Using upper and lower bounds practically | Maths | Quizalize & Oak National Academy

Starter quiz

The ______ bound for a rounded number is the smallest value that would round up to the next rounded value.

'upper' ✓
$x$ = 5.2 correct to 1 decimal place. What is the error interval?

$5.15\leq{x}>5.25$

$5.15\leq{x}<5.25$ ✓

$5.15\leq{x}\leq5.25$

$5.15<{x}\leq5.25$

$5.15\geq{x}<5.25$
$y$ = 45 correct to 2 significant figures. What is the error interval?

$44.5\geq{y}<45.5$

$44.5<{y}\leq45.5$

$44.5\leq{y}>45.5$

$44.5\leq{y}\leq45.5$

$44.5\leq{y}<45.5$ ✓
The error interval of $x$ is $5.15\leq{x}<5.25$ . The error interval of $y$ is $44.5\leq{y}<45.5$ . What are the lower and upper bounds of $xy$ ? (Give you answers to 3 decimal places)

'229.175 and 238.875' ✓
The error interval of $x$ is $5.15\leq{x}<5.25$ . The error interval of $y$ is $44.5\leq{y}<45.5$ . What are the lower and upper bounds of $xover{y}$ ? (Give you answers to 3 s.f.)

'0.168 and 0.178' ✓
Which calculation will give the upper bound of $x={{a^2}\over{b+c}}$

$UB_x={LB_{a^2}\over{LB_b+LB_c}}$

$UB_x={LB_{a^2}\over{UB_b+UB_c}}$

$UB_x={UB_{a^2}\over{LB_b+LB_c}}$ ✓

$UB_x={UB_{a^2}\over{UB_b+UB_c}}$

$UB_x={UB_{a^2}\over{UB_b+LB_c}}$

The degree of ______ determines the upper and lower bounds of a number or measurement.

'acurracy' ✓
Considering the maximum number of boxes to safely fit in a lift. Which of the following should be used? (Where $l$ represents the capacity of the lift and $b$ represents the mass of a box?

$UB_l\div{UB_b}$

$UB_l\div{LB_b}$

$LB_l\div{UB_b}$ ✓

$LB_l\div{LB_b}$
A sack contains 16 kg of flour correct to the nearest kilogram. What are the lower and upper bounds of the mass of the flour?

'15.5 kg and 16.5 kg' ✓
A sack contains 16 kg of flour correct to the nearest kilogram. This is put into smaller bags containing 500 g correct to 10g. What are the lower and upper bounds of the mass of the bags?

'495 g and 505 g' ✓
A sack contains 16 kg of flour correct to the nearest kilogram. This is put into smaller bags containing 500 g correct to 10g. Which calculation is correct to find the minimum number of bags produced?

$UB_f\div{UB_b}$

$LB_f\div{UB_b}$ ✓

$LB_f\div{LB_b}$

$UB_f\div{LB_b}$
A sack contains 16 kg of flour correct to the nearest kilogram. This is put into smaller bags containing 500 g correct to 10g. What is the minimum number of bags produced?

'30' ✓

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When considering safety contexts, you want to be able to guarantee safety limitations (weight of materials).
When considering costs, you may wish to know the maximum cost to you.
When training in sport, you may wish to know the time you need to beat in order to win a race.

For example if a measurement of 12 cm has been given to the nearest centimetre assuming the upper bound is 12.4 cm.

Emphasise the infinite nature of a measurement.

Upper bound - The upper bound for a rounded number is the smallest value that would round up to the next rounded value.
Lower bound - The lower bound for a rounded number is the smallest value that the number could have taken prior to being rounded.
Error interval - An error interval for a number x shows the range of possible values of x. It is written as an inequality a ≤ x < b