What “mixed” means
Each card is a real Advanced-style join: two or more syllabus units in one stem. The knowledge bridge is the exam voice — the chain you should write on rough sheet.
Multi-concept practice
Mixed joins
Advanced rarely tests one chapter alone. Browse by year, open the matching notes hub, then drill the stem — knowledge bridge first, answer second.
Why this page
Brief
30–60 min session
Pick one year → open Math / Physics / Chem notes under that year block → solve 2–3 stems under timer → log the join that broke. Use a subject quick card if you need the daily protocol.
Bank size
35 mixed stems · Math 12 · Physics 13 · Chem 10. Filter below without leaving the year map.
Before you open a stem
Join protocol
- 01Name every chapter the stem touches
≤15s. If you cannot name the join, do not start algebra.
- 02Write the bridge in one line
Same style as the card’s knowledge bridge — then execute Math 60–90s / Physics 60–90s / Chem 45–75s templates.
- 03Defend options / units
MC = independent T/F. NUM = units + limit check. Then open the year review for paper context.
Always one click away
Notes path (PCM)
Mathematics
60–90s methodsClassify in ≤20s, then execute a named template
Physics
60–90s methodsName every chapter join in ≤15s, then run FBD / field / path templates
Chemistry
45–75s methodsName family + joins in ≤15s; Physical numerical vs Inorganic/Organic logic
Year-first map
Years · notes under each
Jump a year, open subject notes, then scroll to its stems in Stems.
2026
14 mixed · M 5 · P 5 · C 42025
5 mixed · M 2 · P 2 · C 12024
4 mixed · M 1 · P 2 · C 12023
3 mixed · M 1 · P 1 · C 12022
3 mixed · M 1 · P 1 · C 12021
3 mixed · M 1 · P 1 · C 12020
3 mixed · M 1 · P 1 · C 1Drill surface
Mixed stems by year
Showing 35 of 35 mixed stems.
Year 2026
14 stems · Math 5 · Physics 5 · Chem 4
Mathematics2026 · Paper 2 · Q15–Q16linked-numerical
Exponential curves + area
Calculus – Curves+Definite Integration – Area+Trigonometric equations
Knowledge bridge
Step 1: set y = e^{-x} equal to y = e^{-x}(sin x + cos x) and cancel the common exponential to get a trig equation for intersection abscissae α_i. Step 2: order those roots and set up the definite integral of the difference of the two curves between α_1 and α_4 for the enclosed area β. Step 3: simplify the given log expression in β to a clean numerical value.
Why it feels hard
The stem hides trig solving inside an exponential envelope; students often integrate before finding exact limits.
What to practise
Drill ‘cancel common positive factor → trig roots → area integral’ as one reflex chain.
Mathematics2026 · Paper 1 · Q16matching
Matching across circle / parabola / ellipse / hyperbola
Circle+Parabola+Ellipse+Hyperbola
Knowledge bridge
Step 1: for each List-I geometric condition, reduce to a standard conic equation or point. Step 2: match coordinates/parameters in List-II without mixing ellipse and hyperbola templates. Step 3: verify one substituted point per match to avoid swap errors.
Why it feels hard
Matching lists punish template mix-ups under time pressure.
What to practise
Keep a one-page conics identity sheet and practise full matching sets weekly.
Mathematics2026 · Paper 2 · Q17–Q18linked-numerical
Ellipse intersection + angle + common area
Coordinate Geometry – Ellipse+Tangents & angle between curves+Area of common region
Knowledge bridge
Step 1: solve the two ellipse equations simultaneously for the first-quadrant intersection P. Step 2: differentiate implicitly to get slopes of both tangents at P; convert the angle formula into 4 tan θ. Step 3: for the common area, set up the integral (or standard ellipse-sector form) of the overlapping region and read cot α from that area.
Why it feels hard
Two different asks on one geometry figure — angle then area — under numerical fatigue.
What to practise
For two conics, always compute intersection → slopes → area in that fixed order.
Mathematics2026 · Paper 1 · Q2single-correct
Parabola points + circumcircle + ellipse
Coordinate Geometry – Parabola+Circle (circumradius)+Ellipse conditions
Knowledge bridge
Step 1: recover points P, Q, R from the slope/tangent conditions on the parabola. Step 2: find the circumcircle of triangle PQR (perpendicular bisectors). Step 3: read the required radius / relation that also ties to an ellipse option.
Why it feels hard
Geometry hops across three curve types in one SC item.
What to practise
Practise ‘points on parabola → circle through them → conic check’ as a single drill.
Mathematics2026 · Paper 2 · Q8multi-correct
DE solution + extrema + intersections
Differential Equations+Functions / AOD+Curve intersections
Knowledge bridge
Step 1: solve x y' = y − x³ (homogeneous/linear in y/x) to get the family y = Cx − x³/2. Step 2: impose the given condition to fix C, then use y' = 0 to locate the local max. Step 3: compare monotonicity on (1,2) and count positive roots of f = g.
Why it feels hard
Multi-correct options test DE, calculus and graph reading together; one sign error in the DE kills several options.
What to practise
After every DE, immediately ask: extrema? monotonicity? intersections with a given g?
Physics2026 · Paper 1 · Q1single-correct
Rolling disks + relative rotation on a large disk
Mechanics – Rotation+Rolling without slipping+Relative angular motion
Knowledge bridge
Step 1: relate arc lengths so the small disks roll without slipping on the large circumference (geometry of contact). Step 2: convert path radius R+r into orbital and spin rates (ω/51-type ratios). Step 3: close the remaining angular gap 2π − Δθ to get the meeting time τ.
Why it feels hard
Easy to use the wrong Δθ (2/51 vs 4/51) if relative rolling sense is mishandled.
What to practise
Always draw contact velocities and write v = ωr for every rolling interface before algebra.
Physics2026 · Paper 2 · Q15–Q16linked-numerical
Fluid flow between chambers + changing capacitance
Fluids – level vs time+Electrostatics – Capacitance+Dielectric / liquid between plates
Knowledge bridge
Step 1: from the linked fluid setup, find liquid height in the left chamber at t = 500 s. Step 2: translate that height (or remaining liquid fraction) into the dielectric fill between capacitor plates. Step 3: compute ΔC = (8−n)ε₀ and extract n.
Why it feels hard
Two chapters share one clock variable t; errors in height propagate into capacitance.
What to practise
Practise fluid+capacitor linked numericals where the same h(t) feeds both answers.
Physics2026 · Paper 2 · Q17–Q18linked-numerical
Disk collision + rotation about pivot + energy loss
Mechanics – Collision+Rotation about a fixed point+Energy & angular momentum
Knowledge bridge
Step 1: apply angular impulse about the pivot C for the particle–disk collision. Step 2: convert post-collision ω into maximum rise of centre O (energy after collision). Step 3: compare mechanical energy before vs after to get the collision energy loss.
Why it feels hard
Choosing the wrong axis or mixing linear KE with rotational KE about C breaks both answers.
What to practise
Linked collision–rotation: conserve angular momentum about the eventual pivot, then energy separately.
Physics2026 · Paper 1 · Q2single-correct
Mutual inductance + LC resonance
EMI – Mutual inductance+AC / LC circuits+Effective inductance
Knowledge bridge
Step 1: read the coupling M = L/2 and series inductance to form L_eff. Step 2: replace the network by one equivalent L_eff (here 3L/4). Step 3: apply ω₀ = 1/√(L_eff C) to get 2/√(3LC).
Why it feels hard
Students remember ω=1/√(LC) but forget to rebuild L_eff from mutual terms.
What to practise
For every coupled-inductor problem, compute L_eff first, then resonate.
Physics2026 · Paper 1 · Q3single-correct
Cylinder rolling off a vertical edge
Rigid body rotation+Loss of contact+Energy conservation
Knowledge bridge
Step 1: use energy to relate ω and θ as the cylinder rolls on the edge. Step 2: write radial (centripetal) condition with normal → 0 at loss of contact. Step 3: solve for v = √(5gR/7) (or the option equivalent).
Why it feels hard
Combines rolling constraint, energy and N=0 in one geometric setting.
What to practise
Memorise the ‘energy + N=0’ template for bodies leaving curved/edge surfaces.
Chemistry2026 · Paper 2 · Q15–Q16linked-numerical
Ideal solution molar volumes + vapour mole fraction
Solutions – colligative / ideal+Raoult’s law+Vapour–liquid composition
Knowledge bridge
Step 1: from the linked ideal-solution data, compute the vapour-to-liquid molar volume ratio for pure B. Step 2: find liquid mole fractions (e.g. from molality). Step 3: apply Raoult to get y_B in the vapour (numerical ~0.16 style).
Why it feels hard
Two numericals share solution data; unit slips (molality vs mole fraction) are common.
What to practise
Convert every molality stem to x_i before touching vapour pressures.
Chemistry2026 · Paper 2 · Q17–Q18linked-numerical
Kjeldahl nitrogen + Carius sulphur on related organics
Organic practical – Kjeldahl+Organic practical – Carius+Stoichiometric estimation
Knowledge bridge
Step 1: from structure/formula of L, count N and convert mass to moles of NH₃, then to mL of 1 M H₂SO₄. Step 2: from M, count S and convert to grams of BaSO₄ via Carius stoichiometry. Step 3: keep atomic masses consistent across both linked estimation asks.
Why it feels hard
NCERT ‘end chapter’ methods under numerical pressure; easy arithmetic slips.
What to practise
Treat Kjeldahl/Carius as fixed stoichiometry templates — practise until automatic.
Chemistry2026 · Paper 2 · Q3–Q4multi-concept
Polymer ozonolysis + biomolecule sweetener
Polymers – natural rubber+Ozonolysis / functional tests+Biomolecules – disaccharide
Knowledge bridge
Step 1: ozonolyse the rubber repeating unit to carbonyl fragments; apply iodoform/Tollens to identify Y. Step 2: read the chlorinated disaccharide sweetener as linked galactose+fructose-type units. Step 3: connect ‘polymer degradation products’ thinking with biomolecule structure reading.
Why it feels hard
Students often skip polymers/biomolecules until too late; stems assume NCERT fluency.
What to practise
Schedule polymers + carbohydrates every fortnight with one Adv-style product ID set.
Chemistry2026 · Paper 1 · Q8multi-correct
Multi-step organic synthesis + functional tests
Organic reaction sequence+Heterocycles+Tollens / qualitative tests
Knowledge bridge
Step 1: push each reagent in order to get intermediates Q, R, S, T. Step 2: recognise the heterocyclic closure in T. Step 3: apply Tollens (and related tests) only to the structure that still has the oxidisable group (S).
Why it feels hard
Mechanism memory plus lab-test logic in one multi-correct/sequence item.
What to practise
After every synthesis map, annotate which intermediates pass Tollens/Fehling/iodoform.
Year 2025
5 stems · Math 2 · Physics 2 · Chem 1
Mathematics2025 · Paper 2 · Q1–Q2multi-concept
Limit/derivative structure + area inequalities
Calculus – Limits / AOD+Definite Integration – Area+Inequalities of regions
Knowledge bridge
Step 1: analyse the given limit expression to identify the correct f(x) / derivative behaviour. Step 2: on a related (or following) stem, sketch the region defined by inequalities. Step 3: integrate carefully (logs appear from 1/x-type boundaries).
Why it feels hard
Back-to-back calculus depth: analytic limit then geometric area.
What to practise
Pair every limit/AOD drill with one area-of-region numerical the same day.
Mathematics2025 · Paper 1 · Q13numerical
Parabola numerical with algebraic constraints
Coordinate Geometry – Parabola+Algebraic parameters+Numerical answer
Knowledge bridge
Step 1: write the parabola in standard form and express the geometric condition algebraically. Step 2: reduce to an equation in the unknown parameter. Step 3: extract the required integer/decimal for the NUM grid.
Why it feels hard
Conic geometry collapses into algebra; diagram alone is not enough.
What to practise
Translate every parabola condition into an equation before computing.
Physics2025 · Paper 1 · Q2–Q3single-correct
Back-to-back rotation SC pair
Rotation+Rigid body dynamics+Energy / torque
Knowledge bridge
Step 1: identify axis and moment of inertia for each stem. Step 2: apply torque = Iα or energy+constraint as needed. Step 3: refuse to reuse numbers from Q2 in Q3 without re-deriving.
Why it feels hard
Similar-looking rotation stems invite copy-paste mistakes.
What to practise
Reset the free-body and axis choice on every new rotation question.
Physics2025 · Paper 1 · Q5multi-correct
EMI/AC multi-correct
Electromagnetic induction+AC circuits+Phase / amplitude
Knowledge bridge
Step 1: write induced emf from flux change. Step 2: place that source in the AC network (reactances). Step 3: test each option for amplitude, phase and limiting behaviour separately.
Why it feels hard
MC options mix Faraday facts with circuit phasors.
What to practise
Separate ‘induction law’ checks from ‘impedance algebra’ checks on paper.
Chemistry2025 · Paper 1 · Q12–Q13multi-concept
Polymers numerical + named organic reactions
Polymers+Named reactions+Stoichiometry of products
Knowledge bridge
Step 1: identify the polymer/monomer relation and compute the asked count or mass. Step 2: on the next item, map the named-reaction sequence to the major product. Step 3: connect functional-group changes across both questions if reagents overlap thematically.
Why it feels hard
End-chapter Organic + mechanism memory in numerical/SC mix.
What to practise
Never isolate polymers from GOC week — Advanced joins them in spirit.
Year 2024
4 stems · Math 1 · Physics 2 · Chem 1
Mathematics2024 · Paper 1 · Q4single-correct
Ellipse single-correct with parametric depth
Ellipse+Tangents / chords+Algebraic conditions
Knowledge bridge
Step 1: place the ellipse in standard form and introduce eccentric angle or slope form. Step 2: impose the geometric condition (tangent/chord/focus). Step 3: match the simplified relation to the correct option.
Why it feels hard
Parametric slips create attractive wrong options.
What to practise
Keep both slope and parametric forms of ellipse tangents fluent.
Physics2024 · Paper 1 · Q6–Q7multi-correct
Waves multi-correct + ray optics multi-correct
Waves / Sound+Ray optics+Multi-correct option logic
Knowledge bridge
Step 1: for waves, check superposition/phase options individually. Step 2: for optics, ray-trace each claim (TIR, magnification, mirror/lens sign). Step 3: never assume ‘exactly two correct’ — mark only proven options.
Why it feels hard
Two consecutive MC items amplify partial-marking risk.
What to practise
Practise MC pairs under a strict ‘prove or leave’ rule.
Physics2024 · Paper 1 · Q9–Q10numerical
Rotation numerical beside wave optics
Mechanics – Rotation+Wave optics+Numerical accuracy
Knowledge bridge
Step 1: finish the rotation NUM with a clear MOI/energy chain. Step 2: switch mental model to interference/diffraction for the next NUM. Step 3: protect calculator/decimal hygiene across both.
Why it feels hard
Topic switch mid-numerical section drains working memory.
What to practise
In NUM blocks, write a one-line topic label before each solve.
Chemistry2024 · Paper 1 · Q10–Q14numerical
Practical organic + coordination + electrochem stretch
Organic practical/analysis+Coordination compounds+Electrochemistry
Knowledge bridge
Step 1: decode the practical/analysis NUM (tests, equivalents). Step 2: count coordination isomers / geometry carefully. Step 3: finish with electrochem NUM using consistent electron/ Faraday stoichiometry.
Why it feels hard
A long NUM corridor mixes three Chem branches.
What to practise
Build a ‘mixed Chem NUM’ set: 1 practical + 1 coordination + 1 electrochem.
Year 2023
3 stems · Math 1 · Physics 1 · Chem 1
Mathematics2023 · Paper 1 · Q7–Q9multi-concept
Parabola/ellipse tangents + area numerical
Conics – common tangents+Calculus – Area+Trigonometric equations
Knowledge bridge
Step 1: for the ellipse–parabola common-tangent MC, write both tangent conditions and compare. Step 2: later area NUM — find intersection limits first. Step 3: integrate difference of functions; keep trig-equation NUM technique nearby for neighbouring items.
Why it feels hard
Classic Advanced join: geometry conditions feeding calculus numerics in the same paper.
What to practise
Any week you revise conics, end with one area-between-curves NUM.
Physics2023 · Paper 1 · Q8–Q10numerical
Modern Physics NUM + ray optics NUM chain
Modern Physics+Ray optics+Linked-style numericals
Knowledge bridge
Step 1: finish photoelectric/nuclear arithmetic cleanly. Step 2: switch to ray-optics formulae (mirror/lens/prism) without reusing constants wrongly. Step 3: track significant figures as required by the grid.
Why it feels hard
Formula-dense corridor; one wrong sign convention costs two questions.
What to practise
Keep a tiny optics sign-convention sticky note on your desk during NUM practice.
Chemistry2023 · Paper 1 · Q5–Q6single-correct
Electrochemistry + chemical equilibrium SC pair
Electrochemistry+Chemical equilibrium+Thermodynamic links
Knowledge bridge
Step 1: relate E_cell / Nernst quantities carefully. Step 2: on equilibrium, write K in terms of activities and compare options. Step 3: note shared thermo language (ΔG, K, E) across both stems.
Why it feels hard
Conceptual overlap tempts overthinking simple algebra.
What to practise
Drill ΔG° = −nFE° = −RT ln K until the three forms feel identical.
Year 2022
3 stems · Math 1 · Physics 1 · Chem 1
Mathematics2022 · Paper 1 · Q1–Q2numerical
Inverse trig NUM + trig equation NUM
Inverse trigonometry+Trigonometric equations+Numerical answers
Knowledge bridge
Step 1: reduce inverse-trig expressions with principal-value care. Step 2: solve the neighbouring trig equation in the stated interval. Step 3: enter integers carefully — range mistakes are common.
Why it feels hard
Heavy NUM opening stresses accuracy before you are warm.
What to practise
Start Math mocks with a 10-minute trig warm-up when the paper is NUM-heavy.
Physics2022 · Paper 1 · Q7numerical
EMI/AC numerical among mechanics NUMs
EMI/AC+Mechanics context switching+Numerical
Knowledge bridge
Step 1: isolate the electromagnetic law needed (flux/induced emf/impedance). Step 2: compute the asked scalar. Step 3: consciously leave rotation kinematics behind so constants are not mixed.
Why it feels hard
Topic island inside a Mechanics-heavy NUM sea.
What to practise
Underline the chapter keywords in each NUM stem before writing equations.
Chemistry2022 · Paper 1 · Q6–Q8numerical
Organic practical + named-reaction NUM burst
Organic practical/analysis+Named reactions+Physical mixed NUM nearby
Knowledge bridge
Step 1: decode practical/analysis data into a count or identification. Step 2: push named-reaction reagents to the major product / stoichiometric ask. Step 3: keep Physical mixed NUMs mentally separate so Organic logic is not diluted.
Why it feels hard
Organic numericals feel unfamiliar if you only practised MCQ mechanisms.
What to practise
Convert two named reactions per week into a numerical ask (moles, isomers, mass).
Year 2021
3 stems · Math 1 · Physics 1 · Chem 1
Mathematics2021 · Paper 1 · Q8–Q10linked-numerical
Straight-line linked numerical stem
Coordinate Geometry – Straight line+Linked numerical stems+Distance / intercept algebra
Knowledge bridge
Step 1: extract all shared geometric data from the paragraph once. Step 2: answer the first NUM (slope/intercept/distance). Step 3: reuse intermediates for the linked follow-ups without re-deriving from scratch.
Why it feels hard
Early example of Advanced’s linked-stem tax on organisation.
What to practise
Box shared quantities at the top of linked stems — treat them as a mini formula sheet.
Physics2021 · Paper 1 · Q6–Q9linked-numerical
Capacitance/field linked numerical chain
Electrostatics – Capacitance+Electric field+Linked numericals
Knowledge bridge
Step 1: draw the capacitor/field configuration and label charge/potential. Step 2: solve the first NUM for a base quantity (C, E, V). Step 3: propagate that value through linked asks (energy, force, series/parallel changes).
Why it feels hard
Long electrostatic chains amplify one early algebra mistake.
What to practise
In linked EM stems, verify units of the first answer before continuing.
Chemistry2021 · Paper 1 · Q5–Q9linked-numerical
Organic linked NUM + Physical thermo/mixed
Organic named/reactions (linked)+Physical thermodynamics+Metallurgy / mixed Physical
Knowledge bridge
Step 1: resolve the Organic linked numerical using reaction stoichiometry. Step 2: switch to thermo/mixed Physical NUMs with fresh variables. Step 3: keep metallurgy facts (if present) as recall, not calculation, items.
Why it feels hard
Branch switching inside one NUM section.
What to practise
Label each Chem NUM as Org/Phy/Inorg in the margin before solving.
Year 2020
3 stems · Math 1 · Physics 1 · Chem 1
Mathematics2020 · Paper 1 · Q3–Q4single-correct
Area calculus beside parabola geometry
Calculus – Area+Coordinate Geometry – Parabola+Single-correct pair
Knowledge bridge
Step 1: for the area item, find intersection limits and integrate. Step 2: for the parabola item, apply focus–directrix or tangent properties. Step 3: notice how often Advanced seats Calculus and Conics as neighbours — train that adjacency.
Why it feels hard
2020’s Calculus weight makes area items feel easy until limits are wrong.
What to practise
Always find limits from geometry before writing ∫.
Physics2020 · Paper 1 · Q2–Q4single-correct
Rotation triple in opening SC block
Rotation+Rigid body+Angular kinematics
Knowledge bridge
Step 1: assign I and axis for each stem independently. Step 2: use rolling/energy/torque as appropriate. Step 3: compare answers only after each FBD is complete — similarity is a trap.
Why it feels hard
Three rotation SCs in a row reward method, not memory of a single formula.
What to practise
Build a rotation checklist: axis → I → constraint → energy/torque.
Chemistry2020 · Paper 1 · Q16–Q17numerical
Physical mixed numerical pair
Physical – Mixed+Mole / gas / thermo blend+Numerical
Knowledge bridge
Step 1: parse which Physical sub-ideas are fused (mole + thermo, gas + equilibrium, etc.). Step 2: write governing equations for each piece. Step 3: combine numerically without dropping stoichiometric factors.
Why it feels hard
‘Mixed’ Physical tags mean the stem will not stay in one textbook chapter.
What to practise
Practise deliberately cross-chapter Physical sets (thermo×gases×equilibrium).
Close the loop