Math 7 · Unit 14: Position and transformation · Cambridge Lower Secondary Maths Stage 7

Questions

1. 1. Question 1a: the shaded 1 by 1 square is enlarged using a scale factor of 2. What are the dimensions of the image?

   • 4 by 4
   • 3 by 3
   • 2 by 2
   • 1 by 2
   Check

2. 2. Question 1b: the shaded rectangle, 2 squares long and 1 square high, is enlarged using a scale factor of 2. What are the dimensions of the image?

   • 3 by 2
   • 4 by 4
   • 4 by 1
   • 4 by 2
   Check

3. 3. Question 2a: the shaded 1 by 1 square is enlarged using a scale factor of 3. What are the dimensions of the image?

   • 4 by 4
   • 9 by 9
   • 3 by 3
   • 1 by 3
   Check

4. 4. Question 2b: the shaded rectangle, 2 squares long and 1 square high, is enlarged using a scale factor of 3. What are the dimensions of the image?

   • 6 by 3
   • 6 by 1
   • 5 by 4
   • 6 by 6
   Check

5. 5. Question 3c: the shaded rectangle, 1 square wide and 2 squares tall, is enlarged using a scale factor of 4. What are the dimensions of the image?

   • 4 by 8
   • 5 by 6
   • 8 by 16
   • 4 by 2
   Check

6. 6. This is part of Dan's homework. He was asked to enlarge the shape using a scale factor of 2. What mistake has Dan made?

   • He drew the shape in the wrong place on the grid; all the lengths are correct.
   • Not every length is doubled: the bottom edge and the slanting edges are the wrong length, so his shape is stretched out of shape.
   • He has made no mistake: his shape is a correct enlargement.
   • He used a scale factor of 3 instead of 2.
   Check

7. 7. Question 6: the object is 4 squares wide and the image is 8 squares wide. What is the scale factor of the enlargement?

   • 8
   • 4
   • 2
   • ½
   Check

8. 8. Question 7a: triangle A is 3 cm by 2 cm and triangle B is 5 cm by 4 cm. Why is B not an enlargement of A?

   • Triangles cannot be enlarged.
   • B is bigger than A.
   • B has the same height as A.
   • The base is not multiplied by the same number as the height: 5 ÷ 3 ≠ 4 ÷ 2.
   Check

9. 9. Question 7b: triangle A is 3 cm by 2 cm. Triangle C is 9 cm by 6 cm and triangle D is 16 cm by 10 cm. Are both C and D enlargements of A?

   • Yes
   • No
   Check

10. 10. A company makes boxes with square bases. The diagram shows the dimensions of the smallest box that it makes, and the other boxes the company makes. Some of the boxes are enlargements of the smallest box and some are not. Tick the 3 boxes that are enlargements of the smallest box.

    Tick all the right answers.

    • ☐ Box A
    • ☐ Box B
    • ☐ Box C
    • ☐ Box D
    • ☐ Box E
    Check

11. 11. Marcus and Arun look at this diagram. Marcus says: "I think that shape B is an enlargement of shape A because all the sides are twice as long." Arun says: "I don't think that shape A is an enlargement of shape B because the shape has been rotated 90°." Who do you think is correct?

    • Marcus: all the sides are twice as long, so B is an enlargement of A
    • Neither: the sides of B are not twice as long as the sides of A
    • Arun: shape B has been turned through 90°, so it is not an enlargement of A
    • Both: B is an enlargement of A only if it faces the same way
    Check

12. 12. Question 10a: Naveen enlarges triangle A (base 3 cm, height 4 cm) to B, B to C, then C to D (base 72 cm, height 96 cm). Which of these could be the sizes of B and C?

    • B 6 cm by 12 cm, C 18 cm by 24 cm
    • B 5 cm by 6 cm, C 36 cm by 48 cm
    • B 6 cm by 8 cm, C 12 cm by 24 cm
    • B 6 cm by 8 cm, C 18 cm by 24 cm
    Check

13. 13. Naveen enlarges triangle A (base 3 cm, height 4 cm) to B, B to C, then C to D (base 72 cm, height 96 cm). One answer is B 6 cm by 8 cm and C 18 cm by 24 cm. Which of these is a different possible answer?

    • B 9 cm by 12 cm, C 20 cm by 30 cm
    • B 9 cm by 12 cm, C 18 cm by 24 cm
    • B 6 cm by 8 cm, C 12 cm by 18 cm
    • B 8 cm by 10 cm, C 24 cm by 32 cm
    Check

14. 14. Naveen enlarges triangle A (base 3 cm, height 4 cm) to B, B to C, then C to D (base 72 cm, height 96 cm). Each enlargement uses a whole-number scale factor greater than 1. How many different base lengths and heights could there be for triangles B and C?

    • Exactly two
    • Only one
    • Four
    • Infinitely many
    Check

15. 15. Question 11a: rectangle A is 2 by 1, B is 4 by 2, C is 6 by 3 and D is 8 by 4. What are the scale factors from A to B, A to C and A to D?

    • 2, 3 and 4
    • 2, 3 and 6
    • 2, 4 and 6
    • 4, 9 and 16
    Check

16. 16. Question 11b: what are the areas of rectangles A (2 by 1), B (4 by 2), C (6 by 3) and D (8 by 4)?

    • 2, 6, 12 and 20
    • 3, 6, 9 and 12
    • 2, 4, 6 and 8
    • 2, 8, 18 and 32
    Check

17. 17. Question 11c: the ratio of lengths A : C is 1 : 3. What is the ratio of areas A : C, in its simplest form?

    • 1 : 6
    • 2 : 18
    • 1 : 3
    • 1 : 9
    Check

18. 18. Question 11d: which rule connects the ratio of lengths to the ratio of areas?

    • The ratio of areas is the ratio of lengths plus 1.
    • The ratio of areas is double the ratio of lengths.
    • They are the same.
    • The ratio of areas is the ratio of lengths squared.
    Check

19. 19. The ratio of areas is the ratio of lengths squared. Will this rule work for any scale factor of enlargement, and in general for any shape?

    • Yes
    • No
    Check