smc-983-10-Rounding

v1 Functions, 2ADV F1 2014 HSC 1 MC

What is the value of `pi^2/12`, correct to 3 significant figures?

`0.823`
`0.82`
`0.822`
`0.83`

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`C`

Show Worked Solution

`pi^2/12`	`= (3.14159…)^2/12`
	`= 9.8696…/12`
	`= 0.8224…`
	`= 0.822\ text{(3 sig. figures)}`

`=> C`

v1 Functions, 2ADV F1 2015 HSC 1 MC

What is `341.56789` written in scientific notation, correct to 4 significant figures?

`3.416 xx 10^2`
`3.415 xx 10^2`
`3.416 xx 10^3`
`3.415 xx 10^1`

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`A`

Show Worked Solution

`341.567\ 89`

`= 3.4156… xx 10^2`

`= 3.416 xx 10^2` (to 4 significant figures)

`=> A`

v1 Functions, 2ADV F1 2007 HSC 1a

Evaluate `sqrt (2pi + 7)` correct to two decimal places. (2 marks)

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`3.34\ \ \ text{(to 2 d.p.)}`

Show Worked Solution

`sqrt (2pi + 7)`	`= sqrt(2 × 3.14159… + 7)`
	`= sqrt(6.28318… + 7)`
	`= sqrt(13.28318…)`
	`= 3.6446…`
	`= 3.64\ \ \ text{(to 2 d.p.)}`

v2 Functions, 2ADV F1 2012 HSC 1 MC

What is `2.49572` correct to three significant figures?

`2.49`
`2.50`
`2.495`
`2.496`

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`B`

Show Worked Solution

`2.50`

`=> B`

v1 Functions, 2ADV F1 2012 HSC 1 MC

What is `7.85179` correct to three significant figures?

`7.85`
`7.86`
`7.851`
`7.852`

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`A`

Show Worked Solution

`7.85`

`=> A`

Functions, 2ADV F1 SM-Bank 53

If `1/(root3(7+pi)) = (7+pi)^x`, find `x`. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
Calculate the value of `1/(root3(7+pi))` to 3 significant figures. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

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`-1/3`
`0.462`

Show Worked Solution

i. `1/(root3(7+pi)) = (7+pi)^(-1/3)`

ii.	`1/(root3(7+pi))`	`=0.4619…`
		`=0.462\ \ text{(to 3 sig. fig.)}`

Functions, 2ADV F1 2019 HSC 1 MC

What is the value of `pi^10` to two significant figures?

`9.36 xx 10^4`
`9.4 xx 10^4`
`9.36 xx 10^5`
`9.4 xx 10^5`

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`B`

Show Worked Solution

`pi^10`	`= 93648.04…`
	`= 9.4 xx 10^4`

`=> B`

Functions, 2ADV F1 2018 HSC 1 MC

What is the value of `7^(-1.3)` correct to two decimal places?

0.07
0.08
-12.54
-12.55

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`B`

Show Worked Solution

`7^(-1.3)`

`= 0.0796…`

`= 0.08\ \ text{(2 d.p.)}`

`=> B`

Functions, 2ADV F1 2007 HSC 1a

Evaluate `sqrt (pi^2 + 5)` correct to two decimal places. (2 marks)

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`3.86\ \ \ text{(to 2 d.p.)}`

Show Worked Solution

`sqrt (pi^2 + 5)`	`= 3.8561…`
	`= 3.86\ \ \ text{(to 2 d.p.)}`

Functions, 2ADV F1 2015 HSC 1 MC

What is `0.005\ 233\ 59` written in scientific notation, correct to 4 significant figures?

`5.2336 xx 10^-2`
`5.234 xx 10^-2`
`5.2336 xx 10^-3`
`5.234 xx 10^-3`

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`D`

Show Worked Solution

`0.005\ 233\ 59`

`= 5.234 xx 10^-3`

`=> D`

Functions, 2ADV F1 2004 HSC 1a

The radius of Mars is approximately `3\ 397\ 000` metres. Write this number in scientific notation, correct to two significant figures. (2 marks)

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`3.4 xx 10^6`

Show Worked Solution

`3\ 397\ 000`

`= 3.397 xx 10^6`

`= 3.4 xx 10^6\ text(m)\ \ text{(2 sig figures)}`

Functions, 2ADV F1 2008 HSC 1a

Evaluate `2 cos (pi/5)` correct to three significant figures. (2 marks)

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`1.62\ text{(3 sig)}`

Show Worked Solution

`2 cos (pi/5)`	`= 1.6180…`
	`= 1.62\ text{(3 sig)}`

Functions, 2ADV F1 2014 HSC 1 MC

What is the value of `(pi^2)/6`, correct to 3 significant figures?

`1.64`
`1.65`
`1.644`
`1.645`

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`A`

Show Worked Solution

`(pi^2)/6`	`= 1.6449…`
	`= 1.64\ text{(3 sig. figures)}`

`=> A`

Functions, 2ADV F1 2011 HSC 1a

Evaluate `root(3)(651/(4pi))` correct to four significant figures. (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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`3.728\ text{(to 4 sig. figures)}`

Show Worked Solution

MARKER’S COMMENT: Show answer to 5 or 6 decimals before rounding. Correct rounding of a wrong answer still receives half marks.

`root(3)(651/(4pi))`	`=3.72783…`
	`=3.728\ text{(to 4 sig. figures)}`

Functions, 2ADV F1 2012 HSC 1 MC

What is `4.097 84` correct to three significant figures?

`4.09`
`4.10`
`4.097`
`4.098`

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`B`

Show Worked Solution

`4.10`

`=> B`

Functions, 2ADV F1 2013 HSC 11a

Evaluate `ln3` correct to three significant figures. (1 mark)

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`1.10\ \ \ text{(to 3 sig. figures)}`

Show Worked Solution

`ln3`	`=1.09861…`
	`=1.10\ \ \ text{(to 3 sig. figures)}`