Real-life graphs

Complete the table of values for y = 2

Draw the graph of y = 2^x for values of x from –1 to 3

14 For a small plane, (a)

• the mass of the empty plane is 800 kg, to the nearest 100kg

• the mass of fuel is 190 kg, to the nearest 5 kg

• the mass of the passengers is 163 kg, to the nearest kg

The total mass of a plane is calculated by adding these three masses. The maximum mass for the plane to take off safely is 1200 kg

Can this plane definitely take off safely? Tick a box.

Show working to support your answer.

A different plane travels 1250 miles in 2 hours 30 minutes at a constant speed.

On the grid, draw a speed/time graph to represent this information.

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.

The graph represents the velocity of a ball as it rolls along the ground.

Work out an estimate for the acceleration of the ball, in m/s², after 2 seconds. You must show your working.

Work out an estimate for the total distance covered by the ball.

Is your estimate from part (b) an overestimate or underestimate? Tick a box.

Give a reason for your 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.

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.

A room is kept at a constant temperature of 21 ° C for 6 hours. The heating is then turned off and the room begins to cool. Here is a sketch graph showing the temperature, y ° C, of the room at time x hours.

Assume the equation of the curved part is y = where k is a constant.

Work out the value of y when x = 12

In fact,

How does this affect the value of y when x = 12 ? Tick one box. You must show working to support your answer.

The graph below is used to convert between pounds (£) and Norwegian krone (kr).

Convert 720 krone into pounds.

Convert £500 into krone.

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

Scarlett leaves home at 10.00 to cycle to the supermarket. Here is part of a distance-time graph of her trip to the supermarket.

She arrives at the supermarket at 10.20 How far is the supermarket from her home?

She leaves the supermarket at 10.35 How long does she stay at the supermarket?

Scarlett cycles home at a constant speed using the same route. It takes her 3 minutes longer than her journey to the supermarket. Complete the distance-time graph.

Here is the distance-time graph for a car between 1 pm and 3 pm

Work out the total time that the car is not moving between 1 pm and 3 pm State the units of your answer.

Work out the total distance the car travels between 1 pm and 3 pm

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.

Helena ran an 800-metre race in 140 seconds. The speed-time graph represents the first 100 seconds of her run.

Helena ran the last 40 seconds with constant deceleration. Work out her speed as she finished the race.

metres per second

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

Here is the speed-time graph for a 50-second journey.

Circle the acceleration, in m/s², halfway through the journey.

0 2 20 25

Work out the total distance travelled.

The cost of making a phone call is a fixed charge and a charge per minute. The costs of phone calls up to 5 minutes are represented by the graph.

Write down the fixed charge.

Work out the charge per minute.

Work out the cost of a phone call lasting 7 minutes.

Here is a sketch of a graph.

Circle the equation of the graph. k is a constant.

The graph shows the height above ground of a toy rocket for 10 seconds.

For how long is the rocket in the air? Circle your answer.

10 seconds 9 seconds 6 seconds 4 seconds

Using the graph, estimate the speed of the rocket after 6 seconds. State the units of your answer.

Jim buys a plant of height 20 cm The graph shows how the height of the plant changes during the next 4 days.

Work out a formula for h in terms of n.

Circle the point that is on the graph of y =

(– 1, 1) (0.3, 3) (0.8, 0.2) (2.5, 0.4)

Leo wants to draw the graph of y = 2^x for values of x from 0 to 4 Here is his graph.

Make one criticism of his graph.

A horse runs in a field. The speed-time graph represents the first 12 seconds of the run.

After how many seconds had the horse run a distance of 75 metres?

Here is a formula.

Draw the graph of y = 3.6 x for values of x from 0 to 20

In the formula y = 3.6 x y is speed in kilometres per hour (km/h) x is speed in metres per second (m/s)

Convert 50 km/h to m/s Give your answer to the nearest whole number.

Convert 30 m/s to miles per hour. Use 1 mile per hour = 1.61 km/h

miles per hour

Chris visits a library. He cycles to the library in half an hour at a speed of 12 miles per hour. He stays at the library for one hour. He then cycles home. The sketch graph represents his visit.

Work out the speed, in miles per hour, at which Chris cycles home.

Here is a sketch of a distance-time graph.

Which of these represents the average speed between A and B ? Tick one box.

Jenny leaves home at 06.00 She runs for 3 hours. Here is a distance-time graph of her run.

How far from home is she after 3 hours?

For the next hour she rests. She then gets a bus home. She arrives home at 11.30 Complete the distance-time graph. Assume the bus travels at a constant speed.

Here is a sketch of a speed-time graph for the first part of a journey.

The total distance for the journey is 130 kilometres. How far is left to travel?

t is the time in minutes the machine takes to make one item. The value of t changes for different types of item.

On the grid below, draw the graph of n = for values of t from 1 to 4

The machine takes 3 minutes 30 seconds to make one item. Use your graph to estimate the value of n.

t is the time in minutes the machine takes to make one item. The value of t changes for different types of item.

On the grid below, draw the graph of n = for values of t from 1 to 4

The machine takes 3 minutes 30 seconds to make one item. Use your graph to estimate the value of n.

The graph below is used to convert between temperature in degrees Fahrenheit (F) and temperature in degrees Celsius (C).

Use the graph to convert 40 degrees Fahrenheit into degrees Celsius.

At one temperature, T, the number of degrees Celsius is double the number of degrees Fahrenheit. The graph of C = 2 F can be drawn to help find this temperature.

On the grid opposite, draw the graph of C = 2 F for values of F from –25 to 25 You may use the table to help you.

Use your graph to estimate the value of T. Give your answer in degrees Celsius.

Leo runs for 12 seconds. The graph shows his speed.

Show that the distance he runs is less than 67.5 metres.

Work out his average acceleration for the first 9 seconds. State the units of your answer.

A ship is sailing in a straight line from its home port. The distance-time graph shows 4 hours of the journey.

Work out the speed of the ship during these 4 hours.

A ship is sailing in a straight line from its home port. The distance-time graph shows 4 hours of the journey.

Work out the speed of the ship during these 4 hours.

Izzy runs an 80-metre race in 14 seconds. During the first 6 seconds her speed increases at a constant rate. During the last 8 seconds her speed increases at a different constant rate. Her speed at 14 seconds is 2 m/s more than her speed at 6 seconds. Here is a sketch of her speed-time graph.

Work out her acceleration during the last 8 seconds. State the units of your answer.

When Izzy finishes the 80-metre race, her speed is v m/s Work out the value of v.

A ball is thrown vertically upwards. The graph shows the height of the ball above the ground after it is thrown.

For how many seconds is the ball at a height of more than 2 metres?

After how many seconds is the ball at instantaneous rest when it is in the air?

Work out the average speed of the ball when it is moving downwards.

The speed-time graph shows 20 seconds of a car journey. Harry wants to estimate the distance the car travels in this time. He uses a triangle and a trapezium, as shown, to estimate the area under the graph.

Complete Harry’s method to estimate the distance the car travels.

For this journey, which of these is true for Harry’s method? Tick one box.

Anil’s home is 1 km from a shop. He walked from home to the shop at a constant speed in 10 minutes. He stayed at the shop for 5 minutes. He walked home at a constant speed in 8 minutes. Anil drew this distance-time graph to represent his journey.

Make two criticisms of his graph.

Beth ran a 200 metre race. Here is a graph of the first 8 seconds of her race. She completed the race at a constant speed of 9 m/s

Amy completed the race in 27 seconds. Did Beth finish before Amy? You must show your working.

Liquid is leaking out of a container. The graph shows the depth of the liquid for 60 seconds.

Use the graph to work out an estimate of the rate of decrease of depth at 10 seconds. You must show your working.

Here is a velocity-time graph of a motorbike for 25 seconds.

After how many seconds was the acceleration zero?

Work out the distance travelled in the last 15 seconds.

Lily goes on a car journey. For the first 30 minutes her average speed is 40 miles per hour. She then stops for 15 minutes. She then completes the journey at an average speed of 60 miles per hour. The total journey time is 1 hour.

Draw a distance-time graph for her journey.

Write down the average speed for the total journey.

Lily goes on a car journey. For the first 30 minutes her average speed is 40 miles per hour. She then stops for 15 minutes. She then completes the journey at an average speed of 60 miles per hour. The total journey time is 1 hour.

Draw a distance-time graph for her journey.

Write down the average speed for the total journey.

The graph shows the depth of water in a harbour for 12 hours. d is the depth of water in a harbour in metres t is the number of hours after 9 am

For how many of the 12 hours is the depth more than 5 metres?

By how much does the depth change between 12 noon and 4 pm?

A ball is thrown from a point 6 metres above the ground. The graph shows the height of the ball above the ground, in metres.

Estimate the speed of the ball, in m/s, after 1 second. You must show your working.