2020 SUMMER ASSIGNMENT - ENTERING 10TH GRADE

SCIENCE PARK HIGH SCHOOL
 MATHEMATICS DEPARTMENT

 ENTERING 10
 TH
 GRADE

 2020 SUMMER ASSIGNMENT
 DUE ON THE FIRST DAY OF SCHOOL
 DIRECTIONS

 Join Google Classroom to submit your work. The code is gv727b3

 The problems in this assignment are designed to help you review topics that are
 essential to your success in Geometry and/or Algebra II. We expect that you come to
 class knowing this material and ready to continue learning.

 Answer all the questions in the space provided. SHOW ALL WORK.

“I pledge on my honor that I have abided by the Science Park HS Academic Integrity Code.”

Printed Name: ____________________________ Signature: _________________

Summer Break Trip
Derrick and his family plan to drive 570 miles from their home outside
Memphis to Chicago over summer break. They agree to leave at 8:00am.

However, his dad can’t find the car keys and they start 2 hours late.

a. Using information from the graph below, create an equation that
 represents the relationship between time and distance for the summer
 break trip and explain the meaning of the terms in the equation.

b. What equation must Derrick solve to answer the following question: If Derrick and his family
 leave their house at 10:00am, in how many hours will they be 150 miles away from home?

c. Use an equation to find out at what time Derrick and his family will reach Chicago if they leave
 their house at 10:00am.

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What’s the Point?
Mr. Williams asks his Algebra I class to find the solutions to an equation in two variables with the
set of real numbers.

Colton correctly creates the table below using values from the domain of the equation. He then uses
this table to create a graph.

a. Determine the equation Colton used to create the table. Use mathematical reasoning to justify
 that the equation is correct.

b. Destiny sees Colton’s work and argues that any table contains some but not all of the solutions
 to Mr. Williams’ equation. Do you agree or disagree with Destiny? Explain why or why not.

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Yes, I Got Multiple Discounts!
Shannon was so happy coming back with her brand new PS5 pre-order. She was able to order from
the only store that lists a price: Play N Trade Vancouver. The listed price is CA$560 (Canadian
dollars). Each Canadian dollar is worth 73 US cents.

Luckily, Shannon was able to find a 20% off coupon for one item purchased
from Play N Trade Vancouver. In addition, she received a 15% off offer for
applying for a new credit card.

Shannon had to pay the 7% provincial sales tax on the initial price before
discounts and 5% Goods and Services tax on the discounted price. She must
also pay 12% for shipping and handling fees on the final bill including taxes.

a. How much did Shannon pay (in USD) in total?

b. Jose, Shannon’s significant other, decided to get a PS5 for himself. He paid a total of $375.46.
 Although Jose received some discounts, he did not get the same discounts as Shannon. What
 percentage discount did Jose get?

To promote the sale of PS5, Sony stated a campaign in the US promising 17% discount and 12%
loyal customers additional discount. Since NJ charges only 6.625% sales tax, Sony promised its NJ
customers to pay only $346.25 for the unit. However, Sony did not list the original price in this
promotion.

c. Calculate the missing list price that Sony will offer to its NJ residents. How much does Sony
 lose per unit of potential income due to the discount?

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Show Me The Money!!!
On March 1st, 2012 of her freshman year at Science Park High School, Jessica started working 2 jobs
after school. (She is working in her parents’ store and does not need working papers.) She works
the same number of hours every week. Jessica decided to save all her money to purchase a new car
after she graduates.

After five weeks of work, she had $1,570 saved. After ten weeks, she saved $2,453.

a. Write a function that represents Jessica’s savings.

At the beginning of the 53rd week, Jessica decided to stop working and invest all her savings in a
corporate bond. The bond pays 9% interest compounded quarterly. Jessica decided to invest the
money for a period of 2 years. Note that Jessica cannot withdraw money or sell the corporate bond
before the end of the term.

b. Write a function that models her investment.

At the end of the 2-year investment, Jessica decided to purchase a new car for $18,000. It will be
financed over a period of 48 months with 0% interest.

c. If she put $2,000 as down payment, how much does she need to pay each month?

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Turns out that this was a lucky car for Jessica! The day she signed the purchase agreement and
drove it out of the lot, she got her long-awaited surprise. Jessica got accepted to MIT! She was
required to move in after 5 months from receiving the acceptance letter. As she moved to
Cambridge, she decided to take a job that pays $3,200 a month. Her employer will deduct 12.6% in
taxes from her paycheck. She also has a grant that pays all her university tuition. However, she
needs to rent a studio for $1,500 per month, including utility. She estimated that her living
expenses will cost $347 per week.

d. With her monthly car payments in mind, create a function of her savings during her 4 years at
 Cambridge, MA. How much money would she have at the end of her 4 years residency in
 Massachusetts?

e. Graph Jessica’s savings since she started working until her graduation from MIT in May 2020.

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Polynomial Farm
Farmer Bob is planting a garden this spring. He wants to plant squash, pumpkins, corn, beans, and
potatoes. His plan for the field layout, in feet, is shown in the figure below. Use the figure and your
knowledge of polynomials, perimeter, and area to solve the following.

a. Write an expression that represents the length of the south side of the field.

b. Write polynomial expressions to represent the perimeter of the pumpkin field. State one
 reason why the perimeter would be useful to Farmer Bob.

c. Write a polynomial expression to represent the area of the potato field.

d. If = 3 feet and = 7 feet, find the area of the bean field. Specify the unit.

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e. Farmer Bob would like to plant six additional fields of produce in another part of his property.
 Find the dimensions of each field, in terms of , given their area.
 ➢ Strawberry field with area 16 2 + 4 

 ➢ Cucumber field with area 2 − 4 − 21

 ➢ Tomato field with area 2 − 36

 ➢ Parsley field with area 2 − 10 + 21

 ➢ Onion field with area 2 − 11 + 30

 ➢ Watermelon field with area 2 + 8 − 20

f. What values of cannot be used if the above six fields are to be built together?

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EXTRA CREDIT! - Social Distancing Revisited
A room with dimensions 20 feet by 26 feet is to be used to host a meeting. Under the CDC
guidelines, we need to design the seats to be six feet apart. John suggested to put people in rows,
with the first row facing the others, and to be used by the hosts.

a. How many rows can be used and what is the maximum number of people that can fit? (Hint:
 Make sure that the distance between any 2 consecutive points is exactly 6 feet.)

Janet suggested to put the attendees on a parabola-like setting, with the zeros of the function on one
edge of the room. The vertices of the parabolas should also be 6 feet apart.

b. How many parabolas can you fit? Write the functions for each one.

c. Assume that the first point on the curve is (0, 0). Use the distance formula and your functions
 from part (b) to find the next possible point with a safe distance of six feet.

d. Write a rule to find the next consecutive points on the parabola with a safe distance.

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e. How many people can you fit in the room if they are only allowed to sit on the designated
 parabolas?

f. Can we add more attendees to the room while keeping a safe distance? Create a graphical
 design for the room to maximize the number of attendees.

g. Is it possible to fit more attendees if they are required to sit on a circular arrangement? Create
 circles that are six feet apart to maximize the number of attendees. Find the coordinates of
 three consecutive seats on each arrangement.

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