2019 senior external examination: mathematics a paper two
TRANSCRIPT
2019 Senior External Examination
Mathematics APaper Two — Question and response book
Monday 28 October 20191:15 pm to 4:25 pm
Time allowed• Perusal time: 10 minutes
• Working time: 3 hours
Examination materials provided• Paper Two — Question and response book
• Paper Two — Resource book
Equipment allowed• QCAA-approved equipment• ruler (metric, parallel or rolling)• protractor• drawing compass• set squares• templates (without formulas)• non-programmable calculator• graphing calculator
Not allowed: Calculators with computer algebra system (CAS) functionality.
DirectionsDo not write during perusal time.
Paper Two has four extended-response questions.
Attempt all questions.
AssessmentPaper Two assesses the following assessment criteria:
• Knowledge and procedures (KP)
• Modelling and problem solving (MP)
• Communication and justification (CJ)
Assessment standards are at the end of this book.
After the examination sessionThe supervisor will collect this book when you leave.
Candidate usePrint your candidate number here
Attach barcode here
Number of books used
Supervisor use only
Supervisor’s initials
QCAA use only
Marker number
1 9 – –
Planning space
12019 Mathematics A — Question and response book — Paper Two
Paper Two has four extended-response questions. Attempt all questions.Write your responses in the spaces provided. Show full working in all responses. Partial credit can be awarded only if working is shown.Additional pages for responses are at the back of this book.
Question 1a. Billy bought a home entertainment unit on a payment plan. The cash price of the unit was $3500.
Billy had to pay 12% deposit and repay the balance at 9% p.a. flat interest in equal monthly instalments for 2 years.
Calculate the amount of each monthly repayment.
(KP)
b. A car is purchased for $24 000. Use the diminishing value formula to calculate the salvage value of the car after 4 years at a depreciation rate of 15% p.a.
(KP)
Question 1 continues over next page ▬►
2 2019 Mathematics A — Question and response book — Paper Two
c. Steven and Michelle borrow $225 000 over 20 years at 4% p.a. reducible rate to purchase a house.
They make the required repayment each month, and after 7 years the balance of the loan has reduced to $195 000.
The interest rate then rises to 5% p.a.
Using the repayment table schedule below, determine whether they will need to increase the size of their monthly repayment and, if so, by how much.
Fully justify your decision with mathematical reasoning.
State one strength and one limitation for this situation.
Monthly repayment per $1000
Years 10 11 12 13 14 15 16 17 18 19 20
4% $12.67 $11.96 $11.38 $10.90 $10.49 $10.14 $9.85 $9.59 $9.36 $9.17 $9.00
5% $13.22 $12.52 $11.95 $11.48 $11.08 $10.75 $10.46 $10.21 $10.00 $9.81 $9.65
(MP)
d. A company’s prospectus predicts that the percentage dividend for the coming year will be 6.25%. Each share has a face value of $16.40.
Calculate the dividend paid if this percentage dividend is paid.
(KP)
32019 Mathematics A — Question and response book — Paper Two
Question 2a. Below are the final heights recorded for two athletes in eight high-jump competitions.
Carl 1.80 m 1.80 m 1.90 m 1.90 m 1.70 m 1.80 m 2.00 m 1.60 m
Richard 2.00 m 1.90 m 1.70 m 2.10 m 2.10 m 1.80 m 1.90 m 2.10 m
i. Calculate the mean height for Carl and the mean height for Richard.
Carl: Richard:
ii. Calculate the interquartile range for Carl and the interquartile range for Richard.
Carl:
Richard:
iii. Calculate the sample standard deviation for each student’s heights.
Carl: Richard:
iv. Determine which student is the most consistent and give a reason for your choice.
v. List the five-number summary for Carl and the five-number summary for Richard.
Carl:
Richard:
vi. Draw adjacent boxplots to represent this data on the scale below.
Jump heights
Question 2 continues over next page ▬►
(KP)
(KP)
(KP)
(KP)
(KP)
(KP)
4 2019 Mathematics A — Question and response book — Paper Two
b. The following data represents the number of goals scored in 16 soccer games.
0 1 0 2 3 0 4 3 3 1 3 0 0 2 4 4
i. Complete the frequency table.
Goals scored Tally Frequency
ii. Draw a frequency histogram to represent this data using the axes below.
iii. Find the mean, median, mode and range for this data.
Mean:
Median:
Mode:
Range:
iv. Describe this data using two words, one from each list below.
List 1: continuous, discrete List 1 word:
List 2: categorical, ordinal List 2 word:(KP)
(KP)
(KP)
(KP)
Spare axes are provided on page 16.
52019 Mathematics A — Question and response book — Paper Two
c. A class of 30 students sat for an Algebra test and a Geometry test. The results are displayed in a scatterplot with a line of best fit below.
i. How many students scored less than 30 on both the Algebra and Geometry tests?
ii. Describe the correlation between the Algebra and Geometry test results.
iii. Explain why the following statement is incorrect.
In this class all students who are near the top in Algebra are also near the top in Geometry.
(KP)
(KP)
(MP)
6 2019 Mathematics A — Question and response book — Paper Two
Question 3a. Below is a floor plan for a house.
i. If the length of the southern wall of the kitchen is 3 m, find the scale used for this plan.
(KP)
ii. What are the actual dimensions of the living room?
(KP)
72019 Mathematics A — Question and response book — Paper Two
iii. The floor of the bathroom is to be tiled. A 600 mm × 600 mm tile costs $29.80 each. Allowing an extra 10% for wastage, calculate the cost of tiling the bathroom.
iv. Wallpaper is to be used to cover the southern and western walls of the bedroom. The walls are 2.4 m high. A 10 m long wallpaper roll is 0.53 m in width.
Calculate the minimum number of rolls of wallpaper needed to cover both the southern and western walls of the bedroom.
Question 3 continues over next page ▬►
(KP)
(KP)
8 2019 Mathematics A — Question and response book — Paper Two
v. Determine the amount of concrete needed for the footings of this house if they are 350 mm wide and 200 mm deep.
(KP)
Note: This is a duplicate image from page 6.
92019 Mathematics A — Question and response book — Paper Two
vi. Calculate the amount of concrete needed for the slab of this house if it is to be 10 cm deep.
vii. The builder has estimated the concrete for the slab and footings will cost $2300.
Concrete costs $300 / m3. Make an informed decision as to whether the builder has allowed sufficient money to pay for the concrete.
(KP)
(MP)
Question 3 continues over next page ▬►
10 2019 Mathematics A — Question and response book — Paper Two
b. After pegging out a rectangular shed, a builder measures one pair of opposite sides of the shed to be 4.8 m and the other pair of opposite sides to be 3.6 m.
Use diagrams and mathematical reasoning to explain how the builder can be sure that the shed is rectangular.
(MP)
112019 Mathematics A — Question and response book — Paper Two
Question 4a. The following network shows the completion time for a project in days.
i. Find the minimum time to complete the project.
ii. State the critical path.
b.
The above network shows connecting paths for a cable network. It costs $65 per metre to lay the cable. Use a minimum spanning tree to determine the least cost to connect this network.
Question 4 continues over next page ▬►
(KP)
(KP)
(KP)
all distances are in metres
not to scale
not to scale
12 2019 Mathematics A — Question and response book — Paper Two
c. The graph below illustrates the waiting time in a queue across a 60-minute period.
i. How many customers were waiting to be served 19 minutes after the start of the 60-minute period?
(KP)
ii. What is the longest time a customer has to queue before being served?
(KP)
d. Spectators arrive at the rate of 60 per minute at a football game. If it takes 20 seconds to check each person through security, how many service points are needed if queues are not to grow?
(KP)
132019 Mathematics A — Question and response book — Paper Two
e. The table below shows the distances in metres between exhibits at a garden show.
A B C D E F GA – 50 70 85 – – –B – – 30 – 70 – –C – – – 50 65 – –D – – – – 45 90 60E – – – – – 40 –F – – – – – – 80
i. Construct a network diagram to represent the information displayed in the table.
(KP)
ii. All exhibits are to be visited only once. This means that visitors enter the show and progress through the exhibits to the exit without revisiting exhibits. Determine if the minimal spanning tree will identify the route that satisfies these conditions. Fully justify your decision with mathematical reasoning and a network diagram.
(MP)
14 2019 Mathematics A — Question and response book — Paper Two
f. A drive-through fast food outlet has two service lanes but only one operator. It takes one minute for the operator to take the order and then a further two minutes to give the customer the order at the service window.
Up to five cars can fit between the order window and the service window in each service lane. When the outlet opens at 6:00 am there are three cars waiting in each service lane to order.
For the first ten minutes after opening, a car arrives every minute. Following this, a car arrives every two minutes.
i. Respond to this question on page 15. A spare grid is provided on page 17. Graph a scenario for the first 30 minutes the outlet opens.
ii. Determine the first time the queue becomes empty.
iii. Calculate the average waiting time between 6:00 am and 6:30 am.
End of Paper Two(KP)
(KP)
(KP)
152019 Mathematics A — Question and response book — Paper Two
Question 4f i.
16 2019 Mathematics A — Question and response book — Paper Two
Spare axes (if required)
172019 Mathematics A — Question and response book — Paper Two
Spare grid (if required)
18 2019 Mathematics A — Question and response book — Paper Two
Question
Additional page for responses (if required)
192019 Mathematics A — Question and response book — Paper Two
Question
Additional page for responses (if required)
20 2019 Mathematics A — Question and response book — Paper Two
Question
Additional page for responses (if required)
Asse
ssm
ent s
tand
ards
from
the M
athe
mat
ics A
Sen
ior E
xter
nal S
yllab
us 200
6
Crite
rion
AB
CD
E
Know
ledg
e and
pr
oced
ures
(KP)
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent
acro
ss th
e ful
l ran
ge w
ithin
th
e con
text
s of a
pplic
atio
n,
tech
nolo
gy an
d co
mpl
exity
, an
d ac
ross
topi
cs, c
onsis
tent
ly de
mon
stra
tes:
• ac
cura
te re
call,
sele
ctio
n an
d us
e of d
efin
ition
s and
rule
s•
use o
f tec
hnol
ogy
• re
call a
nd se
lect
ion
of
proc
edur
es, a
nd th
eir
accu
rate
and
prof
icien
t use
.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent a
cros
s a r
ange
with
in th
e con
text
s of
appl
icatio
n, te
chno
logy
and
com
plex
ity, a
nd ac
ross
topi
cs,
gene
rally
dem
onst
rate
s:•
accu
rate
reca
ll, se
lect
ion
and
use o
f def
initi
ons a
nd ru
les
• us
e of t
echn
olog
y•
reca
ll and
sele
ctio
n of
pr
oced
ures
, and
thei
r ac
cura
te u
se.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent i
n th
e con
text
s of a
pplic
atio
n,
tech
nolo
gy an
d co
mpl
exity
, ge
nera
lly d
emon
stra
tes:
• ac
cura
te re
call a
nd u
se of
ba
sic d
efin
ition
s and
rule
s•
use o
f som
e tec
hnol
ogy
• ac
cura
te u
se of
bas
ic pr
oced
ures
.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent i
n th
e con
text
s of a
pplic
atio
n,
tech
nolo
gy an
d co
mpl
exity
, so
met
imes
dem
onst
rate
s:•
accu
rate
reca
ll and
use
of
som
e def
initi
ons a
nd ru
les
• us
e of s
ome t
echn
olog
y.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent r
arel
y de
mon
stra
tes k
nowl
edge
and
use o
f pro
cedu
res.
Mod
ellin
g and
pr
oble
m so
lving
(MP)
The o
vera
ll qua
lity o
f a
cand
idat
e’s ac
hiev
emen
t acro
ss
the f
ull r
ange
with
in ea
ch co
ntex
t, an
d acro
ss to
pics
gene
rally
de
mon
stra
tes m
athe
mat
ical
thin
king w
hich
inclu
des:
• in
terp
retin
g, cl
arify
ing
and
anal
ysin
g a ra
nge o
f sit
uatio
ns, a
nd id
entif
ying
varia
bles
• se
lect
ing a
nd u
sing e
ffect
ive
stra
tegie
s•
info
rmed
dec
ision
mak
ing
… and
som
etim
es
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des:
• se
lect
ing a
nd u
sing
proc
edur
es to
solve
a wi
de
rang
e of p
robl
ems
• in
itiat
ive in
expl
orin
g the
pr
oble
m•
reco
gnisi
ng st
reng
ths a
nd
limita
tions
of m
odel
s.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent a
cros
s a r
ange
with
in ea
ch co
ntex
t, an
d ac
ross
topi
cs, g
ener
ally
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des:
• in
terp
retin
g, cl
arify
ing
and
anal
ysin
g a ra
nge o
f sit
uatio
ns, a
nd id
entif
ying
varia
bles
• se
lect
ing a
nd u
sing s
trate
gies
… and
som
etim
es
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des:
• se
lect
ing a
nd u
sing
proc
edur
es re
quire
d to
solve
a r
ange
of p
robl
ems
• in
form
ed d
ecisi
on m
akin
g.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des:
• in
terp
retin
g and
clar
ifyin
g a
rang
e of s
ituat
ions
• se
lect
ing s
trate
gies a
nd/o
r pr
oced
ures
.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des
follo
wing
bas
ic pr
oced
ures
and/
or u
sing s
trate
gies.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent r
arel
y de
mon
stra
tes m
athe
mat
ical
thin
king
whi
ch in
clude
s fo
llowi
ng b
asic
proc
edur
esan
d/or
usin
g stra
tegie
s.
212019 Mathematics A — Question and response book — Paper Two
Asse
ssm
ent s
tand
ards
from
the M
athe
mat
ics A
Sen
ior E
xter
nal S
yllab
us 200
6
Crite
rion
AB
CD
E
Know
ledg
e and
pr
oced
ures
(KP)
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent
acro
ss th
e ful
l ran
ge w
ithin
th
e con
text
s of a
pplic
atio
n,
tech
nolo
gy an
d co
mpl
exity
, an
d ac
ross
topi
cs, c
onsis
tent
ly de
mon
stra
tes:
• ac
cura
te re
call,
sele
ctio
n an
d us
e of d
efin
ition
s and
rule
s•
use o
f tec
hnol
ogy
• re
call a
nd se
lect
ion
of
proc
edur
es, a
nd th
eir
accu
rate
and
prof
icien
t use
.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent a
cros
s a r
ange
with
in th
e con
text
s of
appl
icatio
n, te
chno
logy
and
com
plex
ity, a
nd ac
ross
topi
cs,
gene
rally
dem
onst
rate
s:•
accu
rate
reca
ll, se
lect
ion
and
use o
f def
initi
ons a
nd ru
les
• us
e of t
echn
olog
y•
reca
ll and
sele
ctio
n of
pr
oced
ures
, and
thei
r ac
cura
te u
se.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent i
n th
e con
text
s of a
pplic
atio
n,
tech
nolo
gy an
d co
mpl
exity
, ge
nera
lly d
emon
stra
tes:
• ac
cura
te re
call a
nd u
se of
ba
sic d
efin
ition
s and
rule
s•
use o
f som
e tec
hnol
ogy
• ac
cura
te u
se of
bas
ic pr
oced
ures
.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent i
n th
e con
text
s of a
pplic
atio
n,
tech
nolo
gy an
d co
mpl
exity
, so
met
imes
dem
onst
rate
s:•
accu
rate
reca
ll and
use
of
som
e def
initi
ons a
nd ru
les
• us
e of s
ome t
echn
olog
y.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent r
arel
y de
mon
stra
tes k
nowl
edge
and
use o
f pro
cedu
res.
Mod
ellin
g and
pr
oble
m so
lving
(MP)
The o
vera
ll qua
lity o
f a
cand
idat
e’s ac
hiev
emen
t acro
ss
the f
ull r
ange
with
in ea
ch co
ntex
t, an
d acro
ss to
pics
gene
rally
de
mon
stra
tes m
athe
mat
ical
thin
king w
hich
inclu
des:
• in
terp
retin
g, cl
arify
ing
and
anal
ysin
g a ra
nge o
f sit
uatio
ns, a
nd id
entif
ying
varia
bles
• se
lect
ing a
nd u
sing e
ffect
ive
stra
tegie
s•
info
rmed
dec
ision
mak
ing
… and
som
etim
es
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des:
• se
lect
ing a
nd u
sing
proc
edur
es to
solve
a wi
de
rang
e of p
robl
ems
• in
itiat
ive in
expl
orin
g the
pr
oble
m•
reco
gnisi
ng st
reng
ths a
nd
limita
tions
of m
odel
s.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent a
cros
s a r
ange
with
in ea
ch co
ntex
t, an
d ac
ross
topi
cs, g
ener
ally
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des:
• in
terp
retin
g, cl
arify
ing
and
anal
ysin
g a ra
nge o
f sit
uatio
ns, a
nd id
entif
ying
varia
bles
• se
lect
ing a
nd u
sing s
trate
gies
… and
som
etim
es
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des:
• se
lect
ing a
nd u
sing
proc
edur
es re
quire
d to
solve
a r
ange
of p
robl
ems
• in
form
ed d
ecisi
on m
akin
g.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des:
• in
terp
retin
g and
clar
ifyin
g a
rang
e of s
ituat
ions
• se
lect
ing s
trate
gies a
nd/o
r pr
oced
ures
.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent
dem
onst
rate
s mat
hem
atica
l th
inki
ng w
hich
inclu
des
follo
wing
bas
ic pr
oced
ures
and/
or u
sing s
trate
gies.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent r
arel
y de
mon
stra
tes m
athe
mat
ical
thin
king
whi
ch in
clude
s fo
llowi
ng b
asic
proc
edur
esan
d/or
usin
g stra
tegie
s.
22 2019 Mathematics A — Question and response book — Paper Two
(cont
inue
d)
Crite
rion
AB
CD
E
Com
mun
icatio
n an
d ju
stifi
catio
n(C
J)
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent
acro
ss th
e ful
l ran
ge w
ithin
ea
ch co
ntex
t con
siste
ntly
dem
onst
rate
s:•
accu
rate
use
of m
athe
mat
ical
term
s and
sym
bols
• ac
cura
te u
se of
lang
uage
• or
gani
satio
n of
info
rmat
ion
into
vario
us fo
rms s
uita
ble f
or
a give
n us
e•
use o
f mat
hem
atica
l re
ason
ing t
o dev
elop
logic
al
argu
men
ts in
supp
ort o
f co
nclu
sions
, res
ults
and/
or
decis
ions
• ju
stifi
catio
n of
pro
cedu
res.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent a
cros
s a r
ange
with
in ea
ch co
ntex
t ge
nera
lly d
emon
stra
tes:
• ac
cura
te u
se of
mat
hem
atica
l te
rms a
nd sy
mbo
ls•
accu
rate
use
of la
ngua
ge•
orga
nisa
tion
of in
form
atio
n in
to va
rious
form
s sui
tabl
e for
a g
iven
use
• us
e of m
athe
mat
ical
reas
onin
g to d
evel
op si
mpl
e lo
gical
argu
men
ts in
supp
ort
of co
nclu
sions
, res
ults
and/
or
decis
ions
.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent
in so
me c
onte
xts g
ener
ally
dem
onst
rate
s:•
accu
rate
use
of b
asic
mat
hem
atica
l ter
ms a
nd
sym
bols
• ac
cura
te u
se of
bas
ic la
ngua
ge•
orga
nisa
tion
of in
form
atio
n in
to va
rious
form
s•
use o
f som
e mat
hem
atica
l re
ason
ing t
o dev
elop
sim
ple
logic
al ar
gum
ents
.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent
som
etim
es d
emon
stra
tes
evid
ence
of th
e use
of th
e bas
ic co
nven
tions
of la
ngua
ge an
d m
athe
mat
ics.
The o
vera
ll qu
ality
of a
cand
idat
e’s a
chie
vem
ent r
arel
y de
mon
stra
tes u
se of
the b
asic
conv
entio
ns of
lang
uage
or
mat
hem
atics
.
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