Scheme of work: Year 13 A-Level: Pure 2: Functions and Graphs
Students learn how to understand and use the modulus function.
Later, as learning progresses, they use sketched graphs to solve equations involving a modulus function.
Students learn how to categorise the different types of function.
Later, as learning progresses they consider the domain and range of one-to-one and one-to-many functions.
Students learn how to sketch a piecewise function and identify its range.
Later, as learning progresses they solve equations involving piece-wise functions.
Students learn how to combine functions to make a composite function.
Later, as learning progresses they find the domain and range of composite functions.
Students learn how to find and identify the properties of an inverse function.
Later, as learning progresses, they solve equations of inverse functions and identify their domain and range.
Students learn how to sketch modulus functions by exploring transformations such as reflections in the x-axis and y-axis. Initially, they sketch basic graphs to understand how modulus affects negative sections.
As learning progresses, students handle more complex functions, including quadratics and restricted domains. They identify critical points, intersections, and accurately state function ranges.
Students learn how to apply and combine transformations to functions. Starting with modulus graphs like f(|x|), they explore reflections, translations, and stretches.
As learning progresses, they apply multiple transformations in sequence, sketch transformed graphs, and interpret algebraic forms.
Students learn how to solve various problems involving modulus functions.
Later, as learning progresses, they combine transforming modulus functions with composite and inverse functions.
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