## IGCSE | Mathematics

### About this course

IGCSE stands for the International General Certificate of Secondary Education. It is a special educational programme of preparation for IGCSE examinations and getting a qualification that is globally-recognised. This qualification fits into the latest educational developments and trends all over the world and can be an ideal foundation for A Level and the International Baccalaureate Diploma programs. Students normally sit five to seven subjects in the last years of their school.

#### FAQs

###### Why do students need IGCSE?

IGCSE program not only gives students a chance to go to the best colleges and universities, but also helps to develop their critical and creative thinking, independence, cultural and social awareness and thus building the foundation for further academic success. Good IGCSE exam results (points 4-9) is the best way to enter the best educational institutions all over the world.

###### How to choose subjects for study on the IGCSE program?

Traditionally, IGCSEs are taken in 5-6 subjects, depending on which path the students choose for their future profession. The range of IGCSE subjects is really wide but the students usually choose Mathematics, Business, ICT, English, Science (Biology, Physics or Chemistry) or humanities (Literature, Geography or History). When choosing the IGCSE subjects you should also consider your own interests and preferences. As a rule, IGCSE subjects are chosen “in excess”, so that it is possible to abandon disciplines which are more difficult to cope with.

In 2013 our British Online School Knowledge Space was accredited by Edexcel to run the programs in accordance with British educational standards. Since then, our students have studied various subjects at our British School and each year most of them pass IGCSE exams.

Subject Mathematics:

- Understand the importance of Math skills for further education and the ways it can be applied in different subjects and spheres.
- Carry out complex mathematical calculations.
- Solve math problems.
- Find the probability and possibility.
- Process statistical data.

##### Part 1. Algebra and Equations

- Number, products of prime numbers
- Fractions and decimals
- Percentage
- Squares, cubes and roots
- Set language and notation
- Ratio, proportion and speed
- Approximation and limits of accuracy
- Standard form
- Algebraic manipulation
- Factorization, quadratic factorization
- Solutions of equations
- Simultaneous equations
- Cartesian plane and graphs
- Straight line graphs
- Graphs of functions
- Sequence
- Indices
- Direct and inverse proportion
- Inequalities and regions

##### Part 2. Geometry and Trigonometry

- Angles and parallel lines
- Angles in a triangle and in a quadrilateral
- Regular, irregular polygons
- Tangents and chords
- Angles in a circle, cyclic quadrilaterals, alternate segment theorem, intersecting chords
- Measuring and drawing angles, bearings, congruent shapes
- Geometrical constructions
- Pythagoras theorem, trigonometric ratios, calculating angles
- Solving problems using trigonometry
- Angles of elevation and depression,
- Problems in three dimensions, sine, cosine, and tangent of obtuse angle
- The sine rule and the cosine rule, using sine to find the area of a triangle
- Perimeter and area of a rectangle, area of a triangle, a parallelogram, of a trapezium
- Circumference and area of a circle
- Surface area and volume of a cuboid
- Volume of a prism
- Volume and surface area of a cylinder, a cone, and a sphere, arcs and sectors
- Lines of symmetry, rotational symmetry, symmetry of special two-dimensional
- Translation, reflections, rotations, enlargements

##### Part 3. Statistics and probability

- Frequency tables, pictograms, bar charts, pie charts, and histograms
- Statistical measures
- Using frequency tables, grouped data, measuring spread, cumulative frequency diagrams
- Probability
- Probability from data
- Expected frequency
- Combined events
- Tree diagrams

##### Skills

- Simplifying a fraction by cancelling common factors, converting mixed number into improper fraction, converting a decimal into a fraction, converting a fraction to a decimal or a percentage, calculating percentage, increasing or decreasing by a percentage.
- Expressing one quantity as a percentage of another, finding compound interest, repeated percentage change, finding reverse percentage, using brackets and the hierarchy of operations, finding a fraction by a quantity, adding, subtracting, dividing and multiplying fractions.
- Using a number line, operations with directed numbers, finding square and cube roots, calculating with surds, rationalizing a denominator.
- Working with sets, using subsets, the complement of a set.
- Solving problems with sets, expressing ratios as fractions, dividing amounts in a given ratio, reading map scales, and solving motion problems. Finding proportional variables.
- Rounding numbers, solving problems using upper and lower bounds where values are given to a degree of accuracy.
- Converting numbers to standard form, solving tasks with standard form, converting between metric units, reading scales, time, counting exchange rates.
- Applying the language of algebra in the real-life tasks, substituting numbers into formulae, simplifying expressions, expanding brackets.
- Factorizing expression, expanding two brackets.
- Solving linear equations, setting up equations, applying the quadratic formula.
- Solving simultaneous equations using three methods of solving it, reading conversion, travel, and speed-time graphs, plotting graphs.
- Plotting straight line graphs, finding gradient in the straight-line graphs.
- Plotting quadratic graphs, finding the next term and the nth term of the sequence.
- Using indices on a calculator, solving tasks with negative and fractional indices.
- Finding the constant of proportionality.
- Solving linear and quadratic inequalities, defining a region by inequalities.
- Finding domain of functions, inverse and composite functions, finding the gradient of the curve.
- Apply properties of angles, Finding exterior/interior angle in a regular polygon.
- Understand chord and tangent properties of circles, using properties of angles in a circle and in a cyclic quadrilateral to find angles, Using alternate segment theorem to find angles in a circle, using intersecting chords property to find a chord.
- Using protractor to measure angles, finding bearings, using and interpreting maps and scale drawings, finding congruent shapes, Using the geometrical properties about corresponding lengths and corresponding angles of similar shapes and figures.
- Constructing triangles and other two-dimensional shapes using a combination of a ruler, a protractor and compasses, solve problems using scale drawings.
- Using Pythagoras’ Theorem in two dimensions, using sine, cosine and tangent of acute angles to determine lengths and angles of a right-angled triangle.
- Solving problems using trigonometry, solving problems in three dimensions, finding sine, cosine of an obtuse angle, Applying sine and cosine rule formulae, finding the area of triangle using sine.
- Recognizing line and rotational symmetry, identifying any lines of symmetry and the order of rotational symmetry of a given two-dimensional figure, solving vector problems, finding the magnitude of a vector.
- Describing translation and reflection transformation using vectors and the mirror line, plotting these transformations, describing rotation and enlargement transformation, plotting transformations.
- Using different methods of presenting data, using appropriate methods of tabulation to enable the construction of statistical diagrams.
- Calculating the mean, median, mode and range for a discrete data set.
- Working with frequency tables, calculating an estimate for the mean for grouped data, drawing cumulative frequency diagrams.
- Plotting probability scale, calculating probabilities.
- Estimating probabilities from previously collected data, plotting tree diagrams.

IGCSE 14-16 y.o. |

IGCSE preparation, 3 or more subjects from the list (English SL, English1, Math, Physics, Chemistry, ICT, Geography, Economics, Business) |

72 lessons on each subject, every lesson lasts 60 minutes |

Price of the course (3 subjects) 5100 € |

Registration fee 250 € |