Lab: Math Review

Today’s lab will give you a chance to review mathematical concepts that will be important in this course and your future in computer science.

The goal of this lab is to give me an idea of what background material you know well, what material you know less well, and how you think about math. To that end, I ask that you please show all of your work. I also ask that if you realize you did something wrong, you do not erase the old work.

Section 1: Exponential Review

1. What is \(x^{1/2}\times x^{3/2}\times x^{-2}\)
2. Simplify \(x^2y^3xy^{-3}yz\)
3. Simplify \(\frac{x^3}{x^{-2}}\)
4. Simplify \(3\times5\times9\times3^4\)

Section 2: Prime factorization

For each of the following numbers, give the prime factorization

1. 70
2. 108
3. 180
4. 27
5. 64

Section 3: Matrix Review

Given Matrices A and B:

\[A=\begin{bmatrix} 1 & 2\\ 2 & 1\\ \end{bmatrix}\] \[B=\begin{bmatrix} 2 & 1\\ 4 & 3\\ \end{bmatrix}\]

1. What is \(A+B\)? \(B+A\)?
2. What is \(A-B\)? \(B-A\)?
3. What is \(A\times B\) \(B\times A\)

Section 4: Finite sequences

Simplify each of the following sums to an integer:

1. \[\sum_{i=0}^10 i\]
2. \[\sum_{i=0}^10 2i\]
3. \[\sum_{i=0}^10 (2i+1)\]
4. \[\sum_{i=0}^10 2^i\]

Section 5: Solving systems of linear equations

For each set of linear equations below, solve for x and y.

1. \(y=4x-9\) and \(y=x-3\)
2. \(4x+2y=10\) and \(x-y=13\)
3. \(x+y=0\) and \(x-y=0\)
4. \(x+y=2\) and \(x-y=0\)
5. \(x+y=0\) and \(x-y=2\)

Section 6: Two column geometric proofs

Go to mathplane

1. Page 3 problem 6
2. Page 4 problem 3
3. Page 4 problem 5
4. Page 4 problem 6

Some problems taken from kutasoftware and mathplane