Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Solving equations involving functions

      Lesson details

      Learning outcome

      I can solve equations involving functions.

      Key learning points

      1. A function may have a given output.
      2. It is possible to solve to find the input.

      Keywords

      • Function - A function is a mathematical relationship that uniquely maps values of one set to the values of another set.

      • Equation - An equation is used to show two expressions that are equal to each other.

      Common misconception

      Small slips in working can lead to the wrong answer and pupils are not clear on how to check their working.

      The lesson models how to check working so that the correct answer can be verified. This is good practice and helps pupils identify if there is an error.

      Teacher tip

      Pupils need to be able to manipulate equations in order to access this lesson. Consider reviewing these skills before this lesson if you think your pupils would benefit from this.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      An equation is used to show two expressions that are __________ each other.

      unlike
      like
      Correct answer: equal to
      unequal to

      Q2.
      If $${\text{f}}(x)=7x−4$$ evaluate $${\text{f}}(8)$$.

      Correct Answer: 52, f(8)=52

      Q3.
      Solve $$7x-5=-26$$ $$x=$$

      Correct Answer: -3, x=-3

      Q4.
      Solve $$7x-5=31-3x$$ $$x=$$

      Correct Answer: 3.6, x=3.6

      Q5.
      Solve $$x^2+3x-26=7x-5$$.

      Correct answer: $$x=7$$
      $$x=3$$
      Correct answer: $$x=-3$$
      $$x=-7$$
      This equation has no solutions.

      Q6.
      Solve $${4\over{3x+7}}={3\over{x-1}}$$ $$x=$$

      Correct Answer: -5, x=-5

      6 Questions

      Q1.
      If $${\text{f}}(8)=145$$ then $${\text{f}}(x)$$ is a function which __________ $$8$$ to $$145$$.

      multiplies
      scales up
      sums
      Correct answer: maps

      Q2.
      If $${\text{f}}(x)=5(x−11)$$ solve $${\text{f}}(x)=50$$ $$x=$$ .

      Correct Answer: 21, x=21

      Q3.
      If $${\text{f}}(x)=x^2−8x$$ solve $${\text{f}}(x)=-12$$.

      Correct answer: $$x=6$$
      Correct answer: $$x=2$$
      $$x=-2$$
      $$x=-6$$
      This equation has no solutions.

      Q4.
      If $${\text{f}}(x)=5(x−11)$$ and $${\text{g}}(x)=2x+5$$ solve $${\text{f}}(x)={\text{g}}(x)$$ $$x=$$ .

      Correct Answer: 20, x=20

      Q5.
      If $${\text{f}}(x)={7\over{3x}}$$ solve $${\text{f}}(x)=21$$.

      $$x=9$$
      $$x=3$$
      $$x=1$$
      $$x={1\over3}$$
      Correct answer: $$x={1\over9}$$

      Q6.
      If $${\text{f}}(x)={{5x+11}\over{2}}$$ and $${\text{g}}(x)=-{{1}\over{x}}$$ solve $${\text{f}}(x)={\text{g}}(x)$$.

      Correct answer: $$x=-2$$
      Correct answer: $$x=-{1\over5}$$
      $$x={1\over5}$$
      $$x=2$$
      $$x=5$$

      To help you plan your 11 maths lesson on: Solving equations involving functions, download all teaching resources for free and adapt to suit your pupils' needs...