GCSE Maths: Graphs of Functions

Once straight lines are secure, GCSE Mathematics moves on to curves: you are expected to recognise, sketch and interpret the graphs of quadratic, cubic and reciprocal functions and, on the Higher tier, exponential and trigonometric graphs, the circle with centre the origin, and translations and reflections of a graph. This material follows the graphs content of the GCSE subject content for England, beyond the straight-line work covered elsewhere in the category.

The quiz has thirteen questions, each describing the graph in words and symbols so no picture is needed. You find the roots of a quadratic, its y-intercept and line of symmetry, and (Higher) its turning point by completing the square; you recognise a reciprocal graph from a description and find where a cubic crosses the x-axis. Higher-tier questions cover the key features of $y=2^x$ and $y=\sin x$, the equation of a circle with centre the origin, the gradient of a tangent to that circle, and the four standard transformations $y=f(x)+a$, $y=f(x-a)$, $y=-f(x)$ and $y=f(-x)$. The wrong options are the typical sign slips, such as moving $f(x-2)$ to the left, and forgetting a factor of $x$ when solving a cubic.

The flashcards describe the shape of each family of graphs, the circle equation and the tangent property, the rules for the four transformations, and the line of symmetry of a quadratic.

The printable written work has eight longer tasks: a table of values and the key features of a quadratic, completing the square to find a turning point and exact roots, the roots and shape of a cubic, a reciprocal graph and why it has no value at $x=0$, an exponential growth model, the equation of a tangent to a circle, solving trigonometric equations using the symmetry of the sine and cosine graphs, and tracking a point through several transformations. Each task asks you to show method, because sketches and interpretations are marked on the reasoning as well as the final answer.

Quadratic roots and intercepts, cubic and reciprocal graphs are content for both tiers; completing the square for turning points, exponential and trigonometric graphs, circles and transformations are Higher tier, and the quiz marks the circle item accordingly. The material suits Year 10 and Year 11 students, especially Higher-tier candidates preparing for the graph questions near the end of a paper.

• Find roots, intercepts and the line of symmetry of a quadratic graph
• Find the turning point of a quadratic by completing the square (Higher)
• Recognise and sketch cubic, reciprocal and (Higher) exponential and trigonometric graphs
• Use the equation of a circle with centre the origin and find the equation of a tangent (Higher)
• Describe and apply translations and reflections of a graph $y = f(x)$ (Higher)

Practice material written by Zestly, based on the DfE GCSE mathematics subject content (DFE-00233-2013), Algebra: graphs (A11, A12, A13, A16).