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 C) 1x1y D) 2x > 2y
2) Simplify 54 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)-210-4 6) Simplify (4m2n4)(7m8n2)(m5n7)
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) C) (s – 1) D) (4s – 1)
5) Factor 3x3 – 36x2 + 60x 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) 34y – 5 = 10
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) / Length (centimeters)1 / 5.0
2 / 7.4
3 / 9.8
4 / 12.2
5 / 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 D) 9n – 1
2) Which relation is also a function? 3) Find the domain and range for the data
A) {(0, 3), (4, 3), (8, 3)} {(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 T-shirts / 20 / 30 / 40 / 50 / 60Total Cost (dollars) / 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 / 1 / 2 / 3 / 4 / 5Score / 225 / 245 / 222 / 230 / ?
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?