This document serves as the central hub for all IB Math courses under development. Each course entry includes a clear description, SEO keywords for YouTube and website optimization, as well as links to course materials, landing pages, and related resources. It ensures consistency across platforms, streamlines content production, and provides a single reference point for the entire team.

Topics’ pages

Start here

Start by downloading the cheat sheet and the vocabulary below. After that, move to the video lessons with their respective exercise lists.

Video lessons

Learn the content with the videos provided and reinforce your comprehension by practicing with the exercise list above.

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Subtopics’ descriptions

Number and Algebra

Proofs by contradiction

Course description

Proofs by contradiction are a fundamental method of mathematical reasoning in which a statement is proven by assuming the opposite and demonstrating that this assumption leads to a logical inconsistency. By arriving at a contradiction, the original statement is confirmed to be true. In IB Mathematics, this technique is commonly used to establish results involving inequalities, number properties, and divisibility, and it plays an important role in developing rigorous mathematical thinking. Students are expected to structure arguments clearly, use precise notation, and communicate reasoning in a logically coherent sequence.

Keywords

• ib math
• proof by contradiction
• proof by contradiction ib math
• contradiction aa hl
• contradiction ib math
• the ib math teacher

Induction proofs

Course description

Mathematical induction is a proof technique used to establish the truth of statements involving positive integers. It consists of two essential steps: verifying the statement for a base case, and then proving that if the statement holds for an arbitrary integer $k$, it must also hold for $k+1$. In IB Mathematics, induction is commonly applied to results involving sequences, series, inequalities, and divisibility. Students are expected to present arguments with logical precision, clear structure, and correct mathematical notation. A strong understanding of induction also supports deeper reasoning across multiple areas of the syllabus.

SEO description

Keywords

• ib math
• induction proof
• proof by induction
• proof by induction math aa hl
• induction proof math aa hl
• the ib math teacher

Calculus

Optimization

Course description

Optimization problems involve finding maximum or minimum values of quantities subject to given constraints, using differentiation as the primary analytical tool. These problems require students to translate real-world situations into mathematical models, identify relevant variables, and analyze critical points to determine optimal solutions. In IB Mathematics, optimization is a key application of calculus that integrates algebraic modeling, differentiation, and logical reasoning. Success in this topic depends on a clear, structured approach: defining variables, constructing an objective function, applying differentiation correctly, and interpreting results within the given context.

Keywords

• ib math
• aa hl
• ib math calculus optimization
• ib math aa optimization
• aa hl optimization
• optimization problems
• ib math optimization problems
• optimization problem example
• the ib math teacher

Integration by parts

Course description

Integration by parts is like IB Math’s version of a good breakup: you start with a hot mess but, after splitting apart, everything falls back in place (hopefully). The trick is knowing who to select to be your u and to be your dv. Pick wisely and the mess untangles beautifully. Pick wrong and, well, you’ll be stuck in algebraic therapy for hours. Once you get the hang of it, integration by parts feels less like heartbreak and more like magic.

Keywords

• ib math
• aa hl
• ib math aa hl integration by parts
• aa hl integration by parts
• integration by parts
• cyclic integration by parts
• examples integration by parts
• the ib math teacher

From ChatGPT

TOPIC 1 — NUMBER & ALGEBRA

Sequences and Series: Arithmetic & Geometric

Course description

Arithmetic and geometric sequences are the ultimate “pattern-spotting” game. Arithmetic sequences add the same thing every time — like your stress level increasing through the IB. Geometric sequences multiply — like the number of assignments your teachers swear are “quick.” Once you crack the formulas, these questions feel less like magic tricks and more like predictable routines you can control. And series? That’s just the grand total of all your mathematical suffering — elegantly summed.

Keywords

• ib math
• arithmetic sequence
• geometric sequence
• arithmetic series
• geometric series
• sequences ib math
• the ib math teacher

The binomial theorem

Course description

The binomial theorem provides a systematic method for expanding expressions of the form $(a+b)^n$ without repeated multiplication. It introduces binomial coefficients, combinations, and structured expansion patterns that are essential for efficient algebraic manipulation, especially for large powers. In IB Mathematics, this topic is particularly important for problem-solving in algebra and calculus, including approximation techniques and series expansions. A solid understanding of the binomial theorem allows students to recognize patterns quickly, work accurately under exam conditions, and connect algebraic structure with combinatorial reasoning.

Keywords

• ib math
• binomial theorem
• binomial expansion
• pascal triangle ib
• aa hl binomial
• the ib math teacher

Laws of Exponents

Course description

Exponent laws are the grammar rules of mathematics — break them, and nothing makes sense. They tell you how powers behave, multiply, divide, grow, and shrink. Once you learn them, simplifying expressions becomes a breeze instead of a battlefield. Think of them as etiquette rules for numbers: no chaos, no drama, just math behaving itself (for once).

Keywords

• ib math
• exponent laws
• indices rules ib
• laws of exponents aa
• simplifying exponents
• the ib math teacher

Logarithms

Course description

Logarithms look scary until you realize they’re just exponents wearing fancy sunglasses. They answer one simple question: “To what power must we raise this number?” Once that clicks, logs become one of the most satisfying tools in algebra. They tame exponential equations, unlock growth and decay models, and make you feel like you’re hacking the matrix. Master logs, and suddenly everything exponential bows to you.

Keywords

• ib math
• logarithms
• log laws
• solving log equations
• exponential and logarithmic relationships
• the ib math teacher

Simultaneous Equations

Course description

Simultaneous equations are the mathematical equivalent of solving a mystery with two clues: two equations, two unknowns — find the culprits. Sometimes you substitute one into the other; sometimes you eliminate; sometimes you graph and hope for the best. Once you learn the techniques, these problems go from “unsolvable crime scene” to “oh, I’ve got this” in seconds.

Keywords

• ib math
• simultaneous equations
• systems of equations
• substitution ib
• elimination ib
• the ib math teacher

Rational Expressions

Course description

Rational expressions look harmless… until you start simplifying them and realize they’re full of traps. Cancel the wrong thing? The math gods will judge you. But once you learn the rules — factor, simplify, identify restrictions — these expressions become surprisingly elegant. Work with them correctly, and you’ll feel like you’ve unlocked a secret level in algebra.

Keywords

• ib math
• rational expressions
• simplifying rational expressions
• rational algebra ib
• the ib math teacher

Financial Mathematics

Course description

Financial math is the part of the course that suddenly feels real. Compound interest, annuities, loans — it’s all the math behind adulting. Understand these formulas, and not only will you ace the IB exams, you’ll also avoid becoming the person who signs a terrible phone contract or thinks “0% interest” is a gift from heaven. This topic is empowerment disguised as homework.

Keywords

• ib math
• financial math ib
• compound interest
• annuities ib
• loans ib math
• the ib math teacher

TOPIC 2 — FUNCTIONS

Functions and Graphs

Course description

Functions are the backbone of modern mathematics — but in IB Math, they’re more like personalities with quirks. Some are linear and predictable (like that one friend who always arrives on time). Others curve dramatically, flip upside down, or run off to infinity the moment you look away. Once you understand domain, range, transformations, and how to read graphs like a story, functions stop being mysterious creatures and start behaving like old acquaintances.

Keywords

• ib math
• functions
• graph transformations
• domain and range ib
• function notation ib
• the ib math teacher

Quadratics

Course description

Quadratics are where algebra decides to get dramatic: parabolas flying up, swooping down, turning points acting like the emotional peak of a telenovela. Once you understand how to factor, complete the square, and use the quadratic formula without crying, you’ll start seeing quadratics everywhere — in physics, finance, and even in projectile drama when you throw your IB Math notes across the room. Master these, and the rest of algebra suddenly feels much more civilized.

Keywords

• ib math
• quadratics
• quadratic equations ib math
• completing the square ib
• solving quadratics
• the ib math teacher

Transformations of Functions

Course description

Transformations are where functions try on different outfits. Slide left, stretch up, flip over the x-axis — it’s algebraic fashion week. The good news? All transformations follow a neat pattern, and once you memorize the rules, you’ll recognize them instantly. By the end, you’ll be able to look at any transformed function and say, “Ah yes, very chic. A bold horizontal shift with a subtle vertical stretch.”

Keywords

• ib math
• transformations of functions
• function shifts ib
• reflections ib math
• stretches and compressions ib
• the ib math teacher

Inverse Functions

Course description

Inverse functions are the mathematical equivalent of rewinding a movie: whatever the original function does, the inverse undoes. If the function makes your life complicated, the inverse politely un-complicates it — assuming it exists, of course. Before that, you’ll need to prove the function is one-to-one. Once everything is in place, inverses become elegant dance partners, perfectly mirroring each other across the line y=xy=xy=x.

Keywords

• ib math
• inverse functions
• one to one functions
• finding inverses ib
• inverse graphs ib
• the ib math teacher

Polynomial Functions

Course description

Polynomials are functions with attitude. Linear functions go straight to the point, quadratics give you a cute parabola… and then cubic and quartic functions start twisting like they’re auditioning for a dance show. Learn how to spot turning points, end behavior, roots, and factorization patterns, and soon you’ll read polynomials the way some people read horoscopes — instantly and with surprising accuracy.

Keywords

• ib math
• polynomial functions
• higher degree functions
• roots and factors ib
• cubic and quartic behavior
• the ib math teacher

Rational Functions

Course description

Rational functions are the dramatic divas of the function world. They have vertical asymptotes, horizontal asymptotes, holes, and sometimes they blow up to infinity just for the drama. But once you learn to factor, simplify, and analyze behavior near asymptotes, these functions suddenly become predictable — like a diva with a very strict daily routine.

Keywords

• ib math
• rational functions
• asymptotes ib
• holes ib math
• rational graphs aa
• the ib math teacher

Exponential Functions

Course description

Exponential functions are the kings of growth. Whether you're modeling population, money, bacteria, or the number of assignments piling up in the IB, exponentials capture anything that grows (or decays) at alarming speed. Once you know how bases, transformations, and asymptotes work, these graphs become incredibly satisfying to sketch and even more satisfying to manipulate.

Keywords

• ib math
• exponential functions
• exponential growth ib
• e to the x ib
• exponential models
• the ib math teacher

Logarithmic Functions

Course description

Logarithmic functions are exponentials in reverse — the “undo” button for growth. They're ideal for measuring how intense something is, like earthquakes, sound levels, or the emotional crash after a math exam. Once you understand logs, their graphs, and how they pair with exponentials, the whole topic becomes beautifully symmetrical.

Keywords

• ib math
• logarithmic functions
• log graphs ib
• ln x ib math
• exponential and logarithmic relationships
• the ib math teacher

Trigonometric Functions

Course description

Trigonometric functions are the original periodic celebrities. They oscillate, repeat, wave, and behave like the universe’s metronome. Once you understand amplitude, period, phase shift, and all the transformations you can throw at sine, cosine, and tangent, you’ll have everything you need to tame any trigonometric graph that comes your way.

Keywords

• ib math
• trig functions
• sine and cosine ib
• tangent graph ib
• trig transformations
• the ib math teacher

Piecewise Functions

Course description

Piecewise functions are mathematical mosaics — different rules for different parts of the domain. They’re the “choose your own adventure” of the function world. At first, it feels chaotic, but once you learn to read each interval carefully, these become some of the most intuitive and visual graphs in the syllabus.

Keywords

• ib math
• piecewise functions
• piecewise graphs
• domain restrictions ib
• step functions ib math
• the ib math teacher

Functional Equations

Course description

Functional equations are puzzles disguised as algebra: you’re given strange relationships like f(x+2)=3f(x)f(x+2)=3f(x)f(x+2)=3f(x) and told to uncover the secret behind the function. They’re clever, sneaky, and deeply satisfying once you catch the pattern. They test creativity more than brute force — a rare break from the usual IB grind.

Keywords

• ib math
• functional equations
• functions aa hl
• recursive functional relationships
• the ib math teacher

Limits

Course description

Limits are where calculus begins — the art of understanding what a function is “approaching” even if it never gets there. It’s like watching someone almost clean their room but never quite finishing. Limits unlock continuity, derivatives, and a whole universe of ideas. Once you get the intuition, it's one of the most beautiful concepts in the entire IB curriculum.

Keywords

• ib math
• limits
• approaching values ib
• continuity ib math
• limit notation
• the ib math teacher

TOPIC 3 — GEOMETRY & TRIGONOMETRY

Geometry and Shapes

Course description

Geometry is where math decides to get visual — lines, triangles, circles, volumes, and all the beautiful symmetry of the world. But in IB Math, it often feels like geometry is personally offended by you. The trick is learning to see the hidden relationships: angles whispering secrets, parallel lines playing games, similar shapes repeating patterns like they’re trying to get your attention. Once it clicks, geometry becomes less “mysterious art form” and more “wow, this actually makes perfect sense.”

Keywords

• ib math
• geometry ib
• shapes and geometry
• angle rules ib
• congruence and similarity
• the ib math teacher

Coordinate Geometry

Course description

Coordinate geometry is where algebra puts on its hiking boots and goes exploring. Lines get slopes, points get coordinates, and circles suddenly have equations. Everything becomes measurable, graphable, and wonderfully logical. Once you know how to work with gradients, midpoints, distances, and equations of lines, the plane becomes your playground.

Keywords

• ib math
• coordinate geometry
• distance formula ib
• midpoint ib
• equation of a line
• the ib math teacher

Vectors

Course description

Vectors are the superheroes of geometry: they have direction, magnitude, and they save you from messy coordinate calculations. Once you learn how to add, subtract, dot, project, and use them to describe motion, it feels like gaining x-ray vision. Everything becomes simpler, neater, and surprisingly elegant.

Keywords

• ib math
• vectors
• vector geometry ib
• dot product ib
• vector applications
• the ib math teacher

Trigonometry: Identities and Equations

Course description

Trigonometric identities are like secret cheat codes that only make sense after hours of confusion. At first, everything looks random — sines becoming cosines, cosines turning into secants — but eventually you see that trigonometry is a perfectly structured world with identities that fit together like puzzle pieces. Once you master the identities, trig equations start falling apart faster than your motivation during exam week.

Keywords

• ib math
• trig identities
• trig equations ib
• sine cosine identity
• trigonometry aa hl
• the ib math teacher

Right-Angle Trigonometry

Course description

Right-angle trigonometry is your first real taste of trig — SOH-CAH-TOA, triangles that behave, and angles that tell you exactly how long a side should be. These questions are clean, crisp, and deeply satisfying once you get the hang of them. If only the rest of IB Math were this polite.

Keywords

• ib math
• soh cah toa
• right triangle trig
• basic trig ib
• trigonometry aa
• the ib math teacher

Non-Right-Angle Trigonometry (Sine Rule, Cosine Rule, Area)

Course description

Non-right-angle trig is where triangles stop being easygoing and start having opinions. When angles aren’t 90°, the sine rule, cosine rule, and area formulas step in like a cleanup crew — restoring order to geometrical chaos. Once you learn which rule to use when, solving triangles feels like detective work with very precise clues.

Keywords

• ib math
• sine rule
• cosine rule
• area of triangle trig
• non right angle trig
• the ib math teacher

Radian Measure

Course description

Radians are the language of pure mathematics — degrees are cute, but radians are destiny. At first, they feel strange (why is π suddenly everywhere?), but once you understand arc length, sector area, and angle-speed relationships, radians become far more natural than degrees could ever dream of being.

Keywords

• ib math
• radians
• radian measure ib
• arc length ib
• sector area
• the ib math teacher

Trigonometric Graphs

Course description

Trig graphs are beautiful, wavy creatures — rising, falling, repeating, and occasionally going vertical just to mess with you (thanks, tangent). Understanding amplitude, period, and phase shift turns these waves from chaotic squiggles into perfectly predictable patterns. Once you master them, you’ll never look at sound waves, tides, or Ferris wheels the same way again.

Keywords

• ib math
• trig graphs
• sine graph ib
• cosine graph ib
• tangent graph ib
• the ib math teacher

3D Geometry

Course description

3D geometry is where shapes go from flat to fabulous. Distances in 3D, angles between lines, planes crossing each other like dramatic soap opera characters — it’s geometry with depth. The moment you learn how to visualize in three dimensions (or at least pretend convincingly), these problems become incredibly satisfying to solve.

Keywords

• ib math
• 3d geometry
• lines and planes ib
• angle between vectors
• geometry hl
• the ib math teacher

Circular Measure & Arc Calculations

Course description

Circular measure questions take everything you’ve learned about angles and wrap it around a circle. Arc length, sector area, radian measure — it’s all about understanding how far around the circle an angle actually takes you. Once the formulas stick, these problems become beautifully mechanical.

Keywords

• ib math
• circular measure
• arc length ib
• sector area ib
• radian applications
• the ib math teacher

Transformations & Symmetry (Geometry)

Course description

Reflections, rotations, translations, enlargements — geometry transformations are like choreographing a dance routine for shapes. At first they seem messy, but with practice, you’ll start predicting exactly how a shape moves, flips, or scales. It’s hugely visual, deeply satisfying, and one of the few topics where drawing neat diagrams actually pays off.

Keywords

• ib math
• geometric transformations
• symmetry ib
• reflections and rotations
• enlargement ib math
• the ib math teacher

TOPIC 4 — STATISTICS & PROBABILITY

Statistics: Representing Data

Course description

Statistics is what happens when math decides to observe the real world instead of living in a fantasy of perfect circles and straight lines. Bar charts, box plots, histograms — each one is a different way of telling a story with data. Once you understand how to choose the right representation and read it like a detective, statistics stops being a jumble of numbers and becomes a superpower for understanding patterns, trends, and the occasional suspicious outlier.

Keywords

• ib math
• statistics ib
• data representation
• histograms ib
• box and whisker ib math
• the ib math teacher

Measures of Central Tendency and Spread

Course description

Mean, median, mode — the holy trinity of “What’s going on here?” And then we meet their edgy cousins: standard deviation and interquartile range. Together, they tell you not just the “average,” but how wildly (or politely) the data behaves around it. Once you learn these measures, you’ll start interpreting real-world data with the confidence of someone who actually understands the news.

Keywords

• ib math
• standard deviation ib
• mean median mode
• spread of data ib
• iqr ib math
• the ib math teacher

Sets, Venn Diagrams, and Logic

Course description

Sets and Venn diagrams are math’s way of organizing chaos. Instead of drowning in data, you draw circles — and suddenly everything makes sense. Intersections, unions, complements… it’s basically the Instagram of mathematics: grouping, sorting, filtering. Logic ties it all together by teaching you how to argue like a lawyer but with symbols instead of shouting.

Keywords

• ib math
• sets ib
• venn diagrams
• logic ib math
• set notation aa
• the ib math teacher

Counting Principles, Permutations, and Combinations

Course description

Counting principles answer life’s biggest question: “How many ways can this go wrong?” Whether you're arranging books, choosing ice cream flavors, or figuring out how many times you can pick the wrong multiple-choice answer — permutations and combinations have you covered. Once you understand when order matters and when it doesn’t, these questions become beautifully mechanical instead of terrifying.

Keywords

• ib math
• permutations
• combinations
• counting principles
• factorial ib math
• the ib math teacher

Binomial Distribution

Course description

The binomial distribution models situations where things either succeed or fail — basically the story of every IB student. Flip a coin, guess an answer, take a shot at a difficult question: binomial distribution tells you the probability of getting exactly the outcomes you want. It’s simple, elegant, and surprisingly powerful — the statistics equivalent of a Swiss army knife.

Keywords

• ib math
• binomial distribution
• probability distribution ib
• stats aa hl
• bernoulli trials
• the ib math teacher

Probability Rules & Combined Events

Course description

Probability is math’s attempt to quantify uncertainty — because “maybe” isn’t a number. With Venn diagrams, trees, and formulas for combined events, you’ll learn how to calculate the likelihood of all kinds of scenarios: winning games, passing tests, or getting a math question right by accident. Once the rules click, probability becomes incredibly predictable, ironically.

Keywords

• ib math
• probability ib
• venn diagram probability
• conditional probability ib
• combined events
• the ib math teacher

Conditional Probability

Course description

Conditional probability answers the classic question: “Given that this already happened, what are the chances of THAT happening?” It’s the math behind medical tests, spam filters, and all the plot twists in detective shows. Once you understand how to apply the formula and read two-way tables, these questions feel logical and surprisingly intuitive.

Keywords

• ib math
• conditional probability
• probability ib math
• two way tables
• dependent events
• the ib math teacher

Probability Distributions

Course description

Probability distributions describe all the possible outcomes of an experiment and how likely each one is. Think of them as the menu of everything that could happen, with probabilities instead of prices. Whether discrete or continuous, distributions help you organize randomness into something you can analyze — and even predict.

Keywords

• ib math
• probability distribution
• discrete distributions ib
• continuous distributions ib
• the ib math teacher

Binomial Distribution

(already appears under Topic 1 but we include it here since it's part of Statistics)

Course description

The binomial distribution models all the little “success vs failure” moments of life — flipping coins, shooting free throws, and answering multiple-choice questions when you're 50% confident but 100% desperate. Once you understand the conditions and formula, binomial questions go from intimidating to deliciously formulaic.

Keywords

• ib math
• binomial distribution
• stats ib aa
• bernoulli trials
• probability of success
• the ib math teacher

Normal Distribution

Course description

The normal distribution is the superstar of statistics — the smooth, symmetrical bell curve that shows up everywhere: test scores, height, measurement errors, your motivation to study over time (declining toward the mean). With z-scores and standard deviations, everything becomes standardized and predictable. It’s one of the most satisfying topics in the entire IB course.

Keywords

• ib math
• normal distribution
• z scores ib
• standard normal ib
• bell curve statistics
• the ib math teacher

Correlation & Regression (Bivariate Statistics)

Course description

Correlation tells you whether two variables are dancing together or ignoring each other completely. Regression draws the “best fit” line that tries to describe their relationship — kind of like the peacemaker in a messy friendship. Once you understand scatter plots, Pearson’s correlation, and regression equations, you’ll be able to analyze relationships like a pro.

Keywords

• ib math
• correlation ib
• regression ib
• scatter plot ib
• pearson correlation ib math
• the ib math teacher

Expected Value

Course description

Expected value is the mathematical way of asking, “What should I expect on average?” It’s the backbone of fair games, insurance, and every casino’s business model. Once students learn it, they also learn why gambling is a bad idea — and why math is the ultimate party pooper.

Keywords

• ib math
• expected value
• mean of distributions
• statistics aa
• probability expectation
• the ib math teacher

Hypothesis Testing

Course description

Hypothesis testing is statistics’ courtroom drama. You begin with an assumption (the null hypothesis), gather evidence, run tests, and decide whether there’s enough proof to reject it. It’s logical, structured, and surprisingly thrilling once you get the hang of test statistics, p-values, and significance levels. Suddenly, you’re not just solving problems — you’re making decisions with data.

Keywords

• ib math
• hypothesis testing ib
• p value ib
• significance level ib
• test statistic aa hl
• the ib math teacher

Chi-Squared Tests

Course description

Chi-squared tests are what happen when you want to know whether reality matches expectation — or whether life has decided to surprise you. These tests compare observed vs expected frequencies and tell you if differences are meaningful or just random noise. It’s like doing a lie detector test on your data.

Keywords

• ib math
• chi squared test
• observed vs expected
• contingency tables ib
• chi square distribution
• the ib math teacher

TOPIC 5 — CALCULUS

Limits

(Already included under Functions, so this version is short and consistent.)

Course description

Limits are the quiet foundation of calculus — the idea that you can understand what a function is heading toward, even if it never quite gets there. It’s like watching someone walk toward the fridge but never actually open it. Once the concept snaps into place, so does the entire logic of derivatives and integrals.

Keywords

• ib math
• limits
• approaching values
• continuity ib
• limit questions aa
• the ib math teacher

Differentiation Basics

Course description

Differentiation is the art of finding slopes, rates, and how fast things change — basically the heartbeat of calculus. Once you learn the derivative rules, you’ll feel like a mathematical Jedi, slicing through functions to reveal their inner behavior. Suddenly, straight lines, curves, and weird polynomial creatures all bow to your power.

Keywords

• ib math
• differentiation
• derivative rules ib
• rate of change ib
• calculus basics
• the ib math teacher

Product Rule

Course description

The product rule exists because sometimes functions refuse to behave nicely and insist on multiplying themselves together. Instead of expanding everything (and crying), the product rule rescues you with a neat formula. Once you master it, you’ll start seeing products everywhere — and differentiating them with the confidence of someone who Actually Knows What They’re Doing™.

Keywords

• ib math
• product rule
• differentiation ib
• derivative techniques
• calculus aa
• the ib math teacher

Quotient Rule

Course description

The quotient rule is what happens when functions divide instead of multiply — and suddenly get messy. Fortunately, calculus gives you a structured way to tame the chaos. It may look intimidating at first, but once you memorize the pattern (low d-high minus high d-low…), it becomes second nature. And very satisfying.

Keywords

• ib math
• quotient rule
• derivative of quotient
• differentiation ib
• calculus aa hl
• the ib math teacher

Chain Rule

Course description

The chain rule is the ultimate “function inside a function” hack: peel off the outside, multiply by the derivative of the inside, and boom — you’ve just differentiated something that would otherwise take 12 minutes and emotional damage to expand. Once it clicks, you’ll see composite functions everywhere, and the chain rule becomes your best friend.

Keywords

• ib math
• chain rule
• composite functions derivative
• differentiation techniques
• the ib math teacher

Implicit Differentiation

Course description

Implicit differentiation is a technique used to differentiate equations in which the dependent variable is not explicitly expressed as a function of the independent variable. Instead of rearranging the equation to isolate one variable, both sides are differentiated directly, applying the chain rule where necessary. In IB Mathematics, implicit differentiation is essential for working with relations such as circles, curves, and more complex algebraic equations. It also forms the foundation for topics such as related rates and curve analysis. Students must demonstrate careful application of differentiation rules, clear notation, and logical progression of steps to meet IB assessment criteria.

Keywords

• ib math
• implicit differentiation
• implicit derivative ib
• calculus aa
• dy/dx implicitly
• the ib math teacher

Related Rates

Course description

Related rates turn everyday motions into calculus puzzles: water filling a tank, shadows stretching, balloons expanding — if something is changing, calculus wants to measure it. The questions look scary, but the process is always the same: relate the variables, differentiate with respect to time, and plug in the numbers. It’s real-world math with a dramatic twist.

Keywords

• ib math
• related rates
• word problems calculus
• dl/dt ib math
• rates of change ib
• the ib math teacher

Stationary Points & Curve Sketching

Course description

Derivatives describe how one quantity changes with respect to another and form the central concept of differential calculus. They represent instantaneous rates of change and can be interpreted geometrically as the gradient of a tangent to a curve at a given point. In IB Mathematics, understanding the meaning of derivatives is essential for interpreting motion, growth, and change, as well as for applying calculus to real-world problems. Students are expected not only to compute derivatives correctly, but also to explain their significance in context, using appropriate mathematical language and notation.

Keywords

• ib math
• stationary points
• maxima minima ib
• first derivative test
• curve sketching ib
• the ib math teacher

Integration Basics

Course description

If differentiation is about tearing functions apart, integration is about putting them back together — like calculus reconstruction surgery. It measures area, accumulates values, and generally makes sense of everything differentiation dismantled. Once you get the basic rules, integration becomes surprisingly zen.

Keywords

• ib math
• integration
• antiderivatives
• indefinite integrals ib
• calculus integration basics
• the ib math teacher

Definite Integrals

Course description

Definite integrals take the area under curves — even the weird ones — and calculate them precisely. At first it feels impossible, but once you learn the Fundamental Theorem of Calculus (a.k.a. the greatest plot twist in math), everything falls into place. Areas, accumulations, totals — all computed effortlessly.

Keywords

• ib math
• definite integrals
• area under curve ib
• ftc ib math
• integral bounds
• the ib math teacher

Integration by Substitution

Course description

Integration by substitution is a fundamental technique used to simplify integrals by reversing the chain rule. It allows complex integrals to be transformed into standard forms through an appropriate change of variable, making them easier to evaluate accurately and efficiently. In IB Mathematics, this method is essential for solving a wide range of integrals involving composite functions and algebraic expressions. Mastery of substitution helps students recognize underlying structures within integrands, select effective substitutions, and apply limits correctly in definite integrals.

Keywords

• ib math
• substitution integration
• u-substitution ib
• antiderivative techniques
• calculus aa
• the ib math teacher

Integration by Parts

(Earlier version exists — but here’s a fresh, short, fun one for Notion completeness.)

Course description

Integration by parts is what happens when integrals refuse to behave. You split the function into a “u” and a “dv,” and if you choose wisely, the new integral becomes simpler instead of worse. Choose poorly and… well… you’ll learn why mathematicians cry. But with practice, this powerful tool becomes one of the most elegant parts of the entire course.

Keywords

• ib math
• integration by parts
• ib math integration
• uv rule integration
• calculus aa hl
• the ib math teacher

Volumes of Revolution

Course description

Volumes of revolution are where calculus turns art into mathematics. Spin a curve around an axis and suddenly — bam — you’ve created a 3D solid. With a single integral, you calculate the volume of shapes that would make ancient geometers quit in frustration. It’s mesmerizing, powerful, and one of the most satisfying skills in IB Math.

Keywords

• ib math
• volumes of revolution
• solid of revolution ib
• pi integral volume
• calculus hl
• the ib math teacher

Differential Equations

Course description

Differential equations describe how things change — they’re the language of physics, biology, engineering, and everything that moves. In IB Math, you’ll solve simple ones by separating variables, integrating, and applying initial conditions. Once you master the process, you’ll feel like you’ve unlocked the secret code behind real-world behavior.

Keywords

• ib math
• differential equations
• separable equations ib
• dy/dx modeling
• calculus applications
• the ib math teacher

Kinematics

Course description

Kinematics is calculus in motion — literally. Position, velocity, acceleration: three siblings connected by derivatives and integrals. Once you see how they interact, motion problems become intuitive and wonderfully systematic. Suddenly, every moving object is just a calculus question waiting to be solved.

Keywords

• ib math
• kinematics
• velocity and acceleration ib
• calculus motion
• s v a relationships
• the ib math teacher