Draw a scatter plot on to represent the exchange rate (in R/$) versus the oil price (in $).

Describe the relationship between the exchange rate (in R/$) and the oil price (in $).

Determine the mean oil price.

Determine the standard deviation of the oil price.

Generally there is concern from the public when the oil price is higher than two standard deviations from the mean.

In which month(s) would there have been concerns from the public?

Give the range of Peter's scores.

Give the minimum of Vuyani's scores.

Comment on who you think had a more consistent performance throughout the year.

Motivate your answer by referring to values in the box-and-whisker diagrams.

Draw the ogive (cumulative frequency graph) representing the above data.

Use the ogive to approximate the following:

The number of learners who scored less than 85%

Use the ogive to approximate the following:

The interquartile range (Show ALL calculations.)

Calculate the gradient of `AD` .

Determine the equation of `BC` in the form `y = mx + c`

Determine the coordinates of point `F` .

`AB'CD` is a parallelogram with `B'` on `BC` .

Determine the coordinates of `B'` , using a transformation `<<x;y>>-><<x+a;y+b>>` that sends `A ` to `B'`.

Show that `alpha=48,37^o`

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Calculate the area of `DCF`. ``

The coordinates of centre `M.`

The radius of circle `C` ₁

Determine the coordinates of `D` , the point where line `PM` and circle `C` ₁ intersect.

If it is given that `DB =4sqrt(2)` , determine `MB` , the radius of circle `C` ₂.

Write down the equation of `C` ₂ in the form `<<x-a>>^2+<<y-b>>^2=r^2`

Is the point `F<<2sqrt(5);0>>` inside circle `C` ₂?

Support your answer with calculations.

Translation of 3 units downwards and 4 units to the right

Reflection about the `x` -axis

In the above diagram, triangle `KMN` `` is enlarged by a certain factor to form triangle `K'M'N'` .

Determine the factor of enlargement.

Give the general rule for the transformation for the previous question.

Use the answer to the question above to determine the image `P'` of `P(3 ; 2)` .

`M` is the reflection of `K` about the line with equation `x = a` .

Determine the value of the constant `a` .

The area of `KMN` is rotated 180^o about the origin to form```` the area `K''M''N''`

Give the coordinates of `K''`

Area `KMN` is translated 3 units to the right and 1 unit upwards to obtain Area `K'''M'''N'''`.

Write down the ratio of `(K'K''')/(K'M''')` after the translation.

Write down the coordinates of point `K'` in terms of `a` and `b` .

Write down the coordinates of `K''` in terms of `a` , `b` , `sintheta` and `costheta` .

Simplify if necessary.

`T(-4;-2)` is rotated clockwise through an angle of `(90^o + theta )` about the origin to obtain image `T'` .

Determine, in the simplest form, the coordinates of `T'` in terms of `theta` .

Hence, or otherwise, calculate the size of `theta` if it is given that `T'(2sqrt(3)+1;sqrt(3)-2)`  and `90^o<theta<180^o` .

Simplify as far as possible: `1-sin^2theta+3-cos^2theta`

Simplify WITHOUT the use of a calculator:

`sqrt(4^(sin150^o) xx 2^(3tan225^o))`

Prove that:

`(cos^2x+sin^2x+cos^4x)/(1-sinx)=1+sinx`

Prove that for any angle `theta` , `cos3theta=4cos^3theta-3costheta`

(Hint: `3theta= theta +2theta` )

If `x=cos20^o` , use the previous question to show that `8x^3-6x-1=0` .

Simplify to ONE trigonometric function WITHOUT using a calculator:

`(cos160^otan200^o)/(2sin<<-10^o>>)`

Consider: `cos<<x+45^o>>cos<<x-45^o>>` .

Show that: `cos<<x+45^o>>cos<<x-45^o>>=1/2cos2x` .

Consider: `cos<<x+45^o>>cos<<x-45^o>>.`

Hence, determine a value of `x` in the interval `0^o<=x<=180^o` for which `cos<<x+45^o>>cos<<x-45^o>>` is a minimum.

Write down the range of `f` .

Determine the period of `f<<3/2x>>`

Draw the graph of `g(x)=cos(x-30^o)` for`-180^o<=x<=90^o` .

Clearly lable ALL `x` -intercepts and turning points.

Hence, or otherwise, determine the values of `x` in the interval `-180^o<=x<=90^o` for which `f(x).g(x)<0` .

Describe the transformation that graph `f` has to undergo to form `y=sin(2x+60^o)` .

Determine the general solution of `sin 2x=cos(x-30^o)` .

Write down `AB` in terms of `x` and `r` .

Give the size of `Ahat(K)C` in terms of `x` .

If it is given that `(AK)/(AB)=2/3` , calculate the value `x`