Daily Math — 2026-07-09

[Easy] Counting Apples

• EN: There are 7 apples on the table and 5 more in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 de plus dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add 6 + 4, count on from 6: 7, 8, 9, 10.
• Steps:
  • Start at 7 and count on 5 more.
  • 8, 9, 10, 11, 12 — so there are 12 apples in all.
• Answer: 12

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes next: 4, 6, 8, ___?
• FR: Compte par bonds de 2. Quel nombre vient ensuite: 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: To skip count by 2s from 10, the next number is 10 + 2 = 12.
• Steps:
  • Each number goes up by 2.
  • 8 + 2 = 10, so the next number is 10.
• Answer: 10

[Easy] Fewer Stickers

• EN: Mia has 15 stickers. She gives away 6. How many stickers does she have left?
• FR: Mia a 15 autocollants. Elle en donne 6. Combien lui en reste-t-il?
• Choices: A) 7 B) 8 C) 9 D) 21
• Hint: To find 13 − 5, count back 5 from 13: 12, 11, 10, 9, 8.
• Steps:
  • Start at 15 and count back 6.
  • 14, 13, 12, 11, 10, 9 — so Mia has 9 stickers left.
• Answer: 9

[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, and a coin worth twice as much is worth 10 cents.
• Steps:
  • A penny = 1 cent, a nickel = 5 cents, a dime = 10 cents.
  • The coin worth 10 cents is the dime.
• Answer: Dime

[Medium] Hockey Jerseys

• EN: There are 9 kids on a hockey team. 4 kids forgot their jerseys. How many kids have their jerseys?
• FR: Il y a 9 enfants dans une équipe de hockey. 4 enfants ont oublié leur chandail. Combien d'enfants ont leur chandail?
• Choices: A) 4 B) 5 C) 6 D) 13
• Hint: To find 8 − 3, think: what plus 3 equals 8? The answer is 5.
• Steps:
  • We need 9 − 4.
  • Think: 4 + ? = 9, so ? = 5. Five kids have their jerseys.
• Answer: 5

[Medium] Skip Counting by 10s

• EN: Count by 10s. What number comes next: 20, 30, 40, ___?
• FR: Compte par bonds de 10. Quel nombre vient ensuite: 20, 30, 40, ___?
• Choices: A) 41 B) 45 C) 50 D) 60
• Hint: To skip count by 10s from 70, add 10 to get 80.
• Steps:
  • Each number increases by 10.
  • 40 + 10 = 50, so the next number is 50.
• Answer: 50

[Medium] Comparing Numbers

• EN: Which number is greater: 13 or 17?
• FR: Quel nombre est plus grand: 13 ou 17?
• Choices: A) 13 B) 17 C) Both are equal D) Neither
• Hint: When comparing 11 and 15, look at the ones digit — 5 is bigger than 1, so 15 is greater.
• Steps:
  • Both numbers have a 1 in the tens place.
  • In the ones place, 7 is greater than 3, so 17 is greater.
• Answer: 17

[Medium] Pennies and Nickels

• EN: You have 2 nickels and 3 pennies. How many cents do you have in all?
• FR: Tu as 2 pièces de 5 cents et 3 pennies. Combien de cents as-tu en tout?
• Choices: A) 5 cents B) 8 cents C) 13 cents D) 15 cents
• Hint: If you have 3 nickels and 2 pennies, that is 15 + 2 = 17 cents.
• Steps:
  • 2 nickels = 2 × 5 = 10 cents.
  • 3 pennies = 3 cents. 10 + 3 = 13 cents in all.
• Answer: 13 cents

[Hard] Two-Step Story

• EN: Ben had 8 crayons. He found 6 more, then gave away 4. How many crayons does Ben have now?
• FR: Ben avait 8 crayons. Il en a trouvé 6 de plus, puis en a donné 4. Combien de crayons Ben a-t-il maintenant?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: For 5 + 3 − 2, first add: 5 + 3 = 8, then subtract: 8 − 2 = 6.
• Steps:
  • First, add: 8 + 6 = 14 crayons.
  • Then subtract: 14 − 4 = 10 crayons. Ben has 10 crayons now.
• Answer: 10

[Hard] Missing Number

• EN: What number makes this true: ___ + 6 = 14?
• FR: Quel nombre rend ceci vrai: ___ + 6 = 14?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: For ___ + 4 = 11, think: 11 − 4 = 7, so the missing number is 7.
• Steps:
  • Think: what plus 6 equals 14?
  • 14 − 6 = 8, so the missing number is 8.
• Answer: 8

[Easy] Adding Two-Digit Numbers

• EN: What is 34 + 25?
• FR: Combien font 34 + 25?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: For 21 + 36, add tens: 20 + 30 = 50, add ones: 1 + 6 = 7, total = 57.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9. So 50 + 9 = 59.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows 3 o'clock. What time is it?
• FR: L'horloge indique 3 heures. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 4:00
• Hint: When the minute hand points to 12 and the hour hand points to 5, the time is 5:00.
• Steps:
  • The hour hand points to 3, and the minute hand points to 12.
  • When the minute hand points to 12, it is exactly on the hour: 3:00.
• Answer: 3:00

[Easy] Subtracting Two-Digit Numbers

• EN: What is 76 − 43?
• FR: Combien font 76 − 43?
• Choices: A) 23 B) 32 C) 33 D) 43
• Hint: For 58 − 24, subtract tens: 50 − 20 = 30, subtract ones: 8 − 4 = 4, total = 34.
• Steps:
  • Subtract the tens: 70 − 40 = 30.
  • Subtract the ones: 6 − 3 = 3. So 30 + 3 = 33.
• Answer: 33

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A marker is 9 cm long. How much longer is the pencil?
• FR: Un crayon mesure 15 cm de long. Un marqueur mesure 9 cm de long. De combien le crayon est-il plus long?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 24 cm
• Hint: To find how much longer 18 cm is than 11 cm, subtract: 18 − 11 = 7 cm.
• Steps:
  • Subtract to find the difference: 15 − 9.
  • 15 − 9 = 6, so the pencil is 6 cm longer.
• Answer: 6 cm

[Medium] Counting Coins

• EN: You have 1 quarter, 1 dime, and 1 nickel. How many cents do you have?
• FR: Tu as 1 pièce de 25 cents, 1 de 10 cents et 1 de 5 cents. Combien de cents as-tu?
• Choices: A) 35 cents B) 38 cents C) 40 cents D) 45 cents
• Hint: A quarter (25) + nickel (5) + penny (1) = 31 cents.
• Steps:
  • Quarter = 25 cents, dime = 10 cents, nickel = 5 cents.
  • 25 + 10 = 35, then 35 + 5 = 40 cents in all.
• Answer: 40 cents

[Medium] Telling Time — Half Hour

• EN: The clock shows the minute hand pointing to 6 and the hour hand between 7 and 8. What time is it?
• FR: L'horloge montre la petite aiguille entre 7 et 8, et la grande aiguille sur le 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:00
• Hint: When the minute hand points to 6, it means 30 minutes past the hour.
• Steps:
  • The minute hand at 6 means 30 minutes past.
  • The hour hand is between 7 and 8, so the time is 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: What comes next in this pattern: 5, 10, 15, 20, ___?
• FR: Qu'est-ce qui vient ensuite dans ce patron: 5, 10, 15, 20, ___?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: In the pattern 3, 6, 9, 12, each number increases by 3, so the next is 15.
• Steps:
  • Each number increases by 5 (skip counting by 5s).
  • 20 + 5 = 25, so the next number is 25.
• Answer: 25

[Medium] Adding with Regrouping

• EN: What is 47 + 36?
• FR: Combien font 47 + 36?
• Choices: A) 73 B) 82 C) 83 D) 84
• Hint: For 38 + 25, add ones: 8 + 5 = 13, write 3 carry 1; add tens: 3 + 2 + 1 = 6; total = 63.
• Steps:
  • Add the ones: 7 + 6 = 13. Write 3, carry 1.
  • Add the tens: 4 + 3 + 1 (carried) = 8. So the answer is 83.
• Answer: 83

[Hard] Two-Step Money Problem

• EN: Maya buys a juice for 45 cents and a muffin for 35 cents. She pays with a loonie (100 cents). How much change does she get?
• FR: Maya achète un jus pour 45 cents et un muffin pour 35 cents. Elle paie avec un dollar (100 cents). Combien de monnaie reçoit-elle?
• Choices: A) 10 cents B) 15 cents C) 20 cents D) 25 cents
• Hint: For 30 + 40 = 70 spent, change from 100 cents is 100 − 70 = 30 cents.
• Steps:
  • Total spent: 45 + 35 = 80 cents.
  • Change: 100 − 80 = 20 cents.
• Answer: 20 cents

[Hard] Measuring and Comparing

• EN: A ribbon is 62 cm long. Another ribbon is 28 cm long. How long are they together?
• FR: Un ruban mesure 62 cm de long. Un autre mesure 28 cm. Quelle est leur longueur ensemble?
• Choices: A) 34 cm B) 80 cm C) 88 cm D) 90 cm
• Hint: For 54 + 37, add ones: 4 + 7 = 11, carry 1; add tens: 5 + 3 + 1 = 9; total = 91.
• Steps:
  • Add the ones: 2 + 8 = 10. Write 0, carry 1.
  • Add the tens: 6 + 2 + 1 = 9. So the answer is 90 cm.
• Answer: 90 cm

[Easy] Multiplication by 2

• EN: What is 6 × 2?
• FR: Combien font 6 × 2?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: 7 × 2 means 7 groups of 2, or 7 + 7 = 14.
• Steps:
  • 6 × 2 means 6 groups of 2.
  • 6 + 6 = 12.
• Answer: 12

[Easy] Basic Division

• EN: 20 ÷ 4 = ?
• FR: 20 ÷ 4 = ?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: For 18 ÷ 3, think: 3 × ? = 18. Since 3 × 6 = 18, the answer is 6.
• Steps:
  • Think: 4 × ? = 20.
  • 4 × 5 = 20, so 20 ÷ 4 = 5.
• Answer: 5

[Easy] Identifying Fractions

• EN: A pizza is cut into 4 equal slices. You eat 1 slice. What fraction did you eat?
• FR: Une pizza est coupée en 4 tranches égales. Tu en manges 1. Quelle fraction as-tu mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: If a pie is cut into 3 equal parts and you eat 1, you ate 1/3.
• Steps:
  • The pizza has 4 equal parts total.
  • You ate 1 out of 4, which is written as 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: There are 5 bags with 7 apples each. How many apples are there in all?
• FR: Il y a 5 sacs contenant chacun 7 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 12 B) 30 C) 35 D) 40
• Hint: 5 × 6 = 30 because 5 groups of 6 equals 30.
• Steps:
  • 5 × 7 means 5 groups of 7.
  • 5 × 7 = 35 apples in all.
• Answer: 35

[Medium] Perimeter

• EN: A rectangle has a length of 8 cm and a width of 3 cm. What is its perimeter?
• FR: Un rectangle a une longueur de 8 cm et une largeur de 3 cm. Quel est son périmètre?
• Choices: A) 11 cm B) 22 cm C) 24 cm D) 32 cm
• Hint: The perimeter of a rectangle with length 5 and width 2 is 5 + 5 + 2 + 2 = 14.
• Steps:
  • Add all four sides: 8 + 8 + 3 + 3.
  • 16 + 6 = 22 cm.
• Answer: 22 cm

[Medium] Reading a Graph

• EN: A bar graph shows: Monday = 4 books, Tuesday = 7 books, Wednesday = 5 books. How many books were read in total?
• FR: Un diagramme à barres montre: lundi = 4 livres, mardi = 7 livres, mercredi = 5 livres. Combien de livres ont été lus en tout?
• Choices: A) 11 B) 14 C) 16 D) 18
• Hint: To add three numbers like 3 + 6 + 4, first add two: 3 + 6 = 9, then add the third: 9 + 4 = 13.
• Steps:
  • Add: 4 + 7 = 11.
  • Then 11 + 5 = 16 books in total.
• Answer: 16

[Medium] Multiplication by 3

• EN: There are 9 rows of chairs with 3 chairs in each row. How many chairs are there in all?
• FR: Il y a 9 rangées de chaises avec 3 chaises dans chaque rangée. Combien y a-t-il de chaises en tout?
• Choices: A) 12 B) 24 C) 27 D) 30
• Hint: 8 × 3 = 24 because 8 groups of 3 equals 24.
• Steps:
  • 9 × 3 means 9 groups of 3.
  • 9 × 3 = 27 chairs in all.
• Answer: 27

[Medium] Comparing Fractions

• EN: Which fraction is greater: 1/2 or 1/4?
• FR: Quelle fraction est plus grande: 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/2 C) They are equal D) Cannot be determined
• Hint: If a chocolate bar is split into 2 equal pieces, each piece (1/2) is bigger than if it were split into 4 pieces (1/4).
• Steps:
  • The larger the denominator, the smaller each piece.
  • 1/2 means 1 out of 2 pieces; 1/4 means 1 out of 4 pieces. So 1/2 is greater.
• Answer: 1/2

[Hard] Division with Context

• EN: A box of 36 Tim Hortons Timbits is shared equally among 4 friends. How many Timbits does each friend get?
• FR: Une boîte de 36 Timbits de Tim Hortons est partagée également entre 4 amis. Combien chaque ami en reçoit-il?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: For 28 ÷ 4, think: 4 × 7 = 28, so each person gets 7.
• Steps:
  • Divide: 36 ÷ 4.
  • 4 × 9 = 36, so each friend gets 9 Timbits.
• Answer: 9

[Hard] Two-Step Multiplication

• EN: Each shelf holds 5 books. There are 4 shelves in one bookcase and 3 shelves in another. How many books are there in all?
• FR: Chaque étagère contient 5 livres. Il y a 4 étagères dans une bibliothèque et 3 dans une autre. Combien y a-t-il de livres en tout?
• Choices: A) 12 B) 30 C) 35 D) 40
• Hint: For 3 shelves + 2 shelves with 4 books each: (3 + 2) × 4 = 5 × 4 = 20 books.
• Steps:
  • Total shelves: 4 + 3 = 7 shelves.
  • 7 × 5 = 35 books in all.
• Answer: 35

[Easy] Multiplication Facts

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: 6 × 8 = 48, so 7 × 8 is 8 more than that.
• Steps:
  • Recall the fact: 7 × 8.
  • 6 × 8 = 48, and 48 + 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 5.62, the digit 6 is in the tenths place, and the digit 2 is in the hundredths place.
• Steps:
  • In 3.47, the digits after the decimal point are in tenths and hundredths.
  • The digit 4 is in the first decimal place, which is the tenths place.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A rectangle is 9 cm long and 4 cm wide. What is its area?
• FR: Un rectangle a 9 cm de longueur et 4 cm de largeur. Quelle est son aire?
• Choices: A) 13 cm² B) 26 cm² C) 36 cm² D) 40 cm²
• Hint: The area of a rectangle with length 6 and width 5 is 6 × 5 = 30 cm².
• Steps:
  • Area = length × width.
  • 9 × 4 = 36 cm².
• Answer: 36 cm²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/4?
• FR: Quelle fraction est plus grande: 3/4 ou 2/4?
• Choices: A) 2/4 B) 3/4 C) They are equal D) Cannot be determined
• Hint: When denominators are the same, compare numerators: 5/8 > 3/8 because 5 > 3.
• Steps:
  • Both fractions have the same denominator (4).
  • 3 > 2, so 3/4 is greater than 2/4.
• Answer: 3/4

[Medium] Long Division

• EN: What is 84 ÷ 7?
• FR: Combien font 84 ÷ 7?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: For 63 ÷ 9, think: 9 × 7 = 63, so the answer is 7.
• Steps:
  • Think: 7 × ? = 84.
  • 7 × 12 = 84, so 84 ÷ 7 = 12.
• Answer: 12

[Medium] Long Division with Remainder

• EN: What is 50 ÷ 6?
• FR: Combien font 50 ÷ 6?
• Choices: A) 7 remainder 8 B) 8 remainder 2 C) 8 remainder 3 D) 9 remainder 1
• Hint: For 25 ÷ 4, think: 4 × 6 = 24, so the answer is 6 remainder 1.
• Steps:
  • 6 × 8 = 48, which is the largest multiple of 6 that fits into 50.
  • 50 − 48 = 2, so 50 ÷ 6 = 8 remainder 2.
• Answer: 8 remainder 2

[Medium] Elapsed Time

• EN: A movie starts at 2:15 p.m. and ends at 4:45 p.m. How long is the movie?
• FR: Un film commence à 14 h 15 et se termine à 16 h 45. Quelle est la durée du film?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: From 1:20 to 3:50 is 2 hours and 30 minutes.
• Steps:
  • From 2:15 to 4:15 is exactly 2 hours.
  • From 4:15 to 4:45 is 30 more minutes. Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: What is 4.6 + 2.3?
• FR: Combien font 4,6 + 2,3?
• Choices: A) 6.8 B) 6.9 C) 7.0 D) 7.1
• Hint: For 3.4 + 5.2, add the ones: 3 + 5 = 8, add the tenths: 4 + 2 = 6; total = 8.6.
• Steps:
  • Add ones: 4 + 2 = 6.
  • Add tenths: 6 + 3 = 9. So 4.6 + 2.3 = 6.9.
• Answer: 6.9

[Hard] Multi-Step Area and Perimeter

• EN: A rectangular hockey rink is 30 m long and 15 m wide. What is the difference between its perimeter and its area in numbers (not units)?
• FR: Une patinoire rectangulaire est longue de 30 m et large de 15 m. Quelle est la différence entre son périmètre et son aire (en nombres, sans unités)?
• Choices: A) 360 B) 390 C) 400 D) 450
• Hint: For a rectangle of 10 by 4: perimeter = 28, area = 40, difference = 12.
• Steps:
  • Perimeter = 2 × (30 + 15) = 2 × 45 = 90.
  • Area = 30 × 15 = 450. Difference: 450 − 90 = 360.
• Answer: 360

[Hard] Multi-Step Word Problem

• EN: Jake earns $7 per hour shovelling snow. He worked 6 hours on Saturday and 4 hours on Sunday. How much did he earn in total?
• FR: Jake gagne 7 $ de l'heure en pelletant la neige. Il a travaillé 6 heures samedi et 4 heures dimanche. Combien a-t-il gagné en tout?
• Choices: A) $42 B) $63 C) $70 D) $77
• Hint: If you earn $5/hour for 3 + 2 hours, that is 5 × 5 = $25 total.
• Steps:
  • Total hours: 6 + 4 = 10 hours.
  • 10 × $7 = $70 earned in total.
• Answer: $70

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 194 B) 200 C) 204 D) 210
• Hint: For 23 × 4, multiply ones: 3 × 4 = 12, carry 1; multiply tens: 2 × 4 = 8, plus 1 = 9; total = 92.
• Steps:
  • Multiply ones: 4 × 6 = 24. Write 4, carry 2.
  • Multiply tens: 3 × 6 = 18, plus 2 = 20. So 34 × 6 = 204.
• Answer: 204

[Easy] Adding Fractions (Like Denominators)

• EN: What is 2/5 + 1/5?
• FR: Combien font 2/5 + 1/5?
• Choices: A) 3/10 B) 3/5 C) 2/5 D) 4/5
• Hint: For 3/7 + 2/7, add the numerators and keep the denominator: 5/7.
• Steps:
  • The denominators are the same, so add the numerators: 2 + 1 = 3.
  • The answer is 3/5.
• Answer: 3/5

[Easy] Percentage Introduction

• EN: What is 50% of 80?
• FR: Combien font 50% de 80?
• Choices: A) 30 B) 40 C) 50 D) 60
• Hint: 50% of any number means half of it. Half of 60 is 30.
• Steps:
  • 50% means one half.
  • Half of 80 is 80 ÷ 2 = 40.
• Answer: 40

[Easy] Decimal Operations

• EN: What is 7.25 − 3.10?
• FR: Combien font 7,25 − 3,10?
• Choices: A) 3.15 B) 4.10 C) 4.15 D) 4.25
• Hint: For 8.60 − 4.20, subtract ones: 8 − 4 = 4, subtract decimals: 0.60 − 0.20 = 0.40; total = 4.40.
• Steps:
  • Subtract ones: 7 − 3 = 4.
  • Subtract decimals: 0.25 − 0.10 = 0.15. So 7.25 − 3.10 = 4.15.
• Answer: 4.15

[Medium] Multi-Digit Division

• EN: What is 252 ÷ 6?
• FR: Combien font 252 ÷ 6?
• Choices: A) 38 B) 40 C) 42 D) 44
• Hint: For 144 ÷ 4: 4 goes into 14 three times (12), remainder 2; bring down 4: 4 goes into 24 six times; answer = 36.
• Steps:
  • 6 goes into 25 four times (24), remainder 1. Bring down 2 to get 12.
  • 6 goes into 12 twice. So 252 ÷ 6 = 42.
• Answer: 42

[Medium] Subtracting Fractions (Like Denominators)

• EN: What is 7/8 − 3/8?
• FR: Combien font 7/8 − 3/8?
• Choices: A) 4/8 B) 3/8 C) 1/2 D) 5/8
• Hint: For 5/9 − 2/9, subtract numerators and keep the denominator: 3/9.
• Steps:
  • Subtract the numerators: 7 − 3 = 4.
  • Keep the denominator: 4/8. This simplifies to 1/2.
• Answer: 4/8

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte a 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 80 cm³
• Hint: Volume = length × width × height. For a 4 × 3 × 2 box: 4 × 3 × 2 = 24 cm³.
• Steps:
  • Volume = length × width × height.
  • 5 × 4 × 3 = 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage

• EN: What is 25% of 120?
• FR: Combien font 25% de 120?
• Choices: A) 25 B) 30 C) 40 D) 45
• Hint: 25% means one quarter. One quarter of 80 is 80 ÷ 4 = 20.
• Steps:
  • 25% means one quarter, so divide by 4.
  • 120 ÷ 4 = 30.
• Answer: 30

[Hard] Multi-Step Decimal Problem

• EN: At a school supply sale, a binder costs $3.75, a pack of pencils costs $2.50, and an eraser costs $0.85. You pay with a $10 bill. How much change do you receive?
• FR: À une vente de fournitures scolaires, un classeur coûte 3,75 $, une boîte de crayons coûte 2,50 $ et une gomme coûte 0,85 $. Tu paies avec un billet de 10 $. Combien de monnaie reçois-tu?
• Choices: A) $2.90 B) $3.00 C) $3.10 D) $2.80
• Hint: For items costing $4.25 + $1.50 + $0.50 = $6.25, change from $10 is $10 − $6.25 = $3.75.
• Steps:
  • Total cost: $3.75 + $2.50 + $0.85 = $7.10.
  • Change: $10.00 − $7.10 = $2.90.
• Answer: $2.90

[Hard] Multi-Step Fraction and Percentage

• EN: A bag has 40 marbles. 1/4 of them are red and 10% of them are blue. How many marbles are red or blue?
• FR: Un sac contient 40 billes. 1/4 d'entre elles sont rouges et 10% sont bleues. Combien de billes sont rouges ou bleues?
• Choices: A) 10 B) 12 C) 14 D) 16
• Hint: For 20 marbles: 1/4 = 5 red, 10% = 2 blue; total = 7.
• Steps:
  • Red: 1/4 of 40 = 40 ÷ 4 = 10.
  • Blue: 10% of 40 = 4. Total: 10 + 4 = 14 marbles.
• Answer: 14

[Easy] Percent of a Number

• EN: What is 20% of 60?
• FR: Combien font 20% de 60?
• Choices: A) 10 B) 12 C) 15 D) 20
• Hint: 10% of 80 = 8, so 20% of 80 = 16 (just double the 10% value).
• Steps:
  • 10% of 60 = 6.
  • 20% = 2 × 6 = 12.
• Answer: 12

[Easy] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2.
• FR: Calcule: 3 + 4 × 2.
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: In BEDMAS, multiplication comes before addition: for 5 + 2 × 3, do 2 × 3 = 6 first, then 5 + 6 = 11.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
• Answer: 11

[Easy] Ratio

• EN: For every 2 red beads there are 5 blue beads. If there are 6 red beads, how many blue beads are there?
• FR: Pour chaque 2 perles rouges, il y a 5 perles bleues. S'il y a 6 perles rouges, combien y a-t-il de perles bleues?
• Choices: A) 12 B) 13 C) 15 D) 18
• Hint: If the ratio is 3:4 and you have 6 of the first, multiply both by 2: 6:8.
• Steps:
  • The ratio is 2:5. To get from 2 to 6, multiply by 3.
  • Multiply 5 by 3 as well: 5 × 3 = 15 blue beads.
• Answer: 15

[Easy] Integers — Comparing

• EN: Which number is greater: −3 or −7?
• FR: Quel nombre est plus grand: −3 ou −7?
• Choices: A) −7 B) −3 C) They are equal D) 0
• Hint: On a number line, −2 is to the right of −5, so −2 is greater than −5.
• Steps:
  • On a number line, numbers to the right are greater.
  • −3 is to the right of −7, so −3 is greater.
• Answer: −3

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/7 B) 6/12 C) 1/2 D) 2/7
• Hint: For 3/5 × 2/3, multiply numerators: 3 × 2 = 6, multiply denominators: 5 × 3 = 15; result = 6/15 = 2/5.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12. So 6/12 = 1/2.
• Answer: 1/2

[Medium] Fraction Division

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

[Medium] Algebraic Expression

• EN: Evaluate the expression 4x − 3 when x = 5.
• FR: Évalue l'expression 4x − 3 lorsque x = 5.
• Choices: A) 17 B) 18 C) 20 D) 23
• Hint: For 3x + 2 when x = 4, substitute: 3 × 4 + 2 = 12 + 2 = 14.
• Steps:
  • Substitute x = 5: 4 × 5 − 3.
  • 20 − 3 = 17.
• Answer: 17

[Medium] Rate Problem

• EN: A car travels 90 km in 2 hours. What is its speed in kilometres per hour?
• FR: Une voiture parcourt 90 km en 2 heures. Quelle est sa vitesse en kilomètres par heure?
• Choices: A) 40 km/h B) 45 km/h C) 50 km/h D) 55 km/h
• Hint: If a bike travels 60 km in 3 hours, the speed is 60 ÷ 3 = 20 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 90 ÷ 2 = 45 km/h.
• Answer: 45 km/h

[Hard] BEDMAS with Multiple Operations

• EN: Evaluate: (5 + 3)² ÷ 4 − 6.
• FR: Calcule: (5 + 3)² ÷ 4 − 6.
• Choices: A) 10 B) 12 C) 14 D) 16
• Hint: For (2 + 3)² ÷ 5, first brackets: 5, then exponent: 25, then divide: 25 ÷ 5 = 5.
• Steps:
  • Brackets first: 5 + 3 = 8.
  • Exponent: 8² = 64. Divide: 64 ÷ 4 = 16. Subtract: 16 − 6 = 10.
• Answer: 10

[Hard] Percent with Tax

• EN: A hockey stick costs $80. There is a 13% tax (HST). What is the total cost including tax?
• FR: Un bâton de hockey coûte 80 $. Il y a une taxe de 13% (TVH). Quel est le coût total avec la taxe?
• Choices: A) $88.40 B) $90.00 C) $90.40 D) $93.00
• Hint: For a $50 item with 10% tax: 10% of $50 = $5, total = $50 + $5 = $55.
• Steps:
  • Tax = 13% of $80 = 0.13 × 80 = $10.40.
  • Total = $80 + $10.40 = $90.40.
• Answer: $90.40

[Easy] Integer Addition

• EN: What is (−8) + 5?
• FR: Combien font (−8) + 5?
• Choices: A) −13 B) −4 C) −3 D) 3
• Hint: For (−6) + 4, start at −6 and move 4 places right on a number line: you land on −2.
• Steps:
  • Start at −8 and move 5 places to the right.
  • −8 + 5 = −3.
• Answer: −3

[Easy] Percent — Discount

• EN: A $40 jacket is on sale for 25% off. How much is the discount?
• FR: Un manteau à 40 $ est en solde avec 25% de rabais. Quel est le montant du rabais?
• Choices: A) $8 B) $10 C) $12 D) $15
• Hint: 25% of $60 = $60 ÷ 4 = $15.
• Steps:
  • 25% = 1/4, so find 1/4 of $40.
  • $40 ÷ 4 = $10 discount.
• Answer: $10

[Easy] One-Step Equation

• EN: Solve for x: x + 9 = 20.
• FR: Résous pour x: x + 9 = 20.
• Choices: A) x = 9 B) x = 10 C) x = 11 D) x = 29
• Hint: For x + 5 = 13, subtract 5 from both sides: x = 13 − 5 = 8.
• Steps:
  • Subtract 9 from both sides: x = 20 − 9.
  • x = 11.
• Answer: x = 11

[Easy] Integer Subtraction

• EN: What is 3 − (−5)?
• FR: Combien font 3 − (−5)?
• Choices: A) −2 B) 2 C) 7 D) 8
• Hint: Subtracting a negative is the same as adding: 4 − (−3) = 4 + 3 = 7.
• Steps:
  • Subtracting −5 means adding 5: 3 + 5.
  • 3 + 5 = 8.
• Answer: 8

[Medium] Percent — Tax and Tip

• EN: A restaurant bill is $35. You leave a 15% tip. How much is the tip?
• FR: Une addition au restaurant est de 35 $. Tu laisses un pourboire de 15%. Combien est le pourboire?
• Choices: A) $4.25 B) $5.25 C) $5.50 D) $6.25
• Hint: For a 15% tip on $20: 10% = $2, 5% = $1, total tip = $3.
• Steps:
  • 10% of $35 = $3.50; 5% of $35 = $1.75.
  • 15% tip = $3.50 + $1.75 = $5.25.
• Answer: $5.25

[Medium] Surface Area of a Rectangular Prism

• EN: A box is 6 cm long, 4 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte a 6 cm de long, 4 cm de large et 2 cm de haut. Quelle est son aire de surface?
• Choices: A) 48 cm² B) 64 cm² C) 88 cm² D) 96 cm²
• Hint: SA of a box with l=3, w=2, h=1: 2(3×2 + 3×1 + 2×1) = 2(6+3+2) = 2×11 = 22 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(6×4 + 6×2 + 4×2).
  • = 2(24 + 12 + 8) = 2 × 44 = 88 cm².
• Answer: 88 cm²

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Combien font (−6) × (−4)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: A negative times a negative gives a positive: (−3) × (−5) = 15.
• Steps:
  • Negative × negative = positive.
  • 6 × 4 = 24, so (−6) × (−4) = 24.
• Answer: 24

[Medium] Probability

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

[Hard] Two-Step Equation

• EN: Solve for n: 3n − 7 = 14.
• FR: Résous pour n: 3n − 7 = 14.
• Choices: A) n = 5 B) n = 7 C) n = 9 D) n = 11
• Hint: For 2x − 3 = 9, add 3 to both sides: 2x = 12, then divide by 2: x = 6.
• Steps:
  • Add 7 to both sides: 3n = 21.
  • Divide both sides by 3: n = 7.
• Answer: n = 7

[Hard] Multi-Step Percent Problem

• EN: A store has a coat originally priced at $120. It is first reduced by 20%, then an additional 10% is taken off the reduced price. What is the final price?
• FR: Un magasin vend un manteau à 120 $ à l'origine. Le prix est d'abord réduit de 20%, puis encore de 10% sur le prix réduit. Quel est le prix final?
• Choices: A) $84.00 B) $85.20 C) $86.40 D) $90.00
• Hint: For a $100 item: 20% off → $80, then 10% off $80 → $72.
• Steps:
  • After 20% off: $120 × 0.80 = $96.
  • After another 10% off: $96 × 0.90 = $86.40.
• Answer: $86.40

[Easy] Perfect Squares

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

[Easy] Mean of a Data Set

• EN: Find the mean of: 8, 12, 6, 14.
• FR: Trouve la moyenne de: 8, 12, 6, 14.
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Mean of 4, 8, 6: add all (4+8+6=18) then divide by how many numbers (3): 18÷3 = 6.
• Steps:
  • Sum: 8 + 12 + 6 + 14 = 40.
  • Divide by 4: 40 ÷ 4 = 10.
• Answer: 10

[Easy] Pythagorean Theorem — Identify

• EN: A right triangle has legs of 3 cm and 4 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des côtés de 3 cm et 4 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: Use a² + b² = c². For legs of 5 and 12: 25 + 144 = 169, and √169 = 13.
• Steps:
  • a² + b² = c²: 3² + 4² = 9 + 16 = 25.
  • c = √25 = 5 cm.
• Answer: 5 cm

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 5 = 17.
• FR: Résous pour x: 2x + 5 = 17.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 11
• Hint: For 3x + 2 = 11, subtract 2: 3x = 9, then divide by 3: x = 3.
• Steps:
  • Subtract 5 from both sides: 2x = 12.
  • Divide by 2: x = 6.
• Answer: x = 6

[Medium] Percent Increase

• EN: A hockey card was worth $25 last year. This year it is worth $30. What is the percent increase?
• FR: Une carte de hockey valait 25 $ l'année passée. Cette année, elle vaut 30 $. Quel est le pourcentage d'augmentation?
• Choices: A) 15% B) 20% C) 25% D) 30%
• Hint: Percent increase = (new − old) ÷ old × 100. For old = 40, new = 50: (10 ÷ 40) × 100 = 25%.
• Steps:
  • Increase: 30 − 25 = 5.
  • Percent increase: (5 ÷ 25) × 100 = 20%.
• Answer: 20%

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 2, 9, 5.
• FR: Trouve la médiane de: 3, 7, 2, 9, 5.
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: To find the median of 1, 4, 6, 8, 9, arrange in order and pick the middle value: 6.
• Steps:
  • Arrange in order: 2, 3, 5, 7, 9.
  • The middle value (3rd of 5) is 5.
• Answer: 5

[Medium] Slope Introduction

• EN: A line passes through (0, 1) and (3, 7). What is the slope of the line?
• FR: Une droite passe par (0, 1) et (3, 7). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 6
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). For (0,2) to (4,10): (10−2)÷(4−0) = 8÷4 = 2.
• Steps:
  • Rise = 7 − 1 = 6. Run = 3 − 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Pythagorean Theorem — Missing Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et un côté de 5 cm. Quel est l'autre côté?
• Choices: A) 8 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: For hypotenuse 10 and leg 6: a² = 10² − 6² = 100 − 36 = 64, so a = 8.
• Steps:
  • a² + 5² = 13²: a² + 25 = 169.
  • a² = 144, so a = 12 cm.
• Answer: 12 cm

[Hard] Multi-Step Two-Step Equation

• EN: Solve for y: 4(y − 3) = 20.
• FR: Résous pour y: 4(y − 3) = 20.
• Choices: A) y = 5 B) y = 7 C) y = 8 D) y = 23
• Hint: For 3(x − 2) = 12, divide both sides by 3: x − 2 = 4, then add 2: x = 6.
• Steps:
  • Divide both sides by 4: y − 3 = 5.
  • Add 3 to both sides: y = 8.
• Answer: y = 8

[Hard] Percent Decrease with Context

• EN: A snowblower originally costs $450. It is on clearance for 30% off. What is the sale price?
• FR: Une souffleuse à neige coûte à l'origine 450 $. Elle est en liquidation à 30% de rabais. Quel est le prix de vente?
• Choices: A) $295 B) $310 C) $315 D) $320
• Hint: For 20% off a $200 item: discount = $40, sale price = $160.
• Steps:
  • Discount: 30% of $450 = 0.30 × 450 = $135.
  • Sale price: $450 − $135 = $315.
• Answer: $315

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 3 = 22.
• FR: Résous pour x: 5x − 3 = 22.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: For 4x − 2 = 14, add 2: 4x = 16, then divide by 4: x = 4.
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide both sides by 5: x = 5.
• Answer: x = 5

[Easy] Slope-Intercept Form

• EN: A line has equation y = 3x + 2. What is the slope?
• FR: Une droite a l'équation y = 3x + 2. Quelle est la pente?
• Choices: A) 1 B) 2 C) 3 D) 5
• Hint: In y = mx + b, m is the slope. For y = 7x − 4, the slope is 7.
• Steps:
  • The equation is in y = mx + b form.
  • The coefficient of x is 3, so the slope is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 1).
• FR: Simplifie: (3x + 5) + (2x − 1).
• Choices: A) 5x + 4 B) 5x + 6 C) 6x + 4 D) 5x − 4
• Hint: To add (4x + 3) + (x − 2), combine like terms: 4x + x = 5x and 3 − 2 = 1; result = 5x + 1.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−1) = 4. So the answer is 5x + 4.
• Answer: 5x + 4

[Easy] SOH-CAH-TOA

• EN: In a right triangle, the opposite side is 4 cm and the hypotenuse is 5 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 4 cm et l'hypoténuse est 5 cm. Quel est sin(θ)?
• Choices: A) 3/5 B) 4/5 C) 4/3 D) 5/4
• Hint: SOH: sin = opposite ÷ hypotenuse. For opposite = 6 and hypotenuse = 10: sin = 6/10 = 3/5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 4 ÷ 5 = 4/5.
• Answer: 4/5

[Medium] Linear Inequality

• EN: Solve for x: 2x + 3 > 11.
• FR: Résous pour x: 2x + 3 > 11.
• Choices: A) x > 3 B) x > 4 C) x > 5 D) x > 7
• Hint: For 3x − 1 > 8, add 1: 3x > 9, then divide by 3: x > 3.
• Steps:
  • Subtract 3 from both sides: 2x > 8.
  • Divide both sides by 2: x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 4).
• FR: Développe: (x + 3)(x + 4).
• Choices: A) x² + 7x + 12 B) x² + 12x + 7 C) x² + 7x + 7 D) x² + 12
• Hint: (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.
• Steps:
  • x × x = x², x × 4 = 4x, 3 × x = 3x, 3 × 4 = 12.
  • Combine: x² + 4x + 3x + 12 = x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two triangles are similar. The sides of the smaller triangle are 3, 4, and 5 cm. The shortest side of the larger triangle is 9 cm. What is the longest side of the larger triangle?
• FR: Deux triangles sont semblables. Les côtés du plus petit triangle sont 3, 4 et 5 cm. Le côté le plus court du plus grand triangle est 9 cm. Quel est le côté le plus long?
• Choices: A) 12 cm B) 13 cm C) 14 cm D) 15 cm
• Hint: If triangles are similar with scale factor 2, multiply each side by 2.
• Steps:
  • Scale factor: 9 ÷ 3 = 3.
  • Longest side: 5 × 3 = 15 cm.
• Answer: 15 cm

[Medium] Graphing Lines

• EN: A line has equation y = −2x + 6. What is the y-intercept?
• FR: Une droite a l'équation y = −2x + 6. Quel est l'ordonnée à l'origine?
• Choices: A) −6 B) −2 C) 2 D) 6
• Hint: In y = mx + b, b is the y-intercept (where the line crosses the y-axis). For y = 4x − 3, the y-intercept is −3.
• Steps:
  • The equation is y = −2x + 6, which is in y = mx + b form.
  • The y-intercept is b = 6.
• Answer: 6

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 6 cm and the hypotenuse is 10 cm. What is the angle θ? (Use cos⁻¹)
• FR: Dans un triangle rectangle, le côté adjacent est 6 cm et l'hypoténuse est 10 cm. Quel est l'angle θ? (Utilise cos⁻¹)
• Choices: A) 30° B) 45° C) 53° D) 60°
• Hint: CAH: cos(θ) = adjacent ÷ hypotenuse. For adj = 8 and hyp = 10: cos(θ) = 0.8, so θ ≈ 37°.
• Steps:
  • cos(θ) = 6 ÷ 10 = 0.6.
  • θ = cos⁻¹(0.6) ≈ 53°.
• Answer: 53°

[Hard] Systems of Equations (Substitution)

• EN: Solve the system: y = 2x + 1 and y = x + 5. What is x?
• FR: Résous le système: y = 2x + 1 et y = x + 5. Quel est x?
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: For y = 3x and y = x + 4, set equal: 3x = x + 4, so 2x = 4, x = 2.
• Steps:
  • Set equal: 2x + 1 = x + 5.
  • Subtract x: x + 1 = 5, so x = 4.
• Answer: x = 4

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6.
• FR: Factorise: x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 3) D) (x − 2)(x − 3)
• Hint: To factor x² + 7x + 12, find two numbers that multiply to 12 and add to 7: 3 and 4. So (x + 3)(x + 4).
• Steps:
  • Find two numbers that multiply to 6 and add to 5: 2 and 3.
  • So x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry

• EN: In a right triangle, the opposite side is 5 and hypotenuse is 13. What is the adjacent side?
• FR: Dans un triangle rectangle, le côté opposé est 5 et l'hypoténuse est 13. Quel est le côté adjacent?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Use a² + b² = c². For opp = 3 and hyp = 5: adj² = 25 − 9 = 16, so adj = 4.
• Steps:
  • adj² = 13² − 5² = 169 − 25 = 144.
  • adj = √144 = 12.
• Answer: 12

[Easy] Solving a Quadratic by Factoring

• EN: Solve: x² − 7x + 10 = 0.
• FR: Résous: x² − 7x + 10 = 0.
• Choices: A) x = 2 or x = 5 B) x = 2 or x = 7 C) x = 5 or x = 7 D) x = 1 or x = 10
• Hint: For x² − 6x + 8 = 0, factor to (x − 2)(x − 4) = 0, so x = 2 or x = 4.
• Steps:
  • Factor: (x − 2)(x − 5) = 0.
  • Set each factor to zero: x = 2 or x = 5.
• Answer: x = 2 or x = 5

[Easy] System of Equations

• EN: Solve: x + y = 10 and x − y = 4. What is x?
• FR: Résous: x + y = 10 et x − y = 4. Quel est x?
• Choices: A) x = 3 B) x = 5 C) x = 7 D) x = 9
• Hint: For x + y = 8 and x − y = 2, add the equations: 2x = 10, so x = 5.
• Steps:
  • Add the equations: 2x = 14, so x = 7.
  • Check: 7 + y = 10 → y = 3. Confirm: 7 − 3 = 4. ✓
• Answer: x = 7

[Medium] Circle Geometry — Circumference

• EN: A circle has a radius of 7 cm. What is its circumference? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 7 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 21.98 cm B) 43.96 cm C) 44.00 cm D) 153.86 cm
• Hint: Circumference = 2πr. For r = 5: C = 2 × 3.14 × 5 = 31.4 cm.
• Steps:
  • C = 2πr = 2 × 3.14 × 7.
  • C = 6.28 × 7 = 43.96 cm.
• Answer: 43.96 cm

[Medium] Completing the Square

• EN: Complete the square for x² + 6x + ___. What term completes the perfect square trinomial?
• FR: Complète le carré pour x² + 6x + ___. Quel terme complète le trinôme carré parfait?
• Choices: A) 6 B) 9 C) 12 D) 36
• Hint: To complete the square for x² + 8x, take half of 8 = 4, then square it: 4² = 16.
• Steps:
  • Take half of the coefficient of x: 6 ÷ 2 = 3.
  • Square it: 3² = 9.
• Answer: 9

[Medium] Surface Area of a Cylinder

• EN: A cylinder has radius 3 cm and height 10 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 10 cm. Quelle est son aire de surface totale? (Utilise π ≈ 3,14)
• Choices: A) 188.4 cm² B) 194.4 cm² C) 245.0 cm² D) 282.6 cm²
• Hint: SA of cylinder = 2πr² + 2πrh. For r = 2, h = 5: 2π(4) + 2π(10) = 8π + 20π = 28π ≈ 87.9 cm².
• Steps:
  • SA = 2πr² + 2πrh = 2(3.14)(9) + 2(3.14)(3)(10).
  • = 56.52 + 188.4 = 244.92 ≈ 245.0 cm².
• Answer: 245.0 cm²

[Medium] Trigonometry — Finding a Side

• EN: In a right triangle, angle A = 30° and the hypotenuse is 20 cm. What is the side opposite angle A?
• FR: Dans un triangle rectangle, l'angle A = 30° et l'hypoténuse est 20 cm. Quel est le côté opposé à l'angle A?
• Choices: A) 8 cm B) 10 cm C) 14 cm D) 17 cm
• Hint: sin(angle) = opposite ÷ hypotenuse. For sin(45°) = 0.707 and hyp = 10: opposite = 7.07 cm.
• Steps:
  • sin(30°) = 0.5, and sin = opposite ÷ hypotenuse.
  • Opposite = 0.5 × 20 = 10 cm.
• Answer: 10 cm

[Hard] Quadratic Formula

• EN: Solve using the quadratic formula: x² − 4x − 5 = 0. What are the solutions?
• FR: Résous à l'aide de la formule quadratique: x² − 4x − 5 = 0. Quelles sont les solutions?
• Choices: A) x = 5 or x = −1 B) x = 5 or x = 1 C) x = −5 or x = 1 D) x = 4 or x = −5
• Hint: For x² − 3x − 4 = 0, x = (3 ± √(9+16)) ÷ 2 = (3 ± 5) ÷ 2, so x = 4 or x = −1.
• Steps:
  • a=1, b=−4, c=−5. Discriminant: 16 + 20 = 36. √36 = 6.
  • x = (4 ± 6) ÷ 2: x = 5 or x = −1.
• Answer: x = 5 or x = −1

[Hard] Circle Geometry — Inscribed Angle

• EN: An inscribed angle in a circle is 35°. What is the central angle that subtends the same arc?
• FR: Un angle inscrit dans un cercle est de 35°. Quel est l'angle central qui sous-tend le même arc?
• Choices: A) 17.5° B) 35° C) 70° D) 105°
• Hint: The central angle is always twice the inscribed angle that subtends the same arc. For 40°, the central angle is 80°.
• Steps:
  • The central angle theorem: central angle = 2 × inscribed angle.
  • 2 × 35° = 70°.
• Answer: 70°

[Easy] Evaluating an Exponential Function

• EN: Evaluate f(x) = 2^x when x = 5.
• FR: Évalue f(x) = 2^x lorsque x = 5.
• Choices: A) 10 B) 16 C) 25 D) 32
• Hint: For f(x) = 3^x at x = 4: 3 × 3 × 3 × 3 = 81.
• Steps:
  • f(5) = 2^5 = 2 × 2 × 2 × 2 × 2.
  • = 32.
• Answer: 32

[Easy] Logarithm Introduction

• EN: Evaluate: log₂(8).
• FR: Évalue: log₂(8).
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log₂(16) asks "2 to what power equals 16?" Since 2⁴ = 16, the answer is 4.
• Steps:
  • log₂(8) asks: "2 to what power equals 8?"
  • 2³ = 8, so log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• EN: Find the 10th term of the arithmetic sequence: 3, 7, 11, 15, ...
• FR: Trouve le 10e terme de la suite arithmétique: 3, 7, 11, 15, ...
• Choices: A) 37 B) 39 C) 40 D) 43
• Hint: For the sequence 2, 5, 8, 11, ... with d = 3, the nth term is 2 + (n−1) × 3. The 5th term = 2 + 4 × 3 = 14.
• Steps:
  • Common difference d = 4. Use formula: aₙ = a₁ + (n−1)d.
  • a₁₀ = 3 + (10−1) × 4 = 3 + 36 = 39.
• Answer: 39

[Easy] Compound Interest — Single Period

• EN: $500 is invested at an annual interest rate of 6%, compounded annually. What is the amount after 1 year?
• FR: 500 $ sont investis à un taux d'intérêt annuel de 6%, composé annuellement. Quel est le montant après 1 an?
• Choices: A) $506 B) $530 C) $560 D) $580
• Hint: A = P(1 + r). For $200 at 5%: A = 200 × 1.05 = $210.
• Steps:
  • A = P(1 + r)^t = 500 × (1.06)^1.
  • A = 500 × 1.06 = $530.
• Answer: $530

[Medium] Quadratic Function — Vertex

• EN: Find the vertex of the parabola y = x² − 6x + 11.
• FR: Trouve le sommet de la parabole y = x² − 6x + 11.
• Choices: A) (3, 2) B) (3, 6) C) (6, 2) D) (−3, 2)
• Hint: For y = x² − 4x + 7, vertex x = −(−4)/(2×1) = 2, then y = 4 − 8 + 7 = 3. Vertex = (2, 3).
• Steps:
  • x = −b/(2a) = −(−6)/(2) = 3.
  • y = (3)² − 6(3) + 11 = 9 − 18 + 11 = 2. Vertex = (3, 2).
• Answer: (3, 2)

[Medium] Geometric Series — Sum

• EN: Find the sum of the first 4 terms of the geometric series: 2, 6, 18, 54, ...
• FR: Trouve la somme des 4 premiers termes de la série géométrique: 2, 6, 18, 54, ...
• Choices: A) 60 B) 80 C) 160 D) 80
• Hint: Sum of geometric series Sₙ = a(rⁿ − 1)/(r − 1). For a=1, r=2, n=4: S = (16−1)/1 = 15.
• Steps:
  • a = 2, r = 3, n = 4. S₄ = 2(3⁴ − 1)/(3 − 1).
  • = 2(81 − 1)/2 = 80.
• Answer: 80

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ.
• FR: Simplifie: sin²θ + cos²θ.
• Choices: A) 0 B) 1 C) 2 D) sin(2θ)
• Hint: This is one of the most important Pythagorean identities in trigonometry.
• Steps:
  • This is the Pythagorean identity.
  • sin²θ + cos²θ = 1 for any angle θ.
• Answer: 1

[Medium] Exponential Growth

• EN: A town has 2 000 people and grows at 5% per year. What is the population after 2 years?
• FR: Une ville a 2 000 habitants et croît à 5% par an. Quelle est la population après 2 ans?
• Choices: A) 2 100 B) 2 200 C) 2 205 D) 2 250
• Hint: P = P₀(1 + r)^t. For 1000 at 3% for 2 years: 1000 × (1.03)² = 1000 × 1.0609 ≈ 1 061.
• Steps:
  • P = 2000 × (1.05)² = 2000 × 1.1025.
  • P = 2 205 people.
• Answer: 2 205

[Hard] Compound Interest — Annuity

• EN: You deposit $200 at the end of each year for 3 years into an account earning 4% annually. What is the future value of the annuity?
• FR: Tu déposes 200 $ à la fin de chaque année pendant 3 ans dans un compte qui rapporte 4% annuellement. Quelle est la valeur future de l'annuité?
• Choices: A) $600.00 B) $624.32 C) $648.00 D) $664.64
• Hint: FV = R × [(1+r)ⁿ − 1]/r. For R = $100, r = 5%, n = 3: 100 × [(1.05)³ − 1]/0.05 = 100 × 3.1525 = $315.25.
• Steps:
  • FV = 200 × [(1.04)³ − 1] / 0.04.
  • (1.04)³ = 1.124864. FV = 200 × (0.124864/0.04) = 200 × 3.1216 = $624.32.
• Answer: $624.32

[Hard] Logarithm — Solving an Equation

• EN: Solve for x: 3^x = 81.
• FR: Résous pour x: 3^x = 81.
• Choices: A) x = 3 B) x = 4 C) x = 27 D) x = 243
• Hint: For 2^x = 32, write 32 as a power of 2: 2^5 = 32, so x = 5.
• Steps:
  • Write 81 as a power of 3: 81 = 3⁴.
  • So 3^x = 3⁴ means x = 4.
• Answer: x = 4

[Easy] Counting — Permutations

• EN: How many ways can you arrange 5 different books on a shelf?
• FR: De combien de façons peut-on disposer 5 livres différents sur une étagère?
• Choices: A) 25 B) 60 C) 120 D) 240
• Hint: For 4 books, arrangements = 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
• Answer: 120

[Easy] Derivative — Power Rule

• EN: If f(x) = x³, what is f′(x)?
• FR: Si f(x) = x³, quel est f′(x)?
• Choices: A) x² B) 3x C) 3x² D) 3x³
• Hint: The power rule: if f(x) = xⁿ, then f′(x) = n·xⁿ⁻¹. For f(x) = x⁴, f′(x) = 4x³.
• Steps:
  • Apply the power rule: bring down the exponent, reduce by 1.
  • f′(x) = 3x².
• Answer: 3x²

[Easy] Polynomial Evaluation

• EN: Evaluate f(x) = 2x³ − x + 4 when x = 2.
• FR: Évalue f(x) = 2x³ − x + 4 lorsque x = 2.
• Choices: A) 14 B) 18 C) 20 D) 24
• Hint: For g(x) = x² + 3x − 1 at x = 3: 9 + 9 − 1 = 17.
• Steps:
  • f(2) = 2(2)³ − 2 + 4 = 2(8) − 2 + 4.
  • = 16 − 2 + 4 = 18.
• Answer: 18

[Easy] Combinations

• EN: A team of 3 is chosen from 6 students. How many different teams are possible?
• FR: Une équipe de 3 est choisie parmi 6 élèves. Combien d'équipes différentes sont possibles?
• Choices: A) 18 B) 20 C) 30 D) 120
• Hint: C(5,2) = 5! / (2! × 3!) = 10.
• Steps:
  • C(6,3) = 6! / (3! × 3!) = 720 / (6 × 6).
  • = 720 / 36 = 20.
• Answer: 20

[Medium] Rational Function — Asymptote

• EN: Find the vertical asymptote of f(x) = 3/(x − 4).
• FR: Trouve l'asymptote verticale de f(x) = 3/(x − 4).
• Choices: A) x = −4 B) x = 0 C) x = 3 D) x = 4
• Hint: A vertical asymptote occurs where the denominator equals zero. For 1/(x+2), set x+2=0: x = −2.
• Steps:
  • Set the denominator equal to zero: x − 4 = 0.
  • x = 4.
• Answer: x = 4

[Medium] Derivative — Instantaneous Rate of Change

• EN: Find the slope of f(x) = x² at x = 3 using the derivative.
• FR: Trouve la pente de f(x) = x² en x = 3 en utilisant la dérivée.
• Choices: A) 3 B) 6 C) 9 D) 12
• Hint: f′(x) = 2x for f(x) = x². At x = 4, the slope is 2(4) = 8.
• Steps:
  • f′(x) = 2x.
  • f′(3) = 2 × 3 = 6.
• Answer: 6

[Medium] Binomial Distribution

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 2 heads?
• FR: On lance une pièce équitable 4 fois. Quelle est la probabilité d'obtenir exactement 2 fois pile?
• Choices: A) 1/4 B) 3/8 C) 1/2 D) 5/8
• Hint: P(k successes) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ. For n=3, k=1, p=0.5: C(3,1) × 0.5³ = 3/8.
• Steps:
  • P(X=2) = C(4,2) × (0.5)² × (0.5)² = 6 × 0.25 × 0.25.
  • = 6 × 0.0625 = 0.375 = 3/8.
• Answer: 3/8

[Medium] Vectors — Adding

• 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) (1, 3) B) (5, 3) C) (1, −5) D) (5, −5)
• Hint: To add vectors (2, 5) and (−1, 3), add the components: (2+(−1), 5+3) = (1, 8).
• Steps:
  • Add x-components: 3 + (−2) = 1.
  • Add y-components: −1 + 4 = 3. So a + b = (1, 3).
• Answer: (1, 3)

[Hard] Derivatives — Chain Rule

• EN: Find f′(x) if f(x) = (3x + 2)⁴.
• FR: Trouve f′(x) si f(x) = (3x + 2)⁴.
• Choices: A) 4(3x + 2)³ B) 12(3x + 2)³ C) 12(3x + 2)⁴ D) 3(3x + 2)⁴
• Hint: Chain rule: differentiate the outside, keep the inside, multiply by the derivative of the inside. For (2x + 1)³: 3(2x+1)² × 2 = 6(2x+1)².
• Steps:
  • Outside: 4(3x + 2)³. Inside derivative: 3.
  • f′(x) = 4(3x + 2)³ × 3 = 12(3x + 2)³.
• Answer: 12(3x + 2)³

[Hard] Permutations with Restrictions

• EN: How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition if the first digit must be odd?
• FR: Combien de nombres à 4 chiffres peut-on former avec les chiffres 1, 2, 3, 4, 5 sans répétition si le premier chiffre doit être impair?
• Choices: A) 48 B) 60 C) 72 D) 96
• Hint: For a 3-digit number with first digit from {1,3} and remaining 2 from 4 others: 2 × 4 × 3 = 24 ways.
• Steps:
  • Odd digits for first position: {1, 3, 5} = 3 choices.
  • Remaining 3 digits from 4 left, in order: 4 × 3 × 2 = 24. Total: 3 × 24 = 72.
• Answer: 72