First Education

Preparation of a mathematics examination should not mean endless late nights cramming. Start a little earlier, as much as you need to break the subjects in small, easily chewable parts. Focus on understanding concepts only instead of remembering formulas; to explain an idea or to be able to solve a similar problem with different numbers is a great test of mastery. Explain what you are learning to other people, this revising technique is often slept upon, and if you are at a stage where you can explain a topic clearly, you are well on the right track. For the creation of speed and confidence, mix in timed practice papers under examination conditions, and use active study methods such as flashcards, or writing “cheat sheets” from memory instead of re-reading. Give your brain regular brakes, drink water, aim for constant sleep, and as soon as you hit a sticky point, do not hesitate to ask a teacher, parent, classmate or tutor for help. By studying continuously, actively and with proper comfort, you can get set to acing your mathematics!

Starsky Schepers

Studying doesn’t have to look like sitting in front of computers and books at a desk for hours on end, with little progress made each day. Many students study like this, just reading over content learnt in class without actively learning, which prevents this knowledge from entering their long term memory where it can be used in an exam situation. The answer to this issue is studying smarter, not harder using study techniques that work for you.

The main study technique I used to memorise for content heavy subjects during the HSC was active recall. I used different flashcard websites and created by own sets based on the content learnt in class. By doing this, I made sure that I was revising everything that I needed to know in a format that I could understand. Flashcards are a great way to practice active recall so that the brain can form the connections that are necessary for remembering information when it comes to a stressful exam situation. This prevents you from having ‘mind blanks’ during exams because you are used to recalling the content quickly and easily. Additionally, many websites involve spaced repetition which ensures that context is embedded into the long term memory, which makes revision in the weeks leading into the exam less stressful as you are not memorising information for the first time.

Past papers are also an essential tool when studying as they replicate an exam situation and the types of questions that you are going to see when you are sitting in the exam room. Doing these papers in test conditions makes them even more valuable to practice time management and anxiety that can be experienced on exam day. Doing this often can reduce this stress and allow you to feel more prepared when you are stepping into the exam.

Trying these study techniques may help your study days move a little bit faster and allow you to learn more in a shorter amount of time, giving you more time to yourself and to rest!

Maddie Manins

Probability is all about working out how likely something is to happen. It is the maths of chance. We use numbers between 0 and 1 to describe probability, or percentages between 0% and 100%. A probability of 0 means the event is impossible, and a probability of 1 (or 100%) means it is certain. For example, the chance of the sun rising tomorrow is 100%, while the chance of rolling a 7 on a standard six-sided dice is 0%.

Everyday life is full of probability. When you check the weather app, it might say there is a 30% chance of rain. That means rain is possible, but unlikely. If it says 80% chance of rain, then it is quite likely you will need an umbrella.

Probability can also be described in words like impossible, unlikely, even chance, likely, and certain.For instance, pulling a red card from a pack of playing cards is likely, because about half the cards are red. Flipping a coin and landing on heads has an even chance, because heads and tails are equally possible.

In school, probability is often shown with coins, dice, spinners, and cards. If you roll a dice, there are six possible numbers. Each number is equally likely, so the chance of rolling any specific number is the same. If you are asked about rolling an even number, there are three numbers that count as even (2, 4, and 6), so the chance is bigger compared to rolling just one specific number.

Another important idea is opposites in probability. If something has a certain chance of happening, the opposite has no chance. For example, if the chance of choosing a blue marble is 40%, then the chance of not choosing a blue marble must be 60%. Together they always add up to 100%.

Probability is useful in making decisions, playing games fairly, and understanding risks. From sports predictions to weather forecasts, probability helps us make sense of uncertainty in the world around us.

David

Maths is a subject where consistent practice makes all the difference. In tutoring sessions, I often remind students that learning maths is similar to learning a sport or an instrument—the more you practise, the stronger the skill becomes.

One mistake students often make is leaving all their practice until right before an exam. This creates pressure and often leads to confusion. By practising regularly, even in short bursts, students strengthen their understanding step by step. In my sessions, I set small amounts of practice between lessons so that the content stays fresh and does not pile up.

Regular practice also helps students build speed and accuracy. Questions that once felt difficult start to feel routine, and patterns become easier to recognise. This gives them more confidence in exams, where time and pressure can be challenging.

I also encourage students to mix up their practice. Rather than only doing the types of questions they are comfortable with, I help them focus on the areas that need the most attention. That way, they build balance and are prepared for anything that comes up in a test.

In the end, regular practice is not just about passing exams, it is about developing long-term habits that make maths less stressful and more manageable.

James Valiozis

Today I had the opportunity to observe Mateus and his Year 9 Mathematics session, where the focus was on trigonometry, particularly the application of bearings. It was an insightful session that highlighted not only the challenges students face when transitioning from abstract trigonometric concepts to real-world applications, but also the importance of guided practice in building confidence.

Mateus began by revising the fundamentals of sine, cosine, and tangent, ensuring the student was comfortable with the core ratios before extending them to navigation based problems. This foundation was crucial, as many students often find it difficult to link abstract ratios to directional movement. By anchoring the lesson in familiar material, Mateus created a logical bridge to the more complex concept of bearings.

What stood out most was his use of visual aids. Diagrams were drawn, with clear emphasis on orienting from north and applying clockwise measurement. This incremental approach allowed students to see how trigonometry moves beyond the triangle on paper to describe direction, distance, and orientation in practical contexts, such as maps or navigation. The student initially struggled with distinguishing between angles inside the triangle and the bearing required from north, but through repetition and guided questioning, Mateus helped the student be more confident in attempting the questions

Another strength was his pacing. Rather than rushing through worked examples, he gave the student time to attempt problems independently, providing targeted support. This balance between instruction and practice allowed the student to consolidate their understanding while also identifying areas of misconception.

Observing this session reminded me of the value of contextualising mathematics. Bearings, while technical, become far more engaging when framed as a tool for navigation and decision-making. As a tutor, it reinforced for me the importance of blending clarity, patience, and real-world relevance in teaching. The session ultimately highlighted how effective instruction can transform abstract mathematics into a skill set students see as both useful and applicable

Tynan Philmara

The adaptive immune system is a highly specialised defense mechanism that protects the body against pathogens by recognising specific antigens and developing long-term immunity. Unlike the innate immune system, which responds rapidly but non-specifically, the adaptive system is slower on first exposure but produces a specific response and, most importantly, has immunological memory. This feature is key to how vaccinations work.
When a vaccine is introduced into the body, it contains either weakened, inactivated, or non-infectious components of a pathogen, such as proteins or inactivated toxins. These act as antigens that trigger the adaptive immune response without causing illness. B lymphocytes are activated and differentiate into plasma cells, which secrete antibodies that specifically bind to the introduced antigen. At the same time, some B cells become memory B cells, which persist in the body for years. Similarly, helper T cells activate both B cells and cytotoxic T cells, while cytotoxic T cells target and destroy any cells displaying the antigen. Memory T cells also remain in circulation after vaccination.
The first exposure through vaccination mimics the primary immune response, which is relatively slow and produces a moderate level of antibodies. However, the generation of memory cells ensures that, upon later exposure to the actual pathogen, the body can mount a secondary immune response. This response is rapid, producing a larger quantity of highly specific antibodies and activated T cells, often neutralising the pathogen before symptoms appear.
Vaccinations therefore harness the adaptive immune system’s specificity and memory, training the body to recognise and fight disease without the risks of natural infection. This principle not only protects individuals but also contributes to herd immunity, reducing disease spread within the community.

Chris Mylonas

One of the most effective ways to check understanding in maths is to ask students to explain a concept in their own words. It is not enough to simply solve a problem by following steps. True understanding shows when a student can explain why those steps work.

In my tutoring sessions, I often pause after a question and ask, “Can you explain to me what you just did?” At first, many students find this uncomfortable, but with practice they begin to use their own language to describe the process. This reveals how well they grasp the concept and highlights any gaps that need addressing.

For example, when working on fractions, a student might say, “I made the denominators the same so I could add them together.” This simple explanation shows that they understand the reasoning rather than just applying a formula. If they cannot explain it, that is a sign we need to revisit the idea more clearly.

Encouraging students to use their own words also builds confidence. They begin to see themselves not just as learners, but as people who can teach and explain. That shift is powerful, especially when exam pressure makes students doubt themselves.

When students can explain maths in plain language, they have taken the first step towards mastery.

James Valiozis

Today, observed James’ year 7 Maths, as it was the last week, and Owen didn’t have any class work James focused on revision – ensuring that all the content that was taught throughout the semester was well understood and remembered this included, fractions, area and volume, and algebra. Throughout this revision, James identified that Owen struggled and was not as confident in completing worded questions across all topics, he was able to confidently complete more basic questions where the information was given, but struggled to fully comprehend how to extract information for worded problems.

Therefore to help Owen, James focused most of the lesson was based on completing worded problems ranging from easier questions to more challenging. James was super clear when reading the question and really helped him to understand by begin to help him through using the board to help him identify key words and formulas and asking him to explain why he approached the question instead of just telling him to answer. By the end of the lesson, Owen was a bit more confident on answering these questions and was able to complete them more independently.

James also went over factorisation with Owen as he forget the concept , James did this through showing Owen factorisation tree, using the white board again to help explain this concept and make it understandable reminding Owen on how to complete it, he then completed questions on his own. James ensured that the holiday homework was based on worded questions and factorisation to make sure that he has a clear understanding of the next term and is he is ready for next term if these questions potentially come up in next exams or in future years.

To finish the class, he ended with uni a fun game they enjoy playing. Overall James was very clear, using the board to reinforce his ideas and teaching, which really helped owen understand his revision.

Daniella Antoun

I had the opportunity to observe Luka’s Year 10 Mathematics session, which centred on trigonometry, with particular focus on solving problems involving bearings, angles, and sides of right-angled triangles. The lesson began with a recap of the trigonometric ratios — sine, cosine, and tangent — before applying them to more practical navigation-style contexts. Bearings were introduced as a way of expressing direction, and the teacher demonstrated how trigonometry could be used to calculate distances and angles when moving between points on a map.

Luka engaged well with the material, particularly when the problems were framed in real-world terms. He was able to identify the key sides of the triangle (opposite, adjacent, hypotenuse) and select the appropriate trigonometric ratio when solving for unknown side lengths. When tasked with finding unknown angles, Luka showed confidence in rearranging the formula, carefully using the inverse trigonometric functions on his calculator. The introduction of bearings provided an additional layer of complexity, as it required Luka to link his trigonometric calculations with compass directions and standardised angle measurements from north. While he initially found this challenging, he improved as the teacher modelled step-by-step worked examples.

Overall, the session was an effective demonstration of how trigonometry can be taught through scaffolded examples that connect to practical applications. Observing Luka’s learning emphasised the importance of contextual problems, such as bearings, in motivating students and showing the real-world value of mathematics.

Alexander Nikitopoulos

I recently observed Joel working with one of his students and was struck by how thoughtfully she ran the lesson. From the outset, he was very confident and knowledgeable about topic areas from the get-go. He also planned, making sure his student would leave with learning opportunities and areas to work on for the week ahead, while leaving confidently knowing the previous content they had completed during the session.

Joel’s explanations were also very clear and concise. He used everyday language, defined new terms as they came up, and regularly paused to confirm that the student was following along and learning along the way, as he took a hands-off approach, which is a perfect approach for tutors to take from my own learning. Rather than correcting errors straight away, he posed guiding questions that helped to see the source of a mistake. When working through problems, he modelled his own reasoning step by step, letting the student watch his thought process unfold as well as imitate his process with their own working later on.

His time management was equally impressive. He moved the lesson forward at a steady pace, spending just enough time on topics of need as well as practising what they were learning during the session.

Overall, Joel demonstrated a well-balanced blend of preparation and clarity, and an approach that kept the student engaged. This made the session both efficient and encouraging, letting the student walk away benefiting from the session that had just finished with new knowledge and a comprehensive understanding of the content covered.

Lucas Sinnott