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**Scheme of work: GCSE Higher: Year 10: Term 5: Non-Linear Graphical Functions**

- Plot graphs of equations that correspond to straight-line graphs in the coordinate plane
- Recognise, sketch and interpret graphs of linear functions

- Recognise, plot and interpret graphs of quadratic functions, simple cubic functions and the reciprocal function y = 1/x with x not equal to 0.
- Solve quadratic equations by finding approximate solutions using a graph
- Plot and interpret graphs exponential graphs
- Recognise and use the equation of a circle with centre at the origin
- Find the equation of a tangent to a circle at a given point.

- To generate the coordinates students need to have a secure understanding of applying the order of operations to substitute and evaluate known values into equations.
- Quadratic, Cubic and Reciprocal functions are non-linear and therefore do not have straight lines. All graphs of this nature should be drawn with smooth curves.
- When solving equations graphically students should realise solutions are only approximate.
- Students need to gain an understanding of the shape of each function in order to identify incorrectly plotted coordinates.
- The equation of a circle relates very closely to Pythagoras theorem.
- Exponential graphs can be increasing as well as decreasing.
- Students need to understand the equivalence between linear graphs in the form y = mx + c and ax + by + c = 0.

- Students often have difficulty substituting negative values for complex equations. Encourage the use of mental arithmetic.
- Identifying the correct type of function from graphs is often a source of confusion.
- By creating the table of results students will be more able to choose a suitable scale for their axes.
- Students who complete the table of results correctly often have little difficulty plotting the graph correctly.
- Students often have difficulty drawing the equation of a circle correctly in examinations.
- Students often have difficulty stating the equation of a linear graph in the form ax + by + c = 0.

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