VCAA MATHEMATICS PAPER 1 2018 MEMORANDUM CAPS 2018 Prelim Papers/Crawford/… · VCAA 2018 MATHEMAEMATICS PAPER 1 MEMO Page 17 of 17 QUESTION 14 (a) 6 X 5 = 30 ways or Bruce/ Peter

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)