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Papers (30)
2025
yks-ayt 36 yks-tyt 7
2024
yks-ayt 34 yks-tyt 7
2023
yks-ayt 24 yks-tyt 38
2021
yks-ayt 36 yks-tyt 13
2020
yks-ayt 35 yks-tyt 36
2019
yks-ayt 39 yks-tyt 9
2018
yks-ayt 39 yks-tyt 8
2017
lys1-math 56 ygs 18
2016
lys1-math 49 ygs 13
2015
lys1-math 50 ygs 13
2014
lys1-math 50 ygs 17
2013
lys1-math 50 ygs 25
2012
lys1-math 46 ygs 17
2011
lys1-math 49 ygs 19
2010
lys1-math 50 ygs 28
2015 ygs

13 maths questions

Q3 Indices and Surds Simplifying Surd Expressions View
$$\frac { \sqrt [ 3 ] { 2 \cdot \sqrt { 54 } } } { \sqrt { 2 } }$$
What is the result of this operation?
A) $\sqrt { 2 }$ B) $\sqrt { 3 }$ C) $\sqrt { 6 }$ D) $\sqrt [ 3 ] { 4 }$ E) $\sqrt [ 3 ] { 9 }$
Q9 Inequalities Ordering and Sign Analysis from Inequality Constraints View
For real numbers $\mathbf { a }$ and $\mathbf { b }$
$$b ^ { 2 } < a \cdot b < b - a$$
Given that, which of the following orderings is correct?
A) $a < 0 < b$ B) $b < 0 < a$ C) $0 < a < b$ D) $\mathrm { b } < \mathrm { a } < 0$ E) $a < b < 0$
Q12 Modulus function Solving equations involving modulus View
For real numbers x and y
$$\begin{aligned} & 2 x = 7 - | y | \\ & y = \frac { | x | } { 3 } \end{aligned}$$
Given that, what is the sum $\mathbf { x } + \mathbf { y }$?
A) 12 B) 10 C) 8 D) 6 E) 4
Q13 Exponential Functions Exponential Equation Solving View
For integers a and b
$$\frac { 6 ^ { a ^ { 2 } + b ^ { 2 } } } { 9 ^ { a b } } = 96$$
Given that, what is the product $\mathbf { a } \cdot \mathbf { b }$?
A) 1 B) 2 C) 3 D) 4 E) 6
Q14 Composite & Inverse Functions Recover a Function from a Composition or Functional Equation View
For functions $f$ and $g$ defined on the set of positive real numbers
$$\begin{aligned} & ( f \circ g ) ( x ) = f ( x ) \cdot g ( x ) \\ & f ( x ) = 2 x + 3 \end{aligned}$$
Given that, what is the value of $\mathbf { g } ( \mathbf { 1 } )$?
A) 1 B) 2 C) 3 D) 4 E) 5
Q15 Differential equations Qualitative Analysis of DE Solutions View
A function f defined on the set of natural numbers is defined for every n as
$$f ( n ) = \begin{cases} 5 n + 40 , & 0 \leq n < 10 \\ f ( n - 10 ) , & n \geq 10 \end{cases}$$
Example: $f ( 23 ) = f ( 13 ) = f ( 3 ) = 5 \cdot 3 + 40 = 55$
Accordingly, what is the sum of the two-digit numbers AB that satisfy the equation $f ( A B ) = A B$?
A) 75 B) 80 C) 90 D) 100 E) 105
Q18 Combinations & Selection Subset Counting with Set-Theoretic Conditions View
$$\mathrm { X } \subseteq \{ \mathrm { a } , \mathrm {~b} , \mathrm { c } , \mathrm {~d} , \mathrm { e } \}$$
Given that, how many different subsets $X$ are there such that the number of elements in $\mathbf { X } \cap \{ \mathbf { a } , \mathbf { b } \}$ is 1?
A) 10 B) 12 C) 14 D) 16 E) 18
Q19 Proof True/False Justification View
Ali; starting with the equality $x = y$ for non-zero, equal real numbers x and y, follows the following steps in order.
I. Let us multiply both sides of the equality by x: $$x ^ { 2 } = x \cdot y$$
II. Let us subtract $\mathrm { y } ^ { 2 }$ from both sides: $$x ^ { 2 } - y ^ { 2 } = x \cdot y - y ^ { 2 }$$
III. Let us factor both sides: $$( x + y ) ( x - y ) = y ( x - y )$$
IV. Let us divide both sides by $\mathrm { x } - \mathrm { y }$: $$x + y = y$$
V. Let us substitute y for x: $$2 y = y$$
As a result of these steps, Ali arrives at the conclusion "Every number equals twice itself."
Accordingly, in which of the numbered steps did Ali make an error?
A) I B) II C) III D) IV E) V
Q30 Combinations & Selection Selection with Group/Category Constraints View
A school's basketball team has a total of 8 players, two of whom are brothers. 5 of these players will be selected to be in the starting lineup.
In how many different ways can a selection be made such that both brothers are in this lineup?
A) 20 B) 24 C) 30 D) 36 E) 40
Q32 Probability Definitions Finite Equally-Likely Probability Computation View
Deniz randomly colored two of the following four points that are the vertices of a square red and the other two blue, and drew line segments connecting the points she colored the same color.
What is the probability that these line segments intersect?
A) $\frac { 1 } { 6 }$ B) $\frac { 1 } { 4 }$ C) $\frac { 1 } { 3 }$ D) $\frac { 2 } { 3 }$ E) $\frac { 3 } { 4 }$
Q35 Circles Circles Tangent to Each Other or to Axes View
Below, two concentric circles with center $O$ and a circle with center $M$ tangent to both circles are given.
The radius of the small circle with center $O$ is 4 units less than the radius of the large circle with center $O$, and 1 unit more than the radius of the circle with center $M$.
Accordingly, what is the area of the shaded region in square units?
A) $28 \pi$ B) $32 \pi$ C) $36 \pi$ D) $39 \pi$ E) $45 \pi$
Q39 Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane View
In the rectangular coordinate plane, the sides of rectangle $A B C D$ are parallel to the axes.
If the coordinates of vertices A and $C$ are $(1, -1)$ and $(3, 5)$ respectively, what is the area of rectangle ABCD in square units?
A) 8 B) 10 C) 12 D) 15 E) 16
Q40 Straight Lines & Coordinate Geometry Section Ratio and Division of Segments View
According to the given information above, what is the sum of the coordinates of point C?
A) 3 B) 4 C) 5 D) 6 E) 7