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Geometry & Trigonometry - IB Questionbank | RevisionDojo

Practice Geometry & Trigonometry with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SLPaper 1

Consider the function $f(x) = 3 \sin\left(kx + \frac{\pi}{4}\right) - 1$ .

Find the amplitude of $f(x)$ .

[1]

Determine the possible values of $k$ such that $f(x)$ has a period of $12\pi$ .

[3]

Given that $k > 0$ , find the $x$ -coordinates of the maximum and minimum points of $f(x)$ in the domain $0 \le x \le 2\pi$ .

[6]

Question 2

HLPaper 1

The motion of a particle is given by the equation $\vec{r}=\begin{pmatrix} 3 \\ 5 \end{pmatrix}+t\begin{pmatrix} 4 \\ 3 \end{pmatrix}$ , where $t$ is in seconds.

Find initial position of the particle and its position after 2 seconds.

[6]

Find the velocity and the speed of the particle.

[3]

How far from the origin is the particle after 2 seconds?

[4]

How far from its initial position is the particle after 2 seconds?

[4]

Question 3

HLPaper 1

Let $\mathbf{u} = \begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix}$ and $\mathbf{v} = \begin{pmatrix} 3 \\ -1 \\ 1 \end{pmatrix}$ . Let $\mathbf{w}$ be a vector that is perpendicular to both $\mathbf{u}$ and $\mathbf{v}$ .

Find a vector $\mathbf{w}$ that is perpendicular to both $\mathbf{u}$ and $\mathbf{v}$ .

[4]

Question 4

HLPaper 1

The position vectors of points $P$ and $Q$ are $\mathbf{p}=3\mathbf{i}+2\mathbf{j}+\mathbf{k}$ and $\mathbf{q}=\mathbf{i}+3\mathbf{j}-2\mathbf{k}$

Find the vector product $\mathbf{p} \times \mathbf{q}$ . Give your answer in terms of base vectors.

[4]

Using your answer to part 1, or otherwise, find the area of the parallelogram with two sides $\overrightarrow{OP}$ and $\overrightarrow{OQ}$

[5]

Question 5

HLPaper 1

Prove that: $\tan(\arcsin(x)) = \frac{x}{\sqrt{1 - x^2}}$ for $|x| < 1$

[4]

Question 6

HLPaper 1

Consider a triangle $XYZ$ such that $X$ has coordinates $(0, 0, 0), Y$ has coordinates $(0, 1, 2)$ and $Z$ has coordinates $(2b, 0, b - 1)$ where $b < 0$

Let $N$ be the midpoint of the line segment $XZ$ .

Find, in terms of $b$ , a Cartesian equation of the plane $\Pi$ containing this triangle.

[5]

Find, in terms of $b$ , the equation of the line $L$ which passes through $N$ and is perpendicular to the plane $\Pi$ .

[2]

Geometry & Trigonometry Questionbank