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- For any real number $x$, $[x]$ is the greatest integer not exceeding $x$. For example, $[5.78] = 5$ and $[13.1] = 13$. Solve the equation below and find the value of $m$.$$[m] \times m = 70$$
A. 8.25
B. 8.45
C. 8.65
D. 8.75
E. None of the above - Find the last digit of the final result.$$(2024^{2024})^2 + 2024$$
A. 0
B. 2
C. 4
D. 6
E. None of the above - How many numbers appear in both sequences below?$$13, 21, 29, 37, \dots , 773$$ $$13, 18, 23, 28, \dots , 773$$
A. 19
B. 20
C. 21
D. 39
E. None of the above - What is the next number in the sequence below?$$1, 3, 24, 82, 201, 411, \dots$$
A. 784
B. 754
C. 749
D. 748
E. None of the above - The shaded figure below is formed by three identical circles touching one another as shown. If the perimeter of the figure is $120\pi$ in cm, what is the length (in cm) of the radius of one circle?
A. 10
B. 24
C. 48
D. 120
E. None of the above - Given that $|a| + b - a = 200$ and $|b| + b + a = 200$, what is the value of $a + b$?
A. –40
B. 40
C. 80
D. 120
E. None of the above - The six-digit number $A0352B$ is a multiple of 2024. What is the value of $A+B$?
A. 16
B. 12
C. 18
D. 17
E. None of the above - How many integers $a$ satisfy the inequality below? $$(a+12)(a-13)(a+9)(a-8)<0$$
A. 4
B. 5
C. 6
D. 7
E. None of the above - What is the distance from the point $(27, −3)$ to the line $6x − 8y + 4 = 0$?
A. 14
B. 17
C. 18
D. 19
E. None of the above - Find the sum of the digits of $A$. $$ A=\underset{1000\text{ 3}}{\underbrace{333\cdots3}}\times \underset{1000\text{ 6}}{\underbrace{666\cdots6}}$$
A. 9990
B. 9000
C. 8100
D. 7200
E. None of the above - If points $A(-12, -7)$, $B(-6, 8)$ and $C(9, y)$ form a right-angled triangle with $\angle ABC = 90^\circ$, find the value of $y$.
A. –2
B. 2
C. 3
D. 4
E. None of the above - What are the last two digits of $11^{2024}$?
A. 41
B. 51
C. 31
D. 61
E. None of the above - What is the remainder when $(x^{20} + 24)$ is divided by $x + 1$?
A. 25
B. 24
C. 26
D. 2024
E. None of the above - What is the largest integer $a$ such that the expression below is an integer?$$\frac{a^2 - 8a + 15}{a+7}$$
A. 120
B. 113
C. 60
D. 53
E. None of the above - In the diagram below, $AC = 24\text{ cm}$, $AB = 48\text{ cm}$ and $\angle CAB = 120^\circ$. Point $D$ is the midpoint of side $AB$, and $DE$ is perpendicular to $AB$. If $DE = 32\text{ cm}$, find the length (in cm) of $CE$.
A. 72 cm
B. 66 cm
C. 60 cm
D. 20 cm
E. None of the above - Sophia owns a collection of vintage stamps, each with a unique value. She decides to distribute her stamps among her three friends. Sophia gives the 34 most valuable stamps, which collectively account for 49% of the total value, to Jack. She then presents the 19 least valuable stamps, which make up 30% of the total value, to Emily. Finally, she allocates the remaining stamps to Olivia. How many stamps did Olivia receive?
- In a theatre production, 2 directors are collaborating with 6 actors. The entire team decides to divide into 2 groups under the guidance of one director each, ensuring that each director is paired with at least one actor. How many distinct group configurations are possible?
- Solve the equation below and find the value of $x^2$.$$2\log_{54} (x - 3) = 1 - \log_{54} (x + 6)$$
- 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. If $A$ is the greatest value of the smallest number on the line segments, what is the value of $3A$?
- 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 $AD = 84$ and $BC = 210$, what is the length of $EF$?
- In a deck of cards, there are 3 spades and 9 hearts. Ethan draws cards one by one from the deck without replacement until he empties the deck. It is revealed that the second card he draws is a spade, and the fifth card he draws is a heart. Let the probability that the last three cards Ethan draws are all hearts be $\frac{a}{b}$ where $\text{HCF}(a, b) = 1$. What is the value of $a + b$?
- Sarah had 7 quizzes this semester. She received integer scores for each quiz. The lowest score she got was 73, and the highest score was 82. If the mode, median, and average of her scores form an arithmetic sequence with a common difference of 2, find the largest possible value of the sum of her scores.
- In the figure below, point $B$ is on a quarter $ADE$ of a circle and point $C$ is on radius $DE$ such that $\angle ABC = 90^\circ$, $AB = 24$ and $CE = 7$. Find the length of $CD$.
- 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 Discordant 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 $\frac{2024(x+2y)}{\pi}$.$$\left\{ \begin{array}{cl}
\dfrac{\cos x}{\cos y} = 2 \cos^2 y \\
\dfrac{\sin x}{\sin y} = 2 \sin^2 y
\end{array} \right.$$
This topic was modified 7 hari ago 2 times by Admin dot
Posted : 20/05/2026 2:32 am
