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Math Studies Year 1 2013-2014 BELLRINGERS BELLRINGER #1 What is the area, in square feet, of the triangle whose sides have lengths equal to 10, 6 and 8 feet? A) 480 B) 24 C) 48 D) 30 E) 40 BELLRINGER #2 3102 + 9*3100 + 3103/3 = ? A) 3101 B) 3102 C) 3103 D) 3104 E) 3105 BELLRINGER #3 Of the 80 students in class, 25 are studying German, 15 French and 13 Spanish. 3 are studying German and French; 4 are studying French and Spanish; 2 are studying German and Spanish; and none is studying all 3 languages at the same time. How many students are not studying any of the three languages? A) 27 B) 18 C) 53 D) 62 E) 36 BELLRINGER #4 Round (202)2 to the nearest hundred. A) 40,000 B) 48,000 C) 40,800 D) 47,000 E) 49,000 BELLRINGER #5 A number of the form 213ab, where a and b are digits, has a remainder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. Find the digit b. A) 5 B) 7 C) 6 D) 8 E) 9 BELLRINGER #6 Find a negative value of x that satisfies the equation [(x+1)2 - (2x + 1)]1/2 + 2|x| - 6 = 0 A) -5 B) -4 C) -3 D) -2 E) -1 BELLRINGER #7 The inequality x2 - 2x + 1 ≤ 0 has A) no solutions B) a set of solutions C) 1 solution only D) 2 solutions only E) 3 solutions only BELLRINGER #8 12 – n, 12, 12 + n What is the average (arithmetic mean) of the 3 quantities in the list above? a) 4 b) 12 c) 18 d) 4 + 𝑛 3 e) 12 + 𝑛 3 BELLRINGER #9 5 𝑥 If a ≠ 0 and = a) -5 b) -1 5+𝑎 , 𝑥+𝑎 what’s the value of x? c) 1 d) 2 e) 5 BELLRINGER #10 What is the maximum number of rectangular blocks measuring 3 inches by 2 inches by 1 inch that can be packed into a cube-shaped box whose interior measures 6 inches on an edge? a) 24 b) 28 c) 30 d) 36 e) 40 BELLRINGER #11 3x + 2y + 2z = 19 3x + y + z = 14 If the equations above are true, which of the following is the value of y + z? a) -5 b) -4 c) 0 d) 4 e) 5 BELLRINGER #12 A boat costs x dollars, and this cost is to be shared equally by a group of people. In terms of x, how many dollars less will each person contribute if there are 4 people in the group instead of 3? a) 𝑥 12 b) 𝑥 4 c) 𝑥 3 d) 7𝑥 12 e) 7𝑥 BELLRINGER #13 If y = 2x + 3 and x < 2, which of the following represents all the possible values for y? a) y < 7 b) y > 7 c) y < 5 d) y > 5 e) 5 < y < 7 BELLRINGER #14 For all numbers a and b, let aΦb be defined by aΦb = ab + a + b. For all numbers x, y and z, which of the following must be true? 1) xΦy = yΦx 2) (x – 1)Φ(x + 1) = (xΦx) – 1 3) xΦ(y + z) = (xΦy) + (xΦz) a) 1 only b) 2 only c) 3 only d) 1 and 2 only e) 1, 2, and 3 BELLRINGER #15 If 1 y 3 + 9 = 0, then y= a) -27 b) -9 c) -3 d) 3 e) 27 BELLRINGER #16 Let the function of f be defined by f(x) = 5x – 2a, where a is a constant. If f(10) + f(5) = 55, what is the value of a? a) -5 b) 0 c) 5 d) 10 e) 20 BELLRINGER #17 If m is a positive integer, which of the following is NOT equal to (24)m? a) 24m b) 42m c) 2m(23m) d) 4m(2m) e) 16m BELLRINGER #18 A sphere of radius r inside a cube touches each one of the six sides of the cube. What is the volume of the cube, in terms of r? a) r3 b) 2r3 c) 4r3 d) 4 п𝑟3 3 e) 8r3 BELLRINGER #19 n(t) = 500(0.81)t The function above can be used to model the population of a certain endangered species of animal. If n(t) gives the number of the species living t decades after the year 1900, which of the following is true about the population of the species from 1900 to 1920? a) It increased by 1,000 b) It increased by about 320 c) It increased by about 180 d) It increased by about 320 e) It decreased by about 1,000 BELLRINGER #20 How many different ordered pairs (x,y) are there such that x is an even integer, where 4≤x≤10, and y is an integer, where 4<y<10? a) 8 b) 12 c) 20 d) 30 e) 36 BELLRINGER #21 If a, b, c and f are four nonzero numbers, then all of the following proportions are equivalent except: a) a/f = b/c BELLRINGER #22 ( 2 - 3 )2 = a) 5 - 2 6 b) 5 - 6 c) 1 - 2 6 d) 1 - 2 e) 1