iGCSE Mathematics B Edexcel

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Content Overview

95 topics in 10 modules

☑️ Number 11 topics
- The Ordinary Processes of Number Manipulation
- Prime Numbers, Factors, Multiples
- Indices, Powers and Roots
- Simple Manipulation of Surds
- Rationalising the Denominator
- Natural Numbers, Integers and Rational and Irrational Numbers
- Weights, Measures and Money
- Fractions, Decimals, Ratio, Proportion and Percentage
- Expressing Numbers to a Given Degree of Accuracy
- Solve Problems Using Upper and Lower Bounds where Values are Given to a Degree of Accuracy
- Numbers in Standard Form
☑️ Sets 9 topics
- The Idea of a Set
- Set Language and Notation
- Union and Intersection of Sets
- Number of Elements in a Set
- Complementary Sets
- Subsets
- Universal Set, Null Set
- Venn Diagrams and their Use in Simple Logical Problems
- Use of Symbols to Represent Sets
☑️ Algebra 12 topics
- The Basic Processes of Algebra
- The Construction, Interpretation and Use of Formulae and their Manipulation
- The Factorisation of Simple Algebraic Expressions
- Use of the Factor Theorem
- Algebraic Division of a Cubic by a Linear Factor
- The Manipulation of Simple Algebraic Fractions, the Denominators being Numerical, Linear or Quadratic
- Solution of Equations of 1st, 2nd and 3rd Degree Containing One Unknown Quantity
- Solution of Linear Simultaneous Equations in Two Unknowns
- Solve Simultaneous Equations in Two Unknowns, One Linear and the Other Quadratic Equation
- Solution of Linear Inequalities, and the Representations of Solutions on the Number Line and 2D Space
- Solve Quadratic Inequalities in one Unknown and Represent the Solution Set on a Number Line
- The Idea of a Sequence
☑️ Functions 11 topics
- The Idea of a Function of a Variable
- Function as a Mapping or as a Correspondence between the Elements of Two Sets
- Use Functional Notations of the Form f(x) and f: x ->
- Domain and Range of a Function
- Composite Functions
- Inverse Functions
- Variation, Direct and Indirect Proportion
- Rectangular Cartesian Co-ordinates
- Differentiation of Integer Powers of x
- Determination of Gradients, Rates of Change, Maxima and Minima, Stationary Points and Turning Points
- Applications to Linear Kinematics and Other Simple Practical Problems
☑️ Matrices 7 topics
- Representation of Data by a Matrix
- Addition and Multiplication of Matrices
- Multiplication of a Matrix by a Scalar
- Unit (identity) Matrix and Zero (null) Matrix
- Determinants and Inverses of Non-Singular 2x2 Matrices
- Transformation of the Plane Associated with 2x2 Matrices
- Combination of Transformations
☑️ Geometry 14 topics
- Geometrical Properties of Euclidean Space
- Geometrical Reasoning
- Angle Properties of Parallel Lines, Triangles and Polygons
- Properties of the Parallelogram, Rectangle, Square, Rhombus, Trapezium and Kite
- Symmetry about a Point, Line or Plane
- Use of Pythagoras' Theorem in 2D and 3D
- Similarity: Areas and Volumes of Similar Figures
- Prove the Similarity of Two Triangles
- Congruent Shapes
- SSS, SAS, ASA and RHS Conditions
- Chord, Angle and Tangent Properties of Circles
- Properties of a Cyclic Quadrilateral
- Loci in Two Dimensions
- Constructions of Bisector of an Angle and Perpendicular Bisector of a Straight Line
☑️ Mensuration 4 topics
- Length, Area and Volume
- Mensuration of 2D Shapes, Rectangle, Parallelogram, Trapezium, Triangle, Circle
- Mensuration of 3D Shapes, Right Circular Cylinder, Right Circular Cone and Sphere, Cuboid, Pyramid, Prism
- Length of an Arc, Area of a Sector of a Circle
☑️ Vectors and Transformation Geometry 12 topics
- Scalar and Vector Quantities
- Understand and Use Vector Notation
- Representation of a Vector by a Directed Line Segment
- Parallel Vectors, Unit Vectors and Position Vectors
- Sum and Difference of Two Vectors
- Modulus (Magnitude) of a Vector
- Multiplication of a Vector by a Scalar
- Find the Resultant of Two or More Vectors
- Apply Vector Methods to Simple Geometrical Problems
- Transformations of the Plane
- Combination of Transformations
- Multiplication of a Vector by a Matrix
☑️ Trigonometry 4 topics
- Use of Sine, Cosine and Tangent of Angles up to 180 Degrees
- Solution of Problems in 2 and 3D by Calculation and by Drawing
- Angles of Elevation and Depression
- Bearings
☑️ Statistics and Probability 11 topics
- Graphical Representation of Numerical Data
- Determination of the Mean, Median and Mode for a Discrete Data Set
- Calculation of an Estimate of the Mean of a Larger Number of Quantities Given in Grouped Frequencies
- Determination of a Modal Class and the Class Containing the Median for Grouped Data
- Understand the Language and Basic Concepts of Probability
- Use of Addition Rule for Two or More Mutually Exclusive Events
- Use of Product Rule for Two or More Independent Events
- Determination of the Probability of Two or More Independent Events
- Using Simple Conditional Probability for Combined Events
- Finding Very Simple Conditional Probability
- Understand and Use the Term 'Expected Frequency'

iGCSE Mathematics B Edexcel Revision Content

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iGCSE Mathematics B Edexcel - Number - The Ordinary Processes of Number Manipulation Content Preview

Number

Revision ContentExam Question

The Ordinary Processes of Number Manipulation

Basics of Numbers

Place Value: Understand the place value of digits in a number. For example, in the number 456, 4 is in the hundreds place, 5 in the tens place, and 6 in the units place.
Number Types: Identify the different types of numbers such as whole numbers, natural numbers, integers, fractions, and decimals.
Rounding Numbers: Know how to round numbers to the nearest ten, hundred or thousand, and understand the difference between rounding up and rounding down.

Operations with Numbers

Basic Operations: Perform the four basic operations – addition, subtraction, multiplication, and division – with any type of number.
BODMAS/BIDMAS Rule: Understand the importance of following correct order of operations: Brackets, Orders (or Indices), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Negative Numbers: Understand how to add, subtract, multiply, and divide with negative numbers. For example, multiplying two negative numbers results in a positive number.

Fractions, Decimals and Percentages

Equivalent Fractions: Identify and create equivalent fractions. For example, 1/2 is equivalent to 2/4, 3/6, etc.
Decimal and Fraction Conversion: Convert between fractions and decimals. For example, 0.75 is equivalent to 3/4.
Percentage Calculations: Convert between fractions, decimals, and percentages. For example, 0.20 is equivalent to 20% or 1/5.
Operations with Fractions, Decimals, and Percentages: Understand how to add, subtract, multiply, and divide fractions, decimals, and percentages.

Prime factors, Highest Common Factor and Lowest Common Multiple

Prime factors: Understand the concept of prime factors and how to find the prime factorisation of a number.
Highest Common Factor (HCF): Identify the HCF of two or more numbers, which is the greatest number that divides exactly into those numbers.
Lowest Common Multiple (LCM): Identify the LCM of two or more numbers, which is the smallest number that is a multiple of those numbers.

Handling Data

Mean, Median and Mode: Understand how to calculate the mean (average), median (middle value), and mode (most frequently occurring value) of a set of numbers.
Range: Calculate the range of a set of data by subtracting the smallest number from the largest number. This provides a measure of dispersion or spread in the data.
Handling Large Numbers and Standard Form: Be able to manipulate very large and very small numbers and convert numbers into standard form (also known as scientific notation).

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