75-Archetype SyllabusPhysics • ARCH-P-14 • Spec P5

Full 6-Card Lesson 15-Question Timed Drill

UAT-UK SPEC CODE: P5 (Matter)ASSUMED MATHS 1 PREREQUISITE: M1.2FREQUENCY: HIGH

Hydrostatic Fluid Pressure (P = ρgh), Archimedes Upthrust, Composite Density & Ideal Gas Pistons (P_1V_1 = P_2V_2)

Deconstructed from 14 past UAT-UK questions (6.01% of all historical Physics 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 40s (saving 105s per question).

Historical Frequency

14 Past Qs

6.01% of Physics

Classroom Trap Time

145s

+55s over 90s budget

Sub-90 Target Time

40s

Banks +105s on the clock

Dominant UI Format

5-Option A–E

Maths 1 Skill: M1.2

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-P-14.

Launch All 6 Active-Recall Cards

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

Why Students Bleed Time:

Mass of block is

m = \frac{W}{g} = \frac{30}{10} = 3\text{ kg} = 3000\text{ g}

. Net volume of solid material is

V_{\text{net}} = 10^3 - (5^2 \times 10) = 1000 - 250 = 750\text{ cm}^3

. Thus

\rho = \frac{m}{V_{\text{net}}} = \frac{3000}{750} = 4.00\text{ g cm}^{-3}

(~120s).

In 14 past UAT-UK questions (6.01% of Physics), candidates lose 105s by boyle's law p₁*v₁ = p₂*v₂ requires total absolute pressure (atmospheric + piston pressure), never gauge pressure alone. Instead, apply P5 with Maths 1 skill M1.2.

CARD 2 OF 6 • THE 2-LINE SUB-90 HEURISTIC (<40s)

Line 1 (Net Material Volume):

V_{\text{net}} = 10(10^2 - 5^2) = 750\text{ cm}^3

; mass

m = 3000\text{ g}

Line 2 (Divide):

\rho = \frac{3000}{750} = 4.00\text{ g cm}^{-3}

(25s).

Sanity & Limit Check: Verify units/signs against subsystem_isolation_trap (Using piston additional pressure ΔP = mg/A alone instead of total absolute trapped gas pressure P₂ = P_atm + mg/A in Boyle's Law) and sign_or_direction_flip (Dividing density by 1.20 instead of multiplying by 1.20 when isothermal gas pressure increases by 20%).

Examiner Distractor Blueprint for ARCH-P-14

FOIL #1subsystem_isolation_trap

Using piston additional pressure ΔP = mg/A alone instead of total absolute trapped gas pressure P₂ = P_atm + mg/A in Boyle's Law

Boyle's Law P₁*V₁ = P₂*V₂ requires total absolute pressure (atmospheric + piston pressure), never gauge pressure alone.

Open Subsystem Isolation Trap Clinic

FOIL #2sign_or_direction_flip

Dividing density by 1.20 instead of multiplying by 1.20 when isothermal gas pressure increases by 20%

For fixed mass m at constant T, P*V = const and ρ = m/V, so density ρ is directly proportional to pressure P (ρ_2 = 1.20 * ρ_1).

Open Sign / Direction Flip Clinic

FOIL #3fence_post_or_domain_trap

Using Celsius T(°C) instead of Kelvin T(K) = T(°C) + 273 in ideal gas scaling P*V/T = const

Ideal gas law requires absolute temperature in Kelvin.

Open Fence-Post / Domain Trap Clinic

FOIL #4unit_or_prefix_mismatch

Using weight W = 30 N directly as mass m instead of dividing by g = 10 N/kg (m = 3.0 kg = 3000 g) when finding density ρ = m / V_net

Confusing weight in Newtons with mass in kilograms/grams.

Open Unit / Prefix Mismatch 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-P-14)

ARCH-P-14: Hydrostatic Fluid Pressure (P = ρgh), Archimedes Upthrust, Composite Density & Ideal Gas Pistons (P_1V_1 = P_2V_2) (Sample)Physics

00:00.0

SUB-90 ZONE (<40S)

0.0s40s Sub-9090s ESAT Budget150s Classroom

Question 1 of 1ARCH-P-14 (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.

Physics•ARCH-P-14•Standard 5-Option

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