Rates of change

Ola and Pip make orange paint by mixing red paint and yellow paint. The graph shows how much of each colour paint to use.

Ola uses 5 litres of yellow paint.

Write down how much red paint Ola uses.

Pip uses 10 litres of yellow paint.

How much orange paint does Pip make ?

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.

Show this information on the graph.

A lion is sprinting in a straight line away from its den. The graph shows the lion’s distance from the den.

Work out the speed of the lion in metres per second.

A lion is sprinting in a straight line away from its den. The graph shows the lion’s distance from the den.

Work out the speed of the lion in metres per second.

Here is the velocity-time graph of a cyclist for 40 seconds.

By dividing the area under the graph into four sections of equal widths, estimate the distance travelled during the 40 seconds.

Work out the average acceleration of the cyclist during the 40 seconds. State the units of your answer.

Water flows from a tap at a constant rate. A container is filled with water from the tap in 40 seconds.

The graph shows the height, h centimetres, of the water after time, t seconds.

The container is one of these shapes.

Circle the letter of the correct shape.

By drawing a tangent on the graph, estimate the rate at which the height is increasing when t = 10

A tank contains 40 litres of water.

Water leaks out of the tank at a rate of 1.2 litres per minute. The leak is stopped after 20 minutes. Show that, when the leak is stopped, the tank contains 16 litres of water.

The tank is refilled with water from a tap. The graph shows the amount of water in the tank after the leak is stopped.

Complete this report by writing a number in each answer space.

A tank contains 40 litres of water.

Water leaks out of the tank at a rate of 1.2 litres per minute. The leak is stopped after 20 minutes. Show that, when the leak is stopped, the tank contains 16 litres of water.

The tank is refilled with water from a tap. The graph shows the amount of water in the tank after the leak is stopped.

Complete this report by writing a number in each answer space.

A mobile phone takes 2 hours to charge from empty. When the phone is being charged, the current flow into the phone

• starts at full current flow (100%)

• continues at full current flow for a period of time

• gradually decreases until the phone is fully charged.

This is shown on Graph A below.

Graph B shows the percentage charge in the phone when charging from empty.

Megan’s phone is empty of charge. She starts to charge her phone at 10.00 am

Using Graph A, estimate the time when the current flow starts to decrease.

Using Graph A and Graph B, estimate the percentage charge in the phone when the current flow is 40%

Using Graph B, estimate the rate of increase in the percentage charge when the phone has 90% charge.

percent per minute

A and B are points on a curve. A is (2, 7) B is (12, 0)

Work out the instantaneous rate of change of y with respect to x at point A.

The average rate of change of y with respect to x between points A and B is worked out. Which statement is correct? Tick one box.

The table shows the cost of hiring a concrete mixer for up to 5 days.

Eva hires the concrete mixer for 5 days. She says, “The rate is £14 per day because the cost for 1 day is £14” Is she correct? Give a reason for your answer.

In a sport, the number of points is directly proportional to the number of wins. On the axes, sketch a graph to show this relationship.

The diagrams show the position of a tap when off and fully on. The tap is fully on when the angle of turn is 180°

When fully on, water flows out of the tap at 14 litres per minute. The rate at which water flows out is in direct proportion to the angle of turn. The tap is turned 135°

The water flows into a tank with a capacity of 79.8 litres. Will it take less than 7 minutes to fill the tank? You must show your working.

Water is poured into a tank. The graph shows the number of litres of water in the tank.

How much water is poured into the tank each minute? Circle your answer. 1.5 litres 15 litres 30 litres 120 litres