Answers
[Pages:67]Back to Menu >>>
Answers Chapter 1
Exercise 1A
E 5
1a3 b9
c1
d -8 e 5
f2
g 3
-7 7
h
i
20
-10
j
k
14 l
23
3
3
5
L 2 a a + b
b a-b
b c
bc d ab e
a
a
3a 7
b5
c -3 d 14
7 e
14 f
2
3
g 48
3 h
i2
j3 k7
l2
2
4 4a
b -5 c 2
3
P 5a -1 b 18
6 c
d 23 e 0
f 10
5
g 12 h 8
i - 14 5
12 j
5
7 k
2
-b 6a
a
e-d b
c c -b
c
a
b d c-a
ab
b-d
e b+a f a+b g a-c
bd - c h
a
M 7 a -18 d 28
b -78.2 e 34
Exercise 1B
c 16.75 3
f 26
A1a x +2 =6,4
b 3x = 10, 10 3
c 3x + 6 = 22, 16 3
d 3x - 5 = 15, 20 3
e 6(x + 3) = 56, 19 f x + 5 = 23, 87
3
4
2 A = $8, B = $24, C = $16
S3 14 and 28 4 8 kg 5 1.3775 m2
2 a x = 8, y = -2
c x = 7, y = 1 2
3 a x = 2, y = -1
c m = 2, n = 3
e s = 2, t = 5
g
x
=
4 ,
y
=
7
3
2
i x = -1, y = 5 2
b x = -1, y = 4
b x = 2.5, y = -1 d x = 2, y = -1 f x = 10, y = 13 h p = 1, q = -1
Exercise 1D
1 25, 113
2 22.5, 13.5
3 a $70
b $12
c $3
4 a $168
b $45
c $15
5 17 and 28 6 44 and 12
7 5 pizzas, 25 hamburgers
8 Started with 60 and 50; finished with 30 each
9 $17 000
10 120 shirts and 300 ties
11 360 Outbacks and 300 Bush Walkers
12 Mydney = 2800; Selbourne = 3200
13 20 kg at $10, 40 kg at $11 and 40 kg at $12.
Exercise 1E
1 a x < 1 b x > 13 c x 3 d x 12
e x -6 f x > 3
g x > -2
h x -8 2a x>> Answers 705
e x1
1D 2D 3C 4A 5C 6 C 7 B 8 B 9 A 10 B
Short-answer questions
?2 ?1 0 1 2 3 4
(technology-free)
g
x
<
3
1 2
?2 ?1 0 1 2 3 4 h x3
?2 ?1 0 1 2 3 4
i
x
>
1 6
E 0 1
3 a x > -1
b x -5
5 87
L Exercise 1F
1 a 18 b 9
c3
d -18
e3
f 81 g 5
h 20
2 a S = a + b + c b P = xy c C = 5p
d T = dp + cq e T = 60a + b
3 a 15
b 31.4
c 1000
d 12
e 314
f 720
P 4aV = c p
ba= F m
cP= I rt
dr= w-H C
e t = S -lP Pr
f r = R(V - 2) V
5 a T = 48 b b = 8 c h = 3.82 d b = 10
M 6 a (4a + 3w) m
b (h + 2b) m
c 3w h m2
d (4ah + 8ab + 6w b) m2
7 a i T = 2( p + q) + 4h ii 88 + 112
b p= A -q h
8a D= 2 3
bb=2
Acn= 60 29
d r = 4.8
9
a
D
=
1 bc
(1
-
k2)
2
Sc k = 2 = 6
b k = 1 - 2D bc
1a 1
-3 b
2
-2 c
3
e 12
44 f
13
1 g
8
2a t =a-b
cd - b b
a
d -27
h 31 c d +c
a
cb - a d c-1
2b e c-a
1 - cd f
ad
3a x < 2 3
b
x
1 148
2
c x < 22 29
d x -7 17
4 x = 2(z + 3t), -10
5 a d = e2 + 2 f
d - e2 b f=
2
c f=1 2
6 x= a2 + b2 + 2ab = a + b
ac + bc
c
7
x
=
a
ab -b-
c
Extended-response questions
1 a c = -10 9
d x = -62.5
2
a
r
=
2uv u+v
b F = 86
e x = -160 13
bm= v u
c x = -40 fk=5
3 a T = 6w + 6l
b i T = 8w c i y = L - 6x
8 d x = 10, y = 5
ii
l
=
25 ,
w
=
1 12
6
2
ii y = 22
4 a distance that Tom travelled = ut km and
distance Julie travelled = vt km
b
it
=
d u+v
h ii
distance from A =
ud u+v
km
c t = 1.25 h, distance from town A
= 37.5 km
5
a
average
speed
=
uv u+v
b i uT
vT + uT ii
v
v
6a 3 + 3 ab
3 10 a P = 4b
3 b A = 2bc - c2
c b = A + c2 2c
c
i
c
=
2ab a+b
40 ii
3
11 a b = a2 - a 2
b x = -ay b
7a x, y 8 10
80(x + y) b 10x + 8y
c r = 3q - p2x2
x2 d v = u2 1 -
y2
c x = 320 , y = 310
9
9
Cambridge University Press ? Uncorrected Sample Pages ? 2008 ? Evans, Lipson, Wallace TI-Nspire & Casio ClassPad material prepared in collaboration with Jan Honnens & David Hibbard
Answers
706 Essential Mathematical Methods 1 & 2 CAS
Back to Menu >>>
Chapter 2
c
y
d
y
Exercise 2A
1
1a4 b2
1 c
d -4 e 1
f -1
4
5 g
4
h -2
-5 i
4
4 j
3
k0
2 Any line parallel to 3
y
the one shown y
(1, 6)
x 01
0
x
?1
4 a - 1 b - 5 c -2 d -8 e 0 f -1
4
2
E g 7 h 11 i -13 j 11 k 111 l 61
5 a -2
2
5
b
6 a 54
b
5
6
7a x =4
b y = 11
L Exercise 2B
1a
y
2
x
?2
0
P c
y
1
10
x
2
M 2a
y
1
1x 0
c
y
A1 x ?1 0
S3a
y
b
y
2
x 02
d
y
1
x 01
2
b
y
x 01 ?1
d
y
x ?1 0
?1
b
y
4 0
ey
8 x
x
0 21
3
?2
fy
3 0 g
6 y 6
2 x
0
4 x
h
y
x 03
x
?8
?4 0
4 Pairs which are parallel: a, b and c; Non-parallel: dy
4
3 4y ? 3x = 4
1 ?4 0
3
1 ?1 2
3y = 4x ? 3
x 34
5 c only 6 a -1 b 0
c -1 d 1
Exercise 2C
1 a y = 3x + 5 b y = -4x + 6 c y = 3x - 4
2 a y = 3x - 11
b y = -2x + 9
3a 2
b y = 2x + 6
4 a -2
b y = -2x + 6
5 a y = 2x + 4
b y = -2x + 8
6 a y = 4x + 4 b y = - 2 x c y = -x - 2 3
d
y
=
1 x
-
1
e
y
=
1 3
2
2
f x = -2
7 Some possible answers:
a y = 4x - 3 b y = - 2 x - 1 c y = -x - 1
3
d
y
=
1 x
+
1
e
y
=
4
f x = -1
2
Check with your teacher for other answers.
3
3
8
a
y
=
3 x
+
1 9
b y = -1x -1
42
2
x ?3 0
10 ?1 1
3
c y=3
d y = -3
x
9
a
y
=
4 x
+
3
b y = -1x +3
3
2
Cambridge University Press ? Uncorrected Sample Pages ? 2008 ? Evans, Lipson, Wallace TI-Nspire & Casio ClassPad material prepared in collaboration with Jan Honnens & David Hibbard
Answers
Back to Menu >>> Answers 707
c y = -0.7x + 6.7
d
y
=
1 1
x
-
3
2
5 a x + 3y = 11 b 7x + 5y = 20 c 2x + y = 4 d ?11x + 3y = ?61
e y = -3x +6
f y = -x
6 a y = 2x - 9, m = 2
4
10 a y = - 2 x + 4 3
b y = -2x - 6
c y = -1x +4
2
11
a
y
=
2 x
+4
3
d y = -x + 8 b y = 2x - 2
33
c
y
=
1 x
+ 11
22
e y = x + 3.5
d y = -1x +2 2
f y = - 1 x + 0.25 2
12 Yes
13 AB: y = 2x + 1 BC: y = - 3x + 9
33
2
E AC:
y
=
1 x
-
3
84
Exercise 2D
1 a (0, 4), (4, 0)
L c (0, -6), (-6, 0)
2 a y = -2x + 6
c y=x
3a
y
b (0, -4) (4, 0) d (0, 8) (-8, 0)
1
b y = x-2
2
d y = -1 x + 3
2 b
y
P 2
x
x
01
?2 0
?1
c
y
Mx
02 ?4
4a y
by
0
A?4
c
x 6 y
S6
x
0
8
?2
d
y
10
b y = -3x + 5,m = -3
42
4
c y = - 1 x - 2, m = - 1
3
3
d
y
=
5 x
-
2, m
=
5
2
2
7a
y
b
y
5x 0
?10
c
y
d
10
x ?2 0
x 03 ?9 y 10
x 05
8 a = -4, b = 4 , d = -1, e = 14
3
3
Exercise 2E
1 a d = 50t
b d = 40t + 5
2 a V = 5t
b V = 10 + 5t
3 w = 20n + 350, possible values for
n = N {0}
4 a v = 500 - 2.5t
b domain: 0 t 200, range: 0 v 500
cv
500
0
200 t
5 C = 1.5n + 2.6
6 a C = 0.24x + 85
7 d = 200 - 5t
8a w (g)
b $145
51
x ?8 0
x ?4 0
ey
fy
50 0 1 2 3 4 5 6 x (cm)
x
0
15
?5
4
x 0 15
? 15
7
2
b w = 0.2x + 50 9 a C = 0.06n - 1 10 a C = 5n + 175
c x = 12.5 cm b $59 b Yes c $175
Cambridge University Press ? Uncorrected Sample Pages ? 2008 ? Evans, Lipson, Wallace TI-Nspire & Casio ClassPad material prepared in collaboration with Jan Honnens & David Hibbard
Answers
708 Essential Mathematical Methods 1 & 2 CAS
Back to Menu >>>
Exercise 2F
b d (km)
1a
b t =5
57
C
A
B 30
0
90 t (min)
20
c 10.30 am d Maureen 30 km, Anne 27 km
0 2a
d
15
t
dB dA
b 2.00 pm
5
E 0
t
3 a C1 = 210 + 1.6x C2 = 330
b C
300
L 75
200 0 20 40 60 80 x
c Fixed charge method is cheaper when x > 75.
4a d
P 500 B
A
C
0 5 10 15 20 25 t (hours)
b C wins the race
d
C,
leaving
5
hours
after
B,
overtakes
B
13
1 2
hours after B had started and then overtakes A
M 20 hours after A had started. C wins the race
with
a
total
handicap
time
of
22
1 2
hours
(12
1 2
hours for journey + 10 hours handicap) with A
and B deadheating for 2nd, each with a total
handicap time of 25 hours.
5 Both craft will pass over the point
5
1 3
,
-4
A6 a CT = 2.8x, CB = 54 + x
b $C
c >30 students
S54
8 a = 0.28 and b = 0.3, 10 m/s 3
Exercise 2G
1 a 135 b 45
c 26.57 d 135
2 a 45 b 135 c 45
d 135
e 63.43 (to 2 d.p.) f 116.57 (to 2 d.p.)
3 a 45 b 2634 c 16134
d 4924 e 16134 f 135
4 a 7134 b 135 c 45 d 16134
5
m BC
=
-
3 5
,
m
AB
=
5 3
m BC
?
m AB
=
-3 5
?
5 3
= -1
ABC is a right-angled triangle
6 mRS
=
-
1 2
,
m ST
=2
RS ST
m UT
=
-
1 2
,
m ST
=2
UT
ST
(Also need
to show S R = U T .)
RST U is a rectangle.
7 y = 2x + 2
8 a 2x ? 3y = 14
b 2y + 3x = 8
9 l = - 16 , m = 80
3
3
Exercise 2H
1 a 7.07 b 4.12 c 5.83
d 13
2 29.27 3 DN
Exercise 2I
1 a (5, 8) c (1.6, 0.7)
b
1 2
,
1 2
d (?0.7, 0.85)
2 MAB (3, 3). MBC
8,
3
1 2
. MAC
6,
1
1 2
3 Coordinates of C are (6, 8.8)
4 a PM = 12.04
b No, it passes through
0,
3
1 3
5 a (4, 4) b (2, ?0.2) c (?2, 5) d (?4, ?3)
6 1 + a , 4 + b ; a = 9, b = -6 22
0
30 x
7
a
dA
=
1 3
t
,
dM
=
57
-
3 t
10
Exercise 2J
1 a 3441 b 45 c 90 d 4924 e 2633
Multiple-choice questions
1A 2E 3C 4D 5B 6 E 7 D 8 C 9 E 10 E
Cambridge University Press ? Uncorrected Sample Pages ? 2008 ? Evans, Lipson, Wallace TI-Nspire & Casio ClassPad material prepared in collaboration with Jan Honnens & David Hibbard
Answers
Back to Menu >>> Answers 709
Short-answer questions
5 a i C = 0.091n ii C = 1.65 + 0.058n
(technology-free)
1 a 9 b - 10 4 11
c undefined
d -1
b e
a
-b f
a
2 a y = 4x b y = 4x + 5 c y = 4x + 2
d y = 4x - 5
iii C = 6.13 + 0.0356n
b C ($) 15 10
(300, 16.81) (200, 13.25)
5 (50, 4.55)
3 a a = -2
20 b
0 100 200 300 n (kWh)
3 4 4y + 3x = -7 5 3y + 2x = -5
6 a = -3, b = 5, c = 14
7 a y = 11 b y = 6x - 10 c 3y + 2x = -3
8 a midpoint = (3, 2), length = 4
b midpoint =
-1,-9
, length = 74
22
c midpoint = 5, 5 , length = 5 2
E
9 3y - x = 3 3 - 2 10 y + x = 1 11 3752
Extended-response questions
1a
L S
8
1
220
279 l
P b Since the graph is a line of best fit answers
may vary according to the method used; e.g. if
the two end points are used then the rule is
S=
7 l - 25.1
or
l
=
59 S
+
1481
59
7
7
If a least squares method is used the rule is
l = 8.46S + 211.73.
c
M C
41
33 220
273 l
d Again this is a line of best fit. If the two end
Apoints are used then
C=
8
l
-
11
(or
l
=
53C
-
11 )
53 53
8
A least squares method gives
l = 6.65C + 0.6166.
S2 a C = 110+38n
b 12 days
i For 30 kWh, C = 2.73
ii For 90 kWh, C = 6.87
iii For 300 kWh, C = 16.81
c 389.61 kWh
6
a
y
=
-7x
+
2 14
3
3
1 b 20 km south
3
7 a s = 100 - 7x
b s (%)
100
0 5 c% 7
100 7
14.3
2 d 14 %
7
x (%)
e Probably not a realistic model at this value
of s
f
0
x
2 14
7
8 a AB, y = x + 2; CD, y = 2x - 6
b Intersection is at (8, 10), i.e. on the near bank.
128 9a
b y = - 199 x + 128
19
190 19
c No, since gradient of AB is 20 (1.053), 19
whereas the gradient of V C is ?1.047
10 a No
41 b 1 km to the east of H
71
11 a y = x - 38
b B (56, 18)
c y = -2x + 166 d (78, 10)
12 a L = 3n + 7
bL
61
10
01
18 n
13 a C = 40x + 30 000
b $45
c 5000
d R = 80x
e $'000
c Less than 5 days 3 a Cost of the plug
300
R = 80x
200
b Cost per metre of the cable
c 1.8
1 d 11 m
9
100
C = 40x + 30 000
0 1000 2000 3000 x
4 a The maximum profit (when x = 0)
f 751
g P = 40x - 30 000
b 43 seats
c The profit reduces by $24 for every seat empty.
Cambridge University Press ? Uncorrected Sample Pages ? 2008 ? Evans, Lipson, Wallace TI-Nspire & Casio ClassPad material prepared in collaboration with Jan Honnens & David Hibbard
Answers
710 Essential Mathematical Methods 1 & 2 CAS
Back to Menu >>>
14 a Method 1: Cost = $226.75; Method 2: Cost = $227; Method 1 cheaper
b
47 1 -2
=
x7 1 -2
if x = 4
0 1000 2000 3000 b Method 1 100 181.25 262.50 343.75
c
2 x4 -1 10 3
=
y 04 -1 10 3
Method 2 110 185 260 335
=
20 -1 10
4 3
if x = 0, y = 2
Cost the same for approx. 1600 units
c 110
cost ($) 100 300 200 100
343.75 335
0 1000 2000 3000 units 1600
E d C1 = 0.08125x + 100
(1)
C2 = 0.075x + 110
(2)
x = 1600
15 a (17, 12) b 3y = 2x + 2
16
a
PD:
y
=
2 x
+ 120;
DC:
y
=
2 x
+
136;
L 3
5
CB: y = - 5 x + 600
2
AB: y = 2 x + 20; AP: y = - 3 x + 120
5
5
b At B and C since product of gradients is -1
2
5
P e.g.
m DC
=
, 5
m CB
=
-; 2
2 ? - 5 = -1
52
17 a y = 3x + 2 b (0, 2) c y = 3x - 8
d (2, ?2)
e Area = 10 square units
f Area = 40 square units
Chapter 3
M Exercise 3A
1a 2?2 b 2?3 1 0 0 0 1
A2
a
0 0 0
1 0 1
0 1 0
1 0 1
0 0 0
10001
c 1?4 d 4?1 1 1 1 1 1
b
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
11111
1 0 0 0 0
S3
0 0 0
1 0 0
0 1 0
0 0 1
0 0 0
Only the seats for top-left to bottom-right diagonal
0 0 0 0 1 are occupied.
6 a x = 2, y = 3 c x = 4, y = -3
0310
7
3 1
0 2
2 0
1 1
0110
b x = 3, y = 2
d x = 3, y = -2 21 5 5
8
8 4 14
2 1 8
3 1 60
01 2
Exercise 3B
1X+Y=
4 -2
, 2X =
2 -4
,
4Y + X =
13 -2
,X-Y =
-2 -2
,
-3A =
-3 -6
3 -9
, -3A + B =
1 -7
3 -7
2a
6 12 4 8 42
5 1
c 3
3 7
0 13
6
33
b
51 0 18 7 13
3 2A =
2 0
-2 4
, -3A =
-3 3 0 -6
,
-6A =
-6 6 0 -12
4 a Yes
b Yes
5a
64 -4 -4
b
0 -9 12 3
c
6 -5 8 -1
d
-6 -13 16 7
6a
01 23
b
-2 3 63
-9
7X=
2 0
4 -3
,
Y
=
2 -1
c
33 -1 7
-23
2
11
2
4
200 110
180 135 117 98
110 89
56 28 53 33
8X+Y=
310 200
180 220 0 125
90 0
, representing
the total production at two factories in two
5 a [0 x] = [0 4] if x = 4
successive weeks.
Cambridge University Press ? Uncorrected Sample Pages ? 2008 ? Evans, Lipson, Wallace TI-Nspire & Casio ClassPad material prepared in collaboration with Jan Honnens & David Hibbard
Answers
Back to Menu >>>
Answers 711
Exercise 3C
6.00
1 AX =
4 -5
, BX =
4 1
, AY =
-5 8
,
10
8.00 2.00 11.00
represents how much each student spends in a week on magazines.
6.50
IX =
2 -1
, AC =
0 -1 12
,
11 a SC =
s11c1 + s12c2 + s13c3 s21c1 + s22c2 + s23c3
CA =
1 0
-1 1
, (AC)X =
1 0
,
C(BX) =
9 5
, AI =
1 -1
-2 3
,
IB =
32 11
, AB =
10 01
,
BA =
10 01
, A2 =
3 -8 -4 11
,
E B2=
11 8 43
, A(CA) =
1 -3 -1 4
,
A2C =
-2 -5 37
L 2 a AY, CI are defined, YA, XY, X2, XI are not defined.
b AB =
00 00
3 No
4 LX = [7], XL =
4 -2 -6 3
P 5 AB and BA are not defined unless m = n.
6
10 01
7 One possible answer is
A=
12 34
,B =
-2 1 1.5 -0.5
M 8 One possible answer is A =
1 4
2 3
,
B=
01 23
,C =
-1 2 -2 1
,
A(B + C) =
-1 -4
11 24
,
AAB + AC =
-1 -4
11 24
,
(B + C)A =
11 7 16 12
S9
29 8.50
represents John spending 29 minutes
b SC represents the income from car sales for each showroom.
c SC = s11c1 +s12c2 +s13c3 s11u1 +s12u2 +s13u3 s21c1 +s22c2 +s23c3 s21u1 +s22u2 +s23u3
represents the income for each showroom for new car sales and used car sales. d CV gives the profit on each new car and each used car for the three models.
Exercise 3D
1a 1
b
2 -2 -3 2
c2
2a
-1 1 -4 3
1 d
2
22 -3 -2
2 -1
b
7 1
14 3
7 14
10
c
1 0
d
cos sin -sin cos
k
11
3 A-1 = 2 2 , B-1 = 0 -1
10 -3 1
,
1 1
AB =
5 -3
1 -1
,
(AB)-1
=
2 -3
2 -5
,
22
1
A-1B-1 = -1 2 ,
3 -1
11
B-1 A-1
=
2 -3
2 -5
,
(AB)-1
=
B-1 A-1
2
-1
3
4a 2 2
1 -2
5 -7
2
07 b
1 -8
consuming food which cost him $8.50.
29 8.50
22 8.00
12 3.00
John's friends spent
$8.00 and $3.00 and took 22 and 12 minutes respectively to consume their food.
c
2 11
2 -21
2 -3
5 a
8 1
2 11
8 7
-11 17
b
16 -1
16 3
16 16
44
Cambridge University Press ? Uncorrected Sample Pages ? 2008 ? Evans, Lipson, Wallace TI-Nspire & Casio ClassPad material prepared in collaboration with Jan Honnens & David Hibbard
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
Related searches
- ecological succession worksheet answers pdf
- more questions than answers radio
- english answers to questions
- fun trivia questions and answers for kids
- percentage questions and answers pdf
- biology questions and answers pdf
- photosynthesis worksheet answers pdf
- free answers to any question
- more questions than answers podcast
- trivia questions and answers for kids
- printable trivia question and answers for k
- photosynthesis worksheet answers high school