Here, we have discussed the topics covered in MYP Mathematics, Math SL AA, Math HL AA, Math SL AI and Math HL AI. We have checked their differences and we have given tips for studying effectively for the final test.  ## Mathematics for the Middle Year Programme (MYP)

Students aged 11 to 16 are enrolled in the MYP Programme in which IB students “learn how to learn”. Students who seek an MYP math certificate may take a two-hour on-screen examination while carrying out a mid-level personal project and completing community service.

MYP Mathematics Math IB is presented at two levels: standard and extended. Standard Mathematics aims to provide students with knowledge of basic mathematical concepts, while Extended Mathematics supplements the standard level, introducing additional topics and concepts to encourage greater depth and breadth of comprehension. Students planning to take Math AA (either SL or HL) are strongly recommended to take the extended version of MYP 5.

MYP mathematics (1 through 5 (pre-diploma)) consists of four branches of math that include:

1. Numbers
Topics covered in both standard and extended level include forms of number (integers, fractions, decimals, absolute value, etc), number systems, prime number & factors, sets, Venn diagrams, number lines, estimation, ratio & percentage, number sequences, and integer exponents.
Topics only covered in the extended level include fractional exponents, logarithms, and number bases. Four basic operations for whole numbers, integers, decimals and fractions, number lines, rounding, …

2. Algebra

Topics covered in both standard and extended levels include basic algebraic operations, factorization, substitution, simplification, integer & fractional exponents, patterns & sequences, algorithms, functions (linear, quadratic, exponential, trigonometric), domain & range, transformations, and inequalities.
Topics only covered in the extended level include logarithm with different base number, functions & graphs (inverse and composite), arithmetic & geometric sequences.
building expressions, simplifying expressions, expansion rules, solving equations, linear inequalities, factorization, rational equations, …

3. Geometry and Trigonometry

Topics covered in both standard and extended level include distance formula, angle properties, triangle properties (similar triangles, pythagoras’ theorem), perimeter/area/volume, the cartesian plane, trigonometric ratios, simple transformations (rotations, reflection, translation, stretches), circle geometry (chord length, angles & arcs).
Topics only covered in the extended level include 3D coordinate geometry, similarity & congruence, vectors, sine & cosine rules, trigonometric identities, angle measures (use of radians), the unit circle. angles, lines, parallels and perpendicular lines, parallelism, triangles, quadrilaterals, polygons, circles, 3D objects, coordinate geometry, trigonometric ratios, sine and cosine rules, solving a triangle, …

4. Statistics and Probability

Topics covered in both standard and extended level include graphical representation (pie charts, histograms, line graphs, scatter plots, box-and-whisker), population sampling, mean/mode/median, range, interquartile range, probability (of independent, mutually exclusive, combined, successive events).
Topics only covered in the extended level include standard deviation, conditional probability, samples and populations, dot tables, tally and frequency tables, column graphs, pie charts, plots, mean, median, mode and range, experimental probability, Venn diagram, probability of two-way table, multiplying probabilities and compound events…

The new HL pre-diploma curriculum (MYP 5) covers most of the DP Math 11 SL topics. However, different schools have different approaches as the IB organization does not mandate the exact topics.

MYP requires 50-70 hours of teaching time depending on the level. For completing the course students need to complete an end-of-term on-screen examination. The students in MYP math are assessed on a scale from 1 to 8 according to the following four criteria: “Knowing and Understanding, Investigating Patterns, Communicating, and Applying mathematics in real-life contexts.” You can find a sample question released by IB here.

# Mathematics for IB Diploma Programme (IBDP)

From the August 2019, IBO introduced a new change to the curriculum. The 4 old courses (Math Studies, Math SL, Math HL, Further) were replaced by the two routes that can either be taken at Standard Level (SL) or Higher Level (HL); the 2 routes are “Applications & Interpretations (AI)” and “Applications & Approaches (AA)”. Thus, students can now choose from the following 4 courses: AA SL, AA HL, AI SL, and AI HL. The IB Diploma Programme has a wide range of math courses that according to students’ goals and capabilities may be taken. That being said, not all of them are presented in all schools, especially the schools that are not exclusively IB. Currently, the most common offerings at schools are Math AA SL and Math AA HL.
Below we will explore the specifics of the four courses and the differences between them.

### Analysis and Approaches SL (Math AA SL)

Math AA SL is more suitable for students who enjoy math and are interested in pursuing courses involving a reasonable amount of mathematics after high school (for example, Economics or Biology, etc.) However, it should be noted that for students aspiring to study a STEM major in top-ranking universities, it is still recommended to take Math HL. Therefore, ensure to consult with your school or check your interested universities’ websites to rest assured that you are taking the right course.

Syllabus Outline for Math AA SL:

Topic 1: Numbers and Algebra (19 teaching hrs)

● Arithmetic and geometric sequence & series
● Sigma notation
● Financial applications of geometric sequences & series (compound interest, depreciation)
● Logarithms (base 10 and e) & laws
● Simple deduction proofs
● Change of base (log)
● Binomial theorem

Topic 2: Functions (21 teaching hrs)

• Domain & range
• Inverse Functions
• Point of intersections using GDC
• Composite Functions
• Use of discriminant
• Reciprocal & Rational Functions
• Exponential Functions
• Combined Transformations

Topic 3: Geometry & Trigonometry (25 teaching hrs)

• Distance & Midpoint
• Volume, SA of 3D shapes
• Sine, cosine, tangent ratios
• Sine & Cosine rule
• Circle geometry (sector area, arc length)

Topic 4: Statistics and Probability (27 teaching hrs)

• Discrete & continuous data
• Histograms & Box-and-whisker
• Mean/median/mode
• Standard Deviation, variance, interquartile range
• Pearson’s product-moment coefficient
• Regression line
• Probability (mutually exclusive, independent, combined, conditional)
• Binomial & normal distribution
• Inverse normal calculations

Topic 5: Calculus (28 teaching hrs)

• Limit
• Derivative as the rate of change
• Tangents & normals at a given point
• Intro to anti-differentiation
• Chain, product, quotient rules
• Second derivative
• Max/min/inflection points
• Optimization & Kinematics problems
• Indefinite & definite integrals
• Area between curves

Assessment outline for both Math AA SL and Math AI SL

 Assessment Format Of Assessment Time (hr) Weight (%) External Assessment (EA) Paper 1 (GDC Not Allowed) short-response questions based on syllabus 1.5 40 Paper 2 (GDC Required) extended-response questions based on syllabus 1.5 40 Internal Assessment (IA) Project A Personal and Practical Project That Might involve "Collection of Information or Generation of Measurements" Followed by Analysis and Evaluation. IA is assessed by the teacher and moderated by IB. 20

Note: The external assessments (paper 1 and 2) are marked by examiners appointed by IBO, while the internal assessment (mathematical exploration) is assessed by the teacher, then some are moderated by IBO.

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### APPLICATION AND INTERPRETATION SL (Math AI SL)

Math AI SL is the least academically demanding among the four courses as it emphasizes fundamental concepts rather than complex manipulation skills. As such, Math AI SL is more suitable for students who do not plan to take mathematics as an essential part of their studies at university like law, psychology, languages, etc. On the other hand, students who need to take math as a significant component of their studies like engineering or sciences must take Math AA SL or HL. According to IB, students who take Math AA “will be those who enjoy the thrill of mathematical problem solving and generalization.” While students who take AI “ will be those who enjoy mathematics best when seen in a practical context.”

Syllabus Outline for Math AI SL:

Students who anticipate mathematics as a major component of their university studies should take Math HL. IB recommends it if you are aiming for math, engineering and physics majors. Students can choose to take 2 distinct courses under Math HL: Math AA HL and Math AI HL.

Topic 1: Numbers and Algebra (16 teaching hrs vs 19 for AA)

• Arithmetic, geometric sequence & series
• Sigma notation
• Financial applications of geometric sequences & series (compound interest, depreciation)
• Exponent laws
• Logarithms (base 10 and e)
• % error & estimation
• Technology to solve polynomial equations

Topic 2: Functions (31 teaching hrs vs 21 for AA)

• Domain & range
• Point of intersections using GDC
• Sinusoidal & cubic functions
• Exponential Functions

Topic 3: Geometry and Trigonometry (18 teaching hrs vs 25 for AA)

• Distance & Midpoint
• Volume, Surface Area of 3D shapes
• Sine, cosine, tangent ratios
• Sine & Cosine rule
• Circle geometry (sector area, arc length)

Topic 4: Statistics and Probability (36 teaching hrs vs 27 for AA)

• Discrete & continuous data
• Histograms & Box-and-whisker
• Mean/median/mode
• Standard Deviation, variance, interquartile range
• Pearson’s product moment coefficient
• Regression line
• Probability (mutually exclusive, independent, combined, conditional)
• Binomial, normal distribution
• Inverse normal calculations

Topic 5: Calculus (19 teaching hrs vs 28 for AA)

• Limit
• Derivative as the rate of change
• Tangents & normals at a given point
• Intro to anti-differentiation
• Chain, product, quotient rules
• Max/min/inflection points
• Optimization

A quick look at this file will give you a glimpse of the differences in the subject breakdown between Math AA (SL/HL) and AI (SL/HL)

### IB MATHEMATICS HIGHER LEVEL (HL)

Students who anticipate mathematics as a major component of their university studies should take Math HL. IB recommends it if you are aiming for math, engineering and physics majors. Students can choose to take 2 distinct courses under Math HL: Math AA HL and Math AI HL.

### IB MATHEMATICS ANALYSIS AND APPROACHES (MATH AA HL)

Math AA HL is similar to the old Math HL curriculum and is generally recommended for students who are strongest at math and are interested in studying courses that are math-intensive after high school (for example, engineering, computer science, math, etc.)

Syllabus Outline for Math AA HL:

Below are the topics that HL students must learn in addition to the SL topics (see the section under ‘Mathematics: Analysis and Approaches (Math AA SL)’ above for the list of topics that both levels must learn).

Topic 1: Numbers and Algebra (39 teaching hrs.)

• Permutations & Combinations
• Complex Numbers (real & imaginary, conjugate, modulus, argument)
• Modulus-argument (polar) form
• Euler form
• De Moivre’s Theorem
• Mathematical Induction

Topic 2: Functions (32 teaching hours)

• Polynomial functions
• Factor & remainder theorem
• Sum & Product of roots of polynomials
• Odd & even functions
• Self-inverse functions

Topic 3: Geometry & Trigonometry (51 teaching hours)

• Reciprocal trigonometric ratios
• Compound angle identities
• Vectors (magnitude, position & displacement vector)
• Scalar product
• Parallel, intersecting, skew lines
• Vector equations of a plane
• The intersection between planes, line & plane

Topic 4: Statistics & Probability (33 teaching hrs.)

• Bayes’ theorem
• Variance of discrete random variable
• Continuous random variable

Topic 5: Calculus (55 teaching hrs.)

• Continuity & differentiability at a point
• Derivatives from first principles
• Higher derivatives
• L’Hôpital’s rule & Maclaurin series
• Implicit differentiation
• Related rates of change
• Partial fractions
• Integration by substitution & parts
• Area between curves
• Volumes of revolution about x-axis / y-axis
• Euler’s method

Assessment outline for Math AA HL and Math AI HL

 Assessment Format of Assessment Time (hr) Weight (%) External Assessment (EA) 5 Paper 1 (No Calculator) Two Sections of Short & Extended Response Questions 2 30 Paper 2 (GDC Required) Two Sections of Short & Extended Response Questions 2 30 Paper 3 (GDC Required) Extended Response Questions from Options Course 1 20 Internal Assessment (IA) Project A Personal and Practical Project That Might involve "Collection of Information or Generation of Measurements" Followed by Analysis and Evaluation. IA is assessed by the teacher and moderated by IB. 20

Note: The external assessments (paper 1, 2 and 3) are marked by examiners appointed by IBO, while the internal assessment (mathematical exploration) is assessed by the teacher, then some are moderated by IBO.

### IB MATHEMATICS APPLICATIONS AND INTERPRETATION (MATH AI HL)

Math AI HL is an entirely new addition and is unlike any of the old courses. IBO recommends the course for students interested in math and are strong at it but do not plan to study a math-intensive course after high school (for example, Biology, Chemistry, Economics, etc.).

Syllabus Outline for Math AI HL:

Below are the topics that HL students must learn in addition to the SL topics (see the section under ‘Mathematics: Application and Interpretation (Math AI SL) above for the list of topics that both levels must learn).

Topic 1: Numbers and Algebra (29 teaching hrs.)

• Sum of infinite geometric sequences
• Complex Numbers (real & imaginary, conjugate, modulus, argument)
• Polar, exponential, cartesian form
• Matrix
• Eigenvalues & eigenvectors
• 2 x 2 matrices

Topic 2: Functions (42 teaching hrs.)

• Composite & inverse functions
• Combined transformations
• Sinusoidal, logistic, natural logarithmic models
• Piecewise models

Topic 3: Geometry & Trigonometry (46 teaching hrs.)

• Ambiguous case
• Matrix transformations
• Geometric interpretation of determinant of the transformation matrix
• Vector & Scalar
• Vector application to kinematics

Topic 4: Statistics & Probability (52 teaching hrs.)

• Reliability & Validity tests
• Non-linear regression
• Sum of square residuals
• Coefficient of determination
• Central limit theorem
• Confidence intervals
• Poisson distribution
• Tests for population
• Transition matrices

Topic 5: Calculus (41 teaching hrs.)

• Related rates of change
• Second derivative
• Definite/indefinite integrals
• Areas between curves
• The volume of revolution about x-axis and y-axis
• Kinematic problems
• Slope fields
• Euler’s method

At the end of the day, the most important thing to consider when choosing amongst the four courses is the level of interest and skill you currently have in math. However, it is also essential to consider the potential career pathways you may take beyond high school, including the major you may decide to pursue at university; therefore, ensure to check the course requirements for university admissions into your desirable program!

### TIP FOR STUDENTS doing any level of ib math

1)  Instead of memorizing specific types of questions, understand the concepts.

• IBO is standard, but it also changes the problem styles from time to time, so it is crucial to comprehend instead of systematically memorize.

2)  DO NOT ignore the materials you don’t understand — always seek help.

• If you need tutoring help, get it from companies specializing in IB tutoring, not just any company or any tutor. Hack Your Course AP and IB Tutoring Service has been doing online IB tutoring for a long time and all people engaged know about the ins and outs of the programme.

3) Instead of waiting until the last minute to practice, do a little bit of math consistently every day.

• Remember that math is all about practice, practice, practice.

4) Study well in advance for exams.

•  Most of the time, last-minute studying doesn’t work because there is a long process involved, from understanding the concept to practicing basic problems to challenging yourself with harder problems.

5) Review past topics & notes in time for the final and mock exam

• A common occurrence is for students to forget the prior topics learned, which is a problem as the May and mock exams will include ALL topics.

6) Utilize free online materials

• Visit our webpage for a list of free and cheap resources.

7) Practice with past problems!

• Practicing past exam-style questions will allow you to understand the type of questions IB commonly likes to ask. Do not forget to follow the mark schemes.

8) Time yourself

• When practicing with past exams, make sure to time yourself based on the time allowed for the specific exam. This is because time management is a significant problem for many students.

•  Even if you do many problems, ignoring the questions you don’t know how to do is futile. Remember that the whole point of practice is to learn from your mistakes, so when you encounter similar problems in the future, you will finish them with no problem.

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Phone: (437) 998-2533
Email:
info@ibaptutoring.com

WHERE TO FIND US
Hack Your Course AP & IB Tutoring Service
#230, 2030 Marine Drive
North Vancouver, BC, V7P 1V7, Canada
Phone: (604) 971-2533, (437) 998-2533
Email: info@hackyourcourse.com
Hack Your Course AP & IB Tutoring Service
99 Yorkville Avenue
Toronto, ON M5R 1C1
Phone: (437) 998-2533
Email: info@hackyourcourse.com