Revision NotesExam QuestionsFlashcardsPast Papers
GCSEMathsAQAHigherFlashcards2. AlgebraRearranging Formulas

Rearranging Formulas (AQA GCSE Maths)

Flashcards

1/5

0Still learning

Know0

  • FrontFormulas where Subject Appears Once

    Define the term subject in the context of formulas.

Enjoying Flashcards?
Tell us what you think

Cards in this collection (5)

  • 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:Algebraic FractionsNext:Algebraic Proof

    1. Topic 1

      Number Operations

    2. Topic 2

      Prime Factors, HCF & LCM

    3. Topic 3

      Powers, Roots & Standard Form

    4. Topic 4

      Fractions

    5. Topic 5

      Percentages

    6. Topic 6

      Simple & Compound Interest, Growth & Decay

    7. Topic 7

      Fractions, Decimals & Percentages

    8. Topic 8

      Rounding, Estimation & Bounds

    9. Topic 9

      Surds

    10. Topic 10

      Using a Calculator

    1. Topic 1

      Introduction to Algebra

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Linear Equations

    10. Topic 10

      Quadratic Equations

    11. Topic 11

      Simultaneous Equations

    12. Topic 12

      Iteration

    13. Topic 13

      Forming & Solving Equations

    14. Topic 14

      Functions

    15. Topic 15

      Coordinate Geometry

    16. Topic 16

      Linear Graphs

    17. Topic 17

      Graphs of Functions

    18. Topic 18

      Equation of a Circle

    19. Topic 19

      Estimating Gradients & Areas under Graphs

    20. Topic 20

      Real-Life Graphs

    21. Topic 21

      Solving Inequalities

    22. Topic 22

      Graphing Inequalities

    23. Topic 23

      Transformations of Graphs

    24. Topic 24

      Sequences

    1. Topic 1

      Ratios

    2. Topic 2

      Problem Solving with Ratios

    3. Topic 3

      Direct & Inverse Proportion

    4. Topic 4

      Standard & Compound Units

    5. Topic 5

      Exchange Rates & Best Buys

    1. Topic 1

      Symmetry & Shapes

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing, Constructions & Loci

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    13. Topic 13

      Vectors

    14. Topic 14

      Transformations

    1. Topic 1

      Introduction to Probability

    2. Topic 2

      Simple Probability Diagrams

    3. Topic 3

      Tree Diagrams

    4. Topic 4

      Combined & Conditional Probability

    1. Topic 1

      Averages, Ranges & Data

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency & Box Plots

    5. Topic 5

      Scatter Graphs & Correlation