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

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions follow the OCR GCSE (9-1) Mathematics J560 specification, Version 2.1 (August 2026), sections 8.01 and 8.06. Nothing in this set is Higher tier only. You need a ruler, protractor, compasses and squared or isometric paper for some questions. Read the study guide and revision notes first. See also the course hub, the checklist and the free diagnostics.

Questions

1. Classify each angle as acute, right, obtuse or reflex: 36°, 90°, 143°, 251°. [4]

2. In triangle DEF, angle DEF = 97°.

(a) Which side is e? [1] (b) State the type of angle DEF. [1] (c) Find the reflex angle at E on the outside of the triangle. [1] (d) Write the angle between sides FD and FE using three letters. [1]

3. Name each quadrilateral.

(a) Four equal sides, opposite sides parallel, angles not 90°. [1] (b) Exactly one pair of parallel sides. [1] (c) Opposite sides equal and parallel, adjacent sides unequal, no right angles. [1] (d) Four equal sides and four right angles. [1]

4. (a) A pentagonal prism is a solid with pentagon ends. State its numbers of faces, edges and vertices. [3] (b) A pyramid has 14 edges. Name its base and state its number of vertices. [2]

5. Name the solid.

(a) One flat circular face, one curved surface and one vertex. [1] (b) A single curved surface, no edges and no vertices. [1] (c) Six vertices, nine edges and five faces. [1]

6. Triangle ABC has AB = AC = 9 cm and angle BAC = 50°. M is the midpoint of BC.

(a) Sketch the triangle, marking the equal sides, the 50° angle and M. [2] (b) Find angle ABC. [1] (c) Find angle BAM. [1]

7. Construct triangle ABC with AB = 7.2 cm, angle A = 48° and angle B = 64°. [3] Then measure AC to the nearest millimetre. [1]

8. A reflex angle measures 295°.

(a) What angle does your protractor show when you measure the matching acute or obtuse angle? [1] (b) Describe how to construct the 295° angle. [2]

9. A(−3, 1), B(5, 1), C(3, 4) and D(−1, 4) are the vertices of quadrilateral ABCD.

(a) Name the quadrilateral. [1] (b) Find the lengths of AB and DC. [2] (c) Find the coordinates of the midpoint of AC. [2] (d) C is reflected in the y-axis. Write the coordinates of its image. [1]

10. (a) A solid has a circular plan with a dot at its centre. Its front elevation and side elevation are both isosceles triangles. Name the solid. [1] (b) Another solid has a rectangular plan, a rectangular front elevation and a triangular side elevation. Name it and say which kind of face it rests on. [2] (c) Describe the plan of a square-based pyramid. [2]

11. Cubes are stacked on a base 3 cubes wide and 2 deep. The numbers give the stack heights in cubes, seen from above with the front at the bottom.

back    1 3 1
front   2 1 1

(a) Draw the front elevation. [2] (b) Draw the side elevation seen from the right, with the front of the solid on the left of your drawing. [2] (c) How many cubes are used? [1] (d) The solid is to be drawn on isometric paper as seen from the front left. How many unit squares of the solid are exposed on its top, front and left faces in total? [1]

12. A prism has a trapezium as its cross-section. The trapezium ABCD has A(0, 0), B(6, 0), C(4, 3) and D(0, 3), in cm. The prism is 5 cm long, and the trapezium forms its front face.

(a) Explain why ABCD is a trapezium. [1] (b) State the number of faces, edges and vertices of the prism. [3] (c) Describe the plan, with its dimensions. [2] (d) Find the coordinates of the midpoint of BC. [2] (e) On isometric paper, at what angle to the horizontal are the 5 cm edges drawn, and how do you place the slanting edge BC? [2]

Answers

1. 36° is acute [1]. 90° is right [1]. 143° is obtuse [1]. 251° is reflex [1]. [4] Examiner insight: Learn the boundaries exactly: 90° itself is not acute or obtuse, and 180° is neither obtuse nor reflex.

2. (a) e is opposite angle E, so e = FD [1]. (b) 97° is between 90° and 180°: obtuse [1]. (c) 360° − 97° = 263° [1]. (d) The angle at F is angle DFE (or EFD) [1]. Examiner insight: Show the subtraction from 360° in (c). Check each letter set puts the vertex in the middle.

3. (a) Rhombus [1]. (b) Trapezium [1]. (c) Parallelogram [1]. (d) Square [1]. [4] Examiner insight: Match every property in the description. For (a), four equal sides alone could also be a square, so the “angles not 90°” detail decides it.

4. (a) n = 5: faces = 5 + 2 = 7 [1]; edges = 3 × 5 = 15 [1]; vertices = 2 × 5 = 10 [1]. (b) Edges = 2n = 14, so n = 7: the base is a heptagon [1]; vertices = n + 1 = 8 [1]. Examiner insight: Counting the hidden edges and vertices on a drawing is where answers slip. Check with faces + vertices − edges = 2: 7 + 10 − 15 = 2.

5. (a) Cone [1]. (b) Sphere [1]. (c) Triangular prism [1]. [3] Examiner insight: Use every clue. Five faces and six vertices rule out the pyramids, which would have different edge counts.

6. (a) Triangle with AB and AC both marked 9 cm with matching ticks [1]; 50° at A and M marked on BC with BM = MC [1]. (b) Angles at B and C are equal: (180° − 50°) ÷ 2 = 65° [1]. (c) AM bisects angle BAC: 50° ÷ 2 = 25° [1].

        A
       /|\
    9 / | \ 9
     /  |  \
    B---M---C

Examiner insight: Put every given fact on the sketch and keep it neat, so the equal sides, the angle and M are easy to see.

7. AB = 7.2 cm drawn accurately [1]. 48° at A drawn accurately [1]. 64° at B drawn on the same side and C at the crossing [1]. AC measures about 7.0 cm [1]. [4] Examiner insight: Draw long arms so the crossing is clear. Keep construction marks. Angle C = 68°, so a drawing that disagrees with this by a visible amount should be redrawn.

8. (a) 360° − 295° = 65° [1]. (b) Draw a base line and measure 65° from it with the protractor [1]. The reflex angle is the larger angle on the outside, shown by an arc round the outside [1]. [3] Examiner insight: Say which side the 295° angle lies on. A bare 65° label would not show the reflex angle.

9. (a) AB and DC are both horizontal, so parallel, and the sides AD and BC are not parallel. Trapezium [1]. (b) AB = 5 − (−3) = 8 [1]. DC = 3 − (−1) = 4 [1]. (c) Midpoint = ((−3 + 3) ÷ 2, (1 + 4) ÷ 2) = (0, 2.5) [1] [1]. (d) Reflecting in the y-axis changes the sign of x: (−3, 4) [1]. Examiner insight: Subtracting a negative coordinate is the usual slip. Write 5 − (−3) in full.

10. (a) Cone [1]. (b) Triangular prism [1], resting on a rectangular face [1]. (c) A square [1] with lines joining each corner to the centre, which is the apex seen from above [1]. Examiner insight: State the shape of each view separately and give the viewing direction when the question allows. A sketch with correct lines helps when words are unclear.

11. (a) The tallest stack in each column, left to right, is 2, 3 and 1 [1]:

   . # .
   # # .
   # # #

Drawn as three columns of squares with those heights [1]. (b) From the right, the front row reaches 2 and the back row reaches 3, so the front of the solid is on the left [1]:

   . #
   # #
   # #

Drawn with the correct heights [1]. (c) 1 + 3 + 1 + 2 + 1 + 1 = 9 cubes [1]. (d) Top faces: 6. Front faces: 4 from the front row and 2 from the back row, so 6. Left faces: 2 from the front row and 3 from the back row, so 5. Total 6 + 6 + 5 = 17 squares [1]. Examiner insight: An elevation shows the outline, so hidden heights behind a taller stack do not appear. Check which side the front of the solid is on before you draw the side view.

12. (a) AB and DC are both horizontal (y = 0 and y = 3), so they are parallel, while AD and BC are not parallel. That is why ABCD is a trapezium [1]. (b) The cross-section has 4 sides, so n = 4. Faces = 4 + 2 = 6 [1]. Edges = 3 × 4 = 12 [1]. Vertices = 2 × 4 = 8 [1]. (c) The plan is a rectangle 6 cm by 5 cm [1], with a line across it 4 cm from the left edge, where the flat top meets the sloping face [1]. (d) Midpoint of BC = ((6 + 4) ÷ 2, (0 + 3) ÷ 2) = (5, 1.5) [1] [1]. (e) The 5 cm edges are drawn at 30° to the horizontal [1]. BC does not lie along a grid direction, so plot B and C separately (C is 4 units along and 3 up from A) and join them with a straight line [1]. [10] Examiner insight: Multi-part questions need each part labelled. Give dimensions with units and say what each line on a plan represents.

Where marks are usually lost

• Writing the angle in the wrong vertex order: angle ABC has its vertex at B.
• Confusing the angle the protractor reads with the reflex angle you need.
• Calling a trapezium a parallelogram, or a kite a rhombus.
• Forgetting the base when counting faces of a pyramid, or the two ends of a prism.
• Giving a cylinder or cone too many vertices.
• Drawing a side elevation back to front, or leaving out the dividing lines between different heights.
• Drawing isometric edges at 45° or not keeping vertical edges vertical.
• Subtracting negative coordinates incorrectly when finding lengths.
• Constructing without construction marks, or with an arm too short to see the crossing point.

Next steps

• Revise with the revision notes and re-read the study guide.
• Go to the OCR GCSE Mathematics hub and the checklist.
• Take one of the free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

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