| |
Student Edition Lesson(s) |
| 1.0 |
|
Students solve equations and
inequalities involving absolute value. |
|
1-4,
1-6, 2-7 |
| 2.0 |
|
Students solve systems of linear
equations and inequalities (in two or three variables) by substitution,
with graphs, or with matrices. |
|
3-1,
3-2,
3-3, 3-5,
4-1, 4-6,
4-8 |
| 3.0 |
|
Students are adept at operations
on polynomials, including long division. |
|
5-1,
5-2,
5-3, 7-4 |
| 4.0 |
|
Students factor polynomials
representing the difference of squares, perfect square trinomials,
and the sum and difference of two cubes. |
|
5-1,
9-1,
9-2, 9-6 |
| 5.0 |
|
Students demonstrate knowledge
of how real and complex numbers are related both arithmetically and
graphically. In particular, they can plot complex numbers as points
in the plane. |
|
5-9 |
| 6.0 |
|
Students add, subtract, multiply,
and divide complex numbers. |
|
5-9 |
| 7.0 |
|
Students add, subtract, multiply,
divide, reduce, and evaluate rational expressions with monomial and
polynomial denominators and simplify complicated rational expressions,
including those with negative exponents in the denominator. |
|
1-1,
5-1,
5-4, 9-1,
9-2, 9-3 |
| 8.0 |
|
Students solve and graph quadratic
equations by factoring, completing the square, or using the quadratic
formula. Students apply these techniques in solving word problems.
They also solve quadratic equations in the complex number system. |
|
5-9,
6-2,
6-3, 6-4,
6-5 |
| 9.0 |
|
Students demonstrate and explain
the effect that changing a coefficient has on the graph of quadratic
functions; that is, students can determine how the graph of a parabola
changes as a, b, and c vary in the equation y
= a(x - b)2 + c. |
|
6-6,
8-2 |
| 10.0 |
|
Students graph quadratic functions
and determine the maxima, minima, and zeros of the function. |
|
6-1,
6-2 |
| 11.0 |
|
Students prove simple laws of
logarithms. |
|
10-2,
10-3,
10-4 |
| 11.1 |
|
Students understand the inverse
relationship between exponents and logarithms and use this relationship
to solve problems involving logarithms and exponents. |
|
10-2,
10-3,
10-4, 10-5 |
| 11.2 |
|
Students judge the validity
of an argument according to whether the properties of real numbers,
exponents, and logarithms have been applied correctly at each step. |
|
5-1,
10-2,
10-3, 10-5 |
| 12.0 |
|
Students know the laws of fractional
exponents, understand exponential functions, and use these functions
in problems involving exponential growth and decay. |
|
5-7,
10-1,
10-6 |
| 13.0 |
|
Students use the definition
of logarithms to translate between logarithms in any base. |
|
10-4 |
| 14.0 |
|
Students understand and use
the properties of logarithms to simplify logarithmic numeric expressions
and to identify their approximate values. |
|
10-2,
10-3,
10-4 |
| 15.0 |
|
Students determine whether a
specific algebraic statement involving rational expressions, radical
expressions, or logarithmic or exponential functions is sometimes
true, always true, or never true. |
|
5-4,
5-5,
5-6, 9-1,
9-2, 10-1,
10-5 |
| 16.0 |
|
Students demonstrate and explain
how the geometry of the graph of a conic section (e.g., asymptotes,
foci, eccentricity) depends on the coefficients of the quadratic equation
representing it. |
|
8-2,
8-3,
8-4, 8-5 |
| 17.0 |
|
Given a quadratic equation of
the form ax2 + by2 + cx
+ dy + e = 0, students can use the method for completing
the square to put the equation into standard form and can recognize
whether the graph of the equation is a circle, ellipse, parabola,
or hyperbola. Students can then graph the equation. |
|
8-6 |
| 18.0 |
|
Students use fundamental counting
principles to compute combinations and permutations. |
|
12-1,
12-2 |
| 19.0 |
|
Students use combinations and
permutations to compute probabilities. |
|
12-3,
12-5 |
| 20.0 |
|
Students know the binomial theorem
and use it to expand binomial expressions that are raised to positive
integer powers. |
|
11-7,
12-8 |
| 21.0 |
|
Students apply the method of
mathematical induction to prove general statements about the positive
integers. |
|
11-8 |
| 22.0 |
|
Students find the general term
and the sums of arithmetic series and of both finite and infinite
geometric series. |
|
11-1,
11-2,
11-3, 11-4,
11-5 |
| 23.0 |
|
Students derive the summation
formulas for arithmetic series and for both finite and infinite geometric
series. |
|
11-2,
11-4,
11-5 |
| 24.0 |
|
Students solve problems involving
functional concepts, such as composition, defining the inverse function
and performing arithmetic operations on functions. |
|
7-7,
7-8 |
| 25.0 |
|
Students use properties from
number systems to justify steps in combining and simplifying functions. |
|
7-7 |