Download summer math packet 2016 for rising eighth graders who were in pre

SUMMER MATH PACKET
2016
FOR RISING EIGHTH
GRADERS WHO WERE
IN PRE-ALGEBRA
1
DIRECTIONS FOR COMPLETING THE PACKET
• The following page contains the list of help topics available on the Glencoe website. Each
topic includes a brief explanation and review of problems like those you will see in your
packet. If you are having trouble with a specific topic or question, you may use this site as
a resource.
• This work should be attempted without the use of a calculator. However, some sections
will require the use of a calculator. These sections will be noted. If the section is not
noted for use of a calculator, you must show all work.
• Solve part I in June, part II in July, part III in August.
The idea of the review is to do little work (each of these 3 packets should take about 3 –
4 hours of work), but spread in time so it refreshes your memory every now and then
and keeps alive the knowledge you acquired during the year. Of course, you can do
everything in August, but by then your memory will be stale beyond the rejuvenating
power of this packet. Or you can do it all now, but by late August, when classes begin,
you will have trouble to retrieve this knowledge from the dungeons of your memory. If
you want to invest your time poorly, go ahead.
• If a problem or group thereof is still driving you crazy, you will find help at
[email protected]. USE IT! Be explicit about what you did, what you got, and/or what
you find puzzling. A couple of sentences. You may include a scan in your email. Help may
delay a day or two.
• Turn in the packet with your solutions the first day of classes. It will be a conversation
piece the first week of class.
• Enjoy your vacation!
2
MATH REVIEW TOPICS AVAILABLE ONLINE
http://glencoe.mcgraw-hill.com/sites/0078738229/student_view0/math_review.html
Number Sense
Adding and Subtracting Whole Numbers
Comparing and Ordering Whole Numbers
Divisibility Patterns
Estimating with Whole Numbers
Estimation Strategies
Greatest Common Factor
Least Common Multiple
Multiplying and Dividing Whole Numbers
Place Value and Whole Numbers
Powers of 10
Prime Factorization
Decimals
Adding and Subtracting Decimals
Comparing and Ordering Decimals
Dividing Decimals
Estimating Products
Multiplying Decimals
Place Value and Decimals
Rounding Decimals
Fractions
Estimating Products and Quotients of Fractions and Mixed Numbers
Estimating Sums and Differences of Fractions and Mixed Numbers
Expressing Fractions as Decimals and Percents
Mixed Numbers and Improper Fractions
Operations with Fractions: Adding and Subtracting
Operations with Fractions: Multiplying and Dividing
Simplifying Fractions
The Percent Proportion
Integers
Comparing and Ordering Real Numbers
Operations with Integers
Problem-Solving
Guess and Check
Make a Table or List
Solve a Simpler Problem
Work Backward
Measurement
Converting Measurements w/ Customary System
Converting Measurements w/ Metric System
Units of Time
Statistics and Graphs
Box and Whisker Plots
Making Bar and Line Graphs
Making Circle Graphs
Mean, Median and Mode
Stem and Leaf Plots
Algebraic Concepts
Evaluating Algebraic Expressions
Factoring to Solve
Graphing Ordered Pairs
Graphing Using Intercepts and Slope
Multiplying Polynomials
Solving Eqns. w/ the Variable on Both Sides
Solving Inequalities
Solving Multi-Step Equations
Solving One-Step Equations
Solving Systems of Linear Equations
Square Roots and Simplifying Radicals
Geometry
Area and Circumference of Circles
Congruent and Similar Figures
Identifying 3-Dimensional Figures
Identifying 2-Dimensional Figures
Measuring and Drawing Angles
Perimeter and Area of Squares and Rectangles
Pythagorean Theorem
Volume
3
JUNE – Lesson 1: Operations with Fractions: Adding, Subtracting, Multiplying and
Dividing (NO CALCULATORS)
Find each sum or difference.
1.
2 1
+
5 5
2.
2
1
3 −1
7
7
4.
28
40
Simplify.
6
9
3.
Find each sum or difference. Write in simplest form.
5.
2
8
2
−1
9
3
6.
3
2
+5
4
5
8.
6 10
⋅
5 12
Find each product.
7.
2
6
2 ⋅3
3 10
4
Name the reciprocal of each number.
9.
6
7
10.
5
1
3
12.
2
1 1
÷
4 2
Find each quotient.
11.
11
2
÷1
12
3
Lesson 2: Operations with Rational Numbers (NO CALCULATORS)
13.
16 – (–23)
14.
-19 – 8
15.
-12(15)
16.
(-1 )( −2 )
17.
(-64) ÷ (−8)
18.
(32.25) ÷ (−2.5)
5
4
5
1
2
19.
Hannah is making pillows. The pattern states that she needs 1
she has 4
20.
3
yards of fabric for each pillow. If
4
1
yards of fabric, how many pillows can she make?
2
The price of a computer dropped $34.95 each month for 7 months. If the starting price was
$1,450, what was the price after 7 months?
Lesson 3: The Percent Proportion (CALCULATORS PERMITTED)
Express each percent as a reduced fraction.
21.
78%
22.
120%
Use the percent proportion to find each number.
23.
25 is what percent of 125?
24.
50% of what number is 80?
6
25.
Find 12% of 156.
26.
Maddie usually makes 85% of her shots in basketball. If she shoots 20 shots, how many will she
likely make?
27.
A glucose solution is prepared by dissolving 6 millimeters of glucose in 120 milliliters of solution.
What is the percent glucose in the solution?
28.
The U.S. Food and Drug Administration requires food manufacturers to label their products with
a nutritional label. The sample label shown at the right shows a portion of the information from a
package of macaroni and cheese. For a healthy diet, the National Research Council recommends
that no more than 30% of total Calories come from fat. What percent of the Calories in a serving
of this macaroni and cheese come from fat?
7
JULY – Lesson 4: Expressing Fractions as Decimals and Percents. (NO CALCULATORS)
Write each fraction as a decimal.
29.
3
8
30.
2
3
32.
5.24
34.
0.333…
36.
10.5%
Write each decimal as a fraction.
31.
0.9
Write each decimal as a percent.
33.
0.08
Write each percent as a decimal.
35.
68%
Write each fraction as a percent. Round to the nearest tenth of a percent if necessary.
37.
9
20
38.
19
25
40.
0.5%
Write each percent as a fraction.
39.
52%
8
Lesson 5: Mean, Median and Mode (CALCULATORS PERMITTED)
41.
Bill’s scores on his first four science tests are 86, 90, 84, and 91. What is Bill’s average test score
based on these scores?
42.
Sue’s average for 9 games of bowling is 108. What is the lowest score she can receive for the tenth
game to have an average of 110?
43.
The ratings for the top television programs during one week are shown in the table at the right.
Find the mean, median, and mode of the ratings. Round to the nearest hundredth.
(There are no questions #44-53! Go take a break in the sunshine in place of those missing problems.)
Lesson 6: Order of Operations / Evaluating expressions (CALCULATORS PERMITTED)
Evaluate each expression.
54.
3 + 8 ÷2 – 5
55.
9
16 ÷ 2 ⋅ 5 ⋅ 3 ÷ 6
56.
390 ÷ [5(7 + 6)]
57.
15 ÷ 3 ⋅ 5 − 4 2
58.
20 ÷ 5 · 2 – 12 + 7
59.
13 + 7 2 ÷ 7
9 − 20 ÷ 4 + 16
60.
2
2(5 + (30 ÷ 6) )
61.
[(8 + 5)(6 − 2) 2 ] − (4 ⋅ 17 ÷ 2)
[(24 ÷ 2) ÷ 3]
Evaluate each expression if a = 2, b = 5, x = 4 and n = 10.
62.
8a + b
63.
(2x)2 + an – 5b
64.
a(6 – 3n)
65.
[a + 8(b – 2)]2 ÷ 4
10
AUGUST – Lesson 7: Simplifying and Solving Algebraic Expressions (CALCULATORS
PERMITTED)
66.
5(-3a) – 6a
67.
-7(2m – 3n)
68.
65x − 15 y
5
69.
-8(-x) + 13x
71.
9 + x = 19
73.
7p = 35
Solve each equation. Then check your work.
70.
–2 + m = 7
72.
f – (− ) =
1
8
3
10
11
74.
w
=3
5
75.
p −5
=
6 12
76.
4x + 5 = 37
77.
-3t – 9 = -24
78.
4.8m – 3 = 9 – 1.2a
79.
5r + 4r = -72
80.
5x + 1 = 3x – 3
81.
6(y - 5) = 18 – 2y
12
Lesson 8: Plotting Points on the Coordinate Plane (CALCULATORS PERMITTED)
Plot the following points on the coordinate plane to the right.
82.
(2,3)
83.
(-4,1)
84.
(5,-2)
85.
(0, 7)
86.
(-4,0)
Write the ordered pair for point E and point K.
87.
E=(
88.
K=(
,
)
,
)
Fill in the following table of values for each linear equation below. Then graph the points on the
coordinate plane.
89.
y = 2x - 1
x
y
13
90.
y=3–x
x
y
Lesson 10: Mixed Problem Solving
As you ascend in the Earth’s atmosphere, the temperature drops about 3.6 degrees every 1,000 feet in
altitude.
91.
If you ascend 10,000 feet, what is the change in temperature?
92.
If the temperature drops from 70 degrees Fahrenheit at sea level to -38 degrees Fahrenheit, what
is the altitude you have reached?
In the 2000 Olympic games, the winning time for the men’s 400-meter run was approximately 44
seconds. The winning time for the men’s 400-meter freestyle meter swimming event was about 3 minutes
41 seconds. Round your answer to the nearest meter in questions 93 and 94.
93.
What was the speed in meters per second for the 400-meter run?
94.
What was the speed in meters per second for the 400-meter freestlye?
14
95.
How do the speeds of the two events compare?
The Congo River in Africa is 2900 miles long. That is 310 miles longer than the Niger River, which is also
in Africa.
96.
Write an equation you could use to find the length of the Niger River.
97.
What is the length of the Niger River?
98.
Four teachers went to a baseball game. A vendor selling bags of popcorn came by. Dulaney bought
half of the bags of popcorn plus one. DL bought half of the remaining bags of popcorn plus one.
Dan bought half of the remaining bags of popcorn plus one. Riki bought half of the remaining
bags of popcorn plus one, leaving the vendor with no bags of popcorn. If Riki bought 2 bags of
popcorn, how many bags did each of the four teachers buy?
Mike is registering for a ski trip in British Columbia, Canada. The cost of the camp is $1,254, but the
Canadian government imposes a general sales tax of 7%.
99.
What is the total cost of the camp including tax?
100.
As a US Citizen, Mike can apply for a refund of one-half of the tax. What is the amount of the
refund he can receive?
15