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CS 361 Pretest: Math Review and Problem Solving, Exams of Computer Science

University of New Mexico (UNM) - GallupComputer Science

A take-home pretest for the cs 361 course at the university of new mexico, designed to assess students' math background and review needs. It includes graded and ungraded problems on equation solving, function identification, and logical reasoning, as well as requests for student preferences and availability.

Typology: Exams

Pre 2010

Uploaded on 07/23/2009

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koofers-user-2z0 🇺🇸

10 documents

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CS 361, Pretest
Prof. Jared Saia, University of New Mexico
January 21, 2003, Due: Tuesday, January 28
This is a take-home “pretest” to test your math background for this course.
It will be graded! However, if you don’t see an answer to a question, you are
free to ask a friend for help, or use a book or the web as a resource. Please show
all your work.
This test will be used for two purposes: 1) to divide the class up into groups
which are roughly balanced in terms of mathematical background (the class
project and at least some hws will be done in groups) and 2) to see how much
math review we need to do in class.
Graded Problems:
1. Find the solutions to this equation: x2−5x−14 = 0.
2. Find the solutions to this equation x2−x−1 = 0
3. Assume that x+y= 7 and −2x+ 2y= 2 for unknown variables xand y.
What are the values of xand y?
4. Assume you know that some function fis of the form f(x) = ax2+bx,
where the coefficients aand bare unknown. Assume further that f(1) = 2
and f(2) = 10. What are the co efficients aand b?
1
pf3

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Download CS 361 Pretest: Math Review and Problem Solving and more Exams Computer Science in PDF only on Docsity!

CS 361, Pretest

Prof. Jared Saia, University of New Mexico

January 21, 2003, Due: Tuesday, January 28

This is a take-home “pretest” to test your math background for this course. It will be graded! However, if you don’t see an answer to a question, you are free to ask a friend for help, or use a book or the web as a resource. Please show all your work. This test will be used for two purposes: 1) to divide the class up into groups which are roughly balanced in terms of mathematical background (the class project and at least some hws will be done in groups) and 2) to see how much math review we need to do in class. Graded Problems:

  1. Find the solutions to this equation: x^2 − 5 x − 14 = 0.
  2. Find the solutions to this equation x^2 − x − 1 = 0
  3. Assume that x + y = 7 and − 2 x + 2y = 2 for unknown variables x and y. What are the values of x and y?
  4. Assume you know that some function f is of the form f (x) = ax^2 + bx, where the coefficients a and b are unknown. Assume further that f (1) = 2 and f (2) = 10. What are the coefficients a and b?
  1. For each of the following equations, say whether it is always true, or if it may be false. If the equation is always true, say why. If it’s false, give values for which it is false. All logs are base 2 unless stated otherwise.

(a) 2log^ n^ = n (b) alog^ b^ = b log^ a. (c) log 2x = log 2 + log x (d) log x^2 = 2 log x (e) log 8 x = (log 2 x)/4 (that is, log base 8 of x is log base 2 of x divided by 4.

  1. What is

i=0 2 −i (^) = 1 + 1/2 + 1/4 + 1/8 +...

  1. Prove, by induction on n, that

∑n i=1 i^ = 1 + 2 + 3 +^ · · ·^ +^ n^ =^ n(n^ + 1)/2.

  1. Prove, by induction on n, that

∑n i=0 2

i (^) = 2n+1 (^) − 1

  1. Let’s say you have 2 blue blocks, and 2 green blocks, and 1 red block that are otherwise indistinguishable. How many different columns of height 5 can be built from these 5 blocks? For this problem, BRBGG and GGBRB will be considered to be two different columns (i.e. there is a bottom up ordering).

Ungraded Questions:

  1. If there are any students in the class who you’d prefer to work with, or prefer not to work with, please list them here (every effort will be made to honor these requests): Prefer to work with:

Prefer not to work with: