1. Directions

For questions 1 through 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 through 20, solve the problem and enter your answer in the grid on the answer sheet. 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 x for which    f of 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.

If , and k = 3, what is the value of x?

2. For , what is the sum(7 + 3i) + (-8 + 9i)

3. On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?

4. Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation   P = 108 – 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?

5. (x²y-3y²+5xy²)-(-x²y+3xy²-3y²) Which of the following is equivalent to the preceding expression?

6. h=3a+28.6

A pediatrician uses the model above to estimate the height h of a boy, in inches, in terms of the boy’s age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy’s height each year?

7. The formula below gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months. Which of the following gives P in terms of m, r, and N?

.

8. If  the fraction, what is the value of the fraction ?

9.   3 x + 4 y = -23

  2 y – x = -19

What is the solution   parenthesis, x comma y, close parenthesis, to the preceding system of equations?

10.

For the function g defined, a is a constant and  g(4) = 8. What is the value of   g(-4)?

11. b = 2.35 + 0.25 x

 c = 1.75 + 0.40 x

In the preceding equations, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?

12. A line in the xy-plane passes through the origin and has a slope of . Which of the following points lies on the line?

13. If   x >3, which of the following is equivalent to ?

14. If   3x – y = 12, what is the value of ?

15. If for all values of x, and  a + b = 8, what are the two possible values for c?

16. Directions

For questions 16 through 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  7/2. is entered into the grid, 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.

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

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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   t > 0 and t² – 4 = 0, what is the value of t?

17.

Begin skippable figure description.

The figure presents the outline of a lake and some geometric figures with measurements. In the figure, from point A, which is on the top side of the lake, to point E, which is on the bottom side of the lake, the length of the lake, A E, is labeled x feet. To the right of the lake, line segments A C and E D are drawn such that A C slants downward, E D slants upward, and both line segments intersect at point B that is to the right of the lake. In triangle A E B and triangle C D B, angle A E B and angle C D B are both marked with an angle symbol.

End skippable figure description.

Question 17.

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the preceding sketch. The lengths represented by AB, EB, BD, and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and ∠ AEB and ∠ CDB have the same measure. What is the value of x?

18. Question 18 is based on the following system of equations.

x + y = -9

x + 2y = -25

Question 18.

According to the preceding system of equations, what is the value of x?

19. In a right triangle, one angle measures x° where sin x° . What is cos(90° – x°)?

20. If and, , what is the value of x?

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