2. Jan 2010 qu June 2009 qu.8
|
|
- Rudolf Lindsey
- 6 years ago
- Views:
Transcription
1 C3 Functions. June 200 qu.9 The functions f and g are defined for all real values of b f() = and g() = a + b, where a and b are non-zero constants. (i) Find the range of f. [3] Eplain wh the function f has no inverse. (iii) Given that g () = g() for all values of, show that a =. [4] (iv) Given further that gf() < 5 for all values of, find the set of possible values of b. [4] 2. Jan 200 qu.4 3 The function f is defined for all real values of b f() = 2 +. The diagram shows the graph of = f(). (i) Evaluate ff( 26). Find the set of values of for which f() = f(). (iii) Find an epression for f (). [3] (iv) State how the graphs of = f() and = f () are related geometricall. [] 3. June 2009 qu.5 The functions f and g are defined for all real values of b f() = 3 2 and g() = Find the eact coordinates of the point at which (i) the graph of = fg() meets the -ais, [3] the graph of = g() meets the graph of = g (), [3] (iii) the graph of = f() meets the graph of = g(). [4] 4. June 2009 qu.8 The diagram shows the curves = ln and = 2 ln( 6). The curves meet at the point P which has -coordinate a. The shaded region is bounded b the curve = 2 ln( 6) and the lines = a and = 0. (i) Give details of the pair of transformations which transforms the curve = ln to the curve = 2 ln( 6). [3] Solve an equation to find the value of a. [4]
2 5. Jan 2009 qu.6 The function f is defined for all real values of b f() = The graphs of = f() and = f () meet at the point P, and the graph of = f () meets the -ais at Q (see diagram). (i) Find an epression for f () and determine the -coordinate of the point Q. [3] State how the graphs of = f() and = f () are related geometricall, and hence show that the -coordinate of the point P is the root of the equation = Jan 2009 qu.7 The diagram shows the curve = e k a, where k and a are constants. (i) (iii) Give details of the pair of transformations which transforms the curve = e to the curve = e k a. [3] Sketch the curve = e k a. Given that the curve = e k a passes through the points (0, 3) and (ln 3, 3), find the values of k and a. [4] 7. June 2008 qu. Find the eact solutions of the equation 4 5 = 3 5. [4]
3 8. June 2008 qu.2 The diagram shows the graph of = f(). It is given that f( 3) = 0 and f(0) = 2. Sketch, on separate diagrams, the following graphs, indicating in each case the coordinates of the points where the graph crosses the aes: (i) = f (), = 2f(). [3] 9. June 2008 qu.7 It is claimed that the number of plants of a certain species in a particular localit is doubling ever 9 ears. The number of plants now is 42. The number of plants is treated as a continuous variable and is denoted b N. The number of ears from now is denoted b t. (i) Two equivalent epressions giving N in terms of t are N = A 2 kt and N = Ae mt. Determine the value of each of the constants A, k and m. [4] Find the value of t for which N = 00, giving our answer correct to 3 significant figures. (iii) Find the rate at which the number of plants will be increasing at a time 35 ears from now. [3] 0. Jan 2008 qu. Functions f and g are defined for all real values of b f() = and g() = 2 5. Evaluate (i) fg(), f (2). [3]. Jan 2008 qu.6 The diagram shows the graph of = sin ( ). (i) Give details of the pair of geometrical transformations which transforms the graph of = sin ( ) to the graph of = sin. [3] Sketch the graph of = sin ( ). ( ). (iii) Find the eact solutions of the equation sin = π 3 [3]
4 2. June 2007 qu.2 Solve the inequalit 4 3 < 2 +. [5] 3. June 2007 qu.3 The function f is defined for all non-negative values of b f() = 3 +. (i) Evaluate ff(69). Find an epression for f () in terms of. (iii) n a single diagram sketch the graphs of = f() and = f - (), indicating how the two graphs are related. [3] 4. June 2007 qu.5 A substance is decaing in such a wa that its mass, m kg, at a time t ears from now is given b the formula m = 240e 0.04t (i) Find the time taken for the substance to halve its mass. [3] Find the value of t for which the mass is decreasing at a rate of 2. kg per ear. [4] 5. Jan 2007 qu.9 Functions f and g are defined b f() = 2 sin for π π, g() = for. (i) State the range of f and the range of g. Show that gf (0. 5) = 2.6, correct to 3 significant figures, and eplain wh fg (0. 5) is not defined. [4] (iii) Find the set of values of for which f g() is not defined. [6] 6. June 2006 qu.2 Solve the inequalit 2 3 < +. [5] 7. June 2006 qu.6 The diagram shows the graph of = f(), where f() = 2 2, 0. (i) Evaluate ff( 3). [3] Find an epression for f (). [3] (iii) Sketch the graph of = f (). Indicate the coordinates of the points where the graph meets the aes. [3]
5 8. Jan 2006 qu.4 The function f is defined b f() = 2 for 0. The graph of = f() is shown above. (i) State the range of f. [] Find the value of ff(4). (iii) Given that the equation f() = k has two distinct roots, determine the possible values of the constant k. 9. June 2005 qu. The function f is defined for all real values of b f() = 0 ( + 3) 2. (i) State the range of f. [] Find the value of ff( ). [3] 20. June 2005 qu.2 Find the eact solutions of the equation 6 =. [4] 2. June 2005 qu.9 = f ( ) 7 m 4 7 The function f is defined b f () = (m + 7) 4, where and m is a positive constant. m The diagram shows the curve = f(). (i) A sequence of transformations maps the curve = to the curve = f(). Give details of these transformations. [4] Eplain how ou can tell that f is a one one function and find an epression for f (). [4] (iii) It is given that the curves = f() and = f () do not meet. Eplain how it can be deduced that neither curve meets the line =, and hence determine the set of possible values of m. [5]
and hence show that the only stationary point on the curve is the point for which x = 0. [4]
C3 Differentiation June 00 qu Find in each of the following cases: = 3 e, [] = ln(3 + ), [] (iii) = + [] Jan 00 qu5 The equation of a curve is = ( +) 8 Find an epression for and hence show that the onl
More information(a) Show that there is a root α of f (x) = 0 in the interval [1.2, 1.3]. (2)
. f() = 4 cosec 4 +, where is in radians. (a) Show that there is a root α of f () = 0 in the interval [.,.3]. Show that the equation f() = 0 can be written in the form = + sin 4 Use the iterative formula
More informationThe region enclosed by the curve of f and the x-axis is rotated 360 about the x-axis. Find the volume of the solid formed.
Section A ln. Let g() =, for > 0. ln Use the quotient rule to show that g ( ). 3 (b) The graph of g has a maimum point at A. Find the -coordinate of A. (Total 7 marks) 6. Let h() =. Find h (0). cos 3.
More informationChapter XX: 1: Functions. XXXXXXXXXXXXXXX <CT>Chapter 1: Data representation</ct> 1.1 Mappings
978--08-8-8 Cambridge IGCSE and O Level Additional Mathematics Practice Book Ecerpt Chapter XX: : Functions XXXXXXXXXXXXXXX Chapter : Data representation This section will show you how to: understand
More informationGetting ready for Exam 1 - review
Getting read for Eam - review For Eam, stud ALL the homework, including supplements and in class activities from sections..5 and.,.. Good Review Problems from our book: Pages 6-9: 0 all, 7 7 all (don t
More informationExact Differential Equations. The general solution of the equation is f x, y C. If f has continuous second partials, then M y 2 f
APPENDIX C Additional Topics in Differential Equations APPENDIX C. Eact First-Order Equations Eact Differential Equations Integrating Factors Eact Differential Equations In Chapter 6, ou studied applications
More informationRegent College Maths Department. Core Mathematics 4 Trapezium Rule. C4 Integration Page 1
Regent College Maths Department Core Mathematics Trapezium Rule C Integration Page Integration It might appear to be a bit obvious but you must remember all of your C work on differentiation if you are
More informationThe slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope.
LESSON Relating Slope and -intercept to Linear Equations UNDERSTAND The slope of a line is the ratio of the line s vertical change, called the rise, to its horizontal change, called the run. You can find
More informationmeans Name a function whose derivative is 2x. x 4, and so forth.
AP Slope Fields Worksheet Slope fields give us a great wa to visualize a famil of antiderivatives, solutions of differential equations. d Solving means Name a function whose derivative is. d Answers might
More information4.3 Worksheet - Derivatives of Inverse Functions
AP Calculus 3.8 Worksheet 4.3 Worksheet - Derivatives of Inverse Functions All work must be shown in this course for full credit. Unsupported answers ma receive NO credit.. What are the following derivatives
More informationInstructions for Section 2
200 MATHMETH(CAS) EXAM 2 0 SECTION 2 Instructions for Section 2 Answer all questions in the spaces provided. In all questions where a numerical answer is required an eact value must be given unless otherwise
More informationDifferentiating Functions & Expressions - Edexcel Past Exam Questions
- Edecel Past Eam Questions. (a) Differentiate with respect to (i) sin + sec, (ii) { + ln ()}. 5-0 + 9 Given that y =, ¹, ( -) 8 (b) show that = ( -). (6) June 05 Q. f() = e ln, > 0. (a) Differentiate
More information7.4. Characteristics of Logarithmic Functions with Base 10 and Base e. INVESTIGATE the Math
7. Characteristics of Logarithmic Functions with Base 1 and Base e YOU WILL NEED graphing technolog EXPLORE Use benchmarks to estimate the solution to this equation: 1 5 1 logarithmic function A function
More information1. For each of the following, state the domain and range and whether the given relation defines a function. b)
Eam Review Unit 0:. For each of the following, state the domain and range and whether the given relation defines a function. (,),(,),(,),(5,) a) { }. For each of the following, sketch the relation and
More informationSolutions to O Level Add Math paper
Solutions to O Level Add Math paper 4. Bab food is heated in a microwave to a temperature of C. It subsequentl cools in such a wa that its temperature, T C, t minutes after removal from the microwave,
More informationPatterns, Functions, & Relations Long-Term Memory Review Review 1
Long-Term Memor Review Review 1 1. What are the net three terms in the pattern? 9, 5, 1, 3,. Fill in the Blank: A function is a relation that has eactl one for ever. 3. True or False: If the statement
More informationUnit #3 Rules of Differentiation Homework Packet
Unit #3 Rules of Differentiation Homework Packet In the table below, a function is given. Show the algebraic analysis that leads to the derivative of the function. Find the derivative by the specified
More informationCircle. Paper 1 Section A. Each correct answer in this section is worth two marks. 5. A circle has equation. 4. The point P( 2, 4) lies on the circle
PSf Circle Paper 1 Section A Each correct answer in this section is worth two marks. 1. A circle has equation ( 3) 2 + ( + 4) 2 = 20. Find the gradient of the tangent to the circle at the point (1, 0).
More informationMEI STRUCTURED MATHEMATICS 4753/1
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiar General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 4753/ Methods for Advanced Mathematics (C3)
More informationUnit 2 Review. No Calculator Allowed. 1. Find the domain of each function. (1.2)
PreCalculus Unit Review Name: No Calculator Allowed 1. Find the domain of each function. (1.) log7 a) g 9 7 b) hlog7 c) h 97 For questions &, (1.) (a) Find the domain (b) Identif an discontinuities as
More informationSlope Fields and Differential Equations
Slope Fields and Differential Equations Students should be able to: Draw a slope field at a specified number of points b hand. Sketch a solution that passes through a given point on a slope field. Match
More informationFor questions 5-8, solve each inequality and graph the solution set. You must show work for full credit. (2 pts each)
Alg Midterm Review Practice Level 1 C 1. Find the opposite and the reciprocal of 0. a. 0, 1 b. 0, 1 0 0 c. 0, 1 0 d. 0, 1 0 For questions -, insert , or = to make the sentence true. (1pt each) A. 5
More informationAlgebra 1B Assignments Exponential Functions (All graphs must be drawn on graph paper!)
Name Score Algebra 1B Assignments Eponential Functions (All graphs must be drawn on graph paper!) 8-6 Pages 463-465: #1-17 odd, 35, 37-40, 43, 45-47, 50, 51, 54, 55-61 odd 8-7 Pages 470-473: #1-11 odd,
More informationv t t t t a t v t d dt t t t t t 23.61
SECTION 4. MAXIMUM AND MINIMUM VALUES 285 The values of f at the endpoints are f 0 0 and f 2 2 6.28 Comparing these four numbers and using the Closed Interval Method, we see that the absolute minimum value
More information3.1 Exponential Functions and Their Graphs
.1 Eponential Functions and Their Graphs Sllabus Objective: 9.1 The student will sketch the graph of a eponential, logistic, or logarithmic function. 9. The student will evaluate eponential or logarithmic
More information) approaches e
COMMON CORE Learning Standards HSF-IF.C.7e HSF-LE.B.5. USING TOOLS STRATEGICALLY To be proficient in math, ou need to use technological tools to eplore and deepen our understanding of concepts. The Natural
More informationMath 111 Final Exam Review
Math 111 Final Eam Review With the eception of rounding irrational logarithmic epressions and problems that specif that a calculator should be used, ou should be prepared to do the entire problem without
More information4.3 Mean-Value Theorem and Monotonicity
.3 Mean-Value Theorem and Monotonicit 1. Mean Value Theorem Theorem: Suppose that f is continuous on the interval a, b and differentiable on the interval a, b. Then there eists a number c in a, b such
More information2.5 CONTINUITY. a x. Notice that Definition l implicitly requires three things if f is continuous at a:
SECTION.5 CONTINUITY 9.5 CONTINUITY We noticed in Section.3 that the it of a function as approaches a can often be found simpl b calculating the value of the function at a. Functions with this propert
More information2 nd Semester Final Exam Review Block Date
Algebra 1B Name nd Semester Final Eam Review Block Date Calculator NOT Allowed Graph each function. Identif the verte and ais of smmetr. 1 (10-1) 1. (10-1). 3 (10-) 3. 4 7 (10-) 4. 3 6 4 (10-1) 5. Predict
More informationLESSON 12.2 LOGS AND THEIR PROPERTIES
LESSON. LOGS AND THEIR PROPERTIES LESSON. LOGS AND THEIR PROPERTIES 5 OVERVIEW Here's what ou'll learn in this lesson: The Logarithm Function a. Converting from eponents to logarithms and from logarithms
More information4.3 Exercises. local maximum or minimum. The second derivative is. e 1 x 2x 1. f x x 2 e 1 x 1 x 2 e 1 x 2x x 4
SECTION 4.3 HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH 297 local maimum or minimum. The second derivative is f 2 e 2 e 2 4 e 2 4 Since e and 4, we have f when and when 2 f. So the curve is concave downward
More informationAP Calculus. Slope Fields and Differential Equations. Student Handout
AP Calculus Slope Fields and Differential Equations Student Handout 016-017 EDITION Use the following link or scan the QR code to complete the evaluation for the Stud Session https://www.survemonke.com/r/s_sss
More informationTo: all students going into AP Calculus AB From: PUHSD AP Calculus teachers
To: all students going into AP Calculus AB From: PUHSD AP Calculus teachers Going into AP Calculus, there are certain skills that you have been taught to you over the previous years that we assume you
More informationHigher Mathematics (2014 on) Expressions and Functions. Practice Unit Assessment B
Pegass Educational Publishing Higher Mathematics (014 on) Epressions and Functions Practice Unit Assessment B otes: 1. Read the question full before answering it.. Alwas show our working.. Check our paper
More informationCALCULUS AB SECTION II, Part A
CALCULUS AB SECTION II, Part A Time 45 minutes Number of problems 3 A graphing calculator is required for some problems or parts of problems. pt 1. The rate at which raw sewage enters a treatment tank
More informationExponential, Logistic, and Logarithmic Functions
CHAPTER 3 Eponential, Logistic, and Logarithmic Functions 3.1 Eponential and Logistic Functions 3.2 Eponential and Logistic Modeling 3.3 Logarithmic Functions and Their Graphs 3.4 Properties of Logarithmic
More information5A Exponential functions
Chapter 5 5 Eponential and logarithmic functions bjectives To graph eponential and logarithmic functions and transformations of these functions. To introduce Euler s number e. To revise the inde and logarithm
More information5.2 Solving Quadratic Equations by Factoring
Name. Solving Quadratic Equations b Factoring MATHPOWER TM, Ontario Edition, pp. 78 8 To solve a quadratic equation b factoring, a) write the equation in the form a + b + c = b) factor a + b + c c) use
More informationPRE-CALCULUS: by Finney,Demana,Watts and Kennedy Chapter 3: Exponential, Logistic, and Logarithmic Functions 3.1: Exponential and Logistic Functions
PRE-CALCULUS: Finne,Demana,Watts and Kenned Chapter 3: Eponential, Logistic, and Logarithmic Functions 3.1: Eponential and Logistic Functions Which of the following are eponential functions? For those
More informationPACKET Unit 4 Honors ICM Functions and Limits 1
PACKET Unit 4 Honors ICM Functions and Limits 1 Day 1 Homework For each of the rational functions find: a. domain b. -intercept(s) c. y-intercept Graph #8 and #10 with at least 5 EXACT points. 1. f 6.
More informationQuick Review 4.1 (For help, go to Sections 1.2, 2.1, 3.5, and 3.6.)
Section 4. Etreme Values of Functions 93 EXPLORATION Finding Etreme Values Let f,.. Determine graphicall the etreme values of f and where the occur. Find f at these values of.. Graph f and f or NDER f,,
More informationUse Properties of Exponents
4. Georgia Performance Standard(s) MMAa Your Notes Use Properties of Eponents Goal p Simplif epressions involving powers. VOCABULARY Scientific notation PROPERTIES OF EXPONENTS Let a and b be real numbers
More informationEvaluate Logarithms and Graph Logarithmic Functions
TEKS 7.4 2A.4.C, 2A..A, 2A..B, 2A..C Before Now Evaluate Logarithms and Graph Logarithmic Functions You evaluated and graphed eponential functions. You will evaluate logarithms and graph logarithmic functions.
More informationf 0 ab a b: base f
Precalculus Notes: Unit Eponential and Logarithmic Functions Sllabus Objective: 9. The student will sketch the graph of a eponential, logistic, or logarithmic function. 9. The student will evaluate eponential
More informationDaily Lessons and Assessments for AP* Calculus AB, A Complete Course Page 584 Mark Sparks 2012
The Second Fundamental Theorem of Calculus Functions Defined by Integrals Given the functions, f(t), below, use F( ) f ( t) dt to find F() and F () in terms of.. f(t) = 4t t. f(t) = cos t Given the functions,
More informationAQA Higher Practice paper (calculator 2)
AQA Higher Practice paper (calculator 2) Higher Tier The maimum mark for this paper is 8. The marks for each question are shown in brackets. Time: 1 hour 3 minutes 1 One billion in the UK is one thousand
More informationMath 7/Unit 4 Practice Test: Patterns and Functions
Math 7/Unit 4 Practice Test: Patterns and Functions Name: Date: Define the terms below and give an eample. 1. arithmetic sequence. function 3. linear equation 4. What ordered pair represents the origin?.
More information10.4 Nonlinear Inequalities and Systems of Inequalities. OBJECTIVES 1 Graph a Nonlinear Inequality. 2 Graph a System of Nonlinear Inequalities.
Section 0. Nonlinear Inequalities and Sstems of Inequalities 6 CONCEPT EXTENSIONS For the eercises below, see the Concept Check in this section.. Without graphing, how can ou tell that the graph of + =
More informationA11.1 Areas under curves
Applications 11.1 Areas under curves A11.1 Areas under curves Before ou start You should be able to: calculate the value of given the value of in algebraic equations of curves calculate the area of a trapezium.
More informationChapter 18 Quadratic Function 2
Chapter 18 Quadratic Function Completed Square Form 1 Consider this special set of numbers - the square numbers or the set of perfect squares. 4 = = 9 = 3 = 16 = 4 = 5 = 5 = Numbers like 5, 11, 15 are
More informationDiagnostic Tests. (c) (sa sb )(sa sb ) Diagnostic Test: Algebra
Diagnostic Tests Success in calculus depends to a large etent on knowledge of the mathematics that precedes calculus: algebra, analtic geometr, functions, and trigonometr. The following tests are intended
More informationMath 115: Review for Chapter 2
Math 5: Review for Chapter Can ou determine algebraicall whether an equation is smmetric with respect to the - ais, the -ais, or the origin?. Algebraicall determine whether each equation below is smmetric
More informationUnit 5, Day 1: Ratio s/proportions & Similar Polygons
Date Period Unit 5, Da 1: Ratio s/proportions & Similar Polgons 1. If a) 5 7, complete each statement below. b) + 7 c) d) 7 2. Solve each proportion below. Verif our answer is correct. a) 9 12 b) 24 5
More informationMethods of Integration
U96-b)! Use the substitution u = - to evaluate U95-b)! 4 Methods of Integration d. Evaluate 9 d using the substitution u = + 9. UNIT MATHEMATICS (HSC) METHODS OF INTEGRATION CSSA «8» U94-b)! Use the substitution
More informationC3 A Booster Course. Workbook. 1. a) Sketch, on the same set of axis the graphs of y = x and y = 2x 3. (3) b) Hence, or otherwise, solve the equation
C3 A Booster Course Workbook 1. a) Sketch, on the same set of axis the graphs of y = x and y = 2x 3. b) Hence, or otherwise, solve the equation x = 2x 3 (3) (4) BlueStar Mathematics Workshops (2011) 1
More information( 3x. Chapter Review. Review Key Vocabulary. Review Examples and Exercises 6.1 Properties of Square Roots (pp )
6 Chapter Review Review Ke Vocabular closed, p. 266 nth root, p. 278 eponential function, p. 286 eponential growth, p. 296 eponential growth function, p. 296 compound interest, p. 297 Vocabular Help eponential
More informationZETA MATHS. Higher Mathematics Revision Checklist
ZETA MATHS Higher Mathematics Revision Checklist Contents: Epressions & Functions Page Logarithmic & Eponential Functions Addition Formulae. 3 Wave Function.... 4 Graphs of Functions. 5 Sets of Functions
More informationCreated by T. Madas. Candidates may use any calculator allowed by the regulations of this examination.
IYGB GCE Mathematics SYN Advanced Level Snoptic Paper C Difficult Rating: 3.895 Time: 3 hours Candidates ma use an calculator allowed b the regulations of this eamination. Information for Candidates This
More informationMath 121. Practice Problems from Chapter 4 Fall 2016
Math 11. Practice Problems from Chapter Fall 01 1 Inverse Functions 1. The graph of a function f is given below. On same graph sketch the inverse function of f; notice that f goes through the points (0,
More informationMathematics. Mathematics 2. hsn.uk.net. Higher HSN22000
Higher Mathematics UNIT Mathematics HSN000 This document was produced speciall for the HSN.uk.net website, and we require that an copies or derivative works attribute the work to Higher Still Notes. For
More informationTO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet.
MATH TEST 4 REVIEW TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet. PART NON-CALCULATOR DIRECTIONS: The problems
More informationAPPENDIX D Rotation and the General Second-Degree Equation
APPENDIX D Rotation and the General Second-Degree Equation Rotation of Aes Invariants Under Rotation After rotation of the - and -aes counterclockwise through an angle, the rotated aes are denoted as the
More informationLINEARIZATION OF GRAPHS
LINEARIZATION OF GRAPHS Question 1 (**) The table below shows eperimental data connecting two variables and y. 1 2 3 4 5 y 12.0 14.4 17.3 20.7 27.0 It is assumed that and y are related by an equation of
More informationCALCULUS AB/BC SUMMER REVIEW PACKET (Answers)
Name CALCULUS AB/BC SUMMER REVIEW PACKET (Answers) I. Simplify. Identify the zeros, vertical asymptotes, horizontal asymptotes, holes and sketch each rational function. Show the work that leads to your
More informationDIAGNOSTIC TESTS. (c) (sa sb )(sa sb )
DIAGNOSTIC TESTS Success in calculus depends to a large etent on knowledge of the mathematics that precedes calculus: algebra, analtic geometr, functions, and trigonometr. The following tests are intended
More information5. Zeros. We deduce that the graph crosses the x-axis at the points x = 0, 1, 2 and 4, and nowhere else. And that s exactly what we see in the graph.
. Zeros Eample 1. At the right we have drawn the graph of the polnomial = ( 1) ( 2) ( 4). Argue that the form of the algebraic formula allows ou to see right awa where the graph is above the -ais, where
More informationMathematics. Mathematics 2. hsn.uk.net. Higher HSN22000
hsn.uk.net Higher Mathematics UNIT Mathematics HSN000 This document was produced speciall for the HSN.uk.net website, and we require that an copies or derivative works attribute the work to Higher Still
More informationSystems of Linear Equations: Solving by Graphing
8.1 Sstems of Linear Equations: Solving b Graphing 8.1 OBJECTIVE 1. Find the solution(s) for a set of linear equations b graphing NOTE There is no other ordered pair that satisfies both equations. From
More informationMay 27, QUADRATICS.notebook. Apr 26 17:43. Apr 26 18:27. Apr 26 18:40. Apr 28 10:22. Apr 28 10:34. Apr 28 10:33. Starter
1. Factorise: 2 - - 6 2. Solve for : 2( + 1) = - 1 3. Factorise: 2-25 To solve quadratic equations.. Factorise: 2 2-8 5. State the gradient of the line: + 12 = 2 Apr 26 17:3 Apr 26 18:27 Solving Quadratic
More informationChapter 9 Vocabulary Check
9 CHAPTER 9 Eponential and Logarithmic Functions Find the inverse function of each one-to-one function. See Section 9.. 67. f = + 68. f = - CONCEPT EXTENSIONS The formula = 0 e kt gives the population
More information9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson
Chapter 9 Lesson 9-1 The Function with Equation = a BIG IDEA The graph of an quadratic function with equation = a, with a 0, is a parabola with verte at the origin. Vocabular parabola refl ection-smmetric
More informationAll work must be shown in this course for full credit. Unsupported answers may receive NO credit.
AP Calculus 6. Worksheet Da All work must be shown in this course for full credit. Unsupported answers ma receive NO credit. Indefinite Integrals: Remember the first step to evaluating an integral is to
More information*X100/301* X100/301 MATHEMATICS HIGHER. Units 1, 2 and 3 Paper 1 (Non-calculator) Read Carefully
X00/0 NATINAL QUALIFICATINS 007 TUESDAY, 5 MAY 9.00 AM 0.0 AM MATHEMATICS HIGHER Units, and Paper (Non-calculator) Read Carefull Calculators ma NT be used in this paper. Full credit will be given onl where
More informationMATRIX TRANSFORMATIONS
CHAPTER 5. MATRIX TRANSFORMATIONS INSTITIÚID TEICNEOLAÍOCHTA CHEATHARLACH INSTITUTE OF TECHNOLOGY CARLOW MATRIX TRANSFORMATIONS Matri Transformations Definition Let A and B be sets. A function f : A B
More informationNATIONAL QUALIFICATIONS
H Mathematics Higher Paper Practice Paper A Time allowed hour minutes NATIONAL QUALIFICATIONS Read carefull Calculators ma NOT be used in this paper. Section A Questions ( marks) Instructions for completion
More informationLimits 4: Continuity
Limits 4: Continuit 55 Limits 4: Continuit Model : Continuit I. II. III. IV. z V. VI. z a VII. VIII. IX. Construct Your Understanding Questions (to do in class). Which is the correct value of f (a) in
More informationMTH 3311 Test #1. order 3, linear. The highest order of derivative of y is 2. Furthermore, y and its derivatives are all raised to the
MTH 3311 Test #1 F 018 Pat Rossi Name Show CLEARLY how you arrive at your answers. 1. Classify the following according to order and linearity. If an equation is not linear, eplain why. (a) y + y y = 4
More informationSelf- assessment 1010 (Intermediate Algebra)
Self- assessment (Intermediate Algebra) If ou can work these problems using a scientific calculator, ou should have sufficient knowledge to demonstrate master of Intermediate Algebra and to succeed in
More information9.1.1 What else can I solve?
CCA Ch 9: Solving Quadratics and Inequalities Name Team # 9.1.1 What else can I solve? Solving Quadratic Equations 9-1. USE THE ZERO PRODUCT PROPERTY TO SOLVE FOR X. a. 9 3 2 4 6 b. 0 3 5 2 3 c. 2 6 0
More informationAnswers for the problems can be found at the end of this packet starting on Page 12.
MAC 0 Review for Final Eam The eam will consists of problems similar to the ones below. When preparing, focus on understanding and general procedures (when available) rather than specific question. Answers
More informationMathematics Extension 2
Student Number ABBOTSLEIGH AUGUST 007 YEAR ASSESSMENT 4 HIGHER SCHOOL CERTIFICATE TRIAL EXAMINATION Mathematics Etension General Instructions Reading time 5 minutes. Working time 3 hours. Write using blue
More informationNational 5 Mathematics
St Andrew s Academ Mathematics Department National 5 Mathematics UNIT 4 ASSESSMENT PREPARATION St Andrew's Academ Maths Dept 016-17 1 Practice Unit Assessment 4A for National 5 1. Simplif, giving our answer
More informationLesson 8.1 Secret Codes
Lesson 8. Secret Codes. Use this table to code each word. Input A B C D E F G H I J K L M Coded output M N O P Q R S T U V W X Y Input N O P Q R S T U V W X Y Z Coded output Z A B C D E F G H I J K L a.
More informationUNIVERSIDAD CARLOS III DE MADRID MATHEMATICS II EXERCISES (SOLUTIONS )
UNIVERSIDAD CARLOS III DE MADRID MATHEMATICS II EXERCISES (SOLUTIONS ) CHAPTER : Limits and continuit of functions in R n. -. Sketch the following subsets of R. Sketch their boundar and the interior. Stud
More informationMath 111 Final Exam Review KEY
Math Final Eam Review KEY. Use the graph of = f in Figure to answer the following. Approimate where necessar. a Evaluate f. f = 0 b Evaluate f0. f0 = 6 c Solve f = 0. =, =, =,or = 3 d Solve f = 7..5, 0.5,
More information2 nd Semester Final Exam Review Block Date
Algebra 1B Name nd Semester Final Eam Review Block Date Calculator NOT Allowed Graph each function. 1 (10-1) 1. (10-1). (10-1) 3. (10-1) 4. 3 Graph each function. Identif the verte, ais of smmetr, and
More informationIntegration Past Papers Unit 2 Outcome 2
Integration Past Papers Unit 2 utcome 2 Multiple Choice Questions Each correct answer in this section is worth two marks.. Evaluate A. 2 B. 7 6 C. 2 D. 2 4 /2 d. 2. The diagram shows the area bounded b
More informationExponential Growth - Classwork
Exponential Growth - Classwork Consider the statement The rate of change of some quantit is directl proportional to! $ This is like saing that the more mone ou have ( ), the faster it will grow # &, or
More information1. Radium has a half-life of 1600 years. How much radium will be left from a 1000-gram sample after 1600 years?
The Radioactive Deca Eperiment ACTIVITY 7 Learning Targets: Given a verbal description of a function, make a table and a graph of the function. Graph a function and identif and interpret ke features of
More informationAll work must be shown in this course for full credit. Unsupported answers may receive NO credit.
AP Calculus.1 Worksheet Day 1 All work must be shown in this course for full credit. Unsupported answers may receive NO credit. 1. The only way to guarantee the eistence of a it is to algebraically prove
More information* * MATHEMATICS (MEI) 4753/01 Methods for Advanced Mathematics (C3) ADVANCED GCE. Thursday 15 January 2009 Morning. Duration: 1 hour 30 minutes
ADVANCED GCE MATHEMATICS (MEI) 475/0 Methods for Advanced Mathematics (C) Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Eamination Formulae and Tables
More informationMathematics Paper 1 (Non-Calculator)
H National Qualifications CFE Higher Mathematics - Specimen Paper F Duration hour and 0 minutes Mathematics Paper (Non-Calculator) Total marks 60 Attempt ALL questions. You ma NOT use a calculator. Full
More informationAPPM 1360 Final Exam Spring 2016
APPM 36 Final Eam Spring 6. 8 points) State whether each of the following quantities converge or diverge. Eplain your reasoning. a) The sequence a, a, a 3,... where a n ln8n) lnn + ) n!) b) ln d c) arctan
More informationChapter 8 Notes SN AA U2C8
Chapter 8 Notes SN AA U2C8 Name Period Section 8-: Eploring Eponential Models Section 8-2: Properties of Eponential Functions In Chapter 7, we used properties of eponents to determine roots and some of
More information10.3 Solving Nonlinear Systems of Equations
60 CHAPTER 0 Conic Sections Identif whether each equation, when graphed, will be a parabola, circle, ellipse, or hperbola. Then graph each equation.. - 7 + - =. = +. = + + 6. + 9 =. 9-9 = 6. 6 - = 7. 6
More information9.1 The Square Root Function
Section 9.1 The Square Root Function 869 9.1 The Square Root Function In this section we turn our attention to the square root unction, the unction deined b the equation () =. (1) We begin the section
More informationCalculus AB Semester 1 Final Review
Name Period Calculus AB Semester Final Review. Eponential functions: (A) kg. of a radioactive substance decay to kg. after years. Find how much remains after years. (B) Different isotopes of the same element
More information2413 Exam 3 Review. 14t 2 Ë. dt. t 6 1 dt. 3z 2 12z 9 z 4 8 Ë. n 7 4,4. Short Answer. 1. Find the indefinite integral 9t 2 ˆ
3 Eam 3 Review Short Answer. Find the indefinite integral 9t ˆ t dt.. Find the indefinite integral of the following function and check the result by differentiation. 6t 5 t 6 dt 3. Find the indefinite
More informationMATH 2300 review problems for Exam 3 ANSWERS
MATH 300 review problems for Eam 3 ANSWERS. Check whether the following series converge or diverge. In each case, justif our answer b either computing the sum or b b showing which convergence test ou are
More information