# SAT Skills Insight

Next Tests:
10/3 , 11/7

#### 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. 1

Solve problems involving complex fractions

Example

If and , which of the following must be equal to ?

2. 2

Solve problems involving functions defined with unfamiliar symbols in one or more variables

Example

For all numbers , let be defined as . Which of the following is equal to ?

3. 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. 4

Apply properties of non-integer exponents

Example

If , which of the following are equivalent to ?

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5. 5

Solve multistep problems involving algebraic inequalities

Example

If and , which of the following represents all the possible values for ?

6. 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. 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. 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. 9

Transform an equation or expression by raising it to a power

Example

If is an integer and , how many different values of are possible?

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