Differentiating Functions & Expressions - Edexcel Past Exam Questions
|
|
- Scarlett Hicks
- 5 years ago
- Views:
Transcription
1 - Edecel Past Eam Questions. (a) Differentiate with respect to (i) sin + sec, (ii) { + ln ()} Given that y =, ¹, ( -) 8 (b) show that = ( -). (6) June 05 Q. f() = e ln, > 0. (a) Differentiate to find f (). The curve with equation y = f() has a turning point at P. The -coordinate of P is a. (b) Show that a = e a. 6 () June 05 Q4 æ ö. The point P lies on the curve with equation y = ln ç. The -coordinate of P is. è ø Find an equation of the normal to the curve at the point P in the form y = a + b, where a and b are constants. (5) Jan 06 Q
2 4. (a) Differentiate with respect to (i) e +, cos ( ) (ii). (b) Given that = 4 sin (y + 6), find in terms of. (5) Jan 06 Q4 5. Differentiate, with respect to, (a) e + ln, (b) (5 + ). June 06 Q 6. (a) Given that cos A =, where 70 < A < 60, find the eact value of sin A. (5) 4 æ p ö æ p ö (b) (i) Show that cos ç + + cos ç - º cos. è ø è ø Given that y = sin æ p ö æ p ö + cos ç + + cos ç -, è ø è ø (ii) show that = sin. June 06 Q8 7. (i) The curve C has equation y =. 9 + Use calculus to find the coordinates of the turning points of C. (6) (ii)given that y = ( + e ), find the value of at = ln. (5) Jan 07 Q4
3 8. O O P Figure Figure shows part of the curve with equation p y = ( ) tan, 0 <. 4 The curve has a minimum at the point P. The -coordinate of P is k. Show that k satisfies the equation 4k + sin 4k = 0. (6) June 06 Q f() =, > (a) Show that f () =. (7) - (b) Hence, or otherwise, find f () in its simplest form. June 07 Q 0. The curve C has equation = sin y. æ ö (a) Show that the point P ç Ö, p lies on C. () è 4 ø (b) Show that = at P. Ö (c) Find an equation of the normal to C at P. Give your answer in the form y = m + c, where m and c are eact constants. Jan 07 Q
4 . A curve C has equation y = e. (a) Find, using the product rule for differentiation. (b) Hence find the coordinates of the turning points of C. d y (c) Find. () (d) Determine the nature of each turning point of the curve C. () June 07 Q. A curve C has equation y = e p tan, (n + ). (a) Show that the turning points on C occur where tan = -. (6) (b) Find an equation of the tangent to C at the point where = 0. () Jan 08 Q. A curve C has equation The point A(0, 4) lies on C. y = sin + 4 cos, -π π. (a) Find an equation of the normal to the curve C at A. (5) p (b) Epress y in the form R sin( + α), where R > 0 and 0 < a <. Give the value of a to significant figures. (c) Find the coordinates of the points of intersection of the curve C with the -ais. Give your answers to decimal places. Jan 08 Q7
5 4. (a) Differentiate with respect to, (i) e (sin + cos ), (ii) ln (5 + ) Given that y =, ¹, ( + ) 0 (b) show that =. (5) ( + ) d y d y 5 (c) Hence find and the real values of for which =. 4 June 08 Q6 5. (a) Find the value of at the point where = on the curve with equation y = (5 ). (6) sin (b) Differentiate with respect to. Jan 09 Q f() = (a) Epress f() as a single fraction in its simplest form. (b) Hence show that f () = ( - ). Jan 09 Q æ ö 7. Find the equation of the tangent to the curve = cos (y + p) at ç0, p. è 4 ø Give your answer in the form y = a + b, where a and b are constants to be found. (6) Jan 09 Q4
6 8. The functions f and g are defined by f :! + ln, > 0, Î R,! g :, Î R. e (a) Write down the range of g. () (b) Show that the composite function fg is defined by fg :! +, Î R. () e (c) Write down the range of fg. () d (d) Solve the equation [ fg( ) ] = ( e + ). (6) Jan 09 Q5 9. f() = e. The curve with equation y = f() has a turning point P. (a) Find the eact coordinates of P. (5) 0. Rabbits were introduced onto an island. The number of rabbits, P, t years after they were introduced is modelled by the equation t 5 P = 80e, t Î R, t ³ 0. Jan 09 Q7 (a) Write down the number of rabbits that were introduced to the island. () (b) Find the number of years it would take for the number of rabbits to first eceed 000. () dp (c) Find. dt dp (d) Find P when = 50. dt () June 09 Q
7 . (i) Differentiate with respect to (a) cos, ln( + ) (b). + (ii) A curve C has the equation y = (4+), >, y > 0. 4 The point P on the curve has -coordinate. Find an equation of the tangent to C at P in the form a + by + c = 0, where a, b and c are integers. (6). The function f is defined by - 8 f() = +, Î R, 4,. ( + 4) ( - )( + 4) June 09 Q4 - (a) Show that f () =. - (5) The function g is defined by e - g() =, Î R, ln. e - e (b) Differentiate g() to show that g () = (e - ). (c) Find the eact values of for which g () = June 09 Q7. ln( +) (i) Given that y =, find. (ii) Given that = tan y, show that =. + (5) Jan 0 Q4
8 4. d(sec ) (a) By writing sec as, show that = sec tan. cos Given that y = e sec, (b) find. The curve with equation y = e p p sec, < <, has a minimum turning point at (a, b). 6 6 (c) Find the values of the constants a and b, giving your answers to significant figures. Jan 0 Q7 5. A curve C has equation 5 y =,. ( 5 - ) The point P on C has -coordinate. Find an equation of the normal to C at P in the form a + by + c = 0, where a, b and c are integers. (7) June 0 Q
9 6. Figure Figure shows a sketch of the curve C with the equation y = ( 5 + )e. (a) Find the coordinates of the point where C crosses the y-ais. () (b) Show that C crosses the -ais at = and find the -coordinate of the other point where C crosses the -ais. (c) Find. (d) Hence find the eact coordinates of the turning points of C. (5) June 0 Q5
10 7. (a) Epress 4 - ( -) ( -)( -) as a single fraction in its simplest form. Given that 4 - f() =, >, ( -) ( -)( -) (b) show that f() =. () - (c) Hence differentiate f() and find f (). Jan Q 8. The curve C has equation + sin y =. + cos (a) Show that 6sin + 4cos + = ( + cos ) p (b) Find an equation of the tangent to C at the point on C where =. Write your answer in the form y = a + b, where a and b are eact constants. Jan Q7
11 9. Figure Figure shows a sketch of part of the curve with equation y = f(), where f() = (8 ) ln, > 0. The curve cuts the -ais at the points A and B and has a maimum turning point at Q, as shown in Figure. (a) Write down the coordinates of A and the coordinates of B. () (b) Find f (). Jan Q5 0. Given that d (cos ) = sin, d (a) show that (sec ) = sec tan. Given that = sec y, (b) find in terms of y. () (c) Hence find in terms of. Jan Q8
12 . Differentiate with respect to (a) ln ( + + 5), cos (b). () June Q 4-5. f() =, ¹ ±, ¹. ( + )( - ) - 9 (a) Show that 5 f() =. (5) ( + )( + ) æ 5 ö The curve C has equation y = f (). The point P ç-, - lies on C. è ø (b) Find an equation of the normal to C at P. (8) June Q7. (a) Epress cos sin in the form R cos ( + a), where R and a are constants, R > 0 and p 0 < a <. Give your answers to significant figures. f() = e cos. (b) Show that f () can be written in the form f () = Re cos ( + a ), where R and a are the constants found in part (a). (5) (c) Hence, or otherwise, find the smallest positive value of for which the curve with equation y = f() has a turning point. June Q8
13 Differentiating functions
Paper Reference. Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes. Mathematical Formulae (Orange or Green)
Centre No. Candidate No. Paper Reference(s) 6665/01 Edecel GCE Core Mathematics C3 Advanced Thursday 11 June 009 Morning Time: 1 hour 30 minutes Materials required for eamination Mathematical Formulae
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 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 informationTrigonometry (Addition,Double Angle & R Formulae) - Edexcel Past Exam Questions. cos 2A º 1 2 sin 2 A. (2)
Trigonometry (Addition,Double Angle & R Formulae) - Edexcel Past Exam Questions. (a) Using the identity cos (A + B) º cos A cos B sin A sin B, rove that cos A º sin A. () (b) Show that sin q 3 cos q 3
More informationNOTICE TO CUSTOMER: The sale of this product is intended for use of the original purchaser only and for use only on a single computer system.
NOTICE TO CUSTOMER: The sale of this product is intended for use of the original purchaser only and for use only on a single computer system. Duplicating, selling, or otherwise distributing this product
More informationAP Calculus Summer 2017
AP Calculus Summer 017 Welcome to AP Calculus. I hope this course proves to be a challenging, yet rewarding endeavor for you. Calculus will be unlike any other math class you may have taken, filled with
More informationCircles - Edexcel Past Exam Questions. (a) the coordinates of A, (b) the radius of C,
- Edecel Past Eam Questions 1. The circle C, with centre at the point A, has equation 2 + 2 10 + 9 = 0. Find (a) the coordinates of A, (b) the radius of C, (2) (2) (c) the coordinates of the points at
More informationTime: 1 hour 30 minutes
Paper Reference(s) 6665/0 Edecel GCE Core Mathematics C3 Gold Level (Hard) G Time: hour 30 minutes Materials required for eamination Mathematical Formulae (Green) Items included with question papers Nil
More informationy x is symmetric with respect to which of the following?
AP Calculus Summer Assignment Name: Note: Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f () is a real number. Part : Multiple Choice Solve
More informationLimits and Continuity. 2 lim. x x x 3. lim x. lim. sinq. 5. Find the horizontal asymptote (s) of. Summer Packet AP Calculus BC Page 4
Limits and Continuity t+ 1. lim t - t + 4. lim x x x x + - 9-18 x-. lim x 0 4-x- x 4. sinq lim - q q 5. Find the horizontal asymptote (s) of 7x-18 f ( x) = x+ 8 Summer Packet AP Calculus BC Page 4 6. x
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 informationSolutionbank Edexcel AS and A Level Modular Mathematics
Page of Exercise A, Question The curve C, with equation y = x ln x, x > 0, has a stationary point P. Find, in terms of e, the coordinates of P. (7) y = x ln x, x > 0 Differentiate as a product: = x + x
More informationMath 231 Final Exam Review
Math Final Eam Review Find the equation of the line tangent to the curve 4y y at the point (, ) Find the slope of the normal line to y ) ( e at the point (,) dy Find d if cos( y) y 4 y 4 Find the eact
More information( ) - 4(x -3) ( ) 3 (2x -3) - (2x +12) ( x -1) 2 x -1) 2 (3x -1) - 2(x -1) Section 1: Algebra Review. Welcome to AP Calculus!
Welcome to AP Calculus! Successful Calculus students must have a strong foundation in algebra and trigonometry. The following packet was designed to help you review your algebra skills in preparation for
More informationC3 Revision Questions. (using questions from January 2006, January 2007, January 2008 and January 2009)
C3 Revision Questions (using questions from January 2006, January 2007, January 2008 and January 2009) 1 2 1. f(x) = 1 3 x 2 + 3, x 2. 2 ( x 2) (a) 2 x x 1 Show that f(x) =, x 2. 2 ( x 2) (4) (b) Show
More information(i) find the points where f(x) is discontinuous, and classify each point of discontinuity.
Math Final Eam - Practice Problems. A function f is graphed below. f() 5 4 8 7 5 4 4 5 7 8 4 5 (a) Find f(0), f( ), f(), and f(4) Find the domain and range of f (c) Find the intervals where f () is positive
More informationCore Mathematics C3 Advanced Level
Paper Reference(s) 666/0 Edecel GCE Core Mathematics C Advanced Level Wednesda 0 Januar 00 Afternoon Time: hour 0 minutes Materials required for eamination Mathematical Formulae (Pink or Green) Items included
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 10 Conics, Parametric Equations, and Polar Coordinates Conics and Calculus
Chapter 10 Conics, Parametric Equations, and Polar Coordinates 10.1 Conics and Calculus 1. Parabola A parabola is the set of all points x, y ( ) that are equidistant from a fixed line and a fixed point
More informationMath 144 Activity #7 Trigonometric Identities
144 p 1 Math 144 Activity #7 Trigonometric Identities What is a trigonometric identity? Trigonometric identities are equalities that involve trigonometric functions that are true for every single value
More informationIntegration Techniques for the AB exam
For the AB eam, students need to: determine antiderivatives of the basic functions calculate antiderivatives of functions using u-substitution use algebraic manipulation to rewrite the integrand prior
More informationA2 MATHEMATICS HOMEWORK C3
Name Teacher A2 MATHEMATICS HOMEWORK C3 Mathematics Department September 2016 Version 1 Contents Contents... 2 Introduction... 3 Week 1 Trigonometric Equations 1... 4 Week 2 Trigonometric Equations 2...
More informationC3 papers June 2007 to 2008
physicsandmathstutor.com June 007 C3 papers June 007 to 008 1. Find the exact solutions to the equations (a) ln x + ln 3 = ln 6, (b) e x + 3e x = 4. *N6109A04* physicsandmathstutor.com June 007 x + 3 9+
More informationKey- Math 231 Final Exam Review
Key- Math Final Eam Review Find the equation of the line tangent to the curve y y at the point (, ) y-=(-/)(-) Find the slope of the normal line to y ) ( e at the point (,) dy Find d if cos( y) y y (ysiny+y)/(-siny-y^-^)
More informationBook 4. June 2013 June 2014 June Name :
Book 4 June 2013 June 2014 June 2015 Name : June 2013 1. Given that 4 3 2 2 ax bx c 2 2 3x 2x 5x 4 dxe x 4 x 4, x 2 find the values of the constants a, b, c, d and e. 2. Given that f(x) = ln x, x > 0 sketch
More informationF O R SOCI AL WORK RESE ARCH
7 TH EUROPE AN CONFERENCE F O R SOCI AL WORK RESE ARCH C h a l l e n g e s i n s o c i a l w o r k r e s e a r c h c o n f l i c t s, b a r r i e r s a n d p o s s i b i l i t i e s i n r e l a t i o n
More informationEdexcel past paper questions. Core Mathematics 4. Parametric Equations
Edexcel past paper questions Core Mathematics 4 Parametric Equations Edited by: K V Kumaran Email: kvkumaran@gmail.com C4 Maths Parametric equations Page 1 Co-ordinate Geometry A parametric equation of
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 informationThe Fundamental Theorem of Calculus Part 3
The Fundamental Theorem of Calculus Part FTC Part Worksheet 5: Basic Rules, Initial Value Problems, Rewriting Integrands A. It s time to find anti-derivatives algebraically. Instead of saying the anti-derivative
More informationIntegration Techniques for the AB exam
For the AB eam, students need to: determine antiderivatives of the basic functions calculate antiderivatives of functions using u-substitution use algebraic manipulation to rewrite the integrand prior
More informationPreCalculus First Semester Exam Review
PreCalculus First Semester Eam Review Name You may turn in this eam review for % bonus on your eam if all work is shown (correctly) and answers are correct. Please show work NEATLY and bo in or circle
More informationMHF 4UI - Final Examination Review
MHF 4UI - Final Eamination Review Jan 08. If 0, find the possible measure of. tan = cos = (c) sin = 0 (d) cos =. For each function, state the amplitude, period, phase shift, vertical translation, and sketch
More informationH2 Mathematics 2017 Promotion Exam Paper 1 Question (VJC Answer all questions [100 marks]. By using an algebraic approach, solve. 3 x.
H Mathematics 07 Promotion Eam Paper Question (VJC Answer all questions [00 marks]. By using an algebraic approach, solve 0. [] Verify that = 5 i is a root of the equation + 9 9 = 0. Hence, without the
More informationTechnical Calculus I Homework. Instructions
Technical Calculus I Homework Instructions 1. Each assignment is to be done on one or more pieces of regular-sized notebook paper. 2. Your name and the assignment number should appear at the top of the
More informationv ( t ) = 5t 8, 0 t 3
Use the Fundamental Theorem of Calculus to evaluate the integral. 27 d 8 2 Use the Fundamental Theorem of Calculus to evaluate the integral. 6 cos d 6 The area of the region that lies to the right of the
More informationTopic 6: Calculus Integration Markscheme 6.10 Area Under Curve Paper 2
Topic 6: Calculus Integration Markscheme 6. Area Under Curve Paper. (a). N Standard Level (b) (i). N (ii).59 N (c) q p f ( ) = 9.96 N split into two regions, make the area below the -ais positive RR N
More informationMATH140 Exam 2 - Sample Test 1 Detailed Solutions
www.liontutors.com 1. D. reate a first derivative number line MATH140 Eam - Sample Test 1 Detailed Solutions cos -1 0 cos -1 cos 1 cos 1/ p + æp ö p æp ö ç è 4 ø ç è ø.. reate a second derivative number
More informationG r a d e 1 1 P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Final Practice Exam Answer Key
G r a d e P r e - C a l c u l u s M a t h e m a t i c s ( 3 0 S ) Final Practice Eam Answer Key G r a d e P r e - C a l c u l u s M a t h e m a t i c s Final Practice Eam Answer Key Name: Student Number:
More informationC) 2 D) 4 E) 6. ? A) 0 B) 1 C) 1 D) The limit does not exist.
. The asymptotes of the graph of the parametric equations = t, y = t t + are A) =, y = B) = only C) =, y = D) = only E) =, y =. What are the coordinates of the inflection point on the graph of y = ( +
More informationA2 MATHEMATICS HOMEWORK C3
Name Teacher A2 MATHEMATICS HOMEWORK C3 Mathematics Department September 2014 Version 1.1 Contents Contents... 2 Introduction... 3 HW1 Algebraic Fractions... 4 HW2 Mappings and Functions... 6 HW3 The Modulus
More informationand 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 informationCalculus Summer TUTORIAL
Calculus Summer TUTORIAL The purpose of this tutorial is to have you practice the mathematical skills necessary to be successful in Calculus. All of the skills covered in this tutorial are from Pre-Calculus,
More informationThe Definite Integral. Day 5 The Fundamental Theorem of Calculus (Evaluative Part)
The Definite Integral Day 5 The Fundamental Theorem of Calculus (Evaluative Part) Practice with Properties of Integrals 5 Given f d 5 f d 3. 0 5 5. 0 5 5 3. 0 0. 5 f d 0 f d f d f d - 0 8 5 F 3 t dt
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 information2. Jan 2010 qu June 2009 qu.8
C3 Functions. June 200 qu.9 The functions f and g are defined for all real values of b f() = 4 2 2 and g() = a + b, where a and b are non-zero constants. (i) Find the range of f. [3] Eplain wh the function
More informationName Class. 5. Find the particular solution to given the general solution y C cos x and the. x 2 y
10 Differential Equations Test Form A 1. Find the general solution to the first order differential equation: y 1 yy 0. 1 (a) (b) ln y 1 y ln y 1 C y y C y 1 C y 1 y C. Find the general solution to the
More information2 nd ORDER O.D.E.s SUBSTITUTIONS
nd ORDER O.D.E.s SUBSTITUTIONS Question 1 (***+) d y y 8y + 16y = d d d, y 0, Find the general solution of the above differential equation by using the transformation equation t = y. Give the answer in
More information1. Solve for x and express your answers on a number line and in the indicated notation: 2
PreCalculus Honors Final Eam Review Packet June 08 This acket rovides a selection of review roblems to hel reare you for the final eam. In addition to the roblems in this acket, you should also redo all
More information6675/01 Edexcel GCE Pure Mathematics P5 Further Mathematics FP2 Advanced/Advanced Subsidiary
6675/1 Edecel GCE Pure Mathematics P5 Further Mathematics FP Advanced/Advanced Subsidiary Monday June 5 Morning Time: 1 hour 3 minutes 1 1. (a) Find d. (1 4 ) (b) Find, to 3 decimal places, the value of.3
More informationEdexcel Core Mathematics 4 Parametric equations.
Edexcel Core Mathematics 4 Parametric equations. Edited by: K V Kumaran kumarmaths.weebly.com 1 Co-ordinate Geometry A parametric equation of a curve is one which does not give the relationship between
More informationMATH 175: Final Exam Review for Pre-calculus
MATH 75: Final Eam Review for Pre-calculus In order to prepare for the final eam, you need too be able to work problems involving the following topics:. Can you graph rational functions by hand after algebraically
More informationAnswers for NSSH exam paper 2 type of questions, based on the syllabus part 2 (includes 16)
Answers for NSSH eam paper type of questions, based on the syllabus part (includes 6) Section Integration dy 6 6. (a) Integrate with respect to : d y c ( )d or d The curve passes through P(,) so = 6/ +
More informationEdexcel GCE A Level Maths. Further Maths 3 Coordinate Systems
Edecel GCE A Level Maths Further Maths 3 Coordinate Sstems Edited b: K V Kumaran kumarmaths.weebl.com 1 kumarmaths.weebl.com kumarmaths.weebl.com 3 kumarmaths.weebl.com 4 kumarmaths.weebl.com 5 1. An ellipse
More informationMath Exam 1a. c) lim tan( 3x. 2) Calculate the derivatives of the following. DON'T SIMPLIFY! d) s = t t 3t
Math 111 - Eam 1a 1) Evaluate the following limits: 7 3 1 4 36 a) lim b) lim 5 1 3 6 + 4 c) lim tan( 3 ) + d) lim ( ) 100 1+ h 1 h 0 h ) Calculate the derivatives of the following. DON'T SIMPLIFY! a) y
More information* Circle these problems: 23-27, 37, 40-44, 48, No Calculator!
AdvPreCal 1 st Semester Final Eam Review Name 1. Solve using interval notation: 7 8 * Circle these problems: -7, 7, 0-, 8, 6-66 No Calculator!. Solve and graph: 0. Solve using a number line and leave answer
More informationTime: 1 hour 30 minutes
Paper Reference(s) 6665/0 Edecel GCE Core Mathematics C3 Bronze Level B Time: hour 30 minutes Materials required for eamination papers Mathematical Formulae (Green) Items included with question Nil Candidates
More informationM 408 K Fall 2005 Inverse Trig Functions Important Decimal Approximations and Useful Trig Identities Decimal Approximations: p
M 408 K Fall 005 Inverse Trig Fnctions Imortant Decimal Aroimations an Usefl Trig Ientities Decimal Aroimations: 0 0000 0 0 0000 054 0500 6 0577 ( æ ö ç ø è 4 0785 0707 ; 0866 047 4 000 57 6 55 094 8 44
More information2. Find the value of y for which the line through A and B has the given slope m: A(-2, 3), B(4, y), 2 3
. Find an equation for the line that contains the points (, -) and (6, 9).. Find the value of y for which the line through A and B has the given slope m: A(-, ), B(4, y), m.. Find an equation for the line
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 informationMath 170 Calculus I Final Exam Review Solutions
Math 70 Calculus I Final Eam Review Solutions. Find the following its: (a (b (c (d 3 = + = 6 + 5 = 3 + 0 3 4 = sin( (e 0 cos( = (f 0 ln(sin( ln(tan( = ln( (g (h 0 + cot( ln( = sin(π/ = π. Find any values
More informationSolutionbank C2 Edexcel Modular Mathematics for AS and A-Level
file://c:\users\buba\kaz\ouba\c_rev_a_.html Eercise A, Question Epand and simplify ( ) 5. ( ) 5 = + 5 ( ) + 0 ( ) + 0 ( ) + 5 ( ) + ( ) 5 = 5 + 0 0 + 5 5 Compare ( + ) n with ( ) n. Replace n by 5 and
More informationCreated by T. Madas. Candidates may use any calculator allowed by the regulations of this examination.
IYGB GCE Mathematics MP Advanced Level Practice Paper N Difficulty Rating: 3.550/.68 Time: hours Candidates may use any calculator allowed by the regulations of this eamination. Information for Candidates
More informationCalculus B Exam III (Page 1) May 11, 2012
Calculus B Eam III (Page ) May, 0 Name: Instructions: Provide all steps necessary to solve the problem. Unless otherwise stated, your answer must be eact and reasonably simplified. Additionally, clearly
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 informationDirections: Please read questions carefully. It is recommended that you do the Short Answer Section prior to doing the Multiple Choice.
AP Calculus AB SUMMER ASSIGNMENT Multiple Choice Section Directions: Please read questions carefully It is recommended that you do the Short Answer Section prior to doing the Multiple Choice Show all work
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 informationSolutions Exam 4 (Applications of Differentiation) 1. a. Applying the Quotient Rule we compute the derivative function of f as follows:
MAT 4 Solutions Eam 4 (Applications of Differentiation) a Applying the Quotient Rule we compute the derivative function of f as follows: f () = 43 e 4 e (e ) = 43 4 e = 3 (4 ) e Hence f '( ) 0 for = 0
More informationName Please print your name as it appears on the class roster.
Berkele Cit College Practice Problems Math 1 Precalculus - Final Eam Preparation Name Please print our name as it appears on the class roster. SHORT ANSWER. Write the word or phrase that best completes
More informationAll work must be shown in this course for full credit. Unsupported answers may receive NO credit.
AP Calculus 5. Worksheet All work must be shown in this course for full credit. Unsupported answers may receive NO credit.. Suppose an oil pump is producing 8 gallons per hour for the first 5 hours of
More informatione x for x 0. Find the coordinates of the point of inflexion and justify that it is a point of inflexion. (Total 7 marks)
Chapter 0 Application of differential calculus 014 GDC required 1. Consider the curve with equation f () = e for 0. Find the coordinates of the point of infleion and justify that it is a point of infleion.
More informationDepartment of Mathematical Sciences. Math 226 Calculus Spring 2016 Exam 2V2 DO NOT TURN OVER THIS PAGE UNTIL INSTRUCTED TO DO SO
Department of Mathematical Sciences Math 6 Calculus Spring 6 Eam V DO NOT TURN OVER THIS PAGE UNTIL INSTRUCTED TO DO SO NAME (Printed): INSTRUCTOR: SECTION NO.: When instructed, turn over this cover page
More informationNO CALCULATORS: 1. Find A) 1 B) 0 C) D) 2. Find the points of discontinuity of the function y of discontinuity.
AP CALCULUS BC NO CALCULATORS: MIDTERM REVIEW. Find lim 7 7 9. B) C) D). Find the points of discontinuit of the function of discontinuit. 9. For each discontinuit identif the tpe A. Removable discontinuit
More information1 Exam 1 Spring 2007.
Exam Spring 2007.. An object is moving along a line. At each time t, its velocity v(t is given by v(t = t 2 2 t 3. Find the total distance traveled by the object from time t = to time t = 5. 2. Use the
More informationDUNMAN HIGH SCHOOL Preliminary Examination Year 6
Name: Inde Number: Class: DUNMAN HIGH SCHOOL Preliminary Eamination Year 6 MATHEMATICS (Higher ) 970/0 Paper 7 September 05 Additional Materials: Answer Paper Graph paper List of Formulae (MF5) 3 hours
More informationMATH section 3.1 Maximum and Minimum Values Page 1 of 7
MATH section. Maimum and Minimum Values Page of 7 Definition : Let c be a number in the domain D of a function f. Then c ) is the Absolute maimum value of f on D if ) c f() for all in D. Absolute minimum
More informationRecurring Decimals. Mathswatch. Clip ) a) Convert the recurring decimal 036. to a fraction in its simplest form.
Clip Recurring Decimals ) a) Convert the recurring decimal 06. to a fraction in its simplest form. 8 b) Prove that the recurring decimal 07. = ) a) Change 4 9 to a decimal. 9 b) Prove that the recurring
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 informationQuestions Q1. The function f is defined by. (a) Show that (5) The function g is defined by. (b) Differentiate g(x) to show that g '(x) = (3)
Questions Q1. The function f is defined by (a) Show that The function g is defined by (b) Differentiate g(x) to show that g '(x) = (c) Find the exact values of x for which g '(x) = 1 (Total 12 marks) Q2.
More informationAP CALCULUS BC SUMMER ASSIGNMENT
AP CALCULUS BC SUMMER ASSIGNMENT Dear BC Calculus Student, Congratulations on your wisdom in taking the BC course! We know you will find it rewarding and a great way to spend your junior/senior year. This
More informationFP1 PAST EXAM QUESTIONS ON NUMERICAL METHODS: NEWTON-RAPHSON ONLY
FP PAST EXAM QUESTIONS ON NUMERICAL METHODS: NEWTON-RAPHSON ONLY A number of questions demand that you know derivatives of functions now not included in FP. Just look up the derivatives in the mark scheme,
More informationMath 171 Calculus I Spring, 2019 Practice Questions for Exam II 1
Math 171 Calculus I Spring, 2019 Practice Questions for Eam II 1 You can check your answers in WebWork. Full solutions in WW available Sunday evening. Problem 1. Find the average rate of change of the
More informationMATH 175: Final Exam Review for Pre-calculus
MATH 75: Final Eam Review for Pre-calculus In order to prepare for the final eam, you need to be able to work problems involving the following topics:. Can you find and simplify the composition of two
More informationAP Calc Summer Packet #1 Non-Calculator
This packet is a review of the prerequisite concepts for AP Calculus. It is to be done NEATLY and on a SEPARATE sheet of paper. All problems are to be done WITHOUT a graphing calculator. Points will be
More informationSTRATHFIELD GIRLS HIGH SCHOOL TRIAL HIGHER SCHOOL CERTIFICATE MATHEMATICS. Time allowed Three hours (Plus 5 minutes reading time)
STRATHFIELD GIRLS HIGH SCHOOL TRIAL HIGHER SCHOOL CERTIFICATE 00 MATHEMATICS Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of
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 information5 Find an equation of the circle in which AB is a diameter in each case. a A (1, 2) B (3, 2) b A ( 7, 2) B (1, 8) c A (1, 1) B (4, 0)
C2 CRDINATE GEMETRY Worksheet A 1 Write down an equation of the circle with the given centre and radius in each case. a centre (0, 0) radius 5 b centre (1, 3) radius 2 c centre (4, 6) radius 1 1 d centre
More informationJuan Juan Salon. EH National Bank. Sandwich Shop Nail Design. OSKA Beverly. Chase Bank. Marina Rinaldi. Orogold. Mariposa.
( ) X é X é Q Ó / 8 ( ) Q / ( ) ( ) : ( ) : 44-3-8999 433 4 z 78-19 941, #115 Z 385-194 77-51 76-51 74-7777, 75-5 47-55 74-8141 74-5115 78-3344 73-3 14 81-4 86-784 78-33 551-888 j 48-4 61-35 z/ zz / 138
More informationCALCULUS: Graphical,Numerical,Algebraic by Finney,Demana,Watts and Kennedy Chapter 3: Derivatives 3.3: Derivative of a function pg.
CALCULUS: Graphical,Numerical,Algebraic b Finne,Demana,Watts and Kenned Chapter : Derivatives.: Derivative of a function pg. 116-16 What ou'll Learn About How to find the derivative of: Functions with
More informationabc Mathematics Pure Core General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES
abc General Certificate of Education Mathematics Pure Core SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER MATHEMATICS
More informationCALCULUS BASIC SUMMER REVIEW
NAME CALCULUS BASIC SUMMER REVIEW Slope of a non vertical line: rise y y y m run Point Slope Equation: y y m( ) The slope is m and a point on your line is, ). ( y Slope-Intercept Equation: y m b slope=
More informationSolve Quadratics Using the Formula
Clip 6 Solve Quadratics Using the Formula a + b + c = 0, = b± b 4 ac a ) Solve the equation + 4 + = 0 Give our answers correct to decimal places. ) Solve the equation + 8 + 6 = 0 ) Solve the equation =
More information(a) Show that (5) The function f is defined by. (b) Differentiate g(x) to show that g '(x) = (3) (c) Find the exact values of x for which g '(x) = 1
Q1. The function f is defined by (a) Show that (5) The function g is defined by (b) Differentiate g(x) to show that g '(x) = (c) Find the exact values of x for which g '(x) = 1 (Total 12 marks) Q2. (a)
More information( + ) 3. AP Calculus BC Chapter 6 AP Exam Problems. Antiderivatives. + + x + C. 2. If the second derivative of f is given by f ( x) = 2x cosx
Chapter 6 AP Eam Problems Antiderivatives. ( ) + d = ( + ) + 5 + + 5 ( + ) 6 ( + ). If the second derivative of f is given by f ( ) = cos, which of the following could be f( )? + cos + cos + + cos + sin
More informationCalculus 1 - Lab ) f(x) = 1 x. 3.8) f(x) = arcsin( x+1., prove the equality cosh 2 x sinh 2 x = 1. Calculus 1 - Lab ) lim. 2.
) Solve the following inequalities.) ++.) 4 >.) Calculus - Lab { + > + 5 + < +. ) Graph the functions f() =, g() = + +, h() = cos( ), r() = +. ) Find the domain of the following functions.) f() = +.) f()
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 000 MATHEMATICS /3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of equal
More informationC3 PAPER JUNE 2014 *P43164A0232* 1. The curve C has equation y = f (x) where + 1. (a) Show that 9 f (x) = (3)
PMT C3 papers from 2014 and 2013 C3 PAPER JUNE 2014 1. The curve C has equation y = f (x) where 4x + 1 f( x) =, x 2 x > 2 (a) Show that 9 f (x) = ( x ) 2 2 Given that P is a point on C such that f (x)
More informationMATH 174: Numerical Analysis I. Math Division, IMSP, UPLB 1 st Sem AY
MATH 74: Numerical Analysis I Math Division, IMSP, UPLB st Sem AY 0809 Eample : Prepare a table or the unction e or in [0,]. The dierence between adjacent abscissas is h step size. What should be the step
More informationDIFFERENTIAL EQUATION. Contents. Theory Exercise Exercise Exercise Exercise
DIFFERENTIAL EQUATION Contents Topic Page No. Theor 0-0 Eercise - 04-0 Eercise - - Eercise - - 7 Eercise - 4 8-9 Answer Ke 0 - Sllabus Formation of ordinar differential equations, solution of homogeneous
More informationPaper Reference. Core Mathematics C3 Advanced. Wednesday 20 January 2010 Afternoon Time: 1 hour 30 minutes. Mathematical Formulae (Pink or Green)
Centre No. Candidate No. Surname Signature Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced Wednesday 20 January 2010 Afternoon Time: 1 hour 30 minutes Materials required for examination
More informationsin x (B) sin x 1 (C) sin x + 1
ANSWER KEY Packet # AP Calculus AB Eam Multiple Choice Questions Answers are on the last page. NO CALCULATOR MAY BE USED IN THIS PART OF THE EXAMINATION. On the AP Eam, you will have minutes to answer
More information