Cumulative Review_A Name 1-9: Write an equation in the specified form from the given information 1.) Write a quadratic function with a vertex at (5, 11) and passes through the point (13, 27); in Vertex Form 3.) Write a linear function that goes through the points (-5, 6) and (10, 12); in Slope-Intercept Form 2.) Write a circle equation with center at (-3, 6) and a point on the circle (5, -10); in Center-Radius Form 4.) Write a cubic function that passes through at -4 and bounces at 6 and also goes through the point (5, 63); in Intercept Form 5.) Write an absolute value function using the table; in Vertex Form x -4-3 -2-1 0 1 f(x) 9 7 5 7 9 11 6.) Write a piecewise function using the graph 7.) Write a polynomial function using the graph; in Center-Radius Form in Intercept Form 5-5 0 5-5 8.) Write a circle equation from the graph; 9.) Write a quadratic function from the graph; in General Form in Standard Form 10 10 5 5-10 -5 0-5 0
For 10-13, graph and state domain and range 10.) y = (x + 4)( 3, x < 1. / x 5, x 3 11.) y =. 23 x + 6 x + 2 ( x 5 12.) y = / x + 4 + 7 13.) y =. (x + 6)(x 2) ( (
For 14-19, rewrite the function into its inverse; then write the domain and range of both the function and inverse 14.) T x = e 9:; 3 15.) F x = x 5 x + 3 T >. x = F >. x = 16.) P x = ( / x + 7 17.) D x = 2 x + 6 / P >. x = D >. x = 18.) W x = x ( + 8x + 19 19.) Q x = log / ( 2x + 5) W >. x = Q >. x =
For 20-23, answer the application questions 20.) Use the figure of the square pyramid to the right to answer the questions a.) Based on the given height and volume, what be the length of the base? Volume = 10800 cm 3 36 cm b.) What will be the length of the slant height? c.) What will be the surface area of the square pyramid? 21.) A relief effort to help hurricane victims is making care packages. The effort already has made 22 care packages and continues to make more at a steady rate of 4 packages every 10 minutes. a.) Write a function modeling the number of care packages the effort has P(t) over time in minutes t b.) Evaluate P(55) and write a sentence interpreting the meaning of the answer c.) If the effort needs to have made 300 packages, how will it take for them to make that many? 22.) Find the volume. a. b. c. d.
23.) Find the surface area. a. b. c. d. e. f. For 24-31, solve the equation or system of equations 24.) 2 x + 7 3 = 17 25.) 7log ; 6x + 7 = 14 26.) 27 9>( 3 9:I = 9 (9>. 27.) 4 3x + 7 5x = 2x + 19
28.) 4x + 7 11 < 3 29.) 3x y = 28 y = (3x + 2)(x 6) 30.) 8x / 343 = 0 31.) x I + 2x / + 21x ( + 72x 540 = 0 Given 6i is one of the zeroes For 32-34, evaluate the given piecewise function f x = x( + 4, x < 1 3 9 56, x 4 32.) f(-6) 33.) f(-1) 34.) f(4) For 35 38, complete each operation and simplify 35.) / + L 9 : 2 9 > ( 36.) x 2 x > 6 3x > 12 x2 > 4 x > 2 37.) x 2 :10x:16 x 2 >6x>16 x2 >64 x:8
38.) Given the function: f x = >I(9:;)(9>/)(9:()W (9>I) 9:. W (9:;) a) Where are the x-intercepts located and do they bounce or pass through? b) Where are the vertical asymptotes located and do they approach opposite directions or approach the same direction? c) What are the coordinates of the hole? d) Where is the y-intercept? e) Where is the horizontal asymptote? f) What is the domain? For each equation, state the excluded/restricted values and solve. 39.).3 + I = ; 9 W > (9 9 9>( 40.) 2 = 9 9 W :I9:/ 9:/ For each pair of similar triangles, determine the value of the variable(s). 41.) 5.) A 42.) 6.) D 20 x 15 12 y G x I 16 13 H B 14.4 E C ABC ~ y DEF F J 24 18 GHI ~ KJI K
For each pair of triangles and with the given information, complete the following. Determine if they can be proven similar, congruent, neither, or write inconclusive if there is not enough info. If it can be proven similar or congruent, state what theorem you can use to prove it. 43.) 44.) J K M L N 14 11 45.) 46.) 21 O P 5.6 8 4.4 R Given: Figure OPQR is a parallelogram Q 47) Match the point of concurrence with type of lines that form it and its name. (A capital letter, lower case letter, and roman numeral should go in each box provided.) A) B) C) D) i) Angle Bisectors ii) Perpendicular Bisectors iii) Medians iv) Altitudes a) Circumcenter b) Centroid c) Orthocenter d) Incenter
For questions 48 50, solve for the indicated measure. Q R 48.) 49.) S O U Given: mqt = 122 m QUT = 80 Find: mrs = A O B Given m ACB = 41 mbc = 109 Find mac = T C 50.) B D K A O Given mab = 25 mcd = 65 C Find m AKC = For 51 52, solve for the variable. 51.) 52.) x + 13 4 7 -x - 2 53.) x+1 3 8 3x+1 O
Complete a proof for 54 56 54.) Given AC AR and 1 2 55.) Prove 3 4 Given: B E, C is the midpoint of BE vvvv Prove: ABC DEC Statement Reason Statement Reason 56.) Prove EFG ~ IHG E F Statement Reason G H Given: EF HI I Find the arc length for the minor arc for 57-58. s = θr (θ = degree k.l3 (donn t type in π) 57.) 58.)
Graph the sine or cosine function 59.) y = 3 cos x + 2 60.) y = sin 4πθ 61.) y = 2 cos İ x Find the sector area for the shaded region for 62 63. A =. ( θr( (θ = degree k.l3 (donn t type in π):
64.) A Ferris wheel makes 1 revolution in six minutes. The diameter is 62 meters and the midline is at 48 meters. a) What is the tallest height a person will be on the Ferris wheel? b) At what time(s) will the rider be at 17 meters in one revolution? c) What is the period of this function? d) What is the amplitude of this function? e) Sketch a graph of the function. (Use every two squares as one tick mark) f) Write the function that would represent this scenario. 65.) 66.)