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Mensuration and calculation
Mensuration and calculation combines perimeter, area, volume, Pythagoras and trigonometry, requiring formula selection, correct substitution, units and geometric reasoning.
17
Objectives
85
Flashcards
85
Questions
90 min
Study time
AQAGCSEMathematicsGeometry and measures
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Syllabus checklist
What you need to know
17 objective pages available
Measures in geometry1 objectives
- [Foundation and Higher] Use standard units of measure and related concepts including length, area, volume, capacity, mass, time and money.
Angles, maps, scale drawings and bearings2 objectives
- [Foundation and Higher] Measure line segments and angles in geometric figures.
- [Foundation and Higher] Interpret maps, scale drawings and bearings, including compass bearings and three-figure bearings.
Area and volume formulae2 objectives
- [Foundation and Higher] Know and apply formulae for areas of triangles, parallelograms and trapezia.
- [Foundation and Higher] Know and apply formulae for volumes of cuboids and other right prisms, including cylinders.
Circles and composite solids3 objectives
- [Foundation and Higher] Know and use the formulae for circumference and area of a circle.
- [Foundation and Higher] Calculate perimeters of two-dimensional shapes, including circles, and areas of circles and composite shapes.
- [Higher only] Calculate surface area and volume of spheres, pyramids, cones and composite solids, including frustums where required.
Sectors and arcs1 objectives
- [Higher only] Calculate arc lengths, angles and areas of sectors of circles.
Congruence and similarity calculations2 objectives
- [Foundation and Higher] Apply congruence and similarity, including relationships between lengths in similar figures.
- [Higher only] Include relationships between lengths, areas and volumes in similar figures.
Pythagoras and trigonometric ratios2 objectives
- [Foundation and Higher] Know and apply Pythagoras' theorem and the trigonometric ratios to find angles and lengths in right-angled triangles in two-dimensional figures.
- [Higher only] Apply Pythagoras and trigonometric ratios to right-angled and general triangles in two and three dimensions where possible.
Exact trigonometric values2 objectives
- [Higher only] Know exact values of sin and cos for 0, 30, 45, 60 and 90 degrees.
- [Higher only] Know exact values of tan for 0, 30, 45 and 60 degrees.
Sine and cosine rules1 objectives
- [Higher only] Know and apply the sine rule and cosine rule to find unknown lengths and angles.
Area of any triangle1 objectives
- [Higher only] Know and apply Area = 1/2 ab sin C to calculate the area, sides or angles of any triangle.
Key terms
lengthanglemapareavolumecircumferenceperimetersurface areasectorcongruencehigherPythagoras
Exam tips
- Measures in geometry exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to [Foundation and Higher] Use standard units of measure and related concepts including length, area, volume, capacity, mass, time and money..
- Angles, maps, scale drawings and bearings exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to [Foundation and Higher] Measure line segments and angles in geometric figures..
Common mistakes
- Measures in geometry common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Measures in geometry.
- Angles, maps, scale drawings and bearings common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Angles, maps, scale drawings and bearings.
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