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
2007 csat__math-science

17 maths questions

Q1 2 marks Laws of Logarithms Simplify or Evaluate a Logarithmic Expression View
The value of $\left( \log _ { 3 } 27 \right) \times 8 ^ { \frac { 1 } { 3 } }$ is? [2 points]
(1) 12
(2) 10
(3) 8
(4) 6
(5) 4
Q2 2 marks Matrices Linear System and Inverse Existence View
For two matrices $A = \left( \begin{array} { r r } - 1 & 0 \\ 0 & 1 \end{array} \right) , B = \left( \begin{array} { l l } 2 & 1 \\ 3 & 3 \end{array} \right)$, what is the sum of all components of the matrix $( A + B ) ^ { - 1 }$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Q3 2 marks Differentiation from First Principles View
The value of $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } - 1 } { \sqrt { x + 3 } - 2 }$ is? [2 points]
(1) 7
(2) 8
(3) 9
(4) 10
(5) 11
Q4 3 marks Inequalities Integer Solutions of an Inequality View
System of inequalities $$\left\{ \begin{array} { l } x ( x - 4 ) ( x - 5 ) \geqq 0 \\ \frac { x - 3 } { x ^ { 2 } - 3 x + 2 } \leqq 0 \end{array} \right.$$ What is the number of integers $x$ that satisfy the system? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Q5 3 marks Conic sections Focal Distance and Point-on-Conic Metric Computation View
On a parabola $y ^ { 2 } = x$ with focus F, there is a point P such that $\overline { \mathrm { FP } } = 4$. As shown in the figure, point Q is taken on the extension of segment FP such that $\overline { \mathrm { FP } } = \overline { \mathrm { PQ } }$. What is the $x$-coordinate of point Q? [3 points]
(1) $\frac { 29 } { 4 }$
(2) 7
(3) $\frac { 27 } { 4 }$
(4) $\frac { 13 } { 2 }$
(5) $\frac { 25 } { 4 }$
Q6 3 marks Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines View
For a regular hexahedron (cube) $\mathrm { ABCD } - \mathrm { EFGH }$, let $\theta$ be the angle between plane AFG and plane AGH. What is the value of $\cos ^ { 2 } \theta$? [3 points]
(1) $\frac { 1 } { 6 }$
(2) $\frac { 1 } { 5 }$
(3) $\frac { 1 } { 4 }$
(4) $\frac { 1 } { 3 }$
(5) $\frac { 1 } { 2 }$
Q7 3 marks Differentiation from First Principles View
When the function $f ( x )$ is $$f ( x ) = \begin{cases} 1 - x & ( x < 0 ) \\ x ^ { 2 } - 1 & ( 0 \leqq x < 1 ) \\ \frac { 2 } { 3 } \left( x ^ { 3 } - 1 \right) & ( x \geqq 1 ) \end{cases}$$ which of the following statements in are correct? [3 points]
Remarks ㄱ. $f ( x )$ is differentiable at $x = 1$. ㄴ. $| f ( x ) |$ is differentiable at $x = 0$. ㄷ. The minimum natural number $k$ such that $x ^ { k } f ( x )$ is differentiable at $x = 0$ is 2.
(1) ㄱ
(2) ㄴ
(3) ㄱ, ㄷ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ
Q8 3 marks Indefinite & Definite Integrals Net Change from Rate Functions (Applied Context) View
The following is a graph showing the velocity $v ( t )$ at time $t$ ( $0 \leqq t \leqq d$ ) of a point P moving on a number line starting from the origin.
When $\int _ { 0 } ^ { a } | v ( t ) | d t = \int _ { a } ^ { d } | v ( t ) | d t$, which of the following statements in are correct? (Here, $0 < a < b < c < d$.) [3 points]
Remarks ㄱ. Point P passes through the origin again after starting. ㄴ. $\int _ { 0 } ^ { c } v ( t ) d t = \int _ { c } ^ { d } v ( t ) d t$ ㄷ. $\int _ { 0 } ^ { b } v ( t ) d t = \int _ { b } ^ { d } | v ( t ) | d t$
(1) ㄴ
(2) ㄷ
(3) ㄱ, ㄴ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ
Q24 4 marks Vectors Introduction & 2D Magnitude of Vector Expression View
As shown in the figure, on a plane $\alpha$ there is an equilateral triangle ABC with side length 3, and a sphere $S$ with radius 2 is tangent to the plane $\alpha$ at point A. For a point D on the sphere $S$ such that the segment AD passes through the center O of the sphere $S$, find the value of $| \overrightarrow { \mathrm { AB } } + \overrightarrow { \mathrm { DC } } | ^ { 2 }$. [4 points]
Q25 4 marks Exponential Equations & Modelling Geometric Properties of Exponential/Logarithmic Curves View
The graph of the function $y = k \cdot 3 ^ { x }$ ($0 < k < 1$) meets the graphs of the two functions $y = 3 ^ { - x }$ and $y = - 4 \cdot 3 ^ { x } + 8$ at points P and Q, respectively. When the ratio of the $x$-coordinates of points P and Q is $1 : 2$, find the value of $35k$. [4 points]
Q26 (Calculus) 3 marks Small angle approximation View
$\lim _ { x \rightarrow a } \frac { 2 ^ { x } - 1 } { 3 \sin ( x - a ) } = b \ln 2$ is satisfied by two constants $a , b$. What is the value of $a + b$? [3 points]
(1) $\frac { 1 } { 6 }$
(2) $\frac { 1 } { 5 }$
(3) $\frac { 1 } { 4 }$
(4) $\frac { 1 } { 3 }$
(5) $\frac { 1 } { 2 }$
Q26 (Probability and Statistics) 3 marks Independent Events View
For two independent events $A$ and $B$, $$\mathrm { P } ( A \cap B ) = 2 \mathrm { P } \left( A \cap B ^ { c } \right) , \quad \mathrm { P } \left( A ^ { c } \cap B \right) = \frac { 1 } { 12 }$$ find the value of $\mathrm { P } ( A )$. (Given that $\mathrm { P } ( A ) \neq 0$.) [3 points]
(1) $\frac { 1 } { 2 }$
(2) $\frac { 5 } { 8 }$
(3) $\frac { 3 } { 4 }$
(4) $\frac { 7 } { 8 }$
(5) $\frac { 15 } { 16 }$
Q26 (Discrete Mathematics) 3 marks Permutations & Arrangements Distribution of Objects into Bins/Groups View
In how many ways can 9 identical candies be distributed into 5 identical bags such that no bag is empty? [3 points]
(1) 8
(2) 7
(3) 6
(4) 5
(5) 4
Q27 (Calculus) 3 marks Radians, Arc Length and Sector Area View
As shown in the figure, let $\mathrm { Q } _ { 1 }$ be the point where the tangent line to the circle $x ^ { 2 } + y ^ { 2 } = 1$ at point $\mathrm { P } _ { 1 }$ meets the $x$-axis. The area of triangle $\mathrm { P } _ { 1 } \mathrm { OQ } _ { 1 }$ is $\frac { 1 } { 4 }$. Let $\mathrm { P } _ { 2 }$ be the point obtained by rotating $\mathrm { P } _ { 1 }$ about the origin O by $\frac { \pi } { 4 }$, and let $\mathrm { Q } _ { 2 }$ be the point where the tangent line at $\mathrm { P } _ { 2 }$ meets the $x$-axis. What is the area of triangle $\mathrm { P } _ { 2 } \mathrm { OQ } _ { 2 }$? (Here, point $\mathrm { P } _ { 1 }$ is in the first quadrant.) [3 points]
(1) 1
(2) $\frac { 5 } { 4 }$
(3) $\frac { 3 } { 2 }$
(4) $\frac { 7 } { 4 }$
(5) 2
Q28 (Probability and Statistics) 3 marks Approximating Binomial to Normal Distribution View
It is known that $10\%$ of the notebooks displayed in a certain stationery store are products from Company A. When a customer randomly purchases 100 notebooks from this store, find the probability that at least 13 notebooks from Company A are included using the standard normal distribution table below. [3 points]
$z$$\mathrm { P } ( 0 \leqq Z \leqq z )$
0.750.2734
1.000.3413
1.250.3944
1.500.4332

(1) 0.0668
(2) 0.1056
(3) 0.1587
(4) 0.2266
(5) 0.2734
Q29 (Probability and Statistics) 4 marks Confidence intervals Conceptual reasoning about confidence level and sample size effects View
A population follows a normal distribution $\mathrm { N } \left( m , 2 ^ { 2 } \right)$. Let $\overline { X _ { A } }$ and $\overline { X _ { B } }$ be the sample means of samples of size 7 and size 10, respectively, drawn from this population. Using the distributions of $\overline { X _ { A } }$ and $\overline { X _ { B } }$, the 95\% confidence intervals for the population mean $m$ are $[a, b]$ and $[c, d]$, respectively. Choose all correct statements from the given options. [4 points]
Options ㄱ. The variance of $\overline { X _ { A } }$ is greater than the variance of $\overline { X _ { B } }$. ㄴ. $\mathrm { P } \left( \overline { X _ { A } } \leqq m + 2 \right) < \mathrm { P } \left( \overline { X _ { B } } \leqq m + 2 \right)$ ㄷ. $d - c < b - a$
(1) ㄱ
(2) ㄷ
(3) ㄱ, ㄴ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ
Q30 (Probability and Statistics) 4 marks Discrete Probability Distributions Binomial Distribution Identification and Application View
A factory produces products that are sold with 50 items per box. The number of defective items in a box follows a binomial distribution with mean $m$ and variance $\frac { 48 } { 25 }$. Before selling a box, all 50 products are inspected to find defective items, which costs a total of 60,000 won. If a box is sold without inspection, an after-sales service cost of $a$ won is required for each defective item.
When the expected value of the cost of inspecting all products in a box equals the expected cost of after-sales service, find the value of $\frac { a } { 1000 }$. (Given that $a$ is a constant and $m$ is a natural number not exceeding 5.) [4 points]