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Numbers

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Published in: Mathematics
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Upper Bounds and Lower Bounds Solve problems using upper and lower bounds

Divya J / Dubai

15 years of teaching experience

Qualification: CAIE and Pearson Examiner for IGCSE an AS Levels, Masters in Mathematics

Teaches: SAT, ACT, Maths, IGCSE/AS/AL, Physics, Biology, Chemistry, Mathematics

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  1. Mathematics Lecture No.- 07 Numbers Today_'s Targets Upper Bounds and Lower Bounds Solve problems using upper and lower bounds
  2. Bounds Bounds are the smallest (lower bound, LB) and largest (upper bound, UB) numbers that a rounded number can lie between. The bounds for a number, , can be written as The lower bound is included in the range of values of x could have taken but the upper bound is not.
  3. Bounds 4.5 is rounded to one decimal place and therefore any number from 4.45 up to but not including 4.55 would be rounded to 4.5 . On a number line, this would be represented as: 4.4 4.45 4.5 4.55 4.6 As an inequality where x represents the number it would be expressed as: 4.45 < x < 4.55 4.45 is known as the lower bound of 4.5, while 4.55 is known as the upper bound.
  4. Bounds Note that while implies that the number is not included in the solution implies that the number is included in the solution.
  5. Calculations using Bounds Upper bound of T = Uuper bound of a + Upper bound of b Lower bound of T = Lower bound of a + Lower bound of b Upper bound of T = Upper bound of a x Upper bound of b Lower bound of T = Lower bound of a X Lower bound of b Upper bound of T = Upper bound of a — Lower bound of b Lower bound of T = Lower bound of a — Upper bound of b Upper bound of T = Upper bound of a + Lower bound of b Lower bound ofT = Lower bound of a + Upper bound of b
  6. Question The length of each side of a regular pentagon is 8.4 cm to 1 decimal place. Complete the error interval for the length of one side.
  7. Question Write down the lower and upper bounds for each measurement, to the given degree of accuracy: (i) 50, 230, 4560, to the nearest 10. (ii) 6, 17, 123, to the nearest unit.
  8. Question A sheep is weighed by a farmer as 43 kg to the nearest kg. What are the lower and upper bound weights for the sheep?
  9. Question Calculate lower and upper bounds for the following calculations, if each of the numbers is given to 1 d.p. (i) 2A + 4.7 (ii) 176 4.2 (iii) 63 X 4.8 (iv) 6.8
  10. Question The sides of a square are 15.1 cm, correct to 1 decimal place. Find the upper bound of the area of the square.
  11. Question An equilateral triangle has side length 12 cm, correct to the nearest centimetre. Find the lower bound and the upper bound of the perimeter of the triangle.
  12. Question The area of a square is 42.5 cm2, correct to the nearest 0.5 cm2. Calculate the lower bound of the length of the side of the square.
  13. Question Serge walks 7.9 km, correct to the nearest 100 metres. The walk takes 133 minutes, correct to the nearest minute. Calculate the maximum possible average speed of Serge's walk. Give your answer in kilometres/hour.
  14. Question A rectangle measures 8.5 cm by 10.7 cm, both correct to 1 decimal place. Calculate the upper bound of the perimeter of the rectangle.
  15. Question On one day, the number of members using the exercise machines was 40, correct to the nearest 10. Each member used a machine for 30 minutes, correct to the nearest 5 minutes. Calculate the lower bound for the number of minutes the exercise machines were used on this day.
  16. [99, 21, Q4] An equilateral triangle has sides of length 15 cm, correct to the nearest centimetre. Calculate the upper bound of the perimeter of this triangle. .. .. .. ...........cm [1]
  17. [58, 22, Q12] Anna walks 31 km at a speed of 5 km/h. Both values are correct to the nearest whole number. Work out the upper bound of the time taken for Anna's walk. ..... .... ... ... hours [2]
  18. [S17, 22, Q18] A rectangle has length 62 mm and width 47 mm, both correct to the nearest millimetre. The area of this rectangle is A mm2. Complete the statement about the value of A.
  19. [S15, 22, Q0] One year ago Ahmed's height was 114 cm. Today his height is 120 cm. Both measurements are correct to the nearest centimetre. Work out the upper bound for the increase in Ahmed's height. . ............... cm [21
  20. [96, 22, Q13] The base of a triangle is 9 cm correct to the nearest cm. The area of this triangle is 40 cm2 correct to the nearest 5 cm2. Calculate the upper bound for the perpendicular height of this triangle. ....................cm [3]
  21. [WE, 22, Q12] A circle has a radius of 8.5 cm correct to the nearest 0.1 cm. The lower bound for the area of the circle is prcm2. The upper bound for the area of the circle is qrcm2. Find the value of p and the value of q. - [31

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