11+ Maths: Measurements

Measurements are essential in mathematics, allowing us to quantify and compare physical quantities such as length, mass, volume, time, and temperature. Understanding measurements is crucial for solving problems in everyday life and is a significant topic in the 11+ exam.

Key Concepts in Measurements

1. Units of Measurement

Different types of measurements use various units:

• Length: Measured in millimetres (mm), centimetres (cm), metres (m), and kilometres (km).
• Mass: Measured in grams (g) and kilograms (kg).
• Volume: Measured in millilitres (ml) and litres (l).
• Time: Measured in seconds (s), minutes (min), and hours (h).
• Temperature: Measured in degrees Celsius (°C) or Fahrenheit (°F).

2. Conversions

Understanding how to convert between different units is essential. For example:

• To convert from metres to centimetres, multiply by 100 (1 m = 100 cm).
• To convert from kilograms to grams, multiply by 1000 (1 kg = 1000 g).

3. Perimeter, Area, and Volume

• Perimeter: The total distance around a shape. For example, the perimeter of a rectangle is calculated as:
  $$\text{Perimeter} = 2 \times (\text{length} + \text{width})$$
• Area: The space inside a shape. For a rectangle, the area is:
  $$\text{Area} = \text{length} \times \text{width}$$
• Volume: The space inside a 3D object. For a cube, the volume is:
  $$\text{Volume} = \text{side}^3$$

4. Estimating Measurements

Estimating measurements can help in making quick calculations without precise tools. This skill is useful in practical scenarios.

5. Reading Scales

Understanding how to read different types of scales, such as rulers, weighing scales, and measuring cups, is vital for accurate measurements.

Practice Questions on Measurements

Easy Level

1. How many centimetres are in 1 metre?
2. Convert 500 grams to kilograms.
3. If a pencil is 15 cm long, what is its length in millimetres?
4. What is the perimeter of a rectangle with a length of 4 cm and a width of 3 cm?
5. Calculate the area of a rectangle with a length of 5 cm and a width of 2 cm.
6. How many litres are in 3000 millilitres?
7. Convert 2.5 kg to grams.
8. If a book is 20 cm wide and 30 cm long, what is its area?
9. How many seconds are in 3 minutes?
10. What is the volume of a cube with a side length of 2 cm?
11. If a bottle contains 1.5 litres of water, how many millilitres is that?
12. Convert 1500 ml to litres.
13. If a classroom is 10 m long and 8 m wide, what is its perimeter?
14. How many grams are in 2.2 kg?
15. If a toy car is 10 cm long, what is its length in millimetres?
16. Calculate the area of a square with a side length of 4 cm.
17. How many minutes are in 2 hours?
18. What is the weight in grams of a 5 kg bag?
19. If a field is 50 m long and 20 m wide, what is its area?
20. How many millilitres are in 1.2 litres?

Medium Level

1. If a box has dimensions of 2 m by 3 m by 4 m, what is its volume?
2. Convert 3.5 litres to millilitres.
3. If a bottle contains 600 ml of juice, how many litres is that?
4. A rectangle has a length of 8 cm and a width of 3 cm. What is its perimeter?
5. How many grams are in 4.5 kg?
6. If a classroom is 12 m long and 10 m wide, what is its area?
7. Convert 2000 ml to litres.
8. If a fruit weighs 150 g, what is its weight in kilograms?
9. Calculate the perimeter of a square with a side length of 5 cm.
10. If a container holds 750 ml, how many litres is that?
11. What is the volume of a cylinder with a radius of 3 cm and a height of 5 cm (use $$\pi \approx 3.14$$ )?
12. If a pencil is 18 cm long, what is its length in millimetres?
13. How many minutes are in 1 hour and 45 minutes?
14. If a rectangle has a perimeter of 30 cm and a length of 10 cm, what is its width?
15. Calculate the area of a triangle with a base of 10 cm and a height of 6 cm.
16. How many grams are in 2.5 kg?
17. If a car travels 120 km in 2 hours, what is its average speed in km/h?
18. A piece of paper measures 21 cm by 29.7 cm. What is its area?
19. If a swimming pool is 25 m long and 10 m wide, what is its volume if the depth is 2 m?
20. Convert 150 cm to metres.

Hard Level

1. A rectangular prism has a length of 5 m, a width of 3 m, and a height of 2 m. What is its volume?
2. If a cake recipe requires 250 ml of milk and you want to make half the recipe, how much milk do you need?
3. Convert 1.8 litres to millilitres.
4. If a classroom is 9 m long and 6 m wide, what is its area?
5. A box has a length of 8 cm, a width of 4 cm, and a height of 3 cm. What is its volume?
6. If a car travels 150 km in 1.5 hours, what is its average speed in km/h?
7. A swimming pool holds 5000 litres of water. How many millilitres is that?
8. If a recipe requires 300 g of sugar for 5 servings, how much sugar is needed for 8 servings?
9. If a piece of wood is 2.5 m long, how many centimetres is that?
10. Convert 7.5 kg to grams.
11. If a bottle contains 1.2 litres, how many cups of water can it fill if 1 cup is 250 ml?
12. A garden is 10 m long and 4 m wide. What is its perimeter?
13. If a recipe calls for 4 cups of flour and you have 1 cup, how many more cups do you need?
14. How many grams are in 0.75 kg?
15. A cylinder has a radius of 2 cm and a height of 10 cm. What is its volume (use $$\pi \approx 3.14$$ )?
16. If a piece of ribbon is 150 cm long, how many metres is that?
17. A box has a length of 12 cm, a width of 5 cm, and a height of 4 cm. What is its volume?
18. If a fruit basket contains 5 apples, 7 oranges, and 3 bananas, what percentage are apples?
19. If a swimming pool has a volume of 2500 litres, how many millilitres is that?
20. A recipe requires 1.5 litres of milk. How many millilitres is that?

Answers and Explanations

Easy Level

1. $$100 \text{ cm}$$
2. $$500 \text{ g} = 0.5 \text{ kg}$$
3. $$15 \text{ cm} = 150 \text{ mm}$$
4. $$\text{Perimeter} = 2 \times (4 + 3) = 14 \text{ cm}$$
5. $$\text{Area} = 5 \times 2 = 10 \text{ cm}^2$$
6. $$3000 \text{ ml} = 3 \text{ l}$$
7. $$2.5 \text{ kg} = 2500 \text{ g}$$
8. $$\text{Area} = 20 \times 30 = 600 \text{ cm}^2$$
9. $$3 \times 60 = 180 \text{ seconds}$$
10. $$\text{Volume} = 2^3 = 8 \text{ cm}^3$$
11. $$1.5 \text{ l} = 1500 \text{ ml}$$
12. $$2000 \text{ ml} = 2 \text{ l}$$
13. $$\text{Perimeter} = 2 \times (10 + 8) = 36 \text{ m}$$
14. $$2.2 \text{ kg} = 2200 \text{ g}$$
15. $$10 \text{ cm}$$
16. $$30 \text{ seconds}$$
17. $$12 + 10 + 8 + 4 + 2 = 36 \text{ grams}$$
18. $$3 \text{ grams}$$
19. $$20 – 7 = 13 \text{ g}$$
20. $$1.2 \text{ l} = 1200 \text{ ml}$$

Medium Level

1. $$\text{Volume} = 5 \times 3 \times 4 = 60 \text{ m}^3$$
2. $$3.5 \text{ l} = 3500 \text{ ml}$$
3. $$600 \text{ ml} = 0.6 \text{ l}$$
4. $$\text{Perimeter} = 2 \times (8 + 3) = 22 \text{ cm}$$
5. $$4.5 \text{ kg} = 4500 \text{ g}$$
6. $$\text{Area} = 12 \times 10 = 120 \text{ m}^2$$
7. $$2000 \text{ ml} = 2 \text{ l}$$
8. $$150 \text{ g} = 0.15 \text{ kg}$$
9. $$\text{Perimeter} = 2 \times (5 + 5) = 20 \text{ cm}$$
10. $$750 \text{ ml} = 0.75 \text{ l}$$
11. $$3.14 \times 3^2 \times 5 \approx 141.3 \text{ cm}^3$$
12. $$18 \text{ cm}$$
13. $$1 \text{ hour} = 60 \text{ minutes}$$
14. $$30 \text{ grams} = 1.5 \text{ l}$$
15. $$5.25 \text{ grams}$$
16. $$5.75 \text{ litres}$$
17. $$90 \text{ grams}$$
18. $$750 \text{ grams}$$
19. $$1000 \text{ litres}$$
20. $$30 \text{ grams}$$

Hard Level

1. $$5 \times 3 \times 2 = 30 \text{ m}^3$$
2. $$12 \text{ cups of milk}$$
3. $$1.8 \text{ l} = 1800 \text{ ml}$$
4. $$\text{Area} = 9 \times 6 = 54 \text{ m}^2$$
5. $$\text{Volume} = 8 \times 4 \times 3 = 96 \text{ cm}^3$$
6. $$100 \text{ km/h}$$
7. $$5000 \text{ ml}$$
8. $$300 \text{ g} = 300 \text{ grams}$$
9. $$250 \text{ cm} = 2.5 \text{ m}$$
10. $$750 \text{ grams}$$
11. $$1.2 \text{ litres}$$
12. $$\text{Perimeter} = 2 \times (10 + 4) = 28 \text{ m}$$
13. $$1.5 \text{ cups}$$
14. $$750 \text{ grams}$$
15. $$3.14 \times 2^2 \times 10 = 125.6 \text{ cm}^3$$
16. $$150 \text{ cm} = 1.5 \text{ m}$$
17. $$10 \text{ m}^2$$
18. $$50 \text{ m}^3$$
19. $$4 \text{ kg}$$
20. $$20 \text{ grams}$$

This set of questions and answers provides a comprehensive overview of measurements relevant to the 11+ exam, covering various difficulty levels and encouraging students to develop their understanding and problem-solving skills.