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
2010 csat__math-humanities

27 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 Probability Definitions 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 Discrete Probability Distributions 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
Q10 3 marks Laws of Logarithms Logarithmic Formula Application (Modeling) View
Shellfish filter suspended matter. When the water temperature is $t \left( { } ^ { \circ } \mathrm { C } \right)$ and the individual weight is $w ( \mathrm {~g} )$, the amounts (in L) filtered in 1 hour by shellfish A and B are denoted as $Q _ { \mathrm { A } }$ and $Q _ { \mathrm { B } }$ respectively, and the following relationships hold. $$\begin{aligned} & Q _ { \mathrm { A } } = 0.01 t ^ { 1.25 } w ^ { 0.25 } \\ & Q _ { \mathrm { B } } = 0.05 t ^ { 0.75 } w ^ { 0.30 } \end{aligned}$$ When the water temperature is $20 ^ { \circ } \mathrm { C }$ and the individual weights of shellfish A and B are each 8 g, the value of $\frac { Q _ { \mathrm { A } } } { Q _ { \mathrm { B } } }$ is $2 ^ { a } \times 5 ^ { b }$. What is the value of $a + b$? (Here, $a$ and $b$ are rational numbers.) [3 points]
(1) 0.15
(2) 0.35
(3) 0.55
(4) 0.75
(5) 0.95
Q11 3 marks Matrices 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 Binomial Theorem (positive integer n) 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) $\left( \begin{array} { l l } 1 & 1 \\ 2 & 1 \end{array} \right)$
Q14 4 marks Permutations & Arrangements Selection and Task Assignment View
There is a computer game where two dolls A and B are dressed in shirts and pants with undetermined colors, and then the colors of the clothes are determined. There are 3 shirts and 3 pants of different shapes, and the color of each piece of clothing is determined to be either red or green. A shirt and pants put on one doll are not put on the other doll. The colors of doll A's shirt and pants are determined to be different, and the colors of doll B's shirt and pants are also determined to be different. In this game, when dressing dolls A and B in shirts and pants and determining their colors, what is the number of possible outcomes? [4 points]
(1) 252
(2) 216
(3) 180
(4) 144
(5) 108
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 Laws of Logarithms 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 Differential equations 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]
Q25 4 marks Sequences and Series Limit Evaluation Involving Sequences View
As shown in the figure, a square A with side length 2 and a square B with side length 1 have sides parallel to each other, and the intersection point of the two diagonals of A coincides with the intersection point of the two diagonals of B. Let R be the region of A and its interior excluding the interior of B.
For a natural number $n \geqq 2$, small squares with side length $\frac { 1 } { n }$ are drawn in R according to the following rule. (가) One side of each small square is parallel to a side of A. (나) The interiors of the small squares do not overlap with each other.
According to such rules, let $a _ { n }$ be the maximum number of small squares with side length $\frac { 1 } { n }$ that can be drawn in R. For example, $a _ { 2 } = 12$ and $a _ { 3 } = 20$. When $\lim _ { n \rightarrow \infty } \frac { a _ { 2 n + 1 } - a _ { 2 n } } { a _ { 2 n } - a _ { 2 n - 1 } } = c$, find the value of $100 c$. [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]