01-01 Virtual Challenge Meet # - Mathematics Test 1. Evaluate [( + 1) ] {( + 7) 11 (18 9)}. 5 7 11 1. Store A sells 1 pencils for $1.00. Store B sells 15 pencils for $1.5. Store C sells 16 pencils for $1.50. Packages of pencils cannot be broken into smaller units. What is the smallest amount of money need to purchase exactly 170 pencils? $1.50 $15.50 $1.5 $15.00 $1.00. The largest chord of a circle is known as the diameter radius circumference secant tangent. Which of the following is a factor of x x 8x + 1? x 1 x x x x 6 5. The largest triangular number less than 00 is 18 176 188 190 196 6. Which of the following is true of the set {0, 1,,,...}? (1) closed under addition () closed under subtraction () has an additive identity () has a multiplicative identity 1, 1,, 1,, 1,,, 7. It takes 1 feet of ribbon to make each mum for homecoming. How much ribbon is needed to make two dozen mums? 78 yards 5 yards 6 yards 1 yards 6 1 yards Dr Numsen Doug Ray c 01 www.academicmeet.com Twitter: @DrNumsenMath
01-01 Virtual Challenge Meet # - Mathematics Test 8. Angles R and S are supplementary. Angles S and T are complementary. Angles T and U are complementary. If m S = 8, what is m R + m U? 17 168 180 156 1 9. If f(x) = x 5 + 5x + 10x + 10x + 5x + 1, then f(18) = 1568 1889568 119857 76099 68769 10. The length of a rectangle is x + 5 and its width is x 1. What is the perimeter of the rectangle, in terms of x? 8x + 6 6x + 1x + 1x 5 8x + 6x 5 1x + 8 11. A special.5% alcohol solution must be mixed by diluting a 5.% alcohol solution with water. A total of pints of.5% solution must be created. How much water must be used? (Round.) 1.1 pt 0.65 pt 0.7 pt 0.57 pt 0. pt 1. Which formula gives the nth term of this sequence: 7, 10, 1, 19, 5,,...? n + 1 n + 6 n + n + 10 n + n + 7 n + n + 5 1. Two ranger stations are 600 yards apart along a road. Ranger Bob sees a lost hiker 0 yards away from his station. Ranger Tim sees the same hiker 0 yards away from the other station. If the hiker walks straight to the road between the stations, how far must he walk to get to the road? (Round.) 07 yd 1 yd 19 yd yd 8 yd 1. A merry-go-round is rotating at 1 RPM. A child sits on the edge. The radius of the merry-go-round is 6 feet. How far does the child go if he rides for minutes? (Round.) 5 ft 1810 ft 10 ft 8 ft 905 ft 15. If f(x) = e x, what is f 1? 1 e x ln x ln x ln 1 x ln x Page
01-01 Virtual Challenge Meet # - Mathematics Test 16. Two skyscrapers are 0 feet apart. The buildings are 86 feet high and 676 feet high, respectively. A high wire will attach the two buildings at their roofs. How long does the wire need to be? (Round.) 18 ft 187 ft 190 ft 19 ft 196 ft 17. If log x + log x 7 log x 9 =, then x = 6 5 18. A cable company is going to offer 1 new music channels: 5 rock, country, pop, and classical. The channels in their own genre must stay together, but can be re-arranged. The genres can be listed on the channel guide in any order. How many different ways can the channels be listed on the guide? 6910 880 1150 560 10 19. If f(x) = kx x + and f () = 7, then f (6) = 17 11 1 7 0. Let x + y = 1xy. Find dy dx. x + 6y x 6y 6x + y 6x y x 6y x y x + 6y x + y x y 6x 1. The radius of a sphere is increased from 1 cm to 15 cm. By what percent is the sphere s surface area increased? 56 1 % 66 % 5% 50% 75%. Let U = {1,,,,..., 5} be the universal set. Let T = {t t is a triangular number} and S = {s s is a perfect square}. How many elements are in the set (T S)? [X represents the complement of X.] 1 15 16 17 18. If 5x 6 x = 7y, then 6x = 8 y 57y 77y 9y 6y Page
01-01 Virtual Challenge Meet # - Mathematics Test. If a 1 = and a n = n for n, find a a 5. n 1 0 0 7 10 15 5 5. M and N are midpoints of AC and AB, respectively. Find the area of AB A 7 cm 8 cm M N 6 cm C B 6 cm cm 8 cm 96 cm 6. The lines ax + by = c are dx + ey = f are parallel. Which of the following must be true? a = d and b = e c = f a b = d e ae = bd ad = be 7. The orthocenter of ABC lies on the triangle itself. Which of the following is true? ABC is acute ABC is right ABC is obtuse the orthocenter is also the centroid the orthocenter is also the incenter 8. 1 + 6 10 + 15 1 + 8 6 + 5 55 1 + 9 16 + 5 6 + 9 6 + 81 100 = 11 6 18 9 11 7 1 7 9. For flood protection, a trench is dug to contain rain water. The cross section of the trench is a trapezoid with length across the top of 6 feet, base length of 0 feet, and 16 feet deep. If the trench is 00 feet long, how much water can it hold? (Round.) 0.9 milion gallons 1.1 million gallons 1. million gallons 1.5 million gallons 1.7 million gallons Page
01-01 Virtual Challenge Meet # - Mathematics Test 0. If sin θ = 5 and cos θ < 0, then sec θ = 5 5 5 5 1. The unit circle, x + y = 1, has tangent lines drawn at the points that correspond to standard position angles of 0 and 5. Where do these lines intersect? +,,, (1, 1) (1, 1 ). Find the sum of the positive integral divisors of 115. 75 15 895 00 79. BBA 1 + 987 1 = 1 01 BB 1876 A0 1985. Which is true about the graph shown? y 8 x 8 8 the function is odd the function is even the function is neither odd nor even the function is one-to-one it is not a function 8 5. An account earns 1.5% compounded quarterly. How much should be invested to earn $500 in interest over years? $19,78.7 $18,67.5 $17,997.80 $17,1.56 $16,8.57 6. What is the domain of y = sin 1 x? [ 1, 1] [0, ] [0, ] [, ] (, ) Page 5
01-01 Virtual Challenge Meet # - Mathematics Test [ ( 7. Find sin sin 1 a )] c c a where a, b, and c are sides of a right triangle with a < b < c. b c a c ab c ab c 8. Find the equation of the directrix of the parabola (y + ) = 1(x + ). y = 0 y = 6 x = 7 x = 1 x = 16 9. The parametric curves x(t) = t + 1 and y(t) = t + 5 determine a curve in the plane. Find the slope of the line tangent to the curve at the point (17, 1). 17 17 1 17 1 89 90 0. a x a x + 1 dx = 1 ln(a + 1) ln(a + 1) ln(a + 1) 1 0 1. Simplify a b 5 a b 7 a b. a 5 b 1 a 6 b 1 a b 1 b a 6 a b. The circumference of a circle is k cm and its area is k cm. Find the value of k. 8 1 16. If xy = 0 and x y = 7, then x y = 7580 80 76 77. Find the remainder when x + x 7x 8 is divided by x. 5. If 56 1 9 17 11x 65 x 10x + 1 = A x + B x 7, then B = 6 8 11 Page 6
01-01 Virtual Challenge Meet # - Mathematics Test 6. What is the radius of the circle whose center lies on the line 9x 5y = 0 and is tangent to both the x- and y-axes? 5 8 10 1 7. In which quadrant will α terminate if tan α > 0 and sec α < 0? I II III IV on x-axis 8. The population of fruit flies grows exponentially. After 6 days, there were flies. After 10 days, there were flies. How many flies will be present after 0 days? (Round.) 689 81 1005 18 1596 9. Simplify cot θ 1 + csc θ. 1 cos θ cos θ sin θ 1 sin θ 1 sin θ sin θ cos θ 1 sin θ tan θ 1 + sin θ 50. Find the angle between the vectors u =, 5 and v = 1, 9. (Round.) 0.5 7. 9. 6.7 8.1 51. Find the largest number in the 6th row when the pattern shown is extended. 70 1 5 6 7 8 9 10 11 1 1 1 15 16 17 18 19 0... 71 79 77 750 5. Bob has 6 coins, in nickels, dimes, and quarters. He has seven more nickels than dimes and twice as many nickels as quarters. How much money does he have? $11.0 $10.0 $8.0 $9.80 $7.00 5. Find the sum sin k θ for any angle θ, 0 < θ <. k=1 sec θ tan θ cos θ csc θ cot θ Page 7
01-01 Virtual Challenge Meet # - Mathematics Test kx, if x, 5. If f(x) = 1 x Find the value of k so that f is continuous at x =., if x <. 5 6 55. How many solutions are there for the equation 7x+11y = 10 where x and y are both positive integers? 0 1 56. A bag contains 60 pens of different colors. The probability of selecting a red pen is 5%. The probability of selecting a green pen is 0%. One-third of the remaining pens are blue and the rest are black. How many black pens are there? 7 6 0 57. What is the least positive solution to the equation 8 sin x cos(x) = 0? 1 6 8 58. Find the harmonic mean of 78, 91, and 105. 96 95 9 88 90 59. Find the maximum value of f where f(x) = sin(x). 1 8 16 60. The position of a particle is given by s(t) = t t + 1 after t seconds. How fast is the particle traveling after 8 seconds? 1 units/second 1 units/second units/second units/second 1 units/second Page 8