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WJEC Core 3 Maths - Key Facts

Daniel Cox Mathematics A-Level Englisch 41 Karten

WJEC Core 3 Maths - Key Facts

Karten in diesem Stapel (41)

  1. 1\[\sec x\equiv ?\]\[\sec x\equiv \frac{1}{\cos x}\]
  2. 2\[\text{cosec } x\equiv ?\]\[\text{cosec }x\equiv \frac{1}{\sin x}\]
  3. 3\[\cot x\equiv ?\]\[\cot x\equiv \frac{1}{\tan x}\]
  4. 4Write an identity which links together \(\sec \theta\) and \(\tan \theta\)\[\sec^2 \theta \equiv 1 + \tan^2 \theta\]
  5. 5Write an identity which links together \(\text{cosec }\theta\) and \(\cot \theta\)\[\text{cosec}^2 \theta \equiv 1 + \cot^2 \theta\]
  6. 6Sketch the graph of \(y=\sin x\) for \(0\leq x \leq 360^{\circ}\)Sketch the graph of \(y=\sin x\) for \(0\leq x \leq 360^{\circ}\)
  7. 7Sketch the graph of \(y=\cos x\) for \(0\leq x \leq 360^{\circ}\)Sketch the graph of \(y=\cos x\) for \(0\leq x \leq 360^{\circ}\)
  8. 8Sketch the graph of \(y=\tan x\) for \(0\leq x \leq 360^{\circ}\)Sketch the graph of \(y=\tan x\) for \(0\leq x \leq 360^{\circ}\)
  9. 9Sketch the graph of \(y=\sin^{-1}x\). What is its domain and range?Domain \([-1,1]\)
    Range \([-\frac{\pi}{2},\frac{\pi}{2}]\)    Sketch the graph of \(y=\sin^{-1}x\). What is its domain and range?
  10. 10Sketch the graph of \(y=\cos^{-1}x\). What is its domain and range?Domain \([-1,1]\)
    Range \([0,\pi]\)    Sketch the graph of \(y=\cos^{-1}x\). What is its domain and range?
  11. 11Sketch the graph of \(y=\tan^{-1}x\). What is its domain and range?Domain \((-\infty,\infty)\)
    Range \( (-\frac{\pi}{2}, \frac{\pi}{2}) \)    Sketch the graph of \(y=\tan^{-1}x\). What is its domain and range?
  12. 12What does \(|x|\[-a
  13. 13What does \(|x|>a\) mean?\[x>a \text{ or } x<-a\]
    \[\text{NOT } x>\pm a\]
  14. 14Give the definition of a functionA function relates each element of a set
    with exactly one element of another set
  15. 15How are the graphs of \(y=f(x)\) and \(y=f^{-1}(x)\) related?They are reflections of each other in the line \(y=x\)How are the graphs of \(y=f(x)\) and \(y=f^{-1}(x)\) related?
  16. 16The domain of \(f(x)\) equals the range of ...?The domain of \(f(x)\) equals the range of \(f^{-1}(x)\)
  17. 17The range of \(f(x)\) equals the domain of ...?The range of \(f(x)\) equals the domain of \(f^{-1}(x)\)
  18. 18What is meant by the range of a function?The set of all possible output values of a function
  19. 19What is meant by the domain of a function?All the values that could go into a function
  20. 20State the inverse function of \(e^x\)\[\ln x\]
  21. 21Sketch the graph of \(y=e^x\), showing any intersections with the axes. State its domain and range.The \(x\) axis is an asymptote.
    Domain \((-\infty, \infty)\)
    Range \((0, \infty)\)    Sketch the graph of \(y=e^x\), showing any intersections with the axes. State its domain and range.
  22. 22Sketch the graph of \(y=\ln x\), showing any intersections with the axes. State its domain and range.The \(y\) axis is an asymptote.
    Domain \((0, \infty)\)
    Range \((-\infty, \infty)\)    Sketch the graph of \(y=\ln x\), showing any intersections with the axes. State its domain and range.
  23. 23State the inverse function of \(\ln x\)\[e^x\]
  24. 24Differentiate \(e^{f(x)}\) with respect to \(x\)\[f'(x)e^{f(x)}\]
  25. 25Differentiate \(\ln{f(x)}\) with respect to \(x\)\[\frac{f'(x)}{f(x)}\]
  26. 26Differentiate \(\sin {\left(f(x)\right)}\) with respect to \(x\)\[f'(x)\cos{\left(f(x)\right)}\]
  27. 27Differentiate \(\cos {\left(f(x)\right)}\) with respect to \(x\)\[-f'(x)\sin{\left(f(x)\right)}\]
  28. 28Differentiate \(\tan {\left(f(x)\right)}\) with respect to \(x\)\[f'(x)\sec^2{\left(f(x)\right)}\]
  29. 29State the product rule for differentiating \[y=uv\] with respect to \(x\), where \(u\) and \(v\) are functions of \(x\)\[\frac{\text{d}y}{\text{d}x}=uv'+vu'\]
  30. 30State the quotient rule for differentiating \[y=\frac{u}{v}\] with respect to \(x\), where \(u\) and \(v\) are functions of \(x\)\[\frac{\text{d}y}{\text{d}x}=\frac{vu'-uv'}{v^2}\]
  31. 31\[\frac{1}{\left(\frac{\text{d}x}{\text{d}y}\right)}=?\]\[\frac{\text{d}y}{\text{d}x}\]
  32. 32How would you find the first and second derivatives of the parametric equations \(x=f(t)\) and \(y=g(t)\)\[\frac{\text{d}y}{\text{d}x}=\frac{g'(t)}{f'(t)}\]
    \[\frac{\text{d}^2y}{\text{d}x^2}=\frac{\frac{\text{d}}{\text{d}t}\left(\frac{\text{d}y}{\text{d}x}\right)}{\frac{\text{d}x}{\text{d}t}}\]
  33. 33\[\int e^x \, dx =?\]\[\int e^x \, dx = e^x+c\]
  34. 34\[\int \frac{1}{x} \, dx = ?\]\[\int \frac{1}{x} \, dx = \ln x +c\]
  35. 35\[\int \sin x \, dx = ?\]\[\int \sin x \, dx = -\cos x +c\]
  36. 36\[\int \cos x \, dx = ?\]\[\int \cos x \, dx = \sin x +c\]
  37. 37What effect will the transformation \(y=f(x)+a\) have on the graph of \(y=f(x)\)?Translation \(a\) units in the \(y\) direction.
    i.e. the graph will move UP by \(a\) units
  38. 38What effect will the transformation \(y=f(x+a)\) have on the graph of \(y=f(x)\)?Translation \(-a\) units in the \(x\) direction.
    i.e. the graph will move LEFT by \(a\) units
  39. 39What effect will the transformation \(y=af(x)\) have on the graph of \(y=f(x)\)?Stretch, scale factor \(a\) in the \(y\) direction.
    i.e. the \(y\) values will be multiplied by \(a\)
  40. 40What effect will the transformation \(y=f(ax)\) have on the graph of \(y=f(x)\)?Stretch, scale factor \(\frac{1}{a}\) in the \(x\) direction.
    i.e. the \(x\) values will be divided by \(a\)
    [This could also be described as a 'squash', scale factor \(a\) in the \(x\) direction]
  41. 41Sketch the graph of \[y=|x|\]Sketch the graph of \[y=|x|\]

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Beschreibung
Key facts and formulae which must be known for the WJEC Core 3 examination.
Erstellt von
Daniel Cox
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