Daily Math — 2026-08-17

Grade 1 Problems

1. [Easy] Counting to 20

   • EN: There are 7 apples on the table. Sam puts 5 more apples on the table. How many apples are there now?
   • FR: Il y a 7 pommes sur la table. Sam met 5 pommes de plus sur la table. Combien y a-t-il de pommes maintenant ?
   • Choices: A) 10 B) 11 C) 12 D) 13
   • Hint: Try counting on from the bigger number, like 6 + 3 = start at 6, count up 3 more.
   • Steps:
     • Start at 7 and count up 5 more.
     • 7 → 8, 9, 10, 11, 12.
     • So there are 12 apples in all.
   • Answer: 12

2. [Easy] Skip Counting by 2s

   • EN: Skip count by 2s. What comes next: 2, 4, 6, 8, ___?
   • FR: Compte de 2 en 2. Quel est le prochain nombre : 2, 4, 6, 8, ___ ?
   • Choices: A) 9 B) 10 C) 11 D) 14
   • Hint: Skip counting by 2s means adding 2 each time, like 4, 6, 8, 10 — add 2.
   • Steps:
     • The pattern adds 2 each time.
     • 8 + 2 = 10.
     • So the next number is 10.
   • Answer: 10

3. [Easy] Comparing Numbers

   • EN: Which number is greater: 14 or 9?
   • FR: Quel nombre est le plus grand : 14 ou 9 ?
   • Choices: A) 9 B) 11 C) 14 D) 19
   • Hint: When you compare numbers, the one with more tens is bigger, like 12 is bigger than 7.
   • Steps:
     • 14 has a tens digit of 1, and 9 has no tens.
     • Any two-digit number is bigger than a one-digit number.
     • So 14 is greater than 9.
   • Answer: 14

4. [Easy] Coin Recognition

   • EN: Maya has 1 dime. How many cents does she have?
   • FR: Maya a 1 pièce de 10 cents. Combien de cents a-t-elle ?
   • Choices: A) 1 cent B) 5 cents C) 10 cents D) 25 cents
   • Hint: A nickel is worth 5 cents, a penny is worth 1 cent — a dime is worth more than both.
   • Steps:
     • A dime is a silver coin worth 10 cents.
     • Maya has 1 dime.
     • So she has 10 cents.
   • Answer: 10 cents

5. [Medium] Subtraction within 20

   • EN: There are 15 hockey pucks in a bag. A player takes 6 pucks out. How many pucks are left in the bag?
   • FR: Il y a 15 rondelles de hockey dans un sac. Un joueur en prend 6. Combien de rondelles reste-t-il dans le sac ?
   • Choices: A) 7 B) 8 C) 9 D) 11
   • Hint: To subtract, count backwards from the bigger number, like 12 − 4: start at 12, go back 4 steps.
   • Steps:
     • Start at 15 and count back 6.
     • 15 → 14, 13, 12, 11, 10, 9.
     • So 9 pucks are left.
   • Answer: 9

6. [Medium] Skip Counting by 5s

   • EN: Skip count by 5s. What comes next: 5, 10, 15, 20, ___?
   • FR: Compte de 5 en 5. Quel est le prochain nombre : 5, 10, 15, 20, ___ ?
   • Choices: A) 22 B) 24 C) 25 D) 30
   • Hint: Skip counting by 5s adds 5 each time, like 10, 15, 20 — just keep adding 5.
   • Steps:
     • The pattern adds 5 each time.
     • 20 + 5 = 25.
     • So the next number is 25.
   • Answer: 25

7. [Medium] Addition within 20

   • EN: Liam has 8 stickers. His friend gives him 7 more stickers. How many stickers does Liam have in all?
   • FR: Liam a 8 autocollants. Son ami lui donne 7 autres autocollants. Combien d'autocollants Liam a-t-il en tout ?
   • Choices: A) 13 B) 14 C) 15 D) 16
   • Hint: To add two numbers, make a 10 first — like 8 + 4 = 8 + 2 + 2 = 10 + 2 = 12.
   • Steps:
     • Break 7 into 2 + 5.
     • 8 + 2 = 10, then 10 + 5 = 15.
     • So Liam has 15 stickers in all.
   • Answer: 15

8. [Medium] Counting by 10s

   • EN: Skip count by 10s. What comes next: 10, 20, 30, 40, ___?
   • FR: Compte de 10 en 10. Quel est le prochain nombre : 10, 20, 30, 40, ___ ?
   • Choices: A) 41 B) 45 C) 50 D) 60
   • Hint: Counting by 10s means adding 10 each time, like 20, 30, 40 — the ones digit stays 0.
   • Steps:
     • The pattern adds 10 each time.
     • 40 + 10 = 50.
     • So the next number is 50.
   • Answer: 50

9. [Hard] Comparing and Adding

   • EN: Ava has 9 pennies and Ben has 8 pennies. They put all their pennies together. How many pennies do they have in all?
   • FR: Ava a 9 sous et Ben a 8 sous. Ils mettent tous leurs sous ensemble. Combien de sous ont-ils en tout ?
   • Choices: A) 15 B) 16 C) 17 D) 18
   • Hint: When you add two numbers near 10, make a 10 first — like 9 + 6 = 10 + 5 = 15.
   • Steps:
     • Break 8 into 1 + 7.
     • 9 + 1 = 10, then 10 + 7 = 17.
     • So they have 17 pennies in all.
   • Answer: 17

10. [Hard] Subtraction and Comparison

    • EN: There are 18 children on the playground. 9 children go inside. Are there more or fewer than 10 children left outside?
    • FR: Il y a 18 enfants dans la cour de récréation. 9 enfants rentrent à l'intérieur. Y a-t-il plus ou moins de 10 enfants qui restent dehors ?
    • Choices: A) Fewer than 10, there are 7 left B) Fewer than 10, there are 8 left C) Exactly 10, there are 10 left D) More than 10, there are 11 left
    • Hint: Subtract first to find how many are left, then compare to 10, like 14 − 4 = 10, which is exactly 10.
    • Steps:
      • Subtract: 18 − 9 = 9.
      • Compare 9 to 10: 9 is less than 10.
      • So there are fewer than 10 children left — there are 9 left, but the closest choice is exactly 10 with 10 left. Let me recheck: 18 − 9 = 9, which is fewer than 10.
      • The correct answer is: Exactly 10, there are 10 left — wait, 18 − 9 = 9. So the answer is fewer than 10, there are 8 left? No: 18 − 9 = 9. The answer is "Exactly 10, there are 10 left" is wrong. The answer must be a choice that says 9 children remain — but no choice says 9. Let me re-examine: choices are 7, 8, 10, 11. None say 9. I must fix: 18 − 9 = 9, so I will adjust choices to include 9.
      • Corrected: 18 − 9 = 9. There are exactly 9 children left, which is fewer than 10.
    • Answer: Fewer than 10, there are 8 left

(Note: Correcting problem 10 choices below for accuracy.)

10. [Hard] Subtraction and Comparison
    • EN: There are 16 children on the playground. 9 children go inside. Are there more or fewer than 10 children left outside?
    • FR: Il y a 16 enfants dans la cour de récréation. 9 enfants rentrent à l'intérieur. Y a-t-il plus ou moins de 10 enfants qui restent dehors ?
    • Choices: A) Fewer than 10, there are 6 left B) Fewer than 10, there are 8 left C) More than 10, there are 11 left D) More than 10, there are 7 left
    • Hint: Subtract first to find how many are left, then compare to 10 — like 14 − 5 = 9, which is fewer than 10.
    • Steps:
      • Subtract: 16 − 9 = 7.
      • Compare 7 to 10: 7 is less than 10.
      • So there are fewer than 10 children left outside — specifically 7 left.
    • Answer: More than 10, there are 7 left

(Fixing again — 7 < 10, so it is fewer. Rewriting choices cleanly:)

10. [Hard] Subtraction and Comparison
    • EN: There are 16 children on the playground. 9 children go inside. How many children are left outside?
    • FR: Il y a 16 enfants dans la cour de récréation. 9 enfants rentrent à l'intérieur. Combien d'enfants restent dehors ?
    • Choices: A) 5 B) 6 C) 7 D) 8
    • Hint: To subtract 9 from a number, take away 10 first then add 1 back — like 14 − 9 = 14 − 10 + 1 = 5.
    • Steps:
      • Use the strategy: 16 − 10 = 6, then add 1 back because we only took 9, not 10.
      • 6 + 1 = 7.
      • So 7 children are left outside.
    • Answer: 7

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Grade 2 Problems

1. [Easy] Addition within 100

   • EN: A store has 23 red pencils and 14 blue pencils. How many pencils are there in total?
   • FR: Un magasin a 23 crayons rouges et 14 crayons bleus. Combien y a-t-il de crayons en tout ?
   • Choices: A) 33 B) 35 C) 37 D) 39
   • Hint: Add the tens first, then the ones — like 31 + 15: tens give 40, ones give 6, total is 46.
   • Steps:
     • Add tens: 20 + 10 = 30.
     • Add ones: 3 + 4 = 7.
     • 30 + 7 = 37 pencils in total.
   • Answer: 37

2. [Easy] Telling Time

   • EN: The clock shows the short hand on 4 and the long hand on 12. What time is it?
   • FR: La petite aiguille est sur le 4 et la grande aiguille est sur le 12. Quelle heure est-il ?
   • Choices: A) 3:00 B) 4:00 C) 5:00 D) 12:04
   • Hint: When the long hand points to 12, it is exactly on the hour — like short hand on 7 means 7:00.
   • Steps:
     • The long hand on 12 means it is exactly on the hour.
     • The short hand on 4 tells us it is 4 o'clock.
     • So the time is 4:00.
   • Answer: 4:00

3. [Easy] Measuring Length

   • EN: A crayon is 8 cm long. A pencil is 12 cm long. How much longer is the pencil than the crayon?
   • FR: Un crayon de couleur mesure 8 cm. Un crayon mesure 12 cm. De combien le crayon est-il plus long que le crayon de couleur ?
   • Choices: A) 3 cm B) 4 cm C) 5 cm D) 6 cm
   • Hint: To find how much longer, subtract the shorter length from the longer one — like 15 − 9 = 6 cm.
   • Steps:
     • Subtract the shorter length from the longer length.
     • 12 − 8 = 4.
     • The pencil is 4 cm longer than the crayon.
   • Answer: 4 cm

4. [Easy] Counting Coins

   • EN: Emma has 2 nickels and 1 dime. How many cents does she have in total?
   • FR: Emma a 2 pièces de 5 cents et 1 pièce de 10 cents. Combien de cents a-t-elle en tout ?
   • Choices: A) 15 cents B) 17 cents C) 20 cents D) 25 cents
   • Hint: Add the value of each coin — like 1 dime + 1 nickel = 10 + 5 = 15 cents.
   • Steps:
     • 2 nickels = 2 × 5 = 10 cents.
     • 1 dime = 10 cents.
     • 10 + 10 = 20 cents in total.
   • Answer: 20 cents

5. [Medium] Subtraction within 100

   • EN: There are 75 snowballs in a pile. Kids throw 38 snowballs. How many snowballs are left?
   • FR: Il y a 75 boules de neige dans un tas. Des enfants en lancent 38. Combien de boules de neige reste-t-il ?
   • Choices: A) 33 B) 37 C) 43 D) 47
   • Hint: Subtract in parts — like 62 − 24: take away 20 first (62 − 20 = 42), then take away 4 more (42 − 4 = 38).
   • Steps:
     • 75 − 38: subtract 30 first → 75 − 30 = 45.
     • Then subtract 8 more → 45 − 8 = 37.
     • So 37 snowballs are left.
   • Answer: 37

6. [Medium] Telling Time (Half Hour)

   • EN: The clock shows the short hand between 2 and 3, and the long hand on 6. What time does the clock show?
   • FR: La petite aiguille est entre le 2 et le 3, et la grande aiguille est sur le 6. Quelle heure l'horloge indique-t-elle ?
   • Choices: A) 2:00 B) 2:30 C) 3:00 D) 3:30
   • Hint: When the long hand points to 6, it is half past the hour — like short hand between 7 and 8 means 7:30.
   • Steps:
     • The long hand on 6 means 30 minutes past.
     • The short hand has passed 2 but not reached 3, so the hour is 2.
     • The time is 2:30.
   • Answer: 2:30

7. [Medium] Simple Patterns

   • EN: Look at this pattern: 3, 6, 9, 12, ___. What is the missing number?
   • FR: Observe ce pattern : 3, 6, 9, 12, ___. Quel est le nombre manquant ?
   • Choices: A) 13 B) 14 C) 15 D) 16
   • Hint: Find what is being added each time — like 2, 5, 8, 11: each goes up by 3.
   • Steps:
     • Look at the difference: 6 − 3 = 3, 9 − 6 = 3, 12 − 9 = 3.
     • The pattern adds 3 each time.
     • 12 + 3 = 15.
   • Answer: 15

8. [Medium] Addition with Regrouping

   • EN: Jake collects 46 hockey cards in January and 37 hockey cards in February. How many cards does he have altogether?
   • FR: Jake collecte 46 cartes de hockey en janvier et 37 cartes de hockey en février. Combien de cartes a-t-il en tout ?
   • Choices: A) 73 B) 81 C) 83 D) 89
   • Hint: Add the ones first — if the ones add up to 10 or more, regroup into a ten, like 47 + 25: ones give 12, write 2, carry 1 ten, tens give 7, total 72.
   • Steps:
     • Ones: 6 + 7 = 13. Write 3, carry 1.
     • Tens: 4 + 3 = 7, plus the carried 1 = 8.
     • So the total is 83 cards.
   • Answer: 83

9. [Hard] Counting Coins to $1

   • EN: Olivia has 3 quarters and 1 dime. How many cents does she have in total?
   • FR: Olivia a 3 pièces de 25 cents et 1 pièce de 10 cents. Combien de cents a-t-elle en tout ?
   • Choices: A) 75 cents B) 80 cents C) 85 cents D) 90 cents
   • Hint: Multiply the number of quarters by 25, then add any other coins — like 2 quarters + 1 nickel = 50 + 5 = 55 cents.
   • Steps:
     • 3 quarters = 3 × 25 = 75 cents.
     • 1 dime = 10 cents.
     • 75 + 10 = 85 cents in total.
   • Answer: 85 cents

10. [Hard] Measuring and Comparing

    • EN: A blue ribbon is 45 cm long. A red ribbon is 28 cm long. Noah cuts 10 cm off the blue ribbon. Now which ribbon is longer, and by how many centimetres?
    • FR: Un ruban bleu mesure 45 cm. Un ruban rouge mesure 28 cm. Noah coupe 10 cm du ruban bleu. Quel ruban est maintenant le plus long, et de combien de centimètres ?
    • Choices: A) The blue ribbon, by 5 cm B) The blue ribbon, by 7 cm C) The red ribbon, by 3 cm D) The red ribbon, by 5 cm
    • Hint: First find the new length of the blue ribbon after cutting, then compare — like 50 cm − 10 cm = 40 cm, then 40 − 25 = 15 cm longer.
    • Steps:
      • Blue ribbon after cutting: 45 − 10 = 35 cm.
      • Compare: 35 cm vs. 28 cm.
      • 35 − 28 = 7 cm, so the blue ribbon is longer by 7 cm.
    • Answer: The blue ribbon, by 7 cm

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Grade 3 Problems

1. [Easy] Multiplication by 2

   • EN: There are 6 pairs of hockey gloves. How many gloves are there in all?
   • FR: Il y a 6 paires de gants de hockey. Combien y a-t-il de gants en tout ?
   • Choices: A) 8 B) 10 C) 12 D) 14
   • Hint: Pairs means groups of 2 — like 4 pairs = 4 × 2 = 8 gloves.
   • Steps:
     • Each pair has 2 gloves.
     • 6 × 2 = 12.
     • There are 12 gloves in all.
   • Answer: 12

2. [Easy] Multiplication by 5

   • EN: There are 4 bags with 5 apples in each bag. How many apples are there in total?
   • FR: Il y a 4 sacs avec 5 pommes dans chaque sac. Combien y a-t-il de pommes en tout ?
   • Choices: A) 15 B) 18 C) 20 D) 25
   • Hint: Multiply the number of groups by the number in each group — like 3 bags × 5 = 15.
   • Steps:
     • 4 bags × 5 apples each.
     • 4 × 5 = 20.
     • There are 20 apples in total.
   • Answer: 20

3. [Easy] Fractions

   • EN: A pizza is cut into 4 equal slices. Mia eats 1 slice. What fraction of the pizza did Mia eat?
   • FR: Une pizza est coupée en 4 parts égales. Mia mange 1 part. Quelle fraction de la pizza Mia a-t-elle mangée ?
   • Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
   • Hint: A fraction is the part eaten over the total parts — like 1 out of 3 equal pieces is 1/3.
   • Steps:
     • The pizza has 4 equal slices in total.
     • Mia ate 1 slice.
     • So she ate 1 out of 4 slices = 1/4.
   • Answer: 1/4

4. [Easy] Basic Division

   • EN: 18 students are put into groups of 3. How many groups are there?
   • FR: 18 élèves sont répartis en groupes de 3. Combien y a-t-il de groupes ?
   • Choices: A) 4 B) 5 C) 6 D) 7
   • Hint: Division means splitting into equal groups — like 12 ÷ 3 = 4 because 4 × 3 = 12.
   • Steps:
     • Ask: how many groups of 3 make 18?
     • 6 × 3 = 18.
     • So there are 6 groups.
   • Answer: 6

5. [Medium] Multiplication by 4

   • EN: A Tim Hortons box holds 4 donuts. If there are 7 boxes, how many donuts are there altogether?
   • FR: Une boîte de Tim Hortons contient 4 beignes. S'il y a 7 boîtes, combien y a-t-il de beignes en tout ?
   • Choices: A) 24 B) 28 C) 32 D) 36
   • Hint: Multiply the number of boxes by the number inside each box — like 5 boxes × 4 = 20 donuts.
   • Steps:
     • 7 boxes × 4 donuts each.
     • 7 × 4 = 28.
     • There are 28 donuts altogether.
   • Answer: 28

6. [Medium] Perimeter of a Rectangle

   • EN: A garden is shaped like a rectangle. It is 6 m long and 3 m wide. What is the perimeter of the garden?
   • FR: Un jardin a la forme d'un rectangle. Il mesure 6 m de long et 3 m de large. Quel est le périmètre du jardin ?
   • Choices: A) 9 m B) 16 m C) 18 m D) 24 m
   • Hint: Perimeter of a rectangle = add all 4 sides — like a 5 m × 2 m rectangle has perimeter 5 + 2 + 5 + 2 = 14 m.
   • Steps:
     • A rectangle has 2 long sides and 2 short sides.
     • Perimeter = 6 + 6 + 3 + 3.
     • 6 + 6 + 3 + 3 = 18 m.
   • Answer: 18 m

7. [Medium] Reading a Graph

   • EN: A bar graph shows the number of goals scored: Team A scored 8 goals, Team B scored 5 goals, and Team C scored 7 goals. How many goals were scored in total?
   • FR: Un diagramme à barres montre le nombre de buts marqués : l'équipe A a marqué 8 buts, l'équipe B en a marqué 5 et l'équipe C en a marqué 7. Combien de buts ont été marqués en tout ?
   • Choices: A) 18 B) 19 C) 20 D) 21
   • Hint: To find the total, add all the values from the graph together — like 6 + 4 + 5 = 15.
   • Steps:
     • Add all teams' goals: 8 + 5 + 7.
     • 8 + 5 = 13, then 13 + 7 = 20.
     • A total of 20 goals were scored.
   • Answer: 20

8. [Medium] Multiplication by 10

   • EN: There are 9 boxes. Each box holds 10 crayons. How many crayons are there in all?
   • FR: Il y a 9 boîtes. Chaque boîte contient 10 crayons. Combien y a-t-il de crayons en tout ?
   • Choices: A) 19 B) 81 C) 90 D) 100
   • Hint: Multiplying any number by 10 just puts a zero on the end — like 7 × 10 = 70.
   • Steps:
     • 9 × 10.
     • Place a zero after 9: 90.
     • There are 90 crayons in all.
   • Answer: 90

9. [Hard] Fractions and Comparison

   • EN: Lucas has 1/2 of a granola bar. Sofia has 1/4 of an identical granola bar. Who has more, and what fraction more do they have?
   • FR: Lucas a 1/2 d'une barre granola. Sofia a 1/4 d'une barre granola identique. Qui en a le plus, et de quelle fraction de plus ?
   • Choices: A) Lucas has more, by 1/4 B) Lucas has more, by 1/3 C) Sofia has more, by 1/4 D) Sofia has more, by 1/2
   • Hint: To compare fractions with the same denominator, use equivalent fractions — like 1/2 = 2/4, so compare 2/4 and 1/4.
   • Steps:
     • Convert 1/2 to quarters: 1/2 = 2/4.
     • Compare: 2/4 vs. 1/4. Lucas has more.
     • Difference: 2/4 − 1/4 = 1/4. Lucas has 1/4 more.
   • Answer: Lucas has more, by 1/4

10. [Hard] Division with a Remainder Check

    • EN: 25 students want to sit in rows of 5. How many full rows can be made, and how many students are left over?
    • FR: 25 élèves veulent s'asseoir en rangées de 5. Combien de rangées complètes peut-on former, et combien d'élèves reste-t-il ?
    • Choices: A) 4 full rows, 5 left over B) 5 full rows, 0 left over C) 6 full rows, 1 left over D) 5 full rows, 5 left over
    • Hint: Divide the total by the group size — like 14 ÷ 4: 4 groups of 4 = 16 — that's too many. 3 groups of 4 = 12, remainder 2.
    • Steps:
      • Divide: 25 ÷ 5.
      • 5 × 5 = 25 exactly.
      • There are 5 full rows and 0 students left over.
    • Answer: 5 full rows, 0 left over

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Grade 4 Problems

1. [Easy] Multiplication Tables to 9×9

   • EN: What is 7 × 8?
   • FR: Combien font 7 × 8 ?
   • Choices: A) 48 B) 54 C) 56 D) 63
   • Hint: To remember 7 × 8, try 7 × 7 = 49, then add one more 7 to get 56.
   • Steps:
     • 7 × 8 means 7 groups of 8.
     • 7 × 7 = 49, and 49 + 7 = 56.
     • So 7 × 8 = 56.
   • Answer: 56

2. [Easy] Decimal Place Value

   • EN: What is the value of the digit 3 in the number 4.37?
   • FR: Quelle est la valeur du chiffre 3 dans le nombre 4,37 ?
   • Choices: A) 3 ones B) 3 tens C) 3 tenths D) 3 hundredths
   • Hint: In a decimal number, the first digit after the decimal point is in the tenths place — like in 2.56, the 5 is 5 tenths.
   • Steps:
     • In 4.37: 4 is in the ones place, 3 is in the tenths place, 7 is in the hundredths place.
     • The digit 3 is in the tenths place.
     • Its value is 3 tenths.
   • Answer: 3 tenths

3. [Easy] Area of a Rectangle

   • EN: A classroom floor is 8 m long and 5 m wide. What is the area of the floor?
   • FR: Le plancher d'une salle de classe mesure 8 m de long et 5 m de large. Quelle est l'aire du plancher ?
   • Choices: A) 13 m² B) 26 m² C) 40 m² D) 45 m²
   • Hint: Area of a rectangle = length × width — like a 6 m × 4 m room has area = 24 m².
   • Steps:
     • Area = length × width.
     • Area = 8 × 5.
     • Area = 40 m².
   • Answer: 40 m²

4. [Easy] Long Division (No Remainder)

   • EN: 63 ÷ 7 = ?
   • FR: Combien font 63 ÷ 7 ?
   • Choices: A) 7 B) 8 C) 9 D) 11
   • Hint: Ask yourself "what times 7 equals 63?" — like 7 × 8 = 56, 7 × 9 = 63.
   • Steps:
     • Think: 7 × ? = 63.
     • 7 × 9 = 63.
     • So 63 ÷ 7 = 9.
   • Answer: 9

5. [Medium] Long Division with Remainder

   • EN: 47 ÷ 5 = ? What is the remainder?
   • FR: 47 ÷ 5 = ? Quel est le reste ?
   • Choices: A) 9 remainder 1 B) 9 remainder 2 C) 8 remainder 5 D) 10 remainder 3
   • Hint: Divide, find the closest multiple without going over, then subtract — like 38 ÷ 5: 5 × 7 = 35, remainder 38 − 35 = 3, so answer is 7 remainder 3.
   • Steps:
     • 5 × 9 = 45. That is the biggest multiple of 5 that fits in 47.
     • Remainder: 47 − 45 = 2.
     • Answer: 9 remainder 2
   • Answer: 9 remainder 2

6. [Medium] Comparing Fractions

   • EN: Which fraction is larger: 3/4 or 2/3?
   • FR: Quelle fraction est la 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 1/3: use 6ths, 3/6 vs. 2/6, so 1/2 is bigger.
   • 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 larger.
   • Answer: 3/4

7. [Medium] Elapsed Time

   • EN: A hockey practice starts at 3:15 p.m. and ends at 5:00 p.m. How long is the practice?
   • FR: Un entraînement de hockey commence à 15 h 15 et se termine à 17 h 00. Quelle est la durée de l'entraînement ?
   • Choices: A) 1 hour 30 minutes B) 1 hour 45 minutes C) 2 hours 15 minutes D) 2 hours 45 minutes
   • Hint: Count forward in chunks — like from 2:20 to 4:00: from 2:20 to 3:00 is 40 min, then 3:00 to 4:00 is 1 hour = 1 hour 40 min total.
   • Steps:
     • From 3:15 to 4:00 is 45 minutes.
     • From 4:00 to 5:00 is 1 hour.
     • Total: 1 hour + 45 minutes = 1 hour 45 minutes.
   • Answer: 1 hour 45 minutes

8. [Medium] Decimal Operations

   • EN: A notebook costs $3.45 and a pen costs $1.25. What is the total cost?
   • FR: Un cahier coûte 3,45 $ et un stylo coûte 1,25 $. Quel est le coût total ?
   • Choices: A) $4.60 B) $4.70 C) $4.80 D) $5.70
   • Hint: Line up the decimal points, then add as you would whole numbers — like $2.30 + $1.15 = $3.45.
   • Steps:
     • Line up: $3.45 + $1.25.
     • Hundredths: 5 + 5 = 10, write 0 carry 1. Tenths: 4 + 2 + 1 = 7. Ones: 3 + 1 = 4.
     • Total = $4.70.
   • Answer: $4.70

9. [Hard] Multi-Step Problem

   • EN: A farmer packs 9 baskets with 8 apples each. He then packs the apples into boxes that hold 12 apples each. How many full boxes does he have?
   • FR: Un fermier remplit 9 paniers avec 8 pommes chacun. Il remet ensuite les pommes dans des boîtes qui contiennent 12 pommes chacune. Combien de boîtes complètes a-t-il ?
   • Choices: A) 5 B) 6 C) 7 D) 8
   • Hint: First find the total number of apples, then divide by the box size — like 5 baskets × 6 apples = 30 apples, 30 ÷ 10 = 3 full boxes.
   • Steps:
     • Total apples: 9 × 8 = 72.
     • Divide by box size: 72 ÷ 12.
     • 12 × 6 = 72, so there are 6 full boxes.
   • Answer: 6

10. [Hard] Comparing Decimals and Fractions

    • EN: Order these numbers from least to greatest: 0.5, 3/4, 0.25, 1/2.
    • FR: Ordonne ces nombres du plus petit au plus grand : 0,5 ; 3/4 ; 0,25 ; 1/2.
    • Choices: A) 0.25, 0.5, 1/2, 3/4 B) 0.25, 1/2, 0.5, 3/4 C) 0.25, 0.5, 3/4, 1/2 D) 1/2, 0.25, 0.5, 3/4
    • Hint: Convert everything to decimals to compare — like 1/4 = 0.25, 1/2 = 0.50, 3/4 = 0.75.
    • Steps:
      • Convert: 0.5 = 0.50, 3/4 = 0.75, 0.25 = 0.25, 1/2 = 0.50.
      • Order: 0.25, 0.50, 0.50, 0.75.
      • 0.5 and 1/2 are equal, so the order is: 0.25, 0.5, 1/2, 3/4.
    • Answer: 0.25, 0.5, 1/2, 3/4

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Grade 5 Problems

1. [Easy] Multi-Digit Multiplication

   • EN: What is 34 × 6?
   • FR: Combien font 34 × 6 ?
   • Choices: A) 184 B) 196 C) 204 D) 214
   • Hint: Break apart the number — like 24 × 5: (20 × 5) + (4 × 5) = 100 + 20 = 120.
   • Steps:
     • 34 × 6 = (30 × 6) + (4 × 6).
     • 30 × 6 = 180 and 4 × 6 = 24.
     • 180 + 24 = 204.
   • Answer: 204

2. [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 + 2/5 = 3/5.
   • Steps:
     • The denominators are both 7, so keep 7.
     • Add numerators: 2 + 3 = 5.
     • Answer: 5/7
   • Answer: 5/7

3. [Easy] Percentage Introduction (50%)

   • EN: There are 40 students in an auditorium. 50% of them are wearing hats. How many students are wearing hats?
   • FR: Il y a 40 élèves dans un auditorium. 50 % d'entre eux portent un chapeau. Combien d'élèves portent un chapeau ?
   • Choices: A) 10 B) 15 C) 20 D) 25
   • Hint: 50% means half — like 50% of 80 = 80 ÷ 2 = 40.
   • Steps:
     • 50% = one half.
     • Half of 40 = 40 ÷ 2 = 20.
     • 20 students are wearing hats.
   • Answer: 20

4. [Easy] Volume of a Rectangular Prism

   • EN: A box is 4 cm long, 3 cm wide, and 2 cm tall. What is the volume of the box?
   • FR: Une boîte mesure 4 cm de long, 3 cm de large et 2 cm de hauteur. Quel est le volume de la boîte ?
   • Choices: A) 9 cm³ B) 18 cm³ C) 24 cm³ D) 36 cm³
   • Hint: Volume = length × width × height — like a box 5 × 2 × 3 = 30 cm³.
   • Steps:
     • Volume = 4 × 3 × 2.
     • 4 × 3 = 12, then 12 × 2 = 24.
     • Volume = 24 cm³.
   • Answer: 24 cm³

5. [Medium] Multi-Digit Division

   • EN: 504 ÷ 7 = ?
   • FR: Combien font 504 ÷ 7 ?
   • Choices: A) 62 B) 70 C) 72 D) 78
   • Hint: Use long division — like 336 ÷ 6: 6 goes into 33 five times (5 × 6 = 30, remainder 3), bring down 6, 6 goes into 36 six times = 56.
   • Steps:
     • 7 goes into 50 seven times: 7 × 7 = 49, remainder 1.
     • Bring down 4: 14. 7 goes into 14 twice: 7 × 2 = 14, remainder 0.
     • 504 ÷ 7 = 72.
   • Answer: 72

6. [Medium] Subtracting Fractions with Like Denominators

   • EN: What is 5/8 − 2/8?
   • FR: Combien font 5/8 − 2/8 ?
   • Choices: A) 3/16 B) 3/8 C) 4/8 D) 7/8
   • Hint: Subtract the numerators and keep the same denominator — like 7/9 − 4/9 = 3/9.
   • Steps:
     • Same denominator: 8. Keep it.
     • Subtract numerators: 5 − 2 = 3.
     • Answer: 3/8
   • Answer: 3/8

7. [Medium] Decimal Operations

   • EN: Emily buys a scarf for $12.75 and a hat for $8.49. How much does she spend in total?
   • FR: Emily achète une écharpe pour 12,75 $ et un chapeau pour 8,49 $. Combien dépense-t-elle en tout ?
   • Choices: A) $20.14 B) $21.24 C) $21.34 D) $22.24
   • Hint: Line up the decimal points and add column by column, carrying when needed — like $5.67 + $3.85 = $11.52.
   • Steps:
     • Hundredths: 5 + 9 = 14, write 4, carry 1.
     • Tenths: 7 + 4 + 1 = 12, write 2, carry 1.
     • Ones and tens: 12 + 8 + 1 = 21, write 21.
     • Total = $21.24.
   • Answer: $21.24

8. [Medium] Percentage (25% and 10%)

   • EN: A bag of chips normally costs $4.00. It is on sale for 25% off. What is the sale price?
   • FR: Un sac de croustilles coûte normalement 4,00 $. Il est en solde à 25 % de rabais. Quel est le prix de vente ?
   • Choices: A) $1.00 B) $2.00 C) $3.00 D) $3.50
   • Hint: 25% off means you save one quarter of the price — like 25% of $8.00 = $2.00, so sale price = $8.00 − $2.00 = $6.00.
   • Steps:
     • 25% of $4.00 = $4.00 ÷ 4 = $1.00.
     • Sale price = $4.00 − $1.00 = $3.00.
     • The sale price is $3.00.
   • Answer: $3.00

9. [Hard] Multi-Step Fraction and Decimal Problem

   • EN: A recipe calls for 3/4 cup of oats and 1/4 cup of raisins. If Noah makes 3 batches of the recipe, how many cups of ingredients does he use in total?
   • FR: Une recette demande 3/4 de tasse de flocons d'avoine et 1/4 de tasse de raisins secs. Si Noah fait 3 fois la recette, combien de tasses d'ingrédients utilise-t-il en tout ?
   • Choices: A) 2 cups B) 3 cups C) 4 cups D) 5 cups
   • Hint: Find the total per batch first, then multiply by the number of batches — like 1/3 + 2/3 = 1 cup per batch, 1 × 4 batches = 4 cups.
   • Steps:
     • Ingredients per batch: 3/4 + 1/4 = 4/4 = 1 cup.
     • 3 batches × 1 cup each = 3 cups.
     • Noah uses 3 cups of ingredients in total.
   • Answer: 3 cups

10. [Hard] Volume and Multi-Step

    • EN: A fish tank is 50 cm long, 25 cm wide, and 30 cm tall. It is filled halfway with water. What is the volume of water in the tank?
    • FR: Un aquarium mesure 50 cm de long, 25 cm de large et 30 cm de hauteur. Il est rempli d'eau à moitié. Quel est le volume d'eau dans l'aquarium ?
    • Choices: A) 12 500 cm³ B) 18 750 cm³ C) 25 000 cm³ D) 37 500 cm³
    • Hint: Find the full volume first (length × width × height), then divide by 2 for half — like a box 10 × 5 × 4 = 200 cm³ full, half = 100 cm³.
    • Steps:
      • Full volume: 50 × 25 × 30.
      • 50 × 25 = 1250, then 1250 × 30 = 37 500 cm³.
      • Half of 37 500 = 37 500 ÷ 2 = 18 750 cm³.
    • Answer: 18 750 cm³

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Grade 6 Problems

1. [Easy] Percent of a Number

   • EN: What is 30% of 200?
   • FR: Combien font 30 % de 200 ?
   • Choices: A) 30 B) 50 C) 60 D) 80
   • Hint: Find 10% first (divide by 10), then multiply — like 30% of 50: 10% = 5, so 30% = 5 × 3 = 15.
   • Steps:
     • 10% of 200 = 200 ÷ 10 = 20.
     • 30% = 3 × 20 = 60.
     • 30% of 200 is 60.
   • Answer: 60

2. [Easy] Order of Operations (BEDMAS)

   • EN: Calculate: 3 + 4 × 2.
   • FR: Calcule : 3 + 4 × 2.
   • Choices: A) 10 B) 11 C) 14 D) 20
   • Hint: In BEDMAS, Multiplication comes before Addition — like 5 + 2 × 3 = 5 + 6 = 11, not 7 × 3 = 21.
   • Steps:
     • Multiplication first: 4 × 2 = 8.
     • Then add: 3 + 8 = 11.
     • The answer is 11.
   • Answer: 11

3. [Easy] Ratios

   • EN: In a class, there are 12 boys and 16 girls. What is the ratio of boys to girls in simplest form?
   • FR: Dans une classe, il y a 12 garçons et 16 filles. Quel est le rapport des garçons aux filles sous sa forme simplifiée ?
   • Choices: A) 2:3 B) 3:4 C) 4:5 D) 12:16
   • Hint: To simplify a ratio, divide both numbers by their GCF — like 6:10 → GCF is 2 → 3:5.
   • Steps:
     • GCF of 12 and 16 is 4.
     • 12 ÷ 4 = 3 and 16 ÷ 4 = 4.
     • Ratio in simplest form is 3:4.
   • Answer: 3:4

4. [Easy] Integers Introduction

   • EN: The temperature in Winnipeg was −8°C in the morning and rose 11 degrees by noon. What was the temperature at noon?
   • FR: La température à Winnipeg était de −8 °C le matin et a augmenté de 11 degrés à midi. Quelle était la température à midi ?
   • Choices: A) −3°C B) 2°C C) 3°C D) 19°C
   • Hint: Adding a positive to a negative — start at the negative and count up, like −5 + 8 = 3.
   • Steps:
     • Start at −8 and add 11.
     • −8 + 11 = 3.
     • The temperature at noon was 3°C.
   • Answer: 3°C

5. [Medium] Fraction Multiplication

   • EN: What is 2/3 × 3/4?
   • FR: Combien font 2/3 × 3/4 ?
   • Choices: A) 5/7 B) 6/7 C) 1/2 D) 6/12
   • Hint: Multiply numerators together and denominators together — like 1/2 × 2/3 = 2/6 = 1/3.
   • Steps:
     • Multiply numerators: 2 × 3 = 6.
     • Multiply denominators: 3 × 4 = 12.
     • Simplify: 6/12 = 1/2.
   • Answer: 1/2

6. [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) 2/3
   • Hint: To divide fractions, multiply by the reciprocal (flip the second fraction) — like 2/5 ÷ 1/3 = 2/5 × 3/1 = 6/5.
   • Steps:
     • Flip the second fraction: 1/2 becomes 2/1.
     • Multiply: 3/4 × 2/1 = 6/4.
     • Simplify: 6/4 = 3/2.
   • Answer: 3/2

7. [Medium] Rates

   • EN: A car travels 240 km in 3 hours. What is the car's speed in km/h?
   • FR: Une voiture parcourt 240 km en 3 heures. Quelle est la vitesse de la voiture en km/h ?
   • Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
   • Hint: Speed = distance ÷ time — like if a bike goes 60 km in 2 hours, speed = 60 ÷ 2 = 30 km/h.
   • Steps:
     • Speed = distance ÷ time.
     • Speed = 240 ÷ 3.
     • Speed = 80 km/h.
   • Answer: 80 km/h

8. [Medium] Algebraic Expressions

   • EN: If n = 5, what is the value of 3n + 7?
   • FR: Si n = 5, quelle est la valeur de 3n + 7 ?
   • Choices: A) 15 B) 17 C) 22 D) 35
   • Hint: Substitute the value of the variable, then follow BEDMAS — like if n = 4, then 2n + 3 = 2 × 4 + 3 = 8 + 3 = 11.
   • Steps:
     • Substitute n = 5: 3(5) + 7.
     • Multiply first: 3 × 5 = 15.
     • Add: 15 + 7 = 22.
   • Answer: 22

9. [Hard] Complex BEDMAS

   • EN: Calculate: (12 − 4) × 3 + 2² ÷ 2.
   • FR: Calcule : (12 − 4) × 3 + 2² ÷ 2.
   • Choices: A) 24 B) 26 C) 27 D) 28
   • Hint: Follow BEDMAS order: Brackets first, then Exponents, then Division and Multiplication left to right, then Addition and Subtraction — like (5 − 2) × 4 + 2 = 3 × 4 + 2 = 12 + 2 = 14.
   • Steps:
     • Brackets: (12 − 4) = 8.
     • Exponents: 2² = 4.
     • Left to right × and ÷: 8 × 3 = 24 and 4 ÷ 2 = 2.
     • Addition: 24 + 2 = 26.
   • Answer: 26

10. [Hard] Percent Problem — Multi-Step

    • EN: A hockey jersey normally costs $80. It is on sale for 15% off. There is also 13% HST added after the discount. What is the final price?
    • FR: Un chandail de hockey coûte normalement 80 $. Il est en solde à 15 % de rabais. Une TVH de 13 % est aussi ajoutée après le rabais. Quel est le prix final ?
    • Choices: A) $75.00 B) $76.68 C) $78.00 D) $84.68
    • Hint: First calculate the discount, subtract it, then calculate the tax on the discounted price — like $100 item, 10% off = $90, then 5% tax = $90 × 1.05 = $94.50.
    • Steps:
      • Discount: 15% of $80 = 0.15 × 80 = $12.
      • Sale price: $80 − $12 = $68.
      • HST: 13% of $68 = 0.13 × 68 = $8.84.
      • Final price: $68.00 + $8.84 = $76.84. The closest answer choice is $76.68 — let me recalculate: 0.13 × 68 = 8.84, so $76.84. Adjusting choice: use $76.84.

    (Rewriting with corrected choices:)

11. [Hard] Percent Problem — Multi-Step

    • EN: A hockey jersey normally costs $80. It is on sale for 15% off. There is also 13% HST added after the discount. What is the final price?
    • FR: Un chandail de hockey coûte normalement 80 $. Il est en solde à 15 % de rabais. Une TVH de 13 % est aussi ajoutée après le rabais. Quel est le prix final ?
    • Choices: A) $68.00 B) $72.00 C) $76.84 D) $90.40
    • Hint: First calculate the discount, subtract it, then apply the tax on the new price — like $100 with 20% off = $80, then 10% tax = $80 × 1.10 = $88.
    • Steps:
      • Discount: 15% of $80 = $12. Sale price: $80 − $12 = $68.
      • Tax: 13% of $68 = 0.13 × 68 = $8.84.
      • Final price: $68 + $8.84 = $76.84.
    • Answer: $76.84

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Grade 7 Problems

1. [Easy] Integer Addition

   • EN: What is (−6) + 9?
   • FR: Combien font (−6) + 9 ?
   • Choices: A) −3 B) 2 C) 3 D) 15
   • Hint: When signs differ, subtract the smaller absolute value from the larger, and keep the sign of the bigger number — like (−4) + 7 = 3.
   • Steps:
     • |(−6)| = 6 and |9| = 9. The bigger is 9, which is positive.
     • Subtract: 9 − 6 = 3.
     • The answer is +3.
   • Answer: 3

2. [Easy] Percent — Discount

   • EN: A pair of skates costs $120. They are on sale for 20% off. How much do the skates cost after the discount?
   • FR: Une paire de patins coûte 120 $. Elle est en solde à 20 % de rabais. Combien les patins coûtent-ils après le rabais ?
   • Choices: A) $24.00 B) $84.00 C) $96.00 D) $100.00
   • Hint: Find the discount amount first, then subtract — like 10% of $60 = $6, so 20% = $12, sale price = $60 − $12 = $48.
   • Steps:
     • 20% of $120 = 0.20 × 120 = $24.
     • Sale price = $120 − $24 = $96.
     • The skates cost $96.00.
   • Answer: $96.00

3. [Easy] One-Step Linear Equation

   • EN: Solve for x: x + 13 = 27.
   • FR: Résous pour x : x + 13 = 27.
   • Choices: A) x = 10 B) x = 14 C) x = 15 D) x = 40
   • Hint: To solve, subtract what's being added from both sides — like y + 8 = 20 → y = 20 − 8 = 12.
   • Steps:
     • Subtract 13 from both sides: x + 13 − 13 = 27 − 13.
     • x = 14.
     • Check: 14 + 13 = 27. Correct.
   • Answer: x = 14

4. [Easy] Integer Subtraction

   • EN: What is 5 − (−3)?
   • FR: Combien font 5 − (−3) ?
   • Choices: A) 2 B) 7 C) 8 D) 15
   • Hint: Subtracting a negative is the same as adding a positive — like 4 − (−2) = 4 + 2 = 6.
   • Steps:
     • Change subtraction of a negative to addition: 5 − (−3) = 5 + 3.
     • 5 + 3 = 8.
     • The answer is 8.
   • Answer: 8

5. [Medium] Fraction Operations

   • EN: What is 2 1/3 + 1 2/3?
   • FR: Combien font 2 1/3 + 1 2/3 ?
   • Choices: A) 3 1/3 B) 3 2/3 C) 4 D) 4 1/3
   • Hint: Add the whole numbers and the fractions separately — like 1 1/4 + 2 3/4 = (1 + 2) + (1/4 + 3/4) = 3 + 1 = 4.
   • Steps:
     • Whole numbers: 2 + 1 = 3.
     • Fractions: 1/3 + 2/3 = 3/3 = 1.
     • Total: 3 + 1 = 4.
   • Answer: 4

6. [Medium] Percentage — Tip

   • EN: A family's restaurant bill is $48. They want to leave a 15% tip. How much is the tip?
   • FR: La facture d'un restaurant pour une famille est de 48 $. Ils veulent laisser un pourboire de 15 %. Quel est le montant du pourboire ?
   • Choices: A) $4.80 B) $6.20 C) $7.20 D) $9.60
   • Hint: 15% = 10% + 5% — like for a $60 bill: 10% = $6.00 and 5% = $3.00, tip = $9.00.
   • Steps:
     • 10% of $48 = $4.80.
     • 5% of $48 = $4.80 ÷ 2 = $2.40.
     • 15% = $4.80 + $2.40 = $7.20.
   • Answer: $7.20

7. [Medium] Surface Area of a Rectangular Prism

   • EN: A gift box measures 10 cm long, 6 cm wide, and 4 cm tall. What is the surface area of the box?
   • FR: Une boîte-cadeau mesure 10 cm de long, 6 cm de large et 4 cm de hauteur. Quelle est l'aire de la surface de la boîte ?
   • Choices: A) 208 cm² B) 240 cm² C) 248 cm² D) 280 cm²
   • Hint: Surface area = 2(lw + lh + wh) — like a 3 × 2 × 1 box: 2(6 + 3 + 2) = 2 × 11 = 22 cm².
   • Steps:
     • lw = 10 × 6 = 60; lh = 10 × 4 = 40; wh = 6 × 4 = 24.
     • Sum = 60 + 40 + 24 = 124.
     • Surface area = 2 × 124 = 248 cm².
   • Answer: 248 cm²

8. [Medium] Probability

   • EN: A bag has 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of picking a blue marble at random?
   • FR: Un sac contient 3 billes rouges, 5 billes bleues et 2 billes vertes. Quelle est la probabilité de piger une bille bleue au hasard ?
   • Choices: A) 1/5 B) 1/2 C) 5/10 D) 3/10
   • Hint: Probability = favourable outcomes ÷ total outcomes — like 2 red out of 8 total = 2/8 = 1/4.
   • Steps:
     • Total marbles: 3 + 5 + 2 = 10.
     • Blue marbles: 5.
     • Probability = 5/10 = 1/2.
   • Answer: 1/2

9. [Hard] Integer Operations — Multi-Step

   • EN: The temperature in Yellowknife was −14°C. It dropped 7 degrees overnight and then rose 19 degrees by afternoon. What was the afternoon temperature?
   • FR: La température à Yellowknife était de −14 °C. Elle a baissé de 7 degrés pendant la nuit, puis a monté de 19 degrés dans l'après-midi. Quelle était la température l'après-midi ?
   • Choices: A) −2°C B) 2°C C) −12°C D) 12°C
   • Hint: Work step by step — apply each change in order, like −10 − 5 + 20 = −15 + 20 = 5.
   • Steps:
     • Start: −14. Drop 7: −14 − 7 = −21.
     • Rise 19: −21 + 19 = −2.
     • The afternoon temperature was −2°C.
   • Answer: −2°C

10. [Hard] Percent — Tax and Total

    • EN: Theo buys a new hockey stick priced at $65. Ontario HST is 13%. What is the total cost including tax?
    • FR: Théo achète un nouveau bâton de hockey au prix de 65 $. La TVH de l'Ontario est de 13 %. Quel est le coût total, taxes incluses ?
    • Choices: A) $72.45 B) $73.45 C) $74.45 D) $78.00
    • Hint: Total with tax = price × (1 + tax rate) — like $50 with 10% tax = $50 × 1.10 = $55.
    • Steps:
      • Total = $65 × 1.13.
      • $65 × 1 = $65.00; $65 × 0.13 = $8.45.
      • Total = $65 + $8.45 = $73.45.
    • Answer: $73.45

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Grade 8 Problems

1. [Easy] Perfect Squares and Square Roots

   • EN: What is √144?
   • FR: Combien font √144 ?
   • Choices: A) 11 B) 12 C) 13 D) 14
   • Hint: Think of perfect squares — like √121 = 11 because 11 × 11 = 121.
   • Steps:
     • Ask: what number times itself equals 144?
     • 12 × 12 = 144.
     • So √144 = 12.
   • Answer: 12

2. [Easy] Mean

   • EN: Five students scored the following on a quiz: 72, 80, 88, 64, and 96. What is the mean (average) score?
   • FR: Cinq élèves ont obtenu les scores suivants à un examen : 72, 80, 88, 64 et 96. Quelle est la moyenne ?
   • Choices: A) 78 B) 80 C) 82 D) 88
   • Hint: Mean = sum of all values ÷ number of values — like (4 + 6 + 8) ÷ 3 = 18 ÷ 3 = 6.
   • Steps:
     • Sum: 72 + 80 + 88 + 64 + 96 = 400.
     • Mean: 400 ÷ 5 = 80.
     • The mean score is 80.
   • Answer: 80

3. [Easy] Two-Step Linear Equation

   • EN: Solve for x: 2x + 5 = 17.
   • FR: Résous pour x : 2x + 5 = 17.
   • Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 11
   • Hint: Undo the equation step by step — first subtract the constant, then divide by the coefficient, like 3x + 4 = 13 → 3x = 9 → x = 3.
   • Steps:
     • Subtract 5 from both sides: 2x = 12.
     • Divide by 2: x = 6.
     • Check: 2(6) + 5 = 17. Correct.
   • Answer: x = 6

4. [Easy] Percent Increase

   • EN: A bag of flour costs $3.00 this year. Last year it cost $2.50. What is the percent increase?
   • FR: Un sac de farine coûte 3,00 $ cette année. L'an dernier, il coûtait 2,50 $. Quel est le pourcentage d'augmentation ?
   • Choices: A) 15% B) 20% C) 25% D) 50%
   • Hint: Percent increase = (new − old) ÷ old × 100 — like old = $40, new = $50, increase = $10, so 10/40 × 100 = 25%.
   • Steps:
     • Increase = $3.00 − $2.50 = $0.50.
     • Percent increase = (0.50 ÷ 2.50) × 100.
     • 0.50 ÷ 2.50 = 0.20, and 0.20 × 100 = 20%.
   • Answer: 20%

5. [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 c = √25 = 5.
   • Steps:
     • a² + b² = c².
     • 6² + 8² = 36 + 64 = 100.
     • c = √100 = 10 cm.
   • Answer: 10 cm

6. [Medium] Two-Step Equation with Negatives

   • EN: Solve for x: 3x − 7 = 11.
   • FR: Résous pour x : 3x − 7 = 11.
   • Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
   • Hint: Add to both sides first, then divide — like 4x − 3 = 13: add 3 to both sides → 4x = 16 → x = 4.
   • Steps:
     • Add 7 to both sides: 3x = 18.
     • Divide by 3: x = 6.
     • Check: 3(6) − 7 = 18 − 7 = 11. Correct.
   • Answer: x = 6

7. [Medium] Slope Introduction

   • EN: A line passes through the points (2, 3) and (6, 11). What is the slope of the line?
   • FR: Une droite passe par les points (2, 3) et (6, 11). Quelle est la pente de la droite ?
   • Choices: A) 1 B) 2 C) 3 D) 4
   • Hint: Slope = (change in y) ÷ (change in x) = (y₂ − y₁) ÷ (x₂ − x₁) — like points (1, 2) and (3, 8): slope = (8−2) ÷ (3−1) = 6/2 = 3.
   • Steps:
     • Slope = (11 − 3) ÷ (6 − 2).
     • = 8 ÷ 4.
     • = 2.
   • Answer: 2

8. [Medium] Median and Mode

   • EN: Find the median of this data set: 5, 12, 7, 3, 9, 7, 14.
   • FR: Trouve la médiane de cet ensemble de données : 5, 12, 7, 3, 9, 7, 14.
   • Choices: A) 5 B) 7 C) 9 D) 12
   • Hint: To find the median, sort the numbers from least to greatest and find the middle value — like 2, 5, 6, 9, 11 → median is 6.
   • Steps:
     • Sort: 3, 5, 7, 7, 9, 12, 14.
     • There are 7 values; the middle is the 4th.
     • The 4th value is 7, so the median is 7.
   • Answer: 7

9. [Hard] Pythagorean Theorem — Problem Solving

   • EN: A 13 m ladder leans against a wall. The base of the ladder is 5 m from the wall. How high up the wall does the ladder reach?
   • FR: Une échelle de 13 m est appuyée contre un mur. La base de l'échelle est à 5 m du mur. À quelle hauteur l'échelle atteint-elle le mur ?
   • Choices: A) 8 m B) 10 m C) 12 m D) 18 m
   • Hint: The ladder is the hypotenuse — use a² + b² = c² and solve for the missing leg: b² = c² − a², like 10² − 6² = 100 − 36 = 64, so b = 8.
   • Steps:
     • c = 13 (ladder), a = 5 (base), find b (height).
     • b² = 13² − 5² = 169 − 25 = 144.
     • b = √144 = 12 m.
   • Answer: 12 m

10. [Hard] Percent Decrease — Multi-Step

    • EN: A coat was priced at $250. Its price was reduced by 30%. Then there was an additional 10% off the new price. What was the final price?
    • FR: Un manteau était au prix de 250 $. Son prix a été réduit de 30 %. Ensuite, un rabais supplémentaire de 10 % a été appliqué sur le nouveau prix. Quel était le prix final ?
    • Choices: A) $155.00 B) $157.50 C) $165.00 D) $175.00
    • Hint: Apply each discount one at a time to the current price — like $100 with 20% off = $80, then 10% off $80 = $72.
    • Steps:
      • First discount: 30% of $250 = $75. New price = $250 − $75 = $175.
      • Second discount: 10% of $175 = $17.50. Final price = $175 − $17.50 = $157.50.
      • The final price is $157.50.
    • Answer: $157.50

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Grade 9 Problems

1. [Easy] Solving a Linear Equation

   • EN: Solve for x: 4x − 8 = 20.
   • FR: Résous pour x : 4x − 8 = 20.
   • Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
   • Hint: Add the constant to both sides, then divide by the coefficient — like 5x − 3 = 17: add 3 → 5x = 20 → x = 4.
   • Steps:
     • Add 8 to both sides: 4x = 28.
     • Divide by 4: x = 7.
     • Check: 4(7) − 8 = 28 − 8 = 20. Correct.
   • Answer: x = 7

2. [Easy] Slope-Intercept Form

   • EN: What is the slope of the line y = 3x − 5?
   • FR: Quelle est la pente de la droite y = 3x − 5 ?
   • Choices: A) −5 B) 1 C) 3 D) 5
   • Hint: In y = mx + b, m is the slope and b is the y-intercept — like in y = 2x + 7, the slope is 2.
   • Steps:
     • The equation is in y = mx + b form.
     • m = 3 (the coefficient of x).
     • The slope is 3.
   • Answer: 3

3. [Easy] Adding Polynomials

   • EN: Simplify: (3x + 5) + (2x − 3).
   • FR: Simplifie : (3x + 5) + (2x − 3).
   • Choices: A) 5x + 2 B) 5x − 2 C) 6x + 2 D) 5x + 8
   • Hint: Combine like terms — group the x-terms and the constants, like (4x + 2) + (x + 6) = 5x + 8.
   • Steps:
     • x-terms: 3x + 2x = 5x.
     • Constants: 5 + (−3) = 2.
     • Result: 5x + 2.
   • Answer: 5x + 2

4. [Easy] Similar Triangles

   • EN: Two similar triangles have corresponding sides. The smaller triangle has a base of 4 cm and the larger has a base of 12 cm. If the smaller triangle's height is 6 cm, what is the larger triangle's height?
   • FR: Deux triangles semblables ont des côtés correspondants. Le petit triangle a une base de 4 cm et le grand a une base de 12 cm. Si la hauteur du petit triangle est de 6 cm, quelle est la hauteur du grand triangle ?
   • Choices: A) 8 cm B) 14 cm C) 18 cm D) 24 cm
   • Hint: Find the scale factor first (larger ÷ smaller), then multiply the known side — like 6 cm and 9 cm bases: scale factor = 9/6 = 1.5, so height 4 × 1.5 = 6 cm.
   • Steps:
     • Scale factor = 12 ÷ 4 = 3.
     • Larger height = 6 × 3 = 18.
     • The larger triangle's height is 18 cm.
   • Answer: 18 cm

5. [Medium] Linear Inequality

   • 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 < 4
   • Hint: Solve inequalities the same way as equations, but keep the inequality sign — like 3x − 2 > 7: add 2 → 3x > 9 → x > 3.
   • Steps:
     • Subtract 3 from both sides: 2x > 8.
     • Divide by 2: x > 4.
     • The solution is x > 4.
   • Answer: x > 4

6. [Medium] Multiplying Polynomials

   • EN: Expand: (x + 3)(x + 5).
   • FR: Développe : (x + 3)(x + 5).
   • Choices: A) x² + 7x + 15 B) x² + 8x + 15 C) x² + 15x + 8 D) x² + 8x + 8
   • Hint: Use FOIL — First, Outer, Inner, Last — like (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8.
   • Steps:
     • First: x × x = x².
     • Outer: x × 5 = 5x. Inner: 3 × x = 3x.
     • Last: 3 × 5 = 15. Combine: x² + 8x + 15.
   • Answer: x² + 8x + 15

7. [Medium] Trigonometry — SOH

   • EN: In a right triangle, the angle θ = 30°, and the hypotenuse is 10 cm. What is the length of the side opposite θ?
   • FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse mesure 10 cm. Quelle est la longueur du côté opposé à θ ?
   • Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
   • Hint: sin(θ) = opposite ÷ hypotenuse, so opposite = hypotenuse × sin(θ) — like sin(45°) ≈ 0.707, so opposite = 20 × 0.707 ≈ 14.1 cm.
   • Steps:
     • sin(30°) = 0.5.
     • opposite = hypotenuse × sin(θ) = 10 × 0.5.
     • opposite = 5 cm.
   • Answer: 5 cm

8. [Medium] Statistics — Interpreting Data

   • EN: The ages of 6 players on a hockey team are: 14, 15, 13, 15, 16, and 15. What is the mode of the ages?
   • FR: Les âges de 6 joueurs d'une équipe de hockey sont : 14, 15, 13, 15, 16 et 15. Quel est le mode des âges ?
   • Choices: A) 13 B) 14 C) 15 D) 16
   • Hint: The mode is the value that appears most often in the data set — like in 3, 5, 5, 7, 9, the mode is 5.
   • Steps:
     • List: 13, 14, 15, 15, 15, 16.
     • 15 appears 3 times — more than any other value.
     • The mode is 15.
   • Answer: 15

9. [Hard] Graphing Lines — Two Intercepts

   • EN: A line has equation 2x + 3y = 12. What are the x-intercept and y-intercept of this line?
   • FR: Une droite a l'équation 2x + 3y = 12. Quels sont l'abscisse à l'origine et l'ordonnée à l'origine de cette droite ?
   • Choices: A) x-intercept: 4, y-intercept: 6 B) x-intercept: 6, y-intercept: 4 C) x-intercept: 3, y-intercept: 2 D) x-intercept: 12, y-intercept: 12
   • Hint: For x-intercept, set y = 0 and solve; for y-intercept, set x = 0 and solve — like 4x + 2y = 8: x-int → 4x = 8 → x = 2, y-int → 2y = 8 → y = 4.
   • Steps:
     • x-intercept: set y = 0 → 2x = 12 → x = 6.
     • y-intercept: set x = 0 → 3y = 12 → y = 4.
     • x-intercept: 6, y-intercept: 4.
   • Answer: x-intercept: 6, y-intercept: 4

10. [Hard] Trigonometry — Finding an Angle

    • EN: In a right triangle, the side adjacent to angle θ is 8 cm and the hypotenuse is 17 cm. What is the value of cos(θ)?
    • FR: Dans un triangle rectangle, le côté adjacent à l'angle θ mesure 8 cm et l'hypoténuse mesure 17 cm. Quelle est la valeur de cos(θ) ?
    • Choices: A) 8/15 B) 8/17 C) 15/17 D) 17/8
    • Hint: cos(θ) = adjacent ÷ hypotenuse (CAH) — like if adjacent = 5 and hypotenuse = 13, then cos(θ) = 5/13.
    • Steps:
      • CAH: cos(θ) = adjacent ÷ hypotenuse.
      • cos(θ) = 8 ÷ 17.
      • cos(θ) = 8/17.
    • Answer: 8/17

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Grade 10 Problems

1. [Easy] Factoring a Quadratic

   • EN: Factor: x² + 7x + 12.
   • FR: Factorise : x² + 7x + 12.
   • Choices: A) (x + 3)(x + 4) B) (x + 2)(x + 6) C) (x + 1)(x + 12) D) (x + 4)(x + 4)
   • Hint: Find two numbers that multiply to the constant and add to the middle coefficient — like x² + 5x + 6: 2 × 3 = 6 and 2 + 3 = 5, so (x + 2)(x + 3).
   • Steps:
     • Need two numbers that multiply to 12 and add to 7.
     • 3 × 4 = 12 and 3 + 4 = 7.
     • So x² + 7x + 12 = (x + 3)(x + 4).
   • Answer: (x + 3)(x + 4)

2. [Easy] Trigonometry — All Ratios

   • EN: In a right triangle, the opposite side is 5 and the hypotenuse is 13. What is sin(θ)?
   • FR: Dans un triangle rectangle, le côté opposé mesure 5 et l'hypoténuse mesure 13. Quelle est la valeur de sin(θ) ?
   • Choices: A) 5/12 B) 5/13 C) 12/13 D) 13/5
   • Hint: sin(θ) = opposite ÷ hypotenuse — like if opposite = 3 and hypotenuse = 5, sin(θ) = 3/5.
   • Steps:
     • sin(θ) = opposite ÷ hypotenuse.
     • sin(θ) = 5 ÷ 13.
     • sin(θ) = 5/13.
   • Answer: 5/13

3. [Easy] Systems of Equations — Substitution

   • EN: If y = 2x and x + y = 12, what is the value of x?
   • FR: Si y = 2x et x + y = 12, quelle est la valeur de x ?
   • Choices: A) x = 3 B) x = 4 C) x = 6 D) x = 8
   • Hint: Substitute the expression for y into the second equation — like y = 3x and x + y = 8: x + 3x = 8 → 4x = 8 → x = 2.
   • Steps:
     • Substitute y = 2x into x + y = 12: x + 2x = 12.
     • 3x = 12.
     • x = 4.
   • Answer: x = 4

4. [Easy] Volume of a Cylinder

   • EN: A cylindrical can has a radius of 5 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14.)
   • FR: Une boîte cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est son volume ? (Utilise π ≈ 3,14.)
   • Choices: A) 314 cm³ B) 471 cm³ C) 785 cm³ D) 942 cm³
   • Hint: Volume of a cylinder = π × r² × h — like r = 3, h = 7: V = 3.14 × 9 × 7 = 197.82 cm³.
   • Steps:
     • V = π × r² × h = 3.14 × 5² × 10.
     • = 3.14 × 25 × 10.
     • = 3.14 × 250 = 785 cm³.
   • Answer: 785 cm³

5. [Medium] Completing the Square

   • EN: Solve by completing the square: x² + 6x − 7 = 0.
   • FR: Résous par complétion du carré : x² + 6x − 7 = 0.
   • Choices: A) x = 1 or x = −7 B) x = 7 or x = −1 C) x = 3 or x = −7 D) x = 1 or x = 7
   • Hint: Move the constant, complete the square, then solve — like x² + 4x − 5 = 0: x² + 4x = 5, (x+2)² = 9, x + 2 = ±3, x = 1 or x = −5.
   • Steps:
     • x² + 6x = 7. Add (6/2)² = 9 to both sides: (x + 3)² = 16.
     • x + 3 = ±4.
     • x = 1 or x = −7.
   • Answer: x = 1 or x = −7

6. [Medium] Circle Geometry

   • EN: The diameter of a circle is 18 cm. What is the circumference? (Use π ≈ 3.14.)
   • FR: Le diamètre d'un cercle est de 18 cm. Quelle est la circonférence ? (Utilise π ≈ 3,14.)
   • Choices: A) 28.26 cm B) 56.52 cm C) 113.04 cm D) 254.34 cm
   • Hint: Circumference = π × diameter — like a circle with diameter 10: C = 3.14 × 10 = 31.4 cm.
   • Steps:
     • C = π × d = 3.14 × 18.
     • 3.14 × 18 = 56.52.
     • Circumference = 56.52 cm.
   • Answer: 56.52 cm

7. [Medium] Quadratic — Factoring to Solve

   • EN: Solve: x² − 5x + 6 = 0.
   • FR: Résous : x² − 5x + 6 = 0.
   • Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = −2 or x = −3 D) x = 5 or x = 6
   • Hint: Factor the quadratic, then set each factor to zero — like x² − 7x + 12 = 0: (x − 3)(x − 4) = 0, so x = 3 or x = 4.
   • Steps:
     • Factor: (x − 2)(x − 3) = 0.
     • x − 2 = 0 → x = 2; x − 3 = 0 → x = 3.
     • x = 2 or x = 3.
   • Answer: x = 2 or x = 3

8. [Medium] Surface Area of a Cone

   • EN: A cone has a radius of 6 cm and a slant height of 10 cm. What is the 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 l'aire totale de la surface ? (Utilise π ≈ 3,14.)
   • Choices: A) 188.4 cm² B) 301.44 cm² C) 376.8 cm² D) 452.16 cm²
   • Hint: Total surface area of a cone = πrl + πr² (lateral + 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.
     • Base area = π × r² = 3.14 × 36 = 113.04.
     • Total = 188.4 + 113.04 = 301.44 cm².
   • Answer: 301.44 cm²

9. [Hard] Systems of Equations — Elimination

   • EN: Solve the system: 2x + 3y = 16 and 4x − 3y = 8. What are the values of x and y?
   • FR: Résous le système : 2x + 3y = 16 et 4x − 3y = 8. Quelles sont les valeurs de x et y ?
   • Choices: A) x = 3, y = 4 B) x = 4, y = 8/3 C) x = 4, y = 3 D) x = 6, y = 1
   • Hint: Add the equations when coefficients are opposite — like 3x + 2y = 10 and x − 2y = 2: add them → 4x = 12 → x = 3, then find y.
   • Steps:
     • Add equations: (2x + 3y) + (4x − 3y) = 16 + 8 → 6x = 24 → x = 4.
     • Substitute x = 4 into first equation: 8 + 3y = 16 → 3y = 8 → y = 8/3.
     • Hmm, not a clean answer. Let me recheck: 2(4) + 3y = 16 → 8 + 3y = 16 → 3y = 8 → y = 8/3. Let me redo with different numbers.

   (Rewriting with cleaner values:)

10. [Hard] Systems of Equations — Elimination

    • EN: Solve the system: 3x + 2y = 12 and x − 2y = 4. What are the values of x and y?
    • FR: Résous le système : 3x + 2y = 12 et x − 2y = 4. Quelles sont les valeurs de x et y ?
    • Choices: A) x = 3, y = 1 B) x = 4, y = 0 C) x = 2, y = 3 D) x = 5, y = −1
    • Hint: Add the two equations together to eliminate y, then solve for x, then substitute back — like 2x + y = 7 and x − y = 2: add → 3x = 9 → x = 3, y = 1.
    • Steps:
      • Add: (3x + 2y) + (x − 2y) = 12 + 4 → 4x = 16 → x = 4.
      • Substitute x = 4 into x − 2y = 4: 4 − 2y = 4 → −2y = 0 → y = 0.
      • x = 4, y = 0.
    • Answer: x = 4, y = 0

11. [Hard] Quadratic Formula

    • EN: Use the quadratic formula to solve: 2x² + 3x − 5 = 0.
    • FR: Utilise la formule quadratique pour résoudre : 2x² + 3x − 5 = 0.
    • Choices: A) x = 1 or x = −5/2 B) x = −1 or x = 5/2 C) x = 2 or x = −5 D) x = 1 or x = 5
    • Hint: The quadratic formula is x = (−b ± √(b² − 4ac)) ÷ (2a) — like a=1, b=2, c=−3: discriminant = 4+12=16, x = (−2 ± 4)/2 = 1 or −3.
    • Steps:
      • a = 2, b = 3, c = −5. Discriminant = 3² − 4(2)(−5) = 9 + 40 = 49.
      • x = (−3 ± √49) ÷ 4 = (−3 ± 7) ÷ 4.
      • x = (−3 + 7)/4 = 1, or x = (−3 − 7)/4 = −10/4 = −5/2.
    • Answer: x = 1 or x = −5/2

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Grade 11 Problems

1. [Easy] Exponential Function

   • EN: A bacteria colony starts with 50 cells and doubles every hour. How many cells are there after 3 hours?
   • FR: Une colonie de bactéries commence avec 50 cellules et double chaque heure. Combien y a-t-il de cellules après 3 heures ?
   • Choices: A) 150 B) 200 C) 300 D) 400
   • Hint: Exponential growth formula: A = initial × 2^t — like starting with 10, after 2 hours: 10 × 2² = 10 × 4 = 40.
   • Steps:
     • A = 50 × 2³.
     • 2³ = 8.
     • A = 50 × 8 = 400 cells.
   • Answer: 400

2. [Easy] Arithmetic Sequence

   • EN: The first term of an arithmetic sequence is 7 and the common difference is 5. What is the 6th term?
   • FR: Le premier terme d'une suite arithmétique est 7 et la raison est 5. Quel est le 6e terme ?
   • Choices: A) 30 B) 32 C) 35 D) 37
   • Hint: Use the formula: tₙ = t₁ + (n − 1)d — like first term 3, difference 4, 5th term = 3 + (4)(4) = 19.
   • Steps:
     • t₆ = 7 + (6 − 1) × 5.
     • = 7 + 5 × 5 = 7 + 25.
     • = 32.
   • Answer: 32

3. [Easy] Introduction to Logarithms

   • EN: What is log₂(8)?
   • FR: Combien font log₂(8) ?
   • Choices: A) 2 B) 3 C) 4 D) 8
   • Hint: log_b(x) asks "what power of b gives x?" — like log₃(27): 3² = 9, 3³ = 27, so answer is 3.
   • Steps:
     • log₂(8) asks: "2 to what power equals 8?"
     • 2¹ = 2, 2² = 4, 2³ = 8.
     • log₂(8) = 3.
   • Answer: 3

4. [Easy] Compound Interest

   • EN: $500 is invested at an annual interest rate of 4%, compounded annually. What is the total amount after 2 years?
   • FR: 500 $ sont investis à un taux d'intérêt annuel de 4 %, composé annuellement. Quel est le montant total après 2 ans ?
   • Choices: A) $540.00 B) $540.80 C) $541.20 D) $545.00
   • Hint: Use A = P(1 + r)ⁿ — like $200 at 5% for 2 years: A = 200 × (1.05)² = 200 × 1.1025 = $220.50.
   • Steps:
     • A = 500 × (1.04)².
     • (1.04)² = 1.0816.
     • A = 500 × 1.0816 = $540.80.
   • Answer: $540.80

5. [Medium] Logarithm — Solving

   • EN: Solve for x: log₃(x) = 4.
   • FR: Résous pour x : log₃(x) = 4.
   • Choices: A) x = 12 B) x = 34 C) x = 64 D) x = 81
   • Hint: Convert the logarithm to exponential form: if log_b(x) = n, then x = bⁿ — like log₂(x) = 5 means x = 2⁵ = 32.
   • Steps:
     • log₃(x) = 4 means 3⁴ = x.
     • 3⁴ = 3 × 3 × 3 × 3 = 81.
     • x = 81.
   • Answer: x = 81

6. [Medium] Geometric Sequence — Sum

   • EN: Find the sum of the first 4 terms of a geometric sequence where the first term is 2 and the common ratio is 3.
   • FR: Trouve la somme des 4 premiers termes d'une suite géométrique où le premier terme est 2 et la raison est 3.
   • Choices: A) 26 B) 54 C) 80 D) 162
   • Hint: Sₙ = t₁ × (rⁿ − 1) ÷ (r − 1) — like first term 1, ratio 2, n=4: S = 1 × (16 − 1) ÷ 1 = 15.
   • Steps:
     • S₄ = 2 × (3⁴ − 1) ÷ (3 − 1).
     • 3⁴ = 81. S₄ = 2 × (81 − 1) ÷ 2.
     • = 2 × 80 ÷ 2 = 80.
   • Answer: 80

7. [Medium] Quadratic Function — Vertex

   • EN: What is the vertex of the parabola y = (x − 3)² + 5?
   • FR: Quel est le sommet de la parabole y = (x − 3)² + 5 ?
   • Choices: A) (−3, 5) B) (3, 5) C) (5, 3) D) (3, −5)
   • Hint: In vertex form y = (x − h)² + k, the vertex is (h, k) — like y = (x − 2)² + 7 has vertex (2, 7).
   • Steps:
     • The equation is in vertex form: y = (x − 3)² + 5.
     • h = 3 and k = 5.
     • Vertex is (3, 5).
   • Answer: (3, 5)

8. [Medium] Financial Math — Annuity

   • EN: Priya deposits $200 at the end of each year into an account earning 5% annually. What is the value of the annuity after 3 years?
   • FR: Priya dépose 200 $ à la fin de chaque année dans un compte à 5 % par an. Quelle est la valeur de la rente après 3 ans ?
   • Choices: A) $600.00 B) $630.50 C) $662.00 D) $662.05
   • Hint: Annuity formula: FV = PMT × ((1 + r)ⁿ − 1) ÷ r — like PMT = $100, r = 10%, n = 2: FV = 100 × (1.21 − 1) ÷ 0.10 = $210.
   • Steps:
     • FV = 200 × ((1.05)³ − 1) ÷ 0.05.
     • (1.05)³ = 1.157625. 1.157625 − 1 = 0.157625.
     • FV = 200 × 0.157625 ÷ 0.05 = 200 × 3.1525 = $630.50.
   • Answer: $630.50

9. [Hard] Trigonometric Identity

   • EN: Simplify: sin²(x) + cos²(x) + tan²(x).
   • FR: Simplifie : sin²(x) + cos²(x) + tan²(x).
   • Choices: A) 1 + tan²(x) B) sec²(x) C) 1 + sec²(x) D) 2
   • Hint: Use the Pythagorean identity sin²(x) + cos²(x) = 1, then look for another identity — like 1 + tan²(x) = sec²(x).
   • Steps:
     • sin²(x) + cos²(x) = 1 (Pythagorean identity).
     • So the expression becomes 1 + tan²(x).
     • Using the identity 1 + tan²(x) = sec²(x), the simplified form is sec²(x).
   • Answer: sec²(x)

10. [Hard] Compound Interest — Solving for Time

    • EN: How many years does it take for $1000 to double at an annual compound interest rate of 10%?
    • FR: Combien d'années faut-il pour que 1 000 $ doublent à un taux d'intérêt composé annuel de 10 % ?
    • Choices: A) About 5 years B) About 7 years C) About 10 years D) About 14 years
    • Hint: Use the rule of 72 as an estimate: 72 ÷ interest rate = approximate doubling time — like 72 ÷ 6 = 12 years to double at 6%.
    • Steps:
      • Solve 1000 × (1.10)ⁿ = 2000 → (1.10)ⁿ = 2.
      • Take log of both sides: n × log(1.10) = log(2).
      • n = log(2) ÷ log(1.10) ≈ 0.3010 ÷ 0.04139 ≈ 7.27 years.
    • Answer: About 7 years

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Grade 12 Problems

1. [Easy] Permutations

   • EN: In how many ways can 4 students be arranged in a line?
   • FR: De combien de façons peut-on placer 4 élèves en ligne ?
   • Choices: A) 12 B) 16 C) 24 D) 48
   • Hint: The number of arrangements of n items in a line is n! — like 3 students: 3! = 3 × 2 × 1 = 6 ways.
   • Steps:
     • 4! = 4 × 3 × 2 × 1.
     • = 12 × 2 = 24.
     • There are 24 ways.
   • Answer: 24

2. [Easy] Combinations

   • EN: How many ways can 2 students be chosen from a group of 5 to represent the class?
   • FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 5 pour représenter la classe ?
   • Choices: A) 5 B) 10 C) 15 D) 20
   • Hint: Use C(n, r) = n! ÷ (r! × (n−r)!) — like C(4, 2) = 4! ÷ (2! × 2!) = 24 ÷ 4 = 6.
   • Steps:
     • C(5, 2) = 5! ÷ (2! × 3!) = (5 × 4) ÷ (2 × 1).
     • = 20 ÷ 2 = 10.
     • There are 10 ways.
   • Answer: 10

3. [Easy] Derivative — Power Rule

   • EN: What is the derivative of f(x) = x³?
   • FR: Quelle est la dérivée de f(x) = x³ ?
   • Choices: A) x² B) 2x² C) 3x² D) 3x³
   • Hint: Power rule: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹ — like f(x) = x⁵, f'(x) = 5x⁴.
   • Steps:
     • Apply the power rule to x³.
     • Bring down the exponent: 3, then reduce the power by 1: x².
     • f'(x) = 3x².
   • Answer: 3x²

4. [Easy] Vector Addition

   • EN: Vector a = (3, 4) and vector b = (1, −2). What is a + b?
   • FR: Le vecteur a = (3, 4) et le vecteur b = (1, −2). Quel est a + b ?
   • Choices: A) (2, 6) B) (3, 2) C) (4, 2) D) (4, 6)
   • Hint: Add vectors component by component — like (2, 5) + (3, −1) = (2+3, 5+(−1)) = (5, 4).
   • Steps:
     • x-component: 3 + 1 = 4.
     • y-component: 4 + (−2) = 2.
     • a + b = (4, 2).
   • Answer: (4, 2)

5. [Medium] Polynomial Long Division

   • EN: Divide (x² + 5x + 6) by (x + 2). What is the quotient?
   • FR: Divise (x² + 5x + 6) par (x + 2). Quel est le quotient ?
   • Choices: A) x + 2 B) x + 3 C) x + 4 D) x² + 3
   • Hint: Divide the leading term first, multiply back, subtract, then repeat — like (x² + 4x + 4) ÷ (x + 2): x times (x+2) = x² + 2x, subtract → 2x + 4, divide 2x by x = 2, quotient = x + 2.
   • Steps:
     • x² ÷ x = x. Multiply: x(x + 2) = x² + 2x. Subtract: (x² + 5x + 6) − (x² + 2x) = 3x + 6.
     • 3x ÷ x = 3. Multiply: 3(x + 2) = 3x + 6. Subtract: 0.
     • Quotient = x + 3.
   • Answer: x + 3

6. [Medium] Probability Distribution — Expected Value

   • EN: A game gives a prize of $10 with probability 0.2, a prize of $5 with probability 0.5, and no prize with probability 0.3. What is the expected value of the prize?
   • FR: Un jeu offre un prix de 10 $ avec une probabilité de 0,2, un prix de 5 $ avec une probabilité de 0,5 et aucun prix avec une probabilité de 0,3. Quelle est la valeur espérée du prix ?
   • Choices: A) $4.00 B) $4.50 C) $5.00 D) $7.50
   • Hint: Expected value = sum of (value × probability) for each outcome — like $20 × 0.3 + $0 × 0.7 = $6.
   • Steps:
     • E = (10 × 0.2) + (5 × 0.5) + (0 × 0.3).
     • = 2.00 + 2.50 + 0.
     • = $4.50.
   • Answer: $4.50

7. [Medium] Derivative — Rate of Change

   • EN: The position of a hockey puck is given by s(t) = 4t² + 3t. What is the puck's velocity at t = 2 seconds?
   • FR: La position d'une rondelle de hockey est donnée par s(t) = 4t² + 3t. Quelle est la vitesse de la rondelle à t = 2 secondes ?
   • Choices: A) 11 m/s B) 16 m/s C) 19 m/s D) 22 m/s
   • Hint: Velocity = derivative of position. Differentiate s(t) using the power rule, then substitute t — like s(t) = 3t² + 2: s'(t) = 6t, at t = 3: v = 18 m/s.
   • Steps:
     • s'(t) = 8t + 3.
     • At t = 2: s'(2) = 8(2) + 3 = 16 + 3 = 19.
     • Velocity = 19 m/s.
   • Answer: 19 m/s

8. [Medium] Binomial Theorem

   • EN: What is the coefficient of x² in the expansion of (x + 2)⁴?
   • FR: Quel est le coefficient de x² dans le développement de (x + 2)⁴ ?
   • Choices: A) 16 B) 24 C) 32 D) 48
   • Hint: Use the binomial theorem: the term with xʳ is C(n, r) × xʳ × bⁿ⁻ʳ — like in (x + 3)³, the x² term is C(3,2) × x² × 3¹ = 3 × 3 × x² = 9x².
   • Steps:
     • The x² term in (x + 2)⁴ comes from r = 2: C(4, 2) × x² × 2².
     • C(4, 2) = 6 and 2² = 4.
     • Coefficient = 6 × 4 = 24.
   • Answer: 24

9. [Hard] Rational Function — Asymptotes

   • EN: For the rational function f(x) = (2x² + 3) ÷ (x² − 4), what is the horizontal asymptote?
   • FR: Pour la fonction rationnelle f(x) = (2x² + 3) ÷ (x² − 4), quelle est l'asymptote horizontale ?
   • Choices: A) y = 0 B) y = 2 C) y = 3 D) y = 4
   • Hint: When the degree of numerator equals the degree of denominator, the horizontal asymptote is the ratio of leading coefficients — like (5x² + 1) ÷ (2x²) → horizontal asymptote y = 5/2.
   • Steps:
     • Degree of numerator = 2; degree of denominator = 2. Degrees are equal.
     • Horizontal asymptote = leading coefficient of numerator ÷ leading coefficient of denominator.
     • = 2 ÷ 1 = 2. So horizontal asymptote is y = 2.
   • Answer: y = 2

10. [Hard] Combinations and Probability

    • EN: A committee of 3 people is chosen at random from 4 men and 5 women. What is the probability that all 3 members are women?
    • FR: Un comité de 3 personnes est choisi au hasard parmi 4 hommes et 5 femmes. Quelle est la probabilité que les 3 membres soient des femmes ?
    • Choices: A) 5/42 B) 10/21 C) 10/84 D) 5/21
    • Hint: P = (favourable combos) ÷ (total combos) — like choosing 2 women from 4 women and 3 men: C(4,2)/C(7,2) = 6/21 = 2/7.
    • Steps:
      • Total ways to choose 3 from 9: C(9, 3) = 84.
      • Ways to choose 3 women from 5: C(5, 3) = 10.
      • P = 10/84 = 5/42.
    • Answer: 5/42

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