# SAT Practice Test 2 Math Test: No Calculator, for Assistive Technology

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WF-5LSA07-NCM

Math TestNo Calculator20 Questions

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

DirectionsFor questions 1 through 15, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions16 through 20, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 16 on how to enter your answers in the grid. 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.

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 length and widthw. An equation is presented below reference figure2.A equals w.

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 TrianglesReference 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 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 InformationThe 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 S A TPage 1Copyright 2015 by the College BoardW F5LSA07Question 1.If 5x plus 6 equals 10, what is the value of 10x plus 3?A.4B.9C.11D.20

Explanation for question 1.

Question 2 is based on the following set of equations. x plus y equals 0 3x minus 2y equals 10Question 2.Which of the following ordered pairs parenthesis, x comma y, close parenthesis, satisfies the preceding system of equations?A. parenthesis, 3 comma negative 2, close parenthesisB. parenthesis, 2 comma negative 2, close parenthesisC. parenthesis, negative 2 comma 2, close parenthesisD. parenthesis, negative 2 comma negative 2, close parenthesis

Explanation for question 2.

Question 3.A landscaping company estimates the price of a job, in dollars, using the expression 60 plus 12nh, where n is the number of landscapers who will be working and h is the total number of hours the job will take using nlandscapers. Which of the following is the best interpretation of the number 12 in the expression?A.The company charges $12 per hour for each landscaper.B.A minimum of 12 landscapers will work on eachjob.C.The price of every job increases by $12 every hour.D.Each landscaper works 12 hours a day.

Explanation for question 3.Question 4 is based on the following expression. 9a, raised to the power 4, plus 12a, squared, bsquared, plus, 4b raised to the power4Question 4.Which of the following is equivalent to the preceding expression?A. parenthesis, 3a, squared, plus 2b squared, close parenthesis, squaredB. parenthesis, 3a, plus 2b, close parenthesis, raised to the power4C. parenthesis, 9a, squared, plus 4b squared, close parenthesis, squaredD. parenthesis, 9a, plus 4b, close parenthesis, raised to the power4

Explanation for question 4.

Question 5 is based on the following equation. the square root of 2k squared, plus 17, end square root, minusx equals0.Question 5.If k is greater than 0 and x equals 7 in the preceding equation, what is the value ofk?A.2B.3C.4D.5

Explanation for question 5.

Question 6 refers to the following figure.

Begin figure description.The figure presents two lines, k and , that slant upward and to the right on the xyplane. Line is to the left of linek. Two points on line are labeled with coordinates negative5 comma 0, and 0 comma 2. Two points on linek are labeled with coordinates 0 comma negative4, and p comma 0.End figure description.Question 6.In the preceding xyplane, line l is parallel to linek. What is the value ofp?A.4B.5C.8D.10

Explanation for question 6.

Question 7.If the fraction whose numerator is x raised to the power, a, squared, and whose denominator is x raised to the power bsquared, end fraction, equals, xraised to the power16, x is greater than 1, and a, plus b equals 2, what is the value of a, minusb?A.8B.14C.16D.18

Explanation for question 7.

Question 8 is based on the following formula. nA equals 360Question 8.The measureA, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the preceding formula. If the measure of an exterior angle of a regular polygon is greater than , 50degrees, what is the greatest number of sides it canhave?A.5B.6C.7D.8

Explanation for question 8.

Question 9.The graph of a line in the xyplane has slope2 and contains the point with coordinates 1 comma 8. The graph of a second line passes through the points with coordinates 1 comma 2, and 2 comma 1. If the two lines intersect at the point with coordinates a, comma b, what is the value of a, plus b?A.4B.3C. negative 1D. negative 4

Explanation for question 9.

Question 10.Which of the following equations has a graph in the xyplane for which y is always greater than or equal to negative 1?A. y equals the absolute value of x, end absolute value, minus2B. y equals x squared minus2C. y equals, parenthesis, x minus 2, close parenthesis, squaredD. y equals x cubed minus 2

Explanation for question10.

Question 11.Which of the following complex numbers is equivalent to the fraction 3minus 5i over 8 plus 2i, end fraction? (Note: i equals the square root of negative1.)A. the fraction 3 over 8, minus the fraction 5i over 2B. the fraction 3 over 8, plus the fraction 5i over 2C. the fraction 7 over 34, minus the fraction 23i over 34D. the fraction 7 over 34, plus the fraction 23i over 34

Explanation for question11.

Question 12 is based on the following formula. R equals, the fraction F, over N plus F, end fractionQuestion 12.A website uses the preceding formula to calculate a sellers rating,R, based on the number of favorable reviews,F, and unfavorable reviews,N. Which of the following expresses the number of favorable reviews in terms of the other variables?A. F equals the fraction RN over R minus 1, end fractionB. F equals the fraction RN over 1 minus R, end fractionC. F equals the fractionN over 1 minus R, end fractionD. F equals the fractionN over R minus 1, end fraction

Explanation for question12.

Question 13.What is the sum of all values of m that satisfy 2m squared minus 16m, plus 8, equals 0?A. negative 8B. negative 4 times the square root of 3C. 4 times the square root of 3D.8

Explanation for question13.

Question 14.A radioactive substance decays at an annual rate of 13percent. If the initial amount of the substance is 325grams, which of the following functions fmodels the remaining amount of the substance, in grams, tyears later?A. f of t equals 325, parenthesis, 0.87, close parenthesis, raised to the powertB. f of t equals 325, parenthesis, 0.13, close parenthesis, raised to the powertC. f of t equals 0.87, parenthesis, 325, close parenthesis, raised to the powertD. f of t equals 0.13, parenthesis, 325, close parenthesis, raised to the powert

Explanation for question14.

Question 15.The expression for the fraction whose numerator is 5x minus 2, and whose denominator is x plus 3, is equivalent to which of the following?A. the fraction 5 minus 2, over 3, end fractionB. 5 minus the fraction 2 over 3C. 5 minus the fraction, 2, over x plus 3, end fractionD. 5 minus the fraction, 17, over x plus 3, end fraction

Explanation for question15.

DirectionsFor questions 16 through 20, 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 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.The sales manager of a company awarded a total of $3000 in bonuses to the most productive salespeople. The bonuses were awarded in amounts of $250 or $750. If at least one $250 bonus and at least one $750 bonus were awarded, what is one possible number of $250 bonuses awarded?

Explanation for question16.

Question 17 is based on the following equation. 2x, parenthesis, 3x plus 5, close parenthesis, plus 3, parenthesis, 3x plus 5, close parenthesis, equals, a, xsquared, plus bx, pluscQuestion 17.In the preceding equation, a, b, and c are constants. If the equation is true for all values of x, what is the value of b?

Explanation for question17.

Question 18 refers to the following figure.

Begin skippable figure description.The figure presents two triangles formed by two intersecting line segments and two horizontal line segments. The two intersecting line segments intersect at a point labeledB. The upper triangle is labeled CDB, where sideCD is horizontal and C is to the left of D. The lower triangle is labeled AEB, where sideAE is horizontal and A is to the left of E. In the upper triangle, sideDB is labeled5, and in the lower triangle, sideAB is labeled 10 and sideBE is labeled8.End skippable figure description.Question 18.In the preceding figure, line segmentAE is parallel to line segmentCD, and segment AD intersects segment CE at B. What is the length of segment CE?

Explanation for question18.

Question 19 refers to the following figure.

Begin skippable figure description.The figure presents a circle in the xyplane. The horizontal axis is labeledx, the vertical axis is labeledy, and the origin is labeledO. The circle intersects the xaxis to the right of the origin at a point labeledB. A line is drawn from the origin upward and to the right to a point on the circle labeledA. The coordinates of pointA are the squareroot of 3 comma1.End skippable figure description.Question 19.In the preceding xyplane, O is the center of the circle, and the measure of angleAOB is the fraction pi over a,radians. What is the value of a?

Explanation for question19.

Question 20 is based on the following system of equations. a,x plus by, equals 12 2x plus 8y, equals 60Question 20.In the preceding system of equations, a and b are constants. If the system has infinitely many solutions, what is the value of the fraction a, overb?

Explanation for question20.

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

Answers and explanations for questions1 through20 are provided in the next section of this document.

Answers and Explanations for Questions1 through20

Explanation for question 1.Choice C is correct. Subtracting 6 from each side of 5x plus 6 equals10 yields 5x equals4. Dividing both sides of 5x equals4 by 5 yields x equals fourfifths. The value of x can now be substituted into the expression 10x plus 3, giving 10, parenthesis, fourfifths, close parenthesis, plus 3, equals11.

Alternatively, the expression 10x plus 3 can be rewritten as 2,parenthesis, 5x plus 6, close parenthesis, minus9, and 10 can be...

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