Area, volume and mensuration
Build and connect the representations and methods in area, volume and mensuration.
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Before you begin
Build and connect the representations and methods in area, volume and mensuration.
Learning goals
- Calculate and justify area and perimeter
- Convert compatible measurement units
- Calculate and justify volume and surface area
- Calculate circle, arc, sector and segment measures
Syllabus statements covered
- area of parallelogram and trapezium • problems involving perimeter and area of composite plane figures • volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere • conversion between cm^2 and m^2, and between cm^3 and m^3 • problems involving volume and surface area of composite solids • arc length as fraction of the circumference and sector area as fraction of the area of a circle • area of a segment • use of radian measure of angle (including conversion between radians and degrees) • problems involving the arc length, sector area of a circle and area of a segment Radian measure and problems involving arc length, sector area and segment area are tested only in Paper 2 Section B.
- area of parallelogram and trapezium
- problems involving perimeter and area of composite plane figures
- volume and surface area of prism and cylinder
- conversion between cm² and m² , and between cm³ and m³
- problems involving volume and surface area of composite solids
- volume and surface area of pyramid, cone and sphere
- arc length as fraction of the circumference and sector area as fraction of the area of a circle
- area of a segment
- use of radian measure of angle (including conversion between radians and degrees)
- problems involving the arc length, sector area of a circle and area of a segment
Lessons
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About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Units, heights and composite areaG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020Convert squared and cubed units, then use perpendicular heights and non-overlapping regions to calculate area.
- Circles and composite boundariesG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020Use the radius for circle area and trace every part of a composite boundary.
- Cuboids and liquid volumeG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020Use complete layers to derive cuboid volume and measure liquid in a rectangular tank.
- Prisms, cylinders and exposed surfacesG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020Separate cross-sectional area, perpendicular length, volume and the surfaces actually exposed.
- Pyramids, cones and spheresG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021Distinguish perpendicular height, slant height and radius when using volume and surface-area formulae.
- Degree sectors and arc lengthsG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Use the sector’s share of a full turn and distinguish an arc from the complete sector perimeter.
- Radians, sectors and segmentsG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Use radian measure consistently and subtract a triangle only for the matching segment.
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