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N-RN.3If P and S are rational numbers and R and Q are irrational numbers, which of these statements is true?The product of R and Q is always an irrational number.The product of P and S is always a rational number.The sum of R and Q is always an irrational number. The sum of P and Q is always a rational number.Which statement about rational and irrational numbers is always true?Any irrational number added to any rational number is equal to a rational number.Any irrational number added to any irrational number is equal to a rational number.Any irrational number multiplied by any non-zero rational number is equal to a rational number.Any irrational number multiplied by any non-zero rational number is equal to an irrational number.Which expression results in an irrational number when simplified?121+166+12454949The length of a rectangular prism is 43 units. The height is 36 units. If the volume is irrational, which could be the measure of the width of the rectangular prism?A. 250B. 412C. 58D. 718N-CN.2 Which expressions is equivalent to 8-3i-2-9i?6+6i6-12i11+78i18-6iThe circuit law, V=I?Z, is used in circuit analysis. If I=3i and Z=7i, what is the voltage, V?2121i-21-21iWhat is the value of 8i-2i3i+4?-2+8i10+8i-66Which of the following is equivalent to 3-2i2?5-12i6-4i9+4i13-12iWhich of the following expressions is equivalent to 3i-5+2i-25-4i??-16-23i-16-7i-10-i21-4iWhich value is equivalent to i57?-1–i1iA-SSE.3For 1-3: What value of h is needed to complete the square in order to find the vertex?1. x2-4x+9=x-h2+5 2. x2+2x+7=(x-h)2+6 3. x2-2x+4=x-12+3A-APR.2Given the function Px=x3+4x2+kx+15, for what value of k is (x+3) a factor of P(x)?-26-8826When the polynomial 4x4-13x2-2x+1 is divided by the polynomial (x-2), what is the remainder?-231917If px=x4+3x3-2x2+4 and qx=x+1, then g(x) is a polynomial that equals p(x)q(x). What is the remainder of g(x) when it is divided by (x-2)?-461222What is the remainder when px=x3-7x-6 is divided by (x-4)?-42-18930A-APR.3 Which of the following functions has the same zeros as the function fx=x2-6x+8?gx=x-4gx=x2-5x+6gx=2x2-12x+16gx=x3-6x2+8xWhich function, when graphed, would have the same zero(s) as the function below?fx=x(x+6)fx=x(x-6)fx=(x+6)2fx=(x-6)23. What are the zeros of the polynomial function fx=x2-16x+5x?-5, -4, 0, 4-4, 0, 4, 5-5, -4, 4-5, 0, 4Which function has zeros -4, 2, and 0?fx=x3+2x2-8xfx=x3-2x2-8xfx=x2+2x-8fx=x2-2x-8Let the function fx=(x+4)(x2-36)(x2+25). What are all the x-intercepts for the graph of f(x)?-4, 6-6, -4, 6-6, 4, 6-6, -5, 4, 5, 6Which function best represents the graph below?7. Which function best represents the graph below?fx=x+2x-3A. gx=xx-22(x+3)fx=x+3x-2B. gx=x-22(x+3)fx=xx+2x-3C. gx=xx-2x+3fx=xx+3x-2D. gx=(x-2)(x+3A-APR.6 Which fraction is equal to y2+5y+4y2+19y+18 in simplest form?937418y+4y+185y+419y+18What is 2x2-182x2+18 reduced to lowest terms?x-3x+3 B. x+3x-3C. (x-3)(x-3)x2+9 D. (x-3)(x+3)x2+9 5. What value must be substituted for k so that x+4x2+7x+k can be reduced to 1x+3?341228Which of the following is equivalent to x3-7x2x-7?xx2xx-1-6xx-7A-REI.2 Solve 52x-2=15x2-1151, 5No solutionSolve y5+y2=725710Solve xx-5+3x+2=7x(x-5)(x+2)-35-3, 5No solutionSolve x-3+5=x474, 7No solutionSolve 3x+7=x-1-16-1, 6No solutionAfter an accident, police can determine how fast a car was traveling before the driver put on his brakes by using the equation s=30fd. s represents the speed in miles per hour, f represents the coefficient of friction, and d represents the length of the skid in feet. Suppose the coefficient of friction is 0.6, if you were driving 35 miles per hour, how many feet would it take for you to stop?30 feetB. 47 feetC. 68 feetD. 81 feetA-REI.4.a What number should be added to both sides of the equation to complete the square? x2 + 10x = 3A. 5B. 25C. 50D. 100For what value of p is the expression x-p2+5 is equivalent to the expression x2-14x+54?-49-7749The equation 2x2-5x=-12 is rewritten in the form 2(x-p)2+q=0. What is the value of q?16716B. 718C. 258D. 2516A-REI.4.b Solve 5x2-180=0x=-6B. x=6C. x=±6D. No real solutionWhat are the solutions of -4x2-72=0?±2i3 B. ±3i2 C. ±23 D. ±32What are the values of x that satisfy the equation 3-27x2=0?x=±3B. x=±19C. x=±13D. x=±26What are the solutions of x2+10x+40=5?10±i5C. 5±i10-10±i5D. -5±i10Which equation has -3±5i as its solutions?x2+6x=-34C. x2+6x=-14x2+3x=4D. x2+3x=2A-REI.11 1. For what values of x does fx=g(x) if fx=x3+3x2 and gx=x+3?A. -3, -1, 1B. -3, 1, 3C. -1, 1, 3D. -3, -1, 3For what values of x does fx=g(x) if fx=2x-1+5 and gx=-12x+9?-2, 10B. -2, 8C. -2, 2D. 8, 10For what values of x does fx=g(x) if fx=2x and gx=32x+1?2, 4B. 0, 1C. 4, 1D. 2, 0At approximately what point or points do the graphs of fx=x2-3x-8 and gx=-6+log4x intersect?(3.6949, -5.4324)(3.7824, -5.0403)0.0093, -8.0280and (3.6949, -5.4324)0.0507, -8.1497and (3.7824, -5.0403)Since January 2010, a grape farmer has been growing red and green grapes. The number of red grape vines can be modeled by the function fx=1,0001.03x, where x is the number of years since January 2010. The number of green grape vines can be modeled by the function g(x)=20x+1,125, where x is the number of years since January 2010. In what year will the number of each type of grape vine be approximately equal?2013201520172019F-IF.4 During which interval is the graph of fx=-12x2+3x-2.5 positive?1<x<5B. x<1 and x>5C. 1≤x≤5D. x≤1 and x≥5During which of following intervals is the graph of fx=3x3+10x2-x-12=0 positive?x>0B. x>1C. -3<x<-1D. -2<x<0During which of the following intervals is the graph of fx=x3+x2-6x negative?x<-3B. x<0C. -3<x<0D. x>2What is the y-intercept of y=sin(θ+π2)?(0,0)B. (0, 1)C. (π2, 0)D. (0, π2)During which of the following intervals is the graph of y=12cosθ increasing?0<θ<π2B. π2<θ<πC. π2<θ<3π2D. π<θ<2πWhich function has a period of 4π and an amplitude of 8?y=-8sin8θB. y=8sin2θC. y=-8sin12θD. y=4sin8θWhich of the following describes the end behavior of 2x4-20x2+18?x→-∞ fx→+∞, x→+∞ fx→+∞x→-∞ fx→+∞, x→+∞ fx→-∞x→-∞ fx→-∞, x→+∞ fx→+∞x→-∞ fx→-∞, x→+∞ fx→-∞Which rational function is decreasing in the interval (-∞, 1) and is symmetric over the line x=1?39243009207500685800635000 C. 5810251682750039058101206500 D. F-BF.3 The graph fx=3x is translated 2 units to the right and down 6 units resulting in g(x). Which of the following functions represents g(x)?A. gx=3(x-2)-6 B. gx=3(x+2)-6 C. gx=3(x-6)-2 D. gx=3(x+6)-2The function fx=3(2)x models the growth of a bacteria culture. What is the change that occurs to the graph if f(x+k) is graphed and k<0?A. The graph moves up k unitsB. The graph moves down k unitsC. The graph moves left k unitsD .The graph moves right k unitsWhich function is a phase shift of y=sinθ by 5 units to the left?y=5sinθB. y=sinθ+5C. y=sin(θ+5)D. y=sin5θWhich function is a translation of y=cosθ by 5 units down?y=-5cosθB. y=cos(-5θ)C. y=cos(θ-5)D. y=cosθ-5Which function is a translation of y=sinθ that is π3 units up and π2 units to the left?y=sin(θ+π3)+π2B. y=sinθ+π2+π3C. y=sinθ-π2+π3D. y=sinθ-π3-π2The figure below shows the graph of the function g(x). If fx=2x+3, how is g(x)related to f(x)? gx=fx-4gx=fx+4gx=fx-4gx=f(x+4)The cubic function y=x3 is changed to y=-2x3-7. What effect will this have on the function?The graph will be reflected in the y-axis, shifted up 2 units and vertical stretch by a factor of 7.The graph will be reflected in the x-axis, shifted up 7 units and vertical stretch by a factor of 2.The graph will be reflected in the x-axis, shifted down 7 units and vertical stretch by a factor of 2.The graph will be reflected in the y=axis, shifted down 2 units and vertical stretch by a factor of 7.F-BF.4What is the inverse, f-1(x), of the function fx=3x-7?f-1x=x-73f-1x=x+73f-1x=-3x+7f-1x=7x-3Which of the following is the inverse function of y=3x-22?y=x2+23y=2x2+23y=4x2+23y=x23Which expression represents the inverse of fx=8x+13?x8-1318x+13log21xlog8x-13Given that f-1x=g(x) and fx=2x, which expression correctly defines the function g(x) and its domain?x22 for all values of x≥0x24 for all values of x≥0x22 for all real values of xx24 for all real values of xWhat is the inverse of fx=x3+5?f-1x=-x3-5f-1x=3x-5f-1x=3x3-5f-1x=x-35What is the inverse of the equation y=3x-4, x≥43?y=x2+43, x≥0y=4-x3, x≤4y=-x2+43, x≥0y=-x+43, x≥-4F-LE.3 For what positive integer value of x will the value of gx=3x first exceed the value of fx=2x+25?342526Which statement is true about the functions fx=2x2+x+2 and gx=2x+2, when x=0?The value of f(x) and the value of g(x) are the same.The value of f(x) exceeds the value of g(x) by 1.The value of g(x) exceeds the value of f(x) by 1.The value of g(x) exceeds the value of f(x) by 2.fx=1.02x+100; gx=501.02x What is the smallest positive integer in which the value of g(x) exceeds the value of f(x)?60595550George is comparing the graphs of two function fx=3x and gx=3x2+x-1 for different values of x. Which statement best compares the values of the function as the value of x increases?f(x) will eventually exceed g(x) for all real numbers greater than a certain x-value.g(x) will eventually exceed f(x) for all real numbers greater than a certain x-value.f(x) is greater than g(x) for all values of x.g(x) is greater than f(x) for all values of x.What is the largest integer value of x such that the value of fx=x2-6x+40 exceeds the value of gx=21.5x?681012 F-TF.1 The radius of a circle is 2 centimeters. A central angle of the circle intercepts an arc of 8 centimeters. What is the radian measure of the angle?2 B. 3 C. 4 D. 8A circle has a central angle whose radian measure is 2 and an arc length of 6 meters. What is the diameter of the circle in inches?2 B. 3 C. 6 D. 12In a circle, an arc of length 8π is intercepted by a central angle of 2π3 radians. What is the radius of the circle?3π16 cm B. 16π3 cm C. 16π23 cm D. 12 cmThe circle shown below has a diameter of 18 centimeters (cm). If the dotted arc is 33 cm long, what is the measure of angle θ in radians?311611116113F-TF.2 William put the tip of his pencil on the outer edge of a graph of the unit circle at the point (0, -1). He moved this pencil tip through an angle of 4π3 radians in the counterclockwise direction along the edge of the circle. At what angle of the unit circle did William’s pencil tip stop?π3B. 5π6C. 7π6D. 5π3Max put the tip of his pencil on the outer edge of a graph of the unit circle at the point (-1, 0). He moved his pencil tip through an angle of π6 radians in the counterclockwise direction along the edge of the circle. At what angle of the unit circle did Max’s pencil tip stop in radians?7π6 B. π6 C. 5π6 D. 11π6A Ferris wheel has a diameter of 114 feet and is 5 feet off the ground. After a person gets on the bottom car, the Ferris wheel rotates 1700 counterclockwise before stopping. How high above the ground is the car when it has stopped?56 feetB. 62 feet C. 80 feetD. 118 feetHow many radians are 1800o?1010π180180πIn the right triangle pictured below, the measure of angle A, in radians, is θ. The side adjacent to angle A measures 6 cm and the side opposite measures 5 cm. Which value is closest to sin 5θ?A. -0.3260B. 0.6402C. 0.9723D. 3.2009F-TF.5A mark of T is at the top of a small wheel. The graph shows h, the height in centimeters of the T above the ground as a function of x, the angle the wheel has turned.Which function is best represented by the graph?hx=12cosxhx=12sinx-x2hx=6sinx+π2+6hx=6cosx+π2+6An automotive engineer recorded an antilock brake sensor wave with an amplitude of 0.8, a midline of 0.1, and a frequency of π4. Which equation best represents this wave?y=0.1sin8x+0.8y=0.8sin4x+0.1y=0.8sin8x+0.1y=0.1sin4x+0.8A transmitter sends a radio wave from the top of a 70-foot building. The amplitude of the wave is 1.5, the midline of the wave is 4, and the frequency of the wave is π. Which equation best represents this radio wave?y=1.5sin2xy=1.5sin2x+4y=2sin1.5x+4y=2sin4x+1.5G-GO.10 In ?ABC, AD=DB and AE=EC. Which of the following can be proven? A. Triangle ABC is isosceles.B. DE is perpendicular to ACC. The length of DE is half the length of BC.D. Triangle ABC is congruent to triangle ADC.In triangle ABC, m<x and m<B=y. Which of these can be proved using the triangle sum theorem?m<C=ym<C=x+ym<C=180o-x+ym<C=180o-(x+y)3. Find the measure of each angle in the triangle.4. Find SR in the figure belowIf CR=24, what is KR?6 B. 8 C. 12 D. 168. If TR=12, what is CP?16 B. 18 C. 24 D. 36G-GO.11 Which of these properties is enough to prove that a given parallelogram is also a rectangle?The diagonals bisect each other.The opposite angles are equal.The opposite sides are equal.The diagonals are congruent.In the figure below, PO//MN and PM//ON.Which would be a correct way to begin a proof that shows <O?<M?Draw diagonal PN and show that a pair of corresponding angles formed by the transversal are congruent.Draw diagonal OM and show that a pair of adjacent interior angles formed by the transversal are congruent.Draw diagonal PN and show that a pair of alternate interior angles formed by the transversal are congruent.Draw diagonal OM and show that a pair of alternate interior angles formed by the transversal are complementary.G-SRT.2For 1-2, determine if the triangles below are similar. If so, write the similarity statement.1.2. G-SRT.5What is the value of x in the triangle below?532 cm53 cm10 cm15 cmWhich of the figures shown below are similar?If the rectangular prisms are similar, what is the value of x?9101218Triangle MNP is a right triangle. Point X is on MP, Point Y is on PN, and MN is parallel to XY.Which statement must be true??PMN??PXY ?PMN~?PXYm<PMN-m<XPYm<PMN>m<PXYTriangle ABC is similar to ?DEF, AB=12, DE=8, and AC=15. What is the length of DF?A. 6.4B. 10C. 11D. 22.5G-C.5 Which measurement is closest to the area of the shaded sector in the circle shown below?12.56 square inches25.12 square inches50.24 square inches75.36 square inchesThe drawing shows a semicircular window separated into 3 sections of color glass.Approximately how many square inches of the tinted glass are red?15.770.7141.3282.66. The windshield wiper blade on Julia’s car is 21 inches long. Each swipe of the wiper makes an angle of 85 degrees as pictured below.To the nearest inch, how far does the tip of the windshield wiper travel with each swipe of the blade?21 inches30 inches31 inches33 inches7. Sally is creating a flower bed that wraps around the corner of her house. She will put edging around the flower bed 10 feet from the corner of the house in all directions as shown below. Which is the best estimate of the number of feet of edging that Sally will need?24434863G-GPE.1 What is the equation of the circle that has a center at (-1, -3) and a radius of 4 units?x-12+y-32=16x+12+y+32=16x-12+y-32=2x+12+y+32=2A circle is graphed on the coordinate plane below.x2+y-42=9x+42+y2=9x-42+y2=3x2+y+42=3Which equation represents a circle with the center at -1, 7 and a radius of 17?x-12+y+72=17x+12+y-72=17x+12+y+72=17x+12+y-72=17What is the center and the radius of a circle given by the equation x2+y2+4x-10y+20=0?-2, 5 and r=202, -5 and r=20-2, 5 and r=32, -5 and r=3The equation x2+y2-4x-8y-16=0 represents a circle in the standard xy-coordinate plane. What is the radius of the circle?62042S-IC.4 Of 400 teenagers surveyed, 62% do not plan to stay in their communities after finishing their education. Find the margin of error for the sample.±2% B. ±4% C. ±5% D. ±6%In a random survey of 1,000 high school students, 65% said that math is their favorite subject. Based on these survey results, which of these represents a 95% confidence interval for the percentage of all high school students who would choose math as their favorite subject?60% to 70%62.04% to 67.96%62.5% to 67.5%63.52 to 66.48A sample of 121 high school seniors were surveyed on their level of school spirit on a scale of 0-100. The sample mean of this survey is 86. The known population standard deviation is 14 for all seniors in the class. Which of these is a 95% confidence interval for the population mean?[82.72, 89.28][83.51, 88.49][83.91, 88.09][85.92, 86.08]An electrics company conducted a customer satisfaction survey. The survey results showed, with a 95% confidence level, that 62% to 68% of customers are satisfied with their service. What is the margin of error of this survey?3%6%65%95%A state senator requested a survey of registered voters to determine public opinion of a new law. Of the 940 voters who responded to the survey, 61.7% were in favor of the new law, 35.% were opposed, and the rest were undecided. What is the margin of error of this survey with a 95% level of confidence?±1.44%±1.51%±2.98%±3.11%A random sampling of 500 adults showed that 203 preferred Brand A potato chips more than all other brands of potato chips in the survey. Which interval reflects a 95% likelihood of containing p, the population proportion?0.305≤p≤0.508B. 0.356≤p≤0.456C. 0.363≤p≤0.449 D. 0.386≤p≤0.426 ................
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