State the real distance represented by 1 cm on a map with scale 1:20 000.
(1)
2
On a map with scale 1:10 000, what real distance does 5 cm represent? Give your answer in metres.
(1)
3
A map scale is stated as 1 cm = 2 km. What real distance does 6 cm represent?
(1)
4
On a map with scale 1:5000, what real distance does 8 cm represent? Give your answer in metres.
(1)
5
A map scale is 1 cm = 1.5 km. What real distance does 4 cm represent?
(1)
6
On a map with scale 1:100 000, what real distance does 3 cm represent? Give your answer in kilometres.
(1)
7
A distance of 4.5 km in real life is shown on a map with scale 1:50 000. Calculate the map distance in centimetres.
(2)
8
Two points are 2400 m apart in reality. On a map of scale 1:30 000, calculate the distance between them on the map, in centimetres.
(2)
9
A road is 22 cm long on a map with scale 1:25 000. Calculate the real length of the road in kilometres.
(2)
10
The distance between two towns on a map is 6 cm. The scale of the map is 1:200 000. Work out the real distance in kilometres.
(2)
11
A garden is 15 m long in real life. It is drawn on a plan with scale 1:150. Find the length of the garden on the plan, in centimetres.
(2)
12
A model of a building is made using a scale of 1:75. The real height of the building is 22.5 m. Work out the height of the model, in centimetres.
(2)
13
On a map with scale 1:40 000, a lake has a map length of 5.5 cm. Calculate the real length of the lake in kilometres.
(2)
14
A scale drawing uses 1:250. The length of a room on the drawing is 8.4 cm. Work out the real length of the room, in metres.
(2)
15
A hiking trail measures 24 cm on a map with scale 1:50 000. The hiker walks at an average speed of 5 km/h. Work out how long the walk will take, giving your answer in hours and minutes.
(3)
16
A scale drawing of a park uses scale 1:1000. A rectangular field on the drawing measures 6 cm by 4 cm. Work out the real area of the field in square metres.
(3)
17
Two villages are 8.5 km apart in real life. On a map, the distance between them is drawn as 17 cm. Work out the scale of the map, giving your answer in the form 1:n.
(3)
18
A map has scale 1:40 000. A cyclist's route measures 18 cm on the map in a straight line, but the actual route follows bends and is 25% longer than this straight-line distance. Work out the real distance the cyclist rides, in kilometres.
(3)
19
A plan of a car park is drawn to scale 1:500. The car park is rectangular and measures 9 cm by 5 cm on the plan. Local regulations require at least 1 parking space per 12.5 m2 of real car park area. Work out the maximum number of parking spaces the car park can have.
(3)
20
Stretch question. A map is drawn to a scale of 1:25 000. A rectangular nature reserve has a real area of 18 km2. Work out the area of the nature reserve on the map, in square centimetres.
(3)
Mark scheme · KS3.M-R6D Scale Drawings and Maps: Fluency and Exam Drill
Question 1
B1 200 m cao
Answer: 200 m
Question 2
B1 500 m cao
Answer: 500 m
Question 3
B1 12 km cao
Answer: 12 km
Question 4
B1 400 m cao
Answer: 400 m
Question 5
B1 6 km cao
Answer: 6 km
Question 6
B1 3 km cao
Answer: 3 km
Question 7
M1 convert 4.5 km to cm = 450 000 cm
A1 9 cm cao
Answer: 9 cm
Question 8
M1 convert 2400 m to cm = 240 000 cm
A1 8 cm cao
Answer: 8 cm
Question 9
M1 22 x 25 000 = 550 000 cm
A1 5.5 km cao
Answer: 5.5 km
Question 10
M1 6 x 200 000 = 1 200 000 cm
A1 12 km cao
Answer: 12 km
Question 11
M1 convert 15 m to cm = 1500 cm
A1 10 cm cao
Answer: 10 cm
Question 12
M1 convert 22.5 m to cm = 2250 cm
A1 30 cm cao
Answer: 30 cm
Question 13
M1 5.5 x 40 000 = 220 000 cm
A1 2.2 km cao
Answer: 2.2 km
Question 14
M1 8.4 x 250 = 2100 cm
A1 21 m cao
Answer: 21 m
Question 15
M1 convert map length to real distance: 24 x 50 000 = 1 200 000 cm = 12 km
M1 time = 12 / 5 = 2.4 hours
A1 2 hours 24 minutes cao
Answer: 2 hours 24 minutes
Question 16
M1 real dimensions: 6 x 1000 = 6000 cm = 60 m and 4 x 1000 = 4000 cm = 40 m
M1 area = 60 x 40
A1 2400 m2 cao
Answer: 2400 m2
Question 17
M1 convert 8.5 km to cm = 850 000 cm
M1 divide by map length: 850 000 / 17
A1 1:50 000 cao
Answer: 1:50 000
Question 18
M1 straight-line real distance: 18 x 40 000 = 720 000 cm = 7.2 km
M1 apply 25% increase: 7.2 x 1.25
A1 9 km cao
Answer: 9 km
Question 19
M1 real dimensions: 9x500=4500cm=45m and 5x500=2500cm=25m
M1 real area = 45 x 25 = 1125 m2, then divide by 12.5
A1 90 spaces cao
Answer: 90 spaces
Question 20
M1 convert real area to cm2: 1 km2 = 10 000 000 000 cm2, so 18 km2 = 180 000 000 000 cm2
M1 divide by the area scale factor 25 0002 = 625 000 000