The rate of change is how one variable changes with respect to another. If the change is constant, there is a linear relationship between the variables.

Checking and securing understanding of reading from context-based graphs

Maths

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

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

Checking and securing understanding of drawing distance-time graphs

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.

Distance-time graphs

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

Deceleration is the rate at which the speed of an object is decreasing.

Speed-time graphs

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

Non-linear distance-time graphs

Time series graphs show data over a time period. The time period is always shown on the $$x$$-axis. Data points are joined chronologically by line segments.

Extrapolation is the process of estimating unknown values that are outside the range of existing data.

Interpolation is the process of estimating unknown values that are inside the range of existing data.

Interpreting and drawing real-life graphs

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.

Interpreting and drawing more real-life graphs

Calculating the rate of change

Estimating the gradient of a curve

A tangent to a curve at a given point is a line that intersects the curve at that point. Both the tangent and the curve have the same gradient at the given point.

Improving the estimate of the gradient of a curve

The radius is any line segment that joins the centre of a circle to its edge.

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.

Finding the equation of a radius of a circle

A tangent of a circle is a line that intersects the circle exactly once.

Finding the equation of the tangent to a circle

A compound shape is a shape created using two or more basic shapes.

Calculating journeys from linear speed-time graphs

A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure.

Estimating journeys from non-linear graphs

A generalisation is a statement or rule that applies correctly to all relevant cases.

Real-life graphs

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These lessons will be removed by end of Summer Term 2025.