Download Final Exam Review 2nd semester

Final Exam Review 2nd semester
7. Evaluate
for
8. Simplify
.
and
.
1. Tell whether the ordered pair (1, 3) is a solution
of the system
.
9.
2. Solve
9. The planet Earth has an average distance from the
sun of about 93,000,000 miles. Write this number
in scientific notation.
by using substitution.
Express your answer as an ordered pair.
10. Simplify
.
11. Simplify
3. Solve
.
by using elimination.
12. Simplify
.
Express your answer as an ordered pair.
13. The edge of a cube measures
m. What
is the volume of the cube in cubic centimeters?
b
4. Tell whether (4, 8) is a solution of
.
5. Write an inequality to represent the graph.
14. Simplify
y
.
5
4
15. Simplify
answer in scientific notation.
3
2
and write the
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
a
x
–2
–3
–4
–5
6. Tell whether (1, 11) is a solution of
16. The area of Asia is approximately
square kilometers. Its population is approximately
people. What is the approximate
population density (people per square kilometer)
of Asia? Write your answer in standard form. If
necessary, round your answer to the nearest
hundredth.
.
17. Simplify
.
27. Multiply.
18. A toy rocket is launched from a platform 29 feet
above the ground at a speed of 82 feet per second.
The height of the rocket in feet is given by the
polynomial
, where t is the time in
seconds. How high will the rocket be after 3
seconds?
28. Find the GCF of
and
.
29. Factor x2 + 42x + 80.
19. Add or subtract.
20. Add.
30. Factor the trinomial
.
31. Factor the trinomial
21. Subtract.
32. Factor
.
.
22
22
22. Multiply
23. Multiply.
33. Factor
.
24. Multiply.
34. Factor the trinomial
25. Multiply.
26. Multiply.
35. Factor
.
factor out negative first!!
.
36. Tell whether the graph of the quadratic function
opens upward or downward.
Explain.
39. Find the axis of symmetry of the parabola.
y
10
8
6
4
37. Find the domain and range.
2
–10 –8
y
–6
10
–4
–2
–2
–4
8
10
x
–8
4
–6
6
–6
6
–10 –8
4
–4
8
–10
2
(–8, 1)
2
–2
–2
2
4
6
8
40. Find the axis of symmetry of the graph of
.
x
10
–4
–6
–8
–10
41. Find the vertex of the parabola
38. Find the zeros of the quadratic function
from the graph.
.
y
10
8
6
y
10
4
8
2
6
–10 –8
4
–6
–4
–2
–2
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
2
4
6
8
10
–6
x
–8
–4
–10
–6
–8
–10
42. The height of a curved support beam can be
modeled by
. Find the height and
width of the beam.
height
width
x.
43. Order the functions from narrowest graph to
widest graph.
,
51. Solve
. If necessary, round to the
nearest hundredth.
, and
44. Solve the equation
the related function.
by graphing
45. A kicker starts a football game by “kicking off”.
The quadratic function
models the
football’s height after x seconds. How long is the
football in the air?
46. Use the Zero Product Property to solve the
equation
.
47. Solve the quadratic equation
factoring.
52. A gardener wants to create a rectangular vegetable
garden in a backyard. He wants it to have a total
area of 108 square feet, and it should be 12 feet
longer than it is wide. What dimensions should he
use for the vegetable garden? Round to the nearest
hundredth of a foot.
53. Solve
Formula.
by using the Quadratic
by
54. Solve 2x2 + 3x – 4 = 0 by using the Quadratic
Formula. If necessary, round to the nearest
hundredth.
48. Solve the quadratic equation
factoring.
by
55. Find the number of solutions of the equation
by using the discriminant.
49. The height of an arrow that is shot upward at an
initial velocity of 40 meters per second can be
modeled by
, where h is the height in
meters and t is the time in seconds. Find the time
it takes for the arrow to reach the ground.
56. Solve
.
50. Solve 121x2 + 64 = 0 by using square roots.
57. Solve
.
58. Solve
.
59. Simplify the expression
65. Multiply. Write the product in simplest form.
.
60. Simplify the expression
represent nonnegative numbers.
66. Multiply. Write the product in simplest form.
. All variables
67. Multiply. Simplify your answer.
61. Simplify
. The variable represents a
.
nonnegative number.
68. Solve the system
62. Simplify
by graphing.
.
63. A community is building a square park with sides
that measure 125 meters. To separate the picnic
area from the play area, the park is split by a
diagonal line from opposite corners. Determine the
approximate length of the diagonal line that splits
the square. If necessary, round your answer to the
nearest meter.
69. Graph the solutions of the linear inequality
.
70. Graph the system of linear inequalities
. Give two ordered pairs that are
solutions and two that are not solutions.
125 m
Picnic area
Play area
71. Compare the graph of
graph of
.
125 m
64. Simplify
. The variable represents a
nonnegative number.
72. Graph y = x2 – 4x – 1.
2x2 – 5 with the