Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 1 of 17
VCAA MATHEMATICS
PAPER 1
2018
MEMORANDUM
QUESTION 1
(a)
4or 2
3
0432
01252
12)52(
2
xx
xx
xx
xx
(3)
(b)
7
4
0 47
3 3
33.3
1 27.81
0344
0314
1
x
x
xx
xx
xx
(3)
(c)
Rx
x
xx
xx
02
044
44
2
2
2
(3)
QUESTION 2
(a)
xy
xyy
xyTT
xy
2
23
difference common
(2)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 2 of 17
(b) (1)
25 ; 16 ; 9 ; 4
-9 -7 -5
2 2
1
22
a
a
12
93
93
b
b
ba
36
25121
25
c
c
cba
(4)
(b) (2)
0 and
)D(
D(
)D(
rq
ttt
1
036)6(12)6(6
136)5(12)5()5
3612
2
2
2
(2)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 3 of 17
(b) (3)
As t approaches 6 - D(t) is decreasing in value which show that the athlete is moving
towards A. ie D(1) = 25
D(2) = 16
D(3) = 9 etc
As t gets larger than 6 – D(t) is increasing in value which shows that the athlete starts
moving away from A. ie D(7) = 1
D(8) = 4 (4)
D(9) = 9
OR
increasing is ;
decreasing is ;
at value minimum
n
n
n
Tnfor
Tnfor
n
nT
6
60
6
)6( 2
QUESTION 3
(a) (1)
52
1
]4;5(
; : range
: domain
y
x
(4)
(2)
3 is value maximum (1)
(b) (1)
xy 5log (1)
(2)
;yRy or (2)
6
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 4 of 17
(3)
(4)
(4) 10 x (2)
(c)
3
1
013
x
x
(2)
QUESTION 4
(a) (1) pound per 76,1628000
469280R (2)
(2) 5423903650086,14 R
Most expensive is in Europe. (2)
−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
7
8
9
10
x
y
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 5 of 17
(b) (1)
17
2862,17
2
%5,12
)1(1
n
n
i
ixP
n
n
v
2
12,5%1 1 250 96
000 1000 (3)
(2)
488,52 26 R
goutstandin Balance
F - A goutstandin Balance
2
%5,12
12
%5,12196250
2
%5,1211000000
17
17
(4)
(3)
( 1)loan amount = P (1 ) n
v x i
144,06 28 R
2
12,5%
12,5%1 - 196250
000 1000
x
x
)18(
17
2
%5,121
2
(4)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 6 of 17
QUESTION 5
(a)
2
21
346
4
3
4
a
a
a
c
b
(5)
(b)
17
17
4343
xyxy
cc
cc
cxycxy
or
(4)
(c)
34
2)(
xxg (2)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 7 of 17
QUESTION 6
(a) (1)
x
x
hx
h
hxh
h
hxhh
h
xxhxhxhx
h
xghxgxg
hxhxhx
hxhxhx
hxhxhxg
xxxg
h
h
h
h
h
46
)0(246
246lim
246lim
246lim
2624266lim
)()(lim)(
24266
)2(266
)(26)(
26)(
0
0
2
0
222
0
0
22
22
2
2
(5)
(2)
2
3
046
x
x
(2)
(b) (1)
2
3
2
1
2
1
2
1
2
1
2
1
1
1
xxdx
dy
xxy
xx
xy
x
xy
(4)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 8 of 17
(2)
1
3
2
23
2
65
652
652
2
2
2
dx
dy
xy
x
xxy
x
xxy
xxxy
xxyxy
(4)
QUESTION 7
(a)
3
1
8
1
38
038
0245 22
x
y
x
y
xyxy
yxyx
yxyx
or
or (4)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 9 of 17
(b)
4
21
4
7
74
73
7
8
1
77
78
7
x
y
y
yy
yx
or
x
y
y
yy
yx
(4)
QUESTION 8
(a)
4
9
3
21
4
3
1
4
3
3
1
3
2
3
2
3
19
2
2..................9
2
1..................3
1
2
2
3
3
4
2
3
r
aS
a
a
r
ar
ar
equationarT
equationarT
(5)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 10 of 17
(b)
Zx
x
x
x
r
raS
r
x
x
x
n
n
x
n
n
60
6
3
2203log
3
22033
3
220013
440013
1312
1
1
3
...3241083612
44003.4
3
1
(5)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 11 of 17
(c)
nSS
nSS
nnannnanSS
nnanS
nnanS
nanS
nan
S
nnanS
nanS
nan
S
dnan
S
nn
nn
nn
n
n
n
n
n
n
n
n
2
4
4424822
482
81642
48222
4)12(22
2
4422
4422
4)1(22
122
2
2
2
22
2
2
2
2
2
2
2
2
(7)
QUESTION 9
(4)
y
x -1
6
3
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 12 of 17
QUESTION 10
(a) 18 meters (1)
(b)
m
80
4040
160040
800
3181240
121840800
3
2
2
2
x
x
x
x
x
(3)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 13 of 17
(c)
landing. before 46,19m 16,906 - 63,09 be willcovered distance horizontal
m or
906,1609,63
3
4040
3
160040
800
3181640
161840800
3
2
2
2
xx
x
x
x
x
(4)
−40−30−20−10 10 20 30 40 50 60 70 80 90 100110120130
−10−9−8−7−6−5−4−3−2−1
12345678910111213141516171819202122232425
x
y
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 14 of 17
QUESTION 11
(a)
6750 ; 0
6750
456004525453
1 23
y
y
y
(3)
(b)
4666,7) ; 20 ( B 4500) ; 30 ( A
or
7,46664500
206002025203
130600302530
3
1
2030
02030
060050
60050)(
323
2
2
yy
yy
xx
xx
xx
xxxf
(5)
(c)
9333,3 ; 21 and 9000 ; 31
: be willpoints turning (4)
(d)
1,1400013500
7,46663
4500
k
k
(2)
Both the
values of y
Co-ordinate
form
Both the
values of x
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 15 of 17
QUESTION 12
(a)
xx
xxx
hbx
xh
hxx
hblV
686
5,1714
4
5,171
..2
1171
2
2
2
2
2
area surface
(4)
(b)
7 X7 is base the of dimensions
A
A
7
343
06862
0686
2)(
686)(
3
3
2
2
x
x
x
xxx
xxx
(3)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 16 of 17
QUESTION 13
(a)
24% or 0,24 or 175
42 (2)
(b)
36,3% or 0,36 or 102
37 (2)
(c)
TINDEPENDEN NOT
movie) the P(liking 40) P( movie) the liking and 40 P(
0,356175
102
175
107movie) the P(liking 40) ( P
0,371175
65movie) the liking and 40 P(
175
102 movie) the P(liking
175
10740) P(
(4)
VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 17 of 17
QUESTION 14
(a) 6 X 5 = 30 ways or Bruce/ Peter = 1 so 1 X 5 X 6 =30 (3)
(b) In Taxi P there are 5 ways to fill 4th seat but Bruce/Peter can switch therefore 5 X 2 =10
In Taxi Q there are 4 X 3 X 2 X 1 =24 ways but the passengers can be swap therefore
5 X 4 X 3 X 2 X 1 X 2 X 2 = 480 ways (4)