HKIMO 2026 Grade 8 National Preliminary Set 05 Next → A test has 25 questions, worth 2 points for each correct answer. At least how many students must take it to guarantee that four receive the same score?
79
76
101
105
John travels 13 km northwest, then 12 km northeast, then 4 km southeast. How far is he from his starting point?
15 km
29 km
21 km
5 km
Given $\overline{abcd}+\overline{badc}=17688$, find $a+b-c-d$.
9
8
7
10
It is 6 o’clock. How many minutes until the minute hand and hour hand first overlap?
$33\frac{8}{11}$
$32\frac{5}{11}$
$32\frac{8}{11}$
$33\frac{5}{11}$
There are 13 white, 11 yellow and 14 brown chopsticks mixed together. What is the least number to draw without looking to guarantee two non-yellow pairs?
13
14
15
16
Find $y$ if $|2x+6y+8|+|x-3y+4|=0$.
-4
0
4
2
Let $a$ be constant. The coefficient of $x$ in $(2x-a)(x^2-4x)$ is 20. Find $a$.
5
-5
80
-80
How many negative integers $x$ satisfy $-97\le7x+3\le32$?
15
19
14
18
Given that $x-2$ is a factor of $x^3-2x^2+3x+m$, find $m$.
6
-6
22
10
Given $f(x)=ax^2+bx+c$, $f(-1)=3$, $f(2)=18$ and $f(-2)=6$, find $f(1)$.
15
-3
3
9
Find the remainder when $2024^{2024}$ is divided by 5.
4
2
3
1
If $A=30!\div3^n$ is an integer, find the largest value of $n$.
12
10
14
13
Find the units digit of $A=1+7+7^2+7^3+\cdots+7^{99}+7^{100}$.
1
3
7
9
How many positive integers less than 65 are coprime to 65?
45
48
52
47
Find the number of positive divisors of 35000.
30
40
50
60
Right triangles satisfy $\triangle ABC\sim\triangle FED$, with legs $AB=5$ and $BC=12$. Find $DF:EF$.
$\frac{13}{5}$
$\frac{17}{5}$
$\frac{12}{5}$
$\frac{13}{12}$
On a coordinate plane, $A=(9,4)$, $B=(1,3)$ and $C=(9,8)$. Find the area of triangle ABC.
20
12
16
24
A triangle has side lengths 13, 20 and x, where x is an integer. How many possible values of x are there?
27
24
26
25
An exterior angle of a regular n-sided polygon is $(2n+16)^\circ$. Find n.
8
10
16
18
How many diagonals does a convex 80-sided polygon have?
3080
3160
6320
3120
Next →