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MATH 0312
EXAM 1 REVIEW
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the equation.
1) 20x - 1 = 14
1)
2) 5m + 6 + 2(2m - 5) = 5(m + 5)
2)
3) -[3x + (8x + 1)] = 6 - (2x + 4)
3)
Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
4) -12s - 71 + 4(3s + 20) = 0
4)
5) 2(2g + 28) - 4g - 56 = 0
5)
6) 4x + 6(x + 1) + 2 = 8 - 7x
6)
Solve the equation.
3x + 4 6
5x
7)
+ = - 5
5
6
7)
8) 0.01x + 0.14(x + 5000) = 850
8)
Solve the equation for the specified variable. Use the distributive property to factor as necessary.
3t + 4
9) c = for t
t
Solve the formula for the specified variable.
9
10) F = C + 32 for C
5
9)
10)
Solve the inequality. Give the solution set in both interval and graph forms.
11) 15a - 15 > 3(4a + 1)
12) 12z + 5 > 13z + 8
11)
12)
1
13) -21 < 5a + 4 ≤ -1
13)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
14) 6 ≤ 3x - 1
≤ 9
4
14)
Solve the equation.
15) 7m + 2 = 5
15)
1
16) 4 + x = 5
9
16)
Find the x- and y-intercepts. Then graph the equation.
17) -2x - 10y = 10
17)
y
10
5
-10
-5
5
10
x
-5
-10
18) y = -6
18)
y
10
5
-10
-5
5
10
x
-5
-10
2
19) x = 4
19)
y
10
5
-10
-5
5
10
x
-5
-10
Find the slope.
20) m = 11 - 7
-1 - (-1)
20)
Find the slope of the line through the pair of points.
21) (1, -8) and (-4, 3)
21)
Find the slope of the line.
22)
22)
y
10
5
-10
-5
5
10
x
-5
-10
3
23)
23)
y
10
5
-10
-5
5
10
x
-5
-10
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
24)
24)
y
10
-10
10
x
-10
A) -2
B) 0
C) 2
D) Undefined
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Graph the line described.
25) Through (0, 5); m = 1
6
25)
y
10
5
-10
-5
5
10
x
-5
-10
4
Decide whether the pair of lines is parallel, perpendicular, or neither.
26) 3x - 2y = 12 and 2x + 3y = -3
27) 9x + 3y = 12 and 15x + 5y = 23
26)
27)
Find the equation in slope-intercept form of the line satisfying the conditions.
28) m = 2, passes through (7, -1)
2
25
29) Slope - ; b = 7
7
28)
29)
Write the equation in slope-intercept form.
30) 20x + 8y = 5
30)
Find the slope and the y -intercept of the line.
31) 6x + 5y = 28
31)
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
2
32) Through (2, 5); m = - 5
32)
Find an equation of the line passing through the two points. Write the equation in standard form.
33) (7, -3) and (-6, 8)
33)
Graph the linear inequality in two variables.
34) 2x + y ≤ -2
34)
y
10
5
-10
-5
5
10
x
-5
-10
5
35) x - y > -6
35)
y
10
5
-10
-5
5
10
x
-5
-10
Decide whether the relation is a function.
36) {(1, -9), (3, 7), (4, -2), (8, -6), (11, 4)}
36)
37) {(2, -9), (2, -2), (5, -7), (7, -3), (11, -9)}
37)
Determine whether the relation is a function.
38) x -7 -7 1 4 7
y 2 1 -5 -2 4
38)
Solve the problem.
39) Find f(4) when f(x) = -x2 + 2x - 7.
39)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve by the substitution method.
40) x - 7y = -24
2x - 8y = -30
A) (-4, 4)
Solve by elimination.
41) x + y = -9
x - y = 5
A) No solution
42) x + 2y = -1
-5x + 2y = 17
A) (-1, -3)
43) 7x + 5y = 35
5x + 2y = 25
A) (5, 0)
40)
B) (-3, 3)
C) No solution
D) (3, 4)
41)
B) (-3, -6)
C) (-2, -7)
D) (2, -6)
42)
B) (-2, 0)
C) No solution
D) (-3, 1)
43)
B) No solution
C) (5, 1)
44) 3x + 5y = -5
-18x - 30y = 30
A) Infinite number of solutions
C) (-25, -15)
D) (4, 1)
44)
B) No solution
D) (-15, -25)
6
45)
45) 6x - 2y = -4
12x - 4y = 8
A) (24, -8)
C) (-24, 8)
B) No solution
D) Infinite number of solutions
7
Answer Key
Testname: MATH0312EX1REVIEWS2011
1)
3
4
2)
29
4
3) - 1
3
4) Contradiction; ∅
5) Identity; {all real numbers}
6) Conditional; {0}
60
7) - 43
8) {1000}
4
-4
or t = 9) t = c - 3
-c + 3
5
10) C = (F - 32)
9
11) (6, ∞)
-1
0
1
2
3
4
5
6
7
8
9
10 11 12 13
-2
-1
0
1
2
3
4
5
6
7
12) (-∞, 3)
-4
-3
8
9
10
13) (-5, -1]
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
14) 25 37
,
3 3
25
3
15)
37
3
3
, - 1
7
16) {-81, 9}
8
Answer Key
Testname: MATH0312EX1REVIEWS2011
17) (-5, 0); (0, -1)
y
10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
18) None; (0, -6)
y
10
5
-10
-5
-5
-10
19) (4, 0); none
y
10
5
-10
-5
-5
-10
20) Undefined
11
21) - 5
22) 3
23) Undefined
24) B
9
Answer Key
Testname: MATH0312EX1REVIEWS2011
25)
y
10
5
-10
-5
5
10
x
10
x
-5
-10
26) Perpendicular
27) Parallel
28) y = 2x - 15
25
2
29) y = - x + 7
7
5
5
30) y = - x + 2
8
6
28
31) Slope - ; y-intercept 0, 5
5
32) 2x + 5y = 29
33) 11x + 13y = 38
34)
y
10
5
-10
-5
5
-5
-10
10
Answer Key
Testname: MATH0312EX1REVIEWS2011
35)
y
10
5
-10
-5
5
10
x
-5
-10
36) Function
37) Not a function
38) Not a function
39) -15
40) B
41) C
42) D
43) A
44) A
45) B
11