1. WJEC Past Paper Questions (with answers)
Upper and Lower Bounds.
WJEC Past Paper Questions
(with answers)

3. 495
495
505
505
The least volume of the tank is litres
15·45 litres = cm3
The greatest volume of the jug is 505 cm3
30 full jugs is 30 x 505 = 15150cm3 which is less than the minimum volume of the tank.
So you can always pour in 30 jugs without overflowing.

5. 9·45 9·55 The least length of the shelf is 76·5cm
The greatest thickness of the book is 9·55 cm
8 books will measure a maximum of 8 x 9·55 = 76·4cm.
The greatest thickness of the 8 books is less than the minimum length of the shelf so you can always place 8 copies of the textbook on the shelf.

7. 9·5
10·5
Least mass of 100 blocks = 100 x 9·5 = 950
Greatest mass of 100 blocks = 100 x 10·5 = 1050
950
1050
From above 100 of the blocks with the least mass might not be enough.
1000  9·5 = 105·2 so he needs to deliver 106 blocks (106 x 9·5 = 1007kg) to be sure.

9. 245
255
The least capacity of the bucket is 5·05 litres
5·05 litres = 5050 ml
The greatest capacity of the jug is 255 cm3
20 full jugs is 20 x 255 = 5100ml which is more than the minimum capacity of the bucket.
So the bucket cannot always hold 20 jugs of water.

11. 89·5
90·5
The minimum length of the path is 26·5 m.
The maximum length of 30 strides is 30 x 90·5 = 2715 cm = 27·15m
This is longer than the minimum length of the path so she may not always reach the end of the path.

13. 18·45
18·55
Least possible length = 30 x 18·45 = 553·5 cm
Greatest possible length = 30 x 18·55 = 556·5 cm
553·5
556·5

15. 49·5 kg
50·5 kg
Least possible amount = 20 x 49·5 = 990kg
Greatest possible amount = 20 x 50·5 = 1010kg
990
1010

17. Least perimeter = 85·5 + 33·5 + 85·5 + 33·5 = 238
Greatest
Length (L)
85·5
86·5
Width (W)
33·5
34·5
L + W
119
121
119mm
121mm
Least perimeter = 85·5 + 33·5 + 85·5 + 33·5 = 238
Greatest perimeter = 86·5 + 34·5 + 86·5 + 34·5 = 242
238mm
242mm
Least L – W = 85·5 - 34·5 = 51
Greatest L – W = 86·5 - 33·5 = 53
51mm
53mm

18. 17. A tank holds 1800 litres of liquid, correct to 2 significant figures. A bottle holds 60 litres, correct to the nearest litre. Find the least possible number of bottles needed to completely fill the tank.
Minimum capacity of tank is 1750 litres
Maximum capacity of bottle is 60·5 litres
Least number of bottles = 1750  60.5 = 28·93
The least number of bottles needed to fill the tank is 29