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PAP Algebra 2 Fall Semester Exam Review
Answer Section
MULTIPLE CHOICE
1. ANS: B PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.3
STA: 2A.4.F
KEY: writing quadratic functions in vertex form | vertex of a parabola | quadratic function
NOT: Example 5
SHORT ANSWER
2. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 5.4
STA: 2A.7.E KEY: factoring polynomials | factored completely | polynomial
NOT: Example 3
3. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 5.4
STA: 2A.7.D KEY: factoring polynomials | factored completely | polynomial
NOT: Example 1
4. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 5.4
STA: 2A.7.D | 2A.7.E KEY: factoring polynomials | factored completely | polynomial
NOT: Example 2
5. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 5.4
STA: 2A.7.D | 2A.7.E KEY: factoring polynomials | factored completely | polynomial
NOT: Example 2
6. ANS:
f(x)
g(x)
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
The graph of g is a vertical shrink of the parent quadratic function.
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.2
STA: 2A.2.A | 2A.6.C
KEY: graphing functions and parent functions | describing transformations | parent function
NOT: Example 4
7. ANS:
f(x)
g(x)
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
The graph of g is a translation 3 units
right, a vertical shrink, and a translation 3 units up of the parent absolute value function.
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 1.2
STA: 2A.2.A | 2A.6.C
KEY: graphing functions and parent functions | describing transformations | parent function | combinations of
transformations NOT: Example 5
8. ANS:
f(x)
g(x)
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
The graph of g is a vertical stretch of the parent absolute value
function.
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.2
STA: 2A.2.A | 2A.6.C
KEY: graphing functions and parent functions | describing transformations | parent function
NOT: Example 4
9. ANS:
f(x)
g(x)1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
The graph of g is a translation 3 units
right, a vertical stretch, a reflection in the -axis, and a translation 2 units down of the parent quadratic
function.
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 1.2
STA: 2A.2.A | 2A.6.C
KEY: graphing functions and parent functions | describing transformations | parent function | combinations of
transformations NOT: Example 5
10. ANS:
(3, –4)
x = 3
(1, 0) (5, 0)
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 3.2
STA: 2A.4.B
KEY: axis of symmetry | intercept form | quadratic function | parabola | vertex of a parabola | x-intercept
NOT: Example 4
11. ANS:
The minimum value is –2. The domain is all real numbers and the range is . The function is decreasing
to the left of and increasing to the right of .
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 3.2
STA: 2A.4.B
KEY: axis of symmetry | standard form | minimum value | maximum value | quadratic function | parabola |
vertex of a parabola | domain | range | increasing function | decreasing function
NOT: Example 3
12. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 5.2
STA: 2A.7.B KEY: multiplying polynomials | polynomial
NOT: Example 3
13. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 5.2
STA: 2A.7.B KEY: special product patterns | polynomial
NOT: Example 6
14. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 5.2
STA: 2A.7.B KEY: multiplying polynomials | polynomial
NOT: Example 3
15. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 2.2
STA: 2A.3.B
KEY: system of three linear equations | solution of a system of three linear equations | linear equation in
three variables | one solution NOT: Example 1
16. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.1
STA: 2A.6.K | 2A.7.I
KEY: set-builder notation | writing intervals in set-builder notation
NOT: Example 3
17. ANS:
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 4.3
STA: 2A.4.F
KEY: solving quadratic equations by completing the square | quadratic equation | solving quadratic equations
NOT: Example 4
18. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.1
STA: 2A.4.F
KEY: solving quadratic equations using square roots | solving quadratic equations | quadratic equation in one
variable NOT: Example 2
19. ANS:
and
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 5.5
STA: 2A.7.D KEY: solving polynomial equations | polynomial equation
NOT: Example 1
20. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.3
STA: 2A.4.F
KEY: solving quadratic equations using square roots | quadratic equation | solving quadratic equations
NOT: Example 1
21. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.3
STA: 2A.4.F
KEY: solving quadratic equations by completing the square | quadratic equation | solving quadratic equations
NOT: Example 3
22. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.3
STA: 2A.4.F
KEY: solving quadratic equations using square roots | quadratic equation | solving quadratic equations
NOT: Example 1
23. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.1
STA: 2A.4.F
KEY: solving quadratic equations by factoring | solving quadratic equations | quadratic equation in one
variable NOT: Example 3
24. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.1
STA: 2A.4.F
KEY: solving quadratic equations by graphing | solving quadratic equations | quadratic equation in one
variable NOT: Example 1
25. ANS:
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 4.2
STA: 2A.4.F KEY: solving quadratic equations | complex solutions and zeros | quadratic equation
NOT: Example 6
26. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.3
STA: 2A.6.C
KEY: writing functions representing transformations | transformation | combinations of transformations
NOT: Example 4
27. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.3
STA: 2A.6.C KEY: writing functions representing transformations | transformation
NOT: Example 3
28. ANS:
, ;
0 10 200–10–20
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.4
STA: 2A.6.E
KEY: absolute value equation | solving absolute value equations | graphing absolute value solutions
NOT: Example 1
29. ANS:
2 4–2–4 x
2
4
–2
–4
y
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 2.4
STA: 2A.3.F | 2A.3.G
KEY: system of linear inequalities | graph of a system of linear inequalities | graphing systems of linear
inequalities | no solution NOT: Example 3
30. ANS:
2 4–2–4 x
2
4
–2
–4
y
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 2.4
STA: 2A.3.F | 2A.3.G
KEY: system of linear inequalities | graph of a system of linear inequalities | graphing systems of linear
inequalities NOT: Example 2
31. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.1
STA: 2A.6.K | 2A.7.I KEY: writing intervals in interval notation
NOT: Example 1
32. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 2.3
STA: 2A.3.B
KEY: system of three linear equations | augmented matrix | writing augmented matrices | dimensions of a
matrix | elements of a matrix | solving systems of equations | technology
NOT: Example 3
33. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 2.3
STA: 2A.3.B KEY: augmented matrix | writing augmented matrices | dimensions of a matrix
NOT: Example 1
34. ANS:
;
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 3.1
STA: 2A.4.B KEY: quadratic function | parabola | vertex of a parabola | vertex form
NOT: Example 4
35. ANS:
;
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 3.1
STA: 2A.4.B KEY: quadratic function | parabola | vertex of a parabola | vertex form
NOT: Example 3
36. ANS:
(5, 4)
x = 5
2 4 6 8–2–4–6–8 x
2
4
6
8
–2
–4
–6
–8
y
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 3.2
STA: 2A.4.B
KEY: axis of symmetry | quadratic function | parabola | vertex of a parabola | vertex form
NOT: Example 1
37. ANS:
(0, 3)
x = 0
2 4 6 8–2–4–6–8 x
2
4
6
8
–2
–4
–6
–8
y
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 3.2
STA: 2A.4.B
KEY: axis of symmetry | standard form | quadratic function | parabola | vertex of a parabola
NOT: Example 2
38. ANS:
(3, –6)
x = 3
2 4 6 8–2–4–6–8 x
2
4
6
8
–2
–4
–6
–8
y
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 3.2
STA: 2A.4.B
KEY: axis of symmetry | standard form | quadratic function | parabola | vertex of a parabola
NOT: Example 2
39. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.2
STA: 2A.7.A KEY: adding or subtracting complex numbers
NOT: Example 3
40. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.2
STA: 2A.7.A KEY: multiplying complex numbers NOT: Example 5
41. ANS:
2 4–2–4 x
2
4
–2
–4
y
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.6
STA: 2A.4.H
KEY: quadratic inequality in two variables | graphing quadratic inequalities in two variables | graph of a
quadratic inequality NOT: Example 1
42. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 2.4
STA: 2A.3.E | 2A.3.F | 2A.3.G
KEY: application | writing systems of linear inequalities | graphing systems of linear inequalities | solution of
a system of linear inequalities NOT: Example 5-1
43. ANS:
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 2.1
STA: 2A.3.A | 2A.3.B KEY: application | system of three linear equations
NOT: Example 4-2
44. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 2.1
STA: 2A.3.B
KEY: system of three linear equations | solution of a system of three linear equations | linear equation in
three variables | solving three-variable systems of linear equations | solving systems of equations by
substitution | one solution NOT: Example 1
45. ANS:
PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 2.2
STA: 2A.3.B
KEY: system of three linear equations | solving three-variable systems of linear equations | Gaussian
elimination NOT: Example 4
46. ANS:
0 20–2–4–6
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.5
STA: 2A.6.F
KEY: absolute value inequality | solving absolute value inequalities | inequality | solving inequalities | graph
of an inequality | graphing absolute value inequalities NOT: Example 1
47. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 6.2
STA: 2A.7.G
KEY: properties of radicals | writing radical expressions in simplest form | simplest form of a radical
NOT: Example 3
48. ANS:
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 4.2
STA: 2A.7.A KEY: finding square roots of numbers NOT: Example 1
49. ANS:
y = 1, y =
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.4
STA: 2A.6.E KEY: absolute value equation | solving absolute value equations
NOT: Example 2
50. ANS:
0 1 2 3 4 50–1–2–3–4–5
PTS: 1 DIF: Level 1 REF: Algebra 2 Sec. 1.1
STA: 2A.6.K | 2A.7.I KEY: set-builder notation
NOT: Example 2