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
2017 csat__math-humanities

30 maths questions

Q1 2 marks Indices and Surds Evaluating Expressions Using Index Laws View
What is the value of $8 \times 2 ^ { - 2 }$? [2 points]
(1) 1
(2) 2
(3) 4
(4) 8
(5) 16
Q2 2 marks Laws of Logarithms Simplify or Evaluate a Logarithmic Expression View
What is the value of $\log _ { 15 } 3 + \log _ { 15 } 5$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Q3 2 marks Probability Definitions Set Operations View
Two sets $$A = \{ 1,2,3,4,5 \} , B = \{ 2,4,6,8,10 \}$$ What is the value of $n ( A \cup B )$? [2 points]
(1) 6
(2) 7
(3) 8
(4) 9
(5) 10
Q4 3 marks Probability Definitions Probability Using Set/Event Algebra View
For two events $A$ and $B$, $$\mathrm { P } ( A \cap B ) = \frac { 1 } { 8 } , \mathrm { P } \left( A \cap B ^ { C } \right) = \frac { 3 } { 16 }$$ What is the value of $\mathrm { P } ( A )$? (Here, $B ^ { C }$ is the complement of $B$.) [3 points]
(1) $\frac { 3 } { 16 }$
(2) $\frac { 7 } { 32 }$
(3) $\frac { 1 } { 4 }$
(4) $\frac { 9 } { 32 }$
(5) $\frac { 5 } { 16 }$
Q5 3 marks Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
When three numbers $\frac { 9 } { 4 } , a , 4$ form a geometric sequence in this order, what is the value of the positive number $a$? [3 points]
(1) $\frac { 8 } { 3 }$
(2) 3
(3) $\frac { 10 } { 3 }$
(4) $\frac { 11 } { 3 }$
(5) 4
Q6 3 marks Composite & Inverse Functions Evaluate Composition from Diagram or Mapping View
The figure shows a function $f : X \rightarrow X$. What is the value of $f ( 2 ) + f ^ { - 1 } ( 2 )$? [3 points]
(1) 3
(2) 4
(3) 5
(4) 6
(5) 7
Q7 3 marks Inequalities Sufficient/Necessary Conditions Between Inequality Conditions View
For two conditions on the real number $x$: $$\begin{aligned} & p : | x - 1 | \leq 3 , \\ & q : | x | \leq a \end{aligned}$$ What is the minimum value of the natural number $a$ such that $p$ is a sufficient condition for $q$? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Q8 3 marks Curve Sketching Limit Reading from Graph View
The graph of the function $y = f ( x )$ is shown in the figure. What is the value of $\lim _ { x \rightarrow 0 - } f ( x ) + \lim _ { x \rightarrow 1 + } f ( x )$? [3 points]
(1) - 1
(2) - 2
(3) - 3
(4) - 4
(5) - 5
Q9 3 marks Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
What is the value of $\int _ { 0 } ^ { 2 } \left( 6 x ^ { 2 } - x \right) d x$? [3 points]
(1) 15
(2) 14
(3) 13
(4) 12
(5) 11
Q10 3 marks Composite & Inverse Functions Graphical Interpretation of Inverse or Composition View
On the coordinate plane, when the graph of the function $y = \frac { 3 } { x - 5 } + k$ is symmetric with respect to the line $y = x$, what is the value of the constant $k$? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Q11 3 marks Binomial Distribution Compute Exact Binomial Probability View
When rolling a die 3 times, what is the probability that the number 4 appears exactly once? [3 points]
(1) $\frac { 25 } { 72 }$
(2) $\frac { 13 } { 36 }$
(3) $\frac { 3 } { 8 }$
(4) $\frac { 7 } { 18 }$
(5) $\frac { 29 } { 72 }$
Q12 3 marks Variable acceleration (1D) Compute total distance traveled over an interval View
The velocity $v ( t )$ at time $t ( t \geq 0 )$ of a point P moving on a number line is $$v ( t ) = - 2 t + 4$$ What is the distance traveled by point P from $t = 0$ to $t = 4$? [3 points]
(1) 8
(2) 9
(3) 10
(4) 11
(5) 12
Q13 3 marks Probability Definitions Finite Equally-Likely Probability Computation View
The total number of students at a certain school is 360, and each student chose either experiential learning A or experiential learning B. Among the students at this school, those who chose experiential learning A are 90 male students and 70 female students. When one student is randomly selected from the students at this school who chose experiential learning B, the probability that this student is male is $\frac { 2 } { 5 }$. What is the number of female students at this school? [3 points]
(1) 180
(2) 185
(3) 190
(4) 195
(5) 200
Q14 4 marks Curve Sketching Finding Parameters for Continuity View
For two functions $$\begin{aligned} & f ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } - 4 x + 6 & ( x < 2 ) \\ 1 & ( x \geq 2 ) \end{array} , \right. \\ & g ( x ) = a x + 1 \end{aligned}$$ When the function $\frac { g ( x ) } { f ( x ) }$ is continuous on the entire set of real numbers, what is the value of the constant $a$? [4 points]
(1) $- \frac { 5 } { 4 }$
(2) $- 1$
(3) $- \frac { 3 } { 4 }$
(4) $- \frac { 1 } { 2 }$
(5) $- \frac { 1 } { 4 }$
Q15 4 marks Arithmetic Sequences and Series Find Specific Term from Given Conditions View
An arithmetic sequence $\left\{ a _ { n } \right\}$ with positive common difference satisfies the following conditions. What is the value of $a _ { 2 }$? [4 points] (가) $a _ { 6 } + a _ { 8 } = 0$ (나) $\left| a _ { 6 } \right| = \left| a _ { 7 } \right| + 3$
(1) - 15
(2) - 13
(3) - 11
(4) - 9
(5) - 7
Q16 4 marks Confidence intervals Find a specific bound or margin of error from the CI formula View
The weight of pomegranates produced at a certain farm follows a normal distribution with mean $m$ and standard deviation 40. A sample of size 64 was taken from the pomegranates produced at this farm, and the sample mean of the pomegranate weights was $\bar { x }$. Using this result, the 99\% confidence interval for the mean $m$ of the pomegranate weights produced at this farm is $\bar { x } - c \leq m \leq \bar { x } + c$. What is the value of $c$? (Here, the unit of weight is g, and when $Z$ is a random variable following the standard normal distribution, $\mathrm { P } ( 0 \leq Z \leq 2.58 ) = 0.495$.) [4 points]
(1) 25.8
(2) 21.5
(3) 17.2
(4) 12.9
(5) 8.6
Q17 4 marks Sequences and series, recurrence and convergence Summation of sequence terms View
As shown in the figure, there is a circle $O$ with diameter AB of length 4. Let C be the center of the circle, and let D and P be the midpoints of segments AC and BC, respectively. Let E and Q be the points where the perpendicular bisector of segment AC and the perpendicular bisector of segment BC meet the upper semicircle of circle $O$, respectively. Draw a square DEFG with side DE that meets circle $O$ at point A and has diagonal DF, and draw a square PQRS with side PQ that meets circle $O$ at point B and has diagonal PR. Color the $\square$-shaped figure that is the common part of the interior of circle $O$ and the interior of square DEFG, and the $\square$-shaped figure that is the common part of the interior of circle $O$ and the interior of square PQRS to obtain figure $R _ { 1 }$. In figure $R _ { 1 }$, draw circle $O _ { 1 }$ centered at point F with radius $\frac { 1 } { 2 } \overline { \mathrm { DE } }$, and circle $O _ { 2 }$ centered at point R with radius $\frac { 1 } { 2 } \overline { \mathrm { PQ } }$. Color 2 $\square$-shaped figures and 2 $\square$-shaped figures created in the same way as obtaining figure $R _ { 1 }$ on the two circles $O _ { 1 }$ and $O _ { 2 }$ to obtain figure $R _ { 2 }$. Continuing this process, let $S _ { n }$ be the area of the colored part in figure $R _ { n }$ obtained the $n$-th time. What is the value of $\lim _ { n \rightarrow \infty } S _ { n }$? [4 points]
(1) $\frac { 12 \pi - 9 \sqrt { 3 } } { 10 }$
(2) $\frac { 8 \pi - 6 \sqrt { 3 } } { 5 }$
(3) $\frac { 32 \pi - 24 \sqrt { 3 } } { 15 }$
(4) $\frac { 28 \pi - 21 \sqrt { 3 } } { 10 }$
(5) $\frac { 16 \pi - 12 \sqrt { 3 } } { 5 }$
Q18 4 marks Solving quadratics and applications Determining quadratic function from given conditions View
A quadratic function $f ( x )$ with leading coefficient 1 satisfies $$\lim _ { x \rightarrow a } \frac { f ( x ) - ( x - a ) } { f ( x ) + ( x - a ) } = \frac { 3 } { 5 }$$ When the two roots of the equation $f ( x ) = 0$ are $\alpha$ and $\beta$, what is the value of $| \alpha - \beta |$? (Here, $a$ is a constant.) [4 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Q19 4 marks Combinations & Selection Lattice Path Counting View
A jump is defined as moving from a point $( x , y )$ on the coordinate plane to one of the three points $( x + 1 , y )$, $( x , y + 1 )$, or $( x + 1 , y + 1 )$. Let $X$ be the random variable representing the number of jumps that occur when one case is randomly selected from all cases of moving from point $( 0,0 )$ to point $( 4,3 )$ by repeating jumps. The following is the process of finding the mean $\mathrm { E } ( X )$ of the random variable $X$. (Here, each case is selected with equal probability.)
Let $N$ be the total number of cases of moving from point $( 0,0 )$ to point $( 4,3 )$ by repeating jumps. If the smallest value that the random variable $X$ can take is $k$, then $k =$ (가), and the largest value is $k + 3$.
$$\begin{aligned} & \mathrm { P } ( X = k ) = \frac { 1 } { N } \times \frac { 4 ! } { 3 ! } = \frac { 4 } { N } \\ & \mathrm { P } ( X = k + 1 ) = \frac { 1 } { N } \times \frac { 5 ! } { 2 ! 2 ! } = \frac { 30 } { N } \\ & \mathrm { P } ( X = k + 2 ) = \frac { 1 } { N } \times \text { (나) } \\ & \mathrm { P } ( X = k + 3 ) = \frac { 1 } { N } \times \frac { 7 ! } { 3 ! 4 ! } = \frac { 35 } { N } \end{aligned}$$
and $$\sum _ { i = k } ^ { k + 3 } \mathrm { P } ( X = i ) = 1$$ so $N =$ (다). Therefore, the mean $\mathrm { E } ( X )$ of the random variable $X$ is as follows. $$\mathrm { E } ( X ) = \sum _ { i = k } ^ { k + 3 } \{ i \times \mathrm { P } ( X = i ) \} = \frac { 257 } { 43 }$$
When the numbers that fit (가), (나), and (다) are $a$, $b$, and $c$, respectively, what is the value of $a + b + c$? [4 points]
(1) 190
(2) 193
(3) 196
(4) 199
(5) 202
Q20 4 marks Differential equations Qualitative Analysis of DE Solutions View
A cubic function $f ( x )$ with positive leading coefficient satisfies the following conditions. (가) The function $f ( x )$ has a local maximum at $x = 0$ and a local minimum at $x = k$. (Here, $k$ is a constant.) (나) For all real numbers $t$ greater than 1, $\int _ { 0 } ^ { t } \left| f ^ { \prime } ( x ) \right| d x = f ( t ) + f ( 0 )$ Which of the following statements in the given options are correct? [4 points] Options ᄀ. $\int _ { 0 } ^ { k } f ^ { \prime } ( x ) d x < 0$ ㄴ. $0 < k \leq 1$ ㄷ. The local minimum value of the function $f ( x )$ is 0.
(1) ᄀ
(2) ㄷ
(3) ᄀ, ㄴ
(4) ㄴ, ㄷ
(5) ᄀ, ㄴ, ㄷ
Q21 4 marks Curve Sketching Lattice Points and Counting via Graph Geometry View
On the coordinate plane, the function $$f ( x ) = \begin{cases} - x + 10 & ( x < 10 ) \\ ( x - 10 ) ^ { 2 } & ( x \geq 10 ) \end{cases}$$ and for a natural number $n$, there is a circle $O _ { n }$ centered at $( n , f ( n ) )$ with radius 3. Let $A _ { n }$ be the number of all points with integer coordinates that are inside circle $O _ { n }$ and below the graph of the function $y = f ( x )$, and let $B _ { n }$ be the number of all points with integer coordinates that are inside circle $O _ { n }$ and above the graph of the function $y = f ( x )$. What is the value of $\sum _ { n = 1 } ^ { 20 } \left( A _ { n } - B _ { n } \right)$? [4 points]
(1) 19
(2) 21
(3) 23
(4) 25
(5) 27
Q22 3 marks Permutations & Arrangements Factorial and Combinatorial Expression Simplification View
Find the value of ${ } _ { 5 } \mathrm { P } _ { 2 } + { } _ { 5 } \mathrm { C } _ { 2 }$. [3 points]
Q23 3 marks Differentiation from First Principles View
For the function $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 3$, find the value of $f ^ { \prime } ( 2 )$. [3 points]
Q24 3 marks Principle of Inclusion/Exclusion View
The universal set is $U = \{ x \mid x$ is a natural number not exceeding 9 $\}$, and two subsets of $U$ are $$A = \{ 3,6,7 \} , B = \{ a - 4,8,9 \}$$ If $$A \cap B ^ { C } = \{ 6,7 \}$$ find the value of the natural number $a$. [3 points]
Q25 3 marks Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
For the function $f ( x ) = \frac { 1 } { 2 } x + 2$, find the value of $\sum _ { k = 1 } ^ { 15 } f ( 2 k )$. [3 points]
Q26 4 marks Tangents, normals and gradients Normal or perpendicular line problems View
For the curve $y = x ^ { 3 } - a x + b$, the slope of the line perpendicular to the tangent line at the point $( 1,1 )$ is $- \frac { 1 } { 2 }$. For the two constants $a$ and $b$, find the value of $a + b$. [4 points]
Q27 4 marks Combinations & Selection Counting Integer Solutions to Equations View
Find the number of all ordered pairs $( a , b , c )$ of non-negative integers satisfying the following conditions. [4 points] (가) $a + b + c = 7$ (나) $2 ^ { a } \times 4 ^ { b }$ is a multiple of 8.
Q28 4 marks Sequences and series, recurrence and convergence Convergence proof and limit determination View
For a natural number $n$, let $\mathrm { P } _ { n }$ be the point where the line $x = 4 ^ { n }$ meets the curve $y = \sqrt { x }$. Let $L _ { n }$ be the length of the segment $\mathrm { P } _ { n } \mathrm { P } _ { n + 1 }$. Find the value of $\lim _ { n \rightarrow \infty } \left( \frac { L _ { n + 1 } } { L _ { n } } \right) ^ { 2 }$. [4 points]
Q29 4 marks Normal Distribution Finding Unknown Mean from a Given Probability Condition View
The random variable $X$ follows a normal distribution with mean $m$ and standard deviation 5, and the probability density function $f ( x )$ of the random variable $X$ satisfies the following conditions. (가) $f ( 10 ) > f ( 20 )$ (나) $f ( 4 ) < f ( 22 )$ When $m$ is a natural number, $\mathrm { P } ( 17 \leq X \leq 18 ) = a$. Find the value of $1000a$ using the standard normal distribution table below. [4 points]
$z$$\mathrm { P } ( 0 \leq Z \leq z )$
0.60.226
0.80.288
1.00.341
1.20.385
1.40.419
Q30 4 marks Composite & Inverse Functions Find or Apply an Inverse Function Formula View
For a real number $k$, let $g ( x )$ be the inverse function of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 6 x + k$. For the equation $4 f ^ { \prime } ( x ) + 12 x - 18 = \left( f ^ { \prime } \circ g \right) ( x )$ to have a real root in the closed interval $[ 0,1 ]$, let $m$ be the minimum value of $k$ and $M$ be the maximum value of $k$. Find the value of $m ^ { 2 } + M ^ { 2 }$. [4 points]