Texas University
Interscholastic League |
Contest Event:
Mathematics
The 40-minute, 60-question contest is designed to test knowledge and
understanding in the areas of algebra I and
II, geometry, trigonometry, math analysis , analytic geometry,
pre-calculus and elementary calculus. |
The Texas Essential
Knowledge and Skills are categorized by course area and grade level.
The following are course area abbreviations used for the TEKS in
Mathematics:
Algebra 1= Alg1; Algebra 2 = Alg2; Geometry = Geo; Precalculus = Pc;
Mathematical Models = MM.
Each TEKS begins with the outline number for the appropriate course
area. |
Texas Essential Knowledge and
Skills |
Contest Knowledge and Skills |
Foundations for Functions Knowledge
and Skills: A1. Understands that a function
represents a
dependence of one quantity on another and can be
described in a variety of ways. (Alg1)
A2 & 2A1. Uses the properties and attributes of
functions. (Alg1, Alg2)
A3. Understands how algebra can be used to
express generalizations and recognizes and uses
the power of symbols to represent situations.
(Alg1)
A4 & 2A2. Understands the importance of the skills
required to manipulate symbols in order to solve
problems and uses the necessary algebraic skills
required to simplify algebraic expressions and solve
equations and inequalities in problem situations.
(Alg1, Alg2) |
Foundations for Functions Knowledge
and Skills: - Given the value of x find the
value of F(x).
- Find the domains and/or ranges of various
functions.
- Determine if a relation is a function using a given
equation, a domain and range, a set of ordered
pairs, or a graph of the relation .
- Find the factors of algebraic expressions and use
factors of algebraic expressions to solve algebraic
equations.
- Simplify algebraic expressions.
- Use algebraic concepts to solve equations and
inequalities in real -life problem applications.
- Use direct variations and indirect variations to
solve problems.
- Translate word problems into mathematical
symbols and algebraic expressions to solve
problems.
- Identify appropriate examples of real number
properties such as commutative, associative,
closure, distributive, etc. |
Linear Functions Knowledge and
Skills: A5. Understands that linear
functions can be
represented in different ways and translates among
their various representations. (Alg1)
A6. Understands the meaning of the slope and
intercepts of the graphs of linear functions and
zeros of linear functions and interprets and
describes the effects of changes in parameters of
linear functions in real-world and mathematical
situations. (Alg1)
A7 & 2A3. Formulates equations and inequalities
based on linear functions, uses a variety of
methods to solve them, and analyzes the solutions
in terms of the situation. (Alg1, Alg2)
A8 & 2A3. Formulates systems of linear equations
from problem situations, uses a variety of methods
to solve them, and analyzes the solutions in terms
of the situation. (Alg1, Alg2)
2A4. Connects algebraic and geometric
representations of functions. (Alg2) |
Linear Functions Knowledge and
Skills: - Recognize a linear function from
an equation, a
graph, or a set of points.
- Formulate equations or inequalities of linear
equations from a graph, given points and slopes,
or real-world situation.
- Identify the slope of a line from an equation, a
graph, or a pair of points.
- Put equations of lines into standard form, pointslope
form, and slope-intercept form.
- Solve linear equations or inequalities using
algebraic transformations, substitution, plotting
points, etc.
- Find slopes of parallel and perpendicular lines.
- Form systems of linear equations from given
data and find their point of intersection.
- Solve systems of equations using substitution ,
equation transformations, graphs, etc.
- Formulate and solve systems of equations from
real-life situations involving distance/rate/time
problems, mixture problems, age problems, rate of
work problems, etc. |
Other Nonlinear Functions -
Quadratic, Square
Root, Rational, Exponential , Logarithmic,
Trigonometric - Knowledge and Skills:A9.
Understands that the graphs of quadratic
functions are affected by the parameters of the
function and can interpret and describe the effects
of changes in the parameters of quadratic
functions. (Alg1)
A10. Understands there is more than one way to
solve a quadratic equation and solves it using
appropriate methods. (Alg1)
A11. Understands there are situations modeled by
functions that are neither linear nor quadratic and
models the situations. (Alg1)
2A6. Understands that quadratic functions can be
represented in different ways and translates among
their various representations. (Alg2)
2A7. Interprets and describes the effects of
changes in the parameters of quadratic functions in
applied and mathematical situations. (Alg2)
2A8, 2A9, 2A10 & 2A11. Formulates equations and
inequalities based on other nonlinear functions,
uses a variety of methods to solve them, and
analyzes the solutions in terms of the situation.
(Alg2)
P1. Defines functions, describes characteristics of
functions, and translates among verbal, numerical,
graphical, and symbolic representations of
functions. (Pc) |
Other Nonlinear Functions -
Quadratic, Square
Root, Rational, Exponential, Logarithmic,
Trigonometric - Knowledge and Skills:-
Identify and recognize all of the parent functions
given in symbolically and graphically.
- Know and use how the coefficients affect the
parent functions, especially the quadratic function
and the trigonometric functions.
- Know and use how the parameters, domains,
ranges, and limitations affect the parent functions.
- Solve quadratic functions using factoring,
substitution, the quadratic formula, completing the
square, and graphing.
- Determine the nature of the roots of a quadratic
function based on its discriminant.
- Determine the nature of the roots of higher
degree polynomials using Descartes Rule of Signs.
- Identify graphs from given functions or identify
the given function from the given graph.
- Find solutions to other non-linear functions.
- Find the inverses of other non-linear functions
and evaluate the inverses at specified points.
- Work with composite functions, domains and
ranges of functions, and identify special types of
functions.
- Translate verbal problems or graphs into
functions using numerical and symbolic
representations and use various methods to solve
them. |
Algebra and Geometry Connections
Knowledge and
Skills:2A4. Connects algebraic and
geometric
representations of functions. (Alg2)
2A5. Knows the relationship between the geometric
and algebraic descriptions of conic sections. (Alg2) |
Algebra and Geometry Connections
Knowledge
and Skills:- Find complementary or
supplementary angle
measures algebraically and/or given a geometric
representation. |
Geometric Structure Knowledge and
Skills: G1. Understands the structure of,
and relationships
within, an axiomatic system. (Geo)
G2. Analyzes geometric relationships in order to
make and verify conjectures. (Geo)
G3. Applies logical reasoning to justify and prove
mathematical statements. (Geo)
G4. Uses a variety of representations to describe
geometric relationships and solve problems. (Geo) |
Geometric Structure Knowledge and
Skills: - Identify properties from given
examples.
- Solve problems by using geometric properties,
axioms and theorems.
- Given several statements about geometric
figures, drawings, and graphs, find the true or
false statements.
- Translate word problems into mathematical
symbols and geometric representations to solve
problems. |
Geometric Patterns Knowledge and
Skills: G5. Uses a variety of
representations to describe
geometric relationships and solve problems. (Geo) |
Geometric Patterns Knowledge and
Skills: - Formulate algebraic expressions
based on
patterns and figures to solve problems.
- Find missing attributes of various polygons based
on geometric properties and definitions of
polygons.
- Find missing attributes of similar polygons
including common ratios, angle measures, and
side lengths.
- Transform points and/or figures using horizontal
and vertical translations, reflections, and rotations.
- Use Pythagorean relations to find missing parts
of right triangles. |
Two and Three Dimensional Figures
Knowledge
and Skills:G6. Analyzes the relationship
between threedimensional
geometric figures and related twodimensional
representations and uses these
representations to solve problems. (Geo)
G7. Understands that coordinate systems provide
convenient and efficient ways of representing
geometric figures and uses them accordingly.
(Geo) |
Two and Three Dimensional Figures
Knowledge
and Skills:- Identify three dimensional
figures from given
nets.
- Find points of intersections lines, planes, and
various geometric figures.
- Find points, equations of lines, slopes, etc. from
a Cartesian Coordinate system.
- Use properties of parallel lines, perpendicular
lines, intersecting lines to determine equations of
lines.
- Given attributes of polygons identify the specific
polygon. |
Properties and Relationships of
Figures Knowledge
and Skills:G8, 88 and 89. Uses tools to
determine
measurements of geometric figures and extends
measurement concepts to find perimeter, area, and
volume in problem situations. (Geo, PK8)
G9. Analyzes properties and describes relationships
in geometric figures. (Geo)
G10. Applies the concept of congruence to justify
properties of figures and solve problems. (Geo)
G11. Applies the concepts of similarity to justify
properties of figures and solve problems. (Geo) |
Properties and Relationships of
Figures Knowledge
and Skills:- Given the area of various
geometric figures, find
the perimeters, lengths of sides, and heights.
- Use definitions of geometric figures to find
missing data.
- Use theorems to find measures of angles, arcs,
sides, etc.
- Use vocabulary about circles to determine
radius/diameter/chord lengths.
- Use formulas and given data to determine
perimeter and area of polygons.
- Use formulas and given data to determine
circumference, area, and other missing parts of
circles.
- Use formulas and given data to determine
surface area, volume, and missing parts of various
polyhedra and Platonic Solids.
- Determine congruence and similarity of figures
to assist in solving problems.
- Use properties of congruence and/or similarity to
find relationships between geometric figures. |
Symbolic Representation Knowledge and
Skills: P2. Interprets the meaning of the
symbolic
representations of functions and operations on
functions to solve meaningful problems. (Pc) |
Symbolic Representation Knowledge and
Skills: - Work with parent functions by
doing symbolic
transformations and function compositions.
- Find inverses of functions and evaluate functions
and inverse functions at specific points. |
Probability and
Statistics Knowledge and Skills: M4. Uses
probability models to describe everyday
situations involving chance. (MM) |
Probability and
Statistics Knowledge and Skills: - Find the
probability and/or odds of experiments
and situations.
- Use the probability to determine mathematical
expectations of game situations and everyday
problems.
- Use the fundamental counting principle to
determine the number of possible outcomes. |
Problem Solving Knowledge and Skills:
P3. Uses functions and their properties, tools and
technology, to model and solve meaningful
problems. (Pc)
P4. Uses sequences and series as well as tools and
technology to represent, analyze, and solve real-life
problems.
P6. Uses vectors to model physical situations. (Pc)
M1. Uses a variety of strategies and approaches to
solve both routine and non-routine problems. (MM)
M2. Uses graphical and numerical techniques to
study patterns and analyze data. (MM).
M5. Uses functional relationships to solve problems
related to personal income. (MM)
M8. Uses algebraic and geometric models to
describe situations and solve problems. (MM)
M9. Uses algebraic and geometric models to
represent patterns and structures. (MM) |
Problem Solving Knowledge and Skills:
- Find values of the basic trigonometric functions
given an angle or radian measure.
- Apply trigonometric functions to analyze and
solve problems and to make predictions .
- Apply the Laws of Sines, Law of Cosines, and
other trigonometric laws and properties to solve
problems.
- Convert degree measures to radian measures
and vice versa.
- Find missing terms of sequences and series.
- Find the sums and limits of sequences and
series.
- Use sequences and series to find solutions to
problems.
- Use the binomial expansion to find missing
coefficients of polynomials.
- Convert parametric, rectangular, and Complex
forms of numbers and equations to appropriate
forms in order to graph or solve problems.
- Use vectors, bearings, etc. to solve problems
involving directions, locations, and navigation.
- Make conclusions based on graphs and statistical
data.
- Find means, medians, modes, and ranges from
given data.
- Use means, medians, modes, and ranges to find
solutions to everyday problems.
- Use linear functions, direct variations, indirect
variations, etc. to solve everyday problems.
- Use a graphing calculator to graph trigonometric
functions and other periodic functions to
determine solutions and/or make predictions. |