This benchmark test will contribute 5% to your final course grade.
The test will be available September 16. The window-of-opportunity for
Benchmark #1 is September 16 - 26. 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. Although the test is not timed, many students in
the past have found that they can complete this Benchmark test in 30 - 40
minutes.
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 Geometry Formulas
-
You should know and be able to use basic area, perimeter, and volume formulas
of geometry.
- You should be able to find the perimeter of a triangle, rectangle,
square, or other polygon.
- The perimeter of a circle is usually called the circumference. You
should be able to calculate the circumference of a circle given its radius
or diameter.
- You should be able to find the area of a triangle, rectangle,
square, or other polygon.
- You should be able to find the area of a circle.
- You should be able to find the volume of a rectangular box.
- You should be able to use the Pythagorean theorem to find the lengths
of the sides of a right triangle.
- You should be able to apply these formulas to solve perimeter, area,
and volume problems for composite geometric figures constructed from
simpler figures.
- Lines and Linear Equations
-
You should be able to work with both linear expressions and graphs of
linear equations. You should be able to work with points and lines in a
regular two-dimensional coordinate system.
- You should be able to plot points in 2-dimensional space using
rectangular coordinates, (x, y).
- You should be able to find the length of a line segment.
(This is an application of the Pythagorean Theorem.)
- You should be able to find the midpoint of a line segment given its
endpoints.
- You should be able to graph a line, y = a*x + b, given its equation.
- You should be able to find the equation of a line given its slope
and a point on the line.
- You should be able to find the equation of a line given two points
which lie on the line.
- You should be able to find the x- and y-intercepts of a line given
its equation. That is, you should be able to find where it crosses the x- or
y-axis.
- You should be able to find the slope of a straight line from its graph,
its algebraic formula, or a set of points which lie on the line.
- You should be able to determine whether two given lines are parallel or
perpendicular. (Parallel lines have the same slope. The slopes of perpendicular
lines are negative reciprocals of each other; in other words, their product will
be -1.)
- Basic Algebra
-
You should be able to use basic algebra as a tool in solving problems.
- You should be able to simplify an algebraic expression in the process of
solving a problem.
- You should be able to use the rules of exponents to evaluate or
simplify an algebraic expression. (A negative exponent denotes a reciprocal, and
a fractional exponent denotes a root.)
- You should be able to calculate the sum or product of polynomials.
- You should be able to solve a linear equation for a specified value of x or y.
- Trigonometry
-
You should be familiar with basic right-triangle trigonometry for first
quadrant angles.
- You should know the definitions of the six trigonometric relationships
in a right triangle. (It is necessary to memorize these six definitions.)
- Given a diagram of a right triangle with the lengths
of sides marked, you should be able to give the value of the sine, cosine,
and tangent of each of the angles.
- You should be able to convert between degree and radian measure for
an angle. (Pi radians corresponds to 180-degrees.) In particular,
you should be able to convert 0-, 30-, 45-, 60-, and 90-degrees to
radians. You should be able to convert 0, Pi/6, Pi/4,
Pi/3, Pi/2, Pi, 3*Pi/2, and
2*Pi, to degrees.
- You should be able to use the the Pythagorean theorem to find the
length of the third side of a right triangle given the lengths of any two
sides.
- You should be able to use the two standard triangles
(30-60-90 and 45-45-90) to find the value of each of the trigonometric
functions for angles in the first quadrant (0-, 30-, 45-, 60-, and 90-degrees
or 0, Pi/6, Pi/4,
Pi/3, and Pi/2, radians).