IB Maths AI HL Topic 1: Number and algebra 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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Paper 1 Paper 2

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Question 1

Paper 2Easy6 marks

A circular inspection window has a radius recorded as $6.4\text{ cm}$ correct to the nearest $0.1\text{ cm}$

For this question, percentage error is

\frac{|\text{estimated value}-\text{actual value}|}{\text{actual value}}\times 100\%.

(a)

Write down the lower and upper bounds for the radius.

[2]

(b)

Calculate the estimated area of the window, giving your answer to three significant figures.

[2]

(c)

Determine the greatest possible percentage error in this estimated area. Use unrounded values in your calculations and give your answer to three significant figures.

[2]

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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