Problems adapted from questions set for previous Mathematics exams.
The graph shows the height of water in a container over a period time during which the water enters the container at a constant rate.
Which of the following might be a diagram of the container?
a. b. c. d. e.
The diagram is of a container which is filled with water entering at a constant rate.
Which of the following might be the graph of height of the water in the container plotted against time?
a. b. c. d. e.
The following diagram shows a distance-time graph of the movement of a fish.
(a) Work out the average speed between 10 and 20 seconds.
(b) Estimate the speed of the fish at 25 seconds.
A model train is placed on a length of straight track.
(a) Draw a velocity-time graph for the train on graph paper provided below.
(b) Work out the total distance travelled by the model train.
A motorbike moves from rest along a straight road. The graph below shows the speed, \(v\) in metres per second of the motorbike \(t\) seconds after it started to move.
(a) What is the maximum speed achieved by the motorbike.
(b) Calculate an estimate of the gradient of the graph at t = 10.
(c) Describe what your answer to part (b) represents.
(d) Work out an estimate for the distance the motorbike travels in the first 25 seconds of its journey by dividing the area under the graph into five strips of equal width.
The graph shows the temperature (\(T\)) of an unidentified flying object over a period of 10 seconds (\(t\)).
Use the graph to work out an estimate of the rate of decrease of temperature at 7 seconds. You must show your working.
The graph shows the distance travelled, in metres, of a commuter train as it pulls out of a station.
Estimate the speed of the train, in m/s, after 10 seconds. You must show your working.
Here is a speed-time graph for a go kart.
Work out an estimate for the distance the kart travelled in the first 12 seconds by using six strips of equal width.
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