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General Mathematics 2019 v1.2 - IA1: High-level annotated sample response September 2021 - Queensland ...

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The ultimate guide to scoring top marks in QCAA Maths Methods PSMT IA1

Got your QCAA Maths Methods PSMT IA1 coming up? Read along to find our expert tutor and high achieving graduate's top tips to acing your PSMT assignment.

2 months ago   •   6 min read

What is IA1: the Problem Solving and Modelling task?

The IA1, your first internal assessment for Maths Methods, is a Problem Solving and Modelling Task (we will now refer to it as PSMT). The PSMT tasks are generally based on differentiation and integration topics from Year 12. Your markers are looking to see if you can apply the mathematical concepts you have learned to a more practical real life example. The assessment will propose a situation that you have to make a mathematical model for, and then you will need to use this model to estimate or predict an outcome.

In 2022, I completed a QCE with an ATAR of 98.80. I did both Specialist Maths and Maths Methods, and subsequently was faced with lots of PSMT assignments in my senior years. With this practice, I was able to score top marks for my IA1 PSMT and I am going to share the strategies I learned here.

So, how do you start?

Read your task sheet.

This may seem obvious, but your teacher will list everything you are required to do within this document. Pay special attention to the topic the task is based on and make sure that you understand its real-world implications. I recommend spending time highlighting and underlining  key information in your assignment sheet as well as looking at the marking criteria to know exactly what you are gunning for.

Scaffold your report and plan!

This assignment is often given very little time for completion. Check the due dates and plan to have a good draft to hand in to your teacher for feedback. I would recommend focusing on one stage (i.e. formulate, solve, evaluate and verify, and communication (conclusion)) per day.

Make sure you start with an introduction that outlines the task that will be achieved in the report. If your teacher hasn’t told you how to structure your report, it is a good idea to separate the sections based on the dot points in the ISMG. For example, list your assumptions and observations under separate headings so the marker knows exactly what they are looking at.

Make your observations

Read the task again and highlight anything that stands out to you. Observations are often requirements that the model must adhere to, such as a certain measurement. Look for all the values you are given in the task description.

Make your assumptions

Unlike observations, assumptions aren’t listed on the task sheet. Instead, you have to come up with these on your own. Assumptions are often based on how realistic the model needs to be. These may require a quick Google search to find a real-life value that you can base further calculations on. Remember to reference this!!

For a high mark, make sure you have at least three quality assumptions!

Mathematical concepts, techniques and technology

This is where you can list all the formulas and theories you expect to use in your calculations to solve the problem.

For technology, if you are graphing functions, use Desmos. If you are simulating something or making many calculations at once, use Excel (or another spreadsheet program like google sheets).

Now you’re ready to solve!

Understanding the ISMG

Mark your work against the ISMG! When reading through your report ask yourself whether your work has the high-level characteristics outlined, such as “Did I document appropriate assumptions?” Do this from the moment you start working on the report!

The main differences between a top-scoring report and an average one are the complexity and accuracy. You need to be mathematically justifying your decisions, evaluating the results and accurately solving the problem. As such, it is important to not just get the ‘right’ answer but to constantly evaluate and look for improvements and extensions to your model.

Help! My model doesn’t work!

Maybe the result of your model is unrealistic or you do not get the most ideal outcome.

Having a second model in your PSMT is a great way of showing your markers that you have more depth and understand the original task. You are also able to show your knowledge of a larger variety of mathematical concepts by using another equation or theory. Keep the first model in your report to show your evaluation of the result!

Concluding well

To end the report, make sure you have discussed the reasonableness, strengths and limitations of your final model. Your conclusion doesn’t have to be very long but should include an explanation of the models used and the outcome. Ensure you answer the task sheet question and refer to the introduction.

Some final tips and tricks

• Use an appendix for any extra content. For example, if you are repeating a calculation over and over again, you can put the first calculation in the report and all the rest in the appendix. This shows the marker that you know what you’re doing but also doesn’t waste your precious space or words.
• Ask questions and listen to what your teacher says about the task, especially if the task seems vague or not fully explained. Teachers will often tell you what they expect to see in a top-scoring report, such as a certain format or the number of assumptions.
• If you’re struggling with too many words, try to use tables to organise and explain calculations or strategically list improvements and extensions.

Ultimately, remember that this task does not have a ‘right’ answer. The marker is looking for evidence of your critical thinking, justified decision making, and ability to test and evaluate solutions.

Frequently Asked Questions (FAQs)

Where can i find an example of a psmt.

Have a look at the annotated high-level PSMT example on the QCAA website. This will help you figure out how to structure your assessment and help you understand the marking process.

How do I explain the strengths and limitations of my model?

For strengths, you can explain how well the model accurately predicts a value or finds the best outcome. Often limitations are unrealistic results, due to constraints on the model from the original assumptions and observations.

How much are the IA1 marks weighted?

The IA1 is worth 20% of your year 12 Maths Methods grade.

Written by KIS Academics Tutor for QCAA Maths Methods, Specialist Maths, Physics and Chemistry, Anushka Haydon. Anushka is currently pursuing a Bachelor of Chemical Engineering. You can view Anushka’s profile here and request her as a tutor.

Want more personalised study guidance? A private tutor can make the biggest difference!

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Excel Academics Blog

Qce math methods: a comprehensive guide to unlock success.

• 7 months ago

Among the various subjects offered by QCE, Math Methods stands as one of the more challenging ones. This guide aims to help students navigate their way through this subject, offering insights on assessments, exam question types, strategies, and preparation techniques. Whether you’re aiming for top grades or simply looking to pass, these tips will prove invaluable.

What are the assessments included in Math Methods? 📑

The Problem Solving and Modelling Task (PSMT) weights 20% of your final grade.

To approach any math assignment, especially in a course like Math Methods, you should follow these steps:

1. Plan your deadlines: Create a schedule that provides a clear overview of the day you received your assessment, the allotted time for completion in days or weeks, the date for submitting a draft, and the final deadline. This will help you gauge the daily or weekly time commitment necessary to write a high-quality assessment piece that receives an ‘A’ grade.

• Make use of your online calendar, diary, daily planner, or even just a reminder list on your phone to set tiny goals for yourself to finish the assessment without cramming last minute.
• For instance, let’s think of a scenario in which you were given a PSMT assessment on the 1st of September with it being due on the 1st of October; here is my example of a calendar plan to approach this assessment and ace it:

Dedicating an hour each day to chip away at your assignment incrementally can significantly boost your grade, as opposed to waiting until a week or two before the deadline to start working on it.

2. Understand the Assignment: Begin by carefully reading and understanding the assignment brief or guidelines provided by your teacher or institution. Pay attention to the specific requirements, format, and deadlines.

3. Review Relevant Content: Review the relevant content and concepts that are applicable to the assignment. In the case of Math Methods, this might involve reviewing mathematical principles, formulas, and techniques that are relevant to the assignment topic.

Refer to this link to access the official QCAA high-level annotated PSMT exemplar.

4. Plan Your Approach: Plan how you will tackle the assignment. Consider the steps you need to take, the data or information you need to collect, and the calculations or analyses you need to perform.

5. Gather Data and Information: If the assignment involves data or research, collect the necessary data or information. Ensure that your sources are credible and appropriate for the task.

6. Perform Calculations or Analyses: If your assignment requires calculations or mathematical analyses, carry them out accurately. Double-check your work to avoid errors. If your PSMT involves the generation of graphs, using an online graph maker like Desmos can help you make it look clear and keep track of the equations used to generate graphs.

7. Organize Your Work: Organize your work logically. Use clear headings, labels, and a structured format. Ensure that your work is easy to follow for someone else reading it.

8. Explain Your Reasoning: When presenting your solutions or findings, explain your reasoning and methodology. This helps your teacher or examiner understand your thought process.

9. Proofread and Edit : Before submitting your assignment, proofread it for errors in grammar, spelling, and math calculations. Make any necessary revisions.

10. Seek Feedback: If possible, seek feedback from your teacher or peers before submitting the assignment. This can help you identify areas for improvement. One effective strategy for achieving high grades in your assessments is to present a fully polished draft that resembles the final version, allowing you to gain feedback from your teacher. Submitting a comprehensive draft enables you to undergo a preliminary evaluation of your assignment, giving you the opportunity to receive the most extensive feedback possible from your teacher.

11. Submit on Time: Ensure that you meet the submission deadline. Late submissions may result in penalties.

How to study for Math Methods 🤔:

• Simple familiar
• Complex familiar
• Complex unfamiliar

Exam strategies and approach 📖

Math Methods exam, or any math exam for that matter, requires a strategic and systematic approach to maximize your chances of getting the correct answers. Here’s how to approach these types of questions effectively:

1. Read the Question Carefully: Start by reading the question stem carefully. Understand what it’s asking for, and identify any essential information provided in the question.

2. Preview the Answer Choices: Before attempting to solve the problem, glance at the answer choices. This can give you a sense of what you’re looking for and sometimes even help you eliminate obviously incorrect options.

3. Use the Process of Elimination: If you’re unsure about the answer, try to eliminate obviously incorrect answer choices. Narrow down your options by ruling out any choices that don’t make sense based on your calculations or the problem’s context.

4. Work Out the Problem: Now, start solving the problem step by step. Use your knowledge and problem-solving skills to find the correct answer. Pay attention to details and use the information from the question stem.

5. Avoid Second-Guessing: Once you’ve chosen an answer, try to stick with it unless you have a particularly good reason to change your mind. Second-guessing can often lead to changing from the correct answer to an incorrect one.

6. Manage Your Time: Multiple-choice questions can vary in complexity, so don’t get stuck on a single question for too long. If you’re unsure about a particular question, mark it and come back to it later if time allows.

7. Guess Wisely: If you’re running out of time and must guess, do so strategically. Eliminate any obviously incorrect choices and then make your best guess among the remaining options.

How to prepare for math methods exams ✍️

1. Understand the Curriculum: Start by thoroughly understanding the curriculum. Familiarize yourself with the topics, concepts, and skills that will be assessed in the exam. Refer to the official syllabus or curriculum guide provided by your school or educational institution.

• Refer to this link for the official QCE math methods syllabus

2. Organize Your Study Materials: Gather all your textbooks, class notes, and study resources. Ensure that you have access to a calculator, graph paper, and any other materials that may be necessary for the exam.

3. Create a Study Schedule: Develop a study schedule that outlines what topics you will study and when. Allocate more time to challenging areas or topics you find difficult. Be consistent with your study routine and set achievable goals.

• Unit 2: calculus and Further Functions and Unit 3: Further Calculus can be incredibly challenging due to the amount of content covered. Therefore, make sure you don’t leave anything to the last minute and practice problems regularly so that you don’t get overwhelmed for the final exams.

4. Review Class Notes and Textbooks: Review your class notes and textbooks to reinforce your understanding of key concepts. Take clear and organized notes if you haven’t already. Highlight important formulas, theorems, and examples.

• Always clarify your doubts straight away. DO NOT sit on a topic without being completely clear with the concepts.
• Make sure you finish doing all the chapter questions and chapter review questions in the textbook before fishing for more questions on the internet.

Refer to this link for Math Videos Australia. All the concepts of General math, math methods and specialist math are explained clearly.

5. Practice Regularly: Practice is crucial in math. Work through a variety of problems, including those from your textbooks, class assignments, and past exam papers—practice problems from different difficulty levels to ensure a well-rounded preparation.

Refer to this link to access official QCAA math methods past exam papers.

Topic-specific tips and tricks 🤓

UNIT 1: Algebra, Statistics, and Functions

• Practice simplifying algebraic expressions and equations.
• Learn the properties of different algebraic operations and apply them.
• Brush up on factoring techniques, including the difference of squares, trinomial factoring, and grouping.
• Watch videos to refresh your concepts and take notes on any new methodology used to solve problems.

UNIT 2: Calculus and Further Functions.

• Understand the fundamental concepts of limits, continuity, and derivatives.
• Practice differentiation techniques for various functions, including chain rule, product rule, and quotient rule.
• Master integration techniques, including substitution and integration by parts.

Trigonometry:

• Memorize the key trigonometric identities and formulas.
• Understand the unit circle and how to use it for trigonometric calculations.
• Practice solving trigonometric equations and working with trigonometric functions in different contexts.

UNIT 3: Further Calculus

Functions and Graphs:

• Be proficient in graphing several types of functions, including linear, quadratic, exponential, and logarithmic.
• Know the basic shapes of graphs.
• Understand how to find the domain and range of functions and identify key features of their graphs (e.g., intercepts, asymptotes).
• Practice drawing lots and lots of graphs on actual graph paper as this will come in handy not only for the final exam but also in University.

UNIT 4: Further Functions and Statistics

Statistics and Probability:

• Practice calculating measures of central tendency (mean, median, mode) and measures of dispersion (variance, standard deviation).
• Learn probability rules and apply them to solve probability problems.
• Understand the concepts of probability distributions, including normal distribution.
• Sometimes probability can be confusing due to the way the questions are worded, in this case, try to find similarly worded questions to get an idea of how these questions should be approached.

In Conclusion…

The key to success in QCE Math Methods is practice. Solve a wide variety of problems from different topics and difficulty levels. This will help reinforce your understanding and improve your problem-solving skills. Excelling in Math Methods requires a combination of diligent preparation, effective study strategies, and a positive mindset. Understand the various assessments, familiarize yourself with common question types, and implement exam strategies to maximise your chances of success. Remember that consistent practice, seeking help when needed, and maintaining your overall well-being are essential components of your journey to mastering Math Methods.

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