Measures and solids · Ages 13–14
Planning a measurement worksheet
Part of: Errors in measurement
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Planning a measurement worksheet
Measures and solids · Ages 13–14
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A stack of 50 identical cards is measured as 39 mm thick. How thick is one card, in mm?
Answer:
2.A pendulum is timed for 10 swings, taking 8.9 seconds in all. On average, how many seconds does one swing take?
Answer:
3.A stack of 100 identical cards is measured as 48 mm thick. How thick is one card, in mm?
Answer:
4.A pendulum is timed for 20 swings, taking 27.4 seconds in all. On average, how many seconds does one swing take?
Answer:
5.A measuring cylinder holds 38 mL of water; with a stone dropped in (right under the water), the level rises to 66 mL. What is the stone's volume, in cm³?
Answer:
6.20 identical coins are stacked, and a ruler correct to the nearest 1 mm measures the stack as 30 mm tall. One coin is mm thick, with a greatest absolute error of mm.
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
7.A stopwatch is used to time one swing of a pendulum (about 1.7 seconds). Pressing the stopwatch, a person's reaction adds an error. Which way is best?
- A. Time 20 swings and multiply by 20
- B. Time just one swing
- C. Time 20 swings and divide by 20
- D. Time one swing, to the nearest whole second
Choose the right answer
Answer:
8.A stopwatch is used to time one swing of a pendulum (about 2.5 seconds). Pressing the stopwatch, a person's reaction adds an error. Which way is best?
- A. Time 20 swings and divide by 20
- B. Time just one swing
- C. Time 20 swings and multiply by 20
- D. Time one swing, to the nearest whole second
Choose the right answer
Answer:
9.A ruler correct to the nearest 1 mm measures 10 identical sheets together, and the result is divided by 10. The greatest absolute error of one sheet's thickness found this way is less than 0.01 mm.
True or false?
Answer:
10.A letter of about 36 g is to be weighed. Which tool suits best?
- A. Weigh it in the hand and guess
- B. Jewellery scales correct to the nearest 0.01 g, up to 10 g
- C. Bathroom scales correct to the nearest 0.5 kg
- D. Digital scales correct to the nearest 1 g, up to 2 kg
Choose the right answer
Answer:
11.A letter of about 90 g is to be weighed. Which tool suits best?
- A. Digital scales correct to the nearest 1 g, up to 2 kg
- B. Weigh it in the hand and guess
- C. Jewellery scales correct to the nearest 0.01 g, up to 10 g
- D. Bathroom scales correct to the nearest 0.5 kg
Choose the right answer
Answer:
12.With a ruler correct to the nearest 1 mm, a stack of identical sheets is measured and divided by the number of sheets to find one sheet's thickness. Which way gives the most accurate thickness?
- A. Measure 40 sheets
- B. Measure 200 sheets
- C. Measure 10 sheets
- D. Measure 5 sheets
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.An oddly shaped ornament's volume is to be measured. Sunk right under in a tank with a base area of 308 cm², it makes the water rise by 1.8 cm. What is the ornament's volume, in cm³?
Working:
Answer:
14.To measure a thin copper wire's diameter, May winds it tightly round a pencil 20 times, and a ruler correct to the nearest 1 mm measures the coil as 10 mm long. The wire's diameter is about mm, with a greatest absolute error of mm.
Fill in each blank
Working:
Answer:
15.Chi-keung times 10 swings of a pendulum three times with a stopwatch: 15.2 s, 15.9 s and 15.1 s. The mean of the three is s, so one swing takes about s.
Fill in each blank
Working:
Answer:
16.A pack of 100 identical sheets of paper weighs 530 g on scales correct to the nearest 1 g. About how many g does one sheet weigh?
Working:
Answer:
17.Find one sheet of paper's thickness with a ruler correct to the nearest 1 mm, then estimate how thick 400 sheets stacked up would be. Put the steps in order.
- A. 400 sheets ≈ 0.125 × 400 = 50 mm
- B. One sheet = 25 ÷ 200 = 0.125 mm
- C. Thickness of 200 sheets = 25 mm
Write the letters in the right order
Working:
Answer:
18.Chi-keung uses a ruler correct to the nearest 1 mm to measure 50 identical sheets together, then divides by 50. Chi-keung says the greatest absolute error of one sheet's thickness found this way is 0.5 mm.
True or false?
Working:
Answer:
Show the answers and working
Planning a measurement worksheet: Answers and working
Part A: Working out and filling in
1. 0.78 mm
One is too thin to measure, so measure the stack and divide: 39 ÷ 50 = 0.78 mm.
2. 0.89 s
8.9 ÷ 10 = 0.89 seconds. Timing many and dividing shares the stopwatch's error among them.
3. 0.48 mm
One is too thin to measure, so measure the stack and divide: 48 ÷ 100 = 0.48 mm.
4. 1.37 s
27.4 ÷ 20 = 1.37 seconds. Timing many and dividing shares the stopwatch's error among them.
5. 28 cm³
An odd shape has no length, width and height to measure, so measure the water it pushes aside: 66 − 38 = 28 mL = 28 cm³.
6. 1.5, 0.025
30 ÷ 20 = 1.5 mm; the stack's 0.5 mm error is shared among 20 coins: 0.5 ÷ 20 = 0.025 mm.
Part B: Choose, or true or false
7. C. Time 20 swings and divide by 20
The reaction error is about the same each time; time 20 swings and divide by 20, and the error is shared among the 20 too, leaving each a small part.
8. A. Time 20 swings and divide by 20
The reaction error is about the same each time; time 20 swings and divide by 20, and the error is shared among the 20 too, leaving each a small part.
9. False
The stack can be out by 0.5 mm, shared among 10 sheets: 0.5 ÷ 10 = 0.05 mm.
10. D. Digital scales correct to the nearest 1 g, up to 2 kg
The tool must reach (a big enough range) and its unit must suit: with the 1 g scales the relative error is about 0.5 ÷ 36, just right.
11. A. Digital scales correct to the nearest 1 g, up to 2 kg
The tool must reach (a big enough range) and its unit must suit: with the 1 g scales the relative error is about 0.5 ÷ 90, just right.
12. B. Measure 200 sheets
The stack's error is always 0.5 mm, so the more sheets, the smaller each one's share: 0.5 ÷ 200 = 0.0025 mm is the least.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 554.4 cm³
An odd shape has no length, width and height to measure, so measure the water it pushes aside: 308 × 1.8 = 554.4 cm³.
14. 0.5, 0.025
The coil is 20 diameters long: 10 ÷ 20 = 0.5 mm; its 0.5 mm error is shared among 20 turns: 0.5 ÷ 20 = 0.025 mm.
15. 15.4, 1.54
(15.2 + 15.9 + 15.1) ÷ 3 = 15.4 s; 15.4 ÷ 10 = 1.54 s. Measuring again and taking the mean lets chance errors partly cancel.
16. 5.3 g
One sheet is too light, so weigh the pack and divide: 530 ÷ 100 = 5.3 g; the 0.5 g error is shared among 100 sheets too.
17. C → B → A
Measure a stack first (one sheet is too thin), divide by the count for one sheet, and only then multiply by 400.
18. False
The stack can be out by 0.5 mm; divided by 50, so is the error: 0.5 ÷ 50 = 0.01 mm.
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