Algebra 1H Summer Work
These problems should be completed by students enrolled in Algebra 1 Honors only.
Please complete these problems on a separate sheet of paper (or, even better, in the notebook you
have purchased for math this year.) Please show your work along the way. Please note that some
questions say “explain” so be ready to write down your thought process. You will be asked to present
some of these problems in class…make sure that someone else could follow your work. The problem
numbers match up with the beginning of this year’s problem set collection, so don’t worry that they
go #1, #7 etc. Just number your work to match these and go through.
1. Light travels at about 186 thousand miles per second, and the Sun is about 93 million miles
from the Earth. How much time does light take to reach the Earth from the Sun?
7. Your class sponsors a benefit concert and prices the tickets at $8 each. Dale sells 12 tickets,
Andy 16, Morgan 17, and Pat 13. Compute the total revenue brought in by these four people.
Notice there are two ways of doing the calculation.
8. Kelly telephoned Brook about the homework problem. Kelly said, “Four plus three times two is
14, isn’t it?” Brook replied, “No, it’s 10.” Did someone make a mistake? Can you explain where
these two answers come from?
10. Wes bought some school supplies at an outlet store in Maine, a state that has a 6.5% sales
tax. Including the sales tax, how much did Wes pay for two blazers priced at $49.95 each and 3
pairs of pants priced at $17.50 each?
11. (Continuation) A familiar feature of arithmetic is that multiplication distributes over addition.
Written in algebraic code, this property looks like 𝑎(𝑏 + 𝑐) = 𝑎𝑏 + 𝑎𝑐. Because of this property,
there are two equivalent methods that can be used to compute the answer in the previous
problem. Explain, using words and complete sentences.
13. Pick any number. Add 4 to it and then double your answer. Now subtract 6 from that result
and divide your new answer by 2. Write down your answer. Repeat these steps with another
number. Continue with a few more numbers, comparing your final answer with your original
number. Is there a pattern to your answer?
20. Davis says that adding a two-digit number to the two-digit number formed by reversing the
digits of the original number results in a sum of 65. Avery says that’s impossible. Is it impossible?
28. To buy a ticket for the weekly state lottery, a person selects 6 integers from 1 to 36, the order
not being important. There are 1947792 such combinations of six digits. Alex and nine friends
want to win the lottery by buying every possible ticket (all 1947792 combinations), and plan to
spend 16 hours a day doing it. Assume that each person buys one ticket every five seconds. What
do you think of this plan? Can the project be completed within a week?
29. On a map of South Asia, Nepal looks approximately like a rectangle measuring 8.3 cm by 2.0
cm. The map scale is listed as 1: 9,485,000. What is the approximate real world area of Nepal in
𝑘𝑚2 ?
33. Before you are able to take a bite of your new chocolate bar, a friend comes along and takes
¼ of the bar. Then another friend comes along and you give this person 1/3 of what you have
left. Make a diagram that shows the part of the bar left for you to eat.
39. Tory goes shopping and buys pencils and notebooks. If Tory buys a total of 8 items, p of
which are pencils, write an expression for the number of notebooks Tory buys.
40. (Continuation) If each pencil costs 29 cents and each notebook costs $2.59, write expressions
for:
a. how much Tory spends on pencils;
b. how much Tory spends on notebooks;
c. how much Tory spends altogether.
41. (Continuation If Tory’s bill is $9.22, how many pencils does Tory buy?
43. Here is another number puzzle: Pick a number, add 5 and multiply the result by 4. Add
another 5 and multiply the result by 4 again. Subtract 100 from your result and divide your
answer by 8. How does your answer compare to the original number? You may need to do a
couple of examples like this until you see the pattern. Use a variable for the chosen number and
see how the pattern holds for any number.
46. A group of 10 people were planning to contribute equal amounts of money to buy some pizza.
After the pizza was ordered, one person left. Each of the other nine people had to pay 60 cents
extra as a result. How much was the total bill?
53. Write each of the following as a product of x and another number:
a. 16𝑥 + 7𝑥
b. 12𝑥 − 6𝑥
c. 𝑎𝑥 + 𝑏𝑥
d. 𝑝𝑥 − 𝑞𝑥
54. (Continuation) Solve each of the following equations for x:
a. 16𝑥 + 7𝑥=46
b. 12𝑥 − 6𝑥 = 3
c. 𝑎𝑥 + 𝑏𝑥 = 10
d. 𝑝𝑥 − 𝑞𝑥 = 𝑟
88. Ryan earns x dollars every seven days. Write an expression for how much Ryan earns in one
day. Ryan’s spouse Lee is paid twice as much as Ryan. Write an expression for how much Lee
earns in one day. Write an expression for their combined daily earnings.
𝑥+𝑦
104. Using a number line, describe the location of 2 in relation to x and y. Is your answer
affected by knowing whether x and y are positive or not?
108. One of the interscholastic teams has started its season badly, winning 1 game, losing 6 and
tying none. The team will play a total of 25 games this season.
a. What percentage of the seven games played so far have been wins?
b. Starting with its current record of 1 win and 6 losses, what will the cumulative winning
percentage be if the team wins the next 4 games in a row?
c. Starting with its current record of 1 win and 6 losses, how many games in a row must the team
win in order for its cumulative winning percentage to reach at least 60%?
d. How many of the remaining 18 games does the team need to win so that its final winning
percentage is at least 60%? Is it possible for the team to have a final winning percentage of 80%
Explain.