Estimation — Paper 1 · IGCSE Mathematics 0580

19 8.95 − 3.05 × 1.97 2.92 (a) (i) Write the above expression with each number rounded to one significant figure. Answer (a)(i) [1] (ii) Use your answer to find an estimate for the value of the expression. Answer (a)(ii) [1] (b) Use your calculator to work out the value of the original expression. Give your answer correct to 2 decimal places. Answer (b) [1]

3 marks

Mark scheme: 19 (a) (i) 9 – 3 × 2 1 allow slip of denominator as 3.0 or 3.00 3 (not allow zeros in other figures) (ii) (equals) 1 1ft their (a)(i) provided order of operation is as seen and both (a)(i) and (a)(ii) are to a maximum of 1dp apart from zeros (b) 1.01 1

This question in 0580/11 May/June 2005

15 (a) Write 0.48 correct to 1 significant figure. For Examiner's Use Answer(a) [1] (b) (i) Find an approximate answer for the sum 9.87 – 5.79 × 0.48 by rounding each number to 1 significant figure. Show your working. Answer(b)(i) [1] (ii) Use your calculator to find the exact answer for the sum in part (b) (i). Write down all the figures on your calculator. Answer(b)(ii) [1]

3 marks

Mark scheme: 15 (a) 0.5 not 0.50 1 (b) (i) 10 – 6 x c’s 0.5 = 7 1f.t. Only f.t. c’s (a) if it is 0.4 (0) or 0.50 or 0 (ii) 7.0908 1 Allow 7.6 or 8 from 0.4

This question in 0580/11 Oct/Nov 2005

22 13.5 + 16 4.8 − (22 ÷ 13 ) (a) Rewrite this calculation with each number rounded to 1 significant figure. Answer(a) [2] (b) Use your answer to part (a) to estimate the answer to the calculation. Show your working and write your answer correct to 1 significant figure. Answer(b) [1] (c) Use your calculator to find the answer to the original calculation correct to 3 significant figures. Answer(c) [2]

5 marks

Mark scheme: 22 10 + 20 (a) 2 SC1 for 3 or 4 of the numbers given to 1 5 − ( 20 ÷ 10) significant figure. (b) 10 cao. 1 (c) 9.49 cao. 2 B1 for 9.485(5)… to 9.493 seen. (Allows for 22 ÷ 13 rounded to 3sf) If zero, SC1 for 9.5www as final answer 17 (Not 9.50 but check for possible B1)

This question in 0580/11 Oct/Nov 2006

13 (a) Rewrite this calculation with all the numbers rounded to 1 significant figure. For Examiner's 77.8 Use 21.9 − 3.8 × 4.3 Answer(a) [1] (b) Use your answer to part (a) to work out an estimate for the calculation. Answer(b) [1] (c) Use your calculator to find the actual answer to the calculation in part (a). Give your answer correct to 1 decimal place. Answer(c) [2]

4 marks

Mark scheme: 13 80 1 Condone either 78 for 80 or 22 for 20 but not (a) both. 20 − 4 × 4 (b) 20 1 SC1 for answer 13 if clearly from 78 ÷ (22 − 4 × 4) or 78 ÷ (22 − 16). (c) 14.0 2 B1 for 13.9(9……….) or 14 in working or in the answer.

This question in 0580/12 May/June 2011

4.8 # 1.98276 5 p = 16.83 (a) In the spaces provided, write each number in this calculation correct to 1 signifi cant fi gure. Answer(a) … × … … [1] (b) Use your answer to part (a) to estimate the value of p. Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 5× 2 5 (a) 1 20 1 (b) 0.5 or cao 1 2 n

This question in 0580/11 May/June 2014

3.9 # 29.310 By writing each number correct to 1 significant figure, estimate the value of . 8.9 - 2.7 Show all your working. Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 4 × 3010 M1 Allow one error and 2 for 4 and 6 for 9 − 3 9 − 3 10 nfww A1 2 4 2× 4

This question in 0580/11 Oct/Nov 2015

8 Without using your calculator and by rounding each number correct to 1 significant figure, estimate the value of 10.3 # 19.5 . 88.9 - 43.2 You must show all your working. … [2]

2 marks

Mark scheme: 10 × 20 8 M1 90 − 40 4 nfww A1 2

This question in 0580/12 Feb/March 2017

59.2 # 1.9710 By writing each number correct to 1 significant figure, estimate the value of . 2. 04 + 3. 85 … [2]

2 marks

Mark scheme: 10 60 × 2 M1 Allow 1 error 2 + 4 20 A1 Dep on no errors in rounding

This question in 0580/13 Oct/Nov 2017

13 Without using a calculator, estimate, by rounding each number correct to 1 significant figure, 104. 3 . 8.72 - 7. 389 You must show all your working. … [2]

2 marks

Mark scheme: 13 100 and 9 −7 M1 5 A1

This question in 0580/12 Feb/March 2019

1.6 + 9.6213 p = 5.9 - 4.3 (a) By writing each number correct to 1 significant figure, work out an estimate for p. You must show all your working. … [2] (b) Calculate the exact value of p. … [1]

3 marks

Mark scheme: 13(a) 2 + 10 2 M1 6 − 4 51 A1 13(b) 58.6 1

This question in 0580/11 May/June 2019

19 By rounding each number correct to 1 significant figure, estimate the value of 71 # 32.4 2 . 4.8 You must show all your working. … [2]

2 marks

Mark scheme: 19 70 × 30 2 M1 for two of 70, 30, 5 used 5 2 and 84

This question in 0580/13 May/June 2020

49.2 - 9.5912 T = 4.085 # 2.35 By writing each number correct to 1 significant figure, work out an estimate for T. You must show all your working. … [2]

2 marks

Mark scheme: 12 50 − 10 M1 Allow M1 for 3 out of 4 values correctly rounded 4 × 2 or for all correct but with any trailing zeros 5 A1 50 –1 0 dep on 4 × 2

This question in 0580/11 Oct/Nov 2020

15 By writing each number correct to 1 significant figure, estimate the value of 37.8 # 13 .2 . 28.5 + 22.1 You must show all your working. … [2]

2 marks

Mark scheme: 15 40 × 10 M1 Allow M1 for 3 out of 4 values correctly rounded 30 + 20 or for all correct but with any trailing zeros 8 A1 40 × 10 Dep on 30 + 20

This question in 0580/13 Oct/Nov 2020

20 By rounding each number in the calculation correct to 1 significant figure, estimate the value of 38.7 # 3.115 . 20.3 - 4.12 You must show all your working. … [2]

2 marks

Mark scheme: 20 40 × 3 M1 Allow M1 for 3 out of 4 values correctly 2 rounded 20 − 4 or for all correct but with any trailing zeros 30 cao A1 Dep on M1 with no errors or trailing zeros

This question in 0580/11 May/June 2021

15 Sophie buys 73 books for her school. Each book costs $21.95 . (a) By rounding each number correct to 1 significant figure, estimate the total cost of these books. $ … [1] (b) Write down whether this estimate is greater or less than the exact cost. Explain how you decide, without working out the exact cost. … because … … [1]

2 marks

Mark scheme: 15(a) 70 × 20 and 1400 1 15(b) Less than [because] 1 If zero scored, SC1 for both values rounded down oe answer of 73 × 20 and 1460 in (a) with Less than [because] the cost of the book is rounded down oe

This question in 0580/11 Oct/Nov 2021

20 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 4.3 # 30 .7 . 6.6 - 1.8 … [2]

2 marks

Mark scheme: 20 4 ×30 M1 7 –2 24 nfww A1 If 0 scored, SC1 for 3 correct roundings or for all correct but with any trailing zeros

This question in 0580/13 Oct/Nov 2021

18 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 27 - 2 .32 . 845.4 # 0.048 … [2]

2 marks

Mark scheme: 18 30  2 2 M1 800  0.05 0.65 A1 If M0 scored, SC1 for 3 correct values or all correct but with any trailing zeros

This question in 0580/12 May/June 2022

14 By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 6.7 # 2 .1 . 18 - 5.9 You must show all your working. … [2]

2 marks

Mark scheme: 14 7  2 M1 20  6 1 nfww A1 If 0 scored, SC1 for 3 correct roundings or for all correct but with any trailing zeros

This question in 0580/11 May/June 2023

13 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 6.8 # 10.6 . 3.2 - 0. 98 You must show all your working. … [2]

2 marks

Mark scheme: 13 7 10 M1 3  1 35 nfww A1 If 0 scored, SC1 for 3 correct roundings or all correct but with trailing zeros

This question in 0580/13 May/June 2023

14 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 28. 2 - 5. 6 . 4.2 # 1.68 You must show all your working. … [2]

2 marks

Mark scheme: 14 30  6 M1 4  2 3 nfww A1 If 0 scored, SC1 for 3 correct roundings or all correct but with trailing zeros

This question in 0580/11 May/June 2024

17 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 17.8 + 10 .3 . 5 .5 … [2]

2 marks

Mark scheme: 17 20 + 10 M1 nfww 6 5 nfww A1 If 0 scored SC1 for 2 correct roundings or for all correct but with trailing zeros

This question in 0580/12 May/June 2025

13 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 62.5 . 9.7 # 0.52 … [2]

2 marks

Mark scheme: 13 60 M1 10  0.5 12 A1 If 0 scored, SC1 for 2 correct roundings or for all correct but with any trailing zeros

This question in 0580/13 May/June 2025

19 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 5 .3 # 19 .5 . 2.49 … [2]

2 marks

Mark scheme: 19 5  20 M1 2 50 cao A1 If 0 scored SC1 for 2 correct roundings or for all 3 correct but with any trailing zeros

This question in 0580/11 Oct/Nov 2025