Richard Montgomery High School
Summer Math Packet for Students
Entering Algebra 1
Name:
School Last Year:
Summer Math Packet_Algebra 1_RMHS 2015
Algebra 1 Summer Math Packet
Directions
Hello! This packet will help you get ready to succeed in Algebra 1 next year at Richard
Montgomery. Solve each problem and be sure to show your work where possible. Some of the
problems review basic skills that you’ve already seen and others require you to think
creatively. You may find that you need to look up a formula or refresh your memory on certain
skills. There are many online algebra resources that you can use, including:





www.khanacademy.org/math/algebra
www.mathisfun.com
www.math.com
www.coolmath.com
www.purplemath.com
We recommend that you wait until the middle of summer to start so that the review is still
fresh in your mind when you come back to school. All these problems can be done without
using a calculator. Try finding the answer on your own and then using the calculator to check
your arithmetic.
This packet will be checked on the first day of school. Please bring it with you and have it ready
to turn in.
We’re excited to meet you in August!
-
Your RM Algebra Teachers
2
Algebra 1 Summer Math Packet
1. Plot the following points on the grid and label each point with the corresponding letter:
A (2, 6) B (-2, 4) C (0, -3) D (-5, -6) E (3, -2) F (6, 0)
Draw a line connecting points A
and B and find its slope.
Draw a line connecting points B and
E and find its slope.
2. A square, with side length s, has an area of 324 square centimeters. This equation shows the
area of the square. What is the side length of the square in centimeters?
s
𝑠 2 = 324
3. Six friends are buying pizza for dinner. Their choices are to buy 2 medium
10-inch diameter pizzas for $7.00 each, or 1 large 14-inch diameter pizza
for $15.00. Both include tax and tip. The friends agree that they should
choose the one that gives them the most pizza for their money. Which is
the best choice? Explain your answer.
3
Algebra 1 Summer Math Packet
4. Julissa says the sum of a positive number and a negative number always equals a negative
number or zero.
A. Create an example that supports Julissa’s claim.
B. Create an example that that shows Julissa’s claim is false.
Would you conclude that Julissa is correct or incorrect?
5. For each value below, put the corresponding letter over the correct position on the number
line.
𝐴.
√4
5
𝐵.
𝜋
5
𝐶. 0.52
𝐷.
7
10
𝐸. 2−1
6. Four ounces of a breakfast smoothie provide 5 grams of protein. How many ounces of the
product would be needed to provide 75 grams of protein?
4
Algebra 1 Summer Math Packet
1
1
1
7. Justin’s car can travel 77 2 miles using 3 10.gallons of gas. Kim’s car can travel 99 5 miles
1
using 3 5.gallons of gas. At these rates, how far can each car travel with one gallon of gas?
Graph the number of miles for each car on the number line.
8. Jason lives 100 meters from his school. On a recent trip Jason:
A. Walked 50 meters toward school in 2
minutes.
B. After realizing that he left a book at
home, he turned around and walked
home at the same speed.
C. Spent 1 minute at his house looking for
the book.
D. Walked all the way back to school at twice
his original speed.
Finish drawing the graph so that it accurately
represents Jason’s trip. Label each segment
of the graph with the appropriate letter.
9. Kayla asked 10 students in her class whether they owned a dog or a cat or both. Write a
number from 0-9 in each square to complete the table, given this information:



40% of the students own a dog.
30% of the students own a cat.
10% of the students own both a cat and
dog.
5
Algebra 1 Summer Math Packet
10. Coffee costs $2.00 per pound at a coffee
shop. Graph a line that shows the
proportional relationship between the
number of pounds of coffee purchased and
the total cost.
11. You have a birthday present to wrap. The box is in the shape of a rectangular prism with
the dimensions shown in inches.
a. Find the surface area of the box to the
nearest square inch.
b. You only have 225 square inches of
wrapping paper. Will that be enough to
wrap the present? If not, do you have
enough paper to cover just the top and
sides of the box? Explain.
12. Jake has read 6 of the 20 books on his summer reading list. What percent of the books on
his list has he already completed? What percent does he still need to read?
6
Algebra 1 Summer Math Packet
13. Five friends are eating out together and want to buy 3 salads, 5 sandwiches, 2 bowls of
soup, 1 large drink, and 4 medium drinks. If they divide the cost evenly among themselves,
how much will each person pay?
MENU
Sandwich
Salad
Soup
Small Drink
Medium Drink
Large Drink
$7.50
$4.00
$3.50
$1.25
$1.50
$1.75
14. Compare the fractions. (Put a <, >, or = symbol on the line.)
1
4
1
4
_______
1
6
3
12
_______
−1
18
3
5
15. Consider the following fractions:
_______
1
_______
12
5
3
7
8
5
10
2
4
a. Find their least common denominator (LCD).
b. Write equivalent fractions using the LCD.
c. Calculate the sum of the fractions.
16. Find the simplified values of the following expressions using correct order of operations
(“PEMDAS”).
a. 5 + 2(3 + 5) - 10 =
b. -20 + 7 + 4(3) =
c. 8 + (6 – 3)2 =
7
Algebra 1 Summer Math Packet
17. Rewrite each expression using exponents.
a. (x)(x)(x)(x)(y)(y)(y)
b. -3·b·2·c·c·c·b
18. Simplify each expression by combining like terms.
a. 2x + 7y + 3z + 8x – 5y
b. 4(2x + d) – 3x + 10d
19. Evaluate each expression for the given value.
a. 2k + 3 when k = 5
b. x(x +5) when x = -2
c. (y + 4)2 when y = 3
d. (1 + x)x when x = 2
20. Solve each equation by isolating the variable. (Remember to show work.)
a. x + 4 = 11
b. 2w – 8 = 10
c. 5(t - 3) = 20
d. p + 2p = 28 - 4p
8