IB Mathematics Applications & Interpretation Geometry and Trigonometry

Question Type 1: For given 2 points, calculating the distance between the two points

Question Type 2: For given 2 points, calculating the midpoint between the two points

Question Type 3: Calculating the surface area of specific 3D shapes given the parameters

Question Type 4: Calculating the volume of specific 3D shapes given the parameters

Question Type 5: Calculating the surface area of specific complex shapes made by combining two or more shapes

Question Type 6: Calculating the volume of specific complex shapes made by combining two or more shapes

Question Type 1: Using SOH CAH TOA to find one side length given an angle

Question Type 2: Using SOH CAH TOA to find the angle given two sides

Question Type 3: Finding sides and angles using sine rule

Question Type 4: Using cosine rule to find the 3rd side

Question Type 5: Using cosine rule to find all the angles between sides

Question Type 6: Finding the area of a general triangle

Question Type 7: Working with sine, cosine and area of triangle rule all together

Question Type 1: Finding angles using bearings

Question Type 2: Exploring complex formulations using bearings and angles

Question Type 3: Applying values of elevation and depression

Question Type 1: Finding the circumference and area of a circle

Question Type 2: Calculating the arc length given some parameters

Question Type 3: Calculating the area of a sector given parameters

Question Type 1: Finding the equation of a perpendicular bisector given two points

Question Type 2: Finding the equation of a perpendicular bisector given a line segment with a mid point

Question Type 1: Finding the closest site for a given point in a Voronoi Diagram

Question Type 2: Finding the area of a closed region within a Voronoi Diagram

Question Type 3: Constructing Voronoi Diagrams for a given number of points

Question Type 4: Adding sites to update Voronoi Diagrams

Question Type 5: Determining equations of edges with specific domains

Question Type 6: Assigning values to points using Nearest Neighbor Interpolation

Question Type 7: Finding the furthest site still in the region for Voronoi Diagrams

Question Type 8: Drawing the largest empty circle

Question Type 1: Converting from degrees to radians

Question Type 2: Calculating the arc length given a radius and specific angle

Question Type 3: Calculating the area of sector given a radius and specific angle

Question Type 4: Applying both arc length and area of sector in solving equations

Question Type 1: Determining relationship between trigonometric functions using unit circle

Question Type 2: Given an equation of a line, finding the angle of elevation

Question Type 3: Rearranging equations and simplifying equations into either sin or cos only

Question Type 4: Determining if given information on a triangle suffers from Ambigious case of sine rule

Question Type 5: Finding both possible triangles for those suffering with Ambigious case of sine rule

Question Type 6: Applying the golden rule to rewrite values of trigonometric functions

Question Type 7: Solving trigonometric equations for specific domains

Question Type 1: Applying transformations given descriptions

Question Type 2: Finding parameter values for changes in transformations

Question Type 3: Finding the area of an image using matrix transformations

Question Type 4: Visually applying simple matrix transformations

Question Type 1: Formulating path between two points using given vectors on an image

Question Type 2: Sketching a path between two points using two given vectors on a grid

Question Type 3: Performing simple calculations with vectors

Question Type 4: Determining the unit vector of a given vector

Question Type 5: Visually representing vector operations

Question Type 6: Finding the distance between two position vectors

Question Type 1: Finding vector equation of a line passing through two points

Question Type 2: Verifying if a point lies on a specific line

Question Type 3: Converting between different forms of a line

Question Type 1: Determining speed of an object for a given trajectory

Question Type 2: Determining with an object given a trajectory passes a specific point

Question Type 3: Determining whether two objects intersect for their given trajectory

Question Type 4: Finding the time at which two objects are closest each other given some trajectory

Question Type 5: Finding the value of parameters such that two trajectories or objects would intersect

Question Type 6: Determining speed and velocity for trajectories with varying velocities

Question Type 7: Finding the position of a specific object on a trajectory for a given value in time

Question Type 8: Finding the time of change in both directions for a given object

Question Type 1: Finding the dot product of two different vectors

Question Type 2: Finding the angle between two different vectors

Question Type 3: Determining whether two vectors are perpendicular

Question Type 4: Finding for what values of a parameter are two vectors perpendicular

Question Type 5: Finding the cross product for two given vectors

Question Type 6: Finding the area of a parallelogram or triangle spanned by two vectors

Question Type 7: Determining components of vectors that complement another vector

Question Type 8: Determining components of a vector not acting or acting perpendicularly on another vector

Question Type 1: Determining properties of a given simple graph

Question Type 2: Creating simple graphs given information of structures

Question Type 3: Determining properties of a given directed graph

Question Type 4: Creating directed graphs given some descriptions or information

Question Type 5: Finding all the possible Tree subgraphs

Question Type 1: Constructing adjacency matrices for a given simple or directed graph

Question Type 2: Creating adjacency tables for weighted and unweighted graphs

Question Type 3: Using adjacency tables to reconstruct graphs or check graph properties

Question Type 4: Finding lengths of paths between vertices using adjacency matrices

Question Type 5: Applying adjacency matrices with some real world context

Question Type 1: Finding minimum spanning trees by applying Prim's algorithm

Question Type 2: Finding minimum spanning trees by applying Kruskal's algorithm

Question Type 3: Applying minimum spanning trees under real world context

Question Type 4: Finding the shortest path in weighted graphs using Dijkstra's Algorithm

Question Type 5: Using Floyd-Warshall for all pairs shortest path

Question Type 6: Applying algorithm to find the shortest route covering every edge once

Question Type 7: Applying the postman problem to real world contexts

Question Type 8: Applying different approaches to solve the traveling salesman problem

Question Type 9: Applying the traveling salesman problem in real world contexts