# SAT Skills Insight

Next Tests:
1/24 , 3/14

#### 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. 1

Apply the concept of absolute value to algebraic expressions

Example

If , what is one possible value of ?

2. 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. 3

Solve problems involving nonlinear functions and equations (e.g., quadratic, exponential, and rational)

Example

If and , what is the value of ?

4. 4

Solve problems involving fractional and negative exponents

Example

If , which of the following is equivalent to ?

5. 5

Identify solution sets in algebraic situations involving inequalities

Example

If and if , what is one possible value of ?

6. 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)

Example

For all numbers and , let , be defined as . What is the value of ?

7. 7

Solve problems involving variables with operations represented by unfamiliar symbols

Example

For all numbers , , , and , let    be defined by   . If   , what is the value of ?

8. 8

Generalize an exponential pattern from a geometric sequence

Example

After 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. 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. 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 ?

#### 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

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