MGF Topics in Mathematics Name Test #1 - Chapters 2 and 9 Date List the elements in the set. 1) {x | x is a whole number between 1 and 5} A) {1, 2, 3, 4, 5} B) {2, 3, 4, 5} 2) {x | x is an integer greater than -6} A) {-7, -8, -9, ...} B) {-5, -4, -3, -2} Write the set in set-builder notation. 3) {2, 4, 6, 8} A) {x | x is any even integer less than 10} C) {2, 4, 6, 8} D) {2, 3, 4} C) {-7, -8, -9} D) {-5, -4, -3, ...} B) {x | x is an even natural number less than 10} D) {x | x is any even natural number} 4) {-6, -5, -4, -3, ...} A) {x | x is any integer} C) {-6, -5, -4, -3} B) {x | x is an integer greater than -7} D) {x | x is an integer between -7 and -2} Identify the set as finite or infinite. 5) {x | x is a counting number larger than 480} A) Infinite 6) 1, C) {1, 2, 3, 4} B) Finite 5 25 125 3125 , , , ..., 7 49 343 16807 A) Finite Find n(A) for the set. 7) A = {2, 4, 6, 8, 10} A) n(A) = 5 B) Infinite B) n(A) = 4 8) A = {x | x is a second in a minute} A) n(A) = 12 B) n(A) = 60 C) n(A) = 2 D) n(A) = 10 C) n(A) = Infinite D) n(A) = 120 Tell whether the statement is true or false. 9) k {p, a, k, h, v} A) True B) False 10) {s, q, y, o, d} = {o, d, q, s, y} A) True B) False Write true or false for the following statement. Let A = {3, 5, 7, 9, 11, 13} B = {3, 5, 9, 11} C = {5, 9, 13} 11) A = {x | x is an odd counting number greater than 1 and less than 15} A) True B) False 1 12) Every element of C is also an element of A. A) True B) False Decide whether , , both, or neither can be placed in the blank to make a true statement. 13) {11, 12, 13} {10, 11, 12, 13} A) Both and B) Neither C) 14) {0} A) B) Both and D) C) Neither D) B) {w, y, z} C) {y, z} D) {y} B) {r, t, v, x} C) {t, v, x} D) {r, s, t, u, v, w, x, z} B) {q, y, z} C) {q, s, u, w, y, z} D) {q, s, w, y} List the elements in the set . Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. 15) B C A) {q, s, v, w, x, y, z} 16) (A B)' A) {s, u, w} 17) A (B C) A) {q, r, w, y, z} The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. Alabama soybeans (s) peanuts (p) corn (c) hay (h) wheat (w) Arkansas soybeans (s) rice (r) cotton (t) hay (h) wheat (w) Louisiana soybeans (s) sugarcane (n) rice (r) corn (c) cotton (t) Let U be the smallest possible universal set that includes all of the crops listed, and let A, K and L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find each of the following sets. 18) L K A) {c, h, n, w} B) {c, h, n, r, s, t, w} C) {r, s, t} D) {c, n, r, s, t} 19) K' L A) {h, w} B) {r, s, t} C) {c, n, p} Tell whether the statement is true or false. 20) {3, 17, 26, 9, 31} = {31, 17, 9, 62, 3} A) True B) False 21) (11, 9) = (9, 11) A) True B) False 2 D) {c, n} Find the Cartesian product. 22) A = {i, a} B = {t, d, m} Find A × B. A) {(i, t), (t, a), (i, d), (d, a), (i, m), (m, a)} C) {(i, t), (i, d), (i, m), (a, t), (a, d), (a, m)} B) {(t, i), (t, a), (d, i), (d, a), (m, i), (m, a)} D) {(i, t), (a, t), (i, d), (a, d)} Find the number of subsets of the set. 23) {math, English, history, science, art} A) 24 B) 32 C) 16 D) 28 Find the number of proper subsets of the set. 24) {3, 4, 5} A) 2 B) 5 C) 6 D) 7 For the given sets, construct a Venn diagram and place the elements in the proper region. 25) Let U = {c, d, g, h, k, u, q} A = {d, h, g, q} B = {c, d, h, u} A) B) C) D) 3 26) Let U = {1, 2, 3, 4, 5, 6, 7, 8} A = {3, 6, 8} B = {4, 6} C = {1, 6, 7, 8} A) B) C) D) 4 Shade the regions representing the set. 27) A' B' A) B) C) D) Solve the problem. 28) A survey of a group of 116 tourists was taken in St. Louis. The survey showed the following: 66 of the tourists plan to visit Gateway Arch; 50 plan to visit the zoo; 10 plan to visit the Art Museum and the zoo, but not the gateway Arch; 14 plan to visit the Art Museum and the Gateway Arch, but not the zoo; 18 plan to visit the Gateway Arch and the zoo, but not the Art Museum; 9 plan to visit the Art Museum, the zoo, and the Gateway Arch; 14 plan to visit none of the three places. How many plan to visit the Art Museum only? A) 50 B) 37 C) 13 D) 102 29) In a survey of 280 people, a travel company asked people about places they plan to visit in the next 5 years. The results were as follows: 48 plan to visit Europe 58 plan to visit Latin America 34 plan to visit Asia 14 plan to visit Europe and Latin America 12 plan to visit Latin America and Asia 11 plan to visit Europe and Asia 4 plan to visit all three How many people plan to visit exactly two of these places? A) 29 B) 37 C) 18 Find the requested angle. 30) Complement of 65° A) 295° B) 115° C) 130° 5 D) 25 D) 25° Find the measure of the angles. 31) A = (5x - 48)° , B = (3x + 20)° A) 67.5° and 112.5° B) 80° and 100° C) 56° and 124° A = (13f)°, B = (3f)° A) 68.125° and 21.875° C) 36.56° and 8.44° B) 146.25° and 33.75° D) 73.125° and 16.875° A = (7x - 57)°, B = (5x - 25)° A) 55° and 55° B) 125° and 125° C) 125° and 55° D) 82° and 98° 32) 33) Use the properties of parallel lines to solve the problem. 34) If p q and m 8 = 49°, what are the measures of the other angles? A) m B) m C) m D) m 2=m 5=m 2=m 2=m 4=m 6=m 4=m 4=m 6 = 49°, m 7 = 49° , m 6 = 49° , m 6 = 49° , m 1=m 1=m 1=m 1=m 3=m 2=m 3=m 3=m 5=m 3=m 5=m 5=m 6 7 = 131° 4 = 131° 7 = 41° 7 = 141° D) 35° and 35° 35) In the figure, AB CD . Identify all pairs of congruent angles. A) ABE and ABC , FCD and BCD C) ABE and FCD , ABC and BCD B) ABE and FCD D) ABC and FCD , ABE and BCD, Classify the triangle as acute, right, or obtuse and as equilateral, isosceles, or scalene. 36) A) Obtuse, scalene B) Acute, isosceles C) Obtuse, equilateral D) Right, scalene A) Right, scalene B) Acute, scalene C) Obtuse, scalene D) Obtuse, equilateral C) A = B = 45° D) A = 35°, B = 55° C) 169° D) 105° 37) Find the measure of each unknown angle in triangle ABC. 38) A = (45 - x)°, B = (9x - 35)° A) A = 29°, B = 61° B) A = 39°, B = 51° Solve the problem. 39) Find the measure of the indicated exterior angle. x = (199 - 5n)°, y = (5n + 26)°, z = (n + 8)° A) 146° B) 124° 7 Find the area. 40) 5 in. 10 in. (a parallelogram) A) 50 in2 41) B) 15 in2 C) 100 in2 D) 25 in2 B) 63 ft2 C) 126 ft2 D) 49 ft2 B) 294 cm2 C) 588 cm2 D) 220.5 cm2 B) 882 m 2 C) 1008 m 2 D) 1071 m 2 7 ft 6 ft 14 ft (a trapezoid) A) 27 ft2 42) 26 cm 21 cm 28 cm A) 273 cm2 43) 48 m 25.5 m A) 535.5 m 2 42 m Find the area of the circle. Use 3.14 for . Round results to two decimal places in necessary 44) 11 cm A) 34.54 cm2 B) 94.99 cm2 C) 69.08 cm2 8 D) 379.94 cm2 The following figure has perimeter, circumference, or area as indicated. Find the value of x. Use 3.14 as an approximation for . 45) P = 32 2x - 3 x+1 x+1 2x - 3 A) 6 B) 7 C) 9 D) 12 B) 2.5 C) 4 D) 9 B) 5 C) 2.5 D) 13 46) A = 36 x x+5 A) 13 47) A = 27 x 3 A) 18 x+8 9 The two triangles below are similar. Find the unknown side lengths. 48) 18 27 14 A) x = 45 21 28 B) x = 34 C) x = 36 D) x = 28 B) x = 6.4; y = 3.9 C) x = 5.6; y = 3.9 D) x = 1.40; y = 3.6 49) 7.2 A) x = 5.6; y = 3.6 4.8 a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. 50) b = 48 cm, c = 50 cm A) a = 14 cm B) 48 cm C) 15 = cm D) a = 13 cm 10 Answer Key Testname: MGF 1106 - TEST REVIEW 1 (CH 2 AND 9) 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) D D B B A A A B B A A A A C C B D C D B B C B D B C D C D D D D A A C B A D B A B B A B A C B C A A 11