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Partial Fractions – Calculus II

Section 7.4: Partial Fractions Section 7.4: Partial Fractions In this section, we are going to take a look at integrals of rational expressions of polynomials. Let’s begin by reviewing a familiar integral to show why partial fractions can be so helpful. Example 1 Consider the integral $ int frac{2x – 1}{x^2 – x – 6} […]

Integrals Involving Trig Functions – Calculus II

Integrals Involving Trig Functions – Calculus II Integrals Involving Trig Functions In Calculus II, you often encounter integrals that involve various powers of sine, cosine, tangent, or other trigonometric functions. There are several techniques to handle these, including rewriting with trig identities, using substitutions, or applying integration by parts. Below are some examples with detailed […]

Integration by Parts – Calculus II

Integration by Parts – 30 Worked Examples Integration by Parts One of the most important techniques you learn in Calculus II is Integration by Parts. It is used to integrate products of functions (especially when those products do not succumb to a simple substitution). Below is the standard formula: Integration by Parts Formula (Indefinite Integrals): […]

Practice Questions on Sequences & Series (IB Math AA SL Style)

Practice Questions on Sequences & Series (IB Math AA SL Style) Below are five questions, each similar in style to an IB Math AA SL problem on sequences and series. They focus on arithmetic or geometric sequences. Step-by-step solutions are provided, with relevant formulas clearly stated. Question 1 [6 marks] An arithmetic sequence has first […]

Proofs in IB Math AA SL

Proofs in IB Math AA SL: Comprehensive Notes with 30 Examples In IB Mathematics: Analysis & Approaches SL, the concept of proof underpins all areas of mathematics. Although the SL syllabus emphasizes problem-solving and applications, students are also required to demonstrate rigorous understanding of fundamental properties, theorems, and reasoning techniques. This involves not just solving […]

Exponents and Logs – IB Math AA SL

Exponents and Logs – IB Math AA SL: Comprehensive Notes Welcome to this comprehensive set of notes on Exponents and Logarithms for the IB Mathematics: Analysis & Approaches SL curriculum. In these notes, you will find detailed explanations of key concepts, step-by-step examples, and practice questions. Mastering exponents and logarithms is crucial in IB Math […]

Financial Mathematics – IB Math AI SL

Financial Mathematics – IB Math AI SL Table of Contents 1. Introduction 2. Key Concepts & Formulas 3. Examples with Solutions 4. Conclusion 1. Introduction Financial Mathematics is a vital component of the IB Math Analysis & Approaches SL (AI SL) curriculum. It integrates algebraic techniques and real-world applications involving money, investments, interest rates, loans, […]