Peter has to take 80 mg of a drug to control his blood pressure. The following graph shows the initial amount of the drug, and the amount that remains active in Peter’s blood after one, two, three and four days. How much of the drug remains active at the end of the first day?

From the graph for the previous question it can be seen that each day, about the same proportion of the previous day’s drug remains active in Peter’s blood. At the end of each day which of the following is the approximate percentage of the previous day’s drug that remains active?

A water tank has shape and dimensions as shown in the diagram. At the beginning the tank is empty. Then it is filled with water at the rate of one litre per second.  Which of the following graphs shows how the height of the water surface changes over time?

A game in a booth at a spring fair involves using a spinner first. Then, if the spinner stops on an even number, the player is allowed to pick a marble from a bag. The spinner and the marbles in the bag are represented in the diagram below.  Prizes are given when a black marble is picked. Sue plays the game once.  How likely is it that Sue will win a prize?

Lighthouses are towers with a light beacon on top. Lighthouses assist sea ships in finding their way at night when they are sailing close to the shore. A lighthouse beacon sends out light flashes with a regular fixed pattern. Every lighthouse has its own pattern. In the diagram below you see the pattern of a certain lighthouse. The light flashes alternate with dark periods. Which of the following could be the period of the pattern of this lighthouse?

For how many seconds does the lighthouse send out light flashes in 1 minute?

Many scientists fear that the increasing level of CO2 gas in our atmosphere is causing climate change. The diagram below shows the CO2 emission levels in 1990 (the light bars) for several countries (or regions), the emission levels in 1998 (the dark bars), and the percentage change in emission levels between 1990 and 1998 (the arrows with percentages).  In the diagram you can read that in the USA, the increase in CO2 emission level from 1990 to 1998 was 11%. Show the calculation to demonstrate how the 11% is obtained.

Mandy analyzed the diagram and claimed she discovered a mistake in the percentage change in emission levels: “The percentage decrease in Germany (16%) is bigger than the percentage decrease in the whole European Union (EU total, 4%). This is not possible, since Germany is part of the EU.” Do you agree with Mandy when she says this is not possible? Give an explanation to support your answer

Which of the figures has the largest area? Explain your reasoning

A woman in hospital receives an injection of penicillin. Her body gradually breaks the penicillin down so that one hour after the injection only 60% of the penicillin will remain active. This pattern continues: at the end of each hour only 60% of the penicillin that was present at the end of the previous hour remains active. Suppose the woman is given a dose of 300 milligrams of penicillin at 8 o’clock in the morning. 3 Complete this table showing the amount of penicillin that will remain active in the woman’s blood at intervals of one hour from 0800 until 1100 hours.

In a Sprinting event, the ‘reaction time’ is the time interval between the starter’s gun firing and the athlete leaving the starting block. The ‘final time’ includes both this reaction time, and the running time. The following table gives the reaction time and the final time of 8 runners in a 100 metre sprint race.

To date, no humans have been able to react to a starter’s gun in less than 0.110 second. If the recorded reaction time for a runner is less than 0.110 second, then a false start is considered to have occurred because the runner must have left before hearing the gun. If the Bronze medallist had a faster reaction time, would he have had a chance to win the Silver medal? Give an explanation to support your answer

The following table shows the recommended Zedland shoe sizes corresponding to various foot lengths.  Marina’s feet are 163 mm long. Use the table to determine which Zedland shoe size Marina should try on.

In modern architecture, buildings often have unusual shapes. The picture below shows a computer model of a ‘twisted building’ and a plan of the ground floor. The compass points show the orientation of the building.  The ground floor of the building contains the main entrance and has room for shops. Above the ground floor there are 20 storeys containing apartments. The plan of each storey is similar to the plan of the ground floor, but each has a slightly different orientation from the storey below. The cylinder contains the elevator shaft and a landing on each floor.  Estimate the total height of the building, in metres. Explain how you found your answer