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Northern IrelandMaths

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 angle rules at points, lines, triangles, parallel lines and polygons work?

Use angle facts at a point, on a line and in triangles and quadrilaterals, apply the angle properties of parallel lines, and find interior and exterior angles of polygons.
A CCEA GCSE Mathematics answer on angles and polygons, covering angle facts at a point and on a line, angles in triangles and quadrilaterals, the angle properties of parallel lines, and interior and exterior angles of regular and irregular polygons.
10 min answer →

How do you find circle measurements and apply the circle theorems?

Find the circumference and area of circles, the length of an arc and area of a sector, and apply the circle theorems about angles, tangents and cyclic quadrilaterals (theorems at Higher tier).
A CCEA GCSE Mathematics answer on circles, covering circumference and area, arc length and sector area, and the circle theorems about angles at the centre and circumference, the angle in a semicircle, tangents, cyclic quadrilaterals and the alternate segment.
11 min answer →

How do you carry out ruler-and-compass constructions and find loci that satisfy a condition?

Construct perpendicular bisectors, perpendiculars from a point and angle bisectors with ruler and compasses, and find loci and regions defined by distance conditions, including bearings.
A CCEA GCSE Mathematics answer on constructions and loci, covering ruler-and-compass construction of perpendicular bisectors, perpendiculars and angle bisectors, the standard loci, regions defined by distance conditions, and the link to bearings.
10 min answer →

How do you find perimeter, area, surface area and volume of plane shapes and solids?

Find the perimeter and area of triangles, quadrilaterals and compound shapes, the surface area and volume of prisms, cylinders, pyramids, cones and spheres, and convert between units of area and volume.
A CCEA GCSE Mathematics answer on mensuration, covering perimeter and area of plane and compound shapes, surface area and volume of prisms cylinders pyramids cones and spheres, and converting between units of area and volume.
11 min answer →

How do Pythagoras' theorem and right-angled trigonometry find missing sides and angles?

Use Pythagoras' theorem in two and three dimensions, use the sine, cosine and tangent ratios to find sides and angles in right-angled triangles, and use exact trigonometric values.
A CCEA GCSE Mathematics answer on Pythagoras and right-angled trigonometry, covering Pythagoras' theorem in two and three dimensions, the sine cosine and tangent ratios to find sides and angles, and exact trigonometric values.
11 min answer →

How do the sine and cosine rules solve any triangle, and how is its area found using trigonometry?

Use the sine rule and cosine rule to find sides and angles in any triangle, and use the formula for the area of a triangle as one half a b sine C (Higher tier).
A CCEA GCSE Mathematics Higher answer on the sine and cosine rules, covering when to use each rule to find sides and angles in any triangle, and the area of a triangle using one half a b sine C.
11 min answer →

How do you describe and perform transformations, and use congruence and similarity?

Perform and describe reflections, rotations, translations and enlargements (including negative and fractional scale factors), and use congruence and similarity, including area and volume scale factors (Higher tier).
A CCEA GCSE Mathematics answer on transformations and similarity, covering reflections rotations translations and enlargements including negative scale factors, and congruence and similarity with area and volume scale factors.
11 min answer →

How do you use column vectors to add, subtract and scale, and prove geometric results?

Use column vector notation, add and subtract vectors, multiply by a scalar, find the magnitude of a vector, and use vectors to prove geometric facts such as collinearity (Higher tier).
A CCEA GCSE Mathematics Higher answer on vectors, covering column vector notation, addition subtraction and scalar multiplication, the magnitude of a vector, and using vectors to prove geometric results such as parallel lines and collinear points.
11 min answer →