Mathematical Knowledge and Reasoning
General Expectations
Knowing the mathematics
listed in the sections that follow includes knowing how to put that mathematics
to use in common varieties of problem situations. Thus, knowing about
use of variables in linear situations includes knowing how to set up and
analyze such common situations as those involving mixtures or constant
rates. Rational situations include variation and proportion. Transcendental
situations include exponential growth and decay situations. In all cases,
the use includes interpreting, in terms of the situation, results obtained
from mathematical analysis.
Knowing the mathematics
in the detailed listings also means being able to translate or interpret
between different representations: between functions, equations, tables
and graphs; between pictures and the trigonometric functions sine, cosine
and tangent; between pictures of plane regions and equations or inequalities.
Students are expected
to use clear language to express mathematical ideas in written form.
A. Numbers and Data
- Perform arithmetic
operations in proper order, represent real numbers in a variety of forms
and simplify arithmetic expressions. Use arithmetic operations to model
problem situations. Use mental arithmetic and estimation;
- Construct and read
charts, tables and graphs that summarize data from real world situations;
and
- Use calculators
appropriately to aid computation and understanding.
B. Use of Variables In:
Linear Situations
- Solve linear algebraic
equations and inequalities in one variable, including those with literal
coefficients;
- Solve systems of
linear equations in two or three variables and interpret solutions both
symbolically and graphically;
- Relate linear functions
and equations with their graphs and use them to represent appropriate
situations;
- Use matrices to
represent and analyze linear situations;
Algebraic Situations
- Add, subtract,
multiply, divide, and exponential polynomial and rational expressions
and simplify the results;
- Solve algebraic
equations and inequalities in one variable, including those which can
be factored into linear and quadratic expressions, or which contain fractional
expressions, absolute values, radicals or fractional exponents;
- Translate from
a verbal description of a problem situation to a mathematical representation;
- Use the language,
notation and properties of algebraic functions and their graphs, with
particular attention to quadratic functions;
Transcendental
Situations
- Manipulate and
simplify expressions involving exponentials or logarithms. Solve equations
and inequalities involving exponential and logarithmic expressions. Solve
problems such as those involving growth and decay; and
- Use the language,
notation and properties of exponential, logarithmic and trigonometric
(sine, cosine, tangent) functions and their graphs.
C. Geometry
- Solve geometric
problems (with or without coordinates) involving points, lines, angles,
circles, and polygons. Find perimeters and areas of regions composed of
rectangles, triangles and circles;
- Visualize and sketch
points, lines, planes, and simple solids in three-dimensional space. Find
volumes of boxes and cylinders;
- Use knowledge of
parallelism, perpendicularity, and associated angle properties to analyze
and construct figures and to represent problem situations (with or without
coordinates);
- Apply knowledge
of the angle sum and the relationship between sides and angles in a triangle
(including isosceles and equilateral triangles);
- Use knowledge of
similarity and congruence to make a reasoned analysis of relations between
angles, lengths and areas in a figure or problem situation;
- Demonstrate knowledge
of the relationship between triangle properties, the Pythagorean theorem,
and distance (with or without coordinates); and
- Use right triangle
relationships and the trigonometric ratios sine, cosine and tangent to
analyze relationships and to formulate and solve problems.
We welcome your questions and comments. If you would like to discuss the
possibility of using Competency-Based Admission for some or all students
from your high school, please contact:
Page content last updated December 27, 2000. |
