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QCE Maths Methods Questions Thread
Bri MT:
--- Quote from: dzach0 on December 20, 2020, 09:30:21 am ---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!
--- End quote ---
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:
Hi, I was wondering if anybody knew the solution to this question. It’s from the 2020 external exam :)
fun_jirachi:
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.
jasmine24:
--- Quote from: fun_jirachi on March 22, 2021, 07:33:28 am ---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.
--- End quote ---
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:
15 is the correct radial growth (ie. whatever you integrated should've resulted in 15).
Might've just been an algebraic error, unfortunately - it seems to work here :D
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.
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