2016 HSC Mathematics Marking Guidelines
|
|
- Louise Marcia Horn
- 6 years ago
- Views:
Transcription
1 06 HSC Mathematics Marking Guidelines Section I Multiple-choice Answer Key Question Answer B C 3 B 4 A 5 B 6 A 7 A 8 D 9 C 0 D
2 Section II Question (a) Provides correct sketch Identifies radius, or equivalent merit Question (b) Provides correct derivative Attempts to use quotient rule, or equivalent merit d x + (3x 4 )() (x + )( 3) dx 3x 4 (3x 4) 3x 4 3x 6 (3x 4) 0 (3x 4)
3 Question (c) Establishes that x 5, or equivalent merit x 3 3 x 3 x 5 Question (d) Correct primitive, or equivalent merit ( x + ) 3 dx 0 4 ( x + )4 8 ( 3)4 8 ()
4 Question (e) Provides correct solution 3 Obtains x x 8 0 and solves for x, or equivalent merit Attempts to eliminate x or y, or equivalent merit 5 4x 3 x x x x 8 0 (x 4)(x + ) 0 x 4 or Subst x 4 into y 5 4(4) Subst x into y 5 4( ) 3 points of intersection are (4, ) and (,3). Question (f) π Obtains sec, or equivalent merit 8 y tan x dy sec x dx π dy π When x, sec 8 dx 8 π cos 8.7 Gradient of tangent is.7. 4
5 Question (g) Obtains one correct answer, or equivalent merit x sin for 0 x π Note x 0 π x π 5π, 6 6 π 5π x, 3 3 Question (a) (i) Obtains correct slope, or equivalent merit y 4 4 x 6 y 4 3 x 4 4( y 4) 3(x ) 4y 6 3x + 6 3x + 4y 0 5
6 Question (a) (ii) Attempts to calculate perpendicular distance of a point from a line, or equivalent merit BC :3x + 4y 0 3 ()+ 40 ( ) AD Question (a) (iii) Finds distance from B to C, or equivalent merit BC ( 6) + ( 4 ) Area ABC square units 6
7 Question (b) (i) Provides correct explanation BOA x CBO x ( s opposite equal sides in ABO) (exterior of ABO equal to sum of two opposite interior s) Question (b) (ii) Attempts to use the fact that triangle OBC is isosceles, or equivalent merit OC OB (radii) BCO CBO ( s opposite equal sides in CBO) x Then COD CAO + BCO (exterior of CAO equals sum of two opposite interior s) 87 x + x 87 3x x 9 7
8 Question (c) Provides correct solution 3 Substitutes correctly into cosine rule, and finds angle or equivalent merit Identifies the complementary angle to θ, or equivalent merit cosα α 0.77 θ 69 to nearest degree. Question (d) (i) Provides correct derivative 3x y xe dy dx 3x 3xe 3x + e 3x e ( + 3x) 8
9 Question (d) (ii) Attempts to use part (i) or equivalent merit Find exact value of 0 3x e (3 + 9x)dx e 3x 3x (3 + 9x )dx 3e ( + 3x)dx x 3 xe 3x e ( + 3x)dx 0 ( ) ( 0e 0 ) 3 e 6 6e 6 9
10 Question 3 (a) (i) Provides correct solution 4 Finds the x-values at which the stationary points occur and verifies the 3 maximum turning point, or equivalent merit Finds the x-values at which the stationary points occur, or equivalent merit Attempts to solve dy dx 0, or equivalent merit 4 y 4x 3 x Find stationary points and determine nature. dy x 4x 3 dx dy Need 0 x 4x 3 0 dx when x 0 y 0 when x 3 y 7 4x (3 x) 0 when x 0or x 3. Checking the gradients for x 0, x y +ve 0 +ve horizontal point of inflexion at x 0, ie at (0, 0) x 3, x y +ve 0 ve local maximum at x 3, ie at (3, 7) 0
11 Question 3 (a) (ii) Correct solution Locates the stationary points on the sketch of the curve, or equivalent merit Question 3 (b) (i) Attempts to complete the square, or equivalent merit x 4x y + 8 x 4x + 4 y + x 4x + 4 (y + ) (x ) 43 ( )(y + ) focal length 3
12 Question 3 (b) (ii) Provides correct solution focus (,) Question 3 (c) (i) Provides correct answer A 0 Question 3 (c) (ii) Obtains 5 0e 63k, or equivalent merit kt M() t 0e M (63) 5 63k 5 0e 63k e 63k log e log e k
13 Question 3 (d) Provides correct solution 3 Finds the area under the cosine curve, or equivalent merit Finds the area under y x, or equivalent merit π Area cos x dx π sin x π π sin sin 0 π π 4 square units π or 8 π π Question 4 (a) Provides correct solution 3 Attempts to find a difference in areas or equivalent merit Applies Simpson s Rule to the existing heights or equivalent merit The increase in area can be approximated using Simpson s Rule. 3
14 Question 4 (b) (i) Obtains a correct expression for A, or equivalent merit A A A 0.65 A ( ) Question 4 (b) (ii) Provides correct solution A A 0.65 n (0.65 n n + +) n A 0.65 n n ( 0.65 n ) S n 0.35 ( 0.65 n ) 0.35 Question 4 (b) (iii) Provides correct answer ( ) A
15 Question 4 (c) (i) Provides correct solution If w is the total width then Area 70 x w 70 w x Perimeter 5 x + w 70 5x + x Question 4 (c) (ii) Provides correct solution 3 Finds length at stationary point, or equivalent merit d Finds, or equivalent merit dx Stationary points occur when dl 0 dx 70 5 x 70 5 x x 44 x (x is length so ignore ) d 440 dx x 3 d 440 at x > 0 dx 3 so minimum at x
16 Question 4 (d) Sums the series, or equivalent merit + x + x + x 3 x + x 4 a, r x x x 5 for x x x 5 lim lim + x + x + x 3 + x 4 x x x 5 5 Question 4 (e) Expresses terms involving powers of, or equivalent merit log + log4 + log8 + + log5 log + log + log log 9 log + log + 3log + 9log 9 (log + 9log ) 9 0log 45log 6
17 Question 5 (a) Provides correct solution 4 Evaluates the correct integral for the volume when C is revolved, or equivalent merit Recognises the sum of two volumes is required and makes progress with both, or equivalent merit Attempts to find a volume using integration, or equivalent merit Volume of C rotated: 4 V π 3 3 6π 3 3 Volume of C rotated: 3 0 V π y dx 3 x π 4 dx 9 0 x 3 3 4π x 7 0 4π π 6π V + 8π 3 40π 3 7
18 Question 5 (b) (i) Provides correct tree diagram, or equivalent merit 7 7 P (game ends before 4th roll) Alternative solution: P (ends after roll) 8 7 P (ends after rolls) P (ends after 3 rolls) P (ends before 4th roll)
19 Question 5 (b) (ii) Provides correct solution 3 Finds an equation or inequality of probabilities that can be solved for n, or equivalent merit Finds, as a series, the probability that the game ends before the nth roll, or equivalent merit P (ends before nth roll) n n n n 8 7 n 3 Let n (n ) log log 8 4 log n + 4 log For probability of more than, we require n 4 9
20 Question 5 (c) (i) Identifies one pair of equal angles, giving reason(s) In s FCB, BAT FCB BAT (both 90 angles in square ABCD) Now AB DC (opposite sides of a square) CFB ABT (alternate s, AB DC ) FCB BAT ( pairs of equal s). Question 5 (c) (ii) Shows that TAS and BAE are complementary, or equivalent merit TSA BAD AEB 90 TAS + BAE 90 ( sum, straight line SAE) ABE + BAE 90 ( sum ABE) TAS ABE In s TSA, AEB TAS ABE (above) TSA AEB 90 (given) TSA AEB ( pairs of equal s). 0
21 Question 5 (c) (iii) Obtains AT, or equivalent merit x TS TA (matching sides in similar s) AE AB h TA y h y.ta TA BA Also (matching sides in similar s) BC FC TA x TA x Hence h y x y h x Question 6 (a) (i) Provides correct answer When t 0 4 v 0 +
22 Question 6 (a) (ii) Finds the value of t for which v 0, or equivalent merit The particle is stationary when v 0. 4 So v 0 0 t + 4 t + 4 (t + ) 4 t + t t So particle is stationary when t. dv acceleration dt dv 4(t + ) dt 4 (t + ) dv 4 4 when t dt ( + ) 4 acceleration is ms when particle is stationary.
23 Question 6 (a) (iii) Provides correct graph Describes the behaviour of v for large t, or equivalent merit 4 As t, 0 t + v 3
24 Question 6 (a) (iv) Provides correct solution 3 7 Correctly evaluates vdt, or equivalent merit Recognises the particle changes direction at t, or equivalent merit Particle changes direction when t travelling in negative direction for 0 t <, so 7 Distance travelled vdt + vdt dt + dt t + t [t 4log(t + )] + [t 4log(t + 0 )] ( 4log 0 + 4log) + (4 4log8 + 4log) + 4log + 4 4log8 + 4log 0 + 8log 4log 3 ( 0 + 8log log) ( 0 4log) 4
25 Question 6 (b) (i) Attempts to find dy dt, or equivalent merit y 00 ( + 9e 0.5t ) dy Rate of growth dt 0.5t 0.5t 9e 00 ( + 9e ) 900 e 0.5t ( ) + 9e 0.5t Question 6 (b) (ii) Provides correct solution with justification Provides range, or equivalent merit dy All terms in are positive so y is increasing. dt 00 when t 0 y so y 0 for t 0. As t e 0.5t 0 00 so y hence 0 y < 00. 5
26 Question 6 (b) (iii) Provides correct solution y ( y) t + 9e ) + 9e 0.5t ( e 0.5t + 9e + e 0.5t ( 0.5t ) 9 900e 0.5t ( + 9e 0.5t ) dy dt Question 6 (b) (iv) Recognises the importance of the vertex of the parabola in part (iii), or equivalent merit dy y (00 y) dt y y 400 which is a quadratic in y with roots at y 0 and y 00. Since the coefficient of y is negative, the quadratic has a max at y 00. Population growing fastest when population is y 00. 6
27 06 HSC Mathematics Mapping Grid Section I Question Content Syllabus outcomes 4. P5 3. H5 3 9., 9.5 P P4 5.5, 3.5 H H H5 8., 3. H5 9.,. H8 0. H3 Section II Question Content Syllabus outcomes (a) 4.3 P5 (b) 8.9 P7 (c). P3 (d). H5 (e) 3.4, 6.3, 9. P4 (f)., 8.4, 3.5 P6, H5 (g) 3., 3. H5 (a) (i) 6. P4 (a) (ii) 6.5 P4 (a) (iii).3, 6.5 P4 (b) (i).3 P4 (b) (ii).4 P4 (c) P4 (d) (i) 8.8,.4 H3, H5 (d) (ii). H3, H5 3 (a) (i) 4 0., 0.4 H6 3 (a) (ii) 0.5 H6 3 (b) (i).3, 9.5 P5 3 (b) (ii) 9.5 P5 3 (c) (i) 4. H4 3 (c) (ii) 4. H4, H5 7
28 Question Content Syllabus outcomes 3 (d) 3.4, 3.6 H8 4 (a) 3.3 H5, H8 4 (b) (i) 7.5 H4, H5 4 (b) (ii) 7.5 H4, H5 4 (b) (iii) 7.5 H4, H5 4 (c) (i) 0.6 H4, H5 4 (c) (ii) H4, H5 4 (d) 7., 8. P8, H5 4 (e) 7.,. H3, H5 5 (a) 4.4 H8 5 (b) (i) 3.3 H5 5 (b) (ii) 3 3.3, 7.,. H3, H5 5 (c) (i).3,.5 H5 5 (c) (ii).3,.5 H5 5 (c) (iii).3,.5 H5 6 (a) (i) 4.3 H4 6 (a) (ii) 4.3 H4, H5 6 (a) (iii) 4., 0.5 H4, H5, H6 6 (a) (iv) 3.5, 4.3 H4, H5 6 (b) (i).5, 4. H5 6 (b) (ii) 4.,.5 H5 6 (b) (iii).3, 4. H3 6 (b) (iv) 9.,.5, 4. H5, H7 8
2017 HSC Mathematics Marking Guidelines
07 HSC Mathematics Marking Guidelines Section I Multiple-choice Answer Key Question Answer A D 3 C 4 A 5 B 6 D 7 B 8 A 9 C 0 A NESA 07 HSC Mathematics Marking Guidelines Section II Question (a) Provides
More information2013 HSC Mathematics Extension 1 Marking Guidelines
03 HSC Mathematics Extension Marking Guidelines Section I Multiple-choice Answer Key Question Answer C D 3 C 4 D 5 A 6 B 7 A 8 D 9 B 0 C 03 HSC Mathematics Extension Marking Guidelines Section II Question
More information2014 HSC Mathematics Extension 2 Marking Guidelines
04 HSC Mathematics Extension Marking Guidelines Section I Multiple-choice Answer Key Question Answer D A 3 B 4 C 5 C 6 D 7 B 8 B 9 A 0 D BOSTES 04 HSC Mathematics Extension Marking Guidelines Section II
More informationMATHEMATICS. 24 July Section 1 10 marks (pages 3-7) Attempt Questions 1 10 Allow about 15 minutes for this section
MATHEMATICS 24 July 2017 General Instructions Reading time 5 minutes Working time 3 hours Write using black pen. NESA approved calculators may be used. Commence each new question in a new booklet. Write
More information2013 HSC Mathematics Extension 2 Marking Guidelines
3 HSC Mathematics Extension Marking Guidelines Section I Multiple-choice Answer Key Question Answer B A 3 D 4 A 5 B 6 D 7 C 8 C 9 B A 3 HSC Mathematics Extension Marking Guidelines Section II Question
More information2014 HSC Mathematics Extension 1 Marking Guidelines
04 HSC Mathematics Etension Marking Guidelines Section I Multiple-choice Answer Key Question Answer D A 3 C 4 D 5 B 6 B 7 A 8 D 9 C 0 C BOSTES 04 HSC Mathematics Etension Marking Guidelines Section II
More information2017 HSC Mathematics Extension 1 Marking Guidelines
07 HSC Mathematics Extension Marking Guidelines Section I Multiple-choice Answer Key Question Answer A B 3 B 4 C 5 D 6 D 7 A 8 C 9 C 0 B NESA 07 HSC Mathematics Extension Marking Guidelines Section II
More information2016 Notes from the Marking Centre - Mathematics
2016 Notes from the Marking Centre - Mathematics Question 11 (a) This part was generally done well. Most candidates indicated either the radius or the centre. Common sketching a circle with the correct
More informationd (5 cos 2 x) = 10 cos x sin x x x d y = (cos x)(e d (x 2 + 1) 2 d (ln(3x 1)) = (3) (M1)(M1) (C2) Differentiation Practice Answers 1.
. (a) y x ( x) Differentiation Practice Answers dy ( x) ( ) (A)(A) (C) Note: Award (A) for each element, to a maximum of [ marks]. y e sin x d y (cos x)(e sin x ) (A)(A) (C) Note: Award (A) for each element.
More information2017 HSC Mathematics Extension 2 Marking Guidelines
07 HSC Mathematics Etension Marking Guidelines Section I Multiple-choice Answer Key Question Answer C B 3 D 4 C 5 B 6 A 7 A 8 B 9 C 0 B NESA 07 HSC Mathematics Etension Sample Answers Section II Question
More informationSection I 10 marks (pages 2 5) Attempt Questions 1 10 Allow about 15 minutes for this section
017 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time hours Write using black pen NESA approved calculators may be used A reference sheet is provided
More information= π + sin π = π + 0 = π, so the object is moving at a speed of π feet per second after π seconds. (c) How far does it go in π seconds?
Mathematics 115 Professor Alan H. Stein April 18, 005 SOLUTIONS 1. Define what is meant by an antiderivative or indefinite integral of a function f(x). Solution: An antiderivative or indefinite integral
More information, correct to 4 significant figures?
Section I 10 marks Attempt Questions 1-10 Allow about 15 minutes for this section Use the multiple-choice answer sheet for Questions 1-10. 1 What is the basic numeral for (A) 0.00045378 (B) 0.0004538 (C)
More informationMathematics 2017 HSC ASSESSMENT TASK 3 (TRIAL HSC) Student Number Total Total. General Instructions. Mark
Mathematics 017 HSC ASSESSMENT TASK 3 (TRIAL HSC) General Instructions Reading time 5 minutes Working time 3 hours For Section I, shade the correct box on the sheet provided For Section II, write in the
More informationMathematics. Caringbah High School. Trial HSC Examination. Total Marks 100. General Instructions
Caringbah High School 014 Trial HSC Examination Mathematics General Instructions Total Marks 100 Reading time 5 minutes Working time 3 hours Write using a blue or black pen. Black pen is preferred. Board
More informationTABLE OF CONTENTS 2 CHAPTER 1
TABLE OF CONTENTS CHAPTER 1 Quadratics CHAPTER Functions 3 CHAPTER 3 Coordinate Geometry 3 CHAPTER 4 Circular Measure 4 CHAPTER 5 Trigonometry 4 CHAPTER 6 Vectors 5 CHAPTER 7 Series 6 CHAPTER 8 Differentiation
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 informationSec 4 Maths SET D PAPER 2
S4MA Set D Paper Sec 4 Maths Exam papers with worked solutions SET D PAPER Compiled by THE MATHS CAFE P a g e Answer all questions. Write your answers and working on the separate Answer Paper provided.
More informationDIFFERENTIATION RULES
3 DIFFERENTIATION RULES DIFFERENTIATION RULES Before starting this section, you might need to review the trigonometric functions. DIFFERENTIATION RULES In particular, it is important to remember that,
More informationMATHEMATICS 2017 HSC Course Assessment Task 4 (Trial Examination) Thursday, 3 August 2017
MATHEMATICS 2017 HSC Course Assessment Task 4 (Trial Examination) Thursday, 3 August 2017 General instructions Working time 3 hours. (plus 5 minutes reading time) Write using blue or black pen. Where diagrams
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 998 MATHEMATICS / UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of equal value.
More informationIYGB. Special Paper U. Time: 3 hours 30 minutes. Created by T. Madas. Created by T. Madas
IYGB Special Paper U Time: 3 hours 30 minutes Candidates may NOT use any calculator Information for Candidates This practice paper follows the Advanced Level Mathematics Core Syllabus Booklets of Mathematical
More informationAdd Math (4047/02) Year t years $P
Add Math (4047/0) Requirement : Answer all questions Total marks : 100 Duration : hour 30 minutes 1. The price, $P, of a company share on 1 st January has been increasing each year from 1995 to 015. The
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION. Mathematics. Total marks 120 Attempt Questions 1 10 All questions are of equal value
0 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time 3 hours Write using black or blue pen Black pen is preferred Board-approved calculators may
More information2013 Bored of Studies Trial Examinations. Mathematics SOLUTIONS
03 Bored of Studies Trial Examinations Mathematics SOLUTIONS Section I. B 3. B 5. A 7. B 9. C. D 4. B 6. A 8. D 0. C Working/Justification Question We can eliminate (A) and (C), since they are not to 4
More informationName: Index Number: Class: CATHOLIC HIGH SCHOOL Preliminary Examination 3 Secondary 4
Name: Inde Number: Class: CATHOLIC HIGH SCHOOL Preliminary Eamination 3 Secondary 4 ADDITIONAL MATHEMATICS 4047/1 READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work
More informationMathematics 2U HSC Questions
Mathematics 2U HSC Questions SYLLABUS CONTENT Basic arithmetic and algebra ----------------------------------------- Page 2 Real functions ----------------------------------------------------------- Page
More informationMATHEMATICS. NORTH SYDNEY BOYS HIGH SCHOOL 2008 Trial HSC Examination STUDENT NUMBER:... QUESTION Total %
008 Trial HSC Eamination MATHEMATICS General instructions Working time 3 hours. plus 5 minutes reading time) Write on the lined paper in the booklet provided. Each question is to commence on a new page.
More informationNewington College Mathematics Trial HSC 2012 (D) 2 2
Section I Attempt Questions 1-10 All questions are equal value. Use the multiple choice answer sheet for Questions 1-10 1 Evaluated to three significant figures, 1 e 0.1 is (A) 0.095 (B) 0.095 (C) 0.0951
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION. Mathematics
009 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Board-approved calculators may be used A table of standard
More informationAP Calculus BC Chapter 4 AP Exam Problems. Answers
AP Calculus BC Chapter 4 AP Exam Problems Answers. A 988 AB # 48%. D 998 AB #4 5%. E 998 BC # % 5. C 99 AB # % 6. B 998 AB #80 48% 7. C 99 AB #7 65% 8. C 998 AB # 69% 9. B 99 BC # 75% 0. C 998 BC # 80%.
More informationDIFFERENTIATION RULES
3 DIFFERENTIATION RULES DIFFERENTIATION RULES Before starting this section, you might need to review the trigonometric functions. DIFFERENTIATION RULES In particular, it is important to remember that,
More informationMANLY SELECTIVE CAMPUS
NORTHERN BECHES SECONDRY COLLEGE MNLY SELECTIVE CMPUS General Instructions HIGHER SCHOOL CERTIFICTE Reading time 5 minutes Working time 3hours Write using black or blue pen Write your Student Number at
More informationMathematics Extension 1
Teacher Student Number 008 TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Extension 1 General Instructions o Reading Time- 5 minutes o Working Time hours o Write using a blue or black pen o Approved
More informationHSC Marking Feedback 2017
HSC Marking Feedback 017 Mathematics Extension 1 Written Examination Question 11 Part (a) The large majority of responses showed correct substitution into the formula x = kx +lx 1 k+l given on the Reference
More informationPaper2Practice [303 marks]
PaperPractice [0 marks] Consider the expansion of (x + ) 10. 1a. Write down the number of terms in this expansion. [1 mark] 11 terms N1 [1 mark] 1b. Find the term containing x. evidence of binomial expansion
More informationMathematics Extension 2
0 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Etension General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Black pen is preferred Board-approved calculators
More informationYear 12 into 13 Maths Bridging Tasks
Year 1 into 13 Maths Bridging Tasks Topics covered: Surds Indices Curve sketching Linear equations Quadratics o Factorising o Completing the square Differentiation Factor theorem Circle equations Trigonometry
More informationCalculus first semester exam information and practice problems
Calculus first semester exam information and practice problems As I ve been promising for the past year, the first semester exam in this course encompasses all three semesters of Math SL thus far. It is
More informationMathematics 2013 YEAR 11 YEARLY EXAMINATIONS BAULKHAM HILLS HIGH SCHOOL
BAULKHAM HILLS HIGH SCHOOL 03 YEAR YEARLY EXAMINATIONS Mathematics General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Black pen is preferred Board-approved calculators
More information1 The Derivative and Differrentiability
1 The Derivative and Differrentiability 1.1 Derivatives and rate of change Exercise 1 Find the equation of the tangent line to f (x) = x 2 at the point (1, 1). Exercise 2 Suppose that a ball is dropped
More information0114ge. Geometry Regents Exam 0114
0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?
More informationMathematics 2003 HIGHER SCHOOL CERTIFICATE EXAMINATION
00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Board-approved calculators may be used A table of standard
More informationMath 106 Answers to Exam 3a Fall 2015
Math 6 Answers to Exam 3a Fall 5.. Consider the curve given parametrically by x(t) = cos(t), y(t) = (t 3 ) 3, for t from π to π. (a) (6 points) Find all the points (x, y) where the graph has either a vertical
More informationMATHEMATICS HSC Course Assessment Task 3 (Trial Examination) June 21, QUESTION Total MARKS
MATHEMATICS 0 HSC Course Assessment Task (Trial Eamination) June, 0 General instructions Working time hours. (plus 5 minutes reading time) Write using blue or black pen. Where diagrams are to be sketched,
More informationMathematics Extension 1
009 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Board-approved calculators may be used A table
More informationMathematics DAPTO HIGH SCHOOL HSC Preliminary Course FINAL EXAMINATION. General Instructions
DAPTO HIGH SCHOOL 2009 HSC Preliminary Course FINAL EXAMINATION Mathematics General Instructions o Reading Time 5 minutes o Working Time 2 hours Total marks (80) o Write using a blue or black pen o Board
More informationMA 162 FINAL EXAM PRACTICE PROBLEMS Spring Find the angle between the vectors v = 2i + 2j + k and w = 2i + 2j k. C.
MA 6 FINAL EXAM PRACTICE PROBLEMS Spring. Find the angle between the vectors v = i + j + k and w = i + j k. cos 8 cos 5 cos D. cos 7 E. cos. Find a such that u = i j + ak and v = i + j + k are perpendicular.
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 informationMathematics. Total marks 100. Section I Pages marks Attempt Questions 1 10 Allow about 15 minutes for this section
0 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time 3 hours Write using black or blue pen Black pen is preferred Board-approved calculators may
More information2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is
. If P(A) = x, P = 2x, P(A B) = 2, P ( A B) = 2 3, then the value of x is (A) 5 8 5 36 6 36 36 2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time
More informationPart (1) Second : Trigonometry. Tan
Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,
More information1. Find the area enclosed by the curve y = arctan x, the x-axis and the line x = 3. (Total 6 marks)
1. Find the area enclosed by the curve y = arctan, the -ais and the line = 3. (Total 6 marks). Show that the points (0, 0) and ( π, π) on the curve e ( + y) = cos (y) have a common tangent. 3. Consider
More information(b) g(x) = 4 + 6(x 3) (x 3) 2 (= x x 2 ) M1A1 Note: Accept any alternative form that is correct. Award M1A0 for a substitution of (x + 3).
Paper. Answers. (a) METHOD f (x) q x f () q 6 q 6 f() p + 8 9 5 p METHOD f(x) (x ) + 5 x + 6x q 6, p (b) g(x) + 6(x ) (x ) ( + x x ) Note: Accept any alternative form that is correct. Award A for a substitution
More informationMAC 2311 Calculus I Spring 2004
MAC 2 Calculus I Spring 2004 Homework # Some Solutions.#. Since f (x) = d dx (ln x) =, the linearization at a = is x L(x) = f() + f ()(x ) = ln + (x ) = x. The answer is L(x) = x..#4. Since e 0 =, and
More informationAP Calculus AB Winter Break Packet Happy Holidays!
AP Calculus AB Winter Break Packet 04 Happy Holidays! Section I NO CALCULATORS MAY BE USED IN THIS PART OF THE EXAMINATION. Directions: Solve each of the following problems. After examining the form of
More informationCalculus II Practice Test 1 Problems: , 6.5, Page 1 of 10
Calculus II Practice Test Problems: 6.-6.3, 6.5, 7.-7.3 Page of This is in no way an inclusive set of problems there can be other types of problems on the actual test. To prepare for the test: review homework,
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 informationMaths Higher Prelim Content
Maths Higher Prelim Content Straight Line Gradient of a line A(x 1, y 1 ), B(x 2, y 2 ), Gradient of AB m AB = y 2 y1 x 2 x 1 m = tanθ where θ is the angle the line makes with the positive direction of
More informationCatholic Schools Trial Examinations 2007 Mathematics. as a single fraction in its simplest form. 2
0 Catholic Trial HSC Eaminations Mathematics Page Catholic Schools Trial Eaminations 0 Mathematics a The radius of Uranus is approimately 5 559 000m. Write the number in scientific notation, correct to
More informationB O. Year 12 Trial HSC Examination - Mathematics (2U) Question 2. Marks . 2. Simplify: (b) (c) Solve 2sinθ = 1
Year Trial HSC Examination - Mathematics (U) 008 Question Solve for t: 7 4t >. Simplify: x 5 x +. 6 (c) Solve sinθ = for 0 θ. (d) Differentiate with respect to x: 6 y =. x y = x ln x. 5 (e) Evaluate +
More information2001 HSC Mathematics Marking Guidelines
00 HSC Mathematics Marking Guidelines Question (a) ( marks) Outcomes assessed: P Gives correct answer =. Ê 5 ˆ Correct simplification Á or better Ë 87 Correct rounding of incorrect simplification Question
More informationCredits: Four. School. Level 2 Mathematics and Statistics. Practice Assessment B (2.7) Apply calculus methods in solving problems.
Name: Teacher: NZAMT 2 Credits: Four School Level 2 Mathematics and Statistics Practice Assessment B 91262 (2.7) Apply calculus methods in solving problems 5 credits You should answer ALL parts of ALL
More information( ) 2 + ( 2 x ) 12 = 0, and explain why there is only one
IB Math SL Practice Problems - Algebra Alei - Desert Academy 0- SL Practice Problems Algebra Name: Date: Block: Paper No Calculator. Consider the arithmetic sequence, 5, 8,,. (a) Find u0. (b) Find the
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
More informationIYGB. Special Extension Paper A. Time: 3 hours 30 minutes. Created by T. Madas. Created by T. Madas
IYGB Special Extension Paper A Time: 3 hours 30 minutes Candidates may NOT use any calculator Information for Candidates This practice paper follows the Advanced Level Mathematics Core and the Advanced
More informationFree Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom
Free Response Questions 1969-010 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions
More informationLearning Objectives These show clearly the purpose and extent of coverage for each topic.
Preface This book is prepared for students embarking on the study of Additional Mathematics. Topical Approach Examinable topics for Upper Secondary Mathematics are discussed in detail so students can focus
More informationy mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent
Mathematics. The sides AB, BC and CA of ABC have, 4 and 5 interior points respectively on them as shown in the figure. The number of triangles that can be formed using these interior points is () 80 ()
More informationThe High School Section
1 Viète s Relations The Problems. 1. The equation 10/07/017 The High School Section Session 1 Solutions x 5 11x 4 + 4x 3 + 55x 4x + 175 = 0 has five distinct real roots x 1, x, x 3, x 4, x 5. Find: x 1
More informationMath 180 Written Homework Solutions Assignment #4 Due Tuesday, September 23rd at the beginning of your discussion class.
Math 180 Written Homework Solutions Assignment #4 Due Tuesday, September 23rd at the beginning of your discussion class. Directions. You are welcome to work on the following problems with other MATH 180
More informationPossible C4 questions from past papers P1 P3
Possible C4 questions from past papers P1 P3 Source of the original question is given in brackets, e.g. [P January 001 Question 1]; a question which has been edited is indicated with an asterisk, e.g.
More informationARE YOU READY FOR CALCULUS?? Name: Date: Period:
ARE YOU READY FOR CALCULUS?? Name: Date: Period: Directions: Complete the following problems. **You MUST show all work to receive credit.**(use separate sheets of paper.) Problems with an asterisk (*)
More information2013/2014 SEMESTER 1 MID-TERM TEST. 1 October :30pm to 9:30pm PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:
2013/2014 SEMESTER 1 MID-TERM TEST MA1505 MATHEMATICS I 1 October 2013 8:30pm to 9:30pm PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY: 1. This test paper consists of TEN (10) multiple choice questions
More informationMathematics 2004 TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION. Name: Teacher: S T R A T H F I E L D G I R L S H I G H S C H O O L.
Name: Teacher: S T R A T H F I E L D G I R L S H I G H S C H O O L 004 TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions All questions may be attempted. All questions are of
More informationSydney Grammar School
Sydney Grammar School. (a) Evaluate π 0 sinn x cos xdx. (b) Evaluate x 0 x+ dx. (c) (i) Express 6 u in the form A 4 unit mathematics Trial HSC Examination 993 4 u + B 4+u (ii) Use the substitution u =
More informationMathematics 2001 HIGHER SCHOOL CERTIFICATE EXAMINATION
00 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time 3 hours Write using black or blue pen Board-approved calculators may be used A table of standard
More informationAQA Level 2 Certificate in Further Mathematics. Worksheets - Teacher Booklet
AQA Level Certificate in Further Mathematics Worksheets - Teacher Booklet Level Specification Level Certificate in Further Mathematics 860 Worksheets - Teacher Booklet Our specification is published on
More informationMARK SCHEME for the November 2004 question paper 9709 MATHEMATICS 8719 HIGHER MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary and Advanced Level MARK SCHEME for the November 004 question paper 9709 MATHEMATICS 879 HIGHER MATHEMATICS 9709/03, 879/03 Paper
More information1. B (27 9 ) = [3 3 ] = (3 ) = 3 2. D. = c d dy d = cy + c dy cy = d + c. y( d c) 3. D 4. C
HKDSE03 Mathematics (Compulsory Part) Paper Full Solution. B (7 9 ) [3 3 ] (3 ) 3 n + 3 3 ( n + ) 3 n + 5 3 6 n + 5. D y y + c d dy d cy + c dy cy d + c y( d c) c + d c + d y d c 3. D hl kl + hm km hn
More informationTime: 1 hour 30 minutes
Paper Reference (complete below) Centre No. Surname Initial(s) Candidate No. Signature Paper Reference(s) 6663 Edexcel GCE Pure Mathematics C Advanced Subsidiary Specimen Paper Time: hour 30 minutes Examiner
More informationFinal Examination 201-NYA-05 May 18, 2018
. ( points) Evaluate each of the following limits. 3x x + (a) lim x x 3 8 x + sin(5x) (b) lim x sin(x) (c) lim x π/3 + sec x ( (d) x x + 5x ) (e) lim x 5 x lim x 5 + x 6. (3 points) What value of c makes
More informationMathematics Preliminary Course FINAL EXAMINATION Friday, September 6. General Instructions
03 Preliminary Course FINAL EXAMINATION Friday, September 6 Mathematics General Instructions o Reading Time 5 minutes. o Working Time 3 hours. o Write using a black pen. o Approved calculators may be used.
More information1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.
Higher Maths Non Calculator Practice Practice Paper A. A sequence is defined b the recurrence relation u u, u. n n What is the value of u?. The line with equation k 9 is parallel to the line with gradient
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 informationAdvanced Higher Grade
Prelim Eamination / 5 (Assessing Units & ) MATHEMATICS Advanced Higher Grade Time allowed - hours Read Carefully. Full credit will be given only where the solution contains appropriate woring.. Calculators
More informationMTH Calculus with Analytic Geom I TEST 1
MTH 229-105 Calculus with Analytic Geom I TEST 1 Name Please write your solutions in a clear and precise manner. SHOW your work entirely. (1) Find the equation of a straight line perpendicular to the line
More informationAntiderivatives. Definition A function, F, is said to be an antiderivative of a function, f, on an interval, I, if. F x f x for all x I.
Antiderivatives Definition A function, F, is said to be an antiderivative of a function, f, on an interval, I, if F x f x for all x I. Theorem If F is an antiderivative of f on I, then every function of
More informationTRIGONOMETRY OUTCOMES
TRIGONOMETRY OUTCOMES C10. Solve problems involving limits of trigonometric functions. C11. Apply derivatives of trigonometric functions. C12. Solve problems involving inverse trigonometric functions.
More informationTrigonometry. Sin θ Cos θ Tan θ Cot θ Sec θ Cosec θ. Sin = = cos = = tan = = cosec = sec = 1. cot = sin. cos. tan
Trigonometry Trigonometry is one of the most interesting chapters of Quantitative Aptitude section. Basically, it is a part of SSC and other bank exams syllabus. We will tell you the easy method to learn
More informationFormulas that must be memorized:
Formulas that must be memorized: Position, Velocity, Acceleration Speed is increasing when v(t) and a(t) have the same signs. Speed is decreasing when v(t) and a(t) have different signs. Section I: Limits
More informationMathematics 2005 HIGHER SCHOOL CERTIFICATE EXAMINATION
005 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General Instructions Reading time 5 minutes Working time hours Write using black or blue pen Board-approved calculators may be used A table of standard
More informationAB 1: Find lim. x a.
AB 1: Find lim x a f ( x) AB 1 Answer: Step 1: Find f ( a). If you get a zero in the denominator, Step 2: Factor numerator and denominator of f ( x). Do any cancellations and go back to Step 1. If you
More informationCreated by T. Madas. Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications.
IYGB Special Paper Q Time: 3 hours 30 minutes Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications. Information for Candidates This practice paper follows
More informationAS PURE MATHS REVISION NOTES
AS PURE MATHS REVISION NOTES 1 SURDS A root such as 3 that cannot be written exactly as a fraction is IRRATIONAL An expression that involves irrational roots is in SURD FORM e.g. 2 3 3 + 2 and 3-2 are
More informationDEPARTMENT OF MATHEMATICS
DEPARTMENT OF MATHEMATICS AS level Mathematics Core mathematics 1 C1 2015-2016 Name: Page C1 workbook contents Indices and Surds Simultaneous equations Quadratics Inequalities Graphs Arithmetic series
More informationAdd Math (4047) Paper 2
1. Solve the simultaneous equations 5 and 1. [5]. (i) Sketch the graph of, showing the coordinates of the points where our graph meets the coordinate aes. [] Solve the equation 10, giving our answer correct
More informationSolutionbank C1 Edexcel Modular Mathematics for AS and A-Level
Heinemann Solutionbank: Core Maths C Page of Solutionbank C Exercise A, Question Find the values of x for which f ( x ) = x x is a decreasing function. f ( x ) = x x f ( x ) = x x Find f ( x ) and put
More informationAP Calculus Free-Response Questions 1969-present AB
AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions
More information0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?
0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle
More information