Scale Drawings: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

12 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Geometry and Measures

3.11DB Scale Drawings: Fluency and Exam Drill (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 45 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

On a scale drawing, 1 cm represents 40 m in real life. Write this scale as a ratio in the form 1:n.

(Total for Question 1 is 1 mark)

A scale drawing of a car park uses a scale of 1:500. The table below shows two distances, each measured either on the drawing or in real life, with one value missing from each row.

Distance A - length on drawing: 6.4 cm; real length: ?
Distance B - length on drawing: ?; real length: 55 m

Complete the table by working out the two missing values.

(a)Work out the real length of Distance A, in metres.(1)

(b)Work out the length of Distance B on the drawing, in centimetres.(1)

(Total for Question 2 is 2 marks)

A scale drawing has a scale of 1:300. On the drawing, a driveway is 40 mm long. Work out the real length of the driveway, in metres.

(Total for Question 3 is 1 mark)

A scale drawing uses a scale of 1 cm to 20 m. A running track is 340 m long in real life. Work out the length of the running track on the drawing, giving your answer in millimetres.

(Total for Question 4 is 2 marks)

A model train is built to a scale of 1:76. The model engine is 15.8 cm long. Work out the real length of the engine, in metres, correct to 3 significant figures.

(Total for Question 5 is 2 marks)

A rectangular allotment is shown on a plan with scale 1:400. On the plan the allotment measures 5 cm by 3.5 cm. Work out the real perimeter of the allotment, giving your answer in metres.

(Total for Question 6 is 3 marks)

Priya is using a map with scale 1:20 000 to find the real distance represented by a road that measures 8 cm on the map. Her working is shown below:

8 x 20 000 = 160 000
160 000 cm = 16 km

Priya has made an error. Identify what she did wrong, and work out the correct real distance, in kilometres.

(Total for Question 7 is 3 marks)

Two different maps show the same stretch of coastline. On Map A, which has a scale of 1:25 000, a headland measures 6 cm. Map B has a scale of 1:40 000. Work out the length, in centimetres, that the same headland would measure on Map B.

(Total for Question 8 is 3 marks)

The diagram shows a scale drawing of a triangular flower bed, drawn to a scale of 1:150. The three sides of the triangle measure 4.2 cm, 3.6 cm and 3 cm on the drawing. Work out the real perimeter of the flower bed, giving your answer in metres.

Figure (to be drawn): Triangle ABC representing a flower bed on a scale drawing, drawn to a scale of 1:150. Side AB = 4.2 cm, side BC = 3.6 cm, side CA = 3 cm, each labelled next to its side. NOT accurately drawn.

(Total for Question 9 is 3 marks)

A rectangular lawn is shown on a garden plan with scale 1:250. On the plan the lawn measures 3.2 cm by 2 cm. Turf costs 4.50 pounds per square metre. Work out the total cost of turfing the lawn.

(Total for Question 10 is 3 marks)

A rectangular swimming pool is 15 m long and 9 m wide in real life. On a scale drawing the pool is shown 10 cm long. Show that the scale of the drawing is 1:150, and work out the width of the pool on the drawing, in centimetres.

(Total for Question 11 is 4 marks)

A rectangular bedroom is shown on a floor plan with scale 1:50. On the plan the room measures 8.4 cm by 6 cm. A wardrobe has a longest edge of 2.9 m and needs to be carried flat across the room, diagonally from corner to corner. Work out the length of the room's diagonal, in metres, correct to 3 significant figures, and use your answer to determine whether the wardrobe's longest edge is shorter than the diagonal. Give a reason for your answer.

(Total for Question 12 is 5 marks)

Mark scheme · 3.11DB Scale Drawings: Fluency and Exam Drill (Part 2)

Question 1

B1 1:4000 cao
Answer: 1:4000

Question 2

(a) B1 32 m cao
(a) Answer: 32 m
(b) B1 11 cm cao
(b) Answer: 11 cm

Question 3

B1 12 m cao
Answer: 12 m

Question 4

M1 340 / 20 = 17 (cm), or an equivalent complete method
A1 170 mm cao
Answer: 170 mm

Question 5

M1 15.8 x 76 = 1200.8 (cm), or an equivalent method
A1 12.0 m awrt (3 sf) cao
Answer: 12.0 m

Question 6

M1 Convert plan lengths to real lengths: 5 cm -> 2000 cm (20 m) and 3.5 cm -> 1400 cm (14 m)
M1 Use perimeter = 2 x (length + width) with the real values
A1 68 m cao
Answer: 68 m

Question 7

B1 Correctly identifies Priya's error, e.g. she divided by 10 000 instead of 100 000 when converting cm to km (or an equivalent statement of the error) oe
M1 160 000 / 100 000, or an equivalent complete method to convert cm to km
A1 1.6 km cao
Answer: Priya divided by the wrong power of 10 (she used 10 000 instead of 100 000); the correct real distance is 1.6 km.

Question 8

M1 Find the real length of the headland using Map A: 6 x 25 000 = 150 000 (cm) oe
M1 Divide the real length by 40 000 to convert to Map B's scale, or an equivalent method
A1 3.75 cm cao
Answer: 3.75 cm

Question 9

M1 4.2 + 3.6 + 3 = 10.8 (cm), or convert each side to a real length separately
M1 10.8 x 150, or the sum of the three separately converted real lengths, oe
A1 16.2 m cao
Answer: 16.2 m

Question 10

M1 Convert plan lengths to real lengths: 8 m and 5 m oe
M1 Area = 8 x 5 = 40 (m²)
A1 180 pounds cao
Answer: 180 pounds (180.00 pounds)

Question 11

M1 Convert 15 m to 1500 cm oe
B1 1500 / 10 = 150, so the scale is 1:150 (working must be shown, since the answer is given) cso
M1 Convert 9 m to 900 cm and divide by 150, or an equivalent method, to find the plan width
A1 6 cm cao
Answer: Scale confirmed as 1:150; the width of the pool on the drawing is 6 cm.

Question 12

M1 Convert plan lengths to real lengths: 4.2 m and 3 m oe
M1 Use Pythagoras: diagonal² = 4.2² + 3² (= 17.64 + 9 = 26.64)
A1 5.16 m awrt (3 sf) cao ft from candidate's converted dimensions
C1 Correct comparison stated: 2.9 m < 5.16 m oe
C1 Correct conclusion with a reason, e.g. since the wardrobe's longest edge (2.9 m) is shorter than the room's diagonal (5.16 m), it can be carried across the room diagonally oe
Answer: Diagonal = 5.16 m (3 sf); since 2.9 m < 5.16 m, the wardrobe's longest edge is shorter than the room's diagonal.

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Scale Drawings: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

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3.11DB Scale Drawings: Fluency and Exam Drill (Part 2)

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