SAT Skills Insight
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Next Tests:
6/1
Select a score band
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
Example
The 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
Example
If
in the equations above, what is the value of 
in terms of 
? -
10
Work with systems of equations involving three or more variables
Example
If the equations above are true, which of the following is the value of
?
or 
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 non-integer exponents
Solve multistep problems involving algebraic inequalities
Solve word problems involving rate of change in nonlinear or piecewise-linear 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
