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TIMO - 2017 - Grade 8 - Preliminary Round - Paper 5

Question 1

According to the pattern $5,13,37,109,325,\ldots$, what is the next number?
  1. 541
  2. 975
  3. 973
  4. 653

Question 2

A triangle has side lengths 13, 20 and $x$. How many integer values of $x$ are possible?
  1. 25
  2. 26
  3. 32
  4. 27

Question 3

There are 4 students named Andy, Billy, Cindy and Danny entering a 3-day badminton competition. In each day, a student plays one match. Any two students must play with each other once in the whole competition. Given that: 1) Andy wins Billy on the first day. 2) Billy loses to Danny on the second day. Which student does Andy play with on the final day?
  1. Andy
  2. Billy
  3. Cindy
  4. Danny

Question 4

In a library, the ratio of Math books to English books is 5 : 4, the ratio of Science books to Math books is 8 : 7. Given that the total number of Math books, English books and Science books is 309. Find the number of Math books.
  1. 103
  2. 105
  3. 107
  4. 109

Question 5

In a marathon, participants need to run from red flag to blue flag, then from blue flag to green flag. Given that there are 4 different ways from red flag to blue flag and 6 different ways from blue flag to green flag. At least how many participants should join the marathon so that there always exist 3 people running on the same route from start to finish?
  1. 73
  2. 49
  3. 26
  4. 72

Question 6

If $M=\sqrt{15-2\sqrt{15-2\sqrt{15-2\sqrt{15-\cdots}}}}$, find $M$.
  1. 3
  2. 5
  3. 15
  4. 4

Question 7

Factorize $(2x^2-y^2)+xy-(2x-y)$.
  1. $(2x-y)(x+y-1)$
  2. $(2x-y)(x-y-1)$
  3. $(2x+y)(x+y+1)$
  4. $(x-y)(2x+y-1)$

Question 8

Given $f(x)=(x^2-bx)(2x+b)$ whose coefficient of $x^2$ is 5, find $f(1)$.
  1. 5
  2. 140
  3. 18
  4. -18

Question 9

Given that $(x-2)(x-3)$ is a factor of $x^3+5x^2-ax+b$, find $a+b$.
  1. 105
  2. 102
  3. 104
  4. 100

Question 10

Find the maximum value of $\sqrt{21-2x}+\sqrt{2x-3}$.
  1. $6\sqrt{2}$
  2. $3\sqrt{2}$
  3. $\sqrt{17}+1$
  4. 6

Question 11

How many positive integers smaller than 666 and not divisible by 6 are there?
  1. 555
  2. 550
  3. 554
  4. 556

Question 12

If $2x\equiv9\pmod{11}$, find the smallest 3-digit value of $x$.
  1. 110
  2. 109
  3. 108
  4. 107

Question 13

Find the remainder when $26^{27}$ is divided by 15.
  1. 1
  2. 4
  3. 11
  4. 9

Question 14

Find the largest 3-digit prime number.
  1. 999
  2. 998
  3. 997
  4. 991

Question 15

Anna wants to multiply 1836 by a number X to get a perfect square. What is the smallest value of X?
  1. 51
  2. 17
  3. 102
  4. 34

Question 16

Find the area of a triangle with side lengths 12, 15 and 9.
  1. 36
  2. 90
  3. 108
  4. 54

Question 17

How many triangles can be created by joining 8 noncollinear points?
  1. 336
  2. 56
  3. 168
  4. 42

Question 18

Using the dimensions in the figure below, find the area of the shaded region in m².

Question illustration
  1. $\frac{3\sqrt{5066}}{2}$
  2. 106.5
  3. $3\sqrt{5066}$
  4. 213

Question 19

Given a circle with radius 22. Find the area of the largest square inscribed circle.
  1. 242
  2. 484
  3. 968
  4. 1936

Question 20

In the figure, hexagon $ABCDEF$ is equiangular. $ABJI$ and $FEHG$ are squares with areas 18 and 32 respectively. Triangle $JBK$ is equilateral and $FE=BC$. Find the area of triangle $KBC$.

Question illustration
  1. 12
  2. 24
  3. 16
  4. 15