SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Algebra, NAP-A4-CA27

The plan of a square area of land is drawn below.

A mining licence is granted over part of the land.

All measurements are given in kilometres.
 

The area of land the mining licence covers is

`x^2-20` `x^2 + 20` `2x^2-9` `2x^2-20`
 
 
 
 
Show Answers Only

`x^2-20`

Show Worked Solution

`text{Area of original land}\ = x xx x = x^2\ text{km}^2`

`text{Size of non-mining area}\ = 20\ text{km}^2`

`:.\ text(Area of mining)\ = x^2-20\ text{km}^2`

Algebra, NAP-A4-NC11

`ABCD` is a square.
 


 

What is the value of `x`?

1 2 3 4
 
 
 
 
Show Answers Only

`3`

Show Worked Solution

`text(S) text(ince)\ ABCD\ text(is a square),`

`4x – 7` `= x + 2`
`3x` `= 9`
`:. x` `= 3`

Measurement, NAP-J4-CA16

Cecil is designing a rectangular garden bed for growing vegetables in his yard.

He wants the garden bed to be at least 60 square metres.

He has dug out two sides, each 12.7 metres in length.

What is the smallest possible length of each of the other two sides, rounded to one decimal place?

`text(4 metres)` `text(4.7 metres)` `text(4.8 metres)` `text(5 metres)`
 
 
 
 
Show Answers Only

`text(4.8 metres)`

Show Worked Solution

`text(Let)\ \ d =\ text(length of other side)`

`12.7 xx d` `>= 60`
`d` `>= 6/12.7`
`d` `>= 4.72…\ text(m)`

 

`:.\ text{Smallest length is 4.8 m (to 1 d.p.)}`

Measurement, NAP-C4-NC24

The rhombus below has a side length of 8 cm.
 

 

  
Which equation must be true?

`xy = 80` `10x = 8y` `2xy = 40` `5x = 10y`
 
 
 
 
Show Answers Only

`xy=80`

Show Worked Solution

`text(The area of the rhombus can be calculated)`

`text(in two ways:)`

`text(Area)` `= 8 xx 5 =40, or`
`text(Area)`

`=1/2 xx text(product of diagonals)`
  `= 1/2 xx xy`

 

`:. 1/2 xy` `=40`
`xy` `=80`

Measurement, NAP-C4-NC32 SA

The total surface area of a cube is 150 cm².
 

 How long is an edge of the cube?

  cm
Show Answers Only

`text(5 cm)`

Show Worked Solution

`text(Surface area of 1 face of the cube)`

`=150/6`

`=25\ text(cm²)`

 

`text(Let)\ \ x=\ text(length of 1 side)`

`x^2` `=25`
`:.\ x` `=5\ text(cm)`

Measurement, NAP-F4-CA31 SA

Barry pours two identical cubes of cement as foundation for a large sculpture, as shown in the diagram below.
 

 
If 432 cubic metres are required to form the foundation, what is the height of the foundation, as shown on the diagram?

   metres
Show Answers Only

`12\ text(metres)`

Show Worked Solution

`text(Let dimensions of one cube) = x xx x xx x`

`2x^3` `= 432`
`x^3` `= 216`
`x` `= 6\ text(m)`

 

`:. h` `= 2x`
  `= 12\ text(metres)`

Algebra, NAP-F4-NC12

The rhombus below has a side length `d`.
 

 
Which expression cannot be used for the perimeter?

`2 xx (d + d)` `d xx 4` `d xx d` `d + d + 2 xx d`
 
 
 
 
Show Answers Only

`d xx d`

Show Worked Solution

`d xx d`

Measurement, NAP-H4-NC30

David's backyard is in shape of a rectangle and has an area of 50 m².

Tim's backyard is also rectangular but with side lengths that are double those of David's backyard.

What is the area of Tim's backyard.

`25\ text(m²)` `100\ text(m²)` `200\ text(m²)` `300\ text(m²)`
 
 
 
 
Show Answers Only

`200\ text(m²)`

Show Worked Solution

`text(Let the dimensions of David’s yard be:)\ \ x, y`

`text(Area) = xy`

 

`=>\ text(Tim’s yard’s dimensions are:)\ \ 2x, 2y`

`:.\ text(Area)` `= 4xy`
  `= 4 xx 50`
  `= 200\ text(m²)`