SAT Skills Insight
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Next Tests:
5/3
, 6/7
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
Solve problems using multiple strategies, including the following: Visualization
ExampleTriangle is to be drawn so that the length of side is greater than and less than . If the length of the perpendicular drawn from point to side is less than , which of the following CANNOT be the area of the triangle?

2
Solve problems using multiple strategies, including the following: Estimation skills
ExampleIf is the coordinate of the indicated point on the number line above, which of the lettered points has coordinate ?

3
Solve problems using multiple strategies, including the following: Recognizing relevant information
ExampleThe two semicircles in the figure above have centers and , respectively. If , what is the total length of the darkened curve?

4
Solve problems using multiple strategies, including the following: Function notation
ExampleLet the function be defined by , where is a constant. If , what is the value of ?

5
Use insight in solving nonroutine geometric problems involving the following: Triangles
ExampleIn the figure above, is equilateral and and are isosceles. What is the value of ?

6
Use insight in solving nonroutine geometric problems involving the following: Patterns
ExampleIn each of the three square figures above, only the small 1by1 squares that border the outside edges of the figure are shaded. If a square whose side measures 100 were divided into 1by1 squares that are shaded in a similar fashion, how many squares in that figure would be shaded ?

7
Use insight in solving nonroutine geometric problems involving the following: Perimeter
ExampleIn , . If the length of the altitude drawn from , perpendicular to the side , is , what is the perimeter of ?

8
Use insight in solving nonroutine geometric problems involving the following: The Pythagorean Theorem
ExampleIn above, what is the length of side ?

9
Use insight in solving nonroutine geometric problems involving the following: Properties of circles
ExampleIn the coordinate plane, the points , , and lie on a circle with center . What are the coordinates of point ?
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