Algebra 1 Final Exam Topics List (2016/2017)
Chapter 5
5-6 Graphing Linear Inequalities in two variable and applications
Chapter 6
6-1 Graphing Systems of Equations
6-2 Substitution
6-3/6-4 Elimination
6.5 Applying Systems of Linear Equations
6-6 Systems of Inequalities and Applications
Chapter 7
7-1 Multiplication Properties of Exponents
7-2 Division Properties of Exponents
7-4 Scientific Notation
7-5 Exponential Functions
7-6 Growth and Decay
Chapter 8
8-1 Adding and Subtracting Polynomials
8-2 Multiplying a Polynomials by a Monomial
8-3 Multiplying Polynomials
8-4 Special Products
8-5 Using the Distributive Property
8-6 Solving
8-7 Solving
8-8 Differences of Squares
8-9 Perfect Squares & Solving by Square Roots
Chapter 9
9-1 Graphing Quadratic Functions
9-2 Solving Quadratic Equations by Graphing
9-5 Solving Quadratic Equations by Using the Quadratic Formula and Applications
Chapter 10
10-2 Simplifying Radical Expressions
To prepare for the Final Exam, you should complete the problems in the review packet, review old tests/quizzes, and study your notes and homework assignment
Indicate the answer choice that best completes the statement or answers the question.Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
1.
a. / infinitely many
/ b. / no solution
c. / one solution; (0, 1)
/ d. / one solution; (1, 0)
2.
a. / one solution; (2, 1)
/ b. / infinitely many
c. / no solution
/ d. / one solution; (1, 2)
Use substitution to solve the system of equations.
3.y = 5x + 37
2x – 5y = –1
a. / (–8, –3) / b. / (–2, –12)
c. / (–3, –8) / d. / (3, –2)
Use substitution to solve the system of equations.
4.26 = x – 4y–4x – 48 =3y
a. / (–6, –8) / b. / (2, 10)
c. / (5, –10) / d. / infinitely many solutions
5.The length of a rectangular poster is 10 inches longer than the width. If the perimeter of the poster is 124 inches, what is the width?
a. / 16 inches / b. / 26 inches
c. / 28.5 inches / d. / 36 inches
6.The sum of two numbers is 90. Their difference is 12. What are the numbers?
a. / no solution / b. / 31 and 59
c. / 35 and 47 / d. / 39 and 51
7.At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $12.00. Sabrina bought 9 CDs and spent a total of $114.00. How many $12.00 CDs did she purchase?
a. / 9 / b. / 6
c. / 5 / d. / 3
8.Jordan is 3 years less than twice the age of his cousin. If their ages total 48, how old is Jordan?
a. / 15 / b. / 12
c. / 31 / d. / 17
Use elimination to solve the system of equations.
9.–7x + 10y = 101
–7x + 5y = 61
a. / (–3, 8) / b. / (3, –8)
c. / (–12, 7) / d. / (12, –7)
10.10x – 4y = –122
–3x + 6y = 75
a. / (3, –3) / b. / (8, –9)
c. / (–3, 3) / d. / (–9, 8)
11.The cost of 3 large candles and 5 small candles is $6.40. The cost of 4 large candles and 6 small candles is $7.50. Which pair of equations can be used to determine, t, the cost of a large candle, and s, the cost of a small candle?
a. / / b. /
c. / / d. /
Determine the best method to solve the system of equations. Then solve the system.
12.
a. / elimination using subtraction;
b. / elimination using addition;
c. / elimination using subtraction;
d. / elimination using addition;
Solve the system of inequalities by graphing.
13.
a. / / b. /
c. / / d. /
14.
a. / / b. /
c. / / d. /
Simplify. Assume that no denominator is equal to zero.
15.(–2hi3j2)(9h2ij4)
a. / 18h3i4j6 / b. / –18h3i4j6
c. / 18h2i3j8 / d. / –18h2i3j8
16.(2g4h3)4
a. / 8g8h7 / b. / 16g16h12
c. / 16g8h7 / d. / 8g16h12
17.
a. / / b. /
c. / / d. /
18.
a. / / b. /
c. / / d. /
19.
a. / / b. /
c. / / d. /
20.
a. / / b. /
c. / 1 / d. /
21.
a. / / b. /
c. / / d. /
Express the number in scientific notation.
22.0.0028446
a. / 28.45 × 10–4 / b. / 0.2845 × 10–2
c. / 2.845 × 10–3 / d. / 284.5 × 10–5
Express the number in the statement in standard notation.
23.The Library of Congress collection includes 1.26 × 108 items.
a. / 12,600,000 / b. / 126,000,000
c. / 1,260,000,000 / d. / 12,600,000,000
Evaluate. Express the result in scientific notation.
24.(5.2 × 105)(4 × 10–8)
a. / 20.8 × 10–3 / b. / 2.08 × 10–4
c. / 2.08 × 10–2 / d. / 0.208 × 10–1
25.
a. / / b. /
c. / / d. /
Graph the function.
26.
a. /
/ b. /
c. /
/ d. /
27.
a. /
y-intercept = 1
domain: all real numbers
range: y > 0 / b. /
y-intercept = –1
domain: all real numbers
range: y > –2
c. /
y-intercept = 3
domain: all real numbers
range: y > 2 / d. /
y-intercept = –1
domain: all real numbers
range: y > –2
Solve the problem of exponential growth.
28.A company's value increased by 5.75% from 2010 to 2011. Assume this continues. If the company had a value of $11,140,000 in 2010, write an equation for the value of the company for t years after 2010.
a. / / b. /
c. / / d. /
Solve the equation of exponential decay.
29.A car sells for $25,000. If the rate of depreciation is 15%, what is the value of the car after 7 years? Round to the nearest hundred.
a. / $8000 / b. / $9400
c. / $7400 / d. / $9800
Express the area of the figure as a monomial.
33.
Express the volume of the solid as a monomial.
34.
35.The area of the rectangle is square units. Find the width of the rectangle.
Indicate the answer choice that best completes the statement or answers the question.
Write each polynomial in standard form.
36.2x3 + x5 – 3 +7x7
a. / 3 + 2x3 + x5 +7x7 / b. / 7x7 + x5 + 2x3 + 3
c. / 7x7 + 2x3 + x5 – 3 / d. / 7x7 + x5 + 2x3 – 3
Find the sum or difference.
37.(5a – 3b2 – a) + (b – 4 + 7a2)
a. / 4a2+ 4a + b – 4
b. / 7a2 – 3b2 + 5a + b – 4
c. / 7a2 – 3b2 + 4a + b – 4
d. / 7a2 – 3b2 + 4a + b + 4
38.(11p – 5q2 – q) – (q2 – 5p + 7p2)
a. / 7p2 – 6q2 + 16p – q
b. / –7p2 – 6q2 + 6p – q
c. / –7p2 – 4q2 + 16p – q
d. / –7p2 – 6q2 + 16p – q
Find the product.
39.–5s4t3(–6s4t5 – 8st3 – 5t)
a. / 30s16t15 + 40s4t9 + 25s4t3
b. / 30s8t8 + 40s5t6 + 25s4t4
c. / 30s8t8 + 40s5t6 + 25t4
d. / –30s8t8 – 40s5t6 – 25s4t4
Solve the equation.
40.
a. / / b. /
c. / / d. /
Find the product.
41.(–3t – 6v)(–7t – 5v)
a. / 21t2 + 30v2
b. / 21t2 + 57tv + 30v2
c. / –10t – 11v
d. / 21t2 –57tv + 30v2
42.(r – 9)(r + 3)
a. / r2 – 27 / b. / r2 + 12r – 27
c. / r –6 / d. / r2 –6r – 27
43.(6m2 –5m + 5)(–4m2 –2m –8)
a. / 2m2 –7m –3
b. / –24m4 + 8m3 –58m2 +30m –40
c. / –24m2 + 10m –40
d. / –24m4 –32m3 –78m2 –50m –40
44.(b + 5)2
a. / b2 + 10b + 25 / b. / b2 + 25
c. / b2 + 25b + 25 / d. / 2b + 10
Find the product of each sum and difference.
45.(4l + 5)(4l – 5)
a. / 16l2 + 20l – 25 / b. / 16l2 – 25
c. / 16l2 + 25 / d. / 8l
Factor the polynomial.
46.45j2k – 30j5k6 + 15j3
a. / 15j2(3k – 2j3k6 +j)
b. / 15(3j2k – 2j5k6j3)
c. / 15j2k(3 – 2j3k5 +j)
d. / 3j2(3k – 2j3k6 +j)
Factor the trinomial.
47.g2 –8g –48
a. / (g – 4)(g + 12) / b. / (g + 6)(g –14)
c. / (g –16)(g + 3) / d. / (g + 4)(g –12)
Factor the trinomial, if possible. If the trinomial cannot be factored using integers, write prime.
48.t2 + 2t + 4
a. / (t + 4)(t + 4)
b. / (t – 4)(t – 2)
c. / (t+4)(t+2)
d. / prime
Factor the polynomial.
49.b2 –16b +64
a. / (b +8)2
b. / (b +8)(b –8)
c. / (b –8)2
d. / b(b –16)
50.9m4 +33m3 –185m2 +175m
a. / m(m +7)(3m +5)2
b. / m(m +7)(3m –5)2
c. / m(m +7)(3m –5)(3m +5)
d. / (m2 +7m)(3m –5)2
Solve the equation.
51.
a. / / b. /
c. / / d. /
52.
a. / / b. /
c. / / d. /
Solve the trinomial equation.
53.k2 + 3k = 108
a. / {–14, 7} / b. / {12, –9}
c. / {–12, 9} / d. / {–10, 7}
Solve the equation.
54.14x2 –51x+ 7 = 0
a. / {, } / b. / {7, }
c. / {–2, –49} / d. / {2, 49}
Factor the polynomial, if possible. If the polynomial cannot be factored, write prime.
55.12v2 – 27
a. / 3(3v + 2)(3v – 2)
b. / 3(2v + 3)(2v – 3)
c. /
d. / (2v + 3)(2v – 3)
The measures of two sides of a triangle are given. If P is the perimeter, find the measure of the third side.
56.
Find the area of the shaded region in the simplest form.
57.
Find the area of the shaded region for the figure.
58.
Write the equation of the axis of symmetry.
59.y = 3x2 + 5x–6
a. / x = / b. / x =
c. / x = / d. / x =
Find the coordinates of the vertex of the graph of the function.
60.y = 4x2 – 3
a. / (0, –3) / b. / (0, )
c. / (0, ) / d. / (3, 0)
Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function.
61. –+8 3
a. / The function has a minimum value. The minimum value of the function is –45.
b. / The function has a maximum value. The maximum value of the function is 19.
c. / The function has a maximum value. The maximum value of the function is –45.
d. / The function has a minimum value. The minimum value of the function is 19.
Solve the equation by graphing.
62.
a. / –2 / b. / 4, 0
c. / –4, 0
/ d. / –3, –1
Solve the equation by using the Quadratic Formula. Round to the nearest tenth if necessary.
63.h2 + 12h – 9 = 0
64.
65. Simplify compeltely.
66. Simplify. nAnswers should not be written ith negative expoinents.
67. Classify by degree and number of terms.
68. Factor completely.
69. Simplify.
70. Solve by square roots.
71. Solve by square roots
72. Write in simplest radical form
73. Graph the linear inequality
76. The product of two consecutive negative integers is 1122. What are the numbers?
77. The length of a rectangle is 4 less than twice the width. The area of the rectangle is 70. Find the dimensions of the rectangle.
78. Evaluate:
Answer Key
2.d
3.a
4.a
5.b
6.d
7.b
8.c
9.a
10.d
11.a
12.d
13.d
14.c
15.b
16.b
17.d
18.d
19.a
20.c
21.b
22.c
23.b
24.c
25.a
26.b
27.b
28.c
29.a
30.c
31.c
32.a
33.
34.
35. units
36.d
37.c
38.d
39.b
40.a
41.b
42.d
43.b
44.a
45.b
46.a
47.d
48.d
49.c
50.b
51.c
52.a
53.c
54.a
55.b
56.
57.
58.
59.b
60.a
61.b
62.d
63.
64. 13 dimes, 7 nickels
65.
66.
67. quadratic monomial
68.
69. 12
70.
71.
72.-
73. ------
74. 48, 60, 72
75.
76. -33 and -34
77.w = 8 and l = 12
78.
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