Math Test—No Calculator - The SAT Suite of …



Math Test—No Calculator20 QuestionsTurn 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 indicate your answer choice on your answer sheet. For questions?16 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 question?16 on how to record your answers in the spaces provided. 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 numberReferenceBegin skippable figure descriptions.The figure presents information for your reference in solving some of the?problems.Reference figure 1 is a circle with radius?r. Two equations are presented below reference figure?1.A?equals pi times the square of?r.C equals 2 pi?r.Reference figure 2 is a rectangle with length?? and width?w. An equation is presented below reference figure?2.A?equals ??w.Reference figure 3 is a triangle with base?b and height?h. An equation is presented below reference figure?3.A?equals one half?b?h.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 figure?4.c squared equals a?squared plus b?squared.Special Right TrianglesReference figure 5 is a right triangle with a 30?degree angle and a 60?degree angle. The side opposite the 30?degree angle is labeled?x. The side opposite the 60?degree angle is labeled?x?times the square?root of?3. The side opposite the right angle is labeled?2?x.Reference figure 6 is a right triangle with two 45?degree angles. Two sides are each labeled?s. The side opposite the right?angle is labeled?s?times the square?root of?2.Reference figure 7 is a rectangular solid whose base has length?? and width?w and whose height is?h. An equation is presented below reference figure?7.V equals???w?h.Reference figure 8 is a right?circular?cylinder whose base has radius?r and whose height is?h. An equation is presented below reference figure?8.V equals?pi?times the square of r?times?h.Reference figure 9 is a sphere with radius?r. An equation is presented below reference figure?9.V equals?four thirds pi times the cube of?r.Reference figure 10 is a cone whose base has radius?r and whose height is?h. An?equation is presented below reference figure?10.V equals one third times pi times the square of r?times?h.Reference figure 11 is an asymmetrical pyramid whose base has length?? and width?w and whose height is?h. An equation is presented below reference figure?11.V equals?one third???w?h.End skippable figure descriptions.Additional Reference InformationThe number of degrees of arc in a circle is?360.The number of radians of arc in a circle is 2?pi.The sum of the measures in degrees of the angles of a triangle is?180.Question 1 is based on the following equation. 2?z plus 1, equals?zQuestion 1.What value of z satisfies the preceding equation?A.? negative?2B.? negative?1C.? one halfD.?1Question 2.A television with a price of $300 is to be purchased with an initial payment of $60 and weekly payments of $30. Which of the following equations can be used to find the number of weekly payments, w, required to complete the purchase, assuming there are no taxes or fees?A.? 300 equals, 30?w minus?60B.? 300 equals,?30?wC.? 300 equals, 30?w plus?60D.? 300 equals, 60?w minus?30Question 3 is based on the following table.Shipping ChargesMerchandise weight (pounds)Shipping charge5$16.9410$21.8920$31.7940$51.59Question 3.The preceding table shows shipping charges for an online retailer that sells sporting goods. There is a linear relationship between the shipping charge and the weight of the merchandise. Which function can be used to determine the total shipping charge f?of?x, in dollars, for an order with a merchandise weight of x?pounds?A.? f of x equals,?0.99?xB.? f of x equals, 0.99?x, plus?11.99C.? f of x equals,?3.39?xD.? f of x equals, 3.39?x, plus?16.94Question 4 is based on the following figure.Begin skippable figure description.The figure presents the graph of a line in the x?yplane, with the origin labeled O. The numbers 1 through 6, in increments of 1, are indicated on the xaxis. The numbers 7 through 42, in increments of 7, are indicated on the yaxis. The line is labeled “y, equals h of x,” and begins at the origin. The line slants upward and to the right, and passes through the point with coordinates 2 comma 14, and the point with coordinates 5?comma?35.End skippable figure description.Question 4.The line in the preceding x?yplane represents the relationship between the height h?of?x, in feet, and the base diameter?x, in feet, for cylindrical Doric columns in ancient Greek architecture. How much greater is the height of a Doric column that has a base diameter of 5?feet than the height of a Doric column that has a base diameter of 2?feet?A.?7?feetB.?14?feetC.?21?feetD.?24?feetQuestion 5 is based on the following expression. the square root of 9?x?squared, end rootQuestion 5.If x is greater than 0, which of the following is equivalent to the given?expression?A.?3?xB.? 3?x?squaredC.?18?xD.? 18?x to the fourth powerQuestion 6 is based on the following equation. the fraction with numerator x?squared, minus 1, and denominator x?minus 1, end fraction, equals negative?2Question 6.What are all values of x that satisfy the preceding equation?A.? negative?3B.?0C.?1D.? negative?3 and negative?1Question 7 is based on the following figure.Begin skippable figure description.The figure presents the graph of a curve in the x?yplane, with the origin labeled O. The numbers negative?6 through 6, in increments of 2, are indicated on the xaxis. The numbers negative?2 through 4, in increments of 2, are indicated on the yaxis. The curve is labeled “y, equals f of x.” It goes through the point with approximate coordinates one half comma 5, curves downward and to the left, and crosses the yaxis at the point with coordinates 0 comma 4. It curves further downward and to the left, and approaches the xaxis closely at x equals negative?5, moves all the way left closely to, but never touching, the xaxis.End skippable figure description.Question 7.The graph of y equals, f of x is shown in the x?yplane. What is the value of f?of?0??A.?0B.?2C.?3D.?4Question 8 is based on the following figure.Begin skippable figure description.The figure presents horizontal line segment?A?D, with point?D to the right of point?A. Point?B lies on line segment?A?D and point?C is vertically above point?B, such that line segment?B?C is perpendicular to A?D. Two line segments are drawn from point?B between line segments?B?C and B?D, dividing angle?C?B?D into three angles labeled x?degrees, 2?x?degrees, and 2?x?degrees.End skippable figure description.Question 8.In the preceding figure, point?B lies on line segment?A?D. What is the value of?3?x??A.?18B.?36C.?54D.?72Question 9 is based on the following figure.Begin skippable figure description.The figure presents the graph of line?l in the x?yplane, with the origin labeled O. The numbers negative?4 through 4, in increments of 2, are indicated on each axis. The line slants downward and to the right, crossing the xaxis at negative?4, and crossing the yaxis at negative?4.End skippable figure description.Question 9.Which of the following is an equation of line l in the preceding x?yplane?A.? x minus y, equals negative?4B.? x minus y, equals?4C.? x plus y, equals negative?4D.? x plus y, equals?4Question 10 is based on the following figure.Begin skippable figure description.The figure presents the graph of a parabola in the x?yplane, with the origin labeled O. No numbers are indicated on the xaxis. A number k is indicated on the yaxis above the origin. The parabola opens upward. It begins to the left of the yaxis, above the xaxis, and moves downward and to the right. It crosses the xaxis, turns just below the xaxis, crosses the xaxis again, and moves upward and to the right. It crosses the yaxis at k before it ends.End skippable figure description.Question 10.The graph of y equals, 2?x?squared, plus 10?x, plus 12 is shown. If the graph crosses the yaxis at the point with coordinates 0?comma?k, what is the value of?k??A.?2B.?6C.?10D.?12Question 11.A circle in the x?yplane has center with coordinates 5 comma 7 and radius?2. Which of the following is an equation of the circle?A.? open parenthesis, x minus 5, close parenthesis, squared, plus, open parenthesis, y minus 7, close parenthesis, squared, equals?4B.? open parenthesis, x plus 5, close parenthesis, squared, plus, open parenthesis, y plus 7, close parenthesis, squared, equals?4C.? open parenthesis, x minus 5, close parenthesis, squared, plus, open parenthesis, y minus 7, close parenthesis, squared, equals?2D.? open parenthesis, x plus 5, close parenthesis, squared, plus, open parenthesis, y plus 7, close parenthesis, squared, equals?2Question 12 is based on the following figure.Begin skippable figure description.The figure presents triangle?A?B?C and a bigger triangle?D?E?F. Angle?A and angle?D are both marked with the right angle symbol. Side?A?B is labeled 12, side?A?C is labeled 5, and side?B?C is labeled 13. The sides of triangle?D?E?F are not?labeled.End skippable figure description.Question 12.In the preceding figure, triangle?A?B?C is similar to triangle?D?E?F. What is the value of the cosine of?E??A.? 12?over?5B.? 12?over?13C.? 5?over?12D.? 5?over?13Question 13.In the x?yplane, the graph of the function f of x, equals, x?squared, plus 5?x, plus 4 has two xintercepts. What is the distance between the xintercepts?A.?1B.?2C.?3D.?4Question 14 is based on the following equation. the square root of 4?x, end root, equals, x?minus?3Question 14.What are all values of x that satisfy the given equation?Value?1. 1Value?2. 9A.?Value?1 onlyB.?Value?2 onlyC.?Value?1 and value?2D.?Neither value?1 nor value?2Question 15 is based on the following two equations. Equation?1: negative?3?x, plus y, equals 6. Equation?2: a?x, plus 2?y, equals?4.Question 15.In the preceding system of equations, a is a constant. For which of the following values of a does the system have no solution?A.? negative?6B.? negative?3C.?3D.?6DirectionsFor 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 bubbles accurately. You will receive credit only if the bubbles are filled in correctly.2.?Mark no more than one bubble 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 seven slash two. (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 2Begin skippable figure description.Example 1: If your answer is a fraction such as seven twelfths, it should be recorded as follows. Enter 7 in the first space, the fraction?bar (a?slash) 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 3Begin skippable figure description.Example 3: Acceptable ways to record two thirds are: 2 slash 3, .666, and .667.End skippable figure description.Example 4Note: You may start your answers in any column, space permitting. 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 is based on the following equation. T equals, 5?c, plus?12?fQuestion 16.A manufacturer shipped units of a certain product to two locations. The preceding equation shows the total shipping cost?T, in dollars, for shipping c?units to the closer location and shipping f?units to the farther location. If the total shipping cost was $47,000 and 3000?units were shipped to the farther location, how many units were shipped to the closer location?Question 17 is based on the following equation. the absolute value of, 2?x, plus 1, end absolute value, equals?5Question 17.If a and b are the solutions to the preceding equation, what is the value of ?the absolute value of, a, minus b, end absolute value?Question 18.Juan purchased an antique that had a value of $200 at the time of purchase. Each year, the value of the antique is estimated to increase 10% over its value the previous year. The estimated value of the antique, in dollars, 2?years after purchase can be represented by the expression 200?a, where a is a constant. What is the value of?a??Question 19 is based on the following two equations. Equation?1: 2?x, plus 3?y, equals 1200. Equation?2: 3?x, plus 2?y, equals?1300.Question 19.Based on the preceding system of equations, what is the value of ?5?x?plus?5?y??Question 20.If u plus t, equals 5 and u minus t, equals 2, what is the value of open parenthesis, u minus t, close parenthesis, times, open parenthesis, u?squared, minus t?squared, close parenthesis?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. ................
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