74. If log 2 0.3010 = , log3 0.4771 = . How many digits are there in the decimal expansion of the number 50 35 2 3⋅ ?
(A) 31
(B) 32
(C) 33
(D) 34

75. How many integers are there for the equation 2 2 ( 1) 1 n n n + −− = ? (A) 4 (B) 3 (C) 2 (D) 1

76. There are 5 ways to write 4 as a sum of positive numbers, namely 5, 4+1, 3+2, 2+1+1, 1+1+1+1+1. Note that the order of the summands is irrelevant. How many ways are there to write 8 into a sum of positive numbers, with order or the summands irrelevant? (A) 20 (B) 21 (C) 22 (D) 23

77. How many integers n among [0,10] are there such that the equation x −− − + − = 1 22 3 x xn has exactly two solutions? (A) 8 (B) 9 (C) 10 (D) 11 13

78. Find the sum of the coefficients when we write the vector (-1,2,0) as the linear combination of three vectors (2,1,5), (-1,1,3) and (3,1,9). (A) 2 (B) 3 (C) 5 (D) 7

79. Initially in the first box there are 1 black ball and 1 white ball and in the second box there is a white ball. Tom choose a ball randomly from the first box, put it into the second box, then choose a ball randomly from the second box and put it back to the first box. The above process is called a “round”. After the third round, the probability that the two balls in the first box are of the different colors is n m (in the reduced fraction) . Find the value of m n + . (A) 107 (B) 109 (C) 111 (D) 113

80. According to Anna Sfard, a mathematical concept can be conceived in two different ways: structurally and operationally. Which of the following is to view operationally? (A) as an irrational number. (B) as a symbol. (C) as an infinite decimal. (D) as taking a square root of 2.

81. David Tall conducted a study to investigate 16 year old students’ concept image and concept definition. The students were asked to draw the tangent to the following graph at the origin. Some students did not cope with the task and asserted that “…because the tangent should touch the line at one specific point but this tangent would touch it constantly.” Which of the following best describes the cause of the students’ answer? (A)Almost always the concept definition will be evoked by students when solving problems. (B)Almost always the concept image will be evoked by students when solving problems. (C)The concept definition includes a form of words used to specify the concept, however, the students were asked to draw a tangent in this case. (D)The concept image includes a form of words used to specify the concept, however, the students were asked to draw a tangent in this case.

82. Suppose x is a real number. The maximum of is? (A)(B)(C)(D)

83. Five different odd numbers sum up to 85. What is the range of the largest number n among these five? (A)17≤n≤69  (B)23≤n≤67 (C)19≤n≤67 (D)21≤n≤69

84. The following is a statement of “algorithm for square-root multiplication” in a secondary school textbook, “The product of the positive square roots of two positive numbers is equal to the positive square root of the product of the two positive numbers.” After teaching, Ms. Guo found that most students learned the expressional representation of this statement, a b ab × = , but did not understand the above statement. Please choose the most effective teaching activity from the following to help students understand the statement. (A)Thoroughly re-teach the concept of the algorithm. (B)Give students corresponding numerical expressions of the statement, such as 23 6 × = , and ask students to describe it with words. (C)Ask students to start with a part of the statement and gradually expand it and then judge the relations among all mathematical objects in the statement. (D) Ask students to do more exercises pertinent to the algorithm.

115年 - 115 國立高科實驗高級中等學校_專任教師甄選_國中部︰數學領域數學專長#138920

114年 - 114-1 臺北市立松山高級商業家事職業學校_教師甄選題目：數學#138394

114年 - 114 新北市立國民中學_教師聯合甄選試題： 數學科#127346

114年 - 114 國立臺灣藝術大學_綜合學科測驗﹕數學#126930

114年 - 114 國立彰化高級中學_教師甄選初試試題：數學科#126821

114年 - 114 臺北市立陽明高級中學_正式教師甄選試題：高中數學科#126749

114年 - 114 國立師大附中_教師甄選︰數學#126229

113年 - 113 金門縣國民中學正式教師聯合甄選初試試題：數學#120861

113年 - 113 新北市公立高級中等學校教師聯合甄選試題：數學#120730

113年 - 113 桃園市國民中學新進教師甄選試題：數學科#120523