Flashcards
WJEC Core 2 Maths - Key Facts
Cards in this deck (36)
- 1\[\log_a x+\log_a y = ?\]\[\log_a x+\log_a y = \log_a(xy)\]
- 2\[\log_a x-\log_a y = ?\]\[\log_a x-\log_a y = \log_a\left (\frac{x}{y} \right )\]
NOT \(\frac{\log_a x}{\log_a y}\) - 3\[k \log_a x = ?\]\[k \log_a x = \log_a\left (x^k \right )\]
- 4State the sine rule\(\frac{a}{\sin A}=\frac{b}{\sin B}\)
or
\(\frac{\sin A}{a}=\frac{\sin B}{b}\) - 5True or false? \[\log_a\left (xy^k \right )=k \log_a\left ( xy \right )\]FALSE
\[\begin{align*}
\log_a\left (xy^k \right )&=\log_a x +\log_a \left (y^k \right )\\
&=\log_a x + k \log_a y
\end{align*}
\] - 6What is the trigonometric formula for the area of a triangle?\[Area=\frac{1}{2} ab \sin C\]
Here, the sides \(a\) and \(b\) surround the angle \(C\) - 7What is the Pythagorean trigonometric identity? (Hint: it involves \(\sin^2 x\) and \(\cos^2 x\)\[\sin^2 x + \cos^2 x = 1\]
- 8If \(y=a^x\), then \(x=?\)If \(y=a^x\), then \(x=\log_a y\)
- 9State the cosine rule\[a^2=b^2+c^2-2bc \cos A\]
- 10\[\log_a a =?\]\[\log_a a =1\]
- 11\[\log_a 1 =?\]\[\log_a 1 =0\]
- 12State an identity relating \(\sin x\), \(\cos x\) and \(\tan x\)\[\frac{\sin x}{\cos x}=\tan x\]
- 13How many degrees is \(\pi\) radians?\(\pi\) radians is \(180^{\circ}\)
- 14Formula for the area of a sector?\[Area=\frac{1}{2}r^2 \theta \]
- 15Formula for the length of an arc?\[s=r \theta\]
- 16How would you find the area of a segment of a circle?\begin{align*}
\mathrm{Segment}&= \mathrm{Sector}-\mathrm{Triangle}\\
&=\frac{1}{2}r^2\theta-\frac{1}{2}r^2 \sin\theta\\
&=\frac{1}{2}r^2\left ( \theta - \sin\theta \right )
\end{align*}
- 17Formula for the \(n\)th term of an arithmetic sequence... [given in the formulae booklet]\[u_n=a+(n-1)d\]
- 18Formula for the sum of the first \(n\) terms of an arithmetic sequence... [given in the formulae booklet]\[S_n=\frac{n}{2}\left ( 2a+(n-1)d \right )\]
or
\[S_n=\frac{n}{2}\left ( a+l \right )\]
where \(l\) is the last term - 19Formula for the \(n\)th term of a geometric sequence... [given in the formulae booklet]\[u_n=ar^{n-1}\]
- 20Formula for the sum of the first \(n\) terms of a geometric sequence... [given in the formulae booklet]\[S_n=\frac{a\left ( 1-r^n \right )}{1-r}\]
- 21Formula for the sum to infinity of a convergent geometric series (one where \(\left | r \right |<1\)) [given in the formulae booklet]\[S_\infty=\frac{a}{1-r}\]
- 22\[\int ax^n \, dx=\, ?\]\[\int ax^n \, dx= \frac{ax^{n+1}}{n+1}+c\]
- 23How would you find this shaded area?Work out \(\int_{a}^{b} f(x) \, dx\)
- 24General equation of a circle, centre \(\left ( a,b \right )\) and radius \(r\)\[\left ( x-a \right )^2+\left ( y-b \right )^2=r^2\]
- 25If we are given \(\frac{dy}{dx}\) or \(f'(x)\) and told to find \(y\) or \(f(x)\), we need to...Integrate
[remember to include \(+c\)] - 26What is the angle between the tangent and radius at \(P\)?\[90^{\circ}\]
This is always true at the point where a radius meets a tangent
- 27What does the graph of \(y=a^x\) look like? Where does it cross the axes?It goes through the \(y\)-axis at \(\left ( 0,1 \right )\).
It does not cross the \(x\)-axis. The \(x\)-axis is an asymptote.
- 28This is a triangle inside a semicircle, where one side of the triangle is the diameter of the circle. What is the size of angle \(C\)?\[90^{\circ}\]
- 29Draw the graph of \(y=\sin x\) for \(0\leq x \leq 2\pi\)
- 30Draw the graph of \(y=\cos x\) for \(0\leq x \leq 2\pi\)
- 31Draw the graph of \(y=\tan x\) for \(0\leq x \leq 2\pi\)The lines \(x=\frac{\pi}{2}\) and \(x=\frac{3\pi}{2}\) are asymptotes
- 32Differentiation is the reverse of ...?Integration
- 33Integration is the reverse of ...?Differentiation
- 34What is the condition for two circles to touch externally?The distance between their centres is the sum of their radii
- 35What is the condition for two circles to touch internally?The distance between their centres is the difference in their radii
- 36If we draw the perpendicular bisector of any chord on a circle, which point will it definitely go through?The perpendicular bisector of a chord always passes through the centre of the circle
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- Key facts and formulae which must be known for the WJEC Core 2 examination.
- Created by
- Daniel Cox
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