Sec 3 G1 Maths Map scales worksheet with answers

A free Sec 3 G1 Maths worksheet on map scales: 8 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 3 G1 Maths worksheet: Map scales

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

On a map,

4

cm represents

0.5

km. Express the scale of the map in the form

1 : n

Answer[2]

Two towns are

6

km apart. On a map they are

5

cm apart. Express the scale of the map in the form

1 : n

Answer[2]

A map is drawn to a scale of

1 : 10\,000

. Two towns are

6.4

cm apart on the map. Find the actual distance, in kilometres, between the two towns.

Answerkm[2]

A map is drawn to a scale of

1 : 250\,000

. Two towns are

6.4

cm apart on the map. Find the actual distance, in kilometres, between the two towns.

Answerkm[2]

On a map,

5

cm represents

3

km. Express the scale of the map in the form

1 : n

Answer[2]

(a)A map is drawn to a scale of

1 : 500\,000

. Two towns are

6.4

cm apart on the map. Find the actual distance, in kilometres, between the two towns.

Answer (a)km[2]

(b)The plan of a house is drawn to a scale of

1 : 100

. A room is

2.4

cm long on the plan. Find the actual length, in metres, of the room.

Answer (b)m[2]

Section B

(a)The plan of a house is drawn to a scale of

1 : 50

. A room is

7.5

cm long on the plan. Find the actual length, in metres, of the room.

Answer (a)m[2]

(b)The plan of a house is drawn to a scale of

1 : 200

. A room is

3.5

cm long on the plan. Find the actual length, in metres, of the room.

Answer (b)m[2]

(c)(i)A map is drawn to a scale of

1 : 500\,000

. Two towns are

4.2

cm apart on the map. Find the actual distance, in kilometres, between the two towns.

Answer (c)(i)km[2]

(c)(ii)A map is drawn to a scale of

1 : 10\,000

. Two places are

1.2

km apart. Find the distance, in centimetres, between the two places on the map.

Answer (c)(ii)cm[2]

(a)(i)Two towns are

20

km apart. On a map they are

2

cm apart. Express the scale of the map in the form

1 : n

Answer (a)(i)[2]

(a)(ii)Two towns are

1.5

km apart. On a map they are

2

cm apart. Express the scale of the map in the form

1 : n

Answer (a)(ii)[2]

(b)(i)A map is drawn to a scale of

1 : 50\,000

. Two places are

7.2

km apart. Find the distance, in centimetres, between the two places on the map.

Answer (b)(i)cm[2]

(b)(ii)The plan of a house is drawn to a scale of

1 : 200

. A room is

1.6

cm long on the plan. Find the actual length, in metres, of the room.

Answer (b)(ii)m[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

1 : 12\,500

[2]

\mathstrut 4\text{ cm} : 0.5\text{ km}

4\text{ cm} : 50\,000\text{ cm}

That is

4 : 50\,000

\mathstrut 1 : \dfrac{50\,000}{4}

1 : 12\,500

Question 2

Answer:

1 : 120\,000

[2]

\mathstrut 5\text{ cm} : 6\text{ km}

5\text{ cm} : 600\,000\text{ cm}

That is

5 : 600\,000

\mathstrut 1 : \dfrac{600\,000}{5}

1 : 120\,000

Question 3

Answer:

6.4\text{ cm} : 0.64\text{ km}

[2]

\mathstrut 1 : 10\,000

\mathstrut 1\text{ cm} : 10\,000\text{ cm}

1\text{ cm} : 0.1\text{ km}

\mathstrut 6.4\text{ cm} : 6.4 \times 0.1\text{ km}

6.4\text{ cm} : 0.64\text{ km}

Question 4

Answer:

6.4\text{ cm} : 16\text{ km}

[2]

\mathstrut 1 : 250\,000

\mathstrut 1\text{ cm} : 250\,000\text{ cm}

1\text{ cm} : 2.5\text{ km}

\mathstrut 6.4\text{ cm} : 6.4 \times 2.5\text{ km}

6.4\text{ cm} : 16\text{ km}

Question 5

Answer:

1 : 60\,000

[2]

\mathstrut 5\text{ cm} : 3\text{ km}

5\text{ cm} : 300\,000\text{ cm}

That is

5 : 300\,000

\mathstrut 1 : \dfrac{300\,000}{5}

1 : 60\,000

Question 6

(a)Answer:

6.4\text{ cm} : 32\text{ km}

[2]

\mathstrut 1 : 500\,000

\mathstrut 1\text{ cm} : 500\,000\text{ cm}

1\text{ cm} : 5\text{ km}

\mathstrut 6.4\text{ cm} : 6.4 \times 5\text{ km}

6.4\text{ cm} : 32\text{ km}

(b)Answer:

2.4\text{ cm} : 2.4\text{ m}

[2]

\mathstrut 1 : 100

\mathstrut 1\text{ cm} : 100\text{ cm}

1\text{ cm} : 1\text{ m}

\mathstrut 2.4\text{ cm} : 2.4 \times 1\text{ m}

2.4\text{ cm} : 2.4\text{ m}

Question 7

(a)Answer:

7.5\text{ cm} : 3.75\text{ m}

[2]

\mathstrut 1 : 50

\mathstrut 1\text{ cm} : 50\text{ cm}

1\text{ cm} : 0.5\text{ m}

\mathstrut 7.5\text{ cm} : 7.5 \times 0.5\text{ m}

7.5\text{ cm} : 3.75\text{ m}

(b)Answer:

3.5\text{ cm} : 7\text{ m}

[2]

\mathstrut 1 : 200

\mathstrut 1\text{ cm} : 200\text{ cm}

1\text{ cm} : 2\text{ m}

\mathstrut 3.5\text{ cm} : 3.5 \times 2\text{ m}

3.5\text{ cm} : 7\text{ m}

(c)(i)Answer:

4.2\text{ cm} : 21\text{ km}

[2]

\mathstrut 1 : 500\,000

\mathstrut 1\text{ cm} : 500\,000\text{ cm}

1\text{ cm} : 5\text{ km}

\mathstrut 4.2\text{ cm} : 4.2 \times 5\text{ km}

4.2\text{ cm} : 21\text{ km}

(c)(ii)Answer:

12\text{ cm} : 1.2\text{ km}

[2]

\mathstrut 1 : 10\,000

\mathstrut 1\text{ cm} : 10\,000\text{ cm}

1\text{ cm} : 0.1\text{ km}

\mathstrut \dfrac{1.2}{0.1}\text{ cm} : 1.2\text{ km}

12\text{ cm} : 1.2\text{ km}

Question 8

(a)(i)Answer:

1 : 1\,000\,000

[2]

\mathstrut 2\text{ cm} : 20\text{ km}

2\text{ cm} : 2\,000\,000\text{ cm}

That is

2 : 2\,000\,000

\mathstrut 1 : \dfrac{2\,000\,000}{2}

1 : 1\,000\,000

(a)(ii)Answer:

1 : 75\,000

[2]

\mathstrut 2\text{ cm} : 1.5\text{ km}

2\text{ cm} : 150\,000\text{ cm}

That is

2 : 150\,000

\mathstrut 1 : \dfrac{150\,000}{2}

1 : 75\,000

(b)(i)Answer:

14.4\text{ cm} : 7.2\text{ km}

[2]

\mathstrut 1 : 50\,000

\mathstrut 1\text{ cm} : 50\,000\text{ cm}

1\text{ cm} : 0.5\text{ km}

\mathstrut \dfrac{7.2}{0.5}\text{ cm} : 7.2\text{ km}

14.4\text{ cm} : 7.2\text{ km}

(b)(ii)Answer:

1.6\text{ cm} : 3.2\text{ m}

[2]

\mathstrut 1 : 200

\mathstrut 1\text{ cm} : 200\text{ cm}

1\text{ cm} : 2\text{ m}

\mathstrut 1.6\text{ cm} : 1.6 \times 2\text{ m}

1.6\text{ cm} : 3.2\text{ m}

Sec 3 G1 Maths Map scales worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Section B

(a)The plan of a house is drawn to a scale of

1 : 50

. A room is

7.5

cm long on the plan. Find the actual length, in metres, of the room.

Answer (a)m[2]

(b)The plan of a house is drawn to a scale of

1 : 200

. A room is

3.5

cm long on the plan. Find the actual length, in metres, of the room.

Answer (b)m[2]

(c)(i)A map is drawn to a scale of

1 : 500\,000

. Two towns are

4.2

cm apart on the map. Find the actual distance, in kilometres, between the two towns.

Answer (c)(i)km[2]

(c)(ii)A map is drawn to a scale of

1 : 10\,000

. Two places are

1.2

km apart. Find the distance, in centimetres, between the two places on the map.

Answer (c)(ii)cm[2]

Answers and worked solutions

Question 1

Answer:

1 : 12\,500

[2]

\mathstrut 4\text{ cm} : 0.5\text{ km}

4\text{ cm} : 50\,000\text{ cm}

That is

4 : 50\,000

\mathstrut 1 : \dfrac{50\,000}{4}

1 : 12\,500

Question 2

Answer:

1 : 120\,000

[2]

\mathstrut 5\text{ cm} : 6\text{ km}

5\text{ cm} : 600\,000\text{ cm}

That is

5 : 600\,000

\mathstrut 1 : \dfrac{600\,000}{5}

1 : 120\,000

Question 3

Answer:

6.4\text{ cm} : 0.64\text{ km}

[2]

\mathstrut 1 : 10\,000

\mathstrut 1\text{ cm} : 10\,000\text{ cm}

1\text{ cm} : 0.1\text{ km}

\mathstrut 6.4\text{ cm} : 6.4 \times 0.1\text{ km}

6.4\text{ cm} : 0.64\text{ km}

Question 4

Answer:

6.4\text{ cm} : 16\text{ km}

[2]

\mathstrut 1 : 250\,000

\mathstrut 1\text{ cm} : 250\,000\text{ cm}

1\text{ cm} : 2.5\text{ km}

\mathstrut 6.4\text{ cm} : 6.4 \times 2.5\text{ km}

6.4\text{ cm} : 16\text{ km}

Question 5

Answer:

1 : 60\,000

[2]

\mathstrut 5\text{ cm} : 3\text{ km}

5\text{ cm} : 300\,000\text{ cm}

That is

5 : 300\,000

\mathstrut 1 : \dfrac{300\,000}{5}

1 : 60\,000

Question 6

(a)Answer:

6.4\text{ cm} : 32\text{ km}

[2]

\mathstrut 1 : 500\,000

\mathstrut 1\text{ cm} : 500\,000\text{ cm}

1\text{ cm} : 5\text{ km}

\mathstrut 6.4\text{ cm} : 6.4 \times 5\text{ km}

6.4\text{ cm} : 32\text{ km}

(b)Answer:

2.4\text{ cm} : 2.4\text{ m}

[2]

\mathstrut 1 : 100

\mathstrut 1\text{ cm} : 100\text{ cm}

1\text{ cm} : 1\text{ m}

\mathstrut 2.4\text{ cm} : 2.4 \times 1\text{ m}

2.4\text{ cm} : 2.4\text{ m}

Question 7

(a)Answer:

7.5\text{ cm} : 3.75\text{ m}

[2]

\mathstrut 1 : 50

\mathstrut 1\text{ cm} : 50\text{ cm}

1\text{ cm} : 0.5\text{ m}

\mathstrut 7.5\text{ cm} : 7.5 \times 0.5\text{ m}

7.5\text{ cm} : 3.75\text{ m}

(b)Answer:

3.5\text{ cm} : 7\text{ m}

[2]

\mathstrut 1 : 200

\mathstrut 1\text{ cm} : 200\text{ cm}

1\text{ cm} : 2\text{ m}

\mathstrut 3.5\text{ cm} : 3.5 \times 2\text{ m}

3.5\text{ cm} : 7\text{ m}

(c)(i)Answer:

4.2\text{ cm} : 21\text{ km}

[2]

\mathstrut 1 : 500\,000

\mathstrut 1\text{ cm} : 500\,000\text{ cm}

1\text{ cm} : 5\text{ km}

\mathstrut 4.2\text{ cm} : 4.2 \times 5\text{ km}

4.2\text{ cm} : 21\text{ km}

(c)(ii)Answer:

12\text{ cm} : 1.2\text{ km}

[2]

\mathstrut 1 : 10\,000

\mathstrut 1\text{ cm} : 10\,000\text{ cm}

1\text{ cm} : 0.1\text{ km}

\mathstrut \dfrac{1.2}{0.1}\text{ cm} : 1.2\text{ km}

12\text{ cm} : 1.2\text{ km}

Question 8

(a)(i)Answer:

1 : 1\,000\,000

[2]

\mathstrut 2\text{ cm} : 20\text{ km}

2\text{ cm} : 2\,000\,000\text{ cm}

That is

2 : 2\,000\,000

\mathstrut 1 : \dfrac{2\,000\,000}{2}

1 : 1\,000\,000

(a)(ii)Answer:

1 : 75\,000

[2]

\mathstrut 2\text{ cm} : 1.5\text{ km}

2\text{ cm} : 150\,000\text{ cm}

That is

2 : 150\,000

\mathstrut 1 : \dfrac{150\,000}{2}

1 : 75\,000

(b)(i)Answer:

14.4\text{ cm} : 7.2\text{ km}

[2]

\mathstrut 1 : 50\,000

\mathstrut 1\text{ cm} : 50\,000\text{ cm}

1\text{ cm} : 0.5\text{ km}

\mathstrut \dfrac{7.2}{0.5}\text{ cm} : 7.2\text{ km}

14.4\text{ cm} : 7.2\text{ km}

(b)(ii)Answer:

1.6\text{ cm} : 3.2\text{ m}

[2]

\mathstrut 1 : 200

\mathstrut 1\text{ cm} : 200\text{ cm}

1\text{ cm} : 2\text{ m}

\mathstrut 1.6\text{ cm} : 1.6 \times 2\text{ m}

1.6\text{ cm} : 3.2\text{ m}