SAT Skills Insight
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, 3/14
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Algebra and Functions
Skills needed to score in this band
SKILL 1: Formulate and solve problems involving proportions
SKILL 2: Solve multistep problems involving linear and quadratic relationships
SKILL 3: Use and interpret graphs, including graphs of step functions
SKILL 4: Solve problems involving algebraic inequalities
SKILL 5: Solve problems involving exponential growth and decay
SKILL 6: Evaluate an operation in three variables represented by unfamiliar symbols

1
Formulate and solve problems involving proportions
ExampleA fruit salad is made from pineapples, pears, and peaches mixed in the ratio of to to , respectively, by weight. What fraction of the mixture by weight is pineapple ?

2
Solve multistep problems involving linear and quadratic relationships
ExampleIf , what is the value of ?

3
Use and interpret graphs, including graphs of step functions
ExampleA store discounts merchandise by percent of the original price at the end of each week and stops when the merchandise is priced at percent of the original price. Which of the following graphs could correctly represent the price of an article of merchandise over an eightweek period ?

4
Solve problems involving algebraic inequalities
ExampleIf , which of the following is FALSE ?

5
Solve problems involving exponential growth and decay
ExampleSince the beginning of 1990, the number of squirrels in a certain wooded area has tripled during every year period of time. If there were squirrels in the wooded area at the beginning of 1999, how many squirrels were in the wooded area at the beginning of 1990?

6
Evaluate an operation in three variables represented by unfamiliar symbols
ExampleLet be defined as for all nonzero numbers and
. What is the value of ?
Skills needed to score in the next band
Apply the concept of absolute value to algebraic expressions
Identify and analyze the qualitative behavior of graphs of nonlinear functions
Solve problems involving nonlinear functions and equations (e.g., quadratic, exponential, and rational)
Solve problems involving fractional and negative exponents
Identify solution sets in algebraic situations involving inequalities
Solve problems involving composition of functions (e.g., use the output of one function as the input to be evaluated in a second function)
Solve problems involving variables with operations represented by unfamiliar symbols
Generalize an exponential pattern from a geometric sequence
Solve for one variable or expression in terms of another
Work with systems of equations involving three or more variables