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
2021 csat__math-humanities

30 maths questions

Q1 2 marks Indices and Surds Evaluating Expressions Using Index Laws View
What is the value of $3 ^ { 0 } \times 8 ^ { \frac { 2 } { 3 } }$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Q2 2 marks Curve Sketching Limit Computation from Algebraic Expressions View
What is the value of $\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + 2 x - 8 } { x - 2 }$? [2 points]
(1) 2
(2) 4
(3) 6
(4) 8
(5) 10
Q3 2 marks Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
For a geometric sequence $\left\{ a _ { n } \right\}$ with first term $\frac { 1 } { 8 }$, if $\frac { a _ { 3 } } { a _ { 2 } } = 2$, what is the value of $a _ { 5 }$? [2 points]
(1) $\frac { 1 } { 4 }$
(2) $\frac { 1 } { 2 }$
(3) 1
(4) 2
(5) 4
Q4 3 marks Trig Graphs & Exact Values View
What is the maximum value of the function $f ( x ) = 4 \cos x + 3$? [3 points]
(1) 6
(2) 7
(3) 8
(4) 9
(5) 10
Q5 3 marks Independent Events View
Two events $A$ and $B$ are independent and $$\mathrm { P } ( A \mid B ) = \mathrm { P } ( B ) , \quad \mathrm { P } ( A \cap B ) = \frac { 1 } { 9 }$$ What is the value of $\mathrm { P } ( A )$? [3 points]
(1) $\frac { 7 } { 18 }$
(2) $\frac { 1 } { 3 }$
(3) $\frac { 5 } { 18 }$
(4) $\frac { 2 } { 9 }$
(5) $\frac { 1 } { 6 }$
Q6 3 marks Applied differentiation MCQ on derivative and graph interpretation View
For the function $f ( x ) = x ^ { 4 } + 3 x - 2$, what is the value of $f ^ { \prime } ( 2 )$? [3 points]
(1) 35
(2) 37
(3) 39
(4) 41
(5) 43
Q7 3 marks Exponential Functions Exponential Equation Solving View
How many natural numbers $x$ satisfy the inequality $\left( \frac { 1 } { 9 } \right) ^ { x } < 3 ^ { 21 - 4 x }$? [3 points]
(1) 6
(2) 7
(3) 8
(4) 9
(5) 10
Q8 3 marks Probability Definitions Finite Equally-Likely Probability Computation View
A die is rolled three times, and the results are $a$, $b$, and $c$ in order. What is the probability that $a \times b \times c = 4$? [3 points]
(1) $\frac { 1 } { 54 }$
(2) $\frac { 1 } { 36 }$
(3) $\frac { 1 } { 27 }$
(4) $\frac { 5 } { 108 }$
(5) $\frac { 1 } { 18 }$
Q9 3 marks Tangents, normals and gradients Normal or perpendicular line problems View
The tangent line to the curve $y = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 2$ at point $\mathrm { A } ( 0,2 )$ is perpendicular to a line passing through point A. What is the $x$-intercept of this line? [3 points]
(1) 4
(2) 6
(3) 8
(4) 10
(5) 12
Q10 3 marks Sequences and Series Evaluation of a Finite or Infinite Sum View
For two sequences $\left\{ a _ { n } \right\}$ and $\left\{ b _ { n } \right\}$, $$\sum _ { k = 1 } ^ { 5 } a _ { k } = 8 , \quad \sum _ { k = 1 } ^ { 5 } b _ { k } = 9$$ What is the value of $\sum _ { k = 1 } ^ { 5 } \left( 2 a _ { k } - b _ { k } + 4 \right)$? [3 points]
(1) 19
(2) 21
(3) 23
(4) 25
(5) 27
Q11 3 marks Linear combinations of normal random variables View
A sample of size 16 is randomly extracted from a population following a normal distribution $\mathrm { N } \left( 20,5 ^ { 2 } \right)$, and the sample mean is $\bar { X }$. What is the value of $\mathrm { E} ( \bar { X } ) + \sigma ( \bar { X } )$? [3 points]
(1) $\frac { 91 } { 4 }$
(2) $\frac { 89 } { 4 }$
(3) $\frac { 87 } { 4 }$
(4) $\frac { 85 } { 4 }$
(5) $\frac { 83 } { 4 }$
Q12 3 marks Sequences and Series Evaluation of a Finite or Infinite Sum View
A sequence $\left\{ a _ { n } \right\}$ satisfies $a _ { 1 } = 1$ and for all natural numbers $n$, $$\sum _ { k = 1 } ^ { n } \left( a _ { k } - a _ { k + 1 } \right) = - n ^ { 2 } + n$$ What is the value of $a _ { 11 }$? [3 points]
(1) 88
(2) 91
(3) 94
(4) 97
(5) 100
Q13 3 marks Composite & Inverse Functions Counting Functions with Composition or Mapping Constraints View
For the set $X = \{ 1,2,3,4 \}$, how many functions $f : X \rightarrow X$ satisfy the following condition? [3 points] $\square$
(1) 64
(2) 68
(3) 72
(4) 76
(5) 80
Q14 4 marks Variable acceleration (1D) Compute total distance traveled over an interval View
The velocity $v ( t )$ of a point P moving on a number line at time $t ( t \geq 0 )$ is $$v ( t ) = 2 t - 6$$ If the distance traveled by point P from time $t = 3$ to time $t = k$ ($k > 3$) is 25, what is the value of the constant $k$? [4 points]
(1) 6
(2) 7
(3) 8
(4) 9
(5) 10
Q15 4 marks Permutations & Arrangements Circular Arrangement View
There are 6 students including students $\mathrm { A }$, $\mathrm { B }$, and $\mathrm { C }$. These 6 students sit around a circular table at equal intervals satisfying the following conditions. How many ways are there to seat them? (Note: arrangements that coincide by rotation are considered the same.) [4 points] (가) A and B are adjacent. (나) B and C are not adjacent.
(1) 32
(2) 34
(3) 36
(4) 38
(5) 40
Q16 4 marks Quadratic trigonometric equations View
For $0 \leq x < 4 \pi$, what is the sum of all solutions to the equation $$4 \sin ^ { 2 } x - 4 \cos \left( \frac { \pi } { 2 } + x \right) - 3 = 0$$ ? [4 points]
(1) $5 \pi$
(2) $6 \pi$
(3) $7 \pi$
(4) $8 \pi$
(5) $9 \pi$
Q17 4 marks Applied differentiation Finding parameter values from differentiability or equation constraints View
Two polynomial functions $f ( x )$ and $g ( x )$ satisfy $$\lim _ { x \rightarrow 0 } \frac { f ( x ) + g ( x ) } { x } = 3 , \quad \lim _ { x \rightarrow 0 } \frac { f ( x ) + 3 } { x g ( x ) } = 2$$ For the function $h ( x ) = f ( x ) g ( x )$, what is the value of $h ^ { \prime } ( 0 )$? [4 points]
(1) 27
(2) 30
(3) 33
(4) 36
(5) 39
Q18 4 marks Laws of Logarithms Logarithmic Function Graph Intersection or Geometric Analysis View
For a real number $a$ with $\frac { 1 } { 4 } < a < 1$, let A and B be the points where the line $y = 1$ meets the curves $y = \log _ { a } x$ and $y = \log _ { 4 a } x$ respectively, and let C and D be the points where the line $y = - 1$ meets the curves $y = \log _ { a } x$ and $y = \log _ { 4 a } x$ respectively. Which of the following statements in the given options are correct? [4 points]
$\langle$Given Options$\rangle$ ㄱ. The coordinates of the point that divides segment AB externally in the ratio $1 : 4$ are $( 0,1 )$. ㄴ. If quadrilateral ABCD is a rectangle, then $a = \frac { 1 } { 2 }$. ㄷ. If $\overline { \mathrm { AB } } < \overline { \mathrm { CD } }$, then $\frac { 1 } { 2 } < a < 1$.
(1) ㄱ
(2) ㄷ
(3) ㄱ, ㄴ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ
Q19 4 marks Normal Distribution Algebraic Relationship Between Normal Parameters and Probability View
A random variable $X$ follows a normal distribution with mean 8 and standard deviation 3, and a random variable $Y$ follows a normal distribution with mean $m$ and standard deviation $\sigma$. If the two random variables $X$ and $Y$ satisfy $$\mathrm { P } ( 4 \leq X \leq 8 ) + \mathrm { P } ( Y \geq 8 ) = \frac { 1 } { 2 }$$ find the value of $\mathrm { P } \left( Y \leq 8 + \frac { 2 \sigma } { 3 } \right)$ using the standard normal distribution table below.
$z$$\mathrm { P } ( 0 \leq Z \leq z )$
1.00.3413
1.50.4332
2.00.4772
2.50.4938

[4 points]
(1) 0.8351
(2) 0.8413
(3) 0.9332
(4) 0.9772
(5) 0.9938
Q20 4 marks Stationary points and optimisation Find critical points and classify extrema of a given function View
For a real number $a$ ($a > 1$), define the function $f ( x )$ as $$f ( x ) = ( x + 1 ) ( x - 1 ) ( x - a)$$ Define the function $$g ( x ) = x ^ { 2 } \int _ { 0 } ^ { x } f ( t ) d t - \int _ { 0 } ^ { x } t ^ { 2 } f ( t ) d t$$ such that $g ( x )$ has exactly one extremum. What is the maximum value of $a$? [4 points]
(1) $\frac { 9 \sqrt { 2 } } { 8 }$
(2) $\frac { 3 \sqrt { 6 } } { 4 }$
(3) $\frac { 3 \sqrt { 2 } } { 2 }$
(4) $\sqrt { 6 }$
(5) $2 \sqrt { 2 }$
Q21 4 marks Sequences and series, recurrence and convergence Direct term computation from recurrence View
A sequence $\left\{ a _ { n } \right\}$ satisfies $0 < a _ { 1 } < 1$ and the following conditions for all natural numbers $n$: (가) $a _ { 2 n } = a _ { 2 } \times a _ { n } + 1$ (나) $a _ { 2 n + 1 } = a _ { 2 } \times a _ { n } - 2$ If $a _ { 7 } = 2$, what is the value of $a _ { 25 }$? [4 points]
(1) 78
(2) 80
(3) 82
(4) 84
(5) 86
Q22 3 marks Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
Find the coefficient of $x$ in the expansion of $( 3 x + 1 ) ^ { 8 }$. [3 points]
Q23 3 marks Indefinite & Definite Integrals Recovering Function Values from Derivative Information View
For a function $f ( x )$, if $f ^ { \prime } ( x ) = 3 x ^ { 2 } + 4 x + 5$ and $f ( 0 ) = 4$, find the value of $f ( 1 )$. [3 points]
Q24 3 marks Laws of Logarithms Simplify or Evaluate a Logarithmic Expression View
Find the value of $\log _ { 3 } 72 - \log _ { 3 } 8$. [3 points]
Q25 3 marks Stationary points and optimisation Count or characterize roots using extremum values View
Find the positive value of $k$ such that the curve $y = 4 x ^ { 3 } - 12 x + 7$ and the line $y = k$ intersect at exactly 2 points. [3 points]
Q26 4 marks Composite & Inverse Functions Recover a Function from a Composition or Functional Equation View
Consider the function $$f ( x ) = \begin{cases} - 3 x + a & ( x \leq 1 ) \\ \frac { x + b } { \sqrt { x + 3 } - 2 } & ( x > 1 ) \end{cases}$$ If $f ( x )$ is continuous on the entire set of real numbers, find the value of $a + b$. (Here, $a$ and $b$ are constants.) [4 points]
Q27 4 marks Areas Between Curves Compute Area Directly (Numerical Answer) View
Find the area enclosed by the curve $y = x ^ { 2 } - 7 x + 10$ and the line $y = - x + 10$. [4 points]
Q28 4 marks Sine and Cosine Rules Circumradius or incircle radius computation View
In triangle ABC, $\angle \mathrm { A } = \frac { \pi } { 3 }$ and $\overline { \mathrm { AB } } : \overline { \mathrm { AC } } = 3 : 1$. If the circumradius of triangle ABC is 7, let $k$ be the length of segment AC. Find the value of $k ^ { 2 }$. [4 points]
Q29 1 marks Discrete Probability Distributions Probability Computation for Compound or Multi-Stage Random Experiments View
A bag contains 5 balls labeled with the numbers $3, 3, 4, 4, 4$, one each. Using this bag and one die, a trial is performed to obtain a score according to the following rule:
If the ball drawn from the bag is labeled 3, roll the die 3 times and the sum of the three results is the score. If the ball drawn from the bag is labeled 4, roll the die 4 times and the sum of the four results is the score.
What is the probability that the score obtained from one trial is 10 points? Express this as $\frac { q } { p }$. Find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [1 point]
Q30 4 marks Stationary points and optimisation Composite or piecewise function extremum analysis View
The function $f ( x )$ is a cubic function with leading coefficient 1, and the function $g ( x )$ is a linear function. Define the function $h ( x )$ as $$h ( x ) = \begin{cases} | f ( x ) - g ( x ) | & ( x < 1 ) \\ f ( x ) + g ( x ) & ( x \geq 1 ) \end{cases}$$ If $h ( x )$ is differentiable on the entire set of real numbers, and $h ( 0 ) = 0$, $h ( 2 ) = 5$, find the value of $h ( 4 )$. [4 points]