A scale drawing of Priya's bedroom is made using a scale where 1 cm represents 2 m. On the scale drawing, the length of the bedroom is 3 cm.
(Total for Question 1 is 2 marks)
2
A scale drawing of a toy uses a scale of 1 : 10. The real toy is 45 cm tall. Work out the height of the toy on the scale drawing, in cm.
(Total for Question 2 is 2 marks)
3
On a scale drawing, the scale is 1 : 20. A wall is drawn with a length of 4 cm. What is the real length of the wall?
A) 4 cm
B) 24 cm
C) 80 cm
D) 0.2 cm
(Total for Question 3 is 1 mark)
4
On a scale drawing, the scale is 1 : 50. A wall has a real length of 6 m. Work out the length of the wall on the scale drawing, giving your answer in centimetres.
(Total for Question 4 is 3 marks)
5
A map is drawn using a scale of 1 : 25000.
(a)The distance between two villages on the map is 8 cm. Work out the real distance between the villages, in kilometres.(3)
(b)The real distance between two towns is 12.5 km. Work out the distance between the towns on the map, in centimetres.(2)
(Total for Question 5 is 5 marks)
6
A scale drawing of a garden path is made using a scale of 1 : 100. In real life, the path is 15 m long and 2 m wide. Work out the length and width of the path on the scale drawing, in centimetres.
(Total for Question 6 is 3 marks)
7
Which of these scales would give the smallest scale drawing of the same real-life object?
A) 1 : 10
B) 1 : 100
C) 1 : 1000
D) 1 : 10000
(Total for Question 7 is 1 mark)
8
A scale is given as: 1 cm represents 4 km. Write this scale in the ratio form 1 : n.
(Total for Question 8 is 2 marks)
9
A scale drawing is to be made of a school hall that is 30 m long in real life. Explain why a scale of 1 : 1 would not be sensible to use for this drawing.
(Total for Question 9 is 1 mark)
10
A scale drawing of a swimming pool is made using a scale of 1 : 75. The pool is 22.5 m long in real life. Work out the length of the pool on the scale drawing, in centimetres.
(Total for Question 10 is 3 marks)
11
A scale drawing of a nature reserve is made using a scale of 1 : 20000. A straight path is drawn 7.5 cm long. Work out the real length of the path, giving your answer in kilometres.
(Total for Question 11 is 3 marks)
12
A rectangular kitchen measures 4.8 m by 3.6 m in real life. A scale drawing is made using a scale of 1 : 60.
(a)Work out the dimensions of the kitchen on the scale drawing, in centimetres.(3)
(b)Work out the area of the kitchen on the scale drawing, in cm2.(1)
(Total for Question 12 is 4 marks)
13
A scale drawing of a school hall is made using a scale of 1 : 200. On the drawing, the hall is a rectangle measuring 12 cm by 9 cm. Work out the real area of the hall, giving your answer in m2.
(Total for Question 13 is 4 marks)
14
A scale drawing of a garden is made using a scale of 1 : 20. The area of the garden on the scale drawing is 15 cm2. Work out the real area of the garden, giving your answer in m2.
(Total for Question 14 is 3 marks)
15
A model car is built using a scale of 1 : 24. The real car is 4.8 m long. Which of these is the length of the model car, in cm?
A) 20 cm
B) 2 cm
C) 0.2 cm
D) 200 cm
(Total for Question 15 is 1 mark)
16
A scale drawing of a rectangular sports pitch is made using a scale of 1 cm to 25 m. In real life, the pitch is 100 m long and 64 m wide.
(a)Work out the length and width of the pitch on the scale drawing, in centimetres.(2)
(b)Work out the perimeter of the pitch on the scale drawing, in centimetres.(2)
(Total for Question 16 is 4 marks)
17
A map has a scale of 1 : 40000. Two points are 3.5 km apart in real life. Work out the distance between the points on the map, in centimetres. Give your answer correct to 1 decimal place.
(Total for Question 17 is 3 marks)
18
A scale drawing of a building is made using a scale of 1 : 250. On the drawing, the height of the building is 8.4 cm.
(a)Work out the real height of the building, in metres.(2)
(b)A window on the real building has a width of 1.5 m. A different scale drawing of just the window uses a scale of 1 : 20. Work out the width of the window on this second drawing, in centimetres.(2)
(Total for Question 18 is 4 marks)
19
On a scale drawing, a road that is 3.6 km long in real life is drawn as a straight line 4.5 cm long.
(a)Write the scale of the drawing in the form 1 : n.(3)
(b)Another road is 1.9 km long in real life. Work out the length of this road on the same scale drawing, in centimetres, giving your answer correct to 1 decimal place.(2)
(Total for Question 19 is 5 marks)
20
A furniture designer uses a scale drawing with a scale of 1 : 25 to design a wardrobe that is 2 m tall in real life. She then produces a smaller marketing image of the same wardrobe using a scale of 1 : 100. Work out the difference in height between the two scale drawings, in centimetres.
(Total for Question 20 is 4 marks)
Mark scheme · 3.11 Scale Drawings
Question 1
M1 3 x 2 (oe)
A1 6 m cao
Answer: 6 m
Question 2
M1 45 / 10 (oe)
A1 4.5 cm cao
Answer: 4.5 cm
Question 3
B1 C (80 cm) cao
Answer: C) 80 cm
Question 4
B1 6 m = 600 cm
M1 600 / 50
A1 12 cm cao
Answer: 12 cm
Question 5
(a) M1 8 x 25000 (= 200000)
(a) M1 200000 cm converted towards km (/100 then /1000, or /100000)
(a) A1 2 km cao
(a) Answer: 2 km
(b) M1 12.5 km converted to 1250000 cm, then / 25000
(b) A1 50 cm cao
(b) Answer: 50 cm
Question 6
M1 1500 / 100 or 200 / 100
A1 length = 15 cm
A1 width = 2 cm
Answer: Length = 15 cm, width = 2 cm
Question 7
B1 D cao
Answer: D) 1 : 10000
Question 8
M1 4 km converted to 400000 cm
A1 1 : 400000 cao
Answer: 1 : 400000
Question 9
B1 Correct reason, e.g. the drawing would have to be 30 m long (the same size as the real hall), which is too big to fit on a sheet of paper
Answer: The drawing would be the same size as the real hall (30 m long), which is impractically large for a sheet of paper.