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TIMO - 2021 - Grade 7 - Preliminary Round - Paper 5

Question 1

Given a two-digit number $\overline{AB}$ which is a perfect square. If $A+B=10$, what is the difference between $A$ and $B$?
  1. 2
  2. 3
  3. 5
  4. 7

Question 2

There are some chickens and rabbits on a farm. The number of chickens is twice the number of rabbits. They have 96 legs in total. How many chickens are there?
  1. 12
  2. 24
  3. 36
  4. 48

Question 3

At 10 a.m., mother drove from home to her office with a speed of 30km/h. After 10 minutes, father saw mother’s phone left at home, so he drove in the same direction with a speed of 50km/h to catch her. At which time did father and mother meet?
  1. 10:10 a.m.
  2. 10:15 a.m.
  3. 10:25 a.m.
  4. 10:30 a.m.

Question 4

Adam decided to invite some people to his party. At least how many people should Adam invite to make sure that there exists 3 people born in the same month?
  1. 15
  2. 24
  3. 36
  4. 25

Question 5

How much time after 6 a.m. does the minute hand overlap the hour hand for the first time (give the closest answer)?
  1. 30 minutes and 44 seconds
  2. 32 minutes and 44 seconds
  3. 31 minutes and 44 seconds
  4. 33 minutes and 44 seconds

Question 6

Find $1+3+9+\cdots+729+2187$.
  1. 3260
  2. 3270
  3. 3280
  4. 3290

Question 7

Find $\frac1{1\times3}+\frac1{3\times5}+\frac1{5\times7}+\cdots+\frac1{107\times109}+\frac1{109\times111}$.
  1. $\frac{50}{111}$
  2. $\frac{220}{111}$
  3. $\frac{110}{111}$
  4. $\frac{55}{111}$

Question 8

Convert the recurring decimal $1.5555\ldots$ into a fraction in lowest terms.
  1. $\frac{13}{9}$
  2. $\frac{28}{18}$
  3. $\frac{5}{9}$
  4. $\frac{14}{9}$

Question 9

Let $x$ be real with $x^2+\frac1{x^2}=4$. Find $x^4+\frac1{x^4}$.
  1. 18
  2. 16
  3. 14
  4. 12

Question 10

Given that the sum of 10 consecutive natural numbers is 275, find the smallest number among those 10 numbers.
  1. 23
  2. 24
  3. 22
  4. 21

Question 11

If the seven-digit number $\overline{2020A1B}$ is divisible by 12, find the greatest value of $A+B$.
  1. 7
  2. 10
  3. 13
  4. 16

Question 12

Find the units digit of $4\times14\times24\times\cdots\times84\times94$.
  1. 2
  2. 4
  3. 6
  4. 8

Question 13

How many 3-digit numbers divisible by 5 but not divisible by 2 are there?
  1. 90
  2. 89
  3. 99
  4. 100

Question 14

Find the number of positive factors of 2020.
  1. 10
  2. 12
  3. 8
  4. 6

Question 15

Given $n!=1\times2\times3\times\cdots\times(n-1)\times n$, how many zeros does $20!$ end with?
  1. 2
  2. 5
  3. 4
  4. 3

Question 16

It is known as the lengths of shorter sides for a right-angled triangle are 8cm and 15cm respectively. Find the length of the longest length in cm.
  1. 16
  2. 19
  3. 22
  4. 17

Question 17

The total surface area of a cubic box is 2400cm². Find the volume of the box in cm³.

Question illustration
  1. 27000cm³
  2. 8000cm³
  3. 1000cm³
  4. 125cm³

Question 18

Given 2 squares with side lengths of 8cm and 24cm as the figure below. Find the area of the shaded region.

Question illustration
  1. 100cm²
  2. 144cm²
  3. 90cm²
  4. 96cm²

Question 19

The side length of a square is $7\pi$, and its perimeter equals the circumference of a circle. Find the area of the circle. Take $\pi=\frac{22}{7}$.
  1. 616
  2. 2464
  3. 1232
  4. 610

Question 20

Find the sum of all interior angles in a regular hexagon.
  1. $720^\circ$
  2. $540^\circ$
  3. $900^\circ$
  4. $630^\circ$