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December 06, 2021, 02:29:31 pm

### AuthorTopic: QCE Maths Methods Questions Thread  (Read 12770 times)

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#### Bri MT

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##### Re: QCE Maths Methods Questions Thread
« Reply #30 on: December 20, 2020, 10:05:12 am »
0
I have just finished year 10 and got a very unhappy mark for my methods exam (D+). I feel like it is due to me switching from general midway through the year and not being able to keep up with the pace. I want to get ahead on the topics for year 11 so that I am very confident in what I do. However I do not understand what I need to specifically revise on as the unit outlines only consist of hard to understand learning goals.
Does anyone know what specific topics and subtopics I have to revise for unit 1 at least? (I have attached the unit outlines given by my school)

Happy Holidays!

Hey,

Welcome to the forums!

Great to see that you're taking a proactive approach to tackling this.

This is actually a pretty detailed lesson outline, I think it might just be unfamiliarity with the technical maths language that's making it a bit confusing.

For example, when it says "recognise and determine features of the graphs of 𝑦=𝑥2, 𝑦=𝑎𝑥2+𝑏𝑥+𝑐, 𝑦=𝑎(𝑥−𝑏)2+𝑐, and  𝑦=𝑎(𝑥−𝑏)(𝑥−𝑐), including their parabolic nature, turning points, axes of symmetry and intercepts"

You should be able to: take something that looks like $ax^{2} + bx + c$  where a, b and c can be any numbers (but a won't be 0 otherwise it's linear rather than a quadratic) and know that this has a parabolic shape (go here and play around with different values of a, b & c to get a feel for the shape); it can have 0,1, or 2 x-intercepts and 1 y-intercept; and be able to find the turning point. As with other graph forms, if you want to find the y intercept you set x equal to zero & if you want to find the x intercept you set y equal to zero. Finding x-intercepts can be a bit trickier with quadratics than it is for linear equations so you need to learn how to factorise the equation in different ways and use that to help you + the quadratic equation .

I recommend that you do the quadratic section first (you're given textbook chapter numbers and there are heaps of online resources that teach people about quadratics) and make sure you have solid understanding before moving on because it's going to be very hard to understand other polynomials well if you don't get quadratics.

To go super-specific (skip the ones you already know well):
- look at binomial expansion e.g. (3 + a) (2+ b)  or ( x - 5) (x+4)
- look at the reverse, doing basic factorising and rules for this (e.g. difference of two squares, perfect squares)
- be able to factorise things like $x^{2} + 5x + 6$
- use the null factor law to see what the x intercepts are
- be able to deal with having a coefficient of $x^{2}$ that isn't 1. e.g. multiply the whole above example by 2 or 3 or 5
- be able to use completing the square for factorisation
- be able to use completing the square for factorisation with a  coefficient of $x^{2}$ that isn't 1
- be able to use the null factor law on the above
- be able to read from, and make quadratics into turning point form
- be able to use the quadratic equation
- be able to plot quadratics using the above techniques (could have this dot point earlier) & find the equation if given a graph
- be able to use and find the discriminant

^^ All of the above are covered in year 10 maths lectures I gave earlier this year so they might be a good place to look, the slides are available in the free notes section

I hope this helps!

#### jasmine24

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##### Re: QCE Maths Methods Questions Thread
« Reply #31 on: March 22, 2021, 07:08:44 am »
0
Hi, I was wondering if anybody knew the solution to this question. It’s from the 2020 external exam

#### fun_jirachi

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##### Re: QCE Maths Methods Questions Thread
« Reply #32 on: March 22, 2021, 07:33:28 am »
+1
If you're given the rate of change for the trunk's growth, you can find out the amount it has grown by choosing an appropriate upper and lower bound then integrating the rate of change between those bounds.

Once you get this answer, all you really have to do is make sure you obtain a value for the mass and the end of the second stage that seems accurate (ie. by adding the result of the integral to the trunk radius then calculating the new mass.) Note that the density is irrelevant as the volume is almost analogous to the mass. Just remember to have your ratio the right way around as well.

Answer should be 4:1.
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#### jasmine24

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##### Re: QCE Maths Methods Questions Thread
« Reply #33 on: March 22, 2021, 09:01:04 am »
0
If you're given the rate of change for the trunk's growth, you can find out the amount it has grown by choosing an appropriate upper and lower bound then integrating the rate of change between those bounds.

Once you get this answer, all you really have to do is make sure you obtain a value for the mass and the end of the second stage that seems accurate (ie. by adding the result of the integral to the trunk radius then calculating the new mass.) Note that the density is irrelevant as the volume is almost analogous to the mass. Just remember to have your ratio the right way around as well.

Answer should be 4:1.

Thank you so much!
I used 10 and 0 as the bounds which I’m assuming is wrong considering I got 15 as the answer. Also, the method I originally tried was finding the indefinite interval then substituting t=0, r=15 to find c but since it didn’t work, I was wondering if u knew why this wouldn’t work.

#### fun_jirachi

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##### Re: QCE Maths Methods Questions Thread
« Reply #34 on: March 22, 2021, 09:37:26 am »
+3
15 is the correct radial growth (ie. whatever you integrated should've resulted in 15).

$
\text{Choose } R(t) = \int 1.5 + \sin\left(\frac{\pi x}{5}\right) \ dx = 1.5x - \frac{5}{\pi} \dot \ \cos \left(\frac{\pi x}{5}\right) + C
\\ R(0) = 15 \implies C = \frac{5}{\pi} + 15
\\ \text{Hence, } R(10) = 15 - \frac{5}{\pi} \dot \ \cos \left(\frac{\pi (10)}{5}\right) + \frac{5}{\pi} + 15 = 30
$

Might've just been an algebraic error, unfortunately - it seems to work here

EDIT: having thought about it again, you probably haven't read the question properly? This is for radial growth after 10 years, not for the actual radius. While using the method shown above does get you the actual radius, using an upper and lower bound will get you the radial change because we are taking R(10)-R(0) rather than the actual radius using our predefined radius function R(t) at t=10.
« Last Edit: March 22, 2021, 09:42:01 am by fun_jirachi »
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#### justsomerandom21

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##### Re: QCE Maths Methods Questions Thread
« Reply #35 on: May 12, 2021, 08:05:57 pm »
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Hi I'm in grade 11 and I'm super worried about my first Maths Methods exam, I was just wondering if anyone could give me any tips or pointers to what to expect. Thank you in advance

#### fun_jirachi

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##### Re: QCE Maths Methods Questions Thread
« Reply #36 on: May 12, 2021, 11:41:52 pm »
+4
Welcome to the forums!

I can't really give specific tips since I don't have any details, but some general tips:
- Do your best to calm down; it may be difficult to do so (and it's especially easy for me to say) but maintaining a level head is going to do you so much more good. Also, this is your first exam, so don't feel the need to put so much pressure on yourself; base your future performance and tactics on what happens this time
- Remember that whoever is issuing the exam cannot (at least, in theory they shouldn't) test you on something you haven't learned. If there's something that doesn't seem quite right, break it down into smaller bits so you can use the knowledge you do have to solve the question
- Use any reading time you do get effectively
- Any other previous exam tips like if you get stuck move on, etc. also apply here.

Hope this helps!
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#### justsomerandom21

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##### Re: QCE Maths Methods Questions Thread
« Reply #37 on: June 06, 2021, 08:55:48 pm »
0
Welcome to the forums!

I can't really give specific tips since I don't have any details, but some general tips:
- Do your best to calm down; it may be difficult to do so (and it's especially easy for me to say) but maintaining a level head is going to do you so much more good. Also, this is your first exam, so don't feel the need to put so much pressure on yourself; base your future performance and tactics on what happens this time
- Remember that whoever is issuing the exam cannot (at least, in theory they shouldn't) test you on something you haven't learned. If there's something that doesn't seem quite right, break it down into smaller bits so you can use the knowledge you do have to solve the question
- Use any reading time you do get effectively
- Any other previous exam tips like if you get stuck move on, etc. also apply here.

Hope this helps!
Sorry for the long reply, but thanks so much for the advice!!

#### jinx_58

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##### Re: QCE Maths Methods Questions Thread
« Reply #38 on: July 14, 2021, 07:09:13 pm »
0
Howdy.

Could someone please give me some tips on how to do well in a PSMT?

Many thanks.
Currently doing Unit 2: QCE
Physics
Chemistry
Methods
General English
Ancient History
Religion & Ethics

#### K.Smithy

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##### Re: QCE Maths Methods Questions Thread
« Reply #39 on: July 18, 2021, 06:00:25 pm »
+3
Howdy.

Could someone please give me some tips on how to do well in a PSMT?

Many thanks.

Hey Jinx_58,
There are a few things you need to make sure that you do:
• You must state any assumptions and observations you make
Observations are things that you know before coming up with your design (e.g. your design will be two-dimensional whereas the real-life product will be three-dimensional). Assumptions are made after you have finished your design.

• You have to make evident the mathematical and technical procedures used
If you use online programs such as desmos, state that. Also state why you used them (i.e. desmos is a good tool for understanding how the parameters of an equation transform a graph). What mathematical procedures did you use? If you use simultaneous equations, state that. Also make sure your functions have a stated domain and range. You have to address all of the transformations you perform. Start with the parents function and discuss what you have done to them. E.g. it was translated four units upwards.

• Your report must address why your designs are reasonable
This means justifying the functions you used. Its all good saying that a linear equation was used, but why was it used? One way of partially determining the reasonableness of your design is by solving for points of intercept (for one of my PSMTs we design water slides, so it was important that each function intercepted its predecessor). Also, discuss whether your design is realistic.

• You must discuss recommendations for improvement in your evaluation of design and touch on any strengths and limitations

I hope this helps, if you have any questions please don't hesitate to give us a shout
Katelyn

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#### jasmine24

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##### Re: QCE Maths Methods Questions Thread
« Reply #40 on: July 20, 2021, 10:48:44 pm »
0
hi, i was wondering if anyone had a solution to the attached question. The answer key in the textbook skips over it for some reason
TIA

#### fun_jirachi

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##### Re: QCE Maths Methods Questions Thread
« Reply #41 on: July 20, 2021, 11:40:38 pm »
+2
$f'(x) = 3x^2 + 2bx + c \implies \text{stationary points at } x=\frac{-2b\pm\sqrt{4(b^2-3c)}}{6}$.

Note that we are given that $b^2>3c$, so we can see that the case where there is/are one/none stationary points doesn't happen ie. two distinct roots to the derivative at $\frac{-b\pm \sqrt{b^2-3c}}{3}.$

$f''(x)=6x+2b \implies \text{one solution to } f''(x)=0 \implies \text{one inflection point at } x=-\frac{b}{3}.$

Clearly, the inflection point is the midpoint of the two stationary points, a small of computation will let you see that each stationary point is $\frac{\sqrt{b^2-3c}}{3}$ units away from the point of inflection.

Let me know if I've missed anything / screwed up; should be correct!
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#### jasmine24

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##### Re: QCE Maths Methods Questions Thread
« Reply #42 on: August 12, 2021, 09:03:35 pm »
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Hi, my math methods exam is tomorrow and I was wondering if anyone knew how to solve this

#### Bri MT

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##### Re: QCE Maths Methods Questions Thread
« Reply #43 on: August 13, 2021, 10:02:46 am »
+1
Hi, my math methods exam is tomorrow and I was wondering if anyone knew how to solve this

Hey,

Are we told anything that student race times follow a normal distribution?

In that case, what you would want to do is:
- find the distribution using the information from each end ( number in time range / 900 = probability of the time being in that time range)
- then find the place on the distribution for 100/900 (make sure to pick the right end of the distribution )

Hope this helps and let me know if you have any questions

#### Gracey1415

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##### Re: QCE Maths Methods Questions Thread
« Reply #44 on: October 20, 2021, 11:38:18 am »
0
Hi, I'm struggling with this question I'm not sure how the textbook gets to the answer. Would anyone be able to help?

Q: The Apache Orchard grows a very juicy apple called the Fuji apple. Fuji apples are picked and then sorted by diameter into three categories:
•   small — diameter less than 60 mm
•   jumbo — the largest 15% of the apples
•   standard — all other apples.
f) Some apples are selected before sorting and are packed into bags of 6 to be sold at the front gate of the orchard. Determine the probability, correct to 4 decimal places, that one of these bags contains at least 2 jumbo apples.

The answer given is $Y Bi(6, 0.15)$
$P(Y\leq2)=0.2235$