# Graphs and Transformations

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

#### Prerequisite Knowledge

• 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

### Mr Mathematics Blog

#### Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

#### GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

#### Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.