AMP Intensive Precalculus, Summer 2000
The exam will be given on Fri Jul 20. Prizes will be given both
for the highest score and also for the most improved score (as
compared to the first day diagnostic exam).
- Algebra. Rules of exponents (workbook 1). Multiplying
(FOIL) and factoring (workbook 2-3). Simplifying, combining, and
separating fractions of polynomials (workbook 4). Other manipulation,
including completing the square (workbook 5). Solving linear,
fractional, radical, and exponential equations; solving equations by
factoring; quadratic formula (workbook 7). Inequalities: determining
when an expression is +, -, 0, undef; solving other kinds of
inequalities (workbook 8). Absolute values: algebraic and geometric
methods (purple pp. 10-12, 77-78).
- Trigonometry. Angles (purple 6.1). SOHCAHTOA trig:
definitions, solving triangles (purple 6.2). Unit circle trig:
definitions, calculating values (purple 5.1-5.2). Graphs of sin
and cos: amplitude, period, phase shift, applying these to graphing
(purple 5.3). Trig identities: cos2 x+sin2 x=1, double angle
formulas (purple 7.1, 7.3).
- Exponential and log functions. Definition of exponential
functions; basic graphs; e (purple 4.1-4.2). Definition and laws
of logarithms (purple 4.3-4.4). Simplifying log expressions
(workbook 9). Story problems for exponential functions (purple 4.6).
- Functions in general. Function notation; translating
sentences to functions, and vice versa; functions, solving and graphs
(workbook 9-12). Composition and substitution; reverse composition
(breaking a function into "inside" and "outside") (workbook 13,
purple 2.6). Transformations and graphs; shifts and stretches (purple
- Other specific types of functions. Lines: slope,
slope-intercept, point-slope (purple 1.10). Polynomials: shapes of
graphs, factoring higher degree polynomials (purple 3.1-3.2).
Recognizing types of functions (workbook 14).
- Memorization. Common graphs of functions (workbook 15),
formulas and important function values (workbook 16).