SAT 2016

CHAPTER 11

Math Test – No Calculator

25 MINUTES, 20 QUESTIONS

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

DIRECTIONS

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.

NOTES

1. The use of a calculator 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 f is the set of all real numbers for which f(x) is a real number.

REFERENCE

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

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

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

1

If 8x + 6 = 6m, what is the value of 4x + 3 in terms of m?

A) 2m – 3

B) 2m

C) 3m – 3

D) 3m

2

Which of the following ordered pairs (x, y) is a solution of the system of equations above?

A) (2, 3)

B) (3, 2.25)

C) (4, 1.5)

D) (4, 6)

3

Which of the following is equivalent to

A)

B)

C)

D)

4

If x − 3 is a factor of the expression x² + kx + 12, what is the value of k?

A) −7

B) −5

C) 5

D) 7

5

Note: Figure not drawn to scale.

In the figure above, P is the center of a circle and AC is its diameter. What is the value of x?

A) 60

B) 50

C) 40

D) 30

6

The nth term of a sequence is given by the expression bn + 4, where b is a positive constant. Which of the following is necessarily equal to b?

A) the value of the first term

B) the difference between the fourth term and the third term

C) the average (arithmetic mean) of the first three terms

D) the ratio of the second term to the first term

7

If , where n > 0, what is the value of m in terms of n?

A)

B)

C)

D)

8

One bag of grass seed can cover 5,000 square feet of new lawn. If each bag costs p dollars, which of the following expressions gives the cost, in dollars, to cover a new rectangular lawn that measures a feet by b feet?

A)

B)

C)

D) 5,000abp

9

If , where m > 0, what is the least possible value of m?

A) 6.5

B) 7

C) 7.5

D) 8

10

If f (x) = 3x+ n, where n is a constant, and f(2) = 0, then f(n) =

A) -24

B) -18

C) -12

D) 12

11

If s, t, u, and v are the coordinates of the indicated points on the number line above, which of the following is greatest?

A) |s − v|

B) |s − t |

C) |s + v|

D) |u + v|

12

How many solutions to the equation 4 cos x= 1 lie between x= 0 and x= 3π?

A) Two

B) Three

C) Four

D) Six

13

If , which of the following is NOT equal to i³ + i?

A) (2i)² + 4

B) 2 − 2i⁴

C) 2i² − 2

D) i⁴ − 1

14

If m > 1, which of the following could be the graph of y = - (x+ m)² + m in the xy-plane?

A)

B)

C)

D)

15

The values of x that satisfy the system of equations above also satisfy which of the following equations?

A) (x − 5)(x+ 3) = 0

B) (x − 3)(x+ 5) = 0

C) (x − 2)(x − 5) = 0

D) (x+ 2)(x+ 5) = 0

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 must be gridded as 3.5 or .

(If is entered into the grid as , it will be interpreted as , not ).

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.

16

If , and b = 4, what is the value of a?

17

What is the smallest integer value of x such that is less than 1?

18

If the area of the figure above is square units, what is its perimeter?

19

What is one possible solution to the equation

20

In the figure above, triangle ABC has an area of 19. What is the value of tan θ?

STOP

If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test.