IB Maths AI SL Topic 2: Functions questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1Hard8 marks

An urban greenhouse produces and sells seedlings in complete batches of 1000. Let $q$ be the number of batches produced in a year, where $q$ is an integer and $0\leq q\leq80$

The selling price per seedling is modelled by

p(q)=96-1.2q

dollars. The annual operating cost is modelled by

C(q)=0.4q^2+12q+500

thousand dollars. The greenhouse also pays an annual permit fee of $F$ thousand dollars. Assume that all seedlings produced are sold.

Let $P_F(q)$ denote the annual profit, in thousands of dollars. The greenhouse considers a year acceptable if its profit is at least $350 000.

(a)

Write an expression for $P_F(q)$

[1]

(b)

When $F=200$ use your graphic display calculator to determine all allowed values of $q$ for which the year is acceptable.

[2]

(c)

Determine the greatest annual permit fee that would still allow the greenhouse to have an acceptable year, and the corresponding production.

[4]

(d)

State one limitation of this model when it is used to make the decision in part (c).

[1]

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