Still water surprises
For a square of 2116 bacteria, how many bacteria are there per row/column?
What is 46?
Name one type of knot that isn’t a trefoil:
What is a figure-eight, cinquefoil, square/reef knot, unknot, etc ?
Name one function that has a domain restriction:
What is a square root/log/ln/ tan/sec/csc etc function?
Find 2 objects (cannot be the same category, ex: red marker and black marker) that are topologically identical
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If the fugu fish is a sphere with radius R and only two spikes, what is the average distance between the two spikes along the surface? [hint: consider infinite fish-transformations]
What is pi*R/2 ?
A sample of still water initially contains 5 bacteria at hour 1. If this population doubles every hour, how many bacteria are present at hour 10?
What is 2560?
As a team, form a trefoil knot…there should be no “loose ends!” Whichever team completes the knot first will receive the points.
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f(x) = 2x +1, and g(x) = x^2. Find f(g(f(2 )))
What is 51?
Find the angle between the vectors (1, 0) and (-1, sqrt3)
What is 120 degrees / 4pi/3 radians ?
If this fugu fish had 12 spikes, how should they be placed so that the closest distance between two spikes is as far as possible? You may answer verbally or draw this configuration on the board.
What are as the vertices of an icosahedron? (or drawn)
There’s a lake of still water. As an IB risk taker, Sadie takes n independent sips, each sip with a 20% of containing life-threatening bacteria. After how many sips will there be a 51.2% chance of her survival?
What is 3 sips?
A knot is called alternating if, as you trace it, the crossings go over-under-over-under… How many crossings can a closed knot have if it is alternating?
f(x) = |x - 3| + |x + 1|, find the minimum value of f(x) [hint: use a number line]
What is 4?
For 258 and 86, what is the product of their GCF (greatest common factor) and LCM (least common multiple)?
What is 22188?
This fugu fish enjoys swimming, and half of his volume is now underwater. If this fugu fish had 3 randomly placed spikes, what is the probability that all 3 spikes are underwater?
If the concentration of the bacteria is modeled by the function C(t) = -2t^2 + 16t + 10, at what time is the concentration maximized?
What is t = 4?
If a knot has 8 crossings (no three strands meet at one point), how many distinct regions does the knot have? [hint: knots can be represented as planar graphs]
What is 10?
f(x) = (3x - 2)/(x + 1). Find the inverse function
What is (x+2)/(3-x) ?
What is the remainder when 7^100 is divided by 5?
What is 1?
If this fugu fish had 3 randomly placed spikes, they would form a “curvy” triangle on the sphere’s surface. What is the average perimeter of the average triangle?
What is 3pi*R/2 ?
Lake A has a 30% contamination rate, while Lake B has a 10% contamination rate. Amy randomly chose a lake to take 2 sips out of. Given that only ONE of her sips was contaminated, what is the probability that the contaminated sip came from Lake A? [-$100 for purchasing the Baye’s rule formula]
A knot diagram has 24 crossings, with 10 negative crossings. Three crossings are randomly chosen without replacement. What is the probability that exactly 2 of them are positive?
What is 455/1012?
Of all complex roots of f(x) = x^6 + 5x^5 + 24x^4 + 90x^3 - 67x^2 - 875x - 1050, which complex root has the largest magnitude? [hint: i is the square root of -1]
How many ways are there to make change for a dollar with Canadian currency?
What is 30?
As a hula hooper, this fugu fish has 42 distinct hoops wrapped tightly around him, each hoop forming a great circle [-$100 points for the definition of a great circle 😹] What is the maximum number of regions the fish’s surface can be divided into?
What is 1724?