This set covers ratio scales, area from a map, contours, gradient and cross-sections. All data are invented for practice, and none of the questions comes from an exam paper.
You do not need a ruler. Every measurement is given, so you can focus on the calculation and the reasoning.
Cover each answer until you have written your own with units on every line. The questions run from easy to harder.
Questions
1. On a 1:50 000 map, a path measures 5.2 cm. Find the real distance in km.
Show answer
5.2 × 50 000 = 260 000 cm = 2 600 m = 2.6 km. Check: 1 cm is 0.5 km, and 5.2 × 0.5 = 2.6.
2. On a 1:25 000 map, a river measures 8 cm. Find the real length in km.
Show answer
8 × 25 000 = 200 000 cm = 2 000 m = 2 km. Check: 1 cm is 0.25 km, and 8 × 0.25 = 2.
3. A coastal road is 7.5 km long. How long is it on a 1:150 000 map?
Show answer
7.5 km = 750 000 cm. 750 000 ÷ 150 000 = 5 cm. Check: 1 cm is 1.5 km, and 7.5 ÷ 1.5 = 5.
4. A map states that 1 cm represents 2 km. Write this as a ratio scale.
Show answer
2 km = 200 000 cm, so the scale is 1:200 000. Check: 1 cm × 200 000 = 200 000 cm = 2 km.
5. On a 1:50 000 map, a lake covers 5 cm². Find its real area in km².
Show answer
1 cm² is 500 m × 500 m = 250 000 m² = 0.25 km². So 5 × 0.25 = 1.25 km². Check: a 5 cm by 1 cm strip is 2.5 km by 0.5 km, and 2.5 × 0.5 = 1.25.
6. A forest covers 9 km². What area in cm² does it cover on a 1:100 000 map?
Show answer
On 1:100 000, 1 cm is 1 km, so 1 cm² is 1 km². The forest covers 9 cm². Check: a 3 km by 3 km square is 3 cm by 3 cm.
7. The contour interval is 20 m. Point X is on the third line above the 100 m line. Find the height of X.
Show answer
Each line adds 20 m: 120, 140, 160. X is at 160 m. Check: 3 × 20 = 60, and 100 + 60 = 160.
8. The ground rises 60 m over a horizontal distance of 1.2 km. Find the gradient as a fraction.
Show answer
1.2 km = 1 200 m. 60 ÷ 1 200 = 1/20, so 1 in 20 (5%). Check: 1 200 ÷ 20 = 60.
9. Points P and Q are at 85 m and 235 m. They are 3 cm apart on a 1:25 000 map. Find the average gradient.
Show answer
Vertical = 235 − 85 = 150 m. Horizontal = 3 × 25 000 = 75 000 cm = 750 m. Gradient = 150 ÷ 750 = 1/5, so 1 in 5 (20%). Check: 750 ÷ 5 = 150.
10. Heights along a line are 50 m, 90 m and 70 m. The axis starts at 30 m and 1 cm stands for 10 m. How high above the axis is each point?
Show answer
Heights above the start are 20 m, 60 m and 40 m. Dividing by 10 gives 2 cm, 6 cm and 4 cm.
11. One slope falls 150 m over 1 500 m and another falls 100 m over 1 500 m. Which is steeper?
Show answer
The first is 150 ÷ 1 500 = 1/10. The second is 100 ÷ 1 500 = 1/15. The first is steeper, since 1/10 is larger than 1/15.
If you got these wrong
- Questions 1 to 4 (distance and scale): revisit converting a map distance, especially the unit steps.
- Questions 5 and 6 (area): go back to why area scales by the square.
- Question 7 (heights): reread reading contours and relative height.
- Questions 8, 9 and 11 (gradient): work through gradient with compatible units.
- Question 10 (plotting): follow drawing a cross-section.
Log each miss in the mistake log and retest queue, then retest it in a few days. The map scale, contour and gradient practice tool and the statistics and distribution explorer give more questions.
Return to the scale, distance and relief module for the study order. If one question type keeps slipping, our teachers can work through it with you in online one-to-one Geography tuition.