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Functions, 2ADV F1 SM-Bank 53

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

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

  2. Calculate the value of  `1/(root3(7+pi))`  to 3 significant figures.   (1 mark)

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

Show Answers Only
  1. `-1/3`
  2. `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.)}`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Log/Index Laws and Equations (Adv-2027), Log/Index Laws and Equations (Y11) Tagged With: Band 2, Band 3, smc-6213-60-Rounding, smc-6455-50-Exponential Equations, smc-963-50-Exponential Equation, smc-983-10-Rounding

Functions, 2ADV F1 2019 HSC 1 MC

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

  1. `9.36 xx 10^4`
  2. `9.4 xx 10^4`
  3. `9.36 xx 10^5`
  4. `9.4 xx 10^5`
Show Answers Only

`B`

Show Worked Solution
`pi^10` `= 93648.04…`
  `= 9.4 xx 10^4`

`=>  B`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11) Tagged With: Band 3, smc-6213-60-Rounding, smc-983-10-Rounding

Functions, 2ADV F1 2018 HSC 1 MC

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

  1. 0.07
  2. 0.08
  3. -12.54
  4. -12.55
Show Answers Only

`B`

Show Worked Solution

`7^(-1.3)`

`= 0.0796…`

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

`=>  B`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Surds and Rounding Tagged With: Band 2, smc-6213-60-Rounding, smc-983-10-Rounding

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.)}`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Surds and Rounding Tagged With: Band 2, HSC, smc-6213-60-Rounding, smc-983-10-Rounding

Functions, 2ADV F1 2015 HSC 1 MC

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

  1. `5.2336 xx 10^-2`
  2. `5.234 xx 10^-2`
  3. `5.2336 xx 10^-3`
  4. `5.234 xx 10^-3`
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`D`

Show Worked Solution

`0.005\ 233\ 59`

`= 5.234 xx 10^-3`

`=> D`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Surds and Rounding Tagged With: Band 3, HSC, M/C, smc-6213-60-Rounding, smc-983-10-Rounding

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)}`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Surds and Rounding Tagged With: Band 4, smc-6213-60-Rounding, smc-983-10-Rounding

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)}`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Surds and Rounding Tagged With: Band 3, smc-6213-60-Rounding, smc-983-10-Rounding

Functions, 2ADV F1 2014 HSC 1 MC

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

  1. `1.64`
  2. `1.65`
  3. `1.644`
  4. `1.645`
Show Answers Only

`A`

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

`=>  A`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Surds and Rounding Tagged With: Band 3, smc-6213-60-Rounding, smc-983-10-Rounding

Functions, 2ADV F1 2011 HSC 1a

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

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

Show Answers Only

 `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)}`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Surds and Rounding Tagged With: Band 3, smc-6213-60-Rounding, smc-983-10-Rounding

Functions, 2ADV F1 2012 HSC 1 MC

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

  1. `4.09`  
  2. `4.10`  
  3. `4.097`  
  4. `4.098` 
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`B`

Show Worked Solution

`4.10`

`=>  B`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Surds and Rounding Tagged With: Band 3, smc-6213-60-Rounding, smc-983-10-Rounding

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)}`

Filed Under: Algebraic Techniques (Adv-2027), Algebraic Techniques (Y11), Surds and Rounding Tagged With: Band 3, smc-6213-60-Rounding, smc-983-10-Rounding

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