Rates and Ratios Test Prep

Sugar is sold in four different sized packets.

Which is the best buy?

• 100g for $0.40

• 500g for $1.65

• 1kg for $3.50

• 2kg for $6.90

A brand of pasta is sold in two different packets.

What is the difference in price per kilogram between them?

• $1.50

• $3.00

• $3.60

• $7.20

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)  

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)  

There are 8 male chimpanzees in a community of 24 chimpanzees.

What is the ratio of males to females in the community?

• 1.  1 : 3

• 1.  1 : 2

•  3 : 1

•  2 : 1

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)