Everyday maths - Year 1447 till the end of the year Visuvāsuva

Hmmmmmmm hi.
I know, I know. The post of last year just have few tens of maths questions. Not even every week. We even missed some months. Well… let’s continue to reach the goal.

You said it is almost July? Well, let’s count it using Islamic Calendar. It is the first day of Year 1447 today, but it will end in June 2026, and if we are going to have a 2026 maths post there will be a lot of days overlapping. So, let’s end it with another calendar - Tamil Calendar - which New Year Day (Puthandu) will fall in April 2026.

You asked why not a more common used Chinese Lunar Calendar? Because too common :P
Though, New Year for it is earlier (in February).

Well, just, let’s start solving maths. Wish you get an A in whatever Maths subject and, do your best.

If you haven’t noticed yet, 1447 is a prime number

Question 1 - 28th June 2025


Find the value of ∠A+∠B+∠C+∠D+∠E+∠F .

Question in Standard Malay

Cari nilai ∠A+∠B+∠C+∠D+∠E+∠F .

Question in Standard Chinese

求 ∠A+∠B+∠C+∠D+∠E+∠F 之值。

Not too good at math, but in VietNam if we do solve geometry questions, we will need info whether if there’s special condition for the angle or the pyramids, or even the sideline. I will give this a shot when there’s a bit more info

Well, for any 4 triangles with this pattern, no matter how big or small they change, the sum of ∠A+∠B+∠C+∠D+∠E+∠F is fixed at a value.

Try to prove it and you will see (nya~)

ps. Use some simple theories related to triangles, you will see

answer

360 degrees i think

Been awhile since ive done geometry

Correct

Solution 1

∠1+∠2+∠3 = 180° (Sum of interior angles of any triangle)

∠A+∠B+∠1+∠C+∠D∠2+∠E+∠F+∠3=180°+180°+180°
∠A+∠B+∠C+∠D+∠E+∠F + ∠1+∠2+∠3 = 540°
∠A+∠B+∠C+∠D+∠E+∠F + 180° = 540°
∠A+∠B+∠C+∠D+∠E+∠F = 360°

We have had a 2-day rest on weekend, time to refresh our brains :D

Question 2 - 30th June 2025

Question in English

Given that ∠CAB = 60°, ABDE and ACFG are squares, BCH is a equilateral triangle, try to answer the following questions:
(a) Express BC² in terms of AB and AC;
(b) If the area of square ABDE, square ACFG, triangle BCH, and triangle AEG are α, β, γ, δ respectively, find the value of (γ+δ)/(α+β).

Hints here:

a. Use Cosine Rule

b. Area of a triangle = (1/2)ab(sinC)

Question in Malay

Diberi ∠CAB = 60°, ABDE dan ACFG ialah segi empat sama, BCH ialah sebuah segi tiga sama sisi, cuba menjawab soalan-soalan berikut:
(a) Ungkapan BC² dalam sebutan AB dan AC;
(b) Jika luas segi emapt sama ABDE, segi empat sama ACFG, segi tiga BCH, dan segi tiga AEG ialah α, β, γ, δ masing-masing, cari nilai (γ+δ)/(α+β).

Panduan menjawab:

a. Gunakan petua kosinus

b. Luas bagi segi tiga = (1/2)ab(sinC)

Question in Chinese

若 ∠CAB = 60°, ABDE 及 ACFG 爲正方形, BCH 爲等邊三角形, 試回答下列問題:
(a) 以 AB 、AC 表示 BC²;
(b) 設 正方形ABDE, 正方形ACFG, 正三角形 BCH 及三角形 AEG 之面積分別爲 α, β, γ, δ, 則 (γ+δ)/(α+β) 之值爲何?

作答提示:

a. 用 Cosine Rule (餘弦定理)

b. 三角形之面積 = (1/2)ab(sinC)

Answer/Jawapan/答:
a. BC² = AB²+AC²-(AB)(AC) = (AB+AC)²+(AB)(AC)
b. (√3)/4

1 Like
Solution for question (a)

From Cosine Rule,
BC² = AB² + AC² - 2(AB)(AC)(cos∠CAB)
BC² = AB² + AC² - 2(AB)(AC)(cos60°)
BC² = AB² + AC² - 2(AB)(AC)(0.5)
BC² = AB² + AC² - (AB)(AC)
You can stop here or continue
BC² = AB² + AC² - 2(AB)(AC) + (AB)(AC)
BC² = (AB-AC)² + (AB)(AC)

Solution for question (b)


Question 3 - 1st July 2025

Given that a quadratic function y=ax²+bx+c passes through (1, 3), (2, 8) and (3, 15). Find the values of a, b and c.

Question in Malay

Diberi fungsi kuadratik y=ax²+bx+c melalui titik (1, 3), (2, 8) dan (3, 15). Tentukan nilai a, b dan c.

Question in Chinese

已知二次函數 y=ax²+bx+c 通過(1, 3), (2, 8), (3, 15)三點, 求 a, b, c 的值。

Answer: a=1, b=2, c=0

Solution

Question 4 - 2nd July 2025

Question in English

Find the equation of tangent line of 4x² - 4xy + y² + 24x -38y = -13 at point (1, 1).

Question in Malay

Cari persamaan tangen bagi 4x² - 4xy + y² + 24x -38y = -13 di titik (1, 1).

Question in Chinese

求曲線 4x² - 4xy + y² + 24x -38y = -13 在點 (1, 1) 之切線方程。

Modified the question because the original equation does not pass through (1, 1) …

The effect is small though.

Solution

Omg… The one math part I hate: derivation and integral…

yeah i put it in a graphing calculator and gave up lol

1 Like

>.>

sad

Question 5 - 4th July 2025
If n(ξ) = 32, n(A) = 24 and n(B) = 16, find the maximum possible value of n(A∩B).

Question in Malay

Jika n(ξ) = 32, n(A) = 24 dan n(B) = 16, cari nilai berkemungkinan paling tinggi n(A∩B).

Question in Chinese

n(ξ) = 32, n(A) = 24n(B) = 16, 求 n(A∩B) 的最大可能值。