Review for Midterm: Algebra III / Trigonometry
Name___________________________________
Practice Test
Period ____________
BLACK ORANGE
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the given conditions to write an equation for the line in slope-intercept form.
1) Passing through (-4, 1) and (4, -2)
3
1
3
1
A) y = x B) y = - x 8
2
8
2
C) y = mx -
1
2
D) y - 1 = -
3
(x + 4)
8
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
16
10
2)
+2 =
x-6
x-6
A) x ≠ 6; {3}
B) x ≠ -6; {19}
C) x ≠ -6; {3}
D) x ≠ 6; M
C) 3 + 2i
D) 3 - 2i
Divide and express the result in standard form.
22 + 7i
3)
4 + 5i
A) -2 + 3i
B) -2 - 3i
Determine whether the given function is even, odd, or neither.
4) f(x) = x3 - x + 5
A) Odd
B) Neither
C) Even
Find the inverse of the one-to-one function.
5) f(x) = (x - 4)3
A) f-1(x) =
3
x-4
B) f-1(x) =
C) f-1(x) =
x+4
1
3
x + 64
D) f-1(x) =
3
x+4
Find and simplify the difference quotient
f(x + h) - f(x)
, h≠
≠ 0 for the given function.
h
6) f(x) = x2 + 7x + 2
2x2 + 2x + 2xh + h 2 + h + 4
h
A) 1
B)
C) 2x + h + 2
D) 2x + h + 7
Find the average rate of change of the function from x 1 to x 2.
7) f(x) =
2x from x1 = 2 to x2 = 8
A) 7
B)
1
3
C) 2
D) -
3
10
Find the midpoint of the line segment whose end points are given.
1
8) (- 2, 1) and (- 3, )
3
A) (- 5,
4
)
3
1 1
B) ( , )
2 3
C) (-
5 2
, )
2 3
B) {10, 6}
C) {10, -6}
D) (-
1
1
,- )
2
3
Solve the equation by factoring.
9) x2 + 4x - 60 = 0
A) {-10, 1}
2
D) {-10, 6}
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the
x-axis or touches the x-axis at each zero.
1 4
10) f(x) = (x + ) (x + 5)3
2
A) x =
1
has multiplicity 4; The graph crosses the x-axis; x = 5 has multiplicity 3; The graph touches the
2
x-axis and turns around.
1
B) x = has multiplicity 4; The graph touches the x-axis and turns around; x = 5 has multiplicity 3; The
2
graph crosses the x-axis.
1
C) x = - has multiplicity 4; The graph touches the x-axis and turns around; x = -5 has multiplicity 3; The
2
graph crosses the x-axis.
1
D) x = - has multiplicity 4; The graph crosses the x-axis; x = -5 has multiplicity 3; The graph touches the
2
x-axis and turns around.
Perform the matrix row operation and write the new matrix.
11)
1 1 -1 1 5
0 -2 3 -1 0
1 0 -4 -5 3
-2 3 0 2 -5
-2R 1 + R3
4R 1 + R4
1 1 -1 1 5
0 -2 3 -1 0
A)
-1 -2 -2 -7 -7
-2 3 0 2 -5
C)
1 1 -1 1
0 -2 3 -1
-1 -2 -2 -7
2 7 -4 6
5
0
1
5
B)
1 1 -1 1 5
0 -2 3 -1 0
-1 -2 -2 -7 -7
2 7 -4 6 15
D)
1 1 -1 1 5
0 -2 3 -1 0
3 2 -6 -3 13
2 7 -4 6 15
For the given functions f and g , find the indicated compostion.
12) f(x) = 5x + 11,
(f†g)(x)
A) 15x + 32
g(x) = 3x - 1
B) 15x + 10
C) 15x + 16
3
D) 15x + 6
Solve the equation using the quadratic formula.
13) x2 + 7x + 3 = 0
A)
C)
72
37 7 +
,
37
B)
2
-7 - 37 -7 + 37
,
14
14
D)
-7 2
61 -7 + 61
,
2
-7 - 37 -7 + 37
,
2
2
Solve the system of equations.
14) x - y + z = 1
x+y+z=3
x + y - z = -3
A) {(3, -1, 1)}
B) {(-1, 1, 3)}
C) {(1, 3, -1)}
D) {(-1, 3, 1)}
Solve the inequality by first rewriting it as an equivalent inequality without absolute value bars. Graph the solution set
on the number line. Express the solution set using interval notation.
3y + 6
15)
<3
2
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
A) (-«, -4) or (4, «)
B) (-«, -4) or (0, «)
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
C) (-4, 4)
D) (-4, 0)
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
4
Solve the problem.
16) A doctor has told a sick patient to take vitamin pills. The patient needs at least 32 units of vitamin A, at least 10
units of vitamin B, and at least 40 units of vitamin C. The red vitamin pills cost 10É each and contain 6 units of
A, 1 unit of B, and 2 units of C. The blue vitamin pills cost 20É each and contain 2 units of A, 1 unit of B, and 7
units of C. How many pills should the patient take each day to minimize costs?
A) 4 red and 6 blue
B) 6 red and 4 blue
C) 7 red and 3 blue
D) 10 red and 0 blue
17) Solve the equation 2x3 - 19x2 + 32x + 21 = 0 given that 3 is a zero of f(x) = 2x3 - 19x2 + 32x + 21.
1
1
7
7
A) {3, -7, }
B) {3, 7, - }
C) {3, 1, - }
D) {3, -1, }
2
2
2
2
18) Use synthetic division to divide f(x) = x3 + 2x2 - 11x - 12 by x + 4. Use the result to find all zeros of f.
A) {4, -1, 3}
B) {-4, -1, 3}
C) {4, 1, -3}
D) {-4 , 1, -3}
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given
function.
19) f(x) = 6x7 - 2x2 + x + 10
A) 2 or 0 positive zeros, 1 or 0 negative zeros
B) 2 or 0 positive zeros, 2 or 0 negative zeros
C) 2 or 0 positive zeros, 1 negative zero
D) 3 or 1 positive zeros, 3 or 1 negative zeros
Use the Leading Coefficient Test to determine the end behavior of the polynomial function.
20) f(x) = 5x3 - 2x2 + 4x - 2
A) rises to the left and falls to the right
B) falls to the left and falls to the right
C) falls to the left and rises to the right
D) rises to the left and rises to the right
5
Solve the system of equations.
21)
x + 7y = -2
3x + y = 34
A) {(3, 7)}
B) {(12, -2)}
C) {(7, 12)}
D) {(-2, 3)}
Begin by graphing the standard quadratic function f(x) = x 2 . Then use transformations of this graph to graph the given
function.
1
22) g(x) = - (x - 3)2 - 3
2
10
8
y
6
4
2
-10 -8 -6 -4 -2
-2
-4
2
4 6
8 10 x
-6
-8
-10
A)
B)
10
y
10
8
8
6
4
6
4
2
2
-10 -8 -6 -4 -2
-2
2
4 6
8 10 x
y
-10 -8 -6 -4 -2
-2
-4
-4
-6
-8
-6
-8
-10
-10
C)
2
4 6
8 10 x
2
4 6
8 10 x
D)
10
y
10
8
6
8
6
4
4
2
2
-10 -8 -6 -4 -2
-2
-4
2
4 6
8 10 x
-10 -8 -6 -4 -2
-2
-4
-6
-6
-8
-10
-8
-10
6
y
Answer Key
Testname: MIDTERMREVIEW.TST
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
B
A
D
B
D
D
B
C
D
C
B
D
D
B
D
B
B
B
C
C
B
C
1