`( x^2-9)(2x-1)=0`

` `

`x^2+ x-13=0`  

(Leave your answer correct to TWO decimal places)

`2.3^x=81-3^x`

`( x+1)(4-x) > 0`

Given: `2^x+2^(x+2)=-5y+20`

Express `2^x` in terms of `y`

Given: `2^x+2^(x+2)=-5y+20`

How many solutions for `x` will the equation have if `y=-4`

Given: `2^x+2^(x+2)=-5y+20 `

Solve for `x` if `y` is the largest possible integer value for which `2^x+2^(x+2)=-5y+20` will have solutions

Determine the value of `p` .

Calculate the sum of the first 8 terms of the series.

Why does the sum to infinity for this series exist?

Calculate `Soo`

Write down the next term of the sequence.

If the `n^(th)` term of the sequence is 148, determine the value of `n` .

Calculate the smallest value of `n` for which the sum of the first `n` terms of the sequence will be greater than 10 140.

Calculate `sum_(k=1)^30<<3k+5>>`

Explain why Jacob and Vusi could both be correct.

Jacob's sequence

Vusi's sequence

Write down the domain of `f` .

Write down the equation of the asymptote of `f` .

Write down the equation of `f^(-1)` in the form `y = ...`

`
`

Sketch the graph of `f^(-1)` 

Indicate the x-intercept and ONE other point.

Write down the equation of the asymptote of `f^(-1)<<x+2>>`

Prove that:

`<<f<<x>>>>^2- <<f<<-x>>>>^2=f<<2x>>-f<<-2x>>`

For all values of `x`

Determine the equation for `g` in the form
`g<<x>>=(a/(x-p))+q`

F is the reflection of B across C.

Determine the coordinates of F.

Calculate the coordinates of T.

Determine the equation for `f` in the form:

`f<<x>>=ax^2+bx+c`

Show ALL your working.

If:

`f<<x>>=-2x^2+4x+16`

`
Calculate the coordinates of R.
`

`f<<x>>>=g<<x>>`

`-2x^2+4x-2<0`

Raeesa invests R4 million into an account earning interest of 6% per annum,
compounded annually.

How much will her investment be worth at the end of 3 years?

She withdraws an allowance of R30 000 per month. The first withdrawal is exactly one month after she has deposited the R4 million.

How many such withdrawals will Joanne be able to make?

If Joanne withdraws R20 000 per month, how many withdrawals will she be able to make?

Jeffrey invests R700 per month into an account earning interest at a rate of 8% per annum,
compounded monthly. His friend also invests R700 per month and earns interest compounded
semi-annually (that is every six months) at `r%` per annum. Jeffrey and his friend's investments are worth the same at the end of 12 months.

Calculate `r` .

Use the definition of the derivative (first principles) to determine `f'<<x>>` if `f<<x>>=2x^3`

Determine `dy/dx` if `y=(2sqrt(x)+1)/x^2`

Calculate the values of `a` and `b` if `f<<x>>=ax^2+bx+5` has a tangent at `x=-1` which is defined by the equation `y=-7x+3`

Given: `f<<x>>=-x^3-x^2+x+10`

Write down the coordinates of the `y` -intercept of `f` .

Given: `f<<x>>=-x^3-x^2+x+10`

Show that (2 ; 0) is the only `x` -intercept of `f` .

Given: `f<<x>>=-x^3-x^2+x+10`

Calculate the coordinates of the turning points of `f` .

Given: `f<<x>>=-x^3-x^2+x+10`

Sketch the graph of `f` .

Show all intercepts with the axes and all turning points.

Determine an expression for the height (`h` ) of the box in terms of `x` .

Show that the cost to construct the box can be expressed as `C=1200/x+600x^2` ` `

Calculate the width of the box (that is the value of `x` ) if the cost is to be a minimum.

Shade the feasible region on the DIAGRAM SHEET.

Indicate which constraints have no influence on the feasible region.

What is the maximum value of `x` allowed by these constraints?

If `P=4x+y` for `(x ; y)` in the feasible region, determine the maximum value of `P` .

If the objective function `C=kx+y` is minimized at `J` only, determine all possible values of `k`