OCR GCSE Mathematics: Geometry notation and terms, instruments, 3D solids, plans and elevations (J560) – Revision Notes

Quick recall for the OCR GCSE (9-1) Mathematics J560 specification, Version 2.1 (August 2026), sections 8.01 and 8.06. For full explanations and worked examples, read the study guide. Then test yourself with the practice questions, tick off topics on the checklist, and find gaps with the free diagnostics. The course hub lists every page for this course.

The specification says the 8.01 conventions are assessed at both tiers. Nothing in this unit is Higher tier only.

Terms in one table (8.01a to 8.01d)

Term	Meaning
Point	a position, no size
Line segment	part of a line between two points
Plane	a flat surface extending for ever
Vertex	a corner
Edge	where two faces (or two sides) meet
Face	a flat surface of a solid
Parallel	same direction, never meet; marked with matching arrows
Perpendicular	meet at 90°; marked with a small square
Regular polygon	all sides equal and all angles equal

Angles and labels (8.01b)

Name	Size
Acute	under 90°
Right	90°
Obtuse	over 90° but under 180°
Reflex	over 180° but under 360°

• Angle ABC: the vertex is the middle letter, B.
• AB: the segment from A to B, or its length.
• Side a is opposite angle A, so in triangle ABC, a = BC.
• Reflex angle = 360° minus the angle you can measure.

Polygons (8.01c)

• Triangles: equilateral (3 equal sides), isosceles (2 equal sides), scalene (none equal).
• Names by sides: 5 pentagon, 6 hexagon, 8 octagon.

Quadrilateral	One-line test
Square	4 equal sides and 4 right angles
Rectangle	opposite sides equal, 4 right angles
Parallelogram	opposite sides equal and parallel
Rhombus	4 equal sides, opposite sides parallel
Kite	2 pairs of adjacent equal sides
Trapezium	exactly one pair of parallel sides in the usual school definition

Solids (8.01d and 8.06a)

Solid	Faces	Edges	Vertices
Cube, cuboid	6	12	8
Triangular prism	5	9	6
Hexagonal prism	8	18	12
Square-based pyramid	5	8	5
Cylinder	2 flat, 1 curved	2 circular	0
Cone	1 flat, 1 curved	1 circular	1
Sphere	1 curved surface	0	0

Formulas for an n-sided base:

Solid	Faces	Edges	Vertices
Prism	n + 2	3n	2n
Pyramid	n + 1	2n	n + 1

Check for flat-faced solids: faces + vertices − edges = 2.

Method boxes

Drawing from a description (8.01e)

1. Read the whole description once.
2. Sketch a rough shape and put the first fact on it.
3. Add one fact at a time: lengths, equal-length ticks, right-angle squares, parallel arrows.
4. Check that the facts fit together, for example that a triangle’s sides can close.

Using instruments (8.01f)

1. Ruler: start at zero, mark the length, join with a straight line.
2. Protractor: centre on the vertex, base line along one arm, read the scale that starts at 0° on that arm.
3. Compasses: fix the radius on the ruler, point on the centre, turn the pencil through a full turn.
4. Reflex angle x°: draw 360° − x° and use the outside.

Coordinates (8.01g)

1. Write points as (x, y): across then up.
2. Midpoint of (a, b) and (c, d): ((a + c)/2, (b + d)/2).
3. Fourth vertex of a parallelogram ABCD: D = A + C − B.
4. Reflection in the x-axis: (x, y) becomes (x, −y). In the y-axis: (x, y) becomes (−x, y).

Plans and elevations (8.06b)

1. The plan is the view from above. Elevations are views from the front and the side. Mark the viewing arrow.
2. For stacked cubes, an elevation shows the tallest stack in each column of the view.
3. A side elevation from the right has the front of the solid on the left of the picture.

Solid	Plan	Front elevation
Triangular prism on a rectangular face	rectangle	triangle
Cylinder standing	circle	rectangle
Cone standing	circle with centre point	triangle
Square-based pyramid	square with diagonals	triangle
Sphere	circle	circle

Isometric drawing (8.06b)

1. Vertical edges stay vertical.
2. The other two directions go at 30° to the horizontal, one up-right and one up-left.
3. Draw the base outline, then build the heights one stack at a time.
4. Count the visible faces (top, front, left) as a check.

Worked reminder

Three vertices of parallelogram ABCD are A(0, 0), B(4, 1) and C(7, 5). Find D.

D = A + C - B = (0 + 7 - 4, 0 + 5 - 1) = (3, 4)
Check: midpoint of AC = (3.5, 2.5); midpoint of BD = (3.5, 2.5).

Worked reminder: plan and elevations

Cubes stacked on a 2 by 2 base. Plan with heights (back at the top, front at the bottom):

back    1 3
front   2 1

Front elevation: tallest in each column (left 2, right 3)

   . #
   # #
   # #

Side elevation from the right (front on the left): rows front 2, back 3

   . #
   # #
   # #

Total cubes: 1 + 3 + 2 + 1 = 7

Must-know distinctions

• Edge or face: an edge is a line where faces meet; a face is the flat surface itself.
• Prism or pyramid: a prism has the same cross-section along its length, so it has two matching end faces. A pyramid comes to a point at an apex.
• Cube or cuboid: a cuboid has rectangular faces. A cube is the special cuboid whose faces are all squares.
• Rhombus or kite: a rhombus has four equal sides. A kite has two pairs of equal adjacent sides.
• Parallelogram or trapezium: a parallelogram has two pairs of parallel sides. A trapezium has one pair.
• Plan or elevation: plan from above, elevation from the side or front.
• Sketch or draw: a sketch can be freehand. A drawing or construction needs the instruments and the stated measurements.
• Surface or face: a cylinder, cone or sphere has a curved surface, and a cube has flat faces.

Describing a solid from clues

Work from the clue that cuts down the options fastest.

• 2 circular faces and 1 curved surface: cylinder.
• 1 circular face, 1 curved surface and 1 vertex: cone.
• No edges and no vertices: sphere.
• 5 faces, 8 edges, 5 vertices: square-based pyramid.
• 5 faces with two triangles: triangular prism.
• 9 vertices and 9 faces: octagonal pyramid.

Habits that save marks

• Write the units on every length and the degree sign on every angle.
• Label vertices on a sketch before you start, using the letters in the question.
• When a description gives a right angle, show it with a square, not just a 90° label.
• For a counting question on a solid, list faces, then edges, then vertices, and run the check faces + vertices − edges = 2 when all faces are flat.
• On a plan or elevation question, re-read which view is asked for before drawing.
• Keep construction lines and arcs. They show how you drew the diagram.

Quick self-test

1. Name the type of angle of 217°.
2. In triangle XYZ, which side is x?
3. State the faces, edges and vertices of a hexagonal prism.
4. How many edges does a pyramid with an octagonal base have?
5. Find the midpoint of (−3, 4) and (5, 10).
6. A right-angled triangle has one angle of 34° and one angle of 90°. Find the third angle and name the triangle type by sides.
7. Describe the plan of a standing cone.
8. How would you draw an angle of 300° with a protractor?
9. A quadrilateral has four equal sides but no right angles. Name it.
10. What angle do the non-vertical edges make with the horizontal on isometric paper?
11. Two columns of cubes stand side by side at the front, with heights 2 and 1. Directly behind them are columns of 1 and 3. Give the front elevation heights, left to right.
12. How many cubes are in the solid in question 11?

Answers

1. Reflex (it is between 180° and 360°).
2. YZ, the side opposite angle X.
3. 8 faces, 18 edges, 12 vertices (check: 8 + 12 − 18 = 2).
4. 16 edges (2 × 8).
5. (1, 7).
6. 180° − 90° − 34° = 56°. All three angles differ, so it is scalene.
7. A circle with a point marked at its centre.
8. Draw 60° (360° − 300°) and take the reflex angle on the outside.
9. Rhombus.
10. 30°.
11. The tallest column in each position: 2 and 3.
12. 2 + 1 + 1 + 3 = 7 cubes.

Where marks are usually lost

• Putting the angle at the wrong letter: angle ABC is at B.
• Using the wrong protractor scale and reading 180° minus the real value.
• Answering a reflex angle question with the acute or obtuse angle instead of subtracting from 360°.
• Counting a cylinder’s circular edges as vertices.
• Forgetting the base face when counting the faces of a pyramid or prism.
• Drawing a plan or elevation without the correct viewing direction, so left and right swap.
• Leaving hidden or dividing lines out of an elevation, or adding lines that are not there.
• Drawing isometric edges at 45° or leaving construction lines out when the question asks for a drawing.
• Giving only a sketch when the question says to draw accurately with instruments.

Official syllabus

OCR, GCSE (9-1) Mathematics J560 specification, Version 2.1 (August 2026), first assessment 2017, sections 8.01 and 8.06.