ACSI 2025 Year 6 Mathematics HL guidebook

“Do nothing from selfish ambition or conceit, but in humility consider others more significant than yourselves” – Philippians 2:3 (ESV) YEAR 6 HL GUIDEBOOK 2025 MATHEMATICS: ANALYSIS AND APPROACHES For Internal Circulation Only Name : Class :

Anglo-Chinese School (Independent) Year 6 IBDP Mathematics: Analysis and Approaches HL CONTENTS I Aims & Assessment and Syllabus II Formula Booklet III Notes and Worksheets Topic 5 : Calculus 5.1 Limits and Differentiation 5.2 Applications of Differentiation 5.3 Integration 5.4 Area and Volume of Revolution 5.5 Kinematics 5.6 Differential Equations 5.7 Maclaurin’s Series Topic 4 : Statistics and probability 4.1 Descriptive Statistics 4.2 Correlation and regression 1.3 Permutations and combinations 4.3 Probability 4.4 Discrete random variables 4.5 Binomial distribution 4.6 Continuous random variables 4.7 Normal distribution Paper 3 Skills Paper 3 Practice Questions Paper 3 Past Year Papers IV Past Year IB Questions (Topical) V Specimen Papers This guidebook is compiled for use by the students and teachers of ACS (Independent) only. It is meant for internal use only.

IB learner profile I profile IB learner p arner profile IB lea ile IB learner profi IB learner profile I er profile IB learne © International Baccalaureate Organization 2017 International Baccalaureate® | Baccalauréat International® | Bachillerato Internacional® The IB learner pro/f_ile represents 10 attributes valued by IB World Schools. We believe these attributes, and others like them, can help individuals and groups become responsible members of local, national and global communities. We nurture our curiosity, developing skills for inquiry and research. We know how to learn independently and with others. We learn with enthusiasm and sustain our love of learning throughout life. We develop and use conceptual understanding, exploring knowledge across a range of disciplines. We engage with issues and ideas that have local and global signi/f_icance. We use critical and creative thinking skills to analyse and take responsible action on complex problems. We exercise initiative in making reasoned, ethical decisions. We express ourselves con/f_idently and creatively in more than one language and in many ways. We collaborate effectively, listening carefully to the perspectives of other individuals and groups. We act with integrity and honesty, with a strong sense of fairness and justice, and with respect for the dignity and rights of people everywhere. We take responsibility for our actions and their consequences. We critically appreciate our own cultures and personal histories, as well as the values and traditions of others. We seek and evaluate a range of points of view, and we are willing to grow from the experience. We show empathy, compassion and respect. We have a commitment to service, and we act to make a positive difference in the lives of others and in the world around us. We understand the importance of balancing different aspects of our lives /emdash.capintellectual, physical, and emotional/emdash.capto achieve well-being for ourselves and others. We recognize our interde- pendence with other people and with the world in which we live. We thoughtfully consider the world and our own ideas and expe- rience. We work to understand our strengths and weaknesses in order to support our learning and personal development. We approach uncertainty with forethought and determination; we work independently and cooperatively to explore new ideas and innovative strategies. We are resourceful and resilient in the face of challenges and change. IB learner profile The aim of all IB programmes is to develop internationally minded people who, recognizing their common humanity and shared guardianship of the planet, help to create a better and more peaceful world. As IB learners we strive to be: THE IB LEARNER PROFILE

PAUL’S WHEEL OF REASONING Using Paul’s Wheel of Reasoning in Mathematics • Purpose (What do you think is the purpose of giving you that fact?) • Question at Issue (What is the question asking for in your own words?) • Information (Please read and list all the facts and information) • Assumptions (What do you think is the assumption behind the given information?) • Concepts (What are the key concepts you need in order to resolve this question?) • Point of View (Is there any other way of seeing this problem?) • Interpretation and Inference (Given the question and the information, what do you think are the key moves to solve this problem?) • Implication and Consequences (Based on your point of view, what would be the steps you take to solve this maths problem?)

© International Baccalaureate Organization 2023 Diploma Programme Mathematics: analysis and approaches HL formula booklet For use during the course and in the examinations First examinations 2021 Version 1.0 HIGHER LEVEL

Anglo-Chinese School (Independent) Mathematics Department Setting Press-To-Test for TI-Nspire CX II 1) Make sure your GDC is switched OFF 2) Press ESC d and HOME c buttons simultaneously. 3) A pop up box will appear. 4) Change Angle Setting to Radians 5) Unselecting Functions • DO NOT press ENTER · while selecting the functions. • Use only the TAB e button to scroll down the list. • Uncheck by pressing the centre of the scroll button x when the function you want is highlighted. • Applications that are approved (MUST NOT BE TICKED) o Disable inequality graphing o Limit trigonometric functions o Disable logb x template and summation functions o Disable Polynomial Root Finder and Simultaneous Equation Solver o Disable Numerical Solver o Disable Sliders • Applications that are NOT approved (MUST BE TICKED) o Limit geometry functions o Disable function and conic grab and move, and disable change of equation form o Disable vector functions, including eigenvectors and eigenvalues o Disable “isPrime” function o Disable differential equation graphing o Disable 3D graphing o Disable implicit graphing, conic templates, conic analysis and geometric conics. 6) Once done, press ENTER · 7) Your GDC will enter press-to-test mode and the LED will blink Orange

Contents Topic 1: Number and algebra – HL 2 Topic 2: Functions – HL 3 Topic 3: Geometry and trigonometry – HL 4 Topic 4: Statistics and probability – HL 7 Topic 5: Calculus – HL 9

Mathematics: analysis and approaches HL formula booklet 2 Topic 1: Number and algebra – HL 1.2 The nth term of an arithmetic sequence 1 ( 1)=+−nuu n d The sum of n terms of an arithmetic sequence ( )112 ( 1) ; ( )22 n nn nnS u n d S uu= +− = + 1.3 The nth term of a geometric sequence 1 1 n nu ur −= The sum of n terms of a finite geometric sequence 11( 1) (1 ) 11 nn n ur u rS rr −−= = −− , 1r ≠ 1.8 The sum of an infinite geometric sequence 1 ,11 uSr r ∞ = <− 1.4 Compound interest 1 100 kn rFV PV k = ×+  , where FV is the future value, PV is the present value, n is the number of years, k is the number of compounding periods per year, r% is the nominal annual rate of interest 1.5 Exponents and logarithms logx aab x b=⇔= , where 0, 0, 1aba>>≠ 1.7 Exponents and logarithms log log loga aaxy x y= + log log loga aa x xyy = − log logm aaxm x= Exponential and logarithmic functions loglog log b a b xx a= lnex xaa = ; loglog a xx a a xa= = where , 0, 1ax a>≠ 1.9 Binomial theorem n∈  1() C C 1 n n n nr r nnnab a ab a b b r −−+ = + ++ ++  !C !( )! nn r rn r= −

Mathematics: analysis and approaches HL formula booklet 3 1.10 Combinations !C !( )! nn r rn r= − Permutations Extension of binomial theorem, n∈  !P ( )! nn r nr= − ( ) ( ) 2 11 ...2! n n nnbbab a n aa  − += + + +     1.12 Complex numbers iz ab= + 1.13 Modulus-argument (polar) and exponential (Euler) form i(cos isin ) e c