Q: The weight of a bag of sugar is given as 500g, correct to the nearest 10g. Calculate the maximum possible weight of 6 bags of sugar.

First, find the upper bound of a single bag: 505g. Then, multiply by 6: 505g * 6 = 3030g. Therefore, the maximum possible weight is 3030g.

Q: A rectangle has a length of 12 cm and a width of 5 cm, both measured to the nearest cm. Calculate the minimum possible area of the rectangle.

To find the minimum area, use the lower bounds of both measurements. Lower bound of length = 11.5 cm, Lower bound of width = 4.5 cm. Minimum area = 11.5 cm * 4.5 cm = 51.75 cm².

Q: Explain the difference between a 'continuous' and a 'discrete' variable in the context of limits of accuracy.

A continuous variable can take any value within a range (e.g., height). A discrete variable can only take specific, separate values (e.g., number of students). This distinction affects how we determine the bounds.

Q: The height of a tower is 50m, correct to the nearest meter. A student calculates the volume of a cylinder with this height. What is the implication for the accuracy of the volume calculation?

The volume calculation will also have a limit of accuracy. The calculated volume will be between a lower and upper bound depending on whether the lower or upper bound of the height measurement is used.

Q: - Topic: 1.7 Limits of accuracy - Question: A student measures the side of a square as 6 cm. What further information is needed to determine the limits of accuracy of the area?

You need to know the degree of accuracy to which the side length was measured (e.g., to the nearest cm, to the nearest mm). This determines the upper and lower bounds for the side length, and subsequently the area. Example: If the side is 6 cm to the nearest cm, the side could be between 5.5 cm and 6.5 cm.

Q: Topic: 1.7 Limits of Accuracy. Question: A machine produces bolts with a stated length of 5cm, correct to the nearest millimetre. What are the upper and lower bounds for the actual length of a bolt produced by this machine? Why is understanding these limits important?

The upper bound is 5.05cm and the lower bound is 4.95cm. These limits are critical because if bolts are consistently too long or too short, they could cause assembly problems, weaken structures, or lead to malfunctions. For example, if bolts consistently exceeded 5.05cm in a bridge construction, they might not fit properly and compromise the integrity of the structure.

Question 1

Question 2

A length is measured as 8.3 cm to the nearest 0.1 cm. State the error interval for this measurement.

Accepted Answer

The error interval is the range of possible values for the actual length. In this case, the error interval is 8.25 cm ≤ length < 8.35 cm.

Question 3

The weight of a bag of sugar is given as 500g, correct to the nearest 10g. Calculate the maximum possible weight of 6 bags of sugar.

Accepted Answer

First, find the upper bound of a single bag: 505g. Then, multiply by 6: 505g * 6 = 3030g. Therefore, the maximum possible weight is 3030g.

Question 4

A rectangle has a length of 12 cm and a width of 5 cm, both measured to the nearest cm. Calculate the minimum possible area of the rectangle.

Accepted Answer

To find the minimum area, use the lower bounds of both measurements. Lower bound of length = 11.5 cm, Lower bound of width = 4.5 cm.  Minimum area = 11.5 cm * 4.5 cm = 51.75 cm².

Question 5

Explain the difference between a 'continuous' and a 'discrete' variable in the context of limits of accuracy.

Accepted Answer

A continuous variable can take any value within a range (e.g., height). A discrete variable can only take specific, separate values (e.g., number of students). This distinction affects how we determine the bounds.

Question 6

Question 7

The height of a tower is 50m, correct to the nearest meter. A student calculates the volume of a cylinder with this height. What is the implication for the accuracy of the volume calculation?

Accepted Answer

The volume calculation will also have a limit of accuracy. The calculated volume will be between a lower and upper bound depending on whether the lower or upper bound of the height measurement is used.

Question 8

- Topic: 1.7 Limits of accuracy
- Question: A student measures the side of a square as 6 cm. What further information is needed to determine the limits of accuracy of the area?

Accepted Answer

You need to know the degree of accuracy to which the side length was measured (e.g., to the nearest cm, to the nearest mm). This determines the upper and lower bounds for the side length, and subsequently the area. Example: If the side is 6 cm to the nearest cm, the side could be between 5.5 cm and 6.5 cm.

Question 9

Topic: 1.7 Limits of Accuracy. Question: A machine produces bolts with a stated length of 5cm, correct to the nearest millimetre. What are the upper and lower bounds for the actual length of a bolt produced by this machine? Why is understanding these limits important?

Accepted Answer

The upper bound is 5.05cm and the lower bound is 4.95cm. These limits are critical because if bolts are consistently too long or too short, they could cause assembly problems, weaken structures, or lead to malfunctions. For example, if bolts consistently exceeded 5.05cm in a bridge construction, they might not fit properly and compromise the integrity of the structure.

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