SAT Practice Test 6 for Assistive Technology Math Test, No Calculator | SAT Suite of Assessments The College Board

The SATPractice Test #6Math TestNo Calculator

20 Questions

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

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 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 functionf is the set of all real numbersx 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 radiusr. Two equations are presented below reference figure1.

A equals pi times the square ofr.

C equals 2 pir.

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

A equals w.

Reference figure 3 is a triangle with baseb 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 labeleda andb, and the side opposite the right angle is labeledc. 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 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 length and widthw and whose height ish. An equation is presented below reference figure7.

V equalswh.

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 length and widthw and whose height ish. An equation is presented below reference figure11.

V equalsonethirdwh.

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.

Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a onetime service fee for processing the purchase of the tickets. The equation Tequals 15n plus12 represents the total amountT, in dollars, Salim will pay for ntickets. What does 12 represent in the equation?

A.The price of oneticket, in dollars

B.The amount of the service fee, in dollars

C.The total amount, in dollars, Salim will pay for oneticket

D.The total amount, in dollars, Salim will pay for any number of tickets

Question 2.

A gardener buys two kinds of fertilizer. FertilizerA contains 60%filler materials by weight and FertilizerB contains 40%filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240pounds of filler materials. Which equation models this relationship, where x is the number of pounds of FertilizerA and y is the number of pounds of FertilizerB?

A. 0.4x, plus, 0.6y, equals240

B. 0.6x, plus, 0.4y, equals240

C. 40x, plus, 60y, equals240

D. 60x, plus, 40y, equals240

Question 3.

What is the sum of the complex numbers 2plus3i and 4plus8i, where iequals the square root of negative1?

A.17

B.17i

C. 6plus11i

D. 8plus24i

Question 4 refers to the following equation.

4x squared minus9, equals, open parenthesis, px plust, close parenthesis, times, open parenthesis, px minust, close parenthesis

Question 4.

In the preceding equation, p and t are constants. Which of the following could be the valueofp?

A.2

B.3

C.4

D.9

Question 5.

Which of the following is the graph of the equation yequals 2x minus5 in the xyplane?

Each option presents the graph of a line in the xyplane with the origin labeledO. The numbers negative5 and 5 are indicated on each axis.

A.

Begin skippable figure description.

The line begins in quadrant3 and moves upward and to the right. It crosses the xaxis at negative5 and the yaxis at 2.5, ending in quadrant1.

End skippable figure description.

B.

Begin skippable figure description.

The line begins in quadrant2 and moves downward and to the right. It crosses the xaxis at negative2.5 and the yaxis at negative5, ending in quadrant4.

End skippable figure description.

C.

Begin skippable figure description.

The line begins in quadrant3 and moves upward and to the right. It crosses the xaxis at negative2.5 and the yaxis at 5, ending in quadrant1.

End skippable figure description.

D.

Begin skippable figure description.

The line begins in quadrant3 and moves upward and to the right. It crosses the yaxis at negative5 and the xaxis at 2.5, ending in quadrant1.

End skippable figure description.

Question 6.

If xequals twothirdsy and yequals18, what is the value of 2xminus3?

A.21

B.15

C.12

D.10

Question 7.

A bricklayer uses the formula nequals7lh to estimate the number of bricks,n, needed to build a wall that is lfeet long and hfeet high. Which of the following correctly expresses l in terms of nandh?

A. l equals the fraction whose numerator is 7 and whose denominator is nh, end fraction

B. l equals the fraction whose numerator is h and whose denominator is 7n, end fraction

C. l equals the fraction whose numerator is n and whose denominator is 7h, end fraction

D. l equals the fraction whose numerator is n and whose denominator is 7plush, end fraction

Question 8 refers to the following figure.

Begin skippable figure description.

The figure presents a 3column table with 5 rows of data. The heading for column1 is x, the heading for column2 is wofx, and the heading for column3 is tofx. The five rows of data are as follows.

Row 1: x, 1; wofx, negative1; tofx, negative3.

Row 2: x, 2; wofx, 3; tofx, negative1.

Row 3: x, 3; wofx, 4; tofx,1.

Row 4: x, 4; wofx, 3; tofx,3.

Row 5: x, 5; wofx, negative1; tofx,5.

End skippable figure description.Question 8.

The preceding table shows some values of the functionsw andt. For which value ofx is wofx plus tofx equaltox?

A.1

B.2

C.3

D.4

Question 9.

If the square root ofx, end root, plus the square root of9, end root, equals the square root of64, what is the valueofx?

A. the square root of5

B.5

C.25

D.55

Question 10.

Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280miles per week for 4weeks. He bicycled 240miles the firstweek, 310miles the secondweek, and 320miles the thirdweek. Which inequality can be used to represent the number of miles,x, Jaime could bicycle on the 4thweek to meet hisgoal?

A. the fraction whose numerator is 240 plus 310 plus 320, and whose denominator is 3, end fraction, plusx, is greater than or equal to280

B. 240 plus 310 plus 320, is greater than or equal tox times280

C. the fraction 240 over 4, end fraction, plus the fraction 310 over 4, end fraction, plus the fraction 320 over 4, end fraction, plusx, is greater than or equal to280

D. 240 plus 310 plus 320 plusx, is greater than or equal to 4times,280

Question 11 refers to the following figure.

Begin skippable figure description.

The figure presents a parabola labeled, y equals axsquared plusc, in the xyplane with the origin labeledO. The parabola opens upward and its vertex lies on the yaxis a short distance above the origin.

End skippable figure description.Question 11.

The vertex of the preceding parabola in the xyplane is the point with coordinates 0commac. Which of the following is true about the parabola with the equation yequals negativea, times, open parenthesis, xminusb, close parenthesis, squared, plusc?

A.The vertex is the point with coordinates bcommac, and the graph opens upward.

B.The vertex is the point with coordinates bcommac, and the graph opens downward.

C.The vertex is the point with coordinates negativebcommac, and the graph opens upward.

D.The vertex is the point with coordinates negativebcommac, and the graph opens downward.

Question 12.

Which of the following is equivalent to the fraction whose numerator is 4xsquared, plus, 6x, and whose denominator is 4xplus2, end fraction?

A.x

B. x plus 4

C. x minus the fraction whose numerator is 2, and whose denominator is 4x plus2, end fraction

D. x plus 1 minus the fraction whose numerator is 2, and whose denominator is 4xplus2, end fraction

Question 13 refers to the following equation.

2xsquared minus 4x equalst

Question 13.

In the preceding equation, t is a constant. If the equation has no real solutions, which of the following could be the valueoft?

A. negative 3

B. negative 1

C.1

D.3

Question 14.

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300pounds in a shipment. Each container of detergent weighs 7.35pounds, and each container of fabric softener weighs 6.2pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

A.

7.35d, plus, 6.2s, is less than or equal to 300, and,

d is greater than or equal to 2s

B.

7.35d, plus, 6.2s, is less than or equal to 300, and,

2d is greater than or equal tos

C.

14.7d, plus, 6.2s, is less than or equal to 300, and,

d is greater than or equal to 2s

D.

14.7d, plus, 6.2s, is less than or equal to 300, and,

2d is greater than or equal tos

Question 15.

Which of the following is equivalent to open parenthesis, a, plus the fraction b over 2, close parenthesis, squared?

A. a, squared, plus the fraction bsquared over2

B. a, squared, plus the fraction bsquared over4

C. a, squared, plus the fraction ab over 2, end fraction, plus the fraction bsquared over2

D. a, squared, plus ab, plus the fraction bsquared over4

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 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, spacepermitting. Columns you dont 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 a, to the power of the fraction b over 4, end power, equals16 for positive integers a and b, what is one possible valueofb?

Question 17 refers to the following equation.

twothirdst equals fivehalves

Question 17.

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

Question 18 refers to the following figure.

Begin skippable figure description.

The figure presents triangleACE, with horizontal sideAC. SideAE is perpendicular to sideAC such that pointE is above pointA. PointB lies on horizontal sideAC, pointD lies on hypotenuse CE, and linesegmentBD is drawn such that it is parallel to sideAE and forms triangleCDB. SideAE is labeled18, sideBC is labeled8, sideBD is labeled6, and a right angle symbol is at pointA.

End skippable figure description.Question 18.

In the preceding figure, sideBD is parallel to sideAE. What is the length of sideCE?

Question 19.

How many liters of a 25%saline solution must be added to 3liters of a 10%saline solution to obtain a 15%saline solution?

Question 20.

Points A and B lie on a circle with radius1, and arc AB has length piover3. What fraction of the circumference of the circle is the length of arc AB?

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.

2016 The College Board.

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