ARCH-M1-04: Non-Linear Proportionality (y ∝ x^n) & Reverse Percentage Compounding

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-M1-04: Why the 120s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~120s (Blows 90s Clock)

Write

y = kx^3

. Substituting

x = 2, y = 24

gives

24 = k(2^3) = 8k \implies k = 3

. When

x = 3

y = 3(3^3) = 3 \times 27 = 81

(~95s).

The Fast ShortcutTarget: 35s (Saves 85s)

Line 1 (Ratio Scaling):

y_2 = y_1 \left(\frac{x_2}{x_1}\right)^3

.
Line 2 (Evaluate):

24 \times \left(\frac{3}{2}\right)^3 = 24 \times \frac{27}{8} = 3 \times 27 = 81

(20s).

Where Students Lose Time: In 29 past UAT-UK questions (12.89% of Mathematics 1), candidates lose 85s by applying percentage increase to the discounted price instead of dividing by the multiplier (1 - r). Instead, apply M3 with Maths 1 skill M3.4.

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