2.5 Modelling with functionsIB Maths: Applications and Interpretation HL: Flashcards

What these 14 flashcards ask

General form of a linear model?
What is a piecewise model?
Axis of symmetry of f(x)=ax^2+bx+c?
What is the y-intercept of f(x)=ax^2+bx+c?
Another name for a zero of a function?
Horizontal asymptote of f(x)=ka^x+c?
Exponential growth or decay: f(x)=ke^{rx}+c?
Direct variation model?
Inverse variation model, and its vertical asymptote?
General cubic model?
Amplitude of f(x)=a\sin(bx)+d?
Period of f(x)=a\sin(bx)+d (degrees)?
Principal axis of f(x)=a\cos(bx)+d?
What should you check after finding a model's equation?

Exam questions on 2.5 Modelling with functions

A mobile phone plan costs 45 AED per month and includes 5 GB of data. Each extra GB used beyond 5 GB costs 8 AED. The monthly cost is $C$ AED when $d$ GB are used, $d\geq 0$ .
Write down the gradient of the model for $d>5$ and interpret it in context.2 marks
A footballer kicks a ball from the ground. Its height $h$ metres, when it has travelled a horizontal distance $x$ metres, is modelled by $h(x)=-0.04x^2+0.96x$ , for $x\geq 0$ while the ball is in the air.
Use your GDC to find the horizontal distance at which the ball is at a height of 5 m on its way up.2 marks
A cup of coffee is poured at $t=0$ minutes in a room. Its temperature $T$ °C is modelled by $T(t)=22+68e^{-0.05t}$ , for $t\geq 0$ .
(i) Find the temperature of the coffee when it is poured. (ii) Write down the equation of the horizontal asymptote of the graph of $T$ and interpret it in context.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).