State the real distance represented by 1 cm on a map with scale 1:50 000.
(1)
2
On a map with scale 1:25 000, what real distance does 4 cm represent? Give your answer in kilometres.
(1)
3
A town is 3.2 km from a station in real life. On a map with scale 1:10 000, calculate the map distance in centimetres.
(2)
4
A road measures 13 cm on a map and is 6.5 km in reality. Work out the map scale as a ratio in the form 1:n.
(2)
5
A path on a map measures 7.4 cm and in real life it is 1.85 km. Find the scale of the map in the form 1:n.
(2)
6
On a map with scale 1:40 000 the distance between two villages is 3.6 cm. Calculate the real distance in kilometres.
(2)
7
A map uses the statement 1 cm = 0.5 km. What is the real distance represented by 9 cm on this map? Give your answer in kilometres.
(1)
8
A distance on a map at scale 1:25 000 measures 120 mm. Calculate the real distance in kilometres.
(2)
9
A path is measured on a map as 17.6 cm at a scale of 1:25 000. The student estimates the measurement could be off by plus or minus 0.2 cm. Calculate the possible range of the real distance in kilometres.
(3)
10
A rectangular garden is 12 m by 8 m in reality. Drawn to scale 1:200, what are the lengths of the sides on the drawing in centimetres?
(2)
11
On a 1:20 000 map the distance between two shops is 2.75 cm. Give the real distance in metres.
(2)
12
Two towns are 18 km apart. On a map with scale 1:90 000 what is the distance between them on the map, in millimetres?
(2)
13
A site plan shows 8 cm corresponding to 100 m in reality. Write the scale of the plan in the form 1:n.
(2)
14
A hiker will walk 15 km. On a map with scale 1:50 000, how many centimetres long will the route be on the map? If the printed map sheet can show a maximum straight length of 20 cm, how many sheets are needed to show the whole route?
(3)
15
A scale drawing uses 1:500. A rectangle on the drawing has area 18 cm2. Calculate the real area in square metres.
(3)
16
A map shows two landmarks 3.8 cm apart. The scale statement is 1 cm = 750 m. Find the real distance in metres.
(2)
17
A cyclist plans a route that measures 27.5 cm on a map with scale 1:60 000. The cyclist will ride at an average speed of 15 km/h. Estimate the time to complete the route, giving your answer in minutes to the nearest minute.
(4)
18
A school's sports field is a right triangle with legs 90 m and 60 m. A student draws a plan at scale 1:250. Calculate the length of the hypotenuse on the drawing in centimetres, correct to one decimal place.
(4)
Mark scheme · KS3.M-R6 Scale Drawings and Maps
Question 1
B1 500 m or 0.5 km cao
Answer: 500 m
Question 2
B1 1 km cao
Answer: 1 km
Question 3
M1 convert 3.2 km to cm or set up 3.2 km = 320000 cm and divide by 10 000
A1 32 cm cao
Answer: 32 cm
Question 4
M1 convert 6.5 km to cm = 650 000 cm and form ratio 13:650000 or divide both sides by 13
A1 1:50 000 cao
Answer: 1:50 000
Question 5
M1 convert 1.85 km to cm = 185 000 cm and divide by 7.4
A1 1:25 000 cao
Answer: 1:25 000
Question 6
M1 3.6 cm x 40 000 = 144 000 cm = 1.44 km
A1 1.44 km cao
Answer: 1.44 km
Question 7
B1 4.5 km cao
Answer: 4.5 km
Question 8
M1 120 mm = 12 cm, then 12 x 25 000 = 300 000 cm = 3 km
A1 3 km cao
Answer: 3 km
Question 9
M1 find minimum map length 17.6 - 0.2 = 17.4 cm and convert: 17.4 x 25 000 = 435 000 cm = 4.35 km
M1 find maximum map length 17.6 + 0.2 = 17.8 cm and convert: 17.8 x 25 000 = 445 000 cm = 4.45 km
A1 state range 4.35 km to 4.45 km cao
Answer: 4.35 km to 4.45 km
Question 10
M1 convert metres to cm and divide by 200: 1200/200 = 6, 800/200 = 4
A1 6 cm by 4 cm cao
Answer: 6 cm by 4 cm
Question 11
M1 2.75 x 20 000 = 55 000 cm = 550 m
A1 550 m cao
Answer: 550 m
Question 12
M1 convert 18 km to cm = 1 800 000 cm then divide by 90 000 = 20 cm
A1 200 mm cao
Answer: 200 mm
Question 13
M1 100 m = 10 000 cm so ratio 8:10000 then divide by 8
A1 1:1250 cao
Answer: 1:1250
Question 14
M1 convert 15 km to cm = 1 500 000 cm and divide by 50 000 to get 30 cm
M1 compare 30 cm to sheet length 20 cm and compute required number
A1 30 cm; 2 sheets cao
Answer: 30 cm and 2 sheets
Question 15
M1 use area scale factor (5002 = 250 000) and multiply: 18 x 250 000 = 4 500 000 cm2
M1 convert cm2 to m2: 4 500 000 cm2 = 450 m2
A1 450 m2 cao
Answer: 450 m2
Question 16
M1 3.8 x 750 = 2 850 m
A1 2850 m cao
Answer: 2850 m
Question 17
M1 convert map cm to real: 27.5 x 60 000 = 1 650 000 cm = 16.5 km
M1 compute time in hours = 16.5/15 = 1.1 h
M1 convert hours to minutes: 1.1 x 60 = 66 minutes
A1 66 minutes cao
Answer: 66 minutes
Question 18
M1 find real hypotenuse: √902 + 602 = √11 700 = 108.166... m
M1 convert to cm: 108.166... m = 10 816.66... cm then scale by 1/250 giving 43.2666... cm