Interest is money added to savings or loans. Simple interest is always calculated on the original amount.

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

The general form for an exponential equation is $$y = ab^x$$ where $$a$$ is the coefficient, $$b$$ is the base and $$x$$ is the exponent.

Speed is the rate at which something is moving. It is measured as the distance travelled per unit of time.

Acceleration is the rate of change of speed with respect to time.

Interpreting and drawing more real-life graphs

Maths

Checking and securing understanding of reading from context-based graphs

Checking and securing understanding of drawing distance-time graphs

Distance-time graphs

Speed-time graphs

Non-linear distance-time graphs

Interpreting and drawing real-life graphs

Calculating the rate of change

Estimating the gradient of a curve

Improving the estimate of the gradient of a curve

Finding the equation of a radius of a circle

Finding the equation of the tangent to a circle

Calculating journeys from linear speed-time graphs

Estimating journeys from non-linear graphs

Efficiently estimating journeys from non-linear graphs

Advanced problem solving with real-life graphs

The work on gradient in the prior unit is expanded further in this unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In this unit pupils expand upon knowledge developed in the linear graphs unit. Pupils are introduced to rates of change and the gradient of the tangent as a way of estimating the gradient of a curve.

Real-life graphs

Which would be the equation of the line if graphing £300 invested at a simple interest rate of 2% per month?

Which would be the equation of the exponential curve if graphing £500 invested at a simple interest rate of 3% per month?

Which of these equations could model the value of a car depreciating over time? 

Which of these journey segments show deceleration on a displacement-time graph?

Increasing in speed moving away from the fixed start point.

Decelerating moving away from the fixed start point.

Increasing in speed moving towards the fixed start point.

Decelerating moving back towards the fixed start point.

Match the sections of the graph labelled a)-f) with the correct part of the journey.

Here is a displacement-time graph for a journey. Which of these could be a speed-time graph of the same journey?

Interest which is calculated on the original amount and the interest accumulated over the previous period is called __________.

£200 is invested into an account with 3% simple interest each year. How much will be in the account after 5 years?

£200 is invested into an account with 3% compound interest each year. Which of these calculations will give the amount in the account after 5 years?

£1000 is invested into an account with 2% compound interest paid monthly. How much would be in the account after 1 year? Round to the nearest pence.

Select the coordinates that lie on the curve $$y=3^x$$

The general form for an exponential equation is:

Interpreting and drawing more real-life graphs

Lesson outcome