Key facts and formulae which must be known for the WJEC Core 4 examination.
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Erstellt von Daniel Cox
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Erstellt von Daniel Cox
vor mehr als 8 Jahre
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How would you split the following expression into partial fractions?
\[\frac{f(x)}{(ax+b)(cx+d)}\]
How would you split the following expression into partial fractions?
\[\frac{f(x)}{(ax+b)(cx+d)^2}\]
\[\sin(A\pm B)=?\]
(Given in formulae booklet)
\[\cos(A\pm B)=?\]
(Given in formulae booklet)
\[\tan(A\pm B)=?\]
(Given in formulae booklet)
\[\sin 2A = ?\]
Give the 3 identities for \(\cos 2A\)
\[\tan 2A=?\]
How do you find \[\int \sin^2 x \, dx
\]
How do you find \[\int \cos^2 x \, dx
\]
How do you find \[\int \tan^2 x \, dx
\]
What is meant by a Cartesian equation?
When applying the \(R, \alpha\) method, if \(R\sin \alpha =a\) and \(R\cos \alpha =b\), how would you find \(R\) and \(\alpha\)?
What is the greatest value of \(R\sin (x+\alpha)\) and find a value of \(x\) for which this occurs
What is the least value of \(R\sin (x+\alpha)\) and find a value of \(x\) for which this occurs
If \(x=f(t)\) and \(y=g(t)\), how would you find \(\frac{\text{d}y}{\text{d}x}\)?
If the rate of increase of \(P\) over time is directly proportional to \(f(P)\), write down a differential equation that is satisfied by \(P\).
If the rate of decrease of \(P\) over time is directly proportional to \(f(P)\), write down a differential equation that is satisfied by \(P\).
If the rate of increase of \(P\) over time is inversely proportional to \(f(P)\), write down a differential equation that is satisfied by \(P\).
If the rate of decrease of \(P\) over time is inversely proportional to \(f(P)\), write down a differential equation that is satisfied by \(P\).
What is the formula for the volume of revolution of a curve about the \(x\)-axis?
What is the formula for integration by parts?
(given in formulae book)
\[\int \frac{1}{ax+b} \, \text{d}x=?\]
When \(n \neq -1\),
\[\int (ax+b)^n \, \text{d}x=?\]
What is a unit vector?
What is the magnitude of vector \(a\mathbf{i}+b\mathbf{j}+c\mathbf{k}\)
If vectors \(\mathbf{a}\) and \(\mathbf{b}\) are parallel, then...?
If \(\mathbf{a}\) and \(\mathbf{b}\) are the position vectors of points \(\mathbf{A}\) and \(\mathbf{B}\), how would you find \(\mathbf{AB}\)?
A line passes through the point with position vector \(\mathbf{a}\) and is in the direction of \(\mathbf{b}\). What is the vector equation of the line?
What is the formula for the scalar product of vectors \(\mathbf{a}\) and \(\mathbf{b}\)?
If vectors \(\mathbf{a}\) and \(\mathbf{b}\) are perpendicular, \(\mathbf{a} \cdot \mathbf{b}=?\)
