GCSE. UPPER AND LOWER BOUNDS [ESTIMATED TIME: 70 minutes] (+ IGCSE) EXAM QUESTION PRACTICE 1. [2 marks]
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1 UPPER AND LOWER BOUNDS [ESTIMATED TIME: 70 minutes] The length of a fence is 137 metres, correct to the nearest metre. Write down (i) the lower bound for the length of the fence, GCSE (+ IGCSE) EXAM QUESTION PRACTICE 1. [2 marks] (ii) the upper bound for the length of the fence.... metres... metres 2. [5 marks] Zoe s weight is 62 kg, correct to the nearest kilogram. Anu s weight is 85 kg, correct to the nearest kilogram. (a) Write down the upper bound for the weight of Zoe. (b) Write down the lower bound for the weight of Anu.... (1) (c)... Work out the upper bound for the difference between Zoe s weight and Anu s weight. (1)... (3) Questions compiled
2 3. [2 marks] y = 1.8 correct to 1 decimal place. Calculate the lower bound for the value of 4y [3 marks] The volume of oil in a tank is 1000 litres, correct to the nearest 10 litres. The oil is poured into tins of volume 2.5 litres, correct to one decimal place. Calculate the upper bound of the number of tins which will be required.... Q14
3 5. [7 marks] $ Z;A+@$ h%#8(#$+de< #@@,(#5'./+2(#Q& " )i FG+@$ # 0(%#&8.'+"#$+%*+(%8L5c#&8.'2+#5+#; "#+_+FG+@$M+@-(('@5+5-+H+*%8&%?%@#&5+?%8,('; #$+_+Z;A+@$M+@-(('@5+5-+F+*%8&%?%@#&5+?%8,('*; 6#7+ T(%5'+2-Q&+5L'+.-Q'(+O-,&2+?-(+5L'+.'&85L+-?+ + 6%7+ "#M ;;;;;;;;;;;;;;;;;;;;;+@$ + 6%%7+ #$; ;;;;;;;;;;;;;;;;;;;;;+@$ IJK 6O7+ 9#.@,.#5'+5L'+.-Q'(+O-,&2+?-(+5L'+#('#+-?+5(%#&8.'+"#$; ;;;;;;;;;;;;;;;;;;;;;+@$ F IJK 6@7+ 9#.@,.#5'+5L'+.-Q'(+O-,&2+?-(+5L'+P#.,'+-?+5#&+)i; ;;;;;;;;;;;;;;;;;;;; I$K QO!
4 6. [2 marks] A B Glass A contains 122 millilitres of water, correct to the nearest millilitre. Glass B contains 168 millilitres of water, correct to the nearest millilitre. Calculate the upper bound of the difference, in millilitres, between the volume of water in glass A and the volume of water in glass B.... millilitres 7. [3 marks] An athlete runs 400 metres, correct to the nearest metre. The athlete takes 50.2 seconds, correct to the nearest 0.1 of a second. Work out the upper bound of the athlete s average speed. Give your answer correct to 3 significant figures.... m/s
5 8. [3 marks] 2a y = b c a = 42 correct to 2 significant figures. b = 24 correct to 2 significant figures. c = 14 correct to 2 significant figures. Work out the lower bound for the value of y. Give your answer correct to 2 significant figures. Show your working clearly [3 marks] There are 1300 sheets of paper, correct to the nearest 100 sheets, in a pile. Each sheet is of equal thickness. The height of the pile is 160 mm, correct to the nearest 10 mm. Calculate the upper bound, in millimetres, for the thickness of one sheet of paper.... mm
6 10. [4 marks]! Y-/1!*+%1%!#+N1!,-!(1!)$I,13!(0!+!* *#!*+%1!#+%!+!/+%%!-I!_C U8Q!*-221*,!,-!;!%$8.$I$*+.,!I$8'21%9 J+K! E2$,1!3-4.!,#1!'&&12!(-'.3!-I!,#1!/+%%!-I!+!*+%19 D!*2+.1!*+.!)$I,!%+I1)0!+!)-+3!-I!W;<< U8Q!*-221*,!,-!;!%$8.$I$*+.,!I$8'21%9 J(K! l$.3!,#1!821+,1%,!.'/(12!-i!*+%1%!,#+,!,#1!*2+.1!*+.!)$i,!%+i1)0!$.!-.1!)-+39! !u8 IOK! I$K POU 11. [4 marks] The length of a side of a square is 6.81 cm, correct to 3 significant figures. (a) Work out the lower bound for the perimeter of the square. Leave blank (b) Give the perimeter of the square to an appropriate degree of accuracy. You must show working to explain how you obtained your answer.... cm (2)... cm (2) Q15
7 12. [6 marks] N+O! Q+X1!+!,#1!%'(`1*,!-M!,#1!M-2/')+!'!^!!+ ; L!4#121!+!$%!&-%$,$V19 ()+.X "#1!+21+!-M!+!*$2*)1!$%!KH!*/ ; L!*-221*,!,-!;!%$8.$M$*+.,!M$8'21%9 N(O! N$O! D-2X!-',!,#1!)-412!(-'.3!M-2!,#1!2+3$'%!-M!,#1!*$2*)19!! D2$,1!3-4.!+))!,#1!M$8'21%!-.!0-'2!*+)*')+,-2!3$%&)+09 +!^! IJK !*/! N$$O! ]$V1!,#1!2+3$'%!-M!,#1!*$2*)1!,-!+.!+&&2-&2$+,1!318211!-M!+**'2+*09!! Z-'!/'%,!%#-4!4-2X$.8!,-!16&)+$.!#-4!0-'!-(,+$.13!0-'2!+.% !*/ I!K PO!
8 13. [4 marks] Diagram NOT accurately drawn x m 0.18 m x m Trena wants to build a sandpit in the shape of a cuboid. The volume of sand in the sandpit will be 1.0 m 3, correct to 1 decimal place. The depth of sand in the sandpit will be 0.18 metres, correct to 2 decimal places. The sandpit will have a square base with sides of length x metres. Find the upper bound for x Give your answer correct to 3 significant figures. upper bound =...
9 14. [5 marks] (a) Correct to the nearest millimetre, the length of a side of a regular hexagon is 3.6 cm. Calculate the upper bound for the perimeter of the regular hexagon. (b) Correct to 1 significant figure, the area of a rectangle is 80 cm 2 Correct to 2 significant figures, the length of the rectangle is 12 cm. Calculate the lower bound for the width of the rectangle. Show your working clearly.... cm (2) * 9-(('@5+5-+F+*%8&%?%@#&5+?%8,('*M+5L'+#('#+-?+#+*S,#('+%*+FAG+@$ F ; 9#.@,.#5'+5L'+.-Q'(+O-,&2+?-(+5L'+='(%$'5'(+-?+5L'+*S,#(';... cm (3) 15. [3 marks] ;;;;;;;;;;;;;;;;;;;;;+@$ PJ"
10 16. [4 marks] Correct to 2 decimal places, the volume of a solid cube is cm 3 Calculate the lower bound for the surface area of the cube.... cm [3 marks] Correct to 2 significant figures, a = 58, b = 28 and c = 18 a Calculate the upper bound for the value of b c Show your working clearly....
11 18. [5 marks] A metal cube has sides of length 4.5 cm, correct to the nearest 0.5 cm. The cube is melted down and the metal is used to make small spheres. Each sphere has a radius of 3mm, correct to the nearest millimetre. Work out the greatest number of spheres that could be made from the metal. Show your working clearly.... DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO N
12 19. [5 marks] Correct to 1 significant figure, x = 7 and y =9 (a) Calculate the lower bound for the value of xy (b) Calculate the upper bound for the value of x y... (2)... (3) Q [4 marks] In a race, Paula runs 25 laps of a track. Each lap of the track is 400 m, correct to the nearest metre. Paula s average speed is 5.0 m/s, correct to one decimal place. Calculate the upper bound for the time that Paula takes to run the race. Give your answer in minutes and seconds, correct to the nearest second. blank... Q23 (Total 4 marks)
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