Band 10 – Page 5

Algebra, NAP-I4-NC27 SA

Johnno is saving to buy a go-kart.

He created a table to keep track of his savings.

Complete the rule for the linear relationship between the amount of money in Johnno's savings account and the number of months of saving.

`y = `

`x + 520`

Show Answers Only

`40`

Show Worked Solution

`text(After 2 months, $600 in account)`

`600`	`= 2x + 520`
`2x`	`= 80`
`x`	`= 40`

Number, NAP-I4-NC26

Bobby wants to multiply `25 xx 44`.

Which of these expressions will give Bobby the correct answer?

	`(20 xx 40) + (5 xx 4)`
	`(20 xx 4) + (40 xx 5)`
	`(20 xx 44) + (5 xx 44)`
	`(20 xx 40) + (20 xx 4) + (40 xx 5)`

Show Answers Only

`(20 xx 44) + (5 xx 44)`

Show Worked Solution

`25 xx 44 = (20 xx 44) + (5 xx 44)`

Number, NAP-I4-CA32 SA

A design is made using three times as many large beads as small beads.

The mass of each large bead is 140 milligrams.

The mass of each small bead is 40 milligrams.

The total mass of all the beads used is 92 grams.

How many beads are used in total to make the design?

Show Answers Only

`800`

Show Worked Solution

`text(Let)\ \ \ x`	`= text( number of small beads)`
`3x`	`= text( number of large beads)`

`3x (0.14) + x (0.04)`	`= 92`
`0.42x + 0.04 x`	`= 92`
`0.46 x`	`= 92`
`x`	`= 200`

`:.\ text(There are 200 small beads and)`

`text(600 large beads.)`

`:.\ text(Total beads) = 800`

Algebra, NAP-I4-CA31 SA

What is the value of `x` given `5/2 x + 5 = 3x - 1?`

Show Answers Only

`12`

Show Worked Solution

`5x + 10`	`= 6x – 2`
`x`	`= 12`

Measurement, NAP-I4-CA30 SA

A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below.

Each smaller triangular prism is 40 cm³ in size.

What is the maximum number of smaller triangular prisms that can fit inside the box?

Show Answers Only

`text(17 pieces)`

Show Worked Solution

`text(Volume of 1 piece)\ = 1/2 xx 6 xx 7.9 xx text(Width)`

`text(Width)`	`= 40/(1/2 xx 6 xx 7.9)`
	`= 1.688\ text(cm)`

`:.\ text(Maximum number of pieces that fit)`

`= 30/1.688`

`= 17.77`

`= 17\ \ text{(round down)}`

Measurement, NAP-I4-CA29 SA

A target is drawn as follows

What is the area of the entire target?

Round your answer to the nearest square centimetre.

cm²

Show Answers Only

`284\ text(cm)^2`

Show Worked Solution

`text(Area)`	`= pi r^2`
	`= pi (2 + 1.5 xx 5)^2`
	`= pi (9.5)^2`
	`= 283.52…`
	`= 284\ text(cm)^2`

Number, NAP-I4-CA28 SA

Mr. Soros put $500 into a simple interest account for a year.

He did not take any money out or add any money to the account.

At the end of the year he had $530 in the account.

What was the annual percentage interest rate?

Show Answers Only

`text(6%)`

Show Worked Solution

`text(Interest earned)`	`= 530 – 500`
	`= $30`

`:.\ text{Interest rate (annual)}`

`= 30/500`

`= 0.06`

`= 6text(%)`

Measurement, NAP-I4-CA27 SA

A glass aviary is made up of four triangles and a square, as shown in the diagram below.

Harry is hired to clean the interior sides of the aviary, not including the floor.

What is the area that Harry will need to clean?

m²

Show Answers Only

`402\ text(m²)`

Show Worked Solution

`text(Area to clean)`

`= 4 xx 1/2 bh`

`= 4 xx 1/2 xx 15 xx 13.4`

`= 402\ text(m²)`

Geometry, NAP-I4-CA25 SA

The sum of the interior angles of a 6 sided polygon can be found by first dividing it into triangles from one vertex.

What is the sum of the interior angles of this polygon?

degrees

Show Answers Only

`720\ text(degrees)`

Show Worked Solution

`text(Sum of interior angles)`

`= 4 xx 180`

`= 720\ text(degrees)`