Cambridge IGCSE Extended Mathematics 0580

The syllabus aims describe the purposes of a course based on this syllabus. The aims are to develop an understanding of mathematical principles, concepts and methods in a way which encourages confidence, provides satisfaction and enjoyment, and develops a positive attitude towards mathematics, develop a feel for number and understand the significance of the results obtained, apply mathematics in everyday situations and develop an understanding of the part that mathematics plays in learners’ own lives and the world around them, analyse and solve problems, present the solutions clearly, and check and interpret the results, recognise when and how a situation may be represented mathematically, identify and interpret relevant factors, select an appropriate mathematical method to solve the problem, and evaluate the method used, use mathematics as a means of communication with emphasis on the use of clear expression and structured argument, develop an ability to apply mathematics in other subjects, particularly science and technology, develop the ability to reason logically, make deductions and inferences, and draw conclusions, appreciate patterns and relationships in mathematics and make generalisations, appreciate the interdependence of different areas of mathematics and acquire a foundation for further study of mathematics or for other disciplines.

Source: Cambridge IGCSE Extended Mathematics 0580 syllabus booklet

## MODULES : View - Register - Learn

In this module, students extensively learn about Numbers. Students gain in-depth knowledge of Sets, directed numbers, percentages, ratio and proportion. Students benefit from learning deeper insights to earn top grades in paper 1 and paper 2.

**Content: **

- Identify and use Natural numbers, Integers, Prime numbers, Square and Cube numbers, Common factors and common multiples, Rational and Irrational numbers, Real numbers, Reciprocals.
- Sets
- Calculate with squares, square roots, cubes and cube roots and other powers and roots of numbers.
- Use directed numbers in practical situations
- Fractions and percentages.
- Order of quantities by magnitude and demonstrate familiarity with the symbols.
- Indices
- Using standard form.
- Operations of numbers
- Significant and Decimal places
- Upper bounds and Lower bounds
- Ratio and Proportion
- Increasing and Decreasing percentage
- Calculate times in terms of the 24-hour and 12-hour clock.
- Calculate using money and convert from one currency to another.
- Personal and household finance. Simple and Compound Interest.
- Exponential growth and decay relation to population and finance.

**Duration of the module: **10 Hours (Five sessions of 2 hour each)**Fee:** SGD 400/-**Module CODE: **IGEXTMM1**Mode of Teaching: **Online **How to enroll: **Fill in the form and submit for slots and payment details **CLICK HERE**

In this module, students extensively learn about Algebra and Graphs. Students gain in-depth knowledge of direct and inverse proportions, number sequences, quadratic equations, different graphs which are connected to AS/IB Math levels. Students benefit from learning deeper insights to earn top grades in paper 1 and paper 2.

**Content: **

- Construct and rearrange complicated formulae and equations
- Use brackets and extract common factors, Expand products of algebraic expressions
- Factorisation
- Manipulate algebraic fractions.
- Factorise and simplify rational expressions.
- Use and interpret positive, negative and zero indices. Use and interpret fractional indices. Use the rules of indices
- Linear equations
- Simultaneous equations involving one linear and quadratic
- Solving quadratic equations by factorisation, completing the square and by use of the formula
- Derive and solve linear inequalities
- Represent inequalities graphically and use this representation to solve simple linear programming problems.
- Number sequences
- Direct and Inverse proportion
- Functions.
- Drawing graphs from given data
- Rate of change to simple kinematics involving distance-time and speed-time graphs, acceleration and deceleration, calculate distance travelled as area under a speed-time graph
- Draw and interpret graphs representing exponential growth and decay problems
- Estimate gradients of curves by drawing tangents
- Derivative of the function (power rule)

**Duration of the module: **16 Hours (Eight sessions of 2 hours each)**Fee:**** **SGD 640/-**Module CODE: **IGEXTMM2**Mode of Teaching: **Online **How to enroll: **Fill in the form and submit for slots and payment details **CLICK HERE**

In this module, students extensively learn about Coordinate Geometry. Students gain in-depth knowledge of different equations of straight lines. Students benefit from learning deeper insights to earn top grades in paper 1 and paper 2.

**Content: **

- Cartesian coordinates in two dimensions.
- Gradient.
- Distance between two points and midpoint of two points
- Equation of straight line
- Equation of straight lines parallel to a given line.
- Gradient of parallel and perpendicular lines

**Duration of the module: **8 Hours (Four sessions of 2 hours each)**Fee: **SGD 320/-**Mode of Teaching: **Online **Module CODE: **IGEXTMM3**How to enroll: **Fill in the form and submit for slots and payment details **CLICK HERE**

In this module, students extensively learn about Geometry. Students gain in-depth knowledge of similar triangles, congruence of triangles, Rotational and line of symmetry,properties of circles. Students benefit from learning deeper insights to earn top grades in paper 1 and paper 2.

**Content: **

- Use and interpret the geometrical terms: point, line, parallel, bearing, right angle, acute, obtuse and reflex angles, perpendicular, similarity and congruence.
- Use and interpret vocabulary of triangles, quadrilaterals, circles, polygons and simple solid figures including nets.
- Measure and draw lines and angles. Construct a triangle given the three sides using a ruler and a pair of compasses only.
- Scale drawings.
- Calculate lengths of similar figures.
- Use the basic congruence criteria for triangles.
- Rotational and line symmetry in two dimensions.
- Symmetry properties of circles.
- Angles at a point
- Angles at a point on a straight line and intersecting straight lines and intersecting straight lines.
- Angles formed within parallel lines.
- Angle properties of triangles and quadrilaterals.
- Angle properties of regular polygons
- Angle in a semicircle
- Angle between tangent and radius of a circle.
- Angle properties of irregular polygons.
- Angle at the centre of circle is twice the angle at the circumference.
- Angles in the same segment are equal.
- Angles in the same segment are equal.
- Angles in opposite segment are supplementary, cyclic quadrilaterals
- Alternate segment theorem.

**Duration of the module: **14 Hours (Seven sessions of 2 hours each)**Fee: **SGD 560/-**Module CODE: **IGEXTMM4 **Mode of Teaching: **Online **How to enroll: **** **Fill in the form and submit for slots and payment details **CLICK HERE**

In this module, students extensively learn about Mensuration. Students gain in-depth knowledge of two dimensional and three dimensional figures, area of circle, circumference of circle, arc of sector, area of sector and perimeter of sector . Students benefit from learning deeper insights to earn top grades in paper 1 and paper 2.

**Content: **

- Use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units.
- Perimeter and area of rectangle, triangle, parallelogram and trapezium and compound shapes derived from these.
- Arc length and sector area, circumference of circle.
- Surface area and Volume of cuboid, prism and cylinder.
- Surface area volume of a sphere, pyramid and cone.
- Carry out calculations involving the area and volumes of compound shapes.

**Duration of the module: **10 Hours (Five sessions of 2 hours each)**Fee: **SGD 400/-**Module CODE: **IGEXTMM5**Mode of Teaching: **Online **How to enroll: **Fill in the form and submit for slots and payment details** CLICK HERE**

In this module, students extensively learn about Trigonometry. Students gain in-depth knowledge of trigonometric ratios, sine and cosine rules, sketch and interpretation of graphs of simple trigonometric functions, solving trigonometric equations, solving heights and distance sums, bearing problems. Students benefit from learning deeper insights to earn top grades in paper 1 and paper 2.

**Content:**

- Interpret and use three-figure bearings.
- Sine, Cosine and Tan ratios.
- Solve trigonometric problems in two dimensions involving angles of elevation and depression.
- Perpendicular distance from a point to a line is the shortest distance to the line.
- Recognise, sketch and interpret graphs of simple trigonometric functions. Graph and know the properties of trigonometric functions. Solve simple trigonometric equations .
- Sine and Cosine rules
- Solve simple trigonometric problems in three dimensions including angle between a line and a plane.

**Duration of the module: **16 Hours (Eight sessions of 2 hours each)**Fee: **640/-SGD**Module CODE:** IGEXTMM6**Mode of Teaching: **Online **How to enroll: **Fill in the form and submit for slots and payment details **CLICK HERE**

In this module, students extensively learn about Vectors. Students can gain knowledge in depth of vector addition and subtraction, express given vectors in terms of two coplanar vectors, reflection, rotation of points and figures. Students benefit from learning deeper insights to earn top grades in paper 1 and paper 2.

**Content:**

- Translation by using vectors.
- Add and subtract vectors.
- Multiplying vectors with scalars.
- Reflect simple figures.
- Rotations.
- Magnitude of vector.
- Use position vectors.
- Express given vectors in terms of two coplanar vectors

**Duration of the module: **10 Hours (Five sessions of 2 hours each)**Fee: **SGD 400/-**Mode of Teaching: **online**Module CODE:** IGEXTMM7** **

**How to enroll:**Fill in the form and submit for slots and payment details

**CLICK HERE**

In this module, students extensively learn about Mensuration. Students gain in-depth knowledge of measures of central tendencies, a variety of statistical graphs and applications, simple probability, conditional probability. Students benefit from learning deeper insights to earn top grades in paper 1 and paper 2.

**Content: **

- Collect, classify and tabulate statistical data.
- Tables, graphs and statistical measures.
- Construct and interpret bar charts, pie charts, pictograms, stem-and -leaf diagrams, simple frequency distributions, histograms with equal intervals and scatter diagrams.
- Mean, median, mode and range.
- Understand what is meant by positive, negative and zero correlation with reference to a scatter diagram.
- Draw, interpret and use lines of best fit by eye.
- Calculate the probability of a single event as either a fraction, decimal or percentage.
- Understand and use the probability scale from 0 to 1.
- Probability of an event occurring or not occurring.
- Understand relative frequency as an estimate of probability. Expected frequency of occurrences.
- Calculate the probability of simple combined events, using possibility diagrams, tree diagrams and Venn diagrams.
- Calculate conditional probability using Venn diagrams, tree diagrams and and tables.

**Duration of the module: **12 Hours (Six sessions of 2 hours each)**Fee: SGD 480/-****Mode of Teaching: **Online**Module CODE: **IGEXTMM8 **How to enroll:**Fill in the form and submit for slots and payment details **CLICK HERE**

This module prepares students focused on final exam preparation. We take you through some of exam skills, tips, techniques, approaches that enhance your skills and understanding to earn A-A* grades. We revise key concepts and areas of the syllabus and prepare you through planned assignments.

**Duration of the module: **16 Hours ( Seven sessions of 2 hours each)**Fee: **SGD 640/-**Mode of Teaching: **Online**Module CODE: **IGEXTMM9**How to enrol: **Fill in the form and submit for slots and payment details **CLICK HERE**

This module prepares students focusing on the structured question in the final paper 4. We take you through some of exam skills, tips, techniques, approaches that enhance your skill and understanding to earn A-A* grades. Since paper 4 weighting is 65%, it is the key component to get A* in Extended Mathematics. We revise key concepts and areas of the syllabus and prepare you through planned assignments.

**Duration of the module: **22 Hours (Eleven sessions of 2 hours each)**Fee: **SGD 880/-**Module CODE:** IGEXTMM10 **Mode of Teaching: **Online **How to enrol: **Fill in the form and submit for slots and payment details **CLICK HERE**