SAT Skills Insight

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Select a score band

Problem Solving

Skills needed to score in this band

SKILL 1: Solve problems using multiple strategies, including the following:
— Visualization
— Estimation skills
— Recognizing relevant information
— Function notation

SKILL 2: Use insight in solving nonroutine geometric problems involving the following:
— Triangles
— Patterns
— Perimeter
— The Pythagorean Theorem
— Properties of circles

  1. 1

    Solve problems using multiple strategies, including the following: Visualization

    Example

    Triangle A B C is to be drawn so that the length of side line A C is greater than 3 and less than 5. If the length of the perpendicular drawn from point B to side line A C is less than 8, which of the following CANNOT be the area of the triangle?

    Answer Choices
  2. 2

    Solve problems using multiple strategies, including the following: Estimation skills

    Example

    Line

    If x is the coordinate of the indicated point on the number line above, which of the lettered points has coordinate negative 2 times x?

    Answer Choices
  3. 3

    Solve problems using multiple strategies, including the following: Recognizing relevant information

    Example

    Figure

    The two semicircles in the figure above have centers R and S, respectively. If R S = 12, what is the total length of the darkened curve?

    Answer Choices
  4. 4

    Solve problems using multiple strategies, including the following: Function notation

    Example

    Let the function f be defined by function f of x = (5 times x) minus (2 times a), where a is a constant. If function f of 10 + function f of 5 = 55, what is the value of a?

    Answer Choices
  5. 5

    Use insight in solving nonroutine geometric problems involving the following: Triangles

    Example
    500-590_B7_M2-5.png

    In the figure above, triangle A B E is equilateral and triangle E B D and triangle D B C are isosceles. What is the value of x?

    Answer Choices
  6. 6

    Use insight in solving nonroutine geometric problems involving the following: Patterns

    Example

    Squares

    In each of the three square figures above, only the small 1-by-1 squares that border the outside edges of the figure are shaded. If a square whose side measures 100 were divided into 1-by-1 squares that are shaded in a similar fashion, how many squares in that figure would be shaded ?

    Answer Choices
  7. 7

    Use insight in solving nonroutine geometric problems involving the following: Perimeter

    Example

    In triangle P Q R, P Q = Q R = 13. If the length of the altitude drawn from Q, perpendicular to the side P R, is 12, what is the perimeter of triangle P Q R?

    Answer Choices
  8. 8

    Use insight in solving nonroutine geometric problems involving the following: The Pythagorean Theorem

    Example

    Triangle

    In triangle A B C above, what is the length of side line BC ?

    Answer Choices
  9. 9

    Use insight in solving nonroutine geometric problems involving the following: Properties of circles

    Example

    In the coordinate plane, the points F (negative 2 comma 1), G (1 comma 4), and H (4 comma 1) lie on a circle with center P. What are the coordinates of point P?

    Answer Choices

Skills needed to score in the next band

SKILL 1: Solve the first stage of a problem, and then apply that solution to solve the next stage of the problem

SKILL 2: Recognize complexity in problems that appear at first to be routine

SKILL 3: Develop and apply an effective strategy and keep track of information in solving a nonroutine problem

SKILL 4: Identify relevant and irrelevant information when choosing a solution strategy

SKILL 5: Solve multistep problems involving properties of integers

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