A Cartesian plane is shown below.
Which statement is true?

`R` is located where `x < 0` and `y > 0` 

`N` is located where `x < 0` and `y < 0` 

`M` is located where `x > 0` and `y < 0` 

`Q` is located where `x < 0` and `y < 0` 
Aussie Maths Teachers: Save your time with SmarterMaths
A Cartesian plane is shown below.
Which statement is true?

`R` is located where `x < 0` and `y > 0` 

`N` is located where `x < 0` and `y < 0` 

`M` is located where `x > 0` and `y < 0` 

`Q` is located where `x < 0` and `y < 0` 
`N\ text(is located where)\ \ x < 0\ \ text(and)\ \ y < 0`
`text(Points left of the)\ y text(axis): \ x<0`
`text(Points below the)\ x text(axis): \ y<0`
`:. N\ text(is located where)\ \ x < 0\ \ text(and)\ \ y < 0\ \ text(is correct.)`
A manufacturer makes horse floats.
The table below shows how many floats it makes each month.
The number of floats made grows each month and follows the rule:
Double the number made last month and deduct 4
How many horse floats are made in the 5th month?

22 

28 

32 

36 
`36`
`text(Using the rule:)`
`text(Floats made in 5th month)`  `= (20 xx 2)  4` 
`= 40  4`  
`= 36` 
Amelia is making a pattern using nails.
The table below shows the number of nails she needs for the pattern to be complete.

12 

15 

16 

18 
`15`
`text{Each new pattern adds the new pattern number to the previous total.}`
`text{Pattern # 5 is}`
`therefore \ text{Nails needed = 5 + 10 = 15}`
Rica produced a pattern of small circles and trapeziums.
If this pattern continues how many small circles will be in the 10th figure?

10 

11 

19 

21 
`19`
`text{Each succeeding figure adds 2 circles}.`
`text{Number of small circles}`
`text{Figure 4: 7 circles}.`
`text{Figure 5: 9 circles}.`
`vdots`
`:.\ text(Figure 10 contains 19 circles.)`
Sophie makes a pattern using sticks as shown below.
The number of sticks in the first 3 figures are 3, 9, and 18.
What is the number of sticks needed for figure 4?

24  

27  

30  

36 
30
`text{Figure 1}\ = 3`
`text{Figure 2} \ = 3 + 2 xx 3 = 9`
`text{Figure 3} \ = 9 + 3 xx 3 = 18`
`text{Figure 4} \ = 18 + 4 xx 3 = 30`
The prices at a boutique burger shop can be seen below.
Each extra patty in the burger costs the same amount of money.
How much will a burger with 4 patties cost?
$ 
`$38.20`
`text{C} text{ost of 1 extra patty}`  `= 27.40  22.00`  
`= 5.40` 
`text{C} text{ost of burger with 4 patties}`  `= 22.00 + 3.00 \ text{extra patties}`  
`= 22.00 + (3 xx 5.40)`  
`= 22.00 + 16.20`  
`= 38.20` 
The prices of extra large family pizzas can be seen below.
Each extra topping on the pizza costs the same amount of money.
How much will a pizza with 4 toppings cost?
$ 
`$54.50`
`text{C} text{ost of 1 extra topping}`  `= 41.50  35.00`  
`= 6.50` 
`text{C} text{ost of pizza with 4 toppings}`  `= 35 + 3 \ text{extra toppings}`  
`= 35 + (3 xx 6.50)`  
`= 35 + 19.50`  
`= 54.5` 
James is drawing a rectangular prism on an isometric grid.
Which pair of points could James draw as vertices on the prism?
`A and C`  `B and C`  `A and D`  `C and D` 




`A and C`
`A and C`
A Cartesian plane is shown.
Select the correct statement below.

`A` is located where `x > 0` and `y < 0.` 

`B` is located where `x = 0` and `y > 0.` 

`C` is located where `x < 0` and `y < 0.` 

`D` is located where `x < 0` and `y = 0.` 
`C \ text(is located where)\ \ x < 0\ \ text(and)\ \ y < 0.`
`C \ text(is located where)\ \ x < 0\ \ text(and)\ \ y < 0.`
`text(All other statements can be shown to be false.)`
Ariel uses sticks to make a pattern.
She starts with 4 sticks for Design 1.
How many sticks does Ariel need for Design 5?
`40`  `60`  `36`  `56` 




`60`
`text(One strategy:)`
`text(Each new row has one extra square than)`
`text(the row below.)`
`=>\ text(Sticks in design 4)`  `= 24 + 4 xx 4` 
`= 40` 
`:.\ text(Sticks in design 5)`  `= 40 + 5 xx 4` 
`= 60` 
Rambo is using matchsticks to make a pattern of squares.
How many matchsticks will Rambo need to make square 6?
6  20  24  28 




`24`
`text(Square 1 = 4)`
`text(Square 2 = 8)`
`text(Square 3 = 12)`
`=> 4\ text(matchsticks are added each square)`
`:.\ text(Square 6)\ = 6 xx 4 = 24\ text(matchsticks)`
Janis created a number pattern by adding five to a number to get the next number.
Which of these could be the first four numbers of Janis' pattern?
`3, 8, 14, 21`  `15, 25, 35, 45`  `8, 13, 18, 23`  `5, 9, 13, 17` 




`8, 13, 18, 23`
`8 + 5`  `= 13` 
`13 + 5`  `= 18` 
`18 + 5`  `= 23` 
`:.\ text(Pattern is)\ \ 8, 13, 18, 23`
Which of these patterns fits the rule, "Double the previous number and deduct 2"?

`3, 4, 5, 6, 9, …` 

`3, 6, 12, 24, 48, …` 

`4, 6, 10, 18, 34, …` 

`4, 10, 22, 46, 94, …` 
`4, 6, 10, 18, 34, …`
`text(By trial and error, consider option 3:)`
`4 xx 2  2 = 6`
`6 xx 2  2 = 10`
`10 xx 2  2 = 18`
`:.\ 4, 6, 10, 18, 34, …\ text(fits the rule.)`
Ian is enrolled in an intensive summer swimming program.
His swimming program is shown in the table below.
Which statement about Ian's program is true?
Ian's program is to swim:

`text(12 laps more than the previous day.)` 

`text(18 laps more than the previous day.)` 

`text(1.5 times more laps than the previous day.)` 

`text(12 times more laps than the previous day.)` 
`text(1.5 times more laps than the previous day.)`
`text(Day 2 laps) = 1.5 xx 24 = 36`
`text(Day 3 laps) = 1.5 xx 36 = 54`
`text(etc. …)`
`:.\ text(1.5 times more laps than the previous day.)`
Brogan drives a barge that transports sand.
The table below shows the mass of sand, measured in cubic tonnes, of different sand volumes, measured in cubic metres.
Brogan's barge has 130 tonnes of sand loaded on it.
How many cubic metres of sand are on his barge?
`91\ text(m³)`  `95\ text(m³)`  `180\ text(m³)`  `186\ text(m³)` 




`91\ text(m³)`
`text(Cubic metres in 1 tonne)`
`= 35/50`
`= 0.7\ text(m³)`
`:.\ text(Cubic metres in 130 tonnes)`
`= 0.7 xx 130`
`= 91\ text(tonnes)`
A Cartesian plane is shown.
Select the correct statement below.

`A` is located where `x > 0` and `y = 0.` 

`B` is located where `x >0` and `y < 0.` 

`C` is located where `x < 0` and `y < 0.` 

`D` is located where `x < 0` and `y > 0.` 
`x < 0\ text(and)\ y > 0`
`D\ text(occurs when)`
`x < 0\ text(and)\ y > 0`