SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Algebra, NAP-L4-CA02 SA

The table shows the distances Angus swims on four different days.
 


 

Every day, Angus increases the distance he swims by the same amount.

What distance will Angus swim on Thursday?

   km
Show Answers Only

`3.4\ text(km)`

Show Worked Solution

`text(Each day, Angus swims an extra 0.3 km.)`

`:.\ text{Distance (on Thurs)}` `= 3.1 + 0.3`
  `= 3.4\ text(km)`

Algebra, NAP-A4-CA23 SA

Kelly uses this rule to work out the next number in a pattern.
 


 

The first three numbers of the pattern are: 9, 51, 303, …

What is the fifth number in his pattern?

 
Show Answers Only

`10\ 887`

Show Worked Solution
`text(4th number)` `= 6 xx 303`
  `= 1815`
`text(5th number)` `= 6 xx 1815`
  `= 10\ 887`

Algebra, NAP-J4-CA07

Ethan writes the sequence:

`7, \ 0.7, \ 0.07, \ 0.007, …`

Describe the rule he uses to write the next number in this sequence.

 
 `text(add 6.3)`
 
 `text(subtract 6.3)`
 
 `text(multiply by 0.01)`
 
 `text(divide by 0.1)`
 
 `text(multiply by 10)`
 
 `text(divide by 10)`
Show Answers Only

`text(divide by 10)`

Show Worked Solution
`7 ÷ 10` `= 0.7`
`0.7 ÷ 10` `= 0.07`
`0.07 ÷ 10` `= 0.007`

 

`:.\ text(Rule: divide by 10).`

Algebra, NAP-G4-NC25 SA

The table below shows the relationship between the width of a tree's trunk in centimetres and how old it is in months.
 

 
If this pattern continues, how old would you expect a tree with a 4.5 cm wide trunk to be?

  months
Show Answers Only

`30`

Show Worked Solution

`text(Continuing the pattern,)`

`text(24 months) => 4 1/8`

`text(26 months) => 4 1/4`

`text(28 months) => 4 3/8`

`text(30 months) => 4 1/2`

Algebra, NAP-D4-CA28 SA

The table shows the height of the grid on new tyres after being driven different distances.
 

 
The tyres will be replaced when the grid is 11 mm high.

How many kilometres do the tyres need to be driven to be worn down to a 11 mm high grid?

   kilometres
Show Answers Only

`6000\ text(km)`

Show Worked Solution

`text(Grid is initially 20 mm.)`

`text(After 500 km) -> 19.25\ text(mm)`

`text(After 1000 km) -> 18.5\ text(mm)`

`=>\ text(grid decreases 0.75 mm each 500 km.)`

 

`text(Let)\ \ n = text(multiple of 500 km tyres are driven)`

`20 – (n xx 0.75)` `= 11`
`n xx 0.75` `= 9`
`:. n` `= 9/0.75`
  `= 12`

 

`:.\ text(Distance tyres will be driven)`

`= 12 xx 500`

`= 6000\ text(km)`

Algebra, NAP-C4-NC14

The table shows how a sock company grew by selling more and more pairs of socks over 5 years.
 

 

 
Using this data, what is the best estimate for the number of pairs of socks sold in the sixth year?

 
 `3000`
 
 `4000`
 
 `8000`
 
 `16\ 000`
Show Answers Only

`8000`

Show Worked Solution

`text(The number of pairs sold is growing by a)`

`text(multiple of 4 each year.)`

`=>\ text(Socks sold in year 6)` `=2048 xx 4`
  `=8192`

`:.\ text(8000 is the best estimate.)`

Algebra, NAP-D4-NC09

George starts doing push-ups to get stronger.

The table below shows the number of push-ups he does each training session.
 

 
The number of push-ups he does each week increases and follows the rule:

Double the last session's number of push-ups and deduct 3.

What is the number of push-ups George did in session 4?

`12` `15` `17` `19`
 
 
 
 
Show Answers Only

`19`

Show Worked Solution

`text(Using the rule:)`

`text(Push-ups in session 4)`

`= (2 xx 11) – 3`

`= 22 – 3`

`= 19`

Algebra, NAP-E4-CA23 SA

Stewart uses the formulas below to estimate the population of koalas in a habitat over four years.

`text{Population (Year 1)} = 5000`

`text{Population (Year 2)} = text(Year 1) + text(Year 1)/10`

`text{Population (Year 3)} = text(Year 2) + text(Year 2)/10`

`text{Population (Year 4)} = text(Year 3) + text(Year 3)/10`  

What is the estimated population of koalas in year 4?
Show Answers Only

`6655\ text(koalas)`

Show Worked Solution

`text(Year 2) = 5000 + 5000/10 = 5500`

`text(Year 3) = 5500 + 5500/10 = 6050`

`text(Year 4) = 6050 + 6050/10 = 6655`

Algebra, NAP-E4-CA10

The rules of a number game are shown in the flowchart below.
 

 
The output number is 21.

What are two possible values for the input number?

`7 and 16` `16 and 63` `7 and 26` `26 and 63`
 
 
 
 
Show Answers Only

`7 and 26`

Show Worked Solution

`text(Input 7 into the flowchart:)`

`7 xx 3 = 21`

`text(Input 26 into the flowchart:)`

`26 – 5 = 21` 
 

`:. 7 and 26\ \ text(are the possible values.)`

Algebra, NAP-E4-NC22 SA

Dan is a lettuce grower and the cost of fertilising different crop areas is shown in the table below.
 

 
Complete the rule that agrees with the values in the table.

cost of fertilising crop =     × area of crop
Show Answers Only

`70`

Show Worked Solution
`text(C)text(ost of fertilising)` `=\ text(cost of 1 m² × area of crop)`
  `= 2100/30 xx text(area of crop)`
  `= 70 xx text(area of crop)`

Algebra, NAP-F4-CA17

Barry drives a barge that transports sand.

The table below shows the volume of sand, measured in cubic metres, of different sand masses, measured in tonnes.
 

 

Barry's barge has 84 cubic metres of sand loaded on it.

How many tonnes of sand are on his barge?

56 tonnes 58 tonnes 126 tonnes 136 tonnes`
 
 
 
 
Show Answers Only

`126\ text(tonnes)`

Show Worked Solution

`text(Tonnes in 1 cubic metre of sand)`

`=30/20`

`= 1.5`
 

`:.\ text(Tonnes in 84 cubic metres)`

`=84 xx 1.5`

`=126\ text(tonnes)` 

Algebra, NAP-F4-CA13

Charlie swam 250 lengths of a 50 metre pool in 5 days.

After the first day, he swam 5 more laps each day than the day before.

How many laps did he swim on the first day? 

`35` `40` `45` `50`
 
 
 
 
Show Answers Only

`40`

Show Worked Solution

`text(Average laps per day)`

`= 250/5`

`= 50`
 

`=>\ text(Laps swam each of the 5 days:)`

`text(40, 45, 50, 55, 60)`
 

`:.\ text(He swam 40 laps on the 1st day.)`