GCSE Maths Graphs: Key Terms and Equations

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Amy studied at the University of Bristol and is our revision blog guru. She only graduated recently so understands the pressures of being a student better than most, and is here to share her wisdom so that you revise effectively, smash your exams, succeed at school and write cracking university and job applications.

A number of GCSE Maths questions will require you to either draw or interpret graphs, and make calculations based on the values you’ve been given. There are lots of different types of graphs that might crop up in your exam, and a number of formulae you need to remember in order to draw them.  Here’s a quick run-down of some of the key formula you need to know in order to calculate and draw accurate graphs at GCSE Maths level.

Key terms  

Axes: The two perpendicular lines against which a graph is drawn. The vertical axis is ‘y’ and the horizontal axis is ‘x’

Gradient: The slope of the line on a graph

Intercept: The point at which the line crosses the axes

GCSE Maths Graphs Axes

Straight Line Graphs

A straight line graph has equation y = mx +c where:

m is the gradient (slope) of the graph (remember gradient = rise/run)

c is the y-intercept (where the line crosses the y-axis)

(x and y are the variables)

Horizontal lines have equation y = c (because gradient = 0).

Vertical lines have equation x = d (d is where it cuts the x axis).

GCSE Maths Straight Line Graphs

Distance-Time Graphs

Distance-Time Graphs show distance on the vertical (Y) axis and time on the horizontal (X) axis.

The gradient of the line on a distance-time graph is the speed travelled during that period.

For a straight line segment use speed = distance/time.Distance-Time Graphs

Speed-Time Graphs

The gradient of a Speed-Time graph is acceleration. Change in speed (y axis) divided by change in time (x axis) = change in metres per second divided by change in seconds = metres per second per second (or metres per second squared). If the gradient is negative then it is deceleration.

A velocity time graph works in the same way but velocity can be negative.

Speed or Velocity will show on the vertical (y) axis.

Quadratic Graphs

A quadratic graph is produced when you have an equation of the form y = ax² + bx + c , where b and c can be zero but a cannot be zero.

All quadratic graphs have a vertical line of symmetry.

If a > 0, the graph is smiley (as pictured). If a < 0 the graph is grumpy (the other way up).

GCSE Maths Quadratic Graphs

Cubic Graphs 

A cubic equation contains only terms up to and including x³, such as:

y = x³

y = x³ + 5

Cubic graphs are curved but can have more than one change of direction.

GCSE Maths Cubic Graphs

Reciprocal Graphs 

A graph of the form y = 1/x  is known as a reciprocal graph and looks like this when drawn:

GCSE Maths Reciprocal Graphs

Exponential Graphs 

Exponential graphs increase sharply in the y direction and will never fall below the x axis.

GCSE Maths Exponential Graphs

Circle Graphs 

Using Pythagoras’ theorem, the equation of a circle with radius and centre (0, 0) is given by the formula x² + y² = r².

The equation of the tangent is of the form y = mx + c.

GCSE Maths Circle Graphs

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