Introduction
As we move closer and closer towards the exam, my advice to students would be to begin working through practice exams made by external companies and past papers from VCAA. Hopefully people have completed their bound references and can use them whilst working through practice papers.
Disclaimer
These are recommendations and not everyone learns in the same way, so take all advice with a grain of salt.
Practice Exams
I have mentioned this before, but I think it is a really good idea to reiterate it now; I don’t believe students have to be attempting practice exams in strict exam like conditions. At this stage last year, I was splitting up practice exams into ‘chunks’ and working through the exams bit by bit with breaks where necessary. I would also typically be listening to music or a podcast whilst doing exams. I think this is a good way to keep strong motivation levels for Further Maths throughout the next 5 weeks.
Last week, I went through two typical types of questions used in Further Maths exams. This week I will go through another two district styles of questions that I frequently noticed whilst working through past VCAA exam papers.
‘Process of Elimination Questions’
Questions that demand a ‘process of elimination’ are extremely common in Further Exams, particularly in multiple choice examination. I think students sometimes struggle with these questions as they select an answer that makes sense without looking at all the other possible options. To ensure you do not make a mistake on this type of question, always read all given options and chose the ‘most correct answer’. An example of this style of question is given below.
‘Common Mistake Questions’
This type of question is a favourite of exam writers in the multiple-choice exam. The question will typically seem straight forward, however, the corresponding options will all be conceivable answers if made a mistake was made throughout the working out process. This means that if students do make a slight error whilst working out their response, they will still believe their answer is correct as it matches with a corresponding option. To avoid losing marks on this style of question, always double check your working out no matter if your response does match a corresponding multiple-choice answer; examiners may be trying to trick you like this.
Here is an example question in this style. See below how I made two errors in my working out; I used the ‘Z-Score’ formula incorrectly and converted my answer into decimals incorrectly. Even though I made two errors, my answer still matches one of the multiple-choice answers. Always double check your working out even if your answer does match a corresponding option.
Below is the correct working out for this question.
Some final notes on rounding, significant figures and units
Rounding
Rounding is involved in majority of Further Maths exam questions, so it is important to get it right.
The general rule is:
1. ‘0 – 4’ round down
2. ‘5 – 9’ round up
E.g. 3.256 rounded to one decimal places
= 3.3 as ‘.25’ rounds up to ‘.3’
Significant Figures
Typically, in a Further Maths exam, one if not more questions will ask students to round to a level of ‘significant figures’.
The general rule for Significant figures:
1. Any non-zero digit is SIGNIFICANT
2. Zero’s between non-zero digits are SIGNIFCANT
3. Trailing zero’s in decimals are SIGNIFICANT
The general rule for Non-Significant figures:
1. Leading zero’s in decimals are NOT SIGNIFICANT
2. Trailing zero’s in whole numbers are NOT SIGNIFICANT
E.g. 170.0043 = 7 significant figures
E.g. 0.0043 = 2 significant figures
E.g. 0.00430 = 3 significant figures
E.g. 170 = 2 significant figures
Units
This goes without really saying; if a question involves any sort of units, use the units in all answers related to the question.
Don’t miss simple marks as you didn’t write cm, km, hours etc.
Common Sense Units
‘Common sense units’ apply when an examiner doesn’t specifically detail how many decimal places are required in an answer. In Further Maths, if a question does not detail the number of decimal places required; we usually assume 2 decimal places however if the context of the question means 2 decimal places does not make sense, we apply ‘common sense units’ which requires students to round down to the nearest whole number.
E.g. If the question asks how many people were at the event, and your answer is 4.56 people, you should round down to 4 people, unless otherwise specified.
This is because we have 4 full people that have evidently attended the event, we do not have 5 people in attendance, nor do we have 4.56 people in attendance as this is impossible (cannot have .56 of a person).
I do doubt that there will be a situation where the application of ‘common sense units’ is necessary on your exam. However, why not be prepared just in case?
Have a question?
In the final weeks before exams Ned will be hosting 2 Live Q&A sessions to help everyone get fully prepared for exams. If you have a question on how to best get prepared, have been stuck on an exam question or want to clarify an area of content send it through here, and Ned might answer it live!