HSC Math 10 Tips
HSC Math 10 Tips
1. Show working in your answers
2. Sound like you know what you’re doing
3. Choose the simplest and quickest method
4. Read and answer the whole question
5. Check that your answer makes sense
6. Realise when the parts of a question are related
7. Be familiar with the terminology of HSC questions
* = Board of Studies definition
Compare*: show how things are similar or different
Describe*/identify: provide characteristics or features
Estimate/approximate: make an educated guess or give an inexact answer
Evaluate/calculate: find the value, the numerical answer
Expand: rewrite an expression without brackets, for example, 3(2b + 1) = 6b + 3
Explain/give a reason: describe why or how
Express: rewrite in a particular way
Hence (or otherwise): find or prove a result using the answers from the previous part of the question (the ‘or otherwise’ means that there are alternative methods but these are usually more complicated)
Interpret: draw meaning from the mathematical result
Justify*: support an argument or conclusion
Prove/show/deduce that: in questions where the answer is given, prove that the answer is true using formal mathematics and reasoning
Simplify: reduce to a shorter, neater form
Solve: find the value(s) of the unknown variable in an equation or inequality
Verify: show or check that a result is true by substituting back (not a formal proof)
Write down/state: write the answer, formula(usually in a one-mark question)
8. Know how to:
(a) explain your answers in words (General Maths)
(b) set out a proof correctly (Maths and Extensions)
9. Draw big graphs and diagrams
10. Learn the language and formulas of mathematics
1. Show working in your answers
- No. of marks for question = no. of steps/items in solution
- A ‘bald’ wrong answer with no working gets no marks
- A wrong answer with some correct working gets some marks
- When marking your HSC exam, the examiner looks for evidence of your knowledge of maths and aims to award you as many marks as possible (so help him/her)
- Write neatly and clearly, setting out your solution down the page
- If substituting into a formula, show the values being used
- Before rounding the answer, show unrounded answer first: don’t round values partway through your solution or your final answer will be inaccurate
- If you make a mistake, cross out the incorrect work with a neat line: don’t use white-out or scribble it out (sometimes, crossed-out work can earn marks!)
2. Sound like you know what you’re doing
- Really know your theory: don’t cram, don’t bluff
- Imagine the examiners are the judges on The X-Factor: they are impressed by true knowledge and talent, but they can spot a phony straight away
- Aim for deep understanding rather than ‘recipe learning’
- Don’t memorise a method without understanding the theory or meaning behind it, otherwise you will have trouble adapting to an unfamiliar HSC problem
- Students who don’t know their work use formulas incorrectly rather than rely on their experience, intuition and common sense
- Know how to use your calculator to perform the financial calculations involved in superannuation and loan repayments
3. Choose the simplest and quickest method
- Every HSC question has been designed to be answered within a specific time: note the number of marks allocated
- Don’t choose methods that are longer and harder: they may still work but waste time and are more prone to error
- After reading a question, don’t ‘jump in’: spend more time thinking, less time writing
- Not every answer requires a formula: consider a diagram, graph, list or table, guess-and-check, the answer to a previous question, looking for a pattern, a simpler formula or even common sense
- Don’t use the sine and cosine rules on right-angled triangles if you can use basic sin, cos, tan, Pythagoras’ theorem or similar triangles
- If your working-out to a problem is taking too long, then it’s probably wrong or inappropriate
4. Read and answer the whole question
- Read the question carefully and completely: highlight any key words
- Double-check that you’ve actually answered the question
- Don’t leave out part of the answer: beware of double-barrelled questions
- Don’t ‘over-interpret’ the question and do more than what is required
5. Check that your answer makes sense
- Especially if it involves measurement or money
- When calculating an unknown length or angle, see from the diagram whether your answer seems practical and realistic
6. Realise when the parts of a question are related
- HSC questions are often interrelated, where the answer to part (i) leads to the answer to part (ii) and so on
- Sometimes, but not always, the word ‘Hence’ is used
- You are being led step-by-step through the solution, with hints (and even answers) being kindly provided along the way
- Otherwise, it would be odd to have 3-4 unrelated things within the same question
- Common in questions involving trigonometry (General Maths) and coordinate geometry (Maths and Extensions)
- Students who don’t use hints from previous parts of a question often ‘reinvent the wheel,’ start solving the problem from scratch, or use more complicated methods
7. Be familiar with the terminology of HSC questions
* = Board of Studies definition
Compare*: show how things are similar or different
Describe*/identify: provide characteristics or features
Estimate/approximate: make an educated guess or give an inexact answer
Evaluate/calculate: find the value, the numerical answer
Expand: rewrite an expression without brackets, for example, 3(2b + 1) = 6b + 3
Explain/give a reason: describe why or how
Express: rewrite in a particular way
Hence (or otherwise): find or prove a result using the answers from the previous part of the question (the ‘or otherwise’ means that there are alternative methods but these are usually more complicated)
Interpret: draw meaning from the mathematical result
Justify*: support an argument or conclusion
Prove/show/deduce that: in questions where the answer is given, prove that the answer is true using formal mathematics and reasoning
Simplify: reduce to a shorter, neater form
Solve: find the value(s) of the unknown variable in an equation or inequality
Verify: show or check that a result is true by substituting back (not a formal proof)
Write down/state: write the answer, formula(usually in a one-mark question)
- Practise using past HSC exams
- Know how to answer a ‘show that’ question: aim to achieve the answer given as the end result but don’t use the answer in your working-out!
- If you don’t get the answer asked, don’t make dodgy changes to your working to make it look right (examiners call this ‘fudging’), but identify the error and correct it
8. Know how to:
(a) explain your answers in words (General Maths)
(b) set out a proof correctly (Maths and Extensions)
- No. of marks for question = no. of steps/items in solution
- Don’t write a page of work for a 2-mark question
- Use correct terminology, notation and reasoning
- Write straightforward answers that are short and to-the-point: the examiners like this
- The more you write, the more likely you will contradict yourself, ramble on, become confused or make a mistake Write clearly, listing your steps down the page
- Don’t include unnecessary information or everything you know about a topic
- Use mathematical facts and calculations, not opinions
- For General Maths, write 1-2 sentences, not essays
- For Maths and Extensions, when solving a geometry problem, draw a big diagram, identify what needs to be found, sketch a rough proof on the diagram, then write each step and its reasoning formally, presenting your proof as concisely as possible
9. Draw big graphs and diagrams
- Use half a page to draw clear and accurate graphs and diagrams
- Show labels and scales on axes of graphs
- Bring a ruler (and a set square) to the exam for drawing, measuring and graph-reading
- Learn how to draw true bearings and tree diagrams
- Be familiar with the graphs of basic functions, including parabolas, hyperbolas, the cubic and exponential curves
- (Maths and Extensions) When graphing regions or a transformed graph, indicate which graph is rough working and which graph is the final answer
10. Learn the language and formulas of mathematics
- Know the jargon of each topic: compile a glossary with your study notes
- Study and use the formulas sheet (General Maths) and list of standard integrals (Maths and Extensions)
- Memorise all basic formulas precisely (for General Maths, this means all Years 9-10 formulas that are not included on the formulas sheet)