Using Â
with Â
find the values of , andÂ
Explain the relationship between the values of and and the equationÂ
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Using Â
with Â
find the values of , andÂ
Explain the relationship between the values of and and the equationÂ
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A sequence of numbers is formed by the iterative process
     Â
Work out the values of and
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An approximate solution to an equation is found using the iterative formula
=Â Â Â with
Work out the values of and
= ......................
= ......................
Work out the solution to 5 decimal places.
= ......................
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An approximate solution to an equation is found using this iterative process.
   andÂ
Work out the values of andÂ
  = ........................
  = .........................
Work out the solution to 6 decimal places.
= .......................
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Use the formula with x1 = 2 to calculate x2 and x3.
Round your answers correct to 4 decimal places.
x2 = ............. and x3 = ................
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Show that the equation has a solution between andÂ
Show that the equation can be rearranged to giveÂ
Starting withÂ
use the iteration formula three times to find an estimate for a solution of Â
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Show that the equation has a solution between andÂ
Show that the equation can be arranged to give Â
Starting with , use the iteration formula twice ,
to find an estimate for the solution of Â
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Show that the equation can be rearranged to giveÂ
  Â
UsingÂ
      withÂ
find the values of andÂ
Explain what the values of and represent.
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A sphere has radius cm
An approximate value of can be found using the iterative formula
The starting value isÂ
Work out the values of and
Continue the iteration to work out the radius to 1 decimal place.
................................................. cm
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Use a starting value of to work out a solution to
Give your answer to 3 decimal places.
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Show that the equation has a solution between andÂ
Show that the equation can be arranged to giveÂ
Starting with , use the iteration formula three times to find an estimate for the solution ofÂ
By substituting your answer to part (c) intoÂ
comment on the accuracy of your estimate for the solution toÂ
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The number of bees in a beehive at the start of year is
The number of bees in the beehive at the start of the following year is given byÂ
At the start of 2015 there were 9500 bees in the beehive.
How many bees will there be in the beehive at the start of 2018?
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The number of slugs in a garden days from now is where
  Â
Work out the number of slugs in the garden days from now.
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At the start of year , the number of animals in a population is
At the start of the following year, the number of animals in the population is , where
At the start of 2017 the number of animals in the population was 4000
At the start of 2019 the number of animals in the population was 3610
Find the value of the constant .
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Use the iteration formula  to find the values of , andÂ
Start with
.  Â
.  Â
   Â
The values of , and found part (a) are estimates of the solution of an equation of the form where and are integers.
Find the value of and the value of .
.  Â
   Â
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The number of rabbits on a farm at the end of month isÂ
The number of rabbits at the end of the next month is given byÂ
At the end of March there are 200 rabbits on the farm.
Work out how many rabbits there will be on the farm at the end of June.
Considering your results in part (a), suggest what will happen to the number of rabbits on the farm after a long time.
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