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Graphs
Algebraic graphs connect equations, coordinates, gradients and intercepts. Students interpret straight-line, quadratic and other graphs as visual representations of algebraic relationships.
18
Objectives
90
Flashcards
90
Questions
90 min
Study time
AQAGCSEMathematicsAlgebra
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Syllabus checklist
What you need to know
18 objective pages available
Coordinates1 objectives
- [Foundation and Higher] Work with coordinates in all four quadrants.
Straight-line graphs3 objectives
- [Foundation and Higher] Plot graphs of equations corresponding to straight lines in the coordinate plane.
- [Foundation and Higher] Use y = mx + c to identify parallel lines and find equations of lines from points and gradients.
- [Higher only] Use y = mx + c to identify perpendicular lines.
Gradients and intercepts1 objectives
- [Foundation and Higher] Identify and interpret gradients and intercepts of linear functions graphically and algebraically.
Quadratic graph features2 objectives
- [Foundation and Higher] Identify and interpret roots, intercepts and turning points of quadratic functions graphically.
- [Higher only] Deduce quadratic roots algebraically and deduce turning points by completing the square.
Sketching and interpreting function graphs3 objectives
- [Foundation and Higher] Recognise, sketch and interpret graphs of linear and quadratic functions.
- [Foundation and Higher] Include simple cubic and reciprocal functions where tier-appropriate.
- [Higher only] Include exponential functions and trigonometric functions with degree arguments.
Graph transformations1 objectives
- [Higher only] Sketch translations and reflections of a given function.
Real-context and non-standard graphs3 objectives
- [Foundation and Higher] Plot and interpret graphs, including non-standard graphs in real contexts, to find approximate solutions.
- [Foundation and Higher] Apply graph interpretation to contexts such as distance, speed and acceleration.
- [Higher only] Include reciprocal and exponential graphs in real-context graph problems.
Gradients and areas under graphs2 objectives
- [Higher only] Calculate or estimate gradients of graphs and areas under graphs, including non-linear graphs.
- [Higher only] Interpret gradients and areas in contexts such as distance-time, velocity-time and financial graphs.
Circle equation and tangent2 objectives
- [Higher only] Recognise and use the equation of a circle with centre at the origin.
- [Higher only] Find the equation of a tangent to a circle at a given point.
Key terms
coordinatesfoundationgradientperpendicularroothighertranslationapproximate solutionreal-context graphcircle
Exam tips
- Coordinates exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to [Foundation and Higher] Work with coordinates in all four quadrants..
- Straight-line graphs exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to [Foundation and Higher] Plot graphs of equations corresponding to straight lines in the coordinate plane..
Common mistakes
- Coordinates common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Coordinates.
- Straight-line graphs common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Straight-line graphs.
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