A part of a map is shown.

The distance between two points on the above map (not shown) is 3.4 kilometres. How far apart on the map would be the two points be, in centimetres?

(a)  

A map has a scale of  1 : 500 000.

1. Two mountain peaks are 2 cm apart on the map.

    

   i) What is the actual distance between the two mountain peaks, in kilometres?

A map has a scale of  1 : 500 000.

1. Two mountain peaks are 2 cm apart on the map.

2. Given that 2cm=10km (from question i)

3. ii) Two cities are 75 km apart. How far apart are the two cities on the map, in centimetres?

A potting mix is made up of two ingredients, potting soil and manure, in the ratio 5:2.

21 kilograms of potting mix are used to fertilise the  rectangular vegetable garden pictured below.

i) What rate must the whole 21 kilograms of potting mix be applied to be spread evenly over the garden. Give your answer in grams per square metre. 

(a)  

A potting mix is made up of two ingredients, potting soil and manure, in the ratio 5:2.

21 kilograms of potting mix are used to fertilise the  rectangular vegetable garden pictured below.

ii) How much manure is needed to make the required potting mix?

(a)  

Luka is installing a pond in his backyard. The pond will have three straight edges and one curved edge.

The depth of the pond will be 2 metres throughout. Luka took measurements and drew an overhead

view of the pond to assist the builder, as shown in the diagram.

i) Using the trapezoidal rule, estimate the area of the bottom of the pond.

(a)  

Luka is installing a pond in his backyard. The pond will have three straight edges and one curved edge.

The depth of the pond will be 2 metres throughout. Luka took measurements and drew an overhead

view of the pond to assist the builder, as shown in the diagram.

i) Calculate how many litres of water will be required to fill the pond.

(a)  

Richard plays on his game console for three hours every day. The game console uses 350 watts

of energy per hour. The cost of electricity usage is 45 cents per kWh.

Calculate the yearly cost for Richard to play his game console, correct to the nearest cent.

(a)  

Richard plays on his game console for three hours every day. The game console uses 350 watts

of energy per hour. The cost of electricity usage is 45 cents per kWh.

Calculate the yearly cost for Richard to play his game console, correct to the nearest cent.

(a)  

The average flow rate of Stephanie’s shower head is 14 litres per minute. Stephanie has two 8-minute showers each day. The cost of water usage is $2.55 per kilolitre.

Calculate the fortnightly cost of Stephanie’s showers, correct to the nearest cent.

(a)  

A study of the turtles in Centennial Park uses the “capture-recapture” technique to estimate the size of the turtle population.

In the first stage of the study, 36 turtles were caught, tagged and released.

In the second stage of the study, 40 turtles were captured. Six of these turtles were found to be already tagged.

Calculate the estimated number of turtles in Centennial Park.

(a)  

Francis is buying a fridge. The energy usage of his two choices are below:

Fridge 1 (5 star rating): 227 kWh per year

Fridge 2 (2 star rating): 492 kWh per year

Each fridge has an expected life of 8 years.

If electricity costs 32.4 cents per kWh, how much will Francis save in electricity over the expected life of the more energy efficient fridge, to the nearest dollar?

(a)  

The price and the power consumption of two different brands of television are shown.

The average cost for electricity is 25c/kWh. A particular family watches an average of 3 hours of television per day.

1. a) The annual cost of electricity for Television A for this family is $48.18.

2. For this family, what is the difference in the annual cost of electricity between Television A and Television B?

What scale factor has been used to transform Triangle A to Triangle B?

(a)  

The area of a roof is 6 m by 7 m. Any rain that falls on the roof flows directly into a cylindrical tank with a diameter of 3 m.

Calculate depth of the water in the tank (in metres) if 20 mm of rain falls on the roof.  Answer to the nearest cm.

(a)  

The area of a roof is 6 m by 7 m. Any rain that falls on the roof flows directly into a cylindrical tank with a diameter of 3 m.

Calculate the volume of water that will flow into the tank if 20 mm of rain falls.

Give your answer in kilolitres, to the nearest litre.

(a)  

The area of a roof is 6 m by 7 m. Any rain that falls on the roof flows directly into a cylindrical tank with a diameter of 3 m.

0.84 kL of water will flow into the tank after 20 mm of rain.

The water is being emptied into 10 gallon drums. A 10 gallon drum holds approximately 38 L, and costs $10.55.

What is the minimum cost to buy enough drums to hold this volume of water?

(a)