Chapter 5 of 15
Chapter 5: Far and Near
दूर और पास (मानचित्र पैमाना, दूरियाँ एवं दिशा ज्ञान) | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Map Scale: A ratio relating distance on a drawing/map to actual ground distance (e.g., 1 cm = 200 m).
- Converting map measurements: Actual Distance = Map Distance in cm × Scale Value.
- Metric length conversions: 1 km = 1,000 m; 1 m = 100 cm.
- Shortest straight path (aerial distance) vs route distance along road turns.
All Textbook Exercises & In-Text Tasks (24 Questions)
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Q1
Scale Conversion • Map to Ground
On a city tourist map, the scale is given as: 1 cm on map = 250 metres on ground.
(a) If the distance between the Museum and the Zoo on the map is 6 cm, find the actual distance on the ground in metres and kilometres.
(b) If two temples are actually 2,000 metres apart, how many centimetres apart will they appear on the map?
[3 Marks]
(a) If the distance between the Museum and the Zoo on the map is 6 cm, find the actual distance on the ground in metres and kilometres.
(b) If two temples are actually 2,000 metres apart, how many centimetres apart will they appear on the map?
✅ Step-by-Step Solution & Working
Scale Conversions (Scale: 1 cm = 250 m):
• (a) Map Distance = 6 cm:
- Actual distance = 6 × 250 m = 1,500 metres.
- In kilometres = 1,500 ÷ 1,000 = 1.5 km.
• (b) Actual Distance = 2,000 m:
- Map distance = 2,000 ÷ 250 = 8 cm on the map.
• (a) Map Distance = 6 cm:
- Actual distance = 6 × 250 m = 1,500 metres.
- In kilometres = 1,500 ÷ 1,000 = 1.5 km.
• (b) Actual Distance = 2,000 m:
- Map distance = 2,000 ÷ 250 = 8 cm on the map.
CBSE Step-by-Step Marking Scheme
Ground distance = 1,500 m = 1.5 km
1.5 M
Map distance = 8 cm
1.5 M
Q2
Multi-Leg Journey on Map Scale
Rahul travels from home to school. On his neighbourhood map (scale 1 cm = 100 m):
• House to Bus stop is 3.5 cm.
• Bus stop to School is 8.5 cm.
(a) Find the total map distance.
(b) Calculate the total real walking distance in metres.
(c) Express the total distance in kilometres.
[3 Marks]
• House to Bus stop is 3.5 cm.
• Bus stop to School is 8.5 cm.
(a) Find the total map distance.
(b) Calculate the total real walking distance in metres.
(c) Express the total distance in kilometres.
✅ Step-by-Step Solution & Working
Calculations:
• (a) Total Map Distance: 3.5 cm + 8.5 cm = 12 cm.
• (b) Real Ground Distance: 12 cm × 100 m = 1,200 metres.
• (c) In Kilometres: 1,200 ÷ 1,000 = 1.2 km.
• (a) Total Map Distance: 3.5 cm + 8.5 cm = 12 cm.
• (b) Real Ground Distance: 12 cm × 100 m = 1,200 metres.
• (c) In Kilometres: 1,200 ÷ 1,000 = 1.2 km.
CBSE Step-by-Step Marking Scheme
Map distance = 12 cm
1.0 M
Ground distance = 1,200 m
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In km = 1.2 km
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Q3
State Highway Map • Large Scale
On a state highway map with a scale of 1 cm = 60 km, City P and City Q are 7.5 cm apart.
(a) What is the actual distance between the two cities?
(b) If an express train covers this distance in 5 hours, what is its average speed?
[3 Marks]
(a) What is the actual distance between the two cities?
(b) If an express train covers this distance in 5 hours, what is its average speed?
✅ Step-by-Step Solution & Working
Calculations:
• (a) Actual Distance: 7.5 cm × 60 km = 450 km.
• (b) Average Speed: Speed = Distance ÷ Time = 450 km ÷ 5 h = 90 km/h.
• (a) Actual Distance: 7.5 cm × 60 km = 450 km.
• (b) Average Speed: Speed = Distance ÷ Time = 450 km ÷ 5 h = 90 km/h.
CBSE Step-by-Step Marking Scheme
Distance = 450 km
1.5 M
Speed = 90 km/h
1.5 M
Q4
Compass Directions & Navigation
Look at the standard compass rose (North at top):
(a) What direction is directly opposite to North-West?
(b) If you walk 4 km South and then 3 km East, in which general direction are you from your starting point?
(c) What is the angle between East and South?
[3 Marks]
(a) What direction is directly opposite to North-West?
(b) If you walk 4 km South and then 3 km East, in which general direction are you from your starting point?
(c) What is the angle between East and South?
✅ Step-by-Step Solution & Working
Compass Directions:
• (a) Opposite to North-West: Directly opposite (180°) is South-East.
• (b) Position: Moving South then East places you in the South-East direction from the starting point.
• (c) Angle East to South: East is 90° and South is 180°, so the angle is 180° - 90° = 90° (Right angle).
• (a) Opposite to North-West: Directly opposite (180°) is South-East.
• (b) Position: Moving South then East places you in the South-East direction from the starting point.
• (c) Angle East to South: East is 90° and South is 180°, so the angle is 180° - 90° = 90° (Right angle).
CBSE Step-by-Step Marking Scheme
Part (a): South-East
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Part (b): South-East
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Part (c): 90° Right angle
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Q5
Grid Coordinate Navigation
A school campus grid map has columns labeled A to F and rows 1 to 6. Each grid square is 50 m × 50 m.
• Library is at (B, 2)
• Canteen is at (E, 2)
(a) How many grid units apart are the Library and Canteen?
(b) What is the real walking distance along the corridor between them?
[3 Marks]
• Library is at (B, 2)
• Canteen is at (E, 2)
(a) How many grid units apart are the Library and Canteen?
(b) What is the real walking distance along the corridor between them?
✅ Step-by-Step Solution & Working
Grid Calculations:
• (a) Grid Units: Both are in Row 2. Difference in columns from B to E: C, D, E = 3 grid units.
• (b) Ground Distance: 3 grid units × 50 m = 150 metres.
• (a) Grid Units: Both are in Row 2. Difference in columns from B to E: C, D, E = 3 grid units.
• (b) Ground Distance: 3 grid units × 50 m = 150 metres.
CBSE Step-by-Step Marking Scheme
Grid units = 3
1.5 M
Real distance = 150 m
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Q6
Perspective Views • Aerial vs Side View
Explain how an aerial view (top view) of a town differs from a side view. Why are geographical maps always drawn from the top view?
[3 Marks]
✅ Step-by-Step Solution & Working
Perspective Comparison:
1. Top View (Aerial View): Shows objects as viewed from directly overhead. Heights of buildings cannot be seen; only flat boundaries, roofs, streets, and footprints are visible.
2. Side View: Shows vertical height and facade of structures, but objects in front hide objects behind them.
3. Why Maps Use Top View: A top view allows accurate 2D geometric scaling, uninterrupted representation of every road, plot, and landmark without foreground objects blocking background buildings.
1. Top View (Aerial View): Shows objects as viewed from directly overhead. Heights of buildings cannot be seen; only flat boundaries, roofs, streets, and footprints are visible.
2. Side View: Shows vertical height and facade of structures, but objects in front hide objects behind them.
3. Why Maps Use Top View: A top view allows accurate 2D geometric scaling, uninterrupted representation of every road, plot, and landmark without foreground objects blocking background buildings.
CBSE Step-by-Step Marking Scheme
Top view shows footprint without vertical blocking
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Maps require uniform 2D coordinate scaling without obstruction
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Q7
Curved Paths • Thread Measurement
How can you measure the length of a winding, curved river shown on a map using a piece of cotton thread and a ruler?
[3 Marks]
✅ Step-by-Step Solution & Working
Thread Measurement Technique:
1. Take a piece of flexible cotton thread and tie a knot at one end.
2. Place the knot at the starting point of the river on the map.
3. Carefully trace the thread along all bends, curves, and meanders of the river until reaching the endpoint.
4. Mark the endpoint on the thread with a pen or pinch it with fingers.
5. Stretch the thread straight along a calibrated centimetre ruler to measure its length.
6. Multiply the thread length in centimetres by the map scale factor to find the real ground length of the river.
1. Take a piece of flexible cotton thread and tie a knot at one end.
2. Place the knot at the starting point of the river on the map.
3. Carefully trace the thread along all bends, curves, and meanders of the river until reaching the endpoint.
4. Mark the endpoint on the thread with a pen or pinch it with fingers.
5. Stretch the thread straight along a calibrated centimetre ruler to measure its length.
6. Multiply the thread length in centimetres by the map scale factor to find the real ground length of the river.
CBSE Step-by-Step Marking Scheme
Correct procedure tracing bends with flexible thread
1.5 M
Measuring straight thread on ruler & applying scale factor
1.5 M
Q8
Shortest Path • Route Planning
On a road map, there are two routes from Town A to Town B:
• Route 1 (Highway): 14 cm on map.
• Route 2 (Bypass): 11 cm on map.
The map scale is 1 cm = 15 km.
(a) Find the actual distance of both routes.
(b) How many kilometres shorter is Route 2?
[3 Marks]
• Route 1 (Highway): 14 cm on map.
• Route 2 (Bypass): 11 cm on map.
The map scale is 1 cm = 15 km.
(a) Find the actual distance of both routes.
(b) How many kilometres shorter is Route 2?
✅ Step-by-Step Solution & Working
Working:
• (a) Real Distances:
- Route 1: 14 × 15 km = 210 km.
- Route 2: 11 × 15 km = 165 km.
• (b) Difference: 210 km - 165 km = 45 km shorter.
• (a) Real Distances:
- Route 1: 14 × 15 km = 210 km.
- Route 2: 11 × 15 km = 165 km.
• (b) Difference: 210 km - 165 km = 45 km shorter.
CBSE Step-by-Step Marking Scheme
Route 1 = 210 km; Route 2 = 165 km
2.0 M
Difference = 45 km
1.0 M
Q9
Map Area Scale • Square Grid
A botanical garden occupies a square region of 4 cm × 4 cm on a map. The map scale is 1 cm = 50 metres.
(a) What are the real length and width of the garden?
(b) Find the actual ground area of the garden in square metres.
[3 Marks]
(a) What are the real length and width of the garden?
(b) Find the actual ground area of the garden in square metres.
✅ Step-by-Step Solution & Working
Area Scaling Calculations:
• (a) Real Dimensions:
- Length = 4 cm × 50 m = 200 metres.
- Width = 4 cm × 50 m = 200 metres.
• (b) Ground Area: Side × Side = 200 m × 200 m = 40,000 sq m.
• (a) Real Dimensions:
- Length = 4 cm × 50 m = 200 metres.
- Width = 4 cm × 50 m = 200 metres.
• (b) Ground Area: Side × Side = 200 m × 200 m = 40,000 sq m.
CBSE Step-by-Step Marking Scheme
Dimensions: 200 m × 200 m
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Area = 40,000 sq m
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Q10
Floor Plan Interpretation
A house floor plan has scale 1 cm = 1 metre. The living room measures 6 cm by 4.5 cm on the blueprint.
(a) What are the actual dimensions of the living room?
(b) What is its floor area in square metres?
(c) If flooring costs ₹120 per sq m, find the total cost of tiling the room.
[3 Marks]
(a) What are the actual dimensions of the living room?
(b) What is its floor area in square metres?
(c) If flooring costs ₹120 per sq m, find the total cost of tiling the room.
✅ Step-by-Step Solution & Working
Calculations:
• (a) Dimensions: Length = 6 m, Breadth = 4.5 m.
• (b) Floor Area: 6 m × 4.5 m = 27 sq m.
• (c) Tiling Cost: 27 sq m × ₹120 = ₹3,240.
• (a) Dimensions: Length = 6 m, Breadth = 4.5 m.
• (b) Floor Area: 6 m × 4.5 m = 27 sq m.
• (c) Tiling Cost: 27 sq m × ₹120 = ₹3,240.
CBSE Step-by-Step Marking Scheme
Dimensions: 6 m by 4.5 m
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Area = 27 sq m
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Cost = ₹3,240
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Q11
Map Enlargement & Reduction
A square park has side 2 cm on Map 1 (scale 1 cm = 100 m). If the same park is redrawn on Map 2 with scale 1 cm = 50 m:
(a) What will be the side length of the park on Map 2?
(b) How many times larger will the area of the drawing appear on Map 2?
[3 Marks]
(a) What will be the side length of the park on Map 2?
(b) How many times larger will the area of the drawing appear on Map 2?
✅ Step-by-Step Solution & Working
Scale Analysis:
• Real side of park = 2 cm × 100 m = 200 metres.
• (a) Side on Map 2: 200 m ÷ 50 m = 4 cm.
• (b) Area Comparison on Paper:
- Map 1 area = 2 cm × 2 cm = 4 cm².
- Map 2 area = 4 cm × 4 cm = 16 cm².
- Ratio = 16 ÷ 4 = 4 times larger.
• Real side of park = 2 cm × 100 m = 200 metres.
• (a) Side on Map 2: 200 m ÷ 50 m = 4 cm.
• (b) Area Comparison on Paper:
- Map 1 area = 2 cm × 2 cm = 4 cm².
- Map 2 area = 4 cm × 4 cm = 16 cm².
- Ratio = 16 ÷ 4 = 4 times larger.
CBSE Step-by-Step Marking Scheme
Side on Map 2 = 4 cm
1.5 M
Area is 4 times larger on paper
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Q12
India Map • Border State Directions
Refer to an outline map of India:
(a) In which direction from New Delhi is Kerala located?
(b) In which direction from New Delhi is Assam located?
(c) Which sea lies to the West of India?
[3 Marks]
(a) In which direction from New Delhi is Kerala located?
(b) In which direction from New Delhi is Assam located?
(c) Which sea lies to the West of India?
✅ Step-by-Step Solution & Working
Geographical Directions:
• (a) Kerala from Delhi: Kerala lies directly towards the South.
• (b) Assam from Delhi: Assam lies towards the East (North-East).
• (c) Sea to the West: The Arabian Sea lies to the West of the Indian peninsula.
• (a) Kerala from Delhi: Kerala lies directly towards the South.
• (b) Assam from Delhi: Assam lies towards the East (North-East).
• (c) Sea to the West: The Arabian Sea lies to the West of the Indian peninsula.
CBSE Step-by-Step Marking Scheme
Kerala: South
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Assam: East / North-East
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Arabian Sea
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Q13
Speed-Distance-Scale Problem
A cyclist travels along a straight highway at 15 km/h. On his roadmap, the highway has a scale of 1 cm = 5 km.
(a) How many kilometres does he cycle in 2 hours?
(b) How many centimetres of map distance does his 2-hour ride represent?
[3 Marks]
(a) How many kilometres does he cycle in 2 hours?
(b) How many centimetres of map distance does his 2-hour ride represent?
✅ Step-by-Step Solution & Working
Working:
• (a) Distance Covered: 15 km/h × 2 h = 30 km.
• (b) Map Distance: 30 km ÷ 5 km/cm = 6 cm on the map.
• (a) Distance Covered: 15 km/h × 2 h = 30 km.
• (b) Map Distance: 30 km ÷ 5 km/cm = 6 cm on the map.
CBSE Step-by-Step Marking Scheme
Distance = 30 km
1.5 M
Map distance = 6 cm
1.5 M
Q14
Perimeter on a Grid Map
A jogging track on a park grid map follows the boundary: 6 grid units North, 8 grid units East, 6 grid units South, and 8 grid units West.
(a) What shape is the jogging track?
(b) If 1 grid unit = 25 metres, find the total perimeter of the track in metres.
[3 Marks]
(a) What shape is the jogging track?
(b) If 1 grid unit = 25 metres, find the total perimeter of the track in metres.
✅ Step-by-Step Solution & Working
Geometry & Scale:
• (a) Shape: Opposite sides are equal (6 and 8 units) and meet at right angles → Rectangle.
• (b) Perimeter:
- Total grid units = 6 + 8 + 6 + 8 = 28 units.
- Real perimeter = 28 × 25 m = 700 metres.
• (a) Shape: Opposite sides are equal (6 and 8 units) and meet at right angles → Rectangle.
• (b) Perimeter:
- Total grid units = 6 + 8 + 6 + 8 = 28 units.
- Real perimeter = 28 × 25 m = 700 metres.
CBSE Step-by-Step Marking Scheme
Shape = Rectangle
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Total units = 28
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Perimeter = 700 metres
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Q15
Reading a Legend / Key on a Map
What is a 'Legend' or 'Key' on a geographical map? List three common symbols typically used on school or city maps.
[3 Marks]
✅ Step-by-Step Solution & Working
Map Legend:
1. Definition: A map legend (or key) is an explanatory box that explains the meaning of various colours, signs, and symbols used on the map.
2. Common Symbols:
• Blue lines/areas: Rivers, canals, or water bodies.
• Black parallel lines with cross-ties: Railway tracks.
• Red cross (+): Hospital or clinic.
• Small flag or building: School.
1. Definition: A map legend (or key) is an explanatory box that explains the meaning of various colours, signs, and symbols used on the map.
2. Common Symbols:
• Blue lines/areas: Rivers, canals, or water bodies.
• Black parallel lines with cross-ties: Railway tracks.
• Red cross (+): Hospital or clinic.
• Small flag or building: School.
CBSE Step-by-Step Marking Scheme
Clear definition of map legend
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Three accurate symbol examples
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Q16
Compass Angles • Half Cardinal Directions
Between North and East lies North-East.
(a) What angle does North-East make with North?
(b) What angle does North-East make with East?
(c) What is the angle between North-East and South-West?
[3 Marks]
(a) What angle does North-East make with North?
(b) What angle does North-East make with East?
(c) What is the angle between North-East and South-West?
✅ Step-by-Step Solution & Working
Angle Calculations:
• (a) North to North-East: 90° ÷ 2 = 45°.
• (b) North-East to East: 90° ÷ 2 = 45°.
• (c) North-East to South-West: They are directly opposite directions along a straight line = 180° (Straight angle).
• (a) North to North-East: 90° ÷ 2 = 45°.
• (b) North-East to East: 90° ÷ 2 = 45°.
• (c) North-East to South-West: They are directly opposite directions along a straight line = 180° (Straight angle).
CBSE Step-by-Step Marking Scheme
Part (a): 45°
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Part (b): 45°
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Part (c): 180°
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Q17
River Bridge Crossing • Scale Calculation
A major river bridge measures 2.4 cm on a satellite map (scale 1 cm = 500 m).
(a) What is the actual length of the bridge in metres?
(b) Express this length in kilometres.
(c) A car crosses this bridge at 60 km/h. How many seconds does it take to cross?
[3 Marks]
(a) What is the actual length of the bridge in metres?
(b) Express this length in kilometres.
(c) A car crosses this bridge at 60 km/h. How many seconds does it take to cross?
✅ Step-by-Step Solution & Working
Step-by-Step Working:
• (a) Actual Length: 2.4 cm × 500 m = 1,200 metres.
• (b) In Kilometres: 1,200 ÷ 1,000 = 1.2 km.
• (c) Crossing Time:
- Speed = 60 km/h = (60 × 1,000) ÷ 3,600 = 16.67 m/s.
- Time = Distance ÷ Speed = 1,200 m ÷ 16.67 m/s = 72 seconds (1 minute 12 seconds).
• (a) Actual Length: 2.4 cm × 500 m = 1,200 metres.
• (b) In Kilometres: 1,200 ÷ 1,000 = 1.2 km.
• (c) Crossing Time:
- Speed = 60 km/h = (60 × 1,000) ÷ 3,600 = 16.67 m/s.
- Time = Distance ÷ Speed = 1,200 m ÷ 16.67 m/s = 72 seconds (1 minute 12 seconds).
CBSE Step-by-Step Marking Scheme
Length = 1,200 m = 1.2 km
1.5 M
Crossing time = 72 seconds
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Q18
Grid Coordinate Distance • Manhattan Distance
On a city grid where roads only run along North-South and East-West grid lines:
Point A is at (1, 1) and Point B is at (5, 4). Each grid unit is 200 metres.
(a) How many units East must one travel?
(b) How many units North must one travel?
(c) What is the total real travel distance along the streets?
[3 Marks]
Point A is at (1, 1) and Point B is at (5, 4). Each grid unit is 200 metres.
(a) How many units East must one travel?
(b) How many units North must one travel?
(c) What is the total real travel distance along the streets?
✅ Step-by-Step Solution & Working
Grid Street Distance:
• (a) East Units: 5 - 1 = 4 units East.
• (b) North Units: 4 - 1 = 3 units North.
• (c) Total Travel Distance:
- Total grid units = 4 + 3 = 7 units.
- Real distance = 7 × 200 m = 1,400 metres (1.4 km).
• (a) East Units: 5 - 1 = 4 units East.
• (b) North Units: 4 - 1 = 3 units North.
• (c) Total Travel Distance:
- Total grid units = 4 + 3 = 7 units.
- Real distance = 7 × 200 m = 1,400 metres (1.4 km).
CBSE Step-by-Step Marking Scheme
4 units East, 3 units North
1.5 M
Total real distance = 1,400 m
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Q19
HOTS • Map Scale Riddle
On Map X, two cities are 8 cm apart. On Map Y, the same two cities are 4 cm apart. The scale of Map X is 1 cm = 20 km. What is the scale of Map Y?
[3 Marks]
✅ Step-by-Step Solution & Working
Deduction:
1. Actual Ground Distance: From Map X: 8 cm × 20 km = 160 km.
2. Scale of Map Y: On Map Y, 4 cm represents 160 km.
3. Therefore, 1 cm on Map Y represents: 160 km ÷ 4 = 40 km.
Scale of Map Y: 1 cm = 40 km.
1. Actual Ground Distance: From Map X: 8 cm × 20 km = 160 km.
2. Scale of Map Y: On Map Y, 4 cm represents 160 km.
3. Therefore, 1 cm on Map Y represents: 160 km ÷ 4 = 40 km.
Scale of Map Y: 1 cm = 40 km.
CBSE Step-by-Step Marking Scheme
Ground distance = 160 km
1.5 M
Scale of Map Y = 1 cm = 40 km
1.5 M
Q20
Aerial Map Scale Comparison
A circular stadium has diameter 150 metres on the ground.
(a) What diameter will it have on a blueprint with scale 1 cm = 25 m?
(b) What diameter will it have on a city map with scale 1 cm = 50 m?
[3 Marks]
(a) What diameter will it have on a blueprint with scale 1 cm = 25 m?
(b) What diameter will it have on a city map with scale 1 cm = 50 m?
✅ Step-by-Step Solution & Working
Scaling:
• (a) Blueprint (1 cm = 25 m): 150 ÷ 25 = 6 cm.
• (b) City Map (1 cm = 50 m): 150 ÷ 50 = 3 cm.
• (a) Blueprint (1 cm = 25 m): 150 ÷ 25 = 6 cm.
• (b) City Map (1 cm = 50 m): 150 ÷ 50 = 3 cm.
CBSE Step-by-Step Marking Scheme
Blueprint = 6 cm
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City map = 3 cm
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Q21
Scale Factor • Mathematical Definition
(a) What is meant by the 'scale of a map'?
(b) If a map scale says '1:100,000', what does 1 cm on the map represent in kilometres on the ground?
[3 Marks]
(b) If a map scale says '1:100,000', what does 1 cm on the map represent in kilometres on the ground?
✅ Step-by-Step Solution & Working
Scale Concepts:
• (a) Definition: The scale of a map is the constant ratio between the distance measured on the map and the corresponding actual distance measured on the ground.
• (b) Ratio 1:100,000:
- 1 cm on map = 100,000 cm on ground.
- 100,000 cm ÷ 100 = 1,000 metres.
- 1,000 m = 1 kilometre.
- So 1 cm on the map represents exactly 1 km on the ground.
• (a) Definition: The scale of a map is the constant ratio between the distance measured on the map and the corresponding actual distance measured on the ground.
• (b) Ratio 1:100,000:
- 1 cm on map = 100,000 cm on ground.
- 100,000 cm ÷ 100 = 1,000 metres.
- 1,000 m = 1 kilometre.
- So 1 cm on the map represents exactly 1 km on the ground.
CBSE Step-by-Step Marking Scheme
Definition of scale
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100,000 cm = 1 km
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Q22
Elevation Contours & Topography
On a topographical relief map, contour lines indicate height above sea level.
(a) What does it mean when contour lines are drawn very close to each other?
(b) What does it mean when contour lines are far apart?
[3 Marks]
(a) What does it mean when contour lines are drawn very close to each other?
(b) What does it mean when contour lines are far apart?
✅ Step-by-Step Solution & Working
Contour Line Principles:
• (a) Close Contour Lines: Indicate a steep slope or cliff, where the elevation changes rapidly over a very short horizontal ground distance.
• (b) Far Apart Contour Lines: Indicate a gentle slope or flat plain, where elevation changes very gradually over a long distance.
• (a) Close Contour Lines: Indicate a steep slope or cliff, where the elevation changes rapidly over a very short horizontal ground distance.
• (b) Far Apart Contour Lines: Indicate a gentle slope or flat plain, where elevation changes very gradually over a long distance.
CBSE Step-by-Step Marking Scheme
Close lines = Steep slope
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Far lines = Gentle slope / Flat terrain
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Q23
True or False with Map Reasoning
State True or False with reasoning:
(a) A map scale of 1 cm = 10 km represents a larger area than a scale of 1 cm = 100 m on the same size sheet of paper.
(b) East is always 180° clockwise from North.
(c) The top of every official map is always oriented toward North.
[3 Marks]
(a) A map scale of 1 cm = 10 km represents a larger area than a scale of 1 cm = 100 m on the same size sheet of paper.
(b) East is always 180° clockwise from North.
(c) The top of every official map is always oriented toward North.
✅ Step-by-Step Solution & Working
Justifications:
• (a) True: At 1 cm = 10 km, each centimetre covers 10,000 metres of ground, so the same paper sheet covers a vastly larger geographic territory (small-scale map).
• (b) False: East is 90° clockwise from North (180° clockwise is South).
• (c) True: By international cartographic standard convention, the top edge of a map points toward true North (unless explicitly indicated otherwise by a north arrow).
• (a) True: At 1 cm = 10 km, each centimetre covers 10,000 metres of ground, so the same paper sheet covers a vastly larger geographic territory (small-scale map).
• (b) False: East is 90° clockwise from North (180° clockwise is South).
• (c) True: By international cartographic standard convention, the top edge of a map points toward true North (unless explicitly indicated otherwise by a north arrow).
CBSE Step-by-Step Marking Scheme
Part (a): True with explanation
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Part (b): False (East is 90°)
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Part (c): True with standard convention
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Q24
Comprehensive Map Review • Town Tour
A delivery van starts at Central Depot (0, 0). It travels 4 km North to Station 1, then 3 km East to Station 2, then 4 km South to Station 3.
(a) Plot or describe the coordinates of Station 1, Station 2, and Station 3.
(b) In which direction and at what distance is Station 3 from the Central Depot?
(c) What shape is formed by the complete delivery path if the van returns directly from Station 3 to the Central Depot?
[3 Marks]
(a) Plot or describe the coordinates of Station 1, Station 2, and Station 3.
(b) In which direction and at what distance is Station 3 from the Central Depot?
(c) What shape is formed by the complete delivery path if the van returns directly from Station 3 to the Central Depot?
✅ Step-by-Step Solution & Working
Comprehensive Route Analysis:
• (a) Coordinates:
- Depot: (0, 0)
- Station 1: 4 km North → (0, 4)
- Station 2: 3 km East → (3, 4)
- Station 3: 4 km South → (3, 0).
• (b) Relative Position of Station 3: Station 3 is at (3, 0), which is exactly 3 km East of Central Depot.
• (c) Path Shape: The path goes North (4 km), East (3 km), South (4 km), and West back to depot (3 km). This forms a perfect Rectangle (4 km × 3 km) with perimeter = 4 + 3 + 4 + 3 = 14 km.
• (a) Coordinates:
- Depot: (0, 0)
- Station 1: 4 km North → (0, 4)
- Station 2: 3 km East → (3, 4)
- Station 3: 4 km South → (3, 0).
• (b) Relative Position of Station 3: Station 3 is at (3, 0), which is exactly 3 km East of Central Depot.
• (c) Path Shape: The path goes North (4 km), East (3 km), South (4 km), and West back to depot (3 km). This forms a perfect Rectangle (4 km × 3 km) with perimeter = 4 + 3 + 4 + 3 = 14 km.
CBSE Step-by-Step Marking Scheme
Correct coordinates: (0,4), (3,4), (3,0)
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Station 3 is 3 km East of Depot
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Shape is Rectangle (4 km × 3 km)
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🌟 NEP 2020 Competency-Based Case Study
Competency Question: Hiking Trail Map Interpretation
On a hiking map of a nature sanctuary, 1 cm = 400 metres. The trek comprises three sections: Valley Trail = 3.5 cm; Ridge Walk = 4.2 cm; Lake Loop = 2.8 cm.
Analytical Task: (a) Find the total length of the trek on the ground in kilometres.
(b) If a hiker walks at an average speed of 3.5 km/h, how long will the entire hike take?
(b) If a hiker walks at an average speed of 3.5 km/h, how long will the entire hike take?
Evaluation & Model Answer:
Suggested Model Solution:
(a) Total Distance: Total map = 3.5 + 4.2 + 2.8 = 10.5 cm.
Actual = 10.5 × 400 m = 4,200 m = 4.2 km.
Actual = 10.5 × 400 m = 4,200 m = 4.2 km.
(b) Hike Duration: 4.2/3.5 = 1.2 hours = 1 hour 12 minutes.
Rubric: 1M concept identification + 1M step execution + 1M conclusion