The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.

Displacement is the distance from the starting point when measured in a straight line.

Distance-time graphs

Maths

Checking and securing understanding of reading from context-based graphs

Checking and securing understanding of drawing distance-time graphs

Speed-time graphs

Non-linear distance-time graphs

Interpreting and drawing real-life graphs

Interpreting and drawing more 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

This is a distance-time graph for a journey. What was the total distance travelled?

This is a displacement-time graph for a journey. How far was travelled in total?

Here is a distance-time graph for a race car driving on a straight track. How fast is the car going?

What speed is the object travelling at between 4 and 6 hours? Give your answer in km/h.

The distance-time graph shows a two stage journey of an object. What is the average speed of this object?

The average speed for this journey is {{}} km/h.

What number is the arrow pointing to on this number line?

Here is a distance-time graph for a journey. How far had been travelled after 1 hour?

Here is a distance-time graph for a journey. How far had been travelled after 3 hours?

Moving away from the fixed start point at a constant speed.

Moving towards the fixed start point at a constant speed.

On this displacement-time graph what does the line segment marked a) represent?

Starter Quiz

What number is the arrow pointing to on this number line?