Edexcel A-Level Maths 2020 Paper 2 (Pure) Q14 | Circles скачать в хорошем качестве

Edexcel A-Level Maths 2020 Paper 2 (Pure) Q14 | Circles

✅ 𝗙𝗥𝗘𝗘 𝗧𝗥𝗜𝗔𝗟 — 𝗔𝗶𝗺𝗶𝗻𝗴 𝗳𝗼𝗿 𝗔* 𝗼𝗿 𝗚𝗿𝗮𝗱𝗲 𝟵? 🎓 Get weekly structure + live lessons + feedback (small groups). 𝗕𝗼𝗼𝗸 𝘆𝗼𝘂𝗿 𝗳𝗿𝗲𝗲 𝘁𝗿𝗶𝗮𝗹 𝗹𝗲𝘀𝘀𝗼𝗻: https://www.gufficktuition.com/group-... In this video, Lee Guffick works through Edexcel A-Level Maths 2020 Paper 2 (Pure) Question 14 (Circles), showing you how to form the circle equation, substitute the line 2x + y = 12, and prove the x-coordinates of the intersection points satisfy the required quadratic (3 marks). Then, for Part (b), Lee uses the key tangent condition (discriminant = 0) to find the two possible values of the radius r, finishing neatly by completing the square. If you’re revising circles + tangents + discriminant for Edexcel A-Level, this is exactly the sort of exam-style algebra that wins marks. ⏱️ TIMESTAMPS: 00:00 Introduction + what the question is asking 00:20 Sketching the circle in the first quadrant + the line 2x + y = 12 01:42 Finding the centre and equation of the circle: (x - r)^2 + (y - r)^2 = r^2 02:35 Substituting the line into the circle equation 03:01 Expanding and simplifying carefully 04:18 Arriving at the required quadratic in x (Part A complete) 05:46 Part B: Using the tangent condition (discriminant = 0) 06:12 Expanding b^2 - 4ac and simplifying 08:41 Dividing through by a common factor to clean it up 09:24 Completing the square to solve for r 10:20 Final answers + wrap-up ✏️ TOPICS COVERED: Circle in the first quadrant touching both axes Centre and radius reasoning from geometry Forming the circle equation in coordinate geometry Substitution of a line into a circle Simplifying to a quadratic in x Tangency condition using the discriminant (b^2 - 4ac = 0) Solving a quadratic by completing the square 💯 EXAM TIPS: Always sketch first (it clarifies the circle’s position and the centre immediately). If a circle touches both axes in the first quadrant, the centre is (r, r). For tangents, remember the golden rule: discriminant = 0. Before solving, look for a common factor — it often turns a messy quadratic into something clean. Completing the square is a quick, accurate method under exam pressure. 📚 ABOUT GUFFICK TUITION: Lee Guffick is a former Head of Mathematics and A-Level Examiner, helping students achieve A/A grades* and secure places at top universities including Oxford, Cambridge, and the Ivy League. 📅 JOIN OUR PROGRAMME: → 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 US: → Instagram: @leeguffick → Website: https://www.gufficktuition.com → Email: lee@gufficktuition.com #AlevelMaths #EdexcelALevelMaths #PureMaths #Circles #Tangent #Discriminant #ExamRevision #GuffickTuition