Which areas of Maths Methods are the hardest?

[SmellsLikeTeenSpirit]

Really, which areas are the hardest? Based on the VCE Maths Methods exams between 2006 and 2018, a top list is attached. Please note: the areas in the list do not exactly match those in your textbooks. The main reason is: some areas like Basic Geometry, or Equations, or Evaluations, are not explicitly listed as topics in Maths Methods textbooks, but pop up often in VCE exams!
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[^^^111^^^]

Really, which areas are the hardest? Based on the VCE Maths Methods exams between 2006 and 2018, a top list is attached. Please note: the areas in the list do not exactly match those in your textbooks. The main reason is: some areas like Basic Geometry, or Equations, or Evaluations, are not explicitly listed as topics in Maths Methods textbooks, but pop up often in VCE exams!

Tbh with you, I also find integration more difficult than differentiation. I mean, units 1 and 2 of calculus for both components is quite similar in difficulty, but when looking at more advanced aspects, such as improper integrals and contrasting that to Units 3/4 of differentiation (like product, quotient and chain  rule), differentiation (in my perspective) is waaay more easier. I do find functions quite hard as well (mainly piece-wise defined), but for me units 3/4 of integration is gonna be the winner here  . So yh, most of what I think is hard correlates to the data you've just found  .

[SmellsLikeTeenSpirit]

Hi ^^^11^^^,

I agree with you. There are various topics involving differentiation (chain rule, differentiation of products of functions, or their quotients etc), but more than 50 % of students solved the problems involving these topics. The only exception is a group of tough differentiation problems (I classify them as Miscellaneous) that involve absolute values of functions, or discontinuous functions, or finding the maximum of a gradient etc. Those problems do not pop up often of late for some reason, and the examples of them are:
* 2007, Q 3a in Test 1 and Q 3c in Test 2B
* 2009, Q 10a in Test 1, Q 5 in multiple-choices test and Q 1e ii in Test 2B
* 2011, Q 7 and 9 in multiple-choices test
* 2015, Q 2b in Test 2B

As for integration, it also covers quite a few topics. Students generally do well with the approximation of area under curve, or identifying a function if its derivative and a point are given. What seems to cause a lot of grief are topics like:
* If x*f'(x) is given, calculate the integral of x*f(x)
* Calculation of area under a curve, or between two curves
* If function contains a coefficient of unknown value, and and the area under the function is given, calculate the value of the coefficient
* Some really quirky problems like
- 2008: Q 19 in multiple choices test, Q 2d in Test 2B
- 2010: Q 22 in multiple choices test
- 2013: Q14 in in multiple choices test

Cheers

[SmellsLikeTeenSpirit]

And just to add a couple of additional observations:
* For some reason, less than 40 % of students solve the basic geometry problems involving triangle, rectangle and trapezium. They are really not hard, and I guess the reason for the low success rate is that students get focused on the topics taught in Years 11 and 12, while some stuff from Years 7-10 often pops up at the exams.
* While functions are generally the easiest area, they contain both the easiest topic (finding a period of a function), and the hardest one (inequalities). Only 12 % of students solve the inequalities, and they seem to be fairly regular fare of late. The examples are:
- 2016: Q 4d, 4e (iii) and 4i (ii) in Test 2B
- 2017: Q 4i (ii) in Test 2B
- 2018: Q18 in in multiple choices test
* The next two hardest topics are (a) finding whether two events are dependent or independent, and (b) determining the conditions under which an equation would have a single solution. Only about 30 % of students solve them.
* It should be noted that all three hardest topics were encountered in 2018!!

Cheers

[SmellsLikeTeenSpirit]

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