Student Activity: To investigate an ESB bill - Project Maths
Student Activity: To investigate an ESB bill - Project Maths
Student Activity: To investigate an ESB bill - Project Maths
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c. What shape is the graph? Explain your <strong>an</strong>swer._______________________________________________________________d. Where does this graph cut the y axis <strong>an</strong>d what number does this relate to onthe table?_______________________________________________________________e. What is the rate of ch<strong>an</strong>ge of the graph?_______________________________________________________________f. Find 2 points on the line <strong>an</strong>d calculate the slope of the line._____________________________________________________________________________________________________________________________g. Write <strong>an</strong> algebraic formula to represent the cost of <strong>an</strong> <strong>ESB</strong> <strong>bill</strong> using thecharges used in this question?_______________________________________________________________h. Where does the slope appear i) in the table, ii) in the graph <strong>an</strong>d iii) in theformula?_______________________________________________________________Draft 01 © <strong>Project</strong> <strong>Maths</strong> Development Team 2011 <strong>ESB</strong> <strong>bill</strong> Page 3 of 8
13.a. Using the diagram above, calculate the st<strong>an</strong>ding charge <strong>an</strong>d the unit costfrom the information shown.______________________________________________________________________________________________________________________________b. What is the equation of the line in the above diagram?_______________________________________________________________c. Complete the table for the situation represented in the diagram above.Units used Cost of Units St<strong>an</strong>dingcharge050100150200<strong>To</strong>tal Bill14.a. Complete the following table to represent the situation where the st<strong>an</strong>dingcharge for electricity is €0 <strong>an</strong>d the price per unit is €0.10.Unitsused050100150200Cost of UnitsSt<strong>an</strong>dingcharge<strong>To</strong>tal BillDraft 01 © <strong>Project</strong> <strong>Maths</strong> Development Team 2011 <strong>ESB</strong> <strong>bill</strong> Page 6 of 8
. Draw a rough graph to represent the situation where the st<strong>an</strong>ding charge forelectricity is €0 <strong>an</strong>d the price per unit is €0.10.a. What is the formula that represents the situation where the st<strong>an</strong>ding chargefor electricity is €0 <strong>an</strong>d the price per unit is €0.10?_____________________________________________________________________15. Jonath<strong>an</strong> forgot to pay his <strong>ESB</strong> <strong>bill</strong> for the last <strong>bill</strong>ing period <strong>an</strong>d he used 200 unitsthis period. The st<strong>an</strong>ding charge is €21 per 2 month period <strong>an</strong>d the cost per unit is€0.10. If the <strong>bill</strong> for the 4 month period was €300, how m<strong>an</strong>y units did he use in thefirst 2 months assuming the charges remain the same? Show your calculations.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________16. If the <strong>ESB</strong> ab<strong>an</strong>doned its st<strong>an</strong>ding charge, but the amount of a household’s <strong>bill</strong> didnot increase, what 2 things could have happened?__________________________________________________________________________________________________________________________________________Draft 01 © <strong>Project</strong> <strong>Maths</strong> Development Team 2011 <strong>ESB</strong> <strong>bill</strong> Page 7 of 8
17. If you were told the number of units used vs. the total <strong>bill</strong> was represented by alinear graph y=0.17x+10. What does that tell you about the st<strong>an</strong>ding charge <strong>an</strong>d costper unit?__________________________________________________________________________________________________________________________________________18. Describe what happens to the line in the interactive file if the cost of the st<strong>an</strong>dingcharge for a household is increased.__________________________________________________________________________________________________________________________________________19. Describe what happens to the line in the interactive file if the cost per unit isincreased.__________________________________________________________________________________________________________________________________________20.a. Describe the cost of the <strong>bill</strong> Household A receives <strong>an</strong>d the <strong>bill</strong> Household Breceives in the diagram below.b. Write down <strong>an</strong>d then graph a situation where a household has a higherst<strong>an</strong>ding charge th<strong>an</strong> household A in the diagram above but ends up with a<strong>bill</strong> which is below Households A’s <strong>bill</strong> after a certain number of units. Draw arough sketch of this situation.__________________________________________________________________________________________________________________________________________Draft 01 © <strong>Project</strong> <strong>Maths</strong> Development Team 2011 <strong>ESB</strong> <strong>bill</strong> Page 8 of 8
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