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- What is one-third of $9^{2024}$?
A. $3^{2024}$
B. $3^{2023}$
C. $3^{4047}$
D. $3^{4048}$
E. None of the above - Emily wants to construct a rectangular cuboid with dimensions of $192 \times 216 \times 240\text{ cm}$ using identical cubes. What is the least number of cubes she can use?
A. 360
B. 720
C. 810
D. 900
E. None of the above - The value of $\sqrt{125} + \sqrt{150}$ is between two consecutive positive integers. Which of the following are the values of these 2 integers?
A. 23 and 24
B. 22 and 23
C. 24 and 25
D. 26 and 27
E. None of the above - Solve the equation below and find the value of $x + y$. $$(2y^2 - 9y + 8x)^6 + \sqrt{x^3 + 343} = 0$$
A. 1
B. –7
C. 8
D. 15
E. None of the above - What is the remainder when $2024^{2024}$ is divided by 9?
A. 0
B. 1
C. 4
D. 7
E. None of the above - If points $A(-14, -4)$, $B(-8, 5)$, and $C(x, -7)$ form a right-angled triangle with $\angle ABC = 90^\circ$, find the value of $x$.
A. –10
B. 9
C. 10
D. 11
E. None of the above - What is the value of following? $$1^2 - 2^2 + 3^2 - 4^2 + \dots + 29^2 - 30^2 + 31^2$$
A. 465
B. 469
C. 496
D. 961
E. None of the above - Given that $8x^2 + 24xy + 18y^2 = 5000$ and $x + 2y = 31$, find the positive value of $x + y$.
A. 20
B. 19
C. 12
D. 7
E. None of the above - In right-angled triangle $ABC$, points $D$ and $E$ are the midpoints of sides $AB$ and $BC$, respectively. If the area of quadrilateral $BEFD$ is $36\text{ cm}^2$, find the area (in $\text{cm}^2$) of triangle $ABC$.
A. $72\text{ cm}^2$
B. $108\text{ cm}^2$
C. $216\text{ cm}^2$
D. $432\text{ cm}^2$
E. None of the above - Given that positive integers $a$ and $b$ satisfy the equation below, what is the smallest possible value of $a + b$?$$2024^2 + a^2 = 2023^2 + b^2$$
A. 70
B. 213
C. 1349
D. 4047
E. None of the above - Let $a$ be a positive integer such that the sequence below is an arithmetic progression. How many terms are there in the sequence?$$8, 17, 26, \dots , a + 9$$
A. $\frac{a + 9}{9}$
B. $\frac{a + 1}{9}$
C. $\frac{a + 9}{9}$
D. $\frac{a + 10}{9}$
E. None of the above - The standard 6-sided dice is arranged so that the numbers 1 through 6 on one side are paired with a number on the opposite side such that the sum of the numbers on opposite faces is always 7. If six standard dice are stacked on the floor as shown, what is the largest possible sum of numbers on the 21 visible faces?
A. 58
B. 68
C. 89
D. 126
E. None of the above - In right-angled triangle $ABC$ below, $AD$ is the height and $CE$ is the bisector of $\angle BCA$. Lines $AD$ and $CE$ intersect at point $F$. If $CF = FE$, what is the measurement (in degrees) of $\angle ABC$?
A. $15^\circ$
B. $30^\circ$
C. $45^\circ$
D. $60^\circ$
E. None of the above - Find the prime number $p$ such that $16p + 1$ is a perfect cube.
A. 281
B. 283
C. 293
D. 307
E. None of the above - Ella owns a collection of antique coins, each with a distinct weight. She decides to distribute her coins among her three friends. Ella gives the 33 lightest coins, which collectively weigh 53% of the total weight, to Liam. She then presents the 16 heaviest coins, which account for 28% of the total weight, to Mia. Finally, she allocates the remaining coins to Layla. How many coins did Layla receive?
A. 36
B. 32
C. 12
D. 11
E. None of the above - In the numerical representation of dates, January 23, 2024, is expressed as 20240123, and September 2, 2024, is denoted as 20240902. How many occurrences of the digit "2" exist in all 8-digit numbers reprensenting dates in the year 2024?
- How many positive factors of 180000 are not perfect squares?
- In Mathematics, it is given that $n!=n\times (n-1)\times \cdots \times 2\times 1$. For example, $5!=5\times 4\times 3\times 2\times 1=120$. How many consecutive zeros are there at the end $(2026!-2025!)$?
- In the list below, how many fractions are not in their simplest form? $$\frac{1}{2024}, \frac{2}{2024}, \frac{3}{2024}, \cdots \frac{2023}{2024},$$
- What is the remainder when $193^{123}$ is divided by 100?
- Emily's locker combination is a 4-digit number with the following properties:
-The number is greater than 3000.
-The hundreds digit is one less than the tens digit.
-The number is an even number that is divisible by 9.
How many unique locker combinations can Emily set for her locker? - Tom arranges integers from 1 to 16 within the circles illustrated below. He proceeds to write numbers on line segments, where each number represents the sum of the integers in two circles connected by a line segment. What is the greatest value of the smallest number on the line segments?
- In quadrilateral $ABCD$ below, $\angle BAD = 105^\circ$, $\angle ADC = 165^\circ$, $AD$ is parallel to $BC$, and points $E$ and $F$ are the midpoints of sides $AD$ and $BC$, respectively. If $AD = 56$ and $BC = 140$, what is the length of $EF$?
- On a mystical island, inhabitants are divided into two tribes: the Harmonious Tribe, whose members always speak the truth, and the Discordant Tribe, whose members always lie. A circular formation is deemed harmonious if each individual can say that one of their neighbours represents their own tribe. One day, a gathering of 2024 islanders successfully formed a harmonious circle. Subsequently, 2 members of the Discordant Tribe joined them and declared, "Now we can form a harmonious circle." How many members of the Harmonious Tribe were there in the original formation of 2024 people?
- Solve the equation below for $(x,y) \in \left(0, \frac{\pi}{2}\right)$ and find the value of $\frac{12(x+2y)}{\pi}$.$$\left\{ \begin{array}{cl}
\dfrac{\cos x}{\cos y} = 2 \cos^2 y \\
\dfrac{\sin x}{\sin y} = 2 \sin^2 y
\end{array} \right.$$
This topic was modified 7 hari ago 2 times by Admin dot
Posted : 20/05/2026 1:48 am
