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 is based on the following two equations.

2x – y = 8

x + 2y = 4 

Question 1.

For the preceding system of equations, what is the value of   x + y?

2. Which of the following is equivalent to  ?

3. Which of the following statements is true about the graph of the equation   2 y – 3 x, = -4 in the x yplane?

4. The front of a rollercoaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the rollercoaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height h, in feet, of the front of the rollercoaster car s seconds after it starts up the hill?

5. Question 5 is based on the following equation.

  C = 75 h + 125

Question 5.

The preceding equation gives the amount C, in dollars, an electrician charges for a job that takes h hours. Ms. Sanchez and Mr. Roland each hired this electrician. The electrician worked 2 hours longer on Ms. Sanchez’s job than on Mr. Roland’s job. How much more did the electrician charge Ms. Sanchez than Mr. Roland?

6. Question 6 is based on the following figure.

Begin skippable figure description.

The figure presents a circle with center O. There are four points on the circle. Going clockwise around the circle, the four points are A, B, C, and D. Points A and C divide the circle into two arcs, arc ADC and arc ABC. The length of arc ADC is less than the length of arc ABC. Radius OA and radius OC are drawn. Angle AOC, the central angle corresponding to arc ADC, measures x degrees. The measure of angle AOC, the central angle corresponding to arc ABC, is not given.

End skippable figure description.

Question 6.

The preceding circle has center O, the length of arc ADC is , and   x = 100. What is the length of arc   ABC?

7. If    what is the value of x?

8. Question 8 is based on the following equation.

  2 a x – 15 = 3(x + 5) + 5(x – 1)

Question 8.

In the preceding equation, a is a constant. If no value of x satisfies the equation, what is the value of a?

9. Question 9 is based on the following figure.

Begin skippable figure description.

The figure presents the graphs of 2 lines and a curve that appears to be a downward facing parabola in the x yplane, with the origin labeled O. The integers negative 5 through 5 are indicated on the xaxis. The integers negative 2 through 5 are indicated on the yaxis.

The curve intersects the xaxis at negative 2 and 2, and the yaxis at 4.

One line intersects the xaxis at negative 4, and the yaxis at 4.

The other line intersects the xaxis at 2 and the yaxis at 2.

Both lines intersect the curve at the point with coordinates negative 1 comma 3.

End skippable figure description.

Question 9.

A system of three equations is graphed in the preceding x yplane. How many solutions does the system have?

10. Question 10 is based on the following equation.

Question 10.

The preceding equation is true for all x, where a and b are constants. What is the value of a b?

11. Question 11 is based on the following equation.

Question 11.

Which of the following represents all the possible values of x that satisfy the preceding equation?

12. Question 12 is based on the following expression.

Question 12.

Which of the following is equivalent to the preceding expression for   x > 0?

13. Question 13 is based on the following figure.

Begin skippable figure description.

The figure presents an upward facing parabola labeled y equals, f of x, in the x yplane, with the origin labeled O. The parabola lies entirely above the xaxis. The coordinates of the vertex of the parabola are 3 comma 1. The point with coordinates 2 comma 5 and the point with coordinates 4 comma 5 lie on the parabola.

End skippable figure description.

Question 13.

The graph of the function f in the preceding x yplane is a parabola. Which of the following defines f?

14. Question 14 is based on the following two inequalities.

y ≥ x + 2

Question 14.

In which of the following does the shaded region represent the solution set in the x yplane to the preceding system of inequalities?

Each answer choice presents the graph of the same 2 lines in the x yplane, with the origin labeled O, and the integers negative 4 and 4 indicated on both axes. One line begins in the upper left part of the x yplane and slants downward and to the right, intersecting the yaxis at 2 and the xaxis at 3. The other line begins in the lower left part of the plane and slants upward and to the right, intersecting the xaxis at negative 2 and the yaxis at 2. The lines intersect and divide the plane into 4 regions. In each answer choice 1 of the 4 regions is shaded.

15. What is the set of all solutions to the equation  ?

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.

What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?

17. Question 17 is based on the following equation.

  4 x + 2 = 4

Question 17.

If x satisfies the preceding equation, what is the value of   2 x + 1?

18. Question 18 is based on the following figure.

Begin skippable figure description.

The figure presents the graph of y equals, f of x, in the x yplane, with the origin labeled O. The number 1 is indicated on both axes. The graph begins at the point with coordinates negative 4 comma 2, and goes downward and to the right until it reaches the point on the xaxis with coordinates negative 2 comma 0. Then it goes upward and to the right until it reaches the point on the yaxis with coordinates 0 comma 2. It then goes downward and to the right until it reaches the point on the xaxis with coordinates 2 comma 0. Then it goes upward and to the right until it reaches the point with coordinates 4 comma 2, where it ends.

End skippable figure description.

Question 18.

The preceding figure shows the complete graph of the function f in the x yplane. The function g (not shown) is defined by   g(x) = f(x) + 6. What is the maximum value of the function g?

19. Triangle P Q R has right angle Q. If , what is the value of   tanP?

20. Question 20 is based on the following figure.

Begin skippable figure description.

The figure presents a line labeled y equals, f of x, in the x yplane, with the origin labeled O. The integers negative 2 through 3 are indicated on the xaxis. The integers 0 through 3 are indicated on the yaxis. The line begins in the upper left part of the x yplane and slants downward and to the right, passes through the yaxis at the point with coordinates 0 comma 3, then passes through the point with coordinates 1 comma 1, and then passes through the xaxis at the point with coordinates 1.5 comma 0.

End skippable figure description.

Question 20.

The graph of the linear function f is shown in the preceding x yplane. The graph of the linear function g (not shown) is perpendicular to the graph of f and passes through the point (1, 3). What is the value of g(0)?