Scale Drawings: Higher Tier Practice - Worksheets, Questions and Revision

10 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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3.11H Scale Drawings: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 75 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A plan of a classroom is drawn at a scale of 1:50. The length of the classroom on the plan is 8.2 cm.
Work out the actual length of the classroom in metres.
(Total for Question 1 is 1 mark)
2
A map uses a scale of 1:250 000 (1 cm represents 2.5 km). Two villages A and B are 3.6 cm apart on the map.
(a) Work out the actual distance between A and B in kilometres.
(b) A cyclist travels from A to B at an average speed of 18 km/h. Work out the time taken in hours and minutes to two significant figures.
(a)Work out the actual distance between A and B in kilometres.(1)
(b)Work out the time taken in hours and minutes (to two significant figures).(1)
(Total for Question 2 is 2 marks)
3
A rectangular garden is drawn on a plan with scale 1:200. On the plan the garden measures 6.4 cm by 3.0 cm.
Work out the actual area of the garden in square metres. Give your answer to 3 significant figures.
(Total for Question 3 is 3 marks)
4
A model car is similar to the real car. The scale factor of similarity (model : real) for linear dimensions is 1:18.
(a) Work out the area scale factor (model : real).
(b) The model has a painted roof area of 12 cm2. Work out the area of the real car roof in square metres. Give your answer in standard form to 2 significant figures.
(a)Work out the area scale factor (model : real).(1)
(b)The model roof area is 12 cm2. Work out the real roof area in m2, give answer in standard form to 2 s.f.(2)
(Total for Question 4 is 3 marks)
5
A house is shown on a plan drawn at scale 1:1250. The width of the front of the house on the plan is 2.4 cm.
Work out the actual width of the front of the house in metres. Give your answer to the nearest 0.1 m.
(Total for Question 5 is 2 marks)
6
A scaled drawing of a rectangular swimming pool has length 5x cm and width 3x cm on the plan. The scale is 1:100 for linear measurements. The actual pool has an area of 450 m2.
Show that x satisfies the equation x2 = 30. Hence find the value of x to 2 decimal places.
(Total for Question 6 is 4 marks)
7
An architect draws a rectangular plot on a site plan at scale 1:400. On the drawing the diagonal of the rectangle measures 18.2 cm. The actual rectangle has the property that its length is twice its width. Work out the actual dimensions of the rectangle in metres. Give your answers to 3 significant figures where appropriate.
(a)Find the actual length of the diagonal in metres.(2)
(b)Let width = w and length = 2w. Using the diagonal found in part (a), form an equation and solve to find w. Give the width and length to 3 significant figures.(6)
(Total for Question 7 is 8 marks)
8
A surveyor produces a scale drawing of a triangular field. On the drawing the sides are 7.2 cm, 5.4 cm and 4.2 cm. The scale is 1:500 for linear measurements.
(a) Work out the actual perimeter of the field in metres to 3 significant figures.
(b) Hence, or otherwise, find the actual area of the field in square metres. Give your answer to 3 significant figures. (You may use Heron's formula.)
(a)Work out the actual perimeter of the field in metres to 3 significant figures.(3)
(b)Hence, or otherwise, find the actual area of the field in square metres. Give your answer to 3 significant figures.(6)
(Total for Question 8 is 9 marks)
9
A designer creates a scale elevation of a triangular sail on a boat. On the drawing the base is 24.0 cm and the height (from base to apex perpendicular) is 18.0 cm. The actual sail must have an area of 27.0 m2.
Find the linear scale factor (drawing : actual) and hence find the actual base and actual perpendicular height of the sail in metres. Give answers to 3 significant figures.
(a)Find the area of the sail on the drawing in cm2.(2)
(b)Find the linear scale factor k (drawing : actual) and hence find the actual base and height in metres. Give all answers to 3 significant figures.(7)
(Total for Question 9 is 9 marks)
10
A planning officer examines a new development drawn at scale 1:1250. A circular recreational area appears on the plan with radius 2.88 cm. The developer plans to make the actual area a grassed circular area with a perimeter path of constant width 4.32 m around the grass (path lies outside the grass circle and is included in the overall circular area). The total area including the path must be 5000 m2.
(a) Work out the actual radius of the grassed circle in metres.
(b) Hence calculate the width of the path required (in metres) so that the total overall area including the path is 5000 m2. Give your answer to 2 decimal places.
(a)Work out the actual radius of the grassed circle in metres.(3)
(b)Hence calculate the width of the path required (in metres) so that the total overall area including the path is 5000 m2. Give your answer to 2 decimal places.(6)
(Total for Question 10 is 9 marks)
Mark scheme · 3.11H Scale Drawings: Higher Tier Practice

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10