SAT Skills Insight

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Algebra and Functions

Skills needed to score in this band

SKILL 1: Use function notation in simple situations (e.g., evaluation)

SKILL 2: Use variables in multistep abstract settings (e.g., apply the distributive property across several variables)

SKILL 3: Solve problems involving positive-integer exponents

SKILL 4: Solve word problems involving linear relationships

SKILL 5: Substitute values in and simplify systems of equations in two variables

SKILL 6: Solve two-step linear equations

SKILL 7: Evaluate an operation in two variables represented by unfamiliar symbols

  1. 1

    Use function notation in simple situations (e.g., evaluation)

    Example

    For all numbers x let function f of x be defined by function f of x = (x^2) minus x. What is the value of function f of 10 ?

    Answer Choices
  2. 2

    Use variables in multistep abstract settings (e.g., apply the distributive property across several variables)

    Example

    If x and y are positive integers, what are all the solutions (x comma y) of the equation (3 times x) + (2 times y) = 11?

    Answer Choices
  3. 3

    Solve problems involving positive-integer exponents

    Example

    If (7^n) times (7^3) = 7^12, what is the value of n?

    Answer Choices
  4. 4

    Solve word problems involving linear relationships

    Example

    Morgan’s plant grew from 42 centimeters to 57 centimeters in a year. Linda’s plant, which was 59 centimeters at the beginning of the year, grew twice as many centimeters as Morgan’s plant did during the same year. How tall, in centimeters, was Linda’s plant at the end of the year?

  5. 5

    Substitute values in and simplify systems of equations in two variables

    Example

     

    k = 3 times w times x

    m = (w minus 1) times k

    If k and m are defined by the equations above, what is the value of m when w = 4 and x = 1?

    Answer Choices
  6. 6

    Solve two-step linear equations

    Example

     

    If ((1 over 3) times y) + 9 = 0, then y =

    Answer Choices

Skills needed to score in the next band

Formulate and solve problems involving proportions

Solve multistep problems involving linear and quadratic relationships

Use and interpret graphs, including graphs of step functions

Solve problems involving algebraic inequalities

Solve problems involving exponential growth and decay

Evaluate an operation in three variables represented by unfamiliar symbols

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