Download 601 Topics Covered (`14-15)

Math 1 Honors (601)
Topic List
1. Sets, Fields, and Algebraic Proof
Sets of numbers, field properties, solution of equations over stated domain, graphs of solution sets of
inequalities, solutions of absolute value equations and inequalities, and properties of order, algebraic proof*
equivalence relation properties.
2. Introduction to Geometry and Triangle Congruence
Concepts of points, lines, planes, rays, segments, angles, triangles, measurement of segments and angles,
congruent angles and segments, collinearity, betweeness, two-column and paragraph proofs, midpoint,
trisectors and angle bisectors, deductive structure of undefined terms, definitions, postulates and theorems,
logic of converse, inverse and contrapositive, Venn diagrams, chain reasoning, and geometric probability.
Perpendicular lines, rays and segments, complementary and supplementary angles, segment and angle addition,
transitive and substitution properties, vertical angles. Size and shape of congruent figures, introduction to
slides, reflections and rotations, SSS, ASA and SAS triangle congruence postulates and proofs, congruence
proofs involving radii of circles, medians, auxiliary lines and overlapping triangles, classification of triangles,
isosceles triangles and associated theorems, and HLR postulate.
3. Relations, Functions and Linear Functions
Review of point plotting, sketching of real world relations, definition of a function, plotting relations in a
given domain, finding the range, and vertical line test. Review of linear functions including definition, slope
and slope formula, intercepts, and sketching, forms of a linear function, writing equations of lines from given
data, linear functions as mathematical models.
4. Systems of Linear Equations
Linear systems in two variables, solution by graphing, substitution, linear combination, second order
determinants, and matrices. Inconsistent, dependent, independent, reciprocal systems. Linear systems as
mathematical models, graphs of linear equations in three variables, solution of systems of linear equations with
three or more variables by linear combination, substitution and matrices, linear inequalties and linear
programming. Graphs and solutions of systems of linear inequalities with two variables, systems of linear
inequalities as mathematical models (linear programming).
5. Lines in the Plane
Midpoint formula and proofs, drawing diagrams from given information, a right-angle theorem, the
equidistant theorems.
6. Parallel Lines
Indirect proof, exterior angle theorem, proofs involving parallel lines, transversals and their angles,
polygons, convexity and diagonals, classification and properties of quadrilaterals, proofs involving
quadrilaterals, and coordinate geometry.
7. Lines and Planes in Space
Four ways to determine a plane, perpendicularity of a line and a plane , facts about parallel plans and proofs
involving planes.
8. Quadratic Equations and Functions
Solutions of equations by factoring, completing the square and formula, derivation of quadratic formula,
discriminant and nature of roots, sum and product of roots, definition, powers and ASMD of imaginary
numbers, definition and ASMD of complex numbers, complex conjugates, the complex number plane.
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Definition of quadratic functions, sketching, methods of finding the vertex, y-k = a(x-h) with shape,
symmetry, vertex, transformations, max/min value applications, solution by graphing and numerical methods,
Math 1 Honors (601)
Topic List
evaluation of quadratic functions, equations of quadratic functions from their graphs, quadratic functions as
mathematical models.
9. Exponents and Logarithms
Introduction to exponential functions and review of order of operations involving exponentiation,
properties of exponentiation, negative and zero exponents, radicals and fractional exponents, scientific
notation, transformation of graphs of exponential functions, introduction to exponential functions as
mathematical models (growth and decay), logarithmic functions, properties of logarithmic functions,
logarithms with calculators, solution of exponential equations
10. Polygons
Interior and exterior angles of triangles, proof of the sum of the measures of the angles of a triangle,
midlines of triangles, names of polygons, sum of the exterior and interior angles of a polygon, number of
diagonals of a polygon, regular polygons and associated angle measure theorems
11. Similar Polygons
Definitions of ratio and proportion, properties of proportions, geometric and arithmetic means, dilation,
reduction and similarity, definition of similar polygons, calculations with similar polygons, similar triangle
postulates and proofs, congruences and proportions in similar triangles, parallel transversals and
proportionality, angle bisector theorem.
12. Pythagorean Theorem and Right Triangles
Altitude-on-hypotenuse theorems , Pythagorean theorem and it’s converse, special right triangles.
13. Rational Functions
Polynomials, factoring, rational expressions(ASMD), complex fractions, fractional equations, systems of
equations. Graphs of rational functions with non-removable (asymptotes) or removable(holes) discontinuities
14. Irrational Functions
Graphs of irrational functions, solving radical equations, variation functions with non-integer exponents,
functions of more than one independent variable.
15. Quadratic Relations and Systems
Origin centered and translated linear and quadratic relations in two variables including circle, parabola,
ellipse and hyperbola as graphs of relations. Other graphs such as cubic, absolute value and square root.
Domain, range, introduction to increasing, decreasing, bounded, asymptote, and symmetry. Equations from
geometric definitions. Systems of quadratic relations and inequalities