math test—no calculator · web viewmath test—no calculator 13 questions turn to section 3 of...

Math Test—No Calculator13 Questions

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

DirectionsFor questions 1 through 10, solve each problem, choose the best answer from the choices provided, and indicate your answer choice on your answer sheet. For questions 11 through 13, 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 11 on how to record your answers in the spaces provided. You may use scratch paper for scratch work.

Notes1. 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.

P S A T™ 8/9 Copyright 2016 by the College Board W F-5 L R S 0 1

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 one-half 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 30-degree angle and a 60-degree angle. The side opposite the 30-degree angle is labeled x. The side opposite the 60-degree 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 45-degree 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 four-thirds 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 one-third 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 one-third 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 refers to the following equation.

the fraction 3 over 4 equals the fraction x over 60

Question 1.In the preceding equation, what is the value of x ?

A. 25

B. 30

C. 40

D. 45

Question 2 refers to the following table.x y

1 5

2 7

3 9

4 11

Question 2.The preceding table shows some pairs of x values and y values. Which of the following equations could represent the relationship between x and y ?

A. y equals 2 x plus 3

B. y equals 3 x minus 2

C. y equals 4 x minus 1P S A T™ 8/9 Copyright 2016 by the College Board W F-5 L R S 0 1

D. y equals 5 x


Question 3.A discount airline sells a certain number of tickets, x, for a flight for $90 each. It sells the number of remaining tickets, y, for $250 each. For a particular flight, the airline sold 120 tickets and collected a total of $27,600 from the sale of those tickets. Which system of equations represents this relationship between x and y ?

A. open brace, x plus y equals 120, and, 90 x plus 250 y equals 27,600

B. open brace, x plus y equals 120, and, 90 x plus 250 y equals 120 times 27,600

C. open brace, x plus y equals 27,600, and, 90 x plus 250 y equals 120 times 27,600

D. open brace, 90 x equals 250 y, and, 120 x plus 120 y equals 27,600


Question 4 refers to the following expression. x squared minus 17 x minus 60

Question 4.Which of the following is equivalent to the preceding expression?

A. open parenthesis, x minus 5, close parenthesis, times, open parenthesis, x minus 12, close parenthesis

B. open parenthesis, x plus 5, close parenthesis, times, open parenthesis, x minus 12, close parenthesis

C. open parenthesis, x minus 3, close parenthesis, times, open parenthesis, x minus 20, close parenthesis

D. open parenthesis, x plus 3, close parenthesis, times, open parenthesis, x minus 20, close parenthesis


Question 5 refers to the following figure.

Begin skippable figure description.

The figure presents a graph of a line in the x y-plane with the origin labeled O. The numbers negative 5 through 5 are indicated along the x- and y-axes. The line begins in the second quadrant and moves downward and to the right. It crosses the y-axis at 3 and the x-axis at 1.

End skippable figure description.

Question 5.What is the equation of the line shown in the preceding x y-plane?

A. y equals 3 x minus 3

B. y equals negative 3 x plus 3

C. y equals one third x minus 3

D. y equals negative one third x plus 3


Question 6 refers to the following expression. open parenthesis, negative 11 x plus 31 y, close

parenthesis, minus, 2 times, open parenthesis, negative x plus 5 y, close parenthesis

Question 6.Which of the following expressions is equivalent to the preceding expression?

A. negative 13 x plus 21 y

B. negative 13 x plus 36 y

C. negative 9 x plus 21 y

D. negative 9 x plus 36 y

Question 7.The formula for determining the pressure, p, exerted on an object at a depth, h, below the surface of a liquid is p equals s plus, d g h, where s is the atmospheric pressure, d is the density of the liquid, and g is the acceleration due to gravity. Which formula represents h in terms of p, s, d, and g ?

A. h equals the fraction p over s, end fraction, plus, d g

B. h equals the fraction with numerator p minus s, and denominator, d g, end fraction

C. h equals p s, minus, d g

D. h equals p s, plus, d g


Question 8 refers to the following information.Rachel’s costs for automobile maintenance and fuel are shown in the following table.

Cost of Automobile Ownership

Type of cost Average cost

maintenance 5 cents per mile

fuel 14 cents per mile

Question 8.In addition to fuel and maintenance, Rachel pays $1,000 a year for insurance. The equation C equals open parenthesis, 0.05 plus 0.14, close parenthesis, times x, plus 1,000 shows the cost C, in dollars, of owning and operating the car for a year as a function of x, the number of miles driven in a year. What does the slope of the graph of this function represent?

A. The cost of insurance for a year

B. The cost of fuel and insurance for a year

C. The cost of owning and operating per mile

D. The cost of maintenance and fuel per mile


Question 9 refers to the following equation. open parenthesis, negative 4 x plus 5, close parenthesis,

minus, open parenthesis, 6 x plus 7, close parenthesis, equals 0

Question 9.What is the solution to the preceding equation?

A. x equals 6

B. x equals 1

C. x equals negative 0.2

D. x equals negative 1.2

Question 10.A manufacturer makes two different sizes of spherical ball bearings for use in motors. If the radius of the larger ball bearing is twice the radius of the smaller one, then the volume of the larger ball bearing is how many times the volume of the smaller one?

A. 2

B. 3

C. 6

D. 8


DirectionsFor questions 11 through 13, 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

seven slash two. (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


Example 1: If your answer is a fraction such as seven-twelfths, 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.



Example 3


Example 3: Acceptable ways to record two-thirds are: 2 slash 3, .666, and .667.



Example 4

Note: You may start your answers in any column, space permitting. Columns you don’t need to use should be left blank.


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.



Question 11.

If the equation y equals 2 times x squared, minus 5 x, plus 3 is graphed in the x y-plane, what is the value of its y-intercept?

Question 12.The solution to the following system of equations is the ordered pair x comma y.

3 x plus y equals 13, and,

2 x minus 4 y equals 18

What is the value of x ?

Question 13.A group of 12 friends went bowling. They each rented shoes for $3.00 a pair, and 4 friends bowled 2 games each, while 8 friends bowled 3 games each. Each game bowled cost each person the same amount. The total cost for the shoe rentals and the games bowled was $212.00. What was the cost, in dollars, of each game bowled? (Note: Disregard the $ sign when recording your answer.)

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


math test—no calculator · web viewmath test—no calculator 13 questions turn to section 3 of...

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