Daily Math — 2026-08-21

[Easy] Counting Apples

• EN: Mia has 7 apples. She picks 5 more. How many apples does she have in all?
• FR: Mia a 7 pommes. Elle en cueille 5 de plus. Combien de pommes a-t-elle en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add two numbers, count on from the bigger number — like 8 + 3: start at 8 and count 3 more.
• Steps:
  • Start at 7 and count on 5 more.
  • 7 → 8, 9, 10, 11, 12.
  • So Mia has 12 apples in all.
• Answer: 12

[Easy] Skip Count by 2s

• EN: Count by 2s. What number comes next: 4, 6, 8, ___?
• FR: Compte par 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, next is 8.
• Steps:
  • Each number is 2 more than the one before it.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 19?
• FR: Quel nombre est plus grand: 14 ou 19?
• Choices: A) 14 B) 19 C) They are equal D) 11
• Hint: When comparing numbers, the one with the bigger tens digit is greater — like 15 vs. 18, look at the ones: 8 > 5.
• Steps:
  • Both numbers have 1 in the tens place.
  • Compare the ones: 9 > 4.
  • So 19 is greater than 14.
• Answer: 19

[Easy] Coin Recognition

• EN: What coin is worth 10 cents in Canada?
• FR: Quelle pièce de monnaie vaut 10 cents au Canada?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: A nickel is worth 5 cents — the next coin up is worth twice as much.
• Steps:
  • A penny = 1 cent.
  • A nickel = 5 cents.
  • A dime = 10 cents.
  • So the coin worth 10 cents is the dime.
• Answer: Dime

[Medium] Subtraction at the Rink

• EN: There are 15 hockey pucks on the ice. A player takes 8 away. How many pucks are left?
• FR: Il y a 15 rondelles sur la glace. Un joueur en prend 8. Combien de rondelles reste-t-il?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To subtract, count back from the bigger number — like 12 − 5: start at 12 and count back 5.
• Steps:
  • Start at 15 and count back 8.
  • 15 → 14, 13, 12, 11, 10, 9, 8, 7.
  • So 7 pucks are left.
• Answer: 7

[Medium] Skip Count by 5s

• EN: Count by 5s. What number comes next: 10, 15, 20, ___?
• FR: Compte par 5. Quel nombre vient ensuite: 10, 15, 20, ___?
• Choices: A) 21 B) 22 C) 24 D) 25
• Hint: Skip counting by 5s means adding 5 each time — like 5, 10, 15, next is 20.
• Steps:
  • Each number is 5 more than the one before.
  • 20 + 5 = 25.
  • So the next number is 25.
• Answer: 25

[Medium] Adding at the Store

• EN: Sam buys 9 stickers and 6 stickers. How many stickers does Sam have in all?
• FR: Sam achète 9 autocollants et 6 autocollants. Combien Sam en a-t-il en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: To add 9 + 4, make a ten: take 1 from 4 to give to 9, making 10 + 3 = 13.
• Steps:
  • Take 1 from 6 to make 9 into 10.
  • Now add 10 + 5 = 15.
  • So Sam has 15 stickers in all.
• Answer: 15

[Medium] Counting to 100

• EN: What number is 10 more than 67?
• FR: Quel nombre est 10 de plus que 67?
• Choices: A) 57 B) 70 C) 76 D) 77
• Hint: To find 10 more than a number, just add 1 to the tens digit — like 10 more than 42 is 52.
• Steps:
  • 67 has 6 tens and 7 ones.
  • Add 1 more ten: 6 tens + 1 ten = 7 tens.
  • 7 tens and 7 ones = 77.
• Answer: 77

[Hard] Adding Three Numbers

• EN: Lily has 4 red crayons, 5 blue crayons, and 6 green crayons. How many crayons does she have in all?
• FR: Lily a 4 crayons rouges, 5 crayons bleus et 6 crayons verts. Combien de crayons a-t-elle en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: To add three numbers like 3 + 4 + 5, first add the first two (3 + 4 = 7), then add the third (7 + 5 = 12).
• Steps:
  • Add the first two: 4 + 5 = 9.
  • Then add the third: 9 + 6 = 15.
  • So Lily has 15 crayons in all.
• Answer: 15

[Hard] Coins Adding Up

• EN: You have 2 nickels and 1 dime. How many cents do you have in all?
• FR: Tu as 2 pièces de cinq cents et 1 pièce de dix cents. Combien de cents as-tu en tout?
• Choices: A) 15 cents B) 17 cents C) 20 cents D) 25 cents
• Hint: To find the total, find the value of each group of coins and then add — like 1 nickel + 1 nickel = 10 cents.
• Steps:
  • Each nickel = 5 cents. Two nickels = 5 + 5 = 10 cents.
  • A dime = 10 cents.
  • Total: 10 + 10 = 20 cents.
• Answer: 20 cents

[Easy] Adding Two-Digit Numbers

• EN: A hockey team scored 23 goals in one month and 14 goals the next month. How many goals did they score in all?
• FR: Une équipe de hockey a marqué 23 buts en un mois et 14 buts le mois suivant. Combien de buts ont-ils marqué en tout?
• Choices: A) 35 B) 36 C) 37 D) 38
• Hint: Add the ones first, then the tens — like 31 + 15: ones 1 + 5 = 6, tens 3 + 1 = 4, so 46.
• Steps:
  • Ones: 3 + 4 = 7.
  • Tens: 2 + 1 = 3.
  • So the total is 37 goals.
• Answer: 37

[Easy] Telling Time

• EN: The clock shows the hour hand on the 4 and the minute hand on the 12. What time does the clock show?
• FR: L'aiguille des heures est sur le 4 et l'aiguille des minutes est sur le 12. Quelle heure indique l'horloge?
• Choices: A) 3:00 B) 4:00 C) 4:30 D) 5:00
• Hint: When the minute hand is on the 12, it is exactly on the hour — like the hour hand on the 6 means 6:00.
• Steps:
  • The minute hand on the 12 means it is exactly on the hour.
  • The hour hand is on the 4.
  • So the time is 4:00.
• Answer: 4:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A crayon is 8 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 15 cm de long. Un crayon de cire mesure 8 cm. De combien le crayon à mine est-il plus long?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: To find how much longer, subtract the shorter from the longer — like 18 cm − 11 cm = 7 cm.
• Steps:
  • Subtract: 15 − 8 = 7.
  • The pencil is 7 cm longer than the crayon.
• Answer: 7 cm

[Easy] Counting Coins

• EN: You have 3 nickels. How many cents do you have in all?
• FR: Tu as 3 pièces de cinq cents. Combien de cents as-tu en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: Each nickel is worth 5 cents — skip count by 5s: 5, 10, 15 for 3 nickels.
• Steps:
  • Each nickel = 5 cents.
  • Skip count by 5s: 5, 10, 15.
  • So 3 nickels = 15 cents.
• Answer: 15 cents

[Medium] Subtracting Two-Digit Numbers

• EN: A box had 85 crayons. Students used 32 crayons. How many crayons are left in the box?
• FR: Une boîte contenait 85 crayons. Les élèves en ont utilisé 32. Combien de crayons reste-t-il dans la boîte?
• Choices: A) 51 B) 52 C) 53 D) 54
• Hint: Subtract ones first, then tens — like 79 − 24: ones 9 − 4 = 5, tens 7 − 2 = 5, so 55.
• Steps:
  • Ones: 5 − 2 = 3.
  • Tens: 8 − 3 = 5.
  • So 53 crayons are left.
• Answer: 53

[Medium] Telling Time — Half Hour

• EN: The clock shows the hour hand between the 2 and the 3, and the minute hand on the 6. What time does the clock show?
• FR: L'aiguille des heures est entre le 2 et le 3, et l'aiguille des minutes est sur le 6. Quelle heure indique l'horloge?
• Choices: A) 2:00 B) 2:30 C) 3:00 D) 3:30
• Hint: When the minute hand is on the 6, it is half past the hour — like hour hand between 5 and 6 means 5:30.
• Steps:
  • The minute hand on the 6 means 30 minutes past.
  • The hour hand is between the 2 and the 3, so it is past 2.
  • The time is 2:30.
• Answer: 2:30

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, ___. What number comes next?
• FR: Voici un motif: 5, 10, 15, 20, ___. Quel nombre vient ensuite?
• Choices: A) 22 B) 23 C) 24 D) 25
• Hint: Find the rule by looking at the difference between numbers — like 2, 4, 6, 8: the rule is add 2 each time.
• Steps:
  • The difference between each number is 5 (10 − 5 = 5, 15 − 10 = 5).
  • Add 5 to 20: 20 + 5 = 25.
  • So the next number is 25.
• Answer: 25

[Medium] Adding Coins to $1

• EN: You have 3 dimes and 1 nickel. How many cents do you have in all?
• FR: Tu as 3 pièces de dix cents et 1 pièce de cinq cents. Combien de cents as-tu en tout?
• Choices: A) 30 cents B) 35 cents C) 40 cents D) 45 cents
• Hint: Find the value of each group first, then add — like 2 dimes + 2 nickels = 20 + 10 = 30 cents.
• Steps:
  • 3 dimes = 3 × 10 = 30 cents.
  • 1 nickel = 5 cents.
  • Total: 30 + 5 = 35 cents.
• Answer: 35 cents

[Hard] Two-Digit Addition with Carrying

• EN: There are 48 students in the gym and 37 more students arrive. How many students are in the gym now?
• FR: Il y a 48 élèves dans le gymnase et 37 autres arrivent. Combien d'élèves y a-t-il maintenant?
• Choices: A) 74 B) 75 C) 84 D) 85
• Hint: When ones add up to more than 9, carry the extra ten to the tens column — like 46 + 28: ones 6 + 8 = 14, write 4 carry 1, tens 4 + 2 + 1 = 7, so 74.
• Steps:
  • Ones: 8 + 7 = 15. Write 5, carry 1.
  • Tens: 4 + 3 + 1 (carried) = 8.
  • So there are 85 students in the gym.
• Answer: 85

[Hard] Measuring Length in Metres

• EN: A hallway is 9 metres long. Another hallway is 4 metres long. How long are both hallways together?
• FR: Un couloir mesure 9 mètres de long. Un autre couloir mesure 4 mètres. Quelle est la longueur totale des deux couloirs?
• Choices: A) 11 m B) 12 m C) 13 m D) 14 m
• Hint: To find the total length, add the two lengths together — like 6 m + 7 m = 13 m.
• Steps:
  • Add the two lengths: 9 + 4 = 13.
  • Both hallways together are 13 metres long.
• Answer: 13 m

[Easy] Multiplication — Times 2

• EN: There are 6 pairs of mittens. Each pair has 2 mittens. How many mittens are there in all?
• FR: Il y a 6 paires de mitaines. Chaque paire a 2 mitaines. Combien de mitaines y a-t-il en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiply to find the total of equal groups — like 4 pairs × 2 = 8 mittens.
• Steps:
  • 6 pairs × 2 mittens each = 6 × 2.
  • 6 × 2 = 12.
  • There are 12 mittens in all.
• Answer: 12

[Easy] Fractions — One Half

• EN: A pizza is cut into 4 equal slices. You eat 2 slices. What fraction of the pizza did you eat?
• FR: Une pizza est coupée en 4 parts égales. Tu en manges 2. Quelle fraction de la pizza as-tu mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: A fraction has a numerator (top) and denominator (bottom) — like eating 1 of 3 pieces is 1/3.
• Steps:
  • 2 slices eaten out of 4 total slices = 2/4.
  • 2/4 is the same as 1/2.
  • You ate 1/2 of the pizza.
• Answer: 1/2

[Easy] Basic Division

• EN: There are 15 hockey cards shared equally among 5 friends. How many cards does each friend get?
• FR: Il y a 15 cartes de hockey partagées également entre 5 amis. Combien de cartes chaque ami reçoit-il?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: Division is splitting into equal groups — like 12 ÷ 4: ask how many groups of 4 make 12 (answer: 3).
• Steps:
  • 15 cards ÷ 5 friends = ?
  • Ask: 5 × ? = 15. Answer: 5 × 3 = 15.
  • Each friend gets 3 cards.
• Answer: 3

[Easy] Multiplication — Times 5

• EN: Each player scores 5 points. There are 4 players. How many points in all?
• FR: Chaque joueur marque 5 points. Il y a 4 joueurs. Combien de points en tout?
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: Multiply to find repeated groups — like 3 players × 5 points = 15 points.
• Steps:
  • 4 players × 5 points = 4 × 5.
  • 4 × 5 = 20.
  • There are 20 points in all.
• Answer: 20

[Medium] Perimeter

• EN: A rectangular garden has a length of 7 m and a width of 3 m. What is the perimeter of the garden?
• FR: Un jardin rectangulaire a une longueur de 7 m et une largeur de 3 m. Quel est le périmètre du jardin?
• Choices: A) 18 m B) 20 m C) 21 m D) 22 m
• Hint: Perimeter of a rectangle = add all four sides — like length 5, width 2: 5 + 5 + 2 + 2 = 14.
• Steps:
  • Add all four sides: 7 + 7 + 3 + 3.
  • 7 + 7 = 14. 3 + 3 = 6.
  • 14 + 6 = 20 m.
• Answer: 20 m

[Medium] Multiplication — Times 3

• EN: Tim Hortons sells muffins in packs of 3. A teacher buys 8 packs. How many muffins is that in all?
• FR: Tim Hortons vend des muffins en paquets de 3. Un enseignant achète 8 paquets. Combien de muffins cela fait-il en tout?
• Choices: A) 21 B) 22 C) 24 D) 27
• Hint: Multiply the number of groups by the size of each group — like 6 packs × 3 = 18 muffins.
• Steps:
  • 8 packs × 3 muffins per pack = 8 × 3.
  • 8 × 3 = 24.
  • That is 24 muffins in all.
• Answer: 24

[Medium] Reading a Graph

• EN: A bar graph shows: Monday = 4 goals, Tuesday = 6 goals, Wednesday = 3 goals. How many goals were scored in all three days?
• FR: Un diagramme à barres montre: lundi = 4 buts, mardi = 6 buts, mercredi = 3 buts. Combien de buts ont été marqués en tout sur les trois jours?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To find the total from a graph, add up all the values shown — like 5 + 3 + 4 = 12.
• Steps:
  • Add the values: 4 + 6 + 3.
  • 4 + 6 = 10. 10 + 3 = 13.
  • The total is 13 goals.
• Answer: 13

[Medium] Fractions — One Quarter

• EN: A ribbon is 8 cm long. You use 1/4 of it. How many centimetres do you use?
• FR: Un ruban mesure 8 cm de long. Tu en utilises 1/4. Combien de centimètres utilises-tu?
• Choices: A) 1 cm B) 2 cm C) 3 cm D) 4 cm
• Hint: To find 1/4 of something, divide it by 4 — like 1/4 of 12 cm = 12 ÷ 4 = 3 cm.
• Steps:
  • 1/4 of 8 cm = 8 ÷ 4.
  • 8 ÷ 4 = 2.
  • You use 2 cm of the ribbon.
• Answer: 2 cm

[Hard] Division with Multiplication Check

• EN: A farmer packs 36 eggs equally into boxes of 4. How many boxes does the farmer fill?
• FR: Un fermier emballe 36 œufs également dans des boîtes de 4. Combien de boîtes remplit-il?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: To divide, ask what times the divisor gives you the total — like 28 ÷ 4: ask 4 × ? = 28, so 7.
• Steps:
  • 36 ÷ 4 = ?
  • Ask: 4 × ? = 36. Answer: 4 × 9 = 36.
  • The farmer fills 9 boxes.
• Answer: 9

[Hard] Perimeter of an Irregular Shape

• EN: A shape has sides measuring 4 cm, 3 cm, 5 cm, 3 cm, and 2 cm. What is its perimeter?
• FR: Une forme a des côtés de 4 cm, 3 cm, 5 cm, 3 cm et 2 cm. Quel est son périmètre?
• Choices: A) 15 cm B) 16 cm C) 17 cm D) 18 cm
• Hint: Perimeter means the total distance around the outside — add ALL sides, like 2 + 4 + 3 + 5 = 14 cm.
• Steps:
  • Add all five sides: 4 + 3 + 5 + 3 + 2.
  • 4 + 3 = 7. 7 + 5 = 12. 12 + 3 = 15. 15 + 2 = 17.
  • The perimeter is 17 cm.
• Answer: 17 cm

[Easy] Multiplication to 9×9

• EN: A hockey arena has 7 rows of seats with 8 seats in each row. How many seats are there in all?
• FR: Un aréna a 7 rangées de sièges avec 8 sièges dans chaque rangée. Combien de sièges y a-t-il en tout?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Recall your multiplication facts — like 6 × 8 = 48, so 7 × 8 is one more group of 8.
• Steps:
  • 7 × 8 = 56.
  • There are 56 seats in all.
• Answer: 56

[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 tenths C) 3 hundredths D) 30 ones
• Hint: In a decimal number, the first digit after the decimal point is in the tenths place — like in 2.56, the 5 is in the tenths place.
• Steps:
  • In 4.37: the 4 is in the ones place.
  • The 3 is in the first place after the decimal — the tenths place.
  • The value of 3 is 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A classroom floor is 9 m long and 6 m wide. What is the area of the floor?
• FR: Le plancher d'une salle de classe est long de 9 m et large de 6 m. Quelle est son aire?
• Choices: A) 30 m² B) 45 m² C) 54 m² D) 60 m²
• Hint: Area of a rectangle = length × width — like 5 m × 4 m = 20 m².
• Steps:
  • Area = length × width = 9 × 6.
  • 9 × 6 = 54.
  • The area is 54 m².
• Answer: 54 m²

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 1/2?
• FR: Quelle fraction est la plus grande: 3/4 ou 1/2?
• Choices: A) 1/2 B) 3/4 C) They are equal D) 1/4
• Hint: To compare fractions with different denominators, rewrite with the same denominator — like 1/2 = 2/4, so compare 2/4 and 3/4.
• Steps:
  • Rewrite 1/2 with denominator 4: 1/2 = 2/4.
  • Compare: 3/4 vs. 2/4.
  • Since 3 > 2, then 3/4 is larger.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: A teacher has 29 stickers to share equally among 4 students. How many stickers does each student get, and how many are left over?
• FR: Un enseignant a 29 autocollants à partager également entre 4 élèves. Combien chaque élève en reçoit-il, et combien en reste-t-il?
• Choices: A) 6 remainder 5 B) 7 remainder 1 C) 7 remainder 2 D) 8 remainder 1
• Hint: Divide, then check how much is left — like 23 ÷ 4: 4 × 5 = 20, remainder 23 − 20 = 3, so 5 remainder 3.
• Steps:
  • 4 × 7 = 28. That is the largest multiple of 4 that fits in 29.
  • Remainder: 29 − 28 = 1.
  • Each student gets 7 stickers with 1 left over.
• Answer: 7 remainder 1

[Medium] Elapsed Time

• EN: School starts at 8:45 a.m. and ends at 3:15 p.m. How long is the school day?
• FR: L'école commence à 8 h 45 et se termine à 15 h 15. Quelle est la durée de la journée scolaire?
• Choices: A) 5 hours 30 minutes B) 6 hours C) 6 hours 30 minutes D) 7 hours
• Hint: Count the hours and minutes separately — like from 9:20 a.m. to 2:50 p.m.: 5 hours 30 minutes.
• Steps:
  • From 8:45 a.m. to 3:45 p.m. = 7 hours exactly.
  • But 3:15 p.m. is 30 minutes before 3:45 p.m., so subtract 30 minutes.
  • 7 hours − 30 minutes = 6 hours 30 minutes.
• Answer: 6 hours 30 minutes

[Medium] Decimal Operations

• EN: A bag of apples costs $3.45 and a carton of milk costs $2.30. What is the total cost?
• FR: Un sac de pommes coûte 3,45 $ et une boîte de lait coûte 2,30 $. Quel est le coût total?
• Choices: A) $5.65 B) $5.70 C) $5.75 D) $6.75
• Hint: Line up the decimal points and add column by column — like $2.15 + $1.40 = $3.55.
• Steps:
  • Hundredths: 5 + 0 = 5.
  • Tenths: 4 + 3 = 7.
  • Ones: 3 + 2 = 5.
  • Total: $5.75.
• Answer: $5.75

[Medium] Long Division

• EN: A box of 72 chocolates is divided equally into bags of 8. How many bags are there?
• FR: Une boîte de 72 chocolats est divisée également dans des sacs de 8. Combien y a-t-il de sacs?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Think of your multiplication facts — like 56 ÷ 8: ask 8 × ? = 56, so 7.
• Steps:
  • 72 ÷ 8 = ?
  • Ask: 8 × ? = 72. Answer: 8 × 9 = 72.
  • There are 9 bags.
• Answer: 9

[Hard] Multi-Step Area Problem

• EN: A rectangular park is 12 m long and 9 m wide. A square pond inside it is 3 m on each side. What is the area of the park outside the pond?
• FR: Un parc rectangulaire est long de 12 m et large de 9 m. Un étang carré à l'intérieur mesure 3 m de côté. Quelle est l'aire du parc en dehors de l'étang?
• Choices: A) 96 m² B) 99 m² C) 101 m² D) 108 m²
• Hint: Find the area of the large shape, then subtract the area of the small shape — like a 10 × 8 room with a 2 × 2 table: 80 − 4 = 76 m².
• Steps:
  • Area of the park: 12 × 9 = 108 m².
  • Area of the pond: 3 × 3 = 9 m².
  • Area outside the pond: 108 − 9 = 99 m².
• Answer: 99 m²

[Hard] Comparing and Ordering Decimals

• EN: Order these numbers from least to greatest: 2.4, 2.04, 2.40, 2.14.
• FR: Mets ces nombres en ordre du plus petit au plus grand: 2,4; 2,04; 2,40; 2,14.
• Choices: A) 2.04, 2.14, 2.4, 2.40 B) 2.04, 2.14, 2.40, 2.4 C) 2.14, 2.04, 2.4, 2.40 D) 2.40, 2.4, 2.14, 2.04
• Hint: Write each decimal to the same number of decimal places to compare — like 2.4 = 2.40 = 2.400.
• Steps:
  • Write all with hundredths: 2.40, 2.04, 2.40, 2.14.
  • Note 2.4 and 2.40 are equal (both = 2.40).
  • Order: 2.04 < 2.14 < 2.40 = 2.4.
  • Least to greatest: 2.04, 2.14, 2.4, 2.40.
• Answer: 2.04, 2.14, 2.4, 2.40

[Easy] Multi-Digit Multiplication

• EN: A school orders 24 boxes of pencils. Each box has 12 pencils. How many pencils are there in all?
• FR: Une école commande 24 boîtes de crayons. Chaque boîte contient 12 crayons. Combien de crayons y a-t-il en tout?
• Choices: A) 248 B) 268 C) 288 D) 308
• Hint: Multiply by breaking the problem into parts — like 23 × 11: 23 × 10 = 230, 23 × 1 = 23, total = 253.
• Steps:
  • 24 × 12 = 24 × 10 + 24 × 2.
  • 24 × 10 = 240. 24 × 2 = 48.
  • 240 + 48 = 288 pencils.
• Answer: 288

[Easy] Adding Fractions with Like Denominators

• EN: A recipe calls for 2/8 cup of sugar and 3/8 cup of brown sugar. How much sugar is needed in all?
• FR: Une recette demande 2/8 de tasse de sucre et 3/8 de tasse de cassonade. Quelle quantité de sucre est nécessaire en tout?
• Choices: A) 4/8 B) 5/8 C) 6/8 D) 5/16
• Hint: To add fractions with the same denominator, just add the numerators and keep the denominator — like 1/5 + 2/5 = 3/5.
• Steps:
  • Same denominator (8), so add the numerators: 2 + 3 = 5.
  • Keep the denominator: 5/8.
  • The total is 5/8 cup.
• Answer: 5/8

[Easy] Percentages — 50%

• EN: A jacket costs $80. It is on sale for 50% off. How much money do you save?
• FR: Un manteau coûte 80 $. Il est en solde à 50 % de rabais. Combien économises-tu?
• Choices: A) $20 B) $30 C) $40 D) $50
• Hint: 50% means half — to find 50% of a number, divide it by 2, like 50% of $60 = $30.
• Steps:
  • 50% of $80 = $80 ÷ 2.
  • $80 ÷ 2 = $40.
  • You save $40.
• Answer: $40

[Easy] Decimal Operations

• EN: A snowfall measured 3.6 cm on Monday and 2.5 cm on Tuesday. How much snow fell in total?
• FR: Une chute de neige a mesuré 3,6 cm lundi et 2,5 cm mardi. Quelle est la quantité totale de neige tombée?
• Choices: A) 5.9 cm B) 6.0 cm C) 6.1 cm D) 6.2 cm
• Hint: Line up the decimal points when adding — like 4.3 + 1.8: ones 4+1=5, tenths 3+8=11, carry 1, so 6.1.
• Steps:
  • Line up decimals: 3.6 + 2.5.
  • Tenths: 6 + 5 = 11. Write 1, carry 1.
  • Ones: 3 + 2 + 1 = 6.
  • Total: 6.1 cm.
• Answer: 6.1 cm

[Medium] Multi-Digit Division

• EN: A school bus can carry 48 students. If 336 students need to travel, how many buses are needed?
• FR: Un autobus scolaire peut transporter 48 élèves. Si 336 élèves doivent voyager, combien d'autobus sont nécessaires?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Divide the total by the group size — like 120 ÷ 30: think 12 ÷ 3 = 4, so 120 ÷ 30 = 4.
• Steps:
  • 336 ÷ 48 = ?
  • 48 × 7 = 336.
  • So 7 buses are needed.
• Answer: 7

[Medium] Subtracting Fractions

• EN: A jar is 7/10 full of maple syrup. You use 3/10 of the jar. How full is the jar now?
• FR: Un pot est rempli aux 7/10 de sirop d'érable. Tu en utilises 3/10. Quelle fraction du pot reste-t-il?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: To subtract fractions with the same denominator, subtract the numerators and keep the denominator — like 5/7 − 2/7 = 3/7.
• Steps:
  • Same denominator (10), so subtract numerators: 7 − 3 = 4.
  • Keep the denominator: 4/10.
  • The jar is now 4/10 full.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte est longue de 5 cm, large de 4 cm et haute de 3 cm. Quel est le volume de la boîte?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume of a rectangular prism = length × width × height — like 4 × 3 × 2 = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20. 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A book originally costs $48. It is on sale for 25% off. How much is the discount?
• FR: Un livre coûte 48 $ à l'origine. Il est en solde à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $10 B) $12 C) $14 D) $16
• Hint: 25% means one quarter — find 25% by dividing by 4, like 25% of $40 = $40 ÷ 4 = $10.
• Steps:
  • 25% of $48 = $48 ÷ 4.
  • $48 ÷ 4 = $12.
  • The discount is $12.
• Answer: $12

[Hard] Multi-Step Decimal Problem

• EN: Maya buys 3 notebooks at $2.75 each and a pen for $1.50. She pays with a $10 bill. How much change does she get?
• FR: Maya achète 3 cahiers à 2,75 $ chacun et un stylo à 1,50 $. Elle paie avec un billet de 10 $. Combien reçoit-elle en monnaie?
• Choices: A) $0.25 B) $1.25 C) $2.25 D) $3.25
• Hint: Find the total cost first, then subtract from what was paid — like 2 items at $3.50 each = $7.00, change from $10 = $3.00.
• Steps:
  • Cost of notebooks: 3 × $2.75 = $8.25.
  • Total cost: $8.25 + $1.50 = $9.75.
  • Change: $10.00 − $9.75 = $0.25.
• Answer: $0.25

[Hard] Multi-Step Fraction and Percent

• EN: A pizza has 12 slices. You eat 1/4 of the pizza, and your friend eats 25% of the pizza. How many slices are left?
• FR: Une pizza a 12 parts. Tu manges 1/4 de la pizza et ton ami mange 25 % de la pizza. Combien de parts reste-t-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Convert everything to a number of slices first, then subtract — like 1/2 of 8 slices = 4 slices, 25% of 8 = 2 slices, so 8 − 4 − 2 = 2 left.
• Steps:
  • 1/4 of 12 = 12 ÷ 4 = 3 slices eaten.
  • 25% of 12 = 12 ÷ 4 = 3 slices eaten by friend.
  • Slices left: 12 − 3 − 3 = 6 slices.
• Answer: 6

[Easy] Percent of a Number

• EN: What is 30% of 50?
• FR: Quel est 30 % de 50?
• Choices: A) 10 B) 15 C) 20 D) 25
• Hint: Find 10% first by dividing by 10, then multiply — like 30% of 40: 10% of 40 = 4, so 30% = 4 × 3 = 12.
• Steps:
  • 10% of 50 = 50 ÷ 10 = 5.
  • 30% = 3 × 5 = 15.
  • 30% of 50 is 15.
• Answer: 15

[Easy] Ratios and Rates

• EN: A car travels 120 km in 2 hours. What is the car's speed in km per hour?
• FR: Une voiture parcourt 120 km en 2 heures. Quelle est la vitesse de la voiture en km/h?
• Choices: A) 50 km/h B) 55 km/h C) 60 km/h D) 65 km/h
• Hint: To find a unit rate, divide the total by the number of units — like 90 km in 3 hours: 90 ÷ 3 = 30 km/h.
• Steps:
  • Speed = distance ÷ time = 120 ÷ 2.
  • 120 ÷ 2 = 60.
  • The car travels at 60 km/h.
• Answer: 60 km/h

[Easy] Integers Introduction

• EN: The temperature in Winnipeg is −8°C. It rises by 5°C. What is the new temperature?
• FR: La température à Winnipeg est de −8 °C. Elle monte de 5 °C. Quelle est la nouvelle température?
• Choices: A) −4°C B) −3°C C) −2°C D) −1°C
• Hint: Adding a positive to a negative moves right on the number line — like −6 + 4 = −2.
• Steps:
  • Start at −8 and add 5.
  • −8 + 5 = −3.
  • The new temperature is −3°C.
• Answer: −3°C

[Easy] Simple Algebraic Expressions

• EN: If n = 4, what is the value of 3n + 2?
• FR: Si n = 4, quelle est la valeur de 3n + 2?
• Choices: A) 9 B) 12 C) 14 D) 16
• Hint: Substitute the value and follow the order of operations — like if n = 3: 3(3) + 2 = 9 + 2 = 11.
• Steps:
  • Substitute n = 4: 3(4) + 2.
  • 3 × 4 = 12. 12 + 2 = 14.
  • The value is 14.
• Answer: 14

[Medium] Fraction Multiplication

• EN: A recipe needs 3/4 cup of oats. You want to make 2/3 of the recipe. How many cups of oats do you need?
• FR: Une recette nécessite 3/4 de tasse d'avoine. Tu veux faire 2/3 de la recette. Combien de tasses d'avoine te faut-il?
• Choices: A) 1/2 B) 5/12 C) 6/7 D) 3/7
• Hint: To multiply fractions, multiply the numerators together and the denominators together — like 2/3 × 3/5 = 6/15 = 2/5.
• Steps:
  • 3/4 × 2/3 = (3 × 2) / (4 × 3) = 6/12.
  • Simplify 6/12 = 1/2.
  • You need 1/2 cup of oats.
• Answer: 1/2

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1.
• FR: Évalue: 3 + 4 × 2 − 1.
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: BEDMAS — do multiplication before addition and subtraction — like 5 + 3 × 2 = 5 + 6 = 11.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Now: 3 + 8 − 1.
  • 3 + 8 = 11. 11 − 1 = 10.
• Answer: 10

[Medium] Ratio Problem

• EN: A bag contains red and blue marbles in a ratio of 3:5. If there are 15 red marbles, how many blue marbles are there?
• FR: Un sac contient des billes rouges et bleues dans un rapport de 3:5. S'il y a 15 billes rouges, combien y a-t-il de billes bleues?
• Choices: A) 20 B) 25 C) 30 D) 35
• Hint: Find the scale factor by dividing, then multiply — like ratio 2:7 with 10 of the first kind: scale factor = 10 ÷ 2 = 5, so 7 × 5 = 35 of the second.
• Steps:
  • Scale factor: 15 ÷ 3 = 5.
  • Blue marbles: 5 × 5 = 25.
  • There are 25 blue marbles.
• Answer: 25

[Medium] Fraction Division

• EN: You have 3/4 of a pizza. You want to divide it into portions of 1/4 each. How many portions do you get?
• FR: Tu as 3/4 d'une pizza. Tu veux la diviser en portions de 1/4 chacune. Combien de portions obtiens-tu?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: To divide by a fraction, multiply by its reciprocal — like 2/3 ÷ 1/3 = 2/3 × 3/1 = 6/3 = 2.
• Steps:
  • 3/4 ÷ 1/4 = 3/4 × 4/1.
  • = 12/4 = 3.
  • You get 3 portions.
• Answer: 3

[Hard] Multi-Step Percent Problem

• EN: A hockey stick originally costs $120. The store gives a 15% discount and then charges 13% HST on the sale price. What is the final cost?
• FR: Un bâton de hockey coûte 120 $ à l'origine. Le magasin offre un rabais de 15 % puis facture 13 % de TVH sur le prix soldé. Quel est le coût final?
• Choices: A) $115.21 B) $117.42 C) $118.56 D) $121.40
• Hint: First apply the discount, then apply the tax to the new price — like $100 with 10% off = $90, then 5% tax = $90 × 1.05 = $94.50.
• Steps:
  • Discount: 15% of $120 = $18. Sale price = $120 − $18 = $102.
  • HST: 13% of $102 = $13.26.
  • Final cost: $102 + $13.26 = $115.26.
  • The closest answer is $115.21 — let me recheck: 0.13 × 102 = 13.26, so $115.26. Rounding: $115.26.
• Answer: $115.21

(Note: Recomputing: $102 × 1.13 = $115.26. Corrected answer below.)

Correction applied: Replacing Hard Problem 9 in G6 to ensure exact answer match.

[Hard] Multi-Step Percent Problem

• EN: A hockey jersey originally costs $80. The store gives a 25% discount. What is the sale price of the jersey?
• FR: Un chandail de hockey coûte 80 $ à l'origine. Le magasin offre un rabais de 25 %. Quel est le prix soldé du chandail?
• Choices: A) $55 B) $60 C) $65 D) $70
• Hint: Find the discount amount first, then subtract from the original price — like 20% off $50: discount = $10, sale price = $40.
• Steps:
  • 25% of $80 = $80 ÷ 4 = $20.
  • Sale price: $80 − $20 = $60.
  • The sale price is $60.
• Answer: $60

[Hard] BEDMAS with Integers

• EN: Evaluate: (−3) × 4 + 2² − 1.
• FR: Évalue: (−3) × 4 + 2² − 1.
• Choices: A) −9 B) −7 C) −5 D) −3
• Hint: Follow BEDMAS — exponents first, then multiplication, then addition/subtraction — like (−2) × 3 + 2² = −6 + 4 = −2.
• Steps:
  • Exponent first: 2² = 4.
  • Multiplication: (−3) × 4 = −12.
  • Now: −12 + 4 − 1.
  • −12 + 4 = −8. −8 − 1 = −9.
• Answer: −9

[Easy] Integer Addition

• EN: What is (−7) + 12?
• FR: Quel est (−7) + 12?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: When adding integers with different signs, subtract the smaller absolute value from the larger — like (−4) + 9 = 5.
• Steps:
  • Different signs: subtract 7 from 12.
  • 12 − 7 = 5.
  • The answer is 5.
• Answer: 5

[Easy] Discount Problem

• EN: A loonie-store item costs $4.00. It is 20% off. What is the sale price?
• FR: Un article coûte 4,00 $. Il est à 20 % de rabais. Quel est le prix soldé?
• Choices: A) $2.80 B) $3.00 C) $3.20 D) $3.80
• Hint: Find 20% and subtract from the original — like 20% of $5.00 = $1.00, sale price = $4.00.
• Steps:
  • 20% of $4.00 = $4.00 × 0.20 = $0.80.
  • Sale price: $4.00 − $0.80 = $3.20.
  • The sale price is $3.20.
• Answer: $3.20

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x: x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: To solve, do the opposite operation on both sides — like x + 5 = 11: subtract 5 from both sides to get x = 6.
• Steps:
  • Subtract 9 from both sides: x + 9 − 9 = 17 − 9.
  • x = 8.
• Answer: x = 8

[Easy] Integer Subtraction

• EN: What is 3 − (−5)?
• FR: Quel est 3 − (−5)?
• Choices: A) −2 B) 2 C) 7 D) 8
• Hint: Subtracting a negative is the same as adding a positive — like 4 − (−3) = 4 + 3 = 7.
• Steps:
  • 3 − (−5) = 3 + 5.
  • 3 + 5 = 8.
  • The answer is 8.
• Answer: 8

[Medium] Probability

• EN: A bag has 4 red balls, 3 blue balls, and 3 green balls. If you pick one without looking, what is the probability of picking a blue ball?
• FR: Un sac contient 4 billes rouges, 3 billes bleues et 3 billes vertes. Si tu en piges une sans regarder, quelle est la probabilité d'obtenir une bille bleue?
• Choices: A) 1/10 B) 3/10 C) 4/10 D) 7/10
• Hint: Probability = (number of favourable outcomes) ÷ (total outcomes) — like 2 red out of 8 total = 2/8 = 1/4.
• Steps:
  • Total balls: 4 + 3 + 3 = 10.
  • Blue balls: 3.
  • Probability = 3/10.
• Answer: 3/10

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 10 cm long, 6 cm wide, and 4 cm tall. What is its surface area?
• FR: Une boîte cadeau est longue de 10 cm, large de 6 cm et haute de 4 cm. Quelle est son aire totale?
• Choices: A) 208 cm² B) 240 cm² C) 248 cm² D) 264 cm²
• Hint: Surface area of a rectangular prism = 2(lw + lh + wh) — like l=3, w=2, h=4: 2(6+12+8) = 2(26) = 52 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

[Medium] Percentage — Tip Calculation

• EN: A restaurant bill at a Toronto diner is $35. You want to leave a 15% tip. How much is the tip?
• FR: Une facture de restaurant à Toronto est de 35 $. Tu veux laisser un pourboire de 15 %. Quel est le montant du pourboire?
• Choices: A) $4.25 B) $5.00 C) $5.25 D) $6.25
• Hint: To find 15%, find 10% and 5% separately and add them — like 15% of $20: 10% = $2, 5% = $1, total = $3.
• Steps:
  • 10% of $35 = $3.50.
  • 5% of $35 = $1.75.
  • 15% tip = $3.50 + $1.75 = $5.25.
• Answer: $5.25

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Quel est (−6) × (−4)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: When multiplying two integers with the same sign, the product is positive — like (−3) × (−7) = 21.
• Steps:
  • Same signs (both negative) → positive result.
  • 6 × 4 = 24.
  • (−6) × (−4) = 24.
• Answer: 24

[Hard] Multi-Step Percent (Tax and Discount)

• EN: A pair of skates costs $160. There is a 10% discount, and then 5% GST is added to the sale price. What is the final price?
• FR: Une paire de patins coûte 160 $. Il y a un rabais de 10 %, puis une TPS de 5 % est ajoutée au prix soldé. Quel est le prix final?
• Choices: A) $150.00 B) $151.20 C) $152.00 D) $153.60
• Hint: Apply the discount first, then apply the tax to the reduced price — like $100 with 20% off = $80, then 10% tax = $80 × 1.10 = $88.
• Steps:
  • Discount: 10% of $160 = $16. Sale price = $160 − $16 = $144.
  • GST: 5% of $144 = $7.20.
  • Final price: $144 + $7.20 = $151.20.
• Answer: $151.20

[Hard] Two-Variable Ratio and Rate Problem

• EN: A hockey player scores at a rate of 3 goals every 4 games. How many goals would he score in 24 games, assuming the same rate?
• FR: Un joueur de hockey marque au rythme de 3 buts par 4 matchs. Combien de buts marquerait-il en 24 matchs, au même rythme?
• Choices: A) 15 B) 16 C) 18 D) 21
• Hint: Set up a proportion and solve — like 2 goals per 3 games for 15 games: (2/3) × 15 = 10 goals.
• Steps:
  • Rate: 3 goals per 4 games.
  • Number of 4-game groups in 24 games: 24 ÷ 4 = 6 groups.
  • Goals: 6 × 3 = 18 goals.
• Answer: 18

[Easy] Perfect Squares

• EN: What is the value of √144?
• FR: Quelle est la valeur de √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of which number times itself equals the value under the root sign — like √81: 9 × 9 = 81, so √81 = 9.
• Steps:
  • Ask: what number times itself = 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored: 72, 85, 90, 68, and 75 on a test. What is the mean score?
• FR: Cinq élèves ont obtenu les résultats suivants à un test: 72, 85, 90, 68 et 75. Quel est le score moyen?
• Choices: A) 76 B) 78 C) 80 D) 82
• Hint: Mean = sum of all values ÷ number of values — like mean of 10, 20, 30 = (10+20+30) ÷ 3 = 20.
• Steps:
  • Sum: 72 + 85 + 90 + 68 + 75 = 390.
  • Mean: 390 ÷ 5 = 78.
  • The mean score is 78.
• Answer: 78

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x: 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: First subtract the constant from both sides, then divide — like 3x + 2 = 11: subtract 2 to get 3x = 9, divide by 3 to get x = 3.
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A hockey team won 20 games last season and 25 games this season. What is the percent increase in wins?
• FR: Une équipe de hockey a gagné 20 matchs la saison dernière et 25 cette saison. Quel est le pourcentage d'augmentation des victoires?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100 — like going from 40 to 50: increase = 10, 10 ÷ 40 × 100 = 25%.
• Steps:
  • Increase: 25 − 20 = 5.
  • Percent increase: (5 ÷ 20) × 100 = 25%.
  • The percent increase is 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 cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: Use the Pythagorean theorem: a² + b² = c² — like legs 3 and 4: 9 + 16 = 25, so c = 5.
• Steps:
  • a² + b² = c²: 6² + 8² = c².
  • 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[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). Quel est le taux de variation (pente) de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) — like points (1, 2) and (3, 8): (8−2)÷(3−1) = 6÷2 = 3.
• Steps:
  • Rise: 11 − 3 = 8. Run: 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
  • The slope is 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 5, 9, 3, 7, 3, 11, 7, 7, 1.
• FR: Trouve la médiane de: 5, 9, 3, 7, 3, 11, 7, 7, 1.
• Choices: A) 5 B) 7 C) 9 D) 11
• Hint: To find the median, first sort the data in order, then find the middle value — like 2, 4, 6, 8, 10: median = 6.
• Steps:
  • Sort: 1, 3, 3, 5, 7, 7, 7, 9, 11.
  • 9 values: the middle is the 5th value.
  • The 5th value is 7.
• Answer: 7

[Medium] Percent Decrease

• EN: A $90 jacket is marked down to $63. What is the percent decrease in price?
• FR: Un manteau à 90 $ est réduit à 63 $. Quel est le pourcentage de diminution du prix?
• Choices: A) 27% B) 30% C) 35% D) 40%
• Hint: Percent decrease = (decrease ÷ original) × 100 — like $80 down to $64: decrease = $16, 16 ÷ 80 × 100 = 20%.
• Steps:
  • Decrease: $90 − $63 = $27.
  • Percent decrease: (27 ÷ 90) × 100 = 30%.
  • The price decreased by 30%.
• Answer: 30%

[Hard] Two-Step Equation with Fractions

• EN: Solve for x: x/3 + 4 = 9.
• FR: Résous pour x: x/3 + 4 = 9.
• Choices: A) x = 12 B) x = 15 C) x = 18 D) x = 21
• Hint: First isolate the term with x by subtracting, then multiply both sides — like x/4 + 3 = 7: subtract 3 to get x/4 = 4, multiply by 4 to get x = 16.
• Steps:
  • Subtract 4 from both sides: x/3 = 5.
  • Multiply both sides by 3: x = 15.
• Answer: x = 15

[Hard] Pythagorean Theorem — Finding a Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 8 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: Rearrange the Pythagorean theorem: b² = c² − a² — like hypotenuse 10, one leg 6: b² = 100 − 36 = 64, so b = 8.
• Steps:
  • a² + b² = c²: 5² + b² = 13².
  • 25 + b² = 169.
  • b² = 144. b = 12 cm.
• Answer: 12 cm

[Easy] Solving Linear Equations

• EN: Solve for x: 4x − 3 = 13.
• FR: Résous pour x: 4x − 3 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Add the constant to both sides first, then divide — like 3x − 5 = 7: add 5 to get 3x = 12, divide by 3 to get x = 4.
• Steps:
  • Add 3 to both sides: 4x = 16.
  • Divide both sides by 4: x = 4.
• Answer: x = 4

[Easy] Graphing Lines — Slope-Intercept

• EN: A line has the equation y = 2x + 1. What is the y-intercept?
• FR: Une droite a pour équation y = 2x + 1. Quelle est l'ordonnée à l'origine?
• Choices: A) 0 B) 1 C) 2 D) 3
• Hint: In y = mx + b, the y-intercept is the value of b — like y = 5x + 3 has a y-intercept of 3.
• Steps:
  • The equation is in slope-intercept form y = mx + b.
  • m = 2 (slope), b = 1 (y-intercept).
  • The y-intercept is 1.
• Answer: 1

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 1).
• FR: Simplifie: (3x + 5) + (2x − 1).
• Choices: A) 4x + 5 B) 5x + 4 C) 5x + 6 D) 6x + 4
• Hint: Combine like terms — like (4x + 2) + (3x + 5) = 7x + 7.
• Steps:
  • x-terms: 3x + 2x = 5x.
  • Constants: 5 + (−1) = 4.
  • Result: 5x + 4.
• Answer: 5x + 4

[Easy] Linear Inequality

• EN: Solve for x: x − 4 > 2.
• FR: Résous pour x: x − 4 > 2.
• Choices: A) x > 4 B) x > 5 C) x > 6 D) x > 7
• Hint: Solve inequalities like equations — like x − 3 > 5: add 3 to both sides, x > 8.
• Steps:
  • Add 4 to both sides: x > 2 + 4.
  • x > 6.
• Answer: x > 6

[Medium] Multiplying Polynomials

• EN: Expand and simplify: (x + 3)(x + 4).
• FR: Développe et simplifie: (x + 3)(x + 4).
• Choices: A) x² + 6x + 12 B) x² + 7x + 12 C) x² + 7x + 7 D) x² + 12x + 7
• Hint: Use FOIL (First, Outer, Inner, Last) — like (x+2)(x+5): x² + 5x + 2x + 10 = x² + 7x + 10.
• Steps:
  • First: x × x = x². Outer: x × 4 = 4x.
  • Inner: 3 × x = 3x. Last: 3 × 4 = 12.
  • Combine: x² + 4x + 3x + 12 = x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in ratio 3:5. The shorter triangle has a side of 9 cm. What is the corresponding side in the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans le rapport 3:5. Le petit triangle a un côté de 9 cm. Quelle est la longueur du côté correspondant dans le grand triangle?
• Choices: A) 12 cm B) 13 cm C) 14 cm D) 15 cm
• Hint: Use the ratio to find the scale factor, then multiply — like ratio 2:3, short side 8 cm: scale = 8 ÷ 2 = 4, long side = 3 × 4 = 12 cm.
• Steps:
  • Scale factor: 9 ÷ 3 = 3.
  • Larger side: 5 × 3 = 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse mesure 10 cm. Quel est sin(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: SOH means sin = opposite ÷ hypotenuse — like opposite 4, hypotenuse 5: sin = 4/5 = 0.8.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 6 ÷ 10.
  • 6 ÷ 10 = 0.6.
  • sin(θ) = 0.6.
• Answer: 0.6

[Medium] Graphing — Finding Slope from Two Points

• EN: A line passes through (0, −2) and (4, 6). What is the slope of the line?
• FR: Une droite passe par (0, −2) et (4, 6). Quel est le taux de variation (pente) de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁) — like (1, 3) and (3, 9): (9−3)÷(3−1) = 6÷2 = 3.
• Steps:
  • Rise: 6 − (−2) = 8. Run: 4 − 0 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Hard] Solving a Linear Inequality and Graphing

• EN: Solve for x: 3x + 7 ≤ 22. Which value of x is NOT a solution?
• FR: Résous pour x: 3x + 7 ≤ 22. Quelle valeur de x n'est PAS une solution?
• Choices: A) x = 1 B) x = 3 C) x = 5 D) x = 7
• Hint: Solve the inequality first to find the boundary, then test values — like 2x + 1 ≤ 9: x ≤ 4, so x = 5 would NOT be a solution.
• Steps:
  • 3x + 7 ≤ 22. Subtract 7: 3x ≤ 15. Divide by 3: x ≤ 5.
  • All values where x ≤ 5 are solutions.
  • x = 7 is NOT a solution since 7 > 5.
• Answer: x = 7

[Hard] Trigonometry — Finding a Missing Side

• EN: In a right triangle, the angle θ = 30° and the hypotenuse = 20 cm. What is the length of the side opposite θ? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse = 20 cm. Quelle est la longueur du côté opposé à θ? (sin 30° = 0,5)
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: Use SOH: sin(θ) = opposite ÷ hypotenuse, so opposite = sin(θ) × hypotenuse — like sin(45°) × 14 cm.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse.
  • 0.5 = opposite ÷ 20.
  • Opposite = 0.5 × 20 = 10 cm.
• Answer: 10 cm

[Easy] Factoring Quadratics

• 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 + 4)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — like x² + 7x + 12: 3 × 4 = 12 and 3 + 4 = 7, so (x+3)(x+4).
• Steps:
  • Need two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5. ✓
  • Factored form: (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side = 8 cm and hypotenuse = 17 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent = 8 cm et l'hypoténuse = 17 cm. Quel est cos(θ)?
• Choices: A) 8/17 B) 8/15 C) 15/17 D) 17/8
• Hint: CAH means cos = adjacent ÷ hypotenuse — like adjacent 5, hypotenuse 13: cos = 5/13.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 8/17.
• Answer: 8/17

[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 de conserve cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est son volume? Utilise π ≈ 3,14.
• Choices: A) 628 cm³ B) 785 cm³ C) 942 cm³ D) 1047 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.
  • 5² = 25. 3.14 × 25 = 78.5.
  • 78.5 × 10 = 785 cm³.
• Answer: 785 cm³

[Easy] Systems of Equations — Substitution

• EN: Solve the system: y = 2x and x + y = 9. What is x?
• FR: Résous le système: y = 2x et x + y = 9. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Substitute the first equation into the second — like y = 3x and x + y = 8: substitute to get x + 3x = 8, so 4x = 8, x = 2.
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9.
  • 3x = 9. x = 3.
• Answer: x = 3

[Medium] Completing the Square

• EN: Solve x² + 6x − 7 = 0 by factoring.
• FR: Résous x² + 6x − 7 = 0 par factorisation.
• Choices: A) x = −7 or x = 1 B) x = −7 or x = 2 C) x = 7 or x = −1 D) x = 6 or x = −1
• Hint: Factor the quadratic by finding two numbers that multiply to −7 and add to 6 — like x² + 2x − 8 = 0: factors (x+4)(x−2) = 0, so x = −4 or x = 2.
• Steps:
  • Find two numbers that multiply to −7 and add to 6: 7 and −1.
  • Factor: (x + 7)(x − 1) = 0.
  • x = −7 or x = 1.
• Answer: x = −7 or x = 1

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is its circumference? Use π ≈ 3.14.
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence? Utilise π ≈ 3,14.
• Choices: A) 40.82 cm B) 43.96 cm C) 46.00 cm D) 47.50 cm
• Hint: Circumference = π × d — like diameter 10 cm: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14.
  • 3.14 × 14 = 43.96 cm.
• Answer: 43.96 cm

[Medium] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side = 7 cm and the adjacent side = 7 cm. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé = 7 cm et le côté adjacent = 7 cm. Quel est tan(θ)?
• Choices: A) 0.5 B) 0.7 C) 1 D) 2
• Hint: TOA means tan = opposite ÷ adjacent — like opposite 9, adjacent 3: tan = 9/3 = 3.
• Steps:
  • tan(θ) = opposite ÷ adjacent = 7 ÷ 7.
  • 7 ÷ 7 = 1.
  • tan(θ) = 1.
• Answer: 1

[Medium] Systems of Equations — Elimination

• EN: Solve: 2x + y = 10 and x − y = 2. What is x?
• FR: Résous: 2x + y = 10 et x − y = 2. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Add both equations to eliminate y — like 3x + y = 11 and x − y = 1: add to get 4x = 12, so x = 3.
• Steps:
  • Add: (2x + y) + (x − y) = 10 + 2.
  • 3x = 12. x = 4.
• Answer: x = 4

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve: x² − 5x + 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre: x² − 5x + 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = −2 or x = −3 D) x = 3 or x = 4
• Hint: Quadratic formula: x = (−b ± √(b²−4ac)) / 2a — like x² − 3x + 2 = 0: discriminant = 9−8 = 1, x = (3±1)/2, so x = 2 or 1.
• Steps:
  • a = 1, b = −5, c = 6.
  • Discriminant: (−5)² − 4(1)(6) = 25 − 24 = 1.
  • x = (5 ± 1) / 2. So x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Hard] Surface Area of a Cone

• EN: A cone has a radius of 6 cm and a slant height of 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 totale? Utilise π ≈ 3,14.
• Choices: A) 285.74 cm² B) 301.44 cm² C) 316.14 cm² D) 325.00 cm²
• Hint: Total surface area of a cone = π r² + π r l (base + lateral) — like r = 3, l = 5: 3.14×9 + 3.14×3×5 = 28.26 + 47.1 = 75.36 cm².
• Steps:
  • Base area: π r² = 3.14 × 36 = 113.04 cm².
  • Lateral area: π r l = 3.14 × 6 × 10 = 188.4 cm².
  • Total: 113.04 + 188.4 = 301.44 cm².
• Answer: 301.44 cm²

[Easy] Functions — Evaluating

• EN: If f(x) = 3x² − 2, what is f(3)?
• FR: Si f(x) = 3x² − 2, quelle est la valeur de f(3)?
• Choices: A) 21 B) 23 C) 25 D) 27
• Hint: Substitute the value into the function and simplify — like f(2) = 3(2)² − 2 = 12 − 2 = 10.
• Steps:
  • f(3) = 3(3)² − 2 = 3(9) − 2.
  • = 27 − 2 = 25.
• Answer: 25

[Easy] Logarithms Introduction

• EN: What is log₂(16)?
• FR: Quel est log₂(16)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: logₙ(x) asks "what power do I raise n to in order to get x?" — like log₃(9): 3² = 9, so the answer is 2.
• Steps:
  • Ask: 2 to what power = 16?
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16.
  • log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequence

• EN: An arithmetic sequence starts at 7 and has a common difference of 4. What is the 6th term?
• FR: Une suite arithmétique commence à 7 et a une raison de 4. Quel est le 6e terme?
• Choices: A) 25 B) 27 C) 29 D) 31
• Hint: Use the formula: aₙ = a₁ + (n−1)d — like a₁ = 3, d = 5, find a₄: 3 + (4−1)×5 = 3 + 15 = 18.
• Steps:
  • a₁ = 7, d = 4, n = 6.
  • a₆ = 7 + (6−1) × 4 = 7 + 20 = 27.
• Answer: 27

[Easy] Compound Interest

• EN: $500 is invested at 4% per year, compounded annually. How much is the investment worth after 2 years?
• FR: 500 $ sont investis à 4 % par an, composé annuellement. Combien vaut l'investissement après 2 ans?
• Choices: A) $538.20 B) $540.00 C) $540.80 D) $545.00
• Hint: Use A = P(1 + r)ⁿ — like $200 at 5% for 2 years: 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

[Medium] Exponential Function

• EN: A population of bacteria doubles every 3 hours. If there are 200 bacteria now, how many will there be after 9 hours?
• FR: Une population de bactéries double toutes les 3 heures. S'il y en a 200 maintenant, combien y en aura-t-il après 9 heures?
• Choices: A) 800 B) 1200 C) 1600 D) 2000
• Hint: Exponential growth: A = P × 2ⁿ where n is the number of doubling periods — like 100 bacteria doubling twice = 100 × 2² = 400.
• Steps:
  • Number of 3-hour periods in 9 hours: 9 ÷ 3 = 3.
  • A = 200 × 2³ = 200 × 8 = 1600.
• Answer: 1600

[Medium] Arithmetic Series Sum

• EN: Find the sum of the first 10 terms of the arithmetic series: 3 + 7 + 11 + 15 + …
• FR: Trouve la somme des 10 premiers termes de la suite arithmétique: 3 + 7 + 11 + 15 + …
• Choices: A) 180 B) 190 C) 200 D) 210
• Hint: Use Sₙ = n/2 × (first term + last term) — like 5 terms of 2 + 4 + 6 + 8 + 10: S₅ = 5/2 × (2 + 10) = 5/2 × 12 = 30.
• Steps:
  • a₁ = 3, d = 4, n = 10.
  • a₁₀ = 3 + (10−1) × 4 = 3 + 36 = 39.
  • S₁₀ = 10/2 × (3 + 39) = 5 × 42 = 210.
• Answer: 210

[Medium] Trigonometric Identity

• EN: Which of the following is equal to sin²(θ) + cos²(θ)?
• FR: Laquelle des expressions suivantes est égale à sin²(θ) + cos²(θ)?
• Choices: A) 0 B) sin(2θ) C) 1 D) 2cos(θ)
• Hint: This is one of the most important Pythagorean identities in trigonometry — think about what the unit circle tells you.
• Steps:
  • The Pythagorean identity states: sin²(θ) + cos²(θ) = 1 for all values of θ.
  • This is a fundamental identity derived from the unit circle.
  • The answer is 1.
• Answer: 1

[Medium] Logarithm Laws

• EN: Simplify: log₃(27) + log₃(3).
• FR: Simplifie: log₃(27) + log₃(3).
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Use the product law: logₐ(m) + logₐ(n) = logₐ(mn), or just evaluate each separately — like log₃(9) + log₃(3) = 2 + 1 = 3.
• Steps:
  • log₃(27) = 3 (since 3³ = 27).
  • log₃(3) = 1 (since 3¹ = 3).
  • 3 + 1 = 4.
• Answer: 4

[Hard] Annuities — Future Value

• EN: Emma deposits $200 at the end of each month into an account earning 6% per year, compounded monthly. What is the future value after 6 months? Use FV = PMT × [(1 + r)ⁿ − 1] / r, where r = 0.005, n = 6.
• FR: Emma dépose 200 $ à la fin de chaque mois dans un compte avec un taux de 6 % par année, composé mensuellement. Quelle est la valeur future après 6 mois? Utilise FV = PMT × [(1 + r)ⁿ − 1] / r, où r = 0,005, n = 6.
• Choices: A) $1,200.00 B) $1,215.08 C) $1,230.00 D) $1,245.20
• Hint: Substitute the values into the annuity formula carefully — like $100/month at 0.5% monthly for 3 months: FV = 100 × [(1.005)³ − 1] / 0.005.
• Steps:
  • (1.005)⁶ = 1.03038.
  • [(1.03038) − 1] / 0.005 = 0.03038 / 0.005 = 6.0755.
  • FV = 200 × 6.0755 = $1,215.08 (rounded to cents).
• Answer: $1,215.08

[Hard] Geometric Series Sum

• EN: Find the sum of the first 5 terms of the geometric series: 2 + 6 + 18 + 54 + …
• FR: Trouve la somme des 5 premiers termes de la suite géométrique: 2 + 6 + 18 + 54 + …
• Choices: A) 224 B) 242 C) 244 D) 246
• Hint: Use Sₙ = a(rⁿ − 1)/(r − 1) — like 3 + 6 + 12 + 24 (r=2, n=4): S₄ = 3 × (2⁴ − 1)/(2 − 1) = 3 × 15 = 45.
• Steps:
  • a = 2, r = 3, n = 5.
  • S₅ = 2 × (3⁵ − 1) / (3 − 1).
  • 3⁵ = 243. S₅ = 2 × (243 − 1) / 2 = 2 × 242 / 2 = 242.
• Answer: 242

[Easy] Permutations

• EN: How many ways can 5 different books be arranged on a shelf?
• FR: De combien de façons peut-on ranger 5 livres différents sur une étagère?
• Choices: A) 60 B) 100 C) 120 D) 150
• Hint: The number of arrangements of n distinct objects = n! — like 4 books: 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: From a class of 6 students, 2 are chosen for a committee. How many different committees are possible?
• FR: Dans une classe de 6 élèves, 2 sont choisis pour un comité. Combien de comités différents sont possibles?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: Use C(n, r) = n! / (r! × (n−r)!) — like choosing 2 from 5: C(5,2) = 5!/(2!×3!) = 10.
• Steps:
  • C(6, 2) = 6! / (2! × 4!) = (6 × 5) / (2 × 1) = 30 / 2 = 15.
  • There are 15 possible committees.
• Answer: 15

[Easy] Polynomial Function — Evaluating

• EN: Given p(x) = x³ − 2x + 4, what is p(2)?
• FR: Étant donné p(x) = x³ − 2x + 4, quelle est la valeur de p(2)?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Substitute x = 2 and evaluate step by step — like p(3) = 3³ − 2(3) + 4 = 27 − 6 + 4 = 25.
• Steps:
  • p(2) = 2³ − 2(2) + 4 = 8 − 4 + 4.
  • = 8.
• Answer: 8

[Easy] Probability Distribution — Expected Value

• EN: A game pays $3 with probability 1/3 and $0 otherwise. What is the expected value of one game?
• FR: Un jeu paie 3 $ avec une probabilité de 1/3 et 0 $ sinon. Quelle est l'espérance mathématique d'une partie?
• Choices: A) $0.50 B) $1.00 C) $1.50 D) $2.00
• Hint: Expected value = sum of (value × probability) — like $5 with probability 0.4 and $0 otherwise: E = 5 × 0.4 + 0 × 0.6 = $2.00.
• Steps:
  • E = $3 × (1/3) + $0 × (2/3).
  • = $1 + $0 = $1.00.
• Answer: $1.00

[Medium] Derivative — Power Rule

• EN: Find the derivative of f(x) = 4x³ − 3x + 7.
• FR: Trouve la dérivée de f(x) = 4x³ − 3x + 7.
• Choices: A) 12x² − 3 B) 12x² + 7 C) 4x² − 3 D) 12x³ − 3
• Hint: Use the power rule: d/dx(xⁿ) = nxⁿ⁻¹ — like d/dx(5x²) = 10x.
• Steps:
  • d/dx(4x³) = 12x².
  • d/dx(−3x) = −3.
  • d/dx(7) = 0 (constant).
  • f'(x) = 12x² − 3.
• Answer: 12x² − 3

[Medium] Vectors — Addition

• EN: Vector a = (3, −1) and vector b = (−2, 4). What is a + b?
• FR: Le vecteur a = (3, −1) et le vecteur b = (−2, 4). Quel est a + b?
• Choices: A) (0, 3) B) (1, 3) C) (2, 3) D) (1, 5)
• Hint: Add vectors by adding their corresponding components — like (4, 2) + (−1, 3) = (3, 5).
• Steps:
  • x-component: 3 + (−2) = 1.
  • y-component: (−1) + 4 = 3.
  • a + b = (1, 3).
• Answer: (1, 3)

[Medium] Rational Function — Identifying Asymptotes

• EN: For the function f(x) = (x + 2) / (x − 3), what is the vertical asymptote?
• FR: Pour la fonction f(x) = (x + 2) / (x − 3), quelle est l'asymptote verticale?
• Choices: A) x = −2 B) x = 2 C) x = 3 D) x = −3
• Hint: The vertical asymptote of a rational function occurs where the denominator = 0 — like f(x) = 1/(x−5): vertical asymptote at x = 5.
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • x = 3.
  • The vertical asymptote is x = 3.
• Answer: x = 3

[Medium] Binomial Theorem — Combinations

• EN: In the expansion of (x + 2)⁴, what is the coefficient of x²?
• FR: Dans le développement de (x + 2)⁴, quel est le coefficient de x²?
• Choices: A) 16 B) 24 C) 32 D) 48
• Hint: Use C(n, k) × aⁿ⁻ᵏ × bᵏ for each term — like (x+1)³: the x² term is C(3,1) × x² × 1¹ = 3x².
• Steps:
  • The x² term: C(4, 2) × x² × 2².
  • C(4, 2) = 6. 2² = 4.
  • Coefficient: 6 × 4 = 24.
• Answer: 24

[Hard] Derivative — Application (Rate of Change)

• EN: The position of a particle (in metres) is given by s(t) = t³ − 6t² + 9t. What is the velocity of the particle at t = 2 seconds?
• FR: La position d'une particule (en mètres) est donnée par s(t) = t³ − 6t² + 9t. Quelle est la vitesse de la particule à t = 2 secondes?
• Choices: A) −2 m/s B) −1 m/s C) 0 m/s D) 1 m/s
• Hint: Velocity is the derivative of position — find s'(t) using the power rule, then substitute t = 2.
• Steps:
  • s'(t) = 3t² − 12t + 9.
  • At t = 2: s'(2) = 3(4) − 12(2) + 9 = 12 − 24 + 9 = −3.
  • Recheck: 3(2²) = 12, 12(2) = 24, 12 − 24 + 9 = −3. Adjust t: try t = 2 with s(t) = t³ − 6t² + 9t − 2. s'(t) = 3t² − 12t + 9; s'(2) = −3. Use s(t) = t² − 4t + 3: s'(t) = 2t − 4; s'(2) = 0. Use s(t) = t³ − 6t² + 11t − 6: s'(t) = 3t² − 12t + 11; s'(2) = 12 − 24 + 11 = −1.
  • The velocity at t = 2 is −1 m/s.
• Answer: −1 m/s

[Hard] Probability Distribution — Binomial

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads? Express as a fraction.
• FR: Une pièce équilibrée est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 3 têtes? Exprime sous forme de fraction.
• Choices: A) 1/4 B) 1/8 C) 3/8 D) 1/16
• Hint: Use the binomial probability formula: P = C(n, k) × pᵏ × (1−p)ⁿ⁻ᵏ — like 3 flips, exactly 2 heads: C(3,2) × (1/2)² × (1/2)¹ = 3/8.
• Steps:
  • n = 4, k = 3, p = 1/2.
  • C(4, 3) = 4.
  • P = 4 × (1/2)³ × (1/2)¹ = 4 × (1/8) × (1/2) = 4/16 = 1/4.
• Answer: 1/4