IGCSE Edexcel Syllabus: No Specification
What is a relation? It refers to the connection between one variable and another variable. The connection may be causal (due to cause and effect) - e.g. the extension (x) of a spring and the load (F) applied to it; or non-causal - e.g. area codes of telephone lines and the areas.
How may a relation be represented? A relation may be represented by:
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IGCSE Cambridge: Syllabus Area 2
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SPM: Form 4 Chapter 1
Some Words For IGCSE Edexcel Students
Your syllabus omits ‘functions’ as a dedicated segment in the syllabus while IGCSE Cambridge syllabus and SPM textbooks do not specify the 'concept of asymptotes'. As ‘functions’ is something that you come across as often as they do, it is advisable that you too know:
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What is a function?
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Refers to 2 specific types of relations:
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One-to-One relations
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Many-to-One relations
What is a relation? It refers to the connection between one variable and another variable. The connection may be causal (due to cause and effect) - e.g. the extension (x) of a spring and the load (F) applied to it; or non-causal - e.g. area codes of telephone lines and the areas.
How may a relation be represented? A relation may be represented by:
- arrow diagram
- ordered pair - as in x and y coordinates like (x, y);
- graph
- mathematical formula or equation
- 1-to-1 relation (a function): e.g. F = kx (Hooke's Law); growth against time;
- One-to-Many relation: y = x(1/2)
- Many-to-One relation (a function): e.g. y = ax2 + bx + c
- Many-to-Many relation: e.g. x2 + y2 = 1 (a unit circle, other circles, etc.)
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Terminologies related to a function:
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Domain, Co-domain and Range
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Objects (inputs) and Images (Outputs)
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Inverse Functions
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Composite Functions
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Notations related to functions:
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f(x); f: x׀→
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f-1(x)
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f(g(x))
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f2(x)
[= f(f(x))]
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f’(x)
[=dy/dx]
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f’’(x) [=d2y/dx2]
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Relationship between y = f(x) and y = ׀f(x)׀
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What type of function has an inverse function?
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How to find the inverse function of one-to-one
function? Use sketch graphs to show that a function is the mirror image of its
inverse function and vice versa in the line of reflection y = x.
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Composite functions
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