|
|
|
- Willa Ray
- 6 years ago
- Views:
Transcription
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 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.
32 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.
33 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.
34 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 C , 625.
35 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 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.
36 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.
37 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 x y Let p be the smallest angle of a triangle whose angles are in the ratio 210 :1024 : Determine the sum. k w p. Express your answer as a decimal rounded to the nearest thousandths.
38 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.
39 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
40 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 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.
41 FROSH-SOPH 2 PERSON COMPETITION STATE PLAYOFF QUESTIONS ICTM 2017 STATE DIVISION AA LARGE PRINT QUESTION 11
42
43
44 JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 1 ICTM 2017 STATE DIVISION AA 1. Let k log 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.
45 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.
46 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 x Determine the sum k w. Express your answer as an integer or as a common or improper fraction reduced to lowest terms.
47 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 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.
48 JUNIOR-SENIOR 2 PERSON COMPETITION LARGE PRINT QUESTION 5 ICTM 2017 STATE DIVISION AA 5. Consider angles in degree measure, 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.
49 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.
50 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 meet in four points that determine a convex quadrilateral. Determine the exact perimeter of this quadrilateral.
51 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.
52 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 $ Determine the sum of all possible integral values of n.
53 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 cos with in radians. Express your answer rounded to the nearest integer.
54 JUNIOR-SENIOR 2 PERSON COMPETITION STATE PLAYOFF QUESTIONS ICTM 2017 STATE DIVISION AA LARGE PRINT QUESTION 11
55
56
57
58
59
60
61 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.
62 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.
63 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
64 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
65 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 =.
66 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.
67 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.
68 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.
69 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.
70 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.
71 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
72 FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 3 ICTM 2017 DIVISION AA STATE FINALS QUESTION 4 4. Let k = ANS. The line x y = is tangent to a circle given by the equation ( 9) ( 3) Determine the exact y-coordinate of the point of tangency. x + y = k.
73 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.
74 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
75 FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 3. Let k = ANS A certain convex polygon has k diagonals. Determine the number of sides in this polygon.
76 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 ( )
77 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.
78 FRESHMAN-SOPHOMORE RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 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.
79 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.
80 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.
81
82
83
84
85
86 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.
87 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
88 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. ( )
89 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 $ 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.
90 JUNIOR-SENIOR RELAY COMPETITION ROUND 2 ICTM 2017 DIVISION AA STATE FINALS QUESTION 1 1. Determine the exact value of
91 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) = +.
92 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.
93 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
94 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 x.
95 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 )..
96 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
97 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.
98 JUNIOR-SENIOR RELAY COMPETITION ROUND 4 ICTM 2017 DIVISION AA STATE FINALS QUESTION 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.
99 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
100 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
101 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 ( )) 1 3 k Sin Cos + Tan 1 Cot
102 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.
103 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 = + +.
104 JUNIOR-SENIOR RELAY COMPETITION ROUND 5 ICTM 2017 DIVISION AA STATE FINALS QUESTION 3 k Let k = ANS. Determine the value of x if matrix A = 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.
105 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
WRITTEN AREA COMPETITION ICTM STATE 2017 DIVISION A PAGE 1 OF 3
WRITTEN AREA COMPETITION ALGEBRA I ICTM STATE 2017 DIVISION A PAGE 1 OF 3 1. Let x and y be integers such that 13 < x < 15 and 5 < y < 3. Determine the value of ( 2x y) +. 2. Let ( k, w) be the solution
WRITTEN AREA COMPETITION ICTM REGIONAL 2017 DIVISION AA PAGE 1 OF 3
WRITTEN AREA COMPETITION ALGEBRA I ICTM REGIONAL 2017 DIVISION AA PAGE 1 OF 3 y y 1. If 2x 4x, determine the ratio x. Express your answer as an integer or as a 2 4 y common or improper fraction reduced
WRITTEN AREA COMPETITION ICTM STATE 2014 DIVISION A PAGE 1 OF 3. and
WRITTEN AREA COMPETITION ALGEBRA I ICTM STATE 2014 DIVISION A PAGE 1 OF 3 1. The equations x x 4 3 2 2 4 12 and ax 6 21 both have the same solution when solved for x. Find the value of a. 2. Find the greatest
WRITTEN AREA COMPETITION ICTM REGIONAL 2014 DIVISION AA PAGE 1 OF 3
WRITTEN AREA COMPETITION ALGEBRA I ICTM REGIONAL 014 DIVISION AA PAGE 1 OF 3 1. Given x and y 3, find the value of the expression x y 3.. On an algebra test taken by all but one student in a class, the
WRITTEN AREA COMPETITION ICTM REGIONAL 2010 DIVISION A PAGE 1 OF 3.. If one member of Set A is selected at random and substituted for x
WRITTEN AREA COMPETITION ALGEBRA I ICTM REGIONAL 010 DIVISION A PAGE 1 OF 1. Set A = { 1,,, 4}. If one member of Set A is selected at random and substituted for x in the expression x + 1, find the probability
UNCC 2001 Comprehensive, Solutions
UNCC 2001 Comprehensive, Solutions March 5, 2001 1 Compute the sum of the roots of x 2 5x + 6 = 0 (A) (B) 7/2 (C) 4 (D) 9/2 (E) 5 (E) The sum of the roots of the quadratic ax 2 + bx + c = 0 is b/a which,
QUESTION BANK ON STRAIGHT LINE AND CIRCLE
QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,
3. Which of these numbers does not belong to the set of solutions of the inequality 4
Math Field Day Exam 08 Page. The number is equal to b) c) d) e). Consider the equation 0. The slope of this line is / b) / c) / d) / e) None listed.. Which of these numbers does not belong to the set of
Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? A. (1,10) B. (2,7) C. (3,5) D. (4,3) E.
April 9, 01 Standards: MM1Ga, MM1G1b Practice Test Geometry 1. Which of the following points is the greatest distance from the y-axis? (1,10) B. (,7) C. (,) (,) (,1). Points P, Q, R, and S lie on a line
2015 Fall Startup Event Solutions
1. Evaluate: 829 7 The standard division algorithm gives 1000 + 100 + 70 + 7 = 1177. 2. What is the remainder when 86 is divided by 9? Again, the standard algorithm gives 20 + 1 = 21 with a remainder of
a) i b) ii c) iii d) i and ii e) ii and iii a) b) c) d) e)
Math Field Day 07 Page Suppose the graph of a line has a negative y intercept and a positive intercept If the slope is given by m, which of the following could be true? i m > 0 ii m < 0 iii m = 0 a) i
WRITTEN AREA COMPETITION ICTM REGIONAL 2015 DIVISION A PAGE 1 OF 3
WRITTEN AREA COMPETITION ALGEBRA I ICTM REGIONAL 015 DIVISION A PAGE 1 OF 3 a b 3c 1. Determine the value of the expression when a, b 3 and b a c your answer as a common or improper fraction reduced to
Math is Cool Championships
Individual Contest Express all answers as reduced fractions unless stated otherwise. Leave answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on
02)
GRE / GMATmath,! abscissa, scalene, intercept, markup, such that, break even. abscissa. (4, 2) 4abscissa, 2ordinate absolute value acre add adjacent angles altitude ; angle () acute angle (90 ) right angle
Due to the detail of some problems, print the contests using a normal or high quality setting.
General Contest Guidelines: Keep the contests secure. Discussion about contest questions is not permitted prior to giving the contest. Due to the detail of some problems, print the contests using a normal
Indicate whether the statement is true or false.
PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.
(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2
CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5
0114ge. Geometry Regents Exam 0114
0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?
1. LINE SEGMENTS. a and. Theorem 1: If ABC A 1 B 1 C 1, then. the ratio of the areas is as follows: Theorem 2: If DE//BC, then ABC ADE and 2 AD BD
Chapter. Geometry Problems. LINE SEGMENTS Theorem : If ABC A B C, then the ratio of the areas is as follows: S ABC a b c ( ) ( ) ( ) S a b A BC c a a b c and b c Theorem : If DE//BC, then ABC ADE and AD
2018 LEHIGH UNIVERSITY HIGH SCHOOL MATH CONTEST
08 LEHIGH UNIVERSITY HIGH SCHOOL MATH CONTEST. A right triangle has hypotenuse 9 and one leg. What is the length of the other leg?. Don is /3 of the way through his run. After running another / mile, he
Elizabeth City State University Elizabeth City, North Carolina STATE REGIONAL MATHEMATICS CONTEST COMPREHENSIVE TEST BOOKLET
Elizabeth City State University Elizabeth City, North Carolina 7909 011 STATE REGIONAL MATHEMATICS CONTEST COMPREHENSIVE TEST BOOKLET Directions: Each problem in this test is followed by five suggested
TENTH YEAR MATHEMATICS
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION TENTH YEAR MATHEMATICS Tuesday, June 16,1987-1:15 to 4:15 p.m., only The last page of the booklet is the answer sheet. Fold the last
WRITTEN AREA COMPETITION ICTM STATE 2015 DIVISION A PAGE 1 OF 3. of the number, determine that number. 3 x 2x
WRITTEN AREA COMPETITION ALGEBRA I ICTM STATE 015 DIVISION A PAGE 1 OF 3 1. The operation is defined as 11 k 015. a b 3a b. Determine the value of k such that. Mary can work 10 similar problems in 15 minutes.
MATHEMATICS TEST 60 Minutes 60 Questions
MATHEMATICS TEST 60 Minutes 60 Questions DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. Do not linger over problems that take
( 3x 2 y) 6 (6x 3 y 2 ) x 4 y 4 b.
1. Simplify 3 x 5 4 64x Algebra Practice Problems for MDPT Pre Calculus a. 1 18x 10 b. 7 18x 7 c. x 6 3x d. 8x 1 x 4. Solve 1 (x 3) + x 3 = 3 4 (x 1) + 1 9 a. 77 51 b. 3 17 c. 3 17 d. 3 51 3. Simplify
WRITTEN AREA COMPETITION ICTM REGIONAL 2013 DIVISION AA PAGE 1 OF 3., find the value of k.
WRITTEN AREA COMPETITION ALGEBRA I ICTM REGIONAL 2013 DIVISION AA PAGE 1 OF 3 1. If 7 7 7 w w 17 k 2w, find the value of k. 2. Someone stole 5 candy bars and 2 bags of potato chips. Each bag of potato
11 th Philippine Mathematical Olympiad Questions, Answers, and Hints
view.php3 (JPEG Image, 840x888 pixels) - Scaled (71%) https://mail.ateneo.net/horde/imp/view.php3?mailbox=inbox&inde... 1 of 1 11/5/2008 5:02 PM 11 th Philippine Mathematical Olympiad Questions, Answers,
For math conventions used on the GRE, refer to this link:
GRE Review ISU Student Success Center Quantitative Workshop One Quantitative Section: Overview Your test will include either two or three 35-minute quantitative sections. There will be 20 questions in
WRITTEN AREA COMPETITION ICTM REGIONAL 2011 DIVISION A PAGE 1 OF 3. 5, then the solution set is x : x k.. Find the value of
WRITTEN AREA COMPETITION ALGEBRA I ICTM REGIONAL 011 DIVISION A PAGE 1 OF 3 x 3 x 4 1. Find the value of x that satisfies x 7 x 7. If k is a positive integral multiple of four and k 60, find the largest
2018 TAME High School Practice Mathematics Test
018 TAME High School Practice Mathematics Test (1) Arturo took four exams and made grades of 65, 88, 9 and 75. If Arturo wants to have an average of at least 80, which of the following is the lowest grade
Intermediate Mathematics League of Eastern Massachusetts
IMLEM Meet #4 February, 2016 Intermediate Mathematics League of Eastern Massachusetts This is a calculator meet! Category 1 Mystery Calculator Meet 1) Let X be a non-integer that lies between A and G.
QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)
QUESTION BANK ON CONIC SECTION (Parabola, Ellipse & Hyperbola) Question bank on Parabola, Ellipse & Hyperbola Select the correct alternative : (Only one is correct) Q. Two mutually perpendicular tangents
1. How is five hundred twelve and sixteen thousandths written in decimal form? a b c. 512,160 d e f.
1. How is five hundred twelve and sixteen thousandths written in decimal form? a. 51.016 b. 51.16 c. 51,160 d. 51.16 e. 51.0016. 4 1 3 13 4 =? 7 f. 1 5 g. 3 1 h. 3 3 5 i. 1 j. 1 1 8 3. Simplify 3 11 +
Grade XI Mathematics
Grade XI Mathematics Exam Preparation Booklet Chapter Wise - Important Questions and Solutions #GrowWithGreen Questions Sets Q1. For two disjoint sets A and B, if n [P ( A B )] = 32 and n [P ( A B )] =
UNC Charlotte 2005 Comprehensive March 7, 2005
March 7, 2005 1. The numbers x and y satisfy 2 x = 15 and 15 y = 32. What is the value xy? (A) 3 (B) 4 (C) 5 (D) 6 (E) none of A, B, C or D Solution: C. Note that (2 x ) y = 15 y = 32 so 2 xy = 2 5 and
My Math Plan Assessment #1 Study Guide
My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.
1. The sides of a triangle are in the ratio 3 : 5 : 9. Which of the following words best describes the triangle?
UNIVERSITY OF NORTH CAROLINA CHARLOTTE 999 HIGH SCHOOL MATHEMATICS CONTEST March 8, 999 The sides of a triangle are in the ratio : 5 : 9 Which of the following words best describes the triangle? (A) obtuse
HANOI OPEN MATHEMATICAL COMPETITON PROBLEMS
HANOI MATHEMATICAL SOCIETY NGUYEN VAN MAU HANOI OPEN MATHEMATICAL COMPETITON PROBLEMS HANOI - 2013 Contents 1 Hanoi Open Mathematical Competition 3 1.1 Hanoi Open Mathematical Competition 2006... 3 1.1.1
**** NO CALCULATORS IN THIS ROUND ****
A) Evaluate 8 8. CONTEST NOVEMBER 0 ROUN COMLEX NUMBERS (No Trig) ANSWERS A) B) I II III IV C) **** NO CALCULATORS IN THIS ROUN **** B) Let z = x + yi be represented by the point (x, y). In what quadrant
Pre RMO Exam Paper Solution:
Paper Solution:. How many positive integers less than 000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3? Sum of Digits Drivable
American Math Competition 10 Practice Test 10. American Mathematics Competitions. Practice 10 AMC 10 (American Mathematics Contest 10) INSTRUCTIONS
American Math Competition 0 Practice Test 0 American Mathematics Competitions Practice 0 AMC 0 (American Mathematics Contest 0) INSTRUCTIONS. This is a twenty-five question multiple choice test. Each question
Possible C2 questions from past papers P1 P3
Possible C2 questions from past papers P1 P3 Source of the original question is given in brackets, e.g. [P1 January 2001 Question 1]; a question which has been edited is indicated with an asterisk, e.g.
Math Day at the Beach 2017
Math Day at the Beach 017 Multiple Choice Write your name and school and mark your answers on the answer sheet. You have 0 minutes to work on these problems. No calculator is allowed. 1. How many integers
1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle?
1 For all problems, NOTA stands for None of the Above. 1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle? (A) 40 (B) 60 (C) 80 (D) Cannot be determined
Geometry Honors Homework
Geometry Honors Homework pg. 1 12-1 Practice Form G Tangent Lines Algebra Assume that lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. 2. 3. The circle
CDS-I 2019 Elementary Mathematics (Set-C)
1 CDS-I 019 Elementary Mathematics (Set-C) Direction: Consider the following for the next three (03) items : A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the
0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?
0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100
Chapter 2 Polynomial and Rational Functions
SECTION.1 Linear and Quadratic Functions Chapter Polynomial and Rational Functions Section.1: Linear and Quadratic Functions Linear Functions Quadratic Functions Linear Functions Definition of a Linear
SAT Subject Test Practice Test II: Math Level I Time 60 minutes, 50 Questions
SAT Subject Test Practice Test II: Math Level I Time 60 minutes, 50 Questions All questions in the Math Level 1 and Math Level Tests are multiple-choice questions in which you are asked to choose the BEST
Test Corrections for Unit 1 Test
MUST READ DIRECTIONS: Read the directions located on www.koltymath.weebly.com to understand how to properly do test corrections. Ask for clarification from your teacher if there are parts that you are
HANOI OPEN MATHEMATICS COMPETITON PROBLEMS
HANOI MATHEMATICAL SOCIETY NGUYEN VAN MAU HANOI OPEN MATHEMATICS COMPETITON PROBLEMS 2006-2013 HANOI - 2013 Contents 1 Hanoi Open Mathematics Competition 3 1.1 Hanoi Open Mathematics Competition 2006...
(A) 2S + 3 (B) 3S + 2 (C) 3S + 6 (D) 2S + 6 (E) 2S + 12
1 The sum of two numbers is S Suppose 3 is added to each number and then each of the resulting numbers is doubled What is the sum of the final two numbers? (A) S + 3 (B) 3S + (C) 3S + 6 (D) S + 6 (E) S
Solutions Math is Cool HS Championships Mental Math
Mental Math 9/11 Answer Solution 1 30 There are 5 such even numbers and the formula is n(n+1)=5(6)=30. 2 3 [ways] HHT, HTH, THH. 3 6 1x60, 2x30, 3x20, 4x15, 5x12, 6x10. 4 9 37 = 3x + 10, 27 = 3x, x = 9.
Math Contest, Fall 2017 BC EXAM , z =
Math Contest, Fall 017 BC EXAM 1. List x, y, z in order from smallest to largest fraction: x = 111110 111111, y = 1 3, z = 333331 333334 Consider 1 x = 1 111111, 1 y = thus 1 x > 1 z > 1 y, and so x
Hanoi Open Mathematical Competition 2017
Hanoi Open Mathematical Competition 2017 Junior Section Saturday, 4 March 2017 08h30-11h30 Important: Answer to all 15 questions. Write your answers on the answer sheets provided. For the multiple choice
Solutions th AMC 12 A (E) Since $20 is 2000 cents, she pays (0.0145)(2000) = 29 cents per hour in local taxes.
Solutions 2004 55 th AMC 12 A 2 1. (E) Since $20 is 2000 cents, she pays (0.0145)(2000) = 29 cents per hour in local taxes. 2. (C) The 8 unanswered problems are worth (2.5)(8) = 20 points, so Charlyn must
FAIRFIELD COUNTY MATH LEAGUE (FCML) Match 4 Round 1 Arithmetic: Basic Statistics
Match 4 Round 1 Arithmetic: Basic Statistics 1.) 6.4.) 14706.) 85 1.)The geometric mean of the numbers x 1, x, x n is defined to be n x 1 x...x n. What is the positive difference between the arithmetic
Paper Reference. Paper Reference(s) 7361/01 London Examinations GCE. Mathematics Syllabus B Ordinary Level Paper 1
Centre No. Candidate No. Paper Reference 7 3 6 1 0 1 Surname Signature Paper Reference(s) 7361/01 London Examinations GCE Mathematics Syllabus B Ordinary Level Paper 1 Friday 11 January 2008 Afternoon
221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM
Math Refresher Session 3 1 Area, Perimeter, and Volume Problems Area, Perimeter, and Volume 301. Formula Problems. Here, you are given certain data about one or more geometric figures, and you are asked
2017 OHMIO Individual Competition
2017 OHMIO Individual Competition 1. On a winter hike with friends (all of whom were wearing either a scarlet or gray hat), I saw twice as many scarlet hats as gray. That s silly, said a friend. I see
13 th Annual Harvard-MIT Mathematics Tournament Saturday 20 February 2010
13 th Annual Harvard-MIT Mathematics Tournament Saturday 0 February 010 1. [3] Suppose that x and y are positive reals such that Find x. x y = 3, x + y = 13. 3+ Answer: 17 Squaring both sides of x y =
GRE. Advanced GRE Math Questions
Advanced GRE Math Questions Quantitative Arithmetic 1. What is the sum of all integers x, such that 7 < x 5? 7 7 6 6 7 1. C Quantitative Fractions and Ratios 1. The current ratio of boys to girls at a
8 th Grade Exam Scoring Format: 3 points per correct response -1 each wrong response 0 for blank answers
Pellissippi State Middle School Mathematics Competition 8 th Grade Exam Scoring Format: 3 points per correct response -1 each wrong response 0 for blank answers Directions: For each multiple-choice problem
TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad
TARGT : J 01 SCOR J (Advanced) Home Assignment # 0 Kota Chandigarh Ahmedabad J-Mathematics HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP 1. If x + y = 0 is a tangent at the vertex of a parabola and x + y 7 =
IMLEM Meet #3 January, Intermediate Mathematics League of Eastern Massachusetts
IMLEM Meet #3 January, 2017 Intermediate Mathematics League of Eastern Massachusetts Category 1 Mystery 1) In a row of 21 seats numbered consecutively from 1 to 21 at the movie theatre, I sit in seat #13.
Instructions. Do not open your test until instructed to do so!
st Annual King s College Math Competition King s College welcomes you to this year s mathematics competition and to our campus. We wish you success in this competition and in your future studies. Instructions
Meet #4. Math League SCASD. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):
Math League SCASD Meet #4 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Properties of Circles 3. Number Theory: Modular Arithmetic,
0616geo. Geometry CCSS Regents Exam x 2 + 4x = (y 2 20)
0616geo 1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation?
$$$$$$ 3. What is the sum of the units digits of all the multiples of 3 between 0 and 50?
1. Sharon bought a mixture of nuts that was made up of pecans, walnuts and cashews in a ratio by weight of 2:3:1, respectively. If she bought 9 pounds of nuts, how many pounds of walnuts were in the mixture?
MATHCOUNTS State Competition Countdown Round Problems This section contains problems to be used in the Countdown Round.
MATHCOUNTS 2007 State Competition Countdown Round Problems 1 80 This section contains problems to be used in the Countdown Round. National Sponsors Lockheed Martin * Raytheon Company Texas Instruments
2008 Euclid Contest. Solutions. Canadian Mathematics Competition. Tuesday, April 15, c 2008 Centre for Education in Mathematics and Computing
Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario 008 Euclid Contest Tuesday, April 5, 008 Solutions c 008
High School Math Contest
High School Math Contest University of South Carolina February th, 017 Problem 1. If (x y) = 11 and (x + y) = 169, what is xy? (a) 11 (b) 1 (c) 1 (d) (e) 8 Solution: Note that xy = (x + y) (x y) = 169
Academic Challenge 2009 Regional Mathematics Solution Set. #2 Ans. C. Let a be the side of the cube. Then its surface area equals 6a = 10, so
Academic Challenge 009 Regional Mathematics Solution Set #1 Ans. C: x 4 = x 9 = -5 # Ans. C. Let a be the side of the cube. Then its surface area equals 6a = 10, so a = 10 / 6 and volume V = a = ( 10 /
Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems
Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Euclid Contest. Wednesday, April 15, 2015
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 015 Euclid Contest Wednesday, April 15, 015 (in North America and South America) Thursday, April 16, 015 (outside of North America
HIGH SCHOOL - SOLUTIONS = n = 2315
PURPLE COMET! MATH MEET April 018 HIGH SCHOOL - SOLUTIONS Copyright c Titu Andreescu and Jonathan Kane Problem 1 Find the positive integer n such that 1 3 + 5 6 7 8 + 9 10 11 1 = n 100. Answer: 315 1 3
UNC Charlotte 2005 Comprehensive March 7, 2005
March 7, 2005 1 The numbers x and y satisfy 2 x = 15 and 15 y = 32 What is the value xy? (A) 3 (B) 4 (C) 5 (D) 6 (E) none of A, B, C or D 2 Suppose x, y, z, and w are real numbers satisfying x/y = 4/7,
(A) 20% (B) 25% (C) 30% (D) % (E) 50%
ACT 2017 Name Date 1. The population of Green Valley, the largest suburb of Happyville, is 50% of the rest of the population of Happyville. The population of Green Valley is what percent of the entire
Gauss School and Gauss Math Circle 2017 Gauss Math Tournament Grade 7-8 (Sprint Round 50 minutes)
Gauss School and Gauss Math Circle 2017 Gauss Math Tournament Grade 7-8 (Sprint Round 50 minutes) 1. Compute. 2. Solve for x: 3. What is the sum of the negative integers that satisfy the inequality 2x
Mu Alpha Theta National Convention 2013
Practice Round Alpha School Bowl P1. What is the common difference of the arithmetic sequence 10, 23,? P2. Find the sum of the digits of the base ten representation of 2 15. P3. Find the smaller value
The Second Annual West Windsor-Plainsboro Mathematics Tournament
The Second Annual West Windsor-Plainsboro Mathematics Tournament Saturday October 9th, 0 Grade 8 Test RULES The test consists of 0 multiple choice problems and 0 short answer problems to be done in 0 minutes.
Name: Class: Date: c. WZ XY and XW YZ. b. WZ ZY and XW YZ. d. WN NZ and YN NX
Class: Date: 2nd Semester Exam Review - Geometry CP 1. Complete this statement: A polygon with all sides the same length is said to be. a. regular b. equilateral c. equiangular d. convex 3. Which statement
Log1 Contest Round 2 Theta Geometry
008 009 Log Contest Round Theta Geometry Name: Leave answers in terms of π. Non-integer rational numbers should be given as a reduced fraction. Units are not needed. 4 points each What is the perimeter
Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.
Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the
b = 2, c = 3, we get x = 0.3 for the positive root. Ans. (D) x 2-2x - 8 < 0, or (x - 4)(x + 2) < 0, Therefore -2 < x < 4 Ans. (C)
SAT II - Math Level 2 Test #02 Solution 1. The positive zero of y = x 2 + 2x is, to the nearest tenth, equal to (A) 0.8 (B) 0.7 + 1.1i (C) 0.7 (D) 0.3 (E) 2.2 ± Using Quadratic formula, x =, with a = 1,
SAT SHEET (calculators allowed)
. If! 15 = 15! x, then x = A) -0 B) -15 C) 0 D) 15 E) 0 4. A dozen roses cost $15.60 and the cost of one rose and one lily together cost $4.50. What is the cost of one lily? A) $1.0 B) $.0 C) $5.80 D)
QUESTIONS 1-46 REVIEW THE OBJECTIVES OF CHAPTER 2.
MAT 101 Course Review Questions Valid for Fall 2014, Spring 2015 and Summer 2015 MIDTERM EXAM FINAL EXAM Questions 1-86 are covered on the Midterm. There are 25 questions on the midterm, all multiple choice,
4. If (x h)(x + k) = x 2 16, what is the value of h + k? (A) 8 (B) 4 (C) 0 (D) 4 (E) 8
1. In the figure below, the graph of y = kx 2 intersects triangle C at. If = C and the area of triangle C is 6, what is the value of k? y = kx 2 4. If (x h)(x + k) = x 2 16, what is the value of h + k?
A. 180 B. 108 C. 360 D. 540
Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior
HALF YEARLY EXAMINATIONS 2015/2016
FORM 4 SECONDARY SCHOOLS HALF YEARLY EXAMINATIONS 2015/2016 MATHS NON-CALCULATOR PAPER Track 3 Time: 20 min Name: Non-Calculator Paper Class: Answer all questions. Each question carries 1 mark. Question
GREEN SKILL DRILL 1. Answers Name. Show ALL work! 1) Express as a common fraction: 2) Express
GREEN SKILL RILL Name Show LL work! ) Express as a common fraction: 7 ) Express as a common fraction in lowest terms. 7 ) Find the number which appears the way from to on the number line. ) Express in
f(x + y) + f(x y) = 10.
Math Field Day 202 Mad Hatter A A Suppose that for all real numbers x and y, Then f(y x) =? f(x + y) + f(x y) = 0. A2 Find the sum + 2 + 4 + 5 + 7 + 8 + 0 + + +49 + 50 + 52 + 53 + 55 + 56 + 58 + 59. A3
0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
North Seattle Community College Computer Based Mathematics Instruction Math 102 Test Reviews
North Seattle Community College Computer Based Mathematics Instruction Math 10 Test Reviews Click on a bookmarked heading on the left to access individual reviews. To print a review, choose print and the
Thirty-fifth Annual Columbus State Invitational Mathematics Tournament. Instructions
Thirty-fifth Annual Columbus State Invitational Mathematics Tournament Sponsored by Columbus State University Department of Mathematics February 8, 009 ************************* The Mathematics Department
1 Hanoi Open Mathematical Competition 2017
1 Hanoi Open Mathematical Competition 017 1.1 Junior Section Question 1. Suppose x 1, x, x 3 are the roots of polynomial P (x) = x 3 6x + 5x + 1. The sum x 1 + x + x 3 is (A): 4 (B): 6 (C): 8 (D): 14 (E):
0609ge. Geometry Regents Exam AB DE, A D, and B E.
0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible
( ) ( ) Geometry Team Solutions FAMAT Regional February = 5. = 24p.
. A 6 6 The semi perimeter is so the perimeter is 6. The third side of the triangle is 7. Using Heron s formula to find the area ( )( )( ) 4 6 = 6 6. 5. B Draw the altitude from Q to RP. This forms a 454590
SAGINAW VALLEY STATE UNIVERSITY SOLUTIONS OF 2013 MATH OLYMPICS LEVEL II. 1 4n + 1. n < < n n n n + 1. n < < n n 1. n 1.
SAGINAW VALLEY STATE UNIVERSITY SOLUTIONS OF 03 MATH OLYMPICS LEVEL II. The following inequalities hold for all positive integers n: n + n < 4n + < n n. What is the greatest integer which is less than
California 5 th Grade Standards / Excel Math Correlation by Lesson Number
(Activity) L1 L2 L3 Excel Math Objective Recognizing numbers less than a million given in words or place value; recognizing addition and subtraction fact families; subtracting 2 threedigit numbers with