Key facts and formulae which must be known for the WJEC Core 3 examination.
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Erstellt von Daniel Cox
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Erstellt von Daniel Cox
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\[\sec x\equiv ?\]
\[\text{cosec } x\equiv ?\]
\[\cot x\equiv ?\]
Write an identity which links together \(\sec \theta\) and \(\tan \theta\)
Write an identity which links together \(\text{cosec }\theta\) and \(\cot \theta\)
Sketch the graph of \(y=\sin x\) for \(0\leq x \leq 360^{\circ}\)
Sketch the graph of \(y=\cos x\) for \(0\leq x \leq 360^{\circ}\)
Sketch the graph of \(y=\tan x\) for \(0\leq x \leq 360^{\circ}\)
Sketch the graph of \(y=\sin^{-1}x\).
What is its domain and range?
Sketch the graph of \(y=\cos^{-1}x\).
What is its domain and range?
Sketch the graph of \(y=\tan^{-1}x\).
What is its domain and range?
What does \(|x|<a\) mean?
What does \(|x|>a\) mean?
Give the definition of a function
How are the graphs of \(y=f(x)\) and \(y=f^{-1}(x)\) related?
The domain of \(f(x)\) equals the range of ...?
The range of \(f(x)\) equals the domain of ...?
What is meant by the range of a function?
What is meant by the domain of a function?
State the inverse function of \(e^x\)
Sketch the graph of \(y=e^x\), showing any intersections with the axes.
State its domain and range.
Sketch the graph of \(y=\ln x\), showing any intersections with the axes.
State its domain and range.
State the inverse function of \(\ln x\)
Differentiate \(e^{f(x)}\) with respect to \(x\)
Differentiate \(\ln{f(x)}\) with respect to \(x\)
Differentiate \(\sin {\left(f(x)\right)}\) with respect to \(x\)
Differentiate \(\cos {\left(f(x)\right)}\) with respect to \(x\)
Differentiate \(\tan {\left(f(x)\right)}\) with respect to \(x\)
State the product rule for differentiating \[y=uv\] with respect to \(x\), where \(u\) and \(v\) are functions of \(x\)
State the quotient rule for differentiating \[y=\frac{u}{v}\] with respect to \(x\), where \(u\) and \(v\) are functions of \(x\)
\[\frac{1}{\left(\frac{\text{d}x}{\text{d}y}\right)}=?\]
How would you find the first and second derivatives of the parametric equations \(x=f(t)\) and \(y=g(t)\)
\[\int e^x \, dx =?\]
\[\int \frac{1}{x} \, dx = ?\]
\[\int \sin x \, dx = ?\]
\[\int \cos x \, dx = ?\]
What effect will the transformation \(y=f(x)+a\) have on the graph of \(y=f(x)\)?
What effect will the transformation \(y=f(x+a)\) have on the graph of \(y=f(x)\)?
What effect will the transformation \(y=af(x)\) have on the graph of \(y=f(x)\)?
What effect will the transformation \(y=f(ax)\) have on the graph of \(y=f(x)\)?
Sketch the graph of \[y=|x|\]
