\( \DeclareMathOperator{cosec}{cosec} \)

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Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Here are some exam-style questions on this statement:

- "
*\(f(x) = \frac{2x}{5} + 7\) and \(g(x) = 10x^2 - 15\) for all values of \(x\).*" ... more - "
*(a) A function is represented by the following function machine.*" ... more - "
*If \(f(x)=5-4x\) and \(g(x)=4^{-x}\) then:*" ... more - "
*Here is a function machine that produces two outputs, A and B.*" ... more - "
*The functions \(f\) and \(g\) are such that:*" ... more - "
*Part of the function of \(y=f(x)\) is shown in the following diagram.*" ... more - "
*The functions \(f\) and \(g\) are defined for \(x \in \mathbb{R} \) by*" ... more - "
*The diagram shows the graph of \(y=f(x)\), for \(-3\le x \le 4\).*" ... more - "
*The circumference of a given circle \(C\) can be represented by the function \(C(A) = 2 \sqrt{A \pi}\) , \(A \ge 0 \) , where \(A\) is the area of the circle. The graph of the function \(C\) is shown for \(0 \le A \le 10\).*" ... more - "
*The Big Wheel at Fantasy Fun Fayre rotates clockwise at a constant speed completing 15 rotations every hour. The wheel has a diameter of 90 metres and the bottom of the wheel is 6 metres above the ground.*" ... more - "
*The functions f and g are defined as follows:*" ... more - "
*The functions \( f \) and \( g \) are defined for \( x \in \mathbb{R} \) by \( f(x) = 3 + 5x - 2x^2 \) and \( g(x) = x + k \), where \( k \in \mathbb{R} \).*" ... more - "
*The Fun Wheel at the Meller Theme Park rotates at a constant speed.*" ... more - "
*Let \(f(x)=\frac{3x}{x-q}\), where \(x \neq q\).*" ... more - "
*Part of the graph of \(f(x) = {\log _b}(x + 4)\) for \(x > - 4\) is shown below.*" ... more - "
*The functions \(f\) and \(g\) are defined as:*" ... more - "
*Consider the function \(f(x) = k^x \) where \(x, k \in \mathbb{R}\) and \( x \gt 0, k > 1\).*" ... more - "
*The height above the ground, H metres, of a passenger on a Ferris wheel t minutes after the wheel starts turning, is modelled by the following equation:*" ... more

Here are some Advanced Starters on this statement:

**Catering for a Function**

Find f(x) given f(x-1). more**Permutable Functions**

Find pairs of functions that are commutative under composition. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Algebra Pupils begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or many operations. They use brackets, indices and other constructs to apply algebra to real word problems. This leads to using algebra as an invaluable tool for solving problems, modelling situations and investigating ideas. If this topic were split into four sub topics they might be: Creating and simplifying expressions; Expanding and factorising expressions; Substituting and using formulae; Solving equations and real life problems; This is a powerful topic and has strong links to other branches of mathematics such as number, geometry and statistics. See also "Number Patterns", "Negative Numbers" and "Simultaneous Equations".
- Functions A relationship between two sets can be called a mapping. Elements of the first set (domain) are mapped to elements of the second set (range). A function is a special type of mapping for which one value in the domain maps to one, and only one value in the range.Pupils in Primary school will use the concept of function machines to perform calculations. They will then learn to ‘work backwards’ to find the inverse function. The study of functions becomes more formal as pupils become more proficient and able to cope with more complex mathematical ideas.

Transum,

Saturday, August 17, 2019

"There is an Advanced Lesson Starter called Permutable Functions that is open ended but allows students to consolidate their understanding of composite functions."

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