Name _____________________________________
Unit 1 Worksheets
Math 150
College Algebra and Trig
Revised: Fall 2009
Worksheet 1: Integral Exponents
Simplify each expression. Write all answers in exponential form.
1.
(85)4
4.
 3x 
 
 5y 
7.
(-5a2)(-5a3)4
10.
6
3
  (6 y )
7
2.
(x2y)3
3.
(3a2b3)5
5.
(7x8y)5
6.
(4wt)5(4wt)2
8.
(5a2b3c)3(ab3c2)4
9.
(z3)5(z2)6
11.
 9 wx 3
 2
 y
12.
 r 2 st 


 2n 
15.
4
2
  ⋅4
7
18.
1
2
  4ab
3
6
2



4
2
3
2
3
13.
(4x) (4x)
16.
 6b 2

 11
4 3



(-6q) (-6q)
17.
3
4
  (5x )
4
3
2 5
(z ) (z )
22.
 km 2 p 3 


4
 3n 
6
14.
5
19.
3
4
(
)
3
5
20.
(5x y ) (5xy )
21.
 7a 2 b 3 


 2 
23.
(-2pq)3(-2pq)4
24.
(3x2yz3)2(x4y)3
2 3 3
4 2
6
-1-
Evaluate each exponential expression, writing without exponents.
25.
(-2)6
26.
-26
27.
(-1)7
28.
-17
29.
-53
30.
(-5)3
31.
80
32.
(-6)0
33.
-130
34.
1
 
5
35.
50 + 60
36.
70 + (-7)0
37.
 2 1
  − 
 3  3
38.
(-5)0 + (-5)0
39.
-120 + (-12)0
40.
-250- (-25)0
41.
-r0
42.
08
80
0
0
0
-2-
Worksheet 2: Integral Exponents
Simplify each expression, writing with positive exponents
1) 8-2
1
4 −2
3) t7t-9
4) a-1b2
5) (vw )(v w )
b −5 c 2
6)
bc − 3
3 −2
7)
4
8)
3
4 −2
9) (a-1b2)-2
10) (x-2y-2)-1x2
11) (2x -3y2)(-6x2y -4)
12) (5x2y-3)-2
13) (-5a3b-2)2(2a-3b-1)
14)
15)
− 30a −5 b −3
− 5a 2 b −3
2)
-3
-2
 x −1 
16)  −1 
y 
 5x − 2
20)  3
 y



2 -1
7
−1
 w 
17)  −1 
z 
−2
−1
 x2 
21)  −3 
 3y 
2 -2
2 -3
 a5
18)  2
b
2



 a −3
22)  2
 2b
-2 2
23) (2x ) (2x ) (2x )
50 x 8 y −10
10 x 7 y − 2
-2 3
-2 -2
24) (3a ) (3a ) (3a )
−4



 2x 3
19)  3
 y



−2
3
 5xy 6
25)  4
 3z



−2
Express without fractions, using negative exponents where needed:
26)
9
x
27)
5
x3
28)
x2
y2
29)
-3-
a −3
b2
30)
1
x y3
−2
Worksheet 3: Division of Polynomials
Divide, using long division. Write any remainder as a fraction.
1.
(r2 - 2r - 20) ÷ (r - 5)
2.
(2a2 - 11a + 16) ÷ (2a + 3)
3.
2z 3 − 3z 2 + 8z + 6
2z + 1
4.
y3 − 1
y −1
5.
27 x 5 − 3x 3 + 6 x 2 − 2 x
3x − 1
-4-
Worksheet 4: Radicals
I. Evaluate:
1.
3
8
2.
3
64
3.
7.
3
−8
8.
5
32
9.
3
225
4.
− 64
10.
3
−1
3
5.
− 125
11.
4
81
5
3
6.
− 32
12.
125
4
II. Simplify:
13.
72
14.
17.
200
18.
21.
242
22.
50
15.
98
16.
3
16
3
54
19.
128
20.
3
250
3
− 250
23.
− 32
24.
3
− 16
y 14
27.
a 22
28.
3
m 15
3
III: Simplify
25.
x8
26.
29.
3
a 21
30.
3
x 24
31.
4
x8
32.
4
y 28
33.
4
a 20
34.
5
a 10
35.
5
y 15
36.
5
m 20
-5-
16
IV: Simplify
m 21 a 3
39.
5
b 10 z 15
40.
42.
a 19
43.
3
m 17
44.
3
y 23
y 15 z 6
46.
a 13 m 16
47.
a 5 m 17
48.
3
m 22 z 17
a 22 y 14
50.
8x 15 y 21
54.
3
64a 6 y 9
32 x 3 y 11
58.
40m 14 n 16
62.
37.
m 4 y 10
38.
41.
m 21
45.
49.
3
3
3
y 11
m 14 x 25
V: Simplify
16 x 2 y 10
52.
32m 10 y 15
56.
59.
8a 9 b
63.
98a 5 y14
51.
55.
5
81m 4 y 12
53.
3
− 8x 12 y 18
57.
60.
3
54m 16 y 4
61.
64.
3
8m 16 z 12
-6-
3
3
50m 3 y 7
3
16m 9 y 17
Worksheet 5: Radicals
Perform the indicated operations and express answer in simplest form:
3 +2 5 −5 3 + 5
1.
(
10. 2 − 7
)
3
2
19.
3
(
)
20.
5x ⋅ 3 75x 2
21.
9 −2 4 +6 7
11.
3. 2 75 − 5 12 + 48
12.
4. 5 18 − 2 8 + 50
13. 6mn 3 4m 2mn 2
2.
5 2 + 45
3
)(
(
5.
12
75
+
− 3
25
9
14.
(
a+ b
)(
6.
1
8
−
+ 32
2
9
15.
(
a+ b
)
7.
3⋅ 5
16.
8.
11 ⋅ 22
17.
(
)(
9. 5 + 3 5 − 3
)
18.
3
a− b
2
2m 2
)
)
22.
23.
15 80
25.
26.
3 5
5 20
27.
2 5x
-7-
y z2
10
3
9x 2
7
5− 3
7− 2
2+ 2
1
5+ x
18
24.
3⋅ 6⋅ 8
x
2
36
a
3
a2
5 2x − 3 x
x
2+ 3
2 2− 3
Worksheet 6: Literal Equations
1) Solve for x: 3x + m = b
2) Solve for x: 3m + 2x – c = x + d
3) Solve for W: P = 2L + 2W
4) Solve for n: L = a + (n – 1)d
5) Solve for d: L = a + (n – 1)d
6) Solve for m: Ft = m(V2 – V1)
7) Solve for V2: Ft = m(V2 – V1)
8) Solve for a: 7y + 3b = m + 2a
9) Solve for b 1 : A =
1
h (b 1 + b 2 )
2
10) Solve for B : A =
11) Solve for x: 2x – b + c = a2
5
B−C
3
12) Solve for x: a(2x – c) = a + c
-8-
Worksheet 7: Radical Equations
Solve for the variable. Be sure to check your roots.
1.
x − 9 = −6
2.
5y − 4 − 2 = 4
3.
3x − 5 − 5 = 1
4.
3y + 1 + 7 = 2
7a − 1 = 3
6.
x 2 − 4x = x + 3
8.
5.
7.
3
-9-
3
6 x − 4 = −4
a 2 − 16 = 4 + a
9. a + 6 = a 2 + 7a − 4
10.
9a 2 + 4a − 3a = 2
11. The marketing department of a computer manufacturer determines that the demand for its computers
depends on the price it charges. The relationship of price to demand is given by the formula:
p = 1595 − 0.10x + 150 , x ≥ 0, where p is the price and x is the number of computers sold at that price.
Find the number of computers sold if the price is $1295.
12. For a group of 50,000 births, the number of people surviving (N) to age x is given by the formula:
N = 5000 100 − x . To what age will 40,000 in the group survive?
- 10 -
Worksheet 8: Word Problems
Solve each problem algebraically using one variable.
1. Find a number such that the sum of 15 and the number is four times the number.
2. When nine is added to seven times a certain number, the result is equal to the result of subtracting three
from ten times the number. Find the number.
3. The labor costs for a certain project were $3345 per day for a total of 17 technicians and helpers. If the
technicians earned $210 per day and the helpers earned $185 per day, how many technicians were
employed on the project?
4. When seven times the sum of two and some number is subtracted from four times the sum of three and
twice the number, the result is equal to zero. Find the number.
5. Two cars are at the same location. One travels at a speed of 50 mph and the other at 55 mph in the opposite
direction. How long will it take (in hours) for them to be 367.5 miles apart?
6. An item costs $50.32, which includes 8% tax. How much did the item cost, to the nearest cent, before the
tax was added on?
7. A person goes shopping with a certain amount of money and spends one-half of it on clothes, one-quarter
of it on shoes, one-twelfth of it on lunch and has $30 left for gas. How much did the person have to start?
- 11 -
Worksheet 9: Inequalities
1.
When is it necessary to reverse the direction of the inequality sign when solving an inequality?
Solve each inequality. Express the solutions set using INTERVAL NOTATION and GRAPHICALLY.
2.
x+2>6
3.
y - 8 > -6
4.
5x ≤ -20
5.
4x + 1 ≥ 25
6.
5m + 2 ≥ 42
7.
3x − 1
>5
4
8.
-4a < 48
9.
-2b > 10
10.
y + 4(2y - 1) ≥ y
11.
-3(z - 6) > 2z - 2
12.
-4 < x - 5 < 6
13.
-9 ≤ k + 5 ≤ 15
14.
-15 < 3p + 6 < -12
15.
-6 ≤ -2z + 4 ≤ 16
16.
4 ≤ 5 - 9x < 8
17.
−3≤
- 12 -
2m + 1
≤5
3
Review Test #1
Match each vocabulary term on the left with its example on the right.
1. Two term expression
A.
0
a
2. Third degree expression
B.
(2x - 5) + (x + 3)(5 - x)
3. Undefined
C.
(-2)4
4. When evaluated, equals –16
D.
5
0
5. Zero
E.
-24
F.
5x3 - 4x2 + 7
G.
(x + 1)(x - 6)
6. Simplify: (4x3 - 7x2 + 3x - 2) + 2(-3x3 + 4x2 + 1)
7. Subtract 5x2 - 5x + 6 from 12x2 + 5x - 5.
8. Simplify: 2(7x2y0z3)2(2x2y3z4)0
9. Simplify using only positive exponents: -5x-2y3
10. Simplify and express answer with positive exponents:
 2 w −2 
a)  3 −1 
x y 
−2
b) (5x2y-4) -2(7xy2)
11. Multiply: (2x - 3)(4x2 + 6x + 9)
12. a) Square (3x - 8)
b) Cube (2x + 1)
13.
Divide (15x4y3 - 6x3y2 + 3x2y) by (3x2y)
14.
Divide using long division and writing any remainder as a fraction: (6y3 - 8y - 5) ÷ (2y - 4)
- 13 -
15.
Referring to
3
9 x 2 + y , answer the following three questions:
a) What is the radicand?
b) What is the index?
c) Express this radical expression in exponential form.
16.
What is the conjugate of 2 x − 5 ?
17.
One use of the conjugate is to get a __________ number in the denominator of a radical fraction.
18.
Express the following in exponential form:
a)
19.
2 xy
3
b) 9 a
n
c)
a−b
Express the following in radical form:
3
2
( )
b) x 2 y
a) y 5
1
3
4
d) (2 x ) 3
c) 5x 3
20 -25: Simplify each expression as much as possible:
20.
49
21.
23.
80a 3 b 4 c 2
24.
5
32 x 15 y 10
22.
3
2
5
25.
3
26-29: Combine the following expressions:
26.
28.
12 + 3
2 300 x 2 − 48x 2 + 3x 75
27.
3 8 − 4 72 + 5 50
29.
23 54 + 123 16
31.
(
30-31: Multiply:
30.
(
2 3−2 2
)
8−2
32-33: Divide so that the denominator is rational:
32.
3
5−2
33.
5 2
2 +3
- 14 -
)(
8+2
)
32
5
2x 2
34.
Solve for p: 7 – 3(1 – 2p) = 4 + 2p
36.
Solve the formula h = vt – 16t2 for v.
35. Solve for x: 5x – 2(x – 5) = 4x
For problems 36-37, solve the inequality, express the solution set using interval notation and graphically:
37.
3x - 5 ≤ -11
38.
3 - 3x < -6
39.
2 < 3x - 1 ≤ 8
Write the equation for the following number problems using one variable and solve the resulting equation.
Only an algebraic solution will be accepted!
40.
When three times the sum of 6 and an unknown number is subtracted from 15 times the unknown
number, the result is 6. Find the number.
41.
When twice the sum of five and an unknown number is subtracted from 8 times the unknown
number, the result is equal to 4 times the sum of 8 and twice the unknown number. Find the number.
42.
Find 3 consecutive even integers such that 3 times the sum of the last two is 40 more than 5 times
the first.
43-47: Solve the following radical equations for the variable. Check your answers.
43.
45.
47.
x +1 − 4 = 7
x − 9 = x2 − x − 4
44.
46.
x 2 + 2x + 6 = x + 2
- 15 -
3
7a − 1 = 3
x 2 − 16 = 4 + x