4038/02 October/November 2008

Size: px
Start display at page:

Download "4038/02 October/November 2008"

Transcription

1 GCE O Level October/November 008 Suggested Solutions Additional Mathematics (408/0) version 1.1 ADDITIONAL MATHEMATICS Paper Suggested Solutions 1. Topic: Exponential Functions (i) Given: V =10000e -pt When the man bought the motorcycle, t = 0. value of motorcycle when bought = 10000e 0 (ii) When t = 1, v = 4000: 4000 = 10000e 0.4 = e -1p ln 0.4 = 1p ln e ln 0.4 -p (1) p = V = 10000e t. (1) = $ /0 October/November (18) Sub t = 18 into (1): Value after 18 months = 10000e 59.8 $50 ( s.f.) (iii) Sub v = 1000 into (1): 1000 = 10000e t Note: V < $1000 when t = = e t months, since the e pt curve describes the depreciation of value ln 0.1 = t ln e over time. V t = ln months 0 months (nearest month) t. Topic: Quadratic Equations (Sum & Product of Roots) x 4x + = 0 a =, b = 4, c = Sum of roots: α + β = b a = 4 = Product of roots: αβ = c = a New sum of roots: (α + ) + (β + ) = α + β + 4 =[(α + β) αβ] + 4 = () + 4 = 5 New product of roots: (α + )(β + ) = α β + α + β + 4 =(αβ) + (α + β ) + 4 = (αβ) + [(α + β) αβ] + 4 = [4 ] + 4 = = 8 1 = 4 4 equation with roots α +, β + : x 5x + = 0 4 4x 0x + = 0 Sub α + β =, αα = Useful expression: α + β = (α + β) αα Sub α + β =, αα = x (Sum of roots)x + (Product of roots) = 0 age of motorcycle when expected value is $1000 is 0 months / missloi@exampaper.com.sg facebook.com/jossstickstuition twitter.com/missloi Copyright 008 ϕ exampaper.com.sg. All rights reserved. 1 / 8

2 GCE O Level October/November 008 Suggested Solutions Additional Mathematics (408/0) version 1.1. Topic: Trigonometry (Trigonometric Identities & Equations) (i) tan A + cot A = cosec A L.H.S.: sin A cos A (ii) tan A + cot A = + cos A sin A = sin A+cos A cos A sin A = = = From (i): cosec A = sin A = sin A = 1 sin A cos A 1 sin A cos A sin A = cosec A = R.H.S. (Proved) Basic angle α = sin A 41.81, , , , 18.19, , A = 0.9, 69.1, 00.9, 49.1 sin A + cos A = 1 sin A = sin A cos A 90 A 18., 498. A 69.1, S T α A α C 70 α A 60 0 A 70 A 41.8, A 0.9, Topic: Logarithms (i) + log (x 7) = log (x ) log (x ) log (x 7) = (ii) log 5 y log y 5 = log 5 y = log 5 y Let log 5 y = x. 1 log x = x 7 x = x 7 x = 9(x 7) x = 7x 6 60 = 5x x =.4 x 1 = x x 1 = x (x + 1)(x 1) = 0 x = 1 or 1 log 5 y = 1 or 1 y = 5 1 or 5 1 y = 1 or 5 5 Change of Base of Log: log a b = 1 log b a Quotient Law: m log a m log a n = log a n y = a x x = log a y / missloi@exampaper.com.sg facebook.com/jossstickstuition twitter.com/missloi Copyright 008 ϕ exampaper.com.sg. All rights reserved. / 8

3 GCE O Level October/November 008 Suggested Solutions Additional Mathematics (408/0) version Topic: Polynomials (Factor Theorem & Remainder Theorem) Factor Theorem: (i) f(x) = (x x +1) (x + 1) (x ) = (x 6x +) (x f(a) = 0 (x a) is a factor of f(x) x ) = x 4 x - 4x 6x + 6x + 1x + x x 4 = x 4 8x + 4x + 10x 4 (ii) f(x) = 0 Check: f( 1) = ( 1) 4 8( 1) + 4( 1) + 10( 1) 4 = 0 (x x + 1) (x + 1) (x ) = 0 No. of real roots = 4 (iii) f(x) = (x x + 1) (x + 1) (x ) x = ± 9 4(1)(1) or 1 or = ± 5, 1, 6. Topic: Geometric Proofs (i) (ii) When x = 1, f 1 = [1 + 1] 4 = 1 4 = Remainder = Remainder Theorem: f(x) divided by (x a) remainder is f(a) AE = CE (Tangents from a common external point E) AO = CO (Radius of circle) OAE = OCE = 90 (Radius Tangent) AEO CEO (SAS) Let AOE = θ. COE = θ ( AEO CEO) AOC = θ ABC = θ ( at centre = at circumference) EO // DB ( AOE = ABC = θ - corresponding s) By Midpoint Theorem, E is the mid-pt of AD / missloi@exampaper.com.sg facebook.com/jossstickstuition twitter.com/missloi Copyright 008 ϕ exampaper.com.sg. All rights reserved. / 8

4 GCE O Level October/November 008 Suggested Solutions Additional Mathematics (408/0) version Topic: Trigonometry (Trigonometric Functions) (i) Amplitude = 4 60 (ii) Period = = 180 cycles (iii) Minimum point occurs when cos x = 1 x = cos -1 ( 1) x = 180 x = 90 y = 4 ( 1) = 6 y = a cos bx + c: Amplitude = a Period = 60 b coordinates of the minimum point of the curve is (90, 6) (v) (iv) When y = 0, 4cos x - = 0 4cos x = cos x = 1 Basic angle α = 60 x = 60, 00 x = 0, S T A α α 0 C α = 60 0 x x 60 x = 60 x = 0 x = 00 x = 150 (vi) coordinates where curve meets the x-axis are (0, 0)and (150, 0) / missloi@exampaper.com.sg facebook.com/jossstickstuition twitter.com/missloi Copyright 008 ϕ exampaper.com.sg. All rights reserved. 4 / 8

5 GCE O Level October/November 008 Suggested Solutions Additional Mathematics (408/0) version Topic: Applications of Differentiation & Integration (Maxima & Minima, Area Under Curve) (i) y = x ax + b = dx x a From the diagram, minimum point is (, 0) Sub = 0 and x = into : dx dx () a = 0 1 a = 0 a = 1 Sub (, 0) into y: a = 1, b = 16 0 = 1() + b 0 = b b = 16 (ii) From (i), y = x 1x + 16 = dx x 1 At maximum point, = dx x 1 = 0 (x 4) = 0 (x + )(x ) = 0 x = or (rejected max. point occurs when x < 0 in the diagram) Sub x = into y: Check: d y = 6x dx y = ( ) 1 ( ) + 16 Sub x = into d y dx : d = y dx = 6( ) = 1 < 0 = (, ) is a maximum point coordinates of maximum point is (, ). (iii) Area of shaded region = (x 1x + 16) dx 0 = x4 1x x 0 = x4 4 6x + 16x 0 = [ ()4 4 6() + 16()] [ (0)4 4 6(0) + 16(0)] = = 1 units / missloi@exampaper.com.sg facebook.com/jossstickstuition twitter.com/missloi Copyright 008 ϕ exampaper.com.sg. All rights reserved. 5 / 8

6 GCE O Level October/November 008 Suggested Solutions Additional Mathematics (408/0) version Topic: Further Trigonometric Identities (R-Formula) (i) From the diagram, OAD = θ (corresponding s) sin θ = OD 4 OD = 4 sin θ ABC = BAC = ( θ) = θ cos θ = BC BC = cos θ L = OD BC = 4 sin θ cos θ (Shown) (ii) 4 sin θ cos θ = R sin (θ α) = R (sinθ cos α cos θ sin α) = R cos α sinθ R sin α cos θ Comparing coefficients, 4 = R cos α. (1) = R sin α. () () : sin α = (1) cos α 4 tan α = 1 α 6.6 Addition Formula: sin (A B) = sin A cos B cos A sin B (1) + () : R cos α + R sin α = 4 + R (cos α + sin α) = R = 0 R = 0 or 0 (rejected) L = 0 sin (θ 6.6 ) 90 θ S A θ φ φ 0 (iii) When L =, 0 sin (θ 6.6 ) = 70 sin (θ 6.6 ) = φ Basic angle φ 4.1 θ , θ 68.7, (rejected θ is acute) θ 68.7 ( sig. fig.) T C / missloi@exampaper.com.sg facebook.com/jossstickstuition twitter.com/missloi Copyright 008 ϕ exampaper.com.sg. All rights reserved. 6 / 8

7 GCE O Level October/November 008 Suggested Solutions Additional Mathematics (408/0) version Topics: Coordinate Geometry, Integration, Applications of Differentiation (Rate of Change) (i) = 6 dx (x 1) Sub x = into : dx Gradient of curve at P(, 9) = 6 = Gradient of normal = Equation of normal to the curve at P: y 9 = (x ) y = x y = x + 1. (1) At Q(0, y), Gradients m 1 and m of two lines m 1 m = 1 Equation of line with gradient m and point (x 1, y 1 ): (y y 1 ) = m(x x 1 ) (ii) y = dx (x 1) 6 = 6(x 1) dx = 6(x 1) 1 ( 1) = (x 1) c + c y =. () x 1 Since P(, 9) lies on the curve, sub x =, y = 9 into (): 9 = () 1 + c 9 = 1 + c c = 10 y = + 10 x 1 (aa + (aa + b) n b)n+1 dx = + c a(n + 1) Sub x = 0 into (1): y = (0) + 1 = 1 Q = (0, 1) At R(x, 0), Sub y = 0 into (1): x + 1 = 0 x = 1 x = 8 R = (8, 0) Mid-point of QR = 0+8, 1+0 = (4, 6) Midpoint of (x 1, y 1 ) and (x, y ): x 1 + x, y 1 + y (iii) x-coordinate increases at 0.0 units per second dx dt = 0.0 Rate of change of y-coordinate: = dx dt dx dt 6 = 0.0 (x 1) At P(, 9), sub x = into : dt = dt (() 1) = 0.0 units per second Chain Rule: = dx dt dx dt y-coordinate increases at 0.0 units per second / missloi@exampaper.com.sg facebook.com/jossstickstuition twitter.com/missloi Copyright 008 ϕ exampaper.com.sg. All rights reserved. 7 / 8

8 GCE O Level October/November 008 Suggested Solutions Additional Mathematics (408/0) version Topics: Coordinate Geometry, Circles (i) Centre of C 1, O = (0, 0) Radius of C 1, OP = (0 8) + (0 + 6) = 10 units Equation of C 1 : (x 0) + (y 0) = 10 (ii) Center of C, Q = Midpoint of OP = 0+8, 0+( 6) = (4, ) x + y = 100 Radius of C, QP = (4 8) + ( + 6) = 5 units Equation of C : (x 4) + (y + ) = 5 x 8x y + 6y + 9 = 5 x + y 8x + 6y = 0 Length of Line Segment = (x 1 x ) + (y 1 y ) Equation of circle with centre (a, b) and radius r: (x a) + (y b) = r Midpoint of (x 1, y 1 ) and (x, y ): x 1 + x, y 1 + y (iii) Gradient of OP = = 4 Gradient of AB = 4 Using Q(4, ) from (ii): Equation of AB: y + = 4 (x 4) y = 4 x 5. (1) A and B also lie on C 1 with equation obtained in (i): x + y = () Sub (1) into (): x x = 100 x + 16x 00 x + 65 = x 00 x + 65 = x 00 x 75 = 0 x 8x 11 = 0 x = 8 ± 64 4(1)( 11) (1) = 8 ± 108 = 8 ±6 = 4 ± Gradients m 1 and m of two lines m 1 m = 1 Equation of line with gradient m and point (x 1, y 1 ): (y y 1 ) = m(x x 1 ) x-coordinates of A and B are 4 + and 4 respectively / missloi@exampaper.com.sg facebook.com/jossstickstuition twitter.com/missloi Copyright 008 ϕ exampaper.com.sg. All rights reserved. 8 / 8

9740/01 October/November MATHEMATICS (H2) Paper 1 Suggested Solutions. (ii)

9740/01 October/November MATHEMATICS (H2) Paper 1 Suggested Solutions. (ii) GCE A Level October/November 9 Suggested Solutions Mathematics H (97/) version. MATHEMATICS (H) Paper Suggested Solutions. Topic: Matrices (i) Given that u n is a quadratic polynomial in n, Let u n an

More information

4038/02 October/November 2009

4038/02 October/November 2009 Additional Mathematics (408/0) version 1.1 ADDITIONAL MATHEMATIS Paper Suggested Solutions 1. Topic: Further Trigonometric Identities sin(a B) sin A cos B cos A sin B 8 5 8 cos A sin B 8 8 408/0 October/November

More information

Learning Objectives These show clearly the purpose and extent of coverage for each topic.

Learning 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 information

4016/02 October/November 2010

4016/02 October/November 2010 GCE O Level October/November 010 Suggested Solutions Elementary athematics (4016/0) version.1 ELEENTARY ATHEATICS aper Suggested Solutions 4016/0 October/November 010 1. Topics: Trigonometry (Trigonometric

More information

Candidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required.

Candidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required. Revision Checklist Unit C2: Core Mathematics 2 Unit description Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation;

More information

Sec 4 Maths. SET A PAPER 2 Question

Sec 4 Maths. SET A PAPER 2 Question S4 Maths Set A Paper Question Sec 4 Maths Exam papers with worked solutions SET A PAPER Question Compiled by THE MATHS CAFE 1 P a g e Answer all the questions S4 Maths Set A Paper Question Write in dark

More information

Cambridge International Examinations CambridgeOrdinaryLevel

Cambridge International Examinations CambridgeOrdinaryLevel Cambridge International Examinations CambridgeOrdinaryLevel * 2 5 4 0 0 0 9 5 8 5 * ADDITIONAL MATHEMATICS 4037/12 Paper1 May/June 2015 2 hours CandidatesanswerontheQuestionPaper. NoAdditionalMaterialsarerequired.

More information

ADDITIONAL MATHEMATICS

ADDITIONAL MATHEMATICS ADDITIONAL MATHEMATICS GCE NORMAL ACADEMIC LEVEL (016) (Syllabus 4044) CONTENTS Page INTRODUCTION AIMS ASSESSMENT OBJECTIVES SCHEME OF ASSESSMENT 3 USE OF CALCULATORS 3 SUBJECT CONTENT 4 MATHEMATICAL FORMULAE

More information

TABLE OF CONTENTS 2 CHAPTER 1

TABLE 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 information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level *054681477* ADDITIONAL MATHEMATICS 407/11 Paper 1 May/June 017 hours Candidates answer on the Question Paper. No Additional Materials are required.

More information

Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document

Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document Background knowledge: (a) The arithmetic of integers (including HCFs and LCMs), of fractions, and of real numbers.

More information

DEPARTMENT OF MATHEMATICS

DEPARTMENT OF MATHEMATICS DEPARTMENT OF MATHEMATICS AS level Mathematics Core mathematics 2 - C2 2015-2016 Name: Page C2 workbook contents Algebra Differentiation Integration Coordinate Geometry Logarithms Geometric series Series

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level * 3 1 3 1 7 3 6 3 6 2 * ADDITIONAL MATHEMATICS 4037/11 Paper 1 May/June 2015 2 hours Candidates answer on the Question Paper. No Additional

More information

Core Mathematics C1 (AS) Unit C1

Core Mathematics C1 (AS) Unit C1 Core Mathematics C1 (AS) Unit C1 Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, factorisation. Graphs of functions; sketching curves defined by simple equations.

More information

Add Math (4047/02) Year t years $P

Add 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 information

Mathematics 5 SN TRIGONOMETRY PROBLEMS 2., which one of the following statements is TRUE?, which one of the following statements is TRUE?

Mathematics 5 SN TRIGONOMETRY PROBLEMS 2., which one of the following statements is TRUE?, which one of the following statements is TRUE? Mathematics 5 SN TRIGONOMETRY PROBLEMS 1 If x 4 which one of the following statements is TRUE? A) sin x > 0 and cos x > 0 C) sin x < 0 and cos x > 0 B) sin x > 0 and cos x < 0 D) sin x < 0 and cos x

More information

AS PURE MATHS REVISION NOTES

AS 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 information

Lone Star College-CyFair Formula Sheet

Lone Star College-CyFair Formula Sheet Lone Star College-CyFair Formula Sheet The following formulas are critical for success in the indicated course. Student CANNOT bring these formulas on a formula sheet or card to tests and instructors MUST

More information

a Write down the coordinates of the point on the curve where t = 2. b Find the value of t at the point on the curve with coordinates ( 5 4, 8).

a Write down the coordinates of the point on the curve where t = 2. b Find the value of t at the point on the curve with coordinates ( 5 4, 8). Worksheet A 1 A curve is given by the parametric equations x = t + 1, y = 4 t. a Write down the coordinates of the point on the curve where t =. b Find the value of t at the point on the curve with coordinates

More information

Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)

Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0) Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0) First teaching from September 2017 First certification from June 2018 2

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level *8790810596* ADDITIONAL MATHEMATICS 4037/13 Paper 1 October/November 2017 2 hours Candidates answer on the Question Paper. No Additional Materials

More information

CALCULUS ASSESSMENT REVIEW

CALCULUS ASSESSMENT REVIEW CALCULUS ASSESSMENT REVIEW DEPARTMENT OF MATHEMATICS CHRISTOPHER NEWPORT UNIVERSITY 1. Introduction and Topics The purpose of these notes is to give an idea of what to expect on the Calculus Readiness

More information

abc Mathematics Pure Core General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES

abc 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 information

SUBJECT: ADDITIONAL MATHEMATICS CURRICULUM OUTLINE LEVEL: 3 TOPIC OBJECTIVES ASSIGNMENTS / ASSESSMENT WEB-BASED RESOURCES. Online worksheet.

SUBJECT: ADDITIONAL MATHEMATICS CURRICULUM OUTLINE LEVEL: 3 TOPIC OBJECTIVES ASSIGNMENTS / ASSESSMENT WEB-BASED RESOURCES. Online worksheet. TERM 1 Simultaneous Online worksheet. Week 1 Equations in two Solve two simultaneous equations where unknowns at least one is a linear equation, by http://www.tutorvista.com/mat substitution. Understand

More information

ADDITIONAL MATHEMATICS

ADDITIONAL MATHEMATICS ADDITIONAL MATHEMATICS GCE Ordinary Level (06) (Syllabus 4047) CONTENTS Page INTRODUCTION AIMS ASSESSMENT OBJECTIVES SCHEME OF ASSESSMENT 3 USE OF CALCULATORS 3 SUBJECT CONTENT 4 MATHEMATICAL FORMULAE

More information

Higher Mathematics Skills Checklist

Higher Mathematics Skills Checklist Higher Mathematics Skills Checklist 1.1 The Straight Line (APP) I know how to find the distance between 2 points using the Distance Formula or Pythagoras I know how to find gradient from 2 points, angle

More information

HEINEMANN HIGHER CHECKLIST

HEINEMANN HIGHER CHECKLIST St Ninian s High School HEINEMANN HIGHER CHECKLIST I understand this part of the course = I am unsure of this part of the course = Name Class Teacher I do not understand this part of the course = Topic

More information

Review exercise 2. 1 The equation of the line is: = 5 a The gradient of l1 is 3. y y x x. So the gradient of l2 is. The equation of line l2 is: y =

Review exercise 2. 1 The equation of the line is: = 5 a The gradient of l1 is 3. y y x x. So the gradient of l2 is. The equation of line l2 is: y = Review exercise The equation of the line is: y y x x y y x x y 8 x+ 6 8 + y 8 x+ 6 y x x + y 0 y ( ) ( x 9) y+ ( x 9) y+ x 9 x y 0 a, b, c Using points A and B: y y x x y y x x y x 0 k 0 y x k ky k x a

More information

b UVW is a right-angled triangle, therefore VW is the diameter of the circle. Centre of circle = Midpoint of VW = (8 2) + ( 2 6) = 100

b UVW is a right-angled triangle, therefore VW is the diameter of the circle. Centre of circle = Midpoint of VW = (8 2) + ( 2 6) = 100 Circles 6F a U(, 8), V(7, 7) and W(, ) UV = ( x x ) ( y y ) = (7 ) (7 8) = 8 VW = ( 7) ( 7) = 64 UW = ( ) ( 8) = 8 Use Pythagoras' theorem to show UV UW = VW 8 8 = 64 = VW Therefore, UVW is a right-angled

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level *054681477* ADDITIONAL MATHEMATICS 4037/11 Paper 1 May/June 017 hours Candidates answer on the Question Paper. No Additional Materials are

More information

Year 12 into 13 Maths Bridging Tasks

Year 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 information

ADDITIONAL MATHEMATICS

ADDITIONAL MATHEMATICS ADDITIONAL MATHEMATICS GCE Ordinary Level (Syllabus 4018) CONTENTS Page NOTES 1 GCE ORDINARY LEVEL ADDITIONAL MATHEMATICS 4018 2 MATHEMATICAL NOTATION 7 4018 ADDITIONAL MATHEMATICS O LEVEL (2009) NOTES

More information

x n+1 = ( x n + ) converges, then it converges to α. [2]

x n+1 = ( x n + ) converges, then it converges to α. [2] 1 A Level - Mathematics P 3 ITERATION ( With references and answers) [ Numerical Solution of Equation] Q1. The equation x 3 - x 2 6 = 0 has one real root, denoted by α. i) Find by calculation the pair

More information

DESIGN OF THE QUESTION PAPER Mathematics Class X

DESIGN OF THE QUESTION PAPER Mathematics Class X SET-I DESIGN OF THE QUESTION PAPER Mathematics Class X Time : 3 Hours Maximum Marks : 80 Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage

More information

Mathematics, Algebra, and Geometry

Mathematics, Algebra, and Geometry Mathematics, Algebra, and Geometry by Satya http://www.thesatya.com/ Contents 1 Algebra 1 1.1 Logarithms............................................ 1. Complex numbers........................................

More information

2016 SEC 4 ADDITIONAL MATHEMATICS CW & HW

2016 SEC 4 ADDITIONAL MATHEMATICS CW & HW FEB EXAM 06 SEC 4 ADDITIONAL MATHEMATICS CW & HW Find the values of k for which the line y 6 is a tangent to the curve k 7 y. Find also the coordinates of the point at which this tangent touches the curve.

More information

The 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.

The 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 information

Topic Outline for Algebra 2 & and Trigonometry One Year Program

Topic Outline for Algebra 2 & and Trigonometry One Year Program Topic Outline for Algebra 2 & and Trigonometry One Year Program Algebra 2 & and Trigonometry - N - Semester 1 1. Rational Expressions 17 Days A. Factoring A2.A.7 B. Rationals A2.N.3 A2.A.17 A2.A.16 A2.A.23

More information

MATHEMATICS 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 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 information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level *5238158802* MATHEMATICS 9709/31 Paper 3 Pure Mathematics 3 (P3) October/November 2013 Additional Materials:

More information

C4 "International A-level" (150 minute) papers: June 2014 and Specimen 1. C4 INTERNATIONAL A LEVEL PAPER JUNE 2014

C4 International A-level (150 minute) papers: June 2014 and Specimen 1. C4 INTERNATIONAL A LEVEL PAPER JUNE 2014 C4 "International A-level" (150 minute) papers: June 2014 and Specimen 1. C4 INTERNATIONAL A LEVEL PAPER JUNE 2014 1. f(x) = 2x 3 + x 10 (a) Show that the equation f(x) = 0 has a root in the interval [1.5,

More information

Formulae and Summary

Formulae and Summary Appendix A Formulae and Summary Note to student: It is not useful to memorise all the formulae, partly because many of the complicated formulae may be obtained from the simpler ones. Rather, you should

More information

Test Codes : MIA (Objective Type) and MIB (Short Answer Type) 2007

Test Codes : MIA (Objective Type) and MIB (Short Answer Type) 2007 Test Codes : MIA (Objective Type) and MIB (Short Answer Type) 007 Questions will be set on the following and related topics. Algebra: Sets, operations on sets. Prime numbers, factorisation of integers

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/01

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/01 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/01 Paper 1 Additional Materials: Answer Booklet/Paper Electronic

More information

2013 Bored of Studies Trial Examinations. Mathematics SOLUTIONS

2013 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 information

Maths Higher Prelim Content

Maths 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 information

Topic 3 Part 1 [449 marks]

Topic 3 Part 1 [449 marks] Topic 3 Part [449 marks] a. Find all values of x for 0. x such that sin( x ) = 0. b. Find n n+ x sin( x )dx, showing that it takes different integer values when n is even and when n is odd. c. Evaluate

More information

1. 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

1. 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 information

THE COMPOUND ANGLE IDENTITIES

THE COMPOUND ANGLE IDENTITIES TRIGONOMETRY THE COMPOUND ANGLE IDENTITIES Question 1 Prove the validity of each of the following trigonometric identities. a) sin x + cos x 4 4 b) cos x + + 3 sin x + 2cos x 3 3 c) cos 2x + + cos 2x cos

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *1406924476* ADDITIONAL MATHEMATICS 0606/21 Paper 2 May/June 2010 Additional

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/02 Paper 2 Examination from 2013 SPECIMEN PAPER 2 hours Candidates

More information

Sec 4 Maths SET D PAPER 2

Sec 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 information

Mathematics Class X Board Paper 2011

Mathematics Class X Board Paper 2011 Mathematics Class X Board Paper Solution Section - A (4 Marks) Soln.. (a). Here, p(x) = x + x kx + For (x-) to be the factor of p(x) = x + x kx + P () = Thus, () + () k() + = 8 + 8 - k + = k = Thus p(x)

More information

PhysicsAndMathsTutor.com. Centre No. Candidate No. Core Mathematics C2 Advanced Subsidiary Mock Paper. Time: 1 hour 30 minutes

PhysicsAndMathsTutor.com. Centre No. Candidate No. Core Mathematics C2 Advanced Subsidiary Mock Paper. Time: 1 hour 30 minutes Paper Reference (complete below) 6 6 6 4 / 0 1 PhysicsAndMathsTutor.com Centre No. Candidate No. Surname Signature Initial(s) Paper Reference(s) 6664 Edexcel GCE Core Mathematics C2 Advanced Subsidiary

More information

2013/2014 SEMESTER 1 MID-TERM TEST. 1 October :30pm to 9:30pm PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:

2013/2014 SEMESTER 1 MID-TERM TEST. 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 information

Core Mathematics 2 Unit C2 AS

Core Mathematics 2 Unit C2 AS Core Mathematics 2 Unit C2 AS compulsory unit for GCE AS and GCE Mathematics, GCE AS and GCE Pure Mathematics C2.1 Unit description Algebra and functions; coordinate geometry in the (, y) plane; sequences

More information

Time: 1 hour 30 minutes

Time: 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 information

Outline schemes of work A-level Mathematics 6360

Outline schemes of work A-level Mathematics 6360 Outline schemes of work A-level Mathematics 6360 Version.0, Autumn 013 Introduction These outline schemes of work are intended to help teachers plan and implement the teaching of the AQA A-level Mathematics

More information

AQA Level 2 Certificate in Further Mathematics. Worksheets - Teacher Booklet

AQA 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 information

HSC Mathematics - Extension 1. Workshop 2

HSC Mathematics - Extension 1. Workshop 2 HSC Mathematics - Extension 1 Workshop 2 Presented by Richard D. Kenderdine BSc, GradDipAppSc(IndMaths), SurvCert, MAppStat, GStat School of Mathematics and Applied Statistics University of Wollongong

More information

1 / 23

1 / 23 CBSE-XII-017 EXAMINATION CBSE-X-008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question

More information

Name: Index Number: Class: CATHOLIC HIGH SCHOOL Preliminary Examination 3 Secondary 4

Name: 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 information

Higher Mathematics Course Notes

Higher Mathematics Course Notes Higher Mathematics Course Notes Equation of a Line (i) Collinearity: (ii) Gradient: If points are collinear then they lie on the same straight line. i.e. to show that A, B and C are collinear, show that

More information

Cambridge International Examinations Cambridge International General Certificate of Secondary Education

Cambridge International Examinations Cambridge International General Certificate of Secondary Education Cambridge International Examinations Cambridge International General Certificate of Secondary Education * 9 2 4 2 8 1 9 0 7 2 * ADDITIONAL MATHEMATICS 0606/12 Paper 1 February/March 2016 2 hours Candidates

More information

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola) QUESTION BANK ON CONIC SECTION (Parabola, Ellipse & Hyperbola) Question bank on Parabola, Ellipse & Hyperbola Select the correct alternative : (Only one is correct) Q. Two mutually perpendicular tangents

More information

Edexcel New GCE A Level Maths workbook Circle.

Edexcel New GCE A Level Maths workbook Circle. Edexcel New GCE A Level Maths workbook Circle. Edited by: K V Kumaran kumarmaths.weebly.com 1 Finding the Midpoint of a Line To work out the midpoint of line we need to find the halfway point Midpoint

More information

MATHEMATICS: SPECIALIST UNITS 3C AND 3D FORMULA SHEET 2015

MATHEMATICS: SPECIALIST UNITS 3C AND 3D FORMULA SHEET 2015 MATHEMATICS: SPECIALIST UNITS 3C AND 3D FORMULA SHEET 05 Copyright School Curriculum and Standards Authority, 05 This document apart from any third party copyright material contained in it may be freely

More information

Paper 1 (Edexcel Version)

Paper 1 (Edexcel Version) AS Level / Year 1 Paper 1 (Edexcel Version) Set A / Version 1 017 crashmaths Limited 1 y = 3x 4 + x x +1, x > 0 (a) ydx = 3x 3 3 3 + x 3 / x + x {+c} Attempts to integrate, correct unsimplified integration

More information

Cambridge International Examinations CambridgeInternationalGeneralCertificateofSecondaryEducation

Cambridge International Examinations CambridgeInternationalGeneralCertificateofSecondaryEducation PAPA CAMBRIDGE Cambridge International Examinations CambridgeInternationalGeneralCertificateofSecondaryEducation * 7 0 2 4 7 0 9 2 3 8 * ADDITIONAL MATHEMATICS 0606/22 Paper2 May/June 2014 2 hours CandidatesanswerontheQuestionPaper.

More information

Analytic Trigonometry. Copyright Cengage Learning. All rights reserved.

Analytic Trigonometry. Copyright Cengage Learning. All rights reserved. Analytic Trigonometry Copyright Cengage Learning. All rights reserved. 7.4 Basic Trigonometric Equations Copyright Cengage Learning. All rights reserved. Objectives Basic Trigonometric Equations Solving

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level *2047147351* ADDITIONAL MATHEMATICS 4037/22 Paper 2 October/November 2017 2 hours Candidates answer on the Question Paper. No Additional Materials

More information

Circles, Mixed Exercise 6

Circles, Mixed Exercise 6 Circles, Mixed Exercise 6 a QR is the diameter of the circle so the centre, C, is the midpoint of QR ( 5) 0 Midpoint = +, + = (, 6) C(, 6) b Radius = of diameter = of QR = of ( x x ) + ( y y ) = of ( 5

More information

Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level Cambridge International Examinations Cambridge Ordinary Level * 9 4 5 1 6 2 0 9 2 4 * ADDITIONAL MATHEMATICS 4037/12 Paper 1 October/November 2015 2 hours Candidates answer on the Question Paper. No Additional

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *0835058084* ADDITIONAL MATHEMATICS 0606/11 Paper 1 October/November 2012 2 hours Candidates

More information

Pre-Calculus MATH 119 Fall Section 1.1. Section objectives. Section 1.3. Section objectives. Section A.10. Section objectives

Pre-Calculus MATH 119 Fall Section 1.1. Section objectives. Section 1.3. Section objectives. Section A.10. Section objectives Pre-Calculus MATH 119 Fall 2013 Learning Objectives Section 1.1 1. Use the Distance Formula 2. Use the Midpoint Formula 4. Graph Equations Using a Graphing Utility 5. Use a Graphing Utility to Create Tables

More information

Review for Cumulative Test 2

Review for Cumulative Test 2 Review for Cumulative Test We will have our second course-wide cumulative test on Tuesday February 9 th or Wednesday February 10 th, covering from the beginning of the course up to section 4.3 in our textbook.

More information

MATHEMATICS LEARNING AREA. Methods Units 1 and 2 Course Outline. Week Content Sadler Reference Trigonometry

MATHEMATICS LEARNING AREA. Methods Units 1 and 2 Course Outline. Week Content Sadler Reference Trigonometry MATHEMATICS LEARNING AREA Methods Units 1 and 2 Course Outline Text: Sadler Methods and 2 Week Content Sadler Reference Trigonometry Cosine and Sine rules Week 1 Trigonometry Week 2 Radian Measure Radian

More information

It is known that the length of the tangents drawn from an external point to a circle is equal.

It is known that the length of the tangents drawn from an external point to a circle is equal. CBSE -MATHS-SET 1-2014 Q1. The first three terms of an AP are 3y-1, 3y+5 and 5y+1, respectively. We need to find the value of y. We know that if a, b and c are in AP, then: b a = c b 2b = a + c 2 (3y+5)

More information

AS and A-level Mathematics Teaching Guidance

AS and A-level Mathematics Teaching Guidance ΑΒ AS and A-level Mathematics Teaching Guidance AS 7356 and A-level 7357 For teaching from September 017 For AS and A-level exams from June 018 Version 1.0, May 017 Our specification is published on our

More information

Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours

Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours 1. Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Mark scheme Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question

More information

A Library of Functions

A Library of Functions LibraryofFunctions.nb 1 A Library of Functions Any study of calculus must start with the study of functions. Functions are fundamental to mathematics. In its everyday use the word function conveys to us

More information

ICSE Solved Paper, 2018

ICSE Solved Paper, 2018 ICSE Solved Paper, 018 Class-X Mathematics (Maximum Marks : 80) (Time allowed : Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to

More information

IYGB. 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. 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 information

2011 Mathematics Extension 1 HSC Examination Sample Answers

2011 Mathematics Extension 1 HSC Examination Sample Answers 0 Mathematics Extension HSC Examination Sample Answers When examination committees develop questions for the examination, they may write sample answers or, in the case of some questions, answers could

More information

( and 1 degree (1 ) , there are. radians in a full circle. As the circumference of a circle is. radians. Therefore, 1 radian.

( and 1 degree (1 ) , there are. radians in a full circle. As the circumference of a circle is. radians. Therefore, 1 radian. Angles are usually measured in radians ( c ). The radian is defined as the angle that results when the length of the arc of a circle is equal to the radius of that circle. As the circumference of a circle

More information

Part (1) Second : Trigonometry. Tan

Part (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 information

Core Mathematics C12

Core Mathematics C12 Write your name here Surname Other names Core Mathematics C12 SWANASH A Practice Paper Time: 2 hours 30 minutes Paper - E Year: 2017-2018 The formulae that you may need to answer some questions are found

More information

Core 3 (A2) Practice Examination Questions

Core 3 (A2) Practice Examination Questions Core 3 (A) Practice Examination Questions Trigonometry Mr A Slack Trigonometric Identities and Equations I know what secant; cosecant and cotangent graphs look like and can identify appropriate restricted

More information

MATHEMATICS. IMPORTANT FORMULAE AND CONCEPTS for. Summative Assessment -II. Revision CLASS X Prepared by

MATHEMATICS. IMPORTANT FORMULAE AND CONCEPTS for. Summative Assessment -II. Revision CLASS X Prepared by MATHEMATICS IMPORTANT FORMULAE AND CONCEPTS for Summative Assessment -II Revision CLASS X 06 7 Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.), B. Ed. Kendriya Vidyalaya GaCHiBOWli

More information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level www.xtremepapers.com * 7 7 7 2 2 5 1 5 3 4 * ADDITIONAL MATHEMATICS 4037/23 Paper 2 October/November 2013

More information

CBSE QUESTION PAPER CLASS-X MATHS

CBSE QUESTION PAPER CLASS-X MATHS CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1: In figure, AB = 5 3 cm, DC = 4cm, BD = 3cm, then tan θ is (a) (b) (c) (d) 1 3 2 3 4 3 5 3 Question 2: In figure, what values of x will make DE

More information

CONCEPTS FOR ADVANCED MATHEMATICS, C2 (4752) AS

CONCEPTS FOR ADVANCED MATHEMATICS, C2 (4752) AS CONCEPTS FOR ADVANCED MATHEMATICS, C2 (4752) AS Objectives To introduce students to a number of topics which are fundamental to the advanced study of mathematics. Assessment Examination (72 marks) 1 hour

More information

y mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent

y 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 information

Solutions to RSPL/1. Mathematics 10

Solutions to RSPL/1. Mathematics 10 Solutions to RSPL/. It is given that 3 is a zero of f(x) x 3x + p. \ (x 3) is a factor of f(x). So, (3) 3(3) + p 0 8 9 + p 0 p 9 Thus, the polynomial is x 3x 9. Now, x 3x 9 x 6x + 3x 9 x(x 3) + 3(x 3)

More information

PRACTICE PAPER 6 SOLUTIONS

PRACTICE PAPER 6 SOLUTIONS PRACTICE PAPER 6 SOLUTIONS SECTION A I.. Find the value of k if the points (, ) and (k, 3) are conjugate points with respect to the circle + y 5 + 8y + 6. Sol. Equation of the circle is + y 5 + 8y + 6

More information

Created by T. Madas. Candidates may use any calculator allowed by the regulations of this examination.

Created 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 information

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *7560400886* ADDITIONAL MATHEMATICS 0606/22 Paper 2 May/June 2011 2 hours

More information

ICSE QUESTION PAPER Class X Maths (2016) Solution

ICSE QUESTION PAPER Class X Maths (2016) Solution ICSE QUESTION PAPER Class X Maths (016) Solution SECTION A 1. (a) Let f(x) x x kx 5 Using remainder theorem, f() 7 () () k() 5 7 (8) (4) k() 5 7 16 1 k 5 7 k 16 1 5 7 k 6 k 1 (b) A = 9A + MI A 9A mi...

More information

G H. Extended Unit Tests A L L. Higher Still Advanced Higher Mathematics. (more demanding tests covering all levels) Contents. 3 Extended Unit Tests

G H. Extended Unit Tests A L L. Higher Still Advanced Higher Mathematics. (more demanding tests covering all levels) Contents. 3 Extended Unit Tests M A T H E M A T I C S H I G H E R Higher Still Advanced Higher Mathematics S T I L L Extended Unit Tests A (more demanding tests covering all levels) Contents Extended Unit Tests Detailed marking schemes

More information

1 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.

1 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 information