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Papers (30)
2025
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2024
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2023
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2021
yks-ayt 31 yks-tyt 9
2020
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2019
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2018
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2017
lys1-math 44 ygs 10
2016
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2015
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2014
lys1-math 48 ygs 17
2013
lys1-math 45 ygs 21
2012
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2011
lys1-math 47 ygs 17
2010
lys1-math 50 ygs 18
2017 ygs

10 maths questions

Q3 Indices and Surds Simplifying Surd Expressions View
$$\sqrt [ 3 ] { \frac { 32 } { \sqrt { 8 } - \sqrt { 2 } } }$$
What is the result of this operation?
A) $\sqrt { 2 }$ B) $2 \sqrt { 2 }$ C) $\sqrt [ 3 ] { 2 }$ D) 2 E) 4
Q6 Modulus function Solving equations involving modulus View
For non-zero real numbers $x$ and $y$
$$\begin{aligned} & | x \cdot y | = - 2 x \\ & \left| \frac { y } { x } \right| = 3 y \end{aligned}$$
the following equalities are given.
Accordingly, what is the sum $x + y$?
A) $\frac { 3 } { 2 }$ B) $\frac { 5 } { 2 }$ C) $\frac { 5 } { 3 }$ D) $\frac { 7 } { 3 }$ E) $\frac { 5 } { 6 }$
Q8 Exponential Functions Exponential Equation Solving View
$$\begin{aligned} & 4 ^ { x } + 4 ^ { y } = 10 \\ & 4 ^ { x } - 4 ^ { y } = 8 \end{aligned}$$
Accordingly, what is the value of the expression $\mathbf { 2 } ^ { \mathbf { x } + \mathbf { y } }$?
A) 2 B) 3 C) 4 D) 5 E) 6
Q11 Inequalities Integer Solutions of an Inequality View
For real number $x$
$$- 3 < 2 x < 7$$
Accordingly, what is the sum of the integer values that the expression $5 - x$ can take?
A) 5 B) 10 C) 15 D) 20 E) 25
Q13 Composite & Inverse Functions Evaluate Composition from Algebraic Definitions View
Let k be a real number. The functions f and g defined on the set of positive real numbers are
$$\begin{aligned} & f ( x ) = k x ^ { 2 } + 1 \\ & g ( x ) = \sqrt { x } + 2 \end{aligned}$$
defined in the form.
$$( f \circ g ) ( 9 ) = 6$$
Given that, what is the value of f(2)?
A) $\frac { 7 } { 5 }$ B) $\frac { 8 } { 5 }$ C) $\frac { 9 } { 5 }$ D) 2 E) 3
Q14 Factor & Remainder Theorem Remainder by Linear Divisor View
The polynomial $P ( x ) = ( x + 1 ) + ( x + 2 ) + \ldots + ( x + 9 )$
$$Q ( x ) = ( x + 1 ) + ( x + 2 ) + \ldots + ( x + 5 )$$
is divided by the polynomial.
What is the remainder obtained from this division?
A) 10 B) 12 C) 14 D) 16 E) 18
Q19 Combinations & Selection Handshake / Product Counting View
In a tournament with 8 teams, each team played against the other teams once. In the tournament, 3 referees were assigned from 4 available referees for each match, and all referees worked an equal number of matches.
Accordingly, how many matches did each referee work?
A) 14 B) 15 C) 18 D) 20 E) 21
Q38 Volumes of Revolution Volume by Displacement or Composite Solid View
A right circular cone with height 10 units is placed inside a hollow right circular cylinder with height 10 units as shown in Figure 1. Water with volume $\mathrm { V } _ { 1 }$ cubic units is poured between this cylinder and cone, and the water height becomes 5 units. Then this object is inverted as shown in Figure 2, and after adding more water, the water volume becomes $\mathrm { V } _ { 2 }$ cubic units and the height becomes 5 units.
Accordingly, what is the ratio $\frac { \mathrm { V } _ { 1 } } { \mathrm {~V} _ { 2 } }$?
(During this process, water does not enter the cone.)
A) $\frac { 3 } { 7 }$ B) $\frac { 5 } { 11 }$ C) $\frac { 8 } { 15 }$ D) $\frac { 10 } { 21 }$ E) $\frac { 15 } { 31 }$
Q39 Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane View
In the rectangular coordinate plane, a parallelogram whose vertices are the intersection points of the lines $y = 2$ and $y = 6$ with the line $y = 2x$ has diagonals intersecting at the point $(0,4)$.
What is the area of this parallelogram in square units?
A) 16 B) 18 C) 20 D) 22 E) 24
Q40 Vectors Introduction & 2D Magnitude of Vector Expression View
In the figure, squares OABC and ADEF are shown in the rectangular coordinate plane, each with one side on the x-axis. The vertex F is the midpoint of the side on which it lies in square OABC, which has a side length of 4 units.
Accordingly, which of the following is the vector $\overrightarrow { O B } + \overrightarrow { O E }$?
A) $( 4,6 )$ B) $( 8,6 )$ C) $( 10,4 )$ D) $( 10,6 )$ E) $( 10,8 )$