Equations and Inequalities

June 1, 2022

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

Prerequisite Knowledge

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

Success Criteria

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.

Key Concepts

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.

Common Misconceptions

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.

Graphs and Transformations Resources

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