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**Scheme of work: Year 12 A-Level: Pure 1: Equations and Inequalities**

- Sketch a quadratic graph
- Translate a graphical function in form f(x ± a) and f(x) ± a
- Stretch a graphical function in the form f(ax) and af(x)
- Understand and use function notation, including composite functions and inverse functions

- Understand and use graphs of functions;
- Be able to sketch curves defined by simple equations, including polynomials;
- Be able to use intersection points of graphs to solve equations.

- Before plotting cubic and quartic graphs, freehand students should use a graphical software package such as Desmos or Geogebra to understand their properties.
- When finding points of intersection algebraically, students should be encouraged to check their answers using a sketched graph online.
- In addition to plotting a graph from an equation, students should be able to use the properties of the graph to derive the equation.
- Students have not yet encountered long division at this point in the course, so polynomials need to be easily factorised or given in their simplest form.
- When sketching reciprocal functions, students should begin with f(x) = 1/x and use transformations to build it up to the desired function.

- Students are often confused about the number of roots a polynomial has when they involve repeated roots.
- When plotting cubic and quartic graphs, students often confuse the direction of curves.
- Students lose examination marks by not labelling all the key coordinates where the curve passes through the axes.

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