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WalesMaths

Geometry and measures

8 dot points across 8 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you find unknown angles using angle facts, parallel line rules and the interior and exterior angles of polygons?

Use angle facts at a point and on a line, in triangles and quadrilaterals, the corresponding, alternate and co-interior angles in parallel lines, and the interior and exterior angle properties of polygons, giving reasons.
A focused answer to the WJEC GCSE Mathematics geometry content on angles, covering angle facts at a point and on a line, angles in triangles and quadrilaterals, the parallel line rules and the interior and exterior angles of polygons, with reasons.
11 min answer →

How do you find the perimeter, area, surface area and volume of 2-D shapes and 3-D solids, including circles, prisms, cylinders, cones and spheres?

Calculate perimeter and area of 2-D shapes including circles, sectors and compound shapes, and the surface area and volume of prisms, cylinders, pyramids, cones and spheres, with appropriate units.
A focused answer to the WJEC GCSE Mathematics geometry content on mensuration, covering perimeter and area of 2-D shapes including circles and sectors, and the surface area and volume of prisms, cylinders, pyramids, cones and spheres, with units.
12 min answer →

What are the parts of a circle and the circle theorems, and how do you use them to find angles and write reasoned proofs?

Recognise the parts of a circle, and know and use the circle theorems (angle at the centre, angle in a semicircle, angles in the same segment, cyclic quadrilateral, tangent properties and alternate segment) to find angles and construct reasoned proofs (Higher tier).
A focused answer to the WJEC GCSE Mathematics geometry content on circles, covering the parts of a circle and the circle theorems: the angle at the centre, the angle in a semicircle, angles in the same segment, cyclic quadrilaterals, tangent properties and the alternate segment theorem, with reasoned proofs.
12 min answer →

How do you carry out ruler-and-compass constructions, draw loci and use bearings to solve geometric problems?

Use ruler and compasses for standard constructions (perpendicular bisector, angle bisector, perpendicular from a point), draw loci of points satisfying given conditions, and use scale drawings and three-figure bearings.
A focused answer to the WJEC GCSE Mathematics geometry content on constructions and loci, covering ruler-and-compass constructions of perpendicular and angle bisectors, drawing loci of points satisfying conditions, scale drawings and three-figure bearings.
11 min answer →

How do you use Pythagoras' theorem and trigonometry, including the sine and cosine rules, to find missing sides and angles in triangles?

Use Pythagoras' theorem and the trigonometric ratios in right-angled triangles, and the sine rule, cosine rule and area formula in any triangle (Higher tier), to find missing lengths and angles.
A focused answer to the WJEC GCSE Mathematics geometry content on Pythagoras and trigonometry, covering Pythagoras' theorem, the sine, cosine and tangent ratios in right-angled triangles, and the sine rule, cosine rule and area formula for any triangle at Higher tier.
13 min answer →

How do you recognise congruent and similar shapes, prove congruence and use scale factors for lengths, areas and volumes?

Recognise and prove congruence (SSS, SAS, ASA, RHS) and similarity, use scale factors to find missing lengths in similar shapes, and apply area and volume scale factors (Higher tier).
A focused answer to the WJEC GCSE Mathematics geometry content on similarity and congruence, covering the congruence conditions SSS, SAS, ASA and RHS, recognising similar shapes, using linear scale factors and applying area and volume scale factors at Higher tier.
11 min answer →

How do you describe and carry out translations, reflections, rotations and enlargements, and combine them?

Carry out and describe the four transformations - translation, reflection, rotation and enlargement (including negative and fractional scale factors at Higher tier) - and identify the result of combined transformations.
A focused answer to the WJEC GCSE Mathematics geometry content on transformations, covering translations by vectors, reflections in given lines, rotations about a point and enlargements including negative and fractional scale factors, plus describing combined transformations.
11 min answer →

How do you use column vectors, add and subtract vectors, multiply by a scalar and use vectors in geometric proofs?

Use column vector notation, add and subtract vectors and multiply by a scalar, and use vectors to find resultants and to prove that lines are parallel or points are collinear (Higher tier).
A focused answer to the WJEC GCSE Mathematics geometry content on vectors, covering column vector notation, vector addition and subtraction, multiplication by a scalar, finding resultants and using vectors in geometric proofs of parallel lines and collinearity.
12 min answer →