This document contains solutions to mathematics questions from the 2010 HSC exam in Australia. Question 1 involves solving equations, inequalities and finding derivatives. Question 2 involves finding derivatives of trigonometric functions. Question 3 involves vectors, gradients and parallel lines. Question 4 involves arithmetic progressions, integrals and area under curves. Question 5 involves volumes, surface areas, maxima and minima. Question 6 involves factorizing polynomials, discriminants and finding angles and areas of figures.
Presentatie behorende bij de lessen Analytische chemie voor Laboratoriumtechnologen gedoceerd aan de opleiding Biomedische Laboratoriumtechnologie van de UC Leuven-Limburg.
This document provides examples of calculating the pH of various strong acid solutions, including nitric acid, perchloric acid, hydrochloric acid, a mixture of hydrochloric acid and hydroiodic acid, and a solution of bromoacetic acid that is partially ionized. It also asks questions about weak acids, Lewis acids, and which compounds form more acidic solutions based on cation properties.
Presentatie behorende bij de lessen Analytische chemie voor Laboratoriumtechnologen gedoceerd aan de opleiding Biomedische Laboratoriumtechnologie van de UC Leuven-Limburg.
This document provides the solutions to questions from the 2010 General Mathematics Higher School Certificate (HSC) exam in New South Wales, Australia. It includes answers to multiple choice questions, open response questions involving word problems on topics like profit/loss, financial planning, and statistics. Diagrams are provided for some geometry questions. The solutions show step-by-step working and explanations for full and partial marks on the exam.
This document appears to be an exam paper for mathematics from the Caribbean Examinations Council. It consists of two sections, with Section I containing 8 questions and Section II containing 3 questions. Students are instructed to answer all questions in Section I and any two questions from Section II. The paper provides a list of formulas, instructions for required materials, and sample questions on topics including algebra, geometry, trigonometry, and data analysis.
The document contains 50 multiple choice questions testing mathematical concepts such as algebra, geometry, statistics, and trigonometry. The questions cover a wide range of topics including: simplifying expressions, solving equations, finding values based on graphs/tables, properties of shapes, percentages, and probability.
BBMP1103 - Sept 2011 exam workshop - Part 2Richard Ng
This document is a summary of key points from a mathematics exam preparation workshop on differentiation:
1) It provides the solutions to sample differentiation problems, finding the first and second derivatives of functions like f(x)=5x^3 and p(x)=5x^3-3x^2+7/x^2.
2) It also gives the solutions to differentiation questions that were part of past mathematics exams, finding derivatives like dy/dx of functions such as y=(x^3)(4x^2-2x).
3) The document aims to help students preparing for exams by providing worked examples of common differentiation questions and techniques for finding derivatives.
1. The document provides solutions to trigonometric and algebraic equations. It solves equations involving sin, cos, tan functions as well as polynomials with variables x, y, z.
2. The algebraic equations section involves solving polynomials for single variables x or y, as well as systems of equations with variables x and y.
3. The trigonometric equations section expresses the general solutions to equations involving sin, cos, and tan functions in terms of radian angles n*pi/b, where b is the denominator and n is any integer.
Presentatie behorende bij de lessen Analytische chemie voor Laboratoriumtechnologen gedoceerd aan de opleiding Biomedische Laboratoriumtechnologie van de UC Leuven-Limburg.
This document provides examples of calculating the pH of various strong acid solutions, including nitric acid, perchloric acid, hydrochloric acid, a mixture of hydrochloric acid and hydroiodic acid, and a solution of bromoacetic acid that is partially ionized. It also asks questions about weak acids, Lewis acids, and which compounds form more acidic solutions based on cation properties.
Presentatie behorende bij de lessen Analytische chemie voor Laboratoriumtechnologen gedoceerd aan de opleiding Biomedische Laboratoriumtechnologie van de UC Leuven-Limburg.
This document provides the solutions to questions from the 2010 General Mathematics Higher School Certificate (HSC) exam in New South Wales, Australia. It includes answers to multiple choice questions, open response questions involving word problems on topics like profit/loss, financial planning, and statistics. Diagrams are provided for some geometry questions. The solutions show step-by-step working and explanations for full and partial marks on the exam.
This document appears to be an exam paper for mathematics from the Caribbean Examinations Council. It consists of two sections, with Section I containing 8 questions and Section II containing 3 questions. Students are instructed to answer all questions in Section I and any two questions from Section II. The paper provides a list of formulas, instructions for required materials, and sample questions on topics including algebra, geometry, trigonometry, and data analysis.
The document contains 50 multiple choice questions testing mathematical concepts such as algebra, geometry, statistics, and trigonometry. The questions cover a wide range of topics including: simplifying expressions, solving equations, finding values based on graphs/tables, properties of shapes, percentages, and probability.
BBMP1103 - Sept 2011 exam workshop - Part 2Richard Ng
This document is a summary of key points from a mathematics exam preparation workshop on differentiation:
1) It provides the solutions to sample differentiation problems, finding the first and second derivatives of functions like f(x)=5x^3 and p(x)=5x^3-3x^2+7/x^2.
2) It also gives the solutions to differentiation questions that were part of past mathematics exams, finding derivatives like dy/dx of functions such as y=(x^3)(4x^2-2x).
3) The document aims to help students preparing for exams by providing worked examples of common differentiation questions and techniques for finding derivatives.
1. The document provides solutions to trigonometric and algebraic equations. It solves equations involving sin, cos, tan functions as well as polynomials with variables x, y, z.
2. The algebraic equations section involves solving polynomials for single variables x or y, as well as systems of equations with variables x and y.
3. The trigonometric equations section expresses the general solutions to equations involving sin, cos, and tan functions in terms of radian angles n*pi/b, where b is the denominator and n is any integer.
BBMP1103 - Sept 2011 exam workshop - part 4Richard Ng
This document is a summary of Part 4 of a mathematics exam preparation workshop on integration. It provides examples and step-by-step solutions for two exam questions involving integration. The first question from May 2010 involves integrating expressions including (3x3 - 3x2 + x). The second question from January 2010 involves integrating (a) 1/x3, (b) x/x3 - 2, and (c) (4x3 - 2x). The solutions show the integration steps and resulting expressions for each part.
Solving volumes using cross sectional areasgregcross22
This document provides an explanation of how to calculate the volume of a solid with a cross-sectional area that changes along one axis. It gives the example of finding the volume of a solid where the cross-section is a triangle perpendicular to the x-axis, with base that varies as a function of x from 0 to 4. The document provides the formula for the area of the triangle as a function of x, and the integral required to calculate the volume by summing the areas of each cross-sectional slice from x=0 to x=4.
The document contains a mathematics exam with three groups of questions testing different concepts:
Group A contains 10 multiple choice questions covering domains of functions, trigonometric functions, derivatives, integrals, determinants, and properties related to maxima and minima of functions.
Group B contains another 10 multiple choice questions testing concepts like distance between parallel lines, matrix operations, complex numbers, solving equations, properties of concurrent lines, integrals involving logarithms, and solving inequalities.
Group C contains 2 problems to be solved in detail, the first finding the length of a perpendicular from a point to a line, and the second evaluating a definite integral.
To solve quadratic, fractional, irrational, and absolute value inequalities, one should:
1. Make the right-hand side zero by shifting terms to the left-hand side
2. Fully factorize the left-hand side to find critical values
3. Draw a sign diagram for the left-hand side using the critical values
4. Determine the range of values for the variable based on the sign diagram.
1) The volume of the solid region bounded by z = 9 - x^2 - y in the first octant is found using iterated integration.
2) The volume of the region bounded by z = x^2 + y^2, x^2 + y^2 = 25, and the xy-plane is found using polar coordinates.
3) The double integral of sin(x^2) over the region from 0 to 9 in x and y from 0 to x is evaluated.
11 x1 t01 08 completing the square (2013)Nigel Simmons
The document discusses the process of completing the square to solve quadratic equations. It shows examples of solving equations in the form (i) x^2 + bx + c = 0, (ii) ax^2 + bx + c = 0, and (iii) x^2 - 6x + 6 = 0. The method involves grouping like terms and factorizing the equation into the form (x + p)^2 = q to extract the solutions.
The document discusses the second derivative and provides examples of taking the derivative of two functions. It shows that the second derivative of y=x^2 + 3 is 2x.
This document provides instructions for graphing linear equations. It begins with examples of solving linear equations algebraically. Students are then introduced to key properties of linear equations: they contain two variables and graph as straight lines. The document demonstrates graphing various linear equations by plotting their solution sets as points and connecting them with a straight line. It concludes by asking students to reflect on similarities and differences between the graphed linear equations.
This document contains solutions to selected miscellaneous exercises involving calculus concepts like derivatives, logarithms, and integrals. Some key points:
- Exercise 8 involves taking the derivative of an expression involving logarithms and solving for n. The answer is n = 20.
- Exercise 9 proves an identity involving natural logarithms using derivatives.
- Exercise 14 finds the derivative of an expression involving a logarithm.
This document provides a review of key algebra 1 concepts including equations of lines, solving various types of equations, factoring polynomials, expressions and equations involving perimeter, area, and geometry. Students are given examples to solve of each concept, including solving systems of equations, simplifying expressions, graphing lines, and determining equations of lines given points or other criteria. The review covers standard form, slope-intercept form, point-slope form of a line, solving linear and quadratic equations, factoring polynomials, perimeter, area, geometry relationships, graphing, and determining equations of lines from information provided.
This document provides a lesson on factoring trinomials with integer coefficients. It includes 30 problems where students must match trinomials with their factorizations, factor trinomials, solve equations by factoring, and determine if expressions can be factored. It also includes two word problems about the area of a circle that require factoring an expression for the radius and solving for a variable.
This document provides a lesson on factoring trinomials with integer coefficients. It includes 30 problems where students must match trinomials with their factorizations, factor trinomials, solve equations by factoring, and determine if expressions can be factored. It also includes two word problems about finding the radius and value of x for a circle given its area.
This document contains 26 math problems involving derivatives of logarithmic, exponential, and inverse trigonometric functions. The problems include finding derivatives of expressions, setting up and solving differential equations, and determining relationships between derivatives.
PMR Form 3 Mathematics Algebraic FractionsSook Yen Wong
The document provides instructions for expanding and factorizing algebraic expressions involving single and double brackets. It explains how to expand brackets by distributing terms inside brackets to each term outside. For factorizing, it describes finding common factors and grouping terms. It also covers techniques for factorizing quadratic expressions, difference of squares, and grouping. Further sections cover simplifying algebraic fractions through factorizing numerators and denominators and combining like terms.
11X1 T01 09 completing the square (2011)Nigel Simmons
The document discusses the process of completing the square to solve quadratic equations. It shows how to complete the square for a general quadratic equation of the form ax2 + bx + c = 0 by grouping like terms and factorizing into a perfect square form. Examples are worked through, including solving the specific equations x2 + 6x - 7 = 0, x2 - 6x + 6 = 0.
11X1 t01 08 completing the square (2012)Nigel Simmons
The document discusses the process of completing the square to solve quadratic equations. It shows how to complete the square for a general quadratic equation of the form ax2 + bx + c = 0 by grouping like terms and factorizing into a perfect square form. Examples are worked through, including solving the specific equations x2 + 6x - 7 = 0, x2 - 6x + 6 = 0.
This document provides examples of subtracting polynomials. It begins with examples of subtracting terms like x+7 and 3x+9. It then shows how to subtract polynomials by removing corresponding terms and using the opposite sign. For example, (3x^2 + x + 2) - (2x^2 - x + 3) is solved by removing the 2x^2 terms and changing the sign of the remaining terms to get x^2 + x - 1. It provides several more examples and problems for students to solve, including finding the area of a shaded region between a rectangle and square using polynomial subtraction.
The document describes how to solve simultaneous equations using three steps: 1) eliminate a variable from the equations, 2) solve for the remaining variable, and 3) substitute back to find the eliminated variable. It provides an example showing these steps to solve two simultaneous equations for x and y. It then shows another example involving eliminating variables to create two new equations that can be solved simultaneously for y and z. The key points are eliminating variables to reduce the equations, then solving the reduced equations to find the values of the variables.
The document describes how to solve simultaneous equations using three steps: 1) eliminate a variable from the equations, 2) solve for the remaining variable, and 3) substitute back to find the eliminated variable. It provides an example problem demonstrating these steps, eliminating variables through multiplication and addition of the equations until a single variable remains that can be solved for. The document notes that simultaneous equations with the same number of variables and equations can always be solved using this method.
The document describes how to solve simultaneous equations using three steps: 1) eliminate a variable from the equations, 2) solve for the remaining variable, and 3) substitute back to find the eliminated variable. It provides an example showing these steps to solve two simultaneous equations for x and y. It then shows another example involving eliminating variables to create two new equations that can be solved simultaneously for y and z. The key point is that simultaneous equations can be solved when there are as many equations as unknown variables.
Ict in maths presentation for my favourite lessonjharnwell
This document discusses various technologies that teachers can use in mathematics education. It describes tools for tracking homework assignments, communicating with students and parents, flipping the classroom, creating screencasts and applets, using blogs, bookmarking resources, and using programs like Google Sketchup and Google Earth. Examples are provided for how each tool could be implemented in a classroom.
This document contains notes from Joshua Harnwell on using technology in mathematics education. It discusses using tools like OneNote, Google Docs, screencasting, and blogging to flip the classroom and track homework. It also provides examples of using apps, Google Earth, and WolframAlpha in lessons and recommends hardware like Bluetooth mice and tablets. The document aims to communicate ways to incorporate technology to make lessons more engaging for students and help communicate with parents.
BBMP1103 - Sept 2011 exam workshop - part 4Richard Ng
This document is a summary of Part 4 of a mathematics exam preparation workshop on integration. It provides examples and step-by-step solutions for two exam questions involving integration. The first question from May 2010 involves integrating expressions including (3x3 - 3x2 + x). The second question from January 2010 involves integrating (a) 1/x3, (b) x/x3 - 2, and (c) (4x3 - 2x). The solutions show the integration steps and resulting expressions for each part.
Solving volumes using cross sectional areasgregcross22
This document provides an explanation of how to calculate the volume of a solid with a cross-sectional area that changes along one axis. It gives the example of finding the volume of a solid where the cross-section is a triangle perpendicular to the x-axis, with base that varies as a function of x from 0 to 4. The document provides the formula for the area of the triangle as a function of x, and the integral required to calculate the volume by summing the areas of each cross-sectional slice from x=0 to x=4.
The document contains a mathematics exam with three groups of questions testing different concepts:
Group A contains 10 multiple choice questions covering domains of functions, trigonometric functions, derivatives, integrals, determinants, and properties related to maxima and minima of functions.
Group B contains another 10 multiple choice questions testing concepts like distance between parallel lines, matrix operations, complex numbers, solving equations, properties of concurrent lines, integrals involving logarithms, and solving inequalities.
Group C contains 2 problems to be solved in detail, the first finding the length of a perpendicular from a point to a line, and the second evaluating a definite integral.
To solve quadratic, fractional, irrational, and absolute value inequalities, one should:
1. Make the right-hand side zero by shifting terms to the left-hand side
2. Fully factorize the left-hand side to find critical values
3. Draw a sign diagram for the left-hand side using the critical values
4. Determine the range of values for the variable based on the sign diagram.
1) The volume of the solid region bounded by z = 9 - x^2 - y in the first octant is found using iterated integration.
2) The volume of the region bounded by z = x^2 + y^2, x^2 + y^2 = 25, and the xy-plane is found using polar coordinates.
3) The double integral of sin(x^2) over the region from 0 to 9 in x and y from 0 to x is evaluated.
11 x1 t01 08 completing the square (2013)Nigel Simmons
The document discusses the process of completing the square to solve quadratic equations. It shows examples of solving equations in the form (i) x^2 + bx + c = 0, (ii) ax^2 + bx + c = 0, and (iii) x^2 - 6x + 6 = 0. The method involves grouping like terms and factorizing the equation into the form (x + p)^2 = q to extract the solutions.
The document discusses the second derivative and provides examples of taking the derivative of two functions. It shows that the second derivative of y=x^2 + 3 is 2x.
This document provides instructions for graphing linear equations. It begins with examples of solving linear equations algebraically. Students are then introduced to key properties of linear equations: they contain two variables and graph as straight lines. The document demonstrates graphing various linear equations by plotting their solution sets as points and connecting them with a straight line. It concludes by asking students to reflect on similarities and differences between the graphed linear equations.
This document contains solutions to selected miscellaneous exercises involving calculus concepts like derivatives, logarithms, and integrals. Some key points:
- Exercise 8 involves taking the derivative of an expression involving logarithms and solving for n. The answer is n = 20.
- Exercise 9 proves an identity involving natural logarithms using derivatives.
- Exercise 14 finds the derivative of an expression involving a logarithm.
This document provides a review of key algebra 1 concepts including equations of lines, solving various types of equations, factoring polynomials, expressions and equations involving perimeter, area, and geometry. Students are given examples to solve of each concept, including solving systems of equations, simplifying expressions, graphing lines, and determining equations of lines given points or other criteria. The review covers standard form, slope-intercept form, point-slope form of a line, solving linear and quadratic equations, factoring polynomials, perimeter, area, geometry relationships, graphing, and determining equations of lines from information provided.
This document provides a lesson on factoring trinomials with integer coefficients. It includes 30 problems where students must match trinomials with their factorizations, factor trinomials, solve equations by factoring, and determine if expressions can be factored. It also includes two word problems about the area of a circle that require factoring an expression for the radius and solving for a variable.
This document provides a lesson on factoring trinomials with integer coefficients. It includes 30 problems where students must match trinomials with their factorizations, factor trinomials, solve equations by factoring, and determine if expressions can be factored. It also includes two word problems about finding the radius and value of x for a circle given its area.
This document contains 26 math problems involving derivatives of logarithmic, exponential, and inverse trigonometric functions. The problems include finding derivatives of expressions, setting up and solving differential equations, and determining relationships between derivatives.
PMR Form 3 Mathematics Algebraic FractionsSook Yen Wong
The document provides instructions for expanding and factorizing algebraic expressions involving single and double brackets. It explains how to expand brackets by distributing terms inside brackets to each term outside. For factorizing, it describes finding common factors and grouping terms. It also covers techniques for factorizing quadratic expressions, difference of squares, and grouping. Further sections cover simplifying algebraic fractions through factorizing numerators and denominators and combining like terms.
11X1 T01 09 completing the square (2011)Nigel Simmons
The document discusses the process of completing the square to solve quadratic equations. It shows how to complete the square for a general quadratic equation of the form ax2 + bx + c = 0 by grouping like terms and factorizing into a perfect square form. Examples are worked through, including solving the specific equations x2 + 6x - 7 = 0, x2 - 6x + 6 = 0.
11X1 t01 08 completing the square (2012)Nigel Simmons
The document discusses the process of completing the square to solve quadratic equations. It shows how to complete the square for a general quadratic equation of the form ax2 + bx + c = 0 by grouping like terms and factorizing into a perfect square form. Examples are worked through, including solving the specific equations x2 + 6x - 7 = 0, x2 - 6x + 6 = 0.
This document provides examples of subtracting polynomials. It begins with examples of subtracting terms like x+7 and 3x+9. It then shows how to subtract polynomials by removing corresponding terms and using the opposite sign. For example, (3x^2 + x + 2) - (2x^2 - x + 3) is solved by removing the 2x^2 terms and changing the sign of the remaining terms to get x^2 + x - 1. It provides several more examples and problems for students to solve, including finding the area of a shaded region between a rectangle and square using polynomial subtraction.
The document describes how to solve simultaneous equations using three steps: 1) eliminate a variable from the equations, 2) solve for the remaining variable, and 3) substitute back to find the eliminated variable. It provides an example showing these steps to solve two simultaneous equations for x and y. It then shows another example involving eliminating variables to create two new equations that can be solved simultaneously for y and z. The key points are eliminating variables to reduce the equations, then solving the reduced equations to find the values of the variables.
The document describes how to solve simultaneous equations using three steps: 1) eliminate a variable from the equations, 2) solve for the remaining variable, and 3) substitute back to find the eliminated variable. It provides an example problem demonstrating these steps, eliminating variables through multiplication and addition of the equations until a single variable remains that can be solved for. The document notes that simultaneous equations with the same number of variables and equations can always be solved using this method.
The document describes how to solve simultaneous equations using three steps: 1) eliminate a variable from the equations, 2) solve for the remaining variable, and 3) substitute back to find the eliminated variable. It provides an example showing these steps to solve two simultaneous equations for x and y. It then shows another example involving eliminating variables to create two new equations that can be solved simultaneously for y and z. The key point is that simultaneous equations can be solved when there are as many equations as unknown variables.
Ict in maths presentation for my favourite lessonjharnwell
This document discusses various technologies that teachers can use in mathematics education. It describes tools for tracking homework assignments, communicating with students and parents, flipping the classroom, creating screencasts and applets, using blogs, bookmarking resources, and using programs like Google Sketchup and Google Earth. Examples are provided for how each tool could be implemented in a classroom.
This document contains notes from Joshua Harnwell on using technology in mathematics education. It discusses using tools like OneNote, Google Docs, screencasting, and blogging to flip the classroom and track homework. It also provides examples of using apps, Google Earth, and WolframAlpha in lessons and recommends hardware like Bluetooth mice and tablets. The document aims to communicate ways to incorporate technology to make lessons more engaging for students and help communicate with parents.
This document provides a summary of a professional development presentation on various technology tools for teachers. It includes 52 entries with short descriptions and links for tools like screencasting, social bookmarking, URL shorteners, Creative Commons, and more. The tools covered include ways to flip the classroom, backup and share files, create online polls and games, and access educational resources.
1) The document describes a conceptual journey through scales of size from 1 meter to billions of light years and back down to fractions of a nanometer.
2) It explores scales from the size of leaves to the size of galaxies and discusses what can be observed at each scale of magnitude from 10^0 to 10^23 and 10^-16.
3) The journey is meant to illustrate the constancy of natural laws across vast scales and make the reader consider humanity's place in the universe.
The document summarizes the key features of the new draft NSW Mathematics Syllabus which is aligned with the Australian Curriculum. It outlines that the content descriptors from the Australian Curriculum are implemented without change in the NSW syllabus. Teachers only need to refer to the NSW syllabus as implementing it also implements the Australian Curriculum. The syllabus development was informed by the current NSW syllabus and the direction document for syllabus writers. The syllabus sections include the introduction, rationale, aims, objectives and assessment. The content is organized by stages and strands and some content, like Pythagoras' theorem, has been moved to earlier stages. Working mathematically outcomes are more prominent in the new syllabus structure.
Scootle is a digital platform for curriculum resources created by The Le@rning Federation. It contains interactive lessons, assessments, and other materials. The document discusses how teachers can get access to Scootle through their school IT departments. It provides two examples of Scootle resources, one on scientific notation and another on graphs of physical phenomena. Teachers are encouraged to share useful Scootle resources and learning paths with others.
This document contains 32 math word problems ranging in topics from basic arithmetic to geometry and measurement. The problems involve calculating sums, differences, products, quotients, percentages, and solving simple equations. They require applying math operations and concepts like division, multiplication, area, fractions, averages, rates, and angles to reach the answers.
2010 year 7 naplan non calculator solutionsjharnwell
This document contains 32 math word problems or questions from a Year 7 NAPLAN numeracy exam. The questions cover a range of math topics including operations with whole numbers, fractions, decimals, percentages, measurement, geometry, time, and data interpretation. The final question involves using properties of angles on a straight line.
2010 mathematics school certificate solutionsjharnwell
This document contains the solutions to the 2010 Mathematics School Certificate exam for New South Wales, Australia. It includes the answers to multiple choice and free response questions across two sections: the non-calculator section and sections covering parts A and B. The solutions provide brief explanations and workings for obtaining the answers to the math problems on the exam.
Australian curriculum presentation 31 march 2011jharnwell
The document summarizes discussions from an Australian Curriculum Mathematics Heads of Department meeting regarding developments in the Australian Curriculum. Key points include:
- The final Australian Curriculum for Mathematics is planned for release in October with assessment and reporting arrangements to transition between 2010-2013.
- An online platform called Scootle will host curriculum resources. Concerns were raised about several senior mathematics courses having too much content, lack of technology guidance, and need for review of topics.
- States will continue offering non-overlapping subjects and the curriculum may expand over time. New NSW syllabi will be released online and in print with implementation from 2013 and changes to senior years still vague.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
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.
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.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Assessment and Planning in Educational technology.pptxKavitha Krishnan
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
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.
Liberal Approach to the Study of Indian Politics.pdf
2010 mathematics hsc solutions
1. http://www.maths.net.au/ 2010 Mathematics HSC Solutions
2010 Mathematics HSC Solutions
Question 1 (b) x 2 x 12 0
(a) ( x 4)( x 3) 0
x2 4x 0
y
x( x 4) 0
x 0 or x 4 0
–3 4
x4 x
(b) 1 52 52
3 x 4
52 52 54
2 5 (c) y ln 3x
dy 3
a 2 and b 1
dx 3x
(c) ( x 1) 2 ( y 2) 2 25 1
x
(d) 2 x 3 9 1
at x 2, m
2
2x 3 9 or (2 x 3) 9
2 3
(d) (i) 5 x 1 dx 5 5 x 1 2 dx
1
2x 6 2 x 3 9
3 5 2
x3 2 x 12 2
5 x 1 c
3
x 6 15
d 2 x 1 2x
(e) x tan x tan x (2 x) x 2 (sec 2 x) (ii)
dx dx
dx 4 x 2
2 4 x2
x(2 tan x x sec2 x) 1
ln 4 x 2 c
2
a
(f) s
(e) 6
1 r
1
x k dx 30
0
x2
6
1 1
3
2 kx 30
3 0
2 62
6k 30
2
(g) x 8 6k 12
Question 2 k 2
Question 3
d cos x x( sin x) cos x(1)
(a) 2 12 4 6
dx x x2 (a) (i) M ,
x sin x cos x 2 2
5, 1
x2
1
2. http://www.maths.net.au/ 2010 Mathematics HSC Solutions
86 3 1
(ii) mBC ln x dx 0 2 ln 2 ln 3
6 12 1 2
1 1.24 (2 d.p.)
3
(iii) The approximation using the
2 1 trapezoidal rule is less than the
(iii) mMN
25 actual value of the integral, because
1 the shaded area of the trapeziums,
3 is less than the actual area below
since mBC mMN , the curve.
BC || MN
y
Corresponding angles on parallel 2
lines are equal, so
ACB ANM 1
ABC AMN
ABC ||| AMN (equiangular)
1 2 3 4 x
1
(iv) y 2 x 2
3 -1
3y 6 x 2
Question 4
x 3y 8 0
(a) (i) Forms an AP, a 1 , d 0.75
Tn 1 (n 1) 0.75
12 6 6 8
2 2
(v) BC
Tn 0.25 0.75n
2 10
T9 0.25 0.75 9
1 T9 7 km
(vi) Area bh
2 Susannah runs 7 km in the 9th week
1 (ii) Tn 0.25 0.75n
44 2 10h
2 10 0.25 0.75n
22 10 n 13
h
5 In the 13th week.
(b) (i) y
(iii) S 26 26
2 2 1 26 1 0.75
3 269.75 km
2 2
1 (b) Area e 2 x e x dx
0
-1 1 2 3 4 5 x 2
-2 e2 x
e x
-3 2 0
-4
-5 e4 e0
e 2 e0
(ii) x 1 2 3 2 2
0 ln(2) ln(3) 2
f(x) e 2e 3
4
2
2
3. http://www.maths.net.au/ 2010 Mathematics HSC Solutions
(c) (i) P (2 mint)
4 3 4 r 3 20 0
12 11 r3 5 0
1
5
11 r 3
1 1 1
(ii) P (2same) d2A 60
11 11 11 4 3
2
3 dr r
11 5
when r 3 ,
3 2
d A
(iii) P (2 different) 1 16 0, c.c.up,
11 dr 2
8 5
local minimum at r 3
11
(d) f x f x 1 e x 1 e x
1 e x e x 1 1 1 sin x
x (b) (i) sec2 x sec x tan x
2e e x
cos 2 x cos x cos x
f x f x 1 e x 1 e x
1 sin x
cos 2 x
2 e x e x
1 sin x
Question 5 (ii) sec2 x sec x tan x
cos 2 x
1 sin x
(a) (i) V r 2h
1 sin 2 x
10 r 2 h 1 sin x
10 1 sin x 1 sin x
h 2
r 1
1 sin x
A 2 r 2 2 rh
10
2 r 2 2 r 2
1
(iii) I
4
r dx
0 1 sin x
20
2 r 2
4
r sec 2 x sec x tan x dx
0
tan x sec x 0
(ii) dA 20 4
4 r 2
dr r
dA tan sec tan 0 sec 0
let 0 to find stationary points 4 4
dr
1 2 1
2
3
4. http://www.maths.net.au/ 2010 Mathematics HSC Solutions
1 1
(iii)
A1 dx
(c) y
a x
1 ln x a
1
8
1 ln 1 ln a
–2
ln a 1 x
1
a
e (b) (i) l r
9 5
b
1
A2 dx
1.8
1 x
1 ln x 1
b (ii) In OPT and OQT
OP = OQ (equal radii of 5 cm)
1 ln b ln 1 OPT = OQT (both right angles)
ln b 1 OT is a common line
OPT OQT (RHS)
be
(iii) POT 1 POQ
Question 6 2
0.9
(a) (i) f ( x) ( x 2)( x 4)
2
PT
tan(0.9)
f ( x) x3 2 x 2 4 x 8 5
PT 5 tan(0.9)
f ( x) 3 x 2 4 x 4 PT 6.3 cm (1 d.p.)
(iv) PTQ 1.8 2
Consider the discriminate, 2 2
42 4(3)(4) (angle sum of a quadrilateral is 2 )
32
PTQ 1.34
Therefore there are no zeros, and 1
Area (6.3) 2 sin(1.34)
hence, no stationary points. (the 2
derivative function is positive 1
definite) (5) 2 (1.8 sin(1.8))
2
(ii) f ( x ) 6 x 4 9 cm 2
Question 7
The graph is concave down when
6x 4 0
(a) (i) x 4 cos 2t dt
2
x
3 2sin 2t c
The graph is concave up when
2 when t = 0, x 1 ,
x 1 2sin 2(0) c
3
c 1
x 2sin 2t 1
4
5. http://www.maths.net.au/ 2010 Mathematics HSC Solutions
(ii) at x 0
1
0 2sin 2t 1 T is the point , 2 .
2
1 mBT 4
sin 2t
2 Eqn BT: y 4 4( x 2)
y 4x 4
2t
6
13 Since this line is not vertical, if there
t ,
12 12 is one simultaneous solution between
this line and the parabola, it is a
Therefore, the first time it will be at tangent. So, sub y 4 x 4 into
13 y x2
rest is at t = 3.4 s
12 4 x 4 x2
(iii) x 2sin 2t 1 dt x2 4 x 4 0
x 2
2
0
cos 2t t c
x2
at t = 0, x = 0 BT is a tangent to the parabola
0 cos 2(0) 0 c
c 1
x cos 2t t 1
dy Question 8
(b) (i) 2x
dx
at x = –1, m = –2 (a) P Ae kt
P 102e kt
y 1 2( x 1)
when t = 75, P = 200 000 000
2x y 1 0 200000000 102e 75 k
k 0.22
(ii) M ,
1 5
2 2 P 102e0.22t
mAB 1
P 102e0.22(100)
so, to find the x-value on the curve,
where the tangent is 1, let 2x = 1. P 539 311 817 787
1 1 P 539 billion
Therefore the point C is , .
2 4 (b) P ( HH ) 0.36
Since the x-values of M and C are P ( H ) 0.6
the same, then the line MC will be P (T ) 0.4
vertical.
P (TT ) 0.16
x–coordinate of T is 0.5. (c) (i) A 4 (amplitude)
(iii)
2x y 1 0 2
(ii) T
1 b
2 y 1 0 2
2
y 2 b
b2
5
6. http://www.maths.net.au/ 2010 Mathematics HSC Solutions
(iii) y (ii)1 A1 P (1 0.005)1 2000
P (1.005)1 2000
4
3 A2 A1 (1.005)1 2000
2 P (1.005)1 2000 (1.005)1 2000
1
P (1.005) 2 2000(1 1.005)
x A3 A2 (1.005)1 2000
-1
-2 2 P (1.005) 2 2000(1 1.005) (1.005)1 2000
-3
P (1.005)3 2000(1 1.005 1.0052 )
-4
(d) f x x3 3 x 2 kx 8 An P (1.005) n 2000(1 1.005 1.005n 1 )
f x 3x 2 6 x k P (1.005n ) 2000
1(1.005n 1)
1.005 1
P (1.005n ) 400 000 (1.005n 1)
For an increasing function f x 0 , P (1.005n ) 400 000 1.005n 400 000
( P 400 000) 1.005n 400 000
i.e. 3 x 2 6 x k 0
Consider the graph of y 3 x 2 6 x with 2 An ( P 400 000) 1.005n 400 000
0 (232 175.55 400 000) 1.005n 400 000
x-intercepts at 0 and 2. Vertex at x = 1, 400 000
1.005n
y = –3. if k 3 , f x is positive 167824.45
n log1.005 (2.38)
definite and hence f x is an log10 2.38
n
log10 1.005
increasing function.
n 174.1
Question 9
(a) (i) A1 500(1 0.005) 240 Thus there will be money in the
account for the next 175 months
A2 500(1 0.005) 239
. (b) (i) 0 x2
.
. (ii) The maximum occurs at x = 2,
2
A240 500(1 0.005)1
f x dx 4
0
f 2 f 0 4
A A1 A2 A240
f 2 4
500(1.005 1.0052
The maximum value is f x 4
1.005239 1.005240 )
1.005(1.005240 1) (iii) f 6 f 4
500
1.005 1 4
$232 175.55 f x dx 4
2
f 4 f 2 4
f 4 4 4
f 4 0
The gradient is –3, so f 6 6
6
7. http://www.maths.net.au/ 2010 Mathematics HSC Solutions
(iv) 4
y a (1 2 cos )
y a (1 2(1))
2 4 6 y 3a
OA
(b) (i) sin
r
OA r sin
–6 r
V y 2 dx
r sin
Question 10
r x 2 dx
r
2
r sin
(a) (i)In ACD, DAC and DCA = x3
r
r 2 x
90 1 ( sum of )
2 3 r sin
r3 r 3 sin 3
CDB = 180 (suppl. angles) r 3 r 3 sin
3 3
DBC = 90 1 (ABC is isosc.)
2
r 3
DCB = 90 3 ( sum of )
2
3
2 3sin sin 3
ACB = DCB + DCA =
(ii) 1 Initial depth = r. So, find , to give
In ABC and ACD, depth 1 r. From the diagram,
ACB = ADC (both )
2
r
DAC = DBC (both 90 1 )
2 OA r sin
2
ABC ||| ACD (equiangular) 1
sin
AD DC a 2
also note 30
AC CB x
(ii) orresponding sides of similar
C
triangles are in the same proportion. r3
3 1
2
AD AC 3 2 8
2 Fraction
AC AB 2 r 3
a x 3
x a y 5
a (a y ) x 2 16
x 2 a 2 ay
(iii n ACD, by the cosine rule
I
x 2 a 2 a 2 2a 2 cos
a 2 ay a 2 a 2 2a 2 cos
ay a 2 2a 2 cos
y a 2a cos
y a (1 2 cos )
(ivTo get the maximum value of y, cos
must take its minimum value, of –1.
7