Mth 100 Test 1 Practice problems Sec 2.1 - 4.3
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Name: _______________________________
SECTION 3.1
Solve the inequality, giving its solution set in both
interval and graph forms.
11) -9x ≤ 90
SECTION 2.1
Solve the equation.
1) 12t - 34 = 4t - 14
2) -[7x + (6x + 7)] = 4 - (9x + 8)
3)
a 1
- = -4
5 5
4)
r + 6 r + 8
= 3
6
12) -10y + 5 ≤ -11y + 13
13) -(-4x - 2) - 10 + 5x < 7x
Solve.
5) -0.06y + 0.08(1100 - y) = 0.36y
2
9
14) - x ≤ - 3
10
Decide whether the equation is conditional, an identity,
or a contradiction. Give the solution set.
6) 2x + 6(x + 1) + 2 = 8 - 3x
7) -8s + 11 + 4(2s - 1) = 0
15) -30 ≤ 5(x - 1) ≤ 5
SECTION 2.3
Solve the percent problem.
8) At the end of the day, a storekeeper had $1133
in the cash register, counting both the sale of
goods and the sales tax of 3%. Find the
amount that is the tax.
-6
-4
-2
0
2
4
6
8
10
12
16) -10 < 3x + 2 ≤ 2
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Solve the investment problem.
9) Walt made an extra $9000 last year from a
part-time job. He invested part of the money
at 8% and the rest at 7%. He made a total of
$680 in interest. How much was invested at
7%?
17) 6 ≤ 3x - 1
≤ 9
2
SECTION 3.2
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.
18) A ∩ B
Solve the mixture problem.
10) How many liters of a 30% alcohol solution
must be mixed with 20 liters of a 70% solution
to get a 40% solution?
19) C ∪ B
1
14
Graph the requested union or intersection.
20) Intersection
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10
-8
-6
-4
-2
0
2
4
6
8
10
For the given compound inequality, state whether
intersection or union should be used. Then give the
solution set in both interval and graph forms.
30) x - 1 < 2 and x + 2 > 3
31) -6x > 24 or -2x < -10
21) Union
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10 -8
-6
-4
-2
0
2
4
6
8
10
Solve.
32) 4x - 6 = 3
For the compound inequality, give the solution set in both
interval and graph forms.
22) x ≥ 4 and x ≤ 7
1
33) 5 - x = 4
8
SECTION 3.3
Solve the given equation or inequality. If an equation is
given, then write the solution set in set notation. If an
inequality is given, then write the solution set in interval
notation.
34) |5k - 1| - 1 ≥ 6
23) x ≤ -2 and x ≥ 7
Solve.
24) 3x - 6 ≥ -24 and 8x + 3 < -13
-7 -6 -5 -4 -3 -2 -1 0
1
35) |2x - 4 |= 10
2
3
4
5
6
7
36) |8 - 4p|= - 40
25) x ≤ 4 or x ≥ 5
Solve the inequality and graph the solution set.
37) 4x + 2 < 5
-4
-2
0
2
4
26) x < 4 or x < 8
38) 5 - x ≤ 8
-35
-30
-25
-20
-15
-10
-5
0
5
2 4
6 8 10 12 14
27) -6x + 1 ≥ 13 or 7x + 3 ≥ -25
39) -6 + k > 8
-18 -16 -14 -12 -10 -8 -6 -4 -2 0
Express the set in simplest interval form.
28) (-∞, 7] ∩ [-8, ∞)
29) (-6, 5) ∪ [0, 7]
2
SECTION 4.1
Find the x- and y-intercepts. Then graph the equation.
40) 6x - 18y = 18
Find the midpoint of the segment with the given
endpoints.
43) (9, 6) and (-9, 4)
y
10
44) (-8, -3) and (7, 0)
5
-10
SECTION 4.2
Find the slope of the line.
45)
-5
5
10
x
y
10
-5
5
-10
-10
-5
Find the x- and y-intercepts. Then graph the equation.
41) x + 2y = 0
5
10
x
-5
y
10
-10
5
46)
y
-10
-5
5
10
10
x
-5
-10
-10
10
x
42) y = 3
y
10
-10
5
Find the slope of the line through the pair of points.
47) (1, -6) and (-9, -5)
-10
-5
5
10
x
48) (6, 8) and (9, 8)
-5
-10
3
53) x - 5 = 0
Find the slope of the line.
49)
y
10
y
10
5
5
-10
-10
-5
5
10
-5
5
10
x
-5
-5
-10
-10
Graph the line.
54) Through (6, -9); m = 0
Find the slope of the line through the pair of points.
50) (-1, -5) and (-1, 2)
y
10
MULTIPLE CHOICE. Choose the one alternative that
best completes the statement or answers the question.
5
Find the equation in slope-intercept form of the line
satisfying the conditions.
43
4
51) m = - ; y-intercept 0, - 9
9
4
43
A) y = x - 9
9
4
43
B) y = - x - 9
9
4
43
C) y = - x + 9
9
D) y = - -10
-5
5
10
x
5
10
x
-5
-10
43
4
x - 9
9
55) Through (-5, -5); m = SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
1
2
y
10
Find the slope of the line, and sketch the graph.
52) x + 3y = 3
5
y
10
-10
5
-5
-5
-10
-10
-5
5
10
x
-5
-10
4
x
56) Through (0, 6); m = - 1
5
Write the equation in standard form of the line satisfying
the given conditions.
3
61) Through (4, 3); m = - 5
y
10
62) Through (-2, -8); undefined slope
5
-10
-5
5
63) Through (-4, -8); 0 slope
x
10
-5
Write the equation in standard form of the line through
the given points.
64) (7, -4) and (5, 1)
-10
10
Find an equation of the line satisfying the conditions.
Write the equation in slope-intercept form.
65) Through (-3, 8); perpendicular to -3x + 4y =
-23
5
66) Through (-6, 7); parallel to 3x + 7y = 3
57) Through (-2, 9); slope undefined
y
-10
-5
5
x
10
-5
-10
Decide whether the pair of lines is parallel,
perpendicular, or neither.
58) 12x + 4y = 16 and 18x + 6y = 27
59) The line through (3, -5) and (-1, 7) and the line
through (6, -13) and (-2, 11)
SECTION 4.3Write the equation in slope -intercept form,
state the slope and y-intercept, and graph the equation.
60) 3x - 6y = -18
8
y
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
5
Answer Key
Testname: 100 TEST 1 PRAC PROB 2.1 TO 4.3
1)
5
2
2) - 3
4
3) {-19}
4) {-4}
5) {176}
6) Conditional; {0}
7) Contradiction; ∅
8) $33
9) $4000
10) 60 liters
11) [-10, ∞)
-15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-5
12) (-∞, 8]
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
13) (-∞, 4) 0
1
2
3
4
5
6
7
8
27
14) , ∞
20
-2
0
2
15) [-5, 2]
-6
-4
-2
0
2
4
6
8
10
12
14
16) (-4, 0]
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
17) 13 19
,
3 3
13
3
19
3
18) {q, s, y, z}
19) {q, s, v, w, x, y, z}
20)
-10
-8
-6
-4
-2
0
2
4
6
8
10
6
Answer Key
Testname: 100 TEST 1 PRAC PROB 2.1 TO 4.3
21)
-10 -8
-6
-4
-2
0
2
4
6
8
10
22) [4, 7]
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
23) φ
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
24) [-6, -2)
-7 -6 -5 -4
25) (-∞, 4] ∪ [5,∞)
-3 -2 -1 0
1
2
3
4
5
6
7
5
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
26) (-∞, 8)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
4
5
6
7
6
7
8
9 10
27) (-∞,∞)
-7 -6 -5 -4 -3 -2 -1 0
1
2
3
28) [-8, 7]
29) (-6, 7]
30) Intersection; (1, 3)
-7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
31) Union; (-∞, -4) ∪ (5, ∞)
-10
-8
-6
-4
-2
0
2
4
6
8
10
3 9
32) , 4 4
33) {8, 72}
34) -∞, - 8
6
∪ , ∞
5
5
35) - 3, 7
36) - 8, 12
7 3
37) - , 4 4
-4
-2
0
2
4
7
Answer Key
Testname: 100 TEST 1 PRAC PROB 2.1 TO 4.3
38) [-3, 13]
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
20
39) (-∞, -2) ∪ (14, ∞)
-18 -16 -14 -12 -10 -8 -6 -4 -2 0
2 4 6
8 10 12 14 16 18
40) (3, 0); (0, -1)
y
10
5
-10
-5
5
10
x
-5
-10
41) (0, 0); (0, 0)
y
10
5
-10
-5
5
10
x
-5
-10
42) None; (0, 3)
y
10
5
-10
-5
5
10
x
-5
-10
43) 0, 5
8
25
30
35
Answer Key
Testname: 100 TEST 1 PRAC PROB 2.1 TO 4.3
1
3
44) - , - 2
2
45) Undefined
46) 0
1
47) - 10
48) 0
49) -1
50) Undefined
51) B
1
52) Slope: - 3
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
53) Slope: Undefined
y
10
5
-10
-5
-5
-10
9
Answer Key
Testname: 100 TEST 1 PRAC PROB 2.1 TO 4.3
54)
y
10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
55)
y
10
5
-10
-5
-5
-10
56)
y
10
5
-10
-5
-5
-10
10
Answer Key
Testname: 100 TEST 1 PRAC PROB 2.1 TO 4.3
57)
y
10
5
-10
-5
5
10
x
-5
-10
58) Parallel
59) Parallel
1
60) y = x + 3;
2
1
slope: , y-intercept (0, 3)
2
8
y
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
61) 3x + 5y = 27
62) x = -2
63) y = -8
64) 5x + 2y = 27
4
65) y = - x + 4
3
31
3
66) y = - x + 7
7
11