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Rearranging Formulas (Cambridge (CIE) IGCSE Maths)

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  • FrontFormulas where Subject Appears Once

    Define the term subject in the context of formulas.

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  • Define the term subject in the context of formulas.

    The subject is the variable that is by itself on one side of the formula.

    You can find its value if you substitute in the values for all the variables on the other side of the formula.

    Rearranging a formula to get a different variable by itself on one side is known as 'changing the subject'.

  • True or false?

    The methods for changing the subject of a formula are the same as the methods for solving an equation.

    True.

    The methods for changing the subject of a formula are the same as the methods for solving an equation.

    For example, if you want to make a the subject of a formula, 'solve' the formula for a.

    The only difference is that the 'answer' will be another formula, not a number.

  • True or False?

    If a formula contains the power n, e.g. x to the power of 5 equals y plus 3,you can use the nth root to reverse this operation.

    True.

    If a formula contains the power n, you can use the nth root to reverse this operation.

    E.g.

    x to the power of 5 equals y plus 3 x equals fifth root of y plus 3 end root

    Just be careful if n is an even number as you need a plus-or-minus sign, for example if x squared equals... then x equals plus-or-minus square root of... end root

  • True or False?

    To rearrange a formula with fractions, e.g. fraction numerator 2 a over denominator 7 end fraction plus b equals c, you should first multiply both sides of the equation by the denominator(s).

    True.

    To rearrange a formula with fractions, you should first multiply both sides of the equation by the denominator(s).

    This gets rid of the fractions and makes the formula easier to rearrange.

    E.g.

    table row cell fraction numerator 2 a over denominator 7 end fraction plus b end cell equals c row cell 2 a plus 7 b end cell equals cell 7 c end cell end table

  • True or False?

    If the letter you want to make the subject appears twice in a formula,

    e.g. b equals fraction numerator 2 a over denominator c minus a end fraction, you will not need to factorise to change the subject.

    False.

    If the letter you want to make the subject appears twice in a formula, you will often need to factorise to change the subject.

    For example, to make a the subject of b equals fraction numerator 2 a over denominator c minus a end fraction:

    • Multiply both sides by c minus a:   b open parentheses c minus a close parentheses equals 2 a

    • Expand the brackets:   b c minus a b equals 2 a

    • Get the terms with a onto one side:   b c equals 2 a plus a b

    • Factorise the right-hand side:   b c equals a open parentheses 2 plus b close parentheses

    • Divide both sides by 2 plus b:   fraction numerator b c over denominator 2 plus b end fraction equals a

Previous:Quadratic EquationsNext:Simultaneous Equations

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions Toolkit

    6. Topic 6

      Percentages Toolkit

    7. Topic 7

      Simple & Compound Interest, Growth & Decay

    8. Topic 8

      Surds

    9. Topic 9

      Working with FDP

    10. Topic 10

      Working with Ratios

    11. Topic 11

      Compound Measures (Speed, Density, Pressure)

    12. Topic 12

      Time, Currency & Conversions

    13. Topic 13

      Rounding, Estimation & Bounds

    14. Topic 14

      Using a Calculator

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding & Factorising Brackets

    4. Topic 4

      Linear Equations & Inequalities

    5. Topic 5

      Quadratic Equations

    6. Topic 6

      Rearranging Formulas

    7. Topic 7

      Simultaneous Equations

    8. Topic 8

      Algebraic Fractions

    9. Topic 9

      Forming & Solving Equations

    10. Topic 10

      Functions

    11. Topic 11

      Sequences

    12. Topic 12

      Proportion

    1. Topic 1

      Coordinate Geometry

    2. Topic 2

      Linear Graphs

    3. Topic 3

      Quadratic Graphs

    4. Topic 4

      Further Graphs & Tangents

    5. Topic 5

      Solving & Graphing Inequalities

    6. Topic 6

      Real-Life Graphs

    7. Topic 7

      Differentiation

    1. Topic 1

      Geometry Toolkit

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Constructions & Scale Drawings

    4. Topic 4

      Circle Theorems

    1. Topic 1

      Area & Perimeter

    2. Topic 2

      Circles, Arcs & Sectors

    3. Topic 3

      Volume & Surface Area

    4. Topic 4

      Congruence & Similarity

    1. Topic 1

      Right-Angled Triangles (Pythagoras & Trigonometry)

    2. Topic 2

      Sine, Cosine Rule & Area of Triangles

    3. Topic 3

      3D Pythagoras & Trigonometry

    4. Topic 4

      Trigonometric Graphs & Equations

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Basic Probability

    2. Topic 2

      Probability Diagrams (Tree & Venn Diagrams)

    3. Topic 3

      Conditional Probability

    1. Topic 1

      Averages & Range

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency

    5. Topic 5

      Scatter Graphs & Correlation