Exam-useful questions from this chapter, grouped by marks, each with a full model answer. Try writing the answer yourself first, then check it against this one.
1 1-Mark Questions
Q. Define map scale in one line.
Answer: Map scale is the ratio between the distance measured between any two points on a map and the actual distance between those same two points on the ground.
Q. What does the ‘Numerator’ represent in the Representative Fraction?
Answer: In the Representative Fraction, the numerator (the number above the line in the fraction, always 1 unit) represents the distance given on the map, e.g. the ‘1’ in 1:50,000.
Q. What does the ‘Denominator’ represent in the Representative Fraction?
Answer: In the Representative Fraction, the denominator (the number below the line in the fraction) represents the actual ground distance in that same number of units, e.g. the ‘50,000’ in 1:50,000.
Q. Which method of scale is called the universal method, and why?
Answer: The Representative Fraction (R.F.) is called the universal method, because it does not mention any unit, so it can be read after converting it into any system of measurement.
Q. What is a network of lines and polygons drawn without a scale called?
Answer: It is called a sketch, not a map. Scale is an essential element of a map.
Q. How many inches make one mile?
Answer: One mile equals 63,360 inches (8 furlongs × 220 yards × 3 feet × 12 inches).
2 2-Mark Questions
Q. What are the two different systems of measurement?
Answer: The first is the Metric System, which uses the units kilometre, metre, centimetre and millimetre. The second is the English System, which uses the units mile, furlong, yard and foot. India adopted the Metric System after 1957.
Q. Name the three methods of expressing scale.
Answer: The three methods of expressing scale are: (1) Statement of Scale, (2) Graphical or Bar Scale, and (3) Representative Fraction (R.F.).
Q. State one major limitation of the Statement of Scale.
Answer: Its major limitation is that it can be understood only by someone familiar with that same system of measurement, and if the map is enlarged or reduced, its scale becomes invalid and a new scale has to be worked out.
Q. State one major advantage of the Graphical Scale.
Answer: Its major advantage is that it remains valid even when the map is enlarged or reduced, because being a line, it enlarges or reduces along with the map itself.
Q. Why is the Representative Fraction called a universal method?
Answer: Because it does not mention the unit of scale, the same R.F. (say, 1:36,000) can be correctly read by a person familiar with the Metric System in centimetres and by a person familiar with the English System in inches, both readings are equally correct, which is what makes it universal.
Q. What is the main difference between a sketch and a map?
Answer: A map carries a scale, which allows the distances shown on it to be related to actual ground distances; a sketch carries no scale at all, it is merely a network of lines and polygons without one.
Q. 5 cm represents 12.5 km. Convert this statement of scale into a Representative Fraction.
Answer: 12.5 km = 1,250,000 cm (12.5×100,000). This distance is represented by 5 cm, so 1 cm = 1,250,000/5 = 250,000 cm. Therefore R.F. = 1:250,000.
3 4-Mark Questions
Q. Compare the three methods of scale, giving one advantage and one limitation of each.
Answer: (1) Statement of Scale: advantage, the simplest method, explained in a written sentence; limitation, understood only by someone familiar with that system of measurement, and it becomes invalid when the map is enlarged or reduced. (2) Graphical/Bar Scale: advantage, remains valid even when the map is enlarged or reduced; limitation, still useful only to those familiar with the unit marked on it. (3) Representative Fraction: advantage, being unit-free, it is universally valid and considered the most suitable method; limitation, the book names none separately; it only has to be converted into one’s own system (cm or inch) before a distance is read.
Q. Explain the method of converting a Statement of Scale into a Representative Fraction, with a new example: convert ‘3 inches represents 6 miles’ into R.F.
Answer: A distance of 3 inches on the map represents a ground distance of 6 miles. First, convert miles into inches: 6 miles = 6 × 63,360 = 380,160 inches. So 3 inches represents 380,160 inches of ground distance, hence 1 inch = 380,160/3 = 126,720 inches. Replacing ‘inch’ with ‘unit’, the Representative Fraction = 1:126,720.
Q. Explain the method of converting a Representative Fraction into a Statement of Scale, with a new example: convert R.F. 1:75,000 into a Metric statement of scale.
Answer: R.F. 1:75,000 means 1 cm on the map represents 75,000 cm of ground distance. To convert this into kilometres, divide 75,000 by 100,000 (the number of centimetres in a km): 75,000/100,000 = 0.75 km. So the statement of scale is: ‘1 cm represents 0.75 km’.
Q. Explain the universal nature of the Representative Fraction with a new example (R.F. 1:100,000).
Answer: A person familiar with the Metric System will read R.F. 1:100,000 in centimetres: 1 cm on the map equals 100,000 cm on the ground, i.e. ‘1 cm represents 1 km’ (dividing 100,000 by 100,000). A person familiar with the English System will read the same scale in inches: 1 inch on the map equals 100,000 inches on the ground, i.e. 100,000/63,360 ≈ 1.58 miles. Both readings of the same R.F. are equally correct: this is what universality means.
Q. Explain the geometric method of dividing a line of unequal length into N equal parts.
Answer: First, the line of unequal length is drawn. Then, from both its ends (start and finish), two auxiliary lines are drawn at a convenient angle of 40° or 45°. Starting from the same end, N equal small divisions (such as 1 or 1.5 inches each) are marked on these auxiliary lines. Finally, the corresponding division points on the two auxiliary lines are joined with straight lines; wherever these joining lines cut the original unequal line, they mark it into N equal parts.
Q. Explain the importance and definition of map scale.
Answer: Scale is an essential element of every kind of map. A network of lines and polygons drawn without a scale is called merely a sketch, not a map. Scale shows the relationship between the map and the whole or a part of the earth’s surface it depicts, expressed as the ratio between the distance between any two points on the map and the actual distance between the same two points on the ground. This ratio is what makes it possible to correctly work out areas and distances from a map.
Q. Give another example of converting a Statement of Scale into a Representative Fraction: convert ‘2 cm represents 8 km’ into R.F.
Answer: 8 km = 800,000 cm (8×100,000). This distance is represented by 2 cm, so 1 cm = 800,000/2 = 400,000 cm. Therefore R.F. = 1:400,000.
Q. Give an example of converting a Representative Fraction into a Statement of Scale (English System): convert R.F. 1:126,720 into miles.
Answer: R.F. 1:126,720 means 1 inch on the map represents 126,720 inches of ground distance. To convert this into miles, divide 126,720 by 63,360 (the number of inches in a mile): 126,720/63,360 = 2. So the statement of scale is: ‘1 inch represents 2 miles’.
Q. Choosing any two of the three methods of scale, state which of their scales would remain correct if a given map were photocopied at a 50% reduction, and why.
Answer: The Graphical (bar) scale would still remain correct, because being a line, it would shrink along with the photocopy in the same proportion, so its reading would still be accurate. The Statement of Scale, on the other hand (e.g. ‘1 cm represents 10 km’), would become wrong, because the actual distance shown on the map has now been halved but the written statement stays the old one, so a new scale would have to be worked out.
4 6-Mark Questions
Q. For R.F. 1:25,000, explain with a worked example the construction of a Graphical Scale readable in kilometres and metres.
Answer: R.F. 1:25,000 means that 1 unit of distance on the map represents 25,000 units on the ground, i.e. 1 cm represents 25,000 cm. Taking a conventional length of about 15 cm: 15 cm = 25,000×15/100,000 = 3.75 km. Since 3.75 is not a round number, the nearest round number, 4 km, is taken. The new length of the line for 4 km: 15×4/3.75 = 16 cm. Construction: draw a straight line of 16 cm and divide it into 4 equal main parts; leaving out one main part on the left, mark the remaining parts starting from 0 towards the right, each valued at 1 km; divide the left part into 10 equal sub-divisions, each valued at 100 m.
Q. Given the statement of scale ‘1 inch = 2 miles’, explain with a worked example the construction of a Graphical Scale readable in miles and furlongs.
Answer: By convention, a length of about 6 inches is taken for an English-unit reading. Since 1 inch = 2 miles, 6 inches will represent 12 miles. Construction: draw a straight line of 6 inches and divide it into 6 equal parts; give each of the 5 right-hand divisions a value of 2 miles (so 10 miles can be read on the right). Divide the left-hand part (equal to 2 miles, i.e. 16 furlongs) into 8 equal sub-divisions, and starting from 0, give each sub-division a value of 2 furlongs. This way, whole miles can be read on the right and furlongs on the left.
Q. Given R.F. 1:126,720, explain with a worked example the construction of a Graphical Scale for reading distances in miles and furlongs.
Answer: R.F. 1:126,720 means 1 inch = 126,720 inches of ground distance. Taking a conventional length of 6 inches: 6 inches = 126,720×6/63,360 = 12 miles (since 1 mile = 63,360 inches). 12 is already a round number, so no change of length is needed. Construction: draw a line of 6 inches and divide it into 6 equal parts; give each of the 5 right-hand divisions a value of 2 miles (10 of the 12 miles read on the right, the rest of the precision coming from the left part). Divide the left part (2 miles) into 8 sub-divisions, giving each a value of 2 furlongs. Where an unequal length results instead (as in Problem 3 of the chapter), the 40°/45°-angle geometric method is used to divide the line into equal parts.
Q. Compare the three methods of map scale using one example. Suppose a distance of 1 cm on a map represents a ground distance of 5 km. How would each of the three methods express this?
Answer: (1) Statement of Scale: ‘1 centimetre represents 5 kilometres’, a direct written sentence, simple to understand but invalid if the map is enlarged or reduced. (2) Graphical Scale: a horizontal line would be drawn and marked with main and sub-divisions such that each unit length of the line reads 5 km; being self-scaling with the map, it always stays valid. (3) Representative Fraction: 5 km = 500,000 cm, so R.F. = 1:500,000; being unit-free, it can be read in any system of measurement, and is considered the most universal. All three express the same scale in different forms, each suited to a different context of use.
5 Case Studies
(A) 1 mark Explain what R.F. 1:200,000 means.
Answer: It means that 1 unit (centimetre) of the given distance on the map represents 200,000 units (centimetres) of the same distance on the ground.
(B) 2 marks Find the actual ground distance between villages A and B, in kilometres.
Answer: The map distance is 8 cm. Ground distance = 8 × 200,000 = 1,600,000 cm. Converting this into kilometres by dividing by 100,000: 1,600,000/100,000 = 16 km. So the actual distance is 16 km.
(C) 2 marks Convert this R.F. into a Metric statement of scale.
Answer: R.F. 1:200,000 means 1 cm = 200,000 cm. Converting into kilometres: 200,000/100,000 = 2. So the statement of scale is: ‘1 centimetre represents 2 kilometres’.
(D) 4 marks If the student wanted to construct a Graphical Scale for this same map, readable in kilometres and metres, what steps would they follow? Explain briefly.
Answer: Taking a conventional length of about 15 cm: 15 cm = 200,000×15/100,000 = 30 km. Since 30 is already a round number, there is no need to change the length of the line. Draw a straight line of 15 cm and divide it into 3 equal main parts (10 km each); leaving out one main part on the left, mark the remaining parts starting from 0 towards the right, each valued at 10 km; divide the left part into 10 sub-divisions, each valued at 1 km (= 1,000 m), starting from 0. At this scale 1 km is only 0.5 cm long, so the smallest reading on this bar is 1 km (1,000 m); to read 500 m, each of these sub-divisions can be halved.
(A) 2 marks Convert this statement of scale into a Representative Fraction (R.F.).
Answer: 1 mile = 63,360 inches, so 4 miles = 4×63,360 = 253,440 inches. 1 inch on the map represents a ground distance of 253,440 inches. Replacing ‘inch’ with ‘unit’, R.F. = 1:253,440.
(B) 2 marks Based on this statement of scale, can the map’s original Graphical Scale be reconstructed? Give a reason for your answer.
Answer: Yes, it can be reconstructed, because the three methods of scale are mutually convertible: the R.F. can first be worked out from the statement (as done above), and using that same information, taking a suitable length by convention, a new Graphical Scale can be constructed that will be equivalent to the original one.
(C) 4 marks Explain the method of constructing a new Graphical Scale readable in miles and furlongs from this statement of scale (‘1 inch = 4 miles’).
Answer: By convention, a length of about 6 inches can be taken for an English-unit reading. Since 1 inch = 4 miles, 6 inches will represent 24 miles. For convenience, the 6-inch line can be divided into 6 equal parts, with each of the 5 right-hand divisions given a value of 4 miles (so 20 miles can be read on the right). The left-hand part (4 miles, i.e. 32 furlongs) can be divided into 8 sub-divisions, each given a value of 4 furlongs, giving furlong-level precision on the left.