Ratio Proportion and Rates of Change

1 pound = 16 ounces. Work out the number of ounces in 3 pounds.

Write the ratio 6 : 2 in the form n : 1

35 books are either for adults or for children. number for adults : number for children = 6 : 1 How many more books are for adults than for children?

A car travels 4 miles in 5 minutes. Work out the average speed in miles per hour.

In this part, assume that each person works at the same rate. 10 people can complete a job in 9 hours. If 15 people work on the same job, how many hours will it take to complete the job?

In fact, of the 15 people 6 work at a slower rate 9 work at a faster rate. What does this mean about the number of hours it will take to complete the job? Tick one box.

In a house, the floor area of the living room is 26 m² and the floor area of the kitchen is 16.4 m². Express the area of the living room as a fraction of the area of the kitchen. Give your answer in its simplest form.

A, B and C are numbers. Here is some information about B and C. B = 7/4 of A C = A increased by 150% Work out C as a fraction of B. <br/><br/> <table border="1" cellpadding="20" cellspacing="0" style="border-collapse: collapse; font-family: Times New Roman, serif; font-size: 24px;"> <tr> <td style="font-style: italic; width: 80px; text-align: center;"><i>B</i></td> <td style="padding: 20px 40px;">⁷/₄ of <i>A</i></td> </tr> <tr> <td style="font-style: italic; text-align: center;"><i>C</i></td> <td style="padding: 20px 40px;"><i>A</i> <b>increased by 150%</b></td> </tr> </table>

The graph represents the volume of water in a bath. The bath is full after 10 minutes. Work out the rate at which the bath is filled. State the units of your answer.

After the bath is full, the volume of water stays constant for 20 minutes, then all the water empties out at a constant rate in 12 minutes. Complete the graph to show this information.

A map has a scale of 1 : 4000. On the map, the distance from a station to a museum is 7 cm. Is the actual distance from the station to the museum more than 300 m? Show working to support your answer.

X is inversely proportional to Y. Circle the correct statement.

Some oil has a mass of 537 g and a density of 895 000 g/m³. Given that 1 m³ = 1000 litres, work out the volume of the oil. Give your answer in litres.

384 000 electric cars were sold this year. This is 20% more than last year. How many were sold last year?

A map has a scale of 1 : 4000 <br> On the map, the distance from a station to a museum is 7 cm. <br> Is the actual distance from the station to the museum more than 300 m? <br> Show working to support your answer.

X is inversely proportional to Y. <br> Select the correct statement.

Some oil has <br> a mass of 537 g <br> a density of 895 000 g/m³ <br> 1 m³ = 1000 litres <br> Work out the volume of the oil. Give your answer in litres.

At a music festival, four types of instrument are played. <br> guitars, keyboards, drums, trumpets <br> <ul> <li>The total number of instruments is 80</li> <li>Half of the instruments are guitars.</li> <li>keyboards : drums : trumpets = 3 : 4 : 1</li> </ul> How many keyboards are there?

Three shops sell shirts. At which shop is it cheapest to buy 6 shirts? Show working to support your answer. Shop A: Pack of 2, £19.00 Shop B: Was £12.40, Now 25% off (price per shirt) Shop C: Pack of 3, £37.40. Buy one pack, get another pack half price.

At a school there are 912 students. The ratio of students to teachers is 15.2 : 1. The number of students stays the same. The number of teachers increases by 2. Work out the new ratio of students to teachers. Give your answer in the form n : 1.

On a school trip, one teacher is needed for every group of 10 or fewer students. 72 students want to go on the trip. Lexi tries to work out how many teachers are needed. Her working is: 72 ÷ 10 = 7.2 7 teachers are needed. What is wrong with her answer?

A car will travel 60 miles. Draw a graph to show the average speed of the car for times taken between 1 hour and 6 hours. You may use the table to help you.

The population of a country is now 67,200,000. The population is predicted to: - increase by 1% per year for 6 years - and then decrease by 1.2% per year for 2 years. Work out the predicted population of the country 8 years from now. Give your answer to 3 significant figures.

A stone falls vertically from 300 metres above ground. - The stone falls d metres in t seconds. - d is directly proportional to the square of t. - The stone falls 20 metres in the first 2 seconds. Work out the total time taken for the stone to reach the ground.