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Forming & Solving Equations (Cambridge (CIE) IGCSE Maths)

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Cards in this collection (10)

  • Use algebra to represent double the amount of a quantity, given that x is the initial quantity.

    Double the amount of a quantity x can be written as 2 x.

  • Use algebra to represent half the amount of a quantity, given that x is the initial quantity.

    Half the amount of a quantity x can be written as 1 half x or x over 2 or 0.5 x.

  • Use algebra to represent five more than a quantity, given that x is the initial quantity.

    Five more than a quantity x can be written as x plus 5.

    This is not the same as 5 x.

  • Use algebra to represent ten lots of a quantity, given that x is the initial quantity.

    Ten lots of a quantity x can be written as 10 x.

    This is not the same as x plus 10.

  • True or False?

    If my sister is 2 years younger than me, then x is my age and x minus 2 is her age.

    True.

    If my sister is 2 years younger than me, then x is my age and x minus 2 is her age.

    It is also true to say that y plus 2 is my age and y is her age.

  • Three bags contain x, x plus 5 and x plus 10 marbles each.

    If there are 75 marbles in total, explain how to form an equation.

    Three bags contain x, x plus 5 and x plus 10 marbles each.

    If there are 75 marbles in total, then an equation can be formed by adding all the quantities up and setting them equal to 75.

    This gives x plus open parentheses x plus 5 close parentheses plus open parentheses x plus 10 close parentheses equals 75.

    Examiners want to see this full equation (before simplifying or solving).

  • If the total perimeter of the regular pentagon below is 100 cm, show how to form an equation.

    A regular pentagon with side length x + 2.

    The pentagon being regular means the side lengths are all equal.

    If the total perimeter of a regular pentagon with side length open parentheses x plus 2 close parentheses is 100 cm, then:

    1. Find the total perimeter in terms of x by multiplying open parentheses x plus 2 close parentheses by 5

    2. Set this equal to 100

    This forms the equation 5 open parentheses x plus 2 close parentheses equals 100.

  • True or False?

    If the interior angles of an n-sided polygon are given algebraically in terms of x, you can calculate the size of x as the total sum of the angles will always be 180 open parentheses n minus 2 close parentheses.

    True.

    If the interior angles of an n-sided polygon are given algebraically in terms of x, you can calculate the size of x as the total sum of the angles will always be 180 open parentheses n minus 2 close parentheses.

    E.g. for any hexagon (regular or irregular), the sum of its interior angles will always be 180 open parentheses 6 minus 2 close parentheses equals 720 degree.
    So if the interior angles are in terms of x, add them together and set equal to 720 degree.

  • True or False?

    You can use a 'show that' answer from part (a) to do part (b), even if you did not complete part (a) yourself.

    True.

    You can use a 'show that' answer from part (a) to do part (b), even if you did not complete part (a) yourself.

    If part (a) says to show that certain information leads to the equation x squared minus x minus 6 equals 0, then you can use that equation in part (b) without having proved part (a)!

  • Explain the phrase answer the question in context.

    Answer the question in context means that your final answer should

    • be related to the real-life situation in the question

    • be written in sentences

    • use words and phrases from the question

    • state the correct units

    • be rounded appropriately

    The answer should not be, for example:

    • x equals 2 (no explanation)

    • "the length is bigger" (no context)

Previous:Algebraic FractionsNext:Functions

    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