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Algebra, NAP-A4-NC28

The value of  `6t^2`  when  `t = –4`  is

`– 96` `– 48` `96` `576`
 
 
 
 
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`96`

Show Worked Solution

`text(When)\ \ t = -4,`

`6t^2` `= 6 (-4)^2`
  `= 6 xx 16`
  `= 96`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 10, smc-3179-20-Substitution, smc-3179-30-Index laws, smc-683-20-Substitution, smc-683-30-Index laws

Algebra, NAP-B4-NC22 SA

When  `p = 3`  and  `q = –3`, what is the value of  `p^2 + q^2`?

`p^2 + q^2 =`    
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`18`

Show Worked Solution
`p^2 + q^2` `= 3^2 + (-3)^2`
  `= 9 + 9`
  `= 18`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 8, smc-3179-20-Substitution, smc-3179-30-Index laws, smc-683-20-Substitution, smc-683-30-Index laws

Algebra, NAP-B4-CA26

What is the value of  `6 + 2x - x^2`  when  `x = −3`?

`−9` `3` `9` `21`
 
 
 
 
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`−9`

Show Worked Solution
`6 + 2x – x^2` `= 6 + 2(−3) – (−3)^2`
  `= 6 – 6 – 9`
  `= −9`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 9, smc-3179-20-Substitution, smc-3179-30-Index laws, smc-683-20-Substitution, smc-683-30-Index laws

Algebra, NAP-B4-CA17

Ice cream is put into a waffle cone so it fills the cone to the top.
 

The volume, `V`, of the cone is given by the rule  `V = (pir^2h)/3`,

where `r` is the radius of the cone in centimetres and `h` is the height in centimetres.

When  `h = 12`  and   `r = 3`, the volume of the cone is closest to

`38\ text(cm)³` `113\ text(cm)³` `339\ text(cm)³` `452\ text(cm)³`
 
 
 
 
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`113\ text(cm)³`

Show Worked Solution
`V` `= (pi xx 3^2 xx 12)/3`
  `= 113.097…\ text(cm)³`
  `=113\ text{cm³  (nearest cm³)}`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 8, smc-3179-20-Substitution, smc-3179-30-Index laws, smc-683-20-Substitution, smc-683-30-Index laws

Algebra, NAP-D4-CA14

The value of  `y`  can be calculated by using the rule  `y = 8 - x^2`.

What is the value of  `y`  when  `x = 2.5?`

`1.75`  `3` `5.5` `6.25`
 
 
 
 
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`1.75`

Show Worked Solution
`y` `= 8 – x^2`
  `= 8 – (2.5)^2`
  `= 8 – 6.25`
  `= 1.75`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 7, smc-3179-20-Substitution, smc-3179-30-Index laws, smc-683-20-Substitution, smc-683-30-Index laws

Algebra, NAP-E4-CA15

`a`  is a positive whole number.

Which of the equations below is not true?

 
`a + a + a = 3a`
 
`a^3 = 3 xx a`
 
`-a + a = 0`
 
`a ÷ a = 1`
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`a^3 = 3 xx a`

Show Worked Solution
`a^3` `= a xx a xx a`
  `!= 3 xx a`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 8, smc-3179-30-Index laws, smc-683-30-Index laws

Algebra, NAP-E4-NC07

Which expression is equal to  `4a^4`?

 
`8 xx a`
 
`16 xx a`
 
`4 xx a xx a xx a xx a`
 
`4 + a + a + a + a`
 
`4 xx 4 xx 4 xx 4 xx a xx a xx a xx a`
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`4 xx a xx a xx a xx a`

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`4a^4 = 4 xx a xx a xx a xx a`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 6, smc-3179-30-Index laws, smc-683-30-Index laws

Algebra, NAP-G4-NC05

Which expression equals  `a^3`?

`(a + a + a + a)/a` `a^2 + a` `3 × a` `a × a × a`
 
 
 
 
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`a × a × a` 

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`a × a × a` 

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 7, smc-3179-30-Index laws, smc-683-30-Index laws

Algebra, NAP-H4-CA04

`y = 4x^2 - 7`

What is the value of  `y`  when  `x = 3.1?`

`5.4`    `17.8`  `31.44` `146.76`
 
 
 
 
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`31.44`

Show Worked Solution
`y` `= 4 (3.1)^2 – 7`
  `= 38.44 – 7`
  `= 31.44`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 7, smc-3179-20-Substitution, smc-3179-30-Index laws, smc-683-20-Substitution, smc-683-30-Index laws

Algebra, NAP-I4-CA18

Which expression is equivalent to  `4x^2-12x + x^3?`

`4(x^2-3x + x^3)` `4x (x-3 + x^2)` `x^2 (4-12 + x)` `x (4x-12 + x^2)`
 
 
 
 
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`x (4x-12 + x^2)`

Show Worked Solution

 `x (4x-12 + x^2)`

`= 4x^2-12x + x^3`

Filed Under: Basic Algebra, Basic Algebra Tagged With: Band 9, smc-3179-30-Index laws, smc-3179-40-Distributive Law, smc-683-30-Index laws, smc-683-40-Distributive Law

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