Directions for Students: Answer all the questions that are easy FIRST. Then go back and try to figure out the more challenging questions. Please show all your work and make your best guess, if you are unsure.
This is my rough-draft/answer sheet and notes of a pre-test for Math and Technology course in Santiago, Chile. Stanford University sends instructors to countries all over the world to teach exploratory courses. For this one, I have twenty-two 11-13 year old students, grades 6-8. I was going to teach more programming, but there weren't computers, so I decided to bring a bunch of Arduino's with me (Thanks Stanford!). It's a 2 week course.
I basically don't have a clear idea of how much these students know, so I thought I'd pretest them :)
Permutations: How many rainbows can you draw with these colors (red, orange, yellow, green, blue)? Each rainbow can only have 3 colors, no repeated colors.
Where n is the number of things to choose from, and you choose r of them (No repetition, order matters) n!/(n-r)!
Permutations: In how many ways can the letters of the word 'LEADER' be arranged?
The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R. Where n is the number of things to choose from, and you choose r of them (No repetition, order matters) (6!)/(1!2!1!1!1!) = 360
Permutations with Repetition: Each passcode is 5 numbers long. How many passcodes are possible?
Combinations: How many ways can a group of three students be selected from a class of 21 students?
(21!)/(18!)(3!) = 1330 "n choose r" Where n is the number of things to choose from, and you choose r of them (No repetition, order doesn't matter)
Combinations with Repetition: You get 4 scoops of ice cream, how many different combinations can you make from Chocolate, Vanilla, and Strawberry?
"(n + r - 1) choose r"
What is the Prisoners Dilemma according to this image? Try to explain what you thinks this represents.
What game does this matrix represent? Explain what the numbers mean.
rock paper scissors
I have 128 pieces of candy
Cumulative responses are acceptable as are non-cumulative
You give me a quiz, and I get 19 out of 22 problems correct. What percentage did I get correct?
(Independent) My coin has two sides (heads and tails).
p(heads_heads_heads) = p(heads)*p(heads)*p(heads)
(Independent) I roll two dice (each has 6 sides).
p(roll6) = 1/6 p(roll12_2dice) = 1/36 1 + 6 = 7 2 + 5 = 7 3 + 4 = 7 4 + 3 = 7 5 + 2 = 7 6 + 1 = 7 p(roll7_2dice) = 6/36
(Dependent) I have a bag of 5 balls: 2 red and 3 blue. Once I remove a ball, I do not put it back in the bag.
p(A and B) = p(A) * p(B|A) 2/5 * 1/4 = 1/10
Give me the area:
s*s pi*r^2 (1/2)bh
Using the 45°-45°-90° special triangle ratio, the length of the side of the square is 2.
Sum of angles in a triangle = 180°. So, y° + 40° + 80° = 180° y° + 120° = 180° y° = 60°
Two circles both of radii 6 have exactly one point in common. If A is a point on one circle and B is a point on the other circle, what is the maximum possible length for the line segment AB?
If the radius is 6 then the diameter is 2 × 6 = 12 and the distance from A to B would be 2 × 12 = 24
A = 2πrh V = π(r^2)h
Coordinates: You have 2 points on a graph, (2,3) and (4,9). How do you find the distance between the 2 points?
sqrt( (x1-x2)^2 + (y1-y2)^2 )
Prefix Notation: (+ (- 7 8) (/ 10 5) (+ 2 2 (x 9 10))
(7-8) + (10 / 5) + (2 + 2 + (9 x 10))
Game Search: This is a tic-tac-toe game tree
Draw the game tree that starts with:
|o|x| | |x| |o| |o|x| |
Draw a graph that is fully connected with 5 vertices. How many edges does it have?
A complete graph is a graph in which each pair of graph vertices is connected by an edge.
For a given source vertex (node) in the graph, the algorithm finds the path with lowest cost (i.e. the shortest path) between that vertex and every other vertex.
What is Ohm's law?
V = IR
I = V/R
What do we use resistors for?
Resistors are used to limit current in a circuit. It follows the math and the practical implication is to not overload and burn out, for example, LEDs.
What is an Arduino?
What is the difference between a Digital and Analog Clock?
"BTW, a digital clock gives the exact time to it's number of places like any digital device. It's always 6:06 till it's 6:07 LOL. Of course, it's easily possible to construct a digital clock that will allow more accuracy than a 2 or even 3 hand analog clock. (given equally accurate mechanisms)"
"I'm not sure the difference between analog and digital is best described as approximate vs accurate, but that of continuous vs discrete (as Steve points out). Maybe a different choice of object such as what is the difference between an analog signal and a digital signal. One changes smoothly and the other abruptly. Music is digital in an mp3 file, but it's analog when the speaker (and air) moves."
red - 14 black - 7 or gate
Draw the truth table for: ~p v q (not p or q)
00 1 01 1 10 0 11 1
Use DeMorgan's Law to simplify this equation: ~(p ^ q)
~p v ~q
What is another way to represent p → q (p implies q)?
~p v q
Explain what is happening the in diagram above.
Y = ~A v ~B
Explain what is happening the in diagram above.
Y = A(~C) v B
Why do we use Karnaugh Maps?
To detect redundancy
For the following mark whether the argument is inductive or deductive:
It's debatable, but anything that starts with "All observed" is inductive.
Match the logical statement with the English sentence:
|∀x IsABunny(x) ⇒ IsCute(x)||There is at least one student who doesn’t hate (any of) the Math homework|
|∀x IsAStudent(x) ∧ IsTakingMath(x) ⇒ IsCool(x)||Everyone who eats ramen is either very hungry or a student|
|∀x IsABunny(x) ∧ IsAStudent(x) ∧ IsTakingMath(x) ⇒ IsCute(x) ∧ IsCool(x)||Cats rule and dogs drool|
|∀x EatsRamen(x) ⇒ IsVeryHungry(x) ∨ IsStudent(x)||Every bunny who is a student taking Math is cute and cool|
|∃s ∀h IsAStudent(s) ∧ IsTaking(s,Math) ∧ HomeworkFor(h,Math) ∧ ¬Hates(s,h)||All bunnies are cute|
|∀a (IsACat(a) ⇒ Rules(a)) ∧ (IsADog(a) ⇒ Drools(a))||Everyone student who is taking Math is cool|
Write the logical statement for “All men are mortal.”
∀x IsMan(x) -> IsMortal(x)
How do you convert 2 decimal to binary?
How do you convert 31 decimal to hexadecimal?
How do you convert A3D2F in hexadecimal to binary?
What color is:
black red yellow white pink purple