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Now all we need to do as shown in Figure 2 and (7), is find the values of p such that, https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/874b65b7-96ed-4701-a128-37cb830c3c16/Screenshot+2025-11-04+at+1.58.15%E2%80%AFpm.png Resources - Q32 of the 2025 Maths Advanced HSC - Make it stand out Expanding this out, https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/b6f32d86-ce89-4ea6-9c54-e82f82fcdd6d/Screenshot+2025-11-04+at+1.58.23%E2%80%AFpm.png Resources - Q32 of the 2025 Maths Advanced HSC - Make it stand out Thus, because p has to satisfy both of the conditions found in (11) and (16), we can simply combine them, giving us the answer and final range of solutions for p. i.e. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/263ced19-9844-4ed9-a0cd-821a5b7cedd6/Screenshot+2025-11-04+at+2.00.14%E2%80%AFpm.png Resources - Q32 of the 2025 Maths Advanced HSC - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/0a418179-93df-4942-8585-ab6d0a41cf50/Pinnacle+Learners-54.jpg Resources - 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Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://www.pinnaclelearners.com.au/resources/5-steps-to-master-hsc-short-answer monthly 0.5 2025-11-17 https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/2961a33d-c017-472c-8243-8ae18a58c86f/Blog+Post+Covers+%283%29.png Resources - 5 Steps to Master HSC Short Answer - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/2d84cf38-7f70-490f-9cc1-65e96f48813e/Screenshot+2025-08-17+at+10.11.55%E2%80%AFam.png Resources - 5 Steps to Master HSC Short Answer - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/4a790eed-1ade-498c-a099-5703509d20ac/Screenshot+2025-08-17+at+9.36.48%E2%80%AFam.png Resources - 5 Steps to Master HSC Short Answer - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/589acba7-18b1-4f77-9916-04269a640c0e/Pinnacle+Learners-09.jpg Resources - 5 Steps to Master HSC Short Answer - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://www.pinnaclelearners.com.au/resources/how-to-answer-the-question monthly 0.5 2025-11-17 https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/738f4d63-6206-4ea4-bad5-63b5649265aa/Blog+Post+Covers+%281%29.png Resources - How to ‘Answer the Question’ - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/cd375e0b-5385-4b2e-a55b-248fd24fb418/Screenshot+2025-11-17+at+5.50.23%E2%80%AFpm.png Resources - How to ‘Answer the Question’ - Make it stand out Here are the 5 key NESA Glossary terms for English https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/e8645d30-c70a-43a7-ba53-f3596e3190e5/Screenshot+2025-11-17+at+6.42.47%E2%80%AFpm.png Resources - How to ‘Answer the Question’ - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/f548e3d9-443b-42b8-886d-fc7e29a42634/Screenshot+2025-11-17+at+6.44.39%E2%80%AFpm.png Resources - How to ‘Answer the Question’ - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/3bf66d7e-d4d1-4e18-8831-8ec274a0d3fb/Screenshot+2025-11-17+at+7.12.11%E2%80%AFpm.png Resources - How to ‘Answer the Question’ - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/7e16e651-903d-4a56-84cb-729a30f7db8e/Screenshot+2025-11-17+at+7.25.37%E2%80%AFpm.png Resources - How to ‘Answer the Question’ - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/7101f2e8-cedd-4fee-bc2a-c9e30cbd1622/Pinnacle+Learners-50.jpg Resources - How to ‘Answer the Question’ - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://www.pinnaclelearners.com.au/resources/mastering-high-school-organisation monthly 0.5 2025-11-18 https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/cb1f6e62-43ba-4ef0-96d2-72b7a2d22d05/How+%284%29.png Resources - Mastering High School Organisation https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/9218c79a-a3b8-4a07-bd2d-2812785fe048/Pinnacle+Learners-10.jpg Resources - Mastering High School Organisation - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/fcd5d9a1-7597-44ff-9148-43ad075c439f/66a0ce99e47e489d108664fd_IMG_0070.jpg Resources - Mastering High School Organisation - Tips for Organised Notes https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/639f388f-bc76-4d25-96b9-1857ace6b98d/Screen%2BShot%2B2020-07-08%2Bat%2B8.59.54%2BPM.png Resources - Mastering High School Organisation - Pro Tips for Managing Your Timetable Set aside time each week to plan your upcoming schedule. Use apps like Google Calendar or Notion for digital scheduling. Include relaxation and physical activity to maintain a healthy balance. Keep flexibility in your schedule for unexpected assignments or events. Break study sessions into focused blocks, followed by short breaks. Regularly evaluate your timetable and make adjustments as needed. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/4af6d9f1-a457-4035-bd12-ad6d84f410df/istockphoto-466144261-612x612.jpg Resources - Mastering High School Organisation - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/0feed801-021e-489d-a190-e194892ce08d/Screenshot+2025-07-28+at+5.35.42%E2%80%AFpm.png Resources - Mastering High School Organisation - Best Practices for Weekly Revision Sessions https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/92c87b7e-1e81-42f6-84b2-6571d8ec4224/create_study_space.jpg Resources - Mastering High School Organisation https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/88f18d69-81de-48b5-83a1-5b5af5232de8/Pinnacle+Learners-44+%282%29.jpg Resources - Mastering High School Organisation - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://www.pinnaclelearners.com.au/resources/16-practice-essay-questions-for-othello monthly 0.5 2025-11-18 https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/b7e36ccb-d3ed-4776-b39a-1188ca8a5d0b/Blog+Post+Covers+%288%29.png Resources - 16 Practice Essay Questions for Othello - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/7419ac8b-cc59-4991-af84-ebac65facf79/Pinnacle+Learners-82.jpg Resources - 16 Practice Essay Questions for Othello - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://www.pinnaclelearners.com.au/resources/hsc-scaling-explained monthly 0.5 2025-08-17 https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/b4a522a2-f689-4aff-94e8-e37adc4446bc/Blog+Post+Covers+%284%29.png Resources - HSC Scaling Explained - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/4351719f-7538-4142-a717-6fd1dda2bc8e/graph.png Resources - HSC Scaling Explained - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/2e84962d-3bc5-4723-8f02-cfde5eb7b602/Blog+Post+Covers+%286%29.png Resources - HSC Scaling Explained - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/d264c617-90ba-48d2-95ba-a17eda9e4e4b/Screenshot+2025-03-26+164644.png Resources - HSC Scaling Explained - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/7101f2e8-cedd-4fee-bc2a-c9e30cbd1622/Pinnacle+Learners-50.jpg Resources - HSC Scaling Explained - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://www.pinnaclelearners.com.au/resources/5-tips-to-boost-your-essays-from-a-c-to-an-a monthly 0.5 2025-11-22 https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/a123314f-d0fd-4a7d-ae84-22e0e11b45d0/How+%281%29.png Resources - 5 Tips to Write an A Level Essay https://www.pinnaclelearners.com.au/resources/how-to-study-during-the-school-term monthly 0.5 2025-06-23 https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/1737978818463-0YZRG2RP5VGA7029B7I7/3.png Resources - How to Study During the High School Term - If you’re reading this, you’re probably a conscientious student (or parent) and want to ace your high school exams without pulling all-nighters or cramming the week before. Great news: you can! The secret is studying smart throughout the term. This guide is designed to help you develop effective study habits and strategies that will set you up for success—not just during exam week but throughout the entire term. Whether you're in Year 9 starting to find your feet or tackling the high-stakes environment of Year 12, these tips will show you how to stay organized, understand your syllabus, and study smarter, not harder If you’re reading this, you’re probably a conscientious student (or parent) and want to ace your high school exams without pulling all-nighters or cramming the week before. Great news: you can! The secret is studying smart throughout the term. By following these simple tips, you’ll build strong study habits, stay on top of your work, and walk into your exam feeling confident and prepared. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/53a7bb2d-e666-45e0-a0d2-1f38dbc81e40/crime+syl.JPG Resources - How to Study During the High School Term - For example, in the Crime unit of Year 12 Legal Studies, the first section is called ‘nature of crime.’ From the ‘learn to’ column, you can see that the type of questions asked for this section are lower value: ‘describe’ ‘define’ ‘examine.’ This means you’d only ever receive a multiple choice question and not an essay. Your notes for this section should be brief, focusing on practice multiple-choice questions using past papers instead of researching LCMID (Legislation, Cases, Media, Instruments and Documents) for an essay. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/f8a10af6-3a91-4b68-a4da-3eb179cf1654/calend+study+ewe.JPG Resources - How to Study During the High School Term - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/d63a4e14-1261-49e6-9cdf-03c30db360d6/mod+notes.JPG Resources - How to Study During the High School Term - Make it stand out Whatever it is, the way you tell your story online can make all the difference. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/65321f44-e7a3-45bc-8e4d-abdb491e0224/forgetting+curve.JPG Resources - How to Study During the High School Term - According to Ebbinghaus’ forgetting curve, without reinforcement, we forget up to 90% of the new information we learn. However, this is easily combatted by regular review and reinforcement https://www.pinnaclelearners.com.au/resources/top5mathsmistakesandhowtofixthem monthly 0.5 2025-08-21 https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/ba72d0d3-ab54-404e-881a-b40baba6f56c/How+%283%29.png Resources - Top 5 Maths Mistakes and How to Fix Them - Mathematics is a subject that many students struggle with, especially in high school. From Year 7 to Year 12, the complexity of mathematical concepts increases, requiring students to develop critical thinking, problem-solving skills, and a strong conceptual foundation. However, many students face common pitfalls that hinder their ability to excel. By identifying and addressing these mistakes, students can significantly improve their performance and confidence in maths. This blog will explore the top five mistakes students make in maths and provide in-depth, actionable solutions to overcome them. With a combination of strategy, practice, and the right approach, students can not only avoid these mistakes but also develop a long-term understanding that benefits them in higher education and real-world applications. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/1740099699340-7WF2AV3D42YRVLWCWT1P/unsplash-image-aYPtEknQmXE.jpg Resources - Top 5 Maths Mistakes and How to Fix Them - Another common pitfall for students is ineffective problem-solving techniques. Some students rush through problems without properly analyzing them, while others struggle with structuring their approach, leading to confusion and unnecessary mistakes. Problem-solving in maths is not just about applying formulas but also about developing logical thinking skills to navigate different types of problems. A more effective approach involves breaking down complex problems into smaller, more manageable steps. For example, in algebra, rather than trying to solve for a variable immediately, students should first simplify the equation, isolate terms, and methodically apply rules. Similarly, in geometry, drawing accurate diagrams and labelling them appropriately can help in visualizing relationships between different elements. Developing an analytical mindset by working on varied problem types, rather than just repetitive drills of the same formula, can enhance problem-solving skills significantly. https://images.squarespace-cdn.com/content/v1/66f8d6a40f44d11e31fc22c3/1740099785242-MSUG268TLFD8TAGH3X5U/unsplash-image-qDgTQOYk6B8.jpg Resources - Top 5 Maths Mistakes and How to Fix Them - Tips for Better Exam Performance: Practice under timed conditions to improve time management skills. Read questions carefully, highlighting key terms to avoid misinterpretation. 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