Academic & Student Services
UW System Competency Based Admissions - Mathematics
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| 1.01 Perform basic arithmetic operations with whole numbers, rational numbers and decimals, and reduce to lowest terms fractions involving single-digit whole numbers for numerator and denominator | A.1. Perform arithmetic operations in proper order, represent real numbers in a variety of forms and simplify arithmetic expressions Use arithmetic operations to model problem situations Use mental arithmetic and estimation |
| 1.02 Convert between fractions, decimals, and percents | A.1. Perform arithmetic operations in proper order, represent real numbers in a variety of forms and simplify arithmetic expressions Use arithmetic operations to model problem situations Use mental arithmetic and estimation |
| 1.03 Arrange fractions, decimals, and integers in order of size | |
| 1.04 Set up and solve simple verbal problems involving percentages, mixtures, unit conversions, and distance/time/rate |
A.1. Perform
arithmetic operations in proper order, represent real numbers in a variety
of forms and simplify arithmetic expressions Use arithmetic operations
to model problem situations Use mental arithmetic and estimation
B.7. Translate from a verbal description of a problem situation to a mathematical representation |
| 1.05 Find areas and perimeters of geometric figures composed of rectangles, triangles, and circles | C.1. Solve geometric problems (with or without coordinates) involving points, lines, angles, circles, and polygons Find perimeters and areas of regions composed of rectangles, triangles and circles |
| 1.06 Find the surface area and volume of a rectangular prism | C.2. Visualize and sketch points, lines, planes, and simple solids in three-dimensional space Find volumes of boxes and cylinders |
| 1.07 Solve problems involving the measures of angles of triangles |
C. 1 Solve
geometric problems (with or without coordinates) involving points, lines,
angles, circles, and polygons Find perimeters and areas of regions composed
of rectangles, triangles and circles
C.4. Apply knowledge of the angle sum and the relationship between sides and angles in a triangle (including isosceles and equilateral triangles |
| 1.08 Exhibit knowledge of basic geometric vocabulary |
C.1. Solve
geometric problems (with or without coordinates) involving points, lines,
angles, circles, and polygons Find perimeters and areas of regions composed
of rectangles, triangles and circles
C.2. Visualize and sketch points, lines, planes, and simple solids in three-dimensional space Find volumes of boxes and cylinders |
| 2.01 Perform the basic arithmetic operations with integers using symbols of grouping | A.1. Perform arithmetic operations in proper order, represent real numbers in a variety of forms and simplify arithmetic expressions Use arithmetic operations to model problem situations Use mental arithmetic and estimation |
| 2.02 Solve linear equations containing simple fractions and literal numbers |
B.1. Solve
linear algebraic equations and inequalities in one variable, including
those with literal coefficients
B.6. Solve algebraic equations and inequalities in one variable, including those which can be factored into linear and quadratic expressions, or which contain fractional expressions, absolute values, radicals or fractional exponents |
| 2.03 Manipulate formulas containing fractions and several variables | |
|
2.04 Simplify
algebraic expressions involving multiplication and division of exponential
expressions
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B.5. Add, subtract,
multiply, divide, and exponential polynomial and rational expressions and
simplify the results
B.9. Manipulate and simplify expressions involving exponentials or logarithms Solve equations and inequalities involving exponential and logarithmic expressions Solve problems such as those involving growth and decay |
| 2.05 Simplify exponential expressions with negative bases |
B.5. Add, subtract,
multiply, divide, and exponential polynomial and rational expressions and
simplify the results
B.9. Manipulate and simplify expressions involving exponentials or logarithms Solve equations and inequalities involving exponential and logarithmic expressions Solve problems such as those involving growth and decay |
| 2.06 Find products of binomials | B.5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results |
| 2.07 Collect like terms, and perform simple monomial factoring | B.5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results |
| 2.08 Use order of operations to simplify polynomials and rational expressions | B.5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results |
| 2.09 Evaluate polynomials at specific values of the variable | |
| 2.10 Set up and solve verbal problems involving linear equations |
B.1. Solve
linear algebraic equations and inequalities in one variable, including
those with literal coefficients
B.3. Relate linear functions and equations with their graphs and use them to represent appropriate situations B.7. Translate from a verbal description of a problem situation to a mathematical representation |
| 3.01 Recognize and use congruence and similarity correspondences | C.5. Use knowledge of similarity and congruence to make a reasoned analysis of relations between angles, lengths and areas in a figure or problem situation |
| 3.02 Recognize and use conditions that imply congruence and those that imply similarity for triangles |
C. 4. Apply
knowledge of the angle sum and the relationship between sides and angles
in a triangle (including isosceles and equilateral triangles)
C.5. Use knowledge of similarity and congruence to make a reasoned analysis of relations between angles, lengths and areas in a figure or problem situation |
| 3.03 Recognize and use symmetries of isosceles triangles and equilateral triangles |
C.4. Apply
knowledge of the angle sum and the relationship between sides and angles
in a triangle (including isosceles and equilateral triangles)
C.6. Demonstrate knowledge of the relationship between triangle properties, the Pythagorean theorem, and distance (with or without coordinates) and |
| 3.04 Set up and solve proportions derived from similar triangles | C.5. Use knowledge of similarity and congruence to make a reasoned analysis of relations between angles, lengths and areas in a figure or problem situation |
| 3.05 Recognize and use conditions that imply that two lines are parallel or two lines are perpendicular | C.3. Use knowledge of parallelism, perpendicularly, and associated angle properties to analyze and construct figures and to represent problem situations (with or without coordinates) |
| 3.06 Find the area of a sector of a circle given the measure of a central angle | C.1. Solve geometric problems (with or without coordinates) involving points, lines, angles, circles, and polygons Find perimeters and areas of regions composed of rectangles, triangles and circles |
| 3.07 Find measures of angles by using complementary and supplementary relations | |
| 3.08 Use Pythagorean relationships | C.6. Demonstrate knowledge of the relationship between triangle properties, the Pythagorean theorem, and distance (with or without coordinates) and |
| 3.09 Recognize and use the fact that the contrapositive of a conditional statement has the same truth value as the conditional statement | |
| 3.10 Given a generalization, identify examples and counterexamples | |
| 3.11 Use incidence and parallelism properties in three dimensions | C.2. Visualize and sketch points, lines, planes, and simple solids in three-dimensional space Find volumes of boxes and cylinders |
| 3.12 Classify sets of objects by set inclusion, eg, the set of squares is a subset of the set of rectangles | |
| 4.01 Simplify (reduce) rational expressions | B.5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results |
| 4.02 Add, subtract, multiply, and divide rational expressions | B.5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results |
| 4.03 Factor completely: a quadratic trinomial, difference of two squares or the sum of difference of two cubes | B.5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results |
| 4.04 Recognize the relationships between coefficients of perfect-square trinomials | |
| 4.05 Evaluate numerical expressions containing integral and fractional exponents | |
| 4.06 Simplify radical expressions | B.5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results |
| 4.07 Rationalize numerators and denominators of rational expressions containing radicals | |
| 4.08 Rewrite radical expressions using fractional exponents | |
| 4.09 Add, subtract, multiply, and divide radical expressions | |
| 4.10 Simplify algebraic expressions with positive, negative, and zero exponents | B. 5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results |
| 4.11 Convert between decimal and scientific notation | |
| 4.12 Find the slope and y-intercept and be able to graph a straight line given its equation | B.3. Relate linear functions and equations with their graphs and use them to represent appropriate situations |
| 4.14 Graph a parabola given its equation | B.8. Use the language, notation and properties of algebraic functions and their graphs, with particular attention to quadratic functions |
| 4.15 Evaluate numerical expressions and solve equations involving absolute values | B.6. Solve algebraic equations and inequalities in one variable, including those which can be factored into linear and quadratic expressions, or which contain fractional expressions, absolute values, radicals or fractional exponents |
| 4.16 Recognize the graph of y = {x} | B.6. Solve algebraic equations and inequalities in one variable, including those which can be factored into linear and quadratic expressions, or which contain fractional expressions, absolute values, radicals or fractional exponents |
| 4.17 Graph the solution of inequalities such as Ax + B < 0 on the number line |
B.1. Solve
linear algebraic equations and inequalities in one variable, including
those with literal coefficients
B.6. Solve algebraic equations and inequalities in one variable, including those which can be factored into linear and quadratic expressions, or which contain fractional expressions, absolute values, radicals or fractional exponents |
| 4.18 Graph the solution of inequalities such as Ax + By + C < 0 | |
| 4.19 Solve quadratic equations (includes use of quadratic formula) |
B.6. Solve
algebraic equations and inequalities in one variable, including those which
can be factored into linear and quadratic expressions, or which contain
fractional expressions, absolute values, radicals or fractional exponents
B.8. Use language, notation and properties of algebraic functions and their graphs, with particular attention to quadratic functions |
| 4.20 Solve fractional equations, discarding extraneous roots | B.6. Solve algebraic equations and inequalities in one variable, including those which can be factored into linear and quadratic expressions, or which contain fractional expressions, absolute values, radicals or fractional exponents |
| 4.21 Solve a system of two linear equations in two unknowns recognizing cases of no solutions or infinitely many solutions | B.2. Solve systems of linear equations in two or three variables and interpret solutions both symbolically and graphically |
| 4.22 Graph a system of two linear equations in two unknowns | B.2. Solve systems of linear equations in two or three variables and interpret solutions both symbolically and graphically |
| 4.23 Read, analyze, and solve verbal problems |
B.3. Relate
linear functions and equations with their graphs and use them to represent
appropriate situations
B.7. Translate from a verbal description of a problem situation to a mathematical representation B.9. Manipulate and simplify expressions involving exponentials or logarithms. Solve equations and inequalities involving exponential and logarithmic expressions. Solve problems such as those involving growth and decay |
| 4.24 Add, subtract, multiply and divide polynomials | B.5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results |
| 5.01 Use the definitions of the trigonometric functions of angles |
B.10. Use the
language, notation and properties of exponential, logarithmic and trigonometric
(sine, cosine, tangent) functions and their graphs
C.7. Use right triangle relationships and trigonometric ratios, sine, cosine and tangent to analyze relationships and to formulate and solve problems |
| 5.02 Evaluate trigonometric functions for special angles, eg, , |
B.10. Use the
language, notation and properties of exponential, logarithmic and trigonometric
(sine, cosine, tangent) functions and their graphs
C.6. Demonstrate knowledge of the relationship between triangle properties, the Pythagorean theorem, and distance (with or without coordinates) C.7. Use right triangle relationships and the trigonometric ratios sine, cosine and tangent to analyze relationships and to formulate and solve problems |
| 5.03 Use the standard formulas and identities: Pythagorean formulas, quotient and reciprocal formulas, complementary angle formulas, sums and differences formulas, and double- and half-angle formulas | C.7. Use right triangle relationships and the trigonometric ratios sine, cosine and tangent to analyze relationships and to formulate and solve problems |
| 5.04 Solve trigonometric equations (linear and quadratic) | B.10. Use the language, notation and properties of exponential, logarithmic and trigonometric (sine, cosine, tangent) functions and their graphs |
| 5.05 Sketch the graphs of trigonometric functions | B.10. Use the language, notation and properties of exponential, logarithmic and trigonometric (sine, cosine, tangent) functions and their graphs |
| 5.06 Evaluate expressions involving inverse trigonometric functions | B.10. Use the language, notation and properties of exponential, logarithmic and trigonometric (sine, cosine, tangent) functions and their graphs |
| 5.07 Solve triangles (acute, right and obtuse) |
B.10. Use the
language, notation and properties of exponential, logarithmic and trigonometric
(sine, cosine, tangent) functions and their graphs
C.7. Use right triangle relationships and the trigonometric rations since, cosine and tangent to analyze relationships and to formulate and solve problems |
| 5.08 Determine the domain and range of a function from a defining statement or graph | B.8. Use the language, notation and properties of algebraic functions and their graphs, with particular attention to quadratic functions |
| 5.09 Use function notation, perform operations on functions and evaluate functions | B.8. Use the language, notation and properties of algebraic functions and their graphs, with particular attention to quadratic functions |
| 5.10 Work with exponential and logarithmic functions and their graphs |
B.9. Manipulate
and simplify expressions involving exponentials or logarithms. Solve equations
and inequalities involving exponential and logarithmic expressions. Solve
problems such as those involving growth and decay
B.10. Use the language, notation and properties of exponential, logarithmic and trigonometric (sine, cosine, tangent) functions and their graphs |
| 5.11 Solve exponential and logarithmic functions and their graphs |
B.9. Manipulate
and simplify expressions involving exponentials or logarithms. Solve equations
and inequalities involving exponential and logarithmic expressions. Solve
problems such as those involving growth and decay
B.10. Use the language, notation and properties of exponential, logarithmic and trigonometric (sine, cosine, tangent) functions and their graphs |
| 5.12 Solve inequalities of the type [ax + b] < c | B.6. Solve algebraic equations and inequalities in one variable, including those which can be factored into linear and quadratic expressions, or which contain fractional expressions, absolute values, radicals or fractional exponents |
| 5.13 Solve quadratic inequalities one variable, and graph the solutions | B.6. Solve algebraic equations and inequalities in one variable, including those which can be factored into linear and quadratic expressions, or which contain fractional expressions, absolute values, radicals or fractional exponents |
| 5.14 Represent complex numbers geometrically and perform complex number arithmetic | |
| 5.15 Use remainder and factor theorems to find the zeros of polynomials | B.6. Solve algebraic equations and inequalities in one variable, including those which can be factored into linear and quadratic expressions, or which contain fractional expressions, absolute values, radicals or fractional exponents |
| 5.16 Solve systems containing linear and/or quadratic equations in two variables | B.2. Solve systems of linear equations in two or three variables and interpret solutions both symbolically and graphically |
| 5.17 Find the distance between two points | C.6. Demonstrate knowledge of the relationship between triangle properties, the Pythagorean theorem, and distance (with or without coordinates) and |
| 5.18 Determine from the equations of two lines whether they are parallel or perpendicular or neither | C.3. Use knowledge of parallelism, perpendicularly, and associated angle properties to analyze and construct figures and to represent problem situations (with or without coordinates) |
| 5.19 Convert between the equation of a circle in standard form and data on the center and radius | |
| 5.20 Convert between the equation of a parabola in standard form and data on its vertex and axis | B.8. Use the language, notation and properties of algebraic functions and their graphs, with particular attention to quadratic functions |
| 5.21 Distinguish equations of conics | |
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If you have questions or comments, direct them to Academic and Student Services, Phone: (608) 262-8778, Email: acss@uwsa.edu
This
document was last revised on October 14, 1999. ©January 1999 Board of Regents
of the University of Wisconsin System, All Rights Reserved.
dpi\new matrix\math placement-cba-placementdoc