1 Number

1.A Ordinary number operations

1.B Prime numbers, factors and multiples

1.C Indices, powers and roots

1.D Surds

1.E Rationalising denominators

1.F Number sets

1.G Units, measures and money

1.H Fractions, decimals, ratio and percentage

1.I Accuracy

1.J Upper and lower bounds

1.K Standard form

2 Sets

2.A Sets

2.B Set language and notation

2.C Union and intersection

2.D Number of elements

2.E Complementary sets

2.F Subsets

2.G Universal and null sets

2.H Venn diagrams

2.I Set symbols

3 Algebra

3.A Basic algebra processes

3.B Formulae

3.C Factorisation

3.D Factor theorem

3.E Algebraic division

3.F Algebraic fractions

3.G Equations

3.H Linear simultaneous equations

3.I Linear and quadratic simultaneous equations

3.J Linear inequalities

3.K Quadratic inequalities

3.L Sequences

4 Functions

4.A Functions

4.B Functions as mappings

4.C Function notation

4.D Domain and range

4.E Composite functions

4.F Inverse functions

4.G Variation

4.H Cartesian coordinates

4.I Straight-line graphs

4.J Graphs of equations

4.K Graph gradients

4.L Differentiation

4.M Rates of change and stationary points

4.N Kinematics applications

5 Matrices

5.A Matrices

5.B Matrix addition and multiplication

5.C Scalar multiplication of matrices

5.D Identity and zero matrices

5.E Determinants and inverses

5.F Matrices and transformations

5.G Combined transformations

6 Geometry

6.A Euclidean geometry

6.B Geometrical reasoning

6.C Angle properties

6.D Quadrilaterals

6.E Symmetry

6.F Pythagoras in 2D and 3D

6.G Similarity

6.H Triangle similarity

6.I Congruent shapes

6.J Triangle congruence

6.K Circle theorems

6.L Cyclic quadrilaterals

6.M Loci

6.N Constructions

7 Mensuration

7.A Length, area and volume

7.B 2D mensuration

7.C 3D mensuration

7.D Arcs and sectors

8 Vectors and transformation geometry

8.A Scalars and vectors

8.B Vector notation

8.C Directed line segments

8.D Parallel, unit and position vectors

8.E Vector sums and differences

8.F Vector magnitude

8.G Scalar multiplication of vectors

8.H Resultant vectors

8.I Vector geometry

8.J Transformations

8.K Combined transformations

8.L Vectors and matrices

9 Trigonometry

9.A Sine, cosine and tangent

9.B 2D and 3D trigonometry

9.C Elevation and depression

9.D Bearings

10 Statistics and probability

10.A Graphical representation of data

10.B Mean, median and mode

10.C Grouped mean estimates

10.D Modal class and median class

10.E Probability language

10.F Addition rule

10.G Product rule

10.H Independent event probability

10.I Conditional probability

10.J Simple conditional probability

10.K Expected frequency

IGCSE Math B/Notes/1.J Upper and lower bounds

IGCSE Math B 1.J Upper and lower bounds Notes

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