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
2008 gsat__math

9 maths questions

Q1 Exponential Functions MCQ on Function Properties View
1. For any real number $x$, the minimum value of $27 ^ { \left( x ^ { 2 } + \frac { 2 } { 3 } \right) }$ is
(1) 3
(2) $3 \sqrt { 3 }$
(3) 9
(4) 27
(5) $81 \sqrt { 3 }$
Q5 35 marks SUVAT in 2D & Gravity Horizontal Launch or Dropped Object Problems View
5. A red flag and a white flag are placed in a plaza, and Xiaoming stands between them. Using instruments on hand, Xiaoming measures that his distance to the red flag due east is 6 times his distance to the white flag due west. After walking 10 meters due north and measuring again, he finds that his distance to the red flag is now 4 times his distance to the white flag. What is the distance between the red and white flags closest to?
(1) 60 meters
(2) 65 meters
(3) 70 meters
(4) 75 meters
(5) 80 meters
II. Multiple-Choice Questions (35 points)
Instructions: For questions 6 through 12, each of the five options is independent, and at least one option is correct. Select all correct options and mark them on the ``Answer Sheet''. No deductions are made for incorrect answers. Five points are awarded for all five options correct; 2.5 points for one incorrect option; no points for two or more incorrect options.
Q6 Curve Sketching MCQ on Function Properties View
6. Which of the following functions have graphs that lie completely above the $x$-axis?
(1) $y = x + 100$
(2) $y = x ^ { 2 } + 1$
(3) $y = 2 + \sin x$
(4) $y = 2 ^ { x }$
(5) $y = \log x$
Q7 Probability Definitions Verifying Statements About Probability Properties View
7. A high school has 20 classes, each with 40 students: 25 boys and 15 girls. If 80 students are selected from the school's 800 students using simple random sampling, which of the following statements are correct?
(1) At least one student from each class will be selected
(2) The number of boys selected will definitely be greater than the number of girls selected
(3) Given that Xiaowén is a boy and Xiaomei is a girl, the probability that Xiaowén is selected is greater than the probability that Xiaomei is selected
(4) If students A and B are in the same class, and student C is in another class, then the probability that both A and B are selected equals the probability that both A and C are selected
(5) If students A and B are brothers, the probability that both are selected is less than $\frac { 1 } { 100 }$
Q8 Arithmetic Sequences and Series True/False or Multiple-Statement Verification View
8. Let $a _ { 1 } , a _ { 2 } , a _ { 3 }$ form an arithmetic sequence, and $b _ { 1 } , b _ { 2 } , b _ { 3 }$ form a geometric sequence, where all six numbers are real. Which of the following statements are correct?
(1) It is possible for both $a _ { 1 } < a _ { 2 }$ and $a _ { 2 } > a _ { 3 }$ to hold simultaneously
(2) It is possible for both $b _ { 1 } < b _ { 2 }$ and $b _ { 2 } > b _ { 3 }$ to hold simultaneously
(3) If $a _ { 1 } + a _ { 2 } < 0$, then $a _ { 2 } + a _ { 3 } < 0$
(4) If $b _ { 1 } b _ { 2 } < 0$, then $b _ { 2 } b _ { 3 } < 0$
(5) If $b _ { 1 } , b _ { 2 } , b _ { 3 }$ are all positive integers and $b _ { 1 } < b _ { 2 }$, then $b _ { 1 }$ divides $b _ { 2 }$
Q9 Laws of Logarithms Verify Truth of Logarithmic Statements View
9. In a container, there are two types of bacteria, A and B. At any time, the product of the number of bacteria A and B is a constant $10 ^ { 10 }$. For simplicity, scientists use $P _ { A } = \log \left( n _ { A } \right)$ to record data about the number of bacteria A, where $n _ { A }$ is the number of bacteria A. Which of the following statements are correct?
(1) $1 \leq P _ { A } \leq 10$
(2) When $P _ { A } = 5$, the number of bacteria B equals the number of bacteria A
(3) If $P _ { A }$ measured last Monday was 4 and $P _ { A }$ measured last Friday was 8, then the number of bacteria A on Friday is twice the number on Monday
(4) If today's $P _ { A }$ value increases by 1 compared to yesterday, then today's bacteria A count is 10 more than yesterday's
(5) If the scientist controls the number of bacteria B to be 50,000, then $5 < P _ { A } < 5.5$
Q10 Factor & Remainder Theorem True/False or Multiple-Statement Evaluation View
10. Let $f ( x )$ and $g ( x ) = x ^ { 3 } + x ^ { 2 } - 2$ be real coefficient polynomials with a common factor of degree greater than 0. Which of the following statements are correct?
(1) $g ( x ) = 0$ has exactly one real root
(2) $f ( x ) = 0$ must have a real root
(3) If $f ( x ) = 0$ and $g ( x ) = 0$ have a common real root, then this root must be 1
(4) If $f ( x ) = 0$ and $g ( x ) = 0$ have a common real root, then the greatest common divisor of $f ( x )$ and $g ( x )$ is a linear polynomial
(5) If $f ( x ) = 0$ and $g ( x ) = 0$ have no common real roots, then the greatest common divisor of $f ( x )$ and $g ( x )$ is a quadratic polynomial
Q11 Vectors: Lines & Planes True/False or Verify a Given Statement View
11. Let the equations of three lines $L _ { 1 } , L _ { 2 } , L _ { 3 }$ in coordinate space be
$$L _ { 1 } : \frac { x } { 1 } = \frac { y + 3 } { 6 } = \frac { z + 4 } { 8 } ; \quad L _ { 2 } : \frac { x } { 1 } = \frac { y + 3 } { 3 } = \frac { z + 4 } { 4 } ; \quad L _ { 3 } : \frac { x } { 1 } = \frac { y } { 3 } = \frac { z } { 4 }$$
Which of the following statements are correct?
(1) $L _ { 1 }$ and $L _ { 2 }$ intersect
(2) $L _ { 2 }$ and $L _ { 3 }$ are parallel
(3) The distance between points $P ( 0 , - 3 , - 4 )$ and $Q ( 0,0,0 )$ equals the shortest distance from point $P$ to $L _ { 3 }$
(4) The line $L$ : $\left\{ \begin{array} { c } x = 0 \\ \frac { y + 3 } { 4 } = \frac { z + 4 } { - 3 } \end{array} \right.$ is perpendicular to both $L _ { 1 }$ and $L _ { 2 }$
(5) The three lines $L _ { 1 } , L _ { 2 } , L _ { 3 }$ are coplanar
Q12 Circles Circle Identification and Classification View
12. Let $\Gamma : x ^ { 2 } + y ^ { 2 } - 10 x + 9 = 0$ be a circle in the coordinate plane. Which of the following statements are correct?
(1) The center of $\Gamma$ is at $( 5,0 )$
(2) The maximum distance from a point on $\Gamma$ to the line $L : 3 x + 4 y - 15 = 0$ equals 4
(3) The line $L _ { 1 } : 3 x + 4 y + 15 = 0$ is tangent to $\Gamma$
(4) There