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Lessons by Ms Tam

Ms Tam taught secondary mathematics in Hong Kong for more than a decade. She writes spatial geometry lessons that emphasise clear diagrams, perpendicular heights and exam-ready presentation.

27 lessons

1Pyramid volume: identify the base and perpendicular heightSpatial Geometry · Ms Tam · V = (1/3) × base area × perpendicular height2Distance from a point to a plane using volumeSpatial Geometry · Ms Tam · V = (1/3) × base area × height3Finding the angle between a line and a planeSpatial Geometry · Ms Tam · θ = angle between the line and its projection4Cylinder volume and curved surface areaSpatial Geometry · Ms Tam · V = πr²h5Cone volume when slant height is givenSpatial Geometry · Ms Tam · l² = r² + h²6Bearings and a right-triangle journeyApplied & Exam · Ms Tam · bearing measured clockwise from north7Map scales and real distancesApplied & Exam · Ms Tam · real length = map length × scale factor8Prism volume from a cross-sectionSpatial Geometry · Ms Tam · V = cross-sectional area × length9Sphere volume without the fear of πSpatial Geometry · Ms Tam · V = (4/3)πr³10Volume of a triangular pyramidSpatial Geometry · Ms Tam · V = (1/3) × triangle area × height11Frustum of a pyramid: the cut-off topSpatial Geometry · Ms Tam · V = (1/3)h(A₁ + A₂ + √(A₁A₂))12Largest cylinder inside a sphereSpatial Geometry · Ms Tam · r² + (h/2)² = R²13Finding height from a lateral edgeSpatial Geometry · Ms Tam · h = √(ℓ² − d²)14Hemisphere volume and curved surfaceSpatial Geometry · Ms Tam · V = (2/3)πr³15Volume of a hollow pipeSpatial Geometry · Ms Tam · V = π(R² − r²)h16Cone: from slant height to perpendicular heightSpatial Geometry · Ms Tam · ℓ² = r² + h²17Composite solids: add or subtract volumesSpatial Geometry · Ms Tam · V_total = V₁ ± V₂ ± …18Height and area of an equilateral trianglePlane Geometry · Ms Tam · h = (√3/2)a19Area of a trapeziumPlane Geometry · Ms Tam · area = ½(a+b)h20Annotating the exam diagram in the first minuteApplied & Exam · Ms Tam · given → mark → plan → calculate21Map scales and area factorsApplied & Exam · Ms Tam · area factor = (length factor)²22Percentage error in a measured lengthApplied & Exam · Ms Tam · % error = (|approx − true|/true)×100%23Roof pitch as a right triangleApplied & Exam · Ms Tam · tan θ = rise/run24Heights from shadows with similar trianglesApplied & Exam · Ms Tam · h₁/s₁ = h₂/s₂25Water tank problems with consistent unitsApplied & Exam · Ms Tam · 1 m³ = 1000 L26Paint coverage from surface areaApplied & Exam · Ms Tam · litres = area / coverage27Estimating before calculatingApplied & Exam · Ms Tam · estimate → calculate → compare