Flexible Variables: Bend Them to Your Will! | TMUA
JZMaths
4,112 views
This is one of the MOST USEFUL videos I’ve made!
Sometimes, the quickest way through a maths question is to give the letters some convenient values.
In this video, I work through five increasingly challenging TMUA past-paper questions, showing how carefully chosen substitutions can dramatically simplify the work.
This is a legitimate method rooted in logic: the correct general answer must work for every permitted choice of values. If an option fails for our chosen values, we can eliminate it. If only one survives, we have our answer!
We’ll look at when this works and how to choose useful values.
0:00 Introduction — Flexible Variables: Bend Them to Your Will!
0:54 Question 1 — Triangle areas: choosing a convenient scale (TMUA 2023, Paper 1, Q8)
5:28 Question 2 — Cubic roots: simplifying a parameter (TMUA 2023, Paper 1, Q14)
8:21 Question 3 — Graph intersections: choosing the intercept (TMUA 2020, Paper 1, Q17)
10:46 Question 4 — Distance between roots: making a quadratic factorise (TMUA 2016, Paper 2, Q15)
12:50 Question 5 — Quadratic inequalities: turning algebra into numbers (TMUA 2017, Paper 1, Q19)
More TMUA resources, original papers and the free exam simulator:
https://jzmaths.com
10 Comments
here's how I did it (might be slightly slower but can be more reliable if you can't spot similar triangles easily).
by setting a = 1 you will notice that the length XZ forms the hypotenuse of a right angled triangle, this very much means that we can take sqrt{3}/2 as the area of S.
Then after noticing the equilateral triangle on the right, you can note that the top angle is 60 degrees and since its nestled within a right-angle the other angle is 30, making the T triangle isosceles. Using Area = absin(theta)/2 we can discern that T = \sqrt{3}/4
therefore S : T = \sqrt{3}/2 : \sqrt{3}/4
= 1/2 : 1/4
= 2 : 1
Flexible Variables: Bend Them to Your Will! | TMUA
JZMaths
4,112 views
This is one of the MOST USEFUL videos I’ve made!
Sometimes, the quickest way through a maths question is to give the letters some convenient values.
In this video, I work through five increasingly challenging TMUA past-paper questions, showing how carefully chosen substitutions can dramatically simplify the work.
This is a legitimate method rooted in logic: the correct general answer must work for every permitted choice of values. If an option fails for our chosen values, we can eliminate it. If only one survives, we have our answer!
We’ll look at when this works and how to choose useful values.
0:00 Introduction — Flexible Variables: Bend Them to Your Will!
0:54 Question 1 — Triangle areas: choosing a convenient scale (TMUA 2023, Paper 1, Q8)
5:28 Question 2 — Cubic roots: simplifying a parameter (TMUA 2023, Paper 1, Q14)
8:21 Question 3 — Graph intersections: choosing the intercept (TMUA 2020, Paper 1, Q17)
10:46 Question 4 — Distance between roots: making a quadratic factorise (TMUA 2016, Paper 2, Q15)
12:50 Question 5 — Quadratic inequalities: turning algebra into numbers (TMUA 2017, Paper 1, Q19)
More TMUA resources, original papers and the free exam simulator:
https://jzmaths.com