Functions
Term 1 starting in week 11 :: Estimated time: 2 weeks
- Use function machines (review)
- Substitute into expressions and formulae (review)
- Use function notation
- Graphs of quadratic functions
- Understand and use trigonometric functions (review)
For higher-attaining pupils:
- Work with composite functions
- Work with inverse functions
- Solve quadratic inequalities (review)
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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.
Brainbox A puzzle requiring the arrangement of numbers on the function machines to link the given input numbers to the correct output.
Graph Paper Flexible graph paper which can be printed or projected onto a white board as an effective visual aid.
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.
Inequalities Check that you know what inequality signs mean and how they are used to compare two quantities. Includes negative numbers, decimals, fractions and metric measures.
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.
Name that Graph Choose from the given functions the one that best describes the shape of the graph.
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.
Functions An online exercise on function notation, inverse functions and composite functions.
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
- "\(f(x) = \frac{2x}{5} + 7\) and \(g(x) = 10x^2 - 15\) for all values of \(x\)." ... more
- "The function \(f\) is described by the following formula:" ... 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
- "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 - "(a) A function is represented by the following function machine." ... more
- "(a) Solve the simultaneous equations." ... more
- "Four functions have been defined in the following way:" ... more
- "If \(f(x)=5-4x\) and \(g(x)=4^{-x}\) then:" ... more
- "Here is a function machine that produces two outputs, A and B." ... more
- "(a) Find the coordinates of the point at which the curve \(y = k^x\) intersects the y-axis." ... more
- "The functions \(f\) and \(g\) are such that:" ... more
- "The functions f and g are defined as follows:" ... more
Here are some Advanced Starters on this statement:
- Permutable Functions
Find pairs of functions that are commutative under composition. 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.
- Algebra Pupils begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or many operations. They use brackets, indices and other constructs to apply algebra to real word problems. This leads to using algebra as an invaluable tool for solving problems, modelling situations and investigating ideas. If this topic were split into four sub topics they might be: Creating and simplifying expressions; Expanding and factorising expressions; Substituting and using formulae; Solving equations and real life problems; This is a powerful topic and has strong links to other branches of mathematics such as number, geometry and statistics. See also "Number Patterns", "Negative Numbers" and "Simultaneous Equations".
- 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
Inbetweens
Find fractions between two given values.
2nd Lesson
Less Than
This mathematics lesson starter invites pupils to interpret a three part algebraic inequality.
3rd Lesson
Christmas Bells
If all the bells ring together at noon, at what time will they next all ring together? This problem requires the use of LCM.
4th Lesson
Christmas Presents
Work out the total cost of five Christmas presents from the information given.
5th Lesson
Christmas Eve Snow
Each different letter stands for a different digit. Can you make sense of this word sum?
6th Lesson
Christmas Tables
Which of the two shapes has the largest area? You will be surprised!
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.
