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Date November 2017 Marks available 2 Reference code 17N.1.SL.TZ0.T_15
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 0
Command term Find Question number T_15 Adapted from N/A

Question

Maria owns a cheese factory. The amount of cheese, in kilograms, Maria sells in one week, Q , is given by

Q = 882 45 p ,

where p is the price of a kilogram of cheese in euros (EUR).

Maria earns ( p 6.80 )  EUR for each kilogram of cheese sold.

To calculate her weekly profit W , in EUR, Maria multiplies the amount of cheese she sells by the amount she earns per kilogram.

Write down how many kilograms of cheese Maria sells in one week if the price of a kilogram of cheese is 8 EUR.

[1]
a.

Find how much Maria earns in one week, from selling cheese, if the price of a kilogram of cheese is 8 EUR.

[2]
b.

Write down an expression for W in terms of p .

[1]
c.

Find the price, p , that will give Maria the highest weekly profit.

[2]
d.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

522 (kg)     (A1)     (C1)

[1 mark]

a.

522 ( 8 6.80 ) or equivalent     (M1)

 

Note:     Award (M1) for multiplying their answer to part (a) by ( 8 6.80 ) .

 

626 (EUR) (626.40)     (A1)(ft)     (C2)

 

Note:     Follow through from part (a).

 

[2 marks]

b.

( W = )   ( 882 45 p ) ( p 6.80 )     (A1)

OR

( W = ) 45 p 2 + 1188 p 5997.6     (A1)     (C1)

[1 mark]

c.

sketch of W with some indication of the maximum     (M1)

OR

90 p + 1188 = 0     (M1)

 

Note:     Award (M1) for equating the correct derivative of their part (c) to zero.

 

OR

( p = )   1188 2 × ( 45 )     (M1)

 

Note:     Award (M1) for correct substitution into the formula for axis of symmetry.

 

( p = )   13.2  (EUR)     (A1)(ft)     (C2)

 

Note:     Follow through from their part (c), if the value of p is such that 6.80 < p < 19.6 .

 

[2 marks]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 5 —Calculus » SL 5.8—Testing for max and min, optimisation. Points of inflexion
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Topic 5 —Calculus

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