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Introduction

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Math:Introduction

The directions and question numbers below are representative of what students will encounter on test day. Some math sections allow the use of a calculator, while others do not, as indicated in the directions.


Turn to Section 3 of your answer sheet to answer the questions in this section.

For questions 1-15, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 16-20, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 16 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work.

  1. The use of a calculator [is permitted]/[is not permitted].
  2. All variables and expressions used represent real numbers unless otherwise indicated.
  3. Figures provided in this test are drawn to scale unless otherwise indicated.
  4. All figures lie in a plane unless otherwise indicated.
  5. Unless otherwise indicated, the domain of a given function is the set of all real numbers x for which f of x is a real number.

Reference

The figure presents information for your reference in solving some of the problems.   Reference figure 1 is a circle with radius r. Two equations are presented below reference figure 1. A equals pi times the square of r. C equals 2 pi r.  Reference figure 2 is a rectangle with length ℓ and width w. An equation is presented below reference figure 2. A equals ℓ w.  Reference figure 3 is a triangle with base b and height h. An equation is presented below reference figure 3. A equals one half b h.  Reference figure 4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeled c. An equation is presented below reference figure 4. c squared equals a squared plus b squared.  Special Right Triangles Reference figure 5 is a right triangle with a 30 degree angle and a 60 degree angle. The side opposite the 30 degree angle is labeled x. The side opposite the 60 degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2x.  Reference figure 6 is a right triangle with two 45 degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2.   Reference figure 7 is a rectangular solid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 7. V equals ℓ w h.  Reference figure 8 is a right circular cylinder whose base has radius r and whose height is h. An equation is presented below reference figure 8. V equals pi times the square of r times h.  Reference figure 9 is a sphere with radius r. An equation is presented below reference figure 9. V equals four thirds pi times the cube of r.  Reference figure 10 is a cone whose base has radius r and whose height is h. An equation is presented below reference figure 10. V equals one third times pi times the square of r times h.  Reference figure 11 is an asymmetrical pyramid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 11. V equals one third ℓ w h.  Additional Reference Information The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2 pi. The sum of the measures in degrees of the angles of a triangle is 180.

The number of degrees of arc in a circle is 360.

The number of radians of arc in a circle is 2 pi.

The sum of the measures in degrees of the angles of a triangle is 180.


For student-produced response questions, students will also see the following directions:

For questions 16-20, solve the problem and enter your answer in the grid, as described below, on the answer sheet.

  1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.
  2. Mark no more than one circle in any column.
  3. No question has a negative answer.
  4. Some problems may have more than one correct answer. In such cases, grid only one answer.
  5. Mixed numbers such as three and one half must be gridded as 3.5 or seven slash two.
    (If three and one half is entered into the grid as three, one, slash, two,, it will be interpreted as thirty one halves not three and one half
  6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.

Example 1: If your answer is a fraction such as seven twelfths, it should be recorded as follows. Enter seven in the first space, the fraction bar (a slash) in the second space, one in the third space, and two in the fourth space. All four spaces would be used in this example.  Example 2: If your answer is a decimal value such as two point five, it could be recorded as follows. Enter two in the second space, the decimal point in the third space, and five in the fourth space. Only three spaces would be used in this example.  Example 3: Acceptable ways to record two thirds are: two slash three, point six six six, and point six six seven.


If you will be requesting (or have been approved for) the accommodation of Assistive Technology Compatible format (digital testing for use with a screen reader or other assistive technology) for the SAT, you may wish to also review the math sample items in their fully formatted versions which are sorted as questions that permit the use of a calculator and questions that do not permit the use of a calculator. 

Please note that all testing accommodations, including requests for assistive technology and special formats, must be approved by the College Board’s Services for Students with Disabilities in advance of test-day.