2.3 applications of equations (oct 24 pre lesson)
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The document provides information about upcoming assessments and practice problems. It includes a summary of standards on functions and interpreting functions to be covered on a quiz. It also lists exercises identifying functions that will be on the quiz. Additionally, it gives steps for interpreting word problems and recommends practicing similar problems from the textbook.
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College Algebra MATH 107 Spring, 2017, V.1.3
Page 1 of 11
MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function. 1. ______
A. Domain [– 3, 3]; Range [– 1, 3]
B. Domain [– 3, 1]; Range [– 3, 3]
C. Domain [– 1, 0.5]; Range [–1, 0]
D. Domain (–∞, 3]; Range [–1, ∞)
2. Solve: 10 3x x− = − 2. ______
A. –5, 2
B. 5/2
C. –5
D. No solution
2 4 -4
-2
-4
2
4
-2
College Algebra MATH 107 Spring, 2017, V.1.3
Page 2 of 11
3. Determine the interval(s) on which the function is increasing. 3. ______
A. (–∞, –1)
B. (– 2, 2)
C. (–∞, – 3) and (1, ∞)
D. (– 4.5, – 1) and (2.5, ∞)
4. Determine whether the graph of ( )
2
4xy −= is symmetric with respect to the origin,
the x-axis, or the y-axis. 4. ______
A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. symmetric with respect to the origin only
5. Solve, and express the answer in interval notation: | 6 – 5x | ≤ 14. 5. ______
A. (–∞, −8/5] ∪ [4, ∞)
B. (–∞, –8/5]
C. [4, ∞)
D. [–8/5, 4]
College Algebra MATH 107 Spring, 2017, V.1.3
Page 3 of 11
6. Which of the following represents the graph of 7x + 4y = 28 ? 6. ______
A. B.
C. D.
College Algebra MATH 107 Spring, 2017, V.1.3
Page 4 of 11
7. Write a slope-intercept equation for a line parallel to the line x – 3y = 5 which passes through
the point (6, –8). 7. ______
A.
1
8
3
y x= −
B.
1
10
3
y x= −
C.
1
6
3
y x= − −
...
Math 107 College AlgebraName Olufemi Akinyemi Final Examination F.docx
Math 107 College AlgebraName Olufemi Akinyemi Final Examination: Fall, 2019Instructor: Dr.K. Thengumthara Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document. There are 30 problems.
Problems #1-12 are multiple choice. Record your choice for each problem. Problems #13-21 are short answer. Record your answer for each problem.
Problems #22-30 are short answer with work required. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain- text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement.
Please sign (or type) your name below the following honor statement:
I have completed this final examination myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this final examination.
NameDate
Math 107 Final Examination
Fall, 2019
1
MULTIPLE CHOICE. Record your answer choices.
1.7.
2.8.
3.9.
4.10.
5.11.
6.12.
SHORT ANSWER. Record your answers below.
13.
14.
15.
16.
17.
18.
19. (a) (b) (c)
20.(a)
(b)
(c)
(d)
21. (a) (b) (c) (d)
SHORT ANSWER with Work Shown. Record your answers and work.
Problem Number
Solution
22
Answers:
(a)
(b)
Work/for part (a) and explanation for part (b):
23
Answers:
(a)
(b)
(c)
Work for part (a):
24
Answer:
Work:
25
Answer:
Work:
26
Answers:
(a)
(b)
Work for part (a) and for part (b):
27
Answer:
Work:
28
Answer:
Work:
29
Answers: (a)
(b)
Work for (b):
30
Answer:
Work:
Research Paper Guidelines
Due Date: Nov 29th, 2019
An important activity in this course will involve writing a research paper in APA format. This is an exercise in argumentation. This paper will be between 5 - 7 pages in size single-spaced. A list of topics related to software construction are provided below. Each student will select one of the topics from the list. Most of the topics includes papers that provide necessary background. The student would then be required to research and identify at least three academic papers for and three papers against the topic. Please note these papers will be in addition to the ones listed below for the topic. You will be asked to take a position either for or against the topic and argue your position based on the literature collected. As part of your argument, you would be asked to demonstrate using coding o.
GenMath 11_Module 21 Distinguishing EF EE EI or None.pdf
This document provides a module on distinguishing between exponential functions, equations, and inequalities. It begins with an introduction to the topic and learning objectives. It then provides examples of each type of exponential expression and explains the definitions. The document provides practice problems for students to determine which category different exponential expressions fall into. It concludes by summarizing the key differences between exponential functions, equations, and inequalities.
Transformations of functions
This document discusses transformations of functions. It begins by introducing common parent functions like linear, quadratic, absolute value, cubic and square root functions using xy-tables and graphs. It then demonstrates how adding or subtracting values like 1, 5, or 2 to a quadratic function f(x)=x^2 results in a rigid transformation that shifts the graph up, down, left or right but maintains the same basic shape. The document defines rigid transformations as those that only change the position of the graph and lists the three types as vertical shifts, horizontal shifts, and reflections, providing formulas for shifting graphs vertically and horizontally.
GenMath-Lesson-1.pptx
Representing Real-life Situations Using Functions Including Piecewise functions. Lesson 1 in General Mathematics for Grade 11
Theory of Equation
1. The document provides an overview of the key concepts in the Theory of Equations unit, including types of equations, methods for solving different types of equations, and properties of roots.
2. It discusses linear equations, simultaneous equations, quadratic equations and their solving methods like elimination, substitution, and factorization.
3. Examples of equation problems from commercial applications are also presented, involving linear, simultaneous and quadratic equations. Worked examples and practice problems are provided for each topic.
Paper no. 4
This document provides instructions on how to evaluate algebraic expressions using a Casio fx-350ES PLUS calculator. It includes an example of evaluating the expression a2+b3 when a=4 and b=2. The steps shown are to assign the values 4 and 2 to the variables a and b using the calculator's storage function, then using the variables to calculate the expression. Exercises are provided to evaluate other algebraic expressions using the given calculator.
Paper no. 4
This document provides instructions on how to evaluate algebraic expressions using a Casio fx-350ES PLUS calculator. It includes an example of evaluating the expression a2+b3 when a=4 and b=2. The steps shown are to assign the values 4 and 2 to the variables a and b using the calculator's storage function, then using the variables to calculate the expression. Exercises are provided to evaluate other algebraic expressions using the given calculator.
Contextualized Lesson Plan in Math 7 Linear Equation in One Variable
Contextualized Lesson Plan in Math 7 Linear Equation in One VariableDepartment of Education - Philippines
This lesson plan is about solving linear equations and inequalities algebraically. Students will learn to find the solution of linear equations in one variable. They will practice translating between verbal and mathematical phrases and evaluating expressions. The lesson will review properties of equality like the reflexive, symmetric, transitive, addition, and multiplication properties. Students will learn steps to solve various types of linear equations using these properties. They will assess their understanding by solving sample equations on their own. For homework, students will solve equations and determine whether they have unique solutions, no solutions, or infinite solutions.(7) Lesson 3.2 - Add Integers
This document provides examples and step-by-step explanations of how to add, subtract, multiply and divide integers according to their signs. It begins with writing integers for word problems, then evaluates expressions. The main content explains that to add integers with the same sign, add their absolute values and the sum is positive if both are positive or negative if both are negative. To add integers with different signs, subtract the absolute values and the sum is positive if the positive value is greater or negative if the negative value is greater. Several worked examples are provided to illustrate the rules.
Week 1 2 linear equations (2)
The document provides an overview of lessons on linear equations for a math class over 3 days. Key points covered include:
- Day 1 focuses on defining linear equations, properties of equality, and solving linear and rational equations.
- Day 2 covers solving equations involving radicals, absolute values, and literal equations.
- Day 3 involves word problems including number, geometry, digit, investment, age, mixture, uniform motion, work, and clock problems that can be modeled and solved using linear equations.
MATH 10 Week 1 2 linear equations (2)
The document provides an overview of lessons on linear equations for a math class over 3 days. Key points covered include:
- Day 1 focuses on defining linear equations, properties of equality, and solving linear and rational equations.
- Day 2 covers solving equations involving radicals, absolute values, and literal equations.
- Day 3 involves word problems including number, geometry, digit, investment, age, mixture, uniform motion, work, and clock problems, which are modeled and solved using linear equations.
Page 1 of 3 MATH133 Unit 4 Functions and Their Graphs .docx
Page 1 of 3
MATH133 Unit 4: Functions and Their Graphs
Individual Project Assignment: Version 2A
IMPORTANT: Please see Question 3 under Problem 2 for special instructions for this
week’s IP assignment. This is mandatory.
Show all of your work details, explanations, and answers on the Unit 4 IP Answer Form
provided.
Problem 1: Children’s Growth
A study of the data representing the approximate average heights of children from birth to 12
years (144 months) has shown the following two equations. The function is the radical
function representing the girls’ heights in inches after x months, and the function is the radical
function representing the boys’ heights in inches after x months ( months).
( ) √
( ) √
1. Choose five different values of x between 0 and 144 months, and calculate the values of each of
these functions for the chosen x values. Show all of your work and display these calculated values
of ( ) and ( ) in “t-tables” in the Answer Form supplied.
2. Use these five different values of x and the corresponding calculated values of both functions,
together with Excel or another graphing utility, to draw the graphs of these two functions. These
graphs should be drawn on the same coordinate system so that the two functions can be easily
compared. Insert those graphs into the Answer Form.
3. Set the two functions equal to each other, and solve the resulting radical equation for x. This
value of x will be the age in months when boys and girls are the same height. (Show all of the
steps for solving this radical equation on the Answer Form provided.)
4. What is the height in inches when boys and girls (according to these radical functions) are the
same height? (Show all of your work on the Answer Form provided.)
5. Based on each of the two radical functions above, what is the average change in height per
month for girls and the average change in height per month for boys between the two values of
x (x = 30 months and x = 60 months)? (Show all of your work on the Answer Form provided.)
Page 2 of 3
6. Describe the transformations of the radical function ( ) √ that will result in each of these
functions.
7. Which intellipath Learning Nodes helped you with this problem?
Problem 2: Average Cost
Your company is making a product item. The fixed costs for making this product are b, and the variable
costs are mx, where x is the number of items produced. The cost function is the following linear function:
( )
The average cost is the total costs divided by the number of items produced, which is a rational function,
as follows:
̅
1. Based on the first letter of your last name, choose values for m and b from the following tables
(Neither m nor b has to be a whole number):
First letter of your last name Possible values for m
A–F $10–$19
G–L $20–$29
M–R $30–$39
S–Z $40–$49
First letter of .
(7) Lesson 5.5 - Simplify Algebraic Expressions
To simplify the expression 5n + n:
1. Identify the terms: 5n and n.
2. Note that 5n and n are like terms since they have the same variable, n.
3. Use the distributive property to combine the like terms:
5n + n = (5 + 1)n
4. Simplify:
(5 + 1)n = 6n
So, the simplified expression is 6n.
DLL week 1 G9.docx
The document provides a daily lesson log for a Grade 9 mathematics class covering quadratic equations. It includes the objectives, content standards, and performance standards for the lesson. The log details the activities and examples covered each day, which focus on illustrating quadratic equations, solving them by extracting square roots, factoring, and using the quadratic formula. Examples of solving quadratic equations in simplest form and by factoring are provided. Students practice identifying quadratic equations and solving them using different methods.
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Math 107 College AlgebraName Olufemi Akinyemi Final Examination F.docx
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Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
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Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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2.3 applications of equations (oct 24 pre lesson)
- 1. Warm-up 1 Write the function which takes a room of 50 m2 and decreases each dimension by the same value.
- 2. Warm-up 2: translate the following into a mathematical relation • A presidential candidate in Indonesia must be at least 30 years old, while a presidential candidate in the United States of America must be at least 35 years old.
- 3. Applications of equations Wordy word problems which are wrought with words
- 4. Quiz on Wednesday over the following standard CCSS: Mathematics, CCSS: HS: Functions, Interpreting Functions HSF-IF.A. Understand the concept of a function and use function notation. HSF-IF.A.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
- 5. Quiz on Wednesday over the following exercise type • Identify whether each of the relations are functions or not. 1. 2y + 3x = 6 2. y2 + 3x = 6 3. y = x−3 x+2 4. xy = y − x 5. 푥 = 푦−3 2푥2
- 6. FYI: Aligned Common Core State Standards CCSS: Mathematics, CCSS: HS: Algebra, Creating Equations HSA-CED.A. Create equations that describe numbers or relationships. HSA-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
- 7. Steps to interpreting word problems 1. Read the problem closely 2. Label unknown quantities 3. Draw a picture 4. Translate into mathematical language 5. Consolidate information into an equation 6. Solve for at least one variable 7. Find all unknown quantities 8. Check and interpret your answer
- 8. In/Out of class practice Complete the problems from the textbook Write the problem, each step and the solution in your notebook p.105 #1-8
- 9. Number 1