Coordinate Algebra
Unit 1: Relationships between Quantities
Review
Name ________KEY______________________
Date ____________
Knowledge and Understanding (use complete sentences and proper vocabulary)
1. Define the following vocab using complete sentences.
a. Equation - Mathematical statement that says that two expressions have the same value; any number
sentence with an equal sign.
b. Expression - A number, variable, or combination of the two connected by some mathematical
operation such as addition, subtraction, multiplication, division, exponents, and/or root.
c. Constant - A number with no variable is a constant.
d. Coefficient - The number in front of the variable is a coefficient. This number role is to multiple
the unknown value of the variable.
e. Variable - A letter that represents an unknown number
f. Term - A single number or variable, or numbers and variables multiplied together is considered a term.
g. Factor - A number you multiply to get a product is called a factor.
2. Identify the variables, coefficients and the total number of terms in the following expressions. Use
complete sentences.
a. 2x2 + 7x + 3
The variable in this expression is x. There are 3 total terms and the coefficient for x2 is 2, the coefficient
for x is 7 and 3 is a constant.
b. 11a3 + 8a
The variable in this expression is y. There are 2 total terms and the coefficient for a3 is 11 and the
coefficient for a is 8. There is not a constant in this expression.
c. y2 + 3y – 7
The variable in this expression is y. There are 3 total terms and the coefficient for y2 is 1, the coefficient
for y is 3 and -7 is a constant.
3. What is the difference x5 and 5x?
x5 represents the variable, x, being multiplied by itself 5 times. (x*x*x*x*x). 5x represent the number 5 being
multiplied by the unknown value of the variable x: (5*x).
4. How do you identify a solution on a graph?
If there are infinitely many, find a point on the line. If there is one, it is the intersection of two lines.
5. What are two ways to solve a system of equation problem?
Substitution, Elimination, Graphing
Proficiency Skills
6. Solve the formula for A: 𝐵 =
𝑨=
7. If 𝑪 = 𝑨 +
𝟑
𝑷𝒃,
𝟒
𝟗
𝟓
5
9
𝐴 + 64.
(𝑩 − 𝟔𝟒).
solve the equation for P.
8. Solve for m: 𝟐(𝒎 + 𝟑) = 𝟒𝒏 − 𝟔
𝟒(𝑪−𝑨)
𝟑𝒃
=𝑷
m = 2n - 6
9. Elder(x) has three times as much money as Elise(y). Elise has $7 less than Tosan (z). Together they have
$22. Which expression would represent the amount of money Elder would have?
x = 3y ; y = z – 7; x + y + z = 22
This can be done many way. I am going to solve in respect to z
x = 3y  x = 3(z – 7)
y=z–7
So substitute those in: x + y + z = 22  3(z – 7) + (z – 7) + z = 22
3z – 21 + z – 7 + z = 22
5z – 28 = 22
5z = 50; z = 10
Therefore, Tosan has $10, Elise has $3 and Elder has $9: total of $22
10. Explain the role of the coefficient 3 in this problem: x3 – 3x2 + 3x = 4
The coefficient 3 is being multiplied by the unknown variable x.
11. Explain the role 2 in this problem: x2 + 4 = 20
The exponent is multiplying the variable x times itself (x*x)
12. A rectangle is 8ft longer than it is wide. Its perimeter is at least 40ft. a) Determine the model that would
represent the perimeter of the rectangle. b) Find the approximate width of the rectangle.
a) Wide = x ; Length x + 8 Perimeter = l + l + w+ w = 2(x) + 2(x +8) = 4x + 16
b) Perimeter: 4x + 16 ≥ 40 the width is at least 6 ft
13. The graph is show the relationship of the number of bacteria growing (in thousands) over a period of time (in
minutes).
a) Determine the number of bacteria present after 4 minutes.
1500
b) How much time has passed when the bacteria is 8,000?
8 mins
12. Brayan is 5’6” tall and weighs 168 pounds. Many doctors use a person’s body mass index (BMI) as a health
(w  705)  h
risk indicator. The formula, BMI 
, can be used to calculate a person’s BMI where w represents
h
the weight and h represents the height in inches. A person with an index of less than 19 or greater than 27
indicates an increased risk for health problems. Determine if his BMI indicates his health may be at risk.
We did this in class
13. Kiana wants to have an average of at least 95 on her quizzes. If she took three quizzes and earned a 84, 90
and 97, which expression would help Kiana find the grade (x) she would need on her fourth quiz?
We did this in class. Answer: 109
14. Write a model for three consecutive even integers whose sum is 36. Simplify the expression.
n + (n + 2) + (n + 4) = 36  3n + 6 = 36  3n = 30  n = 10
15. Five years ago, Isaiah invested $3,500 in an account that earns 7% interest compounded annually. The
equation y = P(1+I)t describes the balance in the account, where P is the principal, I is the interest and t is time
in years. Isaiah made no additional deposits and no withdrawals. How much is in the account now?
Did in class. Answer: $4,908. 93
16. Using the exponential growth model y  a(1  r)t where a is the initial amount, r is the percent
increase
expressed as a decimal and t is the time, use the model given to find the value after 8 yrs. of a football card that
initially cost $530 and is expected to increase by 10% per year.
Did in class. Answer: $1,136. 10
Determine if the following are solutions to the graph. If it is not a solution then state a solution for the graph.
16. (2, 6)
NO
18. (-4, -4)
YES
Determine if the following are solutions to the graph and explain your answers in complete sentences. If it is
not a solution then state a solution for the graph.
19. (0, 0)
NO
20. (0, 2)
NO
21. (4, 0) YES
Performance Task
21. Lyric is the president of student body. Student body is having a bake sale to raise money for Homecoming. She
has received quotes from two different companies for cookies and cakes. LetsBake charges $4 to print 12 cookies.
BestCakes charges a $15 service fee and an additional $5 per cake. Determine under which conditions Lyric
should choose each company if her goal is to reduce expenses.
Multiple answers. We discussed this in class.
22. Deangelo wants to have a surprise birthday party for his best friend on Saturday. He is planning on having at
least 75 people show up. Typically about 15% of the people who are invited actually attend. Answer the following
questions about his planning:
A. Determine a model that would find how many people Ben would need to invite to have at least 40 people
show up?
B. The table below shows the number of people invited to the party if Deangelo tells one person and asks that
person to tell one other person the next day through the day of the party.
Complete the table below using the pattern described above. Write a model to represent the pattern
you found in the table.
Day
0
1
2
3
4
5
6
# of People that
know
1
2
4
23. In order to make a profit, the school concession stand must have at least $650 in sales.
Prices
Water….……………………………….$2.00
Nachos………………………………….$2.00
French Fries……………………………….$2.50
They sold 175 bottles of water. If they typically sell four times as many French Fries as Nachos, how
many French Fries must the concession stand sell in order to make a profit?
We did this in class