Mathematics
Divisibility by 11 — Alternating sum of digits must be 0 or divisible by 11. For 8415: 8−4+1−5=0, divisible by 11. Quick mental check for factorization problems.
Triangle Inequality Shortcut — Sum of any two sides > third side. Quick check: if given three lengths a, b, c (a≤b≤c), only verify a+b>c. Saves time in geometry validity questions.
30-60-90 Triangle Ratios — Sides are in ratio 1:√3:2 (opposite to 30°, 60°, 90°). Memorize as "1-root3-2". Essential for quick architectural elevation and perspective calculations.
Quadratic Sum-Product — For ax²+bx+c=0, sum of roots = −b/a, product = c/a. When finding roots mentally, list factor pairs of c/a that add to −b/a.
Circle-Tangent Rule — Tangent perpendicular to radius at contact point. In architectural drawings, when finding tangent lengths: (tangent)² = (distance to center)² − radius². Instant right-triangle recognition.
Arithmetic Progression nth Term — Use Tn = a+(n−1)d. For last term problems, rearrange to n = (Tn−a)/d + 1. Avoids calculation errors in sequence problems.
Drawing & Design Aptitude
One-Point Perspective Memory — All receding parallel lines meet at single vanishing point on horizon line. Horizon = eye level. Keep VP centered for symmetrical interior rooms, off-center for dramatic architectural views.
Shading Direction Consistency — Light source top-left (10 o'clock position) is standard. Shadow falls opposite: bottom-right. Keep one imaginary light source throughout drawing to maintain consistency in object studies.
Golden Ratio Quick Check — ≈1.618 or roughly 8:5. Human face: hairline to chin ÷ eyebrow to chin. In rectangles, length:width = 1.6:1 appears most pleasing. Use for proportion evaluation.
Symmetry Line Method — For reflections, every point and its mirror are equidistant from symmetry axis. Count grid squares perpendicular to axis. Doubles speed in pattern completion tests.
Isometric Angle Rule — 30° from horizontal for both axes. Use set-square's 30-60-90 angles. Vertical lines stay vertical. All parallel edges in object remain parallel in drawing—never converge.
Texture Density Principle — Closer objects need detailed texture; distant objects get lighter, sparser marks. In 2D-to-3D problems, dense hatching = foreground, light dots = background. Creates instant depth.
General Awareness (Architecture)
Famous Architects Mnemonic "FOWL-CG" — Frank Lloyd Wright (Fallingwater), Oscar Niemeyer (Brasília), Walter Gropius (Bauhaus), Le Corbusier (Chandigarh), Charles Correa (Jawahar Kala Kendra), Gautam Bhatia. Covers major modern movements.
Indian Heritage "TAJMA" — Taj Mahal (Mughal), Ajanta-Ellora (Rock-cut), Jantar Mantar (Observatory), Meenakshi (Dravidian), Akshardham (Contemporary). Five diverse architectural styles for identification questions.
Architectural Styles Timeline — Ancient (pre-500), Classical (500BCE-500CE), Medieval (500-1500), Renaissance (1400-1600), Modern (1900+). Rome = Classical, Gothic cathedrals = Medieval, glass-steel = Modern. Chronological anchors for style-dating questions.