2.6 Modelling skillsIB Maths: Applications and Interpretation SL: Flashcards

What these 13 flashcards ask

What are the stages of the modelling process?
What is the domain of a model?
How do you choose a model from data?
For f(t)=ka^t, what is f(0)?
Parameters a, d and b of a\sin(bt)+d from a maximum, minimum and period?
How do you find parameters by substitution?
How many equations do you need for y=ax^2+bx+c?
What is the maximum number of linear equations in three variables you must solve at SL?
Do you need to perform non-linear regression at SL?
What does it mean to test and reflect on a model?
What is extrapolation?
What is interpolation?
Give one sign that a model is unreasonable.

Exam questions on 2.6 Modelling skills

A rooftop water tank holds at most 400 litres. A pump starts filling the tank at $t=0$ minutes, and the volume of water $V$ litres in the tank is modelled by $V(t)=40+25t$ .
Find $V(20)$ and comment on the reasonableness of the model at $t=20$ .2 marks
A scientist measures the mass $M$ grams of a radioactive sample $t$ days after the start: 80 g at $t=0$ , 40 g at $t=6$ and 20 g at $t=12$ . She wants to fit a model to these data.
Use the model $M(t)=80a^t$ , with $a$ from part (b), to predict the mass of the sample after 20 days.2 marks
A Ferris wheel has its lowest point 2 m above the ground and its highest point 52 m above the ground, and it completes one revolution every 20 minutes. A passenger is level with the axle, and rising, at $t=0$ minutes. The passenger's height $h$ metres above the ground is modelled by $h(t)=a\sin(bt^\circ)+d$ , where $a,b>0$ .
Find the values of $a$ , $b$ and $d$ .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).