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- Simplify $$\frac{11}{2\sqrt{5}-3}+\frac{5}{\sqrt{5}-2}-7\sqrt{5}$$
- Evaluate $$\sqrt{14+6\sqrt{5}}-\sqrt{14-6\sqrt{5}}$$
- Find the value of$$\cos^{2}\theta+\cos^{2}\left(\theta+\frac{2\pi}{3}\right)+\cos^{2}\left(\theta-\frac{2\pi}{3}\right)$$
- Factorize $x^{3}+4x^{2}+5x+2$
- The 3 sides of a right-angled triangle are all integers. One of the 2 shorter sides is 35. Find the minimum possible perimeter.
- $ABCD$ is a rectangle whose diagonals intersect at point $O$. $E$ is a point on $AB$ such that $CE$ bisects $\angle BCD$. It is known that $\angle ACE=15^{\circ}$. Find $\angle BOE$.
- Suppose $xy=144$ and $\log_{y}x+\log_{x}y=\frac{10}{3}$ with $x,y>0$. Find the value of $\frac{x+y}{2}$, leaving your answer in the simplest form.
- Given that $x+\frac{1}{x}=3$, evaluate $$x^{10}+x^{5}+\frac{1}{x^{5}}+\frac{1}{x^{10}}$$
- Find the remainder when $(257^{33}+46)^{26}$ is divided by 50.
- A positive integer is called friendly if it is divisible by the sum of its digits. For example, 111 is friendly but 123 is not. Find the number of all 2-digit friendly numbers.
- A candidate is required to answer 7 out of 15 questions which are divided into 3 groups $A$, $B$, $C$ each containing 4, 5, 6 questions respectively. He is required to select at least 2 questions from each group. Find the number of choices he can make.
- It is known that $\angle MAN=45^{\circ}$ in square $ABCD$, $M$ and $N$ are points on $BC$, $CD$ respectively. Given that $BM=3.5$ and $DN=2.5$, find the length of $MN$.
- There are 6 questions in Paper E for SEAMO X 2024. Exactly 500 participants answered each question correctly. For any 2 participants, there is at least one question they both got wrong. At least how many participants are there for this paper?
- $ABCD$ is a trapezium with $AD \parallel BC$. $AB=BC$ and $AD=AE$. Given that $\angle ABC=90^{\circ}$ and $E$ is a point on $AB$ such that $\angle BEC=75^{\circ}$, find $\angle DCE$.
- The radii of the 2 circles are 8 and 6 respectively. The distance between the centres of the 2 circles is 12. A line $QR$ is drawn through one of the intersections $P$ such that $QP=PR$. Find $(QP)^{2}$.
This topic was modified 7 hari ago by Admin dot
Posted : 20/05/2026 4:56 am
