FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 1 ICTM 2017 STATE DIVISION AA 1. Determine the sum of all distinct positive integers between 8 and 16 inclusive that can be expressed in one and only one way as the sum of at least two consecutive positive integers.

FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 2 ICTM 2017 STATE DIVISION AA 2. In right ABC with A c B d D a 17 C AB BC and D on AC such that BD AC, CD 17, AC b 20 and BD d. Determine the value of a 2 b 2 c 2 d 2.

FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 3 ICTM 2017 STATE DIVISION AA 3. Line is parallel to the line 2x 6y 15 and contains the point 2, 11. Line m is perpendicular to the line containing points 3,5 and 2,10 and passes through the point 2,3. The point k, w is the point of intersection of lines and m. Determine the sum k w.

FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 4 ICTM 2017 STATE DIVISION AA 4. Determine the area of ABC with coordinate points A 0,0, B 80 16, 16 and 2 2 4 C 12 2 35, 625.

FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 5 ICTM 2017 STATE DIVISION AA 5.Point O is the origin. Points A and B are the coordinates of the x-intercept and y- intercept for the graph of 7x 24y 168 0. The area inside the circle containing O, A, and B, but outside OAB is k w p where k, w, and p are relatively prime integers and p 0. Determine the value of k w p.

FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 6 ICTM 2017 STATE DIVISION AA 6. ABCD is a A E B rectangle O with AD 6 D C and E lies on AB so that AED 45. Circle O is inscribed in trapezoid EBCD. Determine the numeric area of the shaded region. Express your answer as a decimal rounded to four significant digits.

FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 7 ICTM 2017 STATE DIVISION AA 7. Let k, w be the unique solution to the system 5x 2y 10.71 13x y 38.51 Let p be the smallest angle of a triangle whose angles are in the ratio 210 :1024 : 2017. Determine the sum. k w p. Express your answer as a decimal rounded to the nearest thousandths.

FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 8 ICTM 2017 STATE DIVISION AA 8. (Adapted from "Real Life" cartoons) Let k 3x 4y equals when 3xy 2xy 2. Let w equal 4y times 2y when x equals 13 and y equals 2x. Determine the sum k w.

FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 9 ICTM 2017 STATE DIVISION AA 9. A slot car track with two slots that are formed by two rectangles with length 20 meters and semi-circular ends of radii 5 and 9 meters as shown. Two cars start and stop at the same time and place and run a complete lap. Let k be the additional distance traveled by the car in the outer slot. The rate of travel of the outside car is w times the rate of the car on the inside slot. Determine the sum k w as a decimal rounded to four significant digits 9 5 20

FROSH-SOPH 2 PERSON COMPETITION LARGE PRINT QUESTION 10 ICTM 2017 STATE DIVISION AA 10. A sequence of concentric circles is formed such that each whole circle has area in the ratio 25: 9 when compared to the previous whole circle. The circle represented by 2 2 x y 6x 4y 2011 0 is the 5 th such circle. Determine the radius of the first circle. Report your answer as a decimal rounded to the nearest thousandths of a unit.

FROSH-SOPH 2 PERSON COMPETITION STATE PLAYOFF QUESTIONS ICTM 2017 STATE DIVISION AA LARGE PRINT QUESTION 11

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 1 ICTM 2017 STATE DIVISION AA 1. Let k log 8192 8 and w n 1 the product n 1 3. Determine 9 kw. Express your answer as an integer or as a common or improper fraction reduced to lowest terms.

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 2 ICTM 2017 STATE DIVISION AA 2.For the system of equations 3x Ay 3, let k be the 4x 5y 1 value of A such that the system is inconsistent. Let w be the value of A such that this system represents perpendicular lines. Determine the product kw. Express your answer as an integer or as a common or improper fraction reduced to lowest terms.

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 3 ICTM 2017 STATE DIVISION AA 3. g x is the polynomial whose zeros are the negative reciprocals of the zeros of 3 2 f x 3x x 4x 2. Let k be the product of the zeros of g x. Let w be the value x x lim log 4 5 log 12 7 3 3 x Determine the sum k w. Express your answer as an integer or as a common or improper fraction reduced to lowest terms.

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 4 ICTM 2017 STATE DIVISION AA 4.Determine the sum of the distinct real root(s) for x, x 0, when 4 3 2 1 1 1 x 8 x 24 x x x x 1 32 x 16 0 x Express your answer as an integer or as a common or improper fraction reduced to lowest terms.

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 5 ICTM 2017 STATE DIVISION AA 5. Consider angles in degree measure, 0 360. Let k be the sum of all such when 2 10cos 9cos 2 0. Let w be the sum of all such when 2 10sin 9sin 2 0. Determine the sum k w.

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 6 ICTM 2017 STATE DIVISION AA 6. Let k and w be positive integers such that k 1 and w 1. Let A 2,3,4,5,, n,,299 Determine the sum of all distinct members of A that are in the form 3 kw.

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 7 ICTM 2017 STATE DIVISION AA 7. The hyperbolas y 2 x 2 1 and y 2 x 2 1 9 meet in four points that determine a convex quadrilateral. Determine the exact perimeter of this quadrilateral.

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 8 ICTM 2017 STATE DIVISION AA 8. In degree mode, let s( x) 1 Sin x sine function) and (the inverse t x tan x. Determine the exact value of s t s t s t 30.

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 9 ICTM 2017 STATE DIVISION AA 9.A van with n teens, n 3, ordered the following items at a fast-food drive-thru: x sandwiches at $3.50 each, where n x 2 n ; y orders of French fries at $1.80 each, where 0 y n ; and n drinks at $2.70 each. The total bill, not including tax, was $60.20. Determine the sum of all possible integral values of n.

JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 10 ICTM 2017 STATE DIVISION AA 10. Determine the least area of a rectangle with horizontal and vertical sides that encloses the entire graph of the polar equation r 20 1 2cos with in radians. Express your answer rounded to the nearest integer.

JUNIOR-SENIOR 2 PERSON COMPETITION STATE PLAYOFF QUESTIONS ICTM 2017 STATE DIVISION AA LARGE PRINT QUESTION 11

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 1 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 1. All values are in dollars. The value of a mug is one-third the value of a jug. The value of a jug is equal to four-fifths the value of a pot. A pot costs $15. Determine the number of dollars for the cost of a mug.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 1 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2. Let k = ANS. The numeric area of rectangle ABCD is 16. AD = k 2. Determine the numeric perimeter of rectangle ABCD.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 1 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. Let k = ANS. In the diagram shown, but not drawn to scale, B, C, D, and E lie on the circle. AE = k, ED = 7, and AB = 15. Determine the length of BC. A E B D C

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 1 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k = ANS. Isosceles ABC (not drawn to scale) has vertex A on the positive y-axis and base BC on the x-axis. BC = 4 and the altitude of ABC from A has length k. ABC is rotated 180 about the y-axis. The numeric volume of the resulting three-dimensional solid is wπ. Determine the value of w. y-axis A C B x-axis

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 2 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 1. Determine the exact larger solution for 2 2x 7x 5 0 =.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 2 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2. a + b ANS = or can be simplified to that form. Let k = a + b + c. Determine the number of prime c number factors of k.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 2 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. Let k = ANS. In rectangle ABCD, diagonal BD = k and DBC = 30. Determine the exact numeric area of rectangle ABCD.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 2 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k ANS =. Each side of a regular hexagon has length k. Determine the exact numeric area of this regular hexagon.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 3 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 3 x y 19 = 16y. 1. Determine the slope of the line perpendicular to the line whose equation is ( ) Express your answer as an integer or as a common or improper fraction reduced to lowest terms.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 3 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2. Let k = ANS. y varies jointly as x and z. y = 38 when x = k and z = 9. Determine the value of y when x = 7 and z = 16.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 3 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. Let k = ANS. In ACE, AE BD, EB bisects AEC, EC = k, and AE = 42. Determine the length DC. A B E D C

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 3 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k = ANS. The line x y 4 2 2 + = is tangent to a circle given by the equation ( 9) ( 3) Determine the exact y-coordinate of the point of tangency. x + y = k.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 1. Sally's rectangular garden is twice as long as it is wide. The width of the garden is 6 feet. Determine the number of feet in the perimeter of the garden.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2. Let k ANS =. Determine the solution (, ) x y for the system your answer the y-coordinate of this ordered pair ( x, y ). 40x 3y = 21. Report as ky 76x = 18

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. Let k = ANS + 16. A certain convex polygon has k diagonals. Determine the number of sides in this polygon.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k = ANS. In an equilateral triangle with sides of length k, the radius of the inscribed circle is x y when completely reduced and written in simplified radical form where x, y, and z are z x + y + z. integers. Determine the sum ( )

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 1. It takes 5 minutes for Will to work 2 similar calculus problems. At this rate, determine the number of seconds it will take him to work 8 similar calculus problems.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2 2. Let k = ANS. Let 100x + 700x + k = 0. Determine the sum and the product of the solutions for this equation. Report as your answer the smaller of these two quantities.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. Let k ANS =. k is the difference between the squares of the lengths of the two legs of a right triangle. k is also the sum of lengths of these same two legs. Determine the numerical area of this triangle.

FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k ANS =. The apothem of a regular hexagon is k units long. Determine the exact numeric area of this hexagon.

JUNIOR-SENIOR RELAY COMPETITION ROUND 1 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 1. Determine the smallest solution for the equation x 3 + 5x 2 x 5 = 0.

JUNIOR-SENIOR RELAY COMPETITION ROUND 1 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2. Let k = ANS. Determine the exact numerical area of the polygon enclosed by 2 x 3. y k

JUNIOR-SENIOR RELAY COMPETITION ROUND 1 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. Let k = ANS. Let n be a positive integer. The sum of the first n positive odd integers is 2 k. Determine the value of n. ( )

JUNIOR-SENIOR RELAY COMPETITION ROUND 1 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k ANS =. On January 1, 2017, Jeff took out a Certificate of Deposit (CD) with a deposit of $200.00. The CD was for a term of k years and earned an Annual Percentage Rate of interest of 3% compounded annually. Determine the value of the CD at the end of k years. Report your answer in standard dollars & cents notation rounded to the nearest cent.

JUNIOR-SENIOR RELAY COMPETITION ROUND 2 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 1. Determine the exact value of 1 1 3 5 5 2 3 2 2 3 3 2 2 3.

JUNIOR-SENIOR RELAY COMPETITION ROUND 2 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2. Let k ANS =. Determine the value for x such that log ( 5x 12) log( x k ) log ( x 6) = +.

JUNIOR-SENIOR RELAY COMPETITION ROUND 2 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. Let k = ANS. Determine the degree measure for θ, 0 θ 180, so that sin θ + k = cos 180 θ. Report your answer as a decimal rounded to the nearest tenth of ( ) ( ) a degree.

JUNIOR-SENIOR RELAY COMPETITION ROUND 2 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k ANS =. Let ( ) ( x 2) f x = e +. Determine the value of a decimal rounded to the nearest thousandth. f ( 1 ) ( k ). Express your answer as

JUNIOR-SENIOR RELAY COMPETITION ROUND 3 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 1. Determine the smallest integer in the domain of f ( x) = 2x + 3 + 2 3x.

JUNIOR-SENIOR RELAY COMPETITION ROUND 3 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2. Let k = ANS. Let y = k be the equation of the directrix of a parabola Determine the coordinates (, ) x y of the vertex of the parabola if the focus of the parabola is ( 3, 5) Report your answer as the ordered pair ( x, y )..

JUNIOR-SENIOR RELAY COMPETITION ROUND 3 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. ANS ( a, b) measure of =. In ABC BAC, A = ( 1,4 ), B = ( 9,11), and C ( a, b). Report your answer rounded to the nearest degree. =. Determine the degree

JUNIOR-SENIOR RELAY COMPETITION ROUND 3 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k = ANS. In ABC, AB = k, AC = 50, and BAC = 56. In ACD, CAD = 62 and ACD = 45. BAD = 118. Determine the numerical area of polygon ABCD. Report your answer rounded to the nearest integer.

JUNIOR-SENIOR RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 2.5 1.5 1 1. Let A =. 2 1 Determine the value of the determinant of A. Express your answer as an integer or as a common or improper fraction reduced to lowest terms.

JUNIOR-SENIOR RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2. Let k = ANS. Determine the ordered triple that is the solution for the x y + 2z = 7 system: 3x + 2y z = 10. x + 3y + z = k

JUNIOR-SENIOR RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. ANS will be an ordered triple of real numbers, ( a, b, c ). Point P has coordinates ( ) point A has coordinates ( x, 4, 2), point O has coordinates ( 0,0,0 ), and point B has coordinates ( a, b, c ). Determine the value of x such that the vectors equivalent to PA OB are perpendicular. Express your answer as an integer or as a common or improper fraction reduced to lowest terms. 2,3, 4, and

JUNIOR-SENIOR RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k = ANS. All angles are in radians and all inverses are the respective inverse functions. Determine the exact value of the expression 1 3 1 2 ( 1 ( )) 1 3 k Sin Cos + Tan 1 Cot 2 2 3.

JUNIOR-SENIOR RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 1. Aune, Barb, Cindy and Ella are going to sit at a large, empty, circular table for math team practice. Determine the number of distinct ways they can be seated around the table.

JUNIOR-SENIOR RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 2 2. Let w ANS =. f ( x) = ( x + 1)( x + 2)( x + 3) + 25 and g ( x) x( x 3) ( x 1)( x 2) 22( f ( w) ). g ( w) Determine the value of the expression = + +.

JUNIOR-SENIOR RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 k 1 1 3 3. Let k = ANS. Determine the value of x if matrix A = 3 2 2 3 2 x and the determinant of A is 37 (alternately written det A = 37.) Express your answer as an integer or as a common or improper fraction reduced to lowest terms.

JUNIOR-SENIOR RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let w ANS =. Determine the value of the sum ( 4x w) 100. x= 10