csat-suneung

Papers (39)
2026
csat__math 30
2025
csat__math 43
2024
csat__math 44
2023
csat__math 30
2022
csat__math 41
2021
csat__math-humanities 30 csat__math-science 29
2020
csat__math-humanities 30 csat__math-science 30
2019
csat__math-humanities 30 csat__math-science 30
2018
csat__math-humanities 30 csat__math-science 30
2017
csat__math-humanities 30 csat__math-science 30
2016
csat__math-A 30 csat__math-B 30
2015
csat__math-A 30 csat__math-B 30
2014
csat__math-A 30 csat__math-B 30
2013
csat__math-humanities 30 csat__math-science 30
2012
csat__math-humanities 29 csat__math-science 30
2011
csat__math-humanities 30 csat__math-science 36
2010
csat__math-humanities 27 csat__math-science 33
2009
csat__math-humanities 27 csat__math-science 23
2008
csat__math-humanities 29 csat__math-science 14
2007
csat__math-humanities 30 csat__math-science 17
2006
csat__math-humanities 30 csat__math-science 26
2005
csat__math-humanities 27 csat__math-science 32
2008 csat__math-science

14 maths questions

Q1 2 marks Laws of Logarithms Simplify or Evaluate a Logarithmic Expression View
The value of $8 ^ { \frac { 2 } { 3 } } + \log _ { 2 } 8$ is? [2 points]
(1) 5
(2) 6
(3) 7
(4) 8
(5) 9
Q2 2 marks Matrices Matrix Algebra and Product Properties View
For two matrices $A = \left( \begin{array} { r r } 1 & - 2 \\ 3 & 0 \end{array} \right) , B = \left( \begin{array} { r r } 2 & 0 \\ 1 & - 1 \end{array} \right)$, what is the matrix $X$ that satisfies $A = 2 B - X$? [2 points]
(1) $\left( \begin{array} { r r } 3 & 2 \\ - 1 & - 2 \end{array} \right)$
(2) $\left( \begin{array} { r r } 3 & - 2 \\ 1 & 2 \end{array} \right)$
(3) $\left( \begin{array} { r r } - 1 & - 2 \\ 3 & 2 \end{array} \right)$
(4) $\left( \begin{array} { r r } - 2 & - 1 \\ 2 & 3 \end{array} \right)$
(5) $\left( \begin{array} { l l } - 3 & 1 \\ - 2 & 2 \end{array} \right)$
Q3 2 marks Curve Sketching Finding Parameters for Continuity View
Function $$f ( x ) = \left\{ \begin{array} { c c } \frac { x ^ { 2 } + x - 12 } { x - 3 } & ( x \neq 3 ) \\ a & ( x = 3 ) \end{array} \right.$$ When this function is continuous for all real numbers $x$, what is the value of $a$? [2 points]
(1) 10
(2) 9
(3) 8
(4) 7
(5) 6
Q4 3 marks Inequalities Integer Solutions of an Inequality View
Two quadratic expressions $f ( x ) , g ( x )$ with leading coefficient 1 have greatest common divisor $x + 3$ and least common multiple $x ( x + 3 ) ( x - 4 )$. How many integers $x$ satisfy the fractional inequality $\frac { 1 } { f ( x ) } + \frac { 1 } { g ( x ) } \leqq 0$? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Q5 3 marks Conic sections Equation Determination from Geometric Conditions View
The graph of the logarithmic function $y = \log _ { 2 } ( x + a ) + b$ passes through the focus of the parabola $y ^ { 2 } = x$, and the asymptote of the graph of this logarithmic function coincides with the directrix of the parabola $y ^ { 2 } = x$. What is the value of the sum $a + b$ of the two constants $a , b$? [3 points]
(1) $\frac { 5 } { 4 }$
(2) $\frac { 13 } { 8 }$
(3) $\frac { 9 } { 4 }$
(4) $\frac { 21 } { 8 }$
(5) $\frac { 11 } { 4 }$
Q22 4 marks Exponential Equations & Modelling Solve Exponential Equation for Unknown Variable View
In a certain region, the average number of earthquakes $N$ with magnitude $M$ or greater occurring in one year satisfies the following equation. $$\log N = a - 0.9 M \text{ (where } a \text{ is a positive constant)}$$ In this region, earthquakes with magnitude 4 or greater occur on average 64 times per year. Earthquakes with magnitude $x$ or greater occur on average once per year. Find the value of $9 x$. (Use $\log 2 = 0.3$ for the calculation.) [4 points]
Q23 4 marks Vectors 3D & Lines Section Division and Coordinate Computation View
In coordinate space, there is a tetrahedron ABCD with vertices at four points $\mathrm { A } ( 2,0,0 ) , \mathrm { B } ( 0,1,0 ) , \mathrm { C } ( - 3,0,0 )$, $\mathrm { D } ( 0,0,2 )$. For point P moving on edge BD, let the coordinates of point P that minimize $\overline { \mathrm { PA } } ^ { 2 } + \overline { \mathrm { PC } } ^ { 2 }$ be $( a , b , c )$. If $a + b + c = \frac { q } { p }$, find the value of $p + q$. (Here, $p , q$ are coprime natural numbers.) [4 points]
Q24 4 marks Vector Product and Surfaces View
There is a regular tetrahedron OABC with edge length 6. Let $S _ { 1 } , S _ { 2 } , S _ { 3 }$ be the orthogonal projections onto plane ABC of the three circles inscribed in triangles $\triangle \mathrm { OAB } , \triangle \mathrm { OBC } , \triangle \mathrm { OCA }$ respectively. As shown in the figure, let $S$ be the area of the dark region enclosed by the three figures $S _ { 1 } , S _ { 2 } , S _ { 3 }$. Find the value of $( S + \pi ) ^ { 2 }$. [4 points]
Q25 4 marks Combinations & Selection Selection with Group/Category Constraints View
A training center operates five different types of experience programs. Participants A and B each want to select 2 types from the 5 types of experience programs. Find the number of cases where A and B select exactly one type in common. [4 points]
Q26 3 marks Addition & Double Angle Formulae Direct Double Angle Evaluation View
(Calculus) When $\sin \alpha = \frac { 3 } { 4 }$, what is the value of $\cos 2 \alpha$? [3 points]
(1) $- \frac { 1 } { 32 }$
(2) $- \frac { 1 } { 16 }$
(3) $- \frac { 1 } { 8 }$
(4) $- \frac { 1 } { 4 }$
(5) $- \frac { 1 } { 2 }$
Q27 3 marks Applied differentiation Convexity and inflection point analysis View
(Calculus) For the function $f ( x ) = x + \sin x$, define the function $g ( x )$ as $$g ( x ) = ( f \circ f ) ( x )$$ Which of the following in are correct? [3 points]
ㄱ. The graph of function $f ( x )$ is concave down on the open interval $( 0 , \pi )$. ㄴ. The function $g ( x )$ is increasing on the open interval $( 0 , \pi )$. ㄷ. There exists a real number $x$ in the open interval $( 0 , \pi )$ such that $g ^ { \prime } ( x ) = 1$.
(1) ᄀ
(2) ᄃ
(3) ᄀ, ᄂ
(4) ᄂ, ᄃ
(5) ᄀ, ᄂ, ᄃ
Q28 3 marks Radians, Arc Length and Sector Area View
(Calculus) As shown in the figure, for a positive angle $\theta$, there is an isosceles triangle ABC with $\angle \mathrm { ABC } = \angle \mathrm { ACB } = \theta$ and $\overline { \mathrm { BC } } = 2$. Let O be the center of the inscribed circle of triangle ABC, D be the point where segment AB meets the inscribed circle, and E be the point where segment AC meets the inscribed circle. [3 points]
(1) $\frac { \pi } { 4 } - 1$
(2) $\frac { \pi } { 4 }$
(3) $\frac { \pi } { 4 } + \frac { 1 } { 3 }$
(4) $\frac { \pi } { 4 } + \frac { 1 } { 2 }$
(5) $\frac { \pi } { 4 } + 1$
Q29 4 marks Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
(Calculus) Find the length of the curve $y = \frac { 1 } { 3 } \left( x ^ { 2 } + 2 \right) ^ { \frac { 3 } { 2 } }$ from $x = 0$ to $x = 6$. [4 points]
Q30 4 marks Confidence intervals Find a specific bound or margin of error from the CI formula View
(Probability and Statistics) To determine the proportion $p$ of students arriving before 8 AM at a certain high school, 300 students were randomly sampled from the school on a certain day, and the sample proportion $\hat{p}$ of students arriving before 8 AM was obtained. Using the sample proportion $\hat{p}$, the 95\% confidence interval for the proportion $p$ is $[ 0.701, 0.799 ]$. Find the number of students among the 300 randomly sampled students who arrived before 8 AM. (Note: When $Z$ follows the standard normal distribution, $\mathrm { P } ( | Z | \leqq 1.96 ) = 0.95$.) [4 points]