# Syllabus for Basic Arithmetic and Algebra

**Course Description:**

This is a course is a combination of remedial arithmetic skills and elementary
algebra. It includes the

arithmetic of integers, fractions, decimals, and percent. In addition, the
course covers topics such as

algebraic representation, operations with polynomials , solving linear equations,
solving systems of two

linear equations in two variables, exponents and radicals, factoring, graphing
linear equations, and the

Pythagorean theorem. This is an accelerated course for students who have scored
relatively high on the

placement examination in pre-algebra.

**Pre/Co-Requisites:**

Pre-Requisite: ESL 062. Students who score 30 up to 36 on the COMPASS
Pre-algebra exam and less

than 38 on the COMPASS algebra exam are eligible to take MAT 012. Students who
have not yet

obtained a score of 30 or more on the COMPASS pre-algebra exam will be required
to do so before

exiting the course. The COMPASS pre-algebra exam will be scheduled during the
8th week of classes.

**Student Learning Outcomes and Assessment:**

Course Student Learning Outcomes |
Measurements |

1. Students should be able to
correctly compute a variety of operations involving real numbers in a number of different formats , including the correct usage of the order of operations . |
1. Homework, quizzes, online problem assignments, midterm, COMPASS exam, final exam. |

2. Students should be able to
correctly convert between a variety of real number types and formats. |
2. Homework, quizzes, online problem assignments, midterm, COMPASS exam, final exam. |

3. Students should be able to make
estimates and to check the reasonableness of solutions to calculations and problems involving real numbers. |
3. Homework, quizzes, online problem assignments, midterm, COMPASS exam, final exam. |

4. Students should be able to solve
applied word problems, including correctly setting up problems and translating between words and algebraic expressions and equations. |
4. Homework, quizzes, online problem assignments, midterm, COMPASS exam, final exam. |

5. Students should be able to perform
operations and solve equations involving algebraic expressions in the real numbers, including polynomial, rational, and radical expressions and equations, linear inequalities and systems of equations. |
5. Homework, quizzes, online problem assignments, midterm, COMPASS exam, final exam. |

6. Students should be able to
represent equations in the real numbers graphically, and translate between graphical and algebraic forms, and use both graphical and algebraic forms to solve problems. |
6. Homework, quizzes, online problem assignments, midterm, COMPASS exam, final exam. |

Outline of Topics |
Pages in Text |

Arithmetic of Whole Numbers (Week 1) | 1 -77 |

• Writing, rounding, adding, subtracting , multiplying, and
dividing whole numbers.

• Estimating the sum , difference, products and quotients of whole numbers.

• Problems involving exponents, simple averages , and order of operations.

• Prime factorizations of whole numbers.

• Applied problems and word problems.

Fractions (Week 2) | 79-160 |

• Forming, reducing, adding, subtracting, multiplying,
dividing and comparing fractions .

• Converting between mixed numbers and improper fractions.

• Solving applied problems and word problems.

Decimals (Week 3) | 161-219 |

• Writing, rounding, adding, subtracting, multiplying,
dividing and comparing decimals .

• Converting between decimals and fractions .

• Solve applied problems and word problems.

Percent (Week 4) | 220-268 |

• Writing and simplifying ratios and rates as fractions.

• Finding units rates and best buys.

• Setting up and solving proportion problems.

• Solving applied problems and word problems.

• Converting between decimals, percent and fractions.

• Setting up and solving percent problems, including application problems
involving percent.

Basic Statistics (Week 5) | 269-307 |

• Finding the mean median, mode, and range of a given set
of numbers.

• Reading and interpreting tables, line graphs, bar graphs and pie charts.

• Solving applied problems and word problems involving basic statistics and bar
graphs.

Signed numbers (Week 5) | 31-80 (2nd section) |

• Adding, subtracting, multiplying, dividing and comparing
signed numbers.

• Determining absolute value.

• Completing word problems involving signed numbers.

Algebraic Expressions, Translations and Exponents (Week 6) | 81-118 |

• Evaluating algebraic expressions via substitution.

• Adding, subtracting, multiplying, dividing and simplifying algebraic
expressions.

• Using algebraic expressions to solve applied problems.

Solving Linear Equations and Inequalities (Week 7) | 119-195 |

• Solving linear and literal equations .

• Defining a linear equation in x and y using given information.

• Solving applied problems using linear equations in one variable.

Week 7: **Departmental Midterm Exam: Whole umbers, Fractions, Decimals,
Percent, Algebraic
Expressions and Exponents, and Solving Linear Equations/Inequalities**

Graphing Linear Equations and Inequalities (Week 8) | 197-314 |

• Graphing the solution set of a linear inequality.

• Ploting points in the x-y plane.

• Graphing linear equations.

• Finding the slope of a line from given information.

• Graphing linear inequalities in 2 variables .

Solving Systems of Linear Equations (Week 9) | 315-374 |

• Solving systems of linear equations in 2 variables using
graphical, substitution and elimination

methods.

• Solving applied problems involving systems of equations.

Exponents and Polynomials (includes scientific notation) (Week 10) | 375-467 |

• Multiplying, dividing and simplifying expressions
involving exponents.

• Adding, subtracting, multiplying, dividing and evaluating polynomials.

• Converting numbers between standard form and scientific notation.

• Adding, subtracting, multiplying, and dividing numbers in scientific notation.

Factoring Polynomials (Week 11) | 469- 527 |

• Factoring polynomials using the greatest common factor
and grouping.

• Factoring trinomials and difference of squares.

• Solving quadratic equations in one variable by factoring.

• Solving applied problems involving factoring.

Rational Expressions and Equations (Week 12) | 529-612 |

• Simplifying, adding, subtracting, multiplying and
dividing rational expressions.

• Simplifying complex fractions.

• Solving rational equations.

Radical Expressions and Equations (Week 13) | 613- 667 |

• Simplifying, adding, subtracting, multiplying and
dividing radical expressions.

• Rationalizing the denominator of a radical expression.

Week 14: Review for Final Exam; **Department Final Exam**

Week 15: **COMPASS Algebra Exam; Second Try for Department Final Exam**

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