Prepare for the BC Math 10 Provincial Exam by working through this Graphs practice test. This course is also known as BC Math 10 Foundations and Pre-Calculus 10.
Prepare for the BC Math 10 Provincial Exam by working through this Exponents practice test. This course is also known as BC Math 10 Foundations and Pre-Calculus 10.
IIT Jam math 2016 solutions BY TrajectoryeducationDev Singh
The document contains a mathematics exam question paper with 10 single mark questions (Q1-Q10) and 20 two mark questions (Q11-Q30). The questions cover topics like sequences, linear transformations, integrals, permutations, differential equations etc. Some key questions asked about the nature of a sequence involving sines, order of a permutation, evaluating a limit, checking if a differential equation is exact etc. and provided solutions to them.
The document discusses three methods for multiplying polynomials: the distributive property, FOIL (First, Outer, Inner, Last), and the box method. It provides examples of multiplying polynomials using each method. The key steps of FOIL are to multiply the first, outer, inner, and last terms of each binomial being multiplied. The box method involves drawing a box and writing one polynomial above and beside the box before multiplying the terms. The document emphasizes that all three methods will provide the same answer when multiplying polynomials.
Module 10 Topic 4 solving quadratic equations part 1Lori Rapp
This document provides instruction on solving quadratic equations. It begins with an introduction explaining why quadratic equations are useful and includes a video example. It then defines quadratic equations and provides examples of solving quadratic equations by factoring and using the quadratic formula. The document uses examples and "Try It" problems for students to practice each step in solving quadratic equations.
El documento trata sobre el máximo común divisor (MCD) y el mínimo común múltiplo (MCM) de expresiones algebraicas. Explica que el MCD es la expresión formada por los factores comunes elevados a los menores exponentes, mientras que el MCM es la expresión formada por todos los factores primos y los comunes elevados a los mayores exponentes. Incluye ejemplos y problemas propuestos sobre calcular el MCD y MCM de diferentes expresiones algebraicas.
The document summarizes several key properties of exponents:
1) The Product Property states that when multiplying like bases, you add the exponents.
2) The Quotient of Powers Property allows you to divide one power by another by subtracting the exponents.
3) The Power of a Power Property allows you to raise a power to another exponent by multiplying the exponents.
This document provides instruction on solving algebraic equations that have variables on both sides. It begins with a review of solving equations with a variable on one side, such as 6x+4=28. It then demonstrates how to solve equations with variables on both sides through a step-by-step process of combining like terms, moving terms to one side of the equation, and then dividing both sides by the coefficient of the variable. Several examples are worked through and solutions are checked by substituting the solutions back into the original equations. The document concludes by providing additional practice problems for the student to solve.
Addition and subtraction of polynomial functionsMartinGeraldine
To add or subtract polynomial functions:
1. Align like terms of the polynomials being added or subtracted.
2. Combine like terms by adding or subtracting the coefficients.
3. The sum or difference of the polynomials is a new polynomial with terms consisting of the combined like terms.
Prepare for the BC Math 10 Provincial Exam by working through this Exponents practice test. This course is also known as BC Math 10 Foundations and Pre-Calculus 10.
IIT Jam math 2016 solutions BY TrajectoryeducationDev Singh
The document contains a mathematics exam question paper with 10 single mark questions (Q1-Q10) and 20 two mark questions (Q11-Q30). The questions cover topics like sequences, linear transformations, integrals, permutations, differential equations etc. Some key questions asked about the nature of a sequence involving sines, order of a permutation, evaluating a limit, checking if a differential equation is exact etc. and provided solutions to them.
The document discusses three methods for multiplying polynomials: the distributive property, FOIL (First, Outer, Inner, Last), and the box method. It provides examples of multiplying polynomials using each method. The key steps of FOIL are to multiply the first, outer, inner, and last terms of each binomial being multiplied. The box method involves drawing a box and writing one polynomial above and beside the box before multiplying the terms. The document emphasizes that all three methods will provide the same answer when multiplying polynomials.
Module 10 Topic 4 solving quadratic equations part 1Lori Rapp
This document provides instruction on solving quadratic equations. It begins with an introduction explaining why quadratic equations are useful and includes a video example. It then defines quadratic equations and provides examples of solving quadratic equations by factoring and using the quadratic formula. The document uses examples and "Try It" problems for students to practice each step in solving quadratic equations.
El documento trata sobre el máximo común divisor (MCD) y el mínimo común múltiplo (MCM) de expresiones algebraicas. Explica que el MCD es la expresión formada por los factores comunes elevados a los menores exponentes, mientras que el MCM es la expresión formada por todos los factores primos y los comunes elevados a los mayores exponentes. Incluye ejemplos y problemas propuestos sobre calcular el MCD y MCM de diferentes expresiones algebraicas.
The document summarizes several key properties of exponents:
1) The Product Property states that when multiplying like bases, you add the exponents.
2) The Quotient of Powers Property allows you to divide one power by another by subtracting the exponents.
3) The Power of a Power Property allows you to raise a power to another exponent by multiplying the exponents.
This document provides instruction on solving algebraic equations that have variables on both sides. It begins with a review of solving equations with a variable on one side, such as 6x+4=28. It then demonstrates how to solve equations with variables on both sides through a step-by-step process of combining like terms, moving terms to one side of the equation, and then dividing both sides by the coefficient of the variable. Several examples are worked through and solutions are checked by substituting the solutions back into the original equations. The document concludes by providing additional practice problems for the student to solve.
Addition and subtraction of polynomial functionsMartinGeraldine
To add or subtract polynomial functions:
1. Align like terms of the polynomials being added or subtracted.
2. Combine like terms by adding or subtracting the coefficients.
3. The sum or difference of the polynomials is a new polynomial with terms consisting of the combined like terms.
The document provides lessons on complex numbers. It defines a complex number as being of the form z = x + iy, where x and y are real numbers. It discusses operations like addition, subtraction, multiplication and division of complex numbers. It also defines the complex conjugate and gives some examples of performing operations on complex numbers.
The document discusses the factor theorem and how to determine if a polynomial is a factor of another polynomial. It provides examples of using the factor theorem to show that (x + 1) is a factor of 2x^3 + 5x^2 - 3 and that (x - 2) is a factor of x^4 + x^3 - x^2 - x - 18. It also gives an example of finding a polynomial function given its zeros as -2, 1, -1. The document provides exercises for using the factor theorem to determine unknown values in polynomials.
This document discusses using the point-slope form to find the equation of a line given a slope and point. It provides the point-slope form equation, and examples of finding the line equation for different slopes and points. Exercises are provided for the reader to practice finding additional line equations using given slopes and points.
Finding Slope Given A Graph And Two PointsGillian Guiang
The student will learn to find the slope of a line given two points on a graph or explicitly given the points. Slope is defined as the steepness or rise over run of a line between two points. You can find the slope by taking the difference in the y-values and dividing by the difference in the x-values of the two points. Slope can be positive, negative, zero if horizontal, or undefined if vertical. Examples are worked through of finding the slope given two points on a graph or the points explicitly.
This document contains mark schemes for physics examinations from the University of Cambridge International Examinations. It provides the answer keys for multiple choice questions on papers 9702/11, 9702/12, and 9702/13. It also contains mark schemes and guidance for teachers to mark structured questions on papers 9702/21 and 9702/22. The mark schemes are published to aid teachers in understanding how to properly score student responses.
4.2 exponential functions and periodic compound interests pina tmath260
This document discusses compound interest concepts and formulas. It contains:
1) Examples of calculating compound interest with different periodic rates and time periods.
2) Formulas for calculating principal (P), accumulation (A), periodic interest rate (i), and the relationship between annual (r) and periodic rates.
3) Exercises involving using the compound interest formulas to calculate principal, accumulation, and converting between annual and periodic rates for different time periods and rates.
- If a line is perpendicular to the radius of a circle at its outer end, then the line is tangent to the circle.
- If a line is tangent to a circle, then it is perpendicular to the radius at the point of tangency.
- If two segments from the same exterior point are tangent to a circle, then they are congruent.
This document provides an overview of polynomials including classifying polynomials by number of terms, adding and subtracting polynomials, multiplying polynomials, and ordering polynomial terms in ascending and descending order. It discusses key polynomial concepts such as monomials, degrees of polynomials, and factoring polynomials. Examples are provided for adding, subtracting, and multiplying polynomials.
This document provides an overview of integration and how it relates to calculating areas under curves and between functions. Some key points covered include:
- Integration uses the concept of reverse differentiation to calculate the area under a function.
- The area under a function between two x-values a and b is calculated as the definite integral from a to b.
- Integrals may be used to find the area between two curves by subtracting their integrals between the intersection points.
- Integrals can represent either positive or negative areas depending on whether the area is above or below the x-axis.
This document discusses special products and factorization in algebra. It begins by introducing special products like (a ± b)2, (a + b)(a - b), and (x + a)(x + b) that occur frequently in algebra. These special products allow calculations like multiplication to be performed more easily. The document then discusses factorizing polynomials, including expressions of the form a2 - b2 and a3 ± b3. It provides examples of finding special products and using them to more conveniently calculate numerical multiplications. The objectives are to learn formulas for various special products and how to factorize and work with polynomials.
In multiplying rational expressions, we multiply the numerators and denominators, then express the product in its lowest term. This involves:
- Multiplying the numerators and denominators of each rational expression
- Using cross-cancellation to express the product in lowest terms
- Examples are provided to demonstrate multiplying rational expressions and expressing the product in lowest terms through cross-cancellation.
1. The document discusses factoring general trinomials of the form ax^2 + bx + c where a = 1. It provides examples of factoring various trinomial expressions.
2. Students are asked to factor trinomials and check their understanding of the factoring process. Several exercises and activities are provided to help students practice factoring trinomials.
3. The objective is for students to learn how to factor general trinomials of the form ax^2 + bx + c where a = 1.
1) Graphing quadratic equations in vertex form involves identifying the vertex (a, h) and the axis of symmetry (x = h) from the equation.
2) The document provides examples of quadratic equations in vertex form and describes the transformations between the graphs and the standard form equations.
3) Key aspects like the vertex, axis of symmetry, direction of opening, and roots are identified and the transformations including stretches, shifts, reflections and compressions are described.
Class 9 Cbse Maths Sample Paper Model 2Sunaina Rawat
The document is a sample test paper for Class 9 mathematics. It provides general instructions for a 3 hour exam with 37 questions divided into 4 sections. Section A contains 10 one-mark questions, Section B contains 9 two-mark questions, Section C contains 10 three-mark questions, and Section D contains 8 four-mark questions. The questions cover a range of mathematics topics including decimals, polynomials, geometry, trigonometry, and probability.
This document provides an overview of solving linear inequalities. It introduces inequality notation and properties, discusses multiplying and dividing by negative numbers, and provides examples of solving different types of linear inequalities. It also covers interval notation, graphing solutions to inequalities on number lines, and using interactive tools like Gizmos for additional practice with inequalities.
Here are some things you did well and could improve on:
WWW:
- You explained the key concepts around writing the equation of a circle clearly and concisely. Breaking it down step-by-step makes it easy to understand.
- Providing examples with worked solutions is very helpful for reinforcement. The visual diagrams additionally aid comprehension.
- Giving practice problems for students to try on their own, along with answers, allows for application of the material.
EBI:
- Some of the text could be formatted for easier reading (e.g. consistent formatting of equations).
- Adding brief summaries or recaps after sections of explanation may aid retention.
- Providing guidance on common errors
The document discusses radical equations, which contain radical expressions. It explains that a radical equation can be solved by squaring both sides of the equation to remove the radical terms, then solving the resulting equation. Two examples of solving radical equations are shown step-by-step: solving 5x - 1 = 8 by squaring both sides and then solving the equation, and solving 9x + 1 = 4x - 26 using the same method.
This document provides 17 practice problems for the BC Math 10 Provincial Exam. The problems cover topics like solving systems of linear equations, finding points of intersection of lines, setting up equations to solve word problems, and determining rates and percentages from financial information.
Bc Math 10 Functions and Slope Practice TestHun Kim
Prepare for the BC Math 10 Provincial Exam by working through this Functions and Slope practice test. This course is also known as Foundations and Pre-Calculus 10 Math 10.
The document provides lessons on complex numbers. It defines a complex number as being of the form z = x + iy, where x and y are real numbers. It discusses operations like addition, subtraction, multiplication and division of complex numbers. It also defines the complex conjugate and gives some examples of performing operations on complex numbers.
The document discusses the factor theorem and how to determine if a polynomial is a factor of another polynomial. It provides examples of using the factor theorem to show that (x + 1) is a factor of 2x^3 + 5x^2 - 3 and that (x - 2) is a factor of x^4 + x^3 - x^2 - x - 18. It also gives an example of finding a polynomial function given its zeros as -2, 1, -1. The document provides exercises for using the factor theorem to determine unknown values in polynomials.
This document discusses using the point-slope form to find the equation of a line given a slope and point. It provides the point-slope form equation, and examples of finding the line equation for different slopes and points. Exercises are provided for the reader to practice finding additional line equations using given slopes and points.
Finding Slope Given A Graph And Two PointsGillian Guiang
The student will learn to find the slope of a line given two points on a graph or explicitly given the points. Slope is defined as the steepness or rise over run of a line between two points. You can find the slope by taking the difference in the y-values and dividing by the difference in the x-values of the two points. Slope can be positive, negative, zero if horizontal, or undefined if vertical. Examples are worked through of finding the slope given two points on a graph or the points explicitly.
This document contains mark schemes for physics examinations from the University of Cambridge International Examinations. It provides the answer keys for multiple choice questions on papers 9702/11, 9702/12, and 9702/13. It also contains mark schemes and guidance for teachers to mark structured questions on papers 9702/21 and 9702/22. The mark schemes are published to aid teachers in understanding how to properly score student responses.
4.2 exponential functions and periodic compound interests pina tmath260
This document discusses compound interest concepts and formulas. It contains:
1) Examples of calculating compound interest with different periodic rates and time periods.
2) Formulas for calculating principal (P), accumulation (A), periodic interest rate (i), and the relationship between annual (r) and periodic rates.
3) Exercises involving using the compound interest formulas to calculate principal, accumulation, and converting between annual and periodic rates for different time periods and rates.
- If a line is perpendicular to the radius of a circle at its outer end, then the line is tangent to the circle.
- If a line is tangent to a circle, then it is perpendicular to the radius at the point of tangency.
- If two segments from the same exterior point are tangent to a circle, then they are congruent.
This document provides an overview of polynomials including classifying polynomials by number of terms, adding and subtracting polynomials, multiplying polynomials, and ordering polynomial terms in ascending and descending order. It discusses key polynomial concepts such as monomials, degrees of polynomials, and factoring polynomials. Examples are provided for adding, subtracting, and multiplying polynomials.
This document provides an overview of integration and how it relates to calculating areas under curves and between functions. Some key points covered include:
- Integration uses the concept of reverse differentiation to calculate the area under a function.
- The area under a function between two x-values a and b is calculated as the definite integral from a to b.
- Integrals may be used to find the area between two curves by subtracting their integrals between the intersection points.
- Integrals can represent either positive or negative areas depending on whether the area is above or below the x-axis.
This document discusses special products and factorization in algebra. It begins by introducing special products like (a ± b)2, (a + b)(a - b), and (x + a)(x + b) that occur frequently in algebra. These special products allow calculations like multiplication to be performed more easily. The document then discusses factorizing polynomials, including expressions of the form a2 - b2 and a3 ± b3. It provides examples of finding special products and using them to more conveniently calculate numerical multiplications. The objectives are to learn formulas for various special products and how to factorize and work with polynomials.
In multiplying rational expressions, we multiply the numerators and denominators, then express the product in its lowest term. This involves:
- Multiplying the numerators and denominators of each rational expression
- Using cross-cancellation to express the product in lowest terms
- Examples are provided to demonstrate multiplying rational expressions and expressing the product in lowest terms through cross-cancellation.
1. The document discusses factoring general trinomials of the form ax^2 + bx + c where a = 1. It provides examples of factoring various trinomial expressions.
2. Students are asked to factor trinomials and check their understanding of the factoring process. Several exercises and activities are provided to help students practice factoring trinomials.
3. The objective is for students to learn how to factor general trinomials of the form ax^2 + bx + c where a = 1.
1) Graphing quadratic equations in vertex form involves identifying the vertex (a, h) and the axis of symmetry (x = h) from the equation.
2) The document provides examples of quadratic equations in vertex form and describes the transformations between the graphs and the standard form equations.
3) Key aspects like the vertex, axis of symmetry, direction of opening, and roots are identified and the transformations including stretches, shifts, reflections and compressions are described.
Class 9 Cbse Maths Sample Paper Model 2Sunaina Rawat
The document is a sample test paper for Class 9 mathematics. It provides general instructions for a 3 hour exam with 37 questions divided into 4 sections. Section A contains 10 one-mark questions, Section B contains 9 two-mark questions, Section C contains 10 three-mark questions, and Section D contains 8 four-mark questions. The questions cover a range of mathematics topics including decimals, polynomials, geometry, trigonometry, and probability.
This document provides an overview of solving linear inequalities. It introduces inequality notation and properties, discusses multiplying and dividing by negative numbers, and provides examples of solving different types of linear inequalities. It also covers interval notation, graphing solutions to inequalities on number lines, and using interactive tools like Gizmos for additional practice with inequalities.
Here are some things you did well and could improve on:
WWW:
- You explained the key concepts around writing the equation of a circle clearly and concisely. Breaking it down step-by-step makes it easy to understand.
- Providing examples with worked solutions is very helpful for reinforcement. The visual diagrams additionally aid comprehension.
- Giving practice problems for students to try on their own, along with answers, allows for application of the material.
EBI:
- Some of the text could be formatted for easier reading (e.g. consistent formatting of equations).
- Adding brief summaries or recaps after sections of explanation may aid retention.
- Providing guidance on common errors
The document discusses radical equations, which contain radical expressions. It explains that a radical equation can be solved by squaring both sides of the equation to remove the radical terms, then solving the resulting equation. Two examples of solving radical equations are shown step-by-step: solving 5x - 1 = 8 by squaring both sides and then solving the equation, and solving 9x + 1 = 4x - 26 using the same method.
This document provides 17 practice problems for the BC Math 10 Provincial Exam. The problems cover topics like solving systems of linear equations, finding points of intersection of lines, setting up equations to solve word problems, and determining rates and percentages from financial information.
Bc Math 10 Functions and Slope Practice TestHun Kim
Prepare for the BC Math 10 Provincial Exam by working through this Functions and Slope practice test. This course is also known as Foundations and Pre-Calculus 10 Math 10.
Prepare for the BC Math 10 Provincial Exam by working through this Systems practice test. This course is also known as BC Math 10 Foundations and Pre-Calculus 10.
Prepare for the BC Math 10 Provincial Exam by working through this Measurement practice test. This course is also known as BC Math Foundations & Pre-Calculus 10.
Prepare for the BC Math 10 Provincial Exam by working through this Trigonometry practice test. This course is also known as Math 10 Foundations and Pre-Calculus 10.
1. The first piece is 22 feet long, the second is 33 feet long, and the third is 66 feet long.
2. The solutions to the inequality -5<x-4<2 are the values of x between -1 and 6.
3. The document provides examples and explanations of linear equations including standard form, graphing lines, finding intercepts, and determining if an equation represents a linear function based on its form.
The document provides an assessment review with multiple choice questions about math concepts like algebra, geometry, and coordinate planes. It includes 15 questions testing skills like simplifying expressions, solving equations, factoring polynomials, and graphing lines. The questions are formatted with explanations of steps required to arrive at the answers.
1. The document appears to be notes from a math class covering linear equations and graphs. It includes examples of writing equations in standard form, graphing linear equations, finding x- and y-intercepts, and using linear equations to determine if an ordered pair is a solution.
2. The notes define key concepts like what makes an equation linear, how to graph linear equations of the form y=mx, y=mx+c, and horizontal and vertical lines. Examples are provided of finding intercepts and using linear equations to check solutions.
3. Practice problems are included for students to complete involving graphing, finding intercepts, determining if ordered pairs are solutions, and matching linear equations to their graphs.
This document contains a multi-part math exam review with multiple choice and short answer questions. It provides practice problems covering topics like geometry, ratios, equations, expressions, and word problems. The review is designed to help students prepare for their math final exam.
College Algebra MATH 107 Spring, 2015, V4.8 Page 1 of .docxmonicafrancis71118
This document provides instructions and requirements for a PowerPoint presentation project on a student's chosen career. The presentation must include 10-12 slides covering: an introduction of the student and research topic, an outline, background on the career path and reasons for choice, educational requirements, pay ranges in three regions, and a summary and conclusion slide. References must be in MLA format. The presentation will be graded based on inclusion of required elements, design features like themes and visual elements, transitions and animations, and correct spelling and grammar.
Raj and Ajay traveled by car to Ranikhet. Raj's car traveled at speed x km/hr while Ajay's was 5 km/hr faster. Raj took 4 hours more than Ajay to complete the 400 km journey.
A motor boat traveled upstream at a speed of 20 km/hr. To cover 15 km it took 1 hour more than traveling downstream.
A seminar had participants in Hindi (60), English (84) and Math (108). The maximum in each room was 12. The minimum rooms needed was 21.
Real numbers, polynomials, linear equations and quadratic equations word problems were presented as case studies with multiple choice questions to test understanding of concepts. Concise
College Algebra MATH 107 Spring, 2016, V4.7 Page 1 of .docxclarebernice
College Algebra MATH 107 Spring, 2016, V4.7
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 [–1, 3]; Range [–3, 1]
B. Domain [–1, 1]; Range [–1, 3]
C. Domain [–1/2, 0]; Range [–1, 0]
D. Domain [–3, 1]; Range [–1, 3]
2. Solve: 17 3x x+ = − 2. ______
A. No solution
B. −1
C. −7
D. −1, 8
2 4 -4
-2
-4
2
4
-2
College Algebra MATH 107 Spring, 2016, V4.7
Page 2 of 11
3. Determine the interval(s) on which the function is increasing. 3. ______
A. (–2, 4)
B. (–∞, –2) and (4, ∞)
C. (–3.6, 0) and (6.7, ∞)
D. (–3, 1)
4. Determine whether the graph of 7y x −= 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] ∪ [4, ∞)
C. (–∞, –8/5]
D. [4, ∞)
College Algebra MATH 107 Spring, 2016, V4.7
Page 3 of 11
6. Which of the following represents the graph of 8x + 3y = 24 ? 6. ______
A. B.
C. D.
College Algebra MATH 107 Spring, 2016, V4.7
Page 4 of 11
7. Write a slope-intercept equation for a line parallel to the line x – 7y = 2 which passes through
the point (14, –9). 7. ______
A.
1
7
7
y x= − −
B. 7 89y x= − +
C.
1
9
7
y x= −
D.
1
11
7
y x= −
8. Which of the following best describes the graph? 8. ______
A. It is the graph of a function and it is one-to-one.
B. It is the graph of a function and it is not one-to-one.
C. It is not the graph of a function and it is one-to-one.
D. It is not the graph of a function and it is not one-to-one.
College Algebra MATH 107 Spring, 2016, V4.7
Page 5 of 11
9. Express as a single logarithm: 5 log y – log (x + 1) + log 1 9. ______
A.
log(5 )
log( 1)
y
x +
B. ( )log 5 y x−
C.
5
log
1
y
x
+
D.
5 ...
3D Representation
Read chapter 10 in Computer Science: note especially section 10.2. Create a 2-page document which will summarize the three steps involved in producing an image using 3D graphics. After you describe each step, give a good example of each. The examples should be different from the one given in the text.
Find a recent news article (not a tutorial or description) that relates to 3D graphics. Explain how any aspect of the news article relates to one of the steps you summarized above.
The document should be clear and concise, free from syntax and semantic errors.
Please submit the document on time please.
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= − −
...
Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docxSHIVA101531
Lesson 3-7 Equations of Lines in the Coordinate Plane 189
3-7
Objective To graph and write linear equations
Ski resorts often use steepness to rate the difficulty
of their hills. The steeper the hill, the higher the
difficulty rating. Below are sketches of three new hills
at a particular resort. Use each rating level only once.
Which hill gets which rating? Explain.
Difficulty Ratings
Easiest
Intermediate
Difficult
3300 ft 3000 ft 3500 ft
1190 ft 1180 ft 1150 ft
A B C
Th e Solve It involves using vertical and horizontal distances to determine steepness.
Th e steepest hill has the greatest slope. In this lesson you will explore the concept of
slope and how it relates to both the graph and the equation of a line.
Essential Understanding You can graph a line and write its equation when you
know certain facts about the line, such as its slope and a point on the line.
Equations of Lines in the
Coordinate Plane
Think back!
What did you
learn in algebra
that relates to
steepness?
Key Concept Slope
Defi nition
Th e slope m of a line is the
ratio of the vertical change
(rise) to the horizontal change
(run) between any two points.
Symbols
A line contains the
points (x1, y1) and
(x2, y2) .
m 5
rise
run 5
y2 2 y1
x2 2 x1
Diagram
(x2, y2)
(x1, y1)
O
x
y run
rise
Lesson
Vocabulary
• slope
• slope-intercept
form
• point-slope form
L
V
L
V
• s
LL
VVV
• s
hsm11gmse_NA_0307.indd 189 2/24/09 6:49:09 AM
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Problem 1
Got It?
190 Chapter 3 Parallel and Perpendicular Lines
Finding Slopes of Lines
A What is the slope of line b?
m 5
2 2 (22)
21 2 4
5 4
25
5 245
B What is the slope of line d?
m 5
0 2 (22)
4 2 4
5 20 Undefi ned
1. Use the graph in Problem 1.
a. What is the slope of line a?
b. What is the slope of line c?
As you saw in Problem 1 and Got It 1 the slope of a line can be positive, negative,
zero, or undefi ned. Th e sign of the slope tells you whether the line rises or falls
to the right. A slope of zero tells you that the line is horizontal. An undefi ned slope
tells you that the line is vertical.
You can graph a line when you know its equation. Th e equation of a line has diff erent
forms. Two forms are shown below. Recall that the y-intercept of a line is the
y-coordinate of the point where the line crosses the y-axis.
O
y
c
b
d a
x
2
2 86
4
6
( 1, 2)
(4, 2)
(4, 0)
(5, 7)(1, 7)
(2, 3)
Positive slope
O
x
y
Negative slope
O
x
y
Zero slope
O
x
y
Undefined slope
O
x
y
Key Concept Forms of Linear Equations
Defi nition
Th e slope-intercept form of an equation of
a nonvertical line is y 5 mx 1 b, where m
is the slope and b is the y-intercept.
Symbols
Th e point-slope form of an equation of a
nonvertical line is y 2 y1 5 m(x 2 x1),
where m is the slope and (x1, y1) is a point
on the line.
y mx b
slope y-intercept
y y1 m(x x1)
slope x-coordinatey-coordinate
A
...
This document contains a practice exam for Math 220 with 16 multi-part questions covering topics such as functions, inequalities, trigonometry, logarithms, and graphing. The exam instructs students to show their work to receive partial credit and enough work to receive full credit. It tests skills like finding domains of functions, solving inequalities, determining equations of lines and circles, properties of functions, evaluating trigonometric and logarithmic expressions, solving equations, and graphing functions.
1. The document provides worked solutions to mathematical problems involving differentiation, graph sketching, solving quadratic equations, and probability.
2. A key is provided with common statistical formulas and tables for critical values of t and z distributions.
3. The problems cover a range of mathematical topics at an intermediate level, with multiple parts requiring setting up and solving equations as well as interpreting results.
This document provides a review for algebra sections on various topics including:
1) Solving word problems involving equations with one unknown variable.
2) Finding sums, differences, and ratios of numbers.
3) Representing word problems using tables and equations.
4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described.
5) Graphing linear equations and finding slopes of lines from equations or two points.
6) Writing equations of lines in different forms given information like slopes, intercepts, or two points.
This document provides a review for algebra sections on various topics including:
1) Solving word problems involving equations with one unknown variable.
2) Finding sums, differences, and ratios of numbers.
3) Representing word problems using tables and equations.
4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described.
5) Graphing linear equations and finding slopes of lines from equations or two points.
6) Writing equations of lines in different forms given information like slopes, intercepts, or two points.
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
1 Week 2 Homework for MTH 125 Name_______________AbbyWhyte974
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
The document provides examples of calculating angles between lines and planes in 3 dimensions. It includes calculating angles between a line and plane using tangent, and between two planes. It also provides practice questions involving finding angles between lines and planes given dimensional information about the lines and planes.
7.curves Further Mathematics Zimbabwe Zimsec Cambridgealproelearning
The document discusses properties of curves defined by functions. It begins by listing objectives for understanding important points on graphs like maxima, minima, and inflection points. It emphasizes using graphing technology to experiment but not substitute for analytical work. Examples are provided to demonstrate finding maximums, minimums, intersections, and asymptotes of various functions. The key points are determining features of a curve from its defining function.
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
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His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
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This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
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How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
BC Math 10 Graphs Practice Test
1. www.provincialexam.ca | BC Math 10 Provincial Exam Practice Questions
Graph Chapter Practice Test Name: ______________________ Period: _____
1) Sketch 2 1y x
Answer:
2) Write in general form:
2
2 1
3
y x
Answer: 2 3 9 0x y
3) Sketch the line 1y .
Answer:
4) What is the x -intercept of the line: 2 3 1 0x y ?
Answer: 1/ 2
2. 5) The slope of AB is 2 / 3 . The slope of CD is 2 / x .
Given AB is to CD, find x .
Answer: 4 / 3
6) Determine the slope-intercept equation of the line that goes through
( 3,2) and has a y -intercept of 5.
Answer: 5y x
7) You work in sales. You are guaranteed to make $10 a day. However,
for every sale that you make, you make an additional $50. Sketch and
label the units of your graph.
Answer:
8) Sketch a distance-time graph. The y -axis is the distance away from home.
You WALK halfway to work but you RUN back home because you forgot
your lunch. It takes you A WHILE for you to find your lunch at home. You
then JOG all the way to work. Your graph must show the difference between
walking vs. jogging vs. running.
Answer:
3. 9) What is the point of intersection for 2 3y x and 3 1y x ?
Answer:
5 8
,
7 7
10) Test if 1 0x y produces the point (5,4).
Answer: no
11) You want to shoot a laser at a target at ( 5,4) . If your horizontal position
is 2, and the shot needs to have a slope of 2/3, what is your position on
the screen? Provide the ( , )x y coordinate.
Answer: ( 2,6)
12) A line has a slope of 2 / 3 . The line produces the point (2,3). Another
point on this line is ( ,5)x . Solve x .
Answer: 1
13) Find the intercepts of 2 1y x .
Answer: x -int: 1/ 2 ; y -int: 1
14) Does the following line have a negative slope? 3 3(2 5)y x
Answer: yes
4. 15) What quadrant does 2 1y x and 2 5 0x y intersect in?
Answer: QI
16) Line AB contains the points (1,2) and (5, 3). Line CD is to line AB
and intersects the line through ( , 10)x . What is the slope-intercept
equation of Line CD?
Answer:
4
18.48
5
y x
17) Rewrite in general form.
2
2
3 2
y
x
Answer: 4 3 12 0x y
18) Lines 11x Py and 5x Py intersect at (3,4) . What is the value of P ?
Answer: 2