Algebraic Techniques (Adv-X)

Functions, 2ADV F1 2008 HSC 1c (Adapted)

Simplify `2/n-1/(n+1)`. (2 marks)

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`(n + 2)/(n(n+1))`

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`2/n-1/(n+1)`

`= (2(n+1)-1(n))/(n(n+1))`

`= (2n + 2-n)/(n(n+1))`

`= (n+2)/(n(n+1))`

Functions, 2ADV F1 2008 HSC 1e (Adapted)

Expand and simplify `(sqrt5+2)(3 sqrt5-4)`. (2 marks)

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`7 + 2 sqrt 5`

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`(sqrt 5+2)(3 sqrt 5-4)`

`= 3 sqrt 5 xx sqrt 5-4 sqrt 5 + 6 sqrt 5-8`

`= 3 xx 5-4 sqrt 5 + 6 sqrt 5-8`

`= 15-4 sqrt 5 + 6 sqrt 5-8`

`= 15-8 + 2 sqrt 5`

`= 7 + 2 sqrt 5`

Functions, 2ADV F1 2014 HSC 1 MC (Adapted)

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`

Functions, 2ADV F1 2015 HSC 1 MC (Adapted)

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`

Functions, 2ADV F1 2007 HSC 1a (Adapted)

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

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

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

Functions, 2ADV EO-Bank 22

Find the reciprocal of `1/(xy) + 1/y-z/x`. (2 marks)

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`(xy)/(x+y-z)`

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`1/(xy) + 1/y-z/x`	`=1/(xy)+x/(xy)-(zy)/(xy)`
	`=(1+x-zy)/(xy)`

`text(Reciprocal of)\ \ x = x^(-1)`

`:.\ text(Reciprocal of)\ \ (1+x-zy)/(xy)=((1+x-zy)/(xy))^(-1)=(xy)/(1+x-zy)`

Functions, 2ADV EO-Bank 23

Find the reciprocal of `r/p-1/(pq) + 1/q`. (2 marks)

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`(pq)/(p+q-r)`

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`r/p-1/(pq) + 1/q`	`=(qr)/(pq)-1/(pq)+p/(pq)`
	`=(qr-1+p)/(pq)`

`text(Reciprocal of)\ \ x = x^(-1)`

`:.\ text(Reciprocal of)\ \ (qr-1+p)/(pq)=((qr-1+p)/(pq))^(-1)=(pq)/(qr-1+p)`

Functions, 2ADV F1 2004 HSC 1c (Adapted)

Solve `(x+4)/5-(x-2)/6 = 4`. (2 marks)

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`38`

Show Worked Solution

`(x+4)/5-(x-2)/6`	`= 4`
`30((x+4)/5)-30((x-2)/6)`	`= 30 xx 4`
`6x+24-5x+10`	`= 120`
`x+34`	`= 120`
`:. x`	`= 38`

Functions, 2ADV F1 2012 HSC 1 MC (Adapted)

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`

Functions, 2ADV F1 2012 HSC 1 MC (Adapted)

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`