MML Contest #1 ROUND 1: VOLUME & SURFACES

Transcription

1 MML Contest # ROUND : VOLUME & SURFACES A) The base of a right pyramid is a square with perimeter 0 inches. The pyramid s altitude is 9 inches. Find the exact volume of the pyramid. A) The volume of a right circular cylinder is 48π and the circumference of the base is 8π. Find the total surface area in terms of π. A) The radius of a right circular cylinder is 0 inches and its height is 4 inches. Determine the value of x ( > 0) which, when added to either the radius or the height, produces two different right circular cylinders of equal volume. A) Determine the exact length of the interior diagonal of a cube if its total surface area is A) A cone is inscribed in a sphere. The radius of the base of the cone is 3 and the radius of the sphere is 5. Find the ratio of the volume of the sphere to the volume of the cone.

2 ROUND 2: PYTHAGOREAN RELATIONS A) The shortstop fields a batted ball at a point /3 the distance from second base third base. To the nearest 0. ft, how far must she throw the ball to get it to first base? Assume the infield is a square 90 ft on a side. Some of the following approximations should be helpful. 2.44, 3.732, , A) The diagonal of a rectangle with integer dimensions is 25. List all possible perimeters of this rectangle. A) The hypotenuse and long leg of a right triangle have lengths 3 and 7 7 respectively. Compute the length of the short leg. A) A ladder has rungs foot apart, starting foot from each end. The bottom of the ladder is 5 feet from the base of a wall when the top of the ladder reaches a point on the wall 36 feet above the ground. How many rungs on this ladder? A) In square ABCD, AB = 4, E and F are midpoints of BC and CD respectively. Compute the ratio of the area of ΔAEF to the area of ABCD.

3 A) If [ ] MML Contest # ROUND 3 ALG : LINEAR EQUATIONS r represents the largest integer which is less than or equal to r and x + 2 x =, find [ x ]. 9 6 A) Farmer Euclid MacDonald states: I have 360 livestock, horses and chickens. The total number of legs, excluding my own, is 00. How many chickens does farmer MacDonald have? A) Find a simplified expression for the value of x in terms of a and b, given a + b 0: a(a 2x) = b(b + 2x) A) Solve the following equation for x x = Note: 0. x represents a repeating decimal, where x is the repeating digit A number is more than half of its opposite. Compute the reciprocal of this number.

4 ML Contest # ROUND 4 ALG : FRACTIONS & MIXED NUMBERS A) A ream (500 sheets) of letter size paper (eight and a half by eleven inches) is If the volume of a single sheet as a simplified fraction is b a cubic inches, find 2 inches thick. 8 a + b. A) Determine the positive difference between A and B. A = B = A) Compute: A) Given: t = π L g If L is multiplied by 00 and g is divided by 4, what is the effect on t? Circle the correct word and fill in the blank. increase decrease by a factor of A) A triathlete swims 2 miles in three hours, jogs 0 miles in four hours and bicycles 40 miles in 2 hours. The average rate for these three events lies between two consecutive integers A and B, closer to one of these values than the other. Let C denote the closer value. Determine the ordered triple (A, C, B).

5 MML Contest # ROUND 5 INEQUALITIES & ABSOLUTE VALUE A) Find all real x for which 4x x A) It cost a publishing company $250 to setup for the printing of a brochure. After that, the cost of printing, materials, etc. is 9 per brochure. If the publisher sells the brochure for 40 per copy, how many copies minimum must be sold before any profit is realized? A) Find the area of the region defined by y x x 2 x y 0 A) If 2x 5 < 3, compute the average of the largest positive and smallest negative solutions A) The complete set of x-values satisfying the inequality ( x )( x ) 4 9 > 0

6 MML Contest # ROUND 6 ALG : EVALUATIONS A) If we define n m as nm n + m, find the exact value of 2 3. A) Consider the following binary operation: a b = 2a(3 b). Determine the positive difference between (0.5) 4 and 4 (0.5). A) 22/7 and 3.4 are often used as approximations of π. When 22/7 is approximated as 3.4, the error is, where n is a positive integer? n Compute n. A) The first Thursday in 2025 is on New Year s Day, /. Specify in what month the first Thursday falls later than the 5 th for the first time. Circle the correct month above. The numbers of days in each month for a non-leap year are: 3, 28, 3, 30, 3, 30, 3, 3, 30, 3, 30 and A) Compute (3 5) 9 25 Note: a = a