Level 2 Mathematics WJEC

This subject is broken down into 33 topics in 3 modules:

  1. Number and Quantity 12 topics
  2. Algebra and Graphs 11 topics
  3. Geometry and Measures 10 topics
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This page was last modified on 28 September 2024.

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Mathematics

Number and Quantity

Notation and structure of the number system

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Notation and structure of the number system

Notation and Structure of the Number System

Types and Properties of Numbers

  • Understand the different types of numbers in the number system, including natural numbers, integers, rational numbers, irrational numbers, and real numbers.
  • Natural numbers are those used for counting and ordering (e.g., 1, 2, 3).
  • Integers include natural numbers, zero, and their negatives (e.g., -2, -1, 0, 1, 2).
  • Rational numbers can be written as a fraction where both the numerator and denominator are integers (e.g., 7/3, -4/5). This category also includes integers and natural numbers.
  • Irrational numbers cannot be written as a fraction. They do not terminate or repeat, and include numbers like π and √2.
  • The real numbers are a combination of rational and irrational numbers.

Number Notations

  • Get comfortable with standard form (or scientific notation) e.g., 3.4 x 10<sup>5</sup>.
  • Understand the use of surds to represent the root of a number that cannot be simplified to a rational number (e.g., √2 is a surd).
  • Know how to convert between fractions, decimals, and percentages and when to use each.

Order of Operations

  • Remember the order of operations, often remembered by the acronym BIDMAS, standing for Brackets, Indices, Division, Multiplication, Addition, and Subtraction.
  • Note that division and multiplication, as well as addition and subtraction, are of equal precedence and should be performed from left to right.

Sequences and Series

  • Recognize and work with arithmetic sequences, where each term is a certain number (the common difference) more than the previous term.
  • Similarly, understand geometric sequences, where each term is a certain number (the common ratio) times the previous term.
  • Know how to calculate the sum of a finite arithmetic series and the sum of a finite and infinite geometric series.

Each of these key points serves as a solid foundation on which to build a deeper understanding of the notation and structure of the number system. Details of the mathematical operations and workings of these number types can then be studied individually for a comprehensive understanding of the subject.

Course material for Mathematics, module Number and Quantity, topic Notation and structure of the number system

Mathematics

Algebra and Graphs

Represent real-world problems algebraically

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Represent real-world problems algebraically

Algebraic Representation in Real-World Problems

  • Algebraic representation is a vital tool in solving real-world problems. Using variables, constants, and arithmetic operations, you can represent a problem situation with an equation or formula.

  • A variable refers to an unknown quantity while a constant is a known, unchanging quantity. Variables are often represented as letters such as 'x', 'y', 'a', 'b', etc.

  • Remember that the equation or formula you construct should reflect the relationships among the quantities in the problem situation. The objective is to solve for the unknown variable(s).

  • Units of measurement, if any, should be taken into account during the process of setting up and solving the algebraic equation. Conversion may be necessary if units do not match.

Building Algebraic Equations

  • Identify what the problem asks for. This is usually your unknown variable or the quantity you need to solve for.

  • Determine the known quantities within the problem. These could include given values, distances, quantities, times, etc.

  • Understand the relationship between the known and unknown quantities. For instance, are they directly proportional? Or does an increase in one cause a decrease in the other?

  • Use these relationships to construct your equation. For instance, if the known quantity is 'y' and the unknown is 'x', an equation could be

    y = 2x

    if 'y' is twice 'x'.

Using Algebraic Equations to Solve Problems

  • Once your equation is established, you can use algebraic methods to solve for the unknown variable(s). This might involve rearranging the equation, applying inverse operations, or using specific solution methods for complex equations such as factorisation and the quadratic formula.

  • Consider the validity of your solutions by substituting them back into the original equation. The solution is correct if it satisfies the equation.

  • Finally, interpret the solution in the context of the original problem. For example, if the problem involves time, a negative solution would typically be invalid as time cannot be negative.

Use these concepts and strategies to tackle a wide variety of real-world problems algebraically. Remember to practice problems of increasing difficulty to improve your proficiency.

Course material for Mathematics, module Algebra and Graphs, topic Represent real-world problems algebraically

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