 # Cambridge

Cambridge’s International A and AS Levels satisfy the entry criteria for every university around the world and are considered equal in value to UK A and AS Levels. They are recognized by universities in NZ, Australia, Canada, UK (including Oxford and Cambridge) as well as throughout the European Union.

In the USA they are accepted by all Ivy League universities (such as Harvard) and can earn students course credits up to one full year of credit. Cambridge publishes comprehensive lists of all institutions that recognize its qualifications, including details about entry criteria and the grades needed for entrance. If you are considering the overseas study, you are advised to include three A Level subjects in your course of study.

CORE MATHEMATICS FOR CAMBRIDGE IGCSE

1. Basic Number

Learn 1.1 The Structure of Numbers

Learn 2.2 Types of Number

2. Basic Algebra

Learn 2.1 Using Letters for numbers

Learn 2.2 Expressing basic arithmetic processes algebraically

Learn 2.3 Substitution

Learn 2.4 Using Formulae

3. Mensuration: perimeter and area

Learn 3.1 Perimeters and areas of basic 2-D shapes

Learn 3.2 Circles

Learn 3.3 Composite Shapes

4. Mensuration: Volume and surface area

Learn 4.1 Volume of a cube or cuboid

Learn 4.2 Volume of a prism

Learn 4.3 Volume of a cylinder

Learn 4.4 Surface area and nets

5. Numbers and sequences

Learn 5.1 The rules of a sequence

Learn 5.2 The nth term of a sequence

6. Directed numbers

Learn 6.1 Using directed numbers

Learn 6.2 Adding and subtracting positive and negative numbers

learn 6.3 Multiplying and dividing positive and negative numbers

7. Time and Money

Learn 7.1 Time

Learn 7.2 Money

8. Decimals, fractions, and percentages

learn 8.1 Working with decimals

Learn 8.2 Fractions

Learn 8.3 Fractions, decimals and percentages

learn 8.4 Working with fractions: addition and subtraction

learn 8.5 Working with fractions: Multiplication and division

Learn 8.6 Ordering operations

9.Algebra

Learn 9.1 Expanding brackets

learn 9.2 Factorising expressions

learn 9.3 Constructing simple expressions

Learn 9.4 Solving linear equations

10. Transformations 1

Learn 10.1 Reflection

Learn 10.2 Rotation

11. Indices and standard form

Learn 11.1 Squares and cubes

Learn 11.2 indices and powers

Learn 11.3 Standard form

12. Statistical diagrams

Learn 12.1 Collecting and interpreting data

Learn 12.2 Bar charts, histograms, and pictograms

Learn 12.3 Pie charts and scatter diagrams

13. Symmetry

Learn 13.1 line symmetry

Learn 13.2 Rotational Symmetry

Learn 13.3 Special shapes and their symmetries

14. Geometry

Learn 14.1 Angles

Learn 14.2 Angle sum of a triangle and quadrilateral

Learn 14.3 Special triangles and quadrilaterals

15. Percentages

Learn 15.1 Percentage of a quantity

Learn 15.2 Writing one quantity as a percentage of another

Learn 15.3 Percentage increase and decrease

16. Transformations-2

Learn 16.1 Translation

Learn 16.2 Enlargement

Learn 16.3 Recognising and describing transformations

17. Probability

Learn 17.1 Probability and probability scale

Learn 17.2 Experimental probability

18. Measures

Learn 18.1 Metric Units

Learn 18.2 Changing units of area, volume, and capacity

19. Ratio and proportion

Learn 19.1 Simplifying ratios

Learn 19.2 The unitary method

Learn 19.3 Using ratios to find quantities

Learn 19.4 Dividing quantities in a given ratio

Learn 19.5 Compound measures

20. Real-life graphs

Learn 20.1 Cartesian coordinates

Learn 20.2 Conversion graphs

Learn 20.3 Travel graphs

21. Personal finance

Learn 21.1 Earnings

Learn 21.3 Interest

22. Estimation and accuracy

Learn 22.1 Rounding

Learn 22.2 Decimal places

Learn 22.3 Significant figures

Learn 22.4 Upper and lower bounds

23. Constructions

Learn 23.1 Measuring and drawing lines and angles

Learn 23.2 Construction triangles

Learn 23.3 Constructing parallel lines

Learn 23.4 Bisectors and scale drawings

24. Loci

Learn 24.1 describing a locus

Learn 24.2 Constructions and Loci

Learn 24.3 Loci and scale drawing

25. Statistical measures

Learn 25.1 Mean, median and mode

Learn 25.2 using frequency tables

Learn 25.3 Comparing sets of data

26. Straight line graphs

Learn 26.1 Introduction to straight line graphs

Learn 26.2 Gradient of straight line graphs

Learn 26.3 Finding the equation of a straight line graph

27. Angle properties

Learn 27.1 Regular polygons

Learn 27.2 Angle Properties of circles

28. Equations and formulae

Learn 28.1 Transforming simple formulae

Learn 28.2 Equations with the unknown on both sides

Learn 28.3 Equations with brackets

Learn 28.4 Simultaneous equations

29. Graphs of functions

Learn 29.2 Graphs of reciprocal functions

Learn 29.3 Solving equations by graphical methods

30. Trigonometry

Learn 30.1 Pythagoras’s Theorem

Learn 30.2 Trigonometry

Learn 30.3 Bearings

31. Vectors

Learn 31.1 Vector notation

Learn 31.2 Addition, subtraction and multiplication of vectors

Extended Mathematics for Cambridge IGCSE

1. Number

1.1 Arithmetic

1.2 Number facts and sequences

1.3 Approximations and estimation

1.4 Standard form

1.5 Ration and proportion

1.6 Percentages

1.7 Speed, distance and time

1.8 Calculator

1.9 Using a spreadsheet on a computer

2 . Algebra 1

2.1 Negative Numbers

2.2 Directed Numbers

2.3 Formulae

2.4 Brackets and simplifying

2.5 Linear equations

2.6 Problems solved by linear equations

2.7 Simultaneous equations

2.8 Problems solved by Simultaneous equations

2.9 Factorising

2.11 Problems solved by quadratic equations

3.Mensuration

3.1 Area

3.2 the circle

3.3 arc length and sector area

3.4 Chord of a circle

3.5 Volume

3.6 Surface area

4. Geometry

4.1 Fundamental results

4.2 Pythagoras’ theorem

4.3 Symmetry

4.4 similarity

4.5 Circle Theorems

4.6 Constructions and loci

4.7 Nets

5. Algebra-2

5.1 Algebraic fractions

5.2 Changing the subject of a formula

5.3 Variation

5.4 Indices

5.5 Inequalities

5.6 Linear Programming

6. Trigonometry

6.1 Right-angled triangles

6.2 Scale drawing

6.3 Three-dimensional problems

6.4 Sine, cosine, tangent for any angle

6.5 The sine rule

6.6 The cosine rule

7. Graphs

7.1 Drawing accurate graphs

7.3 The form y=mx+c

7.4 Plotting curves

7.5 interpreting graphs

7.6 Graphical solution of equations

7.7 Distance time graphs

7.8 Speed-time graphs

8. Sets, vectors, and functions

8.1 Sets

8.2 logical problems

8.3 vectors

8.4 Column Vectors

8.5 Vector Geometry

8.6 Functions

9. Matrices and Transformations

9.1 Matrix operations

9.2 The inverse of a matrix

9.3 Simple transformations

9.4 Combined transformations

9.5 Transformations using matrices

10. Statistics and Probability

10.1 Data display

10.2 Mean, Median and Mode

10.3 Cumulative frequency

10.4 Simple probability

10.5 Exclusive and independent events

10.6 Tree diagrams

11. investigation Practical Problems, Puzzles

11.1 investigation

11.2 Practical problems

11.3 Puzzles and experiments

Pure Mathematics 2 & 3

Unit P2& P3

1. Polynomials
2. The modulus function
3. Exponential and logarithmic functions
4. Differentiating exponentials and logarithms
5. Trigonometry
6. Differentiating trigonometric functions
7. differentiating Products
8. Solving equations numerically
9. The trapezium rule
10. Parametric equations
11. Curves defined implicitly

Unit P3

1. Vectors: Lines in two and three dimensions
2. Vectors: Planes in three dimensions
3. The binomial expansion
4. Rational functions
5. Complex numbers
6. 17. Complex numbers in polar form
7. Integration
8. Differential equations

Statistics – 1

1. Representation of data
2. Measures of location