1.25 Error intervals and truncation
9 exam questions worth 18 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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The number 2.1 is rounded to 1 decimal place. Which is the error interval for the number?
Choose one answer.
Correct Not quite: the answer is \( 2.05 \le x < 2.15 \)
Mark scheme
B: 2.05 \le x < 2.15
Model answer
2.05 \le x < 2.15 (B). Half a unit either side; the lower bound is included and the upper bound is not.
A number x is 350 correct to the nearest 10. Write down the error interval for x.
Mark scheme
B1: 345 ≤ x; B1: x < 355
Model answer
345 ≤ x < 355.
A number y is 0.8 correct to 1 significant figure. Write down the error interval for y.
Mark scheme
B1: 0.75 ≤ y; B1: y < 0.85
Model answer
0.75 ≤ y < 0.85.
A number n is 4000 correct to 1 significant figure. Write down the error interval for n.
Mark scheme
B1: 3500 ≤ n; B1: n < 4500
Model answer
3500 ≤ n < 4500.
A number x is 2.1 when it is truncated to 1 decimal place. Write down the error interval for x.
Mark scheme
B1: 2.1 ≤ x; B1: x < 2.2
Model answer
2.1 ≤ x < 2.2.
A length is 12.5 cm correct to 3 significant figures. Write down the error interval for the length.
Mark scheme
B1: 12.45 ≤ L; B1: L < 12.55
Model answer
12.45 ≤ L < 12.55.
Show the difference between rounding and truncating by writing 3.78 to 1 decimal place using each method.
Mark scheme
B1: rounded 3.8; B1: truncated 3.7
Model answer
Rounding gives 3.8 (the decider 8 rounds up) but truncating gives 3.7 (the digits are just cut off).
There are 200 cars in a car park, correct to the nearest 100. The number of cars n is a whole number. Write down the error interval for n.
Mark scheme
B1: 150 ≤ n; B1: n ≤ 249 (accept n < 250)
Model answer
150 ≤ n ≤ 249 (or 150 ≤ n < 250).
A box is 20 cm wide, to the nearest centimetre. A shelf is 20 cm wide, to the nearest centimetre. Can you be sure that the box will fit on the shelf? You must show your working.
Mark scheme
B1: box width < 20.5 cm; B1: shelf width ≥ 19.5 cm; B1: No, because the box could be wider than the shelf
Model answer
The box is up to 20.5 cm wide and the shelf could be as narrow as 19.5 cm. The box could be wider than the shelf, so you cannot be sure it fits.
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