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vmnalex.bsky.social
Alex ~ VIC Maths Notes
@vmnalex.bsky.social
520 followers 180 following 270 posts
#mtbos #iteachmath | Engelmann | Free notes & resources @ http://vicmathsnotes.weebly.com | Author for OUP Maths | CL @ Ochre
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vmnalex.bsky.social
Got to test something new in #mathstoday. Normally, to decide which transformation to linearise a data set, I'd just show a circle of transformations where each quadrant has the options listed. I recently stumbled upon Tukey and Mosteller's bulging rule and ladder of powers and it's /so/ much easier
circle of transformations with possible transforms listed. signs indicate the sign of the correlation after transformation (without compensating for the reversal of 1/x) the bulging rule where the ladder is labelled as a scale across each axis ladders going from x^-3 to x^-1 to x^0 treated as log(x) to x^1/2 x^1 then through x^5
October 22, 2025 at 9:01 AM
vmnalex.bsky.social
easy change
October 18, 2025 at 6:36 AM
vmnalex.bsky.social
the (hopefully) fully corrected version and x^n
differentiating x^2, x^3, and x^4 by factorising (x+h)^n - x^n using the factorisation of a^n - b^n and letting h → 0 without expanding the second factor. differentiating x^n by factorising (x+h)^n - x^n using the factorisation of a^n - b^n and letting h → 0 without expanding the second factor, where there are n terms of x^(n-1)
October 18, 2025 at 5:58 AM
vmnalex.bsky.social
This was wrong too, lol #OnARoll
October 18, 2025 at 3:57 AM
vmnalex.bsky.social
differentiating x^2, x^3, and x^4 by factorising (x+h)^n - x^n using the factorisation of a^n - b^n and letting h → 0 without expanding the second factor. *corrected x^4 working
October 18, 2025 at 3:23 AM
vmnalex.bsky.social
Can't say I'd thought to do this before. #mathstoday
differentiating x^2, x^3, and x^4 by factorising (x+h)^n - x^n using the factorisation of a^n - b^n and letting h → 0 without expanding the second factor.
October 18, 2025 at 2:23 AM
vmnalex.bsky.social
Additional example over 2 years, quarterly.

They're out JUST enough that you could get marked incorrectly from an assumption of one method or the other because it looks like a rounding error
average percentage method applied to data over 2 years to determine seasonal indices and deseaonalised sales; sales in millions of dollars simple average method applied to data over 2 years to determine seasonal indices and deseaonalised sales; sales in millions of dollars differences in seasonal indices: -0.0093950283 0.0278223623 -0.0145401985 -0.0038871355 differences in deseasonalised values (in millions of dollars) 0.032382259 -0.04141642 0.025299911 0.017857768 0.019279611 -0.035355481 0.015528388 0.011324438
October 11, 2025 at 4:11 AM
vmnalex.bsky.social
Here's the catch: they're not equivalent (nuisance 2). They produce VERY similar results, but not exactly the same (algebraically distinct). And the difference is enough that it could look like a rounding error to 2-4 decimal places occasionally.
seasonally adjusted time series showing original data, and deseasonalised values using average percentage and simple averages methods which are generally equivalent but have deviations same graph without the original data to exaggerate discrepancies differences between seasonal indices 0.001 0 0.001 0 -0.001 -0.002 -0.002 -0.001 0 0.002 0.002 0.002
October 11, 2025 at 4:11 AM
vmnalex.bsky.social
Some texts describe the "average percentage" method but call it "simple average", but "average percentage" is pretty consistently as above (feels very self-referential tbh).
text refers to average percent method: data as percentages of the average for the year which are then averaged text refers to simple averages method: calculates average for each quarter across all years, then written as a percentage of the overall average text lists average percentage and simple average as the same
October 11, 2025 at 4:11 AM
vmnalex.bsky.social
Some questions we've gotten give the average values for each season (assuming across years) and ask to compute the seasonal indices from those. From what I've found, this is the "simple averages" method.
simple averages method applied to the same data over 8 years, monthly; conveniently the average of the seasonal averages is equal to the average of all the data values Past exam question that refers to long-term monthly average heating costs past exam question referring to long-term quarterly average visitor numbers
October 11, 2025 at 4:11 AM
vmnalex.bsky.social
The method our exams use is the "average percentage" method that determines the yearly average for each year, computes the ratio of each value to its corresponding yearly average, and then averages those to get the seasonal indices. It's clunky with all the averaging but gets the job done.
average percentage method applied to data over 8 years, monthly standard style past exam question provided solution in exam report, uses average percentage method: determines quarterly averages for each year then averages the percentages Q3 are of their respectively yearly averages
October 11, 2025 at 4:11 AM
vmnalex.bsky.social
I've got an annoying stats problem at the moment relating to seasonal adjustment of time series about calculating seasonal indices over multiple years. It feels very niche, so any insights are appreciated #mathstoday #mathsconf39 #iteachmath #ukmathschat
example time series with seasonality and upward trend
October 11, 2025 at 4:11 AM
vmnalex.bsky.social
When we reject the null hypothesis, we consider the results to be statistically significant. Statistically significant means that this sample being so extreme is unlikely due to random chance alone. "In general tests of significance are based on hypothetical probabilities calculated from their null hypotheses. They do not generally lead to any probability statements about the real world, but to a rational well-defined measure of reluctance to the acceptance of the hypotheses they test." - Ronald Fisher In short, getting a p-value of 0.06 does NOT mean there is a 6% chance the null hypothesis is true. Null hypothesis testing doesn't allow us to 'accept' or provide evidence that the null is true, we've only failed to provide evidence that it's false. The absence of evidence is not evidence of absence. 'Failing to reject' the null hypothesis doesn't mean that there isn't a difference, effect, or relationship, it just means we didn't get enough evidence to say there definitely is one. If the two groups have the same mean, that is the null hypothesis is true, we want to know that.
August 27, 2025 at 11:17 PM
vmnalex.bsky.social
Was great to see @carlhendrick.substack.com present on Friday. While mostly reinforcing ideas for me, I'm probably going to focus on is more explicitly considering "what is that last 10–20% needed to get this idea?", i.e., what's the bit that actually gets you over the line in understanding an idea
June 29, 2025 at 11:27 PM
vmnalex.bsky.social
Is there a particular, integral based reason for the sequence?
March 27, 2025 at 10:58 PM
vmnalex.bsky.social
Decided to check the etymology for once... It is mixed bag of helpful and unhelpful. Both are "vaulted" and "arched", but it least convex mentions "when viewed from the outside"
concave(adj.) "incurved," early 15c., from Old French concave (14c.) or directly from Latin concavus "hollow, arched, vaulted, curved," from con-, here perhaps an intensive prefix (see con-), + cavus "hollow" (from PIE root *keue- "to swell," also "vault, hole"). convex(adj.) "curved like a circle or sphere when viewed from outside," 1570s, from French convexe, from Latin convexus "vaulted, arched," past participle of convehere "to bring together," from assimilated form of com "with, together," or "thoroughly" (see com-) + vehere "to bring, carry, convey" (from PIE root *wegh- "to go, move, transport in a vehicle"). Possibly the notion is of vaults "carried together" to meet at the point of a roof. Related: Convexity. Convex lens is from 1822.
February 27, 2025 at 9:57 PM
vmnalex.bsky.social
Yes, they lore dropped in an exam.
February 25, 2025 at 12:16 AM
vmnalex.bsky.social
For several years we had context problems involving Tasmania Jones and his cousin Victoria Jones going on several adventures (yes ripping off that Indiana is a US state and using Aus states instead...).

My favourite is where Tas is trying to save a statue www.vcaa.vic.edu.au/Documents/ex... (p20)
February 25, 2025 at 12:16 AM
vmnalex.bsky.social
Ooo I like this! It's a nifty form of integration by parts for inverse functions. Gives something to pair with the rule for the derivative of them.
∫▒〖f^(−1) (x) dx〗=xy−∫▒〖f(y) dy〗, where y=f^(−1) (x) and x=f(y) Let y=f^(−1) (x)=log_e⁡(x) so that x=f(y)=e^y ∫▒〖log_e⁡(x)dx〗=x log_e⁡(x)−∫▒〖e^y dy〗=x log_e⁡(x)−e^y+c=x log_e⁡(x)−x+c Let y=f^(−1) (x)=arcsin⁡(x) so that x=f(y)=sin⁡(y) ∫▒〖arcsin⁡(x)dx〗=x arcsin⁡(x)−∫▒〖sin⁡(y)dy〗=x arcsin⁡(x)+cos⁡(y)+c=x arcsin⁡(x)+√(1−x^2 )+c as cos⁡(arcsin⁡(x) )=√(1−x^2 )
February 6, 2025 at 3:53 AM
vmnalex.bsky.social
NEW for VCE on VIC Maths Notes:
- Grade boundaries for 2014-2023 for graded assessments
- Graphs of stats of numbers of students, mean scores and grade distributions for graded assessments for 2014-2023
Grade distributions for General Maths GA1 Graph of number of students for General Mathematics Graphs of the mean score for General Mathematics exam 1 Graph of the distributions of grades for General Maths exam 1
January 27, 2025 at 11:02 PM
vmnalex.bsky.social
Currently available are:
- Yearly overviews, showing units scheduled over the course of the year.
- Unit overviews, indicating the contents and curriculum/Syllabus alignment for each unit.

Term 1 lesson materials will be released early in Term 3, ready for teaching in 2026.
Unit overview for the Algebraic expressions and fractions unit for Year 10 core showing the split between the core content and the optional extension
January 17, 2025 at 10:28 PM
vmnalex.bsky.social
Curriculum materials are available for:
- Australian Curriculum v9 (Core and Core+Extension)
- New NSW Syllabus (Core + selected paths (Standard +Advanced), and Core + selected paths (Advanced + Extension))
- Victorian Curriculum version 2.0 (Year 10 and Year 10A)
Precedence diagram showing the connections between the units for Year 10 core
January 17, 2025 at 10:28 PM
vmnalex.bsky.social
Very excited for the first of our Ochre Year 10 resources to go live!

We've designed courses to cover both the core content and the core plus the optional extension for AC9 and VC2 and the pathways for the NSW syllabus with lots of room to adapt them as needed.
Yearly overview of the Year 10 core maths course for the Australian Curriculum
January 17, 2025 at 10:28 PM
vmnalex.bsky.social
And for completeness, you can format as equivalent fractions to leverage that knowledge. But I've found students are too used to only doing integers to multiply/divide by that it can get a little in the way.
December 18, 2024 at 8:49 PM
vmnalex.bsky.social
Like I said, using double-number lines (DNLs) as a catch all. Generally, I'm doing the below sort of format (ratios on sequential lines) once the idea about using the multipliers is established and students don't need the vaguely proportional format anymore.
December 18, 2024 at 8:49 PM