6. A ball starts at a height of 21 metres. It then falls at a constant rate of 3 metres per second.


(i) After how many seconds will the ball hit the ground? (ii) Draw a graph to show this information. (iii) Identify the variables in this question.


7. A bus is carrying 24 people. At each stop, 4 people get off the bus. No one gets on the bus. (i) How many stops must the bus make so all the passengers have gotten off? (ii) Draw a graph to show this information. (iii) At which stop will the bus contain 8 passengers?


8. Mary and John each get a bank account. Mary starts by putting €10 into her account and then adds €2 per week. John doesn’t put anything into his account at the start, but saves €4 into it every week.


(i) Create a table showing Mary’s savings and a table showing John’s savings over the first 7 weeks. (ii) Draw a graph showing the amount that Mary has in her account each week for the first 7 weeks.


(iii) Using the same axes and scale, draw a graph showing the amount that John has in his account each week, for the first 7 weeks.


(iv) During which week will the amounts in their accounts be equal?


9. Two identical containers are being filled with water. Each container is 30 cm tall. Container A is empty at the start of the experiment. Once the experiment starts, the water level rises by 3 cm per minute.


A


Container B already contains water at a height of 5 cm before the experiment begins. Once the experiment starts, the water level rises by 2 cm per minute.


(i) Create a table showing how the water levels in each container change over 5 minutes.


(ii) Draw a graph showing the height of the water in container A over 10 minutes.


(iii) Using the same axes and scale, draw a graph showing the height of the water in container B over 10 minutes.


(iv) Will the containers ever contain exactly the same level of water? Justify your answer.


B


7⋅3 Examining the rate of change of a pattern


There are many different types of pattern, but for now, we will be looking at patterns that have the


By the end of this section you should:


● understand what the slope (rate of change) of a graph is


● be able to calculate the slope of a straight line graph


● understand how the rate of change in a pattern/ graph is linked to its slope


same rate of change in each stage. These are called linear patterns.


A linear pattern exists if the points that make it up form a straight line. A linear pattern has the same difference between stages.


114


Linking Thinking 1


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