August 20, 2019, 12:57:46 pm

### AuthorTopic: 12 Avoidable Mistakes Students Make in Math Exams  (Read 12840 times) Tweet Share

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#### BPunjabi

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #15 on: October 10, 2016, 12:59:26 pm »
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So can you please provide a hand written photo example?

No but ill pull up a HSC Past question, give me a sec
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#### nibblez16

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #16 on: October 10, 2016, 01:12:22 pm »
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Hello, I wanted to ask, for 'area enclosed' or 'area of the shaded region' questions, we are usually given two equations to work with. So when we example have to find the area of the shaded region, how do we know if we have to combine the two equations together or do the maths separartely on the two equations??

#### RuiAce

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #17 on: October 10, 2016, 01:14:30 pm »
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Hello, I wanted to ask, for 'area enclosed' or 'area of the shaded region' questions, we are usually given two equations to work with. So when we example have to find the area of the shaded region, how do we know if we have to combine the two equations together or do the maths separartely on the two equations??
Can you be a bit more specific on what 'combine' and 'separate' are meant to mean

#### nibblez16

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #18 on: October 10, 2016, 01:54:52 pm »
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Can you be a bit more specific on what 'combine' and 'separate' are meant to mean

Example, we hace a graph showing parabolas, one has the equation y=5x-x(squared) and the other y=x(squared)-3x. We have to find the area of the shaded region, so to find the area we use integration, but do we place the two equations together, or do we integrate separately? Because some area questions you have to integrate the equations separately and some you have to put the two equations as one...

#### RuiAce

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #19 on: October 10, 2016, 01:58:14 pm »
+1
Example, we hace a graph showing parabolas, one has the equation y=5x-x(squared) and the other y=x(squared)-3x. We have to find the area of the shaded region, so to find the area we use integration, but do we place the two equations together, or do we integrate separately? Because some area questions you have to integrate the equations separately and some you have to put the two equations as one...
$\text{Both of them give the same answer. This is just the rule}\\ \int_a^bf(x)dx+\int_a^bg(x)dx=\int_a^b(f(x)+g(x))dx$
$\text{For your scenario}\\ \int_0^2 (5x-x^2)dx-\int_0^2(x^2-3x)dx = \int_0^2((5x-x^2)-(x^2-3x))dx\\ \text{They will give the same answer}$
$\text{On the day they will not care which you use, so long as you answer the question.}$

#### nibblez16

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #20 on: October 10, 2016, 02:07:40 pm »
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$\text{Both of them give the same answer. This is just the rule}\\ \int_a^bf(x)dx+\int_a^bg(x)dx=\int_a^b(f(x)+g(x))dx$
$\text{For your scenario}\\ \int_0^2 (5x-x^2)dx-\int_0^2(x^2-3x)dx = \int_0^2((5x-x^2)-(x^2-3x))dx\\ \text{They will give the same answer}$
$\text{On the day they will not care which you use, so long as you answer the question.}$

Ohh Alright! Thank You so much

#### marynguyen18

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #21 on: October 10, 2016, 03:16:41 pm »
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when is it safe to skip steps?

#### RuiAce

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #22 on: October 10, 2016, 03:18:25 pm »
+2
when is it safe to skip steps?
Never.

That's what you should be believing. If you're good enough at algebra and you can skip a few steps in it that's fine, but otherwise skipping steps is never advised.

If you want a specific question considered, please post it.

#### BPunjabi

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #23 on: October 10, 2016, 03:55:26 pm »
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$\text{Both of them give the same answer. This is just the rule}\\ \int_a^bf(x)dx+\int_a^bg(x)dx=\int_a^b(f(x)+g(x))dx$
$\text{For your scenario}\\ \int_0^2 (5x-x^2)dx-\int_0^2(x^2-3x)dx = \int_0^2((5x-x^2)-(x^2-3x))dx\\ \text{They will give the same answer}$
$\text{On the day they will not care which you use, so long as you answer the question.}$

$\int_0^2((5x-x^2)-(x^2-3x))dx\\$
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#### Opengangs

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #24 on: July 05, 2017, 09:18:19 am »
+1
I definitely feel like rounding too early can be avoided entirely if you understand the 'store' button on some calculators.
The default calculator for the HSC is the Casio fx-82 AU Plus, and if you have the time, definitely consider buying it for the HSC.

The store button, which can be accessed via SHIFT + RCL allows you to store exact values for irrational values, which in turn, avoids rounding incorrectly altogether.
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#### RuiAce

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #25 on: July 05, 2017, 09:39:05 am »
+2
I definitely feel like rounding too early can be avoided entirely if you understand the 'store' button on some calculators.
The default calculator for the HSC is the Casio fx-82 AU Plus, and if you have the time, definitely consider buying it for the HSC.

The store button, which can be accessed via SHIFT + RCL allows you to store exact values for irrational values, which in turn, avoids rounding incorrectly altogether.
First note that the Casio fx-82 AU is the default. The plus version is slightly more advanced. (Both are, of course, acceptable by BOSTES.) Edit: Sorry, maybe the Plus is the default; I had forgotten about the existence of Plus II. Fortunately, doesn't change the fact that all are acceptable by NESA though.

(MX2 should consider Casio fx-100 AU Plus.)

The store button is only really advantageous for problems where the numbers are overly bizarre or you have two numbers at once. Note that the calculators always store the previous result by the "Ans" key, and that can be exploited very easily without learning the whole store toolkit. The most common places where rounding errors occur is honestly in exponential growth and decay and financial applications of series, and as you usually only need one previous value (instead of mutiple), this fills all the gaps you need.

However, store has saved me quite a lot at university. To the interested reader, here is a very short demonstration on how to use it. Can be very handy for commerce and engineering. It's easy to learn, just easy to forget as well.
« Last Edit: July 29, 2017, 05:02:03 pm by RuiAce »

#### kemi

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##### Re: 12 Avoidable Mistakes Students Make in Math Exams
« Reply #26 on: August 07, 2017, 11:54:55 am »
+2
Great thread - definitely have lost a few marks for several of those points >.<

These mistakes I used to incur often (more specific to MX1):
- Changing your boundaries for integration by substitution. Do this IMMEDIATELY for definite integrals. Saves you a few marks.
- Changing the 'u' back to the original expression for 'x' for indefinite integrals.
- For dividing an interval in a given ratio, ensure your value is negative for m or n when moving left. Even if the final answer is unaffected, you could lose marks for incorrect working.

This can also apply to 2U:
- For similar triangles, be sure to put the correct sides over each other! Check by looking at the angle opposite to each side or the order of side length.
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