Download St. Michael`s Episcopal School Summer Math for

St. Michael’s Episcopal School
Summer Math
for rising 7th grade pre-algebra students
2016
Students entering pre-algebra should be proficient in working with integers, fractions and
decimals and order of operations.
To maintain skills through the summer, students are expected to complete the attached review
problems, showing all work. The summer skills packet will be collected on the first day of
school and graded.
Students are also encouraged to use math throughout the summer. Suggested activities
include:
*Play games with other people. Board games such as Monopoly, checkers and chess require
logic and/or math skills. Set, 24, Sudoku, and many card games require logic and strategy.
*Worksheets, computer games, and word problems that require students to add, subtract,
multiply, and divide without a calculator provide needed practice. Include operations with
fractions and decimals.
*Real life situations often require math. Measuring and adjusting recipes, figuring a checkbook,
determining a trip’s costs and mileage are all opportunities to use math. Compare the costs of
driving or flying for a vacation trip. Graph swim times or the price of gasoline each week.
Determine tips, change and taxes on purchases.
Summer Review 2016
Name:
Attach notebook paper to show work.
Number your problems.
Simplify.
1.
−6 + 10
15 + 12 ÷ 3
4.
Express as a decimal. Show your work.
2.
3.
23
3
8
Round 538.9043
5. to the hundreds place
__________
6. to the hundredths place
7. to the nearest whole
______________
______________
Evaluate the following expressions when 𝒋 = 𝟏𝟐 and 𝒌 = −𝟒. Watch signs.
8.
𝑗 ÷ 𝑘
10.
2𝑘
9.
11.
𝑗
−
𝑗𝑘 + 40
12. Estimate the product to the nearest whole. 4.12 × 6.8.
13. Write
7
200
as a percent.
Use >, < , o r = to complete each of the following.
14.
−28 ________ − 29
16.
42 ________ 24 Show work to justify your answer.
15.
0.36 _______
𝑘
9
25
17.
Express 0.375 as a fraction in lowest terms.
18.
Name the parts of the circle below.
SP ________________ RQ ___________________
Draw chord SQ.____________________
19.
The radius is 4½ cm.
What is the diameter of the circle? ______cm
What is the circumference? Use the formula, C = πd ________
20.
21. What is the measure of ∠𝑎?
What are the coordinates of the graphed point?
22.
4 −
23.
7
8
• 1
2
5
9
=
11
21
There are 12 cubes in a bag. Four are red, 3 are blue, 2 are orange, and 3 are yellow. Find the
probability of drawing the following:
24.
P( yellow) ____________________
25.
P (red or orange) ____________________
26. To make 24 cookies, a recipe requires ¾ teaspoon of vanilla. How much vanilla is needed for a
dozen cookies?
27.
Write 6,230,000 in scientific notation.
28.
Express the prime factorization of 72.
29.
What is the total cost of an item priced at $12.75 if there is a 5% sales tax?
Find the product and simplify if necessary.
30.
4 •
1
4
31. 8 • 3
3
4
32.
5
1
4
• 4
4
7
Find the quotient and simplify if necessary.
33.
4 ÷
1
4
2
34. 8 ÷ 1 3
𝟑𝟓.
3
24
÷
1
2
36.
What is 12% of 50? Show your work.
37.
One centimeter on a map represents 50 miles. What is the actual distance between two cities that
are 6.5 cm apart on the map?
38.
Find the missing number.
input
output
-5
20
8
-32
10 ³ =
39.
-1
40.
Circle the numbers that are factors of 492?
Use the rules of divisibility.
2,
3,
4,
5,
6,
9,
10
41.
What is the square root of 81?
42.
Find the product of 4.12 × 6.8. Show your work. Go back and compare your answer to your
estimate for #12.
43.
To make green paint, a painter mixed yellow paint and blue paint in the ratio 3:2.
If he used 12 gallons of yellow paint, how much blue paint did he use?
44.
A sum of money was shared between Susan and Nancy in the ratio 2:5. Nancy
received $36 more than Susan. How much money did Susan receive?
You may use unit bars to solve the problem.
45.
What fraction of 2 hours is 20 minutes? Simplify.
46.
What fraction of one pound is12 ounces? Simplify.
Write each fraction as a decimal.
47.
17
20
1
48. 2 5
1
1
49. Jane bought of a cake. She ate of it. She cut the remaining cake into 2 equal slices. What
2
4
fraction of the whole cake was each slice?
50.
Divide.
70.76 ÷ 5.8
Show your work.
51. The Dark Ages ended in 1066. What is the Roman numeral for 1066?
52. Subtract 1066 from 2015. Show your work.
53.
One kilometer = ______________meters.
54.
One meter = ___________________centimeters.
55.
12 : 8 : 20 =
3
: ________: ________
56. The product of two numbers is 48. The sum is 16. What are the numbers?
57.
Find the perimeter of the rectangle below. Label your answer. ______________
58.
Find the area of the rectangle. Label your answer. _______________
59.
Find the perimeter of the square if one side is 8 inches in length.
P = __________inches
Find the area of the square. A = __________ in2
60. The stem-and-leaf plot below shows the ages of guests at a restaurant. Find the following:
Mean _____
61.
3
5
28 + 46
Median____
Mode __________
Express your answer as a mixed number in simplest form.
Range __________
62.
35% of what number is 80?
63.
45 is what percent of 60?
64.
Find the sum of 0.15 + 2.46 + 3.7
65.
Divide.
66.
Express 8 as a decimal _______________and as a percent.______________
67.
Find the GCF of 12, 24, and 42.
4.404 ÷ 0.12
68.
7
Identify the figure.
Be specific.
___________________
69.
What does regular mean in geometry? Draw a regular figure.
70.
Express
71.
Match:
5
16
____ sum
____ quotient
____ product
_____difference
as a decimal.
a. the answer to a subtraction problem
b. the answer to a multiplication problem
c. the answer to an addition problem
d. the answer to a division problem
72.
If a car is traveling at an average speed of 55m/hr. on a 330 mile trip, how long will the trip take?
73.
Simplify.
74.
Draw a figure with horizontal reflection. Draw the line of symmetry.
75.
Draw a figure with rotational symmetry.
76.
8.52 · 0.15
77.
What is the main difference between parallelograms and trapezoids?
78.
Divide. 58.75 ÷ 4.7.
79.
Use >, <, or =.
80.
Multiply.
81.
7
14
5
8
+
14
42
8.098 _____ 8.1
·
9
10
·
2
3
John is packing his lunch. He needs a sandwich and fruit. How many different lunches
can he prepare if he has the choice of cheese or peanut butter on white or whole wheat bread. His
fruit selection includes grapes, an apple, or a banana.
He can make ________________ different lunches. List the lunches or draw a tree diagram.
3
82.
Change 57 to an improper fraction.
83.
Change
84.
18 − 4 · 3 + 9
85.
−7 + 18
86.
−64 ÷ −16
87.
−15 · 24
88.
−12 · −3
89.
A right isosceles triangle has angle measures of __________°, ___________°, and __________°.
90.
Multiply
91.
List the first twelve multiples of 7.
48
17
to a mixed number.
3.385 × 10
3.385 × 100
· −4
3.385 × 1000
0, _______ , _______, ______, ______, _______,
______, ______, ______, _____, _____, ______, ______
2
3
=
𝑥
60
, then 𝑥 = _______
92.
If
93.
Order the fractions from least to greatest. Make equivalent fractions with a common denominator.
7
11
2
3
20
33
94.
Use >, <, or = to complete the statement. 116
____________
161
95.
How many quarter pounders can Ronald McDonald make with 80 pounds of beef?
3
96.
There are 125 students in the Middle School. If of them are girls, how many girls are in the
5
Middle School? _________
How many boys are in the Middle School? __________________
97.
48 ounces = _________pounds.
98.
Express 38 % as a decimal _____________ and as a fraction in lowest terms_______________.
99.
List all of the factors of 24.
100.
Find the sum. Simplify.
3
5
8
+
4
3
4
+
6
5
16