Upper and lower bounds Questionbank

A triangle has a base of $10$ cm, measured to the nearest centimetre, and a height of $5.0$ cm, measured to the nearest $0.1$ cm. Find the lower bound for the area of the triangle.

A measurement is recorded as $x = 0.4$ rounded to $1$ significant figure. Determine the rounding step, $a$, that is used to calculate the upper and lower bounds of this measurement.

A physical frequency is defined as $f = \frac{1}{t}$. If $t = 0.040$ s correct to 2 significant figures, calculate the lower bound of the frequency $f$.

True or False: In a continuous measurement interval $L \le T < U$, if the original value was rounded up to the recorded value, the true value $T$ must have been in the sub-interval $[L, x)$.

The acceleration of a particle is given by the formula

$a = \frac{v^2}{r}$

If $v = 10 \text{ m s}^{-1}$ (to the nearest integer) and $r = 5.0 \text{ m}$ (to the nearest $0.1 \text{ m}$), find the lower bound of the acceleration $a$.

Fill in the blank: On a number line representing the interval of a continuous measurement $x$ with lower bound $L$ and upper bound $U$, the limits of accuracy are represented by a _____ point at $L$ and an _____ point at $U$.

True or False: If a length $L$ is measured as $8$ m to the nearest metre, the value $7.5$ m is a possible value for the actual length, but $8.5$ m is not.

A water tank contains $V = 500$ litres, rounded to the nearest 10 litres. Water is being pumped out at a constant rate $R = 15$ litres per minute, rounded to the nearest 5 litres per minute. Calculate the upper bound for the time $t$ in minutes required to empty the tank.

True or False: If a value $x = 500$ is rounded to the nearest $5$ units, the half-step used to determine the upper and lower bounds is $2.5$.

A runner completes Stage 1 in $t_1 = 45.3\text{ s}$ and Stage 2 in $t_2 = 38.7\text{ s}$, with both values rounded to 1 decimal place. What is the minimum possible difference $(t_1 - t_2)$ between the two times?