IGCSE Mathematics | Practice Test | 25 Questions
What does the term lower bound mean for a rounded measurement?
What does the term upper bound mean for a rounded measurement?
State the rule for finding the lower bound and upper bound of a rounded value. Use the term “degree of accuracy” in your answer.
A measurement is given correct to the nearest metre. What is the degree of accuracy?
A number is given correct to 1 decimal place. What is the degree of accuracy?
A length is $12\text{ m}$, correct to the nearest metre. Write down the upper bound.
A length is $12\text{ m}$, correct to the nearest metre. Write down the lower bound.
A mass is $5.3\text{ kg}$, correct to 1 decimal place. Write down the lower bound.
A number is $600$, correct to the nearest $100$. Write down the upper bound.
A measurement has a lower bound $L$ and an upper bound $U$. Write the inequality that the true value $x$ must satisfy. Use the correct inequality signs ($\leq$ or $<$).
A length is $27\text{ cm}$, correct to the nearest centimetre. Find the upper and lower bounds.
A mass is $480\text{ g}$, correct to the nearest $10\text{ g}$. Find the upper and lower bounds.
A temperature is $36.8^\circ\text{C}$, correct to 1 decimal place. Find the upper and lower bounds.
A number is $7.25$, correct to 2 decimal places. Find the upper and lower bounds.
A time is $90\text{ s}$, correct to the nearest $10\text{ s}$. Find the upper and lower bounds. Then write the inequality for the true time $t$.
A height is $2.0\text{ m}$, correct to 1 decimal place. Find the upper and lower bounds.
A price is $\$8.40$, correct to the nearest $\$0.10$. Find the upper and lower bounds.
A distance is $5000\text{ m}$, correct to the nearest $1000\text{ m}$. Find the upper and lower bounds.
A mass $m$ is recorded as $63\text{ kg}$, correct to the nearest kilogram. Write the inequality for $m$.
A number is $50$, correct to the nearest $10$. A student says: “The upper bound is $60$.” Is the student correct? Show your working and explain any error.
(a) A length is given as $9.4\text{ cm}$, correct to 1 decimal place. Find the upper and lower bounds.
(b) The same length is now given as $9.40\text{ cm}$, correct to 2 decimal places. Find the upper and lower bounds.
(c) Even though $9.4 = 9.40$ as numbers, the bounds in (a) and (b) are different. Explain why.
The true value $x$ of a measurement satisfies the inequality $24.5 \leq x < 25.5$.
(a) Write down the lower bound.
(b) Write down the upper bound.
(c) Write down the rounded value.
(d) What was the degree of accuracy used to round this number? Explain how you know.
A distance is recorded as $7\text{ m}$, correct to the nearest metre.
(a) Find the upper and lower bounds.
(b) Write the inequality for the true distance $d$.
(c) A student says: “The true distance could be $7.4\text{ m}$.” Is this possible? Explain.
(d) A student says: “The true distance could be $7.5\text{ m}$.” Is this possible? Explain.
The number $800$ has been rounded in two different ways:
- Version A: rounded to the nearest $100$
- Version B: rounded to the nearest $10$
(a) Find the upper and lower bounds for Version A.
(b) Find the upper and lower bounds for Version B.
(c) Which version gives a narrower range of possible values? Explain why this makes sense.
A bag of flour has a mass of $2.00\text{ kg}$, correct to 2 decimal places.
(a) Write down the degree of accuracy.
(b) Find the upper and lower bounds.
(c) Write the inequality for the true mass $m$.
(d) The upper bound is $2.005\text{ kg}$. Explain why a true mass of exactly $2.005\text{ kg}$ would not be recorded as $2.00\text{ kg}$.
