College Board

SAT® Math Test—No Calculator

Practice Test #8

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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 lengthℓ and widthw. An equation is presented below reference figure2.

A equals ℓw.

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 lengthℓ and widthw and whose height ish. An equation is presented below reference figure7.

V equalsℓwh.

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

V equalsonethirdℓwh.

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.

3x plus x, plus x, plus x, minus 3, minus 2, equals 7 plus x, plusx

Question 1.

In the preceding equation, what is the value ofx?

A. negative fivesevenths

B.1

C. twelvesevenths

D.3

Question 2 refers to the following figure.

Begin skippable figure description.

The figure presents the graph of a line in the coordinate plane. The horizontal maxis is labeled “Time, in minutes,” and the numbers 0 through 7 are indicated. The vertical daxis is labeled “Distance traveled, in feet,” and the numbers 0 through 7 are indicated. The line passes through the points with coordinates 1 comma 2 and 3 comma6.

End skippable figure description.
Question 2.

The preceding graph shows the distance traveledd, in feet, by a product on a conveyor belt mminutes after the product is placed on the belt. Which of the following equations correctly relates d andm?

A. dequals2m

B. d equals, onehalfm

C. d equals m, plus2

D. d equals 2m, plus2

Question 3 refers to the following information.

The following formula is often used by project managers to compute E, the estimated time to complete a job, where O is the shortest completion time, P is the longest completion time, and M is the most likely completion time.

E equals, the fraction with numerator O, plus 4M, plus P, and denominator6

Question 3.

Which of the following correctly gives P in terms of E, O, andM?

A. P equals, 6E, minus O, minus4M

B. P equals, negative6E, plus O, plus4M

C. P equals, the fraction with numerator O, plus 4M, plus E, and denominator6

D. P equals, the fraction with numerator O, plus 4M, minus E, and denominator6

Question 4 refers to the following figure.

Begin skippable figure description.

The figure presents triangleRTU, with RU horizontal, and U to the right of R. A pointV is on RU, such that V is closer to R than it is to U. VertexT is above RU. The angle at T is labeled 114degrees. SideUT is extended to pointS, above vertexR, and line segmentSV is drawn. The angle to the right of SV and below ST is labeled 31degrees. The angle to the left of SV and above RV is labeled xdegrees.

End skippable figure description.
Question 4.

In the preceding figure, RT equals, TU. What is the value ofx?

A.72

B.66

C.64

D.58

Question 5.

The width of a rectangular dance floor is wfeet. The length of the floor is 6feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms ofw?

A. 2w plus6

B. 4w plus12

C. wsquared plus6

D. wsquared plus6w

Question 6 refers to the following system of inequalities.

y is greater than 2x minus1,

and,

2x is greater than5

Question 6.

Which of the following consists of the ycoordinates of all the points that satisfy the preceding system of inequalities?

A. y is greater than6

B. y is greater than4

C. y is greater than fivehalves

D. y is greater than threehalves

Question 7 refers to the following equation.

the square root of 2x plus 6, end root, plus 4 equals, x plus3

Question 7.

What is the solution set of the preceding equation?

A. set consisting of negative1

B. set consisting of5

C. set consisting of negative1 and5

D. set consisting of 0, negative1, and5

Question 8 refers to the following functions.

f of x equals, xcubed minus,9x,

and,

g of x equals, xsquared, minus 2x, minus3

Question 8.

Which of the following expressions is equivalent to the fraction f of x over gofx, for x is greater than3?

A. the fraction with numerator 1, and denominator x plus 1, end fraction

B. the fraction with numerator x plus 3, and denominator x plus 1, end fraction

C. the fraction with numerator x times, open parenthesis, x minus 3, close parenthesis, and denominator x plus 1, end fraction

D. the fraction with numerator x times, open parenthesis, x plus 3, close parenthesis, and denominator x plus 1, end fraction

Question 9 refers to the following equation.

open parenthesis, x minus 6, close parenthesis, squared, plus, open parenthesis, y plus 5, close parenthesis, squared, equals 16

Question 9.

In the xyplane, the graph of the preceding equation is a circle. PointP is on the circle and has coordinates 10 comma negative5. If line segmentPQ is a diameter of the circle, what are the coordinates of pointQ?

A. 2 comma negative5

B. 6 comma negative1

C. 6 comma negative5

D. 6 comma negative9

Question 10.

A group of 202people went on an overnight camping trip, taking 60tents with them. Some of the tents held 2people each, and the rest held 4people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2person tents?

A.30

B.20

C.19

D.18

Question 11 refers to the following figure.

Begin skippable figure description.

The figure presents the graph of a curve in the xyplane with the origin labeledO. The numbers negative3 through 3 appear along the xaxis. The numbers negative10 and 10 appear on the yaxis. The curve begins to the left of the yaxis and above the xaxis, moves downward and to the right, crossing the xaxis at negative3, continues to go down until it reaches a minimum point. Then it starts going upward and to the right, reaches the origin, and then it curves downward again to another minimum point. The curve goes up again, crossing the xaxis at 2, and extends to the right of the yaxis above the xaxis.

End skippable figure description.

Question 11.

Which of the following could be the equation of the preceding graph?

A. y equals, x times, open parenthesis, x minus 2, close parenthesis, times, open parenthesis, x plus 3, close parenthesis

B. y equals, xsquared times, open parenthesis, x minus 2, close parenthesis, times, open parenthesis, x plus 3, close parenthesis

C. y equals, x times, open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x minus 3, close parenthesis

D. y equals, xsquared times, open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x minus 3, close parenthesis

Question 12.

If the fraction with numerator 2a, and denominator b, end fraction, equals, onehalf, what is the value of the fraction b overa?

A. oneeighth

B. onefourth

C.2

D.4

Question 13.

Oil and gas production in a certain area dropped from 4million barrels in 2000 to 1.9million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functionsf best models the production, in millions of barrels, tyears after the year2000?

A. f of t equals, the fraction 21 over 130, end fraction, times t plus4

B. f of t equals, the fraction 19 over 130, end fraction, times t plus4

C. f of t equals, the negative fraction 21 over 130, end fraction, times t plus4

D. f of t equals, the negative fraction 19 over 130, end fraction, times t plus4

Question 14 refers to the following system of equations.

y equals, xsquared, plus 3x, minus7,

and,

y minus 5x, plus 8, equals0

Question 14.

How many solutions are there to the preceding system of equations?

A.There are exactly 4solutions.

B.There are exactly 2solutions.

C.There is exactly 1solution.

D.There are no solutions.

Question 15 refers to the following functions.

g of x equals, 2x minus1,

and,

h of x equals, 1 minus gofx

Question 15.

The preceding functionsg and h are defined. What is the value of hof0?

A. negative2

B.0

C.1

D.2

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 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 refers to the following equation.

xsquared plus x, minus 12, equals0