MATHS 110: Math for Science, Midterm Test 2019
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MATHS 110: Math for Science, Midterm Test
2019
1. (10 marks)
(a) Convert 0.1 mM s − l µm−2 to units of mM µs − l mm−2 .
(b) Suppose that a current, I (with units of µA/µm2 ) can be written as a function
of V (with units of mV) as
I = aV + b + ce −dV .
What are the units of a, b, c and d?
2. (10 marks)
Suppose that
J = 0.45 土 0.002 mol
(0.22 土 0.003 µm2 )(1.2 土 0.09 s) .
(a) What is the relative error in the calculation of J?
(b) What is the absolute error in the calculation of J?
3. (10 marks)
Typical oscillations in the concentration of calcium ions inside an epithelial cell
look like this. |
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 |
10 3me(s) |
Suppose that you wanted to describe this oscillation by the function F = a cos(b(t - c)) + d.
Estimate a, b, c and d. (You can do this just by eye, by looking at the graph and making reasonable guesses at things like the amplitude and period.)
4. (10 marks)
Nitrogen dioxide, one of the important compounds in smog, has the shape
O
where the coordinates of each atom are given. N denotes the nitrogen atom, and O denotes oxygen atoms.
(a) What are the bond lengths Ll and L2 ?
(b) What is the bond angle, θ?
(c) What is the distance between the two O atoms?
5. (10 marks)
(a) Start with the vector j = 9 、1(1) and the matrix
A = 、.
Calculate Aj. Sketch j and Aj .
(b) Write the linear system
x + y = 1
x - z = 2
2x + 5y - 3z = -4
in matrix form, i.e., write this system as a matrix equation Ax = b, for some matrix A and vectors x and b.
2022-04-07