Level 2 Additional Mathematics WJEC

This subject is broken down into 33 topics in 5 modules:

  1. Algebra 12 topics
  2. Coordinate Geometry 7 topics
  3. Mensuration 1 topics
  4. Calculus 9 topics
  5. Trigonometry 4 topics
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  • 33
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  • 11,720
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  • 1+
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This page was last modified on 28 September 2024.

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Additional Mathematics

Algebra

Simplify numerical expressions involving surds

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Simplify numerical expressions involving surds

Surds Basics

  • Surds are numbers left in 'square root form' (or 'cube root form' etc). They are often used when the square root of a number doesn't have an exact value.
  • A surd can be manipulated with the same mathematical rules as other numerical expressions.

Simplifying Surds

  • To simplify a surd, find the largest square number that divides into the number under the square root sign.
  • For example, to simplify √18, which can be expressed as √(9*2), it becomes 3√2.
  • The process of simplifying surds is called 'rationalising the denominator'.

Multiplying and Dividing Surds

  • When multiplying surds, multiply the numbers under the root. For ​example, √2 * √3 = √6.
  • When dividing surds, divide the numbers under the root. For example, √8 / √2 = √4 = 2.

Adding and Subtracting Surds

  • Surds can be added or subtracted when they are the same type. For example, √3 + √3 = 2√3.
  • If the surds are not the same type, they cannot be added or subtracted directly. For example, √2 + √3 cannot be simplified further.

Rationalising the denominator

  • When a surd is in the denominator of a fraction, the fraction needs to be manipulated until the surd is removed from the denominator. This process is called 'rationalising the denominator'.
  • To rationalise the denominator, multiply the top and bottom of the fraction by the conjugate of the bottom. For example (1/√3) * (√3/√3) = √3/3.

Course material for Additional Mathematics, module Algebra, topic Simplify numerical expressions involving surds

Additional Mathematics

Coordinate Geometry

Equations of lines parallel and perpendicular to a given line

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Equations of lines parallel and perpendicular to a given line

Section 1: Understanding Parallel and Perpendicular Lines

  • Two lines are said to be parallel if their gradients are equal, i.e., they have the same steepness but do not intersect at any point.
  • Conversely, two lines are said to be perpendicular if the product of their gradients is -1, which indicates that they intersect at a right angle (90 degrees).

Section 2: Formula for Equations of Parallel Lines

  • If a line is parallel to another line with a known equation, then the gradient of both lines is the same.
  • The equation of a straight line is given by the format

    y = mx + c

    , where

    m

    represents the gradient and

    c

    is the y-intercept (the point where the line crosses the y-axis).
  • If line 1 has the equation

    y = mx + c1

    and you need to find the equation of a line parallel to it through a given point

    (x1, y1)

    , the equation can be found by substituting

    x1

    and

    y1

    into the equation form:

    (y1) = m(x1) + c

    and then solve for

    c

    , and your equation will be of the form

    y = mx + c

    .

Section 3: Formula for Equations of Perpendicular Lines

  • If a line is perpendicular to another line with a known equation, the gradients of the two lines are negatives reciprocals of each other. The gradient of the line perpendicular to a line with gradient

    m

    is

    -1/m

    .
  • Given an original line with the equation

    y = mx + c1

    , if you need to find the equation of a line perpendicular to the original line and passing through a point

    (x1, y1)

    , the gradient of the new line will be

    -1/m

    .
  • Substitute

    x1

    ,

    y1

    , and the new gradient into the equation

    (y1) = (-1/m)(x1) + c

    and solve for

    c

    , to get the equation of the line in the form of

    y = (-1/m)x + c

    .

Section 4: Practical Applications

  • The concept of parallel and perpendicular lines is frequently used in geometry to prove theories, solve problems and construct figures.
  • In the real world, this forms the basis for various fields such as engineering, architecture, and computer graphics among others.
  • Mastery of this subject enhances problem-solving skills that find use in many advanced fields in mathematics.

Course material for Additional Mathematics, module Coordinate Geometry, topic Equations of lines parallel and perpendicular to a given line

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