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These are the Transum resources related to the statement: "Understand and use graphs of functions; sketch curves defined by simple equations including polynomials. The modulus of a linear function. Reciprocal graphs including their vertical and horizontal asymptotes. Interpret algebraic solution of equations graphically; use intersection points of graphs to solve equations. Understand and use proportional relationships and their graphs".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Direct and Inverse Proportion A self-marking exercise in solving direct and inverse variation problems.
- Graph Equation Pairs Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function.
- Graph Match Match the equations with the images of the corresponding graphs. A drag-and-drop activity.
- Graph Patterns Find the equations which will produce the given patterns of graphs.
- Human Graphs Students should be encouraged to stand up and make the shapes of the graphs with their arms.
- Straight Line Graphs 10 straight line graph challenges for use with computer graph plotting software or a graphical display calculator.

Here are some exam-style questions on this statement:

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*At depths below 900 metres, the temperature of the water in the sea is given by the formula:*" ... more - "
*Match the equation with the letter of its graph*" ... more - "
*The following table shows corresponding values for two variables \(x\) and \(y\).*" ... more - "
*(a) Sketch a graph on the axes below left that shows that \(y\) is directly proportional to \(x\).*" ... more - "
*At a constant temperature, the volume of a gas \(V\) is inversely proportional to its pressure \(p\). By what percentage will the pressure of a gas change if its volume increases by 15% ?*" ... more - "
*Let \(f(x)=5x^2-20x+k\). The equation \(f(x)=0\) has two equal roots.*" ... more - "
*Let \(f(x) = \frac{9x-3}{bx+9}\) for \(x \neq -\frac9b, b \neq 0\).*" ... more

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

- Functions A relationship between two sets can be called a mapping. Elements of the first set (domain) are mapped to elements of the second set (range). A function is a special type of mapping for which one value in the domain maps to one, and only one value in the range.Pupils in Primary school will use the concept of function machines to perform calculations. They will then learn to ‘work backwards’ to find the inverse function. The study of functions becomes more formal as pupils become more proficient and able to cope with more complex mathematical ideas.
- 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.

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