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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
2011 ygs

19 maths questions

Q3 Indices and Surds Evaluating Expressions Using Index Laws View
$\frac { 4 ^ { \frac { 1 } { 2 } } + ( - 8 ) ^ { \frac { 1 } { 3 } } - 1 } { 2 ^ { - 1 } }$
What is the result of this operation?
A) 2 B) 6 C) $-1$ D) 0 E) $-2$
Q5 Laws of Logarithms Simplify or Evaluate a Logarithmic Expression View
$12^{a} = 2$
$$6^{b} = 3$$
Given that, what is the value of the expression $\mathbf{12}^{\boldsymbol{(}\mathbf{1} - \mathbf{a}\mathbf{)2b}}$?
A) 15 B) 16 C) 9 D) 8 E) 4
Q6 Indices and Surds Ordering and Comparing Surd or Numerical Values View
$x = \sqrt[3]{4}$
$$y = \sqrt[4]{8}$$ $$z = \sqrt[5]{16}$$
Given that, which of the following orderings is correct?
A) $x < y < z$ B) $x < z < y$ C) $y < x < z$ D) $z < x < y$ E) $z < y < x$
Q7 Number Theory Divisibility and Divisor Analysis View
If the product $\mathrm{x} \cdot (10!)$ is the square of a positive integer, what is the smallest value that x can take?
A) 21 B) 7 C) 5 D) 10 E) 14
Q8 Simultaneous equations View
$\frac{a - 1}{b} = \frac{c}{a}$
$$\frac{a}{c - 2} = \frac{b + 3}{a - 1}$$
Given that, what is the value of the expression $3c - 2b$?
A) 8 B) 9 C) 6 D) 3 E) 4
Q9 Laws of Logarithms Solve a Logarithmic Equation View
$$\frac{2^{x^{2} - y^{2}}}{4^{x^{2} + xy}} = \frac{1}{2}$$
Given that, what is the value of the expression $(x + y)^{2}$?
A) 2 B) 4 C) 1 D) $\frac{1}{2}$ E) $\frac{1}{4}$
Q10 Differential equations Qualitative Analysis of DE Solutions View
$\frac{1}{x + 1} + x - 1 = \frac{1}{x^{2}}$
Given that, which of the following is the expression $x^{3} - 1$ equal to?
A) $\frac{2}{x - 1}$ B) $\frac{1}{x}$ C) $\frac{x - 1}{x}$ D) $-x$ E) $\frac{1}{x + 1}$
Q11 Simultaneous equations View
For distinct numbers a and b
$$\frac{a^{2}}{b} - \frac{b^{2}}{a} = b - a$$
Given that, what is the value of the expression $\frac{a}{b} + \frac{b}{a}$?
A) $-2$ B) $-1$ C) 0 D) 1 E) 4
Q12 Inequalities Ordering and Sign Analysis from Inequality Constraints View
For integers x and y, $x + 2y = 11$. Given that,
I. x is an odd number. II. x is greater than y. III. Both x and y are positive.
Which of the following statements are always true?
A) Only I B) Only III C) I and II D) I and III E) II and III
Q15 Number Theory Prime Number Properties and Identification View
Let a be a positive integer and $p = a^{2} + 5$. If p is a prime number, which of the following statements are true?
I. a is an even number. II. The remainder when p is divided by 4 is 1. III. $\mathrm{p} - 6$ is prime.
A) I and III B) Only I C) I and II D) Only III E) I, II and III
Q16 Number Theory GCD, LCM, and Coprimality View
Let n be a positive integer, and let $S(n)$ denote the set of positive integers that divide n without remainder.
Accordingly, how many elements does the intersection set $S(60) \cap S(72)$ have?
A) 8 B) 9 C) 6 D) 5 E) 4
Q17 Number Theory Congruence Reasoning and Parity Arguments View
If a number of the form $7k + 4$ is divisible by 3 without remainder, how many positive integers k less than 21 are there?
A) 8 B) 9 C) 7 D) 6 E) 5
Q20 Composite & Inverse Functions Find or Apply an Inverse Function Formula View
The following functions are given:
$f(x) = 3x - 6$
$g(x) = (x - 2)^{2}$
Accordingly, $\left(g \circ f^{-1}\right)(x)$ is equal to which of the following?
A) $\frac{3x^{2}}{2} - 1$ B) $(3x + 4)^{2}$ C) $x^{2} - 4x + 2$ D) $\frac{x^{2}}{9}$ E) $(3x - 8)^{2}$
Q21 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification View
The following functions are defined on the set of real numbers:
I. $f(x) = 2x - 1$ II. $g(x) = x^{2} + 2$ III. $h(x) = x^{3}$
Which of these functions are one-to-one?
A) I and II B) Only I C) I, II and III D) I and III E) Only II
Q23 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
On day 1, Ismail puts one of each of the following coins into his piggy bank: 5 Kr, 10 Kr, 25 Kr, 50 Kr, and 1 TL. On day 2, he puts two of each, and continuing in this manner, on day n he puts n of each.
If Ismail has saved 104.5 TL in his piggy bank, what is n?
A) 10 B) 11 C) 12 D) 13 E) 14
Q37 Radians, Arc Length and Sector Area View
$$|\widehat{AD}| = a \text{ units}$$ $$|\widehat{BC}| = b \text{ units}$$ $$|DC| = c \text{ units}$$
The OAD and OBC circular sectors with center O are given above.
Accordingly, the area of the shaded region is equal to which of the following in terms of $a, b$ and $c$?
A) $\frac{(a + b) \cdot c}{2}$ B) $\frac{(b - a) \cdot c}{2}$ C) $\frac{2(a + b)}{c}$ D) $\frac{2(b - a)}{c}$ E) $\frac{a \cdot b \cdot c}{2}$
Q38 Circles Intersection of Circles or Circle with Conic View
$$|\mathrm{OM}| = 2 \text{ units}$$
In the rectangular coordinate plane, a semicircle with center at point M and a quarter circle with center at the origin intersect at point A as shown in the figure.
Accordingly, what is the x-coordinate of point A?
A) $\frac{5}{3}$ B) $\sqrt{2}$ C) $\frac{\sqrt{3}}{2}$ D) $\frac{3}{2}$ E) $\sqrt{3}$
Q39 Linear transformations View
The reflection of the right triangle ABC given in the rectangular coordinate plane with respect to the y-axis is taken, and the triangle $A'B'C'$ is obtained such that A is paired with $A'$, B with $B'$, and C with $C'$ as symmetric point pairs. This obtained triangle is then rotated $90^{\circ}$ clockwise around point $A'$.
As a result of this rotation, what are the coordinates of the B'' point corresponding to $\mathrm{B}'$?
A) $(0, 3)$ B) $(2, 4)$ C) $(3, 5)$ D) $(4, 6)$ E) $(5, 4)$
Q40 Proof Computation of a Limit, Value, or Explicit Formula View
A rectangular piece of paper ABCD shown below is folded so that vertices B and D coincide. Let E be the folding point on side [AB] such that $|AE| = 1$ unit.
As a result of the folding, the overlapping parts of the paper form a dark-colored equilateral triangular region DEF.
Accordingly, what is the area of the paper in square units?
A) $6\sqrt{2}$ B) $2\sqrt{2}$ C) $4\sqrt{3}$ D) $3\sqrt{3}$ E) $4\sqrt{2}$