OxfordAQA International GCSE Mathematics: Rounding, estimation, bounds and fraction-decimal equivalence (9260) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions are aligned to the OxfordAQA International GCSE Mathematics (9260) specification, Version 5.1 (for exams May/June 2018 onwards), statements N11 (section 3.1.1) and N12 to N14 (section 3.1.2). All content can be assessed on the Extension Tier question papers. Questions on content that appears only in the Extension column are marked “(Extension only)”.

Links: study guide, revision notes, course hub, printable checklist and the free diagnostics.

Questions

1. Round each number as stated.

(a) 0.0507318 to 2 significant figures [1] (b) 4 962.5 to 3 significant figures [1] (c) 12.0498 to 2 decimal places [1]

2. (a) A plank is measured as 2.4 m to 1 decimal place. State the error interval for its length. [2] (b) The mass of a bag is given as 650 g, correct to the nearest 10 g. Write down the error interval for the mass. [2] (c) Zara says the true mass of the bag could be 654.9 g. Is she right? Give a reason. [1]

3. (a) Estimate the value of (5.92 × 41.3) ÷ 0.0396. Show the numbers you use. [3] (b) A builder buys 48 boxes of tiles at £6.95 per box. Estimate the total cost. State whether your estimate is bigger or smaller than the true cost, and why. [2]

4. (Extension only) A force of 240 N, correct to the nearest 10 N, acts on an area of 0.35 m², correct to 2 decimal places. Pressure = force ÷ area, in pascals.

(a) Calculate the upper bound of the pressure. [2] (b) Calculate the lower bound of the pressure. [2] (c) Give the pressure to a suitable degree of accuracy. Justify your answer. [2]

5. (Extension only) p = 12.4 correct to 1 decimal place and q = 0.85 correct to 2 decimal places.

(a) Find the upper bound of p × q. Give your answer to 3 decimal places. [2] (b) Find the lower bound of p − q. [2]

6. (a) Write 0.045 as a fraction in lowest terms. [2] (b) Write 7/32 as a decimal and as a percentage. [2] (c) Write 2.4% as a decimal. [1]

7. (Extension only) (a) Write 0.5̇4̇ as a fraction in lowest terms. [2] (b) Prove that 0.17̇ = 8/45. [3] (c) Write 11/30 as a recurring decimal. [2]

8. A school has 1 260 students. 5/9 of the students are girls. 35% of the girls and 3/8 of the boys take art.

(a) How many girls are there? [1] (b) How many students take art? [3] (c) What percentage of all the students take art? Give your answer to 1 decimal place. [2]

9. (a) Write 36 minutes as a fraction of 1.5 hours, in lowest terms. [2] (b) Write 2.7 kg as a percentage of 900 g. [2] (c) A shop took £7 830 this week and £6 000 last week. Write this week’s takings as a percentage of last week’s. [1]

10. (Extension only) A cyclist rides 72 km, correct to the nearest km, in 4.5 hours, correct to the nearest 0.1 hour.

(a) Write down the error interval for the distance and for the time. [2] (b) Calculate the upper bound of the average speed. [2] (c) Calculate the lower bound of the average speed. [2] (d) Give the average speed to a suitable degree of accuracy. Justify your answer. [2]

11. (a) Estimate the value of (7.2 × 19.6) ÷ (0.48 × 4.9). [3] (b) The exact value is 60. Write your estimate as a percentage of the exact value, to 1 decimal place. [2]

Answers

1. (a) The first two significant figures are 5 and 0, and the next digit is 7, so round up: 0.051 [1] (b) 4 962.5 has digits 4, 9, 6 and the next digit is 2, so keep 4 96 and fill with a zero: 4 960 [1] (c) The third decimal digit is 9, so round the second up: 12.05 [1] Examiner insight: Answers that keep the right digits but lose a place-holding zero, such as writing 496 for 4 960, change the size of the number and are unlikely to earn credit.

2. (a) The rounding unit is 0.1 m, so half a unit is 0.05 m [1]. 2.35 ≤ L < 2.45 [1] (b) The rounding unit is 10 g, so half a unit is 5 g: 645 ≤ m < 655 [2] (c) Yes, because 654.9 is less than 655 and lies inside the interval [1] Examiner insight: Write the lower end with ≤ and the upper end with <. An interval with both ends as ≤ is a common way to lose credit.

3. (a) Round to 1 s.f.: 6, 40 and 0.04 [1]. 6 × 40 = 240 [1]. 240 ÷ 0.04 = 6 000 [1] (b) 48 → 50 and 6.95 → 7, so 50 × 7 = £350 [1]. Each value went up when rounded, so the estimate is bigger than the true cost [1] Examiner insight: Show the rounded numbers. An unsupported estimate that happens to be near the right size gives the examiner nothing to give credit for.

4. (a) Upper bound of force = 245 and lower bound of area = 0.345 [1]. 245 ÷ 0.345 = 710.1… [1] (b) Lower bound of force = 235 and upper bound of area = 0.355 [1]. 235 ÷ 0.355 = 661.97… [1] (c) To 2 s.f. the bounds are 710 and 660, which differ [1]. To 1 s.f. both are 700, so the pressure is 700 Pa (1 s.f.) [1] Examiner insight: For a quotient, the bounds of the numerator and the denominator go in opposite directions. Writing which bound you use for each value shows your method clearly.

5. (a) Upper bound of p = 12.45 and upper bound of q = 0.855 [1]. 12.45 × 0.855 = 10.64475, so 10.645 (3 d.p.) [1] (b) Lower bound of p = 12.35 and upper bound of q = 0.855 [1]. 12.35 − 0.855 = 11.495 [1] Examiner insight: The two values are rounded to different places, so write each error interval before using it. Mixing up 0.05 and 0.005 is an easy slip.

6. (a) 0.045 = 45/1000 [1] = 9/200 [1] (b) 7 ÷ 32 = 0.21875 [1] and 0.21875 × 100 = 21.875% [1] (c) 2.4 ÷ 100 = 0.024 [1] Examiner insight: A fraction left as 45/1000 shows the right conversion but is not in simplest form, so a “simplest form” instruction needs the final cancelling step.

7. (a) Let x = 0.545454…; then 100x = 54.545454… [1]. 99x = 54, so x = 54/99 = 6/11 [1] (b) Let x = 0.17777…; then 10x = 1.7777… and 100x = 17.7777… [1]. 100x − 10x = 16, so 90x = 16 [1]. x = 16/90 = 8/45 [1] (c) 11 ÷ 30 = 0.3666… [1] = 0.36̇ [1] Examiner insight: A proof needs the algebra to be visible. Writing only 8/45 = 0.1777… works backwards and does not show how the fraction is found.

8. (a) 1 260 ÷ 9 × 5 = 700 girls [1] (b) Boys = 1 260 − 700 = 560 [1]. Girls taking art = 0.35 × 700 = 245, and boys taking art = 3/8 × 560 = 210 [1]. Total = 245 + 210 = 455 [1] (c) 455 ÷ 1 260 [1] × 100 = 36.1% (1 d.p.) [1] Examiner insight: A multi-step question rewards a clear layout. Label girls, boys and total so that a reader can follow every stage of your working.

9. (a) 1.5 hours = 90 minutes [1]. 36/90 = 2/5 [1] (b) 2.7 kg = 2 700 g [1]. 2 700 ÷ 900 × 100 = 300% [1] (c) 7 830 ÷ 6 000 × 100 = 130.5% [1] Examiner insight: A comparison between different units earns little credit if the units are not changed first. Convert first, then divide, so that the comparison is between like units.

10. (a) 71.5 ≤ d < 72.5 [1] and 4.45 ≤ t < 4.55 [1] (b) Upper speed uses the largest distance and the smallest time: 72.5 ÷ 4.45 [1] = 16.29… [1] (c) Lower speed uses the smallest distance and the largest time: 71.5 ÷ 4.55 [1] = 15.71… [1] (d) To 2 s.f. the bounds are 16 and 16, so they agree [1]. To 3 s.f. they are 16.3 and 15.7, which differ, so the speed is 16 km/h (2 s.f.) [1] Examiner insight: Give the reason for your final accuracy: both bounds agree to that many figures and not to the next. A bare answer without this comparison is unlikely to be given full credit.

11. (a) 7.2 → 7, 19.6 → 20, 0.48 → 0.5 and 4.9 → 5 [1]. Top 7 × 20 = 140 and bottom 0.5 × 5 = 2.5 [1]. 140 ÷ 2.5 = 56 [1] (b) 56 ÷ 60 × 100 [1] = 93.3% (1 d.p.) [1] Examiner insight: Round to 1 s.f. in the usual way. Rounding 19.6 to 20 gives the simplest working, and estimating with unrounded values gains nothing.

Where marks are usually lost

• Dropping a trailing zero in answers such as 8.000 or 4 960.
• Mixing up decimal places and significant figures when the number has leading zeros.
• Writing the upper end of an error interval with ≤.
• Choosing the wrong bound in a subtraction or division.
• Using half a unit of 0.05 for a value given to 2 decimal places, instead of 0.005.
• Giving a bounds answer to more accuracy than the data supports, or with no justification.
• Not showing the rounded numbers in an estimation.
• Failing to leave out the repeat when subtracting in a recurring decimal proof.
• Leaving a fraction unsimplified when “simplest form” is asked for.
• Comparing quantities in different units without converting first.

Next steps

• Read the revision notes for a short recap.
• Go back to the study guide for any worked example you found hard.
• Check the course hub and the printable checklist.
• Take one of the free 10-minute diagnostics to find your next weak point.
• Book a free trial class if you want to go through these with a teacher.

Official syllabus

OxfordAQA International GCSE Mathematics (9260), specification Version 5.1, for exams May/June 2018 onwards, published by OxfordAQA. Sections 3.1.1 (N11) and 3.1.2 (N12, N13, N14).