NES Test Algebra

106. Evaluate lim x→∞ x²+2x-3/2x²+1 a. 0 b.½ c. -3 d ∞

?

107. Evaluate lim x→3⁺ |x-3|/3-x a. 0 b. -1 c. 1 d.∞

?

48. Solve 3x³y²-45x²y=15x³y-9x²y² for x and y. a. x= {0,-3}, y = {0,5} b. x= {0}, y={0} c. x= {0,-3}, y= {0} d. x= {0}, y= {0,5}

A. X={0,-3}, Y = {0,5}

109. If f(x) = 2x³-3x²+4, what is the lim h→0 f(2+h)-f(2)/h? a. -4 b. 4 c. 8 d. 12

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110. Find the derivative of f(x) =e³ⁿ²⁻¹ a. 6xe⁶ⁿ b. e³ⁿ²⁻¹ c. (3x²-1)e³ⁿ⁻² d. 6xe³ⁿ²⁻¹

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114. If f(x) = 4x³-x²-4x+2, which of the following statements is (are) true of its graph? I. The point (-½, 3¼) is a relative maximum. II. The graph of f is concave upward on the interval (-∞,½). a.I b. II c. I and II d. Neither I nor II

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74. A rainbow pattern is designed from semi-circles as shown below. Which of the following gives the area A of the shaded region as a function of x?

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78. Which of the following equations gives the area A of the triangle below as a function of a and b?

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Find f"(x) if f(x) = 2x⁴+2x²-x+1 a. 24x²-24x+4 b. 8x³-12x²+4x-1 c. 32x²-36x²+8 d. 2/5x⁵-x⁴+2/3x³-½x²+x+c

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9. The path of ball thrown into the air is modleled by the first quarant graph of the equation h= -16t² + 64t +5, where h is the height of the ball in feet and t is time in seconds after the ball is thrown. What is the average rate of change in the ball's height with respect to time over the interval [1,3]? a. 0 feet/ second b. 48 feet/ second c. 53 feet/ second d. 96 feet/ second

a. 0 feet/ second

24. Simplify 2+3i/ 4-2i a. 1/10 + 4/5i b. 1/10 c. 7/6 + 2/3i d. 1/10 + 3/10i

a. 1/10 + 4/5i

58. Simplify √-28x₆/27y⁵ a. 2x³i√21y/9y³ b.2x³i√21y/27y⁴ c. -2x³√21y/9y³ d. 12x³yi√7/ 27y²

a. 2x³i√21y/ 9y³

89. What is the radius of the circle defined by the equation x²+y²-10x+8y+29=0? a. 2√3 b. 2√5 c.√29 d. 12

a. 2√3

33. Find [g ₀ f] x when f(x) = 2x+4 and g(x) = x²-3x+2 a. 4x²+10x+6 b. 2x²-6x+8 c. 4x²+13x +18 d. 2x²-3x+6

a. 4x²+10x+6

37. Which of these statements is (are) true for funciton g(x)? I. g(3) = 0 II. The graph of g(x) is discontinuous at x=2. III. The range of g(x) is all real numbers. a. II b.III c. I, II d. II, III

a. II

85. Which of these represents the equation of a shpere which is centered in the xyz-space at the point (1,0,-2) and which has a volue of 36π cubic units? a. x²+y²+z²-2x+4z=4 b. x²+y²+z²-2x-4z=4 c. x²+y²+z²-2x+4z=-2 d. x²+y²+z²-2x-4z=2

a. x²+y²+z²-2x+4z=4

97. What is the exact value of tan (-2π/3)? a. √3 b. -√3 c.√3.3 d. 1

a. √3

46. Solve the system of equations. 2x-4y+z=10 -3x+2y-4z=-7 x+y-3z=-1 a. (-1,-3,0) b. (1, -2,0) c. (-¾, - 21/8, -1) d. No solution

b. (1,-2,0)

79. Given the figure and the following information, find DE to the nearest tenth. AD is an altitude of Δ ABC DE is an altitude of traingle ΔΑDC BD≅DC BC =24; AD =5 a. 4.2 b. 4.6 c. 4.9 d. 5.4

b. 4.6

10. Zeke drove from his house to a furniture store in Atlanta and then back home along the same route. It took Zeke three hours to drive to the store. By driving an average of 20 mph faster on his return trip, Zeke was able to save an hour of driving time. What was Zeke's average driving speed on his round trip? a. 24 mph b. 48 mph c. 50 mph d. 60 mph

b. 48 mph

5. Two companies offer monthly cell phone plans, both of which include free text messaging. Company A charges $25 monthly fee plus five cents per minute of phone conversation, while Company B charges a duration of monthly calls is a. 500 hours b. 8 hours and 33minutes c. 8 hours and 20 minutes d. 5 hours

b. 8 hours and 33 minutes

65. Which of the following statements is (are) true when f(x) = x²-x-6/x³+2x²-x-2? I. The graph f(x) has vertical asymptotes at x=-2, x= -1, and x=1 II. The x- and y- intercepts of the graph of f(x) are both 3. a. I b. II c. I and II d. neither statements is true

b. II

103. Which of the following statements is true? a. 0<a₂<a₁ b. a₂<0<a₁ c. 0<a₁<a₂ d. a₂<a₁<0

b. a₂<0<a₁

13. Complete the analogy x³ is to ³√y as ... a. x+a is to x-y b. e is to ln y, y > 0. c. 1/x is to y, x, y ≠ 0. d. sin x is to cos y

b. e is to ln y, y>0

91. THe graph of f(x) is a paabola with a focus of (a,b) and a directrix of y=-b, and g (x) represents transformation of f(x). If the vertex of the graph of g(x) is (a,0), which of these is a possible equation for g(x) for nonzero integers a and b? a. g(x)=f(x)+b b.G(x)=-f(x) c.g(x) = f(x+a) d. g(x) =f(x-a) +b

b. g(x) =-f(x)

61. Solve x-2/x-1 = x-1/x+1 + 2/x-1 a. x=2 b. x= -5 c. x=1 d. No solution

b. x= -5

47. Solve x⁴+64 = 20x². a. x= {2,4} b. x= {-2,2,-4,4} c. x= {2i,4i} d. x= {-2i,2i,-4i,4i}

b. x= {-2,2,-4,4}

36. Determine which pair of equations are NOT inverse a. y = x+6;y=x-6 b. y=2x +3; y= 2x-3 c. y= 2x+3/x-1; y= x+3/x-2 d. y=x-1/2; y=2x+1

b. y=2x+3; y=2x-3

26. Which of these sets forms a group under multiplication? a. {-i, 0,i} b. {-1,1,i,-i} c. {i,1} d. {i, -i, 1}

b. {-1, 1, i, -1}

43. Solve the system of equations. 3x + 4y = 2 2x + 6y = -2 a. (0,½) b. (2/5, 1/5) c. (2,-10 d. -1,5/4)

c. (2,-1)

28. If the square of twice the sum of x and three is equal to the product of twenty-four and x, which of these is a possible value of x? a. 6 + 3√2 b. 3/2 c. -3i d. -3

c. -3i

105. Evaluatee lim x→-3 x³+3x²-x-3/x²-9 a. 0 b. 1/3 c. -4/3 d. ∞

c. -4/3

108. If f(x)=¼x²-3, find the slope of the line tangent to graph of f(x) at x=2 a. -2 b. 0 c. 1 d. 4

c. 1

59. Which of these does NOT have a solution set of {x:-1≤x≥1}? a. -4≤2+3(x-1)≤2 b.-2x²+2≥x²-1 c. 11-|3x|/7 ≥ 2 d. 3|2x|+4≤10

c. 11-|3x|/7≥2

44. Which system of linear inequalities has no solution? a. x-y <3 x-y ≥ -3 b. y≤6-2x 1/3y + 2/3x≥2 c. 6x+2y≤12 3x≥8-y d. x+4y≤-8 y+4x>-8

c. 6x+2y≤12 3x≥8-y

11. The graph below Aaron's distance from home at times throughout his morning run. Which of the following statements is (are) true? I. Aaron's average running speed was 6mph II. Aaron's running speed fomr point A to point B was the same as his running speed from point D to E. III. Aaron ran a total distance of four miles.

c. I and II

31. Which of these relationships represents y as a function of x? a. x= y² b. c. y= [[x]]s d.

c. y= [[x]]s

64. Which of these functions includes 1 as an element of the domain and 2 as an element of the range? a. y= 1/x+1 b. y= ⁻√x+2-1 c. y= |x+2|-3 d. y={ x, x<1, -x-3, x≥1

c. y=|x+2|-3

87. If the midpoint of a line segment graphed on the xy-coordinate plane is (3,-1) and the slope of the line segment is -2, which of these is a possible endpoint of the line segment? a. (-1,1) b.(0,-5) c. (7,1) d. (5,-5)

d. (5,-5)

34. Given the partial table of values for f(x) and g(x), find f(g(-4)). (Assume that f(x) and g(x) are the simplest polynomials that fit the data.) a. 69 b. 31 c. 18 d. -3

d. -3

56. A colony of Escheirchia coli is inoculated from a Petri dish into a test tube containing 50ml of nutrient broth. The test tube is placed in a 37⁰C incubator/shaker; after one hour, the number of bacteria in the test tube is determined to be 8×10⁶. Given that the doubling time of E. coli is 20 minutes with agitation at 37⁰C, approximately how many bacteria should the test tube contain after eight hours of growth? a. 2.56 × 10⁸ b. 2.05×10⁹ c. 1.7×10¹⁰ d. 1.7×10¹³

d. 1.7×10¹³

25. Simplify |(2-3i)² - (1-4i)| a.√61 b. -6-8i c. 6+8i d. 10

d. 10

30. If a, b and c are even integers and 3a² + 9b³ = c, which of these is the largest number which must be factor of c? a. 2 b. 3 c. 6 d. 12

d. 12

6. A dress is marked down by 20% and placed on a clearnce rack, on which is posted a sighn reading "Take an extra 25% off already reduced merchandise." What fraction of the original price is the final sales price of the dress? a. 9/20 b. 11/20 c. 2/5 d. 3/5

d. 3/5

35. If f(x) and g(x) are inverse functions, which of these is the value of x when f(g(x))=4? a. -4 b. 1/4 c. 2 d. 4

d. 4

98. If sin θ = ½ when π/2 < θ <π, what is the value of θ? a. π/6 b. π/3 c. 2π/3 d. 5π/6

d. 5π/6

60. Solve 2-√x= √x-20 . a. x=6 b.x=36 c. x=144 d. No solution

d. No solution

12. Use the operation tabel to determine (a×b)×(c×d) a. I only b. II only c. I and II d. I, II, and III

d. d

90. Which of these describes the graph of the equation 2x²+y²+29=0 a. circular b. elliptical c. arabolic d. hyperbolic

d. hyperbolic

42. Solve 7x²+6x=-2 a. x= -3±√23/7 b. x= ±i√5 c. x=±2i√2/7 d. x= -3±i√5/7

d. x= -3±i√5/7