Perplex
Content
  • Exponents & Logarithms
  • Approximations & Error
  • Sequences & Series
  • Matrices
  • Complex Numbers
  • Financial Mathematics
  • Cartesian plane & lines
  • Function Theory
  • Modelling
  • Transformations & asymptotes
  • 2D & 3D Geometry
  • Voronoi Diagrams
  • Trig equations & identities
  • Vectors
  • Graph Theory
  • Probability
  • Descriptive Statistics
  • Bivariate Statistics
  • Distributions & Random Variables
  • Inference & Hypotheses
  • Differentiation
  • Integration
  • Differential Equations
Other
  • Review Videos
  • Blog
  • Landing Page
  • Sign Up
  • Login
  • Perplex
    IB Math AIHL
    /
    Modelling
    /

    Problems

    Edit

    Problem Bank - Modelling

    Access custom-built, exam-style problems for modelling. Each problem has a full solution and mark-scheme, as well as AI grading and support.

    Select a Difficulty:

    24 / 57 problems visible - Upgrade to view all problems

    IB: 5
    14

    !!

    0 / 5

    The voltage of two alternating electrical currents are given by V0​=3sin(ωt) and V1​=8sin(ωt+120°).


    The voltages add to give a total of Vsin(ωt+θ).

    Find V and θ.

    [5]
    15

    !

    0 / 6

    Raymond is riding a ferris wheel. His height h meters above the ground t seconds after the ride starts is given by h(t)=asin(bt+c)+24, where a,b>0 and −π≤c≤π.


    The ferris wheel makes a full revolution in 2 minutes.

    1. Show that b=60π​.

      [1]

    Raymond reaches a maximum height of 45 meters for the first time after 50 seconds.

    1. Find the value of

      1. a

        [1]
      2. c

        [2]
    2. Determine the length of time between when Raymond is first at his lowest point and when he first returns to his starting point.

      [2]
    16

    0 / 8

    Consider the function g(x)=asinbx+c for 0≤x≤24. The graph of g is shown in the diagram below.


    Powered by Desmos

    The x-intercepts are q and r, and the point P lies at the minimum.

    1. Find the coordinates of P.

      [3]
    2. Find the value of q and the value of r.

      [5]
    17

    !

    Plus

    0 / 4

    Upgrade to Plus to solve this problem
    18

    !

    Plus

    0 / 8

    Upgrade to Plus to solve this problem
    19

    !

    Plus

    0 / 8

    Upgrade to Plus to solve this problem
    20

    !

    Plus

    0 / 6

    Upgrade to Plus to solve this problem
    21

    !

    Plus

    0 / 8

    Upgrade to Plus to solve this problem
    22

    !

    Plus

    0 / 7

    Upgrade to Plus to solve this problem

    Ask Plex AI about problem 14

    Get hints, ask questions, and work through this problem step by step