Download Algebra II

Name:____________
Summer Workbook
for any students entering
Algebra II or Algebra II Honors
and it is due on the first day of
your Algebra II class.
There is space provided to do the 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 numbers
and attach to the workbook. You will
receive a grade for the workbook and you
will also be tested on this material during
the first week of class.
Date:_________________
Homeroom:_______
Page 1
The following are sets of real
9)
numbers: (ℕ)Natural numbers,
10
11
9)_______
(W)Whole numbers, (ℤ)Integers,
(ℚ)Rational or (ℙ)Irrational numbers.
10) 14
10)_______
Name the set or sets to which each
number belongs.
11)  13
11)_______
12) 
12)_______
1)  15
2) 11
1)_______
2)_______
80
2
13)_______
14) 77
14)_______
13)
3) 30
17
4)
3
3)_______
4)_______
6
7
15)_______
16)  196
16)_______
15)
5) 6
5)_______
6) 0
6)_______
7)  13
8) 3
7)_______
8)_______
17)
 16
2
17)_______
18)
135
3
18)_______
19) the quotient of 18 and n
19)________________
Page 2
Write each as an algebraic expression
Write each as a verbal expression
1) u decreased by 17
1)
1)_________________
2) the difference of 10 and 5
2)_________________
3) half of 14
3)_________________
4) the quotient of 14 and 7
4)_________________
5) x increased by 6
5)_________________
6) the product of x and 7
6)_________________
x
2
1)___________________________
2) a  9
2)___________________________
3) 19  3
3)___________________________
4) 2 2
4)___________________________
5) n  6
5)___________________________
Evaluate each expression
1) 5 squared
1)_____
2) twice 6
2)_____
3) 10 less than 17
3)_____
7) the sum of q and 8
7)_________________
8) twice q
8)_________________
9) n cubed
9)_________________
9)  4 8x  8
4) the product of 4 and 5
9)_______
4)_____
5) 10 increased by 8
5)_____
10)  67  x
10)______
Page 3
Simplify each expression.
1) 6 5n  7
2) 41  9 x 
3)  4  3n  8
4) 8 b  4
5) 1  7n  5
6)  6x  4
7) 53m  6
8)  6 p  7  4
11)  3x  5
11)_______
12)  510x  1
12)_______
13) 1  2v  5
13)_______
14)  81  5x
14)_______
15)  75k  4
15)_______
16)  57a  6
16)_______
17) 5n  6
17)_______
18) 43r  8
18)_______
1)_______
2)_______
3)_______
4)_______
5)_______
6)_______
7)_______
8)_______
19) 35  5x
19)_______
8) 306 18
8)_______
20) 1  9x  10
20)_______
9)  85  17
9)_______
Page 4
Find each quotient.
1)
2)
3)
10
5
1)_______
 20
2
2)_______
65
5
75
4)
 15
5)
102
 17
6) 153  17
7) 48  6
3)_______
Find each product.
1)  11 9
1)_______
2)  11 8
2)_______
3) 12  12
3)_______
4) 8  6  3
4)_______
5) 33 13
5)_______
6)  7  12
6)_______
7)  3  6  6
7)_______
8) 6  1 2
8)_______
4)_______
5)_______
6)_______
7)_______
9) 11 6  5  4
10)  4  8 53
9)_______
10)_______
9) 6  (7)  (5)  (2)
9)______
10) (-3)+5+(-5)+12
10)_____
11) 10  (10)  7  5
11)______
12) 6  3.908
12)______
13) 5.8  (2.5)
13)______
14) 1.8  (3.7)
14)______
15) 7  2.8
15)______
16) (0.8)  (7.2)  5.4
16)______
17) 1.7  (0.8  4.013
17)______
3
8
18)    
18)______
7  1
  
4  2
19)______
Page 5
Evaluate each expression
1) (2)  3
2) (14)  (7)
3) 3  (8)
4) (9)  14
5) (8)  (2)
6) 5  (8)
1)______
2)______
3)______
4)______
5)______
6)______
7) (11)  (14)  7
7)______
8) 7  (1)  12  7
8)______
 2
19)
5
1
7
20)    
 5
4
20)______
9) p 2 m  4 ; for p=7, and m=4
9)_______
Page 6
Evaluate for the given values.
1) y  2  x ; for x=1, and y=2
1)_______
2) p  m ; for m=1, and p=5
10) z  ( y  3  1) ; for y=3, and z=7
10)______
11) p  (9  (m  q)) ; for m=4, p=5, and
q=3
11)_______
2
2)_______
3) a  5  b ; for a=10, and b=4
12) (a 2  b)  6 ; for a=5, and b=1
12)_______
3)_______
13) 2( p  4)  (m  n) ; for m=4, n=2,
and p=5
4) y  9  x ; for x=1, and y=3
13)_______
4)_______
14) pn  (n  m) 2 ; for m=1, n=4, and
p=6
5) m  p  5 ;for m=1, and p=5
5)_______
6) y  x ; for y=7, and x=7
2
6)_______
7) z ( x  y) ; for x=6, y=8, and z=6
7)_______
8) x  y  y ; for x=9, and y=10
8)_______
14)_______
15) 12k  h 2 ; for h=2, and k=3
15)_______
16) y  z  x  6 ; for x=3, y=4, and z=4
16)_______
17)
y
 x  4  z  y ; for x=7, y=2, and
2
z=4
17)_______
18) c 
bc
 (7  a) ; for a=4, b=8, and
4
9)
27
3
23 4
9)_______
c=5
18)______
10) 8 
Page 7
Evaluate each expression.
1) 3(6+7)
15
 (5  9) 10)______
5
11) 48  (4  4)
11)_______
1)_______
12) 40  4  (5  3) 12)_______
2) 72  9  7
2)_______
13) (5  16)  7  2 13)_______
3) 9  8  7
3)_______
14) 9  32  4
4) 5(10  1)
14)_______
4)_______
15) (8  5) 
35
 6 15)_______
5
5) 20  [4  (10  8)]
5)_______
6) 9  9  6  5
6)_______
7) 7  10  5  10
7)_______
8) (6  4)  49  7
8)_______
16)
45
8(5  4)  3
16)_______
17)
49 60

7 25
17)_______
18) (6  25  7)  6 18)_______
19) (10  2  2)  6  1 19)_______
6) -3(4x + 3) + 4(6x + 1) =43
6)_______
20)
8
 (3  6)  3
5 1
20)_______
7) -5(1 – 5x) + 5(-8x – 2) = -4x – 8x
7)_______
Page 8 - Show work.
Solve each equation.
1) 8x – 2 = -9 + 7x
1)_______
a
4
2) 4m – 4 = 4m
3) -(7 – 4x) = 9
4) 5n + 34 = -2(1-7n)
8) 6   2
8)_______
9) 0  4 
n
5
9)_______
10)  4 
r
5
20
10)_______
n
2
11)_______
2)_______
3)_______
4)_______
11)  6   10
5) 3n – 5 = -8(6 + 5n)
5)_______
v9
8
3
12)
13) 2(n+5) = -2
12)_______
13)_______
Page 9 - Show work.
6)  3 p  15
6)______
7)______
Solve each absolute value equation.
1) 6m  42
1)______
7)  3 r  12
2) k  2  3
2)______
8)
3) 7 n  56
x
3)______
5
4)______
5) 4 n  8  76
5)______
4)
7
a5
5
8)______
9) n  9  4
9)______
10)
8
x
 8  7
7
10)_______
11)  6 x  30
12)
5 2

8 3t
11)_______
12)_______
5)  8  5t  5  3
5)______
6) 10 9 x  60
Page 10 - Show work.
Solve each equation. Remember to
check for extraneous solutions.
1)
6)_______
x  10
7) 10 
m
10
1)_______
2)
v4 3
7)_______
2)_______
8)
3n  4n  1
3) 2  4a
8)_______
3)_______
9)
x
 3x  58
10
4) 5  x  3
9)_______
4)_______
10)
3n  12  n  8
10)______
11)
11  x  x  7
11)______
12)
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?
3)_______
2k  40   16  2k
12)_______
Page 11 - Show work.
Solve the following. Round each
answer to the nearest hundredth.
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?
1)_______
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?
2)_______
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?
4)_______
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?
5)______
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?
6)______
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?
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)________
4)______
Page 12
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?
Solve the following. Show work.
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.
1)______
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.
2)______
5)______
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?
6)______
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.
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?
3)______
7)______
Page 13 - Set up an equation and
solve the following:
1. 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?
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?
4)_______
1)_______
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.
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.
5)_______
2)_______
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?
3)_______
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.
6)______
Page 14
7. 1 
3
3m

m3 m3
Solve each equation. Check for
extraneous solutions. Show work.
1.
4 5 1
 
n2 n n2
1)______
2.
7)______
8.
1 1 n 1


n 5n 5n
4
1
a3
 2
 2
a a  4a a  4a
2)______
3.
x6 x  4

1
x
x
8)______
9.
3)______
4.
6b  18 1 3
 
b b
b2
4)______
5.
9)______
10.
6
1
1
 2

n  6n  8 n  6n  8 n  4
2
3n  15 1 n  3
 2 
4n 2
n
4n 2
5)______
6.
v3
1

2
v  3v v  3
5 x  20
1
x4

 2
2
x  9 x  18 x  6 x  9 x  18
6)______
10)______
11.
6
1
p4

 2
p p  5 p  5p
11)_______
12.
1
1
3

 2
x  3x x  3 x  3x
2
12)______
Page 15
Solve each of the following, round
your answers to the nearest tenth or
tenth of a percent. Show work.
1. What percent of 38 is 4?
1)_______
2. What percent of 28.6 is 22?
7. 73% of 95 lbs. is what?
7)_______
8. 23% of what is 17 minutes?
8)_______
9. 3% of 152 miles is what?
2)_______
9)_______
3. 45% of 58 is what?
10. What is 18% of 42.9 grams?
3)_______
4. 132% of 43.7 is what?
10)______
11. 15 inches is 65% of what?
4)_______
5. 2 is what percent of 62.4
5)_______
11)______
12. 142 hours is 88% of what?
6. What percent of 27 is 13?
12)______
6)_______
Page 16
6.
4 r 3

9
6
Solve the following proportions.
Show work.
1.
9 x

6 14
1)_______
2.
4 8

3 x
2)_______
3.
7 x

5 3
3)_______
4.
7 8

r 7
6)_______
7.
7)_______
8)
5.
n
2

n3 3
8)_______
9.
n6 9

n7 2
9)_______
10.
4)_______
4
7

n2 n
3x  5
4
2x
4
8

m8 2
10)________
5)_______