MATHEMATICS
:: 2003 :: TO BE IMPLEMENTED 9-12 :: INTEGRATED MATHEMATICS IV
High School Grades
Integrated Mathematics 4 provides students
an advanced study of trigonometry, functions, analytic geometry, and
data analysis with a problem-centered, connected approach in preparation
for college-level mathematics. Applications and modeling should be included
throughout the course of study. Appropriate technology, from manipulatives
to calculators and application software, should be used regularly for
instruction and assessment.
Prerequisites
- Describe phenomena as functions graphically, algebraically and
verbally; identify independent and dependent quantities, domain, and
range, and input/output.
- Translate among graphic, algebraic, numeric, tabular, and verbal
representations of relations.
- Define and use linear, quadratic, cubic, exponential, rational,
absolute value, and radical functions to model and solve problems.
- Use systems of two or more equations or inequalities to solve problems.
- Use the trigonometric ratios to model and solve problems.
- Use logic and deductive reasoning to draw conclusions and solve
problems.
|
| Number
and Operations |
| Competency
Goal 1 |
The learner will operate
with complex numbers and vectors to solve problems. |
| |
Objectives 1.01 Operate with vectors in two
dimensions to model and solve problems.
1.02 Define and compute with complex numbers.
|
| Geometry
and Measurement |
| Competency
Goal 2 |
The learner will describe geometric figures
in the coordinate plane algebraically. |
| |
Objectives 2.01 Use the quadratic relations (parabola,
circle, ellipse, hyperbola) to model and solve problems; justify results.
- Solve using tables, graphs, and algebraic properties.
- Interpret the constants and coefficients in the context of the problem.
2.02 Estimate the area and volume of continuously varying quantities.
|
| Data Analysis and Probability |
| Competency
Goal 3 |
The learner will analyze
data to solve problems. |
| |
Objectives 3.01 Analyze univariate data to
solve problems.
- Apply and compare methods of data collection.
- Apply statistical principles and methods in sample surveys.
- Determine measures of central tendency and spread.
- Recognize, define, and use the normal distribution curve.
- Interpret graphical displays of distributions of univariate data.
- Compare distributions of univariate data.
3.02 Create and use calculator-generated models of linear,
polynomial, exponential, trigonometric, power, logistic, and logarithmic
functions of bivariate data to solve problems.
- Interpret the constants, coefficients, and bases in the context
of the data.
- Check models for goodness-of-fit; use the most appropriate model
to draw conclusions or make predictions.
|
| Algebra |
| Competency Goal 4 |
The learner will use relations
and functions to solve problems. |
| |
Objectives 4.01 Use functions (polynomial,
power, rational, exponential, logarithmic, logistic, piecewise-defined,
and greatest integer) to model and solve problems; justify results.
- Solve using graphs and algebraic properties.
- Interpret the constants, coefficients, and bases in the context
of the problem.
4.02 Use recursively-defined functions to model and solve
problems.
- Find the sum of a finite sequence.
- Find the sum of an infinite sequence.
- Determine whether a given series converges or diverges.
- Translate between recursive and explicit representations.
4.03 Use the composition and inverse of functions
to model and solve problems.
4.04 Use trigonometric and inverse trigonometric functions
to model and solve problems.
- Solve using graphs and algebraic properties.
- Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.
4.05 Use polar equations to model and solve problems.
- Solve using graphs and algebraic properties.
- Interpret the constants and coefficients in the context of the problem.
4.06 Use parametric equations to model and solve problems.
4.07 Find the rate of change at any point of a function.
|
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