Question 1: Calculate the reduced length of a line measuring 120 mm when scaled down by a factor of 3.5. Show your working.

Answer: 34.29

Question 2: A drawing of a rectangle has a length of 90 cm. When reduced to fit on a smaller sheet, its length is scaled down to 30 cm. What is the scale factor of the reduction? Show your working.

Answer: 1/3 or 0.33

Question 3: A model of a car is made at a scale of 1:25. If the actual car is 4.5 meters long, what is the length of the model? Show your working.

Answer: 0.18 meters or 18 cm

Question 4: Identify the mistake in this reduction: A student scaled down a drawing by multiplying all dimensions by 2 and labeled it as a reduction.

Answer: Multiplying by 2 is an enlargement, not a reduction. To reduce, dimensions should be divided by the scale factor.

Question 5: A scale drawing has a length of 8 cm. Its real-life length is 32 meters. What is the scale factor used? Show your working.

Answer: 1:4000

Question 6: A diagram is scaled down by a factor of 1/5. If a side measures 15 cm in the drawing, what is the actual length in centimeters? Show your working.

Answer: 75 cm

Question 7: Construct a triangle on the grid with sides measuring 4 cm, 6 cm, and 8 cm. Then create a similar triangle scaled down by a factor of 1/2. Show your work and label the sides.

Answer: Sides: 2 cm, 3 cm, 4 cm

Question 8: A model airplane is built at a scale of 1:60. If the model's wingspan is 12 cm, what is the wingspan of the actual airplane? Show your working.

Answer: 720 cm or 7.2 meters

Question 9: A student incorrectly scaled a drawing by multiplying all dimensions by 3 instead of dividing. What is the mistake, and how should the student correctly perform the reduction?

Answer: Multiplying by 3 enlarges rather than reduces. To reduce, divide dimensions by the scale factor, i.e., divide by 3.

Question 10: A scale drawing measures 7 cm in length. If the scale factor is 1:70, what is the actual length? Show your working.

Answer: 490 cm

Question 11: A photograph of a statue is scaled down by a factor of 1/10. The photograph's height is 9 cm. What is the real height of the statue? Show your working.

Answer: 90 cm

Question 12: Identify and correct the mistake: A student states that to create a reduction, they should multiply all dimensions by the scale factor.

Answer: The mistake is multiplying; to reduce, dimensions should be divided by the scale factor.