The geometry skills and concepts developed in this discipline are useful to all
students. Aside from learning these skills and concepts, students will develop their
ability to construct formal, logical arguments and proofs in geometric settings and
Students demonstrate understanding by identifying and giving examples of
undefined terms, axioms, theorems, and inductive and deductive reasoning.
2.0 Students write geometric proofs, including proofs by contradiction.
Students construct and judge the validity of a logical argument and give
counterexamples to disprove a statement.
4.0 Students prove basic theorems involving congruence and similarity.
Students prove that triangles are congruent or similar, and they are able to use
the concept of corresponding parts of congruent triangles.
6.0 Students know and are able to use the triangle inequality theorem .
Students prove and use theorems involving the properties of parallel lines cut by
a transversal, the properties of quadrilaterals, and the properties of circles.
Students know, derive, and solve problems involving the perimeter, circumference,
area, volume, lateral area, and surface area of common geometric figures.


Students compute the volumes and surface areas of prisms, pyramids, cylinders,
cones, and spheres; and students commit to memory the formulas for prisms,
pyramids, and cylinders.
Students compute areas of polygons, including rectangles, scalene triangles,
equilateral triangles, rhombi, parallelograms, and trapezoids.
Students determine how changes in dimensions affect the perimeter, area, and
volume of common geometric figures and solids.
Students find and use measures of sides and of interior and exterior angles of
triangles and polygons to classify figures and solve problems.
Students prove relationships between angles in polygons by using properties of
complementary, supplementary, vertical, and exterior angles.
14.0 Students prove the Pythagorean theorem.
Students use the Pythagorean theorem to determine distance and find missing
lengths of sides of right triangles.


Students perform basic constructions with a straightedge and compass, such as
angle bisectors, perpendicular bisectors, and the line parallel to a given line
through a point off the line.


Students prove theorems by using coordinate geometry, including the midpoint
of a line segment, the distance formula, and various forms of equations of lines
and circles.


Students know the definitions of the basic trigonometric functions defined by
the angles of a right triangle. They also know and are able to use elementary
relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 +
(cos(x))2 = 1.
Students use trigonometric functions to solve for an unknown length of a side of
a right triangle, given an angle and a length of a side.


Students know and are able to use angle and side relationships in problems with
special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90°


Students prove and solve problems regarding relationships among chords,
secants, tangents, inscribed angles, and inscribed and circumscribed polygons
of circles.
Students know the effect of rigid motions on figures in the coordinate plane and
space, including rotations, translations, and reflections.

Algebra II

This discipline complements and expands the mathematical content and concepts of
algebra I and geometry. Students who master algebra II will gain experience with
algebraic solutions of problems in various content areas, including the solution of
systems of quadratic equations, logarithmic and exponential functions , the binomial
theorem, and the complex number system .
1.0 Students solve equations and inequalities involving absolute value .
Students solve systems of linear equations and inequalities (in two or three variables )
by substitution , with graphs, or with matrices.
3.0 Students are adept at operations on polynomials, including long division.
Students factor polynomials representing the difference of squares, perfect square
trinomials , and the sum and difference of two cubes.


Students demonstrate knowledge of how real and complex numbers are related
both arithmetically and graphically . In particular, they can plot complex numbers
as points in the plane.
6.0 Students add, subtract, multiply , and divide complex numbers.


Students add, subtract, multiply, divide, reduce , and evaluate rational expressions
with monomial and polynomial denominators and simplify complicated
rational expressions, including those with negative exponents in the denominator.


Students solve and graph quadratic equations by factoring, completing the
square, or using the quadratic formula. Students apply these techniques in solving
word problems. They also solve quadratic equations in the complex number


Students demonstrate and explain the effect that changing a coefficient has on
the graph
of quadratic functions; that is, students can determine how the graph
of a parabola changes as a, b, and c vary in the equation y = a(x-b)2+ c.
Students graph quadratic functions and determine the maxima, minima, and
zeros of the function.




Students prove simple laws of logarithms.

11.1 Students understand the inverse relationship between exponents and logarithms
and use this relationship to solve problems involving logarithms and exponents.

11.2 Students judge the validity of an argument according to whether the properties
of real numbers, exponents, and logarithms have been applied correctly at each


Students know the laws of fractional exponents , understand exponential functions,
and use these functions in problems involving exponential growth and
Students use the definition of logarithms to translate between logarithms in any
Students understand and use the properties of logarithms to simplify logarithmic
numeric expressions and to identify their approximate values.


Students determine whether a specific algebraic statement involving rational
expressions, radical expressions, or logarithmic or exponential functions is sometimes
true, always true, or never true.


Students demonstrate and explain how the geometry of the graph of a conic
section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the
quadratic equation representing it.


Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use
the method for completing the square to put the equation into standard form and
can recognize whether the graph of the equation is a circle, ellipse, parabola, or
hyperbola . Students can then graph the equation.
Students use fundamental counting principles to compute combinations and
19.0 Students use combinations and permutations to compute probabilities.
Students know the binomial theorem and use it to expand binomial expressions
that are raised to positive integer powers.
Students apply the method of mathematical induction to prove general statements
about the positive integers.
Students find the general term and the sums of arithmetic series and of both
finite and infinite geometric series.
Students derive the summation formulas for arithmetic series and for both finite
and infinite geometric series.
Students solve problems involving functional concepts, such as composition,
defining the inverse function and performing arithmetic operations on functions.
Students use properties from number systems to justify steps in combining and
simplifying functions.
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