Elizabeth City State University Elizabeth City, North Carolina STATE REGIONAL MATHEMATICS CONTEST COMPREHENSIVE TEST BOOKLET

Size: px

Start display at page:

Download "Elizabeth City State University Elizabeth City, North Carolina STATE REGIONAL MATHEMATICS CONTEST COMPREHENSIVE TEST BOOKLET"

Marcia Perry
5 years ago
Views:

1 Elizabeth City State University Elizabeth City, North Carolina STATE REGIONAL MATHEMATICS CONTEST COMPREHENSIVE TEST BOOKLET Directions: Each problem in this test is followed by five suggested answers When you have decided which of the suggested answer is correct, shade the corresponding circle on the answer sheet Sample question: = A) 6 B) 7 C) 16 D) 1 Sample answer: B C D E Answer A is marked since the difference between 54 and 48 is 6 You will have 80 minutes to work on the 40 questions in this test booklet

2 1 Suppose that b and c are constants and ( x 3)( x b) x cx 1 What is c? A) 4 B) 5 C) 6 D) 7 Completely factor the polynomial x 3 x 6x A) x ( x x 6) B) x ( x 1 7)( x 1 7) C) x ( x 1 7)( x 1 7) D) x ( x 4)( x ) 3 Joy Palmer, a pharmacist, needs 60 liters of 60% alcohol solution She has available a 70% alcohol solution and a 30% alcohol solution How many liters of each solution should she mix to obtain 60 liters of 60% alcohol solution? A) 10 liters of 70% solution and 50 liters of 30% solution B) 0 liters of 70% solution and 40 liters of 30% solution C) 155 liters of 70% solution and 445 liters of 30% solution D) 45 liters of 70% solution and 15 liters of 30% solution E) 8 liters of 70% solution and 3 liters of 30% solution 4 Find the value of the sum: A) 1006 B) C) 0 D) / 3 5 Find the domain of the function f ( x) ( x 4) 1/ (5 x) A) ( 4, ) (5, ) B) ( 4, ) C) (,5) D) ( 4, ) (,5) 6 Determine the value of A so that the line whose equation is x Ay 3is perpendicular to the line containing the points (, 1) and ( 4, ) A) B) 1/ C) 1 / D) 3 7 Given the following equation: 3 x 3 x 0 0, solve for x ln 5 A) B) 4, 5 C) 0, 1 D) ln 3 ln5, ln 4 ln5 ln Let i 1 Simplify i i A) i B) i C) 0 D) i 9 Find the cubic equation with integral coefficients having roots 3 and1 i 3 A) x x 11x 15 3 B) x x 11x 15 C) x 3 5x 11x 15 D) x 3 5x 11x 15

3 lnlnln( x) 10 The domain of the function is ln ln( x) A) { x x 0} B) { x x e} C) { x x e } D) { x 0 x e } 11 In the right triangle ABC with legs of length 5 and 1, the hypotenuse is of length 13 A semicircle is inscribed in the triangle Find the radius of the semicircle A) 17/3 B) 13/5 C) 10/3 D) 1/5 1 Given two similar triangles, the area of the larger triangle is sixteen times the area of the smaller triangle Find the ratio of the perimeter of the larger triangle to the perimeter of the smaller triangle A) 8 : 1 B) 4 : 1 C) 16 : 1 D) 3 : 1 13 In the right triangle ABC, CF is perpendicular to AB Find the length of CF B F 4 C 6 A) 13 / 13 B) 13 / 13 C) 6 13 / 13 D) 1 13 / Find the sum of all solutions of the equation x 4 x 15 0 A) B) 0 C) 5 D) Find the area of a trapezoid in which the bases are 17 m and 4 m and the legs are 15 m and 0 m A) 5 m B) 354 m C) 400 m D) 475 m A 16 The interior angles of a polygon are in arithmetic progression; the least angle is 10 and the common difference is 5 Find the greatest number of sides that this polygon can have A) 0 B) 16 C) 1 D) 9 3

17 In the figure below, two small circles are inscribed and tangent to the large circle at points A and D Let points B and C be the centers of the circles, where AB = BC = CD = Find the area of the

4 17 In the figure below, two small circles are inscribed and tangent to the large circle at points A and D Let points B and C be the centers of the circles, where AB = BC = CD = Find the area of the shaded region A) B) 4 5 C) 3 D) In a triangle ABC, AC = 1 If one of the trisectors of angle B is the median to AC and the other trisector of angle B is the altitude to AC, find the length of the altitude A) 3 B) 3 3 C) 4 3 D) In the circle shown, AB = 4, and the perpendicular chord CD bisects AB How long is BD if DM is 4 times as long as CM? A) 4 5 B) 8 5 C) 1 5 D) If the diameter of a cylindrical can is increased by 30 percent, by approximating what percentage should the height be increased to triple the volume of the can? A) 775 B) 548 C) 500 D) 44 1 An arc of length has length π in and radius 8 in What is the central angle the arc makes? A) 45 B) 90 C) 180 D) 360 Find the amplitude, period, phase shift of y 3sin(x / ) A) Amplitude = 3, period =, phase shift = / 4 B) Amplitude = 3, period =, phase shift = / 4 C) Amplitude = 3, period =, phase shift = / D) Amplitude = 3, period =, phase shift = / 4 4

5 3 sin 4 is A) 3/ 8 (1/ )cos (1/ )cos 4 B) 3/8 (1/ )cos (1/ 4)cos 4 C) 3/ 8 (1/ )cos (1/ 6)cos 4 D) 3/8 (1/ )cos (1/8)cos4 tan cot 4 is tan cot A) sin 1 B) cos 1 C) sec 1 D) csc 1 1 cos 5 is sin 1 sin A) cos B) sin 1 cos C) 1 cos sin D) 1 sin sin sin 1 cos 6 is 1 cos sin A) sin B) cos C) sec D) csc is 1 cos 1 cos A) sin B) cos C) tan D) cot The value of cos tan is: 1 A) 5/13 B) 3/1 C) 5/1 D) 1/13 9 In a triangle ABC, cos C is s ( s a) s ( s b) A) B) bc ca C) s ( s c) ab D) s ( s a) ab 5

6 a b 30 In a triangle ABC, is c A B A B A B A B sin sin sin cos A) B) C C C C sin cos sin cos A B A B A B A B cos sin cos cos C) D) C C C C sin cos sin cos 31 Two similar cones are cut out of a cylinder The cylinder has radius r and height h How much volume is left of the cylinder? A) 1 r h 3 1 B) r h C) r h D) r h Given the square ABCD with M the midpoint of DC The ratio of the area of the triangle MEC to that of the quadrilateral AEMD is: A) 1 : 3 B) 1 : 4 C) 1 : 5 D) 1 : 6 33 What is the y-intercept of the line that is parallel to y x, and which bisects the area of a rectangle with corners at ( 0, 0), (, 0), (, 6), and ( 0, 6)? A) 1 B) 1 5 C) 1 D) 6

7 34 If loga x 4, then log 1/ a ( x / a)? A) 4 B) 1 C) 3 D) 1 / 4 35 The floor of a square hall is tiled with unbroken square tiles Along the two diagonals there are 111 tiles altogether How many tiles are there in the hall? A) 305 B) 3136 C) 349 D) A palindromic number is a natural number that is the same when written forwards or backwards For instance, 33 is palindromic number How many three-digit palindromic numbers are there? A) 100 B) 81 C) 90 D) For all real numbers x, except x 0and x 1, the function f is defined by x 1 f x 1 x Suppose 0 / f cos? What is A) tan B) sin C) cos D) cot E) csc 38 How many subsets X exist such that { 1,,3} X {1,,3,4,5,6,7 }? A) 16 B) 11 C) 10 D) If the number 848 is written out as an ordinary base 10 numeral, then what is the digit in the ones place? A) B) 4 C) 6 D) 8 40 Find the sum of all the three-digit palindromic numbers A) B) C) D)

8 Answers Question Answer 1 D B 3 D 4 A 5 B 6 B 7 A 8 C 9 C 10 B 11 C 1 B 13 D 14 B 15 B 16 B 17 E 18 B 19 C 0 A 1 A D 3 D 4 A 5 B 6 D 7 D 8 D 9 C 30 B 31 B 3 C 33 A 34 C 35 B 36 C 37 A 38 A 39 C 40 A 8

0114ge. Geometry Regents Exam 0114

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?