📌 Title Partial‑Fraction Decomposition — A‑Level P3 Essentials (Linear, Repeated, Quadratic) 📝 Description (≥ 50 characters) This 60‑minute sprint shows you how to break any proper rational function into partial fractions exactly as required by Cambridge International AS & A‑Level Mathematics 9709 (Pure 3): • (ax + b)(cx + d)(ex + f) – three distinct linear factors • (ax + b)(cx + d)² – a repeated linear factor • (ax + b)(cx² + d) – linear × irreducible quadratic We’ll cover: 1. Choosing the correct decomposition template 2. Solving for the constants quickly (cover‑up & comparison methods) 3. Handling an improper fraction by long division first 4. Exam‑style walkthroughs pulled from recent CAIE past papers 5. A timed mini‑practice set where learners try questions and compare solutions live. Scope note: Integration comes later in Calculus; this class focuses on algebraic decomposition only. Prerequisites – solid factorisation skills and comfort simplifying rational expressions. Recommended prep: • KA Algebra → Polynomial division • KA “Partial fraction expansion” videos 1–3 Bring paper, pen, and a calculator/Desmos.

This mini-series (3 hours total) dives straight into the conditional, mutually exclusive, and independent-event portions of CAIE S1 A-level Mathematics. 📘 Session 1: Introduction to Conditional Probability Duration: 1 hour • Objective: To introduce the foundational concept of Conditional Probability. • Structure: 1. Mini Lecture: I will begin with a concise and focused explanation of conditional probability—its meaning, how it works, and its relevance in problem-solving. 2. Guided Problem Solving: After the lecture, I will solve selected problems from actual past papers, demonstrating how to apply the concept to real exam-style questions. 3. Student Practice (if time permits): If we have time remaining, I will encourage students to try out a few similar problems on their own. Afterwards, I will share the correct solutions so you can cross-check and understand your mistakes (if any). ⸻ 📗 Session 2: Practice + New Topics Duration: 2 hours Part 1: Practice from Session 1 • Duration: 1st Hour • We will reinforce our understanding of conditional probability by solving more past paper questions. I will randomly select problems, and you will solve them, either individually or with guidance. • Each solution will be discussed and reviewed, allowing you to correct misconceptions in real-time. Part 2: New Concepts – Mutually Exclusive & Independent Events • Duration: 2nd Hour • I will explain the difference between mutually exclusive events and independent events, including when and how to identify them in problems. • This will be followed by solving selected past paper problems that test understanding of these concepts. ⸻ This structure is designed to ensure a clear flow: starting from concept introduction → guided examples → student practice → new topic → applied practice again. This class is ideal for anyone comfortable with basic probability. 👉 Prerequisite: complete the “Probability” units at Khan Academy (link below) so we can move fast. [https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb](https://schoolhouse.world/redirect?code=aSlvr94juUWYjcpyd5jmT) [](https://schoolhouse.world/redirect?code=aSlvr94juUWYjcpyd5jmT) [https://www.khanacademy.org/math/ap-statistics/probability-ap](https://schoolhouse.world/redirect?code=0OqA37jO2IE-Sq1i_K6LP) You may also benefit from the following link to a document:- [https://drive.google.com/file/d/1SggOBjMBvCDzio9xS6f1Rq0XQqakHAM0/view?usp=sharing](https://schoolhouse.world/redirect?code=lFuzVMPzgpqd_rZnKAj9T) Bring a calculator, paper and a pen. Expect constant problem-solving and Q&A; the sessions are fast-paced “sprints”, not leisurely workshops. [](https://schoolhouse.world/redirect?code=0OqA37jO2IE-Sq1i_K6LP) 🔔 Side Note for Participants:- This series is particularly ideal for any Cambridge International A-Level Mathematics student—especially those taking Statistics—since the topics and practice questions are drawn directly from that curriculum. However, this does not mean the session is limited only to CIE students. Anyone who is interested in learning about Conditional Probability, Mutually Exclusive Events, and Independent Events—regardless of curriculum or academic background—is welcome to join and benefit. That said, I would like to strongly emphasise a few expectations for all participants: • Stay engaged and interactive throughout the session, no matter who you are or what your academic track is. • The sessions will be dense, fast-paced, and target-oriented. We are aiming to cover a large volume of conceptual explanations and past paper practice in a short span of time. • Think of it as a “super sprint”, not a marathon—we’re not stretching it out, but rather moving fast and with full force. • Because of time constraints, I will not be able to monitor each individual participant or constantly check who is following and who is not. That responsibility lies with you. • Therefore, please take initiative: • Ask questions when in doubt. • Let me know immediately if you’re stuck or confused. • Don’t wait for me to call on you—your proactivity is crucial to making the most out of this class. I hope you understand, and I look forward to your active participation and sincere learning, in shā Allāh.[](https://schoolhouse.world/redirect?code=0OqA37jO2IE-Sq1i_K6LP)[](https://schoolhouse.world/redirect?code=0OqA37jO2IE-Sq1i_K6LP)

In this session, we will focus exclusively on the basics of probability as outlined in section 5.3 of the CAIE Probability & Statistics 1 syllabus. Learners will evaluate probabilities in simple cases, such as: The total score when two fair dice are thrown Drawing balls from a bag containing different colors Case enumeration of equally probable outcomes We will not cover permutations or combinations in this session. Our emphasis will be on direct reasoning, tabulation, and real-time problem-solving based on core principles. Learners are expected to engage actively during the session — solving problems live, explaining thought processes, and understanding how to construct sample spaces manually. A calculator, pen, and paper are recommended. This session is ideal for anyone preparing for A-level Statistics 1 or anyone wishing to strengthen foundational probability logic before tackling advanced concepts.

In this session, we will conduct a focused review of the binomial expansion, covering key concepts and challenging problems. This session is ideal for learners who have already completed the Khan Academy Pre-Calculus course on Binomial Theorem and want to deepen their understanding by tackling more advanced questions. We'll briefly revisit the basics, but our primary focus will be on solving complex problems and mastering advanced applications. Please bring a calculator (Desmos or physical), a pen, and paper for note-taking and solving tasks. Active participation will be essential as you’ll be working through problems live. For those unfamiliar with the basics, I recommend completing the Khan Academy Pre-Calculus Binomial Theorem module prior to attending: [Khan Academy Binomial Theorem. ](https://schoolhouse.world/redirect?code=QDlQNeUQYlwwxdELBTXhT) We will also reference problems from Cambridge resources, so please be prepared! we will cover:- use the expansion of (1 + x)^n, where n is a rational number and |x| < 1. Finding the general term in an expansion is not included. Adapting the standard series to expand, e.g. (2 - 1/2 x)^(-1), is included, and determining the set of values of x for which the expansion is valid in such cases is also included.

In this session, we will conduct a focused review of the binomial expansion, covering key concepts and challenging problems. This session is ideal for learners who have already completed the Khan Academy Pre-Calculus course on Binomial Theorem and want to deepen their understanding by tackling more advanced questions. We'll briefly revisit the basics, but our primary focus will be on solving complex problems and mastering advanced applications. Please bring a calculator (Desmos or physical), a pen, and paper for note-taking and solving tasks. Active participation will be essential as you’ll be working through problems live. For those unfamiliar with the basics, I recommend completing the Khan Academy Pre-Calculus Binomial Theorem module prior to attending: [Khan Academy Binomial Theorem. ](https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:binomial/v/binomial-theorem) We will also reference problems from Cambridge resources, so please be prepared!

This series is designed for ambitious learners who are aiming to achieve the highest possible score on the SAT Math section. If you're targeting a score of 800, or simply want to master the most challenging Digital SAT math questions, this is the series for you. We will dive into the hardest questions the SAT has to offer, tackling them through interactive discussions, detailed strategies, and efficient problem-solving techniques. The focus will be on boosting your confidence with these advanced questions, sharpening your mathematical thinking, and ensuring you’re fully prepared for the toughest problems on the test. What We’ll Cover: # Advanced math questions from the official Digital SAT question bank, focusing exclusively on the hard difficulty level. # Strategies, shortcuts, and tips to solve problems quickly and accurately under test conditions. # In-depth breakdowns of challenging problems, including alternative methods to approach them. # Opportunities to engage in discussions, share your approach to problems and ask questions in real-time. Expectations for Learners: # This series is intended for advanced learners who have scored at least 600+ on any official Digital SAT or the Bluebook practice test. If you haven't taken any practice test yet, but feel confident in your math skills, you're welcome to join. # Since this is an advanced series, we won’t cover foundational concepts or theories. The sessions will focus solely on problem-solving, so it’s important that you come with a solid understanding of the core SAT math topics. # Active participation is highly encouraged! Don’t hesitate to ask questions or engage in discussions, even if others seem to be doing well. Your questions are essential for your learning, and they will benefit others too. Materials Required: # Notebook or rough paper and a pen: These will be essential for solving problems and jotting down important notes during the sessions. # Physical calculator (optional, but recommended) or access to Desmos: You’ll need these for solving problems more efficiently during the sessions. Desmos, as the SAT-provided tool, will be the primary calculator used in sessions. Important Notes for learners with low scores: # Although this series is mainly intended for advanced learners, but those with scores below 600 are still welcome to join if they feel up for the challenge. However, please keep in mind that the questions discussed in this series are significantly harder than the typical questions you receive at your level. As a result, you may feel overwhelmed if you’re not yet fully acquainted with the foundational concepts. # Moreover, you might feel like the sessions are moving too quickly, and that I'm not giving you enough time to think or solve the questions, or that I'm not explaining the foundational concepts in enough detail. It's not that I'm intentionally going fast, but rather, you may not be ready to tackle these advanced concepts yet. If you join the sessions without being fully prepared, you may find yourself struggling while others seem to follow along easily. You might end up asking very basic questions about foundational concepts, which isn't a problem for me to explain. However, most of the other learners are at an advanced level, and if I spend too much time on basic explanations, they may feel frustrated or bored because the session is designed for higher-level learners. If I notice that your questions are very basic or that you're not at the same level as the rest of the group, I may have to ignore your questions—not because I don’t want to help, but because I need to keep the session balanced and fair for everyone. The other learners are here to solve advanced problems, and if I spend too much time on foundational concepts, it won’t be fair to them. So, if you decide to join this series despite not being fully prepared for the advanced material, please understand that you’re doing so at your own risk. I won’t be responsible if it negatively affects your score, discourages you, or makes you feel like the SAT is harder than it is. It’s your choice, but just be aware of the challenges. # If you feel that you’re not quite ready for this level of difficulty, I encourage you to focus on building a solid understanding of the foundational SAT math concepts before joining. You may wish to attend foundational-level bootcamps or study these concepts on your own before returning for the advanced content. ---------------------------------------------------------------------- By joining this series, you’ll challenge yourself with the hardest questions the SAT has to offer, ensuring that you’re well-prepared to handle anything that comes your way on test day. Get ready to level up your math skills and aim for that perfect score!