SAT 2016

PRACTICE TEST 2

Images

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 you 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

Images

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 2b − 1 = 5, what is the value of 2b2 − 1?

A)   15

B)   17

C)   24

D)   25

2

Images

In the figure above, points PQRS, and T lie on the same line, and R is the center of the large circle. If the three smaller circles are congruent and the radius of the large circle is 6, what is the radius of one of the smaller circles?

A)   1

B)   2

C)   3

D)   4

3

Jeri has edited Images of her term paper. If she has edited

15 pages, how many pages does she have left to edit?

A)   45

B)   50

C)   60

D)   75

4

7, 12, 22, 42, 82

Which of the following gives a rule for finding each term in the sequence after the first?

A)   Add 5 to the preceding number.

B)   Add 5 to the sum of all of the preceding terms.

C)   Double the preceding term and then subtract 2 from the result.

D)   Add 14 to the preceding term and divide that result by 2.

5

Images

The figure above shows a rectangular box. What is the longest length of a diagonal of one of the faces of this box?

A)   Images

B)   Images

C)   Images

D)   Images

6

Which of the following points is NOT on the graph of the line −2x − 3y = 36 in the xy-plane?

A)   (−9, 6)

B)   (−24, 4)

C)   (6, −16)

D)   (12, −20)

7

During a coyote repopulation study, researchers determine that the equation P = 250(1.32)t describes the population P of coyotes t years after their introduction into a new region. Which of the following gives the values of I, the initial population of coyotes, and r, the annual percent increase in this population?

A)   I = 250, r = 32%

B)   I = 250, r = 132%

C)   I = 330, r = 32%

D)   I = 330, r = 132%

8

Which of the following is equal to Images

A)   Images

B)   Images

C)   Images

D)   Images

9

Which of the following could be the x-intercept and y-intercept of a line that is perpendicular to the line 3x + 6y = 0?

A)   (−6, 0) and (0, 3)

B)   (3, 0) and (0, −6)

C)   (3, 0) and (0, 6)

D)   (6, 0) and (0, 3)

10

The function f is defined by the equation f(x) = x − x2. Which of the following represents a quadratic with no real zeros?

A)   Images

B)   Images

C)   Images

D)   Images

11

In the xy-plane, the graph of the line Images intersects the graph of the equation y = x2 + x at two points. What is the distance between these two points?

A)   Images

B)   Images

C)   Images

D)   4

12

If i2k = 1, and Images, which of the following must be true about k?

A)   k is a multiple of 4.

B)   k is a positive integer.

C)   When 2k is divided by 4, the remainder is 1.

D)   Images is an integer.

13

For all numbers x and y, let z be defined by the equation z = |22 − x2 − y2| + 22. What is the smallest possible value of z?

A)   0

B)   4

C)   8

D)   16

14

If the polynomial P(x) has factors of 12, (x − 5), and (x + 4), which of the following must also be a factor of P(x)?

A)   2x2 + 8

B)   4x2 − 20

C)   6x2 − 6x − 120

D)   x2 − 10x + 25

15

If f(x) = –x + 7 and g(f(x)) = 2x + 1, what is the value of g(2)?

A)   −11

B)   −5

C)   5

D)   11

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 3Images must be gridded as 3.5 or Images.

(If 3Images is entered into the grid as Images, it will be interpreted as Images, not 3Images.)

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.

Images

16

In a writer’s workshop, there are half as many men as women. If there are 24 total men and women in the writer’s workshop, how many men are there?

17

If Images what is the value of b?

18

The square of a positive number is 0.24 greater than the number itself. What is the number?

19

The function f is a quadratic function with zeros at x = 1 and x = 5. The graph of y = f(x) in the xy-plane is a parabola with a vertex at (3, −2). What is the y-intercept of this graph?

20

When graphed in the xy-plane, the line y = mx − 4 intersects the x-axis at an angle of θ. If m > 0, 0° < θ < 90°, and Images, what is the value of m?

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.