Download Algebra 2 Fall Final Review Answer Section

Algebra 2 Fall Final Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Evaluate the given expression if x = 25, y = 10, w = 14, and z = 4.
a. 785
2. Find the value of
b. 575
c. 1785
d. –335
if n = 4, b = 4, and a = 40,000.
a. 156.25
b. 1562.5
3. Find the value of
a. –9000
if
b. 900
c. 2500
,
, and
.
c. 990
4. The flow rate of IV fluids is calculated using the formula
d. 10,000
d. 9000
, where V is the volume of the solution
in milliliters, d is the drip factor in drips per minute, and t is the time in minutes. Determine the flow rate of
1500 milliliter IV fluid for a patient for 24 hours if the drip factor is 1 milliliter per minute.
a. 1.04
b. 25
c. 10.4
d. 6.25
5. The formula to calculate the volume of a cylinder is
the cylinder.
x + 3
. Write an expression to represent the volume of
a.
b.
c.
d.
6. The formulas to find the area of an equilateral triangle are
, and
4
.
4
4
Using these formulas, find the altitude of the given triangle.
a.
b. 4
c.
7. Find the value of
a. 156.25
if n = 3,
b. 15,625
, and
d. 8
.
c. 156,250
d. 250,000
Simplify the given expression.
8.
a.
b.
c.
d.
a.
b.
c.
d.
9.
Write an algebraic expression to represent the following verbal expression.
10. eight more than the product of a number and 100
a.
b.
c.
d.
11. ten less than the cube of a number
a.
b.
c.
d.
12. the cube of the quotient of a number and 24
a.
b.
c.
d.
13. the product of the square of a number and
a.
b.
c.
d.
Write a verbal expression to represent the given equation.
14.
a.
b.
c.
d.
The square of a number is equal to 32.
The square of a number is equal to the product of 23 and that number.
The square of a number is equal to the product of 32 and that number.
The square of a number is equal to the product of that number.
a.
b.
c.
d.
Four times the cube of a number is equal to the number plus two.
Four times a number is equal to the number plus two.
Four times the cube of a number is equal to the number.
The cube of a number is equal to the number plus two.
a.
b.
c.
d.
Three plus half of a number is equal to 4 divided by that number.
Three plus half of a number is equal to 4 divided by the cube of that number.
Three plus half of a number is equal to 4 divided by the square of that number.
Three plus a number is equal to 4 divided by the square of that number.
15.
16.
17. Evaluate the given expression if m = 45.
a. –135
b. 339
c. 135
d. 45
c. –10
d. 706
18. Evaluate the given expression if k = –84.
a. –34
b. 34
Solve the given equation. Check your solution.
19.
a. {35, 29}
b. {35, –19}
c. {35, 19}
d. {–35, –19}
a. {1.97, –3.03}
b. {–1.97, –3.03}
c. {29.5, –3.03}
d. {–1.97, 3.03}
20.
Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the
solution set on a number line.
21.
a. The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
b. The solution set is
–10 –9 –8 –7 –6
c. The solution set is
–10 –9 –8 –7 –6
d. The solution set is
–1
0
1
2
3
4
5
6
7
8
9
10
–1
0
1
2
3
4
5
6
7
8
9
10
–1
0
1
2
3
4
5
6
7
8
9
10
.
–5 –4 –3 –2
.
–5 –4 –3 –2
.
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
–1
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
–1
0
1
2
3
4
5
6
7
8
9
10
–1
0
1
2
3
4
5
6
7
8
9
10
–1
0
1
2
3
4
5
6
7
8
9
10
–1
0
1
2
3
4
5
6
7
8
9
10
22.
a. The solution set is {1.65}.
–10 –9 –8 –7 –6
–5 –4 –3 –2
b. The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
–1
c. The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
–1
d. The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
23.
a.
The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
b.
The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
c.
The solution set is
.
–10 –9 –8 –7 –6
–5 –4 –3 –2
The solution set is
.
d.
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
24.
a. The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
–1
0
b. The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
–1
c. The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
–1
d. The solution set is
–10 –9 –8 –7 –6
.
–5 –4 –3 –2
–1
0
25. The workers in a factory earn $25 an hour. Every week, 20% of each worker’s total pay is deducted for taxes.
If each worker wants a take-home salary of at least $620 a week, solve the inequality
to determine how many hours each worker must work.
a. at the most 31
c. 31
b. at least 31
d. at least 3.1
26. Mary’s parents gave her $60 as pocket money to meet her daily expenses. She spent $20 on clothes and $10
on food. She wishes to buy some books, also. If each book costs $3 each, solve the inequality
to
find how many books she can buy.
a. at the most 10
c. 10
b. at least 10
d. at the most 5
Solve the given inequality. Graph the solution set on a number line.
27.
or
a.
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9 –8 –7 –6
–5 –4 –3 –2
–1
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
b.
c.
d.
28.
or
a.
b.
c.
d.
29.
and
a.
–12 –11 –10 –9 –8 –7 –6 –5 –4
b.
–3 –2 –1
9
10 11 12
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
8
9
10 11 12
c.
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
8
9
10 11 12
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
8
9
10 11 12
1
2
3
4
5
6
7
8
9
10 11 12
d.
30.
a. The solution set is
or
.
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
b. The solution set is
or
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
c. The solution set is
–12 –11 –10 –9 –8 –7 –6 –5 –4
d. The solution set is
0
.
0
1
2
3
4
5
6
7
8
9
10 11 12
1
2
3
4
5
6
7
8
9
10 11 12
0
1
2
3
4
5
0
2
4
6
8
or
–3 –2 –1
.
0
or
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
.
6
7
8
9
10 11 12
31.
a. The solution set is {p | p > 6 or p < 1}.
–24 –22 –20 –18 –16 –14 –12 –10 –8 –6 –4 –2
10 12 14
16 18 20 22
24
b. The solution set is {p | p > –5 or p < 5}.
–24 –22 –20 –18 –16 –14 –12 –10 –8 –6 –4 –2
0
2
4
6
8
10 12 14 16 18 20 22 24
c. The solution set is {p | p > 7 or p < –5}.
–24 –22 –20 –18 –16 –14 –12 –10 –8 –6 –4 –2
d. The solution set is {p | –5 < p < 7}.
0
2
4
6
8
10 12 14 16 18 20 22 24
–22 –20 –18 –16 –14 –12 –10 –8 –6 –4 –2
0
2
4
6
8
10 12 14 16 18 20 22
32. Find the value of f(–9) and g(4) if
a. f(–9) = 44
g(4) = 25.56
b. f(–9) = –16
g(4) = –53.69
and
c. f(–9) = 4
g(4) = 49.06
d. f(–9) = 28
g(4) = 22.44
.
33. Find the value of f(–9) and g(–2) if
a. f(–9) = –7
g(–2) = 19
b. f(–9) = 47
g(–2) = –83
and
c. f(–9) = 43
g(–2) = 54
d. f(–9) = 10
g(–2) = –27
.
24
34. State whether the given equation or function is linear. Write yes or no. Explain your reasoning.
8x + 25y = 5
a. No, the equation is not linear. It is in the form x + y = c.
b. No, the equation is not linear.
c. Yes, the equation is linear. It is in the form Ax + By = C.
d. Yes, the equation is in linear form. It is in the form xy = C.
35. State whether the given equation or function is linear. Write yes or no. Explain your reasoning.
f(x) = 3x + 2
a. No, the equation is not linear. It is not of the form f(x) = mx + b.
b. No, the equation is not linear. It is in the form x + y = c.
c. Yes, the equation is linear. It is of the form f(x) = m + b
d. Yes, the equation is linear. It is of the form f(x)= mx + b
36. Write the equation 10y = 12x + 0.7 in standard form. Identify A, B, and C.
a.
where
,
, and
.
b.
where
,
, and
.
c.
where
,
, and
.
d.
where
,
, and
.
37. Write the equation
a.
b.
c.
d.
where
where
where
where
,
in standard form. Identify A, B, and C.
,
, and
, and
, and
,
,
, and
.
.
.
.
38. Find the slope of the line that passes through the pair of points (17, 11) and (21, 19).
a. 19
c. 19
3
15
b. 2
d.
17
–
8
39. Find the slope of the line that passes through the pair of points (–1, –3) and (–8, 10).
a. 5
c.
8
–
11
13
b. –8
d.
13
–
7
40. Find the slope of the line that passes through the pair of points (5, 12) and (–5.5, –7.5).
a. –1.4
c. 1.86
b. –0.36
d. 0.54
41. Find the slope of the line that passes through the pair of points (–6.1, 1.25) and (0.35, 8.9).
a. 0.06
c. 0.96
b. 1.19
d. 0.84
42. Find the slope of the line that passes through the pair of points (
a.
 18
185
b.
 185
18
c.
 289
3, 330
d. 88, 434
185
10 2
9 13
,
) and ( ,
).
17 17
17 18
43. Write an equation in slope-intercept form for the line that satisfies the following condition.
slope 5 and passes through (2, 28)
a. y =
c. y =
b. y =
d. y =
44. Write an equation in slope-intercept form for the line that satisfies the following condition.
1
slope
and passes through (4, –17)
2
a. y =
c.
1
y=
2
b.
d.
1
4
y=
y=
2
17
45. Write an equation in slope-intercept form for the line that satisfies the following condition.
8
passes through (8, 10), parallel to the graph of y = x + 7
3
a.
c.
34
8
34
y = 6x –
y= x–
3
3
3
b.
d.
8
8
8
y = 16x +
y= x+
3
3
3
46. Write an equation in slope-intercept form for the line that satisfies the following condition.
passes through (6, 11), parallel to the line that passes through (2, 4) and (23, 23)
a.
c.
19
39
19
y=
x
y=
x 6
21
7
21
b.
d.
39
39
19
y=
x
y = 19x +
7
7
21
47. Write an equation in slope-intercept form for the line that satisfies the following condition.
1
passes through (29, 8), perpendicular to the graph of y =
x + 17
13
a.
c.
1
1
y = 385x +
y=
x + 385
13
13
b. y = 13x + 385
d. y = 13x + (13)
48. Write an equation in slope-intercept form for the line that satisfies the following condition.
passes through (10, 16), perpendicular to the graph of 9x + 12y = 15
a.
c.
4
4
4
y= x+
y = 10x +
3
3
3
b.
d. y = 10x + 12
4
8
y= x+
3
3
49. Graph the given inequality.
a.
c.
y
–5
–4
–3
–2
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
–3
–2
–4
–3
–2
–1
–1
–2
–3
–3
–4
–4
–5
–5
d.
y
–4
–5
x
–2
b.
–5
y
5
5
4
4
3
3
2
2
1
1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
50. Graph the given inequality.
y9–|x|
2
3
4
5
x
1
2
3
4
5
x
y
5
–1
–1
1
a.
c.
y
–20 –16 –12 –8
20
20
16
16
12
12
8
8
4
4
–4
–4
4
8
12
16
20
–20 –16 –12 –8
x
–4
–4
–8
–8
–12
–12
–16
–16
–20
–20
b.
d.
y
–20 –16 –12 –8
y
20
16
16
12
12
8
8
4
4
4
8
12
16
20
–20 –16 –12 –8
x
8
12
16
20
x
4
8
12
16
20
x
4
8
12
16
20
x
y
20
–4
–4
4
–4
–4
–8
–8
–12
–12
–16
–16
–20
–20
51. Graph the given inequality.
a.
c.
y
–20 –16 –12 –8
y
20
20
16
16
12
12
8
8
4
4
–4
–4
4
8
12
16
20
x
–20 –16 –12 –8
–4
–4
–8
–8
–12
–12
–16
–16
–20
–20
b.
d.
y
–20 –16 –12 –8
y
20
20
16
16
12
12
8
8
4
4
–4
–4
4
8
12
16
20
x
–20 –16 –12 –8
–4
–4
–8
–8
–12
–12
–16
–16
–20
–20
4
8
12
16
20
x
Solve the following system of equations
52.
a. (–1, 5)
b. (1, 7)
c. (5, 1)
d. (1, 5)
a. (2, 21)
b. (21, 2)
c. (4, 20)
d. (1, 21)
53.
Graph each system of equations and describe it as consistent and independent, consistent and dependent,
inconsistent, or none of these.
54.
a. consistent and independent
b. inconsistent
c. consistent and dependent
d. none of these
a. inconsistent
b. consistent and independent
c. consistent and dependent
d. none of these
55.
Solve each system of equations by using substitution.
56. 8x + 7y = 18
3x – 5y = 22
a. (–2, 4)
b. (3, –2)
c. (4, –2)
d. (4, 0)
57.
a. (4, –0.5)
b. (5.5, 3)
c. (4, –1)
d. (2, –1)
Solve each system of equations by using elimination.
58.
a. (6, –1)
b. (3.75, 2)
c. (5, 0.5)
d. (5, –1)
a. (1, 0)
b. (2, 0)
c. (3, –0.5)
d. (2, 0.25)
59.
Solve the system of inequalities by graphing.
60. x > 2
y>8
a.
14
c.
y
y
12
12
10
10
8
8
6
6
4
4
2
2
–8
–6
–4
–10 –8
–2
–2
2
4
6
8
10
12
–6
–4
–2
–2
x
14
–4
8
10
x
4
6
8
10
12
x
–8
–8
–6
6
–6
–6
–10 –8
4
–4
–4
b.
2
d.
y
14
12
12
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
x
–8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
y
2
Solve the given system of equations.
61. –3a = 36
10a + 3c = 9
2b + 5c = 23
a. a = –12, b = –96, c = 43
b. a = –12, b = 43, c = –96
c. a = 12, b = –96, c = 43
d. a = 43, b = –12, c = –96
62. 11a + 2c = 10
–2a = 32
8b + 10c = 18
a. a = –16, b = –114, c = 93
b. a = 16, b = –114, c = 93
c. a = –16, b = 93, c = –114
d. a = 93, b = –16, c = –114
63. Consider the quadratic function
symmetry.
a. The y-intercept is –2.
. Find the y-intercept and the equation of the axis of
1
The equation of the axis of symmetry is x =  .
2
b.
1
The y-intercept is .
2
The equation of the axis of symmetry is x = 2.
c. The y-intercept is + 2.
The equation of the axis of symmetry is x =
d.
1
.
2
1
The y-intercept is  .
2
The equation of the axis of symmetry is x = –2.
Determine whether the given function has a maximum or a minimum value. Then, find the maximum or
minimum value of the function.
64.
a.
b.
c.
d.
The function has a maximum value. The maximum value of the function is 1.
The function has a maximum value. The maximum value of the function is 5.
The function has a minimum value. The minimum value of the function is 1.
The function has a minimum value. The minimum value of the function is 5.
a.
b.
c.
d.
The function has a minimum value. The minimum value of the function is 8.
The function has a minimum value. The minimum value of the function is 4.
The function has a maximum value. The maximum value of the function is 4.
The function has a maximum value. The maximum value of the function is 8.
65.
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which
the roots are located.
66.
a.
The c.
f(x)
2
2
1
1
–4 –3 –2 –1
–1
1
2
3
4
5
6
7
8
x
–4 –3 –2 –1
–1
–2
–2
–3
–3
–4
–4
–5
–5
–6
–6
–7
–7
–8
–8
–9
–9
–10
–10
solution set is
b.
.
The
f(x)
1
2
3
4
5
solution set is
7
8
x
.
d.
f(x)
6
The
f(x)
2
6
1
5
–4 –3 –2 –1–1
1
2
3
4
5
6
7
8
4
x
–2
3
–3
2
–4
1
–5
–4 –3 –2 –1
–1
–6
1
2
3
4
5
6
7
8
x
–2
–7
–3
–8
–4
–9
–5
–10
–6
The solution set is
.
solution set is
.
67.
a.
6
5
4
4
3
3
2
2
1
1
1
2
3
4
5
6
7
x
–7 –6 –5 –4 –3 –2 –1
–1
–2
–2
–3
–3
–4
–4
–5
–5
–6
–6
.
solution set is
The
f(x)
6
5
–7 –6 –5 –4 –3 –2 –1
–1
solution set is
The c.
f(x)
1
.
2
3
4
5
6
7
x
b.
6
5
5
4
4
3
3
2
2
1
1
–7 –6 –5 –4 –3 –2 –1
–1
solution set is
The d.
f(x)
6
1
2
3
4
5
6
7
x
–7 –6 –5 –4 –3 –2 –1
–1
–2
–2
–3
–3
–4
–4
–5
–5
–6
–6
.
solution set is
The
f(x)
1
2
3
4
5
6
7
x
.
68.
a.
One c.
f(x)
–4
f(x)
6
6
4
4
2
2
–2
2
4
6
8
10
x
–4
–2
2
–2
–2
–4
–4
–6
–6
solution is between 3 and 4, while the other solution is between
0 and 1.
4
6
8
solution is between –3 and 0, while the other so
between –4 and –1.
b.
One d.
f(x)
–4
f(x)
6
6
4
4
2
2
–2
2
4
6
8
10
x
–4
2
–2
–2
–4
–4
–6
–6
solution is between –3 and –1, while the other solution is
between 0 and –4.
69. –5 and 2
a.
b.
c.
d.
5
70.  and 8
4
a.
b.
c.
d.
Solve the equation by factoring.
71.
c.
d.
4
6
8
solution is between –3 and –4, while the other s
between 0 and –1.
Write a quadratic equation with the given roots. Write the equation in the form
and c are integers.
a.
b.
–2
, where a, b,
72.
a.
7
{–4,  }
2
b.
7
{ , 2 }
2
c. {–4, 7}
d. {2, 7}
Solve the equation by completing the square.
73.
a.
b.
c.
d.
a.
b.
c.
d.
74.
Find the exact solution of the following quadratic equation by using the Quadratic Formula.
75.
a.
b.
c.
d.
a.
c.
b.
d.
76.
Find the value of the discriminant. Then describe the number and type of roots for the equation.
77.
a. The discriminant is 196. Because the discriminant is greater than 0 and is a perfect square,
the two roots are real and rational.
b. The discriminant is –204. Because the discriminant is less than 0, the two roots are
complex.
c. The discriminant is 204. Because the discriminant is greater than 0 and is not a perfect
square, the two roots are real and irrational.
d. The discriminant is –188. Because the discriminant is less than 0, the two roots are
complex.
Write the following quadratic function in vertex form. Then, identify the axis of symmetry.
78.
a. The vertex form of the function is
The equation of the axis of symmetry is
b. The vertex form of the function is
The equation of the axis of symmetry is
c. The vertex form of the function is
.
.
The equation of the axis of symmetry is
.
d. The vertex form of the function is
The equation of the axis of symmetry is
.
79.
a. The vertex form of the function is
The equation of the axis of symmetry is
b. The vertex form of the function is
The equation of the axis of symmetry is
c. The vertex form of the function is
The equation of the axis of symmetry is
d. The vertex form of the function is
The equation of the axis of symmetry is
.
.
.
.
.
.
.
.
Algebra 2 Fall Final Review
Answer Section
MULTIPLE CHOICE
1. ANS: A
Evaluate the expression by replacing each variable with its corresponding number and then applying the order
of operations.
Feedback
A
B
C
D
Correct!
Did you calculate correctly?
Did you substitute the correct values?
Did you perform all the calculations?
PTS: 1
DIF: Basic
REF: Lesson 1-1
OBJ: 1-1.1 Use the order of operations to evaluate expressions.
NAT: NA 1 | NA 4 | NA 9 | NA 2
STA: 3.2PO2
TOP: Use the order of operations to evaluate expressions.
KEY: Evaluate Expressions
MSC: 1998 Lesson 1-1
2. ANS: A
Find the value of 4 raised to the power of 4. Then, divide a with the value obtained.
Feedback
A
B
C
D
Correct!
Check the position of the decimal point.
Did you use the correct value of the denominator?
In the denominator the power of b is 4.
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.2 Use formulas.
NAT: NA 1 | NA 4 | NA 9 | NA 2
STA: 3.2PO2
TOP: Use formulas.
KEY: Formulas
MSC: 1998 Lesson 1-1
3. ANS: A
Substitute the values of x, y, and n in the given equation to obtain the value of the given equation.
Feedback
A
B
C
D
Correct!
Did you consider the exponent value of y?
Did you calculate correctly?
Check the sign of the answer.
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.2 Use formulas.
NAT: NA 1 | NA 4 | NA 9 | NA 2
STA: 3.2PO2
TOP: Use formulas.
KEY: Formulas
MSC: 1998 Lesson 1-1
4. ANS: A
Substitute the known values in the formula to find the value of the remaining variable.
Feedback
A
Correct!
B
C
D
Did you divide the numerator by the denominator?
Check the position of the decimal point.
The flow rate should be in minutes.
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.2 Use formulas.
NAT: NA 1 | NA 4 | NA 9 | NA 2
STA: 3.2PO2
TOP: Use formulas.
KEY: Formulas
MSC: 1998 Lesson 1-1
5. ANS: B
Substitute each given value into the formula. Then, evaluate the expression using the order of operations.
Feedback
A
B
C
D
x + 3 is the diameter of the cylinder.
Correct!
What is the formula for finding the volume of the cylinder?
Did you substitute the radius correctly?
PTS:
NAT:
KEY:
6. ANS:
1
DIF: Average
REF: Lesson 1-1
NA 1 | NA 4 | NA 9 | NA 2
STA: 3.2PO2
Formulas
MSC: 1998 Lesson 1-1
C
Find the area using the formula
OBJ: 1-1.2 Use formulas.
TOP: Use formulas.
, and then use the first formula to find the altitude.
Feedback
A
B
C
D
Did you calculate correctly?
Did you use the correct formula to find the area of the triangle?
Correct!
You have used an incorrect formula to find the altitude.
PTS: 1
DIF: Advanced
REF: Lesson 1-1
OBJ: 1-1.2 Use formulas.
NAT: NA 1 | NA 4 | NA 9 | NA 2
STA: 3.2PO2
TOP: Use formulas.
KEY: Formulas
MSC: 1998 Lesson 1-1
7. ANS: B
Substitute the value of n, a, and b in the given expression to find the needed value.
Feedback
A
B
C
D
Did you use the correct value of n in the numerator?
Correct!
Did you calculate correctly?
Use the value of bn, not b.
PTS: 1
DIF: Basic
REF: Lesson 1-1
OBJ: 1-1.2 Use formulas.
NAT: NA 1 | NA 4 | NA 9 | NA 2
STA: 3.2PO2
TOP: Use formulas.
KEY: Formulas
MSC: 1998 Lesson 1-1
8. ANS: B
Use the properties of real numbers to simplify the given expression.
Feedback
A
Did you simplify the entire expression?
B
C
D
Correct!
Did you interchange the coefficients?
Did you calculate correctly?
PTS: 1
DIF: Average
REF: Lesson 1-2
OBJ: 1-2.2 Use the properties of real numbers to evaluate expressions.
NAT: NA 1 | NA 9 TOP: Use the properties of real numbers to evaluate expressions.
KEY: Real Numbers | Evaluate Expressions
MSC: 1998 Lesson 1-2
9. ANS: B
Apply the Distributive Law and simplify the given expression to get the required answer.
Feedback
A
B
C
D
Did you simplify the coefficient of y?
Correct!
You have calculated an incorrect coefficient of y.
Did you simplify the coefficient of x?
PTS: 1
DIF: Advanced
REF: Lesson 1-2
OBJ: 1-2.2 Use the properties of real numbers to evaluate expressions.
NAT: NA 1 | NA 9 TOP: Use the properties of real numbers to evaluate expressions.
KEY: Real Numbers | Evaluate Expressions
MSC: 1998 Lesson 1-2
10. ANS: A
Represent the expression by using appropriate numbers and variables.
Feedback
A
B
C
D
Correct!
The given expression is eight more than the product.
The coefficient of x is incorrect.
You have taken the difference of eight and 100 times the number.
PTS: 1
DIF: Average
REF: Lesson 1-3
OBJ: 1-3.1 Translate verbal expressions into algebraic expressions.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate verbal expressions into algebraic expressions.
KEY: Translate Expressions | Verbal Expressions | Algebraic Expressions
MSC: 1998 Lesson 1-4
11. ANS: A
Read each term of the given expression carefully and represent it algebraically.
Feedback
A
B
C
D
Correct!
Did you interchange 10 and the number?
Did you transform the correct equation?
Find the difference of the cube of the number and 10, not the cube of the difference of
the number and 10.
PTS:
OBJ:
NAT:
KEY:
1
DIF: Basic
REF: Lesson 1-3
1-3.1 Translate verbal expressions into algebraic expressions.
NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate verbal expressions into algebraic expressions.
Translate Expressions | Verbal Expressions | Algebraic Expressions
MSC: 1998 Lesson 1-4
12. ANS: C
Interpret each word of the given expression carefully to get the required expression.
Feedback
A
B
C
D
Find the cube of both numerator and denominator.
Did you interchange the number and 24?
Correct!
Did you transform the correct expression?
PTS: 1
DIF: Basic
REF: Lesson 1-3
OBJ: 1-3.1 Translate verbal expressions into algebraic expressions.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate verbal expressions into algebraic expressions.
KEY: Translate Expressions | Verbal Expressions | Algebraic Expressions
MSC: 1998 Lesson 1-4
13. ANS: D
Read the entire expression carefully and interpret it algebraically.
Feedback
A
B
C
D
Did you find the square of the number?
Did you transform the correct expression?
Check the sign of the expression.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 1-3
OBJ: 1-3.1 Translate verbal expressions into algebraic expressions.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate verbal expressions into algebraic expressions.
KEY: Translate Expressions | Verbal Expressions | Algebraic Expressions
MSC: 1998 Lesson 1-4
14. ANS: C
Read the algebraic expression and represent it verbally.
Feedback
A
B
C
D
You have not written the entire expression.
Check the values in the equation.
Correct!
You have missed one of the values in the equation.
PTS: 1
DIF: Average
REF: Lesson 1-3
OBJ: 1-3.2 Translate algebraic equations into verbal expressions.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate algebraic equations into verbal expressions.
KEY: Translate Equations | Verbal Expressions
MSC: 1998 Lesson 1-4
15. ANS: A
Read the given expression and represent it verbally.
Feedback
A
B
C
Correct!
Did you forget the exponent value of m?
You have not written the complete expression.
D
You have missed one of the values in the equation.
PTS: 1
DIF: Basic
REF: Lesson 1-3
OBJ: 1-3.2 Translate algebraic equations into verbal expressions.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate algebraic equations into verbal expressions.
KEY: Translate Equations | Verbal Expressions
MSC: 1998 Lesson 1-4
16. ANS: C
Read the given expression and represent it verbally.
Feedback
A
B
C
D
Did you forget the exponent value of the number?
Did you write the correct expression?
Correct!
Check the coefficient of x.
PTS: 1
DIF: Average
REF: Lesson 1-3
OBJ: 1-3.2 Translate algebraic equations into verbal expressions.
NAT: NA 1 | NA 4 | NA 6 | NA 9 | NA 2 TOP: Translate algebraic equations into verbal expressions.
KEY: Translate Equations | Verbal Expressions
MSC: 1998 Lesson 1-4
17. ANS: C
For any real number a, if a is positive or zero, the absolute value of a is a. If a is negative, the absolute value
of a is the opposite of a.
Feedback
A
B
C
D
The absolute value cannot be negative.
Did you multiply correctly?
Correct!
This is the absolute value of the given number.
PTS: 1
DIF: Basic
REF: Lesson 1-4
OBJ: 1-4.1 Evaluate expressions involving absolute values.
NAT: NA 1 | NA 9 | NA 10 | NA 2
STA: 3.2PO1
TOP: Evaluate expressions involving absolute values.
KEY: Evaluate Expressions | Absolute Value
MSC: 1998 Lesson 1-5
18. ANS: B
For any real number a, if a is positive or zero, the absolute value of a is a. If a is negative, the absolute value
of a is the opposite of a. Substitute the value of k in the equation and solve it.
Feedback
A
B
C
D
Did you use absolute values in the calculation?
Correct!
You have not performed all of the required calculations.
Did you perform the correct arithmetic operation?
PTS: 1
DIF: Average
REF: Lesson 1-4
OBJ: 1-4.1 Evaluate expressions involving absolute values.
NAT: NA 1 | NA 9 | NA 10 | NA 2
STA: 3.2PO1
TOP: Evaluate expressions involving absolute values.
KEY: Evaluate Expressions | Absolute Value
MSC: 1998 Lesson 1-5
19. ANS: B
For any real numbers a and b, where
, if
, then
, or
.
Feedback
A
B
C
D
Did you calculate correctly?
Correct!
Did you consider the negative value of (m – 1)?
Did you use the correct sign of each value?
PTS: 1
DIF: Average
REF: Lesson 1-4
OBJ: 1-4.2 Solve absolute value equations.
STA: 3.2PO1
TOP: Solve absolute value equations.
MSC: 1998 Lesson 1-5
20. ANS: B
For any real numbers a and b, where
, if
, then
NAT: NA 1 | NA 9 | NA 10 | NA 2
KEY: Solve Equations | Absolute Value
, or
.
Feedback
A
B
C
D
Did you verify the solution in the original equation?
Correct!
Did you use the correct values for calculations?
Did you use the correct sign in the solution?
PTS: 1
DIF: Average
REF: Lesson 1-4
OBJ: 1-4.2 Solve absolute value equations.
STA: 3.2PO1
TOP: Solve absolute value equations.
MSC: 1998 Lesson 1-5
21. ANS: A
Solve the inequality and then graph the solution.
NAT: NA 1 | NA 9 | NA 10 | NA 2
KEY: Solve Equations | Absolute Value
Feedback
A
B
C
D
Correct!
Did you calculate correctly?
Did you verify the solution in the given inequality?
Did you use the correct values for your graph?
PTS: 1
DIF: Basic
REF: Lesson 1-5
OBJ: 1-5.1 Solve inequalities with one operation.
TOP: Solve inequalities with one operation.
MSC: 1998 Lesson 1-6
22. ANS: D
Solve the inequality and then graph the solution.
NAT: NA 1 | NA 6 | NA 9 | NA 2
KEY: Solve Inequalities
Feedback
A
B
C
D
Did you verify the solution in the given inequality?
Did you use the correct values for calculation?
Did you switch the inequality sign when you divided by a negative number?
Correct!
PTS: 1
DIF: Average
REF: Lesson 1-5
OBJ: 1-5.1 Solve inequalities with one operation.
TOP: Solve inequalities with one operation.
NAT: NA 1 | NA 6 | NA 9 | NA 2
KEY: Solve Inequalities
MSC: 1998 Lesson 1-6
23. ANS: D
Solve the inequality and then graph the solution.
Feedback
A
B
C
D
Did you use the correct inequality?
Did you solve the given inequality correctly?
Did you use the correct values for the graph?
Correct!
PTS: 1
DIF: Average
REF: Lesson 1-5
OBJ: 1-5.2 Solve inequalities with fractions with one operation.
NAT: NA 1 | NA 6 | NA 9 | NA 2
TOP: Solve inequalities with fractions with one operation.
KEY: Solve Inequalities | Fractions
MSC: 1998 Lesson 1-6
24. ANS: B
Solve the given inequality and then plot the graph.
Feedback
A
B
C
D
Did you solve the correct inequality?
Correct!
Did you verify the solution in the given inequality?
Did you plot the graph correctly?
PTS: 1
DIF: Average
REF: Lesson 1-5
OBJ: 1-5.4 Solve multi-step inequalities with distribution.
NAT: NA 1 | NA 6 | NA 9 | NA 2
TOP: Solve multi-step inequalities with distribution.
KEY: Solve Inequalities | Distribution
MSC: 1998 Lesson 1-6
25. ANS: B
Solve the given inequality to determine the number of hours each worker must work.
Feedback
A
B
C
D
Did you use the correct inequality?
Correct!
Solve the inequality, not the equation.
Check the position of the decimal point.
PTS: 1
DIF: Average
REF: Lesson 1-5
OBJ: 1-5.5 Solve real-world multi-step inequalities.
TOP: Solve real-world multi-step inequalities.
KEY: Solve Inequalities | Real-World Problems
26. ANS: A
Use the given inequality to find the number of textbooks.
Feedback
A
B
C
D
Correct!
Did you solve the correct inequality?
Solve the inequality, not the equation.
Did you use the correct values for the calculation?
NAT: NA 1 | NA 6 | NA 9 | NA 2
MSC: 1998 Lesson 1-6
PTS: 1
DIF: Advanced
REF: Lesson 1-5
OBJ: 1-5.5 Solve real-world multi-step inequalities.
TOP: Solve real-world multi-step inequalities.
KEY: Solve Inequalities | Real-World Problems
27. ANS: C
Solve the given inequality and then plot the graph.
NAT: NA 1 | NA 6 | NA 9 | NA 2
MSC: 1998 Lesson 1-6
Feedback
A
B
C
D
Did you solve the second equation correctly?
Did you verify the solution in the given inequalities?
Correct!
Did you use the correct inequalities in the calculation?
PTS: 1
DIF: Advanced
REF: Lesson 1-6
OBJ: 1-6.1 Solve compound inequalities with or.
TOP: Solve compound inequalities with or.
KEY: Solve Inequalities | Compound Inequalities
28. ANS: D
Solve the inequalities and then plot the graph.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
MSC: 1998 Lesson 1-7
Feedback
A
B
C
D
Did you solve the second inequality correctly?
Did you solve the first inequality correctly?
Did you solve the inequalities correctly?
Correct!
PTS: 1
DIF: Advanced
REF: Lesson 1-6
OBJ: 1-6.1 Solve compound inequalities with or.
TOP: Solve compound inequalities with or.
KEY: Solve Inequalities | Compound Inequalities
29. ANS: B
Solve the given equation and obtain the required solution.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
MSC: 1998 Lesson 1-7
Feedback
A
B
C
D
Did you solve the second equation correctly?
Correct!
Did you use the given inequality correctly for all of the calculations?
Did you verify the solution?
PTS: 1
DIF: Advanced
REF: Lesson 1-6
OBJ: 1-6.2 Solve compound inequalities with and.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
TOP: Solve compound inequalities with and.
KEY: Solve Inequalities | Compound Inequalities
MSC: 1998 Lesson 1-7
30. ANS: D
Solve the given inequality and plot the solution on a number line.
Feedback
A
B
Did you use the correct information for the calculation?
The value used for the calculation is incorrect.
C
D
You have plotted the graph incorrectly.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 1-6
OBJ: 1-6.3 Solve absolute value inequalities.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
TOP: Solve absolute value inequalities.
KEY: Solve Inequalities | Absolute Value
MSC: 1998 Lesson 1-7
31. ANS: D
Solve the inequality and plot the solution on a number line.
Feedback
A
B
C
D
Did you plot the solution on the number line correctly?
Did you apply the correct values for the calculation?
You have used incorrect symbols to represent the inequality.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 1-6
OBJ: 1-6.3 Solve absolute value inequalities.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
TOP: Solve absolute value inequalities.
KEY: Solve Inequalities | Absolute Value
MSC: 1998 Lesson 1-7
32. ANS: A
Substitute x = –9 in the equation f(x) and x = 4 in the equation g(x).
Feedback
A
B
C
D
Correct!
You have to substitute the values of f(x) and g(x) in the subsequent equations.
Did you substitute the value in f(x) as well?
You have subtracted instead of adding.
PTS: 1
DIF: Average
REF: Lesson 2-1
OBJ: 2-1.2 Find functional values.
NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: 3.2PO2
TOP: Find functional values.
KEY: Functional Values | Functions
MSC: 1998 Lesson 2-1
33. ANS: C
Substitute x = –9 in the equation f(x) and x = –2 in the equation g(x).
Feedback
A
B
C
D
Substitute the value in f(x) as well.
You have subtracted instead of adding.
Correct!
You have to substitute the values of f(x) and g(x) in the subsequent equations.
PTS: 1
DIF: Average
REF: Lesson 2-1
OBJ: 2-1.2 Find functional values.
NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: 3.2PO2
TOP: Find functional values.
KEY: Functional Values | Functions
MSC: 1998 Lesson 2-1
34. ANS: C
The standard form of a linear equation is Ax + By = C.
Feedback
A
B
C
D
What is the standard form for a linear equation?
Did you explain your reasoning?
Correct!
Is this the standard form of a linear equation according to the definition of linear
equations?
PTS: 1
DIF: Average
REF: Lesson 2-2
OBJ: 2-2.1 Identify linear equations and functions.
NAT: NA 1 | NA 4 | NA 8 | NA 10 | NA 2
STA: 3.2PO1
TOP: Identify linear equations and functions.
KEY: Linear Equations | Functions
MSC: 1998 Lesson 2-2
35. ANS: D
Any linear function can be written in the form f(x) = mx + b, where m and b are real numbers.
Feedback
A
B
C
D
Is the given equation in a linear form?
Did you perform the mathematical actions correctly?
What is the form of this equation?
Correct!
PTS: 1
DIF: Average
REF: Lesson 2-2
OBJ: 2-2.1 Identify linear equations and functions.
NAT: NA 1 | NA 4 | NA 8 | NA 10 | NA 2
STA: 3.2PO1
TOP: Identify linear equations and functions.
KEY: Linear Equations | Functions
MSC: 1998 Lesson 2-2
36. ANS: D
The standard form of the equation is Ax + By = C, where
and A and B are non-zero numbers.
Feedback
A
B
C
D
What is the standard form of linear equations?
What is the coefficient of y?
Did you apply the mathematical operators correctly?
Correct!
PTS: 1
DIF: Basic
REF: Lesson 2-2
OBJ: 2-2.2 Write linear equations in standard form.
NAT: NA 1 | NA 4 | NA 8 | NA 10 | NA 2
TOP: Write linear equations in standard form.
KEY: Linear Equations | Standard Form
MSC: 1998 Lesson 2-2
37. ANS: C
The standard form of the equation is Ax + By = C, where
and A and B are non-zero numbers.
Feedback
A
B
C
D
What is the standard form of linear equations?
What is the coefficient of y?
Correct!
Is the equation in standard form?
PTS: 1
DIF: Basic
REF: Lesson 2-2
OBJ: 2-2.2 Write linear equations in standard form.
TOP: Write linear equations in standard form.
NAT: NA 1 | NA 4 | NA 8 | NA 10 | NA 2
KEY: Linear Equations | Standard Form
MSC: 1998 Lesson 2-2
38. ANS: B
The slope of a line is the ratio of the change in the y-coordinates to the corresponding change in the
x-coordinates.
Slope =
Substitute the values of
,
,
, and
to find the slope of the line.
Feedback
A
B
C
D
Did you calculate the ratio of change in the y-coordinates to the change in the
x-coordinates?
Correct!
The values of x- and y-coordinates are to be subtracted and not added.
Is this the correct ratio of change in the y-coordinates to the change in the
x-coordinates?
PTS: 1
DIF: Average
REF: Lesson 2-3
OBJ: 2-3.1 Find and use the slope of a line with integer points. NAT: NA 1 | NA 4 | NA 7 | NA 8 | NA 2
TOP: Find and use the slope of a line with integer points.
KEY: Slope | Integers | Graphs
MSC: 1998 Lesson 2-3
39. ANS: D
The slope of a line is the ratio of the change in the y-coordinates to the corresponding change in the
x-coordinates.
That is, the slope of a line =
Substitute the values of
.
,
,
, and
to find the slope of the line.
Feedback
A
B
C
D
Did you calculate the ratio of change in the y-coordinates to the change in the
x-coordinates?
Is this the correct ratio of change in the y-coordinates to the change in the
x-coordinates?
The values of x- and y-coordinates are to be subtracted and not added.
Correct!
PTS:
OBJ:
TOP:
MSC:
40. ANS:
1
DIF: Average
REF: Lesson 2-3
2-3.1 Find and use the slope of a line with integer points.
Find and use the slope of a line with integer points.
1998 Lesson 2-3
C
The slope of a line is
NAT: NA 1 | NA 4 | NA 7 | NA 8 | NA 2
KEY: Slope | Integers | Graphs
.
Substitute the values of x1, y1, x2, and y2 to find the slope of the line.
Feedback
A
B
C
Find the difference in y values and the difference in x values.
Is this the correct ratio of change in y-coordinates to change in x-coordinates?
Correct!
D
You have to calculate the ratio of change in y-coordinates to the change in
x-coordinates.
PTS:
OBJ:
NAT:
KEY:
41. ANS:
1
DIF: Average
REF: Lesson 2-3
2-3.2 Find and use the slope of a line with decimal points.
NA 1 | NA 4 | NA 7 | NA 8 | NA 2 TOP: Find and use the slope of a line with decimal points.
Slope | Decimals | Graphs
MSC: 1998 Lesson 2-3
B
The slope of a line is
.
Substitute the values of x1, y1, x2, and y2 to find the slope of the line.
Feedback
A
B
C
D
Did you calculate the ratio of change in the y-coordinates to the change in
x-coordinates?
Correct!
Is this the correct ratio of change in y-coordinates to the change in x-coordinates?
You have to calculate the ratio of change in the y-coordinates to ratio of change in the
x-coordinates.
PTS:
OBJ:
NAT:
KEY:
42. ANS:
1
DIF: Advanced
REF: Lesson 2-3
2-3.2 Find and use the slope of a line with decimal points.
NA 1 | NA 4 | NA 7 | NA 8 | NA 2 TOP: Find and use the slope of a line with decimal points.
Slope | Decimals | Graphs
MSC: 1998 Lesson 2-3
B
The slope of a line is
.
Substitute the values of x1, y1, x2, and y2 to find the slope of the line.
Feedback
A
B
C
D
You have to calculate the ratio of change in y-coordinates to the change in
x-coordinates.
Correct!
You have to calculate all the values of fractions to obtain the slope of the line.
Did you calculate the ratio of change in the y-coordinates to the change in the
x-coordinates?
PTS: 1
DIF: Advanced
REF: Lesson 2-3
OBJ: 2-3.3 Find and use the slope of a line with fractional points.
NAT: NA 1 | NA 4 | NA 7 | NA 8 | NA 2 TOP: Find and use the slope of a line with fractional points.
KEY: Slope | Fractions | Graphs
MSC: 1998 Lesson 2-3
43. ANS: D
Substitute the values of the x- and y-coordinates in the equation
. Manipulate the equation
to get it in the slope-intercept form.
Feedback
A
B
Did you calculate the value of the slope correctly?
You have to substitute the values of x- and y-coordinates to obtain the slope-intercept
C
D
equation.
The slope-intercept equation has to include the value of slope as well.
Correct!
PTS: 1
DIF: Advanced
REF: Lesson 2-4
OBJ: 2-4.1 Write an equation of a line given the slope and a point on the line.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
TOP: Write an equation of a line given the slope and a point on the line.
KEY: Equations of Lines | Slope | Graphs
MSC: 1998 Lesson 2-4
44. ANS: B
Substitute values of the x- and y-coordinates in the equation
. Manipulate the equation to
get it in the slope-intercept form.
Feedback
A
B
C
D
You have to substitute the values of x- and y-coordinates to acquire the slope-intercept
equation.
Correct!
Did you calculate the value of y-intercept correctly?
Did you calculate the value of the slope correctly?
PTS: 1
DIF: Advanced
REF: Lesson 2-4
OBJ: 2-4.1 Write an equation of a line given the slope and a point on the line.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
TOP: Write an equation of a line given the slope and a point on the line.
KEY: Equations of Lines | Slope | Graphs
MSC: 1998 Lesson 2-4
45. ANS: C
The point-slope form of the equation of a line is
, where
are the coordinates of a
point on the line and m is the slope of the line.
Feedback
A
B
C
D
Substitute the values of x- and y-coordinates in slope formula to calculate the slope.
You have to calculate the ratio of change in x- and y-coordinates.
Correct!
You have calculated the value of y-intercept incorrectly.
PTS: 1
DIF: Advanced
REF: Lesson 2-4
OBJ: 2-4.2 Write an equation of a line parallel to a given line.
TOP: Write an equation of a line parallel to a given line.
KEY: Parallel Lines | Equations of Parallel Lines
46. ANS: A
The point-slope form of the equation of a line is
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
MSC: 1998 Lesson 2-4
, where
are the coordinates of a
point on the line and m is the slope of the line.
Feedback
A
B
C
D
Correct!
Substitute the values of the x- and y-coordinates in slope formula to calculate the slope.
You have calculated the value of y-intercept incorrectly.
You have to calculate the ratio of change in x- and y-coordinates.
PTS: 1
DIF: Advanced
REF: Lesson 2-4
OBJ: 2-4.2 Write an equation of a line parallel to a given line.
TOP: Write an equation of a line parallel to a given line.
KEY: Parallel Lines | Equations of Parallel Lines
47. ANS: B
The point-slope form of the equation of a line is
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
MSC: 1998 Lesson 2-4
, where
are the coordinates of a
point on the line and m is the slope of the line. The slopes of perpendicular lines are opposite reciprocals.
Feedback
A
B
C
D
What must the slope be if the line is perpendicular to the given line?
Correct!
The slope value is incorrect.
Did you calculate the y-intercept correctly?
PTS: 1
DIF: Advanced
REF: Lesson 2-4
OBJ: 2-4.3 Write an equation of a line perpendicular to a given line.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
TOP: Write an equation of a line perpendicular to a given line.
KEY: Perpendicular Lines | Equations of Perpendicular Lines
MSC: 1998 Lesson 2-4
48. ANS: B
The point-slope form of the equation of a line is
, where
are the coordinates of a
point on the line and m is the slope of the line. The slopes of perpendicular lines are opposite reciprocals.
Feedback
A
B
C
D
Substitute the value for the y-intercept.
Correct!
You have to calculate the slope using slope formula.
The slope value is incorrect.
PTS: 1
DIF: Advanced
REF: Lesson 2-4
OBJ: 2-4.3 Write an equation of a line perpendicular to a given line.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
TOP: Write an equation of a line perpendicular to a given line.
KEY: Perpendicular Lines | Equations of Perpendicular Lines
MSC: 1998 Lesson 2-4
49. ANS: C
Plotting the x-coordinates and the y-coordinates gives a graph of the inequality.
Feedback
A
B
C
D
You have performed the division incorrectly.
Calculate the x- and y-coordinates using correct mathematical operators.
Correct!
You have multiplied instead of divided.
PTS:
NAT:
KEY:
50. ANS:
1
DIF: Average
REF: Lesson 2-8
NA 1 | NA 6 | NA 9 | NA 10 | NA 2
Linear Inequalities | Graphs | Graph Inequalities
B
OBJ: 2-8.1 Graph linear inequalities.
TOP: Graph linear inequalities.
MSC: 1998 Lesson 2-7
Plotting the x-coordinates and the y-coordinates gives a graph of the inequality.
Feedback
A
B
C
D
Choose a point not on the boundary and test it in the inequality.
Correct!
Did you graph the boundary function correctly?.
You have performed addition instead of subtraction.
PTS: 1
DIF: Average
REF: Lesson 2-8
OBJ: 2-8.1 Graph linear inequalities.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
TOP: Graph linear inequalities.
KEY: Linear Inequalities | Graphs | Graph Inequalities
MSC: 1998 Lesson 2-7
51. ANS: B
Plot points for different values of x and y to get a Cartesian graph of the inequality.
Feedback
A
B
C
D
You can test a point on the shaded region to determine which region to shade.
Correct!
Did you substitute the correct values for graphing the inequality?
You have to perform addition and not subtraction.
PTS: 1
DIF: Advanced
REF: Lesson 2-8
OBJ: 2-8.2 Graph absolute value inequalities.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
TOP: Graph absolute value inequalities.
KEY: Absolute Value | Absolute Value Inequalities | Graphs | Graph Inequalities
MSC: 1998 Lesson 2-7
52. ANS: D
Graph the equations and find their point of intersection.
Feedback
A
B
C
D
What is the x-coordinate of the intersection?
Did you graph both equations correctly?
Write the coordinates of the intersection carefully.
Correct!
PTS: 1
DIF: Average
REF: Lesson 3-1
OBJ: 3-1.1 Solve systems of linear equations by graphing.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
STA: 3.3PO3
TOP: Solve systems of linear equations by graphing.
KEY: System of Linear Equations | Graphs
MSC: 1998 Lesson 3-1
53. ANS: A
Graph the equations and find their point of intersection.
Feedback
A
B
C
D
Correct!
Did you plot the graphs correctly?
Did you read the intersection of the graphs correctly?
What is the x-coordinate of the intersection?
PTS: 1
DIF: Average
REF: Lesson 3-1
OBJ: 3-1.1 Solve systems of linear equations by graphing.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
STA: 3.3PO3
TOP: Solve systems of linear equations by graphing.
KEY: System of Linear Equations | Graphs
MSC: 1998 Lesson 3-1
54. ANS: B
Graph the equations and check the number of solutions.
Feedback
A
B
C
D
Did you check the number of solutions?
Correct!
Are the y-intercepts equal?
Did you find the slope of each line?
PTS: 1
DIF: Average
REF: Lesson 3-1
OBJ: 3-1.2 Determine whether a system of linear equations is consistent and independent, consistent and
dependent, or inconsistent.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Determine whether a system of linear equations is consistent and independent, consistent and
dependent, or inconsistent.
KEY: System of Linear Equations | Consistent System | Inconsistent System
MSC: 1998 Lesson 3-1
55. ANS: B
Graph the equations and check the number of solutions.
Feedback
A
B
C
D
Are the slopes equal?
Correct!
Are the y-intercepts equal?
Did you plot the graphs correctly?
PTS: 1
DIF: Average
REF: Lesson 3-1
OBJ: 3-1.2 Determine whether a system of linear equations is consistent and independent, consistent and
dependent, or inconsistent.
NAT: NA 1 | NA 8 | NA 9 | NA 10 | NA 2
TOP: Determine whether a system of linear equations is consistent and independent, consistent and
dependent, or inconsistent.
KEY: System of Linear Equations | Consistent System | Inconsistent System
MSC: 1998 Lesson 3-1
56. ANS: C
By using the method of substitution, solve one equation for one variable in terms of the other variable. Then,
substitute this expression for the variable in the other equation.
Feedback
A
B
C
D
Did you calculate the values correctly?
Recalculate the value of x.
Correct!
Recalculate the value of y.
PTS:
OBJ:
NAT:
KEY:
57. ANS:
1
DIF: Average
REF: Lesson 3-2
3-2.1 Solve systems of linear equations by using substitution.
NA 1 | NA 6 | NA 7 | NA 9 | NA 2 TOP: Solve systems of linear equations by using substitution.
System of Linear Equations | Substitution
MSC: 1998 Lesson 3-2
C
By using the method of substitution, solve one equation for one variable in terms of the other variable. Then,
substitute this expression for the variable in the other equation.
Feedback
A
B
C
D
Recalculate the value of s.
Did you calculate correctly?
Correct!
Recalculate the value of r.
PTS: 1
DIF: Average
REF: Lesson 3-2
OBJ: 3-2.1 Solve systems of linear equations by using substitution.
NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 TOP: Solve systems of linear equations by using substitution.
KEY: System of Linear Equations | Substitution
MSC: 1998 Lesson 3-2
58. ANS: D
Use the method of elimination to obtain the required answer.
Feedback
A
B
C
D
Recalculate the value of p.
Did you calculate the values correctly?
Recalculate the value of q.
Correct!
PTS: 1
DIF: Average
REF: Lesson 3-2
OBJ: 3-2.2 Solve systems of linear equations by using elimination.
NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 TOP: Solve systems of linear equations by using elimination.
KEY: System of Linear Equations | Elimination
MSC: 1998 Lesson 3-2
59. ANS: B
Use the method of elimination to obtain the required answer.
Feedback
A
B
C
D
Recalculate the value of a.
Correct!
Did you calculate the values correctly?
Recalculate the value of b.
PTS: 1
DIF: Average
REF: Lesson 3-2
OBJ: 3-2.2 Solve systems of linear equations by using elimination.
NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 TOP: Solve systems of linear equations by using elimination.
KEY: System of Linear Equations | Elimination
MSC: 1998 Lesson 3-2
60. ANS: C
Both the inequalities should be plotted and the region common to both should be shaded.
Feedback
A
B
C
D
You have plotted the first inequality incorrectly.
You have plotted the second inequality incorrectly.
Correct!
You have plotted the inequalities incorrectly.
PTS: 1
DIF: Average
REF: Lesson 3-3
OBJ: 3-3.1 Solve systems of inequalities by graphing.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: 4.3PO1
TOP: Solve systems of inequalities by graphing.
KEY: System of Inequalities | Graphs
MSC: 1998 Lesson 3-4
61. ANS: A
Solve three equations simultaneously.
Feedback
A
B
C
D
Correct!
Check whether the values of the variables have been interchanged.
Only two of the values are correct.
The values of a, b, and c are interchanged.
PTS: 1
DIF: Average
REF: Lesson 3-5
OBJ: 3-5.1 Solve systems of linear equations in three variables.
NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: 3.3PO3
TOP: Solve systems of linear equations in three variables.
KEY: System of Equations | Three Variables
MSC: 1998 Lesson 3-7
62. ANS: A
Solve three equations simultaneously.
Feedback
A
B
C
D
Correct!
Only two of the values are correct.
Check whether the values of the variables have been interchanged.
The values of a, b, and c are interchanged.
PTS: 1
DIF: Average
REF: Lesson 3-5
OBJ: 3-5.1 Solve systems of linear equations in three variables.
NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2
STA: 3.3PO3
TOP: Solve systems of linear equations in three variables.
KEY: System of Equations | Three Variables
MSC: 1998 Lesson 3-7
63. ANS: C
For the quadratic equation
, the y-intercept is c and the equation of axis of
symmetry is
.
Feedback
A
B
C
D
Did you check the signs?
Did you interchange the y-intercept and the x-coordinate of the vertex?
Correct!
Did you use the correct formulas for the y-intercept and the x-coordinate of the vertex?
PTS: 1
DIF: Average
REF: Lesson 5-1
OBJ: 5-1.1 Graph quadratic functions.
NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3
STA: 3.2PO6
TOP: Graph quadratic functions.
KEY: Quadratic Functions | Graph Quadratic Functions
MSC: 1998 Lesson 6-1
64. ANS: C
The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the
function.
Feedback
A
B
C
D
The coefficient of x2 is greater than zero.
The graph of this function opens up.
Correct!
What is the value of the y-coordinate of the vertex?
PTS: 1
DIF: Average
REF: Lesson 5-1
OBJ: 5-1.2 Find and interpret the maximum and minimum values of a quadratic function.
NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3
TOP: Find and interpret the maximum and minimum values of a quadratic function.
KEY: Maximum Values | Minimum Values | Quadratic Functions
MSC: 1998 Lesson 6-1
65. ANS: D
The y-coordinate of the vertex of a quadratic function is the maximum or minimum value obtained by the
function.
Feedback
A
B
C
D
The graph of the function opens down.
The coefficient of x2 is less than zero.
What is the value of the y-coordinate of the vertex?
Correct!
PTS: 1
DIF: Average
REF: Lesson 5-1
OBJ: 5-1.2 Find and interpret the maximum and minimum values of a quadratic function.
NAT: NA 2 | NA 6 | NA 8 | NA 10 | NA 3
TOP: Find and interpret the maximum and minimum values of a quadratic function.
KEY: Maximum Values | Minimum Values | Quadratic Functions
MSC: 1998 Lesson 6-1
66. ANS: B
The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic
equation because
at those points.
Feedback
A
B
C
D
What are the x-intercepts of the graph?
Correct!
Find the zeros of the function, not the vertex.
The zeros of the function are the solutions of the related equation.
PTS: 1
DIF: Advanced
REF: Lesson 5-2
OBJ: 5-2.1 Solve quadratic equations by graphing.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: 3.2PO1
TOP: Solve quadratic equations by graphing.
KEY: Quadratic Equations | Solve Quadratic Equations
MSC: 1998 Lesson 6-1
67. ANS: A
The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic
equation because
at those points.
Feedback
A
Correct!
B
C
D
The zeros of the function are the solutions of the related equation.
What are the x-intercepts of the graph?
Find the zeros of the function, not the vertex.
PTS: 1
DIF: Advanced
REF: Lesson 5-2
OBJ: 5-2.1 Solve quadratic equations by graphing.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: 3.2PO1
TOP: Solve quadratic equations by graphing.
KEY: Quadratic Equations | Solve Quadratic Equations
MSC: 1998 Lesson 6-1
68. ANS: D
When exact roots cannot be found by graphing, you can estimate solutions by stating the consecutive integers
between which the roots are located.
Feedback
A
B
C
D
Is the coefficient of x2 less than zero?
Did you graph the function correctly?
When the coefficient of x2 is greater than 0, the graph opens up.
Correct!
PTS: 1
DIF: Advanced
REF: Lesson 5-2
OBJ: 5-2.2 Estimate solutions of quadratic equations by graphing.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 2
STA: 3.2PO1
TOP: Estimate solutions of quadratic equations by graphing.
KEY: Quadratic Equations | Solve Quadratic Equations
MSC: 1998 Lesson 6-1
69. ANS: D
A quadratic equation with roots p and q can be written as
, which can be further simplified.
Feedback
A
B
C
D
Did you verify the answer by substituting the values?
Did you calculate the coefficients correctly?
Did you check the signs of the coefficients?
Correct!
PTS: 1
DIF: Average
REF: Lesson 5-3
OBJ: 5-3.1 Write quadratic equations in intercept form.
TOP: Write quadratic equations in intercept form.
KEY: Quadratic Equations | Roots of Quadratic Equations
70. ANS: A
A quadratic equation with roots p and q can be written as
NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2
MSC: 1998 Lesson 6-2 | 1998 Lesson 6-5
, which can be further simplified.
Feedback
A
B
C
D
Correct!
Did you check the signs of the coefficients?
Did you calculate the coefficients correctly?
Did you verify the answer by substituting the values?
PTS:
OBJ:
TOP:
KEY:
1
DIF: Average
REF: Lesson 5-3
5-3.1 Write quadratic equations in intercept form.
Write quadratic equations in intercept form.
Quadratic Equations | Roots of Quadratic Equations
NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2
MSC: 1998 Lesson 6-2 | 1998 Lesson 6-5
71. ANS: B
For any real numbers a and b, if
, then either
,
, or both a and b are equal to zero.
Feedback
A
B
C
D
Did you use the Zero Product Property correctly?
Correct!
Did you verify the answer by substituting the values?
Did you factor the binomial correctly?
PTS: 1
DIF: Average
REF: Lesson 5-3
OBJ: 5-3.2 Solve quadratic equations by factoring.
NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2
STA: 3.2PO1
TOP: Solve quadratic equations by factoring.
KEY: Quadratic Equations | Solve Quadratic Equations | Factoring
MSC: 1998 Lesson 6-2 | 1998 Lesson 6-5
72. ANS: B
For any real numbers a and b, if
, then either
,
, or both a and b are equal to zero.
Feedback
A
B
C
D
Did you use the Zero Product Property correctly?
Correct!
Did you factor the binomial correctly?
Did you verify the answer by substituting the values?
PTS: 1
DIF: Average
REF: Lesson 5-3
OBJ: 5-3.2 Solve quadratic equations by factoring.
NAT: NA 1 | NA 3 | NA 7 | NA 8 | NA 2
STA: 3.2PO1
TOP: Solve quadratic equations by factoring.
KEY: Quadratic Equations | Solve Quadratic Equations | Factoring
MSC: 1998 Lesson 6-2 | 1998 Lesson 6-5
73. ANS: A
To complete the square for any quadratic expression of the form
, find half of b, and square the result.
Then, add the result to
.
Feedback
A
B
C
D
Correct!
Did you make the quadratic expression a perfect square?
Did you verify the answer by substituting the values?
Did you check the signs of the roots?
PTS: 1
DIF: Average
REF: Lesson 5-5
OBJ: 5-5.2 Solve quadratic equations by completing the square.
NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2
STA: 3.2PO1
TOP: Solve quadratic equations by completing the square.
KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square
MSC: 1998 Lesson 6-3
74. ANS: D
To complete the square for any quadratic expression of the form
, find half of b, and square the result.
Then, add the result to
.
Feedback
A
B
C
D
Did you make the quadratic expression a perfect square?
Did you check the signs of the roots?
Find both the solutions.
Correct!
PTS: 1
DIF: Average
REF: Lesson 5-5
OBJ: 5-5.2 Solve quadratic equations by completing the square.
NAT: NA 1 | NA 3 | NA 7 | NA 10 | NA 2
STA: 3.2PO1
TOP: Solve quadratic equations by completing the square.
KEY: Quadratic Equations | Solve Quadratic Equations | Completing the Square
MSC: 1998 Lesson 6-3
75. ANS: D
The solution of a quadratic equation of the form
, where
, is obtained by using the
formula
.
Feedback
A
B
C
D
Did you check the signs of the solution?
Did you use the correct formula?
Did you substitute the values of a, b, and c correctly in the formula?
Correct!
PTS: 1
DIF: Average
REF: Lesson 5-6
OBJ: 5-6.1 Solve quadratic equations by using the Quadratic Formula.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: 3.2PO1
TOP: Solve quadratic equations by using the Quadratic Formula.
KEY: Quadratic Equations | Solve Quadratic Equations | Quadratic Formula
MSC: 1998 Lesson 6-4
76. ANS: D
The solution of a quadratic equation of the form
, where
, is obtained by using the
formula
.
Feedback
A
B
C
D
Did you substitute the values of a, b, and c correctly in the formula?
Did you evaluate the discriminant correctly?
Did you use the correct formula?
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
MSC:
77. ANS:
If
1
DIF: Average
REF: Lesson 5-6
5-6.1 Solve quadratic equations by using the Quadratic Formula.
NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: 3.2PO1
Solve quadratic equations by using the Quadratic Formula.
Quadratic Equations | Solve Quadratic Equations | Quadratic Formula
1998 Lesson 6-4
C
and
is a perfect square, then the roots are rational.
If
and
is not a perfect square, then the roots are real and irrational.
Feedback
A
B
C
D
Did you use the correct formula for the discriminant?
Did you check the sign of the answer?
Correct!
Did you use the correct order of operations while evaluating the discriminant?
PTS: 1
DIF: Basic
REF: Lesson 5-6
OBJ: 5-6.2 Use the discriminant to determine the number and types of roots of a quadratic equation.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP: Use the discriminant to determine the number and types of roots of a quadratic equation.
KEY: Quadratic Equations | Roots of Quadratic Equations | Discriminates
MSC: 1998 Lesson 6-4
78. ANS: A
The vertex form of a quadratic function is
.
The equation of the axis of symmetry of a parabola is
.
Feedback
A
B
C
D
Correct!
Did you check the x-coordinate of the vertex?
Did you identify the coordinates of the vertex correctly?
Did you use the correct equation of the axis of symmetry of a parabola?
PTS: 1
DIF: Basic
REF: Lesson 5-7
OBJ: 5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k.
NAT: NA 2 | NA 7 | NA 8 | NA 10 | NA 6
TOP: Analyze quadratic functions in the form y = a(x - h)^2 + k.
KEY: Quadratic Functions | Axis of Symmetry
MSC: 1998 Lesson 6-6
79. ANS: C
The vertex form of a quadratic function is
.
The equation of the axis of symmetry of a parabola is
.
Feedback
A
B
C
D
Did you use the correct equation of the axis of symmetry?
Did you check the x-coordinate of the vertex?
Correct!
Did you identify the coordinates of the vertex correctly?
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Basic
REF: Lesson 5-7
5-7.1 Analyze quadratic functions in the form y = a(x - h)^2 + k.
NA 2 | NA 7 | NA 8 | NA 10 | NA 6
Analyze quadratic functions in the form y = a(x - h)^2 + k.
Quadratic Functions | Axis of Symmetry
MSC: 1998 Lesson 6-6