In this course, you will learn how arithmetic helps you in these areas. Prerequisites: Basic knowledge of real numbers, ratio, rate and proportion. Basic algebra (algebraic terms and expressions) Duration: 10 hours     |    Self-paced learning                 less Topics covered: Profit and Loss, Discount, Commission, Simple and Compound Interest, Hire Purchase, Taxation, Money Exchange. Students will learn: • That there are a variety of strategies which can be applied to   solve mathematical and real-life problems. • How to solve consumer problems using arithmetic   operations.

US$ 34.99

Mensuration II The volume of a solid object is how much space it occupies. By the end of this course, you will learn the formulas to work out the volume and surface area of cuboids, prisms, pyramids, cones and spheres and apply them to real world problems and to find the volume of compound solids. Prerequisites: Mensuration I Duration: 15 hours     |    Self-paced learning                 more Mensuration II The volume of a solid object is how much space it occupies. By the end of this course, you will learn the formulas to work out the volume and surface area of cuboids, prisms, pyramids, cones and spheres and apply them to real world problems and to find the volume of compound solids. Prerequisites: Mensuration I Duration: 15 hours     |    Self-paced learning                 less Topics covered: Arc length and Area of sectors, Volumes and Surface areas of cube, cuboids, prism, cylinder, cone, sphere and pyramid. Students will learn: • To compare and classify geometric figures. • To calculate arc length and area of a sector. • To calculate and solve problems involving surface area and   volume. • To solve mathematical and real life problems.

US$ 34.99

Intermediate Algebra In this course you will learn to expand algebraic expressions using identities and also to factorise algebraic expressions. You will note that expansion and factorisation are reverse processes of each other. You will also learn to manipulate and simplify algebraic fractions. Prerequisites: Basic Arithmetic Duration: 20 hours     |    Self-paced learning                 more Intermediate Algebra In this course you will learn to expand algebraic expressions using identities and also to factorise algebraic expressions. You will note that expansion and factorisation are reverse processes of each other. You will also learn to manipulate and simplify algebraic fractions. Prerequisites: Basic Arithmetic Duration: 20 hours     |    Self-paced learning                 less Topics covered: Expansion, Identities, Factorisation by grouping, Factorising quadratics, Changing subject of a formula, Algebraic fractions, Equations involving algebraic fractions. Students will learn: • Expansion and factorisation of algebraic expressions can   be represented geometrically. • Expansion and factorisation are reverse processes of each   other. • The use of algebraic identities helps to expedite the solving   of numerical problems. • Manipulate and simplify algebraic fractions. • Manipulate to change the subject of a formula such that   equivalence is maintained.

US$ 44.99

• About
• Ages 10-12
• Ages 11-13
• Ages 12-14
• Ages 13-15
• Ages 14-16

Trigonometry I Trigonometry is an ancient part of mathematics - dealing with triangles, their sides and their angles. Originally its development was spurred on by interest in astronomy and the positions of stars. It remains a vital part of applied mathematics and measurement to this day! Prerequisites: Fractions, ratio and proportion Simple Algebra (algebraic expressions, solving linear equations and powers) Duration: 10 hours     |    Self-paced learning                 more Trigonometry I Trigonometry is an ancient part of mathematics - dealing with triangles, their sides and their angles. Originally its development was spurred on by interest in astronomy and the positions of stars. It remains a vital part of applied mathematics and measurement to this day! Prerequisites: Fractions, ratio and proportion Simple Algebra (algebraic expressions, solving linear equations and powers) Duration: 10 hours     |    Self-paced learning                 less Topics covered: Pythagoras Theorem, Trigonometric ratios for acute angles for a right-angled triangle, Angle of elevation, Angle of depression. Students will learn: • How Pythagoras’ Theorem can be used to solve a variety of   mathematical and real-life problems. • What trigonometric ratios are. • How they can be applied to measure distances and angles   in real-life situations. • How to find the trigonometrical values of sine, cosine and   tangent of an angle with the help of a calculator. • How to solve problems involving trigonometrical ratios in   right-angled triangles. • How to solve problems involving angle of elevation and   angle of depression.

US$ 34.99

Statistics I Whenever large quantities of information need to be summarised we need to use statistics. In this course, we will look at two principal ways of doing this. One way is the use of graphs and charts - these help us understand data quickly in a pictorial form. The second way is concerned with a numerical summary data using different kinds of averages. Prerequisites: Simple Algebra (algebraic expressions, solving linear equations and powers) Duration: 8 hours     |    Self-paced learning                 more Statistics I Whenever large quantities of information need to be summarised we need to use statistics. In this course, we will look at two principal ways of doing this. One way is the use of graphs and charts - these help us understand data quickly in a pictorial form. The second way is concerned with a numerical summary data using different kinds of averages. Prerequisites: Simple Algebra (algebraic expressions, solving linear equations and powers) Duration: 8 hours     |    Self-paced learning                 less Topics covered: Bar graphs, Pictograms, Line Graphs, Pie Chart, Histograms, Mean, Mode and Median. Students will learn: • About how statistics is useful in real-life situations and how   people use statistical data to suit their purposes • That data can be represented in different forms, each with   its own advantages and disadvantages. • How to represent data appropriately e.g. pie chart, bar   graphs, pictograms, dot diagrams, stem and leaf diagrams,   line graphs and histograms with equal intervals. • How to interpret graphs or charts of given situations. • How to evaluate the mean, median and mode for   ungrouped data. • How to select and justify the use of appropriate central   tendencies.

US$ 34.99

Algebra II In Algebra I we learnt about terms, and solving simple equations. Now we need to extend our knowledge to solve harder equations. The kind of equations we will look at now are called quadratic equations. We will see how to draw the graphs of quadratic functions (called 'parabolas') and we will need to develop some interesting new ideas in order to be able to solve the equations! Prerequisites: Algebra I (algebraic formulae, expressions, algebraic fractions, solving linear equations) Duration: 16 hours     |    Self-paced learning                 more Algebra II In Algebra I we learnt about terms, and solving simple equations. Now we need to extend our knowledge to solve harder equations. The kind of equations we will look at now are called quadratic equations. We will see how to draw the graphs of quadratic functions (called 'parabolas') and we will need to develop some interesting new ideas in order to be able to solve the equations! Prerequisites: Algebra I (algebraic formulae, expressions, algebraic fractions, solving linear equations) Duration: 16 hours     |    Self-paced learning                 less Topics covered: Shape of Quadratic graphs, Plotting quadratic graphs, Solving quadratic equations graphically, Factorising quadratics, The quadratic formula for solving any quadratic equation. Students will learn: • About how to plot and sketch quadratic graphs • How the shape of a quadratic graph depends on the   coefficients • That there are different ways that we can solve quadratic   equations • The procedure for factorising a quadratic equation - what   factorising means and how to do it quickly • The derivation of the quadratic formula (for solving any   quadratic equation) and how to use it • That real-life problems can give rise to quadratic equations   and that we can solve the equations using the methods   learnt

US$ 34.99

Congruence and Similarity Geometry has many applications in everyday life, particularly the topics - congruence and similarity. You can find their application in construction especially weight-bearing structures, and in maps and scales. In this course, you will learn how the area and volume of similar objects are related! Prerequisites: Fractions, ratio and proportion, Basic geometry Duration: 8 hours     |    Self-paced learning                 more Congruence and Similarity Geometry has many applications in everyday life, particularly the topics - congruence and similarity. You can find their application in construction especially weight-bearing structures, and in maps and scales. In this course, you will learn how the area and volume of similar objects are related! Prerequisites: Fractions, ratio and proportion, Basic geometry Duration: 8 hours     |    Self-paced learning                 less Topics covered: Congruence and Similarity, Proof of congruent and similar triangles, Area and volume of similar figures and solids. Students will learn: • The meaning of the terms 'similar' and 'congruent' • That a proportional change in the lengths of a shape will   result in a similar shape. • How to derive and apply the relationships between similar   objects.

US$ 34.99

Indices Indices is a useful mathematical notation that is used pervasively in fields such as biology and other sciences. It is interesting to know that different types of quantities, such as population, bank balances, radioactive materials, etc., grow or decrease over time as exponential models. In this course, you will learn the rules to perform basic operations on indices and the ways to apply them in problem solving. Prerequisites: Real number system, Basic algebra Duration: 15 hours     |    Self-paced learning                 more Indices Indices is a useful mathematical notation that is used pervasively in fields such as biology and other sciences. It is interesting to know that different types of quantities, such as population, bank balances, radioactive materials, etc., grow or decrease over time as exponential models. In this course, you will learn the rules to perform basic operations on indices and the ways to apply them in problem solving. Prerequisites: Real number system, Basic algebra Duration: 15 hours     |    Self-paced learning                 less Topics covered: Indices, Laws on indices, Fractional indices, Exponential equations, Applications of indices. Students will learn: • To identify the base and the exponent in an index notation • The meaning of negative, fractional and zero indices. • To use the laws of indices for all rational exponents. • To solve exponential equations of the form a = bx    where a = bn. • The applications of indices and indicial equations in real life   situations.

US$ 34.99

Set Theory This course reviews basic notions of Set Theory that will be needed as a background for most of the advanced mathematics courses. It familiarizes students with abstract mathematical thinking. In this course, you learn basic facts such as subsets, complement, union and intersections and also justify them with the aid of Venn diagram. Prerequisites: Number system, Basic Inequality, Simple geometrical figures Duration: 15 hours     |    Self-paced learning                 more Set Theory This course reviews basic notions of Set Theory that will be needed as a background for most of the advanced mathematics courses. It familiarizes students with abstract mathematical thinking. In this course, you learn basic facts such as subsets, complement, union and intersections and also justify them with the aid of Venn diagram. Prerequisites: Number system, Basic Inequality, Simple geometrical figures Duration: 15 hours     |    Self-paced learning                 less Topics covered: Introduction to Set Notations, Union and Intersection of sets, subsets, complements, Venn Diagrams. Students will learn: • That mathematical information can be represented by set   notations • How Venn diagram helps in organising, recording and   communicating mathematical ideas • That set notations can be used to solve mathematical and   real-life problems • To organise data using set notation and Venn diagram • To formulate and solve problems using set theory

US$ 34.99

• About
• Ages 10-12
• Ages 11-13
• Ages 12-14
• Ages 13-15
• Ages 14-16

Graphs I Sometimes the human brain works best when it has a picture to accompany something more technical. In mathematics we use graphs alongside algebra to help us understand relationships between different quantities. We will look at the algebraic and graphical details of an important sort of equation - the linear equation - and analyse straight line graphs. Prerequisites: Algebra I and II (Solving linear equations, Solving simultaneous linear equations, Solving quadratic equations, Simultaneous non linear equations in 2 unknowns.) Duration: 20 hours     |    Self-paced learning                 more Graphs I Sometimes the human brain works best when it has a picture to accompany something more technical. In mathematics we use graphs alongside algebra to help us understand relationships between different quantities. We will look at the algebraic and graphical details of an important sort of equation - the linear equation - and analyse straight line graphs. Prerequisites: Algebra I and II (Solving linear equations, Solving simultaneous linear equations, Solving quadratic equations, Simultaneous non linear equations in 2 unknowns.) Duration: 20 hours     |    Self-paced learning                 less Topics covered: Cartesian Coordinates, Gradient of a line, Equations of Linear Functions of the form y = mx + c and their sketch, Parallel and perpendicular lines, Solving simultaneous equations graphically, Travel graphs, Distance-time and Speed-time graphs. Students will learn: • About how graphs can help us in analysing trends,   patterns and relationships • How the Cartesian coordinates system is used to represent   algebraic relationships • To use graphs as a pictorial representation of algebraic   equations and to model real-life situations • To use graphs to analyse numerical data for trends,   patterns and relationships • To draw graphs of linear functions • To solve simultaneous linear equations using a graphical   method • To interpret and use graphs in practical situations

US$ 44.99

Quadratic Functions You should have already learnt about quadratic equations, and quadratic graphs, their properties and uses. We know that a number of different real life problems can be turned into a quadratic equation and then solved using factorisation or the quadratic formula. In this module we will look closely at some more details of quadratic functions and graphs. Prerequisites: Algebra II (Expansion and factorisation, identities, algebraic fractions, solving quadratic equations), Graphs of Quadratic Functions and their properties. Duration: 20 hours     |    Self-paced learning                 more Quadratic Functions You should have already learnt about quadratic equations, and quadratic graphs, their properties and uses. We know that a number of different real life problems can be turned into a quadratic equation and then solved using factorisation or the quadratic formula. In this module we will look closely at some more details of quadratic functions and graphs. Prerequisites: Algebra II (Expansion and factorisation, identities, algebraic fractions, solving quadratic equations), Graphs of Quadratic Functions and their properties. Duration: 20 hours     |    Self-paced learning                 less Topics covered: Maximum and minimum values of a quadratic function, Graphs of quadratic functions, Discriminant, Sum and Product of roots, Solving quadratic inequalities. Students will learn: • How to find the maximum or minimum value of quadratic   function by completing the square • How to sketch quadratic functions by observing the value of   'a' and expressing the function in the form y = a(x-h)2+k • To determine the equation of quadratic function from the   graph • To choose and apply different methods to solve quadratic   equations efficiently and elegantly • To investigate how the nature of roots is related to the   'discriminant' and use the results to solve for unknown   constants in an equation • To extend the knowledge on the nature of roots and   discriminant to points of intersection of line and a curve • To establish the relationship between roots and coefficients   of a quadratic equation to solve questions

US$ 44.99

Surds and Logarithms You would have learnt about whole number powers already, such as 2n where 'n' is a whole number. What happens when 'n' is not a whole number? In this module we will look at such numbers and explain how they can be handled. Logarithms are a clever invention, designed to handle these numbers in a different way. Prerequisites: Positive, negative, zero and fractional indices, Laws of indices and indicial equations. Duration: 25 hours     |    Self-paced learning                 more Surds and Logarithms You would have learnt about whole number powers already, such as 2n where 'n' is a whole number. What happens when 'n' is not a whole number? In this module we will look at such numbers and explain how they can be handled. Logarithms are a clever invention, designed to handle these numbers in a different way. Prerequisites: Positive, negative, zero and fractional indices, Laws of indices and indicial equations. Duration: 25 hours     |    Self-paced learning                 less Topics covered: Operations on Surds, Rationalisation of denominator, Laws of Logarithms including change in base, Solving exponential and logarithmic equations, Graphs of exponential and logarithmic functions. Students will learn: • What are Surds and their rules • Simplify numbers/expressions in surds • To convert exponential form to logarithmic form • To simplify logarithmic expressions using the laws of   logarithms • To solve exponential and logarithmic equations • To illustrate exponential and logarithmic functions   graphically and the relationship between the two functions. • To apply the exponential and logarithmic functions to solve   problems in real-life

US$ 44.99

Polynomials and more (The Binomial Theorem, The Remainder and Factor Theorem, Partial fractions) Can you tell me the coefficient of x in (1 + x)2 ? Can you factorise x2 + 3x + 2 ? Pretty easy? What's the coefficient of x6 in (1 + x)10 ? Factorise x3 - 4x2 - 19x - 14. Not so easy! Enter this section to find out how we use some important theorems to help us solve these kinds of questions. Prerequisites: Algebra (Expansion and factorisation, Algebraic Fractions, Solving quadratic equations by factorisation and by formula) Duration: 20 hours     |    Self-paced learning                 more Polynomials and more (The Binomial Theorem, The Remainder and Factor Theorem, Partial fractions) Can you tell me the coefficient of x in (1 + x)2 ? Can you factorise x2 + 3x + 2 ? Pretty easy? What's the coefficient of x6 in (1 + x)10 ? Factorise x3 - 4x2 - 19x - 14. Not so easy! Enter this section to find out how we use some important theorems to help us solve these kinds of questions. Prerequisites: Algebra (Expansion and factorisation, Algebraic Fractions, Solving quadratic equations by factorisation and by formula) Duration: 20 hours     |    Self-paced learning                 less Topics covered: Operations of polynomials, The remainder and factor theorems, Factorising and solving cubic equations, Expressing algebraic fractions as partial fractions, Use the Binomial Theorem for the expansion of (x + y)n. Students will learn: • That the real numbers form an extension of the rational   numbers. • That we can divide polynomials in a similar way to   numbers, getting a quotient and remainder. • Understand, state and use the Remainder and Factor   Theorems to factorise/solve polynomial expressions or   equations. • How to find the remainder when a polynomial is divided by a   linear factor. • How to find factors of polynomials. • How to factorize cubic expressions or polynomials of higher   degree using the Factor Theorem • Translate problems involving remainder and factor   theorems into mathematical equations and solve them. • That rational functions can be written as partial fractions.

US$ 44.99

Probability Probability plays an important role in our daily life. We experience it when we play a casino game or roll a die in a simple board game or when we flip a coin to make a decision. This course introduces the concept of theoritical and experimental probability and presents the different strategies to find the probability of a single event and combined events. Prerequisites: Basic Algebra, Fractions, Decimals and Percentages Duration: 15 hours     |    Self-paced learning                 more Probability Probability plays an important role in our daily life. We experience it when we play a casino game or roll a die in a simple board game or when we flip a coin to make a decision. This course introduces the concept of theoritical and experimental probability and presents the different strategies to find the probability of a single event and combined events. Prerequisites: Basic Algebra, Fractions, Decimals and Percentages Duration: 15 hours     |    Self-paced learning                 less Topics covered: Introduction to probability, Possibility diagrams, Probability Trees, Independent events. Students will learn: • That probability is the mathematical formulation of   likelihood to quantify risks and chance. • To calculate the theoretical probability and make inferences   from data to estimate the probability of an event • To predict possible outcomes of real life situations. • To list all the possible outcomes for more complex   experiments systematically, using possibility diagram and   tree diagrams • To calculate the probability of combined events using   Addition and Multiplication Rules

US$ 34.99

Statistics II The study of Statistics includes collecting, summarizing, organising and drawing conclusions from data. This course will focus upon the statistical methods commonly to represent large set of data such as grouped frequency table, histograms, frequency polygons and cumulative frequency curves. Also you will be introduced to the ways of finding measures of central tendency for such data. Prerequisites: Fractions, Decimals and Percentages, Statistics I, Basic probability Duration: 15 hours     |    Self-paced learning                 more Statistics II The study of Statistics includes collecting, summarizing, organising and drawing conclusions from data. This course will focus upon the statistical methods commonly to represent large set of data such as grouped frequency table, histograms, frequency polygons and cumulative frequency curves. Also you will be introduced to the ways of finding measures of central tendency for such data. Prerequisites: Fractions, Decimals and Percentages, Statistics I, Basic probability Duration: 15 hours     |    Self-paced learning                 less Topics covered: Grouped Frequency Distribution, Histogram, Cumulative frequency curves, quartiles and percentiles, Central Tendencies for grouped data, Box Plot. Students will learn: • That data can be represented effectively by pictorial means • To construct a grouped frequency table • To represent grouped data using histogram with equal and   unequal intervals • To find the central tendencies for grouped data • To draw cumulative curves using a cumulative frequency   table • To find quartiles and percentiles from the cumulative   frequency curves • To use box plots to compare data sets

US$ 34.99

Coordinate Geometry Geometrical relationships involving points and lines can be represented algebraically. Coordinate geometry can be used to model mathematical and real-life situations. In this course you will learn formulae and properties which helps you solve problems in cartesian plane. Prerequisites: Cartesian coordinates, Plotting straight lines on a graph Duration: 15 hours     |    Self-paced learning                 more Coordinate Geometry Geometrical relationships involving points and lines can be represented algebraically. Coordinate geometry can be used to model mathematical and real-life situations. In this course you will learn formulae and properties which helps you solve problems in cartesian plane. Prerequisites: Cartesian coordinates, Plotting straight lines on a graph Duration: 15 hours     |    Self-paced learning                 less Topics covered: Coordinate plane, Length and midpoint of line segments, Equations of straight lines, Area of polygons in coordinate plane. Students will learn: • To derive and apply the formulae for midpoint, distance and   gradient of line joining two points • To find the equation of straight lines and area of plane   figures. • To identify and investigate the relationship between parallel   and perpendicular lines. • To apply these properties and formulae to solve problems   in Cartesian plane.

US$ 34.99

Geometry around circles A circle constitutes the set of all points on a plane equidistant from a fixed point called the centre. What's the geometry around it? Triangles can be used to prove geometrical properties of circles. Learn to derive the properties of circles and to apply them to solve problems. Prerequisites: Basic geometry, Properties of triangles and polygons, Congruency Duration: 20 hours     |    Self-paced learning                 more Geometry around circles A circle constitutes the set of all points on a plane equidistant from a fixed point called the centre. What's the geometry around it? Triangles can be used to prove geometrical properties of circles. Learn to derive the properties of circles and to apply them to solve problems. Prerequisites: Basic geometry, Properties of triangles and polygons, Congruency Duration: 20 hours     |    Self-paced learning                 less Topics covered: Symmetric and angle properties of circles, Cyclic quadrilaterals, Properties of tangents and Alternate segment theorem. Students will learn: • The symmetrical and the geometrical properties of circles. • The angle properties of cyclic quadrilaterals. • To calculate unknown angles and solve problems using the   circle properties.

US$ 44.99

Matrices This course introduces the concept of Matrices. Here you will learn to represent real life data in the form of a matrix; add, subtract, multiply two matrices and to find the inverse of a matrix. Explore the use of matrices as a tool to solve mathematical and real-life problems. Prerequisites: Real numbers, Arithmetic, Algebra Duration: 12 hours     |    Self-paced learning                 more Matrices This course introduces the concept of Matrices. Here you will learn to represent real life data in the form of a matrix; add, subtract, multiply two matrices and to find the inverse of a matrix. Explore the use of matrices as a tool to solve mathematical and real-life problems. Prerequisites: Real numbers, Arithmetic, Algebra Duration: 12 hours     |    Self-paced learning                 less Topics covered: Matrix notation, Addition and subtraction of matrices, Scalar multiple of a matrix, Matrix multiplication, Inverse of a matrix. Students will learn: • To represent data in matrix form • To add, subtract and multiply matrices. • To solve mathematical and real life problems using   matrices.

US$ 34.99

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Trigonometry II In this course, we move trigonometry away from being a subject that deals only with right-angled triangles, and start looking at how we can define sine, cosine and tangent for any angle. In particular, we will see the sine rule and the cosine rule, which are rules that help us find sides and angles in any triangle and hence enable us to look at many more applications. Prerequisites: Pythagoras' theorem and Trigonometry (The sine, cosine and tangent ratios for acute angles in a right-angled triangle.) Duration: 18 hours     |    Self-paced learning                 more Trigonometry II In this course, we move trigonometry away from being a subject that deals only with right-angled triangles, and start looking at how we can define sine, cosine and tangent for any angle. In particular, we will see the sine rule and the cosine rule, which are rules that help us find sides and angles in any triangle and hence enable us to look at many more applications. Prerequisites: Pythagoras' theorem and Trigonometry (The sine, cosine and tangent ratios for acute angles in a right-angled triangle.) Duration: 18 hours     |    Self-paced learning                 less Topics covered: Solving trigonometric equations, Sine rule, Cosine rule, Solution to triangles, Bearings, Angle of Elevation and Depression, Simple three-dimensional problems, Radian measure, Arc length and area of a sector. Students will learn: • How to find the trigonometrical ratios of any angle • What is a basic angle? How to find the basic angle, given   any angle? • To solve simple trigonometric equations of the form   sin x = k, cos x = k and tan x = k where k is a constant • To apply the sine rule, the cosine rule to find unknown   angles or sides in a triangle • How to find the area of a triangle given two sides and an   angle between them • To solve real life problems involving bearings using the   above rules • What is a radian? A radian is a unit of measure for angles   and has a simple relationship with the degree measure • That circular (radian) measure can be used to solve   mathematical and real-life problems

US$ 44.99

Calculus I Calculus is the study of changing quantities. On a graph this is connected with the gradient of the curve, a steep graph means that 'y' is changing quickly and a shallower curve means that 'y' is changing more slowly. Calculus was developed in the Seventeenth Century in order to study this more precisely - we will see how to find gradients of all kinds of different curves. Prerequisites: Algebra, Trigonometry, solving trigonometric equations, Laws of Logarithms, solving exponential and logarithmic equations. Duration: 25 hours     |    Self-paced learning                 more Calculus I Calculus is the study of changing quantities. On a graph this is connected with the gradient of the curve, a steep graph means that 'y' is changing quickly and a shallower curve means that 'y' is changing more slowly. Calculus was developed in the Seventeenth Century in order to study this more precisely - we will see how to find gradients of all kinds of different curves. Prerequisites: Algebra, Trigonometry, solving trigonometric equations, Laws of Logarithms, solving exponential and logarithmic equations. Duration: 25 hours     |    Self-paced learning                 less Topics covered: The idea of Limits, Differentiation of polynomial functions, Functions of the form xn, Trigonometric, Exponential and Logarithmic functions, The Chain rule, The Product rule and The Quotient rule. Students will learn: • About the concept of limits • How limits are essential to the invention of differentiation • That gradients can be formulated using limits • To use differentiation from First Principles to find derivatives   and gradients • To use techniques of differentiation to differentiate many   functions • To extend their knowledge of differentiation to trig functions,   and other functions

US$ 44.99

Calculus II We have seen how to differentiate functions. Why is this important? In the real world a car speeds up and slows down continuously, and smoothly as the accelerator is pressed and released. The rate of a chemical reaction changes with time as the chemicals get used up. In both cases we can use derivatives to understand the process. In this course, we will look at these sorts of applications of differentiation. Prerequisites: Calculus I (Differentiation of polynomial functions, functions of the form xn, Trigonometric, Exponential and Logarithmic functions) Duration: 16 hours     |    Self-paced learning                 more Calculus II We have seen how to differentiate functions. Why is this important? In the real world a car speeds up and slows down continuously, and smoothly as the accelerator is pressed and released. The rate of a chemical reaction changes with time as the chemicals get used up. In both cases we can use derivatives to understand the process. In this course, we will look at these sorts of applications of differentiation. Prerequisites: Calculus I (Differentiation of polynomial functions, functions of the form xn, Trigonometric, Exponential and Logarithmic functions) Duration: 16 hours     |    Self-paced learning                 less Topics covered: Tangent and Normal, Stationary points, Increasing and decreasing functions, Maxima and Minima, Rates of change. Students will learn: • The concept of Tangent and Normal • To describe the graph of non-linear functions and discuss    its appearance in terms of the basic concepts of maxima    and minima, rate of change • To infer, from concepts of approximation and rate   of change, how one change results in other changes and   summarize as accurately as possible, the amount of   change resulted and how fast the change is changing.

US$ 34.99

Calculus III What do we call the reverse process of differentiation? Integration! This course will cover the basic concepts of integration of algebraic, trigonometric, exponential and logarithmic functions. It also introduces the concepts of indefinite and definite integrals. Definite integrals also find application in physics and geometry. Prerequisites: Algebra, Trigonometry, Calculus I Duration: 10 hours     |    Self-paced learning                 more Calculus III What do we call the reverse process of differentiation? Integration! This course will cover the basic concepts of integration of algebraic, trigonometric, exponential and logarithmic functions. It also introduces the concepts of indefinite and definite integrals. Definite integrals also find application in physics and geometry. Prerequisites: Algebra, Trigonometry, Calculus I Duration: 10 hours     |    Self-paced learning                 less Topics covered: Indefinite and definite integrals, Integration of polynomial functions, trigonometric functions and exponential functions. Students will learn: • The relationship between derivatives and integrals; • To derive the formulae for integrating various simple   functions: polynomials, trigonometric, exponential • To find the equation of a curve whose gradient function and   a particular point on the curve are given. • The difference between definite and indefinite integrals and   to evaluate them

US$ 34.99

Calculus IV Integral calculus deals with how quantities accumulate. In this course, you will learn how to apply integration to several types of physical problems; to work out the area bounded by curves, to find how far you have traveled when the speed is continually changing. Integral calculus has its engineering application in construction of dams, highways, roller coaster etc. Prerequisites: Calculus III, Distance, Time & Speed Duration: 14 hours     |    Self-paced learning                 more Calculus IV Integral calculus deals with how quantities accumulate. In this course, you will learn how to apply integration to several types of physical problems; to work out the area bounded by curves, to find how far you have traveled when the speed is continually changing. Integral calculus has its engineering application in construction of dams, highways, roller coaster etc. Prerequisites: Calculus III, Distance, Time & Speed Duration: 14 hours     |    Self-paced learning                 less Topics covered: Area under a curve, Area between two curves, Calculus and Kinematics, Displacement-time, velocity-time and acceleration-time graphs, Problem solving using kinematics. Students will learn: • That finding “area under the curve” is one of the ways to   solve a variety of problems. • To apply the techniques of integration to evaluate the area of   plane figures bounded by one or more curves • To use definite integrals to find the changes in   displacement and velocity of motions. • To solve problems relating to graphs of displacement,   velocity and acceleration as functions of time.

US$ 34.99

Functions In mathematics, the idea of functions is very fundamental and is used to represent the dependence between two or more quantities. In this course, you will learn the different ways of representing a function; different types of functions and their graphs. Prerequisites: Algebraic skills, Sketch linear and quadratic graphs Duration: 12 hours     |    Self-paced learning                 more Functions In mathematics, the idea of functions is very fundamental and is used to represent the dependence between two or more quantities. In this course, you will learn the different ways of representing a function; different types of functions and their graphs. Prerequisites: Algebraic skills, Sketch linear and quadratic graphs Duration: 12 hours     |    Self-paced learning                 less Topics covered: Relations and Functions, Functions and their graphs, Composite, Inverse and Modulus functions. Students will learn: • That functions are relations governed by fixed rules and   domains. • To formulate composite and inverse functions completely   and accurately. • To generate modulus functions.

US$ 34.99

Vectors Vectors are mathematical objects characterized by both magnitude and direction. Vectors have various physical and geometrical applications. In this course you will learn to add and subtract vectors; column vectors and unit vectors. You will explore the possibility of vectors in solving many real life problems. Prerequisites: Real numbers, Basic Arithmetic, Coordinate geometry Duration: 10 hours     |    Self-paced learning                 more Vectors Vectors are mathematical objects characterized by both magnitude and direction. Vectors have various physical and geometrical applications. In this course you will learn to add and subtract vectors; column vectors and unit vectors. You will explore the possibility of vectors in solving many real life problems. Prerequisites: Real numbers, Basic Arithmetic, Coordinate geometry Duration: 10 hours     |    Self-paced learning                 less Topics covered: Vector notation, Column vectors, Position vectors, Addition and subtraction of vectors, Scalar multiple of a vector, Parallel and non-parallel vectors, Collinear vectors, Unit vectors, Ratio theorem. Students will learn: • That vectors are mathematical objects that are   characterized by magnitude and direction. • To model and solve problems involving polygons and   vectors, with the help of vector diagrams. • To solve coordinate geometry problems using column   vectors. • To solve problems involving bearings and proportions   using operations of vectors. • That vectors can be used to represent physical concepts   and to solve mathematical and real life problems.

US$ 34.99

Trigonometry III In this course, we will see other trigonometric ratios, cosecant, secant and cotangent; the relation between degrees and radians; trigonometric identities and to graph these functions. Here you will see the similarities and differences between the amplitudes, periods and symmetries of trigonometric graphs. You will also learn how to use the identities as well as the graphs to solve the trigonometric equations. Prerequisites: Trigonometric ratios of acute angle, Circular measure (angles in radians) Duration: 20 hours     |    Self-paced learning                 more Trigonometry III In this course, we will see other trigonometric ratios, cosecant, secant and cotangent; the relation between degrees and radians; trigonometric identities and to graph these functions. Here you will see the similarities and differences between the amplitudes, periods and symmetries of trigonometric graphs. You will also learn how to use the identities as well as the graphs to solve the trigonometric equations. Prerequisites: Trigonometric ratios of acute angle, Circular measure (angles in radians) Duration: 20 hours     |    Self-paced learning                 less Topics covered: Trigonometric ratios of all angles (in degrees and radians), Solving trigonometric equations, Trigonometric identities, Graphs of trigonometric functions. Students will learn: • How to find the trigonometrical ratios of any angle • What are positive angles and negative angles? How to find   the basic angle, when any angle is given? • What is CAST ? • Trigonometric identities and their applications • How to solve trigonometric equations using basic angles • Graphs of trigonometric functions and their properties. • How we could solve the trigonometric equations using   graphs

US$ 44.99

Trigonometry IV In this course, we will learn about various formulae in trigonometry. In particular, we will see the addition formulae, R-formula, multiple angle formula and factor formula and hence their applications. Prerequisites: Trigonometry III Duration: 15 hours     |    Self-paced learning                 more Trigonometry IV In this course, we will learn about various formulae in trigonometry. In particular, we will see the addition formulae, R-formula, multiple angle formula and factor formula and hence their applications. Prerequisites: Trigonometry III Duration: 15 hours     |    Self-paced learning                 less Topics covered: Trigonometric identities, Addition formulae, R-formulae, Double angle formulae, Factor formulae and their applications. Students will learn: • Trigonometric identities and their applications • Addition formulae and its applications • R-formulae • Double angle formulae • Factor formulae and its applications

US$ 34.99