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Lessons by Mr Wong

Mr Wong focuses on coordinates, vectors and timed HKDSE-style practice. He helps students turn a messy diagram into an organised calculation.

39 lessons

1Writing the equation of a plane in 3DSpatial Geometry · Mr Wong · Ax + By + Cz + D = 02Geometry formula sheet with quick checksApplied & Exam · Mr Wong · triangle area = (1/2)bh3A timed geometry plan for HKDSE-style papersApplied & Exam · Mr Wong · accuracy first, then speed4Gradient of a line through two pointsCoordinates & Vectors · Mr Wong · m = (y₂ − y₁) / (x₂ − x₁)5Section formula with position vectorsCoordinates & Vectors · Mr Wong · If P divides AB in m:n, then OP = (n·OA + m·OB) / (m + n)6Reflection across the axes and y = xCoordinates & Vectors · Mr Wong · reflection in x-axis: (x, y) → (x, −y)7Parallelogram area from two vectorsCoordinates & Vectors · Mr Wong · area = |x₁y₂ − x₂y₁| for a = (x₁, y₁), b = (x₂, y₂)8Space diagonal of a cubeSpatial Geometry · Mr Wong · face diagonal = a√29Shortest distance between skew linesSpatial Geometry · Mr Wong · d = |(P₂−P₁) · n| / |n|10Plane determined by three pointsSpatial Geometry · Mr Wong · n = AB × AC11Space diagonal of a rectangular boxSpatial Geometry · Mr Wong · d = √(a² + b² + c²)12Circular cross-section of a sphereSpatial Geometry · Mr Wong · ρ = √(R² − d²)13Sine rule for a non-right trianglePlane Geometry · Mr Wong · a/sin A = b/sin B = c/sin C14Cosine rule to find a sidePlane Geometry · Mr Wong · c² = a² + b² − 2ab cos C15Distance between two pointsCoordinates & Vectors · Mr Wong · d = √[(x₂−x₁)²+(y₂−y₁)²]16Midpoint and section formula on a lineCoordinates & Vectors · Mr Wong · M = ((x₁+x₂)/2,(y₁+y₂)/2)17Equation of a line through two pointsCoordinates & Vectors · Mr Wong · m = (y₂−y₁)/(x₂−x₁)18Parallel and perpendicular gradientsCoordinates & Vectors · Mr Wong · parallel: m₁=m₂19Area of a triangle from coordinatesCoordinates & Vectors · Mr Wong · area = ½|det form|20Circle equation from centre and radiusCoordinates & Vectors · Mr Wong · (x−h)²+(y−k)²=r²21Intersection of a line and a circleCoordinates & Vectors · Mr Wong · discriminant >0 two points22Vector addition as a parallelogramCoordinates & Vectors · Mr Wong · a + b = diagonal23Position vectors and midpointsCoordinates & Vectors · Mr Wong · OM = (a+b)/224Locus: perpendicular bisectorCoordinates & Vectors · Mr Wong · |PA|=|PB| ⇒ P on perp. bisector of AB25Proving collinearity with vectorsCoordinates & Vectors · Mr Wong · AB = k AC26Dot product and right anglesCoordinates & Vectors · Mr Wong · a · b = |a||b|cos θ27Parametric equation of a lineCoordinates & Vectors · Mr Wong · r = a + t d28Coordinate proof that a quadrilateral is a parallelogramCoordinates & Vectors · Mr Wong · midpoint AC = midpoint BD29Gradient as tan of the inclinationCoordinates & Vectors · Mr Wong · m = tan θ30Dividing a segment in a vector ratioCoordinates & Vectors · Mr Wong · p = (n a + m b)/(m+n)31Command words: find, show, explain, henceApplied & Exam · Mr Wong · read the verb before calculating32A 30-second unit and scale checkApplied & Exam · Mr Wong · length / area / volume → unit33Back bearings and reverse journeysApplied & Exam · Mr Wong · back bearing = bearing ± 180° (mod 360°)34Two-pass timing for a mixed geometry paperApplied & Exam · Mr Wong · pass 1 easy marks → pass 2 constructions35Keeping a one-week geometry error logApplied & Exam · Mr Wong · classify → correct → retest36Choosing formulas by the quantity namedApplied & Exam · Mr Wong · target quantity → formula family37Layout that earns method marksApplied & Exam · Mr Wong · formula → substitute → simplify → conclude38Spider-and-fly shortest path on wallsApplied & Exam · Mr Wong · shortest path = straight line on a suitable net39Rounding lengths without wrecking the next stepApplied & Exam · Mr Wong · round at the end
Mr Wong — Shields Geometry