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TIMO - 2017 - Grade 7 - Preliminary Round - Paper 1

Question 1

According to the pattern shown below, find a number to replace the question mark: $2,3,4,10,38,?,\ldots$
  1. 60
  2. 96
  3. 160
  4. 378

Question 2

There were 50 students who attended a summer camp and they were assigned to five rooms. The numbers of students are indicated in the diagram below. Find the value of $2A+3B+4C+5D+6E$, given that $A,B,C,D,E$ correspond to the number of students in each room.

Question illustration
  1. 130
  2. 154
  3. 177
  4. 200

Question 3

The hour hand of a clock is 3.5 cm long. In 24 hours, how far does its tip travel? Take $\pi=\frac{22}{7}$.
  1. 22cm
  2. 44cm
  3. 24cm
  4. 48cm

Question 4

In a bag, there are 3 green apples, 5 yellow apples, 7 green pears and 2 yellow pears. Simon randomly takes fruits out of the bag one by one. How many fruits must he take out in order to be sure that he has at least one apple and one pear of the same colour?
  1. 5
  2. 9
  3. 13
  4. 10

Question 5

In a sale, each dress is reduced to 49% of its price and if two dresses are purchased at the same time, both are reduced to 45% of their prices. Lily buys two dresses together and pays 90 dollars for both. How many dollars has she saved compared to buying them separately?
  1. 8
  2. 6
  3. 4
  4. 2

Question 6

Given integers $x,y$, find the smallest positive integer value of $x+y$ if $8x+5y=46$.
  1. 1
  2. 2
  3. 6
  4. 8

Question 7

Find the minimum value of $A=3x^2-6x$.
  1. -1
  2. -2
  3. -3
  4. -4

Question 8

Find the value of $3\boxtimes3$. The operation $\boxtimes$ is defined by:
(i) For all $x,y$, $x\boxtimes y=(x-1)\boxtimes(y-1)+x+y$.
(ii) For all $x$, $x\boxtimes1=1$.
  1. 10
  2. 11
  3. 12
  4. 13

Question 9

How many integers $a$ satisfy $\lvert2a+7\rvert+\lvert2a-1\rvert=8$?
  1. 7
  2. 6
  3. 5
  4. 4

Question 10

Given $x<y<0$ and $x^2+y^2=4xy$, find $\frac{x+y}{x-y}$.
  1. $2$
  2. $\sqrt{3}$
  3. $\sqrt{5}$
  4. $\sqrt{6}$

Question 11

Find a number which is under 100. Given that when this number is divided by 2, 3, 4 or 6, there is always a remainder of 1, but when divided by 7 there is no remainder.
  1. 28
  2. 49
  3. 56
  4. 63

Question 12

Find the last digit of $A=13^{2021}+15^{2021}+\cdots+2017^{2021}+2019^{2021}+2021^{2021}$.
  1. 5
  2. 0
  3. 3
  4. 7

Question 13

Find the digit $a$ such that $\overline{8a58a5\ldots8a5}$, formed by repeating the block $8a5$ nine times, is divisible by 11.
  1. 1
  2. 7
  3. 2
  4. 5

Question 14

In how many ways can 31 be expressed in the form a + b + c (a ≤ b ≤ c), where a, b and c are prime numbers?
  1. 4
  2. 5
  3. 6
  4. 7

Question 15

How many factors of 14400 are square number?
  1. 12
  2. 14
  3. 15
  4. 16

Question 16

Cut a cube by two planes parallel to the base of the cube into three rectangular blocks. The ratio of surface areas of these three blocks is 3:4:5. Find the ratio of their volumes in simplified form?
  1. 2 : 3 : 5
  2. 3 : 4 : 5
  3. 3 : 8 : 13
  4. 5 : 8 : 13

Question 17

Find the measure of $\angle BAC$ in the figure, given $AC=CB=CD$.

Question illustration
  1. $70^\circ$
  2. $90^\circ$
  3. $85^\circ$
  4. $95^\circ$

Question 18

The radius of a circle increases by 60%. Find the percentage increase in the area?
  1. 136%
  2. 148%
  3. 156%
  4. 160%

Question 19

In the following figure, E is a point on side AD of the rectangle ABCD. Points F, G, H, and I are midpoints of CE, BF, CG and BH respectively. If the area of the triangle BCI is 1 cm², find the area of the rectangle ABCD in cm².

Question illustration
  1. 16
  2. 32
  3. 24
  4. 18

Question 20

The diagram shows a net of an unfolded rectangular box. Find the volume of this box in cm³. (Figure is used for illustration purpose only).

Question illustration
  1. 40
  2. 80
  3. 100
  4. 120