taiwan-gsat

Papers (23)
2025
ast__math-a 16 ast__math-b 18 gsat__math-a 20 gsat__math-b 18
2024
ast__math-a 17 gsat__math-a 20 gsat__math-b 15
2023
ast__math-a 17 gsat__math-a 20 gsat__math-b 15
2022
ast__math-a 16 gsat__math-a 20 gsat__math-b 19
2021
ast__math-a 13 ast__math-b 10 gsat__math 20
2020
ast__math-a 13 ast__math-b 11
2010
gsat__math 12
2009
gsat__math 10
2008
gsat__math 9
2007
gsat__math 10
2006
gsat__math 9
2006 gsat__math

9 maths questions

Q1 Complex Numbers Arithmetic Geometric Properties of Triangles/Polygons from Affixes View
1. Suppose a quadratic equation with integer coefficients $a x ^ { 2 } + b x + c = 0$ has one root equal to $4 + 3 i$. If the two roots of this equation and the origin are marked on the complex plane, the area of the triangle formed by these three points is
(1) 5
(2) 6
(3) 12
(4) 16
(5) 24
Q2 Probability Definitions Combinatorial Probability View
2. In the checkerboard grid shown on the right, two squares are randomly selected. The probability that the two selected squares are not in the same row (whether or not they are in the same column is irrelevant) is
(1) $\frac { 1 } { 20 }$
(2) $\frac { 1 } { 4 }$
(3) $\frac { 3 } { 4 }$
(4) $\frac { 3 } { 5 }$
(5) $\frac { 4 } { 5 }$
Q3 Sine and Cosine Rules Multi-step composite figure problem View
3. The figure on the right is formed by stacking three right triangles, and $\overline { O D } = 8$. Question: What is the height $\overline { A B }$ of right triangle $O A B$?
(1) 1
(2) $\sqrt { 6 } - \sqrt { 2 }$
(3) $\sqrt { 7 } - 1$
(4) $\sqrt { 3 }$
(5) 2 [Figure]
Q4 Harmonic Form Simplification of Trigonometric Expressions with Specific Angles View
4. Which of the following numbers is closest to $\sqrt { 2 }$?
(1) $\sqrt { 3 } \cos 44 ^ { \circ } + \sin 44 ^ { \circ }$
(2) $\sqrt { 3 } \cos 54 ^ { \circ } + \sin 54 ^ { \circ }$
(3) $\sqrt { 3 } \cos 64 ^ { \circ } + \sin 64 ^ { \circ }$
(4) $\sqrt { 3 } \cos 74 ^ { \circ } + \sin 74 ^ { \circ }$
(5) $\sqrt { 3 } \cos 84 ^ { \circ } + \sin 84 ^ { \circ }$
Q5 30 marks Exponential Functions Applied/Contextual Exponential Modeling View
5. With adequate nutrients, the number of bacteria grows exponentially. Suppose the quantity of bacteria A doubles every two hours, and the quantity of bacteria B triples every three hours. If nutrients are adequate and the initial quantities of both bacteria are equal, approximately how many hours later will the quantity of bacteria B divided by the quantity of bacteria A be closest to 10?
(1) 24 hours.
(2) 48 hours.
(3) 69 hours.
(4) 96 hours.
(5) 117 hours.
II. Multiple-Choice Questions (30 points)
Instructions: For questions 6 to 11, each of the five options is independent, and at least one option is correct. Select the correct options and mark them on the "Answer Section" of the answer sheet. No points are deducted for wrong answers. Five points are awarded for all five options correct, 2.5 points for only one wrong option, and no points for two or more wrong options.
Q7 Conic sections Circle Identification and Classification View
7. Consider all points $( x , y )$ on the coordinate plane satisfying $\sqrt { ( x - 2 ) ^ { 2 } + y ^ { 2 } } + \sqrt { ( x - 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } } = 10$. Which of the following statements is correct?
(1) This figure is an ellipse.
(2) This figure is a hyperbola.
(3) The center of this figure is at $( 2 , - 2 )$.
(4) This figure is symmetric about $x - 2 = 0$.
(5) This figure has a vertex at $( 2,3 )$.
Q8 Arithmetic Sequences and Series Properties of AP Terms under Transformation View
8. Suppose real numbers $a _ { 1 } , a _ { 2 } , a _ { 3 } , a _ { 4 }$ form an arithmetic sequence, and satisfy $0 < a _ { 1 } < 2$ and $a _ { 3 } = 4$. If $b _ { n } = 2 ^ { a _ { n } }$ is defined, which of the following options are correct?
(1) $b _ { 1 } , b _ { 2 } , b _ { 3 } , b _ { 4 }$ form a geometric sequence.
(2) $b _ { 1 } < b _ { 2 }$.
(3) $b _ { 2 } > 4$.
(4) $b _ { 4 } > 32$.
(5) $b _ { 2 } \times b _ { 4 } = 256$.
Q9 Factor & Remainder Theorem Sum of Coefficients and Coefficient Relationships View
9. A student practices calculating the remainder when a cubic polynomial $f ( x )$ is divided by a linear polynomial $g ( x )$. It is known that the coefficient of the cubic term of $f ( x )$ is 3, and the coefficient of the linear term is 2. Student A mistakenly read the coefficient of the cubic term of $f ( x )$ as 2 (other coefficients were read correctly), and Student B mistakenly read the coefficient of the linear term of $f ( x )$ as $- 2$ (other coefficients were read correctly). The remainders calculated by Student A and Student B happen to be the same. Which of the following linear expressions could $g ( x )$ equal?
(1) $x$
(2) $x - 1$
(3) $x - 2$
(4) $x + 1$
(5) $x + 2$
Q10 Normal Distribution Multiple-Choice Conceptual Question on Normal Distribution Properties View
10. The figure below is a histogram based on the weights of 100 women (the percentages in the figure represent the relative frequency of each weight interval, where each interval does not include the left endpoint but includes the right endpoint). The mean weight of the 100 women is 55 kg, and the standard deviation is 12.5 kg. Curve N represents a normal distribution with the same mean and standard deviation as the sample values. In this sample, if "overweight" is defined as weight exceeding the sample mean by 2 or more standard deviations (i.e., weight exceeding 80 kg or more), which of the following statements are correct? [Figure]
(1) In curve N (normal distribution), the proportion at 55 kg or above is approximately 50\%.
(2) In curve N (normal distribution), the proportion at 80 kg or above is approximately 2.5\%.
(3) In this sample, the median weight is greater than 55 kg.
(4) In this sample, the first quartile of weight is greater than 45 kg.
(5) In this sample, the proportion of "overweight" (weight exceeding 80 kg or more) is greater than or equal to 5\%.