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

This guide follows the OCR GCSE (9-1) Mathematics J560 specification, Version 2.1 (August 2026), for first assessment in 2017. It covers section 8.01 (conventions, notation and terms) and section 8.06 (three-dimensional shapes). The specification says the 8.01 conventions are assessed in questions at both tiers. Nothing in this unit is marked Higher tier only. Interpreting plans and elevations is initial learning; constructing them, and drawing solids on isometric paper from them, is listed for Foundation tier learners and so applies to Higher tier learners too.

Other pages for this course: revision notes, practice questions, exam preparation, the course hub and the printable checklist. To find your weak spots first, try the free diagnostics.

What this unit covers

Ref	What you must be able to do
8.01a	Use the terms point, line, line segment, vertex, edge, plane, parallel lines, perpendicular lines
8.01b	Know acute, obtuse, right and reflex angles; use labels such as AB, angle ABC and side a opposite angle A
8.01c	Know the names of regular polygons, triangles, quadrilaterals, pentagon, hexagon, octagon
8.01d	Recognise face, surface, edge, vertex, cube, cuboid, prism, cylinder, pyramid, cone, sphere
8.01e	Draw diagrams from written descriptions
8.01f	Use a ruler, protractor and compasses
8.01g	Use x- and y-coordinates in plane geometry problems, including transformations of simple shapes
8.06a	Recognise and know the properties of the solids above
8.06b	Interpret plans and elevations of simple 3D solids; construct them, and draw solids on isometric paper from them

The specification says all content may be assessed on either the calculator or non-calculator papers. Everything here is done with a pencil, ruler and your head.

Points, lines and planes (8.01a)

A point has position but no size. A line has length and no width. A line segment is the part of a line between two points. A plane is a flat surface that goes on for ever, such as the top of a table extended in every direction. A vertex is a corner. An edge is where two faces, or two sides, meet.

Parallel lines stay the same distance apart and never meet. On a diagram they carry matching arrows. Perpendicular lines meet at a right angle, shown by a small square at the meeting point.

Angles and labelling (8.01b)

Type	Size
Acute	more than 0° and less than 90°
Right	exactly 90°
Obtuse	more than 90° and less than 180°
Reflex	more than 180° and less than 360°

Labelling conventions:

• AB means the line segment from A to B, or its length.
• Angle ABC (written with the angle symbol or in words) is the angle at B, between BA and BC. The middle letter is always the vertex.
• In triangle ABC, the side opposite angle A is written a, so a = BC. Likewise b = CA and c = AB.

Worked example 1

In triangle PQR, angle QPR = 38° and angle PQR = 112°. (a) Which side is r? (b) Name the type of angle PQR. (c) Find the reflex angle at Q on the outside of the triangle.

(a) r is opposite angle R, so r = PQ.
(b) 112° is more than 90° and less than 180°: obtuse.
(c) Reflex angle = 360° - 112° = 248°.

Check the answer to (c) is more than 180°. If it is not, you have used the wrong angle.

Polygons (8.01c)

A polygon is a closed 2D shape with straight sides. A regular polygon has all sides equal and all angles equal.

Sides	Name
3	triangle
4	quadrilateral
5	pentagon
6	hexagon
8	octagon

Triangles: equilateral (three equal sides), isosceles (two equal sides), scalene (no equal sides).

Quadrilaterals, with their key properties:

Name	Key properties
Square	all four sides equal, each corner a right angle
Rectangle	each corner a right angle, so opposite sides are equal
Parallelogram	opposite sides equal and parallel
Rhombus	four equal sides, opposite sides parallel
Kite	two pairs of adjacent equal sides
Trapezium	one pair of parallel sides

A square is also a rectangle and a rhombus, but when a question asks for the most specific name, give the square.

3D solids (8.01d and 8.06a)

A face is a flat surface of a solid. Solids with curved parts have a surface rather than only faces. A prism keeps one cross-section, a fixed polygon, through its whole length. A pyramid has a polygon base and triangular faces that meet at one vertex, the apex.

Solid	Faces or surfaces	Edges	Vertices
Cube	6 square faces	12	8
Cuboid	6 rectangular faces	12	8
Triangular prism	5	9	6
Square-based pyramid	5	8	5
Cylinder	2 flat circular faces, 1 curved surface	2 circular edges	0
Cone	1 flat circular face, 1 curved surface	1 circular edge	1
Sphere	1 curved surface	0	0

For a prism whose cross-section has n sides, the counts are n + 2 faces, 3n edges and 2n vertices. For a pyramid whose base has n sides, they are n + 1 faces, 2n edges and n + 1 vertices. For solids with flat faces, faces + vertices − edges = 2, which is a useful check. It is not listed in the specification, so treat it as a checking tool only.

Worked example 2

Find the faces, edges and vertices of (a) an octagonal prism and (b) a pentagonal pyramid.

(a) n = 8:  faces = 8 + 2 = 10
            edges = 3 x 8 = 24
            vertices = 2 x 8 = 16
    Check: 10 + 16 - 24 = 2
(b) n = 5:  faces = 5 + 1 = 6
            edges = 2 x 5 = 10
            vertices = 5 + 1 = 6
    Check: 6 + 6 - 10 = 2

Drawing diagrams from descriptions (8.01e)

Read the description one fact at a time. Draw a rough sketch first, add each fact as you go, and mark equal lengths, right angles and parallel lines with the standard symbols.

Worked example 3

Sketch kite PQRS, where PQ = PS = 4 cm, QR = SR = 6 cm and the diagonal PR = 8 cm.

Step 1: draw the diagonal PR, 8 cm, vertically.
Step 2: Q and S are on opposite sides of PR.
        PQ = PS = 4 and QR = SR = 6 put Q and S
        at equal distances from P and from R.
Step 3: join P-Q-R-S-P and tick the equal pairs.

        R
       / \
   6  /   \  6
     Q--+--S      PR is the axis of symmetry
      \ | /
     4 \|/ 4
        P

Check: 4 + 6 is more than 8, so triangle PQR can exist.

Instruments (8.01f)

• Ruler: measure and draw straight lines. Start from the zero mark, not the end of the ruler.
• Protractor: line the base line up with one arm and the centre mark on the vertex. Read from the scale that starts at 0° on your arm. Check by asking whether the angle is acute or obtuse.
• Compasses: set the radius against a ruler, put the point on the centre and turn the pencil end through a full turn to draw a circle.

For a reflex angle of x°, draw the angle 360° − x° and the reflex angle is the other side.

Worked example 4

Construct triangle ABC with AB = 7 cm, angle A = 40° and angle B = 75°.

1. Draw AB = 7 cm.
2. At A, measure 40° and draw a long arm.
3. At B, measure 75° on the same side and draw a long arm.
4. C is where the two arms cross.
5. Angle C = 180° - 40° - 75° = 65°.

A measuring check: AC should be about 7.5 cm and BC about 5.0 cm. If yours differ by a lot, re-check the protractor scale. Leave construction lines on the diagram.

Coordinates in plane geometry (8.01g)

Write a point as (x, y): across first, then up or down. Many geometry problems are coordinate problems in disguise.

• The midpoint of the points (a, b) and (c, d) is ((a + c)/2, (b + d)/2).
• Horizontal and vertical distances are found by subtracting coordinates.

Worked example 5

P(1, 2), Q(6, 2) and R(8, 6) are three vertices of parallelogram PQRS. Find S, then reflect the parallelogram in the x-axis and give the image of S.

PQ is horizontal, length 6 - 1 = 5.
In a parallelogram, SR is parallel and equal to PQ,
so S is 5 to the left of R: S = (8 - 5, 6) = (3, 6).
Check: the midpoint of PR is (4.5, 4) and the midpoint of
QS is (4.5, 4). The diagonals bisect each other.
Reflection in the x-axis changes the sign of y:
S' = (3, -6).

Plans and elevations (8.06b)

A plan is the view from directly above. An elevation is a view from the side: the front elevation looks from the front, the side elevation from a side. Mark the viewing direction with an arrow when a question asks you to.

Solid	Plan	Front elevation	Side elevation
Cuboid (standing)	rectangle	rectangle	rectangle
Triangular prism (on a rectangular face, triangular end facing you)	rectangle	triangle	rectangle
Cylinder (standing)	circle	rectangle	rectangle
Cone (standing)	circle with centre point	triangle	triangle
Square-based pyramid	square with lines to the corners	triangle	triangle
Sphere	circle	circle	circle

Hidden edges are often drawn dashed. Edges where two faces at different heights meet appear as lines on the view.

Worked example 6

A solid is built from cubes. The numbers show how many cubes are stacked in each position, viewed from above with the front at the bottom.

Plan (heights)        back    3 2 1
                      front   1 1 2

Draw the front elevation and the side elevation from the right.

Front elevation: tallest stack in each column
columns: left 3, middle 2, right 2

   # . .
   # # #
   # # #

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

   . #
   # #
   # #

The solid has 1 + 1 + 2 + 3 + 2 + 1 = 10 cubes.

Isometric drawings (8.06b)

On isometric dot paper, vertical edges are drawn vertically, and the other two directions go up and to the right, and up and to the left, at 30° to the horizontal. Lengths are drawn to scale along all three directions.

Method for the solid in worked example 6:

1. Choose a front-left viewing position. You will see the top, the front faces and the left faces.
2. Count the exposed faces: 6 top, 7 front and 5 left, so 18 squares in all. Taller stacks hide part of some tops, so treat 18 as a rough check at the end.
3. Draw the base outline first, then add the heights one stack at a time, starting with the stacks nearest to you.
4. Rub out lines that would be hidden behind taller stacks.

A cuboid 3 units by 2 units by 1 unit high needs three edges of 3 units, 2 units and 1 unit drawn from one corner, then the parallel edges completed.

Common errors

• Naming the vertex wrongly: angle ABC is at B, not at A or C.
• Reading the wrong protractor scale, giving an obtuse angle when the angle is acute.
• Calling a trapezium a parallelogram, or a kite a rhombus.
• Giving a cylinder vertices or a cone two vertices. A cylinder has none and a cone has one, at its apex.
• Drawing a side elevation back to front.
• Drawing isometric edges at 45° instead of 30° to the horizontal, or tilting the vertical edges.

Official syllabus

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