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: Solve problems involving complex fractions
SKILL 2: Solve problems involving functions defined with unfamiliar symbols in one or more variables
SKILL 3: Identify, apply, and represent transformations of functions, graphically and algebraically (e.g., vertical shift)
SKILL 4: Apply properties of non-integer exponents
SKILL 5: Solve multistep problems involving algebraic inequalities
SKILL 6: Solve word problems involving rate of change in nonlinear or piecewise-linear settings
SKILL 7: Identify and use the relationship between the slope of a line and algebraic rate of change
SKILL 8: Interpret and solve word problems using multistep proportional reasoning
SKILL 9: Transform an equation or expression by raising it to a power
-
1
Solve problems involving complex fractions
ExampleIf
and 
, which of the following must be equal to 
? -
2
Solve problems involving functions defined with unfamiliar symbols in one or more variables
ExampleFor all numbers
, let 
be defined as 
. Which of the following is equal to 
? -
3
Identify, apply, and represent transformations of functions, graphically and algebraically (e.g., vertical shift)
Example
The graphs of the functions
and 
in the interval from 
to 
are shown above. Which of the following could express 
in terms of 
? -
4
Apply properties of non-integer exponents
ExampleIf
, which of the following are equivalent to 
?
. 
. 
. 
-
5
Solve multistep problems involving algebraic inequalities
ExampleIf
and 
, which of the following represents all the possible values for 
? -
6
Solve word problems involving rate of change in nonlinear or piecewise-linear settings
Example
The function above can be used to model the population of a certain endangered species of animal. If
gives the number of the species living 
decades after the year 1900, which of the following is true about the population of the species from 1900 to 1920? -
7
Identify and use the relationship between the slope of a line and algebraic rate of change
Example
The graph above shows the amount of water remaining in a tank each time a pail was used to remove
gallons of water. If 
gallons were in the tank originally and 
gallons remained after the last pail containing 
gallons was removed, what is the value of 
? -
8
Interpret and solve word problems using multistep proportional reasoning
Example
On the number line above,
and 
represent distances between numbers as shown. If the ratio of 
to 
is 
to 
, what is the value of 
? -
9
Transform an equation or expression by raising it to a power
ExampleIf
is an integer and 
, how many different values of 
are possible?
or 
