SAT® Practice Test #7
Math Test—No Calculator
20 Questions
Turn to Section 3 of your answer sheet to answer the questions in this section.
Directions
For questions1 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 functionfis the set of all real numbersxfor which fofx 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.
Aequals pi times the square ofr.
Cequals 2 pir.
Reference figure 2 is a rectangle with lengthℓand widthw. An equation is presented below reference figure2.
Aequalsℓw.
Reference figure 3 is a triangle with baseband heighth. An equation is presented below reference figure3.
Aequals onehalfbh.
Reference figure 4 is a right triangle. The two sides that form the right angle are labeledaandb, and the side opposite the right angle is labeledc. An equation is presented below reference figure4.
csquared equalsasquared plusbsquared.
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 lengthℓand widthwand whose height ish. An equation is presented below reference figure7.
Vequalsℓwh.
Reference figure 8 is a rightcircularcylinder whose base has radiusrand whose height ish. An equation is presented below reference figure8.
Vequalspitimes the square ofrtimesh.
Reference figure 9 is a sphere with radiusr. An equation is presented below reference figure9.
Vequalsfourthirds pi times the cube ofr.
Reference figure 10 is a cone whose base has radiusrand whose height ish. Anequation is presented below reference figure10.
Vequals onethird times pi times the square ofrtimesh.
Reference figure 11 is an asymmetrical pyramid whose base has lengthℓand widthwand whose height ish. An equation is presented below reference figure11.
Vequalsonethirdℓwh.
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 refers to the following equation.
x plus y, equals75
Question 1.
The preceding equation relates the number of minutes,x, Maria spends running each day and the number of minutes,y, she spends biking each day. In the equation, what does the number 75 represent?
A.The number of minutes spent running each day
B.The number of minutes spent biking each day
C.The total number of minutes spent running and biking each day
D.The number of minutes spent biking for each minute spent running
Question 2.
Which of the following is equivalent to3 times, open parenthesis, xplus 5, close parenthesis, minus6?
A.3x minus3
B.3x minus1
C.3x plus9
D.15x minus6
Question 3 refers to the following system of equations.
x equals, y minus3
and
the fraction x over 2, end fraction, plus 2y, equals6
Question 3.
Which ordered pairx comma y satisfies the preceding system of equations?
A.negative3 comma0
B.0 comma 3
C.6 comma negative3
D.36 comma negative6
Question 4.
Which of the following complex numbers is equal toopen parenthesis, 5 plus 12i, close parenthesis, minus, open parenthesis, 9isquared minus 6i, close parenthesis, foriequals, the square root of negative1?
A.negative14 minus 18i
B.negative4 minus 6i
C.4 plus 6i
D.14 plus 18i
Question 5.
Iff of x equals, the fraction with numerator xsquared minus 6x plus 3, and denominator x minus 1, end fraction, what is f of negative1?
A.negative5
B.negative2
C.2
D.5
Question 6.
A company that makes wildlife videos purchases camera equipment for $32,400. The equipment depreciates in value at a constant rate for 12years, after which it is considered to have no monetary value. How much is the camera equipment worth 4years after it is purchased?
A.$10,800
B.$16,200
C.$21,600
D.$29,700
Question 7 refers to the following expression.
x squared, plus 6x, plus 4
Question 7.
Which of the following is equivalent to the preceding expression?
A.open parenthesis, x plus 3, close parenthesis, squared, plus5
B.open parenthesis, x plus 3, close parenthesis, squared, minus5
C.open parenthesis, x minus 3, close parenthesis, squared, plus5
D.open parenthesis, x minus 3, close parenthesis, squared, minus5
Question 8.
Ken is working this summer as part of a crew on a farm. He earned $8perhour for the first 10hours he worked this week. Because of his performance, his crew leader raised his salary to $10perhour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for theweek?
A.38
B.33
C.22
D.16
Question 9.
Marisa needs to hire at least 10staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640per week, and senior directors, who will be paid $880per week. Her budget for paying the staff members is no more than $9,700per week. She must hire at least 3junior directors and at least 1senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?
A.
640x, plus 880y, is greater than or equal to9,700
x plus y is less than or equal to10
x is greater than or equal to3
y is greater than or equal to1
B.
640x, plus 880y, is less than or equal to9,700
x plus y is greater than or equal to10
x is greater than or equal to3
y is greater than or equal to1
C.
640x, plus 880y, is greater than or equal to9,700
x plus y is greater than or equal to10
x is less than or equal to3
y is less than or equal to1
D.
640x, plus 880y, is less than or equal to9,700
x plus y is less than or equal to10
x is less than or equal to3
y is less than or equal to1
Question 10 refers to the following equation.
a, times xcubed, plus bxsquared, plus cx, plus d, equals0
Question 10.
In the preceding equation, a, b, c, and d are constants. If the equation has roots negative1, negative3, and 5, which of the following is a factor of a, times xcubed, plus bxsquared, plus cx, plusd?
A.x minus1
B.x plus1
C.x minus3
D.x plus5
Question 11.
The expressionthe fraction with numerator x to the power negative2, end power, times y to the power one-half, and denominatorx to the power one-third, end power, times y to the power negative1, end fraction, wherex is greater than 1andy is greater than 1, is equivalent to which of the following?
A.the fraction with numerator the square root of y, and denominator the cube root of xsquared, end root
B.the fraction with numeratory times the square root of y, and denominator the cube root of xsquared, end root
C.the fraction with numeratory times the square root of y, and denominator xtimes the square root ofx, end fraction
D.the fraction with numeratory times the square root of y,and denominator xsquared times, the cube root ofx, end fraction
Question 12.
The function f is defined by f of x equals, open parenthesis, xplus 3, close parenthesis, times, open parenthesis, x plus 1, close parenthesis. The graph of f in the xyplane is a parabola. Which of the following intervals contains the xcoordinate of the vertex of the graphoff?
A.negative4 is less than x, which is less than negative3
B.negative3 is less than x, which is less than1
C.1 is less than x, which is less than3
D.3 is less than x, which is less than4
Question 13.
Which of the following expressions is equivalent to the fraction with numerator x squared, minus 2x, minus 5, and denominator x minus 3, end fraction?
A.x minus 5, minus the fraction with numerator 20, and denominator x minus 3, end fraction
B.x minus 5, minus the fraction with numerator 10, and denominator x minus 3, end fraction
C.x plus 1, minus the fraction with numerator 8, and denominator xminus 3, end fraction
D.x plus 1, minus the fraction with numerator 2, and denominator xminus 3, end fraction
Question 14.
A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. Therestriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130inches. The perimeter of the base is determined using the width and length of the box. Ifa box has a height of 60inches and its length is 2.5times the width, which inequality shows the allowable widthx, in inches, of the box?
A.0 is less than x, which is less than or equal to10
B.0 is less than x, which is less than or equal to 11 and two-thirds
C.0 is less than x, which is less than or equal to 17 and one-half
D.0 is less than x, which is less than or equal to20
Question 15.
The expressionone-third times, xsquared, minus 2can be rewritten asone-third times, open parenthesis, x minus k, close parenthesis, times, open parenthesis, x plus k, close parenthesis, where k is a positive constant. What is the valueofk?
A.2
B.6
C.The square root of2
D.The square root of6
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 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.
Question 16.
If2x plus 8, equals 16, what is the value ofxplus4?
Question 17 refers to the following figure.
Begin skippable figure description.
The figure presents line segments MQ and NR that intersect at pointP,where pointN is above and slightly to the right of pointM and pointQ is above and slightly to the left of pointR. Line segmentsMN, QR, and horizontal line segmentMR are drawn forming trianglesMNR and QMR. The measure of angleQPR is labeled 60degrees and the angle measure of MQR is labeled 70degrees.
End skippable figure description.
Question 17.
In the preceding figure, line segment MQand line segment NRintersect at pointP, NP equals QP, and MP equals PR. What is the measure, in degrees, of angle QMR? (Disregard the degree symbol when indicating your answer.)
Question 18.
The number of radians in a 720degree angle can be written as a,timespi, where a is a constant. What is the valueofa?
Question 19.
The graph of a line in the xyplane passes through the pointwith coordinates 1 comma 4and crosses the xaxis at the pointwith coordinates 2 comma 0. The line crosses the yaxis at the pointwith coordinates 0 comma b. What is the value ofb?
Question 20 refers to the following expression.
open parenthesis, 7,532, plus 100ysquared, close parenthesis, plus, 10, times, open parenthesis, 10ysquared minus 110, close parenthesis
Question 20.
The preceding expression can be written in the forma, times ysquared plus b, where a andb are constants. What is the value ofa, plusb?
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.
© 2017 The College Board.
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