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Year 11
Higher

Evaluating iterative formulas

I can evaluate and interpret iterative formula for various real-world situations.

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New
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Year 11
Higher

Evaluating iterative formulas

I can evaluate and interpret iterative formula for various real-world situations.

Download all resources
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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. Iterative formulae use the previous iteration's output for this iteration's input
  2. A population can be estimated using an iterative formula
  3. Efficient use of the calculator makes this process much faster

Keywords

  • Iteration - Iteration is the repeated application of a function or process in which the output of each iteration is used as the input for the next iteration.

Common misconception

Some pupils want to clear their calculator display and type every single level of iteration in each time.

Encourage the pupils to trust their 'Ans' button. Get them to work on an example whereby they physically type the input value in and type the whole formula again. Then get them to repeat the same question using the 'Ans' button. Time this if you can!


To help you plan your year 11 maths lesson on: Evaluating iterative formulas, download all teaching resources for free and adapt to suit your pupils' needs...

Effective use of a calculator is very helpful for this topic. You may wish to use the Classpad feature from the Casio website to display the Classwiz on the screen to help pupils see what buttons to press.
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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

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Starter quiz

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6 Questions

Q1.
Iteration is the __________ application of a function or process in which the output of each iteration is used as the input for the next iteration.
Correct answer: repeated
mathematical
algebraic
calculative
Q2.
If $$\text{f}(x)=4x-7$$ evaluate $$\text{f}(1)$$
Correct Answer: -3
Q3.
If $$\text{f}(x)=4x-7$$ evaluate $$\text{fff}(1)$$
Correct Answer: -83
Q4.
$$£30\;000$$ is invested at a rate of $$3.25$$% interest for $$4$$ years. Which calculation will work out the value of the investment after $$4$$ years?
Correct answer: $$30\;000\times1.0325^4$$
$$30\;000\times1.04^{3.25}$$
$$30\;000\times103.25^4$$
$$30\;000\times1.0325$$
Q5.
Match the functions to the correct iterative formula we would use if we were to perform multiple repetitions of the same function.
Correct Answer:$$\text{f}(x)=3x-7$$,$$x_{n+1}=3x_{n}-7$$
tick

$$x_{n+1}=3x_{n}-7$$

Correct Answer:$$\text{f}(x)=3x^2-7$$,$$x_{n+1}=3(x_{n})^2-7$$
tick

$$x_{n+1}=3(x_{n})^2-7$$

Correct Answer:$$\text{f}(x)=3x^2-7x$$,$$x_{n+1}=3(x_{n})^2-7(x_{n})$$
tick

$$x_{n+1}=3(x_{n})^2-7(x_{n})$$

Correct Answer:$$\text{f}(x)=x^3-7$$,$$x_{n+1}=(x_{n})^3-7$$
tick

$$x_{n+1}=(x_{n})^3-7$$

Correct Answer:$$\text{f}(x)=x^3-7x^2$$,$$x_{n+1}=(x_{n})^3-7(x_{n})^2$$
tick

$$x_{n+1}=(x_{n})^3-7(x_{n})^2$$

Q6.
$$£150$$ is invested at a rate of $$5.5$$% compound interest p.a. After how many years will the savings first be worth $$£500$$? years.
Correct Answer: 23, 23 years

Exit quiz

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6 Questions

Q1.
Iteration is the repeated application of a function or process in which the of each iteration is used as the input for the next iteration.
Correct Answer: output
Q2.
Using the iterative formula $$x_{t+1}=8x_t-17$$ and $$x_0=5$$ find the value of $$x_1$$
Correct Answer: 23
Q3.
Using the iterative formula $$x_{t+1}=8x_t-17$$ and $$x_0=5$$ find the value of $$x_5$$
Correct Answer: 84263, 84 263
Q4.
Using the iterative formula $$x_{t+1}={3(x_t)^2-12(x_t)+15}$$ and $$x_0=1$$ find the value of $$x_2$$
Correct Answer: 51
Q5.
Using the iterative formula $$x_{t+1}={3(x_t)^2-12(x_t)+15}$$ and $$x_0=1$$ find the value of $$x_4$$
$$7206$$
$$7602$$
$$155\;692$$
$$692\;851$$
Correct answer: $$155\;692\;851$$
Q6.
There are $$20\;000$$ fish in a lake. Every year $$4000$$ fish are fished and removed. The remaining population reproduces and grows by $$12$$%. After how many years will the stock of fish reach zero?
$$5$$ years
$$6$$ years
Correct answer: $$7$$ years
$$8$$ years
$$9$$ years