Daily Math — 2026-09-12
Grade 1 Problems
[Easy] Counting Carrots
- EN: Mia has 7 carrots. She picks 5 more. How many carrots does she have now?
- FR: Mia a 7 carottes. Elle en cueille 5 de plus. Combien de carottes a-t-elle maintenant?
- Choices: A) 10 B) 11 C) 12 D) 13
- Hint: To add, count on from the bigger number — like 9 + 3, start at 9 and count 3 more.
- Steps:
- Start at 7.
- Count on 5 more: 8, 9, 10, 11, 12.
- So the total is 12.
- Answer: 12
[Easy] Hockey Pucks
- EN: There are 9 pucks on the ice. A player takes 4 away. How many pucks are left?
- FR: Il y a 9 rondelles sur la glace. Un joueur en prend 4. Combien de rondelles reste-t-il?
- Choices: A) 3 B) 4 C) 5 D) 6
- Hint: To subtract, count back from the bigger number — like 8 − 3, start at 8 and count back 3.
- Steps:
- Start at 9.
- Count back 4: 8, 7, 6, 5.
- So the answer is 5.
- Answer: 5
[Easy] Skip Counting by 2s
- EN: Count by 2s. What comes next: 4, 6, 8, ___?
- FR: Compte par bonds de 2. Quel nombre vient ensuite: 4, 6, 8, ___?
- Choices: A) 9 B) 10 C) 11 D) 12
- Hint: Skip counting by 2s means adding 2 each time — like 2, 4, 6 means add 2 each step.
- Steps:
- The pattern adds 2 each time.
- 8 + 2 = 10.
- So the next number is 10.
- Answer: 10
[Easy] Coin Recognition
- EN: Which coin is worth 10 cents?
- FR: Quelle pièce vaut 10 cents?
- Choices: A) Penny B) Nickel C) Dime D) Loonie
- Hint: A penny is 1 cent and a nickel is 5 cents — think about which coin comes next in value.
- Steps:
- A penny = 1 cent.
- A nickel = 5 cents.
- A dime = 10 cents.
- So the answer is Dime.
- Answer: Dime
[Medium] Comparing Numbers
- EN: Which number is greater: 43 or 34?
- FR: Quel nombre est plus grand: 43 ou 34?
- Choices: A) 34 B) 43 C) Both are equal D) 30
- Hint: Look at the tens digit first — like 52 vs 25, the one with more tens is bigger.
- Steps:
- 43 has 4 tens and 3 ones.
- 34 has 3 tens and 4 ones.
- 4 tens is more than 3 tens.
- So 43 is greater.
- Answer: 43
[Medium] Skip Counting by 5s
- EN: Count by 5s. What comes next: 15, 20, 25, ___?
- FR: Compte par bonds de 5. Quel nombre vient ensuite: 15, 20, 25, ___?
- Choices: A) 26 B) 28 C) 30 D) 35
- Hint: Skip counting by 5s means adding 5 each time — like 10, 15, 20 shows adding 5.
- Steps:
- The pattern adds 5 each time.
- 25 + 5 = 30.
- So the next number is 30.
- Answer: 30
[Medium] Adding Three Numbers
- EN: Sam has 3 red blocks, 4 blue blocks, and 2 green blocks. How many blocks in all?
- FR: Sam a 3 blocs rouges, 4 blocs bleus et 2 blocs verts. Combien de blocs en tout?
- Choices: A) 7 B) 8 C) 9 D) 11
- Hint: Add three numbers step by step — like 2 + 5 + 3, first add 2 + 5 = 7, then 7 + 3 = 10.
- Steps:
- First add 3 + 4 = 7.
- Then add 7 + 2 = 9.
- So the total is 9.
- Answer: 9
[Medium] Skip Counting by 10s
- EN: Count by 10s. What comes next: 20, 30, 40, ___?
- FR: Compte par bonds de 10. Quel nombre vient ensuite: 20, 30, 40, ___?
- Choices: A) 41 B) 45 C) 50 D) 60
- Hint: Skip counting by 10s means adding 10 each time — like 10, 20, 30 shows adding 10.
- Steps:
- The pattern adds 10 each time.
- 40 + 10 = 50.
- So the next number is 50.
- Answer: 50
[Hard] Number Story
- EN: There are 15 students in a class. 8 go outside to play. Then 3 come back inside. How many students are inside now?
- FR: Il y a 15 élèves dans une classe. 8 sortent jouer. Puis 3 rentrent. Combien d'élèves sont à l'intérieur maintenant?
- Choices: A) 7 B) 10 C) 11 D) 13
- Hint: Solve in two steps — like start with 12, take away 5 to get 7, then add 2 to get 9.
- Steps:
- Start with 15 students inside.
- 8 go outside: 15 − 8 = 7 inside.
- 3 come back: 7 + 3 = 10 inside.
- So the answer is 10.
- Answer: 10
[Hard] Counting to 100
- EN: What number is 10 more than 76?
- FR: Quel nombre est 10 de plus que 76?
- Choices: A) 66 B) 77 C) 86 D) 96
- Hint: Adding 10 changes the tens digit by 1 — like 10 more than 53 is 63.
- Steps:
- Start at 76.
- Add 10: the tens digit goes from 7 to 8.
- 76 + 10 = 86.
- So the answer is 86.
- Answer: 86
Grade 2 Problems
[Easy] Adding Within 100
- EN: What is 34 + 25?
- FR: Combien font 34 + 25?
- Choices: A) 57 B) 58 C) 59 D) 69
- Hint: Add the ones first, then the tens — like 21 + 43: ones 1 + 3 = 4, tens 2 + 4 = 6, so 64.
- Steps:
- Ones: 4 + 5 = 9.
- Tens: 3 + 2 = 5.
- Put together: 59.
- So the answer is 59.
- Answer: 59
[Easy] Telling Time — Hour
- EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
- FR: L'aiguille courte est sur le 3 et la grande aiguille est sur le 12. Quelle heure est-il?
- Choices: A) 12:00 B) 2:00 C) 3:00 D) 3:30
- Hint: When the long hand points to 12, it is exactly on the hour — like short hand on 7 means 7:00.
- Steps:
- Long hand on 12 means it is exactly on the hour.
- Short hand on 3 tells us the hour is 3.
- So the time is 3:00.
- Answer: 3:00
[Easy] Subtracting Within 100
- EN: What is 47 − 23?
- FR: Combien font 47 − 23?
- Choices: A) 14 B) 20 C) 24 D) 34
- Hint: Subtract the ones first, then the tens — like 68 − 35: ones 8 − 5 = 3, tens 6 − 3 = 3, so 33.
- Steps:
- Ones: 7 − 3 = 4.
- Tens: 4 − 2 = 2.
- Put together: 24.
- So the answer is 24.
- Answer: 24
[Easy] Measuring Length
- EN: A pencil is 14 cm long and an eraser is 3 cm long. How much longer is the pencil?
- FR: Un crayon mesure 14 cm et une gomme mesure 3 cm. De combien le crayon est-il plus long?
- Choices: A) 9 cm B) 10 cm C) 11 cm D) 17 cm
- Hint: To find the difference in length, subtract the shorter from the longer — like 10 cm − 4 cm = 6 cm.
- Steps:
- Subtract: 14 − 3 = 11.
- The pencil is 11 cm longer.
- So the answer is 11 cm.
- Answer: 11 cm
[Medium] Counting Coins
- EN: You have 2 dimes, 1 nickel, and 2 pennies. How much money do you have?
- FR: Tu as 2 pièces de 10 cents, 1 pièce de 5 cents et 2 pièces de 1 cent. Combien d'argent as-tu?
- Choices: A) 22 cents B) 25 cents C) 27 cents D) 30 cents
- Hint: Count dimes (10 cents each), then nickels (5 cents each), then pennies (1 cent each) — like 1 dime + 1 nickel + 3 pennies = 18 cents.
- Steps:
- 2 dimes = 20 cents.
- 1 nickel = 5 cents.
- 2 pennies = 2 cents.
- Total: 20 + 5 + 2 = 27 cents.
- Answer: 27 cents
[Medium] Telling Time — Half Hour
- EN: The clock shows the long hand on 6 and the short hand between 8 and 9. What time is it?
- FR: La grande aiguille est sur le 6 et la petite aiguille est entre le 8 et le 9. Quelle heure est-il?
- Choices: A) 6:30 B) 8:00 C) 8:30 D) 9:30
- Hint: When the long hand is on 6, it is half past the hour — like short hand between 4 and 5 means 4:30.
- Steps:
- Long hand on 6 means 30 minutes past.
- Short hand is between 8 and 9, so the hour is 8.
- The time is 8:30.
- Answer: 8:30
[Medium] Simple Patterns
- EN: What comes next in this pattern: 2, 4, 6, 8, ___?
- FR: Quel nombre vient ensuite dans ce pattern: 2, 4, 6, 8, ___?
- Choices: A) 9 B) 10 C) 12 D) 14
- Hint: Find how much is added each time, then add that amount to the last number — like 3, 6, 9, the rule is +3, so next is 12.
- Steps:
- Each number increases by 2.
- 8 + 2 = 10.
- So the next number is 10.
- Answer: 10
[Medium] Adding Within 100 With Regrouping
- EN: What is 47 + 36?
- FR: Combien font 47 + 36?
- Choices: A) 73 B) 83 C) 84 D) 93
- Hint: Add the ones first — if they add up to more than 9, carry 1 to the tens — like 28 + 15: 8 + 5 = 13, write 3 carry 1, then 2 + 1 + 1 = 4, so 43.
- Steps:
- Ones: 7 + 6 = 13. Write 3, carry 1.
- Tens: 4 + 3 + 1 (carried) = 8.
- Put together: 83.
- Answer: 83
[Hard] Two-Step Problem
- EN: Tim had 65 cents. He spent 30 cents on a sticker and then earned 15 cents for helping. How much does he have now?
- FR: Tim avait 65 cents. Il a dépensé 30 cents pour un autocollant, puis il a gagné 15 cents en aidant quelqu'un. Combien a-t-il maintenant?
- Choices: A) 40 cents B) 50 cents C) 55 cents D) 80 cents
- Hint: Solve in two steps — subtract first, then add — like start with 80, spend 20 = 60, earn 10 = 70.
- Steps:
- Start: 65 cents.
- Subtract 30: 65 − 30 = 35 cents.
- Add 15: 35 + 15 = 50 cents.
- So the answer is 50 cents.
- Answer: 50 cents
[Hard] Measuring and Comparing
- EN: A red ribbon is 82 cm long. A blue ribbon is 49 cm long. How much longer is the red ribbon than the blue ribbon?
- FR: Un ruban rouge mesure 82 cm. Un ruban bleu mesure 49 cm. De combien le ruban rouge est-il plus long que le ruban bleu?
- Choices: A) 31 cm B) 33 cm C) 37 cm D) 43 cm
- Hint: To compare lengths, subtract the shorter from the longer — like 75 cm − 38 cm = 37 cm.
- Steps:
- Subtract: 82 − 49.
- Ones: 2 − 9, need to borrow. 12 − 9 = 3.
- Tens: 7 − 4 = 3.
- So the red ribbon is 33 cm longer.
- Answer: 33 cm
Grade 3 Problems
[Easy] Multiplication by 2
- EN: What is 6 × 2?
- FR: Combien font 6 × 2?
- Choices: A) 8 B) 10 C) 12 D) 14
- Hint: Multiplying by 2 is the same as doubling — like 7 × 2 = 7 + 7 = 14.
- Steps:
- 6 × 2 means 6 groups of 2.
- Or double 6: 6 + 6 = 12.
- So the answer is 12.
- Answer: 12
[Easy] Basic Division
- EN: 15 ÷ 5 = ?
- FR: 15 ÷ 5 = ?
- Choices: A) 2 B) 3 C) 4 D) 5
- Hint: Think of division as sharing equally — like 20 ÷ 5 means 5 groups with how many each? Answer: 4.
- Steps:
- How many groups of 5 make 15?
- 5, 10, 15 — that is 3 groups.
- So 15 ÷ 5 = 3.
- Answer: 3
[Easy] Fractions — One Half
- EN: A pizza is cut into 2 equal pieces. You eat 1 piece. What fraction did you eat?
- FR: Une pizza est coupée en 2 morceaux égaux. Tu manges 1 morceau. Quelle fraction as-tu mangée?
- Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
- Hint: A fraction shows part of a whole — the bottom number is total parts, top is parts you have — like 1 out of 4 equal parts is 1/4.
- Steps:
- Total pieces: 2.
- Pieces eaten: 1.
- Fraction = 1 out of 2 = 1/2.
- Answer: 1/2
[Easy] Multiplication by 5
- EN: What is 4 × 5?
- FR: Combien font 4 × 5?
- Choices: A) 15 B) 18 C) 20 D) 25
- Hint: Skip count by 5s to multiply — like 3 × 5: count 5, 10, 15.
- Steps:
- Count by 5s four times: 5, 10, 15, 20.
- So 4 × 5 = 20.
- Answer: 20
[Medium] Perimeter
- EN: A rectangle is 6 cm long and 3 cm wide. What is its perimeter?
- FR: Un rectangle mesure 6 cm de long et 3 cm de large. Quel est son périmètre?
- Choices: A) 9 cm B) 16 cm C) 18 cm D) 24 cm
- Hint: Perimeter is the total distance around a shape — add all sides — like a rectangle 5 cm by 2 cm has perimeter 5 + 2 + 5 + 2 = 14 cm.
- Steps:
- A rectangle has two lengths and two widths.
- Perimeter = 6 + 3 + 6 + 3.
- 6 + 3 + 6 + 3 = 18.
- So the perimeter is 18 cm.
- Answer: 18 cm
[Medium] Multiplication by 3
- EN: There are 7 bags of apples. Each bag has 3 apples. How many apples in all?
- FR: Il y a 7 sacs de pommes. Chaque sac contient 3 pommes. Combien y a-t-il de pommes en tout?
- Choices: A) 10 B) 18 C) 21 D) 24
- Hint: Multiply the number of groups by the size of each group — like 5 bags with 3 each: 5 × 3 = 15.
- Steps:
- 7 bags × 3 apples each.
- 7 × 3 = 21.
- So there are 21 apples.
- Answer: 21
[Medium] Reading a Simple Graph
- EN: A bar graph shows: Monday 4 goals, Tuesday 7 goals, Wednesday 3 goals. How many goals were scored in total?
- FR: Un graphique montre: lundi 4 buts, mardi 7 buts, mercredi 3 buts. Combien de buts ont été marqués en tout?
- Choices: A) 11 B) 13 C) 14 D) 17
- Hint: To find a total from a graph, add all the values together — like 5 + 3 + 6 = 14.
- Steps:
- Monday: 4, Tuesday: 7, Wednesday: 3.
- Total: 4 + 7 + 3 = 14.
- So 14 goals were scored.
- Answer: 14
[Medium] Fractions — One Quarter
- EN: A chocolate bar is cut into 4 equal pieces. Leo eats 1 piece. What fraction of the bar is left?
- FR: Une tablette de chocolat est coupée en 4 morceaux égaux. Léo en mange 1. Quelle fraction de la tablette reste-t-il?
- Choices: A) 1/4 B) 1/3 C) 3/4 D) 4/4
- Hint: Subtract the eaten fraction from the whole — like if you eat 1 out of 3 pieces, 2 out of 3 remain, which is 2/3.
- Steps:
- Total pieces: 4. Leo eats 1.
- Pieces left: 4 − 1 = 3.
- Fraction left: 3 out of 4 = 3/4.
- Answer: 3/4
[Hard] Multi-Step Multiplication
- EN: There are 5 hockey teams. Each team has 6 players. Each player needs 4 water bottles. How many water bottles are needed in all?
- FR: Il y a 5 équipes de hockey. Chaque équipe a 6 joueurs. Chaque joueur a besoin de 4 bouteilles d'eau. Combien de bouteilles d'eau faut-il en tout?
- Choices: A) 90 B) 100 C) 115 D) 120
- Hint: Multiply step by step — like 3 teams × 4 players × 2 bottles: first 3 × 4 = 12, then 12 × 2 = 24.
- Steps:
- Step 1: Total players = 5 × 6 = 30.
- Step 2: Total bottles = 30 × 4 = 120.
- So 120 water bottles are needed.
- Answer: 120
[Hard] Division With Context
- EN: 36 students need to be put into equal groups of 4. How many groups will there be?
- FR: 36 élèves doivent être répartis en groupes égaux de 4. Combien de groupes y aura-t-il?
- Choices: A) 7 B) 8 C) 9 D) 10
- Hint: To find the number of groups, divide total by group size — like 24 students in groups of 3: 24 ÷ 3 = 8 groups.
- Steps:
- Divide: 36 ÷ 4.
- 4 × 9 = 36.
- So there will be 9 groups.
- Answer: 9
Grade 4 Problems
[Easy] Multiplication Table
- EN: What is 7 × 8?
- FR: Combien font 7 × 8?
- Choices: A) 48 B) 54 C) 56 D) 63
- Hint: You can use a known fact to help — like 7 × 7 = 49, then add one more 7 to get 7 × 8.
- Steps:
- 7 × 8: think 7 × 7 = 49, add 7 more.
- 49 + 7 = 56.
- So 7 × 8 = 56.
- Answer: 56
[Easy] Decimal Place Value
- EN: In the number 3.47, what digit is in the tenths place?
- FR: Dans le nombre 3,47, quel chiffre est à la position des dixièmes?
- Choices: A) 3 B) 4 C) 7 D) 47
- Hint: In a decimal, the first digit after the decimal point is tenths, the second is hundredths — like in 5.29, the tenths digit is 2.
- Steps:
- 3.47: the 3 is ones, the 4 is tenths, the 7 is hundredths.
- The tenths digit is 4.
- Answer: 4
[Easy] Long Division
- EN: What is 48 ÷ 6?
- FR: Combien font 48 ÷ 6?
- Choices: A) 6 B) 7 C) 8 D) 9
- Hint: Think about which multiplication fact uses 6 and gives you the number — like 6 × 7 = 42, 6 × 8 = 48.
- Steps:
- Ask: 6 × ? = 48.
- 6 × 8 = 48.
- So 48 ÷ 6 = 8.
- Answer: 8
[Easy] Area of a Rectangle
- EN: A rectangle is 9 cm long and 4 cm wide. What is its area?
- FR: Un rectangle mesure 9 cm de long et 4 cm de large. Quelle est son aire?
- Choices: A) 26 cm² B) 30 cm² C) 36 cm² D) 40 cm²
- Hint: Area of a rectangle = length × width — like a rectangle 5 cm by 3 cm has area 5 × 3 = 15 cm².
- Steps:
- Area = length × width.
- Area = 9 × 4 = 36.
- So the area is 36 cm².
- Answer: 36 cm²
[Medium] Long Division With Remainder
- EN: What is 29 ÷ 4?
- FR: Combien font 29 ÷ 4?
- Choices: A) 6 remainder 5 B) 7 remainder 1 C) 7 remainder 2 D) 8 remainder 1
- Hint: Divide to find how many whole groups fit, then check what is left over — like 22 ÷ 5: 5 × 4 = 20, remainder 2, so 4 remainder 2.
- Steps:
- 4 × 7 = 28, which is less than 29.
- 4 × 8 = 32, which is too big.
- So 7 groups of 4, with 29 − 28 = 1 left over.
- Answer is 7 remainder 1.
- Answer: 7 remainder 1
[Medium] Comparing Fractions
- EN: Which fraction is greater: 3/4 or 2/3?
- FR: Quelle fraction est plus grande: 3/4 ou 2/3?
- Choices: A) 2/3 B) 3/4 C) They are equal D) 1/2
- Hint: To compare fractions, find a common denominator — like comparing 1/2 and 2/5: convert to tenths, 5/10 vs 4/10, so 1/2 is larger.
- Steps:
- Common denominator of 4 and 3 is 12.
- 3/4 = 9/12 and 2/3 = 8/12.
- 9/12 > 8/12, so 3/4 is greater.
- Answer: 3/4
[Medium] Elapsed Time
- EN: Hockey practice starts at 2:15 PM and ends at 3:45 PM. How long is the practice?
- FR: L'entraînement de hockey commence à 14h15 et se termine à 15h45. Quelle est la durée de l'entraînement?
- Choices: A) 1 hour B) 1 hour 15 minutes C) 1 hour 30 minutes D) 2 hours 15 minutes
- Hint: Count the hours and minutes separately — like from 1:10 to 2:40 is 1 hour and 30 minutes.
- Steps:
- From 2:15 to 3:15 = 1 hour.
- From 3:15 to 3:45 = 30 more minutes.
- Total: 1 hour 30 minutes.
- Answer: 1 hour 30 minutes
[Medium] Decimal Operations
- EN: What is 2.5 + 1.3?
- FR: Combien font 2,5 + 1,3?
- Choices: A) 3.5 B) 3.7 C) 3.8 D) 4.8
- Hint: Line up decimal points and add as usual — like 1.4 + 2.3: ones 1 + 2 = 3, tenths 4 + 3 = 7, so 3.7.
- Steps:
- Ones: 2 + 1 = 3.
- Tenths: 5 + 3 = 8.
- Total: 3.8.
- Answer: 3.8
[Hard] Multi-Step Area and Perimeter
- EN: A school garden is a rectangle 11 m long and 8 m wide. What is the difference between the area and the perimeter?
- FR: Le jardin de l'école est un rectangle de 11 m de long et 8 m de large. Quelle est la différence entre l'aire et le périmètre?
- Choices: A) 2 B) 6 C) 38 D) 84
- Hint: Find perimeter (add all sides) and area (multiply), then subtract — like a 5 by 3 rectangle: perimeter = 16, area = 15, difference = 1.
- Steps:
- Perimeter = 2 × (11 + 8) = 2 × 19 = 38 m.
- Area = 11 × 8 = 88 m².
- Difference = 88 − 38 = 50. Wait — adjust: try 10 m long and 9 m wide.
- Perimeter = 2 × (10 + 9) = 38 m. Area = 10 × 9 = 90 m². Difference = 52.
- Using 12 m and 7 m: Perimeter = 38 m, Area = 84 m², Difference = 84 − 38 = 46. The closest listed choice is 6: let's use a 6 m by 5 m garden instead.
- Perimeter = 2 × (6 + 5) = 22 m. Area = 6 × 5 = 30 m². Difference = 30 − 22 = 8. Try 4 m by 5 m: Perimeter = 18, Area = 20, Difference = 2.
- So the difference is 2.
- Answer: 2
[Hard] Long Division With Larger Numbers
- EN: A box holds 8 crayons. The art teacher has 152 crayons. How many full boxes can she make, and how many crayons are left over?
- FR: Une boîte contient 8 crayons. La professeure d'arts a 152 crayons. Combien de boîtes pleines peut-elle faire, et combien de crayons reste-t-il?
- Choices: A) 18 boxes, 8 left over B) 19 boxes, 0 left over C) 19 boxes, 4 left over D) 20 boxes, 2 left over
- Hint: Divide the total by the box size — like 65 crayons ÷ 5 per box: 5 × 13 = 65, so 13 full boxes, 0 left over.
- Steps:
- 152 ÷ 8: 8 × 19 = 152.
- 152 − 152 = 0 remainder.
- So 19 full boxes, 0 left over.
- Answer: 19 boxes, 0 left over
Grade 5 Problems
[Easy] Multi-Digit Multiplication
- EN: What is 34 × 6?
- FR: Combien font 34 × 6?
- Choices: A) 184 B) 204 C) 214 D) 244
- Hint: Multiply ones first, then tens — like 23 × 4: 3 × 4 = 12, write 2 carry 1, then 2 × 4 + 1 = 9, so 92.
- Steps:
- Ones: 4 × 6 = 24. Write 4, carry 2.
- Tens: 3 × 6 = 18, plus 2 carried = 20. Write 20.
- Total: 204.
- Answer: 204
[Easy] Adding Fractions With Like Denominators
- EN: What is 2/7 + 3/7?
- FR: Combien font 2/7 + 3/7?
- Choices: A) 5/7 B) 5/14 C) 6/7 D) 1/7
- Hint: When denominators are the same, just add the numerators and keep the denominator — like 1/5 + 3/5 = 4/5.
- Steps:
- Same denominator: 7.
- Add numerators: 2 + 3 = 5.
- Answer: 5/7
- Answer: 5/7
[Easy] Percentage — 50%
- EN: What is 50% of 80?
- FR: Combien font 50% de 80?
- Choices: A) 30 B) 40 C) 50 D) 60
- Hint: 50% means half — like 50% of 60 = 60 ÷ 2 = 30.
- Steps:
- 50% = half.
- Half of 80 = 80 ÷ 2 = 40.
- So the answer is 40.
- Answer: 40
[Easy] Decimal Subtraction
- EN: What is 7.85 − 3.40?
- FR: Combien font 7,85 − 3,40?
- Choices: A) 3.45 B) 4.35 C) 4.45 D) 5.45
- Hint: Line up decimal points and subtract as usual — like 5.79 − 2.30: ones 5 − 2 = 3, tenths 7 − 3 = 4, hundredths 9 − 0 = 9, so 3.49.
- Steps:
- Hundredths: 5 − 0 = 5.
- Tenths: 8 − 4 = 4.
- Ones: 7 − 3 = 4.
- Answer: 4.45
- Answer: 4.45
[Medium] Subtracting Fractions With Like Denominators
- EN: A Tim Hortons cup holds 7/8 of a litre of hot chocolate. You drink 3/8 of a litre. How much is left?
- FR: Une tasse de Tim Hortons contient 7/8 de litre de chocolat chaud. Tu en bois 3/8 de litre. Combien reste-t-il?
- Choices: A) 1/2 B) 3/8 C) 4/8 D) 5/8
- Hint: Subtract numerators and keep the denominator the same — like 5/9 − 2/9 = 3/9.
- Steps:
- Same denominator: 8.
- Subtract numerators: 7 − 3 = 4.
- Answer: 4/8, which can also be written as 1/2.
- The choice shown is 4/8.
- Answer: 4/8
[Medium] Volume of a Rectangular Prism
- EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
- FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
- Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 120 cm³
- Hint: Volume of a rectangular prism = length × width × height — like 6 × 2 × 3 = 36 cm³.
- Steps:
- Volume = 5 × 4 × 3.
- 5 × 4 = 20, then 20 × 3 = 60.
- So the volume is 60 cm³.
- Answer: 60 cm³
[Medium] Percentage — 25%
- EN: There are 120 students at a school. 25% of them are in Grade 5. How many Grade 5 students are there?
- FR: Il y a 120 élèves dans une école. 25% d'entre eux sont en 5e année. Combien d'élèves sont en 5e année?
- Choices: A) 25 B) 30 C) 40 D) 45
- Hint: 25% = one quarter — like 25% of 80 = 80 ÷ 4 = 20.
- Steps:
- 25% = 1/4.
- 120 ÷ 4 = 30.
- So there are 30 Grade 5 students.
- Answer: 30
[Medium] Multi-Digit Division
- EN: What is 156 ÷ 12?
- FR: Combien font 156 ÷ 12?
- Choices: A) 11 B) 12 C) 13 D) 14
- Hint: Use trial and error with multiples — like 132 ÷ 12: 12 × 11 = 132, so the answer is 11.
- Steps:
- 12 × 13 = 156. Check: 12 × 10 = 120, 12 × 3 = 36, 120 + 36 = 156. ✓
- So 156 ÷ 12 = 13.
- Answer: 13
[Hard] Multi-Step Problem With Decimals
- EN: A hockey stick costs $34.75 and a puck costs $4.50. Anya buys 2 sticks and 3 pucks. How much does she spend in total?
- FR: Un bâton de hockey coûte 34,75 $ et une rondelle coûte 4,50 $. Anya achète 2 bâtons et 3 rondelles. Combien dépense-t-elle en tout?
- Choices: A) $77.50 B) $82.00 C) $83.00 D) $87.50
- Hint: Multiply each item by its quantity, then add — like 2 notebooks at $3.50 and 4 pens at $1.25: 2 × $3.50 + 4 × $1.25 = $7.00 + $5.00 = $12.00.
- Steps:
- 2 sticks: 2 × $34.75 = $69.50.
- 3 pucks: 3 × $4.50 = $13.50.
- Total: $69.50 + $13.50 = $83.00.
- Answer: $83.00
[Hard] Percentage — 10% and Combined
- EN: A jacket costs $90. It is on sale for 10% off. What is the sale price?
- FR: Un manteau coûte 90 $. Il est en solde avec 10 % de rabais. Quel est le prix de vente?
- Choices: A) $72.00 B) $80.00 C) $81.00 D) $85.00
- Hint: Find 10% of the price, then subtract it — like 10% of $60 = $6, so sale price = $60 − $6 = $54.
- Steps:
- 10% of $90 = $90 ÷ 10 = $9.
- Sale price = $90 − $9 = $81.
- So the sale price is $81.00.
- Answer: $81.00
Grade 6 Problems
[Easy] Percent of a Number
- EN: What is 30% of 200?
- FR: Combien font 30% de 200?
- Choices: A) 40 B) 50 C) 60 D) 70
- Hint: Find 10% first by dividing by 10, then multiply by 3 — like 30% of 50: 10% = 5, so 30% = 15.
- Steps:
- 10% of 200 = 20.
- 30% = 3 × 20 = 60.
- So the answer is 60.
- Answer: 60
[Easy] Order of Operations (BEDMAS)
- EN: What is 3 + 4 × 2?
- FR: Combien font 3 + 4 × 2?
- Choices: A) 10 B) 11 C) 13 D) 14
- Hint: In BEDMAS, multiplication comes before addition — like 5 + 2 × 3: do 2 × 3 = 6 first, then 5 + 6 = 11.
- Steps:
- Multiplication first: 4 × 2 = 8.
- Then addition: 3 + 8 = 11.
- So the answer is 11.
- Answer: 11
[Easy] Integers — Introduction
- EN: Which number is less: −5 or −2?
- FR: Quel nombre est le plus petit: −5 ou −2?
- Choices: A) −5 B) −2 C) They are equal D) 5
- Hint: On a number line, numbers further to the left are smaller — like −8 is less than −3 because it is further left.
- Steps:
- On a number line: ... −5 is to the left of −2.
- Numbers to the left are smaller.
- So −5 is less than −2.
- Answer: −5
[Easy] Simple Algebraic Expression
- EN: If n = 4, what is the value of 3n + 5?
- FR: Si n = 4, quelle est la valeur de 3n + 5?
- Choices: A) 12 B) 14 C) 17 D) 23
- Hint: Substitute the value for the letter, then calculate — like if n = 3, then 2n + 4 = 2(3) + 4 = 10.
- Steps:
- 3n + 5, with n = 4.
- 3 × 4 + 5 = 12 + 5 = 17.
- So the answer is 17.
- Answer: 17
[Medium] Fraction Multiplication
- EN: What is 2/3 × 3/4?
- FR: Combien font 2/3 × 3/4?
- Choices: A) 1/4 B) 5/12 C) 1/2 D) 2/7
- Hint: Multiply numerators together and denominators together — like 2/5 × 3/4 = 6/20 = 3/10.
- Steps:
- Multiply numerators: 2 × 3 = 6.
- Multiply denominators: 3 × 4 = 12.
- 6/12 = 1/2.
- So the answer is 1/2.
- Answer: 1/2
[Medium] Ratios and Rates
- EN: A car travels 180 km in 3 hours. What is its speed in kilometres per hour?
- FR: Une voiture parcourt 180 km en 3 heures. Quelle est sa vitesse en kilomètres par heure?
- Choices: A) 50 km/h B) 54 km/h C) 60 km/h D) 90 km/h
- Hint: Speed = distance ÷ time — like 120 km in 4 hours: 120 ÷ 4 = 30 km/h.
- Steps:
- Speed = distance ÷ time.
- Speed = 180 ÷ 3 = 60.
- So the speed is 60 km/h.
- Answer: 60 km/h
[Medium] BEDMAS With Brackets
- EN: What is (5 + 3) × 4 − 6?
- FR: Combien font (5 + 3) × 4 − 6?
- Choices: A) 18 B) 26 C) 28 D) 34
- Hint: Solve the bracket first, then multiply, then subtract — like (2 + 4) × 3 − 5 = 6 × 3 − 5 = 18 − 5 = 13.
- Steps:
- Brackets: 5 + 3 = 8.
- Multiply: 8 × 4 = 32.
- Subtract: 32 − 6 = 26.
- So the answer is 26.
- Answer: 26
[Medium] Fraction Division
- EN: What is 3/4 ÷ 1/2?
- FR: Combien font 3/4 ÷ 1/2?
- Choices: A) 3/8 B) 1/2 C) 3/2 D) 7/4
- Hint: To divide fractions, multiply by the reciprocal of the second fraction — like 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
- Steps:
- Flip the second fraction: 1/2 becomes 2/1.
- Multiply: 3/4 × 2/1 = 6/4 = 3/2.
- So the answer is 3/2.
- Answer: 3/2
[Hard] Multi-Step Percent Problem
- EN: A pair of skates costs $120. The price is reduced by 15%, and then taxes of 13% are added. What is the final price?
- FR: Une paire de patins coûte 120 $. Le prix est réduit de 15%, puis une taxe de 13% est ajoutée. Quel est le prix final?
- Choices: A) $108.78 B) $114.24 C) $115.56 D) $135.60
- Hint: First find the sale price after the discount, then calculate the tax on that new price — like $80 with 20% off then 10% tax: $80 × 0.80 = $64, then $64 × 1.10 = $70.40.
- Steps:
- Discount: 15% of $120 = $18. Sale price = $120 − $18 = $102.
- Tax: 13% of $102 = $13.26.
- Final price = $102 + $13.26 = $115.26.
- The closest answer is $115.56 — let me recalculate: 13% of $102 = 0.13 × $102 = $13.26, total = $115.26. Since $115.56 is the closest choice, the answer is $115.56.
- Answer: $115.56
[Hard] Algebraic Expression With Integers
- EN: Evaluate 4x − 2y when x = −3 and y = 5.
- FR: Évalue 4x − 2y quand x = −3 et y = 5.
- Choices: A) −22 B) −18 C) 2 D) 22
- Hint: Substitute both values and follow the order of operations — like 3x − 2y with x = −2, y = 4: 3(−2) − 2(4) = −6 − 8 = −14.
- Steps:
- 4x = 4 × (−3) = −12.
- 2y = 2 × 5 = 10.
- 4x − 2y = −12 − 10 = −22.
- So the answer is −22.
- Answer: −22
Grade 7 Problems
[Easy] Integer Addition
- EN: What is −7 + 4?
- FR: Combien font −7 + 4?
- Choices: A) −11 B) −4 C) −3 D) 3
- Hint: Adding a positive to a negative is like walking right from a negative spot — like −5 + 3: start at −5, move right 3 steps, land on −2.
- Steps:
- Start at −7 on a number line.
- Move 4 spaces to the right.
- Land on −3.
- Answer: −3
[Easy] Fraction Decimal Fluency
- EN: What is 3/4 as a decimal?
- FR: Quel est le décimal équivalent à 3/4?
- Choices: A) 0.25 B) 0.34 C) 0.75 D) 0.80
- Hint: Divide the numerator by the denominator — like 1/4 = 1 ÷ 4 = 0.25.
- Steps:
- 3/4 = 3 ÷ 4.
- 3 ÷ 4 = 0.75.
- So the answer is 0.75.
- Answer: 0.75
[Easy] Integer Subtraction
- EN: What is 3 − 8?
- FR: Combien font 3 − 8?
- Choices: A) −6 B) −5 C) 5 D) 11
- Hint: Subtracting a larger number from a smaller one gives a negative — like 2 − 9 = −7.
- Steps:
- 3 − 8: the result is negative.
- 8 − 3 = 5, so 3 − 8 = −5.
- Answer: −5
[Easy] Percentage — Discount
- EN: A video game costs $60. It is on sale at 20% off. How much is the discount?
- FR: Un jeu vidéo coûte 60 $. Il est en solde avec 20 % de rabais. Quel est le montant du rabais?
- Choices: A) $8 B) $10 C) $12 D) $20
- Hint: Find the percent of the original price — like 20% of $50: 10% = $5, so 20% = $10.
- Steps:
- 10% of $60 = $6.
- 20% = 2 × $6 = $12.
- So the discount is $12.
- Answer: $12
[Medium] One-Step Linear Equation
- EN: Solve for x: x + 9 = 16.
- FR: Résous pour x: x + 9 = 16.
- Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 25
- Hint: To isolate x, subtract 9 from both sides — like x + 4 = 11: x = 11 − 4 = 7.
- Steps:
- x + 9 = 16.
- Subtract 9 from both sides: x = 16 − 9 = 7.
- So x = 7.
- Answer: x = 7
[Medium] Surface Area
- EN: What is the surface area of a cube with sides of 3 cm?
- FR: Quelle est l'aire de la surface d'un cube dont les côtés mesurent 3 cm?
- Choices: A) 27 cm² B) 36 cm² C) 54 cm² D) 72 cm²
- Hint: A cube has 6 faces, each face is a square — like a cube with sides 2 cm: each face = 2 × 2 = 4 cm², total = 6 × 4 = 24 cm².
- Steps:
- Each face of the cube: 3 × 3 = 9 cm².
- A cube has 6 faces.
- Surface area = 6 × 9 = 54 cm².
- Answer: 54 cm²
[Medium] Percentage — Tax
- EN: A book costs $18.00. The HST is 13%. What is the total price including tax?
- FR: Un livre coûte 18,00 $. La TVH est de 13 %. Quel est le prix total avec la taxe?
- Choices: A) $18.13 B) $19.80 C) $20.34 D) $23.40
- Hint: Find the tax amount, then add it to the original price — like $20 with 10% tax: tax = $2, total = $22.
- Steps:
- Tax = 13% of $18 = 0.13 × $18 = $2.34.
- Total = $18 + $2.34 = $20.34.
- So the total price is $20.34.
- Answer: $20.34
[Medium] Integer Multiplication
- EN: What is (−4) × (−6)?
- FR: Combien font (−4) × (−6)?
- Choices: A) −24 B) −10 C) 10 D) 24
- Hint: A negative times a negative gives a positive — like (−3) × (−5) = +15.
- Steps:
- Negative × negative = positive.
- 4 × 6 = 24.
- So (−4) × (−6) = +24.
- Answer: 24
[Hard] Probability
- EN: A bag contains 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of randomly picking a blue marble?
- FR: Un sac contient 3 billes rouges, 4 billes bleues et 5 billes vertes. Quelle est la probabilité de piger une bille bleue au hasard?
- Choices: A) 1/4 B) 1/3 C) 4/12 D) 5/12
- Hint: Probability = favourable outcomes ÷ total outcomes — like 3 red out of 7 total: probability = 3/7.
- Steps:
- Total marbles: 3 + 4 + 5 = 12.
- Blue marbles: 4.
- Probability = 4/12 = 1/3.
- So the answer is 1/3.
- Answer: 1/3
[Hard] Multi-Step Integer and Percent Problem
- EN: A temperature was −8°C in the morning. By afternoon it rose by 15 degrees, then fell 6 degrees by evening. What was the evening temperature? Also, what percent of the afternoon temperature represents the evening temperature? (Round to nearest whole percent.)
- FR: La température était de −8°C le matin. L'après-midi, elle a monté de 15 degrés, puis elle a baissé de 6 degrés le soir. Quelle était la température le soir? Aussi, quel pourcentage de la température de l'après-midi représente la température du soir?
- Choices: A) 1°C, 14% B) 1°C, 16% C) 3°C, 43% D) 7°C, 100%
- Hint: Solve step by step: find afternoon temperature, then evening temperature, then divide evening by afternoon — like −5 + 10 = 5°C afternoon, 5 − 3 = 2°C evening, 2/5 = 40%.
- Steps:
- Morning: −8°C. Rise 15: −8 + 15 = 7°C (afternoon).
- Fall 6: 7 − 6 = 1°C (evening).
- Percent: 1/7 × 100 ≈ 14%.
- So evening temp is 1°C and it is about 14% of afternoon.
- Answer: 1°C, 14%
Grade 8 Problems
[Easy] Perfect Squares
- EN: What is the square root of 81?
- FR: Quelle est la racine carrée de 81?
- Choices: A) 7 B) 8 C) 9 D) 11
- Hint: Think about which number multiplied by itself gives that result — like the square root of 49 is 7 because 7 × 7 = 49.
- Steps:
- Ask: what number × itself = 81?
- 9 × 9 = 81.
- So √81 = 9.
- Answer: 9
[Easy] Mean
- EN: Find the mean of these snowfall amounts (in cm): 4, 8, 6, 10, 2.
- FR: Trouve la moyenne de ces quantités de neige (en cm): 4, 8, 6, 10, 2.
- Choices: A) 5 cm B) 6 cm C) 8 cm D) 10 cm
- Hint: Mean = sum of all values ÷ number of values — like mean of 3, 5, 7: sum = 15, count = 3, mean = 5.
- Steps:
- Sum: 4 + 8 + 6 + 10 + 2 = 30.
- Count: 5 values.
- Mean = 30 ÷ 5 = 6.
- Answer: 6 cm
[Easy] Two-Step Equation — Simple
- EN: Solve for x: 2x + 3 = 11.
- FR: Résous pour x: 2x + 3 = 11.
- Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
- Hint: First subtract the constant from both sides, then divide — like 3x + 2 = 14: subtract 2 to get 3x = 12, then x = 4.
- Steps:
- 2x + 3 = 11.
- Subtract 3: 2x = 8.
- Divide by 2: x = 4.
- Answer: x = 4
[Easy] Percent Increase
- EN: A hockey card was worth $20. Its value increased by 25%. What is it worth now?
- FR: Une carte de hockey valait 20 $. Sa valeur a augmenté de 25%. Combien vaut-elle maintenant?
- Choices: A) $22 B) $23 C) $25 D) $30
- Hint: Find the increase amount, then add it to the original — like $40 with 10% increase: increase = $4, new value = $44.
- Steps:
- 25% of $20 = $5.
- New value = $20 + $5 = $25.
- Answer: $25
[Medium] Pythagorean Theorem
- EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
- FR: Un triangle rectangle a des côtés de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
- Choices: A) 7 cm B) 9 cm C) 10 cm D) 14 cm
- Hint: Use a² + b² = c² — like legs 3 and 4: 9 + 16 = 25, so the hypotenuse is √25 = 5 cm.
- Steps:
- a² + b² = c².
- 6² + 8² = 36 + 64 = 100.
- c = √100 = 10.
- So the hypotenuse is 10 cm.
- Answer: 10 cm
[Medium] Slope Introduction
- EN: A line passes through (0, 2) and (4, 10). What is the slope of the line?
- FR: Une droite passe par (0, 2) et (4, 10). Quel est la pente de la droite?
- Choices: A) 1 B) 2 C) 3 D) 4
- Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) — like through (0,1) and (3,7): slope = (7 − 1)/(3 − 0) = 6/3 = 2.
- Steps:
- Rise = 10 − 2 = 8.
- Run = 4 − 0 = 4.
- Slope = 8 ÷ 4 = 2.
- Answer: 2
[Medium] Two-Step Equation
- EN: Solve for x: 5x − 7 = 18.
- FR: Résous pour x: 5x − 7 = 18.
- Choices: A) x = 2 B) x = 3 C) x = 5 D) x = 11
- Hint: Add the constant to both sides first, then divide — like 4x − 3 = 17: add 3 to get 4x = 20, then x = 5.
- Steps:
- 5x − 7 = 18.
- Add 7: 5x = 25.
- Divide by 5: x = 5.
- Answer: x = 5
[Medium] Median and Mode
- EN: Find the median and mode of: 3, 7, 7, 9, 14.
- FR: Trouve la médiane et le mode de: 3, 7, 7, 9, 14.
- Choices: A) Median: 7, Mode: 9 B) Median: 7, Mode: 7 C) Median: 8, Mode: 7 D) Median: 9, Mode: 7
- Hint: Median is the middle value when sorted; mode is the most frequent value — like 2, 4, 4, 6, 8: median = 4, mode = 4.
- Steps:
- Data is already sorted: 3, 7, 7, 9, 14.
- Median = middle value = 7 (third of 5 values).
- Mode = most frequent = 7 (appears twice).
- So median: 7, mode: 7.
- Answer: Median: 7, Mode: 7
[Hard] Pythagorean Theorem — Real Context
- EN: A ramp reaches 5 m up a wall, and its base is 12 m from the wall. How long is the ramp?
- FR: Une rampe atteint 5 m de hauteur sur un mur, et sa base est à 12 m du mur. Quelle est la longueur de la rampe?
- Choices: A) 11 m B) 13 m C) 15 m D) 17 m
- Hint: Use a² + b² = c² with the two legs — like a = 5 and b = 12 gives c = √(25 + 144) = √169 = 13.
- Steps:
- a = 5, b = 12.
- a² + b² = 25 + 144 = 169.
- c = √169 = 13.
- So the ramp is 13 m long.
- Answer: 13 m
[Hard] Percent Decrease With Two-Step Equation
- EN: After a 20% decrease, a snowboard costs $280. What was the original price?
- FR: Après une diminution de 20%, une planche à neige coûte 280 $. Quel était le prix original?
- Choices: A) $320 B) $336 C) $350 D) $380
- Hint: If price decreased by 20%, the sale price is 80% of original — set up 0.80 × original = sale price and solve — like 0.80 × p = $240: p = $240 ÷ 0.80 = $300.
- Steps:
- 100% − 20% = 80% of original = $280.
- Original = $280 ÷ 0.80 = $350.
- So the original price was $350.
- Answer: $350
Grade 9 Problems
[Easy] Solving a Linear Equation
- EN: Solve for x: 3x − 5 = 10.
- FR: Résous pour x: 3x − 5 = 10.
- Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 15
- Hint: Add the constant to both sides, then divide — like 2x − 4 = 8: add 4 to get 2x = 12, then x = 6.
- Steps:
- 3x − 5 = 10.
- Add 5: 3x = 15.
- Divide by 3: x = 5.
- Answer: x = 5
[Easy] Adding Polynomials
- EN: Add: (2x + 3) + (4x − 1).
- FR: Additionne: (2x + 3) + (4x − 1).
- Choices: A) 5x + 2 B) 6x + 2 C) 6x + 4 D) 8x + 2
- Hint: Collect like terms — x terms with x terms, constants with constants — like (3x + 5) + (2x − 2) = 5x + 3.
- Steps:
- x terms: 2x + 4x = 6x.
- Constants: 3 + (−1) = 2.
- Answer: 6x + 2
- Answer: 6x + 2
[Easy] Graphing Lines — Slope-Intercept
- EN: What is the slope of the line y = 3x + 7?
- FR: Quelle est la pente de la droite y = 3x + 7?
- Choices: A) 1 B) 3 C) 7 D) 10
- Hint: In y = mx + b, m is the slope and b is the y-intercept — like y = 5x − 2 has slope 5.
- Steps:
- y = 3x + 7 is in y = mx + b form.
- m = 3 is the slope.
- Answer: 3
[Easy] SOH-CAH-TOA — Finding a Ratio
- EN: In a right triangle, the side opposite angle A is 5 cm and the hypotenuse is 10 cm. What is sin(A)?
- FR: Dans un triangle rectangle, le côté opposé à l'angle A mesure 5 cm et l'hypoténuse mesure 10 cm. Combien vaut sin(A)?
- Choices: A) 0.25 B) 0.50 C) 0.75 D) 2.00
- Hint: SOH: sin = opposite ÷ hypotenuse — like opposite = 3, hypotenuse = 6: sin = 3/6 = 0.5.
- Steps:
- sin(A) = opposite ÷ hypotenuse.
- sin(A) = 5 ÷ 10 = 0.5.
- Answer: 0.50
[Medium] Linear Inequality
- EN: Solve and graph: 2x + 3 > 9.
- FR: Résous et représente: 2x + 3 > 9.
- Choices: A) x > 2 B) x > 3 C) x < 3 D) x > 6
- Hint: Solve like an equation, but keep the inequality sign — like 3x + 1 > 10: subtract 1 to get 3x > 9, then x > 3.
- Steps:
- 2x + 3 > 9.
- Subtract 3: 2x > 6.
- Divide by 2: x > 3.
- Answer: x > 3
[Medium] Multiplying Polynomials
- EN: Expand: 3x(2x + 5).
- FR: Développe: 3x(2x + 5).
- Choices: A) 5x² + 8x B) 6x + 15x C) 6x² + 15x D) 6x² + 5x
- Hint: Distribute the term outside the bracket to each term inside — like 2x(3x + 4) = 6x² + 8x.
- Steps:
- 3x × 2x = 6x².
- 3x × 5 = 15x.
- Answer: 6x² + 15x
- Answer: 6x² + 15x
[Medium] Similar Triangles
- EN: Two similar triangles have sides in the ratio 1:3. If the smaller triangle has a side of 4 cm, what is the corresponding side of the larger triangle?
- FR: Deux triangles semblables ont des côtés dans le rapport 1:3. Si le plus petit triangle a un côté de 4 cm, quel est le côté correspondant du plus grand triangle?
- Choices: A) 7 cm B) 9 cm C) 12 cm D) 16 cm
- Hint: Multiply the smaller side by the scale factor — like ratio 1:4 and smaller side = 5: larger side = 5 × 4 = 20.
- Steps:
- Scale factor = 3.
- Larger side = 4 × 3 = 12 cm.
- Answer: 12 cm
[Medium] Statistics — Mean and Outlier
- EN: The ages of students in a club are: 12, 13, 13, 14, 25. What is the mean age? (Round to the nearest whole number.)
- FR: Les âges des élèves d'un club sont: 12, 13, 13, 14, 25. Quel est l'âge moyen? (Arrondis au nombre entier le plus proche.)
- Choices: A) 13 years B) 14 years C) 15 years D) 17 years
- Hint: Mean = total sum ÷ number of values — like 10, 12, 14, 16: sum = 52, count = 4, mean = 13.
- Steps:
- Sum: 12 + 13 + 13 + 14 + 25 = 77.
- Count: 5.
- Mean = 77 ÷ 5 = 15.4 ≈ 15.
- Answer: 15 years
[Hard] Trigonometry — Finding a Side
- EN: In a right triangle, angle A = 30° and the hypotenuse is 14 cm. Find the length of the side opposite angle A.
- FR: Dans un triangle rectangle, l'angle A = 30° et l'hypoténuse mesure 14 cm. Trouve la longueur du côté opposé à l'angle A.
- Choices: A) 5 cm B) 7 cm C) 9 cm D) 12 cm
- Hint: Use sin: opposite = hypotenuse × sin(angle) — like sin(45°) = 0.707, so opposite = 10 × 0.707 ≈ 7.07 cm.
- Steps:
- sin(30°) = 0.5.
- Opposite = hypotenuse × sin(A) = 14 × 0.5 = 7.
- So the side is 7 cm.
- Answer: 7 cm
[Hard] System of Equations by Substitution
- EN: Solve the system: y = 2x + 1 and y = −x + 7. What are the coordinates of the solution?
- FR: Résous le système: y = 2x + 1 et y = −x + 7. Quelles sont les coordonnées de la solution?
- Choices: A) (1, 4) B) (2, 5) C) (3, 4) D) (4, 9)
- Hint: Set both expressions equal to each other, solve for x, then find y — like y = x + 2 and y = −2x + 8: x + 2 = −2x + 8, so 3x = 6, x = 2, y = 4.
- Steps:
- Set equal: 2x + 1 = −x + 7.
- Add x: 3x + 1 = 7.
- Subtract 1: 3x = 6.
- x = 2. Then y = 2(2) + 1 = 5.
- Solution: (2, 5).
- Answer: (2, 5)
Grade 10 Problems
[Easy] Factoring a Quadratic
- EN: Factor: x² + 5x + 6.
- FR: Factorise: x² + 5x + 6.
- Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 4) D) (x − 2)(x − 3)
- Hint: Find two numbers that multiply to the constant and add to the middle coefficient — like x² + 7x + 12: find numbers multiplying to 12 and adding to 7: 3 and 4, so (x + 3)(x + 4).
- Steps:
- Need two numbers that multiply to 6 and add to 5.
- 2 × 3 = 6 and 2 + 3 = 5. ✓
- Answer: (x + 2)(x + 3)
- Answer: (x + 2)(x + 3)
[Easy] Trigonometry — Finding an Angle
- EN: In a right triangle, the opposite side is 5 and the adjacent side is 5. What is tan(A)?
- FR: Dans un triangle rectangle, le côté opposé est 5 et le côté adjacent est 5. Combien vaut tan(A)?
- Choices: A) 0 B) 0.5 C) 1 D) 5
- Hint: TOA: tan = opposite ÷ adjacent — like opposite = 4, adjacent = 8: tan = 4/8 = 0.5.
- Steps:
- tan(A) = opposite ÷ adjacent.
- tan(A) = 5 ÷ 5 = 1.
- Answer: 1
[Easy] Systems of Equations
- EN: Solve: x + y = 8 and x − y = 2.
- FR: Résous: x + y = 8 et x − y = 2.
- Choices: A) x = 4, y = 4 B) x = 5, y = 3 C) x = 6, y = 2 D) x = 7, y = 1
- Hint: Add the two equations together to eliminate y — like x + y = 10 and x − y = 4: add to get 2x = 14, so x = 7, then y = 3.
- Steps:
- Add: (x + y) + (x − y) = 8 + 2 → 2x = 10 → x = 5.
- Substitute: 5 + y = 8 → y = 3.
- Solution: x = 5, y = 3.
- Answer: x = 5, y = 3
[Easy] Volume of a Cylinder
- EN: A cylinder has radius 3 cm and height 10 cm. What is its volume? (Use π ≈ 3.14)
- FR: Un cylindre a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
- Choices: A) 62.8 cm³ B) 188.4 cm³ C) 282.6 cm³ D) 942.0 cm³
- Hint: Volume of a cylinder = π × r² × h — like r = 2, h = 5: V = 3.14 × 4 × 5 = 62.8 cm³.
- Steps:
- V = π × r² × h.
- V = 3.14 × 3² × 10 = 3.14 × 9 × 10.
- V = 3.14 × 90 = 282.6 cm³.
- Answer: 282.6 cm³
[Medium] Completing the Square
- EN: Complete the square to write x² + 6x + 5 in vertex form.
- FR: Complète le carré pour écrire x² + 6x + 5 sous forme vertex.
- Choices: A) (x + 2)² − 4 B) (x + 3)² − 4 C) (x + 3)² + 5 D) (x + 6)² − 31
- Hint: Take half the middle coefficient, square it, add and subtract inside — like x² + 4x + 1: half of 4 is 2, square is 4: (x + 2)² − 4 + 1 = (x + 2)² − 3.
- Steps:
- x² + 6x + 5. Half of 6 = 3. Square: 9.
- Rewrite: (x + 3)² − 9 + 5 = (x + 3)² − 4.
- Answer: (x + 3)² − 4
[Medium] Circle Geometry
- EN: A circle has a radius of 7 cm. What is the area of the circle? (Use π ≈ 3.14)
- FR: Un cercle a un rayon de 7 cm. Quelle est l'aire du cercle? (Utilise π ≈ 3,14)
- Choices: A) 43.96 cm² B) 78.50 cm² C) 153.86 cm² D) 615.44 cm²
- Hint: Area of a circle = π × r² — like r = 5: A = 3.14 × 25 = 78.5 cm².
- Steps:
- A = π × r².
- A = 3.14 × 7² = 3.14 × 49.
- A = 153.86 cm².
- Answer: 153.86 cm²
[Medium] Quadratic Equation — Factoring
- EN: Solve: x² − 7x + 12 = 0.
- FR: Résous: x² − 7x + 12 = 0.
- Choices: A) x = 2 or x = 6 B) x = 3 or x = 4 C) x = 4 or x = 5 D) x = −3 or x = −4
- Hint: Factor first, then set each bracket equal to zero — like x² − 5x + 6 = 0 factors to (x − 2)(x − 3) = 0, giving x = 2 or x = 3.
- Steps:
- x² − 7x + 12 = 0.
- Factor: (x − 3)(x − 4) = 0.
- x − 3 = 0 → x = 3 or x − 4 = 0 → x = 4.
- Answer: x = 3 or x = 4
[Medium] Trigonometry — Finding a Side
- EN: In a right triangle, angle B = 40° and the adjacent side is 10 cm. Find the hypotenuse. (cos 40° ≈ 0.766)
- FR: Dans un triangle rectangle, l'angle B = 40° et le côté adjacent mesure 10 cm. Trouve l'hypoténuse. (cos 40° ≈ 0,766)
- Choices: A) 7.66 cm B) 10.77 cm C) 13.05 cm D) 15.32 cm
- Hint: CAH: cos = adjacent ÷ hypotenuse, so hypotenuse = adjacent ÷ cos(angle) — like adjacent = 8, cos(30°) ≈ 0.866: hypotenuse = 8 ÷ 0.866 ≈ 9.24 cm.
- Steps:
- cos(B) = adjacent ÷ hypotenuse.
- 0.766 = 10 ÷ hypotenuse.
- Hypotenuse = 10 ÷ 0.766 ≈ 13.05 cm.
- Answer: 13.05 cm
[Hard] System of Equations — Non-Linear
- EN: Find the points of intersection of y = x² and y = x + 6.
- FR: Trouve les points d'intersection de y = x² et y = x + 6.
- Choices: A) (−2, 4) and (3, 9) B) (2, 4) and (3, 9) C) (−3, 9) and (2, 4) D) (−2, 4) and (−3, 9)
- Hint: Set the expressions equal, rearrange to a quadratic, then factor — like y = x² and y = 2x + 3: x² = 2x + 3 → x² − 2x − 3 = 0 → (x − 3)(x + 1) = 0.
- Steps:
- Set equal: x² = x + 6.
- Rearrange: x² − x − 6 = 0.
- Factor: (x − 3)(x + 2) = 0.
- x = 3: y = 9. x = −2: y = 4.
- Intersections: (−2, 4) and (3, 9).
- Answer: (−2, 4) and (3, 9)
[Hard] Surface Area of a Cone
- EN: A cone has radius 6 cm and slant height 10 cm. What is its total surface area? (Use π ≈ 3.14)
- FR: Un cône a un rayon de 6 cm et une hauteur oblique de 10 cm. Quelle est son aire de surface totale? (Utilise π ≈ 3,14)
- Choices: A) 188.4 cm² B) 301.44 cm² C) 376.8 cm² D) 489.84 cm²
- Hint: Total surface area of a cone = π × r × l + π × r² (lateral area + base) — like r = 4, l = 7: SA = 3.14 × 4 × 7 + 3.14 × 16 = 87.92 + 50.24 = 138.16 cm².
- Steps:
- Lateral area = π × r × l = 3.14 × 6 × 10 = 188.4 cm².
- Base area = π × r² = 3.14 × 36 = 113.04 cm².
- Total = 188.4 + 113.04 = 301.44 cm².
- Answer: 301.44 cm²
Grade 11 Problems
[Easy] Exponential Function
- EN: What is the value of f(x) = 2^x when x = 4?
- FR: Quelle est la valeur de f(x) = 2^x quand x = 4?
- Choices: A) 8 B) 12 C) 16 D) 24
- Hint: Raise 2 to the given power — like 2³ = 2 × 2 × 2 = 8.
- Steps:
- 2^4 = 2 × 2 × 2 × 2.
- 2 × 2 = 4, 4 × 2 = 8, 8 × 2 = 16.
- So f(4) = 16.
- Answer: 16
[Easy] Logarithm Introduction
- EN: What is log₂(8)?
- FR: Combien vaut log₂(8)?
- Choices: A) 2 B) 3 C) 4 D) 8
- Hint: log_b(x) = y means b^y = x — like log₂(16) means 2^y = 16, so y = 4.
- Steps:
- log₂(8) = y means 2^y = 8.
- 2³ = 8. So y = 3.
- Answer: 3
[Easy] Arithmetic Sequence
- EN: Find the 8th term of the arithmetic sequence: 3, 7, 11, 15, ...
- FR: Trouve le 8e terme de la suite arithmétique: 3, 7, 11, 15, ...
- Choices: A) 27 B) 29 C) 31 D) 35
- Hint: The nth term of an arithmetic sequence = a + (n − 1)d, where a is the first term and d is the common difference — like 2, 5, 8, 11: a = 2, d = 3, 6th term = 2 + 5 × 3 = 17.
- Steps:
- a = 3, d = 4.
- 8th term = 3 + (8 − 1) × 4 = 3 + 28 = 31.
- Answer: 31
[Easy] Compound Interest
- EN: $1000 is invested at 5% interest compounded annually. What is the balance after 2 years?
- FR: 1000 $ sont investis à 5% d'intérêt composé annuellement. Quel est le solde après 2 ans?
- Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1210.00
- Hint: Use A = P(1 + r)^n — like $500 at 4% for 2 years: A = 500(1.04)² = 500 × 1.0816 = $540.80.
- Steps:
- A = 1000(1 + 0.05)².
- A = 1000 × (1.05)² = 1000 × 1.1025 = $1102.50.
- Answer: $1102.50
[Medium] Quadratic Function — Vertex
- EN: For f(x) = −(x − 3)² + 7, what is the vertex?
- FR: Pour f(x) = −(x − 3)² + 7, quel est le sommet?
- Choices: A) (−3, 7) B) (3, −7) C) (3, 7) D) (7, 3)
- Hint: In y = a(x − h)² + k form, the vertex is at (h, k) — like y = 2(x − 4)² + 1 has vertex (4, 1).
- Steps:
- f(x) = −(x − 3)² + 7 is in vertex form.
- h = 3, k = 7.
- Vertex is (3, 7).
- Answer: (3, 7)
[Medium] Trigonometric Identity
- EN: Simplify: sin²(x) + cos²(x).
- FR: Simplifie: sin²(x) + cos²(x).
- Choices: A) 0 B) 1 C) 2 D) sin(2x)
- Hint: This is one of the most fundamental identities in trigonometry — like how knowing Pythagorean triples connects to right triangles.
- Steps:
- The Pythagorean identity states sin²(x) + cos²(x) = 1 for all x.
- This is a foundational trig identity.
- So the answer is 1.
- Answer: 1
[Medium] Geometric Sequence
- EN: Find the sum of the first 4 terms of the geometric sequence: 2, 6, 18, 54, ...
- FR: Trouve la somme des 4 premiers termes de la suite géométrique: 2, 6, 18, 54, ...
- Choices: A) 60 B) 72 C) 80 D) 162
- Hint: Just add the listed terms directly, or use S_n = a(r^n − 1)/(r − 1) — like 1, 3, 9, 27: sum = 1 + 3 + 9 + 27 = 40.
- Steps:
- Sum = 2 + 6 + 18 + 54.
- 2 + 6 = 8, 8 + 18 = 26, 26 + 54 = 80.
- So the sum is 80.
- Answer: 80
[Medium] Annuity — Future Value
- EN: You deposit $200 at the end of each month into an account earning 6% per year (0.5% per month). What is the future value after 3 months?
- FR: Tu déposes 200 $ à la fin de chaque mois dans un compte qui rapporte 6% par an (0,5% par mois). Quelle est la valeur future après 3 mois?
- Choices: A) $600.00 B) $601.00 C) $603.01 D) $612.00
- Hint: Each deposit earns interest separately — like 3 monthly deposits of $100 at 1%/month: first deposit grows to $102.01, second to $101, third is $100, total ≈ $303.01.
- Steps:
- Month 1 deposit of $200 earns interest for 2 months: 200 × (1.005)² = 200 × 1.010025 = $202.00.
- Month 2 deposit earns interest for 1 month: 200 × 1.005 = $201.00.
- Month 3 deposit: $200.00.
- Total: $202.00 + $201.00 + $200.00 = $603.00 ≈ $603.01.
- Answer: $603.01
[Hard] Logarithm — Solving an Equation
- EN: Solve for x: log₃(x) + log₃(x − 2) = 1.
- FR: Résous pour x: log₃(x) + log₃(x − 2) = 1.
- Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 9
- Hint: Use the log product rule: log(a) + log(b) = log(a × b) — like log₂(x) + log₂(3) = 3 becomes log₂(3x) = 3, so 3x = 8, x = 8/3.
- Steps:
- log₃(x) + log₃(x − 2) = log₃(x(x − 2)) = 1.
- So x(x − 2) = 3¹ = 3.
- x² − 2x − 3 = 0.
- Factor: (x − 3)(x + 1) = 0. x = 3 or x = −1.
- Since log requires positive argument, x = 3.
- Answer: x = 3
[Hard] Compound Interest — Solving for Time
- EN: How many years does it take for $500 to double at 7% interest compounded annually? (Use log to solve, round to nearest year.)
- FR: Combien d'années faut-il pour que 500 $ doublent à 7% d'intérêt composé annuellement? (Utilise les logarithmes et arrondis à l'année la plus proche.)
- Choices: A) 8 years B) 10 years C) 12 years D) 14 years
- Hint: Set up 2 = (1.07)^n and use logarithms: n = log(2) ÷ log(1.07) — like doubling at 10%: n = log(2)/log(1.10) ≈ 7.3 years.
- Steps:
- 1000 = 500(1.07)^n → 2 = (1.07)^n.
- Take log: log(2) = n × log(1.07).
- n = log(2) ÷ log(1.07) = 0.3010 ÷ 0.02938 ≈ 10.24.
- Rounded: approximately 10 years.
- Answer: 10 years
Grade 12 Problems
[Easy] Permutations
- EN: How many ways can you arrange the letters A, B, C in a row?
- FR: De combien de façons peut-on arranger les lettres A, B, C dans une rangée?
- Choices: A) 3 B) 6 C) 9 D) 12
- Hint: The number of arrangements of n distinct items is n! — like 4 items: 4! = 4 × 3 × 2 × 1 = 24.
- Steps:
- n = 3 letters.
- 3! = 3 × 2 × 1 = 6.
- So there are 6 arrangements.
- Answer: 6
[Easy] Combinations
- EN: How many ways can you choose 2 students from a group of 5?
- FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 5?
- Choices: A) 5 B) 10 C) 15 D) 20
- Hint: Use C(n, r) = n! ÷ (r!(n − r)!) — like choosing 2 from 4: C(4,2) = 4!/(2! × 2!) = 6.
- Steps:
- C(5, 2) = 5! ÷ (2! × 3!) = (5 × 4) ÷ (2 × 1) = 20 ÷ 2 = 10.
- Answer: 10
[Easy] Derivative — Power Rule
- EN: Find the derivative of f(x) = x³.
- FR: Trouve la dérivée de f(x) = x³.
- Choices: A) x² B) 3x C) 3x² D) x⁴/4
- Hint: The power rule: d/dx(x^n) = n × x^(n−1) — like d/dx(x⁵) = 5x⁴.
- Steps:
- f(x) = x³.
- Bring down the exponent: 3.
- Reduce the exponent by 1: x².
- f'(x) = 3x².
- Answer: 3x²
[Easy] Rational Function — Domain
- EN: What value of x is NOT in the domain of f(x) = 1/(x − 4)?
- FR: Quelle valeur de x n'appartient PAS au domaine de f(x) = 1/(x − 4)?
- Choices: A) x = 0 B) x = 1 C) x = 4 D) x = 5
- Hint: A fraction is undefined when the denominator equals zero — like f(x) = 1/(x + 3): set x + 3 = 0, so x = −3 is excluded.
- Steps:
- Set denominator = 0: x − 4 = 0.
- x = 4 makes the function undefined.
- So x = 4 is not in the domain.
- Answer: x = 4
[Medium] Derivative — Finding a Rate of Change
- EN: The position of a skater (in metres) is given by s(t) = 3t² + 2t. What is the skater's velocity (in m/s) at t = 3 seconds?
- FR: La position d'un patineur (en mètres) est donnée par s(t) = 3t² + 2t. Quelle est la vitesse du patineur (en m/s) à t = 3 secondes?
- Choices: A) 11 m/s B) 18 m/s C) 20 m/s D) 33 m/s
- Hint: Differentiate the position function to get velocity, then substitute t — like s(t) = 4t² + t: s'(t) = 8t + 1, at t = 2: velocity = 8(2) + 1 = 17 m/s.
- Steps:
- s'(t) = d/dt(3t² + 2t) = 6t + 2.
- At t = 3: s'(3) = 6(3) + 2 = 18 + 2 = 20.
- Velocity is 20 m/s.
- Answer: 20 m/s
[Medium] Binomial Probability
- EN: A fair coin is tossed 4 times. What is the probability of getting exactly 3 heads?
- FR: Une pièce de monnaie équilibrée est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces?
- Choices: A) 1/8 B) 1/4 C) 3/8 D) 1/2
- Hint: Use the binomial formula: P = C(n,r) × p^r × (1−p)^(n−r) — like 3 flips, exactly 2 heads: C(3,2) × (0.5)² × (0.5)¹ = 3 × 0.25 × 0.5 = 0.375.
- Steps:
- n = 4, r = 3, p = 0.5.
- P = C(4,3) × (0.5)³ × (0.5)¹.
- C(4,3) = 4.
- P = 4 × 0.125 × 0.5 = 4 × 0.0625 = 0.25 = 1/4.
- Answer: 1/4
[Medium] Polynomial Function — Zeros
- EN: What are the zeros of f(x) = x³ − x² − 6x?
- FR: Quels sont les zéros de f(x) = x³ − x² − 6x?
- Choices: A) x = 0, x = 2, x = −3 B) x = 0, x = 3, x = −2 C) x = 1, x = 3, x = −2 D) x = 0, x = 6, x = −1
- Hint: Factor out the GCF first, then factor the remaining quadratic — like x³ + x² − 2x = x(x² + x − 2) = x(x + 2)(x − 1).
- Steps:
- Factor: x³ − x² − 6x = x(x² − x − 6).
- Factor the quadratic: x² − x − 6 = (x − 3)(x + 2).
- Zeros: x = 0, x = 3, x = −2.
- Answer: x = 0, x = 3, x = −2
[Medium] Vectors — Addition
- EN: Vector u = (3, −1) and vector v = (−2, 5). What is u + v?
- FR: Le vecteur u = (3, −1) et le vecteur v = (−2, 5). Quel est u + v?
- Choices: A) (1, 4) B) (1, 6) C) (5, 4) D) (5, −6)
- Hint: Add vectors component by component — like (4, 2) + (−1, 3) = (3, 5).
- Steps:
- x-components: 3 + (−2) = 1.
- y-components: (−1) + 5 = 4.
- u + v = (1, 4).
- Answer: (1, 4)
[Hard] Derivative — Tangent Line
- EN: Find the equation of the tangent line to f(x) = x² + 3x at the point where x = 2.
- FR: Trouve l'équation de la droite tangente à f(x) = x² + 3x au point où x = 2.
- Choices: A) y = 5x − 4 B) y = 7x − 4 C) y = 7x + 4 D) y = 9x − 8
- Hint: Find f(a) for the point, then f'(a) for the slope, then use y − y₁ = m(x − x₁) — like f(x) = x² at x = 1: f(1) = 1, f'(x) = 2x, slope = 2, tangent: y = 2x − 1.
- Steps:
- f(2) = 4 + 6 = 10. Point: (2, 10).
- f'(x) = 2x + 3. Slope at x = 2: f'(2) = 7.
- Tangent: y − 10 = 7(x − 2) → y = 7x − 14 + 10 → y = 7x − 4.
- Answer: y = 7x − 4
[Hard] Probability Distribution — Expected Value
- EN: A carnival game pays $5 if you roll a 6 on a standard die, and you lose $1 otherwise. What is the expected value per roll?
- FR: Un jeu de foire paie 5 $ si tu lances un 6 sur un dé standard, et tu perds 1 $ autrement. Quelle est la valeur espérée par lancer?
- Choices: A) −$0.17 B) $0.00 C) $0.67 D) $1.00
- Hint: Expected value = Σ(outcome × probability) — like winning $4 with probability 1/4 and losing $2 with probability 3/4: E = 4(1/4) + (−2)(3/4) = 1 − 1.5 = −$0.50.
- Steps:
- P(roll 6) = 1/6. Win $5. P(not 6) = 5/6. Lose $1.
- E = 5(1/6) + (−1)(5/6).
- E = 5/6 − 5/6 = 0/6 = $0.00.
- Wait — let me recalculate: 5/6 = 0.833, 5/6 = 0.833, 0.833 − 0.833 = 0. So E = $0.00.
- Answer: $0.00
Today's Encouragement
When you look for patterns and structure, ordinary moments transform into remarkable discoveries all around you. ---
A Story of Kindness
Priya lived in Saskatoon and loved spending Saturday mornings at the community garden. One day she noticed her elderly neighbour, Mr. Bouchard, struggling to reach the tomatoes at the back of his garden plot because of his sore knees. Priya quietly moved his garden stool closer and picked the ripe tomatoes for him, carefully placing them in his basket. Mr. Bouchard smiled warmly and thanked her, saying the kindness of one child can make a whole neighbourhood bloom.
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