Name:
Class:
Date:
CA2 Review/Semester 1 Final Exam Review
Indicate the answer choice that best completes the
statement or answers the question.
Simplify the given expression.
2. (5x2 – 10x – 20) + (9x2 – 4)
1. Graph the given relation or equation and find the domain and range.
Then
2 – 24
determine whether
a. 14x
b. 14x2 – 10x – 24
the relation or equation is a function.
c. 14x2 – 10x + 24
d. 14x2 – 10x – 16
(3.1, 5.1), (–1.9, 5.1), (–4.9, 3.1), (–4.9, –2.9)
a.
b.
3. (–3x2 – 7x + 17) – (20x2 + 25x – 9)
a. –23x2 – 32x + 8
b. –23x2 – 32x + 26
c. –23x2 – 18x + 26
d. –23x2 – 27x + 8
4. –5xy(4xy3 – 8xy + 6y2)
a. –20x2y4 – 8x2y2 +
6x2y3
c. –20x2y4 + 40x2y2
– 30xy3
b. –20x2y4 + 40xy
+ 30y2
d. –20x2y4 – 8xy
+ 6y2
Simplify the expression using synthetic
division.
5. (9x3 – 151x2 + 566x – 600) ÷ (x – 12)
Domain: {–4.9, –1.9, 3.1}
Range: {–2.9, 3.1, 5.1}
The equation is a function.
c.
a. quotient 9x2 – 259x – 2542 and
remainder 29,904
d.
b. quotient 117x2 + 1253x – 15,602 and
remainder 186,624
c. quotient 9x2 – 43x + 50 and remainder 0
d. quotient 108x2 + 1145x + 14,306 and
remainder 171,072
Factor the polynomial completely.
6. 26xy – 39y – 40x + 60
a. 13y(2x – 3) –
b. 13y(2x – 3) –
40x + 60
20(2x – 3)
c. (13y – 20)(2x –
d. (26xy – 39y) –
3)
(40x – 60)
Domain: {–4.9, 5.1, 3.1}
Range: {–2.9, 3.1, –1.9}
The equation is not a function.
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7. 7x2 – 19x + 10
a. 7x(x – 2) – 5(x –
2)
b. 7x2 – 13x – 6x +
10
c. (7x – 5)(x – 2)
d. 7x2 – 14x – 5x +
10
Page 1
Name:
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CA2 Review/Semester 1 Final Exam Review
8. 64x3 + 125y3
a. (4x – 5y)(16x2 –
b. (4x + 5y)(16x2 –
20xy + 25y2)
20xy + 25y2)
c. (4x – 5y)(16x2 +
d. (4x + 5y)(16x2 +
20xy + 25y2)
11. Graph the quadratic function
a.
b.
25y2)
9. x4 – 34x2 + 225 = 0
a. 3, –3, 5, –5
c. 5, –5
b. 3, –3, 7, –7
d. 2, –2, 9, –9
10. Graph the quadratic function
a.
b.
c.
c.
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d.
d.
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CA2 Review/Semester 1 Final Exam Review
12. Consider the quadratic function f(x) = –2x2 + 4x
– 4. Find the y-intercept and the equation of the
axis of symmetry.
a. The y-intercept is 4.
The equation of the axis of symmetry is x
= –1.
b. The y-intercept is 1.
The equation of the axis of symmetry is x
= –4.
Solve the equation by graphing. If exact
roots cannot be found, state the consecutive
integers between which the roots are located.
14.
a.
b.
c. The y-intercept is –4.
The equation of the axis of symmetry is x
= 1.
d. The y-intercept is –1.
The equation of the axis of symmetry is x
= 4.
Factor the polynomial completely.
13. 4a 4b 2 – 6a 3b 2
a. 2(2a 4b 2 – 3a 3b 2)
b. 2a 3b 2(2a – 3)
c. a 3b 2(4a – 6)
d. 2a 2b 2(2a 2 – 3)
One solution is between –1 and –2,
while the other solution is between 0 and
1.
c.
d.
One solution is between 0 and –1, while
the other solution is between 1 and 2.
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CA2 Review/Semester 1 Final Exam Review
Determine whether the given function has a
maximum or a minimum value. Then, find the
maximum or minimum value of the function.
15. f(x) = –x2 + 10x + 2
a. The function has a minimum value. The
minimum value of the function is –73.
b. The function has a maximum value. The
maximum value of the function is –73.
c. The function has a maximum value. The
maximum value of the function is 27.
d. The function has a minimum value. The
minimum value of the function is 27.
18. Write an equation for the parabola whose vertex
is at (4, 6) and which passes through (5, 24).
a. y = 18(x – 4)2 +
6
b. y = (x + 4)2 – 6
c. y = 18(x + 4)2 –
6
d. y = –18(x – 4)2 +
6
19. Graph the quadratic function
.
a.
b.
c.
d.
Write the following quadratic function in
vertex form. Then, identify the axis of
symmetry.
16. y = x2 + 10x – 3
a. The vertex form of the function is y = (x
+ 5)2 – 28.
The equation of the axis of symmetry is x
= –5.
b. The vertex form of the function is y = (x
– 5)2 – 28.
The equation of the axis of symmetry is x
= –5.
c. The vertex form of the function is y = (x
+ 5)2 – 28.
The equation of the axis of symmetry is x
= –28.
d. The vertex form of the function is y = (x
+ 5)2 + 28.
The equation of the axis of symmetry is x
= –28.
17. Write an equation for the parabola whose vertex
is at (2, 8) and which passes through (4, 4).
a. y = (x + 2)2 – 8
b. y = 1(x – 2)2 + 8
c. y = –1(x – 2)2 +
8
d. y = –1(x + 2)2 –
8
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CA2 Review/Semester 1 Final Exam Review
Graph the quadratic inequality.
21.
20.
a.
b.
c.
d.
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a.
b.
c.
d.
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Name:
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CA2 Review/Semester 1 Final Exam Review
22. Graph the given function. State the domain and range.
a.
b.
23. Graph the given function. State the domain and range.
a.
The domain is x ≤ and the range is y
4.
c.
b.
The domain is x ≤
and the range is
y ≤ 1.
d.
c.
The domain is x
4.
d.
and the range is y
The domain is x ≤
y
and the range is
1.
24. Determine whether each pair of functions are
inverse functions.
1) f(x) =
, g(x) =
2) f(x) = x – 12, g(x) = x + 12
a. Both 1 and 2 are inverse functions.
b. Only 2 is an inverse function.
c. Neither 1 nor 2 is an inverse function.
d. Only 1 is an inverse function.
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CA2 Review/Semester 1 Final Exam Review
Find the inverse of the given function.
25. f(x) =
a. f –1(x) =
b. f –1(x) =
c. f –1(x) =
d. f –1(x) =
Write the given expression in radical form.
26.
a.
b.
c.
d.
27.
a.
b.
c.
d.
28.
Find the value of the discriminant. Then
describe the number and type of roots for the
equation.
29. –x2 – 20x + 5 = 0
a. The discriminant is 400. Because the
discriminant is greater than 0 and is a
perfect square, the two roots are real and
rational.
b. The discriminant is –420. Because the
discriminant is less than 0, the two roots
are complex.
c. The discriminant is 420. Because the
discriminant is greater than 0 and is not a
perfect square, the two roots are real and
irrational.
d. The discriminant is –380. Because the
discriminant is less than 0, the two roots
are complex.
Find the exact solution of the following
quadratic equation by using the Quadratic
Formula.
30. –x2 + 5x + 7 = 0
a.
b.
a. {(5
c.
d.
c. {(–5
)/–2}
)/–2}
b. {(–5
)/–2}
d. {(–5
)/–2}
Solve the equation by completing the square.
31. 2x2 + x = 0
a. {–1, 0}
c. {0}
b. {0, 0.5}
d. {–0.5, 0}
Solve the equation by factoring.
32. x2 + 2x – 35 = 0
a. {–5, 7}
b. {–7, 5}
c. {5, 7}
d. {–5, –7}
Factor the polynomial completely.
33. 5x4y – 10x2y2
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a. 5x2y(x2 – 2y)
b. 5x2(x2y – 2y2)
c. x2y(5x2 – 10y)
d. 5(x4y – 2x2y2)
Page 7
Name:
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Date:
CA2 Review/Semester 1 Final Exam Review
Simplify the given expression. Assume that no
variable equals 0.
34.
35. Graph the given inequality.
y ≤ –3 – | x |
a.
b.
8x 16y8
16x 11y12
a.
b.
x 20
2y16
c.
x 20
16y16
d.
x5
16y4
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x 20y–16
16
c.
d.
Page 8
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CA2 Review/Semester 1 Final Exam Review
36. Graph the given inequality.
y ≤ 6 – | x |
a.
c.
37. Graph the given inequality.
b.
a.
b.
d.
c.
d.
Use substitution to solve each system of
equations.
38. x + y = –12
–5x – 6y = 64
a. (–4, –8)
b. (–3, –5)
c. (–8, –4)
d. (–5, –3)
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CA2 Review/Semester 1 Final Exam Review
Use the elimination method to solve each
system of equations.
39. 2x – 2y = –26
2x + 6y = 70
a. (12, –1)
b. (–1, 12)
c. (5, 6)
d. (6, 5)
45. Find
and
.
g(x) = 8x
h(x) = –4x3 + 8x2 – 11x + 8
a.
= –32x4 + 64x3 – 88x2 + 64x
= –2048x4 + 512x3 – 88x2 + 8x
b.
= –32x3 + 64x2 – 88x + 64
= –2048x3 + 512x2 – 88x + 64
Simplify.
40. (3 + 5i)(8 – 6i)
c.
= 32x3 + 64x2 – 88x + 64
= –2048x3 + 512x2 – 88x + 8
+ 22i – 30i2
a. 24
c. 33 + 40i
b. 24 + 22i + 30
d. 54 + 22i
41. (–2 + 8i)(–10 – 9i)
a. 92 – 62i
c. 20 – 62i – 72i2
d.
= –32x3 + 64x2 – 88x + 64
= –2048x3 + 512x2 – 88x + 8
b. 74 + 80i
d. 20 – 62i + 72
42.
a.
+
c.
+
a.
–
i
i
b.
– i
d.
– i
b.
–
i
d.
– i
43.
c.
+
i
i
44. Find
and
g(x) = 6x
h(x) = –3x – 6
a.
=–
.
18x – 36
18x2 – 36x
=–
= –18x2
18x – 6
– 6x
= –18x
c.
=–
b.
+ 36
=–
d.
18x – 36
= –18x
+6
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=–
18x – 36
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CA2 Review/Semester 1 Final Exam Review
Answer Key
27. c
1. d
28. a
2. b
29. c
3. b
30. d
4. c
31. d
5. c
32. b
6. c
33. a
7. c
34. b
8. b
35. b
9. a
36. b
10. d
37. b
11. b
38. c
12. c
39. b
13. b
40. d
14. a
41. a
15. c
42. b
16. a
43. b
17. c
44. b
18. a
45. d
19. b
20. d
21. c
22. b
23. a
24. b
25. b
26. c
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