AQA GCSE Mathematics 8300: Measures and accuracy – 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 cover section 3.1.3, Measures and accuracy (N13 to N16), of the AQA GCSE Mathematics (8300) specification, for teaching from September 2015 with exams from May/June 2017 onwards (version 1.0). Questions 1 to 7 and 11 use content assessed at both Foundation and Higher tier. Questions 8 and 9, and parts 10(a) and 10(b), use upper and lower bounds, which are Higher tier only, and are labelled (Higher); part 10(c) is a unit conversion for both tiers. Each question says whether it is non-calculator (like Paper 1) or calculator (like Papers 2 and 3).

These questions are different from the ones in the topic-level Number practice questions, so you can use both. Learn the methods first in the Measures and accuracy study guide and the Measures and accuracy revision notes. The course hub is AQA GCSE Mathematics and the printable checklist lists every statement.

Questions

1. (non-calculator)

(a) Change 4.6 km to metres. [1] (b) Change 0.38 litres to millilitres. [1] (c) Change 0.09 m² to cm². [1] (d) 1 kg is approximately 2.2 pounds. Change 15 kg to pounds. [1]

2. (non-calculator)

(a) Round 0.0060825 to 3 significant figures. [1] (b) Round 7.8649 to 2 decimal places. [1]

3. (non-calculator)

(a) By rounding each number to 1 significant figure, estimate the value of (82.4 × 5.97) ÷ 0.398. [3] (b) Kim works out the exact value on a calculator and writes 123.6. Use your estimate to explain why Kim must be wrong. [1]

4. (non-calculator)

(a) A height, h cm, is 17.3 cm, rounded to 1 decimal place. Write down the error interval for h. [2] (b) A time, t seconds, is 42 seconds, truncated to a whole number of seconds. Write down the error interval for t. [2]

5. (calculator) A plumber charges £46.50 per hour.

(a) A job takes 2 hours 40 minutes. Work out the charge. [3] (b) The plumber drives 52 km to the job in 40 minutes. Work out the average speed in km/h. [2]

6. (calculator) A rectangular floor measures 5.35 m by 3.8 m. One pack of tiles covers 1.44 m². Ravi buys enough tiles to cover the floor plus an extra 10% for cutting. Work out how many packs he must buy. [4]

7. (calculator) A bag of flour has a mass of 1.5 kg, correct to the nearest 10 grams.

(a) Write down the error interval for the mass, m kg. [2] (b) A recipe needs at least 1.49 kg of flour. Can you be sure the bag holds enough? Give a reason. [1]

8. (Higher) (calculator) A metal block has a mass of 640 g, to the nearest 10 g, and a volume of 82 cm³, to the nearest cm³.

(a) Work out the upper bound and the lower bound of the density of the block. [3] (b) Write down the density to a suitable degree of accuracy. Give a reason for your answer. [2]

9. (Higher) (calculator) A pipe is 3.6 m long, to the nearest 0.1 m. A piece 1.25 m long, to the nearest centimetre, is cut from it. Work out the least possible length of pipe left. [3]

10. (calculator) A rectangular field is 86 m long and 54 m wide, each to the nearest metre. Jess runs 5 laps of the edge of the field in 9 minutes 20 seconds, to the nearest second.

(a) (Higher) Work out the upper bound of the perimeter of the field. [2] (b) (Higher) Work out the lower bound of Jess’s average speed in m/s. Give your answer to 3 significant figures. [4] (c) The upper bound of her average speed is 1410 ÷ 559.5 m/s. Convert this to km/h, giving your answer to 3 significant figures. [2]

11. (calculator) A garden pond is a cuboid, 2.4 m long, 1.6 m wide and 45 cm deep.

(a) Work out the volume of the pond in litres. [3] (b) A hose fills the pond at 12.5 litres per minute. Work out how long it takes to fill the empty pond. Give your answer in hours and minutes, to the nearest minute. [3] (c) Ali estimates the time using a volume of 2 × 2 × 0.5 m³ and a rate of 10 litres per minute. Is his estimate an overestimate or an underestimate of the true time? Explain how his rounding of the rate affects the estimate. [2]

Answers

1. (a) 4.6 × 1000 = 4600 m [1] (b) 0.38 × 1000 = 380 ml [1] (c) 1 m² = 10 000 cm², so 0.09 × 10 000 = 900 cm² [1] (d) 15 × 2.2 = 33 pounds [1] Examiner insight: Part (c) is the discriminating mark: × 100 gives 9 cm², a common wrong answer that scores nothing because the area factor must be squared.

2. (a) 0.00608 [1] (b) 7.86 [1] Examiner insight: Each part is a single accuracy mark, so 0.006 08 written as 0.0061 (2 s.f.) or 7.865 rounded twice to 7.87 earns nothing; round once from the original digits.

3. (a) Rounded values 80, 6 and 0.4 [1]; 80 × 6 = 480 [1]; 480 ÷ 0.4 = 1200 [1] (b) The estimate is 1200 but Kim’s answer is about ten times smaller, so Kim’s answer cannot be right (the true value is 1236) [1] Examiner insight: The first mark needs all three rounded values seen; using a calculator or rounding 82.4 to 82 means the method mark for 1 s.f. rounding is not given.

4. (a) 17.25 ≤ h [1]; h < 17.35 [1], so 17.25 ≤ h < 17.35 (b) 42 ≤ t [1]; t < 43 [1], so 42 ≤ t < 43 Examiner insight: One mark is usually available for each correct end; writing 41.5 ≤ t < 42.5 in (b) treats truncation as rounding and loses both marks.

5. (a) 40 minutes = 40/60 = 2/3 hour, so time = 2 2/3 hours [1]; 46.50 × 2 2/3 [1] = £124.00 [1] (b) 40 minutes = 2/3 hour [1]; 52 ÷ 2/3 = 78 km/h [1] Examiner insight: Using 2.40 hours in (a) gives £111.60 and earns no marks for the method; the time must be converted to hours (or the rate to pence per minute) first.

6. Area = 5.35 × 3.8 = 20.33 m² [1]; with 10% extra: 20.33 × 1.1 = 22.363 m² [1]; 22.363 ÷ 1.44 = 15.53… [1]; so 16 packs [1] Examiner insight: The last mark is for rounding up in context; 15.53 written as 15 or 15.5 packs does not get it, even with all the working correct.

7. (a) 10 g = 0.01 kg, half of which is 0.005 kg [1]; 1.495 ≤ m < 1.505 [1] (b) Yes, because the least possible mass is 1.495 kg, which is more than 1.49 kg [1] Examiner insight: “Yes” on its own scores nothing; the mark is for quoting the lower limit (1.495) and comparing it with 1.49.

8. (a) Mass 635 ≤ m < 645 and volume 81.5 ≤ V < 82.5 [1]; UB density = 645 ÷ 81.5 = 7.914… g/cm³ [1]; LB density = 635 ÷ 82.5 = 7.696… g/cm³ [1] (b) 8 g/cm³ [1], because both bounds round to 8 to 1 significant figure (but to 7.9 and 7.7 to 2 s.f.) [1] Examiner insight: In (a), the upper bound must use the lower bound of the volume; 645 ÷ 82.5 gives 7.818…, which loses the accuracy mark. In (b) the reason mark needs both bounds compared.

9. Bounds: pipe LB 3.55 m; piece UB 1.255 m [1]; least length = LB pipe − UB piece = 3.55 − 1.255 [1] = 2.295 m [1] Examiner insight: 3.55 − 1.245 = 2.305 m uses the wrong bound of the piece and scores only the first mark.

10. (a) Upper bounds 86.5 m and 54.5 m [1]; perimeter = 2 × (86.5 + 54.5) = 282 m [1] (b) LB perimeter = 2 × (85.5 + 53.5) = 278 m, so LB distance = 5 × 278 = 1390 m [1]; UB time = 9 × 60 + 20.5 = 560.5 s [1]; LB speed = LB distance ÷ UB time [1] = 1390 ÷ 560.5 = 2.4799… = 2.48 m/s [1] (c) 1410 ÷ 559.5 = 2.5201… m/s [1]; × 3.6 = 9.072… = 9.07 km/h [1] Examiner insight: In (b) a mark is usually given for choosing the correct pair of bounds even if an arithmetic slip follows; forgetting to change 9 minutes 20 seconds into seconds (or using 9.2 minutes) loses the time mark.

11. (a) 45 cm = 0.45 m [1]; volume = 2.4 × 1.6 × 0.45 = 1.728 m³ [1]; 1.728 × 1000 = 1728 litres [1] (b) 1728 ÷ 12.5 = 138.24 minutes [1]; 138 minutes to the nearest minute [1]; = 2 hours 18 minutes [1] (c) His estimate is 2000 ÷ 10 = 200 minutes, which is more than the true time, so it is an overestimate [1]. Rounding the rate down to 10 litres per minute makes the time longer, because he is dividing by a smaller number [1] Examiner insight: In (b), 138.24 minutes written as 1.38 hours or 1 hour 38 minutes loses the final mark: convert minutes to hours and minutes with ÷ 60, not by moving the decimal point.

Where marks are usually lost

• Using the length factor for areas and volumes (× 100 for m² to cm²).
• Treating 2 hours 40 minutes as 2.40 hours.
• Not showing the 1 s.f. values in an estimate, so the method mark cannot be awarded.
• Rounding in two stages (7.8649 to 7.865, then to 7.87) instead of once from the original digits.
• Rounding to the nearest whole number when the context needs rounding up, as with packs of tiles.
• Using half a unit for a truncated value, or ≤ at both ends of an error interval.
• Answering “can you be sure?” with no limit quoted.
• (Higher) Pairing UB with UB for a division or a subtraction.
• (Higher) Mixing metres with centimetres, or minutes with seconds, inside a bounds calculation.
• (Higher) Giving a suitable degree of accuracy without comparing both bounds.

Next steps

• Measures and accuracy revision notes
• Measures and accuracy study guide
• Number practice questions for the rest of Topic 1
• AQA GCSE Mathematics course hub
• Printable AQA GCSE Mathematics checklist
• All free 10-minute diagnostics
• Book a free trial class

Official syllabus

AQA GCSE Mathematics (8300) specification, for teaching from September 2015 onwards, for exams in May/June 2017 onwards, version 1.0 (AQA), section 3.1.3 Measures and accuracy, references N13 to N16.