iGCSE Mathematics B Edexcel

This subject is broken down into 95 topics in 10 modules:

  1. Number 11 topics
  2. Sets 9 topics
  3. Algebra 12 topics
  4. Functions 11 topics
  5. Matrices 7 topics
  6. Geometry 14 topics
  7. Mensuration 4 topics
  8. Vectors and Transformation Geometry 12 topics
  9. Trigonometry 4 topics
  10. Statistics and Probability 11 topics
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This page was last modified on 28 September 2024.

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Mathematics B

Number

The Ordinary Processes of Number Manipulation

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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).

Course material for Mathematics B, module Number, topic The Ordinary Processes of Number Manipulation

Mathematics B

Matrices

Transformation of the Plane Associated with 2x2 Matrices

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Transformation of the Plane Associated with 2x2 Matrices

Understanding Transformation of the Plane

  • A 2x2 matrix can represent a linear transformation of the plane.
  • This transformation maps each point in the plane to a new location according to a particular set of rules.
  • Two main types of transformations can be represented by 2x2 matrices: rotations and scaling.
  • A transformation associated with a 2x2 matrix preserves parallelism. This means that if two vectors are parallel before transformation, they remain parallel after transformation.

Performing Transformation of the Plane

  • To transform a point using a 2x2 matrix, we perform matrix multiplication with the 2x2 matrix and a column vector representing the original point.
  • The original point's coordinates are replaced with the result of the multiplication to find the new location of the point.
  • For a given transformation matrix [a b; c d], multiplying [a b; c d] and a column vector [x; y] will result in a new column vector [ax + by; cx + dy].

Rotations and Scalings

  • Rotation matrices transform the plane by rotating points around the origin. A 2x2 rotation matrix can be represented as [cos(θ) -sin(θ); sin(θ) cos(θ)] where θ is the angle of rotation.
  • Scaling matrices transform the plane by stretching or compressing it along the axes. A 2x2 scaling matrix can be represented as [s 0; 0 s], where s is the scaling factor.
  • Combined rotations and scalings can be represented by multiplying respective matrices together.

Special Types of Transformation Matrices

  • An identity matrix does not change any point in the plane. It is represented as [1 0; 0 1].
  • The zero matrix maps all points to the origin. It is represented as [0 0; 0 0].

Remember, matrix transformations can be very useful in computer graphics, physics and engineering. Rotations and scalings are important for manipulating objects within a 2D space.

Course material for Mathematics B, module Matrices, topic Transformation of the Plane Associated with 2x2 Matrices

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