Скачать или смотреть Algebraic Tree Diagrams: The Next Level

🚀 Ready for the toughest GCSE probability questions? In this video, former Head of Maths and A-Level examiner Lee Guffick takes you step-by-step through a Grade 9 algebraic tree diagram question.

Tree diagrams at this level can look intimidating — but Lee shows you how to break them down using clear algebraic methods, substitution, and factorisation, so you can confidently tackle the hardest exam questions worth 6 marks at the end of the paper.

This question is a classic exam-board favourite because it really separates the top students. By the end of the lesson, you’ll see how to:

Set up a probability tree with algebraic terms (G and B for green and blue pens)

Use simultaneous equations to eliminate variables

Simplify complex fractions and denominators

Factorise quadratics to find the correct solution

Apply exam strategies to spot and rule out incorrect answers

Whether you’re aiming for a Grade 9 at GCSE Maths or simply want to push your probability skills further, this video will give you the structure and confidence you need.

⏱️ TIMESTAMPS:
00:00 – Introduction to Grade 9 probability questions
00:32 – Setting up the algebraic tree diagram
03:00 – Using probability rules with algebra
06:00 – Substituting the ‘3 more blue pens’ condition
09:00 – Simplifying and cross-multiplying fractions
11:00 – Solving the quadratic equation step-by-step
12:15 – Identifying the valid solution (21 pens)
12:24 – Final exam tip & wrap-up

✏️ TOPICS COVERED:

Harder probability tree diagrams

Algebraic manipulation with probability

Simultaneous equations & substitution

Quadratic factorisation in exam context

💯 EXAM TIPS:

Always look for extra conditions in the question (like “3 more pens”) — they’re key to forming a solvable equation.

Check your solutions against the context of the question (e.g. ruling out 4 pens because “more than 12” is required).

Don’t panic when the algebra looks messy — examiners expect you to simplify step-by-step.

📚 ABOUT GUFFICK TUITION:
Lee Guffick is a former Head of Mathematics and A-Level Examiner who helps students achieve A*/A grades and win places at top universities including Oxford, Cambridge, and the Ivy League.

📅 JOIN OUR PROGRAMMES:
→ Personalised 1:1 tutoring: https://www.gufficktuition.com/tutoring

→ Small group classes: https://www.gufficktuition.com/group-...

→ Summer intensive courses: https://www.gufficktuition.com/tutoring

📱 CONNECT WITH LEE:
→ Instagram: @leeguffick
→ Website: https://www.gufficktuition.com

→ Email: [email protected]

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