Download Math 1325: Test 1 Review

Math 1325: Test 1 Review
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor completely.
1) u2 - 2uv - 35v2
A) (u - 5v)(u + v)
1)
B) (u - 5v)(u + 7v)
C) Prime
2) 6x2 - 18xy - 24y2
A) (6x - 6y)(x + 4y)
C) 6(x + y)(x - 4y)
D) (u + 5v)(u - 7v)
2)
B) Prime
D) 6(x - y)(x + 4y)
3) 49x2 - 9
3)
A) (7x - 3)2
B) Prime
C) (7x + 3)(7x - 3)
D) (7x + 3)2
4) -100x3 + 45x2 - 5x
4)
A) -5x(4x - 1)(5x - 1)
B) x(4x - 1)(-25x + 5)
D) -5(4x2 - 1)(5x - 1)
C) x(-5x + 5)(5x - 1)
5) x2 + 9x - 36
A) Prime
B) (x + 12)(x - 3)
C) (x - 12)(x + 1)
D) (x - 12)(x + 3)
6) 4x2 - 4x - 24
A) Prime
B) (4x + 8)(x - 3)
C) 4(x - 2)(x + 3)
D) 4(x + 2)(x - 3)
5)
6)
Factor out the greatest common factor.
7) 12m 9 - 24m 4 + 28m 2
7)
B) 4(3m 9 - 6m 4 + 7m 2 )
D) 4m 2 (3m 7 - 6m 2 + 7)
A) No common factor
C) m 2 (12m 7 - 24m 2 + 28)
Use the given data points to construct a linear model, then use the model to find the appropriate Celsius or Fahrenheit
temperature.
8) Degrees Fahrenheit 32 140 212
8)
Degrees Celsius
0 60 100
Choose any two data points and use them to construct a linear equation that models the data, with
x being Fahrenheit and y Celsius. Then use the equation to find the Celsius temperature
corresponding to 176° Fahrenheit.
5
9
A) y = (x + 32); 116° Celsius
B) y = (x - 32); 259° Celsius
9
5
C) y =
9
(x + 32); 374° Celsius
5
D) y =
5
(x - 32); 80° Celsius
9
Solve the problem.
9) Suppose the sales of a particular brand of appliance satisfy the relationship S(x) = 160x + 3100,
where S(x) represents the number of sales in year x, with x = 0 corresponding to 1982. Find the
number of sales in 1991.
A) 4540
B) 8920
C) 4380
D) 9080
1
9)
10) A biologist recorded 6 snakes on 10 acres in one area and 13 snakes on 29 acres in another area. Let
y be the number of snakes in x acres. Write an equation for the number of snakes.
A) 19y = 7x + 4
B) 19y = 7x - 44
C) 19y = 7x + 44
D) y = x + 4
Graph the rational function.
1
11) f(x) =
(x - 4)(x - 2)
10)
11)
6
y
6 x
-6
-6
A)
B)
6
y
6
6 x
-6
y
6 x
-6
-6
-6
C)
D)
6
y
6
6 x
-6
6 x
-6
-6
-6
2
y
12) f(x) =
x-4
x
12)
6
y
6 x
-6
-6
A)
B)
6
y
6
6 x
-6
y
6 x
-6
-6
-6
C)
D)
6
y
6
6 x
-6
y
6 x
-6
-6
-6
Give the equation of the vertical asymptote(s) of the rational function.
x+2
13) g(x) =
2
x + 3x - 4
A) x = -2
C) x = -4, x = 1, y = 0
14) g(x) =
13)
B) x = -4, x = 1
D) x = 4, x = -1
8x + 9
x-6
A) y = 8
14)
B) x = -6
C) x = 6
3
D) y = 6
15) g(x) =
x-3
15)
x2 - 1
A) x = -1
B) x = 3
C) x = 1, x = -1
D) x = 1
Give the equation of the horizontal asymptote of the rational function.
5
16) g(x) =
9x + 5
A) x = -
17) g(x) =
5
9
B) y = 0
5
9
17)
B) x = 9
C) y = 0
D) y = 7
3x2 + 9
3x2 - 9
18)
A) y = 9
19) h(x) =
D) y =
7x + 9
x-9
A) y = 9
18) f(x) =
C) y = 5
16)
B) y = -9
C) None
D) y = 1
27x2
9x2 - 6
19)
A) y = 6
B) None
C) y = 3
Graph the function.
20) f(x) = 2 -x
6
20)
y
4
2
-4
D) y =
-2
2
4
6x
-2
-4
-6
4
A)
B)
y
-4
y
4
4
2
2
-2
2
4
6x
-4
-2
-2
-2
-4
-4
-6
-6
C)
2
4
6x
2
4
6x
D)
y
-4
y
4
4
2
2
-2
2
4
6x
-4
-2
-2
-2
-4
-4
-6
-6
Solve the problem.
21) Use the formula P = Iekt. A bacterial culture has an initial population of 500. If its population grows
to 7000 in 4 hours, what will it be at the end of 6 hours?
A) 26,192
B) 105
C) 2250
D) 207,063
Graph the function.
22) f(x) = -(8 x)
22)
y
4
2
-4
21)
-2
2
4
6x
-2
-4
-6
5
A)
B)
y
-4
y
4
4
2
2
-2
2
4
6x
-4
-2
-2
-2
-4
-4
-6
-6
C)
2
4
6x
2
4
6x
D)
y
-4
y
4
4
2
2
-2
2
4
6x
-4
-2
-2
-2
-4
-4
-6
-6
Solve the problem.
23) The decay of 276 mg of an isotope is given by A(t)= 276e-0.023t, where t is time in years. Find the
amount left after 5 years.
A) 270
B) 123
C) 246
D) 240
Convert to exponential form.
1
24) log5
= -3
125
A) 5 -3 =
1
125
24)
1 3
=5
125
B) 5 125 = 3
C)
B) 3 = log4 64
C) 4 = log3 64
D) 35 =
1
125
Write in logarithmic form.
25) 4 3 = 64
A) 3 = log64 4
26) 2 -3 =
25)
D) 64 = log4 3
1
8
A) 2 = log-3
23)
26)
1
8
B) -3 = log1/8 2
C)
6
1
= log2 -3
8
D) -3 = log2
1
8
Find the value of the expression.
1
27) log7
7
A) 7
27)
B) 0
C) 1
D) -1
28) log8 32
A)
3
2
28)
B)
5
4
C)
4
3
D)
5
3
Write the expression as a sum and/or a difference of logarithms with all variables to the first degree.
29) ln 5t16v2
1
A) ln 5 + 4 ln t + ln v
2
C)
30) ln
1
ln 80t + 2 ln v
2
D)
1
ln 5 + 4 ln t + 2 ln v
2
fz
30)
z 10
A) ln f - 10 ln z
Solve the equation.
31) log (x - 9) = 1 - log x
A) 10, 1
B) ln f -
19
ln z
2
C)
1
ln fz - 10 ln z
2
D)
1
19
ln f ln z
2
2
31)
B) -1, 10
C) -10
D) 10
32) log4 (x - 7) + log4 (x - 7) = 1
A) 9
32)
B) -9, 9
C)
50
D) - 50,
33) log (4 + x) - log (x - 4) = log 3
A) - 8
C) 8
D) ∅
7
B)
3
C) 243
3
D)
7
B) 6.319
C) 0.933
D) 2.933
34)
Solve the equation.
35) 7 x + 1 = 43
A) 1.933
50
33)
3
B)
2
Solve the exponential equation.
34) 5 7x = 125
A) 125
29)
1
B) ln 5 + 16 ln t + ln v
2
35)
7
Answer Key
Testname: 1325-1-REVIEW
1) D
2) C
3) C
4) A
5) B
6) D
7) D
8) D
9) A
10) C
11) B
12) A
13) B
14) C
15) C
16) B
17) D
18) D
19) C
20) D
21) A
22) D
23) C
24) A
25) B
26) D
27) D
28) D
29) A
30) D
31) D
32) A
33) C
34) D
35) C
8