Another week done! Here’s everything we covered: ✅ Problem of the Week #10: EA-style mixed questions ✅ The last 24 hours before your EA ✅ How to review your mistakes after a practice paper ✅ Solving trig equations in 5 steps ✅ Worked solution covering calculus and the normal distribution If you missed any of these, scroll back through the feed and catch up. Everything is there for you. Ten weeks ago this community was brand new. Since then the feed has built up into a library of: - Weekly EA-style problems with full worked solutions - Step-by-step methods for the topics that come up every year - Exam technique, revision checklists and mistake breakdowns - A complete QCAA-aligned course in the Classroom tab If you have been working through even part of that, you are further ahead than most students. This weekend’s task: Pick one past paper question that you got wrong recently and redo it from scratch, without looking at the solution. If you can do it cold, the gap is closed. If you can’t, post the question below and we’ll work through it together. One more thing: If this community has helped you, share it with one friend who is also sitting ATAR maths. The more students we have here, the more questions get asked and answered, and everyone benefits. How are you feeling heading into the final stretch? Drop it below 👇

The fan opens to a right angle—but what happens when it folds? Use the clues to find the blue triangle’s apex angle. 👀 👇 Comment A, B, C, D or E—and tell us how you worked it out! #AStarMaths #MathsChallenge #GeometryPuzzle #AngleChallenge #ProblemSolving #BrainTeaser #MathsIsFun #BrisbaneTutoring

From towering buildings to rivers you can’t cross, a right triangle can help you find the missing measurement. Spot the triangle. Label the sides. Choose your ratio. ✅ 💾 Save this for your next revision session! Which example would you like us to break down step by step? 👇 #AStarMaths #Trigonometry #Year10Maths #MathsMadeSimple #MathsTips #MathsRevision #HighSchoolMaths #BrisbaneMathsTutor #RealWorldMaths

QUESTION 1: Calculus y = x³ - 6x² + 9x + 1 Part a) Stationary points and classification Differentiate: dy/dx = 3x² - 12x + 9 Set equal to zero: 3x² - 12x + 9 = 0 3(x² - 4x + 3) = 0 3(x - 1)(x - 3) = 0 x = 1 or x = 3 Find the y-coordinates: When x = 1: y = 1 - 6 + 9 + 1 = 5 When x = 3: y = 27 - 54 + 27 + 1 = 1 Second derivative: d²y/dx² = 6x - 12 At x = 1: 6(1) - 12 = -6, which is less than 0, so it is a local maximum at (1, 5) ✅ At x = 3: 6(3) - 12 = 6, which is greater than 0, so it is a local minimum at (3, 1) ✅ Part b) Point of inflection Set the second derivative equal to zero: 6x - 12 = 0, so x = 2 Check for a sign change: At x = 1: d²y/dx² = -6 (negative) At x = 3: d²y/dx² = 6 (positive) The sign changes, so it is a genuine point of inflection. When x = 2: y = 8 - 24 + 18 + 1 = 3 Point of inflection at (2, 3) ✅ Part c) Tangent at x = 0 When x = 0: y = 1, so the point is (0, 1) Gradient: dy/dx at x = 0 is 3(0) - 12(0) + 9 = 9 y - 1 = 9(x - 0) y = 9x + 1 ✅ QUESTION 2: Normal distribution Let X be the height of a Year 12 student in cm. X follows a Normal distribution with mean 168 and variance 81, so the standard deviation is 9. Part a) P(X > 175) Calculator: normalCDF(175, 9999, 168, 9) P(X > 175) = 0.2183 ✅ Sanity check: 175 is a little under one standard deviation above the mean, so a probability a bit above 0.16 makes sense. Part b) The height only 10% of students exceed P(X > h) = 0.10, so P(X < h) = 0.90 Calculator: invNorm(0.90, 168, 9) h = 179.5 cm ✅ Part c) Sample of 25, find P(sample mean > 170) By the Central Limit Theorem: Standard error = 9 divided by √25 = 9/5 = 1.8 The sample mean follows a Normal distribution with mean 168 and standard deviation 1.8. Calculator: normalCDF(170, 9999, 168, 1.8) P(sample mean > 170) = 0.1333 ✅ Common mistakes to avoid: Mistake 1: Q1 part b: never call f''(x) = 0 a point of inflection without checking the sign change. Mistake 2: Q1 part c: you need BOTH the point (0, 1) and the gradient 9 before writing the tangent.

Four men. Four wives each. Four children per wife. 🧠💥 Sounds simple… but have you counted EVERYONE? 👀 Drop your answer below—and show us how you worked it out! 👇⭐ #AStarMaths #MathsChallenge #BrainTeaser #MathsPuzzle #MentalMaths #ProblemSolving #BrisbaneMathsTutor #MathsIsFun