Turn to Section 3 of Your Answer Sheet to Answer the Questions in This Section

Math Test—No Calculator

20 Questions

Turn to Section 3 of your answer sheet to answer the questions in this section.

Directions

For questions1 through 15, solve each problem, choose the best answer from the choices provided, and indicate your answer choice on your answer sheet. For questions16 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 question16 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 functionfis the set of all real numbersxfor which fofx is a real number.

Reference

Begin skippable figure descriptions.

The figure presents information for your reference in solving some of theproblems.

Reference figure 1 is a circle with radiusr. Two equations are presented below reference figure1.

Aequals pi times the square ofr.

Cequals 2 pir.

Reference figure 2 is a rectangle with lengthℓand widthw. An equation is presented below reference figure2.

Aequalsℓw.

Reference figure 3 is a triangle with baseband heighth. An equation is presented below reference figure3.

Aequals onehalfbh.

Reference figure 4 is a right triangle. The two sides that form the right angle are labeledaandb, and the side opposite the right angle is labeledc. An equation is presented below reference figure4.

csquared equalsasquared plusbsquared.

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 labeledx. The side opposite the 60degree angle is labeledxtimes the squareroot of3. The side opposite the right angle is labeled2x.

Reference figure 6 is a right triangle with two 45degree angles. Two sides are each labeleds. The side opposite the rightangle is labeledstimes the squareroot of2.

Reference figure 7 is a rectangular solid whose base has lengthℓand widthwand whose height ish. An equation is presented below reference figure7.

Vequalsℓwh.

Reference figure 8 is a rightcircularcylinder whose base has radiusrand whose height ish. An equation is presented below reference figure8.

Vequalspitimes the square ofrtimesh.

Reference figure 9 is a sphere with radiusr. An equation is presented below reference figure9.

Vequalsfourthirds pi times the cube ofr.

Reference figure 10 is a cone whose base has radiusrand whose height ish. Anequation is presented below reference figure10.

Vequals onethird times pi times the square ofrtimesh.

Reference figure 11 is an asymmetrical pyramid whose base has lengthℓand widthwand whose height ish. An equation is presented below reference figure11.

Vequalsonethirdℓwh.

End skippable figure descriptions.

Additional Reference Information

The number of degrees of arc in a circle is360.

The number of radians of arc in a circle is 2pi.

The sum of the measures in degrees of the angles of a triangle is180.

Question 1 refers to the following graph.

Begin skippable figure description.

The figure presents the graph of a line, labeledl, in the xyplane with the origin labeledO. The number 1 is indicated on both axes. The graph begins in the third quadrant. It moves upward and to the right, crossing the xaxis at the point with coordinates negative1 comma 0, and crossing the yaxis at the point with coordinates 0 comma 1. The line ends in the first quadrant.

End skippable figure description.

Question 1.

Which of the following is an equation of line lin the preceding xyplane?

A.x equals1

B.yequals1

C.yequalsx

D.y equals x plus1

Question 2 refers to the following figure.

Begin skippable figure description.

The figure presents a circle with centerO. PointsA and C are indicated on the circle, creating minor arcAC. A diameter is drawn from pointA to a point on the other side of the circle. Similarly, a diameter is drawn from pointC to a point on the other side of the circle. The two lines intersect at the origin, forming a right angle at angleAOC.

End skippable figure description.

Question 2.

The preceding circle with centerO has a circumference of 36. What is the length of minor arcAC?

A.9

B.12

C.18

D.36

Question 3.

What are the solutions of the quadratic equation4xsquared, minus 8x, minus 12, equals0?

A.x equals negative1andx equals negative3

B.xequals negative1andxequals3

C.x equals 1andxequals negative3

D.x equals 1andxequals3

Question 4.

Which of the following is an example of a function whose graph in the xyplane has no xintercepts?

A.A linear function whose rate of change is not zero

B.A quadratic function with real zeros

C.A quadratic function with no real zeros

D.A cubic polynomial with at least one real zero

Question 5 refers to the following equation.

the square root of k plus 2, end root, minus x, equals0

Question 5.

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

A.1

B.7

C.16

D.79

Question 6.

Which of the following is equivalent to the sum of the expressionsasquared minus1andaplus1?

A.asquared plusa

B.acubed minus1

C.2, asquared

D.acubed

Question 7.

Jackie has two summer jobs. She works as a tutor, which pays $12per hour, and she works as a lifeguard, which pays $9.50per hour. She can work no more than 20hours per week, but she wants to earn at least $220per 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?

12x plus 9.5y is less than or equal to 220,

and,

x plus y is greater than or equal to20

12xplus 9.5y is less than or equal to 220,

and,

x plus y is less than or equal to20

12xplus 9.5y is greater than or equal to 220,

and,

x plus y is less than or equal to20

12x plus 9.5y is greater than or equal to 220,

and,

x plus y is greater than or equal to20

Question 8.

In air, the speed of soundS, in meters per second, isa linear function of the air temperatureT, in degrees Celsius, and is given byS of T, equals, 0.6T plus 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

A.The speed of sound, in meters per second, at0degreesCelsius

B.The speed of sound, in meters per second, at 0.6degreeCelsius

C.The increase in the speed of sound, in meters per second, that corresponds to an increase of1degreeCelsius

D.The increase in the speed of sound, in meters per second, that corresponds to an increase of 0.6degreeCelsius

Question 9 refers to the following system of equations.

y equals xsquared,

and,

2y plus 6, equals, 2 times, open parenthesis, x plus 3, close parenthesis

Question 9.

Ifx comma y is a solution of the preceding system of equations andx is greater than 0, what is the value ofxy?

A.1

B.2

C.3

D.9

Question 10.

Ifasquared plus bsquared equals zanda times b equals y, which of the following is equivalent to4zplus 8y?

A.open parenthesis, aplus 2b, close parenthesis, squared

B.open parenthesis, 2a plus 2b, close parenthesis, squared

C.open parenthesis, 4aplus 4b, close parenthesis, squared

D.open parenthesis, 4a plus 8b, close parenthesis, squared

Question 11.

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

A.11

B.22

C.44

D.66

Question 12.

Which of the following is equivalent to9, raised to the power, three fourths?

A.the cube root of9

B.the fourth root of9

C.the square root of3

D.3 times, the square root of3

Question 13.

At a restaurant, ncups of tea are made by adding ttea bags to hot water. Ift equals n plus 2, how many additional tea bags are needed to make each additional cup of tea?

A.None

B.One

C.Two

D.Three

Question 14 refers to the following equation.

f of x, equals, 2 raised to the power x, end power, plus1

Question 14.

The function f is defined by the preceding equation. Which of the following is the graph ofy equals negativef of xin the xyplane?

Each answer choice presents the graph of a curve in the xyplane. The number1 is indicated on both axes.

Begin skippable figure description.

The curve begins in quadrant2. It moves downward and to the right, crossing the yaxis at the point with coordinates 0 comma 2. As the graph moves to the right, it approaches ayvalue of 1. The curve ends in quadrant1.

End skippable figure description.

Begin skippable figure description.

The curve begins in quadrant3, just above the yvalue of negative2. It moves upward and to the right, crossing the yaxis at the point with coordinates 0 comma negative1. It then passes through quadrant4, crossing the xaxis at the point with coordinates 1 comma 0. The curve ends in quadrant1.

End skippable figure description.

Begin skippable figure description.

The curve begins in quadrant3, just below the yvalue of negative1. It moves downward and to the right, crossing the yaxis at the point with coordinates 0 comma negative2. The curve ends in quadrant4.

End skippable figure description.

Begin skippable figure description.

The curve begins in quadrant2, just below the yvalue of 1. It moves downward and to the right, crossing the xaxis at the point with coordinates negative1 comma 0. It then passes through quadrant3, crossing the yaxis at the point with coordinates 0 comma negative1. The curve ends in quadrant4.

End skippable figure description.

Question 15.

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

A.the fraction 25 over 4, end fraction, times m, equals,95

B.the fraction 25 over 4, end fraction, times m, equals,5

C.the fraction 4 over 25, end fraction, times m, equals,95

D.the fraction 4 over 25, end fraction, times m, equals,5

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 three and one half must be recorded as 3.5 or sevenslashtwo. (If three,one,slash,two, is recorded in the spaces provided on the answer sheet, it will be interpreted as thirty one halves, not three and one half.)

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 fractionbar (aslash) 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 secondspace, the decimal point in the third space, and 5 in the fourth space. Only three spaces would be used in thisexample.

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, spacepermitting. 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 $60per hour, and she will also have to pay for a water safety course that costs $10. Maria wants to spend no more than $280for 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?

Question 17 refers to the following equation.

2 times, open parenthesis, p plus 1, close parenthesis, plus, 8 times, open parenthesis, p minus 1, close parenthesis, equals,5p

Question 17.

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

Question 18 refers to the following system of equations.

onehalf times, open parenthesis, 2x plus y, close parenthesis, equals the fraction 21 over2,

and

yequals 2x

Question 18.

The preceding system of equations has solutionx comma y. What is the value ofx?

Question 19 refers to the following expression.

the fraction with numerator 2x plus 6, and denominator, open parenthesis, x plus 2, close parenthesis, squared, end fraction, minus, the fraction with numerator 2, and denominator x plus 2, end fraction

Question 19.

The preceding expression is equivalent tothe fraction with numerator a, and denominator, open parenthesis, x plus 2, close parenthesis, squared, end fraction, where a is a positive constant andxis not equal to negative2. What is the value ofa?

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. Lines begins near the top of the figure and extends downward and slightly to the left. Linet begins to the left of lines, and extends downward and to the right, intersecting lines. Liner begins below linet and to the left of lines. Liner extends upward and to the right, first intersecting lines and then linet. The angle formed to the right of lines and above linet measures 106degrees, and the angle formed to the left of lines and above liner measures xdegrees. The angle formed below linet and above liner measures 23degrees.

End skippable figure description.

Question 20.

What is the value ofx?

Stop.

If you finish before time is called, you may check your work on this section only.Do not go on to any other section.

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