---
tags: 225-spr22, mth225, lt-quiz
---
# Learning Target Quiz 2
:::info
This quiz contains *new versions of questions* for **Learning Targets 1 and 2** and *new questions* for **Learning Targets 3 and 4**.
* It's to your advantage to attempt as many problems as possible. But you *do not* need to attempt all the problems. Only attempt the ones you believe you are ready to take.
* Do your work on separate pages with **each Learning Target on its own separate page**. *Please do not put multiple Learning Targets on the same page.*
* Make sure to consult the [Standards for Assessments in MTH 225](/KoT83ezHRYO3DqPyXMMMag) document before starting on your work, so you're clear on what is expected and what constitutes a "successful" attempt.
* When you are done: **Scan** each Learning Target to a clear, legible, black-and-white PDF and **upload the PDF** to the designated folder on Blackboard. Remember *do not just take a picture with your camera* --- use a scanning app to create a PDF, and upload the PDF.
:::
## Learning Target 1
:::warning
I can represent an integer in base 2, 8, 10, and 16 including negative integers in base 2.
:::
Do **all** of the following:
1. Convert the base 10 integer $167$ to binary. *Show your work and circle your answer*.
2. Convert the base 16 integer $55FA$ to decimal. *Show your work and circle your answer*.
3. Convert the base 2 integer `10011000` to octal. *Show your work and circle your answer*.
4. The 8-bit binary representation of the decimal number $121$ is `01111001`. Write the 8-bit binary representation of $-121$ using two's complement notation. *Show your work and circle your answer*.
**Success criteria:** All four answers are correct, and the work leading to each answer is clear and legible. Up to two simple errors are allowed.
## Learning Target 2
:::warning
(**CORE**) I can add, subtract, multiply, and divide numbers in base 2.
:::
Do **all** of the following:
1. Add the base-2 integers `11001011` and `10010110`. *Show your work and circle your answer*.
2. Subtract the base-2 integers `11001011` and `10010110`. *Show your work and circle your answer*.
3. Multiply the base-2 integers `10101` and `11`. *Show your work and circle your answer*.
4. Divide the base-2 integer `11000110` by `10`. *Show your work and circle your answer*.
**Success criteria:** All four answers are correct, and the work leading to each answer is clear and legible. Up to two simple errors are allowed.
## Learning Target 3
:::warning
(**CORE**) Given a conditional statement, I can state its hypothesis, conclusion, negation, converse, inverse, and contrapositive.
:::
Consider the conditional statement: *If $n$ is even, then its binary representation ends in a 0.*
1. State the **hypothesis** of this statement.
2. State the **conclusion** of this statement.
3. State the **converse** of this statement.
4. State the **inverse** of this statement.
5. State the **contrapositive** of this statement.
6. State the **negation** of this statement (without simply putting "Not" or "It is not the case that" in the front of the statement).
**Success criteria:** All answers are given in clear and correct English (*not* in symbolic notation). The negation and contrapositive must be correct, and no more than one error is allowed in the others.
## Learning Target 4
:::warning
I can construct a truth table for propositions involving 2, 3, or 4 statements.
:::
Construct a correct truth table for each of the following statements.
1. $\neg (p \wedge q)$
2. $p \rightarrow (q \vee r)$
**Success criteria:** Both truth tables have the correct number of rows with no duplicated rows. All intermediate columns are shown. No more than three total errors are permitted. (If you make a mistake in an intermediate column but the rest of the row is correct given that mistake, then the mistake only counts once.)

:::info Welcome to MTH 201! I'm Dr. Robert Talbert, Professor of Mathematics, and I am grateful that you are signed up for the course and am looking forward to working with you this semester. ::: What's MTH 201 all about? MTH 201 is a first course in Calculus, which is all about modeling and understanding change. Change is maybe the most important facet of the world around us, and we care about it more than we realize. For example, we care a lot about the number of Covid-19 cases in our community, but we might care even more about how fast the number of cases is changing (either up or down). In MTH 201, you'll learn the mathematical language of change and apply it to models that you build to draw conclusions, make predictions, and give meaningful answers to real problems. MTH 201 goes beyond just computation. In MTH 201, you'll build skills with understanding complex concepts, communicating those concepts and the meaning of your results to appropriate audiences, using professional tools to help you in your work, and practice working with others to improve your learning (and theirs). These are valuable skills no matter where you go next. Success in this course doesn't come easy, and you can expect to be pushed and stretched intellectually. But the struggle you experience is normal and healthy, a sign of growth and that you are doing things the right way. And you will receive tireless support from me and your classmates in the process. Above all, my top priority is to support you in your work and help you succeed.

11/11/2023Initial due date: Sunday, April 9 at 11:59pm ET Overview Our final miniproject reaches back into linear algebra to look at diagonalizable matrices and their uses in solving systems of differential equations. Prerequisites: You'll need to be able to solve basic systems of differential equations and find the eigenvalues and eigenvectors for a small matrix. You'll also need a basic comfort level with concepts of linear independence and matrix arithmetic from earlier in the course. Background This entire problem comes from Section 3.9.1 in your textbook. Here is a rephrased version of the introduction to that section.

3/29/2023Initial due date: Sunday, April 9 at 11:59pm ET Overview This miniproject will teach you about the Runge-Kutta method, a standard numerical solution technique for differential equations. Prerequisites: A strong grasp of Euler's Method for single DE's is needed. You will also need to be comfortable using a spreadsheet. Miniproject 6 (Euler's Method for systems) is also recommended. Background A description of the Runge-Kutta method along with an example is given in this tutorial. Read it carefully and make sure you can work along with the example before proceeding.

3/29/2023Initial due date: Sunday, April 9 at 11:59pm ET Overview This miniproject introduces a version of Euler's Method as a numerical solution technique for systems. Prerequisites: You will need to be comfortable with using Euler's method for single differential equations. You'll also benefit from some familiarity with spreadsheets or Python in order to automate the calculations. Background This tutorial gives you the background you need for this assignment. Please read it and make sure you understand the concepts and the example: https://github.com/RobertTalbert/linalg-diffeq/blob/main/assignments/Euler's_Method_for_Systems.ipynb

3/22/2023
Published on ** HackMD**