Stony Brook University New York Algebra Questions

I have an algebra midterm. It is 6 questions. I will submit photos of the exam . All work needs to be recorded and everything must be correct please.

Stony Brook University
Mathematics Department
Thomas Rico, Julia Viro
Proficiency Algebra
MAP 103
Spring 2021
Midterm 2
Directions: You must submit all your work through Gradescope.com. In order to receive
full credit for each question, you must properly tag each of your submissions with the
appropriate question number. If you tag the wrong question, or you do not tag your
problem at all, you will not receive credit for your answer. All work for all parts of
each question must be shown to receive full credit.
Student Identification. Upload a picture of yourself holding up your official Stony
Brook ID so that your face, and identification are clearly visible. If you do not
have your school ID, then your driver’s license or passport will do just fine, but for your
privacy, you should cover your address with your finger. Standard procedure at Stony
Brook is to check IDs for in-person exams. Without this identification, the exam will not
be graded.
Academic Integrity Statement. Read, fill in, scan, and submit the following academic
integrity statement:
I,
,
First and Last Name
understand that the following are acts of academic dishonesty during the exam:
• Using problems solving websites and phone applications to get solutions.
• Getting help in any form from other people.
• Sharing solutions with other people.
• Using any calculator or graphing utility unless it is explicitly permitted by the
problem.
I understand that if I violate academic integrity, then this incident will be reported
immediately to the Academic Judiciary and I will face
• failure of the course,
• a dishonesty report on your transcript, and
• an obligation to take the Q course.
Signature
1
2
Problem 1) Consider the following equation:
4(x − 1) = 2x − 2(2 − x)
a) [1 Point.] Alice claims that x = 0 is a solution of the equation. Is she right? Substitute
x = 0 into the equation and check.
b) [1 Point.] Ben says that x = −3 is a correct solution. Is he right? Substitute x = −3
into the equation and check.
c) [1 Point.] Can a linear equation in one variable have exactly two solutions? Why or
why not?
3
Problem 1d) [5 Points.] Cara solves the equation by the following steps:
4(x − 1) = 2x − 2(2 − x)
4x − 4 = 2x − 4 + 2x
4x − 4 = 4x − 4
4x − 4 = 0
4x = 4
x=1
Then Cara verifies (checks) the answer by substitution into the original equation:
4(1 − 1) = 2 · 1 − 2(2 − 1)
4·0=2−2
0=0 X
Is Cara’s solution to the equation 4(x − 1) = 2x − 2(2 − x) correct? If not, indicate
the point where Cara was wrong and present a correct solution. Check your solution by
substitution (if possible). If your solution is impossible to check, then explain why.
4
Problem 2) Tom is running a marathon which is a race that covers a total distance of
26.2 miles. For the entire race, Tom will either walk or run at different speeds, and there
will be no breaks where he is at rest. He plans to pace his race by breaking it into 5
intervals along the following parameters:
• Interval 1: He runs at a constant speed of 6.5 miles per hour for a certain amount
of time.
• Interval 2: He walks for 15 minutes at a constant speed of 3 miles per hour.
• Interval 3: He repeats what he did in Interval 1.
• Interval 4: He repeats what he did in interval 2.
• Interval 5: He finishes the race running at a constant speed of 5.2 miles per hour
for an amount of time that is two-thirds the time spent in Interval 1.
a) [2 Points.] Introduce a variable x. Draw a picture or chart showing the intervals. For
each interval on your drawing, indicate the information given in the problem in terms of
x. Compose an equation (in terms of x) which models Tom’s marathon.
5
Problem 2b) [5 Points.] How much time did he spend running in intervals 1, 3, and 5?
Hint: Solve the equation from 2a.
? You are allowed to use a calculator for this part only to add/subtract/multiply/divide, but you
must provide the steps you took while working on the calculator.
c) [1 Point.] How long will the marathon take Tom based on his planned intervals?
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Problem 3) Write down your Stony Brook ID number:

Let q = the seventh digit of your ID number.
Let r = the eighth digit of your ID number.
Let s = the ninth digit of your ID number.
? If any of these digits is equal to 0, then replace 0 with the number 8 ?
q=
r=
s=
[6 Points.] Rashida is looking to sell a boat that retailed for r · 10, 000 dollars on January
1, 2020. After doing some research online, she learns that her boat decreases in value $s
every day. In what time frame should Rashida sell her boat if she wants to avoid selling
her boat for less than 35% of the price she paid on January 1, 2020? Introduce a variable
x, set up an inequality, and solve this inequality for x. Represent this time frame by use
of a number line, and state this time frame in interval notation.
? You are allowed to use a calculator for this part only to add/subtract/multiply/divide, but you
must provide the steps you took while working on the calculator.
7
Problem 4) Write down your Stony Brook ID number:

Let q = the seventh digit of your ID number.
Let r = the eighth digit of your ID number.
Let s = the ninth digit of your ID number.
? If any of these digits is equal to 0, then replace 0 with the number 8 ?
q=
r=
s=
a) [4 Points.] Give an equation of a line that has a negative slope and a does not pass
through Quadrant I. State your equation in standard form.
b) [4 Points.] Give an equation of the line that is perpendicular to the line from Problem
4a, and goes through the point (q, r). State your equation in slope-intercept form.
8
Problem 5) Write down your Stony Brook ID number:

Let q = the seventh digit of your ID number.
Let r = the eighth digit of your ID number.
Let s = the ninth digit of your ID number.
? If any of these digits is equal to 0, then replace 0 with the number 8 ?
q=
r=
s=
Consider the line l1 given by the equation:




sr x − qr y = s2 + q 2


s q
,
belong to the line? Provide an
a) [3 Points.] Does the point P with coordinates
r r
algebraic justification.
b) [2 Points.] Write down an equation of a horizontal line passing through P and refer
to this line as l2 . Write down an equation of a vertical line passing through P and refer
to this line as l3 .
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Problem 5c) [1 Point.] Use Desmos to draw l1 , l2 , and l3 on the the same coordinate
plane. Label your graphs appropriately. Provide a screenshot with graphs and command
lines (equations). Make sure the intersection points of l1 , l2 , and l3 are labeled as well.
10
Problem 5d) [6 Points.] Lines l1 , l2 , and l3 create a triangle with three vertices where
the intersection of l2 and l3 is one of these vertices (point P ). Find the coordinates of the
other two vertices by solving two separate systems of equations. Answers alone will give
no credit.
? You are allowed to use a calculator for this part only to add/subtract/multiply/divide, but you
must provide the steps you took while working on the calculator.
11
Problem 6) Consider a number line of x-values.
a) [3 Points.] Mr. X is hiding somewhere on the number line. It is known that he is at
a distance not more than 7 from the point -2. Show on the number line all places where
Mister X can be located. Describe his location using an absolute value inequality. Solve
the inequality, and give your answer in interval notation.
b) [3 Points.] Mrs. X is hiding somewhere on the number line. It is known that she is
at a distance more than 5 units away from 8. Show on the number line all places where
Mrs. X can be located. Describe her location using an absolute value inequality. Solve
the inequality, and give your answer in interval notation.
c) [2 Points.] Show on a number line where a common meeting place would be for both
Mr. and Mrs. X? Express this common location in interval notation.
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1
meno
8. describe and perform elementary transformations of an equation
9 eynlain what a linear equation is
rithm for solving a linear equation
6 of 10 y solutions a linear equation may have and why it is so
ations and verify whether a solution is correct.
Week 6 (March 8-12)
Video lecture: 16.
Section in the textbook: 2.4.
Learning objectives. Word problems leading to linear equations.
Learning outcomes. A student should be able to
1. solve linear equations originated in geometry and physics
2. adopt a general scheme for solving a word problem
3. understand how to choose a variable and compose an equation
3. apply appropriate formulas for problem solving.
Week 7 (March 15-19)
Video lectures: 17-18.
Sections in the textbook: 1.2, 2.5, 2.6, 2.7.
Learning objectives. Number line. Intervals. Absolute value of a real number. Linear
equations involving absolute value. Linear inequalities. Equivalent inequalities. What is a
solution of an inequality. Double inequalities and systems of inequalities.
Learning outcomes. A student should be able to
1. adopt the interval notations for intervals on the real line
2 describe what a linear inequality is
3. explain what is the solution set of an inequality
4. describe the solution of an inequality in different rs: in interval notation, using set
builder notation, and graphically on the number line
7
5. explain what it means that two inequalities are equivalent and what the elementary
transformations of inequalities are
6. use the ivalence sign correctly
7. explain why multiplying both sides of the inequality by a negative number results in
reversing the sign of the inequality
8. solve linear inequalities by performing elementary transformations
9. write down the solution of a solved inequality in different ways: using inequality signs,
as a set, and as an interval on the number line
10. solve a system of linear inequalities and give a geometric interpretation of the solution
11. interpret a double inequality as a system of inequalities and solve it.
12. interpret the absolute value of a number as a distance
13. comprehend the general formula defining the absolute value of a variable
14. state and explain the properties of absolute value
15. perform calculations involving absolute values
16. solve linear equations involving absolute value
17. solve linear inequalities involving absolute value
Week 8 (March 22-26)
Video lectures: 19-20.
Sections in the textbook: 3.1, 3.2, 3.3.
Learning objectives. Rectangular coordinate system. Linear equations in two variables.
Graph of a linear equation. Lines on a plane. Intercepts, slope, vertical and horizontal lines.
Various forms of a linear equation: standard, two intercept, slope-intercept, point-slope form,
two-points form. Parallel and perpendicular lines.
Learning outcomes. A student should be able to
1. explain what a Cartesian coordinate system on a plane is
2. describe the points on C
3. recognize the equations of vertical and horizontal lines
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12. interpret the absolute value of a number as a distance
13. comprehend the general formula defining the absolute value of a variable
in the properties of absolute value
7 of 10 tions involving absolute values
ations involving absolute value
11. suive meal mequalities involving absolute value
Week 8 (March 22-26)
Video lectures: 19-20.
Sections in the textbook: 3.1, 3.2, 3.3.
Learning objectives. Rectangular coordinate system. Linear equations in two variables.
Graph of a linear equation. Lines on a plane. Intercepts, slope, vertical and horizontal lines.
Various forms of a linear equation: standard, two intercept, slope-intercept, point-slope form,
two-points form. Parallel and perpendicular lines.
Learning outcomes. A student should be able to
1. explain what a Cartesian coordinate system on a plane is
2. describe the points on Cartesian planes by their coordinates
3. recognize the equations of vertical and horizontal lines
4. present the general form of a linear equation in two variables and describe what a given
linear equation represents geometrically
5. explain how two draw a straight line by its equation
6. understand what the intercepts of a line are and how to find their coordinates
7. present a line equation in two-intercept form
8. operate with linear equations in the slope-intercept form
9. provide algebraic and geometric description of the slope of a line
10. explain why parallel lines have the same slope
11. verify if two given equations represent parallel lines
12. write an equation of a line passing through two given points
13. use the point-slope form of the equation of a line
14. explain why perpendicular lines have negative reciprocal slopes.
Week 9 (March 29-April 2)
Video lectures: 21-22.
Sections in the textbook: 4.1, 4.7.
8
Learning objectives. Systems of two linear equations and their geometrical interpretation.
Inconsistent and dependent systems.
Learning outcomes. A student should be able to
1. explain what a linear system of two equations in two variables is
2. explain what it means to solve a system
3. give geometric description of a linear system and its solution
4. explain how many solutions a linear system may have
5. 6. perform elementary transformations of a system
7. solve a system by substitution
8. solve a system by elimination
9. use combined methods for solving a system
10. check a solution of a system
11. write down the solution of a system with infinitely many solutions.
Week 10 (April 5-9)
Video lecture: 23.
Sections in the textbook: 4.2, 4.3.
Learning objectives. Word problems leading to systems of linear equations.
Learning outcomes. A student should be able to
1. choose variables appropriately
2. compose a system of equations according to the text of the problem
3. solve the system
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MAP103_Syllabus_Spring20…
14. expran why perpendicular mes have negauve reciprocar siopes.
8 of 10 9-April 2)
1-22.
Sections in the textbook: 4.1, 4.7.
8
Learning objectives. Systems of two linear equations and their geometrical interpretation.
Inconsistent and dependent systems.
Learning outcomes. A student should be able to
1. explain what a linear system of two equations in two variables is
2. explain what it means to solve a system
3. give geometric description of a linear system and its solution
4. explain how many solutions a linear system may have
5. 6. perform elementary transformations of a system
7. solve a system by substitution
8. solve a system by elimination
9. use combined methods for solving a system
10. check a solution of a system
11. write down the solution of a system with infinitely many solutions.
Week 10 (April 5-9)
Video lecture: 23.
Sections in the textbook: 4.2, 4.3.
Learning objectives. Word problems leading to systems of linear equations.
Learning outcomes. A student should be able to
1. choose variables appropriately
2. compose a system of equations according to the text of the problem
3. solve the system
4. verify the solution.
Week 11 (April 12-16) Midterm 2
Video lecture: 24.
Sections in the textbook: 8.1, 8.2, 8.5.
Learning objectives. Notion of radical. Rules for radicals.
Learning outcomes. A student should be able to
1. know the definition of a principal square root of a non-negative number
2. use the radical sign correctly
3. identify perfect squares
4. comprehend taking the principal square root as an operation opposite to squaring
5. list the properties of radicals
6. explain how to calculate the radical of the square of a variable
7. be aware about typical misconceptions related to radicals
8. explain what is the simplest radical form and how to operate with radical expressions.
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13. use geometric formulas (perimeter, area, volume), physical formulas (unliorm motion),
and common facts about percentage and pricing in word problems
14 analuze the obtained result.
6 of 10
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Week 5 (March 1-5) Midterm 1
Video lectures: 14-15.
Sections in the textbook: 2.1, 2.3.
Learning objectives. Notion of equation. Equivalent equations. Solution of an equation.
Linear equations. Number of solutions of a linear equation.
Learning outcomes. A student should be able to
1. explain what an algebraic equality is
2. classify equalities with variables as identities, contradictions and equations
3. list some commonly used algebraic identities
4. prove algebraic identities
5. understand what an equation in one variable is and what its solution is
6. explain what it means to solve an equation
7. explain what does it mean that two equations are equivalent
8. describe and perform elementary transformations of an equation
9. explain what a linear equation is
10. present an algorithm for solving a linear equation
11. explain how may solutions a linear equation may have and why it is so
12. solve linear equations and verify whether a solution is correct.
Week 6 (March 8-12)
Video lecture: 16.
Section in the textbook: 2.4.
Learning objectives. Word problems leading to linear equations.
Learning outcomes. A student should be able to
1. solve linear equations originated in geometry and physics
2. adopt a general scheme for solving a word problem
3. understand how to choose a variable and compose an equation
3. apply appropriate formulas for problem solving.
Week 7 (March 15-19)
Video lectures: 17-18.
Sections in the textbook: 1.2, 2.5, 2.6, 2.7.
Learning objectives. Number line. Intervals. Absolute value of a real number. Linear
equations involving absolute value. Linear inequalities. Equivalent inequalities. What is a
solution of an inequality. Double inequalities and systems of inequalities.
Learning outcomes. A student should be able to
1. adopt the interval notations for intervals on the real line
2 describe what a linear inequality is
3. explain what is the solution set of an inequality
4. describe the solution of an inequality in different ways: in interval notation, using set
builder notation, and graphically on the number line
7
5. explain what it means that two inequalities are equivalent and what the elementary
transformations of inequalities are
6. use the equivalence sign correctly
7. explain why multiplying both sides of the inequality by a negative number results in
reversing the sign of the inequality
8. solve linear inequalities by performing elementary transformations
9. write down the solution of a solved inequality in different ways: using inequality signs,
as a set, and as an interval on the number line
10. solve a system of linear mequalities and give a geometric mterpretation of the solution