Mathematics Test—No Calculator
Turn to Section 3 of your answer sheet to answer the questions in this section.
Directions
For questions 1 through 13, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions14 through 17, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 14 on how to enter your answers in the grid. 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 theproblems.
Reference figure 1 is a circle with radius r. Two equations are presented below reference figure1.
A equals pi times the square of r.
C equals 2 pi r.
Reference figure 2 is a rectangle with lengthℓ and widthw. An equation is presented below reference figure2.
A equals ℓw.
Reference figure 3 is a triangle with base b and heighth. An equation is presented below reference figure3.
A equals onehalfbh.
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 figure4.
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 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 labeled stimes the squareroot of2.
Reference figure 7 is a rectangular solid whose base has lengthℓ and widthw and whose height ish. An equation is presented below reference figure7.
V equalsℓwh.
Reference figure 8 is a rightcircularcylinder whose base has radiusr and whose height ish. An equation is presented below reference figure8.
V equalspitimes the square of rtimesh.
Reference figure 9 is a sphere with radiusr. An equation is presented below reference figure9.
V equalsfourthirds pi times the cube ofr.
Reference figure 10 is a cone whose base has radiusr and whose height ish. Anequation is presented below reference figure10.
V equals onethird times pi times the square of rtimesh.
Reference figure 11 is an asymmetrical pyramid whose base has lengthℓ and widthw and whose height ish. An equation is presented below reference figure11.
V equalsonethirdℓwh.
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.
The Redesigned P S A T/N M S Q T® Page 21
Copyright 2015 by the College Board W F-5 K P T 0 6
Question 1.
A babysitter earns $8 an hour for babysitting 2children and an additional $3tip when both children are put to bed on time. If the babysitter gets the children to bed on time, what expression could be used to determine how much the babysitter earned?
A. 8x plus3, where x is the number of hours
B. 3x plus 8, where x is the number of hours
C. x open parenthesis, 8 plus 2, close parenthesis, plus 3, where x is the number of children
D. 3x plus open parenthesis, 8 plus 2, close parenthesis, where x is the number of children
Answer and Explanation. (Follow link to explanation of question 1.)
Question 2.
3 open parenthesis, xplusy, close parenthesis, equalsy
If x comma y, is a solution to the equation above and y is not equal to zero, what is the ratio of x to y?
A. negative four to 3
B. negative two to 3
C. one to 3
D. two to 3
Answer and Explanation. (Follow link to explanation of question 2.)
Question 3.
One half x minus one fourth y, equals 10.
One eighth x minus one eighth y, equals 19.
Which ordered pair x comma y, satisfies the system of equations above?
A. , negative 112 comma negative 264
B. 64 comma 88
C. the fraction 232 over 3, comma, the fraction 224 over3
D. 288 comma 536
Answer and Explanation. (Follow link to explanation of question 3.)
Question 4 refers to the following figure.
Begin skippable figure description.
The figure presents triangle ABC with vertexA above sideBC and vertexB to the left of vertexC. PointD lies on sideBC and point E lies on side AB. Line segmentDE extends from pointD upward and to the left, intersecting sideAB at pointE, forming righttriangleBED with the right angle at vertexE. Point F lies on side AC. Line segmentDF extends from pointD upward and to the right, intersecting sideAC at pointF, forming right triangleDFC with the right angle at vertexF. The figure is not drawn to scale.
End skippable figure description.
Question 4.
The preceding triangle ABC is isosceles with AB equalsAC and BC equals48. The ratio of DE to DF is 5:7. What is the length of line segmentDC ?
A.12
B.20
C.24
D.28
Answer and Explanation. (Follow link to explanation of question 4.)
Question 5.
In a certain game, a player can solve easy or hard puzzles. A player earns 30points for solving an easy puzzle and 60points for solving a hard puzzle. Tina solved a total of 50puzzles playing this game, earning 1,950points in all. How many hard puzzles did Tina solve?
A.10
B.15
C.25
D.35
Answer and Explanation. (Follow link to explanation of question 5.)
Question 6.
2x squared, plus 7x minus 15, equalszero.
If r and s are two solutions of the equation above and ris greater thans, which of the following is the value of rminuss?
A. fifteen halves
B. thirteen halves
C. eleven halves
D. three halves
Answer and Explanation. (Follow link to explanation of question 6.)
Question 7.
To cut a lawn, Allan charges a fee of $15 for his equipment and $8.50 per hour spent cutting a lawn. Taylor charges a fee of $12 for his equipment and $9.25 per hour spent cutting a lawn. If xrepresents the number of hours spent cutting a lawn, what are all the values of xfor which Taylor’s total charge is greater than Allan’s total charge?
A. x is greater than 4.
B. x is greater than or equal to 3 and less than or equal to 4.
C. x is greater than or equal to 4 and less than or equal to 5.
D. x is less than 3.
Answer and Explanation. (Follow link to explanation of question 7.)
Question 8.
n equals, 456 minus 3T
The equation above is used to model the relationship between the number of cups,n, of hot chocolate sold per day in a coffee shop and the average daily temperature,T, in degrees Fahrenheit. According to the model, what is the meaning of the 3 in the equation?
A.For every increase of 3°F, one more cup of hot chocolate will be sold.
B.For every decrease of 3°F, one more cup of hot chocolate will be sold.
C.For every increase of 1°F, three more cups of hot chocolate will be sold.
D.For every decrease of 1°F, three more cups of hot chocolate will be sold.
Answer and Explanation. (Follow link to explanation of question 8.)
Question 9.
A truck enters a stretch of road that drops 4 meters in elevation for every 100meters along the length of the road. The road is at 1,300meters elevation where the truck entered, and the truck is traveling at 16meters per second along the road. What is the elevation of the road, in meters, at the point where the truck passes tseconds after entering the road?
A. 1,300 minus 0.04t
B. 1,300 minus 0.64 t
C. 1,300 minus 4 t
D. 1,300 minus 16t
Answer and Explanation. (Follow link to explanation of question 9.)
Question 10.
If f of x minus 1, equals 2x plus3 for all values ofx, what is the value of f of negative3?
A. negative7
B. negative5
C. negative3
D. negative1
Answer and Explanation. (Follow link to explanation of question10.)
Question 11.
Which of the following is equivalent to open parenthesis, sminust, close parenthesis, times, open parenthesis, the fraction sovert, close parenthesis?
A. the fraction sovert, minuss
B. the fraction sovert, minusst
C. the fraction ssquared overt, minuss
D. the fraction ssquared overt, minusthe fraction whose numerator is s and whose denominator is tsquared
Answer and Explanation. (Follow link to explanation of question11.)
Question 12.
pofx equals3, open parenthesis, xsquared plus 10x plus5, close parenthesis, minus5, open parenthesis, xminusk, close parenthesis.
In the polynomial pofx defined above, k is a constant. If pofx is divisible byx, what is the value ofk?
A. negative 3
B. negative 2
C.0
D.3
Answer and Explanation. (Follow link to explanation of question12.)
Question 13.
In the xyplane, if the parabola with equation yequals axsquared, plusbx, plusc, where a, b, and c are constants, passes through the point with coordinates negative1 comma 1, which of the following must be true?
A. a minus b, equals1
B. negative b plus c, equals1
C. a plus b plus c, equals1
D. a minus b plus c, equals1
Answer and Explanation. (Follow link to explanation of question13.)
The Redesigned P S A T/N M S Q T® Page 21
Copyright 2015 by the College Board W F-5 K P T 0 6
Directions
For questions 14 through 17, 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 three and one half must be gridded as 3.5 or sevenslashtwo. (If three,one,slash,two, is entered into the grid, 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 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 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.
The Redesigned P S A T/N M S Q T® Page 21
Copyright 2015 by the College Board W F-5 K P T 0 6
Question 14.
For what value of h is 24 equals, the fraction h over 10 minus 6?
Answer and Explanation. (Follow link to explanation of question14.)
Question 15.
What is the value of a if open parenthesis, 2a, plus 3, close parenthesis, minus, parenthesis, 4a, minus 8, close parenthesis, equals7?
Answer and Explanation. (Follow link to explanation of question15.)
Question 16.
If x is not equal to zero, what is the value of the fraction whose numerator is 4, open parenthesis 3x close parenthesis, squared, and whose denominator is, open parenthesis 2x close parenthesis, squared?
Answer and Explanation. (Follow link to explanation of question16.)
Question 17.
If xminus2 is a factor of xsquared minus bx plusb, where bis a constant, what is the value ofb?
Answer and Explanation. (Follow link to explanation of question17.)