Nelson Functions 11 Errata - PBworksmrkennedy.pbworks.com/f/3U+Textbook+Answer+Corrections.pdf ·...
Transcript of Nelson Functions 11 Errata - PBworksmrkennedy.pbworks.com/f/3U+Textbook+Answer+Corrections.pdf ·...
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Nelson Functions 11 Errata Chapter 1: Introduction to Functions Location Question Correct Answer Getting Started 6a Graph is correct but vertex and axis of symmetry are not
labelled. Add blue point labelled (in black) (0, –6) and add broken black line on top of y-axis, labelled (in black) x = 0.
Getting Started 6b Graph is correct but vertex and axis of symmetry are not labelled. Add blue point labelled (in black) (2, –1) and add broken red vertical line, labelled (in black) x = 2.
Getting Started 6c Graph is correct but vertex and axis of symmetry are not labelled. Add blue point labelled (in black) (–4, 2) and add broken black vertical line, labelled (in black) x = –4.
Getting Started 6d Graph is correct but vertex and axis of symmetry are not labelled. Add blue point labelled (in black) (3, 9) and add broken black vertical line, labelled (in black) x = 3.
Getting Started 7c Vertical compression, scale factor
21 , then translate right
1 unit and down 4 units Getting Started 9 In the table, right column, “Number of quadrants” should
be: 2, 3, or 4 Last line of non-table text should be changed to: … linear relations may only enter 2 or 3 quadrants, quadratic relations must enter at least 2 quadrants.
1.1 3 Insert at start of answer: y = 6; y = 2 or 3; 1.1 7c The text answer is correct. Change graph to a
graph with x-scale –10 to 2, y-scale –8 to 4, standard labels
+ graph of 1)3(43 2 ++−= xy , labelled with this equation.
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1.1 13b Use graph with x-scale –1 to 11, y-scale –6 to 6, standard
labels + rays as shown:
1.1 15d In line 2, change “more” to: less 1.2 6a domain = {–2, 2, 3, 5, 7}, 1.2 14 f(x) =& 0.0036x(281 – x) 1.2 18 Add between 1st and 2nd sentences: Advantages: function
notation connects input with output; can write expressions involving more than one function. Change student examples will vary to: Function notation makes relations clearer, for example, T(d) = 11 + 0.015d helps show that the temperature depends on the depth and T(3585) = 11 + 0.015d shows that the temperature at a depth of 3585 m is being determined.
1.4 2f Change last part to: range = {y ∈ R | y = –6, –2 ≤ y < 2, y ≥ 4}
1.4 6 Above graph, insert table: Speed (km/h) 1 2 3 4 5 6 8 10 15 20
Time (h) 15.0 7.5 5 3.75 3 2.5 1.875 1.5 1 0.75 1.4 17d Change last part to: range = {P ∈ R | 5 2 ≤ P ≤ 40} 1.5 2de Switch the entire answers for parts d and e; that is, graphs
and text. 1.5 14 y = 0.38x + 0.49 1.7 7a
Change label on graph from ⎟⎠⎞
⎜⎝⎛−= xy
41 to: ⎟
⎠⎞
⎜⎝⎛−= xy
31
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1.7 7b Use graph with x-scale –12 to 12, y-scale –2 to 6, standard
labels + graphs as shown; label right hand graph xy = ,
upper left graph xy21
−= , lower left graph xy31
−= ]
1.7 8a g(x) = | 3x | 1.7 10a Insert before “g(x)”: f(x): domain = {x ∈ R},
range = {y ∈ R | y ≥ 0} 1.7 10b Insert before “g(x)”: f(x): domain = {x ∈ R | x ≥ 0},
range = {y ∈ R | y ≥ 0} 1.7 10c Insert before “g(x)”: f(x): domain = {x ∈ R | x ≠ 0},
range = {y ∈ R | y ≠ 0} 1.8 1
Replace C with: C: horizontal compression, factor 31 ;
1.8 7b Replace with graph with x-scale –14 to 10, y-scale –6 to 4, standard labels + graphs as shown; label curve
( ) 2141
+⎥⎦⎤
⎢⎣⎡ +−= xfy ]
Change range to: range = {y ∈ R | y ≤ 2}
1.8 7c Change range to: range = {y ∈ R | y ≥ –1} 1.8 9c Change range to: range = {y ∈ R | y ≤ 4}
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1.8 14 Graph the following with unchanged scale, labels:
1.8 16 Change the radical sign to:
2)5(3 −−−= xy 1.8 19b
a = 21 , k = –1, c = –4, d = –3
1.8 20c –6, 15 1.8 21 In 2nd line, before “apply vertical stretch…”, insert: C. 1.8 22a Change translation 3 units left and 1 unit up to:
translation 6 units left and 2 units up 1.8 22b
2)6(41 2 ++−= xy
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎥⎦
⎤⎢⎣⎡ +−= 2)6(21or
2
xy
Chapter Review 14a Yes; vertical stretch must be done before vertical translation Chapter Review 19a Change inequality sign in domain to: ≥ Chapter Review 19b Change inequality sign in domain to: ≤ Chapter Review 19c Change inequality sign in domain to: ≥ Chapter Review 19d domain = {x ∈ R | x ≤ 9}, range = {y ∈ R | y > 3} Chapter Self-Test
6a Replace with the following graph with x-scale –5000 to 25 000, y-scale –500 to 2500, x, y labels + ray with point as shown, label ray “f(x) = 0.04(x – 2500) + 1500” + scale exactly as shown:
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Chapter Self-Test
6c Replace graph with the following graph with x-scale –500 to 2500, y-scale –5000 to 25 000, x, y labels + ray with point as shown, label ray “f –1(x) = 25(x – 1500) + 2500” + scale exactly as shown:
Chapter Self-Test
6e Replace the final value with: = $8500
Chapter Self-Test
8a Insert after “d = 2”: ; )2(
21
−−= xy
Change function label on graph to: )2(21
−−= xy
Chapter Self-Test
8b Insert after “d = –2”: ; 3
24
−+−
=x
y
Change function label on graph to: 32
4−
+−
=x
y
Chapter 2: Equivalent Algebraic Expressions Location Question Correct Answer 2.1 7 Add: Answers may vary. For example, 2.1 15c Replace answer with:
5x + 24, where x is the number in the top left corner; 5x + 18, where x is the number in the top right corner; 5x 24, where x is the number in the bottom right corner
2.1 17a Add: Answers may vary. For example, 2.1 17b Add: Answers may vary. For example, 2.2 9a 2.2 14a Add: Answers may vary. For example, 2.2 14b Add: Answers may vary. For example,
will have terms. 2.2 16a Answers may vary. For example,
45 i) 4 ii) 4 + 42 = 20 iii) 2025 = 452
2.3 12b The area of the region between the outside of the inner ring and the outside of the outer ring.
2.3 15c 2.3 15d
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Mid-Chapter Review
2a The answer is just: no
Mid-Chapter Review
2b The answer is just: yes
Mid-Chapter Review
2c The answer is just: yes
Mid-Chapter Review
2d The answer is just: no
2.4 4d
2.4 5a
2.4 5b
, 2.4 6a Add: denominator cannot equal zero 2.4 6b Add: the denominator cannot equal zero 2.4 6c Add: the denominator cannot equal zero 2.4 6d Add: the denominator cannot equal zero 2.4 6e Add: the denominator never equals zero 2.4 6f Add: 2.4 14a iii
2.4 14b
yes; 2.4 16a and 2.4 16b
and 2.4 16c and 2.4 17b
Add
2.7 2d
2.7 9d
2.7 14b Factor the quadratic denominators and determine the common denominator by taking the product of the unique factors of each denominator. Answers will vary. For example,
and factor to;
and . The LCD is
2.7 15b Answers may vary. For example, or
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Chapter Review
17a or
Chapter Review
17bi
Chapter Review
17bii , so he cannot win
Chapter 3: Quadratic Functions Location Question Correct Answer 3.1 16
3.2 11c between $22 971 and $57 029 3.2 12 It is possible, because maximum rectangular area occurs
when rectangle is 125 m by m 3.3 6a b The graph is correct but replace with and replace
with . 3.3 8 3.3 10c
3.3 13a iv 3.3 13c iv Mid Chapter Review
10
Mid Chapter Review
12a
Mid Chapter Review
12b
3.5 5a about (2.59, 0), about (–0.26, 0) 3.5 6c 836 or 10 163 3.5 6d 900 or 11 099 3.5 8c 2016 3.5 12 Add "about": about 2.1 m 3.5 13a Add "about": about 1.68 s and about 17.09 s 3.5 14 Add to the answer of $2.75: (It is unreasonable to raise the
fare to $14.25.) 3.6 12 A: break-even at x = 4.8
B: break-even at about x = 0.93 or 5.22 C: break-even at about x = 2.24 or 6.19 Buy Machine B. It has the earliest break-even point.
3.7 13c Change equation to: f(x) = –443(x – 1.35)2 + 442
3.8 4b about (1.91, 8.91), about ( 1.57, 5.43)
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3.8 4d about (–1.59, –3.97), about (–0.16, 3.22) 3.8 6 either $3.00 or $4.00 3.8 7 Before the answer, add: Answers may vary. For example, 3.8 10 Add "about": about 7.20 s 3.8 12 Add "about": Yes, at about 0.18 s after kick at (0.18, 4.0) Chapter Review 16 Use k instead of x: k < –0.5 or k > 3.5 Chapter Review 20b Add "about": about 8.8 m Chapters 1–3 Cumulative Review Location Question Correct Answer Cumulative Review Chapters 1–3
24a.–d. The answer in the book is correct, but in each part of the equation, change 1 in the inequality to: 0
Cumulative Review Chapters 1–3
35a 8 or 30 students
Chapter 4: Exponential Functions Location Question Correct Answer 4.1 2c They are similar in that both first difference tables show a
multiplicative pattern. They are different in that in the first case the values decrease sharply and then level off while in the second case the values start level and then increase sharply.
4.2 1e
4.2 1f
4.2 18c b(m + 4n)
4.3 3d 7-1 4.3 6c 4.3 6d
4.3 6f 82 = 64 4.3 15a Answers may vary. For example, m = 1, n = 2 4.3 15b n = 0 4.4 3b x2y2 = 36 4.4 10d y < 0 Mid-Chapter Review
1b
4.5 2a exponential; the values decrease at a fast rate 4.6 2c
The base function is . Vertical stretch factor 7 and translation of 1 unit down and 4 units to the right.
4.6 7 Replace graph, graph should not show x < 0:
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4.6 13 Replace graph with the following.
4.7 8c 16 years ago 4.7 13b Add the word "about": 49.3% 4.7 17b Answers may vary. For example, y = 4.25x. 4.7 17c There are too few pieces of data to make a model, and the
exponential growth cannot continue indefinitely. 4.7 18b Add the word "about": 32.2% Chapter Review 5a a0 Chapter Review 5b b1
Chapter Review 5f
Chapter Review 6 ; therefore
for a, b > 0 Chapter Review 7b
Chapter Review 11b The graph is correct, but type should be: y = 2x; vertical
compression by a factor of , reflection in the y-axis, and translation of 1 unit up
Chapter Review 11c The graph is correct, but type should be: y = 3x; reflection in the x-axis, vertical stretch by a factor of 2, horizontal
compression by a factor of , and a translation of 2 units left
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Chapter Review 11d The graph is correct, but: y = 5x; reflection in the x-axis,
vertical compression by a factor of , horizontal
compression by a factor of , and a translation of 3 units right and 10 units up
Chapter Review 12 Change equation to: y = 0.5-x + 1 Chapter Review 14c Graph should not show x < 0. Change y to: f(t) Chapter Review 14f There would be a horizontal compression of the graph; that
is, the values would decrease more quickly. Chapter Review 17d about 7.2% Chapter Self-Test
1b If the second differences are 0 then the relationship is linear. If the second differences are equal but non-zero then the relationship is quadratic. If the second differences show a multiplicative pattern then the relationship is exponential.
Chapter Self-Test
1c reflection in the x-axis, vertical compression of , horizontal
compression of , and a translation of 2 units left and 5 units up.
Chapter 5: Trigonometric Ratios Location Question Correct Answer 5.1 5b ii 45° 5.1 5b iii 56° 5.2 9
5.2 13
5.2 15c
5.3 2 Add: Answers may vary. For example, … 5.3 3b
5.4 2a For r, sin θ, cos θ, and θ, replace = by =& 5.4 2b For r, sin θ, cos θ, and θ, replace = by =& 5.4 2c For r, sin θ, cos θ, and θ, replace = by =& 5.4 2d For θ, replace = by =& 5.4 5abcd For sin, cos, and tan, replace = by =& 5.4 6abcdef For θ, β, replace = by =& 5.4 7b –37° 5.4 7c –104° 5.4 7e –48° 5.4 7f –107° 5.4 16ab For θ, replace = by =&
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Mid-Chapter Review
3 tan 54° or 234°, csc 46° or 134°, sec 44° or 316°, cot 36° or 216°
5.5 1b add: except 90° and 270° 5.5 1d add: except 90° and 270° 5.5 4
= R.S. 5.5 5d L.S. and R.S. are reversed, but the identify is proven. 5.5 10 not an identity; for example, csc2 45° + sec2 45° ≠ 1 5.5 12b Last line should read: “where sin α ≠ ± 1” 5.5 14b iv sin β ≠ –cos β 5.5 14b vi sin x ≠ 0, cos x ≠ −1 5.6 4b 68° or 112° 5.6 8 4139 m 5.6 9 about 299.7 m 5.6 10 13 m 5.6 11 Carol on same side as 66° only. Distance to 66° is 11 m:
a) 28 m b) 36 m c) 63 m Carol on same side as 66° only. Distance to 35° is 11 m: a) 5 m b) 6 m c) 2 m Carol on same side as 35° only. Distance to 66° is 11 m: a) 9 m b) 11 m c) 5 m Carol on same side as 35° only. Distance to 35° is 11 m: a) 19 m b) 24 m c) 24 m All on same side. Distance to 35° is 11 m: a) 19 m b) 24 m c) 7m All on same side. Distance to 66° is 11 m: a) 28 m b) 36 m c) 16 m Carol on same side as neither. Distance to 35° is 11 m: a) 5 m b) 6 m c) 6 m Carol on same side as neither. Distance to 66° is 11 m: a) 9 m b) 11 m c) 19 m
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5.6 14
5.6 15b 3 km 5.7 5 The art in the question should have 8.8 m, 6.5 m, not cm. 5.7 9a Add: (Answer: 85°) 5.7 9b Add: (Answer: 273 m)
In art for the answer, change: 85.2° to 85° 5.7 10 101 m 5.7 14b A is higher by 210 m 5.8 3b 38 cm 5.8 3d 65° 5.8 4a 520.2 m
Determine angle D using the sum of angles rule. Then, determine b using the sine law. Finally, determine h using the sine trigonometric ratio.
5.8 9 The question needs to change 13.5 m to: 8.8 m 5.8 9 Add to current answer:
First, calculate the distance from Tara to the boat. Since the angle of elevation for both girls is the same, the distance between each girl and the boat is the same. Then, the cosine law can be applied to determine the angle between Tara and
a)
b)
c)
or L
L
L
L
M
M M
M
N
N
N
N
l > m, m
Ml
L sinsin=
height = msin L
h = msin L msin L < l < m
h = msin L l < h
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the boat. 5.8 12b You need the altitude of the balloon and the angle formed by
the horizontals of the friends’ sight lines. 5.8 14 605 m Chapter Review
3cii Graphic should show β = 55°, not θ = 55° (keep in fourth quadrant); show θ = 55° (in first quadrant) on diagram too
Chapter Review
6 Add: β ≠ 0°, 180°, 360°
Chapter Review
7a Add: α ≠ 90° or 270°
Chapter Review
7b Change last line to: φ ≠ 0°, 90°, 180°, 270°, or 360°
Chapter Review
7c Change last line to: x ≠ 0°, 90°, 180°, 270°, or 360°
Chapter Review
7d Change last line to: θ ≠ 90° or 270°
Chapter Review
9 5.7 km or 30.5 km
Chapter Review
11 9.4 m
Chapter Review
13 46°
Chapter Self-Test
4ai θ should be replaced by: φ Add: φ ≠ 90°, 270°
Chapter Self-Test
4bi
, α ≠ 0°, 180°, 360°
Chapter 6: Sinusoidal Functions Location Question Correct Answer Getting Started
3a 31°
Getting Started
3b 153°
Getting Started
7 Replace “≠” by: or
6.1 4a period: about 6.5 6.1 4b period: about 3.1 6.1 4e period: 5 6.1 9 Graph should show more than one cycle, and add: Answers may
vary. For example, 6.1 10 Graph should show more than one cycle, and add: Answers may
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vary. For example, 6.1 13c period: 7 min; axis: d = 25; amplitude: 15 cm 6.1 15c Change domain to: domain: 6.2 3a The graph x-axis should be adjusted to show max and min at +1
and –1. 6.2 12 Add: Answers may vary. For example, 6.2 14 Replace “circle” with: function 6.2 16b Dots should be removed from the graph. 6.2 16d The amplitude is the maximum positive or negative
displacement from rest. 6.3 1e Answers may vary. For example, yes, because she is never
closer than 2 m from the motion detector. 6.3 6a Graph should be horizontally translated so that there is a
minimum at 0 s, and should be extended to 120 s. 6.3 6b Graph should be horizontally translated so that there is a
minimum at 0 s, and should be extended to 45 s. 6.3 6d Replace graph with the following, with x-label t and y-label h (to
match other graphs in this question):
6.3 8a Graph should be shifted up so that the range is from 0 to 52 cm. 6.3 8b approximately 50 cm 6.3 8c approximately 337 cm 6.3 10 In the question, the ° in the equation should be after 2sin(12t). 6.3 15c Table for displacement of small gear should be extended to 24 s. 6.3 15d –0.52 m 6.3 15e –0.87 m Mid-Chapter Review
2e Add units: psi
Mid-Chapter Review
5e Change last part to: 2: 503 cm/s
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Mid-Chapter Review
6a Graph should be replaced by a screen (and window settings):
Mid-Chapter Review
6c axis: P = 0; the average position is 0° with respect to due west
6.4 2d Remove: horizontal translation of –30°; 6.5 1abcd Add the words: in any order 6.5 1e Add the words: in any order, as long as the horizontal translation
is after the horizontal stretch 6.5 4 Add the words: Order may vary, as long as any horizontal
translations are after any horizontal stretches or compressions and any vertical translations are after any vertical stretches or compressions.
6.5 7d The 335° on the x-axis should be replaced by 360° 6.5 7f Graph should extend to (–12.4, 720). Replace these: “6” has
been dropped from 360 on x-axis and –16 on y-axis 6.5 8c Change X max to: 4° 6.5 8d Switch Y min and Y max values. 6.5 10 Add: Answers may vary. For example, 6.5 11
Reflection in x-axis, vertical compression of , vertical
translation of 30 upward, horizontal compression of . 6.6 1 Add: Answers may vary. For example, 6.6 3 Add: Answers may vary. For example, 6.6 4 Add: Answers may vary. For example, 6.6 5b y = –4cos(0.5x) + 17 6.6 5c y = 3sin(1.5x) – 4 6.6 7 Add: Answers may vary. For example, 6.6 8a Graph should be horizontally shifted so that it runs from
0 to 11 months. Also, graph should show data points listed so it represents a scatter plot with a line of good fit drawn.
6.6 8b A sinusoidal model can be used because the data is wave-shaped.
6.6 8d Answers may vary. For example, 8.1° or 10.3° using the chart. 6.6 9c The fit is somewhat close. 6.6 9e Answers may vary. For example, 0.8 s and 2.2 s from model or
0.6 s and 2.4 s interpolating from the chart.
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6.6
10a Graph should show sinusoidal curves drawn to represent these points.
6.6 10c Latitude affects average temperature as well as maximum and
minimum temperatures. 6.6 11a y = 3 sin(9000t)° + 8 6.6 13 59.8 cm 6.6 14 h = 7 cos(22.74t)° + 8, t in seconds, h in metres 6.7 1d The range is correct. For the equation, change to: d = 0.5
sin(180t)° + 1.5 6.7 2e Add: Answers may vary. For example, 6.7 3 Add: Answers may vary. For example, 6.7 4c Add: Answers may vary. For example, 6.7 5a Add: Answers may vary. For example, d = 30 cos[18(t – 12)] 6.7 5b Add: Answers may vary. For example, d = 9 cos[18(t – 12)] 6.7 6ae Add: Answers may vary. For example, 6.7 7 Add: Answers may vary. For example, 6.7 8a Add: Answers may vary. For example, 6.7 9a Add: Answers may vary. For example, h = –30 cos(1.43d) + 40 6.7 10 The periods are the same. The rabbit population has a higher
average value and amplitude. The fox population increases when the rabbit population is above average and decreases when the rabbit population is below average.
6.7 11 The period, amplitude, location of the axis, and horizontal shift. 6.7 12 Add: Answers may vary. For example, assuming the paint drop
started at the lowest point 6.7 13a Add: Answers may vary. For example, Chapter Review
9a Graph should be extended to 360°.
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Chapter Review
9b Graph should be replaced with the graph below but with the degree symbol for 90°, 180°, 270°, and 360°, x on the horizontal axis, and f(x) on the vertical axis.
Chapter Review
11a Graph should show data points listed so it represents a scatter plot with a line of good fit drawn.
Chapter Review
11g Add: Answers may vary. For example,
Chapter Review
11h Change February to: March
Chapter Review
13f Add: Answers may vary. For example,
Chapter Review
14 To determine the equation of a sinusoidal function, calculate the period, amplitude, equation of the axis, and horizontal translation. This information will help you to determine the values of k, a, c, and d, respectively, in the equations g(x) = a sin(k(x – d)) + c and h(x) = a cos(k(x – d)) + c.
Chapter Self-Test
1f No. Since the period is 40 s, at 300 s the stair will be at the same level as it is at 20 s, which is 4 m.
Chapter 7: Discrete Functions: Sequences and Series Location Question Correct Answer 7.1 14 Add: Answers may vary. For example, 7.2 15 Add: Answers may vary. For example, 7.2 22 Add: about 7.3 1 Change “Yes,” to: Yes, for n > 2, 7.4 2a
; the positive root 2
51+=r approximates the ratio
of as n increases 7.4 3b Add: about Mid-Chapter Review
4f-ii change recursive formula (leave general term and t6 = …):
, where n > 1
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Mid-Chapter Review
5b-i Change “geometric” to: neither
Mid-Chapter Review
10b t1 = 3, t2 = 2, tn = tn-2 + tn-1, where n > 2
7.5 8a Add: where n > 2 7.6 3e For both, change = to: =& 7.6
18b
Using , . As n approaches infinity,
. 7.7 4e
7.7 5e Trailing + should be – (i.e. “+ …” to “– …”) Chapter Review
22e Add: about
Chapter Self-Test
8b p6+ 6q, p7 – 7q, p8 + 8q
Chapter 8: Discrete Functions: Financial Applications Location Question Correct Answer Getting Started 8 Add: Answers may vary. For example, 8.1 10c 24 years and 158 days 8.2 9 Plan B: Plan A = $1139.99, Plan B = $1049.25 8.2 16 $4534.14 8.2 17 Answers may vary slightly depending on rounding. For
example, $3427.09 or $3427.08 8.3 15 Answers may vary slightly depending on rounding. For
example, $1695.15 or $1695.16 Mid-Chapter Review
5 about 11 years and 5 months
8.4 5d Answers may vary slightly depending on rounding. For example, $57 347.06 or $57 347.07
8.4 8 about 5 years and 9 months 8.4 11 Add: Answers may vary. For example; 8.4 12b Answers may vary slightly depending on rounding. For
example, $918.87 or $918.30 8.4 13 Answers may vary slightly depending on rounding. For
example, $924.32 or $924.31
( ) 276542706120180624832 234566++++++=+ xxxxxx
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8.5 13 $19 070.96 8.6 1a Add "about": about 12 years 8.6 1b Add "about": about 7 years 8.6 1c Add "about": about 19 years 8.6 1d Add "about": about 8 years 8.6 4b about 5 years and 5 months 8.6 4c $53 154.40 Chapter Review 2c Add "about": about 18 years and 6 months Chapter Review 12 about 12 years and 3 months Chapter Review 19 Add "about": about 4 years Chapter Self-Test
5 5.88%/a compounded monthly. This is equivalent to 6.04%/a compounded annually
Chapter Self-Test
7 Answers may vary slightly depending on rounding. For example, $201.01 or $205.30
Chapters 7–8 Cumulative Review Location Question Correct Answer Cumulative Review Chapters 7–8
12 (d)
Cumulative Review Chapters 7–8
18c Change right-hand column head from C to: D
Cumulative Review Chapters 7–8
17 Add "about": about 5.4 h
Appendix A – Review of Essential Skills Location Question Correct Answer A–5 2a Replace graph, exactly the same scales, grid, and labels as
before, but redrawing blue line (which is y = 3x – 1), slope of 3, y-intercept –1:
A–6 3e
⎟⎠⎞
⎜⎝⎛−
1128,
119
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A–6 3f
⎟⎠⎞
⎜⎝⎛
25,
21
A–9 3c (5a – 3)(a + 2) A–14 2c (–2, 1) A–14 2d (–5, 4) A–14 3d y = –x2 – 2 A–16 5d 24.3° A–17 2a 16.0° A–17 2c Add unit cm: 23.4 cm A–17 2d Add unit cm: 13.2 cm A–17 2f Add unit cm: 30.3 cm A–17 3a t =& 6.1 cm, ∠A =& 74°, ∠C =& 47° A–17 3b ∠A =& 34°, ∠B =& 42°, ∠C =& 104° A–17 3c ∠F =& 32°, ∠E =& 109°, DF =& 25.8 cm