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Systems of Equations; Inequalities 1.   Solve the equation |6x + 3| = 15       MACROBUTTON HTMLDirect image1.png A. x = –3 or x = 2 MACROBUTTON HTMLDirect image2.png B. x = 2 MACROBUTTON HTMLDirect image3.png C. x = –3 MACROBUTTON HTMLDirect image4.png D. x = 4 2.   When solving a system of equations using Cramer's Rule, if Dx = 0, Dy = –1, Dz = 1, and D = 0, then what can you conclude?       MACROBUTTON HTMLDirect image5.png A. The system has one solution, (0, –1, 1). MACROBUTTON HTMLDirect image6.png B. The system has one solution, (0, 0, 0). MACROBUTTON HTMLDirect image7.png C. The system is dependent. MACROBUTTON HTMLDirect image8.png D. The system is inconsistent.  Solve the inequality –2 (3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it.       MACROBUTTON HTMLDirect image9.png A. image10.png MACROBUTTON HTMLDirect image11.png B. image12.png MACROBUTTON HTMLDirect image13.png C. image14.png MACROBUTTON HTMLDirect image15.png D. image16.png MACROBUTTON HTMLDirect image17.png  Mark for review (Will be highlighted on the review page) 4.   Solve the system of equations 2x − 2y − 2z = 3, x + 4y − z = 2, and –2x − 8y + 2z = –4.       MACROBUTTON HTMLDirect image18.png A. There are infinitely many solutions, of the form (0.1, 0.1, –1.5). MACROBUTTON HTMLDirect image19.png B. There is no solution. MACROBUTTON HTMLDirect image20.png C. There are infinitely many solutions, of the form (x, 0.1, x −1.6). MACROBUTTON HTMLDirect image21.png D. There is one solution, (0.1, 0.1, –1.5). 5.   If the edge isn't included in the graph of an inequality, you should draw it as a/an _______ line.       MACROBUTTON HTMLDirect image22.png A. closed MACROBUTTON HTMLDirect image23.png B. dashed MACROBUTTON HTMLDirect image24.png C. open MACROBUTTON HTMLDirect image25.png D. solid What is the formula for the determinant of a 3 x 3 matrix image26.png?       MACROBUTTON HTMLDirect image27.png A. image28.png MACROBUTTON HTMLDirect image29.png B. image30.png MACROBUTTON HTMLDirect image31.png C. image32.png MACROBUTTON HTMLDirect image33.png D. image34.png 7.   Solve the inequality |5x + 10| ≥ 15. Write the solution in interval notation and graph it.       MACROBUTTON HTMLDirect image35.png A. image36.png MACROBUTTON HTMLDirect image37.png B. image38.png MACROBUTTON HTMLDirect image39.png C. image40.png MACROBUTTON HTMLDirect image41.png D. image42.png 8.   Solve the equation |x| = 7.       MACROBUTTON HTMLDirect image43.png A. x = 7 or x = –7 MACROBUTTON HTMLDirect image44.png B. x = 7 MACROBUTTON HTMLDirect image45.png C. Undefined MACROBUTTON HTMLDirect image46.png D. x = –7   9.   Graph the following solution set: x ≤ y2 y ≥ x       MACROBUTTON HTMLDirect image47.png A. image48.png MACROBUTTON HTMLDirect image49.png B. image50.png MACROBUTTON HTMLDirect image51.png C. image52.png MACROBUTTON HTMLDirect image53.png D. image54.png 10.   Aunt Jane's Pies had a tent at the county fair. Unfortunately their cash register broke, so they have no receipts. They know from counting their left over paper plates that they made 413 sales. They know from the cash box that they made $2,243. If they only sell two kinds of items at the fair tent, a piece of pie for $4 and pie á là mode for $7, help them figure out how many of each kind they sold.       MACROBUTTON HTMLDirect image55.png A. They sold 355 pieces of pie and 58 pies á là mode. MACROBUTTON HTMLDirect image56.png B. They sold 610 pieces of pie and 4683 pies á là mode. MACROBUTTON HTMLDirect image57.png C. The system of equations is inconsistent, and therefore their plate counting or money counting must have an error. MACROBUTTON HTMLDirect image58.png D. They sold 216 pieces of pie and 197 pies á là mode. 11.   Graph the inequality y ≥ –3.       MACROBUTTON HTMLDirect image59.png A. image60.png MACROBUTTON HTMLDirect image61.png B. image62.png MACROBUTTON HTMLDirect image63.png C. image64.png MACROBUTTON HTMLDirect image65.png D. image66.png   12.   Solve the system of equations x − 4y = –8 and –3x + 12y = 24.       MACROBUTTON HTMLDirect image67.png A. There is one solution, and it is (0, 2). MACROBUTTON HTMLDirect image68.png B. There is one solution, and it is (–4, 1). MACROBUTTON HTMLDirect image69.png C. There are infinitely many solutions. MACROBUTTON HTMLDirect image70.png D. There is no solution. 13.   Choose the correct ways to fill in the blanks in the following sentence. To solve a system of equations using the matrix method, use __________ to transform the augmented matrix into one with __________, then proceed to back-substitute.       MACROBUTTON HTMLDirect image71.png A. elementary row operations, zeros below the diagonal MACROBUTTON HTMLDirect image72.png B. the coefficient matrix, Gaussian elimination MACROBUTTON HTMLDirect image73.png C. the coefficient matrix, an inverse MACROBUTTON HTMLDirect image74.png D. multiplication and addition, zeros in its final column 14.   Find the equation of the boundary line in the graph below. Then give the inequality represented by the shaded area. image75.png       MACROBUTTON HTMLDirect image76.png A. image77.png MACROBUTTON HTMLDirect image78.png B. image79.png MACROBUTTON HTMLDirect image80.png C. image81.png MACROBUTTON HTMLDirect image82.png D. image83.png 15.   Find the value of the expression –|–18|.       MACROBUTTON HTMLDirect image84.png A. –18 MACROBUTTON HTMLDirect image85.png B. 0 MACROBUTTON HTMLDirect image86.png C. 18 MACROBUTTON HTMLDirect image87.png D. Undefined 16.   Are the two equations –6 + y = 2x and 2y − 4x = 12 dependent?       MACROBUTTON HTMLDirect image88.png A. Yes, because they have the same graph. MACROBUTTON HTMLDirect image89.png B. No, because they are not parallel. MACROBUTTON HTMLDirect image90.png C. No, because the equations are not written the same. MACROBUTTON HTMLDirect image91.png D. Yes, because both are the equations of straight lines. 17.   Solve the inequality |2x − 4| < 10. Write the solution in interval notation and graph it.       MACROBUTTON HTMLDirect image92.png A. image93.png MACROBUTTON HTMLDirect image94.png B. image95.png MACROBUTTON HTMLDirect image96.png C. image97.png MACROBUTTON HTMLDirect image98.png D. image99.png 18.   Graph the inequality y < 3x + 1.       MACROBUTTON HTMLDirect image100.png A. image101.png MACROBUTTON HTMLDirect image102.png B. image103.png MACROBUTTON HTMLDirect image104.png C. image105.png MACROBUTTON HTMLDirect image106.png D. image107.png   19.   Which of the following phrases correctly describes the graph of the system of equations image108.png and y = 2 − x?       MACROBUTTON HTMLDirect image109.png A. The graph is of two lines that intersect at a single point. MACROBUTTON HTMLDirect image110.png B. The graph is of two lines that coincide. MACROBUTTON HTMLDirect image111.png C. The graph is of two parallel lines that do not intersect. MACROBUTTON HTMLDirect image112.png D. The graph is of a line and a parabola, which intersect at two points 20.   Graph the following solution set: y ≤ x − 1 y ≥ 2x       MACROBUTTON HTMLDirect image113.png A. image114.png MACROBUTTON HTMLDirect image115.png B. image116.png MACROBUTTON HTMLDirect image117.png C. image118.png MACROBUTTON HTMLDirect image119.png D. image120.png   21.   Graph the solution set of x + 2y ≤ 3  x + 2y ≤ 4       MACROBUTTON HTMLDirect image121.png A. image122.png MACROBUTTON HTMLDirect image123.png B. image124.png MACROBUTTON HTMLDirect image125.png C. image126.png MACROBUTTON HTMLDirect image127.png D. image128.png 22.   When solving the system of equations 6x + 2y = –1 and –x + 10y = 5 by Cramer's Rule, what are the values of D, Dx, and Dy?       MACROBUTTON HTMLDirect image129.png A. D = 58, Dx = –20, Dy = –29 MACROBUTTON HTMLDirect image130.png B. D = 58, Dx = 20, Dy = –28 MACROBUTTON HTMLDirect image131.png C. D = 62, Dx = 20, Dy = 28 MACROBUTTON HTMLDirect image132.png D. D = 62, Dx = –20, Dy = 29 23.   Solve the system of equations 2x − y + z = –7, x − 3y + 4z = –19, and –x + 4y − 3z = 18.       MACROBUTTON HTMLDirect image133.png A. There is one solution, (1, 2, 3). MACROBUTTON HTMLDirect image134.png B. There is one solution, (–1, 2, –3). MACROBUTTON HTMLDirect image135.png C. There is one solution, (1, –2, 3). MACROBUTTON HTMLDirect image136.png D. There is one solution, (–1, –2, –3). 24.   Graph the inequality 3x ≤ –4y − 4.       MACROBUTTON HTMLDirect image137.png A. image138.png MACROBUTTON HTMLDirect image139.png B. image140.png MACROBUTTON HTMLDirect image141.png C. image142.png MACROBUTTON HTMLDirect image143.png D. image144.png   25.   The matrix below is the augmented matrix of a system of three equations in the variables x and y. Solve for x and y. image145.png       MACROBUTTON HTMLDirect image146.png A. Infinitely many solutions MACROBUTTON HTMLDirect image147.png B. One solution (0, 9) MACROBUTTON HTMLDirect image148.png C. One solution, image149.png MACROBUTTON HTMLDirect image150.png D. No solution Radicals and Rational Exponents 1.   What are the mean and standard deviation of the data – 6, 12, 2, – 4, 1, 6, 0, 3?       MACROBUTTON HTMLDirect image151.png A. The mean is 4.86 and the standard deviation is 5.63. MACROBUTTON HTMLDirect image152.png B. The mean is image153.png and the standard deviation is approximately 5.6252. MACROBUTTON HTMLDirect image154.png C. The mean is image155.png and the standard deviation is 5. MACROBUTTON HTMLDirect image156.png D. The mean is image157.png and the standard deviation is approximately 5.6252.   2.   To solve image158.png for x, begin with which of these steps?       MACROBUTTON HTMLDirect image159.png A. Isolate one radical expression. MACROBUTTON HTMLDirect image160.png B. Square both sides of the equation. MACROBUTTON HTMLDirect image161.png C. Combine the two like radicals, then square both sides. MACROBUTTON HTMLDirect image162.png D. Eliminate the negative in the second radical expression. 3.   Solve image163.png for x.       MACROBUTTON HTMLDirect image164.png A. image165.png MACROBUTTON HTMLDirect image166.png B. image167.png MACROBUTTON HTMLDirect image168.png C. image169.png MACROBUTTON HTMLDirect image170.png D. image171.png 4.   What best describes the triangle whose corners are located at the points (1, 1), (2, 2), and (0, 16)?       MACROBUTTON HTMLDirect image172.png A. It is a right triangle. MACROBUTTON HTMLDirect image173.png B. None of the above. MACROBUTTON HTMLDirect image174.png C. It has area 22 square units. MACROBUTTON HTMLDirect image175.png D. It is isosceles. 5.   Which of these expressions is in simplified form?       MACROBUTTON HTMLDirect image176.png A. image177.png MACROBUTTON HTMLDirect image178.png B. image179.png MACROBUTTON HTMLDirect image180.png C. image181.png MACROBUTTON HTMLDirect image182.png D. image183.png   6.   Simplify image184.png.       MACROBUTTON HTMLDirect image185.png A. image186.png MACROBUTTON HTMLDirect image187.png B. image188.png MACROBUTTON HTMLDirect image189.png C. image190.png MACROBUTTON HTMLDirect image191.png D. image192.png   7.   Which of the following best describes imaginary numbers?       MACROBUTTON HTMLDirect image193.png A. They are the complex numbers. MACROBUTTON HTMLDirect image194.png B. They are the values of expressions of the form image195.png for various real numbers a, as long as a ≠ 0. MACROBUTTON HTMLDirect image196.png C. They consist of two values, the principal imaginary number i and its negative –i. MACROBUTTON HTMLDirect image197.png D. They are not numbers, but are useful in solving equations. 8.   Which of these points is 5 units away from the point (6, –1)?       MACROBUTTON HTMLDirect image198.png A. image199.png MACROBUTTON HTMLDirect image200.png B. image201.png MACROBUTTON HTMLDirect image202.png C. image203.png MACROBUTTON HTMLDirect image204.png D. image205.png   Simplify image206.png assuming the variables represent non-negative numbers.       MACROBUTTON HTMLDirect image207.png A. image208.png MACROBUTTON HTMLDirect image209.png B. image210.png MACROBUTTON HTMLDirect image211.png C. image212.png MACROBUTTON HTMLDirect image213.png D. image214.png 10.   Simplify image215.png.       MACROBUTTON HTMLDirect image216.png A. image217.png MACROBUTTON HTMLDirect image218.png B. image219.png MACROBUTTON HTMLDirect image220.png C. image221.png MACROBUTTON HTMLDirect image222.png D. image223.png 11.   Expand image224.png and simplify. Assume c ≥ 0 and d ≥ 0.       MACROBUTTON HTMLDirect image225.png A. image226.png MACROBUTTON HTMLDirect image227.png B. image228.png MACROBUTTON HTMLDirect image229.png C. image230.png MACROBUTTON HTMLDirect image231.png D. image232.png 12.   Combine like radicals in image233.png.       MACROBUTTON HTMLDirect image234.png A. image235.png MACROBUTTON HTMLDirect image236.png B. image237.png MACROBUTTON HTMLDirect image238.png C. image239.png MACROBUTTON HTMLDirect image240.png D. image241.png   13.   Simplify image242.png.       MACROBUTTON HTMLDirect image243.png A. image244.png MACROBUTTON HTMLDirect image245.png B. image246.png MACROBUTTON HTMLDirect image247.png C. image248.png MACROBUTTON HTMLDirect image249.png D. image250.png   14.   Two children in nearby houses attempt to use walkie-talkies to communicate. The walkie-talkies reach one quarter of a mile (1320 feet). From one child's house to the other, the walk along the city sidewalks is as follows: Proceed 450 feet from the first house to the nearest corner, turn right 90° and proceed another 1050 feet. Are the children's houses within the 1320-foot range of one another? Choose the best answer.       MACROBUTTON HTMLDirect image251.png A. No, but if the turn were to the left instead, they would be within range. MACROBUTTON HTMLDirect image252.png B. Yes, as the distance formula indicates. MACROBUTTON HTMLDirect image253.png C. Yes, because city blocks are much smaller than one quarter of a mile. MACROBUTTON HTMLDirect image254.png D. No, because the distance is greater than 1320 feet.   15.   Simplify image255.png.       MACROBUTTON HTMLDirect image256.png A. image257.png MACROBUTTON HTMLDirect image258.png B. image259.png MACROBUTTON HTMLDirect image260.png C. image261.png MACROBUTTON HTMLDirect image262.png D. image263.png   16.   Which of these expressions simplifies to image264.png?       MACROBUTTON HTMLDirect image265.png A. image266.png MACROBUTTON HTMLDirect image267.png B. image268.png MACROBUTTON HTMLDirect image269.png C. image270.png MACROBUTTON HTMLDirect image271.png D. image272.png 17.   Which expression has the same value as 25½?       MACROBUTTON HTMLDirect image273.png A. image274.png MACROBUTTON HTMLDirect image275.png B. image276.png MACROBUTTON HTMLDirect image277.png C. image278.png MACROBUTTON HTMLDirect image279.png D. image280.png 18.   Simplify i23.       MACROBUTTON HTMLDirect image281.png A.  i MACROBUTTON HTMLDirect image282.png B. i MACROBUTTON HTMLDirect image283.png C. 1 MACROBUTTON HTMLDirect image284.png D. –1 19.   Simplify (6 − i)(2 + i).       MACROBUTTON HTMLDirect image285.png A. 13 + 4i MACROBUTTON HTMLDirect image286.png B. 11 + 4i MACROBUTTON HTMLDirect image287.png C. 13 − 8i MACROBUTTON HTMLDirect image288.png D. 11 + 8i 20.   Which of these radical expressions simplifies to x?       MACROBUTTON HTMLDirect image289.png A. image290.png MACROBUTTON HTMLDirect image291.png B. image292.png MACROBUTTON HTMLDirect image293.png C. image294.png MACROBUTTON HTMLDirect image295.png D. image296.png 21.   Rationalize the denominator of image297.png assuming x ≥ 0 and y ≥ 0.       MACROBUTTON HTMLDirect image298.png A. image299.png MACROBUTTON HTMLDirect image300.png B. image301.png MACROBUTTON HTMLDirect image302.png C. image303.png MACROBUTTON HTMLDirect image304.png D. image305.png 22.   Simplify image306.png by rationalizing the denominator.       MACROBUTTON HTMLDirect image307.png A. image308.png MACROBUTTON HTMLDirect image309.png B. image310.png MACROBUTTON HTMLDirect image311.png C. image312.png MACROBUTTON HTMLDirect image313.png D. image314.png 23.   Solve image315.png for x.       MACROBUTTON HTMLDirect image316.png A.  x = 2 or x = 8 MACROBUTTON HTMLDirect image317.png B. The two solutions for are complex numbers. MACROBUTTON HTMLDirect image318.png C.  x = 4 or x = –4 MACROBUTTON HTMLDirect image319.png D.  x = 2   24.   Solve image320.png for x.       MACROBUTTON HTMLDirect image321.png A. 50 MACROBUTTON HTMLDirect image322.png B. 40 MACROBUTTON HTMLDirect image323.png C. 4 MACROBUTTON HTMLDirect image324.png D. –41 25.   Which of these phrases best describes the standard deviation?       MACROBUTTON HTMLDirect image325.png A. It increases as more measurements are taken. MACROBUTTON HTMLDirect image326.png B. It is a radical expression using n variables. MACROBUTTON HTMLDirect image327.png C. It is equal to the mean squared. MACROBUTTON HTMLDirect image328.png D. It is a measure of variability.   Polynomials and Polynomial Functions    Solve the equation image329.png       MACROBUTTON HTMLDirect image330.png A. image331.png MACROBUTTON HTMLDirect image332.png B. image333.png MACROBUTTON HTMLDirect image334.png C. image335.png MACROBUTTON HTMLDirect image336.png D. image337.png   2.   Completely factor the expression 7(x − y) − z(x − y).       MACROBUTTON HTMLDirect image338.png A. (x − y)(7 + z) MACROBUTTON HTMLDirect image339.png B. Prime MACROBUTTON HTMLDirect image340.png C. (x − y)2(7 − z)3 MACROBUTTON HTMLDirect image341.png D. (x − y)(7 − z) 3.   Completely factor the expression 16x4 − 81y4.       MACROBUTTON HTMLDirect image342.png A. (4x2 − 9y2)(4x2 + 9y2) MACROBUTTON HTMLDirect image343.png B. 0 MACROBUTTON HTMLDirect image344.png C. (2x + 3y)(2x − 3y)(4x2 + 9y2) MACROBUTTON HTMLDirect image345.png D. Prime 4.   Perform the indicated operations on the expression below. (5a3 + 3a - 2) - (4a3 + a2 + 5)       MACROBUTTON HTMLDirect image346.png A. 20a3 + 3a2 − 10 MACROBUTTON HTMLDirect image347.png B.  a3 − a2 + 3a − 7 MACROBUTTON HTMLDirect image348.png C. 3a6 − 7 MACROBUTTON HTMLDirect image349.png D.  a3 + a2 + 3 5.   Find the product of –3a3b(2a0b4 − 4a2b3)       MACROBUTTON HTMLDirect image350.png A. –6b4 + 12a6b3 MACROBUTTON HTMLDirect image351.png B. 12a5b4 − 6a3b5 MACROBUTTON HTMLDirect image352.png C. 14a5b4 − 6b5 MACROBUTTON HTMLDirect image353.png D. –6b5 + 14a5b4 6.   Completely factor the expression r2 − 2r + 1.       MACROBUTTON HTMLDirect image354.png A. (r + 1)(r − 1) MACROBUTTON HTMLDirect image355.png B. (r − 1)(r − 1) MACROBUTTON HTMLDirect image356.png C. Prime MACROBUTTON HTMLDirect image357.png D.  r(r − 2) + 1 7.   Graph the polynomial function f(x) = x3 − 1.       MACROBUTTON HTMLDirect image358.png A. image359.png MACROBUTTON HTMLDirect image360.png B. image361.png MACROBUTTON HTMLDirect image362.png C. image363.png MACROBUTTON HTMLDirect image364.png D. image365.png 8.   Completely factor the expression y2 + 12y + 35.       MACROBUTTON HTMLDirect image366.png A. (y + 7)(y + 5) MACROBUTTON HTMLDirect image367.png B. Prime MACROBUTTON HTMLDirect image368.png C. (y + 7)(y − 5) MACROBUTTON HTMLDirect image369.png D. (y − 7)(y − 5) 9.   Completely factor the expression 2a3 − 128.       MACROBUTTON HTMLDirect image370.png A. Prime MACROBUTTON HTMLDirect image371.png B. 2(a3 − 64) MACROBUTTON HTMLDirect image372.png C. 2(a − 4)3 MACROBUTTON HTMLDirect image373.png D. 2(a − 4)(a2 + 4a + 16) 10.   Solve the equation x2 + 4x − 45 = 0.       MACROBUTTON HTMLDirect image374.png A.  x = 9 and x = –5 MACROBUTTON HTMLDirect image375.png B.  x = –9 and x = 5 MACROBUTTON HTMLDirect image376.png C.  x = 15 and x = 30 MACROBUTTON HTMLDirect image377.png D. No solution 11.   Find the product of (2a + 3b)(2a − 3b).       MACROBUTTON HTMLDirect image378.png A. 4a2 + 12ab − 9b2 MACROBUTTON HTMLDirect image379.png B. 4a2 − 9b2 MACROBUTTON HTMLDirect image380.png C. 2a2 − 3b2 MACROBUTTON HTMLDirect image381.png D. 4a2 − 6b2 12.   Completely factor the expression 4q2 + 27r4.       MACROBUTTON HTMLDirect image382.png A. 27r4(4q2 + 1) MACROBUTTON HTMLDirect image383.png B. 4q(q + 27r) MACROBUTTON HTMLDirect image384.png C. Prime MACROBUTTON HTMLDirect image385.png D. 31q2r4 13.   Find the product of (x − 2y)2.       MACROBUTTON HTMLDirect image386.png A.  x2 + 4y2 MACROBUTTON HTMLDirect image387.png B.  x2 + 2xy + 4y2 MACROBUTTON HTMLDirect image388.png C.  x2 + 4xy + 4y2 MACROBUTTON HTMLDirect image389.png D.  x2 − 4xy + 4y2 14.   Completely factor the expression 16t3 − 50t2 + 36t.       MACROBUTTON HTMLDirect image390.png A. Prime MACROBUTTON HTMLDirect image391.png B. 2t(8t − 25t + 18) MACROBUTTON HTMLDirect image392.png C. 2t(8t − 9)(t − 2) MACROBUTTON HTMLDirect image393.png D. 2t(8t + 9)(t + 2) 15.   Find the value of the expression 2xy − x2y when x = 2 and y = 3.       MACROBUTTON HTMLDirect image394.png A. –24 MACROBUTTON HTMLDirect image395.png B. 6 MACROBUTTON HTMLDirect image396.png C. 0 MACROBUTTON HTMLDirect image397.png D. 24 16.   Solve the equation 3z3 − 300z = 0.       MACROBUTTON HTMLDirect image398.png A.  z = 0 MACROBUTTON HTMLDirect image399.png B.  z = –4 and z = 1 MACROBUTTON HTMLDirect image400.png C. Prime MACROBUTTON HTMLDirect image401.png D.  z = 0, z = 10, and z = –10 17.   Completely factor the expression a2 + 4b − ab − 4a.       MACROBUTTON HTMLDirect image402.png A. Prime MACROBUTTON HTMLDirect image403.png B. (a − b)(a − 4) MACROBUTTON HTMLDirect image404.png C. (a + b)(a + 4) MACROBUTTON HTMLDirect image405.png D. (a + b)(a − 4)   18.   Completely factor the expression 48u4v4 − 18u2v2 − 3u8v5.       MACROBUTTON HTMLDirect image406.png A. Nonfactorable MACROBUTTON HTMLDirect image407.png B. 3u2v2(16u2v2 − 6 − u6v3) MACROBUTTON HTMLDirect image408.png C.  u2v2(48u2v2 − 18 − 3u6v3) MACROBUTTON HTMLDirect image409.png D. 3(16u4v4 − 6u2v2 − u8v5) 19.   Simplify the expression 2ab4 − 3a2b2 − ab4 + a2b2.       MACROBUTTON HTMLDirect image410.png A.  a2b8 − a2b8 − 2a4b4 MACROBUTTON HTMLDirect image411.png B. 0 MACROBUTTON HTMLDirect image412.png C. 2a2b8 − 3a4b4 MACROBUTTON HTMLDirect image413.png D.  ab4 − 2a2b2 20.   Simplify the expression –2(4y2 + 3z3 + 5) + 3(2y2 − 5z3 + 3).       MACROBUTTON HTMLDirect image414.png A. 9z3 − 14y2 + 19 MACROBUTTON HTMLDirect image415.png B. –14y2z3 + 6y2 − 1 MACROBUTTON HTMLDirect image416.png C. –21z3 − 2y2 − 1 MACROBUTTON HTMLDirect image417.png D. 21z3 + 2y2 + 1 Rational Expressions 1.   Simplify the following expression:  image418.png       MACROBUTTON HTMLDirect image419.png A. image420.png MACROBUTTON HTMLDirect image421.png B. image422.png MACROBUTTON HTMLDirect image423.png C. image424.png MACROBUTTON HTMLDirect image425.png D. image426.png   After t hours of work, Group A completes image427.png of a job and Group B completes image428.png of the same job. What expression represents the amount the two teams would complete after tseconds, working together?       MACROBUTTON HTMLDirect image429.png A. image430.png MACROBUTTON HTMLDirect image431.png B. image432.png MACROBUTTON HTMLDirect image433.png C. image434.png MACROBUTTON HTMLDirect image435.png D. image436.png 3.   Express this sentence as a formula: z varies directly with the square of s.       MACROBUTTON HTMLDirect image437.png A. image438.png MACROBUTTON HTMLDirect image439.png B. image440.png MACROBUTTON HTMLDirect image441.png C. image442.png MACROBUTTON HTMLDirect image443.png D. image444.png 4.   Perform the indicated operations and simplify the following expression:  image445.png       MACROBUTTON HTMLDirect image446.png A. image447.png MACROBUTTON HTMLDirect image448.png B. image449.png MACROBUTTON HTMLDirect image450.png C. image451.png MACROBUTTON HTMLDirect image452.png D. image453.png 5.   Solve this proportion for the variable: image454.png       MACROBUTTON HTMLDirect image455.png A.  x = 7 MACROBUTTON HTMLDirect image456.png B.  x = 10 MACROBUTTON HTMLDirect image457.png C.  x = –7 MACROBUTTON HTMLDirect image458.png D.  x = –10 6.   Perform the indicated operations and simplify the following expression:  image459.png       MACROBUTTON HTMLDirect image460.png A. image461.png MACROBUTTON HTMLDirect image462.png B. image463.png MACROBUTTON HTMLDirect image464.png C. image465.png MACROBUTTON HTMLDirect image466.png D. image467.png   Simplify the expression image468.png       MACROBUTTON HTMLDirect image469.png A. image470.png MACROBUTTON HTMLDirect image471.png B. image472.png MACROBUTTON HTMLDirect image473.png C. image474.png MACROBUTTON HTMLDirect image475.png D. image476.png 8.   Solve the following equation:  image477.png       MACROBUTTON HTMLDirect image478.png A. { } MACROBUTTON HTMLDirect image479.png B.  t = –1 MACROBUTTON HTMLDirect image480.png C.  t = 1 MACROBUTTON HTMLDirect image481.png D.  t = 2 Divide the following expression:  image482.png       MACROBUTTON HTMLDirect image483.png A. 5z2 + 7z MACROBUTTON HTMLDirect image484.png B. 3z2 + 7z + 3 and a remainder of –9 MACROBUTTON HTMLDirect image485.png C. 3z + 7 MACROBUTTON HTMLDirect image486.png D. 3z2 + 16z + 3 and a remainder of 6   10.   The total resistance R of two resistors in parallel is given by image487.png where R1 is the resistance of the first and R2 the resistance of the second. Solve that equation for R1 and simplify.      MACROBUTTON HTMLDirect image488.png A. image489.png MACROBUTTON HTMLDirect image490.png B. image491.png MACROBUTTON HTMLDirect image492.png C. image493.png MACROBUTTON HTMLDirect image494.png D. image495.png  11 Solve this proportion for the variable: image496.png       MACROBUTTON HTMLDirect image497.png A. y = 2 MACROBUTTON HTMLDirect image498.png B. y = 4 MACROBUTTON HTMLDirect image499.png C. y = –2 MACROBUTTON HTMLDirect image500.png D. y = –4 12.   Simplify image501.png.       MACROBUTTON HTMLDirect image502.png A. a8b–7 MACROBUTTON HTMLDirect image503.png B. a4b–7 MACROBUTTON HTMLDirect image504.png C. a4b3 MACROBUTTON HTMLDirect image505.png D. a8b3 13  Solve the following equation:  image506.png       MACROBUTTON HTMLDirect image507.png A.  z = –4 MACROBUTTON HTMLDirect image508.png B.  z = 4 MACROBUTTON HTMLDirect image509.png C.  z = 6 MACROBUTTON HTMLDirect image510.png D.  z = –6 14.   Perform the indicated operations and simplify the following expression:  image511.png       MACROBUTTON HTMLDirect image512.png A. image513.png MACROBUTTON HTMLDirect image514.png B. image515.png MACROBUTTON HTMLDirect image516.png C. image517.png MACROBUTTON HTMLDirect image518.png D. image519.png 15.   Factor and simplify image520.png.       MACROBUTTON HTMLDirect image521.png A. image522.png MACROBUTTON HTMLDirect image523.png B. image524.png MACROBUTTON HTMLDirect image525.png C. It is already fully simplified. MACROBUTTON HTMLDirect image526.png D. image527.png 16.   Which sum yields image528.png?       MACROBUTTON HTMLDirect image529.png A. image530.png MACROBUTTON HTMLDirect image531.png B. image532.png MACROBUTTON HTMLDirect image533.png C. image534.png MACROBUTTON HTMLDirect image535.png D. image536.png 17.   Simplify the following expression:  image537.png       MACROBUTTON HTMLDirect image538.png A. image539.png MACROBUTTON HTMLDirect image540.png B. image541.png MACROBUTTON HTMLDirect image542.png C. image543.png MACROBUTTON HTMLDirect image544.png D. image545.png 18.   Simplify the expression image546.png       MACROBUTTON HTMLDirect image547.png A. image548.png MACROBUTTON HTMLDirect image549.png B. image550.png MACROBUTTON HTMLDirect image551.png C. image552.png MACROBUTTON HTMLDirect image553.png D. image554.png 19.   Perform the indicated operations and simplify the following expression:  image555.png       MACROBUTTON HTMLDirect image556.png A. image557.png MACROBUTTON HTMLDirect image558.png B. image559.png MACROBUTTON HTMLDirect image560.png C. image561.png MACROBUTTON HTMLDirect image562.png D. image563.png 20.   Divide the following expression:  image564.png       MACROBUTTON HTMLDirect image565.png A. image566.png MACROBUTTON HTMLDirect image567.png B. image568.png MACROBUTTON HTMLDirect image569.png C. image570.png MACROBUTTON HTMLDirect image571.png D. image572.png