An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.

Checking and securing understanding of non-linear sequences

Maths

Extending thinking about sequences

Exploring the shapes of graphs using technology

Equations and their graphs

Efficiently drawing linear graphs

Reading from graphs

Modelling with graphs

Graphically solving two linear graphs that intersect

Problem solving with graphical representations

In this unit, pupils studied the graphical representation of a geometric sequence and linked features of the graph to its equation. In the future unit, other types of graphs are introduced and their key features identified.

In the prior unit, pupils considered geometric sequences and how they might be represented graphically. In this unit, pupils study the graphical representation to link features of the graph to its equation.

In this unit pupils draw, interpret and utilise linear graphs to solve problems. This knowledge is further extended to look at intersecting graphs.

Graphical representations

An arithmetic (or linear) sequence is a sequence where the difference between terms is a constant.

A quadratic is an equation whereby the highest exponent of the variable is 2; the graph of which forms a parabola.

A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus) and a fixed straight line (a directrix).

The gradient is a measure of how steep a line is.

An intercept is the coordinate where a line or curve meets a given axis.

The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

A quadratic is a an equation, graph, or sequence whereby the highest exponent of the variable is 2.

A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).

The rate of change is how quickly one variable changes in relation to another.

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

Graphical representations

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