IB Maths AI HL AI 1.3 Exponents, logarithms and equations 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 2Easy6 marks

A theatre records the total revenue from three group ticket sales. Let $a$ $s$ and $c$ be the prices, in dollars, of one adult, student and child ticket, respectively. The records are shown in Figure 1.

For a later performance, the regular adult ticket price is $p$ dollars. If the discount is $d$ dollars, the estimated number of discounted adult tickets sold is $4d+12$ The revenue from these tickets is modelled by

R=(p-d)(4d+12),

where $0<d<p$

(a)

Use your GDC to determine the values of $a$ $s$ and $c$

[3]

(b)

Using your answer to (a), use your GDC to find all values of $d$ for which $R=280$ Give your answers to the nearest cent.

[3]

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