Learn how to integrate by inspection using the reverse chain rule, recognize the required derivative factor, adjust constants, and avoid IB exam errors.

SL 5.11-Definite integrals, areas under curve onto x-axis and areas between curves

How Do You Find the Area Between a Curve and the X-Axis When the Function Is Negative?

Learn why a negative definite integral must be made positive to find area, when to split at roots, and how to show full working in IB Math AA exams.

SL 5.11-Definite integrals, areas under curve onto x-axis and areas between curves

How Do You Find the Area Between Two Curves?

Learn how to find the area between two curves using intersections, upper-minus-lower integration, split intervals, and clear IB Math AA exam steps.

AHL 5.13-Limits and L’Hopitals

What Is L'Hôpital's Rule and When Do You Use It?

What is L'Hôpital's rule and when should IB Math AA HL students use it? Learn the valid indeterminate forms, method, examples, and key exam pitfalls.

AHL 5.12-First principles, higher derivatives

What Does It Mean for a Function to Be Continuous at a Point?

Learn the three conditions for continuity at a point, see a worked piecewise example, and understand the exact IB Mathematics AA HL exam scope for AHL 5.12.

AHL 5.12-First principles, higher derivatives

How Do You Find the Derivative From First Principles Using Limits?

Learn how to find a derivative from first principles using the limit definition, with a worked IB Math AA HL example, common errors, and exam tips.

AHL 5.12-First principles, higher derivatives

What Does It Mean for a Function to Be Differentiable at a Point?

Learn what differentiability at a point means, how the derivative limit works, why continuity is necessary, and what IB Math AA HL exams expect from students.

AHL 5.12-First principles, higher derivatives

What Are Higher Derivatives?

Learn what higher derivatives are, how to calculate and interpret them, and how IB Mathematics AA HL students should show correct working in examinations.

AHL 5.13-Limits and L’Hopitals

How Do You Evaluate a Limit of the Indeterminate Form \(0/0\) or \(\infty/\infty\)?

Learn how IB Math AA HL students identify indeterminate quotient limits, apply L’Hôpital’s rule correctly, repeat it, and present full exam working.

AHL 5.14-Implicit functions, related rates, optimisation

How Do You Differentiate an Implicit Function?

Learn implicit differentiation for IB Math AA HL, including chain and product rules, worked examples, common errors, exam technique, and scoring advice.

AHL 5.14-Implicit functions, related rates, optimisation

What Is a Related Rates Problem and How Do You Solve One?

Learn what a related rates problem is, how implicit differentiation connects changing quantities, and the IB Math AA HL method, with a clear example.

AHL 5.15-Further derivatives and indefinite integration of these, partial fractions

What Are the Derivatives of Tan x, Sec x, Arcsin x, Arccos x, and Arctan x?

Learn the IB Math AA HL derivatives of tan x, sec x, arcsin x, arccos x and arctan x, with chain-rule examples and exam tips for Papers 1 and 2.

AHL 5.16-Integration by substitution, parts and repeated parts

How Do You Integrate by Substitution?

Learn IB Math AA HL integration by substitution: choose a variable, transform the integral and limits, integrate, back-substitute, and avoid exam errors.

AHL 5.16-Integration by substitution, parts and repeated parts

How Do You Integrate by Parts?

Learn how to integrate by parts in IB Math AA HL, choose u and dv using LIATE, and apply the formula with clear exam-ready working and key pitfalls.

AHL 5.15-Further derivatives and indefinite integration of these, partial fractions

How Do You Use Partial Fractions to Integrate a Rational Function?

Learn the IB Math AA HL method for decomposing rational functions into partial fractions, integrating logarithmic terms, and avoiding common exam errors.

AHL 5.16-Integration by substitution, parts and repeated parts

How Do You Do Repeated Integration by Parts?

Learn repeated integration by parts for IB Math AA HL with the correct formula, a worked example, sign control, common errors, and key exam tips.

AHL 5.18-1st order DE’s – Euler method, variables separable, integrating factor, homogeneous DE using sub y=vx

How Do You Use Euler's Method to Numerically Solve a Differential Equation?

Learn Euler's method for approximating differential equation solutions using recurrence formulas, a worked example, and IB Math AA HL exam guidance.

AHL 5.18-1st order DE’s – Euler method, variables separable, integrating factor, homogeneous DE using sub y=vx

What Is a First Order Differential Equation?

Learn what a first-order differential equation is, how IB Math AA HL solves separable, homogeneous and linear forms, and what examiners expect in AHL 5.18.

AHL 5.18-1st order DE’s – Euler method, variables separable, integrating factor, homogeneous DE using sub y=vx

How Do You Solve a Differential Equation Using an Integrating Factor?

Learn the integrating factor method for first-order linear differential equations in IB Math AA HL, with a complete worked example and focused exam advice.

AHL 5.18-1st order DE’s – Euler method, variables separable, integrating factor, homogeneous DE using sub y=vx

How Do You Solve a Homogeneous Differential Equation Using the Substitution y = vx?

Learn the IB AA HL method for solving homogeneous differential equations using y = vx, including substitution, separation, integration, and exam pitfalls.

AHL 5.19-Maclaurin series

How Do You Find the Maclaurin Series for e^x, sin x, cos x, and ln(1+x)?

Learn to derive Maclaurin series for exponential, sine, cosine, and logarithmic functions using derivatives, patterns, and IB AA HL exam methods.

AHL 5.19-Maclaurin series

What Is a Maclaurin Series and How Do You Use It to Approximate a Function?

Learn how derivatives generate a Maclaurin series and how IB Math AA HL students truncate it to approximate function values accurately in exams.

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