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**Scheme of work: GCSE Higher: Year 11: Term 2: Working with Algebraic Fractions**

- Plot graphs of equations that correspond to straight-line graphs in the coordinate plane
- Recognise, sketch and interpret graphs of linear and non-linear functions
- Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement.

- Where appropriate, interpret simple expressions as functions with inputs and outputs; interpret the reverse process as the inverse function; interpret the succession of two functions as a composite function.
- Sketch translations and reflections of a given function
- Calculate or estimate gradients of graphs (including quadratic and other non-linear graphs),
- Find approximate solutions to equations numerically using iteration

- A function is any algebraic expression in which x is the only variable. It is denoted as f(x)
- Understanding the notation for transformation of functions is critical to accessing this topic.
- f(x) ± a = Vertical Translation
- f(x ± a) = Horizontal Translation
- af(x) = Horizontal stretch
- f(ax) = Vertical stretch

- Composite functions combine more than one function to an input.
- Inverse functions perform the opposite operation to a function.
- A gradient function calculates and approximate the instantaneous rate of change for given values of x.
- Iterative solutions can diverge or converge.

- -f(x) is often incorrectly taken as a reflection in the y-axis rather than the x.
- f(x + a) translates a unit to the left rather than to the right.
- Students often struggle with writing the equation of the new function after a transformation.
- Students need to be precise when drawing the transformed function.
- The order of a composite function is often confused, fg(x) -> g acts on x first, then f acts on the result.
- Students can often differentiate functions with little understanding of how to apply the gradient function correctly.

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