Calculations with Lower and Upper Bounds
1. a = 60 rounded to the nearest 10 b = 5.7 rounded to one decimal place.
What are the lower and upper bounds of a and b?
Use these to work out the following. a+b a-b ab a b
Least
Greatest
(Grade B)
2. The length and width of a field have been measured as 78m and 35m to the nearest metre. a) Find the greatest possible amount of fencing needed to surround the field b) Find the least possible area of the field (Grade B)
3. The distance travelled by an object is 18 metres in a time of 1.8 seconds. Both measurements have been given correct to 2 significant figures. Calculate the minimum and maximum possible speed of the object in m/s. (Grade B)
4. A sheet of paper is 0.08mm thick correct to 2 decimal places. Calculate the difference between the least and greatest possible heights if 2000 pieces of paper are stacked on top of each other. (Grade B)
5. The mass of a block of wood is 480g rounded to the nearest 10g. The volume of the block is 1000cm 3 rounded to 1 significant figure. Calculate the difference between the least and greatest possible density of the block. (Grade B)
6. The area of a circle is 140cm 2 rounded to 2 significant figures. Calculate the greatest possible length of the diameter of the circle. (Grade A*)
7. The base of a right -triangle is 24cm rounded to 2 significant figures and the height of the triangle is 8.6cm rounded to 1 decimal place. Calculate the minimum possible length of the hypotenuse. (Grade A*)
8. The volume of a cylinder is 500cm 3 . The height of the cylinder is 8.6cm. Both measurements have been rounded to 2 significant figures. Calculate the minimum possible length of the radius of the cylinder. (Grade A*)
9.
The angle has been given correct to the nearest degree
5.7cm x and the hypotenuse has been given to 1 decimal place.
30º
Calculate the greatest possible length of side x
(Grade A*)
The measurements of the cuboid have all been given
10.
9.4cm
B correct to 2 significant figures. a) Calculate the maximum possible volume of the cuboid
A
14cm
6.8cm b) Calculate the minimum possible length of the diagonal A (Grade A*)