Download Name

Name __________________________________________
Date ___________________
Algebra 1 – Review for Algebra 1 Final Exam June 2008
Chapter 7 – Solving Systems of Linear Equations
Graph each system of equations. Then determine whether the system has no solution, one
solution, or infinitely many solutions. If it has one solution, name it.
1.
y=–x+4
y=x–4
2.
2x – y = – 3
6x – 3y = – 9
3.
x+y=–2
x+y=3
Use substitution to solve each system of equations. If the system does not have exactly one
solution, state whether it has no solution or infinitely many solutions.
4.
y = 3x
5.
x+y=4
6.
x – 6y = 4
5x – y = 10
7x – 2y = 11
7.
3x – 18y = 4
x – 5y = 10
2x – 10y = 20
Use elimination to solve each system of equations.
8.
2x + 5y = 3
– x + 3y = – 7
10.
x – 3y = 10
x + 2y = 15
9.
2x + 5y = 9
2x + y = 13
Solve each system of inequalities by graphing.
11.
y<x–1
y ≤ 2x + 1
13.
12.
x+y≥2
2x – y < 1
Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. 321
tickets were sold altogether for $937.50. How many of each kind of ticket were sold?
Chapter 8 – Polynomials
Simplify.
14.
3y 5  y 3
16.
(w5y4)3
18.
16r 3 s 5
4r 1 s 2
20.
Express 0.00098 in scientific notation.
21.
Express 1.27 × 105 in standard notation.
22.
Evaluate (2.5 × 10-2) (4 × 106).
Find each sum or difference.
23.
(5n2 – 2ny + 3y2) – (9n2 – 8ny – 10y2)
24.
(11m2 – 2mn + 8n2) + (8m2 + 4mn – 2n2)
15.
17.
19.
(9m3n5) (– 2mn2)
p6q 2
p3q
 8x y 
4x y
2
2 2
3
3
25.
(x2 + 5y) – (2x2 + 6y)
Find each product.
26.
5hk2 (2h2k – hk3 + 4h2k2)
27.
(4x2 + 2y2) (2x2 – y2)
28.
(3s + 5) (2s2 – 8s + 6)
29.
(5c – 4)2
30.
(7a – 3b) (7a + 3b)
31.
(4n + 1)2
Chapter 9 – Factoring
Factor each polynomial. If the polynomial cannot be factored, write prime.
32.
35a3bc2 – 45a2b2c
33.
3xy – 4x + 6y – 8
34.
x2 – 11x + 24
35.
n2 + n – 42
36.
10y2 – 31y + 15
37.
8n2 – 36n + 40
38.
36m2 – 49
39.
2x4 – 18x2
40.
25w2 – 60w + 36
41.
9a2 + 42a – 49
Solve each equation.
42.
(3n + 2) (n – 2) = 0
43.
16y2 – 8y = 0
44.
x2 = x + 110
45.
8n2 + 4 = 12n
46.
36x2 + 49 = 84x
47.
4y2 + 16y + 7 = 0
48.
49w2 – 25 = 0
49.
5d3 – 80d = 0
Chapter 11 – Radicals
Simplify each expression.
50.
24  3
51.
75y 4 w 3
52.
14
45
53.
2 3
6 2
54.
3 x 4 x 7 x
56.
Find

6 7

21  2
55.
20  2 45  3 80
58.
2 x  14  13   7

Solve each equation.
57.
59.
x2 3
10 
x8x
Chapter 10 – Quadratics
Find the vertex, axis of symmetry, x-intercepts, and y-intercept of each quadratic. Identify
whether the vertex is a minimum or maximum.
60.
y = x2 – 4x + 3
61.
y = -x2 + 4x + 5
62.
Miranda throws a set of keys up to her brother, who is standing on a third-story balcony
with his hands 38 feet above the ground. If Miranda throws the keys with an initial
velocity of 40 feet per second, the equation h = -16t2 + 40t + 5 gives the height of the keys
after t seconds.
a.
How long does it take the keys to reach their highest point?
b.
How high do the keys reach?
c.
Will her brother be able to catch the keys? Explain.
Chapter 12 – Rational Expressions
Simplify each expression.
63.