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EnglandMaths

Geometry and measures

7 dot points across 7 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you use angle facts on lines and in triangles, and find the interior and exterior angles of polygons?

Angle facts: angles on a line and around a point, vertically opposite angles, angles in parallel lines (alternate, corresponding and co-interior), angles in triangles and quadrilaterals, and the interior and exterior angles of polygons.
A focused answer to the Edexcel GCSE Mathematics geometry content on angles and polygons, covering angle facts on lines and in parallel lines, angles in triangles and quadrilaterals, and the interior and exterior angles of polygons.
10 min answer →

How do you find the area of 2D shapes and the surface area and volume of prisms, cylinders, cones and spheres?

Area of triangles, parallelograms and trapeziums; circumference and area of circles; volume and surface area of prisms and cylinders; and the volume and surface area of cones, spheres and pyramids (Higher tier).
A focused answer to the Edexcel GCSE Mathematics geometry content on area and volume, covering the areas of 2D shapes, the circumference and area of circles, and the volume and surface area of prisms, cylinders, cones and spheres.
10 min answer →

How do you find arc lengths and sector areas, and apply the circle theorems to find angles?

Parts of a circle, arc length and sector area, and the circle theorems including the angle at the centre, angles in a semicircle, angles in the same segment, cyclic quadrilaterals, the tangent-radius angle and the alternate segment theorem (Higher tier).
A focused answer to the Edexcel GCSE Mathematics geometry content on circles, covering arc length and sector area and the circle theorems used to find angles, including the angle at the centre, cyclic quadrilaterals and the alternate segment theorem at Higher tier.
10 min answer →

How do you carry out standard ruler-and-compass constructions and use them to find loci and regions?

Standard constructions with ruler and compasses (perpendicular bisector of a line, perpendicular from a point, angle bisector), constructing triangles, and finding loci and regions satisfying given conditions.
A focused answer to the Edexcel GCSE Mathematics geometry content on constructions and loci, covering the standard ruler-and-compass constructions, constructing triangles, and finding loci and regions that satisfy given conditions.
9 min answer →

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

Pythagoras' theorem in right-angled triangles, the trigonometric ratios sine, cosine and tangent, exact trig values, and the sine rule, cosine rule and area formula for any triangle (Higher tier).
A focused answer to the Edexcel GCSE Mathematics geometry content on Pythagoras and trigonometry, covering Pythagoras' theorem, the sine, cosine and tangent ratios, exact values, and the sine rule, cosine rule and triangle area formula at Higher tier.
11 min answer →

How do you describe and carry out translations, reflections, rotations and enlargements, including negative and fractional scale factors?

The four transformations: translation by a vector, reflection in a line, rotation about a point, and enlargement by a scale factor including fractional and negative scale factors (Higher tier), and describing a single transformation fully.
A focused answer to the Edexcel GCSE Mathematics geometry content on transformations, covering translation, reflection, rotation and enlargement, including fractional and negative scale factors, and describing a single transformation fully.
9 min answer →

How do you add, subtract and scale vectors, and use them to prove geometric results such as parallel or collinear points?

Vectors: column vectors, adding, subtracting and multiplying vectors by a scalar, the magnitude of a vector, and using vectors in geometric proofs including parallel lines and points lying on a straight line (Higher tier).
A focused answer to the Edexcel GCSE Mathematics geometry content on vectors, covering column vectors, adding, subtracting and scaling vectors, magnitude, and using vectors in geometric proofs such as showing lines are parallel or points collinear.
9 min answer →