!"#$%&'()*$+,'&,*&-.$/-'012((*$
MPM1D%
Jensen%
%
%
%
#"%Determine%the%constant%of%variation%for%each%direct%variation.%%%%%%%%%%%%%%%%%%%%π‘š =
βˆ†!"#"$!"$%
βˆ†!"#$%$"# $ " &
%
%
a)%The%distance%travelled%by%a%bus%varies%directly%with%time.%The%bus%travels%240%km%in%3%hours.%%
%
%
%
%
%
%
%
%
b)%The%total%cost%varies%directly%with%the%number%of%books%bought.%Five%books%cost%$35.%%
%
%
%
%
%
%
%
%
c)%The%volume%of%water%varies%directly%with%time.%A%swimming%pool%contains%500%L%of%water%after%5%
minutes.%%
%
%
%
%
%
%
%
%
%
3"%The%cost,%𝐢,%in%dollars,%of%building%a%concrete%sidewalk%varies%directly%with%its%length,%𝑠,%in%meters.%%
%
a)%Find%an%equation%relating%𝐢%and%𝑠%if%a%200Km%sidewalk%costs%$4500.%%
%
%
%
%
%
%
%
%
%
%
b)%What%does%the%constant%of%variation%represent?%%%
%
%
%
%
c)%Use%the%equation%to%determine%the%cost%of%a%700Km%sidewalk.%%
%
%
%
%
%
%
%
%
4"%Passent’s%pay%varies%directly%with%the%time,%in%hours,%she%works.%She%earns%$8/h.%%
%
a)%Complete%the%following%table%of%values%
%
5-6'1$
/-'0(7$
8,9$
:$
$
#$
$
3$
$
4$
$
%%
%
b)%Graph%the%relation.%Choose%an%appropriate%scale%and%label%your%axes.%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
c)%Write%an%equation%in%the%form%𝑦 = π‘šπ‘₯.%
%
%
%
%
;"%The%total%cost%of%apples%varies%directly%with%the%mass,%in%kilograms,%bought.%Apples%cost%$1.50/%kg.%%
%
a)%Complete%the%following%table%of%values:%
%
<,11$=0>?$
@-1*$=A?$
:$
$
#$
$
3$
$
4$
$
%
b)%Graph%the%relation.%Choose%an%appropriate%scale%and%label%the%axes.%%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
c)%Write%an%equation%in%the%form%𝑦 = π‘šπ‘₯%
%
!"%A%parking%garage%charges%$2.75/h%for%parking.%%
%
a)%Describe%the%relationship%between%the%cost%of%parking%and%the%time,%in%hours,%parked.%%
%
%
%
%
b)%Illustrate%the%relationship%graphically%and%represent%it%with%an%equation.%%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
Equation:%_____________________________________%
%
%
%
c)%Use%your%graph%to%estimate%the%cost%of%7%hours%of%parking.%
%
%
%
%
%
%
%
d)%Use%your%equation%to%determine%the%exact%cost%for%7%hours%of%parking.%%
%
%
%
%
%
B"%The%cost%of%oranges%varies%directly%with%the%total%mass%bought.%2%kg%of%oranges%costs%$4.50.%%
%
a)%Describe%the%relationship%in%words.%%
%
%
%
%
b)%Write%an%equation%relating%the%cost%and%the%mass%of%oranges.%What%does%the%constant%of%variation%
represent?%
%
%
%
%
%
%
%
%
%
%
c)%What%is%the%cost%of%30%kg%of%oranges?%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
C"%The%volume%of%water%in%a%swimming%pool%varies%directly%with%time.%500%L%of%water%is%in%the%pool%after%4%
minutes.%%
%
a)%Write%an%equation%relating%the%volume%of%water%and%time.%What%does%the%constant%of%variation%
represent?%
%
%
%
%
%
%
%
%
%
%
%
%
b)%Graph%this%relationship.%Choose%an%appropriate%scale%and%label%your%axes.%%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
c)%What%volume%of%water%is%in%the%swimming%pool%after%20%minutes?%
%
%
%
%
%
%
%
%
d)%How%long%will%it%take%to%fill%a%swimming%pool%that%holds%115%000%L%of%water?%
%
%
%
%
%
%
%
%
e)%Describe%the%changes%to%the%equation%and%graph%if%only%400%L%of%water%is%in%the%pool%after%4%minutes.%%
%
%
%
D"%[BONUS]%From%a%bag%of%disks%numbered%1%through%100,%one%disk%is%chosen.%What%is%the%probability%that%
the%number%on%the%disk%contains%a%3?%Justify%your%answer.%
%
%
%
%
%
%
%
%
%
%
E.1F('1$
%
% C"$$