csat-suneung

Papers (39)
2026
csat__math 29
2025
csat__math 43
2024
csat__math 43
2023
csat__math 29
2022
csat__math 38
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 29 csat__math-science 30
2016
csat__math-A 28 csat__math-B 29
2015
csat__math-A 30 csat__math-B 30
2014
csat__math-A 26 csat__math-B 30
2013
csat__math-humanities 27 csat__math-science 29
2012
csat__math-humanities 29 csat__math-science 30
2011
csat__math-humanities 30 csat__math-science 33
2010
csat__math-humanities 24 csat__math-science 32
2009
csat__math-humanities 27 csat__math-science 32
2008
csat__math-humanities 29 csat__math-science 26
2007
csat__math-humanities 29 csat__math-science 32
2006
csat__math-humanities 30 csat__math-science 26
2005
csat__math-humanities 22 csat__math-science 31
2010 csat__math-humanities

24 maths questions

Q1 2 marks Indices and Surds Evaluating Expressions Using Index Laws View
What is the value of $27 ^ { \frac { 1 } { 3 } } + \log _ { 2 } 4$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Q2 2 marks Matrices Matrix Algebra and Product Properties View
For two matrices $A = \left( \begin{array} { l l } 3 & 0 \\ 0 & 3 \end{array} \right) , B = \left( \begin{array} { r r } - 1 & 1 \\ 1 & 1 \end{array} \right)$, what is the sum of all components of the matrix $A B + 2 B$? [2 points]
(1) 10
(2) 8
(3) 6
(4) 4
(5) 2
Q3 2 marks Sequences and series, recurrence and convergence Multiple-choice on sequence properties View
What is the value of $\lim _ { n \rightarrow \infty } \frac { ( n + 1 ) ( 3 n - 1 ) } { 2 n ^ { 2 } + 1 }$? [2 points]
(1) $\frac { 3 } { 2 }$
(2) 2
(3) $\frac { 5 } { 2 }$
(4) 3
(5) $\frac { 7 } { 2 }$
Q4 3 marks Exponential Equations & Modelling Solve Exponential Equation for Unknown Variable View
What is the sum of all real roots of the exponential equation $2 ^ { x } + 2 ^ { 2 - x } = 5$? [3 points]
(1) - 2
(2) - 1
(3) 0
(4) 1
(5) 2
Q5 3 marks Independent Events Probability Using Set/Event Algebra View
Two events $A$ and $B$ are mutually exclusive, and $$\mathrm { P } ( A ) = \mathrm { P } ( B ) , \quad \mathrm { P } ( A ) \mathrm { P } ( B ) = \frac { 1 } { 9 }$$ What is the value of $\mathrm { P } ( A \cup B )$? [3 points]
(1) $\frac { 1 } { 6 }$
(2) $\frac { 1 } { 3 }$
(3) $\frac { 1 } { 2 }$
(4) $\frac { 2 } { 3 }$
(5) $\frac { 5 } { 6 }$
Q6 3 marks Permutations & Arrangements Selection and Task Assignment View
A company employee has 6 types of tasks to handle, including tasks $\mathrm { A }$ and $\mathrm { B }$. The employee wants to handle 4 types of tasks today, including $\mathrm { A }$ and $\mathrm { B }$, and task $\mathrm { A }$ must be handled before task $\mathrm { B }$. What is the number of ways to select the tasks to handle today and determine the order of handling the selected tasks? [3 points]
(1) 60
(2) 66
(3) 72
(4) 78
(5) 84
Q7 3 marks Conditional Probability Bayes' Theorem with Production/Source Identification View
10\% of the emails Cheol-su receives contain the word ``travel.'' 50\% of emails containing ``travel'' are advertisements, and 20\% of emails not containing ``travel'' are advertisements. Given that an email Cheol-su received is an advertisement, what is the probability that this email contains the word ``travel''? [3 points]
(1) $\frac { 5 } { 23 }$
(2) $\frac { 6 } { 23 }$
(3) $\frac { 7 } { 23 }$
(4) $\frac { 8 } { 23 }$
(5) $\frac { 9 } { 23 }$
Q8 3 marks Measures of Location and Spread Probability Distribution Table Completion and Expectation Calculation View
The probability distribution table of the random variable $X$ is as follows.
$X$012Total
$\mathrm { P } ( X = x )$$\frac { 2 } { 7 }$$\frac { 3 } { 7 }$$\frac { 2 } { 7 }$1

What is the value of the variance $\mathrm { V } ( 7 X )$ of the random variable $7 X$? [3 points]
(1) 14
(2) 21
(3) 28
(4) 35
(5) 42
Q9 4 marks Normal Distribution Process Capability or Quality Compliance Assessment View
The internal pressure strength of bottles produced at a certain factory follows a normal distribution $\mathrm { N } \left( m , \sigma ^ { 2 } \right)$, and bottles with internal pressure strength less than 40 are classified as defective. The process capability index $G$ for evaluating the factory's process capability is calculated as $$G = \frac { m - 40 } { 3 \sigma }$$ When $G = 0.8$, what is the probability that a randomly selected bottle is defective, using the standard normal distribution table on the right? [4 points]
$z$$\mathrm { P } ( 0 \leqq Z \leqq z )$
2.20.4861
2.30.4893
2.40.4918
2.50.4938

(1) 0.0139
(2) 0.0107
(3) 0.0082
(4) 0.0062
(5) 0.0038
Q11 3 marks Invariant lines and eigenvalues and vectors Determinant and Rank Computation View
The system of linear equations in $x$ and $y$ $$\left( \begin{array} { c c } 5 - \log _ { 2 } a & 2 \\ 3 & \log _ { 2 } a \end{array} \right) \binom { x } { y } = \binom { 0 } { 0 }$$ has a solution other than $x = 0 , y = 0$. What is the sum of all values of $a$? [3 points]
(1) 8
(2) 10
(3) 12
(4) 16
(5) 20
Q12 3 marks Proof by induction Evaluate a Summation Involving Binomial Coefficients View
The following is a proof by mathematical induction that the equality $$\sum _ { k = 0 } ^ { n } \frac { { } _ { n } \mathrm { C } _ { k } } { { } _ { n + 4 } \mathrm { C } _ { k } } = \frac { n + 5 } { 5 }$$ holds for all natural numbers $n$.
(1) When $n = 1$, $$( \text { LHS } ) = \frac { { } _ { 1 } \mathrm { C } _ { 0 } } { { } _ { 5 } \mathrm { C } _ { 0 } } + \frac { { } _ { 1 } \mathrm { C } _ { 1 } } { { } _ { 5 } \mathrm { C } _ { 1 } } = \frac { 6 } { 5 } , ( \text { RHS } ) = \frac { 1 + 5 } { 5 } = \frac { 6 } { 5 }$$ so the given equality holds.
(2) Assume that when $n = m$, the equality $$\sum _ { k = 0 } ^ { m } \frac { { } _ { m } \mathrm { C } _ { k } } { { } _ { m + 4 } \mathrm { C } _ { k } } = \frac { m + 5 } { 5 }$$ holds. When $n = m + 1$, $$\sum _ { k = 0 } ^ { m + 1 } \frac { { } _ { m + 1 } \mathrm { C } _ { k } } { { } _ { m + 5 } \mathrm { C } _ { k } } = \text { (가) } + \sum _ { k = 0 } ^ { m } \frac { { } _ { m + 1 } \mathrm { C } _ { k + 1 } } { { } _ { m + 5 } \mathrm { C } _ { k + 1 } }$$ For a natural number $l$, $${ } _ { l + 1 } \mathrm { C } _ { k + 1 } = \text { (나) } \cdot { } _ { l } \mathrm { C } _ { k } \quad ( 0 \leqq k \leqq l )$$ so $$\sum _ { k = 0 } ^ { m } \frac { { } _ { m + 1 } \mathrm { C } _ { k + 1 } } { { } _ { m + 5 } \mathrm { C } _ { k + 1 } } = \text { (다) } \cdot \sum _ { k = 0 } ^ { m } \frac { { } _ { m } \mathrm { C } _ { k } } { { } _ { m + 4 } \mathrm { C } _ { k } }$$ Therefore, $$\begin{aligned} \sum _ { k = 0 } ^ { m + 1 } \frac { { } _ { m + 1 } \mathrm { C } _ { k } } { { } _ { m + 5 } \mathrm { C } _ { k } } & = \text { (가) } + \text { (다) } \cdot \sum _ { k = 0 } ^ { m } \frac { { } _ { m } \mathrm { C } _ { k } } { { } _ { m + 4 } \mathrm { C } _ { k } } \\ & = \frac { m + 6 } { 5 } \end{aligned}$$ Thus, the given equality holds for all natural numbers $n$.
What are the correct values for (가), (나), and (다) in the above process? [3 points] $\begin{array} { l l l l } & \text { (가) } & \text { (나) } & \text { (다) } \\ \text { (1) } & 1 & \frac { l + 2 } { k + 2 } & \frac { m + 4 } { m + 4 } \end{array}$
(2) $1 \quad \frac { l + 1 } { k + 1 } \quad \frac { m + 1 } { m + 5 }$
(3) $1 \quad \frac { l + 1 } { k + 1 } \quad \frac { m + 1 } { m + 4 }$
(4) $m + 1 \quad \frac { l + 1 } { k + 1 } \quad \frac { m + 1 } { m + 5 }$
(5) $m + 1 \quad \frac { l + 2 } { k + 2 } \quad \frac { m + 1 } { m + 4 }$
Q13 4 marks Matrices Matrix Algebra and Product Properties View
For a $2 \times 2$ square matrix $A$ and matrix $B = \left( \begin{array} { l l } 1 & 0 \\ 1 & 1 \end{array} \right)$ such that $( B A ) ^ { 2 } = \left( \begin{array} { l l } 1 & 1 \\ 1 & 2 \end{array} \right)$, what is the matrix $( A B ) ^ { 2 }$? [4 points]
(1) $\left( \begin{array} { l l } 1 & 1 \\ 1 & 2 \end{array} \right)$
(2) $\left( \begin{array} { l l } 2 & 1 \\ 1 & 2 \end{array} \right)$
(3) $\left( \begin{array} { l l } 2 & 1 \\ 1 & 1 \end{array} \right)$
(4) $\left( \begin{array} { l l } 1 & 2 \\ 2 & 1 \end{array} \right)$
(5) $\left( \begin{array} { l l } 1 & 1 \\ 2 & 1 \end{array} \right)$
Q15 4 marks Circles Area and Geometric Measurement Involving Circles View
As shown in the figure, draw a circle $\mathrm { O } _ { 1 }$ centered at the origin with radius 3, and let the four points where circle $\mathrm { O } _ { 1 }$ meets the coordinate axes be $\mathrm { A } _ { 1 } ( 0,3 )$, $\mathrm { B } _ { 1 } ( - 3,0 ) , \mathrm { C } _ { 1 } ( 0 , - 3 ) , \mathrm { D } _ { 1 } ( 3,0 )$ respectively. Two circles passing through both points $\mathrm { B } _ { 1 }$ and $\mathrm { D } _ { 1 }$ and centered at points $\mathrm { A } _ { 1 }$ and $\mathrm { C } _ { 1 }$ respectively meet the $y$-axis inside circle $\mathrm { O } _ { 1 }$ at points $\mathrm { C } _ { 2 }$ and $\mathrm { A } _ { 2 }$ respectively. Let $S _ { 1 }$ be the area of the region enclosed by arc $\mathrm { B } _ { 1 } \mathrm { A } _ { 1 } \mathrm { D } _ { 1 }$ and arc $\mathrm { B } _ { 1 } \mathrm { A } _ { 2 } \mathrm { D } _ { 1 }$, and let $T _ { 1 }$ be the area of the region enclosed by arc $\mathrm { B } _ { 1 } \mathrm { C } _ { 1 } \mathrm { D } _ { 1 }$ and arc $\mathrm { B } _ { 1 } \mathrm { C } _ { 2 } \mathrm { D } _ { 1 }$. Draw circle $\mathrm { O } _ { 2 }$ with diameter $\mathrm { A } _ { 2 } \mathrm { C } _ { 2 }$, and let the two points where circle $\mathrm { O } _ { 2 }$ meets the $x$-axis be $\mathrm { B } _ { 2 }$ and $\mathrm { D } _ { 2 }$ respectively. Two circles passing through both points $\mathrm { B } _ { 2 }$ and $\mathrm { D } _ { 2 }$ and centered at points $\mathrm { A } _ { 2 }$ and $\mathrm { C } _ { 2 }$ respectively meet the $y$-axis inside circle $\mathrm { O } _ { 2 }$ at points $\mathrm { C } _ { 3 }$ and $\mathrm { A } _ { 3 }$ respectively. Let $S _ { 2 }$ be the area of the region enclosed by arc $\mathrm { B } _ { 2 } \mathrm { A } _ { 2 } \mathrm { D } _ { 2 }$ and arc $\mathrm { B } _ { 2 } \mathrm { A } _ { 3 } \mathrm { D } _ { 2 }$, and let $T _ { 2 }$ be the area of the region enclosed by arc $\mathrm { B } _ { 2 } \mathrm { C } _ { 2 } \mathrm { D } _ { 2 }$ and arc $\mathrm { B } _ { 2 } \mathrm { C } _ { 3 } \mathrm { D } _ { 2 }$. Continuing this process, let $S _ { n }$ be the area of the region enclosed by arc $\mathrm { B } _ { n } \mathrm { A } _ { n } \mathrm { D } _ { n }$ and arc $\mathrm { B } _ { n } \mathrm { A } _ { n + 1 } \mathrm { D } _ { n }$, and let $T _ { n }$ be the area of the region enclosed by arc $\mathrm { B } _ { n } \mathrm { C } _ { n } \mathrm { D } _ { n }$ and arc $\mathrm { B } _ { n } \mathrm { C } _ { n + 1 } \mathrm { D } _ { n }$. What is the value of $\sum _ { n = 1 } ^ { \infty } \left( S _ { n } + T _ { n } \right)$? [4 points]
(1) $6 ( \sqrt { 2 } + 1 )$
(2) $6 ( \sqrt { 3 } + 1 )$
(3) $6 ( \sqrt { 5 } + 1 )$
(4) $9 ( \sqrt { 2 } + 1 )$
(5) $9 ( \sqrt { 3 } + 1 )$
Q16 4 marks Curve Sketching Logarithmic Function Graph Intersection or Geometric Analysis View
For a natural number $n ( n \geqq 2 )$, let the $x$-coordinates of the two distinct points where the line $y = - x + n$ and the curve $y = \left| \log _ { 2 } x \right|$ meet be $a _ { n }$ and $b _ { n }$ respectively ($a _ { n } < b _ { n }$). Which of the following statements in are correct? [4 points]
ㄱ. $a _ { 2 } < \frac { 1 } { 4 }$ ㄴ. $0 < \frac { a _ { n + 1 } } { a _ { n } } < 1$ ㄷ. $1 - \frac { \log _ { 2 } n } { n } < \frac { b _ { n } } { n } < 1$
(1) ㄱ
(2) ㄴ
(3) ㄷ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ
Q17 4 marks Laws of Logarithms Characteristic and Mantissa of Common Logarithms View
For a natural number $n$ less than 10, when $\left( \frac { n } { 10 } \right) ^ { 10 }$ has a non-zero digit appearing for the first time in the sixth decimal place, what is the value of $n$? (Use $\log 2 = 0.3010 , \log 3 = 0.4771$ for calculations.) [4 points]
(1) 2
(2) 3
(3) 4
(4) 5
(5) 6
Q18 3 marks Arithmetic Sequences and Series Find Common Difference from Given Conditions View
An arithmetic sequence $\left\{ a _ { n } \right\}$ satisfies $a _ { 2 } + a _ { 4 } = 8$ and $a _ { 7 } = 52$. Find the common difference. [3 points]
Q19 3 marks Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
In the expansion of the polynomial $( 1 + x ) ^ { n }$, the coefficient of $x ^ { 2 }$ is 45. Find the natural number $n$. [3 points]
Q20 3 marks Laws of Logarithms Solve a Logarithmic Inequality View
Find the number of natural numbers $x$ that satisfy the logarithmic inequality $$\log _ { 2 } x \leqq \log _ { 4 } ( 12 x + 28 )$$ [3 points]
Q21 4 marks Continuous Probability Distributions and Random Variables PDF Graph Interpretation and Probability Computation View
A continuous random variable $X$ has a range of $0 \leqq X \leqq 4$, and the graph of the probability density function of $X$ is as shown in the figure. Find the value of $100 \mathrm { P } ( 0 \leqq X \leqq 2 )$. [4 points]
Q22 3 marks Arithmetic Sequences and Series Qualitative Analysis of DE Solutions View
For a natural number $n$, point $\mathrm { A } _ { n }$ is a point on the $x$-axis. Point $\mathrm { A } _ { n + 1 }$ is determined according to the following rule. (가) The coordinates of point $\mathrm { A } _ { 1 }$ are $( 2,0 )$. (나) (1) Let $\mathrm { P } _ { n }$ be the point where the line passing through point $\mathrm { A } _ { n }$ and parallel to the $y$-axis meets the curve $y = \frac { 1 } { x } ( x > 0 )$.
(2) Let $\mathrm { Q } _ { n }$ be the point obtained by reflecting point $\mathrm { P } _ { n }$ about the line $y = x$.
(3) Let $\mathrm { R } _ { n }$ be the point where the line passing through point $\mathrm { Q } _ { n }$ and parallel to the $y$-axis meets the $x$-axis.
(4) Let $\mathrm { A } _ { n + 1 }$ be the point obtained by translating point $\mathrm { R } _ { n }$ by 1 unit in the direction of the $x$-axis. Let the $x$-coordinate of point $\mathrm { A } _ { n }$ be $x _ { n }$. When $x _ { 5 } = \frac { q } { p }$, find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [3 points]
Q23 4 marks Geometric Sequences and Series Sum of an Infinite Geometric Series (Direct Computation) View
A geometric sequence $\left\{ a _ { n } \right\}$ satisfies $a _ { 2 } = \frac { 1 } { 2 }$ and $a _ { 5 } = \frac { 1 } { 6 }$. When $\sum _ { n = 1 } ^ { \infty } a _ { n } a _ { n + 1 } a _ { n + 2 } = \frac { q } { p }$, find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [4 points]
Q24 4 marks Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
For two natural numbers $a$ and $b$, the three numbers $a ^ { n } , 2 ^ { 4 } \times 3 ^ { 6 } , b ^ { n }$ form a geometric sequence in this order. Find the minimum value of $a b$. (Here, $n$ is a natural number.) [4 points]
Q26 3 marks Arithmetic Sequences and Series Sequence Defined by Recurrence with AP Connection View
A sequence $\left\{ a _ { n } \right\}$ satisfies $a _ { n + 1 } - a _ { n } = 2 n$. When $a _ { 10 } = 94$, what is the value of $a _ { 1 }$? [3 points]
(1) 5
(2) 4
(3) 3
(4) 2
(5) 1
Q30 4 marks Arithmetic Sequences and Series Sequence Defined by Recurrence with AP Connection View
For a sequence $\left\{ a _ { n } \right\}$, let $S _ { n }$ denote the sum of the first $n$ terms. The sequence $\left\{ S _ { 2 n - 1 } \right\}$ is an arithmetic sequence with common difference $-3$, and the sequence $\left\{ S _ { 2 n } \right\}$ is an arithmetic sequence with common difference $2$. When $a _ { 2 } = 1$, find the value of $a _ { 8 }$. [4 points]