SAT Skills Insight
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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 noninteger exponents
SKILL 5: Solve multistep problems involving algebraic inequalities
SKILL 6: Solve word problems involving rate of change in nonlinear or piecewiselinear 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)
ExampleThe 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 noninteger 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 piecewiselinear settings
ExampleThe 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
ExampleThe 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
ExampleOn 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?