In 2nd grade, children begin to get acquainted with three-digit numbers and math problems. Math has longer text. This is also the time when many families let their children try mental math exams like TIMO. This type of test does not require grade-level knowledge, but challenges the ability to read carefully, reason and count systematically.

The 15 questions below are tests prepared by the Karotto team, divided equally into 5 areas: logic, arithmetic, number theory, geometry, and combinatorics. This is not an official exam and Karotto is not affiliated with the TIMO organizing committee. If you want to understand more about the exam, parents should read the lesson What is TIMO?.

All answers have been checked again by machine: try all cases, especially the picture counting test, count on the coordinates of each line segment of the drawing.

How to use this practice question

The test has 15 questions, number range up to 1000. In each array, the previous sentence is easier than the next sentence. Parents can use the question paper in three steps:

Timer: print the question paper or copy it on paper, and let your child do it in about 45 minutes (Karotto's suggestion, about 3 minutes per question). Just write down the answer, don't open the solution yet. If your child is not yet fluent in reading, parents can read the questions for you.
Do it in sections: If your child is new or gets tired easily, divide the problem into several short sessions, each session with one or two sections (3 to 6 sentences). Complete one area and then move on to the next, so your child can focus on one type of thinking.
Correction: for each question, have your child tell you how to do it first, then open "See solution". If the question is wrong, find the correct step that the child misunderstood, write it down, and let the child do it again the next day.

Tips for parents: don't judge just by the answer. A correct sentence thanks to a guess is not as rewarding as an incorrect sentence in which the child explains what he thinks. The solution below is written so that parents can read it once and explain it in their own words.

Part 1: Logic (sentences 1 to 3)

Question 1

It takes 5 minutes to saw a piece of wood into 2 pieces. How many minutes does it take to saw that log into 5 pieces? (Each saw takes 5 minutes.)

See solution

Answer: 20 minutes.

  1. Saw 1 time to get 2 pieces. Saw twice to get 3 pieces. Each time you cut 1 more piece.
  2. To have 5 pieces, you need 5 − 1 = 4 saws.
  3. 4 times, 5 minutes each time: 5 + 5 + 5 + 5 = 20 minutes.

Common incorrect answers is 25 minutes. Parents take a long piece of paper, let the child draw 4 cut lines, the child will immediately see that 4 lines create 5 parts.

Question 2

You guys line up in a vertical line. Na is 8th from the front of the line and 12th from the back of the line. Ask: How many people are there?

See solution

Answer: 19 people.

  1. Na is 8th from the beginning: in front of Na there are 7 people.
  2. Na is 12th from the end: behind Na there are 11 you.
  3. The whole line includes 7 people in front, 11 people in the back and Na herself: 7 + 11 + 1 = 19 friends.

Another way: 8 + 12 = 20, but Na is counted twice so 1 less, leaving 19. A common mistake is to answer 20.

Verse 3

Of the three friends, Ti, Teo, and Tun, exactly one person ate the cake. Ti said: "I eat cake". Teo said: "I don't eat". Tun said: "I don't eat." Know that only one person is telling the truth. Ask who ate the cake?

See solution

Answer: Tún.

Try each person in turn to eat the cake, then count how many sentences are true:

  1. If Ti eats: Ti's sentence is wrong, Teo's sentence is right, Teo's sentence is right, Tun is right. There are 2 correct and incorrect sentences.
  2. If Teo eats: Ti's sentence is correct, Teo's sentence is incorrect, Tun's sentence is correct. There are 2 correct and incorrect sentences.
  3. If Tún eats: Ti's sentence is wrong, Teo's sentence is right, Tún's sentence is wrong. There is exactly 1 correct sentence, matching the problem.

So Tún has eaten the cake. This "assume then check" method is the key to all truth-telling and lying. Have your child draw 3 lines on the board, each line write true or false for each sentence.

Part 2: Arithmetic (questions 4 to 6)

Question 4

Quick calculation: 125 + 238 + 75 + 62 = ?

See solution

Answer: 500.

  1. Find pairs that add up to a hundred: 125 + 75 = 200 and 238 + 62 = 300.
  2. Exchanging terms does not change the sum, so We add in pairs: 200 + 300 = 500.

Signs to recognize pairs: look at the units digit. 5 and 5 add up to ten, and 8 and 2 also add up to ten. Practicing "looking at the end of numbers" helps children calculate much faster.

Question 5

Find the next number in the sequence: 2, 5, 11, 23, ...

See solution

Answer: 47.

  1. Try to find the distance: 5 − 2 = 3, 11 − 5 = 6, 23 − 11 = 12. The distance doubles after each step.
  2. The next distance is 24, so the next number is 23 + 24 = 47.

The pattern can also be seen "double then add 1": 2 doubled is 4, adding 1 is 5; 5 doubled is 10, adding 1 is 11; 11 becomes 23; 23 becomes 47. Two ways give the same answer, parents encourage children to try finding both.

Question 6

Two buckets have a total of 150 liters of water. The first barrel is 30 liters more than the second barrel. How many liters of water are in the first bucket?

See solution

Answer: 90 liters.

  1. Remove 30 liters from the first bucket (the larger part), the two buckets will be equal. The total remains 150 − 30 = 120 liters.
  2. Two equal buckets, each bucket is half of 120: 60 liters. That's the second bucket.
  3. First bucket: 60 + 30 = 90 liters.

Check: 90 + 60 = 150 and 90 − 60 = 30. Drawing two straight lines, the upper one 30 degrees longer than the lower one, is the most intuitive way so your child can understand why 30 must be subtracted first.

Part 3: Number theory (questions 7 to 9)

Question 7

How many three-digit numbers are there where all three digits are the same?

See solution

Answer: 9 numbers.

  1. The same three-digit number has the form 111, 222, 333, ...
  2. The hundreds digit cannot be 0 (because 000 is not a three-digit number), so the common digit can only be from 1 to 9.
  3. There are 9 numbers: 111, 222, 333, 444, 555, 666, 777, 888, 999.

Question 8

Find the largest even number with three different digits.

See solution

Answer: 986.

  1. Largest hundreds place: 9.
  2. Largest tens place, other than 9: 8.
  3. Units place must be an even digit (0, 2, 4, 6, 8) and other than 9, 8. The largest remaining even digit is 6.

The number to search for is 986. Children often answer 988 (two 8s overlap) or 987 (odd number). Let your child underline three requirements in the problem: even, largest, three different digits.

Question 9

How many three-digit numbers have the sum of three digits equal to 3?

See solution

Answer: 6 number.

Hundreds digit must be 1 or more. Consider each case in turn:

  1. Hundreds place is 1: the remaining two digits have a sum of 2, giving 102, 111, 120. There are 3 numbers.
  2. Hundreds place is 2: the remaining two digits have a sum of 1, giving 201, 210. There are 2 numbers.
  3. The hundredth place is 3: the remaining two digits are both 0, making 300. There is 1 number.

Total: 3 + 2 + 1 = 6 numbers. Dividing cases into hundreds is a way to list without omissions or duplicates.

Part 4: Geometry (questions 10 to 12)

Question 10

The Bear arranges equal cubes into stairs as shown. How many blocks did Bear use?

The stairs are made of cubes: the left column is 3 blocks high, the middle column is 2 blocks high, the right column is 1 block high
Question 10. The stairs have three columns, each column is only 1 block thick.
See solution

Answer: 6 blocks.

  1. Count by column: left column 3 blocks high, middle column 2 blocks, right column 1 block.
  2. Sum up: 3 + 2 + 1 = 6 blocks.

Counting by column (or by floor: lower floor 3, middle floor 2, upper floor 1) helps children not double count. If you have a puzzle at home, let your child arrange it exactly like the picture and count.

Question 11

How many triangles are there in the picture?

Triangle ABC, has two more straight lines connecting vertex A to two points D and E located on side BCABCDE
Question 11. Triangle ABC has two more line segments AD and AE.
See solution

Answer: 6 triangles.

  1. Every triangle in the picture has vertex A and one side on base BC. So just count the number of straight segments on the bottom.
  2. Short segment (1 segment): BD, DE, EC. There are 3 triangles: ABD, ADE, AEC.
  3. 2 segment: BE, DC. There are 2 triangles: ABE, ADC.
  4. 3-segment segment: BC. There is 1 triangle: ABC.
  5. Total: 3 + 2 + 1 = 6 triangles.

The "counting segments on the base" tip turns the counting of shapes into counting of straight segments, much easier. Children can use this trick for shapes with 3 or 4 lines.

Question 12

The rectangle on the side is divided into equal squares. How many squares are there in the picture?

The rectangle is divided into a grid of 2 rows and 3 columns of equal small squares
Question 12. The rectangle consists of 2 rows, each row of 3 squares.
See solution

Answer: 8 squares.

  1. Small square (1 cell): 2 rows, each row of 3 cells, has 6 pictures.
  2. Large square (sides equal to 2 cells, includes 4 cells): can be located on the left or one cell to the right, has 2 pictures.
  3. Square with sides of 3 cells: not available, because the shape is only 2 cells high.
  4. Total: 6 + 2 = 8 squares.

Parents can cut a square piece of paper with 4 cells, let the child place it on the picture and slide it to the right to count the number of positions. Children will remember this method longer than any explanation.

Part 5: Combination (sentences 13 to 15)

Verse 13

There are 4 people, An, Binh, Chi, Dung. Every two of you take a photo together. How many photos were taken in total?

See answer

Answer: 6 photos.

  1. An took photos with Binh, Chi, Dung: 3 photos.
  2. Binh took photos with An, but also took photos with Chi, Dung: 2 photos.
  3. Only photos taken with Dung: 1 photo.
  4. Total: 3 + 2 + 1 = 6 photos.

Photo "An and Binh" and photo "Binh and An" are the same photo. Listing names in order helps children avoid counting twice.

Question 14

From the four digits 1, 2, 3, 4, how many different two-digit numbers can be formed?

See solution

Answer: 12 numbers.

  1. Choose the tens digit: there are 4 ways (1, 2, 3 or 4).
  2. For each way of choosing the tens, the units must be different from the tens, there are 3 ways. For example, if the tens is 1, there are 12, 13, 14.
  3. Number of numbers: 4 groups, each group has 3 numbers, yield 3 + 3 + 3 + 3 = 12 numbers.

Let your child write in 4 lines: 12, 13, 14 / 21, 23, 24 / 31, 32, 34 / 41, 42, 43. Writing neatly in a table is the first step in combinatorial thinking.

Verse 15

How many two-digit numbers are there in which the tens digit is larger than the ones digit?

See solution

Answer: 45 numbers.

Consider the tens digits one by one, see how many ways you can count the ones place (must be smaller than tens, can be 0):

  1. Tens 1: unit has only 0, gets 1 number (10).
  2. Tens 2: unit is 0 or 1, gets 2 numbers.
  3. Tens 3: gets 3 numbers. Just like that, the tens of 9: get 9 numbers (90 to 98).
  4. Total: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 numbers.

The last addition is a "quick calculation" that pairs the sum with 10. Parents can show their children how the math areas are related to each other.

Round rubric

Each correct sentence gets 1 point. Record the number of correct sentences for each array in the third column. The results by array are more useful than the total score, because it shows what kind of thinking the child needs to practice more.

ArraySentenceChildren are correctIf less than 2 sentences are correct, practice
Logic1, 2, 3…/3Practice drawing diagrams, drawing tables or arranging real objects before answering; Read each fact sentence slowly.
Arithmetic4, 5, 6…/3Practice finding pairs of numbers round tens and hundreds and drawing line diagrams for sums and differences.
Number theory7, 8, 9…/3List in order (by tens, hundreds) and underline all conditions in the problem.
Geometry10, 11, 12…/3Count from small to large shapes, name the shapes using real letters, sticks or blocks to check.
Combinations13, 14, 15…/3List in tables or branch diagrams; Be careful of double counting (An-Binh and Binh-An are one).
Total1 to 15…/15From 12 sentences or more: your child has mastered this form. From 8 to 11 sentences: practice more weak areas. Less than 8 questions: back to more basic lessons, no need to take exam questions.

The above levels are just suggestions from Karotto for parents to choose the next step, not the scoring scale of any exam. If you want to see more about each type of lesson and how to teach it, parents should read the article Common forms of mental math in elementary schools.

Continue practicing in the Karotto app

Transparency: Karotto is the app of the team that makes this website. In the "Number Garden" Math course, the 2nd grade TIMO-style practice session is located on island M6 (for 7-year-old children), interspersed between regular courses, with all 5 areas of logic, arithmetic, number theory, geometry, and combinatorics as above.

Number theory question in the Karotto app: how many two-digit numbers have the unit digit greater than 4
A number theory question in the TIMO-style practice phase of Karotto: "How many two-digit numbers have the unit digit greater than 4?"
  • Automatically generated practice questions: at the end of the island there are exam-style practice questions. The questions are generated by the app itself, without copying the actual exam questions, so each time you take the test it's a different question and your child can't memorize the answers.
  • There is a timer, marking in arrays: the child does the test with a clock like taking an exam, then sees the score of each section like the self-scoring table above.
  • Review the wrong sentences: after submitting the exam, the child reopens the correct incorrect sentences to see the answers. solution.
  • Voice reading the questions: The questions and instructions are read out loud in Vietnamese, so children who are not fluent in reading can still practice on their own.
  • 3-step hint: When stuck, the child is gently reminded first, then the illustration, Finally, there is the answer with explanation.

Every day children can learn a suitable amount of lessons for free, all islands are open. If you want unlimited training, the Premium package is a one-time purchase, lifetime use, no monthly or yearly subscription, no periodic deduction. The app has no ads.

In short

Let your child take a timed test, grade each section, then carefully correct each wrong sentence. One problem solved carefully is more useful than three problems done hastily. If you get less than 2 questions correct, practice that area more before taking a new test.

Frequently Asked Questions

Is this a real TIMO test?

No. This is a question prepared by the Karotto team in 5 areas of logic, arithmetic, number theory, geometry, and combinatorics, with the same format as common articles. Karotto is not affiliated with TIMO organizers. If you want to see the real test, parents should find the official documents of the organizer.

How long should your child take this test?

Suggest about 45 minutes for all 15 questions, or about 3 minutes per question. The first time can be divided into two sessions, each session has 2 or 3 segments. The important thing is that your child gets used to doing homework on time while still reading the problem carefully.

How to correct your child's homework effectively?

Let your child explain how to do it before opening the solution. For a wrong sentence, find the correct step that your child misunderstood and then let your child try the sentence again the next day. Record scores for each array to know which arrays need more practice.

What if a 2nd grade child gets the whole combination array wrong?

Combination is a new array for most 2nd grade children, many mistakes are normal. Practice the habit of listing in tables or diagrams, re-do each question with your child, then move on to more difficult problems.

Practice mental math every day with Thỏ Bông

Automatically generated TIMO-style practice tests, with timer, array marking, Vietnamese voice reading and solutions for each wrong question.

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