ESAT Syllabus & Archetype Encyclopedia
Mathematics 1 (13 Archetypes)
Take 40-Min Mathematics 1 MockARCH-M1-01 • Spec M17.56% Share (17 Qs)
Compound Units, Alloy Density Mixing & Area/Volume Prefix ScalingWrite dimensional grid [Total Top / Total Bottom] first: for equal-distance average speed use harmonic mean 2v1*v2/(v1+v2); for prefix conversions square/cube the power of 10 immediately (1 cm² = 10⁻⁴ m², 1 cm³ = 10⁻⁶ m³).
Trap: 135s → Sub-90: 40sStudy Guide
ARCH-M1-02 • Spec M27.56% Share (17 Qs)
Surd Rationalisation, Difference-of-Squares & Laws of IndicesFactor out common surds before rationalising; memorise (a + b*sqrt(n))(a - b*sqrt(n)) = a² - n*b² and convert all base powers (4^x, 8^x, 9^x) to prime bases (2²x, 2³x, 3²x) in Line 1.
Trap: 125s → Sub-90: 35sStudy Guide
ARCH-M1-03 • Spec M22.22% Share (5 Qs)
Truncation vs. Rounding Error Intervals, Standard Form & BoundsFor rounding to unit u: [x - u/2, x + u/2); for truncation to unit u: [x, x + u). For extreme bounds of A/B or A-B, always cross-pair: Max = UB(A)/LB(B) and UB(A)-LB(B).
Trap: 130s → Sub-90: 40sStudy Guide
ARCH-M1-04 • Spec M312.89% Share (29 Qs)
Non-Linear Proportionality (y ∝ x^n) & Reverse Percentage CompoundingNever solve for proportionality constant k: write y2/y1 = (x2/x1)^n directly using fractional multipliers (e.g. +20% = 6/5, -25% = 3/4). For reverse percentages, divide by the multiplier.
Trap: 120s → Sub-90: 35sStudy Guide
ARCH-M1-05 • Spec M33.56% Share (8 Qs)
Two-Component Mixing, Dilution Alligation & Combined Work RatesLock onto the invariant quantity (pure solute or pure metal) that does not change during dilution: C1*V1 = C2*V2. For two mixtures C1 and C2 making C_m, the volume ratio is |C2 - C_m| : |C_m - C1|.
Trap: 150s → Sub-90: 45sStudy Guide
ARCH-M1-06 • Spec M34% Share (9 Qs)
2D/3D Geometric Similarity Scaling (k, k^2, k^3) & FrustumsWrite the scaling triad L : A : V = k : k² : k³ immediately. For a frustum cut at fraction k of height from apex, V_frustum = (1 - k³) * V_whole.
Trap: 145s → Sub-90: 35sStudy Guide
ARCH-M1-07 • Spec M413.78% Share (31 Qs)
Algebraic Subject Rearrangement, Rational Fractions & Completing the SquareFor y = (ax+b)/(cx+d), the inverse rearrangement swaps (a, d) with a sign flip: x = (-dy+b)/(cy-a). For p(x+q)²+r, evaluate at x=0 and x=-q to find r in 10 seconds without full expansion.
Trap: 140s → Sub-90: 40sStudy Guide
ARCH-M1-08 • Spec M410.22% Share (23 Qs)
Simultaneous Linear Combinations, Straight-Line Gradients & InequalitiesCheck if the target expression (e.g. 6a+2c) is a direct linear combination of the given equations (2*(4a+4c) - (2a+3c)) before solving for individual variables. For ax+by=c, gradient is -a/b.
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-M1-09 • Spec M57.11% Share (16 Qs)
Circle Theorems, Tangent-Radius Right Angles & Shaded Sector Mensuration (Degrees)Draw auxiliary radii to every tangent contact point (90 deg) and chord endpoint (isosceles triangle) first. Eliminate options by matching the pi term vs. the surd/rational triangle term separately.
Trap: 150s → Sub-90: 45sStudy Guide
ARCH-M1-10 • Spec M58.89% Share (20 Qs)
3D Mensuration (Cylinder/Sphere/Cone) & Right-Triangle Trigonometry in DegreesCancel pi on both sides before substituting numbers when equating cylinder/cone/sphere volumes. For 3D space diagonals, use d = sqrt(x² + y² + z²) in one step.
Trap: 155s → Sub-90: 45sStudy Guide
ARCH-M1-11 • Spec M64% Share (9 Qs)
Mean Deviation Balancing, Grouped Median Interpolation & Unequal-Width HistogramsNever multiply large means: balance deviations from the target mean so sum(x_i - mean) = 0. In histograms, Area = Frequency (F = FD * width).
Trap: 135s → Sub-90: 40sStudy Guide
ARCH-M1-12 • Spec M78.89% Share (20 Qs)
Multi-Stage Conditional Probability Trees (Without Replacement) & Algebraic Venn OverlapsFor 'at least one', always compute 1 - P(none). For 2-Group overlaps without formal set notation, use Total - Neither = Group1 + Group2 - Both.
Trap: 140s → Sub-90: 40sStudy Guide
ARCH-M1-13 • Spec M59.33% Share (21 Qs)
Regular Polygon Exterior Angles (360°/n), 3-Figure Bearings, Clock Angles & 2D Vectors/TransformationsAlways work with exterior angles (360°/n): each clockwise vertex turn on a regular n-gon adds +360°/n to the bearing (mod 360°). On a clock at H:M, angle = |30H - 5.5M|°.
Trap: 135s → Sub-90: 35sStudy Guide
Mathematics 2 (15 Archetypes)
Take 40-Min Mathematics 2 MockARCH-MM-01 • Spec MM14.88% Share (20 Qs)
Polynomial Division by a Quadratic & Linear Remainder Theorem (R(x) = mx + n)Never perform long division: write P(x) = Q(x)(x-a)(x-b) + mx + n, substitute x = a and x = b to get two instant linear equations ma + n = P(a) and mb + n = P(b).
Trap: 165s → Sub-90: 45sStudy Guide
ARCH-MM-02 • Spec MM13.66% Share (15 Qs)
Disguised Radical Equations & Principal Square Root Domain Filtering (√x ≥ 0)In ESAT/TMUA, sqrt(u) is strictly >= 0. Before squaring sqrt(f(x)) = g(x), write the mandatory filter g(x) >= 0 on your notepad and discard any root that fails it.
Trap: 150s → Sub-90: 40sStudy Guide
ARCH-MM-03 • Spec MM29.02% Share (37 Qs)
Coupled Arithmetic & Geometric Progressions and Sum to Infinity (S_∞)Use the mean identities directly: three terms x, y, z are in AP iff 2y = x + z, and in GP iff y² = xz. Always verify |r| < 1 if S_infinity is mentioned.
Trap: 160s → Sub-90: 45sStudy Guide
ARCH-MM-04 • Spec MM22.2% Share (9 Qs)
Sigma Notation (Fence-Post n-m+1 Terms) & Periodic Recurrence Relations (u_{n+1} = f(u_n))For recurrence relations u_{n+1} = f(u_n) asking for u₁₀₀ or sum_{n=1}^{100}, compute u₁, u₂, u₃, u₄ first—90% of ESAT/TMUA recurrences are periodic with period 2, 3, 4, or 6. In sum_{r=m}^n, count = n - m + 1.
Trap: 155s → Sub-90: 45sStudy Guide
ARCH-MM-05 • Spec MM35.61% Share (23 Qs)
Circle Coordinate Geometry, Tangent Discriminants & Extremal DistancesNever substitute y = mx + c into a circle if you can use geometry: a line is tangent iff perpendicular distance from centre (a,b) equals radius r, and shortest distance to an external point P is |CP| - r.
Trap: 170s → Sub-90: 45sStudy Guide
ARCH-MM-06 • Spec MM412.93% Share (53 Qs)
Radian Sector Mensuration & Counting Trigonometric Roots in Transformed IntervalsTo count roots of trig(kx + a) = c in [0, 2*pi], never solve for x: substitute u = kx + a, transform the interval to [a, 2k*pi + a], and count wave intersections per 2*pi cycle.
Trap: 160s → Sub-90: 45sStudy Guide
ARCH-MM-07 • Spec MM511.46% Share (47 Qs)
Laws of Logarithms, Disguised Exponential Quadratics (a^{2x} + b a^x + c = 0) & Log InequalitiesSpot disguised quadratics immediately: 4^x = (2^x)² and 2^(x+k) = 2^k * (2^x). By Vieta's formulas, if u₁*u₂ = a^(x₁ + x₂) = c/A, then x₁ + x₂ = log_a(c/A) directly without finding x₁ or x₂!
Trap: 150s → Sub-90: 40sStudy Guide
ARCH-MM-08 • Spec MM65.85% Share (24 Qs)
Power-Rule Differentiation of Expanded Rational Powers (x^n) & Tangent/Normal GeometryESAT/TMUA restricts differentiation to rational powers x^n: always split fractions over a single-term denominator x^k*sqrt(x) into separate powers x^(a - k - 1/2) first, then apply n*x^(n-1) term-by-term.
Trap: 155s → Sub-90: 45sStudy Guide
ARCH-MM-09 • Spec MM67.07% Share (29 Qs)
Stationary Point Classification, Monotonic Cubics & Constrained 2D/3D OptimisationA cubic ax³+bx²+cx+d (a>0) is increasing for all x iff its derivative 3ax²+2bx+c >= 0 everywhere, which reduces to discriminant (2b)² - 4(3a)(c) <= 0 => b² <= 3ac.
Trap: 175s → Sub-90: 50sStudy Guide
ARCH-MM-10 • Spec MM75.37% Share (22 Qs)
Definite Integration of Rational Powers (x^n, n ≠ -1) & Area Enclosed Between CurvesFor the area enclosed between a parabola y = ax² + bx + c and a line intersecting at x = alpha and x = beta, use Archimedes' 1/6 shortcut: Area = |a|/6 * (beta - alpha)³ in 10 seconds!
Trap: 180s → Sub-90: 50sStudy Guide
ARCH-MM-11 • Spec MM74.88% Share (20 Qs)
Odd/Even Function Integral Symmetry over [-a, a] & Linear Integral TransformationsOver symmetric limits [-a, a], cross out all odd powers (x, x³, x⁵) immediately (= 0) and double the integral of even powers from [0, a]. For vertical shift +c, add rectangle area c*(b-a).
Trap: 145s → Sub-90: 35sStudy Guide
ARCH-MM-12 • Spec MM85.37% Share (22 Qs)
Multi-Step Graph Transformations (af(bx+c)+d), Modulus Reflections & Root CountingTrack a single landmark point (vertex or intercept) through the equation: if (x₀, y₀) is on y = f(x), solve bx_new + c = x₀ for x_new and set y_new = a*y₀ + d.
Trap: 150s → Sub-90: 40sStudy Guide
ARCH-MM-13 • Spec MM28.29% Share (34 Qs)
Binomial Expansion (a + bx)^n Term Isolation, Constant Terms & Multi-Bracket CoefficientsNever expand the full bracket: write the general term T_r = nCr * a^(n-r) * b^r * x^(p(n-r) + qr), set the exponent p(n-r) + qr equal to the target power (0 for constant term), solve for r in 5 seconds, and evaluate only that single term.
Trap: 150s → Sub-90: 40sStudy Guide
ARCH-MM-14 • Spec MM45.37% Share (22 Qs)
Sine Rule, Cosine Rule, Triangle Area (½ab sin C), The Ambiguous Case & 3D Pyramid AnglesAmbiguous Case (SSA) condition for 2 non-congruent triangles given angle A, adjacent side c, and opposite side a: require c * sin(A) < a < c, giving roots c*cos(A) ± sqrt(a² - c²*sin²(A)).
Trap: 165s → Sub-90: 45sStudy Guide
ARCH-MM-15 • Spec MM18.05% Share (33 Qs)
Quadratic Discriminant (b^2 - 4ac), Root-Difference Identities & Parameter Range InequalitiesFor ax² + bx + c = 0, the positive difference between roots is ALWAYS |alpha - beta| = sqrt(b² - 4ac) / |a|. For two distinct positive roots, intersect three conditions: Δ > 0, -b/a > 0, and c/a > 0.
Trap: 155s → Sub-90: 40sStudy Guide
Physics (15 Archetypes)
Take 40-Min Physics MockARCH-P-01 • Spec P19.87% Share (23 Qs)
Series-Parallel Resistor Networks, Potential Dividers & Variable Sensor Meter TablesUse the product-over-sum shortcut R_p = (R1*R2)/(R1+R2) (and R/n for n identical parallel resistors). In meter trend tables, take the extreme limit R_var -> infinity (open circuit) to read ammeter/voltmeter changes in 5 seconds.
Trap: 145s → Sub-90: 40sStudy Guide
ARCH-P-02 • Spec P14.72% Share (11 Qs)
Electrical Power Dissipation (P = IV = I^2R = V^2/R), Grid Efficiency & Energy (E = VIt)Match the formula to the invariant: use P = I²*R for series components and transmission lines (same I); use P = V²/R for parallel branches connected across a fixed supply (same V).
Trap: 140s → Sub-90: 40sStudy Guide
ARCH-P-03 • Spec P23.86% Share (9 Qs)
Magnetic Flux Patterns & Motor Effect Force on Current-Carrying Conductors (F = BIL)In F = BIL = B(Q/t)L, L is strictly the perpendicular segment inside the magnetic field (in metres) and t must be in seconds. Parallel current wires attract; antiparallel wires repel.
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-P-04 • Spec P35.15% Share (12 Qs)
1D Multi-Stage Kinematics (v–t Graph Areas/Gradients) & Constant-Acceleration SUVATNever use algebraic SUVAT if a v-t sketch gives a triangle/trapezium: displacement is simply average velocity (u+v)/2 * t. Always use g = 10 N/kg for vertical free-fall.
Trap: 145s → Sub-90: 40sStudy Guide
ARCH-P-05 • Spec P34.72% Share (11 Qs)
1D Coupled Multi-Body Resultant Force (F_net = ma), Lifts & Internal TensionTwo-line coupled-body rule: Line 1 (Whole System) a = F_net_total / (m1 + m2). Line 2 (Trailing Body only) T - F_drag_2 = m2 * a. If resistive force is proportional to mass, tension split is purely T = F_drive * m_rear / (m1 + m2).
Trap: 150s → Sub-90: 40sStudy Guide
ARCH-P-06 • Spec P36.01% Share (14 Qs)
Equilibrium of Coplanar Forces, Drag/Terminal Velocity Balancing & Tension-Spring/Pulley SystemsIn static or dynamic equilibrium (at rest or constant terminal velocity), net force in every direction is zero: upward tension/drag balances downward weight (T = mg or F_drag = mg), and pulley rope tension is uniform throughout a frictionless massless cord.
Trap: 140s → Sub-90: 35sStudy Guide
ARCH-P-07 • Spec P32.15% Share (5 Qs)
Hooke's Law, Springs in Series (½k) vs. Parallel (2k) & Elastic Potential Energy (½kx^2)Spring stiffness behaves OPPOSITE to resistors: two identical springs in parallel are stiffer (k_eff = 2k, half the extension); in series they are softer (k_eff = k/2, double the extension). Always compute x = |L - L₀| first.
Trap: 140s → Sub-90: 35sStudy Guide
ARCH-P-08 • Spec P34.29% Share (10 Qs)
1D Momentum Conservation, Vector Rebound Impulse (FΔt = Δp) & CollisionsDraw a (+) arrow on the page before writing a single number: rebounding off a wall ALWAYS gives |Δp| = m(|v| + |u|), and kinetic energy relates to momentum via E_k = p² / (2m).
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-P-09 • Spec P37.3% Share (17 Qs)
Work-Energy-Power Conservation (ΔE_p = mgΔh, E_k = ½mv^2) & Resistive Drag WorkWrite the Master Energy Accounting line: E_k_initial + mgh_initial = E_k_final + mgh_final + F_drag * d (with g = 10 N/kg). For constant velocity v against drag F, Mechanical Power is simply P = F * v.
Trap: 140s → Sub-90: 40sStudy Guide
ARCH-P-10 • Spec P44.72% Share (11 Qs)
Specific Heat Capacity (Q = mcΔT), Latent Heat (Q = mL) & Electrical Heating Curves (Pt = mcΔT)Check mass units first: if c is in J/(kg °C), convert grams -> kg (÷1000) immediately. On a ΔT vs t graph with constant heater power P, gradient k = ΔT/t = P/(Mc).
Trap: 140s → Sub-90: 40sStudy Guide
ARCH-P-11 • Spec P615.02% Share (35 Qs)
Wave Equation (v = fλ), Refraction Invariance, Pulse-Echo Sonar (d = ½vt), Relative Waves & RedshiftRefraction invariant: frequency f NEVER changes across a boundary (v1/λ1 = v2/λ2). For echo/ultrasound, halve time (t/2) immediately; for a particle on a transverse wave, distance per cycle = 4 * Amplitude.
Trap: 130s → Sub-90: 35sStudy Guide
ARCH-P-12 • Spec P717.17% Share (40 Qs)
Nuclear Decay Chains (α, β⁻, γ), Isotope Algebra & Background-Corrected Half-Life CalculusDecay chain 2-step rule: (1) Mass number A only changes via alpha: N_alpha = (A_start - A_end)/4. (2) Proton number: N_beta = Z_end - (Z_start - 2*N_alpha). For count rates: Net = Raw - Background.
Trap: 130s → Sub-90: 30sStudy Guide
ARCH-P-13 • Spec P23.43% Share (8 Qs)
Electromagnetic Induction (Faraday/Lenz Coil Graphs), AC Generators & Transformer Scaling (V_p/V_s = N_p/N_s)For any magnet-coil motion graph: (1) Induced V = 0 whenever magnet velocity v = 0; (2) V flips sign on return journey; (3) Faster return = taller, narrower peak (same area ∫V dt = ΔΦ).
Trap: 140s → Sub-90: 35sStudy Guide
ARCH-P-14 • Spec P56.01% Share (14 Qs)
Hydrostatic Fluid Pressure (P = ρgh), Archimedes Upthrust, Composite Density & Ideal Gas Pistons (P_1V_1 = P_2V_2)Isothermal gas shortcut: since P*V = const and ρ = m/V, gas density ρ scales directly with absolute pressure: ρ_2 / ρ_1 = P₂ / P₁ = (P_atm + mg/A) / P_atm.
Trap: 145s → Sub-90: 40sStudy Guide
ARCH-P-15 • Spec P45.58% Share (13 Qs)
Thermal Conduction Rod Scaling (Q̇ ∝ AΔT/L), Convection Density Currents & Radiative Power (P ∝ R^2 T^4)Thermal Conduction Scaling Law: Rate Q̇ ∝ A * ΔT / L ∝ d² * (T2 - T1) / L. Radiation Law: Dull/black = best emitter & absorber; Shiny/white = worst emitter & best reflector.
Trap: 135s → Sub-90: 35sStudy Guide
Chemistry (17 Archetypes)
Take 40-Min Chemistry MockARCH-C-01 • Spec C111.11% Share (25 Qs)
Subatomic Isoelectronic Ions, Isotopic A_r Weighted Means & Comma Electron Configs (Z ≤ 20)For two isotopes of mass M1 and M2 with average A_r, use the lever rule: % of M2 = (A_r - M1)/(M2 - M1) * 100%. Isoelectronic species (N³-, O²-, F^-, Ne, Na^+, Mg²+) all share 2,8 (10 e^-).
Trap: 125s → Sub-90: 30sStudy Guide
ARCH-C-02 • Spec C172.22% Share (5 Qs)
Diatomic Mass Spectrometry (m/z Peak Ratios 9:6:1 & 1:2:1) & Molecular Ion CombinationsDiatomic mass spectra follow (p + q)² = p² : 2pq : q². Memorise the two canonical ESAT ratios: Br2+ (1:1 isotopes at 79,81) -> 1 : 2 : 1 at m/z 158, 160, 162; Cl2+ (3:1 isotopes at 35,37) -> 9 : 6 : 1 at m/z 70, 72, 74.
Trap: 140s → Sub-90: 35sStudy Guide
ARCH-C-03 • Spec C43.56% Share (8 Qs)
Hydrocarbon Combustion Gas Volumes (Avogadro's Law), Excess O2 & Limiting ReactantsBy Avogadro's Law, gas volume ratios equal mole ratios directly: for 1 volume of C_xH_y burned, x = V(CO2)/V(alkane) immediately, and O2 consumed is (x + y/4) volumes. At rtp, H2O(l) volume = 0.
Trap: 150s → Sub-90: 40sStudy Guide
ARCH-C-04 • Spec C48% Share (18 Qs)
Molar Gas Volume (24 dm^3 at rtp), Ideal Gas Scaling, Percentage Yield & Atom EconomyMemorise: 1 mol gas at rtp = 24 dm³ = 24,000 cm³, so 1 mmol gas = 24 cm³. Atom economy depends purely on the balanced equation (desired M_r / total reactant M_r), independent of experimental yield.
Trap: 150s → Sub-90: 40sStudy Guide
ARCH-C-05 • Spec C55.78% Share (13 Qs)
Oxidation State Assignment, Redox Disproportionation & Ionic Half-Equation BalancingFor disproportionation, look for a free element (e.g. Cl2, Br2, Cu+) or intermediate oxide (NO2, H2O2) on the LEFT that appears in TWO different products on the RIGHT with one higher and one lower oxidation state.
Trap: 130s → Sub-90: 35sStudy Guide
ARCH-C-06 • Spec C64% Share (9 Qs)
Chemical Bonding, Giant vs. Simple Lattice Property Tables & Allotropes (Graphite/Diamond)In structure tables, scan the Conductivity columns first: (Solid=No, Liquid=Yes) -> Giant Ionic; (Solid=Yes, Liquid=Yes) -> Metallic; (High MP, Solid=Yes) -> Graphite; (High MP, Solid=No, Liquid=No) -> SiO2/Diamond.
Trap: 125s → Sub-90: 30sStudy Guide
ARCH-C-07 • Spec C84.44% Share (10 Qs)
Solubility Curves (g per 100 g Water), Recrystallisation Mass & Paper/TLC Chromatography R_fCheck the exact wording on the mass given: if given M grams of WATER, Precipitate = (M/100)*(S_hot - S_cold). If given M grams of SATURATED SOLUTION at T_hot, Precipitate = M * (S_hot - S_cold) / (100 + S_hot).
Trap: 145s → Sub-90: 40sStudy Guide
ARCH-C-08 • Spec C94.44% Share (10 Qs)
Strong Acid Factor-of-10 pH Dilutions, Weak vs. Strong Acid Foils & Salt Preparation MethodsEvery 10-fold increase in total volume V_final / V_initial = 10^k increases strong acid pH by +k units (capped at pH 7). To shift pH by +k, you must add (10^k - 1)*V_initial of water.
Trap: 130s → Sub-90: 35sStudy Guide
ARCH-C-09 • Spec C104.44% Share (10 Qs)
Reaction Rate Tangent Gradients, Volume-Time Plateau Curves & Catalyst FoilsDecompose any rate graph into two independent numbers: (1) Initial Slope at t=0 = Concentration / Temp / Catalyst / Surface Area; (2) Final Plateau Height = Moles of Limiting Reactant (n = cV).
Trap: 130s → Sub-90: 35sStudy Guide
ARCH-C-10 • Spec C118.44% Share (19 Qs)
Calorimetry (q = mcΔT, ΔH = -q/n), Hess's Law Cycles & Mean Bond Enthalpies (ΣE_broken - ΣE_formed)For bond energies: ΔH = Broken (Left) - Formed (Right); cancel any bonds that remain unchanged on both sides before multiplying. In q = mcΔT, m is ALWAYS the mass of water/total aqueous solution being heated.
Trap: 150s → Sub-90: 40sStudy Guide
ARCH-C-11 • Spec C1210.22% Share (23 Qs)
Molten vs. Aqueous Electrolysis Discharge Competition & Electron Mole StoichiometryAqueous discharge rules in 10s: Cathode (-) gives H2 unless metal is Cu, Ag, or Au. Anode (+) gives Halogen (Cl2, Br2, I2) if halide present, otherwise O2. For series cells, n(product) = n(e^-) / (electrons per product in half-equation).
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-C-12 • Spec C134.44% Share (10 Qs)
C1–C6 Organic Functional Groups, Structural Isomers, Alcohol Oxidation, Esterification & PolymersFor addition polymers, redraw any monomer as C(R1)(R2)=C(R3)(R4) first -> change = to - and extend bonds outside brackets. For ester R1-COO-R2, split the single C-O bond: R1-COOH (acid) + HO-R2 (alcohol).
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-C-13 • Spec C163.56% Share (8 Qs)
Qualitative Ion Identification, Gravimetric Halide Precipitates & Strict Anion Test Sequence (CO3^2- → SO4^2- → X^-)Qualitative Anion Law: ALWAYS test Carbonate (HNO3 -> CO2 effervescence) -> Sulfate (Ba(NO3)2 -> white BaSO4) -> Halide (AgNO3 -> white AgCl / cream AgBr / yellow AgI) using NITRIC acid only.
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-C-14 • Spec C152.22% Share (5 Qs)
Kinetic Particle Theory, Heating/Cooling Phase Curves, Fractional Distillation & Gas DiffusionFor state-at-T tables, write T_target directly between the MP and BP columns: Liquid strictly requires MP < T_target < BP (watch negative signs: -70 is between -100 and -40!). In diffusion tubes, lighter gas (smaller M_r) travels further.
Trap: 120s → Sub-90: 30sStudy Guide
ARCH-C-15 • Spec C144% Share (9 Qs)
Periodic Table Trends (Groups 1, 17, 18), Metal Reactivity Displacement & Extraction SeriesGroup 1 vs Group 17 opposite rules: Down Group 1 -> Reactivity UP, Melting Point DOWN. Down Group 17 -> Reactivity DOWN, Boiling Point UP. Extraction threshold: above Carbon (Al, Mg, Na) = Molten Electrolysis; below Carbon (Fe, Zn, Cu) = Carbon Reduction.
Trap: 125s → Sub-90: 30sStudy Guide
ARCH-C-16 • Spec C910.22% Share (23 Qs)
Multi-Step Acid-Base Back-Titrations, Diprotic Ratios (H2SO4/Ca(OH)2), Thermometric Titration & PurityWork in millimoles (mmol = c [mol dm⁻³] × V [cm³]) throughout! Proton-balance law: (# of H+ in acid) × c_acid × V_acid = (# of OH- in base) × c_base × V_base. Always multiply aliquot moles by (V_flask / V_pipette) at the end.
Trap: 160s → Sub-90: 45sStudy Guide
ARCH-C-17 • Spec C38.89% Share (20 Qs)
Empirical/Molecular Formula from Reacting Mass Fractions & Hydrated Salt Water of Crystallisation (M·xH2O)For hydrated salts M·xH2O heated from m_hydrated to m_anhydrous: m_water = m_hydrated - m_anhydrous, and x = (m_water / 18) ÷ (m_anhydrous / M_r(anhydrous)). Watch for 1 : 1.33 -> 3 : 4 (Fe3O4) and 1 : 1.5 -> 2 : 3 (Fe2O3).
Trap: 150s → Sub-90: 40sStudy Guide
Biology (15 Archetypes)
Take 40-Min Biology MockARCH-B-01 • Spec B18.15% Share (19 Qs)
Eukaryotic vs. Prokaryotic Ultrastructure (No Bacterial Mitochondria) & Magnification (I = A × M)Scan statements for 'bacteria + mitochondria/nucleus' or 'root hair + chloroplasts'—eliminating that single false statement typically kills 3 of 5 options in 5 seconds. For I = A*M, convert mm -> µm (×1000) first.
Trap: 115s → Sub-90: 30sStudy Guide
ARCH-B-02 • Spec B27.3% Share (17 Qs)
Osmosis Water Potential Gradients, Active Transport & Cube SA:V Diffusion RatiosFor a cube of side L, SA:V = 6/L (halving side length doubles SA:V). On an osmosis % mass change graph, the x-intercept (0% change) is the exact isotonic intracellular solute concentration.
Trap: 130s → Sub-90: 35sStudy Guide
ARCH-B-03 • Spec B315.02% Share (35 Qs)
Mitosis vs. Meiosis Chromosome (2n/n) & DNA Mass (4c/2c/1c) Tracking + Stem Cell PotencyTrack (Chromosomes, DNA mass) as a pair: Somatic G1 = (2n, 2c) -> After S-phase / Metaphase = (2n, 4c) -> Mitosis daughter = (2n, 2c); Meiosis I daughter = (n, 2c); Meiosis II gamete = (n, 1c).
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-B-04 • Spec B49.87% Share (23 Qs)
Autosomal & Sex-Linked Pedigree Probability Trees & Conditional Carrier Calculus (⅔ Trap)Pedigree 10-second rules: (1) Two unaffected parents -> affected child = RECESSIVE (both parents are obligate carriers). (2) Unaffected father + affected daughter = AUTOSOMAL (cannot be X-linked recessive). (3) Unaffected sibling of aa child has P(Aa) = 2/3.
Trap: 160s → Sub-90: 45sStudy Guide
ARCH-B-05 • Spec B42.15% Share (5 Qs)
Non-Mendelian Ratios (2:1 Lethal Alleles, Codominance, Dihybrid & Multi-Cross Phenotypic Ratio Tables)Spot non-standard ratios immediately: 2:1 live offspring ratio = homozygous lethal allele (1/4 die in utero); 1:2:1 phenotypic ratio = codominance/incomplete dominance (e.g. I^A I^B or coat colour); in multi-cross tables, identify the homozygous recessive test-cross row first.
Trap: 130s → Sub-90: 35sStudy Guide
ARCH-B-06 • Spec B58.15% Share (19 Qs)
DNA Base Composition (%A = %T, %G = %C), Triplet Coding Ratios & Point MutationsIn double-stranded DNA, %A + %G = 50% ALWAYS (so if %A = 18%, %G = 50% - 18% = 32% in 2 seconds!). For coding length: N amino acids = 3N template bases = 6N total double-stranded bases.
Trap: 125s → Sub-90: 30sStudy Guide
ARCH-B-07 • Spec B62.15% Share (5 Qs)
Recombinant DNA: Restriction Endonucleases, Sticky Ends, Ligase & Plasmid Marker ScreeningMemorise the 3 recombinant rules: (1) Same restriction enzyme cuts both donor & plasmid -> complementary sticky ends (H-bonds form spontaneously). (2) DNA ligase seals the sugar-phosphate phosphodiester backbone. (3) n cuts in a circular plasmid = n fragments.
Trap: 130s → Sub-90: 35sStudy Guide
ARCH-B-08 • Spec B812.02% Share (28 Qs)
Enzyme Kinetics, Thermal/pH Denaturation & Aerobic vs. Anaerobic RespirationRespiration gas check: Mammals (Anaerobic) = 0 O2 in, 0 CO2 out (Lactate only). Yeast (Anaerobic) = 0 O2 in, CO2 out (+ Ethanol). Low temp = low KE (reversible); High temp = active site denatured (irreversible).
Trap: 130s → Sub-90: 35sStudy Guide
ARCH-B-09 • Spec B96.44% Share (15 Qs)
Cardiac Cycle Pressure/Valve Traces, ECG Intervals & Thorax Ventilation MechanicsValve Rule: Valves are passive one-way doors that open when upstream P > downstream P and snap shut at the exact graph intersection where downstream P > upstream P. Inhalation = Contract -> Flatten -> Volume UP -> Pressure DOWN.
Trap: 145s → Sub-90: 40sStudy Guide
ARCH-B-10 • Spec B92.15% Share (5 Qs)
Renal Vessels, Nephron Ultrafiltration, Selective PCT Reabsorption & ADH OsmoregulationADH Rule: More ADH = More Collecting Duct Permeability = More Water Reabsorbed into Blood = Less, More Concentrated Urine. In a healthy nephron: Protein in filtrate = 0; Glucose in urine = 0.
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-B-11 • Spec B103.86% Share (9 Qs)
Carbon/Nitrogen Cycle Bacteria, Trophic Energy Efficiency & Eutrophication Cascade SequencesNitrogen bacteria 3-way check: N2 -> NH4+ (Nitrogen-fixing, root nodules/lightning); NH4+ -> NO2- -> NO3- (Nitrifying, aerobic); NO3- -> N2 (Denitrifying, anaerobic waterlogged soil). Eutrophication O2 drop is caused by AEROBIC DECOMPOSERS.
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-B-12 • Spec B119.01% Share (21 Qs)
Photosynthesis Inverse-Square Law (I ∝ 1/d^2), Limiting Factors & Capillary Potometers (πr^2h/t)Potometer 2-step check: (1) Halve capillary diameter to radius r = d/2 before computing V = pi*r²*h; (2) Divide by time in minutes/hours. For lamp distance d1 -> d2, multiply light intensity by (d1 / d2)².
Trap: 145s → Sub-90: 40sStudy Guide
ARCH-B-13 • Spec B73% Share (7 Qs)
Natural Selection, Antibiotic Resistance, Heterozygote Advantage & Speciation Sequence FoilsInstant Lamarckian eliminator: any statement saying an organism 'mutates in order to survive' or 'antibiotics cause mutations' is 100% FALSE. Mutation is always random and precedes the selection pressure.
Trap: 120s → Sub-90: 30sStudy Guide
ARCH-B-14 • Spec B96.44% Share (15 Qs)
Nervous Reflex Arc, Synaptic Neurotransmission & Endocrine Homeostasis (Insulin/Glucagon, Thermoregulation & Menstrual Cycle)Two classic physiology traps to eliminate immediately: (1) Blood vessels NEVER move closer to the skin; (2) Electrical impulses NEVER cross a synapse (neurotransmitters diffuse). Reflex arc order: Stimulus -> Receptor -> Sensory -> Relay (CNS) -> Motor -> Effector.
Trap: 135s → Sub-90: 35sStudy Guide
ARCH-B-15 • Spec B104.29% Share (10 Qs)
Belt Transect Kite Diagrams, Quadrat/Lincoln Index Population Sampling & Sigmoid Growth CurvesQuadrat scaling: Total Population = (Mean per quadrat) × (Total Area / Quadrat Area)—for a 0.5 m × 0.5 m quadrat, Area = 0.25 m² so multiply per-quadrat mean by 4 to get density per m²! Lincoln index: N = (n1 × n2) / m2.
Trap: 135s → Sub-90: 35sStudy Guide