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Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra 2: Final Exam
Solve the equation.
____
1. y − 4 = 2(y + 8)
= −12
a.
____
b.
=−
1
20
2. x 2 − 4x + 4 = 100
a. –8, 8
b. –12, 12
1
12
c.
=−
c.
d.
–8, 12
–12, 8
d.
= −20
Use an algebraic equation to solve the problem.
____
3. A rectangle is 5 times as long as it is wide. The perimeter is 80 cm. Find the dimensions of the rectangle.
Round to the nearest tenth if necessary.
a. 6.7 cm by 33.3 cm
c. 13.3 cm by 33.3 cm
b. 16 cm by 80 cm
d. 6.7 cm by 73.3 cm
Solve the inequality. Graph the solution set.
____
4. 5r + 7 ≤ 18
a.
r≥5
b.
r≤2
1
5
c.
r≥2
d.
r≤5
1
5
Solve the absolute value equation. Graph the solution.
____
5. What is the sum of the solutions of 2 |x − 1| − 3 = −1 ?
1
c. 1
a. 2
2
b.
0
d.
1
2
Name: ________________________
ID: A
Solve the system by graphing.
____
ÏÔÔ
ÔÔ −3x = y + 5
6. ÌÔ
ÔÔ 2x − 4y = 6
Ó
a.
c.
(–2, –1)
(–1, –2)
d.
b.
(–1, 2)
____
(2, –1)
7. A jet ski company charges a flat fee of $36.00 plus $1.75 per hour to rent a jet ski. Another company charges
a fee of $31.00 plus $2.75 per hour to rent the same jet ski.
Find the number of hours for which the costs are the same. Round your answer to the nearest whole hour.
a.
b.
5
9
c.
d.
2
10
2
Name: ________________________
ID: A
Solve the system by substitution.
____
ÏÔÔ
ÔÔ −2.5x + y = 13.5
8. ÌÔ
ÔÔ 2.25x − y = −12.25
Ó
a. (–5, 1)
b. (–1, 5)
c.
d.
(1, –5)
(5, –1)
c.
d.
(–5, –1, 0)
(–5, –1, –2)
Solve the system by elimination.
____
ÔÏÔÔ x + 5y − 4z = −10
ÔÔ
ÔÔ
9. ÔÔÌ 2x − y + 5z = −9
ÔÔ
ÔÔÔ 2x − 10y − 5z = 0
Ó
a. (5, –1, 0)
b. (–5, 1, 0)
____ 10. Describe the vertical asymptote(s) and hole(s) for the graph of y =
a.
b.
c.
d.
x−1
.
x 2 + 6x + 8
asymptotes: x = –4, –2 and hole: x = 1
asymptote: x = 1 and no holes
asymptote: x = 1 and holes: x = –4, –2
asymptotes: x = –4, –2 and no holes
____ 11. Write an explicit formula for the sequence 8, 6, 4, 2, 0, ... Then find a 14 .
a. a n = −2n + 10; –16
c. a n = −2n + 8; –20
b. a n = −2n + 8; –18
d. a n = −2n + 10; –18
____ 12. Which of the following angles is not coterminal with the other three?
a.
94°
b.
86°
c.
454°
d.
–266°
c.
−
1
2
d.
2
2
ÊÁ 7π
ˆ˜
____ 13. Find the exact value of cos ÁÁÁÁ −
radians ˜˜˜˜ .
Ë 4
¯
a.
1
2
b.
3
2
3
Name: ________________________
ID: A
Graph the function in the interval from 0 to 2 π.
____ 14. y = sin (θ − 2)
a.
b.
c.
d.
4
Name: ________________________
____ 15. y = sin (θ + 2) − 5
a.
b.
ID: A
c.
d.
5
Name: ________________________
ÁÊ
π ˜ˆ
____ 16. y = 2 cos ÁÁÁÁ θ − ˜˜˜˜ + 2
6¯
Ë
a.
b.
ID: A
c.
d.
What are the vertex and the axis of symmetry of the equation?
____ 17. y = 2x 2 + 24x − 16
a.
b.
vertex: ( –6, –88)
axis of symmetry: x = −6
vertex: ( –6, 88)
axis of symmetry: y = −6
c.
d.
vertex: ( 6, –88)
axis of symmetry: x = −88
vertex: ( –6, –88)
axis of symmetry: x = −88
What is the maximum or minimum value of the function? What is the range?
____ 18. y = −2x 2 + 28x − 10
a.
b.
minimum: –88
range: y ≥ −88
minimum: 88
range: y ≥ 88
c.
d.
6
maximum: 88
range: y ≤ 88
maximum: –88
range: y ≤ −88
Name: ________________________
ID: A
What is the equation, in standard form, of a parabola that contains the following points?
____ 19. (–2, 18), (0, 4), (4, 24)
d.
y = −3x 2 + 2x + 4
y = −4x 2 − 3x − 2
____ 20. x 2 − 6x + 8
a. (x + 4)(x + 2)
b. (x − 2)(x − 4)
c.
d.
(x − 4)(x + 2)
(x − 2)(x + 4)
____ 21. −x 2 − x + 42
a. −(x − 7)(x + 6)
b. (x + 7)(x + 6)
c.
d.
(x − 6)(x − 7)
−(x − 6)(x + 7)
____ 22. 3x 2 + 26x + 35
a. (x + 5)(3x + 7)
b. (3x + 7)(x − 5)
c.
d.
(3x + 5)(x − 7)
(3x + 5)(x + 7)
____ 23. 9x 2 − 18x + 9
a. (3x + 3) 2
c.
(3x − 3) 2
(−3x − 3) 2
a.
b.
y = −2x 2 + 3x − 4
y = 2x 2 − 3x + 4
c.
What is the expression in factored form?
What is the expression in factored form?
b.
(3x − 3)(−3x + 3)
____ 24. Which sum is equal to
a.
b.
x+5
1
+
x+5 x−5
1
x2
+
x+5 x−5
d.
x 2 + 6x − 5
?
x 2 − 25
c.
d.
7
x
1
+
x+5 x−5
1
x
+
x−5 x+5
Name: ________________________
ID: A
____ 25. The figure below shows a container that is a square prism with base area B and a hollow section (shaded
region) that is a square prism with base area b. If the height h of both prisms is the same, write an expression
to represent the volume of the container. Express your answer in completely factored form.
a.
b.
h(B 2 + 2bB − b 2 )
h(B − b)(B − b)
c.
d.
h(B + b)(B + b)(B − b)(B − b)
h(B + b)(B − b)
What are the solutions of the quadratic equation?
____ 26. x 2 + 11x = −28
a. –4, –7
b. –4, 7
____ 27. 3x 2 + 25x + 42 = 0
7 1
a. − , −
3 2
1
b. 6, −
2
c.
d.
4, 7
4, –7
c.
–6, 3
d.
–6, −
7
3
What value completes the square for the expression?
____ 28. x 2 − 18x
a.
b.
9
−9
c.
d.
81
−81
Solve the quadratic equation by completing the square.
____ 29. −3x 2 + 7x = −5
a.
7
±
6
b.
7
− ±
3
109
6
109
3
c.
7
±
3
d.
7
− ±
6
8
67
3
22
6
Name: ________________________
ID: A
Use the Quadratic Formula to solve the equation.
____ 30. −2x 2 − 5x + 5 = 0
a.
5
− ±
2
65
2
c.
4
− ±
5
130
4
b.
5
− ±
4
32
2
d.
5
− ±
4
65
4
____ 31. 2x 2 + x − 4 = 0
a.
1
− ±
2
33
4
c.
1
− ±
4
33
4
b.
−4 ±
66
4
d.
1
− ±
2
33
2
____ 32. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3
yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to
be 155 square yards. The situation is modeled by the equation h 2 + 5h = 155. Use the Quadratic Formula to
find the height that will give the desired area. Round to the nearest hundredth of a yard.
a. 320 yards
c. 20.4 yards
b. 10.2 yards
d. 12.7 yards
Simplify the number using the imaginary unit i.
____ 33.
a.
b.
−144
12
−12
c.
d.
12i
144i
c.
d.
3 + 18i
(8 + 18i)
Simplify the expression.
____ 34. (4 − i)(2 + 5i)
a. 2(4 + 9i)
b. (13 + 18i)
____ 35.
−2 + i
−4 − 5i
a.
b.
1 5
− +1 i
3 9
3 14
− i
41 41
c.
d.
9
3
−
41
13
−
41
6
i
41
14
i
41
Name: ________________________
____ 36.
ID: A
−2 − 3i
6i
a.
b.
1
−
2
1
+
2
1
i
3
1
i
3
c.
d.
1
− +
2
1
− +
2
1
i
3
1
i
3
What is the solution of the quadratic system of equations?
ÏÔÔ
ÔÔ
ÔÔ y = x 2 + 16x + 32
____ 37. ÌÔ
ÔÔ
ÔÔÔ y = −x 2 + 2
Ó
a.
b.
(–7, –3)
(–23, –5)
(–3, 89)
(–5, 137)
c.
d.
(–3, –7)
(–5, –23)
(3, –7)
(5, –23)
What are the zeros of the function? What are their multiplicities?
____ 38. f(x) = x 4 − 4x 3 + 3x 2
a.
b.
c.
d.
the numbers –1 and –3 are zeros of multiplicity 2; the number 0 is a zero of multiplicity
1
the number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeros of multiplicity 1
the numbers 0 and 1 are zeros of multiplicity 2; the number 3 is a zero of multiplicity 1
the number 0 is a zero of multiplicity 2; the numbers –1 and –3 are zeros of multiplicity
1
____ 39. f(x) = 4x 3 − 12x 2 − 16x
a. the numbers 1, –4, and 0 are zeros of multiplicity 2
b. the numbers –1, 4, and 0 are zeros of multiplicity 2
c. the numbers –1, 4, and 0 are zeros of multiplicity 1
d. the numbers 1, –4, and 0 are zeros of multiplicity 1
____ 40. Divide −3x 3 − 2x 2 − x − 2 by x – 2.
a. −3x 2 + 4x + 15, R 32
b. −3x 2 + 4x + 15
c.
d.
−3x 2 − 8x − 17
−3x 2 − 8x − 17, R –36
____ 41. Determine which binomial is not a factor of 4x 4 − 21x 3 − 46x 2 + 219x + 180.
a. x + 4
c. x – 5
b. x + 3
d. 4x + 3
10
Name: ________________________
ID: A
Divide using synthetic division.
____ 42. Divide −4x 3 + 21x 2 − 23x + 6 by (x − 4).
−4x 2 + 5x − 3, R –6
4x 2 − 5x + 3
a.
b.
c.
d.
−4x 2 + 37x − 43, R 18
4x 2 − 37x + 43
____ 43. Use synthetic division to find P(–2) for P(x) = x 4 + 9x 3 − 9x + 2.
a. –2
b. 0
c. –36
d.
68
d.
3x 6
Find all the zeros of the equation.
____ 44. −x 3 − x 2 = 11x + 11
a. i 11 , −i 11 , 1
i 11 , −i 11 , –1
b.
d.
i 11 , 1
11 , − 11 , –1
c.
d.
2, −2, 5i, 0
−2, −5i
c.
____ 45. 21x 2 − 100 = −x 4
a. 2, −2, 5i, −5i
b. 2, 5i
Use the Binomial Theorem to expand the binomial.
____ 46. What is the fourth term of (d + 4b) 3 ?
a. −b 3
b. −64b 3
c. b 3
d. 64b 3
3
____ 47.
270x 20
3
a.
5x
2x 3 3x 6
b.
3x 6 3 2x
c.
3
c.
5x 3x 8
none of these
135x 19
90x 18
____ 48.
2x
a.
b.
3x 8 5x
18x 17
d.
What is the product of the radical expression?
Ê
ˆ2
____ 49. ÁÁÁ −5 − 3 ˜˜˜
Ë
¯
a. 28 + 10 3
c.
28 − 10 3
d.
b.
11
−13 + 5 3
25 − 10 3
135x
Name: ________________________
ID: A
Simplify.
1
1
3
____ 50. 3 ⋅ 9 3
a. 9
b.
3
3
c.
3
c.
d.
–28
–18
c.
4
3
d.
What is the simplest form of the number?
2
3
____ 51. −27
a. 9
b. 57
What is the solution of the equation?
____ 52.
x + 10 − 7 = −5
a. 14
b.
–8
d.
–6
____ 53. The area of a circular trampoline is 112.07 square feet. What is the radius of the trampoline? Round to the
nearest hundredth.
a. 3.37 feet
c. 5.97 feet
b. 10.59 feet
d. 35.67 feet
____ 54. The function d = 4.9t 2 represents the distance d, in meters, that an object falls in t seconds due to Earth’s
gravity. Find the inverse of this function. How long, in seconds, does it take for a cliff diver who is 70
meters above the water to reach the water below?
a. 3.8 seconds
c. 8.1 seconds
b. 5.9 seconds
d. 13.8 seconds
Write the equation in logarithmic form.
____ 55. 2 5 = 32
a. log 32 = 5 ⋅ 2
b. log 2 32 = 5
c.
d.
log 32 = 5
log 5 32 = 2
Evaluate the logarithm.
____ 56. log 3 243
a. 5
b.
–5
c.
4
d.
3
____ 57. log 0.01
a. –10
b.
–2
c.
2
d.
10
12
Name: ________________________
ID: A
Expand the logarithmic expression.
____ 58. log 3
d
12
a.
log 3 d − log 3 12
c.
log 3 d
log 3 12
b.
−d log 3 12
d.
log 3 12 − log 3 d
c.
log3 11 + 3 log 3 p
d.
11 log 3 p 3
c.
7
12
____ 59. log 3 11p 3
a. log 3 11 ⋅ 3 log 3 p
b.
log 3 11 − 3 log 3 p
Solve the exponential equation.
____ 60.
1
= 64 4x − 3
16
1
a.
12
b.
1
4
d.
11
12
Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
____ 61. Solve log(4x + 10) = 3.
7
b.
a. −
4
495
2
c.
250
____ 62. Solve ln 2 + ln x = 5. Round to the nearest tenth, if necessary.
a. 50,000
b. 74.2
c. 10
d.
990
d.
3
Use natural logarithms to solve the equation. Round to the nearest thousandth.
3
4
–0.288
____ 63. e x =
a.
b.
–0.275
c.
13
0.275
d.
0.288
Name: ________________________
ID: A
Sketch the asymptotes and graph the function.
____ 64. y =
5
−1
x−1
a.
c.
b.
d.
3x 6 − 7x + 9
.
7x 2 + 7x + 9
c. y = 0
____ 65. Find the horizontal asymptote of the graph of y =
a.
b.
y=3
3
y=
7
d.
−2x 3 + 3x + 2
.
2x 3 + 6x + 2
c. no horizontal asymptote
d. y = 0
____ 66. Find the horizontal asymptote of the graph of y =
a.
b.
y=1
y = −1
no horizontal asymptote
14
Name: ________________________
ID: A
What is the product in simplest form? State any restrictions on the variable.
____ 67.
y2 − y − 6
y2
⋅
y−3
y 2 + 1y
a.
y 2 + 2y
, y ≠ 3, − 1
y+1
c.
y+2
, y ≠ 3, 0, − 1
y+1
b.
y 2 + 2y
, y ≠ 3, 0, − 1
y+1
d.
y+2
, y ≠ 3, − 1
y+1
What is the quotient in simplified form? State any restrictions on the variable.
____ 68.
a+1
a+2
÷
a − 5 a 2 − 8a + 15
(a + 2)(a − 3)
, a ≠ 5, − 1, 3
a.
a+1
(a + 2)(a + 1)
, a ≠ 5, 3, − 1
b.
(a − 5) 2 (a − 3)
c.
d.
(a + 2)(a − 3)
, a ≠ 3, − 1
a+1
(a + 2)(a + 1)
, a ≠ 5, 3
(a − 5) 2 (a − 3)
____ 69. Find the least common multiple of x 3 − x 2 + x − 1 and x 2 − 1 . Write the answer in factored form.
a. (x + 1) 2 (x − 1)
c. (x 3 − x 2 + x − 1)(x 2 − 1)
b.
(x + 1)(x − 1)(x 2 + 1)
d.
(x + 1)(x − 1)(x 2 − 1)
Simplify the sum.
____ 70.
4
5
+
m + 9 m2 − 81
9
a.
(m − 9)(m + 9)
4m − 31
b.
(m − 9)(m + 9)
c.
d.
9
m + m − 72
4m + 41
(m − 9)(m + 9)
2
Simplify the difference.
____ 71.
9
n 2 − 10n + 24
−
n 2 − 13n + 42 n − 7
n − 13
a.
n−7
n−4
b.
n−7
c.
n − 13
d.
n 2 − 10n + 15
n 2 − 13n + 42
15
Name: ________________________
ID: A
Simplify the complex fraction.
3
1
−
3b 2b
____ 72.
4
2
+
3b 4b
10
a.
3
b.
7
15
c.
15
7
d.
3
10
Generate the first five terms in the sequence using the explicit formula.
____ 73. y n = −5n − 5
a.
b.
c.
d.
–30, –25, –20, –15, –10
30, 25, 20, 15, 10
–10, –15, –20, –25, –30
10, 15, 20, 25, 30
____ 74. Write a recursive formula for the sequence 7, 13, 19, 25, 31, ... Then find the next term.
a. a n = a n − 1 + 6, where a 1 = 7; 37
b. a n = a n − 1 + 6, where a 1 = 37; 7
c. a n = a n − 1 − 6, where a 1 = 6; –23
d. a n = a n − 1 − 6, where a 1 = 7; 37
Is the sequence arithmetic? If so, identify the common difference.
____ 75. 14, 21, 42, 77, ...
a. yes; 7
b.
yes; –7
c.
yes; 14
____ 76. Find the 2nd and 3rd term of the sequence –7, ___, ___, –22, –27, ...
b. –17, –12
c. –10, –17
a. –12, –15
d.
no
d.
–12, –17
d.
no
Is the sequence geometric? If so, identify the common ratio.
____ 77. 6, 12, 24, 48, ...
a. yes; 2
b.
yes; –2
c.
yes; 4
____ 78. Kaylee is painting a design on the floor of a recreation room using equilateral triangles. She begins by
painting the outline of Triangle 1 measuring 50 inches on a side. Next, she paints the outline of Triangle 2
inside the first triangle. The side length of Triangle 2 is 80% of the length of Triangle 1. She continues
painting triangles inside triangles using the 80% reduction factor. Which triangle will first have a side length
of less than 29 inches?
a. Triangle 4
c. Triangle 5
b. Triangle 3
d. Triangle 6
16
Name: ________________________
ID: A
What is a possible value for the missing term of the geometric sequence?
____ 79. 1250, ___, 50, ...
a. 1200
b.
650
c.
250
d.
125
____ 80. A large asteroid crashed into a moon of a planet, causing several boulders from the moon to be propelled into
space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance
(in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic
sequence 26, 44, 62, 80, . . . . Find the total distance that the projectile traveled in seven seconds.
a. 534 feet
b. 560 feet
c. 212 feet
d. 426 feet
8
____ 81. Evaluate the series
∑ 5n.
n = 3
a.
125
b.
38
c.
210
d.
165
____ 82. Justine earned $26,000 during the first year of her job at city hall. After each year she received a 3% raise.
Find her total earnings during the first five years on the job.
a. $138,037.53
b. $1,004,704.20
c. $4,020.51
d. $108,774.30
____ 83. The screen below shows the graph of a sound recorded on an oscilloscope. What are the period and the
amplitude? (Each unit on the t-axis equals 0.01 seconds.)
a.
b.
0.05 seconds; 4.5
0.05 seconds; 9
c.
d.
17
0.025 seconds; 9
0.025 seconds; 4.5
Name: ________________________
ID: A
Find the measure of the angle.
____ 84.
a.
155°
b.
315°
c.
18
90°
d.
205°
Name: ________________________
ID: A
Sketch the angle in standard position.
____ 85. –95°
a.
c.
b.
d.
____ 86. Find the cosine and sine of 180°. Round your answers to the nearest hundredth if necessary.
a.
0, –1.1
b.
–0.71, –0.71
c.
19
–0.71, 0.71
d.
–1, 0
Name: ________________________
ID: A
____ 87. Find the cosine 315°. Round your answers to the nearest hundredth if necessary.
a. 0
b. 0.71
c. 1
d. –0.78
____ 88. Find the radian measure of an angle of –340°.
9
9π
b.
c.
a.
−17π
−17
−17π
9
d.
−17
9π
d.
−
ÊÁ 3π
ÊÁ 3π
ˆ˜
ˆ˜
____ 89. Find the exact values of cos ÁÁÁÁ
radians ˜˜˜˜ and sin ÁÁÁÁ
radians ˜˜˜˜ .
Ë 4
Ë 4
¯
¯
a.
2
2
,−
2
2
b.
3
1
− ,
2 2
c.
−
2
2
,
2
2
3 1
,
2 2
Use the given circle. Find the length s to the nearest tenth.
____ 90.
a.
6.3 m
b.
2.0 m
c.
3.1 m
d.
12.6 m
a.
4.4 ft
b.
70.4 ft
c.
35.2 ft
d.
11.2 ft
____ 91.
20
Name: ________________________
ID: A
____ 92. Find the period of the graph shown below.
a.
2π
b.
π
c.
1
π
2
d.
2
π
3
2
d.
8
____ 93. Find the amplitude of the sine curve shown below.
a.
4
π
3
b.
4
c.
21
Name: ________________________
____ 94. y = sin 3θ
a.
b.
ID: A
c.
d.
Find the domain, period, range, and amplitude of the cosine function.
____ 95. y =
a.
b.
c.
d.
3
t
cos
2
2
3
3
3
domain = all real numbers, period = 4π ; range: − ≤ y ≤ ; amplitude =
2
2
2
1
3
3
3
domain = all real numbers, period = ; range: − ≤ y ≤ ; amplitude = −
2
2
2
2
3
3
3
3
3
domain = − ≤ x ≤ , period = 4π ; range: − ≤ y ≤ ; amplitude = −
2
2
2
2
2
3
3
1
3
3
domain = − ≤ x ≤ , period = ; range: y ≤ ; amplitude =
2
2
2
2
2
22
Name: ________________________
ID: A
What is the value of the expression? Do not use a calculator.
____ 96. tan
5π
3
3
a.
b.
-
3
c.
1
d.
1
3
Write an equation for the translation of the function.
____ 97. y = cos x; translated 6 units up
a. y = cos (x + 6)
b. y = cos (x − 6)
c.
d.
y = cos x − 6
y = cos x + 6
Find the exact value. If the expression is undefined, write undefined.
____ 98. csc 135°
a.
0
b.
undefined
c.
1
2
Evaluate the expression for the given value of the variable(s).
99.
4(3h − 6)
1+h
; h = −2
Solve the system using elimination.
ÔÏÔÔ 7x + 2y = 11
Ô
100. ÌÔ
ÔÔ 4x − 7y = −10
Ó
23
d.
2
ID: A
Algebra 2: Final Exam
Answer Section
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REF: 1-4 Solving Equations
1-4.1 To solve equations
NAT: CC A.CED.1| CC A.CED.4| A.2.a| A.4.c
1-4 Problem 2 Solving a Multi-Step Equation
equation | solution of an equation | inverse operations
C
PTS: 1
DIF: L2
REF: 4-6 Completing the Square
4-6.1 To solve equations by completing the square
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
NC 2.02a
TOP: 4-6 Problem 3 Solving a Perfect Square Trinomial Equation
A
PTS: 1
DIF: L3
REF: 1-4 Solving Equations
1-4.2 To solve problems by writing equations
CC A.CED.1| CC A.CED.4| A.2.a| A.4.c
1-4 Problem 3 Using an Equation to Solve a Problem
KEY: equation | solution of an equation
B
PTS: 1
DIF: L2
REF: 1-5 Solving Inequalities
1-5.1 To solve and graph inequalities
CC A.CED.1| A.2.a| A.3.b| A.3.d| A.4.c
1-5 Problem 2 Solving and Graphing an Inequality
D
PTS: 1
DIF: L2
1-6 Absolute Value Equations and Inequalities
1-6.1 To write and solve equations and inequalities involving absolute value
CC A.SSE.1.b| CC A.CED.1| N.1.g| N.3.c| A.2.a| A.4.c
STA: NC 2.08a| NC 2.08b
1-6 Problem 2 Solving a Multi-Step Absolute Value Equation
absolute value
C
PTS: 1
DIF: L2
3-1 Solving Systems Using Tables and Graphs
3-1.1 To solve a linear system using a graph or a table
CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d
NC 2.10
TOP: 3-1 Problem 1 Using a Graph or Table to Solve a System
system of linear equations | graphing | solution of a system
A
PTS: 1
DIF: L2
3-1 Solving Systems Using Tables and Graphs
3-1.1 To solve a linear system using a graph or a table
CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d
NC 2.10
TOP: 3-1 Problem 3 Using Linear Regression
system of linear equations | word problem | problem solving | multi-part question
A
PTS: 1
DIF: L2
REF: 3-2 Solving Systems Algebraically
3-2.1 To solve linear systems algebraically
CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d
NC 2.10
TOP: 3-2 Problem 1 Solving by Substitution
system of linear equations | substitution method
C
PTS: 1
DIF: L2
REF: 3-5 Systems With Three Variables
3-5.1 To solve systems in three variables using elimination
CC A.REI.6| A.4.d
STA: NC 2.10
3-5 Problem 2 Solving an Equivalent System
system with three variables | solve by elimination
1
ID: A
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DIF: L2
8-3 Rational Functions and Their Graphs
8-3.1 To identify properties of rational functions
CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h STA: NC 2.05a| NC 2.05b| NC 2.05c
8-3 Problem 2 Finding Vertical Asymptotes
KEY: rational function
D
PTS: 1
DIF: L3
REF: 9-1 Mathematical Patterns
9-1.2 To use a formula to find the nth term of a sequence NAT: CC A.SSE.4| A.1.a
9-1 Problem 3 Writing an Explicit Formula for a Sequence
sequence | explicit formula | term of a sequence
B
PTS: 1
DIF: L3
REF: 13-2 Angles and the Unit Circle
13-2.1 To work with angles in standard position
NAT: CC F.TF.2
13-2 Problem 3 Identifying Coterminal Angles
KEY: coterminal angles
D
PTS: 1
DIF: L3
REF: 13-3 Radian Measure
13-3.1 To use radian measure for angles
NAT: CC F.TF.1| M.3.e
13-3 Problem 2 Finding Cosine and Sine of a Radian Measure
central angle | intercepted arc | radian
B
PTS: 1
DIF: L3
13-7 Translating Sine and Cosine Functions
13-7.1 To graph translations of trigonometric functions
NAT: CC F.IF.7.e| CC F.TF.5| A.2.d
13-7 Problem 2 Graphing Translations
KEY: phase shift
A
PTS: 1
DIF: L3
13-7 Translating Sine and Cosine Functions
13-7.1 To graph translations of trigonometric functions
NAT: CC F.IF.7.e| CC F.TF.5| A.2.d
13-7 Problem 3 Graphing a Combined Translation
KEY: phase shift
D
PTS: 1
DIF: L4
13-7 Translating Sine and Cosine Functions
13-7.1 To graph translations of trigonometric functions
NAT: CC F.IF.7.e| CC F.TF.5| A.2.d
13-7 Problem 4 Graphing a Translation of y = sin 2x
KEY: phase shift
A
PTS: 1
DIF: L2
4-2 Standard Form of a Quadratic Function
4-2.1 To graph quadratic functions written in standard form
CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
NC 2.02a| NC 2.02b
4-2 Problem 1 Finding the Features of a Quadratic Function
Graph functions expressed symbolically | standard form | vertex of a parabola | axis of symmetry
C
PTS: 1
DIF: L3
4-2 Standard Form of a Quadratic Function
4-2.1 To graph quadratic functions written in standard form
CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
NC 2.02a| NC 2.02b
4-2 Problem 1 Finding the Features of a Quadratic Function
standard form | minimum value | maximum value
B
PTS: 1
DIF: L3
4-3 Modeling With Quadratic Functions
4-3.1 To model data with quadratic functions
NAT: CC F.IF.4| CC F.IF.5| A.2.f
NC 2.02a| NC 2.02b| NC 2.04a| NC 2.04b
4-3 Problem 1 Writing an Equation of a Parabola
KEY: quadratic function | quadratic model
2
ID: A
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PTS: 1
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4-4 Factoring Quadratic Expressions
4-4.1 To find common and binomial factors of quadratic expressions
CC A.SSE.2| N.5.c| A.2.a
TOP: 4-4 Problem 1 Factoring ax^2+bx+c when a=+/-1
factoring | quadratic expression
D
PTS: 1
DIF: L3
4-4 Factoring Quadratic Expressions
4-4.1 To find common and binomial factors of quadratic expressions
CC A.SSE.2| N.5.c| A.2.a
TOP: 4-4 Problem 1 Factoring ax^2+bx+c when a=+/-1
factoring | quadratic expression
D
PTS: 1
DIF: L3
4-4 Factoring Quadratic Expressions
4-4.1 To find common and binomial factors of quadratic expressions
CC A.SSE.2| N.5.c| A.2.a
TOP: 4-4 Problem 3 Factoring ax^2+bx+c when abs(a) not = 1
factoring
C
PTS: 1
DIF: L3
4-4 Factoring Quadratic Expressions
4-4.2 To factor special quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a
4-4 Problem 4 Factoring a Perfect Square Trinomial
KEY: factoring | perfect square trinomial
C
PTS: 1
DIF: L2
4-4 Factoring Quadratic Expressions
4-4.2 To factor special quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a
4-4 Problem 5 Factoring a Difference of Two Squares
KEY: identify ways to rewrite expressions
D
PTS: 1
DIF: L2
4-4 Factoring Quadratic Expressions
4-4.2 To factor special quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a
4-4 Problem 5 Factoring a Difference of Two Squares
factoring | identify ways to rewrite expressions
A
PTS: 1
DIF: L2
REF: 4-5 Quadratic Equations
4-5.1 To solve quadratic equations by factoring
CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
NC 2.02a| NC 2.02b
TOP: 4-5 Problem 1 Solving a Quadratic Equation by Factoring
Zero-Product Property
D
PTS: 1
DIF: L3
REF: 4-5 Quadratic Equations
4-5.1 To solve quadratic equations by factoring
CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
NC 2.02a| NC 2.02b
TOP: 4-5 Problem 1 Solving a Quadratic Equation by Factoring
Zero-Product Property
C
PTS: 1
DIF: L2
REF: 4-6 Completing the Square
4-6.2 To rewrite functions by completing the square
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
NC 2.02a
TOP: 4-6 Problem 4 Completing the Square
completing the square
A
PTS: 1
DIF: L3
REF: 4-6 Completing the Square
4-6.1 To solve equations by completing the square
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
NC 2.02a
TOP: 4-6 Problem 5 Solving by Completing the Square
completing the square
3
ID: A
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REF: 4-7 The Quadratic Formula
4-7.1 To solve quadratic equations using the Quadratic Formula
CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
STA: NC 2.02a
4-7 Problem 1 Using the Quadratic Formula
KEY: Quadratic Formula
C
PTS: 1
DIF: L3
REF: 4-7 The Quadratic Formula
4-7.1 To solve quadratic equations using the Quadratic Formula
CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
STA: NC 2.02a
4-7 Problem 1 Using the Quadratic Formula
KEY: Quadratic Formula
B
PTS: 1
DIF: L3
REF: 4-7 The Quadratic Formula
4-7.1 To solve quadratic equations using the Quadratic Formula
CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
STA: NC 2.02a
4-7 Problem 2 Applying the Quadratic Formula
KEY: Quadratic Formula
C
PTS: 1
DIF: L2
REF: 4-8 Complex Numbers
4-8.1 To identify, graph, and perform operations with complex numbers
CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
NC 1.02
TOP: 4-8 Problem 1 Simplifying a Number using i
imaginary number | imaginary unit
B
PTS: 1
DIF: L3
REF: 4-8 Complex Numbers
4-8.1 To identify, graph, and perform operations with complex numbers
CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
NC 1.02
TOP: 4-8 Problem 4 Multiplying Complex Numbers
complex number
B
PTS: 1
DIF: L3
REF: 4-8 Complex Numbers
4-8.1 To identify, graph, and perform operations with complex numbers
CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
NC 1.02
TOP: 4-8 Problem 5 Dividing Complex Numbers
complex number | complex conjugates
C
PTS: 1
DIF: L2
REF: 4-8 Complex Numbers
4-8.1 To identify, graph, and perform operations with complex numbers
CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
NC 1.02
TOP: 4-8 Problem 5 Dividing Complex Numbers
complex number | complex conjugates
C
PTS: 1
DIF: L3
REF: 4-9 Quadratic Systems
4-9.1 To solve and graph systems of linear and quadratic equations
CC A.CED.3| CC A.REI.7| A.4.a| A.4.d
STA: NC 2.10
4-9 Problem 3 Solving a Quadratic System of Equations
B
PTS: 1
DIF: L3
5-2 Polynomials, Linear Factors, and Zeros
5-2.2 To write a polynomial function from its zeros
CC A.SSE.1| CC A.APR.3| CC F.IF.7| CC F.IF.7.c| CC F.BF.1
5-2 Problem 4 Finding the Multiplicity of a Zero
KEY: multiple zero | multiplicity
C
PTS: 1
DIF: L3
5-2 Polynomials, Linear Factors, and Zeros
5-2.2 To write a polynomial function from its zeros
CC A.SSE.1| CC A.APR.3| CC F.IF.7| CC F.IF.7.c| CC F.BF.1
5-2 Problem 4 Finding the Multiplicity of a Zero
KEY: multiple zero | multiplicity
4
ID: A
40. ANS: D
PTS: 1
DIF: L3
REF: 5-4 Dividing Polynomials
OBJ: 5-4.1 To divide polynomials using long division
NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e
STA: NC 1.03
TOP: 5-4 Problem 1 Using Polynomial Long Division
41. ANS: A
PTS: 1
DIF: L4
REF: 5-4 Dividing Polynomials
OBJ: 5-4.1 To divide polynomials using long division
NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e
STA: NC 1.03
TOP: 5-4 Problem 2 Checking Factors
42. ANS: A
PTS: 1
DIF: L3
REF: 5-4 Dividing Polynomials
OBJ: 5-4.2 To divide polynomials using synthetic division
NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e
STA: NC 1.03
TOP: 5-4 Problem 3 Using Synthetic Division
KEY: synthetic division
43. ANS: C
PTS: 1
DIF: L3
REF: 5-4 Dividing Polynomials
OBJ: 5-4.2 To divide polynomials using synthetic division
NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e
STA: NC 1.03
TOP: 5-4 Problem 5 Evaluating a Polynomial
KEY: synthetic division | remainder theorem
44. ANS: B
PTS: 1
DIF: L2
REF: 5-6 The Fundamental Theorem of Algebra
OBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex
solutions
NAT: CC N.CN.7| CC N.CN.8| CC N.CN.9| CC A.APR.3
TOP: 5-6 Problem 2 Finding All the Zeros of a Polynomial Function
KEY: Rational Root Theorem
45. ANS: A
PTS: 1
DIF: L3
REF: 5-6 The Fundamental Theorem of Algebra
OBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex
solutions
NAT: CC N.CN.7| CC N.CN.8| CC N.CN.9| CC A.APR.3
TOP: 5-6 Problem 2 Finding All the Zeros of a Polynomial Function
KEY: Fundamental Theorem of Algebra
46. ANS: D
PTS: 1
DIF: L3
REF: 5-7 The Binomial Theorem
OBJ: 5-7.2 To use the Binomial Theorem
NAT: CC A.APR.5| D.4.k
TOP: 5-7 Problem 2 Expanding a Binomial
KEY: Binomial Theorem | expand
47. ANS: B
PTS: 1
DIF: L3
REF: 6-2 Multiplying and Dividing Radical Expressions
OBJ: 6-2.1 To multiply and divide radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-2 Problem 4 Dividing Radical Expressions
KEY: simplest form of a radical
48. ANS: A
PTS: 1
DIF: L3
REF: 6-2 Multiplying and Dividing Radical Expressions
OBJ: 6-2.1 To multiply and divide radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-2 Problem 4 Dividing Radical Expressions
KEY: simplest form of a radical
49. ANS: A
PTS: 1
DIF: L3
REF: 6-3 Binomial Radical Expressions
OBJ: 6-3.1 To add and subtract radical expressions
NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.e
TOP: 6-3 Problem 4 Multiplying Binomial Radical Expressions
KEY: like radicals
5
ID: A
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PTS: 1
DIF: L3
REF: 6-4 Rational Exponents
6-4.1 To simplify expressions with rational exponents
NAT: CC N.RN.1| CC N.RN.2
NC 1.01
TOP: 6-4 Problem 1 Simplifying Expressions with Rational Exponents
rational exponents
A
PTS: 1
DIF: L3
REF: 6-4 Rational Exponents
6-4.1 To simplify expressions with rational exponents
NAT: CC N.RN.1| CC N.RN.2
NC 1.01
TOP: 6-4 Problem 5 Simplifying Numbers With Rational Exponents
rational exponent
D
PTS: 1
DIF: L2
6-5 Solving Square Root and Other Radical Equations
6-5.1 To solve square root and other radical equations
NAT: CC A.CED.4| CC A.REI.2| A.2.a
NC 2.07a
TOP: 6-5 Problem 1 Solving a Square Root Equation
square root equation
C
PTS: 1
DIF: L3
6-5 Solving Square Root and Other Radical Equations
6-5.1 To solve square root and other radical equations
NAT: CC A.CED.4| CC A.REI.2| A.2.a
NC 2.07a
TOP: 6-5 Problem 3 Using Radical Equations
square root equation
A
PTS: 1
DIF: L4
REF: 6-7 Inverse Relations and Functions
6-7.1 To find the inverse of a relation or function
NAT: CC F.BF.4.a| CC F.BF.4.c| A.1.j
NC 2.01
TOP: 6-7 Problem 5 Finding the Inverse of a Formula
inverse function
B
PTS: 1
DIF: L2
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.h
NC 1.01
TOP: 7-3 Problem 1 Writing Exponential Equations in Logarithmic Form
write a function in different but equivalent forms
A
PTS: 1
DIF: L2
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.h
NC 1.01
TOP: 7-3 Problem 2 Evaluating a Logarithm
logarithm
B
PTS: 1
DIF: L4
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.h
NC 1.01
TOP: 7-3 Problem 2 Evaluating a Logarithm
logarithm
A
PTS: 1
DIF: L2
REF: 7-4 Properties of Logarithms
7-4.1 To use the properties of logarithms
NAT: CC F.LE.4| N.1.d| A.3.h
NC 1.01
TOP: 7-4 Problem 2 Expanding Logarithms
C
PTS: 1
DIF: L3
REF: 7-4 Properties of Logarithms
7-4.1 To use the properties of logarithms
NAT: CC F.LE.4| N.1.d| A.3.h
NC 1.01
TOP: 7-4 Problem 2 Expanding Logarithms
6
ID: A
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7-5 Exponential and Logarithmic Equations
7-5.1 To solve exponential and logarithmic equations
CC A.REI.11| CC F.LE.4| A.3.h| A.4.c
STA: NC 2.03a
7-5 Problem 1 Solving an Exponential Equation-Common Base
exponential equation
B
PTS: 1
DIF: L3
7-5 Exponential and Logarithmic Equations
7-5.1 To solve exponential and logarithmic equations
CC A.REI.11| CC F.LE.4| A.3.h| A.4.c
STA: NC 2.03a
7-5 Problem 5 Solving a Logarithmic Equation
KEY: logarithmic equation
B
PTS: 1
DIF: L4
REF: 7-6 Natural Logarithms
7-6.2 To solve equations using natural logarithms
NAT: CC F.LE.4| A.3.h
NC 1.01
TOP: 7-6 Problem 2 Solving a Natural Logarithmic Equation
natural logarithmic function
A
PTS: 1
DIF: L2
REF: 7-6 Natural Logarithms
7-6.2 To solve equations using natural logarithms
NAT: CC F.LE.4| A.3.h
NC 1.01
TOP: 7-6 Problem 3 Solving an Exponential Equation
natural logarithmic function
C
PTS: 1
DIF: L3
8-2 The Reciprocal Function Family
8-2.2 To graph translations of reciprocal functions
CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c
STA: NC 1.05
8-2 Problem 3 Graphing a Translation
KEY: reciprocal function
D
PTS: 1
DIF: L3
8-3 Rational Functions and Their Graphs
8-3.1 To identify properties of rational functions
CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h STA: NC 2.05a| NC 2.05b| NC 2.05c
8-3 Problem 3 Finding Horizontal Asymptotes
KEY: rational function
B
PTS: 1
DIF: L3
8-3 Rational Functions and Their Graphs
8-3.1 To identify properties of rational functions
CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h STA: NC 2.05a| NC 2.05b| NC 2.05c
8-3 Problem 3 Finding Horizontal Asymptotes
KEY: rational function
B
PTS: 1
DIF: L3
REF: 8-4 Rational Expressions
8-4.2 To multiply and divide rational expressions
CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
NC 1.03
TOP: 8-4 Problem 2 Multiplying Rational Expressions
rational expression | simplest form
A
PTS: 1
DIF: L3
REF: 8-4 Rational Expressions
8-4.2 To multiply and divide rational expressions
CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
NC 1.03
TOP: 8-4 Problem 3 Dividing Rational Expressions
rational expression | simplest form
B
PTS: 1
DIF: L3
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
NC 1.03
TOP: 8-5 Problem 1 Finding the Least Common Multiple
7
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PTS: 1
DIF: L2
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
NC 1.03
TOP: 8-5 Problem 2 Adding Rational Expressions
A
PTS: 1
DIF: L3
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
NC 1.03
TOP: 8-5 Problem 3 Subtracting Rational Expressions
D
PTS: 1
DIF: L2
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
NC 1.03
TOP: 8-5 Problem 4 Simplifying a Complex Fraction
complex fraction
C
PTS: 1
DIF: L3
REF: 9-1 Mathematical Patterns
9-1.1 To identify mathematical patterns found in a sequence
CC A.SSE.4| A.1.a
9-1 Problem 1 Generating a Sequence Using an Explicit Formula
sequence | term of a sequence | explicit formula
A
PTS: 1
DIF: L2
REF: 9-1 Mathematical Patterns
9-1.1 To identify mathematical patterns found in a sequence
CC A.SSE.4| A.1.a
9-1 Problem 2 Writing a Recursive Definition for a Sequence
sequence | recursive formula | term of a sequence
D
PTS: 1
DIF: L2
REF: 9-2 Arithmetic Sequences
9-2.1 To define, identify, and apply arithmetic sequences NAT: CC F.IF.3| A.1.a
9-2 Problem 1 Identifying Arithmetic Sequences
arithmetic sequence | common difference
D
PTS: 1
DIF: L3
REF: 9-2 Arithmetic Sequences
9-2.1 To define, identify, and apply arithmetic sequences NAT: CC F.IF.3| A.1.a
9-2 Problem 2 Analyzing Arithmetic Sequences
KEY: arithmetic sequence
A
PTS: 1
DIF: L2
REF: 9-3 Geometric Sequences
9-3.1 To define, identify, and apply geometric sequences NAT: CC A.SSE.4| A.1.a
9-3 Problem 1 Identifying Geometric Sequences
KEY: geometric sequence | common ratio
A
PTS: 1
DIF: L3
REF: 9-3 Geometric Sequences
9-3.1 To define, identify, and apply geometric sequences NAT: CC A.SSE.4| A.1.a
9-3 Problem 3 Using a Geometric Sequence
KEY: geometric sequence
C
PTS: 1
DIF: L3
REF: 9-3 Geometric Sequences
9-3.1 To define, identify, and apply geometric sequences NAT: CC A.SSE.4| A.1.a
9-3 Problem 4 Using a Geometric Mean
geometric sequence | geometric mean
B
PTS: 1
DIF: L3
REF: 9-4 Arithmetic Series
9-4.1 To define arithmetic series and find their sums
NAT: CC F.IF.3| A.1.a| A.3.g
9-4 Problem 2 Using the Sum of a Finite Arithmetic Series
series | finite series | limits
D
PTS: 1
DIF: L3
REF: 9-4 Arithmetic Series
9-4.1 To define arithmetic series and find their sums
NAT: CC F.IF.3| A.1.a| A.3.g
9-4 Problem 4 Finding the Sum of a Series
KEY: series | finite series
8
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PTS: 1
DIF: L2
REF: 9-5 Geometric Series
9-5.1 To define geometric series and find their sums
NAT: CC A.SSE.4| A.1.a| A.3.g
9-5 Problem 2 Using the Geometric Series Formula
KEY: geometric series
A
PTS: 1
DIF: L3
REF: 13-1 Exploring Periodic Data
13-1.2 To find the amplitude of periodic functions
NAT: CC F.IF.4| CC F.TF.5
13-1 Problem 4 Using Periodic Functions to Solve a Problem
periodic function | cycle | period | amplitude
A
PTS: 1
DIF: L3
REF: 13-2 Angles and the Unit Circle
13-2.1 To work with angles in standard position
NAT: CC F.TF.2
13-2 Problem 1 Measuring Angles in Standard Position
standard position | initial side | terminal side
B
PTS: 1
DIF: L3
REF: 13-2 Angles and the Unit Circle
13-2.1 To work with angles in standard position
NAT: CC F.TF.2
13-2 Problem 2 Sketching Angles in Standard Position
standard position | initial side | terminal side
D
PTS: 1
DIF: L3
REF: 13-2 Angles and the Unit Circle
13-2.2 To find coordinates of points on the unit circle
NAT: CC F.TF.2
13-2 Problem 4 Finding the Cosines and Sines of Angles KEY: cosine of theta | sine of theta
B
PTS: 1
DIF: L3
REF: 13-2 Angles and the Unit Circle
13-2.2 To find coordinates of points on the unit circle
NAT: CC F.TF.2
13-2 Problem 4 Finding the Cosines and Sines of Angles KEY: cosine of theta
C
PTS: 1
DIF: L3
REF: 13-3 Radian Measure
13-3.1 To use radian measure for angles
NAT: CC F.TF.1| M.3.e
13-3 Problem 1 Using Dimensional Analysis
central angle | intercepted arc | radian
C
PTS: 1
DIF: L3
REF: 13-3 Radian Measure
13-3.1 To use radian measure for angles
NAT: CC F.TF.1| M.3.e
13-3 Problem 2 Finding Cosine and Sine of a Radian Measure
central angle | intercepted arc | radian
A
PTS: 1
DIF: L3
REF: 13-3 Radian Measure
13-3.2 To find the length of an arc of a circle
NAT: CC F.TF.1| M.3.e
13-3 Problem 3 Finding the Length of an Arc
central angle | intercepted arc | radian
C
PTS: 1
DIF: L3
REF: 13-3 Radian Measure
13-3.2 To find the length of an arc of a circle
NAT: CC F.TF.1| M.3.e
13-3 Problem 3 Finding the Length of an Arc
central angle | intercepted arc | radian
A
PTS: 1
DIF: L3
REF: 13-4 The Sine Function
13-4.1 To identify properties of the sine function
CC F.IF.4| CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c
13-4 Problem 2 Finding the Period of a Sine Curve
KEY: sine function | sine curve
B
PTS: 1
DIF: L3
REF: 13-4 The Sine Function
13-4.1 To identify properties of the sine function
CC F.IF.4| CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c
13-4 Problem 3 Finding the Amplitude of a Sine Curve
KEY: sine function | sine curve
A
PTS: 1
DIF: L3
REF: 13-4 The Sine Function
13-4.2 To graph sine curves
NAT: CC F.IF.4| CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c
13-4 Problem 5 Graphing From a Function Rule
KEY: sine function | sine curve
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13-5.1 To graph and write cosine functions
CC F.IF.4| CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c
13-5 Problem 1 Interpreting a Graph
B
PTS: 1
DIF: L3
13-6.1 To graph the tangent function
CC F.IF.7.e| CC F.TF.2| CC F.TF.5| M.3.c
13-6 Problem 1 Finding Tangents Geometrically
D
PTS: 1
DIF: L3
13-7 Translating Sine and Cosine Functions
13-7.2 To write equations of translations
13-7 Problem 5 Writing Translations
D
PTS: 1
DIF: L3
13-8 Reciprocal Trigonometric Functions
13-8.1 To evaluate reciprocal trigonometric functions
13-8 Problem 1 Finding Values Geometrically
REF: 13-5 The Cosine Function
KEY: cosine function
REF: 13-6 The Tangent Function
KEY: tangent of theta | tangent function
NAT: CC F.IF.7.e| CC F.TF.5| A.2.d
KEY: phase shift
NAT: CC F.IF.7.e
KEY: cosecant
1
DIF: L4
REF: 1-3 Algebraic Expressions
1-3.1 To evaluate algebraic expressions
CC A.SSE.1.a| N.1.d| N.3.a| N.3.b| A.3.b| A.3.d
1-3 Problem 3 Evaluating Algebraic Expressions
KEY: evaluate
1
DIF: L2
REF: 3-2 Solving Systems Algebraically
3-2.1 To solve linear systems algebraically
CC A.CED.2| CC A.CED.3| CC A.REI.5| CC A.REI.6| A.4.d
NC 2.10
TOP: 3-2 Problem 3 Solving by Elimination
system of linear equations | solve by elimination
10