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Mathematics SL

Runs for 2 years and 4 semesters

Presented by

Firat Vaux Lobut

IB 1 - Semester 1

  • Presumed Knowledge

Use of Technology

  • Functions and Equations 1
  • Trigonometry 1
  • Algebra
  • Statistics 1

IB 1 - Semester 1

Presumed knowledge and use of technology

Number systems and symbols/notations

Finding the general term (nth term)

Simultaneous Equations (including non-linear)

Simplifying Expressions

Parallel and Perpendicular Lines

Solving Equations (including quadratic)

(SL Guide, 2014)

Presumed knowledge and use of technology

Detailed Notes

Presumed knowledge and use of technology

  • Presumed Knowledge

Much of the topic should be covered in pre-DP courses. Fluency is essential in algebraic manipulation for Maths SL. Extra work might be helpful for some students to improve their skills. If possible, it is a good idea to give students a booklet to complete during the summer break before Maths SL begins.

  • Use of technology

Practices on linear, quadratic and simultaneous equations are useful to gain technology skills. Focus is on graphs of these equations, NOT algebra.

Detailed Notes

Internationalism

None

Presumed knowledge and use of technology

Internationalism

Learner Profile

Presumed knowledge and use of technology

None

Learner Profile

Core Subjects and Other Disciplines

Presumed knowledge and use of technology

Core Subjects and Other Disciplines

None

Functions and Equations 1

Quadratic Functions and Equations

Functions

Families of Functions and Transformations of Graphs

(SL Guide, 2014)

Functions and Equations 1

Detailed Notes

Functions and Equations 1

Detailed Notes

  • Quadratic Equations

Students are to factorise, complete the square, use formula and graphical solutions with quadratic equations. They use the discriminant and present graphically. They sketch graphs and retrieve the equation from the graph. Students are to model and optimise quadratic functions.

  • Functions

Students are to learn the concept of function, domain, range, composite function, inverse function, one-to-one and one-to-many functions, and domain restriction.

  • Families of Functions and Transformations of Graphs

Students are to understand the general shape and features of Linear, Quadratic and Cubic functions. They do transformations (reflection, translation and stretch).

The discriminant and modeling should be the main aim. Graphing functions and transforming will be visited later in the course. Geogebra (Graphing/mathematics software) can be used to show trasformation and other properties.

Internationalism

Functions and Equations 1

  • The development of functions

Rene Descartes (France), Gottfried Wilhelm Leibniz (Germany) and Leonhard Euler (Switzerland) (SL Guide, 2014)

  • Use of functions by different civilizations

(Mastin, 2010)

Internationalism

Learner Profile

Functions and Equations 1

Inquirers: Students work on a mini project which is related to real life. The aim must be displaying results as a graphic of a function with Geogebra (or another graphic software).

Communicators: Students are to sketch or draw mathematical functions and equations. They graph both on paper and using technology and record methods, solutions and conclusions using standardized mathematical notation. Students are to interpret and describe transformations of graphs.

Thinker: Students are to apply their function and equation skills to solve unfamiliar and complex problems. (SL Guide, 2014)

Learner Profile

Core Subjects and Other Disciplines

Functions and Equations 1

  • Core Subjects

Is zero the same as nothing?

Is mathematics formal language?

How accurate is a visual representation of a mathematical concept? (SL Guide, 2014)

  • Other Disciplines

Chemistry (sketching and interpreting graphs, equilibrium law)

Geographic skills

Economics (shifting of supply and demand curves)

Physics (kinematics, simple harmonic motion )

Core Subjects and Other Disciplines

Trigonometry 1

The circle: radian measure of angles; length of an arc; area of a sector

Solution of triangles

Cos, sin and tan and the unit circle

Trig identities tan x = sin x / cos x and sin^2x + cos^2x = 1

Definition of cosθ and sinθ in terms of the

unit circle

(SL Guide, 2014)

Trigonometry 1

Detailed Notes

Trigonometry 1

Students are to work on the sine rule, cosine rule and area of a triangle.

They are to solve equations with trig identities. The connection between Pythagoras' theorem and the cosine rule needs to be explained.

Students are to solve questions with triangles and to work on real life applications.

They are to understand the relationship between trig ratios. For example, given sinx, find possible values of tanx without finding "x".

Students are to work with radian, find length of an arc and area of a sector.

Detailed Notes

Internationalism

Trigonometry 1

Internationalism

  • Seki Takakazu calculating π to ten decimal places
  • Why are there 360 degrees in a complete turn? Links to Babylonian mathematics.
  • Hipparchus developed first detailed trigonometry tables
  • Menelaus
  • Ptolemy developed even more detailed trigonometry tables
  • Aryabhata defined trigonometric functions, complete and accurate sine tables, accurate approximation for π (and recognition that π is an irrational number)
  • Cosine rule: Al-Kashi and Pythagoras

(SL Guide, 2014)

(Mastin, 2010)

Learner Profile

Trigonometry 1

Knowledgeable: Students have a chance to understand and explain how things work around us by using trigonometry. (GoogleMap, Engineering, Construct buildings)

Thinker: Students are to apply their trigonometry skills to solve unfamiliar and complex problems.

(SL Guide, 2014)

Learner Profile

Core Subjects and Other Disciplines

Trigonometry 1

Core Subjects and Other Disciplines

  • Core Subjects

Which is a better measure of angle: radian or degree? What are the “best” criteria by which to decide?

Euclid’s axioms as the building blocks of Euclidean geometry. Link to non-Euclidean geometry.

Trigonometry was developed by successive civilizations and cultures. How is mathematical knowledge considered from a sociocultural perspective? (SL Guide, 2014)

  • Other Disciplines

Chemistry (sketching and interpreting graphs, equilibrium law)

Geographic skills

Physics (simple harmonic motion )

Algebra

Sequences and Series

Binomial Theorem and Counting Principles

Elementary treatment of exponents and

logarithms

(SL Guide, 2014)

Algebra

Detailed Notes

Algebra

Detailed Notes

  • Elementary treatment of exponents and logarithms

Students are to review the laws of exponents. They are to learn definitions of logs, change of base and laws of logs. They solve a^x=b using graphical and log methods.

  • Sequences and Series

Students are to learn arithmetic sequences and series, finding the nth term, convergent and divergent sequences as well as periodic and oscillating sequences, sum of finite arithmetic series, sigma notation, geometric sequences and series, sum of finite and infinite geometric series. They work on applications.

  • Binomial Theorem and Counting Principles

Students are to investigate Pascal's triangle and patterns. They learn about factorial notations and understand the relationship between nCr notation and Pascal's triangle. They do the expansion of (a+b)^n up to the 7th degree and see the pattern for coefficients.

Internationalism

Algebra

Internationalism

  • The chess legend (Sissa ibn Dahir)
  • Aryabhatta is sometimes considered the

“father of algebra”. Compare with al-Khawarizmi.

  • The so-called “Pascal’s triangle” was known in China much earlier than Pascal.
  • Babylonian were dealing with algebra on clay tablets.
  • Diophantine analysis of complex algebraic problems, to find rational solutions to equations with several unknowns
  • Muhammad Al-Khwarizmi; the Hindu numerals 1 - 9 and 0 in Islamic world, foundations of modern algebra, including algebraic methods of “reduction” and “balancing”, solution of polynomial equations up to second degree

(SL Guide, 2014)

(Mastin, 2010)

Learner Profile

Algebra

Knowledgeable: Students are to understand the impact of algebra in computing and how it changes our lives.

Thinker: Students are to apply their algebraic skills to solve unfamiliar and complex problems.

(SL Guide, 2014)

Learner Profile

Core Subjects and Other Disciplines

Algebra

  • Core Subjects

How did Gauss add up integers from 1 to 100? Discuss the idea of mathematical intuition as the basis for formal proof.

Debate over the validity of the notion of “infinity”: finitists such as L. Kronecker consider that “a mathematical object does not exist unless it can be constructed from natural

numbers in a finite number of steps”.

What is Zeno’s dichotomy paradox? How far can mathematical facts be from intuition?

Are logarithms an invention or discovery?

  • Other Disciplines

Chemistry (Calculation of pH)

Physics (Motion, Gravity)

(SL Guide, 2014)

Core Subjects and Other Disciplines

Statistics 1

Introduction to Statistics

Central tendency - Applications

Cumulative frequency

(SL Guide, 2014)

Statistics 1

Detailed Notes

Statistics 1

Students are to cover the following contents: population, sample, random sample, discrete and continuous data. They use frequency distributions (tables), frequency histograms with equal class intervals, box-and-whisker plots to present the data.

Students are to find mean-mode-median-range-quartiles. They use technology to interperet and display data.

Students are to do cumulative frequency.

Detailed Notes

Internationalism

Statistics 1

  • The St Petersburg paradox, Chebychev, Pavlovsky
  • Discussion of the different formulae for variance.
  • Contribution of Richard Dawkins

(Mastin, 2010)

(SL Guide, 2014)

Internationalism

Learner Profile

Statistics 1

Learner Profile

Inquirers: The topic offers a good chance for students to work on a mini project which is related to real life. They collect their own data and conduct inquiry. Students work independently.

Communicators: Students are to write conclusions about their outcomes. They mention assumptions, limitations and strengths of their findings. They are required to give evidence for their outcomes with mathematical facts.

Thinker: Students are to understand that a problem can have more than one answer.

(SL Guide, 2014)

Core Subjects and Other Disciplines

Statistics 1

Core Subjects and Other Disciplines

  • Core Subjects

Do different measures of central tendency express different properties of the data? Are these measures invented or discovered? Could mathematics make alternative, equally true, formulae? What does this tell us about mathematical truths?

How easy is it to lie with statistics?

  • Other Disciplines

Psychology (descriptive statistics, random sample)

Biology (calculating mean and standard deviation; comparing means and spreads between two or more samples; correlation does not imply causation)

Statistical calculations to show patterns and changes; geographic skills; statistical graphs

Chemistry (Curves of best fit)

Geography (Geographic skills).

(SL Guide, 2014)

The Exploration/Internal Assessment

Introduction to the Exploration. Explain assessment criteria. Get students to start thinking about a possible exploration topic.

Students are to decide on their exploration titles at the end of the first semester.

Summative and Formative Exams

  • Functions, Algebra and Trigonometry

Formative: Quiz and Mock Exam

Summative: Mid Semester Exam and End of Semester Exam

Summative and Formative Exams

Extended Essay

  • Introductory Meeting during TOK class
  • Research Session with EE Coordinator during TOK class
  • Mandatory meeting with EE Coordinator
  • Individual check-in meetings
  • IB subject area choice

(Extended essay guide, 2007)

("EE Timeline", 2012)

(According to West Sound Academy Extended Essay Timeline, 2018)

IB 1 - Semester 2

  • Probability 1
  • Functions 2 and Graphing
  • Trigonometry 2
  • Statistics 2

IB 1 - Semester 2

Probability 1

Concepts of trial, outcome, equally likely

outcomes, sample space (U) and event

Combined events, P(A U B), intersection

Probability 1

Detailed Notes

Probability 1

Students are to review trial, outcome, equally likely outcomes, sample space (U) and event. They are to work on complementary events, use Venn diagrams, tree diagrams and two-ways tables.

Students are to find answers for combined events, mutually exclusive events, conditional probability, independent events and probabilities with and without replacement.

Students are to make correlations between mathematical notation and English expressions, such as "and", "or", "none", "neither".

Detailed Notes

Internationalism

Probability 1

  • The development of probability

Pierre de Fermat (France), Blaise Pascal (France), Jacob Bernoulli (Switzerland), Abraham de Moivre(France)

(Mastin, 2010)

Internationalism

Learner Profile

Probability 1

Inquirers: Students might do an experiment to find differences between theoretical and experimental probability.

Communicators: Students are to gain an understanding of probability notations and their corresponding meanings in English.

Thinker: Students are to apply their probability skills to solve unfamiliar and complex problems.

Learner Profile

Core Subjects and Other Disciplines

Probability 1

  • Core Subjects

To what extent does mathematics offer models of real life? Is there always a function to model data behaviour?

Is mathematics useful to measure risks?

Can gambling be considered as an application of mathematics?

  • Other Disciplines

Biology (Genetics)

Economy

("Probability - GeneEd - Genetics, Education, Discovery", 2017)

(Myerson, 2005)

Core Subjects and Other Disciplines

Functions 2 and Graphing

Exponential functions and their graphs

Applications of graphing skills and solving

equations that relate to real-life situations

The reciprocal function

Rational functions and their graphs

(SL Guide, 2014)

Functions 2 and Graphing

Detailed Notes

Functions 2 and Graphing

Students are to work on logarithmic functions and their graphs.

Students are to develop a good understanding of real life applications of functions (NOT only logarithmic).

Geometric series.

Students are to graph rational and reciprocal functions.

Students are to use technology for real life applications' graphs and interpret them.

(SL Guide, 2014)

Detailed Notes

Internationalism

Functions 2 and Graphing

  • The Babylonian method of multiplication
  • Sulba Sutras in ancient India and the Bakhshali Manuscript contained an algebraic formula for solving quadratic equations

(SL Guide, 2014)

Internationalism

Learner Profile

Functions 2 and Graphing

Inquirers: Students work on a mini project which is related to real life. The aim must be displaying results as a graphic of a function with Geogebra.

Communicators: Students are to sketch or draw mathematical functions and equations. They graph both on paper and using technology and record methods, solutions and conclusions using standardised mathematical notation.

Thinker: Students are to apply their function skills to solve unfamiliar and complex problems.

(SL Guide, 2014)

Learner Profile

Core Subjects and Other Disciplines

Functions 2 and Graphing

  • Core Subjects

Is zero the same as nothing?

Is mathematics formal language?

How accurate is a visual representation of a mathematical concept?

  • Other Disciplines

Economy (Compound interest, growth and decay)

Physics (Projectile motion; braking distance; electrical

circuits, radioactive decay)

Biology (Half-life)

Core Subjects and Other Disciplines

Trigonometry 2

Radian measure

Cosx, sinx, tanx and unit circle

Trigonometric equations

Double angle formula

Sinx, cosx, tanx and their graphs, composite functions of sinx and cosx

Modelling with trig functions

(SL Guide, 2014)

Trigonometry 2

Detailed Notes

Trigonometry 2

Detailed Notes

Students are to understand the relationship between radian and degree.

They can show cosx, sinx and tanx on the unit circle.

Equations leading to quadratic equations in

sin x, cos x or tan x .

Students become confident using double angle formulas.

They are to use technology to show the circular functions sinx, cosx and tanx, their domains and ranges, amplitude, their periodic nature, and their graphs.

They work with composite functions of the form

f (x) = asin (b(x + c) ) + d, its transformation and applications.

(SL Guide, 2014)

Internationalism

Trigonometry 2

Internationalism

  • Seki Takakazu calculating π to ten decimal places
  • Why are there 360 degrees in a complete turn? Links to Babylonian mathematics.
  • Hipparchus developed first detailed trigonometry tables
  • Menelaus
  • Ptolemy developed even more detailed trigonometry tables
  • Aryabhata defined trigonometric functions, complete and accurate sine tables, accurate approximation for π (and recognition that π is an irrational number)
  • Cosine rule: Al-Kashi and Pythagoras
  • (SL Guide, 2014)
  • (Mastin, 2010)

Learner Profile

Trigonometry 2

Knowledgeable: Students have a chance to understand and explain how things work around us by using trigonometry. (Soundwaves, wave, change of temperature)

Thinker: Students are to apply their trigonometry skills to solve unfamiliar and complex problems.

Communicators: Students are to graph their findings by using technology and interpret the important points.

(SL Guide, 2014)

Learner Profile

Core Subjects and Other Disciplines

Trigonometry 1

Core Subjects and Other Disciplines

  • Core Subjects

Which is a better measure of angle: radian or degree? What are the “best” criteria by which to decide?

Euclid’s axioms as the building blocks of Euclidean geometry. Link to non-Euclidean geometry.

Trigonometry was developed by successive civilizations and cultures. How is mathematical knowledge considered from a sociocultural perspective? (SL Guide, 2014)

  • Other Disciplines

Chemistry (sketching and interpreting graphs, equilibrium law)

Geographic skills

Physics (simple harmonic motion, motion of sound )

Statistics 2

Linear correlation of brivate data

Correlation coefficient r

Scatter diagrams

Line of best fit

Equation of the regression line of y on x

Use of the equation for prediction purposes

(SL Guide, 2014)

Detailed Notes

Statistics 2

Students are to work with bivariate analysis and scatter diagrams. They reflect their findings with the line of best fit.

They predict equations' outcomes by using different methods, for exmaple, least squares regression and measuring correlation.

Students are to understand and work with correlation coefficient r. They draw scatter diagrams and the line of best fit.

Detailed Notes

Internationalism

Statistics 2

  • The St Petersburg paradox, Chebychev, Pavlovsky
  • Discussion of the different formulae for variance.
  • Contribution of Richard Dawkins

(Mastin, 2010)

(SL Guide, 2014)

Internationalism

Learner Profile

Statistics 2

Learner Profile

Inquirers: The topic offers a chance for students to work on a mini project which is related to real life. They collect their own data and conduct inquiry. Students work independently.

Communicators: Students are to write conclusions about their outcomes. They mention assumptions, limitations and strengths of their findings. They are required to give evidence for their outcomes with mathematical facts.

Thinker: Students are to understand that a problem can have more than one answer.

(SL Guide, 2014)

Core Subjects and Other Disciplines

Statistics 2

Core Subjects and Other Disciplines

  • Core Subjects

Can we predict the value of x from y, using this equation?

Can all data be modelled by a (known) mathematical function? Consider the reliability

and validity of mathematical models in describing real-life phenomena.

  • Other Disciplines

Psychology (descriptive statistics, random sample)

Biology (calculating mean and standard deviation; comparing means and spreads between two or more samples; correlation does not imply causation)

Statistical calculations to show patterns and changes; geographic skills; statistical graphs

Chemistry (Curves of best fit)

Geography (Geographic skills).

(SL Guide, 2014)

The Exploration/Internal Assessment

Students are to work on exploration in class. Their progress is monitored.

They are requiered to complete their draft.

The Exploration/Internal Assessment

Summative and Formative Exams

  • Statistics and Probability

Formative: Quiz

Summative: Written assignment

  • Probability, Functions and Graphing, Trigonometry and Statistics

Formative: Quiz and Mock Exam

Summative: End of Semester Exam

Extended Essay

  • First reflection session
  • Due first reflection
  • Research Session
  • Check-in Session
  • First draft due
  • Check-in Session

(Extended essay guide, 2007)

("EE Timeline", 2012)

(According to West Sound Academy Extended Essay Timeline, 2018)

IB 2 - Semester 1

  • Calculus 1 - Differentiation
  • Vectors
  • Calculus 2 - Integration

IB 2 - Semester 1

Calculus 1 -Differentiation

Limits

Differentiation from first principles

Derivative interpreted as gradient function and as rate of change

Tangents and normals, and their equations

Derivatives of polynomial functions

Differentiation of a sum

The chain rule for composite functions

The product and quotient rules

The second derivative

Local maximum and minimum points

Points of inflexion with zero and non-zero

gradients

Optimization

(SL Guide, 2014)

Detailed Notes

Calculus 1 -Differentiation

Detailed Notes

Students are to work with limit and understand limit notation. They learn the meaning and graphics of first principles. Students find the derivative by using first principles.

They use the derivative rules and find the derivative of x^n, sinx, cosx, tanx, e^x and ln x.

They use derivative to find equations of tangents and normals.

Students are to interpret derivative as gradient and rate of change.

They derivate a sum of functions.

They use the chain rule, product and quotient rules.

Second derivative.

They find local maximum and minimum points and test their results.

Students are to work on applications of derivative. Optimization.

They are to show the relationship between behaviour of functions and thier graphs. f, f' and f''.

Internationalism

Calculus 1 -Differentiation

  • The debate over whether Newton or

Leibnitz discovered certain calculus concepts

  • Liu Hui discovered early forms of integral and differential calculus
  • Bhaskara II introduced some preliminary concepts of calculus
  • Isaac Newton developed infinitesimal calculus (differentiation and integration)
  • Gottfried Leibniz independently developed infinitesimal calculus (his calculus notation is still used).

(SL Guide, 2014)

(Mastin, 2010)

Internationalism

Learner Profile

Calculus 1 -Differentiation

Inquirers: Students are to understand the meaning of differentiation by working on a real situation. For example, they can find the optimum volume of a soft drink can, cost of building a house, area of a farm, possible lifetime of a cell etc.

Knowledgeable: Students are to explore the use of derivative in our lives. For example, the stock exchange, the population growth, how fast someone must run to break the 100m World record etc.

Thinker: Students are to apply their differentiation skills to solve unfamiliar and complex problems.

(SL Guide, 2014)

Learner Profile

Core Subjects and Other Disciplines

Calculus 1 -Differentiation

Core Subjects and Other Disciplines

  • Core Subjects

What value does the knowledge of

limits have? Is infinitesimal behaviour

applicable to real life?

Opportunities for discussing hypothesis

formation and testing, and then the formal proof can be tackled by comparing certain cases, through an investigative approach.

  • Other Disciplines

Economics (marginal cost, marginal revenue, marginal profit)

Chemistry (interpreting the gradient of a curve, particle motion)

Phsyics (velocity, acceleration, planetary motion)

Profit, area and volume

(SL Guide, 2014)

Vectors

Vectors as displacements

Components of vectors, base vectors I, j, k

Algebraic and geometric approaches to vector properties

The scalar product of two vectors

Vector equation of a line

Determining whether two lines intersect

Distinguishing between coincident and parallel lines

Applications

(SL Guide, 2014)

Vectors

Detailed Notes

Vectors

Detailed Notes

Students are introduced to the components of a vector and work with 2 and 3 dimension vectors. They understand the vectors as displacements in space.

They solve the sum and difference of two vectors, zero vector and the vector -v. They multiply a vector by its scalar.

Students find the magnitude of a vector. They discuss the meaning of magnitude. They develop an understanding of base vectors, i, j and k and position vector.

They are to work with questions on scalar product of two vectors, perpendicular and parallel vectors and find an angle between two vectors.

They are to develop a strong understanding of vector equation of a line.

Students can show the difference between coincident and parallel lines. They can find the intersection of two vectors or determine if two vectors intersect.

(SL Guide, 2014)

Internationalism

Vectors

  • Who developed vector analysis:

JW Gibbs or O Heaviside?

  • Which is the first used of vectors the lost work of Aristotle or the Mechanics of Heron of Alexendria?

(SL Guide, 2014)

("Vectors", 2017)

Internationalism

Learner Profile

Vectors

Communicators: Students are to sketch vectors. They understand that they can display mathematical results with vectors as well. For example, distance between two points, parallel and perpendicular lines, intersection of two lines.

Thinker: Students are to apply their vector skills to solve unfamiliar and complex problems.

Learner Profile

Core Subjects and Other Disciplines

Vectors

  • Core Subjects

How do we relate a theory to the author?

Are algebra and geometry two separate domains of knowledge?

  • Other Disciplines

Physics (vector sums and differences, vector resultants)

(SL Guide, 2014)

Core Subjects and Other Disciplines

Calculus 2 - Integration

Indefinite integration – anti-differentiation

Indefinite integral of of x^n, e^x, sinx, cosx and 1/x

Composites

Definite integrals and boundary conditions

Areas under curves

Volumes of revolution

Calculus 2 - Integration

Detailed Notes

Calculus 2 - Integration

Detailed Notes

Students are to understand the relationship between differentiation and integration.

They are to solve questions with indefinite integrations, find c. They work with indefinite integral of of x^n, e^x, sinx, cosx and 1/x.

Students are to integrate by inspection.

They do integration with boundary conditions. They find areas under curves or between curves.

They find the volume of an object or a shape after the revolution around x-axis.

Students are to do definite integrals using technology.

(SL Guide, 2014)

Internationalism

Calculus 2 - Integration

  • Successful calculation of the volume of

the pyramidal frustum by ancient Egyptians

(Egyptian Moscow papyrus)

  • Use of infinitesimals by Greek geometers
  • Accurate calculation of the volume of a

cylinder by Chinese mathematician Liu Hui

  • Ibn Al Haytham: first mathematician to

calculate the integral of a function, in order to

find the volume of a paraboloid.

(SL Guide, 2014)

Internationalism

Learner Profile

Calculus 2 - Integration

Inquirers: Students are to understand the meaning of integration by working on a real situation. For example, they can find the exact volume of a soft drink can or the speed of a spaceship.

Knowledgeable: Students are to explore the use of integration in life. For example, volume of production in factories, electric charges and universal gravitation.

Thinker: Students are to apply their integration skills to solve unfamiliar and complex problems.

(SL Guide, 2014)

Learner Profile

Core Subjects and Other Disciplines

Calculus 2 - Integration

Core Subjects and Other Disciplines

  • Core Subjects

Mathematics and knowledge claims. Euler was able to make important advances in mathematical analysis before calculus had been put on a solid theoretical foundation by Cauchy and others. However, some work was not possible until after Cauchy’s work. What does this tell us about the importance of proof and the nature of mathematics?

Mathematics and the real world. The seemingly abstract concept of calculus allows us to create mathematical models that permit human feats, such as getting a man on the Moon. What does this tell us about the links between mathematical models and physical reality?

(Eastaugh & Sternal-Johnson, 2013)

Other Disciplines

Physics (velocity, acceleration, universal gravitation)

(SL Guide, 2014)

The Exploration/Internal Assessment

Students are to complete the exploration by the end of semester 3.

The Exploration/Internal Assessment

Summative and Formative Exams

  • Calculus and Vectors

Formative: Quiz and Mock Exam

Summative: Mid Semester and End of Semester Exam

Summative and Formative Exams

Extended Essay

  • Second reflection session
  • Due second reflection
  • Check-in Session
  • Final draft due

(Extended essay guide, 2007)

("EE Timeline", 2012)

(According to West Sound Academy Extended Essay Timeline, 2018)

Extended Essay

IB 2 - Semester 2

  • Calculus 3 - Kinematics and Trig Functions
  • Statistics 3
  • Revision
  • Mock external exams
  • External Exam

IB 2 - Semester 2

Calculus 3 - Kinematics and Trig Functions

Derivatives of trig functions

Integrals of sinx and cosx

Kinematics

(SL Guide, 2014)

Calculus 3 - Kinematics and Trig Functions

Detailed Notes

Calculus 3 - Kinematics and Trig Functions

Students are to revisit and derivate and integrate trig functions in more detail.

They work with displacement s, velocity v and acceleration a to solve kinematic problems.

(SL Guide, 2014)

Detailed Notes

Internationalism

Calculus 3 - Kinematics and Trig Functions

  • The debate over whether Newton or
  • Leibnitz discovered certain calculus concepts
  • Liu Hui discovered early forms of integral and differential calculus
  • Bhaskara II introduced some preliminary concepts of calculus
  • Isaac Newton developed infinitesimal calculus (differentiation and integration)
  • Gottfried Leibniz independently developed infinitesimal calculus (his calculus notation is still used).

(SL Guide, 2014)

(Mastin, 2010)

Internationalism

Learner Profile

Calculus 3 - Kinematics and Trig Functions

Inquirers: Students are to understand the meaning of differentiation by working on a real situation. For example, they can find the distance of a particle after a certain time, speed of a car or acceleration of a spaceship.

Knowledgeable: Students are to explore the use of derivative and integral in life. For example, finding the necessary force to leave the earth with a spaceship or the distance required to stop while travelling at a certain speed.

Thinker: Students are to apply their skills to solve unfamiliar and complex problems.

(SL Guide, 2014)

Learner Profile

Core Subjects and Other Disciplines

Calculus 3 - Kinematics and Trig Functions

  • Core Subjects

Mathematics and the real world. The seemingly abstract concept of calculus allows us to create mathematical models that permit human feats, such as getting a man on the Moon. What does this tell us about the links between mathematical models and physical reality?

(Eastaugh & Sternal-Johnson, 2013)

  • Other Disciplines

Physics (kinematics)

Core Subjects and Other Disciplines

Statistics 3

Discrete random variables

Binomial distribution

Normal distributions and curves

Standardization of normal variables (z-values, z-scores)

(SL Guide, 2014)

Statistics 3

Detailed Notes

Statistics 3

Detailed Notes

Students are to work on discrete random variables and their probability distributions.

They are to do expected value, E(x) for discrete data. They work under real life application, games of chance, fair game etc.

Students are to understand the concept of binomial distribution.

They do mean, variance and standard deviation.

Continuous random variables and their probability distributions.

Students are to work with Normal and Standard Normal distributions and their curves.

(SL Guide, 2014)

Internationalism

Statistics 3

  • The St Petersburg paradox, Chebychev, Pavlovsky
  • Discussion of the different formulae for variance.
  • Contribution of Richard Dawkins

(Mastin, 2010)

(SL Guide, 2014)

Internationalism

Learner Profile

Statistics 3

Inquirers: The topic offers a chance for students to work on a mini project which is related to real life. They collect their own data and conduct inquiry. Students work independently.

Thinker: Students are to apply their statistics skills to solve unfamiliar and complex problems.

(SL Guide, 2014)

Learner Profile

Core Subjects and Other Disciplines

Statistics 3

  • Core Subjects

How easy is it to lie with statistics?

  • Other Disciplines

Biology (links to normal distribution)

Psychology (descriptive statistics)

Core Subjects and Other Disciplines

Revision

Mock Exams

Mock Exams

  • 3 hours in total
  • Paper 1 (without calculator) and Paper 2 (with calculator) - different days

External Exam

External Exam - Exam Block

From 27 October to November 17

(According to IB Diploma Programme November 2017 examination schaedule)

Extended Essay

  • Draft session
  • Final Copy
  • Final reflection session
  • Final reflection due

(Extended essay guide, 2007)

("EE Timeline", 2012)

(According to West Sound Academy Extended Essay Timeline, 2018)

Extended Essay

Timeline

Semester 1 IB 1

Semester 2 IB 2

Semester 1 IB 1

Semester 2 IB 2

Timeline

Algebra 9 hours

Functions and equations 24 hours

Circular functions and trigonometry 16 hours

Vectors 16 hours

Statistics and probability 35 hours

Calculus 40 hours

Exploration 10 hours

Total 150 hours

Semester 1 IB 1

The items in the timeline are arranged in chronicle order.

Semester 1 IB 1

Presumed Knowledge - Use of Technology

  • 3 hours

Functions and Equations 1

  • 14 hours

Trigonometry 1

  • 9 hours

Summative Exam 1

  • Functions and Equations and Intro to Trigonometry (1.5 hours)

Algebra

  • 9 hours

Statistics 1

  • 12 hours

The Exlporation

  • 2 hours

Summative Exam 2

  • Trigonometry, Algebra and Statistics (1.5 hours)

Extended Essay

  • 5 hours

The Formative and Summative Assessments

  • Formative assessments are class quizes. They are used during or/and at beginning of subjects to enhance learning.
  • Summative assessments are one in the middle of the semester and one at the end of the semester, class exams.

Semester 1 IB 2

The items in the timeline are arranged in chronicle order.

Semester 1 IB 2

Probability 1

  • 9 hours

Summative assessment 3 - Written assignment

  • Statistics and Probability - 5.5 hours

Functions 2

  • 10 hours

Trigonometry 2

  • 7 hours

Statistics 2

  • 9 hours

The Exlporation

  • 6 hours - Draft

Summative assessment 4

  • Functions, trigonometry and statistics (1.5 hours)

Extended Essay

  • 10 hours

The Formative and Summative Assessments

  • Formative assessments are class quizes. They are used during or/and at beginning of subjects to enhance learning.
  • Summative assessments are one in the first half of the semester and one at the end of the semester, class exam and written assignment.

Semester 2 IB 1

The items in the timeline are arranged in chronicle order.

Semester 2 IB 1

Calculus 1

  • 18 hours

Vectors

  • 16 hours

Summative Assessment 5

  • Calculus and vectors (1.5 hours)

Calculus 2

  • 12 hours

The Exlporation

  • 2 hours - Due at the end of the term

Summative Assessment 6

  • Calculus (1.5 hours)

Extended Essay

  • 8 hours

The Formative and Summative Assessments

  • Formative assessments are class quizes. They are used during or/and at beginning of subjects to enhance learning.
  • Summative assessments are one in the middle of the semester and one at the end of the semester, class exams. (3 hours in total)

Semester 1 IB 2

The items in the timeline are arranged in chronicle order.

Calculus 3

  • 10 hours

Statistics 3

  • 5 hours

Extended Essay

  • 10 hours

Revision

  • 4 hours

Mock Exams

  • 9 hours

External Exams - Block of Exam Time

  • 21 hours or a term (half a semester)

Semester 1 IB 2

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