4. (i)


A plant is 2 cm tall and grows 1 cm each month. Write a formula to calculate its height for any month.


(ii) A baker has 5 cakes and bakes a further 3 every hour. Write a formula to calculate the number of cakes he will have at a given time.


(iii) Gerry has read 50 pages of his book and he will read a further 8 pages every hour. Write a formula to calculate the number of pages he will have read in a given time.


(iv) A pyramid has a base with 100 blocks (layer 0). For each new layer, 8 blocks are removed, i.e. layer 1 will contain 92 blocks, layer 2 will contain 84 blocks, etc. Write a formula to calculate the number of blocks in any given layer.


5. Tom’s wages are calculated using the following formula:


wages = 3 + 9·8(h)


where h represents the number of hours worked. Calculate Tom’s wages if he worked the following number of hours:


(i) one hour (ii) fi ve hours


(iii) nine hours (iv) 38 hours (a week of work)


6. A taxi fare is calculated using the following rule:


€4⋅00 pick-up fee and €1⋅10 per kilometre travelled.


(i) Write a formula to represent this information, explaining the meaning of the letters you have used.


(ii) Using your formula, calculate the total cost of a 10 km journey.


(iii) Use trial and improvement – or any other valid mathematical method – to fi nd how many kilometres you could travel if you had €27⋅10.


7. (i)


Draw the next two stages of the pattern of blocks shown.


Stage 1 Stage 2 Stage 3


(ii) Copy the table below and complete it for the fi rst six stages of the pattern.


Stage


1 2


Number of green dots


1


Number of black dots


4 (iii) Identify the variables in the table.


(iv) Write a word formula to explain how to fi nd the total number of dots in any stage of the pattern.


(v) Write a mathematical formula to fi nd the total number of dots in any stage of the pattern. Explain the meaning of any letters you use.


(vi) (a) Stage 1 Stage 2 Stage 3


How many dots in total are there in stage 57?


(b) How many of those dots are green? (c) How many of those dots are black?


(vii) Use trial and improvement – or any other valid mathematical method – to fi nd which stage of the pattern contains exactly 77 dots.


138 Linking Thinking 1 Total


number of dots


5 … … … 8. (i)


(ii) Copy the table below and complete it for the fi rst six stages of the pattern.


Stage


1 2


Number of red blocks


2


Number of blue blocks


4 (iii) Identify the variables in the table.


(iv) Write a word formula to explain how to fi nd the total number of blocks in any stage of the pattern.


(v) Write a mathematical formula to fi nd the total number of blocks in any stage of the pattern. Explain the meaning of any letters you use.


(vii) (a) How many blocks in total are there in stage 100?


(b) How many of those blocks are red? (c) How many of those blocks are blue?


Draw the next stage of the pattern of dots shown.


Total


number of blocks


6 … … …


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