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.

Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a onetime service fee for processing the purchase of the tickets. The equation   T =15 n + 12 represents the total amount T, in dollars, Salim will pay for n tickets. What does 12 represent in the equation?

2. A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials by weight and Fertilizer B contains 40% filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?

3. What is the sum of the complex numbers   2 + 3 i and   4 + 8 i, where  ?

4. Question 4 refers to the following equation.

Question 4.

In the preceding equation, p and t are constants. Which of the following could be the value of p?

5. Which of the following is the graph of the equation   y = 2 x – 5 in the xyplane?

Each option presents the graph of a line in the xyplane with the origin labeled O. The numbers negative 5 and 5 are indicated on each axis.

6. If    and   y = 18, what is the value of   2 x – 3?

7. A bricklayer uses the formula   n = 7 l h to estimate the number of bricks, n, needed to build a wall that is  l feet long and h feet high. Which of the following correctly expresses l in terms of n and h?

8. Question 8 refers to the following figure.

Begin skippable figure description.

The figure presents a 3column table with 5 rows of data. The heading for column 1 is “x,” the heading for column 2 is “w of x,” and the heading for column 3 is “t of x.” The five rows of data are as follows.

Row 1: x, 1; w of x, negative 1; t of x, negative 3.

Row 2: x, 2; w of x, 3; t of x, negative 1.

Row 3: x, 3; w of x, 4; t of x, 1.

Row 4: x, 4; w of x, 3; t of x, 3.

Row 5: x, 5; w of x, negative 1; t of x, 5.

End skippable figure description.

Question 8.

The preceding table shows some values of the functions w and t. For which value of x is   w (x) + t (x) = x?

9. If , what is the value of x?

10. Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week, and 320 miles the third week. Which inequality can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal?

11. Question 11 refers to the following figure.

Begin skippable figure description.

The figure presents a parabola labeled, y equals a x squared plus c, in the x yplane with the origin labeled O. The parabola opens upward and its vertex lies on the yaxis a short distance above the origin.

End skippable figure description.

Question 11.

The vertex of the preceding parabola in the xyplane is (0, c). Which of the following is true about the parabola with the equation ?

12. Which of the following is equivalent to ?

13. Question 13 refers to the following equation.

Question 13.

In the preceding equation, t is a constant. If the equation has no real solutions, which of the following could be the value of t?

14. A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

15. Which of the following is equivalent to ?

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

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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.

If   for positive integers a and b, what is one possible value of b?

17. Question 17 refers to the following equation.

Question 17.

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

18. Question 18 refers to the following figure.

Begin skippable figure description.

The figure presents triangle ACE, with horizontal side AC. Side AE is perpendicular to side AC such that point E is above point A. Point B lies on horizontal side AC, point D lies on hypotenuse CE, and line segment BD is drawn such that it is parallel to side AE and forms triangle CDB. Side AE is labeled 18, side BC is labeled 8, side BD is labeled 6, and a right angle symbol is at point A.

End skippable figure description.

Question 18.

In the preceding figure ,   is parallel to . What is the length of  ?

19. How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?

20. Points A and B lie on a circle with radius 1, and arc AB has length . What fraction of the circumference of the circle is the length of arc  AB?