SAT Skills Insight

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Algebra and Functions

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 0 less than x less than y and x over y = r, which of the following must be equal to (x + y) over x ?

    Answer Choices
  2. 2

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

    Example

    For all numbers x, let symbol x be defined as symbol x = negative x + 1. Which of the following is equal to function symbol of symbol x?

    Answer Choices
  3. 3

    Identify, apply, and represent transformations of functions, graphically and algebraically (e.g., vertical shift)

    Example
    700-800_B3_M1-16.png

    The graphs of the functions f and g in the interval from x equals negative 2 to x equals 2 are shown above. Which of the following could express function g in terms of function f?

    Answer Choices
  4. 4

    Apply properties of non-integer exponents

    Example

    If x greather than 0, which of the following are equivalent to x ^ (3 over 2)?

    Roman numeral 1. x times square root x

    Roman numeral 2. square root x^3

    Roman numeral 3. (x ^ 2) over square root x

    Answer Choices
  5. 5

    Solve multistep problems involving algebraic inequalities

    Example

    If y = (2 times x) + 3 and x less than 2, which of the following represents all the possible values for y?

    Answer Choices
  6. 6

    Solve word problems involving rate of change in nonlinear or piecewise-linear settings

    Example

    function n of t = 500 times (0.81)^t

    The function above can be used to model the population of a certain endangered species of animal. If function n of t gives the number of the species living t decades after the year 1900, which of the following is true about the population of the species from 1900 to 1920?

    Answer Choices
  7. 7

    Identify and use the relationship between the slope of a line and algebraic rate of change

    Example

    Graph

    The graph above shows the amount of water remaining in a tank each time a pail was used to remove x gallons of water. If 5 gallons were in the tank originally and 2 and 1 over 3 gallons remained after the last pail containing x gallons was removed, what is the value of x?

  8. 8

    Interpret and solve word problems using multistep proportional reasoning

    Example

    Figure

    On the number line above, a and b represent distances between numbers as shown. If the ratio of a to b is 1 to 6, what is the value of b?

    Answer Choices
  9. 9

    Transform an equation or expression by raising it to a power

    Example

    If m is an integer and 3 less than square root (m + 1) less than 5, how many different values of m are possible?

    Answer Choices

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