Daily Math — 2026-07-01

[Easy] Counting Candles

• EN: Mia has 7 candles on her birthday cake. She gets 5 more. How many candles are there in all?
• FR: Mia a 7 bougies sur son gâteau d'anniversaire. Elle en reçoit 5 de plus. Combien y a-t-il de bougies en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add 6 + 4, start at 6 and count up 4 more: 7, 8, 9, 10.
• Steps:
  • Start at 7 and count up 5: 8, 9, 10, 11, 12.
  • 7 + 5 = 12.
• Answer: 12

[Easy] Hockey Pucks

• EN: There are 9 hockey pucks on the ice. 3 are taken away. How many are left?
• FR: Il y a 9 rondelles de hockey sur la glace. On en enlève 3. Combien en reste-t-il?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: To subtract 8 − 3, count back 3 from 8: 7, 6, 5.
• Steps:
  • Start at 9 and count back 3: 8, 7, 6.
  • 9 − 3 = 6.
• Answer: 6

[Easy] Skip Counting by 2s

• EN: Count by 2s: 2, 4, 6, 8, ___. What number comes next?
• FR: Compte par 2: 2, 4, 6, 8, ___. Quel nombre vient ensuite?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When counting by 2s, add 2 each time: 4, 6, 8, 10, 12...
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
• Answer: 10

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents in Canada?
• FR: Quelle pièce vaut 10 cents au Canada?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: A nickel is worth 5 cents; a dime is worth double that.
• Steps:
  • A penny = 1 cent, a nickel = 5 cents.
  • A dime = 10 cents.
• Answer: Dime

[Medium] More or Less?

• EN: Emma has 14 stickers. Noah has 18 stickers. How many MORE stickers does Noah have?
• FR: Emma a 14 autocollants. Noah en a 18. Combien d'autocollants de PLUS Noah a-t-il?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: To find how many more, subtract: 17 − 13 = 4.
• Steps:
  • Subtract to compare: 18 − 14.
  • 18 − 14 = 4.
• Answer: 4

[Medium] Skip Count by 5s

• EN: Luc counts by 5s: 5, 10, 15, 20, ___. What is the missing number?
• FR: Luc compte par 5: 5, 10, 15, 20, ___. Quel est le nombre manquant?
• Choices: A) 22 B) 23 C) 25 D) 30
• Hint: Counting by 5s: 10, 15, 20, 25, 30 — add 5 each time.
• Steps:
  • Each number goes up by 5.
  • 20 + 5 = 25.
• Answer: 25

[Medium] Comparing Numbers

• EN: Which number is GREATER: 13 or 31?
• FR: Quel nombre est PLUS GRAND: 13 ou 31?
• Choices: A) 13 B) 31 C) They are equal D) Cannot tell
• Hint: Look at the tens digit first: 1 ten is less than 3 tens.
• Steps:
  • 13 has 1 ten; 31 has 3 tens.
  • 3 tens is more, so 31 is greater.
• Answer: 31

[Medium] Adding Three Numbers

• EN: Ayla has 3 apples, 4 oranges, and 6 bananas. How many pieces of fruit in all?
• FR: Ayla a 3 pommes, 4 oranges et 6 bananes. Combien de fruits en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To add 2 + 5 + 3, first add 2 + 5 = 7, then 7 + 3 = 10.
• Steps:
  • Add 3 + 4 = 7.
  • Then 7 + 6 = 13.
• Answer: 13

[Hard] Counting Back

• EN: There are 20 children in a class. 8 go to the library. How many stay in the class?
• FR: Il y a 20 enfants dans une classe. 8 vont à la bibliothèque. Combien restent dans la classe?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To find 15 − 6, count back 6 from 15: 14, 13, 12, 11, 10, 9.
• Steps:
  • Start at 20 and count back 8: 19, 18, 17, 16, 15, 14, 13, 12.
  • 20 − 8 = 12.
• Answer: 12

[Hard] Coins and Total

• EN: Sanjay has 1 dime and 2 nickels. How many cents does he have in all?
• FR: Sanjay a 1 pièce de 10 cents et 2 pièces de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 15 cents B) 17 cents C) 20 cents D) 25 cents
• Hint: A dime = 10¢, a nickel = 5¢. For 1 dime + 1 nickel: 10 + 5 = 15¢.
• Steps:
  • 1 dime = 10 cents; 2 nickels = 5 + 5 = 10 cents.
  • 10 + 10 = 20 cents.
• Answer: 20 cents

[Easy] Adding Within 100

• EN: A store has 34 red mittens and 25 blue mittens. How many mittens in all?
• FR: Un magasin a 34 mitaines rouges et 25 mitaines bleues. Combien de mitaines en tout?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: To add 32 + 24, add tens first (30 + 20 = 50), then ones (2 + 4 = 6): 56.
• Steps:
  • Tens: 30 + 20 = 50. Ones: 4 + 5 = 9.
  • 50 + 9 = 59.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre la petite aiguille sur 3 et la grande aiguille sur 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 12:15
• Hint: When the minute hand is on 12, it is exactly on the hour — like 5:00 or 7:00.
• Steps:
  • Hour hand on 3 → it is 3 o'clock.
  • Minute hand on 12 → exactly 00 minutes.
• Answer: 3:00

[Easy] Subtraction Within 100

• EN: There are 67 snowflakes drawn on a poster. 23 are erased. How many are left?
• FR: Il y a 67 flocons de neige dessinés sur une affiche. 23 sont effacés. Combien en reste-t-il?
• Choices: A) 40 B) 43 C) 44 D) 45
• Hint: For 58 − 21, subtract tens (50 − 20 = 30) then ones (8 − 1 = 7): 37.
• Steps:
  • Tens: 60 − 20 = 40. Ones: 7 − 3 = 4.
  • 40 + 4 = 44.
• Answer: 44

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A crayon is 9 cm long. How much longer is the pencil?
• FR: Un crayon est long de 15 cm. Un crayon de cire est long de 9 cm. Combien le crayon est-il plus long?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: To find how much longer, subtract: 14 − 8 = 6 cm.
• Steps:
  • 15 − 9 = 6.
  • The pencil is 6 cm longer.
• Answer: 6 cm

[Medium] Counting Coins to $1

• EN: Fatima has 3 quarters. How many cents does she have in all?
• FR: Fatima a 3 pièces de 25 cents. Combien de cents a-t-elle en tout?
• Choices: A) 55 cents B) 65 cents C) 75 cents D) 80 cents
• Hint: A quarter = 25 cents; 2 quarters = 50 cents; 3 quarters = 75 cents.
• Steps:
  • 1 quarter = 25¢; 2 quarters = 50¢.
  • 3 quarters = 75¢.
• Answer: 75 cents

[Medium] Telling Time to Half-Hour

• EN: The hour hand is between 7 and 8. The minute hand is on 6. What time is it?
• FR: La petite aiguille est entre 7 et 8. La grande aiguille est sur 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the minute hand points to 6, it is 30 minutes past the hour — like 4:30.
• Steps:
  • Minute hand on 6 = 30 minutes past.
  • Hour hand past 7 → 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: Look at the pattern: 10, 20, 30, 40, ___. What comes next?
• FR: Regarde le motif: 10, 20, 30, 40, ___. Qu'est-ce qui vient ensuite?
• Choices: A) 44 B) 45 C) 50 D) 55
• Hint: Count by 10s: 10, 20, 30, 40, 50, 60 — add 10 each time.
• Steps:
  • The pattern adds 10 each time.
  • 40 + 10 = 50.
• Answer: 50

[Medium] Adding with Regrouping

• EN: A class collects 47 cans of food on Monday and 36 cans on Tuesday. How many cans in total?
• FR: Une classe ramasse 47 boîtes de conserve lundi et 36 mardi. Combien de boîtes en tout?
• Choices: A) 73 B) 82 C) 83 D) 84
• Hint: For 38 + 25, add ones first (8 + 5 = 13, carry the 1), then tens (3 + 2 + 1 = 6): 63.
• Steps:
  • Ones: 7 + 6 = 13. Write 3, carry 1.
  • Tens: 4 + 3 + 1 = 8. So 83.
• Answer: 83

[Hard] Two-Step Problem

• EN: Marcus has 50 cents. He spends 15 cents on a sticker and 20 cents on a pencil. How much money does he have left?
• FR: Marcus a 50 cents. Il dépense 15 cents sur un autocollant et 20 cents sur un crayon. Combien d'argent lui reste-t-il?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: First add what you spent: 10 + 15 = 25 cents. Then subtract from your start: 40 − 25 = 15 cents.
• Steps:
  • Total spent: 15 + 20 = 35 cents.
  • Money left: 50 − 35 = 15 cents.
• Answer: 15 cents

[Hard] Measuring and Comparing

• EN: A bookshelf is 90 cm wide. Three books are 28 cm, 35 cm, and 22 cm wide. Do all three books fit on the shelf?
• FR: Une étagère fait 90 cm de large. Trois livres font 28 cm, 35 cm et 22 cm de large. Les trois livres entrent-ils tous sur l'étagère?
• Choices: A) Yes, with 5 cm to spare B) Yes, with 4 cm to spare C) No, they are 5 cm too wide D) No, they are 10 cm too wide
• Hint: Add the books: 25 + 30 + 20 = 75 cm; then compare 75 to the shelf size.
• Steps:
  • Add widths: 28 + 35 = 63; 63 + 22 = 85 cm.
  • 90 − 85 = 5 cm to spare. Yes, they fit!
• Answer: Yes, with 5 cm to spare

[Easy] Multiplication by 2

• EN: A hockey team has 6 players on the ice. Each player has 2 gloves. How many gloves in all?
• FR: Une équipe de hockey a 6 joueurs sur la glace. Chaque joueur a 2 gants. Combien de gants en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: To find 5 × 2, think "5 groups of 2": 2, 4, 6, 8, 10.
• Steps:
  • 6 players × 2 gloves each.
  • 6 × 2 = 12.
• Answer: 12

[Easy] Basic Division

• EN: There are 15 cookies shared equally among 5 friends. How many cookies does each friend get?
• FR: Il y a 15 biscuits partagés également entre 5 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: Division is sharing equally: 12 ÷ 4 means 4 groups from 12, so 3 in each group.
• Steps:
  • 15 ÷ 5 = how many in each group?
  • 5 × 3 = 15, so each friend gets 3.
• Answer: 3

[Easy] Fractions — One Half

• EN: A pizza is cut into 4 equal slices. Theo eats 2 slices. What fraction did he eat?
• FR: Une pizza est coupée en 4 tranches égales. Théo mange 2 tranches. Quelle fraction a-t-il mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: If you eat 3 out of 6 equal pieces, that is 3/6, which equals 1/2.
• Steps:
  • 2 slices eaten out of 4 total = 2/4.
  • 2/4 = 1/2.
• Answer: 1/2

[Easy] Multiplication by 5

• EN: There are 4 bags of apples. Each bag has 5 apples. How many apples in all?
• FR: Il y a 4 sacs de pommes. Chaque sac contient 5 pommes. Combien de pommes en tout?
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: Skip-count by 5 four times: 5, 10, 15, 20.
• Steps:
  • 4 × 5 = ?
  • Count by 5s four times: 5, 10, 15, 20.
• Answer: 20

[Medium] Perimeter

• EN: A rectangular garden is 8 m long and 3 m wide. What is its perimeter?
• FR: Un jardin rectangulaire a 8 m de long et 3 m de large. Quel est son périmètre?
• Choices: A) 11 m B) 22 m C) 24 m D) 27 m
• Hint: Perimeter of a rectangle: add all 4 sides. For 6 m × 4 m: 6 + 4 + 6 + 4 = 20 m.
• Steps:
  • Perimeter = 8 + 3 + 8 + 3.
  • = 22 m.
• Answer: 22 m

[Medium] Reading a Graph

• EN: A bar graph shows: Monday = 5 books, Tuesday = 8 books, Wednesday = 3 books returned to the library. How many books were returned in all three days?
• FR: Un diagramme à barres montre: lundi = 5 livres, mardi = 8 livres, mercredi = 3 livres retournés à la bibliothèque. Combien de livres ont été retournés en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: To find a total from a graph, add all the bars: 4 + 7 + 2 = 13.
• Steps:
  • 5 + 8 = 13; 13 + 3 = 16.
  • Total = 16 books.
• Answer: 16

[Medium] Multiplication by 3

• EN: A Tim Hortons worker puts 3 chocolate chips on each muffin. She makes 7 muffins. How many chocolate chips does she use?
• FR: Une employée de Tim Hortons met 3 pépites de chocolat sur chaque muffin. Elle fait 7 muffins. Combien de pépites de chocolat utilise-t-elle?
• Choices: A) 18 B) 21 C) 24 D) 28
• Hint: For 3 × 6, skip-count by 3 six times: 3, 6, 9, 12, 15, 18.
• Steps:
  • 7 × 3 = ?
  • 3, 6, 9, 12, 15, 18, 21.
• Answer: 21

[Medium] Fractions — One Quarter

• EN: A ribbon is 12 cm long. Sophie cuts off 1/4 of it. How many centimetres does she cut?
• FR: Un ruban mesure 12 cm de long. Sophie en coupe 1/4. Combien de centimètres coupe-t-elle?
• Choices: A) 2 cm B) 3 cm C) 4 cm D) 6 cm
• Hint: To find 1/4 of 8, divide by 4: 8 ÷ 4 = 2.
• Steps:
  • 1/4 of 12 means divide by 4.
  • 12 ÷ 4 = 3 cm.
• Answer: 3 cm

[Hard] Multiplication and Subtraction Together

• EN: A store has 4 boxes of pencils. Each box holds 10 pencils. The store sells 17 pencils. How many pencils are left?
• FR: Un magasin a 4 boîtes de crayons. Chaque boîte contient 10 crayons. Le magasin vend 17 crayons. Combien de crayons restent-ils?
• Choices: A) 20 B) 23 C) 27 D) 30
• Hint: First find the total: 3 × 10 = 30; then subtract what was sold: 30 − 8 = 22.
• Steps:
  • Total pencils: 4 × 10 = 40.
  • Left after selling: 40 − 17 = 23.
• Answer: 23

[Hard] Division with Fractions

• EN: Ella has 24 grapes. She gives 1/3 to her brother and 1/4 to her sister. How many grapes does she give away altogether?
• FR: Ella a 24 raisins. Elle en donne 1/3 à son frère et 1/4 à sa sœur. Combien de raisins donne-t-elle en tout?
• Choices: A) 12 B) 13 C) 14 D) 16
• Hint: Find each part separately: 1/3 of 12 = 4; 1/4 of 12 = 3; add them: 4 + 3 = 7.
• Steps:
  • 1/3 of 24 = 24 ÷ 3 = 8 grapes to brother.
  • 1/4 of 24 = 24 ÷ 4 = 6 grapes to sister.
  • Total given away: 8 + 6 = 14.
• Answer: 14

[Easy] Multiplication Facts

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To remember 6 × 8 = 48, then 7 × 8 is one more group of 8: 48 + 8 = 56.
• Steps:
  • 7 × 8 = 8 + 8 + 8 + 8 + 8 + 8 + 8.
  • = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 40
• Hint: In 2.58, the 5 is in the tenths place and the 8 is in the hundredths place.
• Steps:
  • 3 is in the ones place; 4 is in the tenths place; 7 is in the hundredths place.
  • The digit 4 = 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A hockey rink practice area is 9 m long and 5 m wide. What is its area?
• FR: Une zone d'entraînement de patinoire de hockey a 9 m de long et 5 m de large. Quelle est son aire?
• Choices: A) 28 m² B) 40 m² C) 45 m² D) 50 m²
• Hint: Area = length × width. For 6 m × 7 m, area = 42 m².
• Steps:
  • Area = 9 × 5.
  • = 45 m².
• Answer: 45 m²

[Easy] Long Division Without Remainder

• EN: 48 ÷ 6 = ?
• FR: 48 ÷ 6 = ?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Think: what times 6 equals 42? 6 × 7 = 42, so 42 ÷ 6 = 7.
• Steps:
  • Ask: 6 × ? = 48.
  • 6 × 8 = 48, so the answer is 8.
• Answer: 8

[Medium] Long Division with Remainder

• EN: 53 ÷ 7 = ? with a remainder.
• FR: 53 ÷ 7 = ? avec un reste.
• Choices: A) 7 remainder 3 B) 7 remainder 4 C) 8 remainder 4 D) 7 remainder 5
• Hint: For 29 ÷ 4: 4 × 7 = 28, remainder = 29 − 28 = 1. Answer: 7 remainder 1.
• Steps:
  • 7 × 7 = 49; 49 is the closest multiple of 7 below 53.
  • 53 − 49 = 4. Answer: 7 remainder 4.
• Answer: 7 remainder 4

[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) Cannot compare
• Hint: To compare 2/5 and 3/7, convert to decimals: 2/5 = 0.4, 3/7 ≈ 0.43, so 3/7 is bigger.
• Steps:
  • 3/4 = 0.75; 2/3 ≈ 0.667.
  • 0.75 > 0.667, so 3/4 is larger.
• Answer: 3/4

[Medium] Elapsed Time

• EN: Soccer practice starts at 2:15 PM and ends at 4:00 PM. How long is the practice?
• FR: L'entraînement de soccer commence à 14h15 et se termine à 16h00. Combien de temps dure l'entraînement?
• Choices: A) 1 hour 30 minutes B) 1 hour 45 minutes C) 2 hours D) 2 hours 15 minutes
• Hint: From 3:20 to 5:00 — count 40 min to 4:00, then 1 more hour = 1 hour 40 min.
• Steps:
  • From 2:15 to 4:00 PM: count 45 min to reach 3:00, then 1 more hour to 4:00.
  • Total = 1 hour 45 minutes.
• Answer: 1 hour 45 minutes

[Medium] Decimal Operations

• EN: A book costs $4.35 and a bookmark costs $1.20. What is the total cost?
• FR: Un livre coûte 4,35 $ et un signet coûte 1,20 $. Quel est le coût total?
• Choices: A) $5.45 B) $5.50 C) $5.55 D) $5.60
• Hint: Line up the decimal points: 3.25 + 2.40 → ones: 3+2=5, tenths: 2+4=6, hundredths: 5+0=5 → $5.65.
• Steps:
  • $4.35 + $1.20: align decimals.
  • 4 + 1 = 5; .35 + .20 = .55. Total = $5.55.
• Answer: $5.55

[Hard] Multi-Step Division and Area

• EN: A classroom floor is 72 m². If the length is 9 m, what is the width? Then find the perimeter.
• FR: Le plancher d'une salle de classe fait 72 m². Si la longueur est de 9 m, quelle est la largeur? Ensuite, trouvez le périmètre.
• Choices: A) 24 m B) 26 m C) 28 m D) 34 m
• Hint: For area 60 m² and length 10 m: width = 60 ÷ 10 = 6 m; perimeter = 2 × (10 + 6) = 32 m.
• Steps:
  • Width = 72 ÷ 9 = 8 m.
  • Perimeter = 2 × (9 + 8) = 2 × 17 = 34 m.
• Answer: 34 m

[Hard] Multi-Digit Multiplication

• EN: A Canadian school orders 24 boxes of crayons. Each box has 32 crayons. How many crayons are ordered in all?
• FR: Une école canadienne commande 24 boîtes de crayons. Chaque boîte contient 32 crayons. Combien de crayons sont commandés en tout?
• Choices: A) 668 B) 748 C) 768 D) 778
• Hint: For 23 × 12: 23 × 10 = 230; 23 × 2 = 46; 230 + 46 = 276.
• Steps:
  • 24 × 32 = 24 × 30 + 24 × 2.
  • 720 + 48 = 768.
• Answer: 768

[Easy] Multi-Digit Multiplication

• EN: A school buys 15 calculators at $12 each. What is the total cost?
• FR: Une école achète 15 calculatrices à 12 $ chacune. Quel est le coût total?
• Choices: A) $160 B) $170 C) $180 D) $190
• Hint: For 14 × 11: 14 × 10 = 140, 14 × 1 = 14; 140 + 14 = 154.
• Steps:
  • 15 × 12 = 15 × 10 + 15 × 2.
  • 150 + 30 = 180. Total = $180.
• Answer: $180

[Easy] Adding Fractions with Like Denominators

• EN: 3/8 + 2/8 = ?
• FR: 3/8 + 2/8 = ?
• Choices: A) 5/16 B) 5/8 C) 6/8 D) 1/2
• Hint: For 2/7 + 3/7, add only the numerators: 2 + 3 = 5; keep the denominator: 5/7.
• Steps:
  • Denominators are the same (8), so add numerators: 3 + 2 = 5.
  • Answer: 5/8
• Answer: 5/8

[Easy] Decimal Subtraction

• EN: A snowfall of 8.6 cm fell overnight. By morning, 3.2 cm had melted. How many cm remain?
• FR: Une chute de neige de 8,6 cm est tombée pendant la nuit. Le matin, 3,2 cm avaient fondu. Combien de centimètres restent-ils?
• Choices: A) 4.4 cm B) 5.2 cm C) 5.4 cm D) 5.6 cm
• Hint: Line up decimals: 7.9 − 2.5 → 7 − 2 = 5, 0.9 − 0.5 = 0.4 → 5.4.
• Steps:
  • 8.6 − 3.2: line up decimal points.
  • 8 − 3 = 5; 0.6 − 0.2 = 0.4. Answer: 5.4 cm.
• Answer: 5.4 cm

[Easy] Introduction to Percentage — 50%

• EN: A jacket costs $60. It is on sale for 50% off. How much is the discount?
• FR: Une veste coûte 60 $. Elle est en solde à 50 % de réduction. Quel est le rabais?
• Choices: A) $20 B) $25 C) $30 D) $35
• Hint: 50% means half. Half of $40 = $20.
• Steps:
  • 50% of $60 = $60 ÷ 2.
  • = $30.
• Answer: $30

[Medium] Volume of Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume = length × width × height. For 2 × 6 × 3 = 36 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions with Like Denominators

• EN: 7/10 − 3/10 = ?
• FR: 7/10 − 3/10 = ?
• Choices: A) 4/20 B) 4/10 C) 3/10 D) 1/2
• Hint: For 6/9 − 2/9, subtract numerators only: 6 − 2 = 4; keep the 9: 4/9.
• Steps:
  • Denominators are the same (10). Subtract numerators: 7 − 3 = 4.
  • Answer: 4/10
• Answer: 4/10

[Medium] Multi-Digit Division

• EN: A hockey team needs to share 756 cards equally among 9 players. How many cards does each player get?
• FR: Une équipe de hockey doit partager 756 cartes également entre 9 joueurs. Combien de cartes chaque joueur obtient-il?
• Choices: A) 74 B) 82 C) 84 D) 86
• Hint: For 480 ÷ 6: 6 × 80 = 480, so 480 ÷ 6 = 80.
• Steps:
  • 756 ÷ 9: 9 × 80 = 720; 756 − 720 = 36; 36 ÷ 9 = 4.
  • 80 + 4 = 84.
• Answer: 84

[Medium] Percentage — 25%

• EN: There are 80 students at a school event. 25% are wearing green shirts. How many students wear green?
• FR: Il y a 80 élèves à un événement scolaire. 25 % portent des chemises vertes. Combien d'élèves portent du vert?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: 25% = 1/4. To find 25% of 60, divide by 4: 60 ÷ 4 = 15.
• Steps:
  • 25% = 1/4 of the total.
  • 80 ÷ 4 = 20 students.
• Answer: 20

[Hard] Multi-Step Problem — Fractions and Decimals

• EN: Zara had $15.50. She spent 2/5 of her money at a store. How much does she have left?
• FR: Zara avait 15,50 $. Elle a dépensé 2/5 de son argent dans un magasin. Combien lui reste-t-il?
• Choices: A) $8.30 B) $9.00 C) $9.30 D) $10.50
• Hint: For 2/5 of $20, first find 1/5: 20 ÷ 5 = 4; then 2/5 = 4 × 2 = $8. Left: 20 − 8 = $12.
• Steps:
  • 1/5 of $15.50 = $15.50 ÷ 5 = $3.10.
  • 2/5 = 2 × $3.10 = $6.20.
  • Left: $15.50 − $6.20 = $9.30.
• Answer: $9.30

[Hard] Volume and Decimal Combined

• EN: A fish tank is 1.5 m long, 0.6 m wide, and 0.4 m tall. What is the volume in cubic metres?
• FR: Un aquarium mesure 1,5 m de long, 0,6 m de large et 0,4 m de haut. Quel est le volume en mètres cubes?
• Choices: A) 0.24 m³ B) 0.36 m³ C) 0.48 m³ D) 0.60 m³
• Hint: For 2.0 × 0.5 × 0.3: first 2.0 × 0.5 = 1.0; then 1.0 × 0.3 = 0.3 m³.
• Steps:
  • Volume = 1.5 × 0.6 × 0.4.
  • 1.5 × 0.6 = 0.9; 0.9 × 0.4 = 0.36 m³.
• Answer: 0.36 m³

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien font 30 % de 200?
• Choices: A) 40 B) 50 C) 60 D) 70
• Hint: 10% of 200 = 20; multiply by 3 for 30%: 20 × 3 = 60.
• Steps:
  • 10% of 200 = 20.
  • 30% = 3 × 20 = 60.
• Answer: 60

[Easy] Simple Algebraic Expression

• EN: If x = 5, what is the value of 3x + 4?
• FR: Si x = 5, quelle est la valeur de 3x + 4?
• Choices: A) 17 B) 18 C) 19 D) 20
• Hint: For 2x + 3 when x = 4: replace x with 4 → 2(4) + 3 = 8 + 3 = 11.
• Steps:
  • 3x + 4 with x = 5: 3 × 5 + 4.
  • = 15 + 4 = 19.
• Answer: 19

[Easy] Ratio

• EN: A recipe calls for 2 cups of flour for every 3 cups of oats. What is the ratio of flour to oats?
• FR: Une recette demande 2 tasses de farine pour chaque 3 tasses d'avoine. Quel est le ratio farine:avoine?
• Choices: A) 3:2 B) 2:3 C) 1:2 D) 2:1
• Hint: A ratio compares two amounts in order. 4 red to 5 blue is written 4:5.
• Steps:
  • Flour : Oats = 2 : 3.
  • The ratio is 2:3.
• Answer: 2:3

[Easy] Integers — Introduction

• EN: Which integer is the smallest? –3, 0, 2, –7, 5
• FR: Quel entier est le plus petit? –3, 0, 2, –7, 5
• Choices: A) –3 B) 0 C) –7 D) 2
• Hint: On a number line, numbers further left are smaller. –10 is smaller than –4.
• Steps:
  • Negative numbers are less than zero.
  • The most negative is –7, which is the smallest.
• Answer: –7

[Medium] Fraction Multiplication

• EN: 3/4 × 2/5 = ?
• FR: 3/4 × 2/5 = ?
• Choices: A) 5/9 B) 6/20 C) 3/10 D) 6/9
• Hint: To multiply fractions, multiply the numerators and multiply the denominators: 2/3 × 4/5 = 8/15.
• Steps:
  • Multiply numerators: 3 × 2 = 6.
  • Multiply denominators: 4 × 5 = 20. Result: 6/20 = 3/10.
• Answer: 3/10

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1
• FR: Évalue: 3 + 4 × 2 − 1
• Choices: A) 10 B) 12 C) 14 D) 13
• Hint: BEDMAS — Multiplication before Addition. For 5 + 2 × 3 − 1: multiply first → 5 + 6 − 1 = 10.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then: 3 + 8 − 1 = 10.
• Answer: 10

[Medium] Rate Problems

• EN: A car travels 240 km in 3 hours. What is its speed in km/h?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km/h?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: Speed = distance ÷ time. For 150 km in 2 hours: 150 ÷ 2 = 75 km/h.
• Steps:
  • Speed = 240 ÷ 3.
  • = 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: 3/4 ÷ 1/2 = ?
• FR: 3/4 ÷ 1/2 = ?
• Choices: A) 3/8 B) 3/4 C) 3/2 D) 2
• Hint: To divide fractions, multiply by the reciprocal: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
• Steps:
  • Flip the second fraction and multiply: 3/4 × 2/1.
  • = 6/4 = 3/2.
• Answer: 3/2

[Hard] Multi-Step BEDMAS

• EN: Evaluate: (12 − 4)² ÷ 4 + 3 × 2
• FR: Évalue: (12 − 4)² ÷ 4 + 3 × 2
• Choices: A) 18 B) 20 C) 22 D) 24
• Hint: Work inside brackets first, then exponents, then division/multiplication, then addition/subtraction.
• Steps:
  • Brackets: 12 − 4 = 8; then 8² = 64.
  • 64 ÷ 4 = 16; 3 × 2 = 6; 16 + 6 = 22.
• Answer: 22

[Hard] Ratio and Rate Word Problem

• EN: In a Grade 6 class, the ratio of girls to boys is 3:4. There are 21 girls. How many students are in the class in total?
• FR: Dans une classe de 6e année, le ratio filles:garçons est 3:4. Il y a 21 filles. Combien y a-t-il d'élèves en tout?
• Choices: A) 42 B) 45 C) 48 D) 49
• Hint: If ratio is 2:5 and there are 10 in the first group, each part = 10÷2 = 5; total parts = 7; total = 7 × 5 = 35.
• Steps:
  • Each part = 21 ÷ 3 = 7; boys = 4 × 7 = 28.
  • Total = 21 + 28 = 49 students.
• Answer: 49

[Easy] Integer Addition

• EN: –8 + 5 = ?
• FR: –8 + 5 = ?
• Choices: A) –4 B) –3 C) 3 D) 13
• Hint: On a number line, start at –6 and move right 4 steps: –6, –5, –4, –3, –2. Answer: –2.
• Steps:
  • Start at –8, add 5 (move right).
  • –8 + 5 = –3.
• Answer: –3

[Easy] Integer Subtraction

• EN: 4 − (–6) = ?
• FR: 4 − (–6) = ?
• Choices: A) –2 B) 2 C) 8 D) 10
• Hint: Subtracting a negative is the same as adding: 3 − (–5) = 3 + 5 = 8.
• Steps:
  • 4 − (–6) = 4 + 6.
  • = 10.
• Answer: 10

[Easy] Percentage — Discount

• EN: Skates regularly cost $80. They are on sale for 20% off. What is the sale price?
• FR: Des patins coûtent habituellement 80 $. Ils sont en solde à 20 % de rabais. Quel est le prix de vente?
• Choices: A) $56 B) $60 C) $64 D) $68
• Hint: 20% of $50 = $10; sale price = $50 − $10 = $40.
• Steps:
  • 20% of $80 = 0.20 × 80 = $16.
  • Sale price = $80 − $16 = $64.
• Answer: $64

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 13 = 25
• FR: Résous pour x: x + 13 = 25
• Choices: A) x = 10 B) x = 11 C) x = 12 D) x = 13
• Hint: To solve y + 9 = 20, subtract 9 from both sides: y = 20 − 9 = 11.
• Steps:
  • x + 13 = 25 → subtract 13 from both sides.
  • x = 25 − 13 = 12.
• Answer: x = 12

[Medium] Integer Multiplication

• EN: (–6) × (–7) = ?
• FR: (–6) × (–7) = ?
• Choices: A) –42 B) –13 C) 42 D) 13
• Hint: Negative × negative = positive. (–4) × (–5) = 20.
• Steps:
  • Negative × negative = positive.
  • 6 × 7 = 42. Answer: 42.
• Answer: 42

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 10 cm long, 5 cm wide, and 4 cm tall. What is the total surface area?
• FR: Une boîte-cadeau mesure 10 cm de long, 5 cm de large et 4 cm de haut. Quelle est l'aire totale?
• Choices: A) 180 cm² B) 200 cm² C) 220 cm² D) 240 cm²
• Hint: Surface area = 2(lw + lh + wh). For 3×4×5: 2(12+15+20) = 2(47) = 94 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(10×5 + 10×4 + 5×4).
  • = 2(50 + 40 + 20) = 2(110) = 220 cm².
• Answer: 220 cm²

[Medium] Fraction and Decimal Fluency

• EN: Convert 7/8 to a decimal. Round to the nearest hundredth.
• FR: Convertis 7/8 en décimal. Arrondi au centième près.
• Choices: A) 0.75 B) 0.85 C) 0.875 D) 0.88
• Hint: To convert 3/4 to a decimal, divide: 3 ÷ 4 = 0.75.
• Steps:
  • 7 ÷ 8 = 0.875.
  • Rounded to hundredths: 0.875 → 0.88.
• Answer: 0.88

[Medium] Percentage — Tax

• EN: A book costs $12.00 before tax. The HST is 13%. What is the total cost including tax?
• FR: Un livre coûte 12,00 $ avant taxes. La TVH est de 13 %. Quel est le coût total avec taxes?
• Choices: A) $13.36 B) $13.56 C) $13.76 D) $14.00
• Hint: For $20 with 10% tax: 10% of 20 = 2; total = $20 + $2 = $22.
• Steps:
  • 13% of $12.00 = 0.13 × 12 = $1.56.
  • Total = $12.00 + $1.56 = $13.56.
• Answer: $13.56

[Hard] Integer All Operations

• EN: Evaluate: (–3)² + (–4) × 2 − (–5)
• FR: Évalue: (–3)² + (–4) × 2 − (–5)
• Choices: A) 4 B) 6 C) 8 D) 10
• Hint: Work step by step: exponents first, then multiplication, then add/subtract. (–2)² = 4; 4 + (–3)×2 − (–1) = 4 − 6 + 1 = –1.
• Steps:
  • (–3)² = 9; (–4) × 2 = –8; subtracting –5 = +5.
  • 9 + (–8) + 5 = 6.
• Answer: 6

[Hard] Probability

• EN: A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 bleues et 2 vertes. Quelle est la probabilité de choisir une bille bleue?
• Choices: A) 1/2 B) 5/10 C) 1/3 D) 5/8
• Hint: Probability = favourable outcomes ÷ total outcomes. For 4 red out of 12 total: 4/12 = 1/3.
• Steps:
  • Total marbles = 3 + 5 + 2 = 10.
  • P(blue) = 5/10 = 1/2.
• Answer: 1/2

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think: what number times itself equals 121? 11 × 11 = 121.
• Steps:
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of: 8, 12, 10, 14, 6
• FR: Trouve la moyenne de: 8, 12, 10, 14, 6
• Choices: A) 8 B) 9 C) 10 D) 11
• Hint: Mean = sum ÷ count. For 4, 7, 9: sum = 20, count = 3, mean = 20 ÷ 3 ≈ 6.7.
• Steps:
  • Sum = 8 + 12 + 10 + 14 + 6 = 50.
  • Mean = 50 ÷ 5 = 10.
• Answer: 10

[Easy] Two-Step Equation

• EN: Solve: 2x + 3 = 11
• FR: Résous: 2x + 3 = 11
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: For 3y + 2 = 14: subtract 2 first → 3y = 12; divide by 3 → y = 4.
• Steps:
  • 2x + 3 = 11 → subtract 3: 2x = 8.
  • Divide by 2: x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A hockey jersey cost $50 last year. This year it costs $60. What is the percent increase?
• FR: Un chandail de hockey coûtait 50 $ l'an dernier. Cette année, il coûte 60 $. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: Percent increase = (new − old) ÷ old × 100. For old = 40, new = 48: (8 ÷ 40) × 100 = 20%.
• Steps:
  • Increase = 60 − 50 = 10.
  • % increase = (10 ÷ 50) × 100 = 20%.
• Answer: 20%

[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) 9 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: For legs 3 and 4: 3² + 4² = 9 + 16 = 25; √25 = 5. The hypotenuse is 5.
• Steps:
  • a² + b² = c² → 6² + 8² = c².
  • 36 + 64 = 100; c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation — Harder

• EN: Solve: 5x − 7 = 23
• FR: Résous: 5x − 7 = 23
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: For 4x − 3 = 17: add 3 → 4x = 20; divide by 4 → x = 5.
• Steps:
  • Add 7 to both sides: 5x = 30.
  • Divide by 5: x = 6.
• Answer: x = 6

[Medium] Slope Introduction

• EN: A line passes through points (2, 4) and (6, 12). What is the slope?
• FR: Une droite passe par les points (2, 4) et (6, 12). Quelle est la pente?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). For (1,3) and (3,7): (7−3)÷(3−1) = 4÷2 = 2.
• Steps:
  • Slope = (12 − 4) ÷ (6 − 2) = 8 ÷ 4.
  • = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 5, 9, 1, 5, 11
• FR: Trouve la médiane de: 3, 7, 5, 9, 1, 5, 11
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: Order the data first, then find the middle value. For 2, 4, 6, 8, 10, the median is 6.
• Steps:
  • Ordered: 1, 3, 5, 5, 7, 9, 11.
  • Middle value (4th of 7) = 5.
• Answer: 5

[Hard] Pythagorean Theorem Application

• EN: A ladder 13 m long leans against a wall. The base is 5 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 13 m de long s'appuie contre un mur. La base est à 5 m du mur. À quelle hauteur l'échelle atteint-elle le mur?
• Choices: A) 10 m B) 11 m C) 12 m D) 13 m
• Hint: For a right triangle with hypotenuse 10 and one leg 6: other leg = √(100 − 36) = √64 = 8.
• Steps:
  • a² + 5² = 13² → a² = 169 − 25 = 144.
  • a = √144 = 12 m.
• Answer: 12 m

[Hard] Percent Decrease Word Problem

• EN: A store had 250 items. After a sale, only 175 items remain. What percent decrease in items is this?
• FR: Un magasin avait 250 articles. Après une vente, il n'en reste que 175. Quel est le pourcentage de diminution?
• Choices: A) 25% B) 28% C) 30% D) 32%
• Hint: % decrease = (original − new) ÷ original × 100. For 80 to 60: (20÷80) × 100 = 25%.
• Steps:
  • Decrease = 250 − 175 = 75.
  • % decrease = (75 ÷ 250) × 100 = 30%.
• Answer: 30%

[Easy] Solving Linear Equations

• EN: Solve: 3x − 6 = 15
• FR: Résous: 3x − 6 = 15
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: For 4x − 8 = 20: add 8 → 4x = 28; divide by 4 → x = 7.
• Steps:
  • Add 6: 3x = 21.
  • Divide by 3: x = 7.
• Answer: x = 7

[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: Add like terms: (4x + 3) + (x − 1) = (4x + x) + (3 − 1) = 5x + 2.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 − 3 = 2.
  • Answer: 5x + 2
• Answer: 5x + 2

[Easy] Slope-Intercept Form

• EN: What is the y-intercept of the line y = 4x − 7?
• FR: Quel est l'ordonnée à l'origine de la droite y = 4x − 7?
• Choices: A) 4 B) –4 C) 7 D) –7
• Hint: In y = mx + b, the b value is the y-intercept. For y = 3x + 5, the y-intercept is 5.
• Steps:
  • The equation is in y = mx + b form.
  • b = –7, so the y-intercept is –7.
• Answer: –7

[Easy] Similar Triangles

• EN: Two triangles are similar. One has a side of 6 cm, and the corresponding side of the other is 9 cm. If another side of the first triangle is 4 cm, what is the corresponding side of the second?
• FR: Deux triangles sont semblables. L'un a un côté de 6 cm et le côté correspondant de l'autre est 9 cm. Si un autre côté du premier triangle est 4 cm, quel est le côté correspondant du second?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: Find the scale factor: 9 ÷ 6 = 1.5. Multiply each side by 1.5: 3 × 1.5 = 4.5 cm.
• Steps:
  • Scale factor = 9 ÷ 6 = 1.5.
  • 4 × 1.5 = 6 cm.
• Answer: 6 cm

[Medium] Linear Inequalities

• EN: Solve: 2x + 4 > 12
• FR: Résous: 2x + 4 > 12
• Choices: A) x > 3 B) x > 4 C) x < 4 D) x > 8
• Hint: For 3x − 6 > 9: add 6 → 3x > 15; divide → x > 5.
• Steps:
  • Subtract 4: 2x > 8.
  • Divide by 2: x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5)
• FR: Développe: (x + 3)(x + 5)
• Choices: A) x² + 8x + 15 B) x² + 15x + 8 C) x² + 8x + 8 D) x² + 6x + 15
• Hint: Use FOIL: (x+2)(x+4) = x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • F: x × x = x²; O: x × 5 = 5x; I: 3 × x = 3x; L: 3 × 5 = 15.
  • x² + 5x + 3x + 15 = x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Trigonometry — SOH

• EN: In a right triangle, the angle is 30°, the hypotenuse is 10 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, l'angle est de 30°, l'hypoténuse est de 10 cm. Quelle est la longueur du côté opposé?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: SOH: sin(angle) = opposite ÷ hypotenuse. For sin(45°) = 0.707, opposite = 0.707 × hypotenuse.
• Steps:
  • sin(30°) = opposite ÷ 10; sin(30°) = 0.5.
  • opposite = 0.5 × 10 = 5 cm.
• Answer: 5 cm

[Medium] Graphing Lines

• EN: A line has slope 2 and passes through (0, –3). Which equation represents this line?
• FR: Une droite a une pente de 2 et passe par (0, –3). Quelle équation représente cette droite?
• Choices: A) y = 2x + 3 B) y = 2x − 3 C) y = –3x + 2 D) y = 3x − 2
• Hint: The slope-intercept form is y = mx + b, where m is slope and b is y-intercept. For slope 3, y-intercept 5: y = 3x + 5.
• Steps:
  • m = 2, b = –3.
  • Equation: y = 2x − 3.
• Answer: y = 2x − 3

[Hard] Trigonometry — CAH

• EN: A right triangle has an adjacent side of 12 cm and a hypotenuse of 15 cm. Find the angle using CAH (round to the nearest degree).
• FR: Un triangle rectangle a un côté adjacent de 12 cm et une hypoténuse de 15 cm. Trouve l'angle avec CAH (arrondi au degré le plus proche).
• Choices: A) 37° B) 41° C) 45° D) 53°
• Hint: CAH: cos(θ) = adjacent ÷ hypotenuse. Then θ = cos⁻¹(ratio). For adj=8, hyp=10: cos(θ)=0.8, θ≈37°.
• Steps:
  • cos(θ) = 12 ÷ 15 = 0.8.
  • θ = cos⁻¹(0.8) ≈ 37°.
• Answer: 37°

[Hard] Systems of Equations (Substitution)

• EN: Solve the system: y = 2x + 1 and y = –x + 7
• FR: Résous le système: y = 2x + 1 et y = –x + 7
• Choices: A) x = 1, y = 3 B) x = 2, y = 5 C) x = 3, y = 7 D) x = 2, y = 4
• Hint: Set the two expressions equal: if y = 3x − 2 and y = x + 4, then 3x − 2 = x + 4 → 2x = 6 → x = 3.
• Steps:
  • Set equal: 2x + 1 = –x + 7 → 3x = 6 → x = 2.
  • y = 2(2) + 1 = 5. So x = 2, y = 5.
• Answer: x = 2, y = 5

[Easy] Factoring Quadratics

• 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 + 3)(x + 5)
• Hint: Find two numbers that multiply to 10 and add to 7 for x² + 7x + 10: those are 5 and 2.
• Steps:
  • Find two numbers that multiply to 12 and add to 7: 3 and 4.
  • x² + 7x + 12 = (x + 3)(x + 4).
• Answer: (x + 3)(x + 4)

[Easy] Trigonometry — TOA

• EN: In a right triangle, the opposite side is 7 cm and the adjacent side is 7 cm. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 7 cm et le côté adjacent est 7 cm. Combien vaut tan(θ)?
• Choices: A) 0.5 B) 0.7 C) 1 D) 2
• Hint: TOA: tan(θ) = opposite ÷ adjacent. For opposite=4, adjacent=8: tan(θ) = 4/8 = 0.5.
• Steps:
  • tan(θ) = opposite ÷ adjacent = 7 ÷ 7.
  • = 1.
• Answer: 1

[Easy] Systems of Equations

• EN: Solve: x + y = 10 and x − y = 2
• FR: Résous: x + y = 10 et x − y = 2
• Choices: A) x = 5, y = 5 B) x = 6, y = 4 C) x = 7, y = 3 D) x = 8, y = 2
• Hint: Add both equations together to eliminate y: (x+y) + (x–y) = sum → 2x = sum; solve for x.
• Steps:
  • Add: 2x = 12 → x = 6.
  • Substitute: 6 + y = 10 → y = 4.
• Answer: x = 6, y = 4

[Easy] Volume of a Cylinder

• EN: A cylinder has radius 5 cm and height 10 cm. What is the volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 5 cm et une hauteur de 10 cm. Quel est le volume? (Utilise π ≈ 3,14)
• Choices: A) 628 cm³ B) 785 cm³ C) 942 cm³ D) 1,570 cm³
• Hint: Volume of cylinder = π × r² × h. For r=3, h=4: V = 3.14 × 9 × 4 = 113.04 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 25 × 10.
  • = 3.14 × 250 = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Complete the square to rewrite x² + 6x + 4 in vertex form.
• FR: Complète le carré pour réécrire x² + 6x + 4 sous la forme vertex.
• Choices: A) (x + 3)² − 5 B) (x + 3)² + 5 C) (x + 6)² − 4 D) (x + 3)² − 4
• Hint: For x² + 4x + 1: half of 4 is 2; (x+2)² = x² + 4x + 4; subtract 4, add 1: (x+2)² − 3.
• Steps:
  • Half of 6 = 3; (x+3)² = x² + 6x + 9.
  • x² + 6x + 4 = (x+3)² − 9 + 4 = (x+3)² − 5.
• Answer: (x + 3)² − 5

[Medium] Circle Geometry — Arc Length

• EN: A circle has a radius of 10 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 10 cm. Quelle est la circonférence? (Utilise π ≈ 3,14)
• Choices: A) 31.4 cm B) 62.8 cm C) 94.2 cm D) 314 cm
• Hint: Circumference = 2πr. For r = 5: C = 2 × 3.14 × 5 = 31.4 cm.
• Steps:
  • C = 2 × π × r = 2 × 3.14 × 10.
  • = 62.8 cm.
• Answer: 62.8 cm

[Medium] Quadratic Formula

• EN: Solve x² − 5x + 6 = 0 by factoring.
• FR: Résous x² − 5x + 6 = 0 en factorisant.
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = –2 and x = –3 D) x = 3 and x = 4
• Hint: Factor x² − 7x + 12: find two numbers that multiply to 12 and add to –7: –3 and –4. So (x–3)(x–4) = 0.
• Steps:
  • Find two numbers that multiply to 6 and add to –5: –2 and –3.
  • (x − 2)(x − 3) = 0 → x = 2 or x = 3.
• Answer: x = 2 and x = 3

[Medium] Surface Area of a Cone

• EN: A cone has radius 6 cm and slant height 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? (Utilise π ≈ 3,14)
• Choices: A) 226.08 cm² B) 301.44 cm² C) 376.80 cm² D) 452.16 cm²
• Hint: SA = πrl + πr². For r=4, l=8: π(4)(8) + π(16) = 3.14 × 32 + 3.14 × 16 = 150.72 cm².
• Steps:
  • SA = π × r × l + π × r² = 3.14 × 6 × 10 + 3.14 × 36.
  • = 188.4 + 113.04 = 301.44 cm².
• Answer: 301.44 cm²

[Hard] Completing the Square — Finding Roots

• EN: Use completing the square to solve: x² + 4x − 12 = 0
• FR: Utilise la complétion du carré pour résoudre: x² + 4x − 12 = 0
• Choices: A) x = 2 and x = –6 B) x = 3 and x = –4 C) x = 4 and x = –3 D) x = 6 and x = –2
• Hint: For x² + 6x − 7 = 0: (x+3)² − 9 − 7 = 0 → (x+3)² = 16 → x = 1 or x = –7.
• Steps:
  • (x+2)² − 4 − 12 = 0 → (x+2)² = 16.
  • x + 2 = ±4 → x = 2 or x = –6.
• Answer: x = 2 and x = –6

[Hard] Circle Geometry — Chord and Radius

• EN: A chord is 16 cm long. The radius of the circle is 10 cm. How far is the centre of the circle from the midpoint of the chord?
• FR: Une corde mesure 16 cm. Le rayon du cercle est de 10 cm. À quelle distance le centre du cercle est-il du milieu de la corde?
• Choices: A) 4 cm B) 6 cm C) 8 cm D) 10 cm
• Hint: The radius, half-chord, and distance from centre form a right triangle. Use Pythagorean theorem: d² + half_chord² = radius².
• Steps:
  • Half-chord = 8 cm. d² + 8² = 10².
  • d² = 100 − 64 = 36; d = 6 cm.
• Answer: 6 cm

[Easy] Quadratic Function — Vertex

• EN: Find the vertex of y = (x − 3)² + 5.
• FR: Trouve le sommet de y = (x − 3)² + 5.
• Choices: A) (3, 5) B) (–3, 5) C) (3, –5) D) (5, 3)
• Hint: For y = (x − 2)² + 7, the vertex is at (2, 7) — the h and k values.
• Steps:
  • In y = (x − h)² + k, vertex is (h, k).
  • h = 3, k = 5 → vertex = (3, 5).
• Answer: (3, 5)

[Easy] Logarithm Introduction

• EN: Evaluate: log₂(32)
• FR: Évalue: log₂(32)
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log_b(x) asks "what power of b gives x?" For log₃(27): 3³ = 27, so the answer is 3.
• Steps:
  • log₂(32) asks: 2 to what power = 32?
  • 2⁵ = 32, so log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequence

• EN: Find the 8th term of the arithmetic sequence: 3, 7, 11, 15, ...
• FR: Trouve le 8e terme de la suite arithmétique: 3, 7, 11, 15, ...
• Choices: A) 29 B) 31 C) 33 D) 35
• Hint: For a sequence 2, 6, 10, 14..., common difference d = 4; nth term = 2 + (n−1)×4.
• Steps:
  • Common difference d = 4; first term a = 3.
  • 8th term = 3 + (8 − 1) × 4 = 3 + 28 = 31.
• Answer: 31

[Easy] Compound Interest — Basic

• EN: $1,000 is invested at 5% compound interest per year. What is the amount after 1 year?
• FR: 1 000 $ est investi à 5 % d'intérêt composé par an. Quel est le montant après 1 an?
• Choices: A) $1,005 B) $1,050 C) $1,100 D) $1,500
• Hint: After 1 year: A = P(1 + r). For $2,000 at 3%: A = 2000 × 1.03 = $2,060.
• Steps:
  • A = 1000 × (1 + 0.05) = 1000 × 1.05.
  • = $1,050.
• Answer: $1,050

[Medium] Exponential Function

• EN: A population doubles every 4 years. If it starts at 500, what is the population after 12 years?
• FR: Une population double tous les 4 ans. Si elle commence à 500, quelle est la population après 12 ans?
• Choices: A) 2,000 B) 3,000 C) 4,000 D) 6,000
• Hint: Doubling 3 times: start × 2³. For start = 100, 3 doublings: 100 × 8 = 800.
• Steps:
  • 12 years ÷ 4 years per doubling = 3 doublings.
  • Population = 500 × 2³ = 500 × 8 = 4,000.
• Answer: 4,000

[Medium] 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 série géométrique: 2, 6, 18, 54, ...
• Choices: A) 182 B) 222 C) 242 D) 252
• Hint: Sum of geometric series: Sₙ = a(rⁿ − 1)/(r − 1). For a=1, r=2, n=4: S = 1(16−1)/(2−1) = 15.
• Steps:
  • a = 2, r = 3, n = 5.
  • S = 2(3⁵ − 1)/(3 − 1) = 2(243 − 1)/2 = 242.
• Answer: 242

[Medium] Logarithm Properties

• EN: Simplify: log₃(9) + log₃(3)
• FR: Simplifie: log₃(9) + log₃(3)
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: logb(x) + logb(y) = log_b(xy). Also, log₃(3) = 1.
• Steps:
  • log₃(9) = 2 (since 3² = 9); log₃(3) = 1.
  • 2 + 1 = 3.
• Answer: 3

[Medium] Compound Interest — Multiple Years

• EN: $2,000 is invested at 4% compound interest per year. What is the total amount after 3 years? Round to the nearest dollar.
• FR: 2 000 $ sont investis à 4 % d'intérêt composé par an. Quel est le montant total après 3 ans? Arrondi au dollar le plus proche.
• Choices: A) $2,200 B) $2,240 C) $2,249 D) $2,280
• Hint: A = P(1 + r)ⁿ. For P=$1,000, r=0.06, n=2: A = 1000 × (1.06)² = 1000 × 1.1236 = $1,124.
• Steps:
  • A = 2000 × (1.04)³ = 2000 × 1.124864.
  • ≈ $2,249.73 ≈ $2,249.
• Answer: $2,249

[Hard] Trigonometric Identity

• EN: Simplify: sin²(x) + cos²(x) + tan²(x) − sec²(x) + 1
• FR: Simplifie: sin²(x) + cos²(x) + tan²(x) − sec²(x) + 1
• Choices: A) 0 B) 1 C) 2 D) –1
• Hint: Use sin²(x) + cos²(x) = 1, and sec²(x) = 1 + tan²(x), so tan²(x) − sec²(x) = −1.
• Steps:
  • sin²(x) + cos²(x) = 1.
  • tan²(x) − sec²(x) = −1.
  • Total: 1 + (−1) + 1 = 1.
• Answer: 1

[Hard] Annuity Calculation

• EN: You deposit $200 at the end of each month into an account earning 6% annual interest, compounded monthly. What is the value after 12 months? (Use formula: FV = PMT × [(1+r)ⁿ − 1] / r where r = 0.005)
• FR: Tu déposes 200 $ à la fin de chaque mois dans un compte à 6 % d'intérêt annuel, composé mensuellement. Quelle est la valeur après 12 mois? (Utilise: FV = PMT × [(1+r)ⁿ − 1] / r où r = 0,005)
• Choices: A) $2,400.00 B) $2,467.11 C) $2,536.45 D) $2,600.00
• Hint: FV = 100 × [(1.005)¹² − 1] / 0.005. For $100/month, r=0.005, n=12: compute (1.005)¹² ≈ 1.0617; FV ≈ 100 × 12.34 = $1,234.
• Steps:
  • r = 0.005, n = 12, PMT = 200.
  • (1.005)¹² ≈ 1.06168; FV = 200 × (0.06168/0.005) = 200 × 12.3356 ≈ $2,467.11.
• Answer: $2,467.11

[Easy] Polynomial Function — End Behaviour

• EN: For the polynomial f(x) = −2x³ + 5x − 1, what happens as x → +∞?
• FR: Pour le polynôme f(x) = −2x³ + 5x − 1, que se passe-t-il quand x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → –∞ C) f(x) → 0 D) f(x) → 1
• Hint: For odd-degree polynomials with negative leading coefficient: as x→+∞, f(x)→−∞; as x→−∞, f(x)→+∞.
• Steps:
  • Leading term is −2x³ (odd degree, negative coefficient).
  • As x → +∞, −2x³ → −∞.
• Answer: f(x) → –∞

[Easy] Permutations

• EN: In how many ways can 5 students line up for a photo?
• FR: De combien de façons 5 élèves peuvent-ils s'aligner pour une photo?
• Choices: A) 25 B) 60 C) 120 D) 240
• Hint: For 4 students lining up: 4 × 3 × 2 × 1 = 24 ways.
• Steps:
  • Number of arrangements = 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
• Answer: 120

[Easy] Derivative Introduction — Power Rule

• EN: Find the derivative of f(x) = x³.
• FR: Trouve la dérivée de f(x) = x³.
• Choices: A) x² B) 3x² C) 3x D) x³
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n × xⁿ⁻¹. For x⁴, derivative = 4x³.
• Steps:
  • Power rule: bring down the exponent, reduce by 1.
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Combinations

• EN: How many ways can you choose 3 students from a group of 7?
• FR: De combien de façons peut-on choisir 3 élèves dans un groupe de 7?
• Choices: A) 21 B) 35 C) 42 D) 210
• Hint: C(n, r) = n! / (r! × (n−r)!). For C(5,2) = 5!/(2!×3!) = 10.
• Steps:
  • C(7,3) = 7! / (3! × 4!) = (7 × 6 × 5) / (3 × 2 × 1).
  • = 210 / 6 = 35.
• Answer: 35

[Medium] Rational Function — Vertical Asymptote

• EN: Find the vertical asymptote of f(x) = (x + 2) / (x − 4).
• FR: Trouve l'asymptote verticale de f(x) = (x + 2) / (x − 4).
• Choices: A) x = 2 B) x = –2 C) x = 4 D) x = –4
• Hint: Vertical asymptotes occur where the denominator equals zero. For (x − 3) in the denominator: x = 3.
• Steps:
  • Set denominator = 0: x − 4 = 0.
  • x = 4 is the vertical asymptote.
• Answer: x = 4

[Medium] 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). Combien vaut a + b?
• Choices: A) (2, 6) B) (4, 6) C) (2, 2) D) (4, 2)
• Hint: Add component by component: (3,5) + (2,–1) = (3+2, 5+(–1)) = (5, 4).
• Steps:
  • Add x-components: 3 + (–1) = 2.
  • Add y-components: 4 + 2 = 6.
  • a + b = (2, 6).
• Answer: (2, 6)

[Medium] Probability Distribution — Expected Value

• EN: A game gives $10 with probability 0.3 and $0 with probability 0.7. What is the expected value?
• FR: Un jeu donne 10 $ avec une probabilité de 0,3 et 0 $ avec une probabilité de 0,7. Quelle est l'espérance?
• Choices: A) $2.00 B) $3.00 C) $4.00 D) $5.00
• Hint: E(X) = sum of (value × probability). For $20 at 0.4 and $0 at 0.6: E = 20 × 0.4 + 0 × 0.6 = $8.
• Steps:
  • E(X) = 10 × 0.3 + 0 × 0.7.
  • = 3 + 0 = $3.00.
• Answer: $3.00

[Medium] Derivative — Rate of Change

• EN: If f(x) = 4x² − 3x + 1, find f'(x).
• FR: Si f(x) = 4x² − 3x + 1, trouve f'(x).
• Choices: A) 8x − 3 B) 4x − 3 C) 8x + 3 D) 4x² − 3
• Hint: Differentiate term by term: for 5x³ − 2x + 7, derivative = 15x² − 2.
• Steps:
  • Derivative of 4x² = 8x; derivative of –3x = –3; derivative of 1 = 0.
  • f'(x) = 8x − 3.
• Answer: 8x − 3

[Hard] Binomial Theorem / Probability Distribution

• EN: A fair coin is flipped 6 times. What is the probability of getting exactly 4 heads?
• FR: Une pièce équitable est lancée 6 fois. Quelle est la probabilité d'obtenir exactement 4 têtes?
• Choices: A) 15/64 B) 6/64 C) 20/64 D) 1/4
• Hint: P = C(n,k) × (0.5)ⁿ. For 5 flips, exactly 3 heads: C(5,3) × (0.5)⁵ = 10/32 = 5/16.
• Steps:
  • C(6,4) = 15; P = 15 × (0.5)⁶ = 15 × (1/64).
  • = 15/64.
• Answer: 15/64

[Hard] Dot Product and Angle Between Vectors

• EN: Find the angle between vectors u = (1, 0) and v = (0, 1).
• FR: Trouve l'angle entre les vecteurs u = (1, 0) et v = (0, 1).
• Choices: A) 0° B) 45° C) 90° D) 180°
• Hint: cos(θ) = (u · v) / (|u| × |v|). If the dot product is 0, cos(θ) = 0, so θ = 90°.
• Steps:
  • u · v = (1)(0) + (0)(1) = 0.
  • |u| = 1, |v| = 1; cos(θ) = 0 ÷ 1 = 0 → θ = 90°.
• Answer: 90°