75-Archetype SyllabusMathematics 2 • ARCH-MM-11 • Spec MM7

Full 6-Card Lesson 15-Question Timed Drill

UAT-UK SPEC CODE: MM7 (Integration)ASSUMED MATHS 1 PREREQUISITE: M4.14FREQUENCY: HIGH

Odd/Even Function Integral Symmetry over [-a, a] & Linear Integral Transformations

Deconstructed from 20 past UAT-UK questions (4.88% of all historical Mathematics 2 papers). Students using standard A-Level classroom methods spend an average of 145s on this archetype—blowing past the 90s ESAT budget. Using the 2-line Sub-90 heuristic below compresses solve time to 35s (saving 110s per question).

Historical Frequency

20 Past Qs

4.88% of Mathematics 2

Classroom Trap Time

145s

+55s over 90s budget

Sub-90 Target Time

35s

Banks +110s on the clock

Dominant UI Format

5-Option A–E

Maths 1 Skill: M4.14

Card 1 & Card 2 Preview: The Classroom Time Trap vs. Sub-90 2-Line Rule

Excerpted from our interactive 6-Step Topic Lesson for ARCH-MM-11.

Launch All 6 Active-Recall Cards

CARD 1 OF 6 • THE CLASSROOM TIME TRAP (145s)

Why Students Bleed Time:

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

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.

CARD 2 OF 6 • THE 2-LINE SUB-90 HEURISTIC (<35s)

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).

Sanity & Limit Check: Verify units/signs against factor_of_two_or_stoichiometry_trap (Multiplying the integral by b instead of dividing by b when stretching horizontally: int f(bx) dx = (1/b) int f(u) du) and fence_post_or_domain_trap (Computing int_a^b (f(x) + c) dx as I + c instead of I + c*(b - a)).

Examiner Distractor Blueprint for ARCH-MM-11

FOIL #1factor_of_two_or_stoichiometry_trap

Multiplying the integral by b instead of dividing by b when stretching horizontally: int f(bx) dx = (1/b) int f(u) du

Applying horizontal stretch factor b instead of 1/b to the area.

Open Factor-of-2 / Stoichiometry Clinic

FOIL #2fence_post_or_domain_trap

Computing int_a^b (f(x) + c) dx as I + c instead of I + c*(b - a)

Adding constant c instead of integrating c over the interval width (b - a).

Open Fence-Post / Domain Trap Clinic

FOIL #3sign_or_direction_flip

Failing to negate the integral when swapping limits int_b^a f(x) dx = -int_a^b f(x) dx

Ignoring reversed integration bounds.

Open Sign / Direction Flip Clinic

FOIL #4intermediate_stop_trap

Expanding and integrating odd terms x³, x⁵ over [-a, a] instead of cancelling them to 0 immediately

Wasting 90 seconds integrating odd polynomial terms over a symmetric interval.

Open Intermediate Stop Trap Clinic

Try 1 Live Sample Question Under the 90-Second Stopwatch

Press W to open the 2-line dry-wipe scratchpad, select A–E, and lock in to reveal the Dual-View solution.

Full 6-Card Lesson Launch All 15 Questions (ARCH-MM-11)

ARCH-MM-11: Odd/Even Function Integral Symmetry over [-a, a] & Linear Integral Transformations (Sample)Mathematics 2

00:00.0

SUB-90 ZONE (<35S)

0.0s35s Sub-9090s ESAT Budget150s Classroom

Question 1 of 1ARCH-MM-11 (6-Card Lesson)Format: Standard 5-Option

Right-click any option to cross out • Keys A–E + Enter

Question 1 of 1 • 90s Target

Ready to Start Question 1?

The question stem, diagram, and answer options are hidden behind this pre-start gate. When you click below, the question will reveal and your 90-second split stopwatch will immediately begin ticking.

Mathematics 2•ARCH-MM-11•Standard 5-Option

or press Enter to start