1. Directions

For questions 1 through 15, solve each problem, choose the best answer from the choices provided, and indicate your answer choice on your answer sheet. For questions 16 through 20, solve the problem and indicate your answer, which is to be recorded in the spaces provided on the answer sheet. Please refer to the directions before question 16 on how to record your answers in the spaces provided. You may use scratch paper 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 x for which  f (x) is a real number.

Reference

Begin skippable figure descriptions.

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 onehalf 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 30degree angle and a 60degree angle. The side opposite the 30degree angle is labeled x. The side opposite the 60degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2 x.

Reference figure 6 is a right triangle with two 45degree 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 fourthirds 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 onethird 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 onethird ℓ w h.

End skippable figure descriptions.

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.

Question 1.

Which of the following is an equation of line   l in the preceding xyplane?

2. Question 2 refers to the following figure.

Begin skippable figure description.

The figure presents a circle with center O. Points A and C are indicated on the circle, creating minor arc AC. A diameter is drawn from point A to a point on the other side of the circle. Similarly, a diameter is drawn from point C to a point on the other side of the circle. The two lines intersect at the origin, forming a right angle at angle AOC.

End skippable figure description.

Question 2.

The preceding circle with center O has a circumference of 36. What is the length of minor arc AC?

3. What are the solutions of the quadratic equation ?

4. Which of the following is an example of a function whose graph in the x yplane has no xintercepts?

5. Question 5 refers to the following equation.

Question 5.

In the preceding equation, k is a constant. If   x = 9, what is the value of k ?

6. Which of the following is equivalent to the sum of the expressions   and   a + 1 ?

7. Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

8. In air, the speed of sound S, in meters per second, is a linear function of the air temperature T, in degrees Celsius, and is given by   S(T) = 0.6 T + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

9. Question 9 refers to the following system of equations.

 2y + 6 = 2(x + 3)

Question 9.

If   (x, y) is a solution of the preceding system of equations and   x > 0, what is the value of x y?

10. If    and ab= y, which of the following is equivalent to   4 z + 8 y?

11. The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

12. Which of the following is equivalent to  ?

13. At a restaurant, n cups of tea are made by adding t tea bags to hot water. If   t = n + 2, how many additional tea bags are needed to make each additional cup of tea?

14. Question 14 refers to the following equation.

Question 14.

The function f is defined by the preceding equation. Which of the following is the graph of   y = – f (x) in the x yplane?

Each answer choice presents the graph of a curve in the x yplane. The number 1 is indicated on both axes.

15. Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?

16. Directions

For questions 16 through 20, solve the problem and record your answer in the spaces provided on the answer sheet, as described in the following directions and examples.

1. Although not required, it is suggested that your answer be recorded in the boxes at the top of the columns to help 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, indicate only one answer.

5. Mixed numbers such as must be recorded as 3.5 or  7/2.

 ( is recorded in the spaces provided on the answer sheet, it will be interpreted as not )

6. Decimal answers: If you obtain a decimal answer with more digits than the spaces on the answer sheet can accommodate, it may be either rounded or truncated, but it must fill all four spaces.

The following are four examples of how to record your answer in the spaces provided. Keep in mind that there are four spaces provided to record each answer.

Examples 1 and 2

Begin skippable figure description.

Example 1: If your answer is a fraction such as seventwelfths, it should be recorded as follows. Enter 7 in the first space, the fraction bar (a slash) in the second space, 1 in the third space, and 2 in the fourth space. All four spaces would be used in this example.

Example 2: If your answer is a decimal value such as 2.5, it could be recorded as follows. Enter 2 in the second space, the decimal point in the third space, and 5 in the fourth space. Only three spaces would be used in this example.

End skippable figure description.

Example 3

Begin skippable figure description.

Example 3: Acceptable ways to record twothirds are: 2 slash 3, .666, and .667.

End skippable figure description.

Example 4

Note: You may start your answers in any column, space permitting. Columns you don’t need to use should be left blank.

Begin skippable figure description.

Example 4: It is not necessary to begin recording answers in the first space unless all four spaces are needed. For example, if your answer is 201, you may record 2 in the second space, 0 in the third space, and 1 in the fourth space. Alternatively, you may record 2 in the first space, 0 in the second space, and 1 in the third space. Spaces not needed should be left blank.

End skippable figure description.

Question 16.

Maria plans to rent a boat. The boat rental costs $60 per hour, and she will also have to pay for a water safety course that costs $10. Maria wants to spend no more than $280 for the rental and the course. If the boat rental is available only for a whole number of hours, what is the maximum number of hours for which Maria can rent the boat?

17. Question 17 refers to the following equation.

  2(p + 1) + 8(p – 1) + 5p

Question 17.

What value of p is the solution of the preceding equation?

18. Question 18 refers to the following system of equations.

 y = 2x

Question 18.

The preceding system of equations has solution   (x,  y). What is the value of x?

19. Question 19 refers to the following expression.

Question 19.

The preceding expression is equivalent to  , where a is a positive constant and  xx≠ -2. What is the value of a ?

20. Question 20 refers to the following information.

Intersecting lines r, s, and t are shown in the following figure.

Begin skippable figure description.

The figure presents three intersecting lines, labeled r, s, and t. Line s begins near the top of the figure and extends downward and slightly to the left. Line t begins to the left of line s, and extends downward and to the right, intersecting line s. Line r begins below line t and to the left of line s. Line r extends upward and to the right, first intersecting line s and then line t. The angle formed to the right of line s and above line t measures 106 degrees, and the angle formed to the left of line s and above line r measures x degrees. The angle formed below line t and above line r measures 23 degrees.

End skippable figure description.

Question 20.

What is the value of x?