Math Test

25 Minutes-20 Questions

NO-CALCULATOR SECTION

This section corresponds to Section 3 of your answer sheet.

Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding oval on the answer sheet. You may use any available space for scratch work.

Notes:

1. Calculator use is NOT permitted.

2. All numbers used are real numbers, and all variables used represent real numbers, unless otherwise indicated.

3. Figures are drawn to scale and lie in a plane unless otherwise indicated.

4. Unless stated otherwise, the domain of any function f is assumed to be the set of all real numbers x, for which f (x) is a real number.

The sum of the degree measures of the angles in 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 2π.

1. The graph above shows the amount that a new, high-tech video arcade charges its customers. What could the y-intercept of this graph represent?

A) The cost of playing 5 games

B) The cost per game, which is $5

C) The entrance fee to enter the arcade

D) The number of games that are played

2. Which of the following is equivalent to the expression above, given that x ≠ −5 ?

A) 2x

B)

C)

D) 2x + 4

3. The graph of the equation above is a circle. What is the area, in square units, of the circle?

A) 4π

B) 5π

C) 16π

D) 25π

4. The figure above shows the graph of f(x). For which value(s) of x does f(x) equal 0 ?

A) 3 only

B) −3 only

C) −2 and 3

D) −3, −2, and 3

5. In the equation above, what is the value of d ?

A) 

B) 

C) 

D) 

6. One indicator of a declining economy is a continued decline in birth rates. In 2010, birth rates in Europe were at an all-time low, with the average number of children that a woman has in her lifetime at well below two. In the figure above, f(t) represents birth rates for Portugal between 1960 and 2010, and g(t) represents birth rates in Slovakia for the same time period. For which value(s) of t is f(t) > g(t) ?

A) 1960 < t < 1980 only

B) 1980 < t < 2000 only

C) 1960 < t < 1980 and 1990 < t < 2000

D) 1960 < t < 1980 and 2000 < t < 2010

7. The blue whale is the largest creature in the world and hasbeen found in every ocean in the world. A marine biologist surveyed the blue whale population in Monterey Bay, off the coast of California, every three years between 1995 and 2010. The figure above shows her results. If w is the number of blue whales present in Monterey Bay and t is the number of years since the study began in 1995, which of the following equations best represents the blue whale population of Monterey Bay?

A) w = 100 + 2t

B) 

C) 

D) 

8. The figure above shows the straight-line depreciation of a laptop computer over the first five years of its use. According to the figure, what is the average rate of change in dollars per year of the value of the computer over the five-year period?

A) −1,100

B) −220

C) −100

D) 100

9. What is the coefficient of x² when   is multiplied by

A) −4

B) −2

C) 2

D) 4

10. The graph above could represent which of the following equations?

A) −6x − 4y = 5

B) −6x − 4y = −5

C) −6x + 4y = 5

D) −6x + 4y = −5

11. If the system of linear equations above has no solution, and k is a constant, what is the value of k ?

A) 

B) 

C) 3

D) 4

12. In Delray Beach, Florida, you can take a luxury golf cart ride around downtown. The driver charges $4 for the first mile, plus $1.50 for each additional mile. Which inequality represents the number of miles, m, that you could ride and pay no more than $10 ?

A) 3.25 + 1.5m ≤ 10

B) 3.25 + 3m ≤ 10

C) 4 + 1.5m ≤ 10

D) 4 + 3m ≤ 10

13. The graph of g(x) is shown in the figure above. If h(x) = −g(x) + 1, which of the following statements is true?

A) The range of h(x) is −3 ≤ y ≤ 3.

B) The minimum value of h(x) is −4.

C) The coordinates of point A on the function h(x) are (2, 4).

D) The graph of h(x) is increasing between x = −5 and x = −2.

14. If a + bi represents the complex number that results from multiplying 3 + 2i times 5 − i, what is the value of a ?

A) 2

B) 13

C) 15

D) 17

15. In order to create safe drinking water, cities and towns use water treatment facilities to remove contaminants from surface water and groundwater. Suppose a town has a treatment plant but decides to build a second, more efficient facility. The new treatment plant can filter the water in the reservoir four times as quickly as the older facility. Working together, the two facilities can filter all the water in the reservoir in 72 hours. The equation above represents the scenario. Which of the following describes what the term represents?

A) The portion of the water the older treatment plant can filter in 1 hour

B) The time it takes the older treatment plant to filter the water in the reservoir

C) The time it takes the older treatment plant to filter of the water in the reservoir

D) The portion of the water the new treatment plant can filter in 4 hours

16. If  what is the value of x + 2y ?

17. If (a, b) is a point in the solution region for the system of inequalities shown above and a = 6, what is the minimum possible value for b ?

18. If  is the simplified form of the expression above, what is the value of n ?

19. In the figure above, the area of the shaded region is 52 square units. What is the height of the larger triangle?

20. If    passes through the points (−3, 10), (0, 1), and (2, 15), what is the value of a + b + c ?