Math 130
Exam 1 Study Guide
Name:
Date:
Must show work for credit.
1. Evaluate each expression.
p
(a)
81
(b)
p
3
125
2. Simplify the expression. Assume that the letters denote any real number.
p
p
4
(a)
16x8
(b)
36x2 y 4
3. Simplify the expression. Assume that all letters denote positive numbers.
p
p
p
p
3
3
(a)
125
45
(b)
x4 + 8x
4. Evaluate each expression.
(a) ( 8)1/3
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(b) 52/3 · 51/3
1/6
Math 130 Exam 1 Study Guide.pdf (#22)
5. Simplify the expression and express the answer using rational exponents. Assume that all
letters denote positive numbers.
p
4
p
x7
p
5
3
(b) p
(a)
y y
4
x3
6. Find the sum, di↵erence, or product.
(a) (3x2
7x)
(x2
9x + 4)
(b) 2(3
4t) + t(t + 6)
(b) (3x
5y)2
7. Multiply the algebraic expressions.
(a) (7r
1)(r + 2)
8. Factor out the common factor.
(a) 5x
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(b) 2x4 + 8x3
35
2/6
10x2
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9. Factor by groupings.
(a) x3 + x2 + 4x + 4
(b) 3x3
2x2 + 18x
(b) 6y 2
5y
(b) 9u2
6uv + v 2
12
10. Factor the trinomial.
(a) x2 + 2x
15
6
11. Factor.
(a) x2
25
12. Simplify the rational expression.
(a)
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15x4
5x
(b)
3/6
x2 + 6x + 8
x2 + 5x + 4
Math 130 Exam 1 Study Guide.pdf (3/6)
13. Perform the indicated operation.
(a)
x2
2x
x2
15 x + 3
·
9
x 5
14. Perform the addition or subtraction.
1
2
(a)
+
x+4 x 3
(b)
y 2 + 6y + 5
2y 2 + 3y + 1
÷
y 2 + 2y 15 2y 2 7y + 3
(b)
2
x+3
1
x2 + 7x + 12
15. Solve the equation.
(a)
1
y
2
(c)
1
5
2
+
=
x + 3 x2 9
x 3
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1
2= y
3
(b) 2x
x x+1
+
= 6x
2
4
(d) (x + 3)2 = 16
4/6
Math 130 Exam 1 Study Guide.pdf (4/6)
16. Find an equation of the line in slope-intercept form that satisfies the given conditions.
(a) Through (1, 7) and ( 2, 5)
(b) Through ( 4, 5); perpendicular to the line 2x + 5y + 10 = 0
17. The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs
in one day and $4800 to produce 300 chairs in one day. Assuming that the relationship
between cost and the number of chairs produced is linear, find an equation that expresses this
relationship.
18. Find all real solutions of the equation factoring or by completing the square.
(a) x2
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6x
(b) 4x2
11 = 0
5/6
4x
15 = 0
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19. Find all real solutions of the equation.
(a) 3x2 + 7x + 4 = 0
(b) w2 = 3(w
1)
20. A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length
and width of the garden if its areas is 2400 ft2 .
21. The sum of the squares of two consecutive even integers is 1252. Find the integers.
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6/6
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