Non-linear graphs

Term 1 starting in week 3 :: Estimated time: 2 weeks

Plot and read from quadratic graphs
Plot and read from cubic graphs
Plot and read from reciprocal graphs
Recognise graph shapes
Identify and interpret roots and intercepts of quadratics

For higher-attaining pupils:

Understand and use exponential graphs
Find and use the equation of a circle centre (O, O)
Find the equation of the tangent to any curve

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Activities for pupils

Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

Graph Paper Flexible graph paper which can be printed or projected onto a white board as an effective visual aid.

Plotting Graphs Complete a table of values then plot the corresponding points to create a graph.

Straight Line Graphs Video After drawing a straight line graph learn about its equation in the form y = mx + c.

Graph Equation Pairs Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function.

Hurdles Race An animated distance time graph to be viewed while a student interprets the graph and comments on the race that produced the graph.

Graph Patterns Find the equations which will produce the given patterns of graphs.

Straight Line Graphs 10 straight line graph challenges for use with computer graph plotting software or a graphical display calculator.

Graph Match Match the equations with the images of the corresponding graphs. A drag-and-drop activity.

Graph Plotter An online tool to draw, display and investigate graphs of many different kinds.

Human Graphs Students should be encouraged to stand up and make the shapes of the graphs with their arms.

Circle Equations Recognise and use the equation of a circle with centre at the origin and the equation of a tangent to a circle.

Here are some exam-style questions on this topic:

"Sketch the graph of \(y=0.5^x +1\) for \(0 \le x \le 5\) labeling the y intercept." ... more

"(a) Use the red graphs to solve the simultaneous equations:" ... more

"The images below show a graphic display calculator screen with different functions displayed as graphs." ... more

"Match the equation with the letter of its graph" ... more

"Marilou and Sam had a skiing race. Here is Marilou’s speed-time graph from the start of the race." ... more

\(x\)	-3	-2	-1	-0.5	0.5	1	2	3	4
\(y\)	3.2	2.5		8.5	7.5	1.0		-2.8

"The table shows some values (rounded to one decimal place) for the function \(y=\frac{2}{x^2}-x, x\neq 0\).

\(x\) -3 -2 -1 -0.5 0.5 1 2 3 4

\(y\) 3.2 2.5 8.5 7.5 1.0 -2.8

(a) Complete the table of values." ... more

"What is the equation of a circle, centered at the origin, that has a tangent passing through the points (-30, 0) and (0, -15)?" ... more

"The graph shows the distance travelled, in metres, of a commuter train as it pulls out of a station." ... more

"The diagram shows a circle with equation \(x^2+y^2=13\)." ... more

"(a) Find the coordinates of the point at which the curve \(y = k^x\) intersects the y-axis." ... more

"A circle with equation \(x^2 + y^2 = 6 \) meets a one of its tangents at point \(S\)." ... more

" (a) The circumference of a circle is \(16 \pi \) cm and its centre is at the origin. Find the equation of the circle." ... more

See all these questions

Here are some Advanced Starters on this statement:

Average Cycling Speed
Work out the average speed of two journeys. The obvious answer is not the correct answer. more

Venn Graphs
Type the equation of a graph into each section of the Venn diagram. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

Graphs This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts. A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops. Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.

Lesson Starters

Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.

1st Lesson

Two Twins and Tim

A tricky problem set on a coordinate grid.

2nd Lesson

Four Factors

Find four single digit numbers that multiply together to give 120. How many different ways are there of answering this question?

3rd Lesson

Freemason's Cipher

Find symmetric words in this ancient cipher.

4th Lesson

Dice Reflections

A dice is reflected in two mirrors. What numbers can be seen?

5th Lesson

9:50 Puzzle

A little lateral thinking might help you solve this puzzle.

6th Lesson

Refreshing Revision

It is called Refreshing Revision because every time you refresh the page you get different revision questions.

Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.

White Rose Resources

End of block assessments provide a quick progress check at the end of each block of learning to make sure students have understood the content covered.