29 April 2000
First Round Knowdown 2000
"I will read the question twice then you will have 10 seconds to answer and your last answer given in the ten seconds will be the accepted one. If the answer is incorrect you will be asked to turn in your nametag and leave the competition. Any questions? Let's begin."
Factor: 4 'x' squared minus 9 { 4x2-9 }
(2x+3)(2x-3) Solve: 3 'x' minus 6 equals 12 { 3x-6=12 }
6 Find the probability of getting three heads when dropping three fair coins on the smooth floor. 1/8 Simplify: 4 times the quantity 'x' minus 2 (pause) plus 3 'x' { 4(x-2)+3x }
7x-8 Multiply: 5 'x' times the quantity 'x' squared plus 2 'x' { 5x(x2+2x) } 5 x3+ 10x2 Solve: 3 'x' minus 8 equals 5 'x' { 3x-8=5x }
-4 Simplify: 2 'x' to the third times 3 'x' to the second { (2 x3 )(3 x2 ) }
6 x5 Evaluate: negative 2 times 3 times the quantity negative 2 to the third { (-2)(3)(-2)3 }
48 Find the slope of the line represented by the equation 2 'y' equals 3 'x' –1 { 2y=3x-1 } 3/2 or 1.5 or 1 1/2
Find the coordinates of the y intercept for the line represented by the equation 5 'x' plus 6 'y' equals 15 { 5x+6y=15 }
(0, 5/2) Simplify to an exact value the square root of 50 5(2)(1/2) Simplify 12 'x' 'y' squared all divided by the quantity 4 'x' { 12xy 2/4x }
3y2 Evaluate: 2 thirds of 3 fourths { 2/3 of 3/4 }
1/2 When rolling a fair six sided standard die twice, find the probability that both throws show a value greater than 2 4/9 Find the decimal value of 5 ninths { 5/9 }
0.5555555555... Find the exact length of the hypotenuse of a right triangle with legs of lengths 5 and 6 (61)(1/2) Solve: negative 3 'x' is less than 12 { -3x<12 }
x > -4 Find the coordinates of the 'x' intercept for the line represented by the equation 7 'x' plus 3 'y' equals 42 { 7x+3y=42 }
(6,0) Evaluate four fifths minus one third { 4/5 - 1/3 }
7/15 In a right triangle one angle is 37 degrees and 20 minutes, find the measure of the other acute angle. 52 degrees 40' Factor: 2 'x' squared minus 25 'x' { 2x2 –25x }
x(2x-25) Simplify to an exact value the square root of 75 5(3)(1/2) Find the decimal value of 12 minus 3 fourths plus 1 half { 12-(3/4)+(1/2) }
11.75 Give the quadrant or quadrants that the graph of 'x' equals -4 would pass through.
{ x=-4 }
2 and 3 (need both) Find the other leg of a right triangle if the hypotenuse is 100 feet and a leg is 60 feet 80 feet Simplify to an exact value: 2 square root of 3 times 4 square root of 2 { (2(3)(1/2))(4(2)(1/2) ) } 8(6)(1/2) Simplify negative 4 'x' 'y' divided by the quantity 8 'x' { -4xy/8x }
-0.5y or -y/2 etc. Solve: 3 minus 2 'x' equals nine { 3-2x=9 }
-3 Factor: 9 'x' squared minus 1 { 9x2 -1 }
(3x-1)(3x+1) Find the exact value of the area of a circle with a diameter of 26 centimeters 169(pi) sq. cm. Fine the slope of the line represented by 3 'x' equals 5 'y' plus 6 { 3x=5y+6 } 3/5 What is the decimal value of 11 eighths { 11/8 }
1.375 Find the mean for these four numbers: 12, 8, 11, 19 12.5 Simplify to an exact value the square root of 48 4(3)(1/2) Evaluate 3 eighths divided by nine eighths { 3/8 ÷ 9/8 }
1/3 Find the area of a right triangle with a hypotenuse of 5 meters and a leg of 4 meters 6 sq. m. Simplify 3 times negative 2 times the quantity negative 3 to the second { (3)(-2)(-3)2 } -54 Simplify to an exact value the square root of 14, times 5 square root of 2 { (14(1/2))(5(2(1/2) )) } 10(7)(1/2) The line represented by the equation 'y' equals 4 'x' minus 2 intercepts the 'x' axis at what coordinates { y=4x-2 }
(1/2, 0) Find the sum of the measures of the interior angles of a hexagon 720 degrees Find the decimal value of 7.2 plus three fourths minus one fifth { 7.2+3/4-1/5 } 7.75 Factor 3 'x' 'y' minus 'y' { 3xy-y }
y(3x-1) Simplify: 4 'x' squared times 2 'x' to the fifth { (4x2)(2x5 ) }
8 x7 Simplify to an exact value the square root of 40 2(10)(1/2) Find the coordinates of the intersection of the x axis and the line represented by 'y' equals 7 'x' plus 14 { y=7x+14 } (-2,0) Factor 7 'x' squared minus 49 'x' { 7 x2–49x }
7x(x-7) Factor 25 'x' squared minus 1 { 25 x2–1 }
(5x+1)(5x-1) Find the exact value of the length of the hypotenuse on a right triangle with legs of lengths 30 and 20 (1300)(1/2) or 10(13)(1/2) Solve: negative 28 is less than or equal to -7 'x' { -28 <= -7x }
x <= 4 Find the measure of one exterior angle on a regular octagon 45 degrees Simplify to an exact value 2 square root of 7 times 5 square root of 7 { (2(7(1/2))(5(7(1/2) ) } 70 Simplify 3 'x' divided by the quantity 12 'x' squared 'z' { 3x/12x2z }
1/(4xz) Give the decimal value of 7/3 2.33333333... If one angle of a right triangle is 12 degrees 57 minutes find the measure of the other acute angle 77 degrees 3' How many marbles are in a bag if there are 16 black marbles and the probability of drawing a black is 2 thirds 24 marbles Second Round Knowdown 2000
"The second round will consist of five questions. In this round I will read the question and all of you will write your final answer on the pad of paper in front of you. You will have 15 seconds to answer and I will count down the final three seconds; 3, 2, 1, 0. When I say zero your pencil must be on the desk in front of you or you will be disqualified. Before each question, put your name at the top of the piece of paper. I (we) will collect the papers after each question and those persons with the correct answers will continue. I will collect the nametags for those that are eliminated. Are there any questions? Let's begin."
Find all the real solutions to 'x' squared minus 3 'x' plus 2 equals zero { x2–3x+2=0 }
1 and 2 Two regular six sided dice are rolled, find the probability that the sum of the dice is greater than 8 10/36 of 5/18 Find the exact volume of a cylinder with a diameter of 10 meters and a height of 8 meters. 200(pi) cubic meters Find to the nearest integer, the number of cubic yards of concrete in a slab 30 feet by 10 feet by 4 inches. 4 Find the sum of the first 6 terms of the series: one half plus one fourth plus one eight and so on. 63/64 Find 'f' of 'f' of 3 if 'f' of 'x' is 4 'x' minus 6 { find f(f(3)) if f(x)=4x-6 }
18 The mean of five test scores is 80. Three of the scores are 75, 80 and 90. What is the sum of the other two scores? 155 The area of a sector of the circle with a radius 8 centimeters is 16¹ centimeters squared. What is the measure of the central angle? 90 degrees Find the median of the following numbers: 45, 32, 73, 42, 19, 12. 37 One runner finished the race in 3 hours 17 minutes 43 seconds and the other finished in 3 hours 26 minutes 27 seconds. How many minutes and seconds separated them? 8 minutes 44 seconds
State Knowdown questions
If f is a linear function and f(1)=5 and f(3)=9, what is f(4)?
f(4) = 11
You have three socks under the bed. Two are clean and one is dirty. You reach under the bed and draw out one sock and then another. You put them on. What is the probability that you are wearing two clean socks?
p = 1/3
The first computer screen has a viewable area of 12x15 inches. The second has a viewable area of 18x15. What is the percent increase from the first to the second?
50% larger
There are four laps in a 1 mile race. If you run the first lap in 71 seconds and on each additional lap, you slow down by two seconds, how many minutes and seconds will you take to complete the race?
4 minutes 56 seconds
You can write 80 lines on a standard sheet of paper. On the average, each line has 10 words. You've used up 3/5 of the page so far. How many words have you written?
480 words
To the nearest square foot, give the area of the smallest square window that a 4'x8' sheet of plywood will fit through.
8 square feet
© 2000 WSMC, Jim Miller, and Richard Edgerton