IB Maths AI HL AI 3.1 Trigonometry and 3D geometry 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.

Paper

Paper 1 Paper 2

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Question 1

Paper 1Medium6 marks

A mapping team approximates a wetland by triangle $ABC$ The horizontal distance between survey stations $A$ and $B$ is $1.80\text{ km}$ The measured interior angles are $\angle BAC=52.6^\circ$ and $\angle ABC=68.3^\circ$

The wetland qualifies for a reserve if its mapped area is at least $1.20\text{ km}^2$

(a)

Find $\angle ACB$

[1]

(b)

Show that $AC=1.95\text{ km}$ correct to three significant figures.

[2]

(c)

Hence, using your answer to part (b), calculate the area of triangle $ABC$ correct to three significant figures, and state whether the wetland qualifies for a reserve.

[3]

Question 2

Paper 1Medium6 marks

A surveyor uses triangulation to estimate the area of a triangular wetland $ABC$ Points $A$ and $B$ lie on an accessible straight bank, and $AB=d$ metres. The measured interior angles are $\angle BAC=48^\circ$ and $\angle ABC=67^\circ$

(a)

Find $\angle ACB$

[1]

(b)

Show that the area $T$ in $\text{m}^2$ is approximately given by $T=0.377d^2$

[2]

(c)

The surveyor wants to map a region with an area of at least $6000\text{ m}^2$ Determine the required value of $d$ to 3 significant figures. Hence state whether a baseline of $125\text{ m}$ is sufficient.

[3]

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