2012 SUMMER WORKBOOK FOR STUDENTS
ENTERING ALGEBRA 2 OR ALGEBRA 2 HONORS
This workbook is to be done by any student taking Algebra 2 or Algebra 2 Honors
(courses 322 or 324).
There is space provided to do work for each problem and for each answer. If you
require more space then you are to do the work on a separate piece of loose leaf
indicating the page and problem number being done and attach to this workbook.
This workbook is due on the first day of your Algebra 2 class (September 2012).
You will receive a grade for the workbook and you will also be tested on this
material during the first week of class.
Name:____________________________ Homedroom:___________
Page 1
The following are sets of real numbers:
(N)atural numbers, (W)hole numbers,
(I)ntegers, Rational or Irrational numbers.
Name the set or sets to which each number
belongs. Answers
10) 14
11)  15
12) 
1)  15
80
2
13)
2) 11
3) 30
17
4)
3
5) 6
6) 0
7)  13
8) 3
9)
10
11
14) 77
15)
6
7
16)  196
17)
 16
2
18)
135
3
Page 2 – (answer on the lines)
Write each as a verbal expression
Write each as an algebraic expression
1)
x
2
1) u decreased by 17
2) a  9
2) the difference of 10 and 5
3) 19  3
3) half of 14
4) 2 2
4) the quotient of 14 and 7
5) n  6
5) x increased by 6
Evaluate each expression
6) the product of x and 7
7) the sum of q and 8
8) twice q
9) n cubed
10) the quotient of 18 and n
1) 5 squared
2) twice 6
3) 10 less than 17
4) the product of 4 and 5
5) 10 increased by 8
Page 3 (answer on the lines)
Simplify each expression.
11)  3x  5
1) 6 5n  7
12)  510 x  1
2) 41  9 x 
13) 1  2v   5
3)  4  3n  8
14)  81  5x 
4) 8 b  4
15)  75k  4
5) 1  7n  5
16)  57a  6
6)  6x  4
17) 5n  6
7) 53m  6
18) 43r  8
8)  6 p  7  4
19) 35  5x 
9)  4 8x  8
20) 1  9 x   10
10)  67  x 
Page 4
Find each quotient. Answers
1)
10
5
 20
2)
2
Find each product.
1)  11 9
2)  11 8
3) 12  12
3)
65
5
4) 8  6  3
4)
75
 15
5)
102
 17
6) 153  17
7) 48  6
8) 306  18
9)  85  17
5) 33 13
6)  7  12
7)  3  6  6
8) 6  1 2
9) 11 6  5  4
10)  4  8 53
Page 5
Evaluate each expression Answers
11) 10  (10)  7  5
1) (2)  3
Work
12) 6  3.908
2) (14)  (7)
13) 5.8  (2.5)
3) 3  (8)
14) 1.8  (3.7)
4) (9)  14
15) 7  2.8
5) (8)  (2)
16) (0.8)  (7.2)  5.4
6) 5  (8)
17) 1.7  (0.8  4.013)
7) (11)  (14)  7
3
8
18)    
 2
5
8) 7  (1)  12  7
9) 6  (7)  (5)  (2)
10) (-3)+5+(-5)+12
19)
7  1
  
4  2
1
7
20)    
 5
4
Page 6
Evaluate for the given values. Answers
1) y  2  x ; for x=1, and y=2
11) p  (9  (m  q)) ; for m=4, p=5, and q=3
2) p 2  m ; for m=1, and p=5
12) (a 2  b)  6 ; for a=5, and b=1
3) a  5  b ; for a=10, and b=4
13) 2( p  4)  (m  n) ; for m=4, n=2, and p=5
4) y  9  x ; for x=1, and y=3
14) pn  (n  m) 2 ; for m=1, n=4, and p=6
5) m  p  5 ;for m=1, and p=5
15) 12k  h 2 ; for h=2, and k=3
6) y 2  x ; for y=7, and x=7
16) y  z  x  6 ; for x=3, y=4, and z=4
7) z( x  y) ; for x=6, y=8, and z=6
17)
y
 x  4  z  y ; for x=7, y=2, and z=4
2
8) x  y  y ; for x=9, and y=10
18) c 
9) p 2 m  4 ; for p=7, and m=4
10) z  ( y  3  1) ; for y=3, and z=7
bc
 (7  a) ; for a=4, b=8, and c=5
4
11) 48  (4  4)
Page 7
Evaluate each expression.
Answers
1) 3(6+7)
12) 40  4  (5  3)
2) 72  9  7
13) (5  16)  7  2
3) 9  8  7
14) 9  32  4
4) 5(10  1)
15) (8  5) 
35
6
5
5) 20  [4  (10  8)]
16)
45
8(5  4)  3
17)
49 60

7 25
6) 9  9  6  5
7) 7  10  5  10
8) (6  4)  49  7
18) (6  25  7)  6
19) (10  2  2)  6  1
27
3
9)
23 4
20)
10) 8 
15
 (5  9)
5
8
 (3  6)  3
5 1
Page 8
Solve each equation.
Answers
1) 8x – 2 = -9 + 7x
a
4
8) 6   2
Work
2) 4m – 4 = 4m
9) 0  4 
n
5
10)  4 
r
5
20
3) -(7 – 4x) = 9
4) 5n + 34 = -2(1-7n)
n
2
11)  6   10
5) 3n – 5 = -8(6 + 5n)
12)
v9
8
3
6) -3(4x + 3) + 4(6x + 1) =43
13) 2(n+5) = -2
7) -5(1 – 5x) + 5(-8x – 2) = -4x – 8x
Page 9
Solve each absolute value equation.
Answers
1) 6m  42
7)  3 r  12
Work
2) k  2  3
3) 7 n  56
4)
x
7
5
5) 4 n  8  76
8)
a 5
8
5
9) n  9  4
10)
x
 8  7
7
11)  6 x  30
6)  3 p  15
12)
5 2

8 3t
Page 10
Solve each equation. Remember to check
for extraneous solutions. Answers
1)
x  10
7) 10 
m
10
Work
2)
v4 3
3) 2  4a
8)
3n  4n  1
9)
x
 3x  58
10
4) 5  x  3
10)
3n  12  n  8
11)
11  x  x  7
12)
2k  40   16  2k
5)  8  5t  5  3
6) 10 9 x  60
Page 11
Answers
Solve the following. Round each answer to
the nearest hundredth.
5) Working alone it takes Susan 11 hours to
harvest a field. Viola can harvest the same
field in 16 hours. How long would it take
them working together?
1) Jim can paint a house in 5 hours and Bill
can do the same job in 6 hours. How long
would it take them if they worked
together?
Work
6) Brenda can wax a floor in 16 minutes.
One day her friend Pat helped her and it
took only 5.76 minutes. How long would it
take Pat alone?
2) It takes Manny 10 hours to clean an attic
and Moe can do it in 7 hours. How long
would it take them working together?
3) Working together Mary and Jill can paint
a fence in 6 hours. Mary can paint it by
herself in 10 hours. How long would it take
Jill working alone?
4) Jason can tar a roof in 9 hours. With help
from his friend Terry it takes 4.74 hours.
How long would it take Terry alone?
7) Working together Jen and Liz can mop a
warehouse in 5.14 hours. Had she done it
alone it would have taken Jen 12 hours.
How long would it take Liz working alone?
8) Bob painted his house for 2 hours when
Al joined him. Together they finished 6
hours later. How long would it take Al
alone?
Page 12
Solve the following.
Answers
1) 5 oz. of a 2% alcohol solution was mixed
with 11 oz. of a 66% alcohol solution. Find
the concentration of the new mixture.
5) How many mg. of a metal containing
45% nickel must be combined with 6 mg. of
pure nickel to form an alloy containing 78%
nickel?
Work
2) How much soil containing 45% sand do
you need to add to a cubic ft. of soil
containing 15% sand in order to make a soil
containing 35% sand.
6) 2 yd .3 of soil containing 35% sand was
mixed into 6 yd .3 of soil containing 15% sand.
What is the sand content of the mixture?
3) 9 quarts of a sugar solution was mixed 6
quarts of a 90% sugar solution to make an
84% sugar solution. Find the percent
concentration of the first solution.
4) 9 lbs. of mixed nuts containing 55%
peanuts were mixed with 6 lbs. of another
kind of mixed nuts that contain 40%
peanuts. What percent of the new mixture
is peanuts?
7) A metallurgist needs to make 12.4 lbs. of
an alloy containing 50% gold. He is going to
melt and combine one metal that is 60%
gold with another metal that is 40% gold.
How much of each should he use?
Page 13
1. Set up an equation and solve the
following. A UPS je t transport made a trip
to Miami and back. On the trip there it flew
at 432 mph and on the return trip it flew at
480 mph. How long was the flight there if
the return trip was 9 hours? Answers
4. A delivery truck left its terminal and
traveled west at 40 mph, another truck left
an hour later and traveled east at 50 mph.
After how many hours was the second truck
400 miles from the first?
Work
2. A Coast Guard ship made a trip to NYC
and back. The trip there took 3 hours and
the return trip took 4 hours. It averaged 6
knots on the return trip. Find the average
speed of the trip there.
3. A Mag-Lev train traveled from Paris to
Berlin and back. It took 1 hour less time to
Berlin than back to Paris. The average speed
on the trip was 220 k/h. The average speed
on the way back was 200 k/h. How many
hours did the trip there take?
5. An ambulance left the hospital and
drove south. 3 hours later a police car left
driving 42 k/h faster attempting to catch up
to the ambulance. The officer caught up
after 2 hours. Find the average speed of the
ambulance.
6. Joe left the hotel and traveled towards
the mountains. Mary left 2.1 hours later
driving 35 mph faster than Joe. After 1.2
hours she caught up. Find Joe’s average
speed.
Page 14
7. 1 
3
3m

m3 m3
Solve each equation. Check for extraneous
solutions.
1.
4 5 1
Answers
 
n2 n n2
Work
2.
3.
4.
8.
4
1
a3
 2
 2
a a  4a a  4a
9.
v3
1

2
v  3v v  3
1 1 n 1


n 5n 5n
x6 x4

1
x
x
10.
6
1
1
 2

n  6n  8 n  6n  8 n  4
11.
6
1
p4

 2
p p  5 p  5p
12.
1
1
3

 2
x  3x x  3 x  3x
2
6b  18 1 3
 
b b
b2
5.
3n  15 1 n  3
 2 
4n 2
n
4n 2
6.
5 x  20
1
x4

 2
2
x  9 x  18 x  6 x  9 x  18
2
Page 15
Solve each of the following, round your
answers to the nearest tenth or tenth of a
percent.
2. What percent of 28.6 is 22?
1. What percent of 38 is 4?
Work
Answers
3. 45% of 58 is what?
4. 132% of 43.7 is what?
5. 2 is what percent of 62.4
6. What percent of 27 is 13?
7. 73% of 95 lbs. is what?
8. 23% of what is 17 minutes?
9. 3% of 152 miles is what?
10. What is 18% of 42
11. 15 inches is 65% of what?
12. 142 hours is 88% of what? 9 grams?
Page 16
Solve the following proportions.
Answers
9 x

6 14
2.
4 8

3 x
3.
7 x

5 3
4.
7 8

r 7
5.
4
8

m8 2
6.
4 r 3

9
6
7.
4
7

n2 n
8.
n
2

n3 3
9.
n6 9

n7 2
10.
1.
Work
3x  5
4
2x
Answers to odd problems
for the Alg.II Summer
Workbook.
Page 1
1) Int, R
3) Irr
5) N, W, Int, R
7) Int, R
9) R
11) Int, R
13) Irr
15) R
17)N, W, Int, R
Page 2
Algebraic expressions
1) u-17
3)
1
 14
2
5) 18
1) 1
Page 3
3) 11
1) -30n+42
5) -6
3) 24n+32
7) 10
5) -35n+5
9) -4
7) 15m-30
11) 8
9) 32x+32
13) 3.3
Page 3 (cont.)
15) 4.2
11) -3x+15
17) -3.113
13) 10v+5
15) -35k+28
17) 5n+30
19) 15x+15
Pqge 4
Quotients
1) 2
3) 13
5) x+6
5) -6
7) q+8
7) 8
9) n
3
Verbal Expressions
1) x divided by 2
3) 19 decreased by 3
5) a number times 6
Evaluate
1) 25
3) 7
19)
9) 5
Products
1) -99
3) -144
5) -27
7) 108
9) -1320
Page 5
9
4
or
2
Page 6
1) 2
3) 1
5) 2
Page 6 (cont.)
7) 84
9) 49
11) 3
13) 12
15) 32
17) 18
Page 7
1) 39
3) 10
5) 10
7) 67
1
4
9) 6
7) 1000
3) 26.1
11) 6
9) 20
5) 3.2 %
13) 1
11) 9
7) 69.4 lbs.
15) 97
Page 11
9) 4.6
17) 42
1) 2.73 hrs.
Page 15 (cont.)
19) 59
3) 15 hrs.
11) 23.1
Page 8
5) 6.52 hrs.
Page 16
1) -7
7) 8.99 hrs
1) 21
3) 4
Page 12
5) -1
1) 46 %
7) -5
3) 80 %
9) -20
5) 4 mg.
11) 8
7) 6.2 lbs. of each
3) 4
5) 9
7) 
9)
13) -6
Page 13
Page 9
1) 10 hrs.
1) 7 or -7
3) 11 hrs.
3) 5 or -1
5) 28 k/h
5) 11 or -27
Page 14
7) 4 or -4
1) 1
9) 
3) -1
11) 5 or -5
5) -2
7) 0
9) 
Page 10
1) 100
3) 1
5) 6
11) 4
1
3
Page 15
1) 10.5 %
1
5
14
3
51
7
4
or
or
7
2
7
2
3