Math 7 · Unit 8: Shapes and symmetry · Cambridge Lower Secondary Maths Stage 7

Questions

1. 1. Does this diagram show a chord or a tangent?

   • a chord
   • a tangent
   Check

2. 2. Does this diagram show a chord or a tangent?

   • a tangent
   • a chord
   Check

3. 3. Does this diagram show a chord or a tangent?

   • a tangent
   • a chord
   Check

4. 4. Does this diagram show a chord or a tangent?

   • a chord
   • a tangent
   Check

5. 5. Alun draws this diagram of a circle with a chord and a tangent. What is incorrect about it?

   • Nothing is incorrect.
   • The labels are the wrong way round.
   • The tangent should go through the centre.
   • The chord is too short.
   Check

6. 6. Ffion draws this diagram of a circle with a chord and a tangent. What is incorrect about it?

   • The tangent is too long.
   • The labels are the wrong way round.
   • Nothing is incorrect.
   • The 'tangent' cuts through the circle, and the 'chord' stops at the centre.
   Check

7. 7. Complete this statement: a tangent to a circle and the radius of a circle always meet at ☐°.

   • 45°
   • 60°
   • 90°
   • 180°
   Check

8. 8. Match each polygon to its correct name and number of sides. The first one is done for you: A is a pentagon and has 5 sides.

   • A
   • B
   • C
   • D

   • decagon, 10 sides
   • pentagon, 5 sides
   • octagon, 8 sides
   • hexagon, 6 sides
   Check

9. 9. The arrows point to the parts of this circle. Which list names them in order, 1 to 6?

   • 1 chord, 2 diameter, 3 centre, 4 radius, 5 circumference, 6 tangent
   • 1 tangent, 2 diameter, 3 centre, 4 radius, 5 circumference, 6 chord
   • 1 tangent, 2 radius, 3 centre, 4 diameter, 5 circumference, 6 chord
   • 1 tangent, 2 radius, 3 circumference, 4 chord, 5 centre, 6 diameter
   Check

10. 10. Sofia says 'Inside a circle I can draw four chords that make an isosceles trapezium.' Which of these shapes can you also make from four chords inside a circle?

    • a rhombus that is not a square
    • a trapezium with no equal sides
    • a rectangle
    • a parallelogram that is not a rectangle
    Check

11. 11. Three tangents to a small circle make an equilateral triangle. Which sentence describes this triangle?

    • It has 0 sides the same length, 0 angles the same size, 0 lines of symmetry and rotational symmetry of order 1.
    • It has 2 sides the same length, 2 angles the same size, 1 line of symmetry and rotational symmetry of order 1.
    • It has 3 sides the same length, 3 angles the same size, 3 lines of symmetry and rotational symmetry of order 3.
    • It has 3 sides the same length, 3 angles the same size, 1 line of symmetry and rotational symmetry of order 1.
    Check

12. 12. Which of these describes the properties of a regular pentagon?

    • 5 equal sides, 5 equal angles, 5 lines of symmetry and order 5 rotational symmetry
    • 5 equal sides, angles of 90°, 5 lines of symmetry
    • 5 equal sides, 5 equal angles, 1 line of symmetry and order 1
    • 5 sides, 2 pairs of parallel sides and order 2
    Check

13. 13. A regular dodecagon has 12 sides. Complete the properties that characterise it.

    Fill the blanks with these.

    • 24
    • 1
    • 6
    • 12
    Check

14. 14. The diagram shows a circle with centre C. A tangent touches the circle at D. The line CD is a … of the circle.

    • tangent
    • chord
    • diameter
    • radius
    Check

15. 15. A tangent touches the circle at D, and C is the centre. Write down the size of ∠CDE.

    • 58°
    • 32°
    • 180°
    • 90°
    Check

16. 16. In triangle CDE, ∠CDE = 90° and ∠CED = 32°. Work out the size of ∠DCE.

    • 32°
    • 68°
    • 122°
    • 58°
    Check

17. 17. The diagram shows a regular hexagon with side length 5 cm. Arun thinks the perimeter of the hexagon is 35 cm. Is Arun correct?

    • Yes
    • No
    Check

18. 18. The diagram shows a regular octagon and a regular decagon. The perimeters of the shapes are the same. Work out the side length of the decagon.

    • 12 mm
    • 18.75 mm
    • 10 mm
    • 15 mm
    Check

19. 19. Belinda splits a regular pentagon into five identical triangles from its centre and finds x = 72°, y = 54° and z = 108°. Use her method to work out x, y and z in this regular hexagon.

    • x = 60°, y = 60°, z = 120°
    • x = 72°, y = 54°, z = 108°
    • x = 45°, y = 67.5°, z = 135°
    • x = 60°, y = 30°, z = 60°
    Check

20. 20. Use Belinda's method (x = 360° ÷ the number of triangles, 2y = 180° − x, z = y + y) to complete the table without drawing any more shapes. Which list gives x, y and z correctly?

    • hexagon 60°, 120°, 60°; octagon 45°, 135°, 67.5°; nonagon 40°, 140°, 70°; decagon 36°, 144°, 72°
    • hexagon 60°, 120°, 240°; octagon 45°, 135°, 270°; nonagon 40°, 140°, 280°; decagon 36°, 144°, 288°
    • hexagon 60°, 60°, 120°; octagon 45°, 67.5°, 135°; nonagon 40°, 70°, 140°; decagon 36°, 72°, 144°
    • hexagon 60°, 60°, 60°; octagon 45°, 67.5°, 67.5°; nonagon 40°, 70°, 70°; decagon 36°, 72°, 72°
    Check