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UW System Competency Based Admissions - Mathematics

MATHEMATICS ALIGNMENT: PLACEMENT
UW System Competency Based Admissions - Mathematics
Placement Objectives
A. Numbers and Data  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; 1.01 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

1.02 Convert between fractions, decimals, and percents

1.04 Set up and solve simple verbal problems involving percentages, mixtures, unit conversions, and distance/time/rate

2.01 Perform the basic arithmetic operations with integers using symbols of grouping
2. Construct and read charts, tables and graphs that summarize data from real world situations; and
3. Use calculators appropriately to aid computation and understanding.
B. Use of Variables In:

Linear Situations

1. Solve linear algebraic equations and inequalities in one variable, including those with literal coefficients; 		2.02 Solve linear equations containing simple fractions and literal numbers

2.10 Set up and solve verbal problems involving linear equations

4.17 Graph the solution of inequalities such as Ax + B < 0
2. Solve systems of linear equations in two or three variables and interpret solutions both symbolically and graphically; 4.21 Solve a system of two linear equations in two unknowns recognizing cases of no solutions or infinitely many solutions

4.22 Graph a system of two linear equations in two unknowns

5.16 Solve systems containing linear and/or quadratic equations in two variables
3. Relate linear functions and equations with their graphs and use them to represent appropriate situations;  2.10 Set up and solve verbal problems involving linear equations

4.12 Find the slope and y-intercept and be able to graph a straight line given its equation

4.23 Read, analyze, and solve verbal problems
4. Use matrices to represent and analyze linear situations;
Algebraic Situations

5. Add, subtract, multiply, divide, and exponential polynomial and rational expressions and simplify the results;

 		2.04 Simplify algebraic expressions involving multiplication and division of exponential expressions

2.05 Simplify exponential expressions with negative bases

2.06 Find products of binomials

2.07 Collect like terms, and perform simple monomial factoring

2.08 Use order of operations to simplify polynomials and rational expressions

4.01 Simplify (reduce) rational expressions

4.02 Add, subtract, multiply, and divide rational expressions

4.03 Factor completely: a quadratic trinomial, difference of two squares or the sum of difference of two cubes

4.06 Simplify radical expressions

4.10 Simplify algebraic expressions with positive, negative, and zero exponents

4.24 Add, subtract, multiply and divide polynomials
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;


2.02 Solve linear equations containing simple fractions and literal numbers

4.15 Evaluate numerical expressions and solve equations involving absolute values

4.16 Recognize the graph of y = {x}

4.17 Graph the solution of inequalities such as Ax + B < 0 on the number line

4.19 Solve quadratic equations (includes use of quadratic formula)

4.20 Solve fractional equations, discarding extraneous roots

5.12 Solve inequalities of the type [ax + b] < c

5.13 Solve quadratic inequalities one variable, and graph the solutions

5.15 Use remainder and factor theorems to find the zeros of polynomials
7. Translate from a verbal description of a problem situation to a mathematical representation;


1.04 Set up and solve simple verbal problems involving percentages, mixtures, unit conversions, and distance/time/rate

2.10 Set up and solve verbal problems involving linear equations

4.23 Read, analyze, and solve verbal problems
8. Use the language, notation and properties of algebraic functions and their graphs, with particular attention to quadratic functions; 4.14 Graph a parabola given its equation

4.19 Solve quadratic equations (includes use of quadratic formula)

5.08 Determine the domain and range of a function from a defining statement or graph

5.09 Use function notation, perform operations on functions and evaluate functions

5.20 Convert between the equation of a parabola in standard form and data on its vertex and axis
Transcendental Situations

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; and

 		2.04 Simplify algebraic expressions involving multiplication and division of exponential expressions

2.05 Simplify exponential expressions with negative bases

4.23 Read, analyze, and solve verbal problems

5.10 Work with exponential and logarithmic functions and their graphs

5.11 Solve exponential and logarithmic functions and their graphs
10. Use the language, notation and properties of exponential, logarithmic and trigonometric (sine, cosine, tangent) functions and their graphs. 5.01 Use the definitions of the trigonometric functions of angles

5.02 Evaluate trigonometric functions for special angles, eg., , 

5.04 Solve trigonometric equations (linear and quadratic)

5.05 Sketch the graphs of trigonometric functions

5.06 Evaluate expressions involving inverse trigonometric functions

5.07 Solve triangles (acute, right and obtuse)

5.10 Work with exponential and logarithmic functions and their graphs

5.11 Solve exponential and logarithmic functions and their graphs
C. Geometry 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; 1.05 Find areas and perimeters of geometric figures composed of rectangles, triangles, and circles

1.07 Solve problems involving the measures of angles of triangles

1.08 Exhibit knowledge of basic geometric vocabulary

3.06 Find the area of a sector of a circle given the measure of a central angle
2. Visualize and sketch points, lines, planes, and simple solids in three-dimensional space. Find volumes of boxes and cylinders; 1.06 Find the surface area and volume of a rectangular prism

1.08 Exhibit knowledge of basic geometric vocabulary

3.11 Use incidence and parallelism properties in three dimensions
3. Use knowledge of parallelism, perpendicularly, and associated angle properties to analyze and construct figures and to represent problem situations (with or without coordinates); 3.05 Recognize and use conditions that imply that two lines are parallel or two lines are perpendicular

5.18 Determine from the equations of two lines whether they are parallel or perpendicular or neither
4. Apply knowledge of the angle sum and the relationship between sides and angles in a triangle (including isosceles and equilateral triangles); 1.07 Solve problems involving the measures of angles of triangles

3.02 Recognize and use conditions that imply congruence and those that imply similarity for triangles

3.03 Recognize and use symmetries of isosceles triangles and equilateral triangles
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; 3.01 Recognize and use congruence and similarity correspondences

3.02 Recognize and use conditions that imply congruence and those that imply similarity for triangles

3.04 Set up and solve proportions derived from similar triangles
6. Demonstrate knowledge of the relationship between triangle properties, the Pythagorean theorem, and distance (with or without coordinates); and 3.03 Recognize and use symmetries of isosceles triangles and equilateral triangles

3.08 Use Pythagorean relationships

5.02 Evaluate trigonometric functions for special angles, eg., , 

5.17 Find the distance between two points
7. Use right triangle relationships and the trigonometric ratios sine, cosine and tangent to analyze relationships and to formulate and solve problems. 5.01 Use the definitions of the trigonometric functions of angles

5.02 Evaluate trigonometric functions for special angles, eg., , 

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

5.07 Solve triangles (acute, right and obtuse)

 

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UWSA LogoThis 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-placement.doc