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TIMO - 2018 - Grade 7 - Preliminary Round - Paper 2

Question 1

A cyclist moves uphill at a speed of 10 km/h. When he reaches the top of the hill, he returns and passes the same track downhill at a speed of 40 km/h. What is the average speed of the cyclist in the whole journey given that the hill is 8km long?
  1. 16km/h
  2. 25km/h
  3. 30km/h
  4. 36km/h

Question 2

Given that A : B = 4 : 3, B : C = 6 : 5 and A – B + C = 21. Find A.
  1. 12
  2. 28
  3. 24
  4. 14

Question 3

There were 5 Mondays but just 4 Tuesdays in March some years ago. The first day of that month falls on which day of the week?
  1. Tuesday
  2. Saturday
  3. Sunday
  4. Monday

Question 4

If each letter represents a different one-digit number, calculate $M+A+T+H$ in the addition $\overline{MATH}+\overline{MATH}=\overline{HABIT}$.

Question illustration
  1. 10
  2. 14
  3. 15
  4. 12

Question 5

A teddy bear costs 4 dollars and a doll cost 5 dollars. Teacher bought some toys including both teddy bears and dolls to give her students. She had to pay 36 dollars altogether. How many toys did she buy?
  1. 8
  2. 12
  3. 9
  4. 10

Question 6

Find $x$ if $(2020-2x)+(x-2021)=0$.
  1. $1$
  2. $4041$
  3. $-1$
  4. $-4041$

Question 7

Find $A$, given $A=\sqrt{30+\sqrt{30+\sqrt{30+\cdots}}}$.
  1. 5
  2. 6
  3. 30
  4. 5.5

Question 8

Let $x,y$ be positive integers with $10x+7y=224$. How many possible pairs $(x,y)$ are there?
  1. 20
  2. 21
  3. 3
  4. 4

Question 9

Find $P$ if $18P=1\times2\times3+2\times3\times4+3\times4\times5+\cdots+18\times19\times20$.
  1. 1990
  2. 1995
  3. 2000
  4. 2005

Question 10

How many integers $x$ satisfy $-25\le2x+27\le62$?
  1. 53
  2. 43
  3. 44
  4. 54

Question 11

How many prime factors does the number 10920 have?
  1. 5
  2. 4
  3. 6
  4. 7

Question 12

A 4-digit number divided by 8 or 12 leaves a remainder 4. Find its smallest value.
  1. 1008
  2. 1012
  3. 1920
  4. 1924

Question 13

If the ten-digit number $\overline{20212022AB}$ is divisible by 36, find the sum of all possible values of $A$, given $A,B$ are different digits.
  1. 6
  2. 14
  3. 16
  4. 4

Question 15

To write all page numbers of a book with 1000 pages, how many digits “2” do we use?
  1. 480
  2. 200
  3. 300
  4. 271

Question 16

Anna has one square with side length 15cm and two identical right-angled triangles. She combines them to get a trapezium with area 345cm² as below. Find its perimeter.

Question illustration
  1. 110cm
  2. 80cm
  3. 82cm
  4. 112cm

Question 17

Combine 8 cubes of side length 4cm to form a bigger cube. Find the decrease of the total surface area in cm² after combination.
  1. 384
  2. 192
  3. 768
  4. 96

Question 18

A rectangle has area 240 and integral side lengths. How many different values of perimeter the rectangle can have?
  1. 24
  2. 12
  3. 20
  4. 10

Question 19

A triangle has three interior angles with ratio 2 : 3 : 4. Find the size of the smallest exterior angle.
  1. $80^\circ$
  2. $140^\circ$
  3. $100^\circ$
  4. $40^\circ$

Question 20

Given a triangle ABC with AM = MB and AN : NC = 1 : 2. If the area of ABC is 60cm², what is the area of the triangle EBC in cm²?

Question illustration
  1. 28
  2. 21
  3. 30
  4. 24