SAT Skills Insight

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Algebra and Functions

Skills needed to score in this band

SKILL 1: Formulate and solve problems involving proportions

SKILL 2: Solve multistep problems involving linear and quadratic relationships

SKILL 3: Use and interpret graphs, including graphs of step functions

SKILL 4: Solve problems involving algebraic inequalities

SKILL 5: Solve problems involving exponential growth and decay

SKILL 6: Evaluate an operation in three variables represented by unfamiliar symbols

  1. 1

    Formulate and solve problems involving proportions

    Example

    A fruit salad is made from pineapples, pears, and peaches mixed in the ratio of 2 to 3 to 5, respectively, by weight. What fraction of the mixture by weight is pineapple ?

    Answer Choices
  2. 2

    Solve multistep problems involving linear and quadratic relationships

    Example

    If (x plus 2)^2 = 9, what is the value of (x + 1) times (x + 3)?

    Answer Choices
  3. 3

    Use and interpret graphs, including graphs of step functions

    Example

    A store discounts merchandise by 10 percent of the original price at the end of each week and stops when the merchandise is priced at 50 percent of the original price. Which of the following graphs could correctly represent the price of an article of merchandise over an eight-week period ?

    Answer Choices
  4. 4

    Solve problems involving algebraic inequalities

    Example

    If 0 less than x less than 1, which of the following is FALSE ?

    Answer Choices
  5. 5

    Solve problems involving exponential growth and decay

    Example

    Since the beginning of 1990, the number of squirrels in a certain wooded area has tripled during every 3-year period of time. If there were 5400 squirrels in the wooded area at the beginning of 1999, how many squirrels were in the wooded area at the beginning of 1990?

  6. 6

    Evaluate an operation in three variables represented by unfamiliar symbols

    Example

    Let (a comma b) delta n be defined as (((a^n) times b) + (a times (b^n))) over a^2 for all nonzero numbers a and

    b. What is the value of (10 comma 10) delta 2?

    Answer Choices

Skills needed to score in the next band

Apply the concept of absolute value to algebraic expressions

Identify and analyze the qualitative behavior of graphs of nonlinear functions

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

Solve problems involving fractional and negative exponents

Identify solution sets in algebraic situations involving inequalities

Solve problems involving composition of functions (e.g., use the output of one function as the input to be evaluated in a second function)

Solve problems involving variables with operations represented by unfamiliar symbols

Generalize an exponential pattern from a geometric sequence

Solve for one variable or expression in terms of another

Work with systems of equations involving three or more variables

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