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ACSEE (Form 6) Calculating Devices — practice questions

Explore 5 free Calculating Devices questions in ACSEE (Form 6) Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Calculating Devices questions and exercises with answers

Showing questions 1–5 of 5.

Using a scientific calculator on the constants $\pi,\sqrt2,e,\sqrt3,1.414213,2.718282,3.1415,1.732051$, the mean to six decimal places is:Read the answer and worked solution →A frequency distribution is entered into a calculator's statistics mode. If the mean is 120.200 and the variance 3455.960, the standard deviation is:Read the answer and worked solution →A calculation gives $T^2=37.86083836$. Reported to nine significant figures, $T$ is:Read the answer and worked solution →Read the calculator outputRead the answer and worked solution →Decimal places or significant figures?Read the answer and worked solution →

Worked practice questions

Using a scientific calculator on the constants $\pi,\sqrt2,e,\sqrt3,1.414213,2.718282,3.1415,1.732051$, the mean to six decimal places is:

  1. 2.035017
  2. 2.425894
  3. 2.251523
  4. 4.457024
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Correct answer: C. 2.251523

1. Enter all eight constants into the calculator's statistics mode. 2. The list is $\pi,\sqrt2,e,\sqrt3,1.414213,2.718282,3.1415,1.732051$ — note $\sqrt2$ and $1.414213$ are separate entries. 3. Read off the mean key, which returns $\bar{x}=2.251523$ to six decimal places. 4. The other three values come from entering the wrong count of items or mixing the mean and standard deviation keys. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 1: Calculating Devices_

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A frequency distribution is entered into a calculator's statistics mode. If the mean is 120.200 and the variance 3455.960, the standard deviation is:

  1. 1727.980
  2. 58.787
  3. 3455.960
  4. 120.200
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Correct answer: B. 58.787

1. Standard deviation is the square root of the variance. 2. So $\delta=\sqrt{3455.960}$. 3. Evaluating gives $58.787$ to three decimal places. 4. Halving the variance, which gives $1727.980$, is not a step in any statistical formula. 5. Reporting the variance itself as the standard deviation confuses the two measures of spread. _Source: NECTA ACSEE 2022 Advanced Mathematics 142/1, Question 1: Calculating Device_

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A calculation gives $T^2=37.86083836$. Reported to nine significant figures, $T$ is:

  1. 37.8608384
  2. 6.15311615
  3. 6.15000000
  4. 1432.44311
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Correct answer: B. 6.15311615

1. The quantity computed is $T^2$, not $T$ itself. 2. So the final step is to take the square root: $T=\sqrt{37.86083836}$. 3. That gives $T=6.15311615$ to nine significant figures. 4. Stopping at $T^2$ and reporting $37.86083836$ as $T$ was a recorded error. 5. Writing $6.15$ is correct in value but carries only three significant figures, so it fails the instruction. _Source: NECTA ACSEE 2022 Advanced Mathematics 142/1, Question 1: Calculating Device_

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