SAT Skills Insight
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Algebra and Functions
Skills needed to score in this band
SKILL 1: Apply the concept of absolute value to algebraic expressions
SKILL 2: Identify and analyze the qualitative behavior of graphs of nonlinear functions
SKILL 3: Solve problems involving nonlinear functions and equations (e.g., quadratic, exponential, and rational)
SKILL 4: Solve problems involving fractional and negative exponents
SKILL 5: Identify solution sets in algebraic situations involving inequalities
SKILL 6: Solve problems involving composition of functions (e.g., use the output of one function as the input to be evaluated in a second function)
SKILL 7: Solve problems involving variables with operations represented by unfamiliar symbols
SKILL 8: Generalize an exponential pattern from a geometric sequence
SKILL 9: Solve for one variable or expression in terms of another
SKILL 10: Work with systems of equations involving three or more variables

1
Apply the concept of absolute value to algebraic expressions
ExampleIf , what is one possible value of ?

2
Identify and analyze the qualitative behavior of graphs of nonlinear functions
ExampleThe figure above shows the graph of a quadratic function in the . Of all the points on the graph, for what value of is the value of greatest?

3
Solve problems involving nonlinear functions and equations (e.g., quadratic, exponential, and rational)
ExampleIf and , what is the value of ?

4
Solve problems involving fractional and negative exponents
ExampleIf , which of the following is equivalent to ?

5
Identify solution sets in algebraic situations involving inequalities
ExampleIf and if , what is one possible value of ?

6
Solve problems involving composition of functions (e.g., use the output of one function as the input to be evaluated in a second function)
ExampleFor all numbers and , let , be defined as . What is the value of ?

7
Solve problems involving variables with operations represented by unfamiliar symbols
ExampleFor all numbers , , , and , let be defined by . If , what is the value of ?

8
Generalize an exponential pattern from a geometric sequence
ExampleAfter the first term in a sequence of positive integers, the ratio of each term to the term immediately preceding it is to . What is the ratio of the term in this sequence to the term?

9
Solve for one variable or expression in terms of another
ExampleIf in the equations above, what is the value of in terms of ?

10
Work with systems of equations involving three or more variables
ExampleIf the equations above are true, which of the following is the value of ?
Skills needed to score in the next band
Solve problems involving complex fractions
Solve problems involving functions defined with unfamiliar symbols in one or more variables
Identify, apply, and represent transformations of functions, graphically and algebraically (e.g., vertical shift)
Apply properties of noninteger exponents
Solve multistep problems involving algebraic inequalities
Solve word problems involving rate of change in nonlinear or piecewiselinear settings
Identify and use the relationship between the slope of a line and algebraic rate of change
Interpret and solve word problems using multistep proportional reasoning
Transform an equation or expression by raising it to a power