GCSE Maths Functions and Advanced Graphs: lesson and practice questions

By the end of this chapter you will be able to

• Use function notation f(x), evaluate functions and solve equations of the form f(x) = k
• Find inverse functions and composite functions such as fg(x), and solve equations involving them
• Sketch the graphs of y = f(x) + a, y = f(x + a), y = −f(x), y = f(−x), and recognise stretches y = af(x) and y = f(ax)
• Recognise, sketch and use the graphs of y = sin x, y = cos x and y = tan x (shape, period, key values), and solve trigonometric equations
• Recognise and use exponential graphs y = kx and solve growth and decay problems, including compound interest
• Use the equation x2 + y2 = r2 of a circle and find the equation of a tangent at a point
• Estimate gradients of curves with tangents, and understand average and instantaneous rates of change
• Estimate the area under a graph with trapezia and rectangles, and interpret it in context
• Solve equations numerically by iteration, and work with general iterative processes

You should already know

• Substituting into expressions and rearranging formulae (Chapter 8)
• Gradients and equations of straight lines, including perpendicular lines (Chapter 12)
• Quadratic and reciprocal graphs (Chapter 13) and solving quadratics (Chapter 14)
• Compound interest and percentage multipliers (Chapter 5)
• Trigonometry in right-angled triangles (Chapter 20)
• Speed–time graphs (Chapters 13 and 16)

Where this leads

• Circle theorems, including the tangent–radius theorem (Chapter 26)
• A-level maths: calculus, which finds exact gradients and areas
• Further work on sequences, series and growth models