Readings and homework

Here are the assigned readings and exercises (Reading 1, Reading 2, Reading 3, Reading 4, Reading 5, Reading 6, Reading 7, Reading 8, Reading 9, Reading 10, Reading 11, Reading 12, Reading 13, Reading 14, Reading 15, Reading 16, Reading 17); but anything whose assigned date is in the future is subject to change!

1. Introduction:
   • Date assigned: July 12 Thursday.
   • Date due: July 17 Tuesday.
   • Reading: My online introduction.
   • Exercises due: none.
2. The language of algebra:
   • Date assigned: July 17 Tuesday.
   • Date due: July 19 Thursday.
   • Reading:
     • My online notes on the real numbers;
     • Section 1.2 (pages 21–36) from the textbook.
   • Exercises due:
     1. Fill in the blank with a word: ab is the ___ of a and b.
     2. Fill in the blank with a symbol to indicate that 2 is less than 3: 2 ___ 3.
     3. Write yyy in exponential notation.
     4. To evaluate the expression 2 + 3 ⋅ 4, do you add or multiply first?
3. Exponentiation:
   • Date assigned: July 19 Thursday.
   • Date due: July 24 Tuesday.
   • Reading:
     • My online notes on exponentiation;
     • Section 6.2, objective 1 (simplify expressions with exponents, page 687 through the very top of page 689);
     • Section 6.5, objective 2 (simplify expressions with zero exponents, the bottom half of page 733 through the top half of page 735);
     • Section 6.7, objective 1 (use the definition of a negative exponent, page 760 through the top half of page 766);
     • Section 1.8, objective 1 (simplify expressions with square roots, page 126 through the top of page 128).
   • Exercises due:
     1. Fill in the blanks with vocabulary words: In the expression a³, a is the ___ and 3 is the ___.
     2. Fill in the blank with a number: a⁰ = ___.
     3. Fill in the blank with an algebraic expression involving division: If a ≠ 0, then a⁻ⁿ = ___.
     4. Fill in the blank with a three-word vocabulary term: √a is the ___ of a.
4. Identities for arithmetic:
   • Date assigned: July 24 Tuesday.
   • Date due: July 26 Thursday.
   • Reading:
     • My handout on identities for arithmetic;
     • Section 6.7, objectives 3–5 (scientific notation, from the bottom of page 769 to page 774).
   • Exercises due:
     1. Fill in the blanks with algebraic expressions (note that the blanks are in superscripts): If m and n are integers, then a^m aⁿ = a^___, (a^m)ⁿ = a^___.
     2. Fill in the blank with an English word: If you write 4.5 × 10⁻³ (rather than 0.0045 or 9/2000), then you are using ___ notation.
5. Algebraic expressions:
   • Date assigned: July 26 Thursday.
   • Date due: July 31 Tuesday.
   • Reading:
     • Section 6.1 (pages 673–682);
     • my online notes on polynomials.
   • Exercises due:
     1. Fill in the blanks with vocabulary words: A ___ is an algebraic expression that may be built out of constants and variables using only multiplication. A ___ expression may be built out of constants and variables using only addition and multiplication by constants. A ___ may be built out of monomials using addition.
     2. What is the coefficient of the monomial x³?
     3. What is the degree of the monomial 4?
6. Simplifying algebraic expressions:
   • Date assigned: July 31 Tuesday.
   • Date due: August 2 Thursday.
   • Reading:
     • The rest of Section 6.2 (the rest of page 689 through page 696);
     • Section 6.3 (pages 701–712);
     • my handout on identities for simplifying algebraic expressions.
   • Exercises due: Fill in the blanks with simplified algebraic expressions in standard form:
     1. 6x + 7x = ___, and x⁷x⁶ = ___.
     2. 5 + 7x = ___, and x⁷5 = ___.
     3. 2(3x) = ___, and (x³)² = ___.
     4. 2(x + y) = ___, and (xy)² = ___.
     5. 2(x + 5) = ___, and (5x)² = ___.
7. Solving linear equations:
   • Date assigned: August 2 Thursday.
   • Date due: August 7 Tuesday.
   • Reading:
     • My notes on solving equations;
     • Section 2.1 (pages 197–208);
     • Section 2.2 (pages 212–222);
     • Section 2.3 (pages 226–233);
     • Section 2.4 (pages 236–245).
   • Exercises due:
     1. Fill in the blank with a vocabulary word: A(n) ___ consists of two expressions with an equality symbol (‘=’) between them.
     2. Fill in the blank with a vocabulary word: A(n) ___ of an equation with one variable is a value of the variable at which both sides of the equation are defined and equal each other.
     3. Fill in the blank with a number: One method to turn an equation into an equivalent equation is to multiply both sides by the same constant, but the constant cannot be ___.
8. More solving:
   • Date assigned: August 7 Tuesday.
   • Date due: August 9 Thursday.
   • Reading:
     • Section 2.5 (pages 249–257);
     • Section 2.7 (pages 270–281).
   • Exercises due:
     1. Fill in the blank with a number: To clear fractions from the equation x/2 + 1/4 = 3/2, multiply both sides of the equation by ___.
     2. Write x ≤ 0 in interval notation.
     3. Multiply both sides of a < b by −1 to get an equivalent inequality.
9. Word problems:
   • Date assigned: August 9 Thursday.
   • Date due: August 14 Tuesday.
   • Reading:
     • Section 3.1 (pages 295–308);
     • My online notes on word problems;
     • Section 3.6 (pages 382–387).
   • Exercises due:
     1. Which letters can you use to stand for the fundamental unknown quantity in a word problem?
     2. Fill in the blanks with algebraic expressions: If n is the first of three consecutive odd integers, then the other two are ___ and ___.
     3. If x is a variable quantity, use an algebraic inequality to say that x cannot exceed 100.
10. Special word problems:
    • Date assigned: August 14 Tuesday.
    • Date due: August 16 Thursday.
    • Reading:
      • Section 3.2 (pages 312–325);
      • Section 3.3 (pages 330–342);
      • Section 3.5 (pages 369–378).
    • Exercises due:
      1. Fill in the blank with an algebraic expression: a% means ___.
      2. Fill in the correct operation (addition, subtraction, multiplication, division, etc): original price ___ discount = sale price,
      3. If you travel at a speed r for a time period t, then what distance d will you travel?
11. Equations with several variables:
    • Date assigned: August 16 Thursday.
    • Date due: August 21 Tuesday.
    • Reading:
      • Section 2.6 (pages 260–266);
      • Section 4.1 (pages 403–418);
      • Section 4.2 (pages 424–440).
    • Exercises due:
      1. Solve d = rt for t, assuming that all variables take only positive values.
      2. In which number quadrant are both coordinates positive?
      3. Given a graph in a coordinate plane, a point on the graph that lies on at least one coordinate axis is a(n) ___ of that graph.
12. Lines:
    • Date assigned: August 21 Tuesday.
    • Date due: August 23 Thursday.
    • Reading:
      • Section 4.3 (pages 444–454);
      • Section 4.4 (pages 459–479);
      • Section 4.5 (pages 486–506);
      • Section 4.6 (pages 512–524);
      • my online notes on lines.
    • Exercises due:
      1. A line with positive slope will move ___ as it moves to the right and will move ___ as it moves to the left.
      2. The slope of a horizontal line is ___, while the slope of a vertical line is ___.
      3. If a line has slope m and has (0, b) as an intercept, then its equation in x and y is ___.
13. Dividing monomials and polynomials:
    • Date assigned: August 23 Thursday.
    • Date due: August 28 Tuesday.
    • Reading:
      • Section 6.5, objective 1 (Simplify expressions using the Quotient Property for Exponents, page 730 through the top half of page 733);
      • The rest of Section 6.5 (the rest of page 735 through page 743);
      • Section 6.7, objective 2 (Simplify expressions with integer exponents, the rest of page 766 through most of page 769);
      • Section 6.6 (pages 748–757).
    • Exercises due:
      1. Fill in the blank superscript with an algebraic expression: a^m ÷ aⁿ = a^___.
      2. Suppose that you divide a by b, getting a quotient q and a remainder r. Fill in the blanks with variable names to get an equation that checks your result: ___ · ___ + ___ = ___. (The same equation works whether a, b, q, and r are all constant whole numbers or whether they are all polynomials in one variable with real coefficients.)
14. Basic factoring:
    • Date assigned: August 28 Tuesday.
    • Date due: August 30 Thursday.
    • Reading:
      • my online factoring overview;
      • Section 7.1 (pages 789–800);
      • Section 7.2 (pages 803–813);
      • Section 7.3 (pages 816–830).
    • Exercises due:
      1. Fill in the blank with a vocabulary phrase: Given a polynomial, the product of everything that is a factor of every term of the polynomial is called the ___ of that polynomial (or of its terms).
      2. Fill in the blanks with algebraic expressions: If a, b, and c are integers, then to factor ax² + bx + c by grouping, you should find two integers whose product is ___ and whose sum is ___.
15. More factoring:
    • Date assigned: August 30 Thursday.
    • Date due: September 4 Tuesday.
    • Reading:
      • Section 6.4 (pages 717–726);
      • Section 7.4 (pages 834–847);
      • Section 7.5 (pages 850–858);
      • my online summary of factoring techniques.
    • Exercises due: Expand the following; try to think of them all as patterns that you recognize rather than problems to work out step by step:
      1. (A + B)² = ___;
      2. (A − B)(A + B) = ___;
      3. (A − B)(A² + AB + B²) = ___.
16. Solving by factoring:
    • Date assigned: September 4 Tuesday.
    • Date due: September 6 Thursday.
    • Reading:
      • Section 7.6 (pages 861–873);
      • my online notes on solving equations by factoring.
    • Exercises due:
      1. A polynomial equation of degree 2 (or sometimes less) is called a ___ equation.
      2. If ab = 0, then either ___ or ___.
17. Rational expressions:
    • Date assigned: September 6 Thursday.
    • Date due: September 11 Tuesday.
    • Reading:
      • Section 8.1 (pages 883–896);
      • my online notes on rational expressions;
      • Section 8.2 (pages 901–910).
    • Exercises due:
      1. Fill in the blank with a vocabulary word: A ___ expression is the result of dividing two polynomials.
      2. Fill in the blank with a number (or a kind of number): The result of evaluating a rational expression is undefined if and only if the denominator evaluates to ___.
      3. Fill in the blank: to divide by a rational expression, multiply by its _____.

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