Geometry and measures

Topics

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Sample objectives

What this unit covers

• Properties and constructions: [Foundation and Higher] Use standard conventions for triangle sides and angles and draw diagrams from written descriptions.
• Properties and constructions: [Foundation and Higher] Use conventional geometric terms and notation for points, lines, vertices, edges, planes, angles, polygons and symmetries.
• Properties and constructions: [Foundation and Higher] Use standard ruler and compass constructions, including perpendicular bisectors, perpendiculars and angle bisectors.
• Properties and constructions: [Foundation and Higher] Know that perpendicular distance from a point to a line is the shortest distance to the line.
• Properties and constructions: [Foundation and Higher] Apply angle facts at a point, on a straight line and for vertically opposite angles.
• Properties and constructions: [Foundation and Higher] Use alternate and corresponding angles on parallel lines.
• Properties and constructions: [Foundation and Higher] Derive and apply properties and definitions of special quadrilaterals, triangles and other plane figures using appropriate language.
• Properties and constructions: [Foundation and Higher] Use basic triangle congruence criteria: SSS, SAS, ASA and RHS.
• Properties and constructions: [Foundation and Higher] Apply angle facts, congruence, similarity and quadrilateral properties to conjecture and derive results about angles and sides.
• Properties and constructions: [Foundation and Higher] Use known results including Pythagoras' theorem and isosceles base angles to obtain simple proofs.
• Properties and constructions: [Higher only] Include negative scale factors.
• Properties and constructions: [Foundation and Higher] Identify, describe and construct congruent and similar shapes, including on coordinate axes, using rotations, reflections, translations and enlargements.
• Properties and constructions: [Foundation and Higher] Use column vector notation for translations.
• Properties and constructions: [Foundation and Higher] Describe changes and invariance from combinations of rotations, reflections and translations.
• Properties and constructions: [Foundation and Higher] Include tangent, arc, sector and segment where tier-appropriate.
• Properties and constructions: [Foundation and Higher] Identify and apply circle definitions and properties including centre, radius, chord, diameter and circumference.
• Properties and constructions: [Higher only] Use circle theorems to prove related geometric results.
• Properties and constructions: [Higher only] Apply and prove standard circle theorems concerning angles, radii, tangents and chords.
• Properties and constructions: [Foundation and Higher] Solve geometrical problems on coordinate axes.
• Properties and constructions: [Foundation and Higher] Identify properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.
• Properties and constructions: [Foundation and Higher] Construct plans and elevations of three-dimensional shapes where tier-appropriate.
• Properties and constructions: [Foundation and Higher] Interpret plans and elevations of three-dimensional shapes.
• Mensuration and calculation: [Foundation and Higher] Use standard units of measure and related concepts including length, area, volume, capacity, mass, time and money.
• Mensuration and calculation: [Foundation and Higher] Interpret maps, scale drawings and bearings, including compass bearings and three-figure bearings.
• Mensuration and calculation: [Foundation and Higher] Measure line segments and angles in geometric figures.
• Mensuration and calculation: [Foundation and Higher] Know and apply formulae for volumes of cuboids and other right prisms, including cylinders.
• Mensuration and calculation: [Foundation and Higher] Know and apply formulae for areas of triangles, parallelograms and trapezia.
• Mensuration and calculation: [Foundation and Higher] Know and use the formulae for circumference and area of a circle.
• Mensuration and calculation: [Foundation and Higher] Calculate perimeters of two-dimensional shapes, including circles, and areas of circles and composite shapes.
• Mensuration and calculation: [Foundation and Higher] Apply congruence and similarity, including relationships between lengths in similar figures.
• Mensuration and calculation: [Higher only] Include relationships between lengths, areas and volumes in similar figures.
• Mensuration and calculation: [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.
• Mensuration and calculation: [Higher only] Apply Pythagoras and trigonometric ratios to right-angled and general triangles in two and three dimensions where possible.
• Mensuration and calculation: [Higher only] Know exact values of sin and cos for 0, 30, 45, 60 and 90 degrees.
• Mensuration and calculation: [Higher only] Know exact values of tan for 0, 30, 45 and 60 degrees.
• Mensuration and calculation: [Higher only] Know and apply the sine rule and cosine rule to find unknown lengths and angles.
• Mensuration and calculation: [Higher only] Know and apply Area = 1/2 ab sin C to calculate the area, sides or angles of any triangle.
• Mensuration and calculation: [Higher only] Calculate arc lengths, angles and areas of sectors of circles.
• Vectors: [Foundation and Higher] Describe translations as two-dimensional vectors.
• Vectors: [Higher only] Apply addition and subtraction of vectors and multiplication of vectors by a scalar.
• Vectors: [Higher only] Use diagrammatic and column vector representations to construct geometric arguments and proofs.