Chapter 6.1
Linear graphs (gradient, intercept, parallel, perpendicular)
Review linear functions and transformations of lines in multiple forms.
Chapters20
Graph families, transformations, curve sketching, and exam technique.
Time invested15 hrs
Approximate guided learning for GCSE mastery.
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Chapter 6.2
Quadratic graphs (standard form, vertex form, completing the square)
Sketch and identify key features of parabolas in all forms.
Chapter 6.3
Cubic graphs and shape recognition
Identify turning points, roots, and end behavior for cubic functions.
Chapter 6.4
Reciprocal functions and asymptotes
Sketch y = 1/x and rational functions with asymptote analysis.
Chapter 6.5
Exponential and logarithmic functions
Understand growth/decay patterns and inverse relationships.
Chapter 6.6
Trigonometric graphs (sine, cosine, tangent)
Sketch trig functions and identify period, amplitude, phase shift.
Chapter 6.7
Translations and reflections of graphs
Apply y = f(x) + k, y = f(x + k), y = -f(x), y = f(-x) transformations.
Chapter 6.8
Stretches and combined transformations
Apply y = k·f(x), y = f(kx) and combine multiple transformations.
Chapter 6.9
Graphical solutions to equations and inequalities
Use graph intersections to solve equations and identify solution regions.
Chapter 6.10
Iteration and finding approximate solutions graphically
Use graphs to find roots and test convergence of iterative methods.
Chapter 6.11
Composite and inverse functions
Find f(g(x)) and sketch inverse functions with reflection in y=x.
Chapter 6.12
Piecewise functions and modulus functions
Sketch functions defined in parts and functions with |x| expressions.
Chapter 6.13
Parametric equations and curves
Eliminate parameters to find Cartesian form and sketch parametric curves.
Chapter 6.14
Polar curves (Higher tier)
Understand polar coordinates and sketch curves in polar form.
Chapter 6.15
Sketching techniques and multiple representations
Connect equations, tables, and graphs to deepen function understanding.
Chapter 6.16
Real-world applications of functions
Apply functions to model distance-time, speed-time, and financial situations.
Chapter 6.17
Graphs exam technique and common pitfalls
Master exam-style questions with clear labeling, correct notation, and accuracy.
Chapter 6.18
Graphs and transformations problem-solving
Combine multiple transformation techniques for complex composite functions.
Chapter 6.19
Past paper practice - Graphs (Papers 1, 2)
Exam-style questions covering all graph families and transformations.
Chapter 6.20
Graphs mastery and mock exam questions
Final assessment covering all Section 6 topics at GCSE level.
Next steps
Continue building your GCSE revision journey through the remaining topics.