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Quiz Time!

  

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Here is a thread where you can go to revise your mathematics, from algebra to calculus!

You can either have a read through the questions and answers, or you can contribute and write your own tutorials on how to do questions that you found difficult! Not only will you benefit but further remembering the question that you're teaching, but you are helping others' revision!

Rules:

  • Must use the built-in maths tools for questions/working. Tutorial Here and Here.
  • All questions must be accommodated with full working and explanations, to help the reader.
  • All answers must be wrapped in [/ spoiler] tags, available from the "Other Styles" menu.

Tips:

  • Wrap your questions and answers in separate [/ note] tags, as well as size 4 font, so that the question and answer are clear and concise.

Also, as a way to try and keep this topic as clean as possible, could I please ask that you refrain from replying to this topic unless you are writing a quiz question with answers. That way people can easily read the questions without seeing unhelpful comments.

If you spot an error or have any further questions, contact the author of the post.

I'll get this started with an easy one!

Finding the inverse of a function.

If: gif.latex?f(x)=2\sqrt{x}+3

Calculate gif.latex?f^{-1}(x)

Answer:

Replace f-1(x) with y:

gif.latex?y=2\sqrt{x}+3

Solve for x:

gif.latex?y=2\sqrt{x}+3

gif.latex?y-3=2\sqrt{x}

gif.latex?{y-3 \over2}=\sqrt{x}

gif.latex?x=\left({y-3 \over2}\right)^2

Swap x for y:

gif.latex?y=\left({x-3 \over2}\right)^2

Replace y with f-1(x):

gif.latex?f^{-1}(x)=\left({x-3 \over2}\r

Edited by Ezeh

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The Unit Circle

Let gif.latex?p=\sin40^{\circ} and gif.latex?q=\cos110^{\circ}

a) Write down an expression (in terms of q and/or p) for:

i)
gif.latex?\sin140^{\circ}

ii)
gif.latex?\cos70^{\circ}

Answer:

a)

i)

Since sin represents the y-axis in the unit circle, this means that angles on both the left and right side of the unit circle will have the same y value (symmetry) (i.e
gif.latex?\sin0^{\circ}
and
gif.latex?\sin180^{\circ}
both equal zero) Therefore it can be seen that
gif.latex?\sin40^{\circ}
and
gif.latex?\sin140^{\circ}
are symmetrical, and thus have the same sin value.

So:

gif.latex?\sin140^{\circ} = p

ii)

The same concept can be applied to cos, however cos represents the x-axis on the unit circle. As it can be seen,
gif.latex?\cos70^{\circ}
and
gif.latex?\cos110^{\circ}
are both 20 degrees away from 90 degrees. Therefore the x-axis values of these two expressions are the opposite of each other.

So:

gif.latex?\cos70^{\circ} = -\cos110^{\ci

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