Review answers

Review answers

1 sin θ= , cos θ=

tan θ=

2 a 26.1 m b 15.3 m

3 a 37.8 b 38°6′

c 47.7 d 47°4′

e 31.2 f 55°45′

4 a 66.93 km b 32.37 km 5 A

6 a ∠B≈ 59.4°, ∠C≈ 78.6°, c≈ 41.0 m or ∠B≈ 120.6°, ∠C≈ 17.4°, c≈ 12.5 m b ∠G= 93.4°, e≈ 23.8 cm, g≈ 49.9 cm c ∠N≈ 22.1°, ∠K≈ 122.9°, k≈ 42.4 m 7 About 47.8°, 59.1°, 73.2°

8 a a≈ 28.1 m, θ≈ 95.1° b b≈ 79.9 m, φ≈ 41.2° c α≈ 56.6°, β≈ 75.1°

9 a 116 cm b 17.1 m

10 6500 mm, 2 × 3126 mm, 871 mm; w= 29 mm, x=y= 277 mm, z= 15 mm 11 16 km at 277°T

12 1965 m 13 91.1 km

14 208.16 m 15 150 m

16 111 mm from the ends and 44 mm from the sides

1 Nominal

2 Systematic sampling of households in the suburbs would be relatively cheap and probably give a reasonable result. Otherwise the council could use stratified sampling based on ABS data about the suburbs.

3 a 38, 58, 74, 67, 55

b 262, 229, 346, 204, 215, 248, 343 (continuing on after part a)

c 3328, 3905, 3983, 4249, 6902, 5777, 3117, 3307, 4865

4 a TV viewers in general

b TV viewers in Mackay who watched that news program, have their phone number in the book, and were interviewed by the market research company.

c A sample may give some bias, but a census would be too expensive and take too long.

Chapter 1

opposite hypotenuse

--- adjacent hypotenuse

---opposite adjacent

---Chapter 2

5 a Pregnant women who took DES and pregnant women who didn’t

b About 16 per 1000 c About 8 per 1000

6 The people on one page could all be of a particular group. For example, they might all have the family name Singh.

7 This survey is to find information about people employed in restaurants.

9

10

11 D

12 Answers may vary within 0.1 or 0.2.

a 97.8 b 101.2 c 98.9

d 96.7 e 90.5 f 104.2

8 Airline f

J 9

Q 14

T 5

V 12

Stem Leaf

4 5 6 7 8 9 10 11

0 2 7 8 9

0 0 0 0 1 2 2 2 3 0 0 0 2 2 5 6 7 7 8 9 2 4 5 6 6 7 8

0 0 0 0 0 4 5 9 9 9 0 0 0 2 4

8 0 6

Please circle your answers. 1What is your age group?

15–25 26–35 36–45 46–55 56–65

2 What is your sex? M F

3What is the highest level of education you completed?

Year 9 Year 10 Year 11 Year 12 TAFE Trade Diploma University degree

Use of council funds

Total = $1 800 000

Roads

Salaries & wages Street lights

Other

Rubbish

Water & sewerage Inspections & reports

b

c

14 a Mean = 15, median = 14.5, mode = 14 b Mean = 21.3, median = 21.25,

modal class = 15–19

15 a Range = 32, interquartile Range = 12.5, σ= 7.56

b Range = 110, interquartile Range = 37.75, σ= 25.24

16 C 17

13 a Weight (kg) Frequency

40–44 4

45–49 6

50–54 9

55–59 12

60–64 12

65–69 15

70–74 10

75–79 11

80–84 9

85–89 5

90–94 3

95–99 2

100–104 1

105–109 1

Masses of people

110 90 100

Frequenc

y

8 6 4 2 0

40 50 60 70 80 16

14 12 10

Mass (kg)

Masses of people

Cumulati

v

e frequenc

y

100 80 60 40 20 0

40 50 60

Mass (kg)

70 80 90 100 110 120

0 20 30 50 60 80

Cricket score

10 40 70

18 Income of people in the area, number of two-person households, number of existing outlets

19 a

$45.5 million b P75

c Q1= $6.3 million, Q2= $13 million,

Q3= $24.5 million

20 Mean = 14.56, median = 14, modes = 12 and 14; typical size = 14 (median)

21 47.57 kg

22 No, using standard deviation or IQ range 23 He did slightly better in Maths, at 1.625 standard

deviations above the mean, compared to 1.6 for English.

24 The men’s results are more spread and lower than the women’s results.

1 a Linear b Not linear

c Not linear d Linear e Not linear f Not linear

2 a b= 4 b p= 6

c x=−4 d v= 6

e m = 3 f d = 8

3 a x-intercept = 2

y-intercept =−5

b x-intercept = 4 y-intercept = 6

Cumulati

v

e frequenc

y

25 20 15 10 5 0

5 10 15

Sales ($ millions) 2025 3035 40 30

35 40

45 50

Chapter 3

y = 2x − 5

y

x

−4

−2

−4

4 6

1 2

---3x + 2y = 12

x 2

2

3 1 4

4 5 y

4 Note: Y scale = 5 a y = 17x + 16

b 9y − 14x + 31 = 0

5 a Domain =−1, 1, 2, 6, 9 Range = 2, 3, 4

b Domain = Mon, Tue, Wed, Thu, Fri, Sat, Sun Range = [20, 50]

c Domain = (4,∞] Range = [−5, 10] 6 c is a function.

7 b and d are functions.

8 a d = 5, tn= 5n − 2

b d = , tn=

c d =−4, tn= 31 − 4n d d = a + 3, tn= n(a + 3) − 1 9 167

10 a 27 b 38

11 a −3 b c 6

12 B

13 a 2.5 b − c

14 a 1.73 b −5.67 c 1

15 About 71.6°

16 x-intercept =−4, y-intercept = 3

17 a Yes b Yes

18 Yes

19 a 2x + y − 5 = 0 b 7x + 3y − 26 = 0 c x + 2y + 10 = 0 d 2x − y + 4 = 0

20 a 9 b −4 c 123.7°

21 3x + y − 7 = 0

22 a mAB= , mCD=−2 b mAB× mCD=−1

c 26.6° d 116.6°

23 a b

c 5 d

24 a AB = =2 , AC = , BC = b BC c AB2+ _AC2= ₅₂ + ₁₃

= 65 = BC2

25 a E(1, 4.5), F(3.5, 3.5), G(3,−1), H(0.5, 0) b Both (2, 1.75) c Diagonals bisect.

26 (−1, 12) 27 C

28 a x =−1, y = 6 b x = −1, y = 2 c x = −9, y = 6

1 2

--- 2n+19

4

---2 5

---5 6

--- 2

5

---1 2

---65 65

a2_{+1 2a}2_–14a+25

52 13 13 65

29 m =−2, p = 5 30 a ≈−3.14, b ≈−2.86 31 7 L

32 Wife receives $320,000, son and daughter both receive $140,000.

33 a

b C = 160d + 220 c

d C = 190d

e For tours between 3 and 7 days the second operator is cheaper. For tours between 8 and 12 days the first operator is cheaper.

34 a 145 frogs b 31 frogs c 5 weeks

d No. The model suggests that due to resistance and other factors, the population reaches a minimum value of about 25 frogs. 35 16

36 a 425 m b 60 m, 0.14

c 0.2 d 2 cm

e

Answers may vary, but the path should be at least 1 cm between contours

37 a b q c p − b

d Midpoints are both .Therefore, the

diagonals bisect each other. 38 Washing powder 280 kg, sugar 160 kg

2 4 10 12

Ski tours 1

Days 6 8 400

1600

Cost ($)

800 1200 2000

0 2400

Ski tours 2

4 8 20

Days 12 16

Cost ($)

0 3000

1000 2000 4000

Scale 1 cm = 200 m

q p–b

---p 2 --- ,q

2

---⎝ ⎠

1 a Yes b About 1.1 ms

c 1.4 ms d About 4.4 ms

e About 1.4 V

2 a T = 1 s, a = 12 cm b About 7.1 cm c About 0.31 s, 0.98 s, 1.31 s, 1.98 s, 2.31 s,

2.98 s, 3.31 s, 3.98 s 3 a y = 4 sin 2πx

b y = 5 cos 2πx

4 a y=7 sin

b y=6 cos

5 a The months are of equal length. b January

c 4.4°C to 17.8°C d 11.1°C

e December, January and February f May and September

6 Midnight to 2:03 am, 10:17 am to 2:23 pm, and 10:37 pm to after the next midnight 7 a Maximum = 12 m, minimum = 2 m

b 120

c a = 5, b = 4π, c = 7

8 a y = 2 + 3 sin πx b y = 5 + 2 cos

1 D 2 E 3 B

4

The results are consistent with a fixed rate.

Chapter 4

2π(x–3) 5

---2π(x+4) 3

---3πx 2

---Chapter 5

50 100 150 4

2

Flo

w rate (L/min)

6

Rainwater tank

Water height (cm) 8

0

200 10

250

5 a 58.9 N/cm b 294 N

c 442 N d 1060 N

6

7 a C b B

8 D

9 a D b B c B

10 A

11 a 340 m/s b 25 m/s

c 13.6 m/s

12 a D and C b B and E

c A d A

13 C

14 a 6.4 b 0.4 c 3.4

15

a i −4 ii −2 iii 0

b The rate of change increases steadily as x increases. It is negative when x 2, zero at x = 2 and positive when x 2.

16

Rate of change = 8 17

5 10 15 200

100

Displacement (m)

300

Police chase

Time (s) 400

0

20 25

−1 1 x

y

3 5

2 4

0

(1, 2) (2, 1)

5 f (x) = x

2− _4x + ₅

y

x 1 2

−1

−2 3

3

4 (4, 15)

(−2,−15)

f(x) = x3− _3x2− _x + ₃

2 4 6

Mass on spring

t v

18 a 5 m b −0.4 m/s c

19 a The gradient is: positive and decreasing for values of x less than −1.8, zero at x =−1.8, negative between x =−1.8 and x = 0, zero at x = 0 and positive and increasing for values of x greater than 0.

b

20 A 21

Gradient 0 for x 1.5; gradient = 0 for x = 1.5; gradient 0 for x 1.5. The gradient is constantly increasing.

22

23 a −3, −2 and 2 b

c 2

0

−2

1 3 5

Moving object

V

elocity (m/s) Time (s)

x 2 y

−2 −1

−3 1 3

5

−5

Gradient function

y

x 1 2

−1

−2 3

−10

4 5

f(x) = x2− _3x − ₁₀

y

x

−5 6

---5

x 2 y

(−4, −12)

−2

−3 1

−12 3

(3, 30)

f(x)

−1

−4

x 2 y

−4 −3 −2 −1 1

Gradient function

3

24 a 16 b 16

c They are equally good approximate rates of change.

25 C 26 −23

27 a −18 b −37.000 001

28 a 18 km/h, 17.14 km/h, 19.2 km/h

b 18 km/h c 0

29 a

b From 7:30 am to 8:15 am c On the way home

30 a −32 cm/s b 7 cm/s

c −14 cm/s d 2 cm/s

31 a The velocity is positive at a constant rate of 2. b The displacement is increasing.

c The velocity is negative at a constant rate of −3.

d The displacement is decreasing. e +2 units f −1 unit g +1 unit h

32 a

b They are the same. c

12 10 8 6 4 2 0

10 12

8

7 9 11

Time (am) Distance from home (km)

14

6

Jogger 16

1 2 3

Nuclear particle

t s

2

0

−1 1

f (x) = 3x2− _x − ₂

g (x) = 3x2− _x + ₄

d They are the same.

e It does not change the gradient function. f They differ only by the constant term.

33 a 1.5 m/s b +3 m

c −2 m/s d −2 m

e

34 a i $240 ii $240.67

b $0.67

c i $675 ii $676.07

d $1.07

e i $1310 ii $1311.47

f $1.47

g C′(n) = 0.0008n + 0.27

1 a −1.3, 3.8 b −0.4, 3.9

2 B 3 D

4 a −1, 0.75 b −1.12, 1.79

5 −1.5, 4 6 B

7 −3, 1.67

8 a (x − 2)(2x + 3) b (x + 2)(3x − 4) c (2x − 5)(5x + 3)

9 D 10 C

11 4 ± ≈ 0.26, 7.74

12 C 13 − , 3

14 a

,

b

,

15 x − = 16, $20 or $80

g (x) = x2+ _x + ₆

8

6

4

2

0

4 6

2

1 3 5 7 8

Time (s)

Displacement (m)

Moving object

Chapter 6

y

−3 −1 1 2 x

y = 3x2+ _4x − ₁₅

−2

14

2 3

--- 1

2

---−7± 41

4

---−1± 13

2

---x2

100

---16 D

17 a −3.30, 0.30 b −3.93, 0.93 c −1.31, 3.81 d −2.37, 3.37 18 a (1.2, −14) minimum

b (−1.3, 9) maximum

19 B 20 B

21 a (3, −5) b (−2, 4) c (4, −3) d (−1, −2) 22 A

23 Maximum at (1 , 13 )

24 The factors are (x − zero1) and (x − zero2).

25 a

b

c

d

1 4

--- 1

8

---y

x

y = 5x + 2x2 _{+ 10} 10

−1.31 3.81

(1 , 13 )1 8 1 4

y

x

(5,−4) 3

y = x2− _10x + ₂₁ 7

y

y =−x2_{− 2x +15} x (−1,16)

−5 3

15

y

x

(1.5,−6.25)

−1 4

y = x2− _3x − ₄

−4

y

y = −x2+ _6x − ₄ x

(3, 5)

−4

26 a [−6, 10] b [−5, 4] c [−30,−5] d [2, 18] 27 a (0.5, −4.8), (3.3, −3.3)

b (−0.6, −2.6), (4.2, −5.2) 28 D

29 (4, 19), (−2, 1)

30 (2 , 7), (−1, 0)

31 a (3, 1), (5, 5) b (−2 ,−4 ), (2, 0)

c (−2,−8), (1 , 2) d ( , 5 ), (−2 , 12)

32 a (−4, 6), ( , 1 )

b (1, 0), (−5,−6)

c (−0.91, 2.19), (2.57, 9.15) d (−1.47,−8.41), (1.14,−0.59)

33 a y = x − 1 and y = b x =

c x2− _x − ₁ = _{0 d} ≈ _1.618

e 3.09 m or 8.09 m

b y =−0.0125x2+ _0.5x + ₅

c k ≈ 33.

d y ≈−13. t2+ _{16. t} + ₅

e About 48.3 m 35 a V = 6w(w + 4)

b S = w(w + 4) + 6(4w + 8) = w2+ _28w + ₄₈

c

d 3.5 cm

e S is greater in ratio to V initially but decreases as w increases until w = 3.5 cm when S = V. As w increases beyond 3.5 cm V becomes increasingly greater in ratio to S.

34 a x (m) 0 20 40

y (m) 5 10 5

1 2

---1 2

--- 1

2

---1 3

--- 2

3

--- 2

3

--- 1

2

---2 3

--- 1

3

---1 x

--- 1

x–1

---5+1 2

---1 3

---8 9

--- 2

3

---1 2 5

Open box

Width, w (cm)

3 4

100 400

V

olume (cm

3)

200 300

Surf

ace area (cm

2)

6 S V

0

1 C 2 C

3 4 4 6x + 5

5 A 6 E

7 a 4 b −3 c 6

d 1 e −2 f −13

8 a 7 b −10 c 14x

d 6x − 9 e 9 − 8x f 12x2− ₁

9 C

10 a 4x3− _6x + _{5 b 95}

c 5

11 a 30x5− _6x + _{1 b} −₁ − _6u + _18u2

c 7q6+ _12q2− _{1 d 90y}5− _4y3− ₂₈

e 1 − 6w + 3w2

12 f′(4) = 23, g′(4) =−43, h′(4) = 48, i(4) =−88, so i(x) is steepest.

13 a 20x3− _{3 b 20 c} −₁₂₅₆

d 20 e 0

14 a −30v−7

b 48(4x − 6)3− _60(4x − ₆₎2+ ₂₈

c 90(3w − 8)5

d 63t6+ _54t5− _80t4+ _4t3− _36t2+ _46t − ₅₆

e −288(5 − 4e)7

f −90(5y − 7)−7

g 8(3v − 7)3 _(2v + ₉₎4 _(27v + ₁₉₎

h

i

j 24(2w − 11)3− _4(2w − ₁₁₎ − ₂ −

15 a −1 b 54 c −2

d 3 e 118

16 a −13 b 27 c −3

d −33 e 97

17 a x − y − 4 = 0 b 23x + y + 20 = 0 c x − y − 3 = 0 d 49x − y − 83 = 0 e 143x + y + 211 = 0

18 B 19 2

20 a 17 b −244 c −1768

d 2633 e 8

21 a 23 b −25 c −1

d 5 e 53

22 B 23 D

24 D 25 A

26 E

Chapter 7

21 3 x–1

( )2

---6g7_(3g–32)

g–4

( )6

---4 2w–11

( )3

---27 Maximum (−3, −35), minimum (−2, −36) 28 Minimum (−1, −14), maximum (5, 94) 29 C

30 a Increasing b Increasing c Decreasing d Decreasing e Decreasing f Increasing g Increasing

31 D 32 B

33 B 34 x 3

35 E

36 a 33.12 Ω b 0.0576 Ω/ºC

c 39 Ω d 0.0588 Ω/ºC

e 6.4128 Ω f 0.0451 Ω/ºC g A high-temperature gauge: any reasonable

answer that does not expose the wire to temperatures above ≈ 1760°C is acceptable. 37 Approximate error in volume would be 80 cc, so

the capacity would be 2080 cc. 38 h(x) = x3− _x2− _5x + ₉

39 y = 36x − 3x2− _2x3+ ₅

1 a 50° b c

d 225° e f

2 a b c

d e f

3 D 4 B

5 a 0.8203 b 3.8528

6 a 135° b 24.6°

7 is larger 8 a and c

h(x)

x 9

−2.48

(−1,12)

2 3

1

−1

−2

−3

2 3 ---(1 , 214)

27

---x y

5

(−3, −76)

(2, 45)

Chapter 8

11π 6

--- 2π 3

---5π 6

--- 7π

6

---3π 2

--- 5π

4

--- 4π

3

---8π 9

--- 11π

6

--- 8π 5

---π 3

---9 a b

c

10 a 2 and 3 b 2 and 4

c 1 and 2 11 sin 270° =−1

cos −60° =

12 tan =

sin =−

13

and have cosines of the same

magnitude, but cos is positive. 11π

6 --- _11π

6

---x

y _2π

3

---2π 3

---x y

7π 4

---x y

7π 4

---O y

x

P(270°) 1

1 2

---O y

x

P(−60°) 1

60°

1 2

---3 2

---3

1 2

π 6

---π 3

---π 3 --- 3

1 1

π 4

---2 7π

4 --- 1

2

---O y

x

π 6

---5π 6

---7π 6

--- 11π 6

---14 D 15 C

16 a − b − c −

d e − f −1

17 a sinθ=− , cosθ=− , tanθ=

b sinθ=− , cosθ= , tanθ=− =−2

18 a cosθ=− , tanθ=−

b sinθ=− , tanθ=−

19 a sinβ= , cosβ=−

b sinβ=− , cosβ=

c sinβ= , cosβ=−

20 4 21 D

22 −4 y 2 23 B

24 A 25 D

26 a y = 3 sin x

b y =−cos 4x

c y =−sin

d y = cos x + 3

1 2 --- 1 2 --- 3 3 2 --- 1 2 ---3 5 --- 4 5 --- 3 4 ---12 13 --- 5 13 --- 12 5 --- 2 5 ---12 13 --- 5 12 ---4 5 --- 4 3 ---4 5 --- 3 5 ---5 13 --- 12 13 ---24 25 --- 7 25 ---x y 3π 2 ---π 2 ---0 3 −3 2π π y 1 −1 0 x 3π 8 ---π 8 --- π 4 --- π 2 ---x π 4 ---– ⎝ ⎠ ⎛ ⎞ y 1 −1 0 x 3π 2 ---π 2

--- π 2π

π 4 ---y 4 3 0 2 x 3π 2 ---π 2

--- π 2π

e y = 5 − 3 sin

f y = 6 cos + 4

27 E

28 a 14° b Midnight

c 24 hours

29 a s b 240 ≈ 340 V

c 240 V

30 8 tan x

31 a 15°C, January

b 10.5°C, April and October c August to December 32 a 12 h

b 12 am–3 am, 9 am–3 pm, 9 pm–12 am c 4 am–8 am, 4 pm–8 pm

33 d = 15 + 10 cos . The tip is 10 cm above the

shelf 48 times a day (20 past and 20 to the hour).

1 a x11 _{b 5k}9 _{c 27a}12_b6

d 4 t6 _{e 4}

2 a b c d 5

3 E 4 E

5 D 6 B

7 a y = 7 × 3x _{b 5103}

8 C 9 A

10 D

11 a A decay function b 0.85 c f(x) = 48 × 0.85x _{d 15.4} 12 a A growth function b 1.1

c f(x) = 60 × 1.1x _{d 116.9} 2 x π

6 ---+ ⎝ ⎠ ⎛ ⎞ y 8 5 0 2 x 3π 4 ---π 4 --- π π 2

---3 x π 4 ---– ⎝ ⎠ ⎛ ⎞ y 10 0 −2 4 x π 2 ---π 6 --- π 3 ---π 12 ---2π 3 ---1 50 --- 2 2 πt 30 ---Chapter 9 1 2 --- 4 7

---8 p14

---13 a V = 11 953 × 1.064y

b $11 953 c $18 454

d About 15 years from the start. 14 a V = 32 000 × 0.88y

b $19 190 c $11 508

d About 14 years from the start.

15 E 16 C

17 B 18 B

19 a

b

c

d

All values of the functions are positive. a, c and d are always increasing as x increases. b is decreasing as x increases. The y-intercepts are 3, 4, 0.6 and 1.5 respectively.

20 B 21 C

22 A 23 C

24 D

25 a x = 4 b x = 3

c x = d x = 1

26 a x = 2 b x = 1 or 4

c x = 1 or 2 d x = or 1 27 x = 19.68

1 2

---1 2

−2 −1 0

5 10 15 y

x

y = 3 × 2x

1 2 3

−3 −2 −1 0

5 15 20 y

x 10

y = 4 × 0.6x

1 2 3 4

−4−3 −2−1 0 0.5 1.5 2 y

x 1

y = 0.6 × 1.2x

1 2

−2 −1 0

2 4 6 8 10 y

x

y = 1.5 × 2.4x

1 2

---1 6

--- 1

9

---2 3

--- 1

3

---28 a x ≈ 1.68 b x ≈ 4.63 c x ≈ 1.39 d x ≈ 1.22

29 B 30 E

31 f(x) and g(x) are mirror images reflected in the line y = x. g(x) is the inverse function of f(x).

32 a

b

c

d

In each case, the first is a reflection of the second in the line y = x. All demonstrate inverse relationships.

33 7 min

34 a A = 100 × 0.5n _{b A(d)} = ₁₀₀ × c Initial value = 100, growth factor ≈ 0.871

d A(d) = 300 × e A(d) = G ×

5 10 20

5 10 15 20

−5 y

x

−5 15

y = x

g(x) f(x)

5 10 5

10 y

x

−5

−10

−10

y = 10x + 1

y = log x − 1

y = x

5 10 5

10 y

x

−5

−10

−10

y = x

y = 10x+ ₁

y = log(x − 1)

5 10 5

10 y

x

−5

−10

−10

y = x

y = 100.5x− ₂

y = 2 log (x + 2)

5 10 5

10 y

x

−5

−10

−10

y = x

y = 3.32 log x

y = 2x

0.5 d

5

---0.5 d

9

---0.5 d h

---35 a A = 12 × 1.12y _{assaults per 1000} b 360 assaults c 2021 36 50 000 000 000 operation per second 37 a 6.48 mg b 0.000 236 9 mg

c About 9:48 am d About 4:39 pm e About 3.52 kg

38 12 min

1 D 2 A 3 D

4 {P, P, P, G, G, G, G, G, O, O}

5 a 1060 b 207

c 519 d 0.51

6 E 7 C 8 D

9 B 10

11 a ≈ 0.308 b ≈ 0.385

c ≈ 0.308 d 1

12 B 13

14 a

b 30 c = 0.2 d ≈ 0.733

Chapter 10

1 3

---4 13

--- 5

13

---4 13

---27 32

---Blue Blue Black Red Red

Blue Blue Black Red Red

Blue Blue Black Red Red

Blue Blue Blue Red Red

Blue Blue Blue Black Red

Blue Blue Blue Black Red Blue

Blue

Blue

Black

Red

Red

1 5

--- 11

15

---15 a

b c d

16 a ≈ 0.011 b ≈ 0.0004

17 B 18 0.784

19 0.121

20 a 0.206 b 0.144

c 0.000 03 d 0.985

21 a No b 6 c

d e 1

22 0.000 004

23 a 0.107 b 0.268

c 0.879

24 a 0.016 b 0.022

c 0.170

25 a 0.087 b 0.681

c 0.823

26 a 0.463 b 0.135

c 0.171 d 0.964

1 a F1(x) = x3 – x2+ 5x + 3

F2(x) = x3 – x2+ 5x – 6

b H1(x) = 3x – x6+ 3

H2(x) = 3x – x6 – 6

2 E 3 D 4 C

5 a y = x2 _{– x}3+ _{c b y} = _x5+ _x2+ _c

6 a F1(x) = x2− 5x

F2(x) = x2− 5x − 2

F3(x) = x2− 5x + 2

b G1(x) = 2x −

G2(x) = 2x − + 5

G3(x) = 2x − − 5 H

T

H

T

T H

H T H T H T H T

1 8

--- 3

8

--- 1

2

---1 88

--- 1

2728

---1 6 ---1

12

---Chapter 11

4 3

---4 3

---2 3

---2 3

---7 2

---3 2

---3 2

---3 2

---x3 3

---x3

3

---x3

---7 F1(x) = x3− x2− 4x

F2(x) = x3− x2− 4x + 4

8 E

9 Find the antiderivative

m(x) = − + 4x + c

Sub in point (5, 0) to solve for c = 25

10

3 x2 2 --- 2 x

3

3

---5 6

---y

x

F(x)

11 a C(x) = 400x − x2+ _c

b C(x) = 400x − x2+ ₁₅₀₀

c $37 900 d $41 100

e Unit cost of producing 140 is $270.71. Unit cost of producing 180 is $228.33, which is $42.38 cheaper per chair.

f Unit cost of x chairs = 400 − x + .

g Lowest unit cost is at maximum production, $228.33.