SAT Practice Test 3 Math Test: No Calculator, for Assistive Technology
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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.
Begin skippable figure descriptions.The figure presents information for your reference in solving some of theproblems.
Reference figure1 is a circle with radiusr. Two equations are presented below reference figure1.A equals pi times the square ofr.C equals 2 pir.
Reference figure2 is a rectangle with length and widthw. An equation is presented below reference figure2.A equals w.
Reference figure3 is a triangle with baseb and heighth. An equation is presented below reference figure3.A equals onehalfbh.
Reference figure4 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 bsquared.
Special Right TrianglesReference figure5 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 labeledx times the squareroot of3. The side opposite the right angle is labeled2x.
Reference figure6 is a right triangle with two 45degree angles. Two sides are each labeleds. The side opposite the rightangle is labeleds times the squareroot of2.
Reference figure7 is a rectangular solid whose base has length and widthw and whose height ish. An equation is presented below reference figure7.V equalswh.
Reference figure8 is a right circularcylinder whose base has radiusr and whose height ish. An equation is presented below reference figure8.V equalspitimes the square of rtimesh.
Reference figure9 is a sphere with radiusr. An equation is presented below reference figure9.V equalsfourthirds pi times the cube ofr.
Reference figure10 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 figure11 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 21Copyright 2015 by the College BoardW F5LSA08Question 1.A painter will paint n walls with the same size and shape in a building using a specific brand of paint. The painters fee can be calculated by the expression nKlh, where n is the number of walls, K is a constant with units of dollars per square foot, l is the length of each wall in feet, and h is the height of each wall in feet. If the customer asks the painter to use a more expensive brand of paint, which of the factors in the expression would change?A.h
Explanation for question 1.
Question 2.If 3r equals18, what is the value of 6r plus 3?A.6B.27C.36D.39
Explanation for question 2.
Question 3.Which of the following is equal to a, raised to the power two thirds, for all values ofa?
A. the square root of a, raised to the power one third, end root
B. the square root of a, cubed, end root
C. the cube root of a, raised to the power one half, end root
D. the cube root of a, squared, end root
Explanation for question 3.
Question 4.The number of states that joined the UnitedStates between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30states joined the UnitedStates between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true?
A. 30x equals 2
B. 2x equals 30
C.the fractionx over 2 equals 30
D.x plus 30 equals 2
Explanation for question 4.
If the fraction 5 over x equals the fraction whose numerator is 15 and whose denominator is x plus 20 end fraction, what is the value of the fraction x over5?
D. one half
Explanation for question 5.
Question 6 refers to the following equations.
2x minus 3y equals negative 14
3x minus 2y equals negative 6Question 6.
If the ordered pair x comma y is a solution to the preceding system of equations, what is the value of x minusy?
A. negative 20
B. negative 8
C. negative 4D.8
Explanation for question 6.Question 7 refers to the following table.x fofx
The function f is defined by a polynomial. Some values of x and f of x are shown in the preceding table. Which of the following must be a factor of fofx?
A. x minus 2
B. x minus 3
C. x minus 4
D. x minus 5
Explanation for question 7.
The line y equals kx plus 4, where k is a constant, is graphed in the xyplane. If the line contains the point with coordinates c comma d, where c is not equal to 0 and d is not equal to 0, what is the slope of the line in terms of candd?
A. the fraction d minus 4, over c
B. the fraction c minus 4, over d
C. the fraction 4 minus d, over c
D. the fraction 4 minus c, over d
Explanation for question 8.
Question 9 refers to the following system of equations. kx minus 3y equals 4 4x minus 5y equals 7Question 9.In the preceding system of equations, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?
A. the fraction 12 over 5
B. the fraction 16 over 7
C. the negative fraction 16 over 7
D. the negative fraction 12 over 5
Explanation for question 9.
In the xyplane, the parabola with equation y equals, parenthesis, xminus 11, close parenthesis, squared, intersects the line with equation yequals 25 at two points, A and B. What is the length of line segment AB?A.10B.12C.14D.16
Explanation for question10.
Question 11 refers to the following figure.
Begin skippable figure description.The figure presents three lines k, l, and m that intersect at a point. The three lines form six angles at the point of intersection. The horizontal line is labeledm, the line that slants upward and to the right is labeledl, and the line that slants downward and to the right is labeledk. Of the 6 angles, 3 angles are above linem, and 3 angles are below linem. Starting from the leftmost angle above linem and going clockwise, the 6 angles are labeled xdegrees, ydegrees, zdegrees, tdegrees, udegrees, and wdegrees, respectively.End skippable figure description.
In the preceding figure, lines k, l, and m intersect at a point. If xplus y equals u plus w, which of the following must be true?
I. x equals z
II. y equals w
III. z equals t
A.I and II onlyB.I and III onlyC.II and III onlyD.I, II, and III
Explanation for question11.
Question 12 refers to the following quadratic equation.
y equals a, parenthesis, x minus 2, close parenthesis, times, parenthesis, x plus 4, close parenthesis
In the preceding quadratic equation, a is a nonzero constant. The graph of the equation in the xyplane is a parabola with vertex with coordinates ccommad. Which of the following is equal tod?
A. negative 9 a
B. negative 8 a
C. negative 5 a
D. negative 2 a
Explanation for question12.
The equation with the fraction whose numerator is 24x squared, plus 25x minus 47, and whose denominator is a,x minus 2, equals, negative 8x minus 3, minus, the fraction whose numerator is 53, and whose denominator is a,x minus 2, is true for all values of x that do not equal the fraction, 2 over a, where a is a constant. What is the value ofa?
A. negative 16
B. negative 3C.3D.16
Explanation for question13.
What are the solutions to 3x squared, plus 12x plus 6, equals0?
A. x equals negative 2, plus or minus the square root of 2
B. x equals negative 2, plus or minus, the fraction the square root of 30, end square root, over 3
C. x equals negative 6, plus or minus the square root of 2
D. x equals negative 6, plus or minus, 6 times the square root of 2
Explanation for question14.
Question 15 refers to the following equation.
C equals five ninths, parenthesis F minus 32 close parenthesisQuestion 15.The preceding equation shows how a temperatureF, measured in degrees Fahrenheit, relates to a temperatureC, measured in degrees Celsius. Based on the equation, which of the following must be true?
I.A temperature increase of 1degree Fahrenheit is equivalent to a temperature increase of five ninths degree Celsius.II.A temperature increase of 1degree Celsius is equivalent to a temperature increase of 1.8degrees Fahrenheit.
III.A temperature increase of five ninths degree Fahrenheit is equivalent to a temperature increase of 1degree Celsius.A.I onlyB.II onlyC.III onlyD.I and II only
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.
Begin skippable figure description.Example 3: Acceptable ways to record twothirds are: 2 slash 3, .666, and .667.End skippable figure description.
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 refers to the following equation.
x cubed, parenthesis, x squared minus 5, close parenthesis, equals negative 4xQuestion 16.
If x is greater than 0, what is one possible solution to the preceding equation?
Explanation for question16.
If seven ninths x, minus four ninths x, equals, one fourth plus five twelfths what is the value ofx?
Explanation for question17.
Question 18 refers to the following figure.
Begin skippable figure description.The figure presents two triangles that have one vertex in common. The two triangles, one on the left and one on the right, each have a vertical side opposite the common vertex, and the other two sides in each triangle are marked showing that both sides are equal in length. In the triangle on the left, the angle at the common vertex is labeled ydegrees, and in the triangle on the right, the angle at the common vertex is labeled zdegrees. The exterior angle of the triangle on the right that is between one of the equal sides and the vertical line extended from the vertical side is labeled xdegrees.End skippable figure description.
Two isosceles triangles are shown in the preceding figure. If 180minus z equals 2y and y equals 75, what is the value ofx?
Explanation for question18.
Question 19.At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2hamburgers and 3orders of fries have a total of 1700calories, how many calories does a hamburger have?
Explanation for question19.
In triangle ABC, the measure of angle B is 90 degrees, BCequals 16, and AC equals 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is one third the length of the corresponding side of triangle ABC. What is the value of sineF?
Explanation for question20.
StopIf 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. The painters fee is given by nKlh where n is the number of walls, K is a constant with units of dollars per square foot, l is the length of each wall in feet, and h is the height of each wall in feet. Examining this equation shows that l and h will be used to determine the area of each wall. The variable n is the number of walls, so n times the area of the walls will give the amount of area that will need to be painted. The only remaining variable is K, which represents the cost per square foot and is determined by the...