Download Math-130-Exam #1 Practice Exam

Math-130-Exam #1
Practice Exam
Name___________________________________
Date: ______________________
Instructions: Show all work neatly. Answers without support will receive no credit. Your answers will be evaluated on
the correctness, completeness and use of mathematical concepts we have covered.
Perform the indicated operations. Write the resulting polynomial in standard form.
1) (3x + 4)2
2) (x - 5)(x2 + 5x + 25)
1)
2)
Factor the polynomial by removing any common monomial factor.
3) 24ax9 + 12ax6 - 60ax2
3)
Factor the polynomial completely. If a polynomial cannot be factored, state that it is irreducible.
4) 4x3 + 8x2 - 60x
4)
Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational
expression.
3x + 3
5)
5)
12x2 + 21x + 9
Multiply. Simplify and leave the numerator and denominator in your answer in factored form.
10x2 - 3x - 4 15x2 + 12x
·
6)
5x2 - x - 4
1 - 4x2
6)
Divide and/or multiply as indicated. Simplify and leave the numerator and denominator in your answer in factored form.
x2 - 12x + 36 5x - 30
÷
7)
7)
11x - 66
55
Add and subtract as indicated. Simplify and leave the numerator and denominator in your answer in factored form.
3
5
+
8)
8)
x2 - 3x + 2 x2 - 1
Evaluate the radical expressions or indicate that the root is not a real number.
3
9) 64
9)
Simplify the expression using the product and quotient properties of square roots. Assume that any variables represent
positive real numbers.
10) 294x2
10)
11)
5
x18y9 z 13
11)
1
Simplify the expression. Assume that all variables represent nonnegative real numbers.
12) 3x2 + 7 12x2 - 2 12x2
12)
Evaluate the expression without using a calculator.
13) -2431/5
13)
Simplify the expression, leaving your answer with only positive exponents. Assume that all variables represent positive
numbers.
14) x1/3 · x2/3
14)
Solve the rational equation.
6
12
+3=
15)
x+5
x+5
15)
Solve the equation by multiplying both sides by the LCD.
5
-2
=
16) 2 +
6z - 1 (6z - 1)2
16)
Solve the equation.
17) -3x - 5 - 6(x + 1) = 3x + 5
17)
18) -9.9x + 1.3 = -23.6 - 1.6x
18)
Solve the equation by the zero-factor property.
19) 3x2 - 2x - 5 = 0
19)
Solve and graph the inequality. Give answer in interval notation.
20) 7x - 9 6x - 12
20)
21) 4 < 3x + 4
21)
16
Solve the quadratic inequality. Write the solution set in interval notation.
22) (x - 2)(x + 4) > 0
23) x2 - 6x + 8 > 0
22)
23)
2
Answer Key
Testname: MATH-130-E1-F15-PRACTICE
1) 9x2 + 24x + 16
2) x3 - 125
3) 12ax2 (2x7 + x4 - 5)
4) 4x(x - 3)(x + 5)
3
1
,x - ,x
5)
4
4x + 3
6)
-1
3x(5x - 4)
(1 - 2x)(x - 1)
7) 1
8)
8x - 7
(x - 1)(x + 1)(x - 2)
9) 4
10) 7x 6
11) x3 yz 2
12) 11x 3
13) -3
5
x3 y4 z 3
14) x
15) {-3}
1 1
16) - ,
6 12
17) -
4
3
18) {3}
5
, -1
19)
3
20) [-3, )
21) (0, 4]
22) (- , -4) (2, )
23) (- , 2) (4, )
3