Curve Sketching Worksheet With Answers

answers to odd questions answers to even questions U-substitution (Feb 4/6) U-sub with definite integrals (Feb 6) answers to odd questions answers to even questions Inverse Trigonometric Functions (Feb 11)  Area Between Curves  (Feb 13) extra practice: area between curves. Shed the societal and cultural narratives holding you back and let free step-by-step Stewart Calculus textbook solutions reorient your old paradigms. y = f(x − 1) crosses the coordinate axes. This will be useful when finding vertical asymptotes and determining critical numbers. Available for Pre-Algebra, Algebra 1, Geometry, Algebra 2, Precalculus, and Calculus. 1) f (x) = x x 2) f (x) =. Which is it? Give several reasons why the other func-tion graphed cannot be the derivative of the function given above. Being able to solve quadratic equations is an essential skill necessary for a number of topics such as curve sketching, and for finding the minimum or maximum values to solve real-life problems. Only links colored green currently contain resources. Showing top 8 worksheets in the category - Curve Sketching. Graphing trigonometric functions lesson plans and worksheets from thousands of teacher-reviewed resources to help you inspire Answers are not included. Graphing Mathematical Functions. 25 scaffolded questions on equation, graph involving amplitude and period. Every time a quadratic expression may not be factorized to provide rational solutions as we have observed in the examples up to now, we want to locate other methods to address the quadratic equation. 3 Worksheet. 5b worksheet answer key 3. I may help you answer it but since the solution is complex, I doubt you will really understand the whole process of solving it so it’s recommended that you really have to ask someone to explain it to you in person to make the explaining clearer. Curve Sketching Curve Sketching - Purpose Absolute Extreme Values - GRAPH The Min/Max Thm - Notes Mean Value Theorem. (a) (b) Answer: The derivative is the graph in (b). Answers to Calculus Manual 12/25/17 W e have added answers to the AB and BC Calculus manuals. Name a feature of the graph of B : T ; L| T| that is not shared by the graphs of polynomial functions. f(x) = p 3 x2 ln(x + 1) ( 1;0) [ 0; p 3 i Where might you expect f(x) to have a vertical asymptote? What does the function look like nearby?. (2) 8 y c By sketching another suitable curve on your diagram in part b,. ©a T2C0l1 j3 B HKIu atHat gSKobfyt Bwa6rweu pL PLrCN. The accompanying figure shows the graph of the derivative of a function f. Example Sketch the graph of the function: f(x) = x2. Curve Sketching Problems For the following functions, f, find all local extrema, inflection points, vertical and horizontal asymptotes. You may also use any of these materials for practice. Mathematics SKE: STRAND F UNIT F4 Solving Quadratic Equations: Text F4. HW: Practicing Properties of Logs Worksheet (1-8 only) 5: Properties of Logarithms Practicing Properties of Logs Assignment (Here's a video of problems from the assignment). Sketching Trigonometric Graphs Today we are learning How to sketch a variety of trigonometric graphs. AP Calculus: Curve Sketching with First and Second Derivatives Web Exploration II. For 1 & 2, use all your math skills to analyze and. Curve Sketching Using Calculus - Part 1 of 2 This video discusses the following topics to help produce the graph of a function: domain, x-y intercepts, symmetry of the function, intervals of increase/decrease, local maximums and minimums, concavity, inflection points, horizontal and vertical asymptotes. These elegant curves,. Helpful when doing math worksheets Me and my dad use this app when we want to make sure our answer on a worksheet is correct, and we get the same answer if it’s correct ! Thank you for making this app !!. The Problems tend to be computationally intensive. Core, Maths, A level, aqa, ocr. If you are having any trouble with these problems, it is recommended that you review the curve sketching tutorial at the link below. In the definition of the slope, vertical lines were excluded. Curve Sketching Whether we are interested in a function as a purely mathematical object or in connection with some application to the real world, it is often useful to know what the graph of the function looks like. com useful for school or work? I built this website and developed the material it contains on my own time, and it's entirely free to use. Simply click on a topic below to see all resources in that collection. Piecewise Function Grapher. It is also available in download form as a stand-alone product. Therefore the domain is D f = R. Curve Sketching. Meaning of Derivative Practice Test 2012 Form B. (Download each Chapter below) Odd Solution Manual Introduction: General Preview of Analytic Geometry and Calculus (pdf). uk A sound understanding of Parabolas is essential to ensure exam success. Welcome; Class Calendars & Syllabi; AP Calculus. AP Calculus: Curve Sketching with First and Second Derivatives Web Exploration II. Zeros The zeros of the. Select more plots in areas where you think you need information to inform your curve. Curve sketching enrichment. Combined exam - Curve Sketching, Related Rates, Optimization Problems (114 kb pdf file), Answer Key - Part 1( 308 kb pdf file) and part 2 (80 kb pdf file) Definite Integral. Derivative Review Maze Description: Great end of topic review for Derivatives or as a review for the AP Exam. 9 - Curve Sketching. Have you found korpisworld. Some of the worksheets for this concept are Curve sketching date period, 201 103 re, Curve sketching, Math 1 section 006, Curve sketching example, Work for week 10 sketching curves, Curve sketching work, Work for week 3 graphs of f x and. b) Hence, sketch the graph of C. You can find C1 Solomon worksheets and answers below. 25 scaffolded questions on equation, graph involving amplitude and period. Calculus Appendix. Explain your reasoning. Worksheet 10, Math 1551, Fall 2017 Sections from Thomas 13th Edition: 4. (3) (b) Find the coordinates of the points where the curve with equation. Open link. This series of quadratic formula worksheets requires students to identify the nature of the roots of the quadratic equation as equal, unequal, real or complex. y = f(x − 1) crosses the coordinate axes. In Part I, students graph equilibrium vapor pressures of three different substances and interpret the graphs. In the definition of the slope, vertical lines were excluded. You can find C1 Solomon worksheets and answers below. Try the quiz at the bottom of the page! go to quiz. Vectors Appendix. I needed a quick worksheet (actually for my Further Maths Qualification students in year 11) to practice graph sketching so knocked this one up. Solutions to Worksheets 6. How to access resources. Worksheets 1 to 15 are topics that are taught in MATH108. t!8, water continues to flow into and out. Search this site. f(x) = 1/3(x-1) 3 + 2. Navigation. Since there is no textbook for this course, it is highly recommended that you have a 3-inch BINDER and develop a system TO FILE YOUR HOMEWORK, QUIZZES, AND HANDOUTS. Being able to solve quadratic equations is an essential skill necessary for a number of topics such as curve sketching, and for finding the minimum or maximum values to solve real-life problems. Volume (8) Worksheet. Curve Sketching Practice With a partner or two and without the use of a graphing calculator, attempt to sketch the graphs of the following functions. The constant k is what causes the vertical shift to occur. Quadratic Formula Worksheets. To nd p 2 on the real line you draw a square of sides 1 and drop the diagonal onto the real line. Worksheet on Optimization Problems Some comments: 1. They also sketch the graph of the equation. The distributive laws discussed in worksheet 1. 2) Given that q ≠ 0, find the value of the constant q such that the equation x² + 2qx - q = 0 has a repeated root. Write the following quadratic equation worksheet with answers pdf. (Solution of this worksheet will be available at the course website after all the tutorials of that week) 1. 7 For the equation y = 2(x 1)2 –3: (a) state the coordinates of the turning point (b) state whether it is a maximum or minimum (c) state the y-intercept (d) state if it is wider or narrower than y = x2 (e) sketch the curve. 2: CURVE SKETCHING RATIONAL FUNCTIONS EXERCISES Give a complete graph of the following functions. 3 ~~~~~ Chapter Six. This innovative activity is designed for Calculus 1, AP Calculus , and Calculus Honors and is an introduction to Unit 3. com!!!!!"#!$%&'()%*+!!!!!R-!,!!!!! Stu Schwartz Function Analysis - Classwork. Answer Key; Applications of Curve Sketching Notesheet Showing 20 items from page AP Calculus Applications of Derivatives Part 1 Homework sorted by Assignment. 4 Concavity and inflection points [Jump to exercises] Collapse menu 1 Analytic Geometry. Lesson 4 - Eight Functions Worksheet Eight Functions soln Lesson 4 - Factoring Review (You don't have to do all of these, just make sure you are comfortable with these kinds of questions) Questions 37, and 39-42 are a bit tricky. ©6 xKruht1aG 4SVoDfet1wyaOrceZ GLPLXCZ. First then, some general advice: Make it big!. M Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Curve Sketching Date_____ Period____. Studying Math 1000 Calculus I at Memorial University Of Newfoundland? On StuDocu you find all the study guides, past exams and lecture notes for this course. 10 g 10 g 10 g 10 g 10 g 10 g CHEMISTRY HEATING CURVE WORKSHEET-50-40-30-20-10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150-50-40-30-20-10 0 10 20 30. A general solution to a differential equation will have a _____in the solution. Answer Key; Applications of Curve Sketching Notesheet Showing 20 items from page AP Calculus Applications of Derivatives Part 1 Homework sorted by Assignment. The best videos and questions to learn about Examples of Curve Sketching. After completing the chart, graph the ordered pairs in the chart. Take a quick interactive quiz on the concepts in Curve Sketching Derivatives, Intercepts & Asymptotes or print the worksheet to practice offline. Sketching curves of functions and their derivatives. Unsupported answers may receive NO credit. Solutions to Worksheets 5. AP CALCULUS REVIEW WORKSHEETS ACCELERATION, VELOCITY AND POSITION In problems 1-4, determine the position function, x(t), from the given information. Graphing Trig Functions Practice Worksheet With Answers Students will practice graphing sine and cosine curves : a) identify period and amplitude based on equation or on the graph b) write equation from graph c) write. -1-For each problem, find the: x and y intercepts, x-coordinates of the critical points, open. Here is a set of practice problems to accompany the Parametric Equations and Curves section of the Parametric Equations and Polar Coordinates chapter of the notes for Paul Dawkins Calculus II course at Lamar University. -1-For each function: (a) determine the end behavior by applying the Leading Coefficient Test,. linearization lesson. Note: For practice only; not to be submitted. Wk 1: Mon 9/4 First Class. Curve Sketching Example 1 Example 1: Sketch the graph of f(x) = 3x − x3. New: School administrations are increasingly concerned with standards. Navigation. Maxima And Minima Problems Prepared by Sue Millet for HSC Revision Day UOW. Click on pop-out icon or print icon to worksheet to print or download. I am currently trying to revise curve sketching, as it seems to be an area in which I could gain a significant amount of easy marks. If you are having any trouble with these problems, it is recommended that you review the curve sketching tutorial at the link below. e t QADlRll erOi^ghhittsp lrhefsyejrovSezdK. 1: Areas Between Curves. Worksheets 16 and 17 are taught in MATH109. Showing top 8 worksheets in the category - Curve Sketching. -1-For each problem, find the: x and y intercepts, x-coordinates of the critical points, open. The accompanying figure shows the graph of the derivative of a function f. i Preface This book is a revised and expanded version of the lecture notes for Basic Calculus and other similar courses o ered by the Department of Mathematics, University of Hong Kong, from the first semester of the academic. 5a worksheet. Chapter 9: Relationships between Points, Lines, and Planes. CW Curve sketching Shape mix and match CLICK HERE FOR PAGE 1 OF SKETCH A GRAPH PRACTICE PAGE CLICK HERE FOR PAGE 2 OF SKETCH A GRAPH PRACTICE PAGE CLICK HERE FOR ANSWERS TO PRACTICE PAGE FOR GRAPH PRACTICE HW 5 steps book:pg. WORKSHEETS AND REVIEWS 3. a) Describe geometrically the three transformations that map the graph of y x= 2 onto the graph of C. Curve Sketching: Level 3 Challenges. Worksheets are 07, Area between two curves, Heating curves work, Work for week 10 sketching curves, The lake, Curve sketching date period, Math 1a calculus work, Work surfaces grid curves and surface elements. Small curves called runouts (i. INTRODUCTION. Example Sketch the graph of the function: f(x) = x2. For higher values of x, the value of the second derivative, 30x + 60, will be positive so the curve is concave up. b) When the graph of. Solutions to Worksheets 6. Limit of the Area Between Two Curves - Notes Chapter Notes - Chapter 5 Constant Difference Thm - Notes Estimate the Area Under a Curve - NotesC, NotesBW Estimate the Area Under a Curve - Numerical Techniques (2 pages) Area under a Curve - Summation , Infinite Sum Motion along a straight line - Worksheet. CURVE SKETCHING EXAMPLES. No calculator unless otherwise stated. Graph the function given that and. You can graph a Quadratic Equation using the Function Grapher, but to really understand what is going on, you can make the graph yourself. This handout contains three curve sketching problems worked out completely. Answer Key; Applications of Curve Sketching Notesheet Showing 20 items from page AP Calculus Applications of Derivatives Part 1 Homework sorted by Assignment. SOLUTION 1 : The domain of f is all x-values. Curve Sketching Whether we are interested in a function as a purely mathematical object or in connection with some application to the real world, it is often useful to know what the graph of the function looks like. 3 T MMQaqd Het Mw2istGh T UIXnzf7i Knji 5t yeB hC eaXlRc4uClQuMsG. Answer: Points like that aren’t called critical points, but they are very. Please not that you may be required to share your summary with the class. Ticket Out the Door Curve Sketching Day 1. Search this site. I teach mathematics to 11 - 18 year olds in the UK. The purpose of this website is to provide a place for students to keep up with classwork and homework each day and to find resources such as worksheets, answer keys, and videos. Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. It is covered in Math 1552. More about me. Justify your answer. Worksheet - Graphing Sin and Cos Functions (Answers) Free worksheet(pdf) and answer key on graphing sine and cosine curves. Identify what the problem is asking. About: Beyond simple math and grouping (like "(x+2)(x-4)"), there are some functions you can use as well. -1-For each problem, find the: a) intercepts b) domain c) symmetry of the function d) equation of any vertical asymptotes e) behavior near the vertical asymptotes. Your answer seems If A A A and B B B are two distinct arbitrary. Consider a continuous function f with the following properties: 1. Calculus 1, summary of curve sketching help please, test tomorrowf(x)=x^6-10x^5-400x^4+ please help? I am having trouble finishing certain steps about sketching the curve. a y = x2 – 4x b y = x2 – 6x + 5 c y = x2 + 2x – 8 d y = 16 – x2. The Exponential Curve: Some fun(ish) worksheets. The curve sketching steps presented in this lesson are but a few essential ones needed to graph a function. VCE MATHS METHODS UNIT 3 &4 AREA OF STUDY: EXAM PREPARATION Functions and graphs, Algebra, Calculus, Probability, covering past and its use in sketching curves. Fundamental theorem of calculus. EXTRA PRACTICE WORKSHEETS CALC AB/BC. 2: The Fundamental Theorem of Calculus. Worksheet by Kuta Software LLC Precalculus Worksheet Section 2. Parabolas Welcome to national5maths. 5 Arithmetic with Surds Section 1 Expanding Expressions Involving Surds Fractional powers and the basic operations on them are introduced in worksheet 1. Home Faculty & Staff Faculty FrontDoor Worksheets on factoring with answers Chapter 3 (part 1) -- Mins and Maxs, Concavity, Curve Sketching. It is very easy to do, and once you master it, the possibilities are endless!. Upload failed. We can obtain a good picture of the graph using certain crucial information provided by derivatives of the function and certain. When a student works through the exercise and comes up with an answer that doesn’t look anything like a p 3+ ˇ b, he/she has been given an obvious invitation to check his/her work. Based on information gained so far, select x values and determine y values to create a chart of points to plot. Give a thorough answer: In order to find a local maximum or minimum for a function, I would…Find where f ' is either zero or undefined. Worksheet and Solutions--This also has the solution to the warm-up. Curve Sketching. Write the following quadratic equation worksheet with answers pdf. Worksheet On Extrema And Curve Sketching Math 1000 Calculus I. Topical worksheets. Videos designed for the site by Steve Blades, retired Youtuber and owner of m4ths. 25 scaffolded questions on equation, graph involving amplitude and period. 6 worksheet answer key Curve sketching overview in chart form Quiz review with solutions Quiz Trig 3 review Quiz Trig 3 review answer key Test rvw w/answrs (no Newton or prop err) Extra Test review Optimization practice Kahoot questions. Example Sketch the graph of the function: f(x) = x2. 2: The Fundamental Theorem of Calculus. 1 Worksheet All work must be shown in this course for full credit. How to access resources. Prerequisite: Grade of C or better in Math 1404 or Math 1505 or placement by exam taken at the University Houston-Downtown. Try to decide: a) Where minimums and maximums occur b) What original function could yield such a derivative graph. HW: Practicing Properties of Logs Worksheet (1-8 only) 5: Properties of Logarithms Practicing Properties of Logs Assignment (Here's a video of problems from the assignment). Math 111 Section 006 Worksheet 2: Curve Sketching Deadline: Wednesday 11/09/15 Instructions: Please write your answers neatly on a separate sheet of paper and show any relevant work. Worksheet 5. The diagram below illustrates the steps involved to convert 10 g of solid ice at -20°C to 10 g of gaseous steam at 140°C. Use l'Hospital's Rule where appropriate but rst check that no easier. Some of the worksheets displayed are Curve sketching date period, 201 103 re, Curve sketching, Math 1 section 006, Curve sketching example, Work for week 10 sketching curves, Curve sketching work, Work for week 3 graphs of f x and. For the graphs that are functions, nd Answers 1. In the list below, you'll see some steps grouped if they are based on similar methods. We can obtain a good picture of the graph using certain crucial information provided by derivatives of the function and certain. EXTRA PRACTICE WORKSHEETS CALC AB/BC. C1 GRAPHS OF FUNCTIONS Worksheet C giving a reason for your answer. The curve sketching steps presented in this lesson are but a few essential ones needed to graph a function. Chapter 20 - 2 Derivatives in Curve Sketching. It is very easy to do, and once you master it, the possibilities are endless!. f(-2) = 0 2. Home Faculty & Staff Faculty FrontDoor Worksheets on factoring with answers Chapter 3 (part 1) -- Mins and Maxs, Concavity, Curve Sketching. Sketching the curve With the above information, we should draw the asymptotes, plot the xand y intercepts, local maxima, local minima and points of in ection. of the pipe at the given rates until the pipe begins to overflow. Chapter 17 Cartesian Geometry 343 Activity 2 Check this sketch by using a graphic calculator or graph plotting program. This chapter covers finding Max and Min solutions for one variable functions, second and higher derivative tests, and curve sketching (Ignore Taylor Series) Scanned Lecture Notes. It is not always possible to express the function y=f(x) in terms of x=f(y). 5 - Examples of Curve Sketching with Step by Step Instructions; Curve. In this worksheet,. Try for free. AP Calculus AB/BC - M. All worksheets created with Infinite Calculus. Horizontal and vertical asymptotes may be calculated by taking the. Visit the Year 12 Pure page for new specification resources. Students find the derivative of a function and then find the slope of a tangent line at a particular point. Do not use your calculator. -1-For each problem, find the: a) intercepts b) domain c) symmetry of the function d) equation of any vertical asymptotes e) behavior near the vertical asymptotes. Write the following quadratic equation worksheet with answers pdf. Solving Quadratic Equations by Factoring. Home-> Teaching-> Math 1401. Welcome; Class Calendars & Syllabi; AP Calculus. Making statements based on opinion; back them up with references or personal experience. Horizontal and vertical asymptotes may be calculated by taking the. The curve sketching steps presented in this lesson are but a few essential ones needed to graph a function. This package is a useful mathematical tool which we will use throughout the course. In this sketching polar equations worksheet, students solve 5 short answer and graphing problems. Time and Acceleration vs. ©a T2C0l1 j3 B HKIu atHat gSKobfyt Bwa6rweu pL PLrCN. Summary Beginning Derivatives. domain and range worksheet 2 answer key unique calculus archive november 06 2017. (Check your answer with your graphing calculator!) f x x( ) 2 sin= − +. This saves time and avoids controversial material. Prefacing each Topic is an info-sheet detailing each each worksheet and activity with descriptions and suggestions for the instructor. Try to sketch it below the € f "(x) graph. org helps support GraphSketch and gets you a neat, high-quality, mathematically-generated poster. Huge thanks to all individuals and organisations who share teaching. Unit 1: Limits & Continuity. Name a feature of the graph of B : T ; L| T| that is not shared by the graphs of polynomial functions. Try the quiz at the bottom of the page! go to quiz. some of the content is on the new a level but this is not for the new a level that started in september 2017. You do not need to attach this sheet when you turn it in. (a) (b) Answer: The derivative is the graph in (b). Course management details, syllabus, student questionnaire. Curve Sketching. Begin reviewing for the end of quarter test Thursday 10/24: p. Reference Material. Unsupported answers may receive NO credit. New: In addition, a set of answer pages (no shown work, just the answer) comes with the solution manual for the homework problems. 1) Given the graph of f(x) below, complete the chart, estimating the derivative (slope of the tangent line) at the given values of x. The larger displacement-time graph shows the motion of some hypothetical object over time. The first derivative of a function is the slope of the tangent line for any point on the function!. Introduction and Objectives. An old Worksheet on Derivative Formulas Curve Sketching Instructions The S-Curve Review Sheet on Curve Sketching The Seasons -- Curve sketching Methods for Finding Critical Points Right Angle Puzzle (1st Semester Vocabulary) Matchboxes Puzzle (1st Semester Vocabulary) Volume of a Box (Max/Min) Maxima / Minima Procedures Worksheet on Maxima. Quadratic graphs - Quiz 1. Justify your answer. 05 x where x is the number of smartphones manufactured per day. Test and Worksheet Generators for Math Teachers. At this point students will be asked to solve worksheet 2: z-scores in groups of 2 students (di erent from worksheet 1 group activity). 25 scaffolded questions on equation, graph involving amplitude and period. fis decreasing, f ' is ( positive , negative ). Purchasers of the AB and BC solution manuals were sent download links and new purchasers of solutions will automatically receive the answers as well. After completing the chart, graph the ordered pairs in the chart. Learning to Work with Charts and Graphs. 3 Higher Degree Polynomials and Curve Sketching Name_____ Period____ ©m m2G0d1i7Q lKVuMtYal FSsovfktjwla\rVey DLmLlCm. Solution: Optimization Problem Worksheet. b) Find all relative maximum(s) or minimum(s). 201-NYA-05 - Calculus 1 WORKSHEET: LIMITS 1. Unit 1: Limits & Continuity. Derivatives can help graph many functions. Only links colored green currently contain resources. UNIT 5 - Curve Sketching. Antiderivative Worksheet With Answers. Modules A - Functions and Graphs Review Worksheet Answers. Worksheet by Kuta Software LLC Precalculus Worksheet Section 2. See the adjoining sign chart for the first derivative, f'. Curve Sketching Example 1 Example 1: Sketch the graph of f(x) = 3x − x3. Time graph. (b) Find the locations of the local extrema for f. Mean Value and Roll’s Thm. c) find regions where the function rises and falls. Graphing the Rational Function. Graphs - Worksheet #1 The first of five worksheets covering curve sketching. 5: Asymptotes and Other Things to Look For. In the definition of the slope, vertical lines were excluded. In this worksheet,. Solution: Optimization Problem Worksheet. View Homework Help - NYA_worksheet_limits from MATH 210 at Cégep John Abbott College. Explain your reasoning. To obtain a grade of 3 or higher, you need to answer about 50 percent of the multiple-choice questions correctly and do acceptable work on the free-response section. A Few Definitions and Theorems from Sections 4. To sketch the curve, we have to complete serveral steps to the problem. AP Calculus AB Name: _____ Unit 4 Worksheet 2 1. 9 - Curve Sketching. Characteristics Video. If you're interested, take a look. A Collection of Problems in Di erential Calculus Problems Given At the Math 151 - Calculus I and Math 150 - Calculus I With Review Final Examinations Department of Mathematics, Simon Fraser University 2000 - 2010 Veselin Jungic Petra Menz Randall Pyke Department Of Mathematics Simon Fraser University c Draft date December 6, 2011. Curve Sketching Worksheet. f(–2) = 0 2. Find the graph of f from f' b. If you are looking for Curious George Worksheets you've come to the right place. After completing the chart, graph the ordered pairs in the chart. Solutions to Worksheets 6. Your answer seems reasonable. Then eliminate the parameter. The best videos and questions to learn about Examples of Curve Sketching. 960x720 Curve Sketching Lesson 5. b) Find all relative maximum(s) or minimum(s). On the current page, there are tips for how to get started. Chapter 5: Derivatives of Exponential and Trigonometric Functions. Worksheet 2. Huge thanks to all individuals and organisations who share teaching. Curve Sketching Problems For the following functions, f, find all local extrema, inflection points, vertical and horizontal asymptotes. -1-For each problem, find the: x and y intercepts, x-coordinates of the critical points, open. 1) Given the graph of f(x) below, complete the chart, estimating the derivative (slope of the tangent line) at the given values of x. Passing the fast paced Higher Maths course significantly increases your career opportunities by helping you gain a place on a college/university course, apprenticeship or even landing a job. -1-For each problem, find the: a) intercepts b) domain c) symmetry of the function d) equation of any vertical asymptotes e) behavior near the vertical asymptotes. Vectors Appendix. Curve sketching. some of the content is on the new a level but this is not for the new a level that started in september 2017. It is important in this section to learn the basic shapes of each curve that you meet. 3 Completing the Square Completing the square is a technique which can be used to solve quadratic equations that do not factorise. Worksheet 6. -1-For each problem, find the: x and y intercepts, asymptotes, x-coordinates of the critical points,.