Download NEED HELP: Middle School teachers will be available on August

NAME ___________________________
SUMMER PACKET
UPPER MERION AREA MIDDLE SCHOOL
Preparation for 8th grade mathematics
JUNE 2013
Attached is a summer packet designed for students
who have completed their 7th grade math course and
who will be taking algebra in the fall. The goal of this
packet is to keep skills sharp and prepare students for
the transition to 8th grade.
This packet is designed to be completed in several
sittings. To be most effective, it is recommended that
you set aside a small amount of time weekly to
complete each section. The majority of the questions
require you to show your work. The work must be
done neatly on the pages of the packet or on looseleaf
paper.
You may NOT use a calculator.
The packet will be collected by your math teacher
on the first day of school and will be worth 30
points. (extra credit = 10 maximum pts) You must
show your work to receive full credit.
NEED HELP: Middle School teachers
will be available on August 13th and
14th from 10-12 in the Middle School
1
Library
NAME _______________________________________________
Write an expression representing the quantity described.
1. The sum of 6 and a number. ____________________
2. The difference of 6 and a number. ___________________
3. The product of 6 and a number, increased by 5. _____________
4. The quotient of 6 and a number. ______________________
5. Seven plus one half of a number. ______________________
6. Seven plus twice a number. _______________________
7. Five times a number cubed. _____________
8. Subtract 9 from the product of 5 and a number. __________
9. Five times the sum of 4 and a number. __________________
10. A number increased by six times the number cubed.
_________________________
2
Evaluate by substituting the given value of the variable. SHOW ALL
WORK
11.
13.
3 x
2x
x2
6
4
if x is (-4)
12.
if x is 4
3
4x2 + 3x if x is 5
Write an equation:
Four times a number decreased by 7 equals 29.
_____________
b. Solve the equation.
Write an expression:
Nine less than 7 times a number. _____________________
b)
Evaluate the expression for the value of (-9)
c)
Solve the equation formed if the expression equals 12.
4
Solve each equation of the following equations. Show work.
5x + 12 = 32
-2x – 7 = -31
3x 16 26
4
45 =
5
2x + 11
3
Graph the following numbers on the number line:
½ -2
5
3.5
-2 2
5
3
-4
-3
-2
-1
0
1
2
3
4
Solve. Show all work.
The ratio of boys to girls in a science class is 2:3. There are 18
girls in the class. How many students in the class are boys?
6
The cost of sending 20 pages using a commercial fax machine is
$18. At this rate, how much will it cost to send 30 pages using
the same fax machine?
During the first day of a trip, Mario drove 168 miles and used 6
gallons of gasoline. At this rate, how many gallons of gasoline
will Mario use for a 588 mile trip?
7
Isabel worked 32 hours last week and was paid $192. At the same
rate, what will Isabel be paid if she works 40 hours this week?
Elena answered 47 items correctly on a 50 item test. What
percent of the items did she get correct?
8
A high school play was attended by a total of 1250 adults and
children. The audience contained 75 adults. What percent of the
audience were adults?
Masao bought a VCR whose price is $496. The sales tax rate is
7.5%. How much sales tax did he pay?
Of the 680 students at Textor Middle School, 55% are female.
How many females attend Textor Middle School?
9
EXTRA CREDIT
In algebra it is assumed that all students can add,
subtract, multiply and divide fractions without using a
calculator. Students should also be able to perform
the basic operations with percents and operate with
integers.
The following pages are EXTRA and are provided for
students who need the review on INTEGERS, fractions
and percents. Again all work should be done in the
space provided. The FRACTION pages should be
done without a calculator. The calculator may be
used for some of the conversions on the percent
page.
10
NAME ____________________________
Fill in the missing number.
1. 28
=
44
11
2.
=
75
15
11
128
6.
8
Compare. Write <, >, or =.
8. 2
5
8
5
80
=
Write each fraction in simplest form.
4. 24
5. 2
40
3.
120
Fractions
9.
5
4
19
20
Complete.
11.
3
Give 3 fractions that reduce to .
5
77
7. 20
121
28
10.
8
6
12
9
12. Explain the difference between a proper
fraction and an improper fraction, and
give an example of each type.
3
Show that your fractions reduce to .
5
Order the fractions from least to greatest.
13 2
14 5
1
8
2
13
,
,
,
,
19
2
9
4
3
16
15.
Write each improper fraction as a mixed number in simplest form.
16. 27
17. 32
18. 56
11
12
3
,
15
4
,
6
19. 26
8
11
10
12
14
Write each mixed number as an improper fraction in simplest form.
20.
21. 2
232. 1
23. 12
3
6
3
2
4
19
3
5
14
Fill in the missing number.
24. 9
1
= 4
2
25. 9
= 1
5
Add or subtract. Write the answer in simplest form.
26. 8
27. 3
5
2
+
9 + 4
22
22
5
5
12
5
28.
1
19
3
- 2
7
7
Multiply. Write the answer in simplest form.
29.
30.
9
7
8
12
10
8
Multiply. Write the answer in simplest form.
32. 1
33. 1
2
5
3
6
2
9
Multiply. Write the answer in simplest form.
35.
36. 2
9
7
3
2
3
1
14
13
9
4
13
31.
8
18
14
34.
3
6
11
8
37. 5
1
4
7
11
Divide. Write the answer in simplest form.
38. 2
39.
7
1
÷ 4
12
÷
4
12
8
Add or subtract. Write the answer in simplest form.
41. 5
42. 7
+ 13
+ 7
7
13
Add or subtract. Write the answer in simplest form.
44. 2
45. 2
5
6
+
+
10
6
3
18
Add or subtract. Write the answer in simplest form.
47.
48.
8
9
1
3
+ 7
1
8
4
12
4
6
14
40.
4
5 ÷
17
43.
1
15 12
46. 6
1
-
9
49.
2
6
2
1
+
10
5
NAME ________________________
Percent
Write each percent as a fraction in simplest form.
1. 99%
2. 20%
3. 30%
Write each percent as a decimal.
4. 14%
5. 80%
6. 90.2%
Write each decimal as a percent.
7. 0.62
8. 0.604
9. 0.3040
Write each fraction as a percent. Round to the nearest hundredth of a percent.
10. 481
11. 7
12. 3
13. 3
100
25
4
10
Complete. Numbers are rounded to the nearest hundredth of a percent.
14. decimal 0.56
15.
16. percent 941%
3
fraction
percent ________
fraction ________
5
decimal
________
15
Find the percent of each number.
17. 30% of 260
18. 89% of 799
19. 330% of 75
Complete. Round your answer to the nearest tenth.
20. What number is 318% of 12?
21. 216 is 54% of what number?
16
NAME _______________________________________ INTEGERS
1. What is the opposite of -2 ?
2. What is the reciprocal of -2?
ADDITION RULES
SIGNS THE SAME ADD AND USE THAT SIGN
SIGNS DIFFERENT SUBTRACT VALUES AND USE THE SIGN OF THE
LARGER
SUBTRACTION RULE:
CHANGE TO ADDITION OF THE OPPOSITE
MULTIPLICATION OR DIVISION:
SIGNS THE SAME THE ANSWER IS POSITIVE
SIGNS DIFFERENT THE ANSWER IS NEGATIVE
EVALUATE – SHOW WORK WHERE NECESSARY
3.
4.
5.
16 + ( - 12)
10.
11.
– 23 + 67 + (- 48)
8–5
12.
5–4
13.
– 8 – 12
14.
–8+9
15.
10 – ( - 3)
16.
– 7 – ( - 4)
– 16 + 15
– 16 + ( - 18)
6.
- 89 + 56
7.
2 + ( - 3) + 4
8.
12 + 6 + ( - 8) + ( - 4)
9.
– 37 + 45 + (- 25)
17
17.
0 – 15
18.
( 8 – 12) – ( 17 – 4)
19.
20.
26.
(4)(-2)
– 12 + 5 + 12 – 5
27.
( - 4)( - 9)
( - 2) ( 4)
28.
18
9
29.
18
9
21.
( - 2)( - 4)
22.
2( - 4)
23.
24.
30.
8( 7)
14
31.
8 8
15
(-2)3
( - 4)( - 5)( - 6)
32.
25.
(4)(9)
18
15
8 8