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Algebra 1 Enriched ~ Final Exam Topics (2013-2014)
Chapter 7 – Systems of Equations and Inequalities
Section 7.1 – Solving Systems by Graphing
Section 7.2 – Solving Systems by Substitution
Section 7.3 – Solving Systems by Elimination
Section 7.4 – Applications of Linear Systems
Section 7.5 – Linear Inequalities
Section 7.6 – System of Linear Inequalities
Chapter 8 – Exponents and Exponential Functions
Section 8.1 – Zero and Negative Exponents
Section 8.2 – Scientific Notation
Section 8.3 – Multiplication Properties of Exponents
Section 8.4 – More Multiplication Properties of Exponents
Section 8.5 – Division Properties of Exponents
Chapter 9 – Polynomials and Factoring
Section 9.1 – Adding and Subtracting Polynomials (degree of a polynomial)
Section 9.2 – Multiplying and Factoring
Section 9.3 – Multiplying Binomials
Section 9.4 – Multiplying Special Cases
Section 9.5 – Factoring Trinomials of the Type x2+bx+c
Section 9.6 – Factoring Trinomials of the Type ax2+bx+c
Section 9.7 – Factoring Special Cases
Section 9.8 – Factoring by Grouping
Chapter 10 – Quadratic Equations and Functions
Section 10.1 – Exploring Quadratic Graphs
Section 10.2 – Quadratic Functions
Section 10.4 – Solving Quadratic Equations (Square Root Method)
Section 10.5 – Factoring to Solve Quadratic Equations (Zero-Product Property)
Section 10.7 – Using the Quadratic Formula
Section 10.8 – Using the Discriminant
Chapter 11 – Radical Expressions and Equations
Section 11.1 – Simplifying Radicals
Chapter 12 – Rational Expressions and Functions
Section 12.3 – Simplifying Rational Expressions
Section 12.4 – Multiplying and Dividing Rational Expressions
Section 12.8 – Counting Methods
1.
2.
3.
4.
5.
How to prepare for the exam:
Do the review packet and check your answers. Correct your mistakes and ask for help if necessary.
Re-do some of the problems from old quizzes and tests.
Try the odd problems in your textbook from the sections above.
Read over your notes and create index cards.
Ask questions during the review session in class or during extra help.
“Math is not a spectator sport.” You must PRACTICE, PRACTICE, PRACTICE!!!
Algebra 1 Enriched Final Exam Review 2014
1. Is (-1, 2) a solution of the system? Explain
2. Is (-4, 3) a solution of the system? Explain.
3. Solve by graphing. Check your solution.
Graph the system. Tell whether the system has no solution or infinitely many solutions.
4.
5.
6. Without graphing, decide whether the system has one solution, no solution, or
infinitely many solutions. Explain.
Solve the system using substitution.
7.
8.
9. Solve the system using elimination.
10. The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this
situation. Solve by elimination to find the two numbers.
11. An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates.
John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00.
Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was
charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?
12. You decide to market your own custom computer software. You must invest $3,255 for computer
hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, how many copies
must you sell to break even?
13. Graph the inequality on a coordinate plane.
14. Graph the inequality on a coordinate plane.
15. Write the linear inequality shown in the graph to the right.
16. You have $47 to spend at the music store. Each cassette tape costs $5 and each CD costs $10. Write
and graph a linear inequality that represents this situation. Let x represent the number of tapes and y
the number of CDs.
17. Find a solution of the system of linear inequalities.
18. Solve the system of linear inequalities by graphing.
19. Write a system of inequalities for the graph to the right.
Simplify each expression.
20.
30.
21.
31.
22.
32.
23.
33.
24.
25.
34.
26.
27.
35.
28.
29.
36.
37. Evaluate
for x = –3 and y = 2.
Write the number in scientific notation.
38. 8,670,000,000
39.
0.0805
Write the number in standard notation.
41.
40.
Simplify the expression. Write the answer using scientific notation.
42.
43.
44.
45. Evaluate the function rule for the given value.
for x = –5
46. Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.
2 – 11x2 – 8x + 6x2
47. Find the degree of the monomial.
6x8y5
48. Name the polynomial based on its degree and number of terms. 6x3 – 9x + 3
49. Find the perimeter of the figure to the right.
Simplify the difference.
50. (–7x – 5x4 + 5) – (–7x4 – 5 – 9x)
51. (4w2 – 4w – 8) – (2w2 + 3w – 6)
Simplify the product.
52. 2n(n2 + 3n + 4)
53.
7a3(5a6 – 2b3)
55.
54c3d4 + 9c4d2
Factor the polynomial.
54.
56. Find the GCF of the terms of the polynomial.
8x6 + 32x3
57. The Johnsons want to cover their backyard with new grass. Their backyard is rectangular, with a length of
3x – 5 feet and a width of 4x – 10 feet. However, their rectangular swimming pool, along with its surrounding
patio, has dimensions of x + 8 by x – 2 feet. What is the area of the region of the yard that they want to cover
with new grass?
Simplify.
60.
(2x – 6)2
58. (3x – 7)(3x – 5)
61.
(2n2 + 4n + 4)(4n – 5)
59.
62.
(4m2 – 5)(4m2 + 5)
63. Find the area of the UNSHADED region. Write your answer in standard form.
64.
Find the volume of the cube.
Factor the expression.
65. w2 + 18w + 77
71.
16j2 + 24j + 9
66. k2 + kf – 2f2
72.
r2 – 49
67. x2 – 10xy + 24y2
73.
4x2 – 81y2
68. 12d2 + 4d – 1
74.
6g3 + 8g2 – 15g – 20
69.
75.
50k3 – 40k2 + 75k – 60
70. 36y2 – 84y – 147
76.
6x4 – 9x3 – 36x2 + 54x
77. Identify the vertex of the graph to the right. Tell whether it is a minimum or maximum
78. Order the group of quadratic functions from widest to narrowest graph.
,
,
79. Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function.
80. Graph
81. Simplify
82. Simplify
. Label the axis of symmetry and vertex.
.
.
Solve the equation using square roots.
83. 7
+ 6 = 13
84.
85. Find the value of x. If necessary, round to the nearest tenth.
86. Solve the equation using the zero-product property.
Solve the equation by factoring.
87.
88.
89.
90.
Use the quadratic formula to solve the equation. Write your answers in simplest radical form.
91.
92.
Find the number of real number solutions for the equation.
93.
94.
Simplify the radical expression.
95.
96.
97.
98. A square garden plot has an area of 24 ft2.
a. Find the length of each side in simplest radical form.
b. Calculate the length of each side to the nearest tenth of a foot.
99. Prestige Builders has a development of new homes. There are four different floor plans, seven exterior colors,
and an option of either a two-car or a three-car garage. How many choices are there for one home?
100. In how many ways can 12 basketball players be listed in a program?
101. How many different arrangements can be made with the letters in the word POWER?
102. At a pizza parlor, Jerome has a choice of pizza toppings and sizes. The topping choices are sausage, onions,
and pineapple. The size choices are mini and small. Draw a tree diagram that shows the number of possible
pizza combinations that Jerome can order.
Simplify the rational expression.
103.
104.
105.
Algebra 1 Enriched Final Exam Review
ANSWERS
1.
Yes, (−1, 2) makes both equations true.
2.
No, (−4, 3) is not a solution to the system. It is not on y = -3
3.
(8, 1)
4.
No Solution
5.
Infinitely Many solutions
6.
The system has one solution., A system of linear equations has no solution when the equa-
tions are of parallel lines and infinitely many solutions when the equations are of the same line. The
slopes of the lines are not equal, so neither case applies.
7.
(−6, −24)
8.
(2, -2)
9.
(15,-10)
10.
11.
12.
13.
x + y = 82
x – y = 24
53 and 29
admission fee: $3.25
skate rental fee: $2.50
300 copies
14.
15.
16 .
17. (2, 17)
18.
19.
20. 1
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40. 90,000
41. 0.0907
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
–5x2 – 8x + 2; quadratic trinomial
13
cubic trinomial
14x + 2
2x4 + 2x + 10
2w2 – 7w – 2
2n3 + 6n2 + 8n
35a9 – 14a3b3
2x(x2 + 2x + 4)
9c3d2(6d2 + c)
8x3
11x2 – 56x + 66 ft2
9x2 – 36x + 35
59.
60.
61.
62.
63.
64.
65.
4x2 – 24x + 36
8n3 + 6n2 – 4n – 20
16m4 – 25
10x + 25 square units
64x3 – 240x2 + 300x – 125 cubic units
(w + 7)(w + 11)
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
(k + 2f)(k – f)
(x – 6y)(x – 4y)
(6d – 1)(2d + 1)
2(5x – 2)(2x + 3)
3(2y – 7)(6y + 7)
(4j + 3)2
(r – 7)(r + 7)
(2x + 9y)(2x – 9y)
(2g2 – 5)(3g + 4)
5(2k2 + 3)(5k – 4)
3x(x2 – 6)(2x – 3)
(1, –1); minimum
78.
,
79.
,
; vertex:
80.
Axis of symmetry:
Vertex:
81.
82.
83.
84.
85.
–50
x=
no real number solutions
10.3 in.
86. n = 0 or n =
87. z = –3 or z = 9
88.
89.
90.
91. 9, 14
92.
93. 2 real solutions
94. no real solutions
95.
96.
97.
98.
ft; 4.9 ft
99. 56
100. 479,001,600
101. 120
102.
or
103.
104.
105.