ARCH-MM-11: Odd/Even Function Integral Symmetry over [-a, a] & Linear Integral Transformations

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-MM-11: Why the 145s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~145s (Blows 90s Clock)

Finding the full antiderivative

\left[\frac{7}{6}x^6 + \frac{-5}{4}x^4 + \frac{3}{3}x^3 + \frac{-9}{2}x^2 + 4x\right]_{-2}^{2}

and evaluating all ten terms at

x = 2

and

x = -2

takes ~150s and simplifies to

32

The Fast ShortcutTarget: 35s (Saves 110s)

Line 1 (Kill Odd Powers): Over

[-2, 2]

, cross out

x^5,\, x^3,\, x

immediately (

= 0

).
Line 2 (Double Even Powers):

2\int_0^{2} (3x^2 + (4))\,dx = 2\left[1(2^3) + (4)(2)\right] = 32

(20s).

Where Students Lose Time: In 20 past UAT-UK questions (4.88% of Mathematics 2), candidates lose 110s by applying horizontal stretch factor b instead of 1/b to the area. Instead, apply MM7 with Maths 1 skill M4.14.

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