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Mathematics Analysis and Approaches (AA)

AHL 4.13-Bayes theorem

How Is Bayes' Theorem Used in Medical Testing to Assess Risk?

Learn how Bayes' theorem combines prevalence, sensitivity and specificity to calculate medical risk after a positive test in IB Math AA HL exams.

SL 4.12-Z values, inverse normal to find mean and standard deviation

How Do You Use Z-Values to Find an Unknown Mean or Standard Deviation?

Learn how to use z-values and normal probabilities to calculate an unknown mean or standard deviation in IB Mathematics AA exam questions.

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AHL 4.14-Properties of discrete and continuous random variables

What Is a Probability Density Function?

Learn what a probability density function is, how area gives probability, its validity conditions, and key IB Math AA HL exam misconceptions clearly.

AHL 4.14-Properties of discrete and continuous random variables

How Do You Calculate the Mean, Variance, and Standard Deviation of a Discrete or Continuous Random Variable?

Learn the IB Math AA HL formulas and exam steps for calculating the mean, variance, and standard deviation of discrete and continuous random variables.

AHL 4.14-Properties of discrete and continuous random variables

How Do You Find the Mode and Median of a Continuous Random Variable?

Learn how to find the mode and median of a continuous random variable from its probability density function, with a worked IB Mathematics AA HL example.

AHL 4.14-Properties of discrete and continuous random variables

How Does a Linear Transformation Affect E(X) and Var(X)?

Learn how the linear transformation Y = aX + b changes expected value, variance and standard deviation in IB Mathematics AA HL, with an example.

SL 5.1-Introduction of differential calculus

What Are the Different Notations for a Derivative (dy/dx; f'(x))?

Learn how derivative notations such as dy/dx, f'(x), y', ds/dt and dV/dr are used and interpreted in IB Mathematics: Analysis and Approaches.

SL 5.4-Tangents and normal

How Do You Find the Equation of a Normal Line at a Point?

Learn how to find a normal line equation using derivatives, perpendicular gradients, point-gradient form, and correct IB Mathematics AA exam working for full marks.

SL 5.5-Integration introduction, areas between curve and x axis

How Do You Calculate a Definite Integral Using Technology?

Learn how to evaluate a definite integral on a GDC, enter bounds correctly, interpret the result, and show the working IB Mathematics AA examiners expect.

AHL 4.13-Bayes theorem

What Is Bayes' Theorem and How Do You Apply It?

Learn Bayes' theorem for IB Math AA HL, reverse conditional probabilities step by step, and apply it correctly in a worked exam-style example.

SL 5.5-Integration introduction, areas between curve and x axis

What Is Integration as the Anti-Derivative?

Learn how integration reverses differentiation, why the constant of integration is required, and how to show the method in IB Mathematics AA SL exams.

SL 5.4-Tangents and normal

How Do You Find the Equation of a Tangent Line at a Point?

Learn how to find a tangent line using derivatives and point-gradient form, with a worked IB Mathematics AA SL example and precise exam advice.

SL 5.6-Differentiating polynomials n E Q. Chain, product and quotient rules

How Do You Use the Product Rule?

Learn how to apply the product rule in IB Math AA, identify two multiplied functions, differentiate each correctly, simplify, and show working clearly.

SL 5.7-The second derivative

What's the Relationship Between the Graphs of f, f', and f''?

Learn how the graphs of f, f', and f'' reveal gradients, stationary points, increasing intervals, concavity, and points of inflexion in IB Math AA.

SL 5.6-Differentiating polynomials n E Q. Chain, product and quotient rules

What Are the Derivatives of x^n, sin x, cos x, e^x, and ln x?

Learn the five core IB Math AA derivative rules for powers, sine, cosine, exponential and logarithmic functions, with clear examples and exam tips.

SL 5.8-Testing for max and min, optimisation. Points of inflexion

How Do You Find Local Maximum and Minimum Points Using the First or Second Derivative?

Learn how to find and classify local maximum and minimum points using first- and second-derivative tests for IB Mathematics AA SL exams.

SL 5.8-Testing for max and min, optimisation. Points of inflexion

What Is an Optimization Problem and How Do You Solve One?

Learn the IB Math AA optimization method: define variables, use constraints, differentiate, classify stationary points, and check endpoints in exams.

SL 5.3-Differentiating polynomials, n E Z

How Do You Differentiate a Polynomial Function?

Learn how to differentiate polynomial functions using the power rule, with an IB Math AA SL worked example, common errors, and exam technique tips.

SL 5.9-Kinematics problems

How Are Displacement, Velocity, and Acceleration Related Through Differentiation and Integration?

Learn how displacement, velocity, and acceleration are linked by differentiation and integration in IB Mathematics AA SL kinematics questions.

SL 5.6-Differentiating polynomials n E Q. Chain, product and quotient rules

How Do You Use the Quotient Rule?

Learn how to apply the quotient rule in IB Mathematics AA, simplify derivatives correctly, and avoid common sign and denominator errors in exams.

SL 5.6-Differentiating polynomials n E Q. Chain, product and quotient rules

How Do You Use the Chain Rule for Composite Functions?

Learn how to apply the chain rule to composite functions in IB Math AA SL, with worked examples, common errors, and Paper 1 and Paper 2 exam technique.

SL 5.5-Integration introduction, areas between curve and x axis

How Do You Find the Area Under a Curve Using Integration?

Learn how to find the area under a positive curve with a definite integral, evaluate it using an antiderivative, and show full working in IB Math AA exams.

SL 5.8-Testing for max and min, optimisation. Points of inflexion

What Is a Point of Inflection?

Learn how a point of inflection is identified using concavity and sign changes in the second derivative, with IB Math AA examples and exam tips.

SL 5.9-Kinematics problems

What's the Difference Between Distance and Displacement in a Kinematics Problem?

Learn how distance differs from displacement in IB Math AA SL 5.9, including velocity integrals, direction changes, and an exam-style worked example.

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