Exam
Name___________________________________
Provide an appropriate response.
1) The additive inverse of 2 is
1
A) .
2
1)
B) -1.
C) -2.
1
D) - .
2
E) none of the above
2) Find the multiplicative inverse of 3.
2)
3) Simplify: 0(2 + x)
3)
4) Simplify: -4 - (-10)
4)
5
4
5) Simplify: + 6
7
5)
2x - 4
6 - 3x
6)
6) Simplify: 7)
7)
Simplify: 2
3
4
9
8) Find the value and simplify: 3
-64
8)
9) Simplify: 20
9)
10) Simplify: x 6 x 2 (3x 3 )
11) Find the value and simplify: 12) Simplify: (7x)
10)
3 8
27
11)
4
7x
12)
13) (y 4 + 2y 3 + y 2 ) - (4y 2 + 8y +4)
13)
1
14) Completely factor: 3ax + 9ay
14)
15) Completely factor: x 2 - 36
15)
16) Completely factor: x 2 + 4x + 3
16)
17)
17)
Simplify: 1
2 + 3
3 - 2
3
18) Completely factor: 4y 2 - 25
18)
19) Completely factor: 4x 2 + 5x - 6
19)
20) Perform the operation and simplify your answer: x+7
6
· x
3x + 21
21)
20)
21)
Perform the operation and simplify your answer: x
2
x - 4
2
(x + 2)2
22) Perform the operation and simplify your answer: 23) Rationalize the denominator and simplify: 2
3
2
+ - x - 1 x 2 - 1 x + 1
2 + x
2 - x
22)
23)
x 3
24) Solve: + = x
2 4
24)
3
25) Solve: (4x - 3) = 2 x - (4x - 3)
2
25)
26) Solve: x 2 - 6x + 9 = 0
26)
27) Solve: 2x 2 - 9x + 4 = 0
27)
28) Find the slope of the line passing through the points (5, -3) and (2, -1).
28)
2
29) Find the slope of the line 4x - 8y + 5 = 0.
29)
30) What is the slope of a horizontal line?
30)
2
31) Find the equation of the line with y-intercept 4 and slope - .
3
31)
32)
32) The y-intercept of the line 3x + 5y + 4 = 0 is
4
4
B) 4.
C) .
A) - .
3
5
D) -4.
4
E) - .
5
33) The slope of a certain line is 4. If the x-value of a point on the line increases by 3 units, by
how many units does the y-value increase?
33)
34) Graph the equation 3x + 4y - 12 = 0.
34)
y
10
5
-10
-5
5
10
x
-5
-10
35) Graph the equation 5x + y + 8 = 0.
35)
y
10
5
-10
-5
5
10
x
-5
-10
3
36) Sketch the graph of x = 4.
36)
y
10
5
-10
-5
5
10
x
-5
-10
37) Sketch the graph of y = 3.
37)
y
10
5
-10
-5
5
10
x
-5
-10
38) Sketch the graph of 5(x + 3) - 3(y - 1) = 0.
38)
y
10
5
-10
-5
5
10
x
-5
-10
4
39) For the straight line 2x + y - 3 = 0 find: (a) the slope; (b) the y-intercept; and
(c) sketch the graph.
39)
y
10
5
-10
-5
5
10
x
-5
-10
40) Determine an equation of the vertical line that passes through the point (3, -6).
40)
41) Find an equation of the horizontal line that passes through the point (5, 6).
41)
42) The slope of the line passing through the points (-4, 5) and (3, -2) is
A) -7.
B) 1.
C) 3.
D) -1.
42)
E) -3.
43) The slope and y-intercept of the line 6x - 5y + 4 = 0 are
6
A) and 4, respectively.
5
B)
4
6
and , respectively.
5
5
C)
5
5
and , respectively.
4
6
43)
D) -5 and 4, respectively.
2
5
E) - and , respectively.
3
6
44) Determine whether the following lines are parallel, perpendicular or neither.
3x - 2y = -1
2x + 3y = -20
44)
45) Determine whether the following lines are parallel, perpendicular or neither.
3x - 2y = 19
2x + 3y = 4
45)
46) Determine whether the following lines are parallel, perpendicular or neither.
12x + 4y = 16
15x + 5y = 23
46)
47) Determine whether the following lines are parallel, perpendicular or neither.
12x + 4y = 16
24x + 8y = 36
47)
5
48) Determine whether the following lines are parallel, perpendicular or neither.
3x - 4y = 3
12x + 6y = 12
48)
49) Determine whether the following lines are parallel, perpendicular or neither.
0.1x - 7y + 81 = 0
2x - 140y + 9 = 0
49)
50) Determine whether the following lines are parallel, perpendicular or neither.
0.21x - 0.35y + 8 = 0
x + 0.6y - 9 = 0
50)
51) Find the equation of a line which is parallel to the line 2x + 3y - 7 = 0 and passes through
the point (-1, 2).
51)
52) Find the equation of a line which is perpendicular to the line 2x + 3y - 57 = 0 and passes
through the point (1, -1).
52)
53) The relationship between temperature on the Fahrenheit scale and the temperature on the
5
Celsius scale is C = (F - 32). Find the slope and y-intercept of the equation.
9
53)
54) An orthodontist charges $3000 for the phase of treatment for a nine -year old which will
provide better alignment and more room for permanent teeth in the future. What is an
equation for the relationship between cost C of the treatment and the number of visits
required to attain the desired result?
54)
55) When the temperature T (in degrees Celsius) of a certain laboratory animal is reduced, its
heart rate r (in beats per minute) decreases. At a temperature of 37°C, the animal had a
heart rate of 200, and at a temperature of 32°C its heart rate was 140. If r is a linear function
of T for 26 ≤ T ≤ 38, (a) determine this function and (b) determine the heart rate at a
temperature of 30°C.
55)
56) For the parabola y = f(x) = x 2 - 2x - 8, find: (a) the vertex, (b) the y-intercept, and (c) the
x-intercepts.
56)
57) For the parabola y = f(x) = 2x 2 - 4x - 6, find: (a) the vertex, (b) the y-intercept, and (c) the
x-intercepts.
57)
58) For the parabola y = f(x) = -x 2 + 7x - 6, find: (a) the vertex, (b) the y-intercept, and (c) the
x-intercepts.
58)
59) For the parabola y = f(x) = 4 - x - 3x 2 , find: (a) the vertex, (b) the y-intercept, and (c) the
x-intercepts.
59)
6
60) Graph the function y = f(x) = 2x 2 + 2x - 12 and indicate the coordinates of the vertex and
intercepts.
60)
y
10
5
-10
-5
5
10
x
-5
-10
61) Graph the function y = f(x) = -x 2 + 5 - 4 and indicate the coordinates of the vertex and
intercepts.
61)
y
10
5
-10
-5
5
10
x
-5
-10
62) Graph the function y = f(x) = 3 - 2x - x 2 and indicate the coordinates of the vertex and
intercepts.
62)
y
10
5
-10
-5
5
10
x
-5
-10
63) State whether f(x) = 12x 2 - 24x + 10 has maximum or minimum value and find that value.
63)
64) State whether f(x) = 10 + 16x - 4x 2 has maximum or minimum value and find that value.
64)
7
65) Find x and express your answer in terms of common logarithms: 4 x = 3
65)
66) Find x and express your answer in terms of common logarithms: 102x-3 = 4
66)
67) Find x and express your answer in terms of natural logarithms: 2 -x - 3 = 8
67)
68) Solve for x: ln(x + 3) = ln(2x)
68)
69) Solve for x: log x = log 3 + 2 log 4
69)
70) Solve for x: 4 2x = 2
70)
71) Solve for x: ln x + ln 3 = ln(x + 1)
71)
72) Solve for x: ln(x + 1) - ln x = ln 2
72)
73) Solve for x: log(x + 1) - log(x - 2) = 1
73)
74) Solve for x: 4 x+1 = 8 3x
74)
75) Solve for x: log2 (x - 4) + log2 3 = log2 x
75)
76) If 2 2x+1 = 8 x-3 , then x =
A) 10.
B) log2 3.
76)
D) -4.
C) 6.
8
E) -7.
Answer Key
Testname: MATH155
1) C
1
2)
3
3) 0
4) 6
59
5)
42
6) - 7)
2
3
3
2
8) -4
9) 2 5
10) 3x 11
11)
2
3
12) 4
13) (y + 2)(y - 2)(y + 1)2
14) 3a(x + 3y)
15) (x + 6)(x - 6)
16) (x + 1)(x + 3)
17) 1
18) (2y + 5)(2y - 5)
19) (4x - 3)(x + 2)
2
20)
x
21)
x(x + 2)
2(x - 2)
22)
7
(x + 1)(x - 1)
23)
4 + 4 x + x
4 - x
24) x = 3
2
25) x =
7
8
26) x = 3
27) x = 4, 28) - 29)
1
2
2
3
1
2
30) 0
2
31) y = - x + 4
3
9
Answer Key
Testname: MATH155
32) E
33) 12
34)
35)
36)
37)
10
Answer Key
Testname: MATH155
38)
y
10
5
-10
-5
5
10
x
-5
-10
39) (a) -2
(c)
(b) 3
40) x = 3
41) y = 6
42) D
43) B
44) perpendicular
45) perpendicular
46) parallel
47) parallel
48) neither
49) parallel
50) perpendicular
51) 2x + 3y - 4 = 0
52) 3x - 2y - 5 = 0
160
5
53) slope = ; y-intercept = - 9
9
54) C = 3000
55) (a) r = 12T - 244
56) (a) (1, -9)
57) (a) (1, -8)
7 25
, 58) (a)
2 4
59) (a)
1 49
- , 6 12
(b) 116
(b) -8
(b) -6
(c) -2 and 4
(c) -1 and 3
(b) -6
(c) 1 and 6
(b) 4
(c) 1 and - 4
3
11
Answer Key
Testname: MATH155
60)
61)
62)
63) minimum value; -2
64) maximum value; 26
log3
65)
log4
66)
3 + log 4
2
67) - ln 11
ln 2
68) 3
69) 48
1
70)
4
71)
1
2
72) 1
7
73)
3
12
Answer Key
Testname: MATH155
74)
2
7
75) 6
76) A
13