For: Year 5 and Year 6 | Exams: KS2 SATs and 11+ | Calculator: not allowed
Jump to: Level 1 – SATs core · Level 2 – SATs stretch · Level 3 – 11+ standard · Level 4 – 11+ selective
📌 KEY FACTS TO KNOW BY HEART
3D shapes: faces are flat surfaces, edges are where two faces meet, vertices are corners. Cube/cuboid: 6 faces, 12 edges, 8 vertices.
Triangles: equilateral (3 equal sides) · isosceles (2 equal sides) · scalene (no equal sides) · right-angled (one 90° angle).
Quadrilaterals: parallel lines never meet; perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Regular shapes: all sides and angles equal, with as many lines of symmetry as sides. Circle: diameter = 2 × radius.
Level 1 – SATs core: naming shapes, faces, edges, vertices and symmetry
Matches the shape questions in KS2 SATs Papers 2 and 3. Learn the names and count carefully.
✏️ WORKED EXAMPLE: A triangular prism is shown below. How many faces, edges and vertices does it have?
Step 1: faces: 2 triangle ends + 3 rectangles = 5
Step 2: edges: 3 round each triangle end + 3 joining the ends = 9
Step 3: vertices: 3 corners on each triangle end = 6
Answer: 5 faces, 9 edges and 6 vertices
Common mistake: forgetting the hidden (dashed) edges at the back. Count each end separately, then the edges that join them.
Your turn
Q1.1 How many sides does a hexagon have?
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A hexagon has 6 sides.
Q1.2 Name the 2D shape that has 8 straight sides.
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An 8-sided shape is an octagon.
Q1.3 What is the name of the 3D shape that has 6 square faces, all the same size?
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It is a cube.
Q1.4 How many edges does a cuboid have?
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4 edges round the top, 4 round the bottom and 4 joining them: 12
Q1.5 How many faces, edges and vertices does a square-based pyramid have?
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Faces: 1 square + 4 triangles = 5. Edges: 4 round the base + 4 up to the top = 8. Vertices: 4 base corners + 1 top = 5. 5 faces, 8 edges, 5 vertices
Q1.6 How many lines of symmetry does a regular pentagon have?
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A regular shape has as many lines of symmetry as sides: 5
Q1.7 I am a 3D shape. I have one flat circular face, one curved face and one vertex. What am I?
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A circle base and a curved surface that comes to a point: a cone
Q1.8 How many lines of symmetry does this shape have?
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One vertical line, one horizontal line and two diagonal lines through the centre: 4
Q1.9 Quadrilateral ABCD is drawn on a square grid.
(a) Which side is parallel to side AB?
(b) Which two sides are perpendicular to side AD?
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(a) DC runs the same direction as AB and never meets it: DC. (b) AD is vertical, AB and DC are horizontal, so they meet AD at right angles: AB and DC
Q1.10 A prism has two hexagon-shaped ends. How many faces does it have altogether?
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2 hexagon ends + 6 rectangles (one for each side of the hexagon) = 8 faces
Level 2 – SATs stretch: triangles, quadrilaterals, nets and diagonals
Matches the harder reasoning questions in SATs Papers 2 and 3. Know the properties, not just the names.
✏️ WORKED EXAMPLE: This net folds up to make a 3D shape. Name the shape.
Step 1: the middle face is a square, so the base is a square.
Step 2: the four triangles fold up and their tips meet at one point at the top.
Step 3: a square base with four triangles meeting at a point is a square-based pyramid
Common mistake: calling it a triangular prism because it has triangles. A prism has two identical ends joined by rectangles.
Your turn
Q2.1 A triangle has three sides that are all 6 cm long. What type of triangle is it?
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All three sides are equal: equilateral
Q2.2 A triangle has sides of 5 cm, 7 cm and 9 cm. What type of triangle is it?
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No two sides are equal: scalene
Q2.3 A triangle has angles of 40°, 70° and 70°. What type of triangle is it?
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Two equal angles means two equal sides: isosceles
Q2.4 Which quadrilateral has exactly one pair of parallel sides?
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A trapezium has exactly one pair of parallel sides.
Q2.5 A quadrilateral has four equal sides but no right angles. What is it called?
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Four equal sides with no right angles: a rhombus
Q2.6 A regular hexagon has a perimeter of 42 cm. How long is one side?
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Regular means all sides are equal. 42 ÷ 6 = 7 cm
Q2.7 A diagonal joins two corners of a shape that are not next to each other. How many diagonals does a pentagon have?
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From each corner you can draw 2 diagonals. 5 × 2 = 10, but each diagonal has been counted twice: 10 ÷ 2 = 5
Q2.8 Which of these shapes has diagonals that are equal in length and cross at right angles?
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A (rectangle): diagonals equal but not at right angles. C (rhombus): at right angles but not equal. B (square): both. B
Q2.9 Name the 3D shape that this net folds up to make.
Show answer
Two triangles for the ends and three rectangles round the sides: a triangular prism
Q2.10 How many diagonals does a hexagon have?
Show answer
From each corner you can draw 3 diagonals. 6 × 3 = 18, and each one is counted twice: 18 ÷ 2 = 9
Level 3 – 11+ standard: property puzzles, cube nets, rotational symmetry and circles
Typical of grammar-school 11+ papers. Use every clue and rule shapes out one by one.
✏️ WORKED EXAMPLE: I am a quadrilateral. I have two pairs of equal sides, but the equal sides are next to each other, not opposite. I have no parallel sides. What am I?
Step 1: no parallel sides rules out squares, rectangles, rhombuses, parallelograms and trapeziums.
Step 2: two pairs of equal sides that are next to each other is the shape of a kite.
Answer: a kite
Common mistake: answering parallelogram. A parallelogram has two pairs of equal sides too, but they are opposite each other and parallel.
Your turn
Q3.1 What is the name for the distance from the centre of a circle to its edge?
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This is the radius.
Q3.2 What is the name for the distance all the way round the edge of a circle?
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This is the circumference.
Q3.3 A circle has a radius of 7 cm. How long is its diameter?
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The diameter goes right across through the centre, so it is two radii: 2 × 7 = 14 cm
Q3.4 What is the order of rotational symmetry of an equilateral triangle?
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It looks the same 3 times in one full turn: order 3
Q3.5 I am a quadrilateral. I have two pairs of parallel sides and no right angles. My sides are not all the same length. What am I?
Show answer
Two pairs of parallel sides with no right angles is a parallelogram or a rhombus. A rhombus has all sides equal, so I am a parallelogram
Q3.6 Which of these nets will not fold up to make a cube?
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In C there is a square above each end of the row of four. When the row folds round into a loop, both of these squares become the top face and overlap, leaving the bottom open. C
Q3.7 A regular octagon has how many lines of symmetry, and what is its order of rotational symmetry?
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Regular shapes have as many lines of symmetry as sides, and the same order of rotational symmetry: 8 lines of symmetry, order 8
Q3.8 This shape is made of squares on a grid. How many lines of symmetry does it have, and what is its order of rotational symmetry?
Show answer
The windmill arms point in a turning direction, so no mirror line works: 0 lines. It looks the same after every quarter turn: order 4. 0 lines of symmetry, order 4
Q3.9 Which one of these shapes always has diagonals that cut each other exactly in half: kite, parallelogram or trapezium?
Show answer
A parallelogram has diagonals that meet at their midpoints. A kite and a trapezium do not always. Parallelogram
Q3.10 I am a triangle with exactly one line of symmetry, and one of my angles is a right angle. What size are my other two angles?
Show answer
One line of symmetry means isosceles, so the other two angles are equal. 180° − 90° = 90°, and 90° ÷ 2 = 45°. 45° and 45°
Level 4 – 11+ selective: Euler counting, hidden shapes and cube-net logic
The style of selective independent-school papers. Be systematic: count in an order so nothing is missed or counted twice.
✏️ WORKED EXAMPLE: This net folds to make a cube. Which number is on the face opposite 1?
Step 1: 3, 4 and 5 are in a row, with 4 in the middle, so 3 is opposite 5.
Step 2: imagine 3 as the bottom face. 2 folds up as the back wall, 4 folds up as the right wall and 5 folds over to become the top.
Step 3: 1 is attached to the side of 2, so it folds round to become the left wall. The left wall is opposite the right wall, which is 4.
Answer: 4 (and 6 ends up opposite 2)
Common mistake: choosing a face that touches 1 on the net, such as 2. Faces that share an edge on the net are always next to each other on the cube, never opposite.
Your turn
Q4.1 A prism has 7 faces. How many edges and vertices does it have?
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A prism has 2 end faces, so there are 5 side faces and the ends are pentagons. Edges: 5 + 5 + 5 = 15. Vertices: 5 + 5 = 10. 15 edges and 10 vertices
Q4.2 A pyramid has 10 edges. How many faces does it have?
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Half the edges are round the base and half go up to the top, so the base has 5 sides. Faces: 1 base + 5 triangles = 6
Q4.3 For an octagonal prism, work out: faces + vertices − edges.
Show answer
Faces: 2 + 8 = 10. Vertices: 8 + 8 = 16. Edges: 8 + 8 + 8 = 24. 10 + 16 − 24 = 2
Q4.4 How many squares of any size are there in this 3 by 3 grid?
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1 by 1: 9. 2 by 2: 4. 3 by 3: 1. Total 9 + 4 + 1 = 14
Q4.5 This net folds to make a cube. Which face is opposite P?
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Q, R, S, T are in a row: Q is opposite S and R is opposite T. That leaves P and U, which must be opposite each other. U
Q4.6 How many triangles of any size are there in this figure?
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6 small triangles round the centre, 2 made by joining two small ones (one along the top side and one along the bottom side), and 4 large ones that each use one diagonal and two sides of the square. 6 + 2 + 4 = 12
Q4.7 How many rectangles of any size are there in this grid? (Squares count as rectangles.)
Show answer
Choose 2 of the 4 upright lines (6 ways) and 2 of the 3 flat lines (3 ways): 6 × 3 = 18
Q4.8 This net folds to make a dice. On a dice, opposite faces add up to 7. What number goes on face X?
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In the row of four (4, 1, X, blank), faces with one face between them are opposite, so X is opposite 4. 7 − 4 = 3
Q4.9 A polygon has 20 diagonals. How many sides does it have?
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An n-sided shape has n × (n − 3) ÷ 2 diagonals. Try 8: 8 × 5 ÷ 2 = 20. 8 sides (an octagon)
Q4.10 How many triangles of any size are there in this figure?
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Small triangles: 9 (6 pointing up and 3 pointing down). Triangles with sides of 2: 3. The whole triangle: 1. 9 + 3 + 1 = 13