smc-4228-10-Positive integers

Indices, SMB-013

Simplify the expression `36t^7 -: 27t^3`. (2 marks)

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`(4t^4)/3`

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`36t^7 -: 27t^3`	`= (9 xx 4 xxt^7)/(9xx3xxt^3)`
	`= (4t^4)/3`

Indices, SMB-012

Simplify the expression `24a^8 -: 3a^2`. (2 marks)

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`8a^6`

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`24a^8 -: 3a^2`	`= (8xx3xxa^8)/(3 xx a^2)`
	`= 8a^6`

Indices, SMB-004 MC

Which expression is equal to `6^3 xx 36^2`?

`6 xx 3 xx 36 xx 2`
`6 xx 6 xx 6 xx 6 xx 6`
`6 xx 6 xx 6 xx 36 xx 6`
`6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`

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`D`

Show Worked Solution

`6^3 xx 36^2`	`= (6xx6xx6) xx (6xx6)^2`
	`= (6xx6xx6) xx (6xx6) xx (6 xx6)`
	`=6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`

`=>D`

Indices, SMB-003 MC

`7 xx 2^3 =`

`28`
`42`
`56`
`2744`

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`C`

Show Worked Solution

`7 xx 2^3`	`= 7 xx 2 xx 2 xx 2`
	`= 56`

`=>C`

Inices, SMB-002 MC

`30^2` is equal to which of the following?

`60^2 ÷ 3`
`3^2 xx 2 xx 5 xx 2 xx 5`
`9 xx 5^2`
`3 xx 10 xx 10`

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`B`

Show Worked Solution

`30^2 = 900`

`3^2 xx 2 xx 5 xx 2 xx 5`

`= 3^2 xx 10 xx 10`

`= 900`

`=>B`

Indices, SMB-001 MC

Which of the following is equal to 32?

`2^3 xx 2^2`
`2^3 + 2^2`
`3^2 + 2^2`
`3^2 xx 2^2`

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`=>A`

Show Worked Solution

`2^3 xx 2^2`	`= 8 xx 4`
	`= 32`

`=>A`

Algebra, 2UG 2016 HSC 26b

Simplify `(8x^4y)/(24x^3y^5)`. (2 marks)

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`x/(3y^4)`

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`(8x^4y)/(24x^3y^5)`	`=(x^((4-3))y^((1-5)))/3`
	`=(xy^(-4))/3`
	`=x/(3y^4)`

Algebra, 2UG 2006 HSC 23a

Simplify `(ab^2)/w xx (4w)/(3b).` (2 marks)

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`(4ab)/3`

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`(ab^2)/w xx (4w)/(3b)`	`=(4ab^2w)/(3bw)`
	`=(4ab)/3`

Algebra, 2UG 2005 HSC 7 MC

Simplify `2m^2 × 3m p^2`

`5m^2p^2`
`5m^3p^2`
`6m^2p^2`
`6m^3p^2`

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`D`

Show Worked Solution

`2m^2 × 3m p^2`	`= 6m^((2+1))p^2`
	`=6m^3p^2`

`=> D`

Algebra, 2UG 2008 HSC 1 MC

Which expression is equivalent to `12k^3 ÷ 4k`?

`3k^2 `
`3k^3`
`8k^2`
`8k^3`

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`A`

Show Worked Solution

`12k^3 -: 4k`	`=(12k^3)/(4k)`
	`=3k^2`

`=> A`

Algebra, 2UG 2014 HSC 11 MC

Simplify `6w^4 xx 1/3 w^2`.

`2w^6`
`2w^8`
`18w^6`
`18w^8`

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`A`

Show Worked Solution

`6w^4 xx 1/3w^2`	`= (6w^4w^2)/3`
	`= 2w^6`

`=> A`

Algebra, 2UG 2010 HSC 27a

Fully simplify `(4x^2)/(3y) -: (xy)/5`. (3 marks)

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

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`(20x)/(3y^2)`

Show Worked Solution

♦♦ Mean mark 33%.
MARKER’S COMMENT: Remember to “invert and multiply” when dividing a fraction by a fraction (see Worked Solution).

`(4x^2)/(3y) -: (xy)/5`	`= (4x^2)/(3y) xx 5/(xy)`
	`= (20x^2)/(3xy^2)`
	`= (20x)/(3y^2)`

Algebra, 2UG 2012 HSC 28b

Simplify fully `(18ab)/(3a^2) xx c/b`. (2 marks)

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`(6c)/a`

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♦ Mean mark 35%!

`(18ab)/(3a^2) xx c/b`	`= (18abc)/(3a^2b)`
	`=(6c)/a`

Algebra, 2UG 2011 HSC 12 MC

Which of the following expresses `(6x^2y)/3-:(2y)/5` in its simplest form?

`5x^2`
`30x^2y`
`1/(5x^2)`
`5/(4x^2y^2)`

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`A`

Show Worked Solution

ALGEBRA TIP: When you divide by a fraction, invert the divisor and multiply as shown in the Worked Solution.

`(6x^2y)/3-:(2y)/5`	`=(6x^2y)/3xx5/(2y)`
	`=(30x^2y)/(6y)`
	`=5x^2`

`=>A`

Algebra, 2UG 2013 HSC 5 MC

Which of the following is `(12T^2)/(3Txx2W)` in its simplest form?

`(2T)/W`
`2TW`
`(8T)/W`
`8TW`

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`A`

Show Worked Solution

`(12T^2)/(3Txx2W)=(12T^2)/(6TW)=(2T)/W`

`=>\ A`