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Page 54

(b) Use your graph to find:

(i) the values of x when x

2

– 2x – 3 = 5

(ii) the value of x that gives the minimum value of x2 – 2x – 3

(Total 4 marks)

39. The profit (P) in Swiss Francs made by three students selling homemade lemonade is modelled

by the function

P = –

2

20

1

x

+ 5x – 30

where x is the number of glasses of lemonade sold.

(a) Copy and complete the table below

x 0 10 20 30 40 50 60 70 80 90

P 15 90 75 50

(3)

(b) On graph paper draw axes for x and P, placing x on the horizontal axis and P on the

vertical axis. Use suitable scales. Draw the graph of P against x by plotting the points.

Label your graph.

(5)

(c) Use your graph to find

(i) the maximum possible profit;

(1)

(ii) the number of glasses that need to be sold to make the maximum profit;

(1)

(iii) the number of glasses that need to be sold to make a profit of 80 Swiss Francs;

(2)

(iv) the amount of money initially invested by the three students.

(1)

IB Questionbank Mathematical Studies 3rd edition 54

(b) Use your graph to find:

(i) the values of x when x

2

– 2x – 3 = 5

(ii) the value of x that gives the minimum value of x2 – 2x – 3

(Total 4 marks)

39. The profit (P) in Swiss Francs made by three students selling homemade lemonade is modelled

by the function

P = –

2

20

1

x

+ 5x – 30

where x is the number of glasses of lemonade sold.

(a) Copy and complete the table below

x 0 10 20 30 40 50 60 70 80 90

P 15 90 75 50

(3)

(b) On graph paper draw axes for x and P, placing x on the horizontal axis and P on the

vertical axis. Use suitable scales. Draw the graph of P against x by plotting the points.

Label your graph.

(5)

(c) Use your graph to find

(i) the maximum possible profit;

(1)

(ii) the number of glasses that need to be sold to make the maximum profit;

(1)

(iii) the number of glasses that need to be sold to make a profit of 80 Swiss Francs;

(2)

(iv) the amount of money initially invested by the three students.

(1)

IB Questionbank Mathematical Studies 3rd edition 54