SAT Skills Insight

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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. 1

    Apply the concept of absolute value to algebraic expressions

    Example

    If absolute value of ((negative 2 times x) + 1) less than 1, what is one possible value of x?

  2. 2

    Identify and analyze the qualitative behavior of graphs of nonlinear functions

    Example

    Figure

    The figure above shows the graph of a quadratic function in the x y-plane. Of all the points (x comma y) on the graph, for what value of x is the value of y greatest?

  3. 3

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

    Example

    If a not equal to 0 and 5 over x = (5 + a) over (x + a), what is the value of x?

    Answer Choices
  4. 4

    Solve problems involving fractional and negative exponents

    Example

    If (k^(1 over 3)) times (k^(1 over 3)) times (k^(1 over 3)) = 1, which of the following is equivalent to x^k?

    Answer Choices
  5. 5

    Identify solution sets in algebraic situations involving inequalities

    Example

    If x greather than 0 and if 0 less than x^2 less than 1 over 64, what is one possible value of x?

  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 x and y, let x delta y, be defined as x delta y = (x times y) + y ^ 2. What is the value of (3 delta 1) delta 1?

    Answer Choices
  7. 7

    Solve problems involving variables with operations represented by unfamiliar symbols

    Example

    For all numbers w, x, y, and z, let (w comma x) symbol (y comma z) be defined by (w comma x) symbol (y comma z) = (w times y) minus (x times z). If (3 comma 4) symbol (k comma 2) = 4, what is the value of k?

    Answer Choices
  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 2 to 1. What is the ratio of the eighth term in this sequence to the fifth term?

    Answer Choices
  9. 9

    Solve for one variable or expression in terms of another

    Example

    a equals 2 times b
    3 times b equals 10 times c
    (2 times a) times (10 times c) equals k times b

    If b not equal to 0 in the equations above, what is the value of k in terms of b?

    Answer Choices
  10. 10

    Work with systems of equations involving three or more variables

    Example

    (3 times x) plus (2 times y) plus (2 times z) equals 19

    (3 times x) plus y plus z equals 14

    If the equations above are true, which of the following is the value of y plus z?

    Answer Choices

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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