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Upper and Lower Bounds

Determine the upper and lower bounds when rounding quantities used in calculations.

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This is level 5: calculations involving upper and lower bounds. You can earn a trophy if you get at least 9 questions correct.

1. The sides of a square are measured to be 3cm to the nearest centimetre. What is the largest possible area the square could have? cm2 Correct Wrong
2. A rectangle is 2cm wide and 4cm long. Both lengths have been rounded to the nearest centimetre. What is the smallest possible area the rectangle could have? cm2 Correct Wrong
3. A triangle has a base of 4.5cm and a height of 3.4cm. Both lengths have been rounded to one decimal place. What is the largest possible area of the triangle? Give your answer to three significant figures. cm2 Correct Wrong
4. The radius of a circle is measured to be 4.92cm to three significant figures. What is the largest possible circumference the circle could have? Give your answer to three significant figures. cm Correct Wrong
5. For the circle mentioned in the previous question. What is the smallest possible area the circle could have? Give your answer to three significant figures. cm2 Correct Wrong
6. The area of a square is 8.65cm2 to three significant figures. What is the largest possible perimeter the square could have? Give your answer to three significant figures. cm Correct Wrong
7. An isosceles right-angled triangle has two sides of length 5.54cm to three significant figures. What is the largest possible length of the third side? Give your answer to three significant figures. cm Correct Wrong
8. If a = 77, b = 72 and c = 26 (all given to the nearest integer) find the largest possible value for a + b − c. Correct Wrong
9. If d = 52, e = 38 and f = 85 (all given to the nearest integer) find the largest possible value for (d − e) ÷ f. Give your answer to three significant figures. Correct Wrong
10. A car travels for 290 miles in 6 hours 15 minutes. The distance was rounded to the nearest five miles and the time was rounded to the nearest 15 minutes. What is the upper bound for the average speed of the car? Give your answer in miles per hour to three significant figures. mph Correct Wrong
11. A total of 9700 attended a festival. This number is given to the hearest hundred. Each person paid £12 entrance fee. What is the maximum amount of money that could have been collected from entrance fees? pounds Correct Wrong
12. Fifty thousand fans attend a football match. This number is correct to the nearest 500. The number of Wolves fans attending the match is thirty three thousand. This number is correct to the nearest 1000. The rest of those attending support West Bromwich Albion. Work out the maximum number of West Bromwich Albion fans in the crowd. Correct Wrong
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This is Upper and Lower Bounds level 5. You can also try:
Level 1 Level 2 Level 3 Level 4

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Description of Levels

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Level 1 - Numbers truncated or rounded up or down to a given multiple.

Level 2 - Quantities rounded to the nearest multiple.

Level 3 - Numbers rounded to a number of decimal places.

Level 4 - Discrete and continuous quantities rounded to a number of significant figures.

Level 5 - Calculations involving upper and lower bounds.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Extension

Students who are also studying Physics may want to investigate a topic called Propagation of Uncertainties that uses these formulas.

$$ \text{If} \quad y= a \pm b \quad \text{then} \quad \Delta y = \Delta a + \Delta b $$ $$ \text{If} \quad y= \frac{ab}{c} \quad \text{then} \quad \frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c} $$ $$ \text{If} \quad y= a^n \quad \text{then} \quad \frac{\Delta y}{y} = \begin{vmatrix} n \frac{\Delta a}{a} \end{vmatrix} $$

The triangular symbols are the Greek letter delta and represent the errors or, more accurately, uncertainties.

Help Video

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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