This benchmark test will contribute 5% to your final course grade.
The test will be available September 3. The window-of-opportunity for
Benchmark #1 is September 3 and September 13. You may arrange with the
instructor to take this test outside of class any time during this
window-of-opportunity.
This test will have ten problems on material which is prerequisite for this
course. The sample benchmark questions
give an idea of the difficulty level and type of question to expect on this
test. To pass this benchmark, a student must get at least nine problems
correct, with no partial credits.
Although
the passing score for the Benchmarks is very high, you do have an
opportunity to retake this test if you don't pass
it on the first attempt. Since there is a requirement that you study
between two attempts of this test, you cannot take and retake the test
twice on the same day.
If you want to take advantage of being able to retake this benchmark, you
should attempt it early in this window-of-opportunity.
You may NOT use a calculator or computer as you work on the benchmark test.
- Basic Algebra
-
- You should be able to:
- use the rules of exponents to simplify an algebraic expression;
- calculate the sum or product of polynomials;
- factor a quadratic or cubic polynomial;
- evaluate a given function, f(x), at particular values
(such as at x = 5,
x = x+h, and x = g(x));
- find the slope of a straight line from its graph, its algebraic
formula, or a set of points which lie on the line;
- find the length and the midpoint of a line segment, given its
endpoints;
- graph a line or a polynomial given its equation;
- determine whether two given lines are parallel or perpendicular;
- find the product of a given pair of polynomial expressions;
- simplify algebraic expressions;
- solve a linear equation;
- solve quadratic or cubic equations (by factoring and/or using the quadratic
formula);
- locate (plot) points in 2-dimensional space using rectangular
coordinates;
- find the equation of a line given its slope and a point on the line;
- find the equation of a line given two points which lie on it;
- give the equation of the line which is tangent to a given curve at a
specified point.
- You should know and be able to use:
- formulas for length of a line segment;
- formulas for area of a square, rectangle, triangle, or circle;
- formulas for volume of a rectangular box, or ordinary cylinder;
- formulas for perimeter and circumference of simple geometric figures.
- Trigonometry
-
- You should be familiar with basic right-triangle trigonometry:
- the six trigonometric relationships,
- the relationship between degrees and radians,
- the two "standard" triangles and the "unit circle,"
- the values of the trigonometric relationships of the angles in
the two standard triangles,
- the trigonometric relationships which can be verified in the unit
circle,
- the Pythagorean theorem, and the trigonometric versions of the Pythagorean
theorem.
- Difference Quotient
-
- You should be able to set up and simplify a difference quotient for a
given function.
- Derivatives
-
- You should be able to:
- calculate derivatives for polynomials, and for the six
trigonometric functions;
- use the product rule, the
quotient rule, and the chain rule to calculate derivatives for simple
combinations of functions.
- Antiderivatives and Definite Integrals
-
- You should be able to:
- use the power rule to integrate an expression of
the form x^n, both for n /= 1 and for n = 1;
- calculate antiderivatives and definite integrals
for polynomials,
and for the derivatives of the six trigonometric functions;
- use simple substitutions to calculate an
antiderivative;
- evaluate the definite integral of an expression
of the form e^u du;
- find any local maxima or minima on the graph of a given curve;
- find the area bounded by a given curve and the x-axis.