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.

Building on composite functions

Maths

Checking and securing understanding of compound interest calculations

Evaluating iterative formulas

Approximating solutions to equations

Signs of a solution

Problem solving with iteration

In this unit, pupils continue to explore composite functions, thereby building on their work from the prior unit. Pupils need to understand function notation from the prior unit as this is used in iteration.

In this unit, pupils continue to explore composite functions and develop understanding of iteration, building on their work on functions and proof.

Iteration

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

In iteration notation how do we communicate 'Year 6'?

In iteration notation we use $$y_t$$ to express the current year. How do we express the next year?

$$£250$$ is invested at a rate of $$4$$% interest for $$3$$ years. Which iterative formula links the current term to the next term?

Match the iterative formulae to their matching scenario.

If we were simplifying multiple representations of the function $$\text{f}(x)=3x^2-7x+1$$ which iterative formula would we use?

__________ interest is when the interest is calculated on the original amount and the interest accumulated over the previous period.

Which of the below is the formula for compound interest?

$$£2000$$ is invested at a rate of $$6.5$$% interest for $$3$$ years. How much is the investment worth at the end of the $$3$$ years? £{{}}

If $$\text{f}(x)=13x-17$$ evaluate $$\text{f}(3)$$

$$\text{f}(x)=10-3x$$ Match the composite functions to their respective values.

This table shows the yearly values when $$£800$$ is invested in a savings account with compound interest. What is the unknown value of 'Year $$1$$'?

Building on composite functions

Lesson outcome