Download Keystone Algebra I Summer Session

Keystone Algebra I
Summer Session: Day 1
Operations with Real Numbers and Expressions
Warm Up
1) Suppose that x and y are rational numbers such that x > y. Which of the following
inequalities must be true?
A) x2 > y2
B) -x > -y
2) Simplify √54
C)
1
𝑥
1
>𝑦
D) 2x > 2y
3) For which value of x should the following
expression be further simplified: √39𝑥
A) x = 2 B) x = 6 C) x = 10
D) x = 11
4) Find the greatest common factor and the least common multiple for the following monomials:
60xy3
and 100x2y2
5) Simplify the expression
(10−6 )−2
10−4
6) Simplify
(4𝑚2 𝑛4 )(7𝑚8 𝑛2 )
(𝑚5 𝑛7 )
A) 1/ 103
B) 1/102
A) 28m5n
B) 28m2n-1
C) 108
D) 1016
C) 28m2/n-1
D) 28m5/n
Keystone Algebra I
Summer Session: Day 1
Operations with Real Numbers and Expressions
Wrap Up: Constructed-Response Problem
The following expressions all use the same values for n, p, and q.



32·3n simplifies to 320
7n/75 simplifies to 7p
(4p·41)3 simplifies to 4q
A) What is the value of the exponent n?
B) What is the value of the exponent p?
C) What is the value of the exponent q?
D) Explain how you found your answers.
Keystone Algebra I
Summer Session: Day 2
Operations with Real Numbers and Expressions
Warm Up
1) One month, 53% of the dinner entrees sold at a restaurant cost $28 or more. That month, the
restaurant sold 2,635 dinner entrees of all prices. What is the best estimate of the least total
amount the $28-or-more dinner entrees brought in?
A) $39,000
B) $40,500
C) $42,000
D) $45,000
2) Find the perimeter and the area for the rectangle with a length of x2 + 3x – 2 and a width of
2x + 1
3) What values of a, b, and c make this equation true?
(2x – 5)(x + 2) + (ax2 + bx + c) = 6x2 – 4x – 7
A) a = 4, b = -3, c = 3
B) a = 4, b = 1, c = -4
C) a = -4, b = -3, c = 3
4) A rectangle has an area equal to 4s2 – 1 square units. When this expression is factored, which
is one of its factors?
A) (s + 1)
B) (2s – 1)
5) Factor 3x3 – 36x2 + 60x
C) (s – 1)
D) (4s – 1)
6) Simplify (x2 – 16)/(x2 + 5x + 4)
Keystone Algebra I
Summer Session: Day 2
Operations with Real Numbers and Expressions
Wrap Up: Constructed-Response Problem
1) A physicist needs to know the values of x for which the trinomial below equals zero. Her
first step is to factor the trinomial:
x2 + 10x + 24
A) Factor the trinomial
B) Explain how you found your answer to part A.
C) The physicist also needs to factor the trinomial x2 – 10x + 24. What is the factored form?
D) The physicist must factor several trinomials that are all of the form x2 – mx + n, where m and
n are whole numbers greater than zero.
She wonders if any of these trinomials factor as (x + a)(x + b), where a > 0 and b < 0. Is that
possible? Explain why or why not.
Keystone Algebra I
Summer Session: Day 3
Linear Equations
Warm Up
Solve the equations:
1) -6z + 1 = 13
2)
3
y – 5 = 10
4
3) A restaurant meal for a group of people cost $85 total. This amount included a 6% tax and an
18% tip, both based on the price of the food. Which equation could be used to find f, the cost of
the food?
A) 85 = 0.24c
B) 85 = 1.06f + 0.18
C) 85 = f + 0.24
D) 85 = 1.24f
4) Jackson 75 cents in dimes, d and nickels, n in his pocket. Which equation could be solved to
find the possible combinations of dimes and nickels Jackson has?
A) 75 = d + n
B) 75 = dn
C) 75 = 10d·5n
D) 75 = 10d + 5n
Solve the linear systems:
5) y = 2x – 1
6) 2x + 2y = 12
4x + y = 2
6x – 2y = 20
Keystone Algebra I
Summer Session: Day 3
Linear Equations
Wrap Up: Constructed-Response Problem
Padma rented a bike for x hours and a kayak for y hours while she was on vacation.
A) She rented the bike and kayak for a total of 7 hours. Write an equation to represent the
situation.
B) The bike cost $6 an hour and the kayak cost $10 an hour. Padma spent a total of $60 for
the bike and the kayak rentals. Write an equation to represent the situation.
C) How many hours did Padma rent the kayak? Show or explain your work.
Keystone Algebra I
Summer Session: Day 4
Linear Equations
Warm Up
1) Graph the linear system: x + 2y = 5
2) What is the solution to the linear
3x + 3y = 6
system: x – 2y = 4 and -x + 2y = 7
3) What is th solution to the system of equations:
x – 4y = 9
2x + 3y = -4
A) (1, -4)
B) (1, -2)
C) (5, -1)
D) ( 7, -6)
4) The growth of a kitten is described by the equation y = 2.5x + 4, where y represents the
kitten’s weight in ounces x weeks after it was born. What is the meaning of the fact that the
point (4, 14) lies on the graph of the equation?
A) The kitten had an initial weight of 4 ounces?
B) The kitten is growing at a rate of 4 ounces per week?
C) The kitten weighed 4 ounces when it was 14 weeks old?
D) The kitten weighed 14 ounces when it was 4 weeks old?
Keystone Algebra I
Summer Session: Day 4
Linear Equations
Wrap Up: Constructed-Response Problem
The table shows how the length of Alex’s pet lizard is changing over time.
Age (years)
1
2
3
4
5
Length (centimeters)
5.0
7.4
9.8
12.2
14.6
A) Write an equation using x and y to find the length of the lizard based on its age.
B)
Describe what the x and y variables represent in your equation
C) Use your equation to predict the length of the lizard when it is 12 years old. Show your
work.
Keystone Algebra I
Summer Session: Day 5
Linear Inequalities
Warm Up
Solve and graph the inequalities on a number line.
1) -6x – 4(3x – 2) ≥ 20
2) 2 < 5 – 3y ≤ 14
3) What is the solution to the absolute value inequality: |5q + 20| > 15
A) -1 < q < 1
B) -7 < q < -1
C) q > -1 or q > 1
D) q < -7 or q > -1
4) Graph the system of inequalities: y ≥ 2x – 3
x+y<4
5) Ellis can spend up to $40 for gasoline and a carwash at a service station. The carwash will
cost $6 and gasoline costs $4.50 per gallon. The inequality 4.5g + 6 ≤ 40 can be solved for g, the
number of gallons of gasoline Ellis can buy. Which of the following is a true statement?
A) Ellis can buy over 10 gallons of gasoline.
B) Ellis can buy at most 7 gallons of gasoline.
C) Ellis can buy 6 gallons of gasoline, but not 7 gallons.
D) Ellis can buy 7 gallons of gasoline, but not 8 gallons.
Keystone Algebra I
Summer Session: Day 5
Linear Inequalities
Wrap Up: Constructed-Response Problem
Michelle is a photographer. She sells framed photographs for $100 each and greeting cards for
$5 each. The materials for each framed photograph cost $30 and the materials for each greeting
card cost $2. Michele can sell up to 8 framed photographs and 40 greeting cards each week, but
this week she has only $200 to spend on materials. Michele hopes to earn a profit of at least
$400 this week after paying for materials.
Let x = the number of framed photographs and y = the number of greeting cards Michele will
make and sell this week. Two of the inequalities that model this situation are x ≤ 8 and y ≤ 40.
A) Write two more inequalities to complete the system of inequalities modeling the
situation.
B) Graph the solution set to your system of inequalities on the coordinate plane. Shade the
area that represents the solution set.
C) Michele plans to make and sell 5 framed photographs and 25 greeting cards. Is that a
solution to the system of inequalities? If so, is it the solution that will produce the most
profit? Explain your answers.
Keystone Algebra I
Summer Session: Day 6
Functions
Warm Up
1) Look at the pattern: 8, 17, 26, 35, 44, …. Which expression represents this pattern
algebraically?
A) n + 9
B) n – 9
C) 9n + 1
2) Which relation is also a function?
A) {(0, 3), (4, 3), (8, 3)}
D) 9n – 1
3) Find the domain and range for the data
{(1, 3), (2, -1), (3, 9), (-5, 0)}
B) {(1, 2), (2, 3), (1, 4)}
C) {(4, 5), (4, 7), (4, 9)}
D) {(6, 0), (8, 1), (8, 5)}
4) Graph 2x + 3y = -6
5) A jet is traveling at 800 km per hour. Sketch a graph that shows the relationship between
time and distance for this jet.
Keystone Algebra I
Summer Session: Day 6
Functions
Wrap Up: Constructed-Response Problem
Justin works at a shop that prints T-shirts. The table shows how the cost of printing T-shirts
depends on the number printed.
Number of Tshirts
Total Cost
(dollars)
20
30
40
50
60
110
135
160
185
210
A) Write an equation to show the relationship between n, the number of t-shirts printed, and C,
the total cost in dollars.
B) Graph your equation on the coordinate plane. Be sure to include an appropriate scale on each
axis.
C) What would be the total cost of an order of 120 T-shirts?
D) Explain how you found your answer to part C.
Keystone Algebra I
Summer Session: Day 7
Coordinate Geometry
Warm Up
1) A pole is placed against a house, 6 feet from the base of the wall. In this position, the pole
has a slope of 5/3. What height off the ground does the top of the pole rest against the house?
A) 2.5 feet
B) 5 feet
C) 10 feet
D) 30 feet
2) A snowstorm laid down more snow on top of an existing base. The equation below can be
used to find the total inches of snow s, on the ground after any number of hours, h, of the storm.
s = 0.75h + 4.
What does the number 0.75 represent? What does the number 4 represent?
3) Which is the equation of the line that contains the points (0, 3) and (-2, 4)?
A) 2x + y = 3
B) x + 2y = 6
C) 2x + y = 0
D) x – 2y = 6
4) A musician charges $45 per hour to play at a party, plus a certain set-up fee. Her total charge
for playing 3 hours is $223. Which equation describes the relationship between x, the time in
hours she plays, and y the total charge in dollars?
A) y + 3 = 45(x + 223)
B) y – 3 = 45(x – 223)
C) y + 223 = 45(x + 3)
D) y – 223 = 45(x – 3)
Keystone Algebra I
Summer Session: Day 7
Coordinate Geometry
Wrap Up: Constructed-Response Problem
There is a linear relationship between the number of people in a group and the cost to enter a
museum. The museum charges $20 for two people and $28 for three people.
A) Write the equation in slope-intercept form that relates the number of people in a group to the
cost of entering the museum. Show your work.
B) How much will it cost for a single individual to enter the museum?
C) How many people can enter the museum for $100?
Keystone Algebra I
Summer Session: Day 8
Data Analysis
Warm Up
1) Eight judges rated a movie on a scale of 1 to 10. Their ratings are given below:
6, 8, 9, 10, 6, 9, 9, 8
Find the mean, median, mode, and range of the data set.
2) The prices of the five most popular big screen television sets at an electronics store are listed
as follows: $2,499 $1,359 $2,299 $2,999 $1,789. If the price of the next most popular
television set is included with this data, the range in prices increases by $800. What could be the
price of the next most popular television set?
A) $2,159
B) $2,199
C) $3,799
D) $3,859
3) Draw a stem and leaf plot for the following test scores in an Algebra class:
83, 75, 92, 65, 78, 90, 92, 70, 66, 78, 85, 89, 75, 99, 58
4) Using the data in # 3, draw a box and whisker plot.
Keystone Algebra I
Summer Session: Day 8
Data Analysis
Wrap Up: Constructed-Response Problem
Isaac’s bowling scores for April are shown below. His mean score after all five games was 221.
Game
Score
1
225
2
245
3
222
4
230
5
?
A) What was Isaac’s score in game 5?
B) What was Isaac’s median score for the five games?
C) Isaac bowls a sixth game and his median score changes to 227. What is Isaac’s score on the
sixth game?
D) Explain how you know your answer to part C is correct?
Keystone Algebra I
Summer Session: Day 9
Probability
Warm Up
1) There is a 10% chance it will rain on Saturday and a 30% chance it will rain on Sunday.
What percent chance is there that it will rain on both Saturday and Sunday?
A) 3%
B) 15%
C) 20%
D) 40%
2) Stefan rolls a 1- 6 number cube and flips a coin. What is the probability that he rolls a
number less than 5 and the coin lands on tails?
1
1
A) 8 3 %
2
B) 33 3 %
C) 41 3 %
2
D) 66 3 %
3) A cafeteria has 5 turkey sandwiches, 6 cheese sandwiches, and 4 tuna sandwiches. There are
two students in line and each will take a sandwich. What is the probability that the first student
takes a cheese sandwich and the next student takes a turkey sandwich?
A)
1
7
B)
1
14
C)
2
15
D)
2
21
Keystone Algebra I
Summer Session: Day 9
Probability
Wrap Up: Constructed-Response Problem
There are 3 black marbles and 4 red marbles in a bag. Trevor will take out 2 marbles without
looking.
A) What is the probability that both marbles will be black? Show your work.
B)
Explain how you found your answer in part A.
C) Suppose that Trevor takes out 1 marble, replaces it in the bag, then takes out another
marble. What is the probability that both marbles will be black in this situation? Show
your work.
D) Explain how you found your answer to part C.
Keystone Algebra I
Summer Session: Day 10
Scatter Plots and Lines of Best Fit
Warm Up
1. MUSIC The scatter plot shows the number of CDs (in millions) that were sold from 1999 to
2005. If the trend continued, about how many CDs were sold in 2006?
2. FAMILY The table below shows the predicted annual cost for a middle income family to raise
a child from birth until adulthood. Draw a scatter plot and describe what relationship exists within
the data.
3. Make a scatter plot of the data in the table. Draw a line of best fit. What is the equation of the
line of best fit?
X
Y
-2
2
-2
3
-1
2
0
1
1
0
1
1
1
-1
2
-1
2
-2
3
-2
Keystone Algebra I
Summer Session: Day 10
Scatter Plots and Lines of Best Fit
Wrap Up: Constructed-Response Problem
EDUCATION The table below gives the number of hours spent studying for a science exam and
the final exam grade.
a. Draw a scatter plot of the data and draw in the line of best fit.
b. What is the equation for the line of best fit?
c. Predict the grade for a student who studied for 6 hours.
d. Could this line go on forever? Why or why not?
Study Hours
Grade
3
84
2
77
5
92
1
70
0
60
4
90
3
75
Keystone Algebra I
Summer Session: Day 11
Functions
Warm Up
Determine if the following are functions, then state the domain and range.
Keystone Algebra I
Summer Session: Day 11
Functions
Wrap Up:
Determine if the following are functions and give the domain and range