Mathematic Proficiency Statements

Arithmetic Proficiency Statements

Total Right Score of about 38 – 64
Students at this level have minimal arithmetic skills. These students can:
• perform simple operations with whole numbers and decimals (addition, subtraction, and multiplication)
• calculate an average , given integer values
• solve simple word problems
• identify data re presented by simple graphs

Total Right Score of about 65 – 92
Students at this level have basic arithmetic skills. These students can:
• perform the basic arithmetic operations of addition, subtraction, multiplication, and division using whole numbers, fractions, decimals, and mixed numbers
• make conversions among fractions, decimals, and percents

Total right score of about 93 – 109
Students at this level have adequate arithmetic skills. These students can:
estimate products and squares of decimals and square roots of whole numbers and decimals
• solve simple percent problems of the form p% of q = ? and ?% of q = r
• divide whole numbers by decimals and fractions
• solve simple word problems involving fractions, ratio, percent increase and decrease, and area

Total right score of about 110 or higher
Students at this level have substantial arithmetic skills. These students can:
• find equivalent forms of fractions
• estimate computations involving fractions
• solve simple percent problems of the form p% of ? = r
• solve word problems involving the manipulation of units of measurement
• solve complex word problems involving percent, average, and proportional reasoning
• find the square root of decimal numbers
• solve simple number sentences involving a variable

Elementary Algebra Proficiency Statements

Total right score of about 28 – 43
Students at this level have minimal pre-algebra skills. These students demonstrate:
• a sense of order relationships and the relative size of signed numbers
• the ability to multiply a whole number by a binomial

Total right score of about 44 – 81
Students scoring at this level have minimal elementary algebra skills. These students can:
• perform operations with signed numbers
• combine like terms
• multiply binomials
• evaluate algebraic expressions

Total right score of about 82 – 108
Students at this level have sufficient elementary algebra skills. By this level, the skills that were beginning to emerge at a Total Right Score of 57 have been developed. Students at this level can:
• add radicals , add algebraic fractions, and evaluate algebraic expressions
• factor quadratic expressions in the form ax² + bx + c, where a = 1
• factor the difference of squares
• square binomials
• solve linear equations with integer coefficients

Total right score of about 109 or higher
Students at this level have substantial elementary algebra skills. These students can:
• simplify algebraic expressions
• factor quadratic expressions where a = 1
• solve quadratic equations
• solve linear equations with fractional and literal coefficients and linear inequalities with integer coefficients
• solve systems of equations
• identify graphical properties of equations and inequalities

College-Level Mathematics Proficiency Statements

Total Right Score of about 39 or less
These students should take the Elementary Algebra test before any placement decisions are finalized.

Total Right Score of about 40 - 62
Students scoring at this level can:
• identify common factors
• factor binomials and trinomials
• manipulate factors to simplify complex fractions.
These students should be considered for placement into intermediate algebra. For further guidance in placement, have these students take the Elementary Algebra test.

Total Right Score of about 63 - 85
Students scoring at this level can demonstrate the fol lowing additional skills:
• work with algebraic expressions involving real number exponents
• factor polynomial expressions
• simplify and perform arithmetic operations with rational expressions, including complex fractions
• solve and graph linear equations and inequalities
• solve absolute value equations
• solve quadratic equations by factoring
• graph simple parabolas
• understand function notation, such as determining the value of a function for a specific number in the domain
• a limited understanding of the concept of function on a more sophisticated level, such as determining the value of the composition of two functions
• a rudimentary understanding of coordinate geometry and trigonometry

These students should be considered for placement into college algebra or a credit-bearing course immediately preceding calculus.

Total Right Score of about 86 - 102
Students scoring at this level can demonstrate the following additional skills:
• understand polynomial functions
• evaluate and simplify expressions involving functional notation, including composition of functions
• solve simple equations involving:
trigonometric functions
logarithmic functions
exp onential functions

These students can be considered for a Pre-calculus course or a non-rigorous course in beginning calculus.

Total Right Score of about 103 or higher
Students scoring at this level can demonstrate the following additional skills:
• perform algebraic operations and solve equations with complex numbers
• understand the relationship between exponents and logarithms and the rules
that govern the manipulation of logarithms and exponents
• understand trigonometric functions and their inverses
• solve trigonometric equations
• manipulate trigonometric identities
• solve right-triangle problems
• recognize graphic properties of functions such as absolute value, quadratic, and logarithmic

These students should be considered for placement into calculus.