Test 1 Review
Sections R.1 - 1.1
Fall 2010
Math 009
Name___________________________________
Directions: Read each question carefully and answer as clearly as possible. Place your answers on the given space(s) and
staple all work to the back of the page. All work must be included in order to receive credit. This is a sample of problems. If
you feel comfortable on these and on the assignments that I have handed out, then you should be fine on the test. This
review sheet is longer than the actual test.
Enouraging Quote: "D'Oh!"---Homer Simpson
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Write interval notation.
1) { x 7 < x ≤ 18 }
1)
Answer: (7, 18]
Calculate.
2) 6 · 8 2 + 4 · 7 - 8( 4 + 6)
2)
Answer: 332
Convert to decimal notation.
3) 8.0658 × 10-7
3)
Answer: 0.00000080658
Express the number in scientific notation.
4) 0.00000035301
4)
Answer: 3.5301 × 10-7
Simplify and write the answer using scientific notation.
15 × 104
5)
5 × 105
5)
Answer: 3 × 10-1
Simplify.
6) 3 -5 · 3 3· 3 -6
6)
Answer: 3 -8
7) (2n)3 · (5n)2
7)
Answer: 200n 5
8)
64x4 y-3
8x7 y-8
Answer:
8)
8y5
x3
1
9)
25 a 7 b-8 c-3 3
5 a 2 b-2 c2
Answer:
9)
125a15
b18 c15
10) (-7)0
10)
Answer: 1
Write an equivalent expression without negative exponents.
x-2 y11
11)
z -8
Answer:
11)
y11z 8
x2
Perform the indicated operations.
12) ( 9x4 + 7x2 - 5x ) - ( -8x3 + 2x2 - 5x - 3)
12)
Answer: 9x4 + 8x3 + 5x2 + 3
Determine the terms and degree of the polynomial.
13) 4x3 - 7x2 - x + 13
13)
Answer: Terms: 4x3 , -7x2 , -x, 13; degree: 3
Multiply.
14) (x + 4y)(x - 9y)
14)
Answer: x2 - 5xy - 36y2
15) (11a + 2c)(11a - 2c)
15)
Answer: 121a 2 - 4c2
16) (2x2 - 10y)(5x2 + 9y + z)
16)
Answer: 10x4 - 32x2 y + 2x2z - 90y2 - 10yz
17) (w - 3)2
17)
Answer: w2 - 6w + 9
Factor by grouping.
18) 9a3 - 9a 2 + 18a - 18
18)
Answer: 9(a - 1)(a 2 + 2)
Factor completely.
19) 27x2 - 117x - 90
19)
Answer: 9(3x + 2)(x - 5)
2
Factor out a common factor.
20) 3a2 - 12a + 27
20)
Answer: 3( a 2 - 4a + 9)
Factor the trinomial.
21) 12y2 - 17y + 6
21)
Answer: (4y - 3)(3y - 2)
Factor.
22) z 2 + 14z + 49
22)
Answer: (z + 7)2
Factor the trinomial.
23) 4x2 + 8x - 60
23)
Answer: 4(x - 3)(x + 5)
Perform the indicated operation.
y
7
24)
+
y-6
6-y
Answer:
24)
y- 7
y- 6
Divide and simplify.
4y2 - 64
8y - 32
25)
÷
y+ 5
y2 - 25
Answer:
25)
(y + 4)(y - 5)
2
Find the domain of the rational expression.
7x2 - 9x - 10
26)
x ( x2 + 3x - 10)
Answer: x
26)
x is a real number and x ≠ 0 and x ≠ -5 and x ≠ 2
Perform the indicated operation and simplify.
z 2 - 8z + 16 z2 + 2z
27)
·
z-4
z2 - 4
Answer:
27)
z(z - 4)
z-2
Simplify.
28)
64 - k2
28)
k2 - 10k + 16
Answer: -
k+ 8
k- 2
3
Simplify. Assume that no radicands were formed by raising negative quantities to even powers.
29) 5 5 - 2 125
Answer: -5
29)
5
Simplify.
30) ( 2 +
2)2
30)
Answer: 6 + 4 2
Rationalize the denominator.
5
31)
6
31)
30
6
Answer:
Simplify. Assume that variables can represent any real number.
3
32)
-216b3
32)
Answer: -6b
33)
4
768x6 y10
Answer: 4 x y2
33)
4
3x2 y2
Solve.
34) 7x + 10 = -2 - 3x
Answer: -
34)
6
5
35) -4x - 23 = -55
35)
Answer: 8
36) 4x - (2x - 1) = 2
Answer:
36)
1
2
37) 4(5x + 4) - 20 = 16x + 4
37)
Answer: 2
38) n 2 + 12n + 36 = 0
38)
Answer: -6
39) x2 + 6x - 27 = 0
39)
Answer: -9, 3
4
40) 30b2 + 37b - 3 = -13
Answer: -
40)
5
2
,6
5
41) 5x2 - 16x = 16
Answer: -
41)
4
,4
5
42) 4x2 - 24x + 32 = 0
42)
Answer: 2, 4
Find the center and radius of the circle.
43) (x - 3)2 + y2 = 49
43)
Answer: Center: (3, 0); radius: 7
Find the distance between the pair of points. Give an exact answer, and, where appropriate, an approximation to two
decimal places.
44) (3, -1) and (5, -5)
44)
Answer: 2 5
Find the equation of the circle. Express the equation in standard form
45)
45)
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4
-6
-8
-10
Answer: (x - 2)2 + (y - 2)2 = 4 2
Find an equation for the circle.
46) Endpoints of a diameter (-2, -1), (4, -9). Note: The diameter is all the way across the circle.
46)
Answer: (x - 1)2 + (y + 5)2 = 25
Find the midpoint of the segment having the given endpoints.
47) (-2, -8) and (4, 7)
1
Answer: 1, 2
5
47)
Plot the two points given by the ordered pairs.
48) A(-3, -3), B(-5, 3)
6
48)
y
6 x
-6
-6
6
y
4
B
2
-6
-4
-2
A
2
4
6 x
-2
-4
Answer:
-6
6
49) A(-5, 0), B(0, 6)
49)
6
y
6 x
-6
-6
Answer:
6
A
y
B
6 x
-6
-6
7
Graph the equation.
50) y = x2 - 8x + 10
50)
y
10
5
-10
-5
5
10
x
-5
-10
Answer:
y
10
5
-10
-5
5
10
x
-5
-10
8