exercises functions

8/13/2019 Exercises Functions

1/3

Exercise #1 :

To clean the upstairs window on the side of a house, it is necessary to position the ladder so

hat it just touches the edge of the lean-to shed as shown in the diagram. The co-ordinates

epresent distances from O in metres, in the x and y directions shown.

Find :

1/ The gradient and the euation of the line of he ladder.

!/ The height of the point " reached #y the top of the ladder.

$/ The length of the ladder to the nearest centimetre.

Exercise #1 :




Find :

1/ The gradient and the euation of the line of he ladder.!/ The height of the point " reached #y the top of the ladder.


Exercise #1 :




Find :

1/ The gradient and the euation of the line of he ladder.

!/ The height of the point " reached #y the top of the ladder.


Exercise #1 :




Find :

1/ The gradient and the euation of the line of he ladder.!/ The height of the point " reached #y the top of the ladder.



2/3

Exercise #2 :

Team A :

%n the ancient times, some people thought that all rectangular plots of land

with the same perimeter had the same area.

&ere those peoples right ' (ustify

Find the dimensions for a rectangle of perimeter 1))m with maximum area.

Team B :

*+etch the graph of the function fdefined on the domain ) ) #y

f(x )=x!+)x0a+e sentences to descri#e this graph

Exercise #3

" stone is thrown into the air and its height in metres a#oe the ground is

gien #y the function h2t3 4 5 t!6 $)t 6 ! where t is the time in seconds

from when the stone is thrown.

Team A :

*+etch the graph of h on the domain ) 1).

0a+e sentences to descri#e this graph

Team B :

&hat is the maximum height reached #y the stone '

&hen does the stone come #ac+ to earth '

Exercise #2 :

Team A :

%n the ancient times, some people thought that all rectangular plots of land

with the same perimeter had the same area.

&ere those peoples right ' (ustify

Find the dimensions for a rectangle of perimeter 1))m with maximum area.

Team B :

*+etch the graph of the function fdefined on the domain ) ) #y

f(x )=x!+)x0a+e sentences to descri#e this graph

Exercise #3

" stone is thrown into the air and its height in metres a#oe the ground is

gien #y the function h2t3 4 5 t!6 $)t 6 ! where t is the time in seconds

from when the stone is thrown.

Team A :

*+etch the graph of h on the domain ) 1).

0a+e sentences to descri#e this graph

Team B :

&hat is the maximum height reached #y the stone '

&hen does the stone come #ac+ to earth '


3/3

Exercise # 4

Team A :

" carpenter wants to ma+e a #ox to hold toys. This #ox is to #e made so that

its olume is as large as possi#le.

" rectangular sheet of thin plywood 273 measuring 1.m #y 1m is aaila#leto cut into pieces as shown :

1/ &rite down the dimensions of one of the four rectangular faces of the #ox

in terms of x . 8etween which num#ers isx'

!/ Form the expression in terms of x for the olume of the made-up #ox.

273 : plywood : contreplau9

Team B :

Vis the function such that V(x)=x!!x$

1/ One needs #oth x and V(x) to #e positie.&hat is conseuently its domain '

!/ Find x that gies the maximum alue for Vand compute this maximum

alue.

Exercise #5

Team A :

Find the domainDwhere the expression )x!x! is greater than or eual

to ;ero.

Ais the function defined onD#y : A(x)=)x!x!

Find x such that A(x) is maximum.

*+etch the graph of A .

Team B :

" new children slide is to #e #uilt in a playground.

" long strip of metal )cm wide is aaila#le for this slide and will #e #ent toform its #ase 2y 3 and two sides 2x 3.

*ee #elow the cross-section of the slide made of this strip of metal :

The designer thin+s that for maximum safety, the "rea of the rectangular

cross-section should #e as large as possi#le.

exercises functions

Documents