Download Math 100 practice test 1.tst

Practice Test #1: These are practice problems to help for the test. This all of the quizzes and homework and the book should
be reviewed for the test._
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the equation.
1) 2(x + 7) = (2x + 14)
1)
2) (y - 4) - (y + 3) = 8y
2)
3) 4(y + 8) = 5(y - 5)
3)
4)
2x x
- =5
5
3
4)
5)
b
- 6 = -2
17
5)
6)
6x
-7x + 6 5
+ =7
7
7
6)
Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
7) 5(4g + 3) - 20g - 15 = 0
7)
8) 20k + 42 = 5(4k + 8)
8)
9) 4(24t + 12) = 16(4t + 5)
9)
Use the variable x for the unknown. Write an equation representing the verbal sentence and solve the problem.
10) If 5 times a number is added to -8, the result is equal to 13 times the number.
10)
11) When
1
of a number is added to 24, the result is 37.
4
Solve the problem.
12) A biologist collected 298 fern and moss samples. There were 102 fewer ferns than moss
samples. How many fern samples did the biologist collect?
11)
12)
13) In a local election, 47,600 people voted. This was an increase of 13% over the last election.
How many people voted in the last election?
13)
14) It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator
now has 20 liters of 20% solution. How many liters of this should be drained and replaced
with 100% antifreeze to get the desired strength?
14)
1
Solve the investment problem.
15) Roberto invested some money at 8%, and then invested $2000 more than twice this amount
at 12%. His total annual income from the two investments was $4720. How much was
invested at 12%?
16) How many liters of a 30% alcohol solution must be mixed with 20 liters of a 70% solution
to get a 40% solution?
Solve the inequality, giving its solution set in both interval and graph forms.
17) -9x ≤ 90
15)
16)
17)
18) 8 + 4x + 8 ≥ 3x + 18
18)
19) -2(5z + 4) < -12z + 2
19)
20) -30 ≤ 5(x - 1) ≤ 5
20)
-6
-4
-2
0
2
4
6
8
10
12
14
21) -10 < 3x + 2 ≤ 2
21)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
22) 6 ≤
3x - 1
≤9
2
22)
Let A = {q, s, u, v, w, x, y, z}, B = {q, s, y, z}, C = {v, w, x, y, z}, and D = {s}. List the elements in the following set.
23) C ∪ B
23)
24) B ∩ C
24)
25) C ∩ D
25)
2
For the compound inequality, give the solution set in both interval and graph forms.
26) x ≤ -2 and x ≥ 7
27) 5x + 1 ≥ 11 and 5x + 1 ≤ 31
-7 -6 -5 -4 -3 -2 -1 0
27)
1
2
3
4
5
6
7
28) 4x > 4 and x + 5 < 5
-6
-5
-4
-3
-2
26)
28)
-1
0
1
2
3
4
5
6
29) x < 4 or x < 8
29)
30) 2x + 2 ≤ -8 or 2x + 2 ≥ -2
30)
Express the set in simplest interval form.
31) (-6, 5) ∪ [0, 7]
31)
Solve.
32)
b-9 =9
33) 5 -
32)
1
x =4
8
33)
Solve the inequality and graph the solution set.
34) k + 8 > 7
-18 -16 -14 -12 -10 -8 -6 -4 -2 0 2
4
34)
6 8 10 12 14 16 18
35) 5 - x ≤ 8
-35
-30
35)
-25
-20
-15
-10
-5
0
5
10
15
20
25
36) m - 5 < 0
30
35
36)
-10
-5
0
5
37) |h - 9|+ 4 ≤ 9
10
37)
3
38) 4x - 1 ≥ 2
-14 -12 -10 -8
38)
-6
-4
-2
0
2
4
6
8
10
12
14
Solve the equation.
39) 2s + 3 = s - 2
39)
Solve the equation or inequality.
40) |5x - 5| > -4
40)
41) |6x - 5| < -8
41)
Graph the equation by determining the missing values needed to plot the ordered pairs.
42) y + x = 4; (3, ), (4, ), (1, )
42)
y
10
5
-10
-5
5
10
x
-5
-10
Find the x- and y-intercepts. Then graph the equation.
43) 6x - 18y = 18
43)
y
10
5
-10
-5
5
10
x
-5
-10
Find the midpoint of the segment with the given endpoints.
44) (-8, -3) and (7, 0)
44)
4
45) (-5.3, 2.2) and (-0.8, -6.8)
45)
Find the slope of the line.
46)
46)
y
10
5
-10
-5
5
10
x
-5
-10
47)
47)
y
10
5
-10
-5
5
10
x
-5
-10
Find the slope of the line through the pair of points.
48) (7, -4) and (9, 1)
48)
5
Find the slope of the line, and sketch the graph.
49) y = 4x
49)
y
10
5
-10
-5
5
10
x
-5
-10
50) y + 4 = 0
50)
y
10
5
-10
-5
5
10
x
-5
-10
Graph the line.
51) Through (-2, 9); slope undefined
51)
y
10
5
-10
-5
5
10
x
-5
-10
6
52) Through (-2, -1); m = 3
52)
y
10
5
-10
-5
5
10
x
-5
-10
Decide whether the pair of lines is parallel, perpendicular, or neither.
53) The line through (-20, 5) and (-4, 7) and the line through (-5, 5) and (7, 4)
53)
54) 3x - 6y = 19 and 18x + 9y = 14
54)
55) 12x + 4y = 16 and 18x + 6y = 27
55)
Solve the problem. Round your answer, as needed.
56) A deep sea diving bell is being lowered at a constant rate. After 8 minutes, the bell is at a
depth of 300 ft. After 40 minutes the bell is at a depth of 1900 ft. What is the average rate of
lowering per minute?
Find the equation in slope-intercept form of the line satisfying the conditions.
1
57) m = ; through (0, 4)
2
56)
57)
Write the equation in slope-intercept form, state the slope and y-intercept, and graph the equation.
58) 3x - 6y = -18
58)
8
y
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
7
59) x + 6y = 30
59)
8
y
6
4
2
-8
-6
-4
-2
2
4
8 x
6
-2
-4
-6
-8
Write the equation in standard form of the line satisfying the given conditions.
3
60) Through (0, 5); m = 4
61) Through (-4, 0); m = -9
61)
Write the equation in standard form of the line through the given points.
62) (6, 0) and (-3, 5)
63) (7, -4) and (5, 1)
65) Through (-3, 8); perpendicular to -3x + 4y = -23
66)
y
10
5
5
10
64)
65)
Graph the linear inequality in two variables.
66) 5x - y ≤ -1
-5
62)
63)
Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form.
64) Through (-6, 5); parallel to -7x + 5y = 57
-10
60)
x
-5
-10
8
Graph the compound inequality.
67) x + y ≥ 2 and y ≤ 2
67)
y
4
2
-4
-2
2
6x
4
-2
-4
-6
68) 2x + y ≤ 4 and x - 1 > 0
68)
y
4
2
-4
-2
2
6x
4
-2
-4
-6
69) 2x + y < 6 or 3x - 2y > 5
69)
y
10
5
-10
-5
5
10
x
-5
-10
9
70) 3x + y ≥ 3 or x - 4y ≤ 1
70)
y
10
5
-10
-5
5
10
x
-5
-10
Decide whether the relation is a function.
71) {(-6, -1), (-2, -9), (3, 9), (6, -1)}
71)
72) {(-8, 2), (-8, 8), (1, -5), (4, -6), (8, -2)}
72)
Give the domain and range of the relation.
73) {(3, 3), (-3, -3), (-7, -7), (5, 5)}
73)
Decide whether the relation is a function, and give the domain and range.
74)
74)
y
10
5
-10
-5
5
10
x
-5
-10
Determine whether the relation defines y as a function of x. Give the domain.
75) y = 4x - 2
76) 3x = 13 - 5y
77) y =
75)
76)
3
x + 19
77)
Solve the problem.
78) Find g(a - 1) when g(x) = 2x - 5.
78)
10
79) Find f(1) when f(x) = x2 - 2x - 4.
79)
80) Find f(-6) when f = {(2, 9), (-2, -8), (-6, -4), (6, 0)}.
80)
An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation
f(x).
81) 5x - 6y = 5
81)
Graph the linear or constant function. Give the domain and range.
1
82) g(x) = x
6
6
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
11
82)
Answer Key
Testname: MATH 100 PRACTICE TEST 1
1) {All real numbers}
7
2) 8
26) φ
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
3) {57}
4) {75}
5) {68}
6) 11
7) Identity; {all real numbers}
8) Contradiction; ∅
9) Conditional; {1}
10) 5x + (-8) = 13x; -1
1
11) x + 24 = 37; 52
4
27) [2, 6]
-7 -6 -5 -4 -3 -2 -1 0
2
3
4
5
6
7
28) ∅
29) (-∞, 8)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
30) (-∞, -5] ∪ [-2, ∞)
12) 98 fern samples
13) 42,124 people
14) 5 liters
15) $30,000
16) 60 liters
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
31) (-6, 7]
32) {18, 0}
33) {8, 72}
34) (-∞, -15) ∪ (-1, ∞)
17) [-10, ∞)
-15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-18 -16 -14 -12 -10 -8 -6 -4 -2 0
-5
2
4 6
8 10 12 14 16 18
35) [-3, 13]
18) [2, ∞)
-5
1
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
-35
9
-30
-25
-20
-15
-10
-5
0
5
10
36) ∅
19) (-∞, 5)
37) [4, 14]
-2
-1
0
1
2
3
4
5
6
7
8
9
10 11 12
38) -∞, -
20) [-5, 2]
-6
-4
-2
0
2
4
6
8
10
12
14
-14 -12 -10 -8
21) (-4, 0]
39) - 5, 40) (-∞, ∞)
41) ∅
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
22)
1
3
∪ ,∞
4
4
13 19
,
3 3
13
3
19
3
23) {q, s, v, w, x, y, z}
24) {y, z}
25) ∅
12
1
3
-6
-4
-2
0
2
4
6
8
10 12 14
15
Answer Key
Testname: MATH 100 PRACTICE TEST 1
42)
49) Slope: 4
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
43) (3, 0); (0, -1)
44) -
10
x
5
10
x
50) Slope: 0
y
-10
5
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
1
3
,2
2
51)
y
45) (-3.05, -2.3)
46) 1
47) Undefined
5
48)
2
10
5
-10
-5
5
-5
-10
13
10
x
Answer Key
Testname: MATH 100 PRACTICE TEST 1
52)
1
x + 5;
6
59) y = -
y
10
slope: -
1
, y-intercept (0, 5)
6
5
8
y
6
-10
-5
5
10
x
4
-5
2
-8
-10
2
4
8 x
6
-6
-8
60) 3x + 4y = 20
61) 9x + y = -36
62) 5x + 9y = 30
63) 5x + 2y = 27
7
67
64) y = x +
5
5
1
, y-intercept (0, 3)
2
8
-2
-4
1
x + 3;
2
slope:
-4
-2
53) Neither
54) Perpendicular
55) Parallel
56) 50.0 ft per minute
1
57) y = x + 4
2
58) y =
-6
65) y = -
y
4
x+4
3
66)
6
y
4
10
2
-8
-6
-4
-2
2
4
6
5
8 x
-2
-4
-10
-5
5
-6
-5
-8
-10
14
10
x
Answer Key
Testname: MATH 100 PRACTICE TEST 1
67)
70)
y
y
10
4
5
2
-10
-4
-2
2
-5
5
x
-5
-2
-10
-4
71) Function
72) Not a function
73) Domain: {-7, -3, 3, 5}; Range: {-7, -3, 3, 5}
74) Not a function; domain: (-∞, 2] ; range: (-∞, ∞)
1
75) Function; domain: , ∞
2
-6
68)
y
4
76) Function; domain: (-∞, ∞)
77) Function; domain: (-∞, -19) ∪ (-19, ∞)
2
-4
10
6x
4
-2
2
78) 2a - 7
79) -5
80) -4
6x
4
-2
81) f(x) =
5 - 5x
-6
-4
82) domain: (-∞, ∞); range: (-∞, ∞)
y
-6
69)
6
y
4
10
2
5
-6
-4
-2
2
-2
-10
-5
5
10
x
-4
-6
-5
-10
15
4
6
x