# SAT Skills Insight

Next Tests:
12/6 , 1/24

#### 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 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. 2

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

Example

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

3. 3

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

Example

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

4. 4

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

Example

Let the function be defined by , where is a constant. If , what is the value of ?

5. 5

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

Example

In the figure above, is equilateral and and are isosceles. What is the value of ?

6. 6

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

Example

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 ?

7. 7

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

Example

In , . If the length of the altitude drawn from , perpendicular to the side , is , what is the perimeter of ?

8. 8

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

Example

In above, what is the length of side ?

9. 9

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

Example

In 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

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