Daily Math — 2026-08-27

[Easy] Counting Carrots

• EN: Liam has 7 carrots. He picks 5 more. How many carrots does he have now?
• FR: Liam a 7 carottes. Il en cueille 5 de plus. Combien de carottes a-t-il maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add, start at the bigger number and count up (e.g., 6 + 3: start at 6, count 7, 8, 9).
• Steps:
  • Start at 7.
  • Count up 5 more: 8, 9, 10, 11, 12.
  • So Liam has 12 carrots.
• Answer: 12

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes after 8?
• FR: Compte par bonds de 2. Quel nombre vient après 8?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Skip counting by 2s means add 2 each time (e.g., 4, 6, 8, …).
• Steps:
  • The pattern goes: 2, 4, 6, 8, …
  • Add 2 to 8: 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 18
• Hint: The number that is farther along a number line is greater (e.g., 12 is greater than 7).
• Steps:
  • Place both numbers on a number line.
  • 14 is farther to the right than 9.
  • So 14 is greater.
• Answer: 14

[Easy] Coin Recognition

• EN: Maya has one dime. How many cents does she have?
• FR: Maya a une pièce de dix cents. Combien de cents a-t-elle?
• Choices: A) 1 cent B) 5 cents C) 10 cents D) 25 cents
• Hint: A nickel is worth 5 cents, a dime is worth 10 cents, a quarter is worth 25 cents.
• Steps:
  • A dime is a small silver coin.
  • Its value is 10 cents.
  • So Maya has 10 cents.
• Answer: 10 cents

[Medium] Hockey Goals

• EN: The Maple Leafs scored 6 goals on Monday and 4 goals on Tuesday. How many goals did they score in total?
• FR: Les Maple Leafs ont marqué 6 buts lundi et 4 buts mardi. Combien de buts ont-ils marqué en tout?
• Choices: A) 8 B) 9 C) 10 D) 11
• Hint: To add two numbers, start at the first and count on (e.g., 3 + 5: start at 3, count 5 more).
• Steps:
  • Start at 6.
  • Count on 4 more: 7, 8, 9, 10.
  • So the total is 10.
• Answer: 10

[Medium] Snowball Subtraction

• EN: There are 15 snowballs. Kids throw away 8 of them. How many are left?
• FR: Il y a 15 boules de neige. Des enfants en lancent 8. Combien en reste-t-il?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To subtract, count back from the bigger number (e.g., 12 – 4: count back 4 from 12).
• Steps:
  • Start at 15.
  • Count back 8: 14, 13, 12, 11, 10, 9, 8, 7.
  • So 7 snowballs are left.
• Answer: 7

[Medium] Skip Counting by 5s

• EN: Ava counts by 5s starting at 5. What is the fourth number she says?
• FR: Ava compte par bonds de 5 en commençant à 5. Quel est le quatrième nombre qu'elle dit?
• Choices: A) 15 B) 20 C) 25 D) 30
• Hint: Counting by 5s: 5, 10, 15, 20 — the third number is 15, so what is the fourth?
• Steps:
  • First: 5. Second: 10. Third: 15. Fourth: 20.
  • So the fourth number Ava says is 20.
• Answer: 20

[Medium] Counting to 100

• EN: Noah counts by 10s. He says 30, 40, 50. What number comes next?
• FR: Noah compte par bonds de 10. Il dit 30, 40, 50. Quel nombre vient ensuite?
• Choices: A) 55 B) 60 C) 65 D) 70
• Hint: Counting by 10s means adding 10 each time (e.g., 20, 30, 40 — add 10).
• Steps:
  • The pattern adds 10 each time.
  • 50 + 10 = 60.
  • So the next number is 60.
• Answer: 60

[Hard] Two Coins

• EN: Zoe has one nickel and one dime. How many cents does she have altogether?
• FR: Zoé a une pièce de cinq cents et une pièce de dix cents. Combien de cents a-t-elle en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: Add the value of each coin together (e.g., a nickel = 5 cents, a penny = 1 cent, so together they are 6 cents).
• Steps:
  • A nickel is worth 5 cents.
  • A dime is worth 10 cents.
  • 5 + 10 = 15 cents.
• Answer: 15 cents

[Hard] Addition and Subtraction Together

• EN: There are 12 mittens on a shelf. 3 fall off, then 4 more are added. How many mittens are on the shelf now?
• FR: Il y a 12 mitaines sur une étagère. 3 tombent, puis 4 autres sont ajoutées. Combien de mitaines y a-t-il maintenant?
• Choices: A) 11 B) 13 C) 15 D) 17
• Hint: Do the subtraction first, then the addition (e.g., 10 – 2 = 8, then 8 + 3 = 11).
• Steps:
  • Start with 12. Subtract 3: 12 – 3 = 9.
  • Then add 4: 9 + 4 = 13.
  • So there are 13 mittens on the shelf.
• Answer: 13

[Easy] Adding Within 100

• EN: A student has 34 stickers and gets 25 more. How many stickers does she have now?
• FR: Une élève a 34 autocollants et en reçoit 25 de plus. Combien d'autocollants a-t-elle maintenant?
• Choices: A) 57 B) 59 C) 61 D) 63
• Hint: Add the tens first, then the ones (e.g., 21 + 35: 20 + 30 = 50, 1 + 5 = 6, total = 56).
• Steps:
  • Add tens: 30 + 20 = 50.
  • Add 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 l'aiguille des heures sur le 3 et l'aiguille des minutes sur le 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 6:15
• Hint: When the minute hand is on 12, it is exactly on the hour (e.g., hour hand on 7 = 7:00).
• Steps:
  • The hour hand on 3 tells us it is 3 o'clock.
  • The minute hand on 12 means 0 minutes.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A crayon is 9 cm long. How much longer is the pencil?
• FR: Un crayon mesure 14 cm. Une craie de couleur mesure 9 cm. De combien le crayon est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: Subtract the shorter length from the longer length (e.g., 11 cm – 7 cm = 4 cm).
• Steps:
  • Subtract: 14 – 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Counting Coins

• EN: Ben has 2 dimes and 1 nickel. How much money does he have?
• FR: Ben a 2 pièces de dix cents et 1 pièce de cinq cents. Combien d'argent a-t-il?
• Choices: A) 20 cents B) 22 cents C) 25 cents D) 30 cents
• Hint: Count each coin's value and add them (e.g., 1 dime + 1 dime = 10 + 10 = 20 cents).
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • 1 nickel = 5 cents.
  • 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtracting Within 100

• EN: There are 72 students at school. 38 go home for lunch. How many are still at school?
• FR: Il y a 72 élèves à l'école. 38 rentrent chez eux pour dîner. Combien restent à l'école?
• Choices: A) 24 B) 30 C) 34 D) 40
• Hint: Subtract ones first, then tens — borrow if needed (e.g., 53 – 27: borrow from the tens).
• Steps:
  • 72 – 38: ones: 2 – 8, borrow 1 ten. Now 12 – 8 = 4.
  • Tens: 6 – 3 = 3 (after borrowing, 7 becomes 6).
  • So 72 – 38 = 34.
• Answer: 34

[Medium] Simple Patterns

• EN: What is the next shape in this pattern: circle, square, circle, square, _____?
• FR: Quelle est la prochaine forme dans ce motif : cercle, carré, cercle, carré, _____?
• Choices: A) triangle B) circle C) rectangle D) diamond
• Hint: Look at what repeats — find the rule, then apply it (e.g., red, blue, red, blue, then red).
• Steps:
  • The pattern is: circle, square, repeating.
  • After square comes circle.
  • So the next shape is circle.
• Answer: circle

[Medium] Telling Time at the Half-Hour

• EN: Mia starts reading at 2:00. She reads for 30 minutes. What time does she finish?
• FR: Mia commence à lire à 2 h 00. Elle lit pendant 30 minutes. À quelle heure termine-t-elle?
• Choices: A) 2:00 B) 2:30 C) 3:00 D) 3:30
• Hint: Adding 30 minutes to an o'clock time gives a half-hour time (e.g., 4:00 + 30 min = 4:30).
• Steps:
  • Start time: 2:00.
  • Add 30 minutes: 2:00 + 30 minutes = 2:30.
  • So Mia finishes at 2:30.
• Answer: 2:30

[Medium] Counting Coins to $1

• EN: Emma has 3 quarters. How many cents does she have?
• FR: Emma a 3 pièces de 25 cents. Combien de cents a-t-elle?
• Choices: A) 60 cents B) 70 cents C) 75 cents D) 80 cents
• Hint: A quarter is worth 25 cents — add 25 for each quarter you have (e.g., 2 quarters = 50 cents).
• Steps:
  • 1 quarter = 25 cents.
  • 3 quarters = 25 + 25 + 25 = 75 cents.
  • So Emma has 75 cents.
• Answer: 75 cents

[Hard] Measuring and Comparing

• EN: A desk is 80 cm wide. A bookshelf is 1 m wide. How many centimetres wider is the bookshelf?
• FR: Un bureau fait 80 cm de largeur. Une bibliothèque fait 1 m de largeur. De combien de centimètres la bibliothèque est-elle plus large?
• Choices: A) 10 cm B) 20 cm C) 25 cm D) 30 cm
• Hint: Convert metres to centimetres first — 1 m = 100 cm — then subtract (e.g., 100 – 70 = 30 cm).
• Steps:
  • 1 m = 100 cm.
  • 100 – 80 = 20.
  • The bookshelf is 20 cm wider.
• Answer: 20 cm

[Hard] Two-Step Problem

• EN: Jake had 45 hockey cards. He gave 12 to his friend and then bought 8 more. How many cards does he have now?
• FR: Jake avait 45 cartes de hockey. Il en a donné 12 à son ami, puis en a acheté 8 de plus. Combien de cartes a-t-il maintenant?
• Choices: A) 37 B) 39 C) 41 D) 43
• Hint: Solve in two steps — subtract first, then add (e.g., 30 – 5 = 25, then 25 + 4 = 29).
• Steps:
  • Step 1: 45 – 12 = 33.
  • Step 2: 33 + 8 = 41.
  • Jake now has 41 cards.
• Answer: 41

[Easy] Multiplication — 2 Times Table

• EN: What is 2 × 7?
• FR: Combien font 2 × 7?
• Choices: A) 12 B) 13 C) 14 D) 16
• Hint: Multiply by 2 means add the number to itself (e.g., 2 × 6 = 6 + 6 = 12).
• Steps:
  • 2 × 7 means 7 + 7.
  • 7 + 7 = 14.
  • So 2 × 7 = 14.
• Answer: 14

[Easy] Basic Fractions

• EN: A pizza is cut into 4 equal slices. Chloe eats 1 slice. What fraction did she eat?
• FR: Une pizza est coupée en 4 parts égales. Chloé mange 1 part. Quelle fraction a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: A fraction shows part of a whole — the bottom number is how many equal parts total (e.g., 3 parts total and you take 1 = 1/3).
• Steps:
  • The pizza has 4 equal slices total.
  • Chloe ate 1 slice.
  • So she ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Perimeter

• EN: A rectangle is 5 cm long and 3 cm wide. What is its perimeter?
• FR: Un rectangle mesure 5 cm de long et 3 cm de large. Quel est son périmètre?
• Choices: A) 12 cm B) 14 cm C) 16 cm D) 18 cm
• Hint: Perimeter = add all sides. A rectangle has 2 long sides and 2 short sides (e.g., 4 cm and 2 cm: 4+4+2+2 = 12 cm).
• Steps:
  • Two long sides: 5 + 5 = 10.
  • Two short sides: 3 + 3 = 6.
  • Perimeter = 10 + 6 = 16 cm.
• Answer: 16 cm

[Easy] Reading a Bar Graph

• EN: A graph shows: apples = 6, oranges = 4, bananas = 8. Which fruit has the most?
• FR: Un graphique montre : pommes = 6, oranges = 4, bananes = 8. Quel fruit est le plus nombreux?
• Choices: A) apples B) oranges C) bananas D) grapes
• Hint: Compare the numbers and find the largest value on the graph.
• Steps:
  • Apples: 6, Oranges: 4, Bananas: 8.
  • 8 is the largest number.
  • So bananas is the most common fruit.
• Answer: bananas

[Medium] Multiplication — 5 Times Table

• EN: There are 6 bags, each holding 5 apples. How many apples are there in total?
• FR: Il y a 6 sacs contenant chacun 5 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 25 B) 28 C) 30 D) 35
• Hint: Multiply to find the total when groups are equal (e.g., 4 bags × 5 apples = 20 apples).
• Steps:
  • 6 × 5 = ?
  • Count by 5s six times: 5, 10, 15, 20, 25, 30.
  • There are 30 apples in total.
• Answer: 30

[Medium] Basic Division

• EN: 24 students are placed into equal groups of 4. How many groups are there?
• FR: 24 élèves sont placés en groupes égaux de 4. Combien y a-t-il de groupes?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Division means splitting into equal groups (e.g., 18 ÷ 3 = 6 because 3 × 6 = 18).
• Steps:
  • 24 ÷ 4 = ?
  • Think: 4 × ? = 24. 4 × 6 = 24.
  • So there are 6 groups.
• Answer: 6

[Medium] Multiplication — 10 Times Table

• EN: A store gets 7 boxes of Tim Hortons cups. Each box has 10 cups. How many cups are there?
• FR: Un magasin reçoit 7 boîtes de gobelets Tim Hortons. Chaque boîte contient 10 gobelets. Combien y a-t-il de gobelets?
• Choices: A) 60 B) 65 C) 70 D) 75
• Hint: Multiplying by 10 is easy — just put a 0 after the number (e.g., 9 × 10 = 90).
• Steps:
  • 7 × 10 = ?
  • Place a zero after 7: 70.
  • There are 70 cups.
• Answer: 70

[Medium] Fractions — Comparing

• EN: Which fraction is larger: 1/2 or 1/4?
• FR: Quelle fraction est plus grande : 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/4
• Hint: When the numerator is the same, the fraction with the smaller denominator is larger (e.g., 1/3 > 1/5).
• Steps:
  • Both fractions have a numerator of 1.
  • The smaller the denominator, the bigger each piece.
  • So 1/2 is larger than 1/4.
• Answer: 1/2

[Hard] Multiplication and Addition Together

• EN: A hockey team scores 3 goals per game for 4 games, then scores 5 goals in the final game. How many goals total?
• FR: Une équipe de hockey marque 3 buts par partie pendant 4 parties, puis marque 5 buts lors du dernier match. Combien de buts en tout?
• Choices: A) 14 B) 15 C) 17 D) 20
• Hint: Multiply first, then add the extra (e.g., 2 goals × 3 games = 6, then 6 + 4 = 10).
• Steps:
  • 3 × 4 = 12 goals in the first 4 games.
  • Add 5 goals from the final game: 12 + 5 = 17.
  • The total is 17 goals.
• Answer: 17

[Hard] Division with Reasoning

• EN: Mrs. Tremblay has 36 crayons to share equally among 4 students. How many crayons does each student get?
• FR: Mme Tremblay a 36 crayons à partager également entre 4 élèves. Combien de crayons chaque élève reçoit-il?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: To divide, think of what times-table fact fits (e.g., 28 ÷ 4: think 4 × ? = 28, so ? = 7).
• Steps:
  • 36 ÷ 4 = ?
  • Think: 4 × ? = 36. 4 × 9 = 36.
  • Each student gets 9 crayons.
• Answer: 9

[Easy] Multiplication to 9×9

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: You can break it apart: 7 × 8 = 7 × 4 + 7 × 4 (e.g., 6 × 8 = 6 × 4 + 6 × 4 = 24 + 24 = 48).
• Steps:
  • 7 × 8: think of the times table.
  • 7 × 8 = 56.
  • So the answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, what digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre est à la position des dixièmes?
• Choices: A) 3 B) 4 C) 5 D) 7
• Hint: In a decimal, the first digit after the point is tenths, the second is hundredths (e.g., in 5.82, the tenths digit is 8).
• Steps:
  • 3.47: the digits after the decimal point are 4 and 7.
  • The first digit after the point (4) is in the tenths place.
  • So the answer is 4.
• Answer: 4

[Easy] Area of a Rectangle

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

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 2/4?
• FR: Quelle fraction est plus grande : 3/4 ou 2/4?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) 4/4
• Hint: When denominators are the same, compare the numerators — the bigger numerator wins (e.g., 5/8 > 3/8).
• Steps:
  • Both fractions have denominator 4.
  • Compare numerators: 3 > 2.
  • So 3/4 is larger.
• Answer: 3/4

[Medium] Long Division with Remainder

• EN: 47 children need to sit in rows of 5. How many complete rows are there, and how many children are left over?
• FR: 47 enfants doivent s'asseoir en rangées de 5. Combien de rangées complètes y a-t-il et combien d'enfants restent-ils?
• Choices: A) 8 rows remainder 5 B) 9 rows remainder 2 C) 9 rows remainder 4 D) 10 rows remainder 3
• Hint: Divide, then find the remainder by multiplying back and subtracting (e.g., 23 ÷ 4 = 5 remainder 3 because 4 × 5 = 20, 23 – 20 = 3).
• Steps:
  • 47 ÷ 5: 5 × 9 = 45, which is the biggest multiple of 5 not exceeding 47.
  • Remainder: 47 – 45 = 2.
  • So there are 9 complete rows with 2 children left over.
• Answer: 9 rows remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 PM and ends at 3:45 PM. How long does the game last?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps dure le match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: Count hours first, then minutes (e.g., from 2:10 PM to 4:40 PM: 2 hours + 30 minutes = 2 hours 30 minutes).
• Steps:
  • From 1:15 PM to 3:15 PM = 2 hours.
  • From 3:15 PM to 3:45 PM = 30 minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A book costs $4.75 and a pencil costs $1.20. How much do they cost together?
• FR: Un livre coûte 4,75 $ et un crayon coûte 1,20 $. Combien coûtent-ils ensemble?
• Choices: A) $5.85 B) $5.90 C) $5.95 D) $6.05
• Hint: Line up the decimal points and add like regular numbers (e.g., $3.50 + $2.25 = $5.75).
• Steps:
  • $4.75 + $1.20: line up decimals.
  • Ones: 4 + 1 = 5. Tenths: 7 + 2 = 9. Hundredths: 5 + 0 = 5.
  • Total = $5.95.
• Answer: $5.95

[Medium] Multiplication — Multi-Digit

• EN: A farmer plants 8 rows of corn with 23 plants in each row. How many plants are there?
• FR: Un fermier plante 8 rangées de maïs avec 23 plants dans chaque rangée. Combien y a-t-il de plants?
• Choices: A) 164 B) 174 C) 184 D) 194
• Hint: Multiply each part separately and add (e.g., 7 × 24 = 7 × 20 + 7 × 4 = 140 + 28 = 168).
• Steps:
  • 8 × 23 = 8 × 20 + 8 × 3.
  • 8 × 20 = 160; 8 × 3 = 24.
  • 160 + 24 = 184.
• Answer: 184

[Hard] Multi-Step Word Problem

• EN: Tyler has $20.00. He buys a notebook for $6.49 and a ruler for $2.75. How much money does he have left?
• FR: Tyler a 20,00 $. Il achète un cahier à 6,49 $ et une règle à 2,75 $. Combien d'argent lui reste-t-il?
• Choices: A) $10.76 B) $10.96 C) $11.16 D) $11.26
• Hint: Add the two costs, then subtract from the total (e.g., $5.10 + $3.40 = $8.50; $20.00 – $8.50 = $11.50).
• Steps:
  • Add the costs: $6.49 + $2.75 = $9.24.
  • Subtract from $20.00: $20.00 – $9.24 = $10.76.
  • Tyler has $10.76 left.
• Answer: $10.76

[Hard] Long Division and Area Combined

• EN: A rectangular garden has an area of 96 m² and is 8 m wide. What is its length?
• FR: Un jardin rectangulaire a une aire de 96 m² et une largeur de 8 m. Quelle est sa longueur?
• Choices: A) 10 m B) 11 m C) 12 m D) 14 m
• Hint: Use the area formula backwards: length = area ÷ width (e.g., area = 48 m², width = 6 m, length = 48 ÷ 6 = 8 m).
• Steps:
  • Area = length × width, so length = area ÷ width.
  • Length = 96 ÷ 8 = 12.
  • The length is 12 m.
• Answer: 12 m

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 5?
• FR: Combien font 34 × 5?
• Choices: A) 150 B) 160 C) 165 D) 170
• Hint: Break it apart: 30 × 5 + 4 × 5 (e.g., 22 × 5 = 20 × 5 + 2 × 5 = 100 + 10 = 110).
• Steps:
  • 34 × 5 = 30 × 5 + 4 × 5.
  • 30 × 5 = 150; 4 × 5 = 20.
  • 150 + 20 = 170.
• Answer: 170

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/8 + 3/8?
• FR: Combien font 2/8 + 3/8?
• Choices: A) 4/8 B) 5/8 C) 5/16 D) 6/8
• Hint: When denominators are the same, just add the numerators and keep the denominator (e.g., 1/5 + 2/5 = 3/5).
• Steps:
  • The denominators are both 8.
  • Add the numerators: 2 + 3 = 5.
  • Answer: 5/8
• Answer: 5/8

[Easy] Percentage — 50%

• EN: What is 50% of 60?
• FR: Combien font 50 % de 60?
• Choices: A) 20 B) 25 C) 30 D) 35
• Hint: 50% means half, so divide by 2 (e.g., 50% of 80 = 80 ÷ 2 = 40).
• Steps:
  • 50% = half.
  • 60 ÷ 2 = 30.
  • So 50% of 60 is 30.
• Answer: 30

[Easy] Decimal Operations

• EN: What is 4.6 + 2.3?
• FR: Combien font 4,6 + 2,3?
• Choices: A) 6.7 B) 6.8 C) 6.9 D) 7.1
• Hint: Add whole numbers, then decimals, keeping the decimal point in place (e.g., 3.2 + 1.5 = 4.7).
• Steps:
  • Ones: 4 + 2 = 6.
  • Tenths: 6 + 3 = 9.
  • So 4.6 + 2.3 = 6.9.
• Answer: 6.9

[Medium] Multi-Digit Division

• EN: A school orders 144 pencils to be shared equally among 6 classes. How many pencils does each class get?
• FR: Une école commande 144 crayons à partager également entre 6 classes. Combien de crayons chaque classe reçoit-elle?
• Choices: A) 22 B) 24 C) 26 D) 28
• Hint: Divide by breaking into parts (e.g., 126 ÷ 6: 120 ÷ 6 = 20, 6 ÷ 6 = 1, total = 21).
• Steps:
  • 144 ÷ 6: 120 ÷ 6 = 20, 24 ÷ 6 = 4.
  • 20 + 4 = 24.
  • Each class gets 24 pencils.
• Answer: 24

[Medium] Subtracting Fractions

• EN: What is 7/10 – 3/10?
• FR: Combien font 7/10 – 3/10?
• Choices: A) 3/10 B) 4/10 C) 4/20 D) 5/10
• Hint: Same denominators: just subtract the numerators and keep the denominator (e.g., 5/9 – 2/9 = 3/9).
• Steps:
  • The denominators are both 10.
  • Subtract numerators: 7 – 3 = 4.
  • Answer: 4/10
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is 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) 40 cm³ B) 48 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height (e.g., a box that is 4 × 3 × 2 = 24 cm³).
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25% and 10%

• EN: A bag of chips normally costs $2.80. Today it is 25% off. How much is the discount?
• FR: Un sac de croustilles coûte normalement 2,80 $. Aujourd'hui, il y a 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $0.60 B) $0.70 C) $0.75 D) $0.80
• Hint: 25% = one quarter; divide the price by 4 (e.g., 25% of $3.20 = $3.20 ÷ 4 = $0.80).
• Steps:
  • 25% of $2.80 = $2.80 ÷ 4.
  • $2.80 ÷ 4 = $0.70.
  • The discount is $0.70.
• Answer: $0.70

[Hard] Multi-Step Fraction and Decimal Problem

• EN: Sophia runs 1.5 km on Monday, 2/4 km on Tuesday, and 1.25 km on Wednesday. How far does she run in total?
• FR: Sofia court 1,5 km lundi, 2/4 km mardi et 1,25 km mercredi. Quelle distance court-elle en tout?
• Choices: A) 2.75 km B) 3.00 km C) 3.25 km D) 3.50 km
• Hint: Convert the fraction to a decimal first, then add all three (e.g., 1/2 = 0.5, so 1.5 + 0.5 + 1.0 = 3.0).
• Steps:
  • 2/4 = 0.5 km.
  • Add: 1.5 + 0.5 + 1.25 = 3.25.
  • Sophia runs 3.25 km in total.
• Answer: 3.25 km

[Hard] Multi-Digit Multiplication — Two Steps

• EN: A school store sells 48 packs of markers at $3.25 each. What is the total amount of money collected?
• FR: La papeterie de l'école vend 48 paquets de marqueurs à 3,25 $ chacun. Quel est le montant total recueilli?
• Choices: A) $144.00 B) $152.00 C) $156.00 D) $160.00
• Hint: Multiply the price by the number of packs — break it into parts (e.g., 20 × $3.25 = $65.00, then double for 40).
• Steps:
  • 48 × $3.25: 40 × $3.25 = $130.00; 8 × $3.25 = $26.00.
  • $130.00 + $26.00 = $156.00.
  • Total collected is $156.00.
• Answer: $156.00

[Easy] Percent of a Number

• EN: What is 10% of 250?
• FR: Combien font 10 % de 250?
• Choices: A) 20 B) 25 C) 30 D) 35
• Hint: 10% means divide by 10 — just move the decimal point one place to the left (e.g., 10% of 180 = 18).
• Steps:
  • 10% of 250 = 250 ÷ 10.
  • 250 ÷ 10 = 25.
  • So 10% of 250 is 25.
• Answer: 25

[Easy] Ratio

• EN: For every 2 teachers there are 30 students. What is the ratio of teachers to students?
• FR: Pour chaque 2 enseignants, il y a 30 élèves. Quel est le rapport enseignants/élèves?
• Choices: A) 1:12 B) 1:15 C) 2:30 D) 2:15
• Hint: A ratio compares two quantities — write teacher : student (e.g., 3 teachers and 12 students = 3:12 or simplified to 1:4).
• Steps:
  • Ratio = teachers : students = 2 : 30.
  • Simplify by dividing both by 2: 1 : 15.
  • The ratio is 1:15.
• Answer: 1:15

[Easy] Order of Operations (BEDMAS)

• EN: Solve: 3 + 4 × 2.
• FR: Résous : 3 + 4 × 2.
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: In BEDMAS, multiplication comes before addition — do the × first, then + (e.g., 5 + 2 × 3 = 5 + 6 = 11).
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • So the answer is 11.
• Answer: 11

[Easy] Integers Introduction

• EN: The temperature in Winnipeg was –8°C in the morning and rose 5°C by noon. What is the noon temperature?
• FR: La température à Winnipeg était de –8 °C le matin et a monté de 5 °C à midi. Quelle est la température à midi?
• Choices: A) –4°C B) –3°C C) –2°C D) –1°C
• Hint: Adding a positive number to a negative number moves you towards zero on a number line (e.g., –6 + 4 = –2).
• Steps:
  • –8 + 5: start at –8 and move 5 steps right.
  • –8 + 5 = –3.
  • The noon temperature is –3°C.
• Answer: –3°C

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 6/12 C) 5/7 D) 6/7
• Hint: Multiply numerators together and denominators together (e.g., 1/2 × 2/3 = 2/6 = 1/3).
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 simplifies to 1/2, but the exact form is 6/12.
• Answer: 6/12

[Medium] Rate Problems

• EN: A car travels 90 km in 2 hours. What is its speed in km/h?
• FR: Une voiture parcourt 90 km en 2 heures. Quelle est sa vitesse en km/h?
• Choices: A) 40 km/h B) 42 km/h C) 45 km/h D) 50 km/h
• Hint: Speed = distance ÷ time (e.g., 60 km in 3 hours = 60 ÷ 3 = 20 km/h).
• Steps:
  • Speed = 90 ÷ 2.
  • 90 ÷ 2 = 45.
  • The speed is 45 km/h.
• Answer: 45 km/h

[Medium] Simple Algebraic Expressions

• EN: If n = 6, what is the value of 4n – 3?
• FR: Si n = 6, quelle est la valeur de 4n – 3?
• Choices: A) 20 B) 21 C) 22 D) 24
• Hint: Substitute the value into the expression and calculate (e.g., if n = 5, then 3n – 2 = 15 – 2 = 13).
• Steps:
  • Replace n with 6: 4(6) – 3.
  • 4 × 6 = 24; 24 – 3 = 21.
  • The value is 21.
• Answer: 21

[Medium] Percent of a Number — Discount

• EN: A pair of hockey skates costs $120. They are on sale for 30% off. How much is the discount?
• FR: Une paire de patins de hockey coûte 120 $. Ils sont en solde à 30 % de rabais. Quel est le montant du rabais?
• Choices: A) $30 B) $32 C) $36 D) $40
• Hint: Find the percent of the price (e.g., 20% of $80 = 80 × 0.20 = $16).
• Steps:
  • 30% of $120 = 120 × 30 ÷ 100.
  • 120 × 30 = 3600; 3600 ÷ 100 = 36.
  • The discount is $36.
• Answer: $36

[Hard] Fraction Division

• EN: A recipe needs 3/4 of a cup of flour. If you want to make half the recipe, how much flour do you need?
• FR: Une recette nécessite 3/4 de tasse de farine. Si tu veux faire la moitié de la recette, de quelle quantité de farine as-tu besoin?
• Choices: A) 1/4 B) 3/8 C) 1/2 D) 3/4
• Hint: Multiplying by 1/2 is the same as dividing by 2 — multiply numerators and denominators (e.g., 2/3 × 1/2 = 2/6 = 1/3).
• Steps:
  • Half the recipe: 3/4 × 1/2.
  • Numerators: 3 × 1 = 3. Denominators: 4 × 2 = 8.
  • You need 3/8 of a cup.
• Answer: 3/8

[Hard] BEDMAS with Integers

• EN: Solve: (–2 + 8) × 3 – 4².
• FR: Résous : (–2 + 8) × 3 – 4².
• Choices: A) –2 B) 0 C) 2 D) 4
• Hint: Use BEDMAS — solve brackets first, then exponents, then multiply, then subtract (e.g., (3 + 1) × 2 – 2² = 4 × 2 – 4 = 8 – 4 = 4).
• Steps:
  • Brackets: –2 + 8 = 6.
  • Exponents: 4² = 16.
  • Multiply: 6 × 3 = 18.
  • Subtract: 18 – 16 = 2.
• Answer: 2

[Easy] Integer Addition

• EN: What is –9 + 15?
• FR: Combien font –9 + 15?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: On a number line, start at –9 and move 15 steps to the right (e.g., –4 + 10 = 6).
• Steps:
  • Start at –9.
  • Move 15 to the right: –9 + 15 = 6.
  • So the answer is 6.
• Answer: 6

[Easy] Percent — Tip Calculation

• EN: A meal costs $20. You want to leave a 15% tip. How much is the tip?
• FR: Un repas coûte 20 $. Tu veux laisser un pourboire de 15 %. Quel est le montant du pourboire?
• Choices: A) $2.00 B) $2.50 C) $3.00 D) $3.50
• Hint: Find 10%, then find 5%, and add them together (e.g., 15% of $40: 10% = $4, 5% = $2, total = $6).
• Steps:
  • 10% of $20 = $2.00.
  • 5% of $20 = $1.00.
  • 15% tip = $2.00 + $1.00 = $3.00.
• Answer: $3.00

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x : x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: To solve, subtract the number being added from both sides (e.g., x + 4 = 10: x = 10 – 4 = 6).
• Steps:
  • x + 9 = 17.
  • Subtract 9 from both sides: x = 17 – 9.
  • x = 8.
• Answer: x = 8

[Easy] Fraction Fluency

• EN: What is 5/6 – 1/6?
• FR: Combien font 5/6 – 1/6?
• Choices: A) 3/6 B) 4/6 C) 5/12 D) 6/6
• Hint: Same denominator — just subtract the numerators (e.g., 7/9 – 3/9 = 4/9).
• Steps:
  • Denominators are both 6.
  • Subtract numerators: 5 – 1 = 4.
  • Answer: 4/6
• Answer: 4/6

[Medium] Integer Multiplication

• EN: What is –4 × 7?
• FR: Combien font –4 × 7?
• Choices: A) –32 B) –28 C) –24 D) –20
• Hint: A negative times a positive gives a negative result (e.g., –3 × 5 = –15).
• Steps:
  • 4 × 7 = 28.
  • One factor is negative, so the answer is negative.
  • –4 × 7 = –28.
• Answer: –28

[Medium] Percentage — Discount

• EN: A winter jacket normally costs $160. It is on sale for 20% off. What is the sale price?
• FR: Un manteau d'hiver coûte normalement 160 $. Il est en solde à 20 % de rabais. Quel est le prix de vente?
• Choices: A) $120 B) $124 C) $128 D) $132
• Hint: Find the discount first, then subtract from the original price (e.g., 25% off $80 = discount of $20, sale price = $60).
• Steps:
  • 20% of $160 = 160 × 0.20 = $32.
  • Sale price = $160 – $32 = $128.
  • The sale price is $128.
• Answer: $128

[Medium] Surface Area of a Rectangular Prism

• EN: A rectangular box is 6 cm long, 4 cm wide, and 3 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 6 cm de long, 4 cm de large et 3 cm de haut. Quelle est son aire totale?
• Choices: A) 96 cm² B) 108 cm² C) 120 cm² D) 144 cm²
• Hint: Surface area = 2(lw + lh + wh) — add three pairs of faces and multiply by 2 (e.g., 2 × 3 × 1 box: SA = 2(6+2+3) = 22).
• Steps:
  • lw = 6 × 4 = 24; lh = 6 × 3 = 18; wh = 4 × 3 = 12.
  • Sum = 24 + 18 + 12 = 54.
  • SA = 2 × 54 = 108 cm².
• Answer: 108 cm²

[Medium] Probability

• EN: A bag has 3 red marbles and 7 blue marbles. What is the probability of picking a red marble?
• FR: Un sac contient 3 billes rouges et 7 billes bleues. Quelle est la probabilité de choisir une bille rouge?
• Choices: A) 3/7 B) 3/10 C) 7/10 D) 1/3
• Hint: Probability = favourable outcomes ÷ total outcomes (e.g., 2 red out of 8 total = 2/8 = 1/4).
• Steps:
  • Total marbles = 3 + 7 = 10.
  • Red marbles = 3.
  • P(red) = 3/10.
• Answer: 3/10

[Hard] Integer Division and Multi-Step

• EN: The temperature dropped 3°C every hour for 6 hours, then rose 8°C. If it started at 5°C, what is the final temperature?
• FR: La température a chuté de 3 °C par heure pendant 6 heures, puis a monté de 8 °C. Si elle était de 5 °C au départ, quelle est la température finale?
• Choices: A) –5°C B) –3°C C) 0°C D) 3°C
• Hint: Calculate the total drop, subtract it, then add the rise (e.g., start at 10°C, drop 2°C for 3 hours: 10 – 6 = 4, then add 5°C = 9°C).
• Steps:
  • Total drop: –3 × 6 = –18°C.
  • Starting at 5°C: 5 + (–18) = –13°C.
  • Then rise 8°C: –13 + 8 = –5°C.
• Answer: –5°C

[Hard] One-Step Equations with Fractions

• EN: Solve for x: x/4 = 9.
• FR: Résous pour x : x/4 = 9.
• Choices: A) x = 32 B) x = 36 C) x = 40 D) x = 45
• Hint: Multiply both sides by the denominator to isolate x (e.g., x/3 = 7 means x = 7 × 3 = 21).
• Steps:
  • x/4 = 9.
  • Multiply both sides by 4: x = 9 × 4.
  • x = 36.
• Answer: x = 36

[Easy] Square Roots

• EN: What is √64?
• FR: Combien fait √64?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: The square root asks "what number times itself equals this?" (e.g., √49 = 7 because 7 × 7 = 49).
• Steps:
  • Ask: what number × itself = 64?
  • 8 × 8 = 64.
  • So √64 = 8.
• Answer: 8

[Easy] Perfect Squares

• EN: Which of the following is a perfect square?
• FR: Lequel des nombres suivants est un carré parfait?
• Choices: A) 20 B) 36 C) 50 D) 72
• Hint: A perfect square is a number that is the product of a whole number times itself (e.g., 25 = 5 × 5).
• Steps:
  • Check each: 20 – no; 36 = 6 × 6 – yes; 50 – no; 72 – no.
  • 36 is the perfect square.
• Answer: 36

[Easy] Mean of a Data Set

• EN: Five students scored 70, 80, 60, 90, and 50 on a quiz. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 80, 60, 90 et 50 à un quiz. Quel est le score moyen?
• Choices: A) 65 B) 70 C) 72 D) 75
• Hint: Mean = sum of all values ÷ number of values (e.g., 4, 6, 8 → (4+6+8) ÷ 3 = 6).
• Steps:
  • Sum: 70 + 80 + 60 + 90 + 50 = 350.
  • Mean = 350 ÷ 5 = 70.
  • The mean score is 70.
• Answer: 70

[Easy] Two-Step Equation

• 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 = 6
• Hint: Subtract the constant first, then divide (e.g., 3x + 2 = 14: subtract 2 → 3x = 12, divide by 3 → x = 4).
• Steps:
  • Subtract 3: 2x = 11 – 3 = 8.
  • Divide by 2: x = 8 ÷ 2 = 4.
  • x = 4.
• Answer: x = 4

[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 jambes 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: Use a² + b² = c² to find the hypotenuse (e.g., legs 3 and 4: 9 + 16 = 25, √25 = 5).
• Steps:
  • a² + b² = c²: 6² + 8² = c².
  • 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Percent Increase

• EN: A hockey player scored 25 goals last season and 30 goals this season. What is the percent increase?
• FR: Un joueur de hockey a marqué 25 buts la saison dernière et 30 buts cette saison. Quel est le pourcentage d'augmentation?
• Choices: A) 15% B) 18% C) 20% D) 25%
• Hint: Percent increase = (change ÷ original) × 100 (e.g., from 40 to 48: change = 8, 8/40 × 100 = 20%).
• Steps:
  • Change = 30 – 25 = 5.
  • Percent increase = (5 ÷ 25) × 100 = 20%.
  • The increase is 20%.
• Answer: 20%

[Medium] Slope Introduction

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

[Medium] Median and Mode

• EN: The data set is: 4, 7, 2, 7, 9. What is the mode?
• FR: L'ensemble de données est : 4, 7, 2, 7, 9. Quel est le mode?
• Choices: A) 2 B) 4 C) 7 D) 9
• Hint: The mode is the value that appears most often in the data set (e.g., in 3, 5, 3, 8, the mode is 3).
• Steps:
  • List the data: 2, 4, 7, 7, 9.
  • 7 appears twice — all others appear once.
  • The mode is 7.
• Answer: 7

[Hard] Pythagorean Theorem — Word Problem

• EN: A ladder is 13 m long and leans against a wall. The bottom 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. Le bas 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) 14 m
• Hint: Use a² + b² = c², solving for a leg: a² = c² – b² (e.g., hypotenuse = 10, one leg = 6: 100 – 36 = 64, √64 = 8).
• Steps:
  • a² + 5² = 13²: a² + 25 = 169.
  • a² = 169 – 25 = 144.
  • a = √144 = 12 m.
• Answer: 12 m

[Hard] Two-Step Equations — Multi-Step

• EN: Solve for x: 3(x – 4) = 18.
• FR: Résous pour x : 3(x – 4) = 18.
• Choices: A) x = 8 B) x = 9 C) x = 10 D) x = 12
• Hint: Divide both sides by 3 first, then add 4 (e.g., 2(x – 3) = 10: x – 3 = 5, x = 8).
• Steps:
  • Divide both sides by 3: x – 4 = 6.
  • Add 4 to both sides: x = 6 + 4 = 10.
  • x = 10.
• Answer: x = 10

[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: Add the constant to both sides, then divide (e.g., 4x – 2 = 14: add 2 → 4x = 16, divide → x = 4).
• Steps:
  • Add 3: 5x = 22 + 3 = 25.
  • Divide by 5: x = 25 ÷ 5 = 5.
  • x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Add: (3x + 4) + (2x – 1).
• FR: Additionne : (3x + 4) + (2x – 1).
• Choices: A) 4x + 3 B) 5x + 3 C) 5x + 5 D) 6x + 3
• Hint: Combine like terms — add x-terms together and constant terms together (e.g., (2x + 1) + (3x + 4) = 5x + 5).
• Steps:
  • x-terms: 3x + 2x = 5x.
  • Constants: 4 + (–1) = 3.
  • Result: 5x + 3.
• Answer: 5x + 3

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x + 7?
• FR: Quelle est la pente de la droite y = 3x + 7?
• Choices: A) 3 B) 7 C) 10 D) 21
• Hint: In y = mx + b, m is the slope and b is the y-intercept (e.g., in y = 5x + 2, the slope is 5).
• Steps:
  • The equation is in y = mx + b form.
  • m = 3 (the coefficient of x).
  • The slope is 3.
• Answer: 3

[Easy] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 4 cm and the hypotenuse is 8 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 4 cm et l'hypoténuse mesure 8 cm. Combien fait sin(θ)?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: SOH means sin = Opposite ÷ Hypotenuse (e.g., opposite = 3, hypotenuse = 6: sin = 3/6 = 1/2).
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 4 ÷ 8 = 1/2.
  • So sin(θ) = 1/2.
• Answer: 1/2

[Medium] Solving Inequalities

• EN: Solve for x: 2x + 5 > 13.
• FR: Résous pour x : 2x + 5 > 13.
• Choices: A) x > 2 B) x > 3 C) x > 4 D) x > 5
• Hint: Solve like an equation — subtract, then divide — the inequality sign stays the same when dividing by a positive (e.g., 3x + 1 > 10: 3x > 9, x > 3).
• Steps:
  • Subtract 5: 2x > 13 – 5 = 8.
  • Divide by 2: x > 4.
  • So x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5).
• FR: Développe : (x + 3)(x + 5).
• Choices: A) x² + 7x + 12 B) x² + 8x + 15 C) x² + 9x + 15 D) x² + 8x + 18
• Hint: Use FOIL — First, Outer, Inner, Last (e.g., (x+2)(x+4) = x² + 4x + 2x + 8 = x² + 6x + 8).
• Steps:
  • First: x × x = x².
  • Outer: x × 5 = 5x. Inner: 3 × x = 3x. Last: 3 × 5 = 15.
  • Combine: x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Triangle A has sides 3, 4, and 5. Triangle B is similar with shortest side 9. What is the longest side of Triangle B?
• FR: Le triangle A a des côtés de 3, 4 et 5. Le triangle B lui est semblable avec le côté le plus court de 9. Quel est le côté le plus long du triangle B?
• Choices: A) 10 B) 12 C) 15 D) 18
• Hint: Find the scale factor first, then multiply each side (e.g., if a triangle with sides 2, 3, 4 is scaled by 3, the sides become 6, 9, 12).
• Steps:
  • Scale factor = 9 ÷ 3 = 3.
  • Longest side of A = 5; B = 5 × 3 = 15.
  • The longest side is 15.
• Answer: 15

[Medium] Graphing Lines

• EN: What is the y-intercept of the line y = –2x + 6?
• FR: Quel est l'ordonnée à l'origine de la droite y = –2x + 6?
• Choices: A) –2 B) 4 C) 6 D) 8
• Hint: In y = mx + b, b is the y-intercept — the point where the line crosses the y-axis (e.g., y = 4x – 3 has y-intercept –3).
• Steps:
  • The equation is y = –2x + 6.
  • The y-intercept is b = 6.
  • So the y-intercept is 6.
• Answer: 6

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, one angle is 30° and the hypotenuse is 20 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, un angle est de 30° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Use SOH: sin(angle) = opposite/hypotenuse, so opposite = hypotenuse × sin(angle) (e.g., sin(60°) ≈ 0.866, so opposite ≈ hypotenuse × 0.866).
• Steps:
  • sin(30°) = 0.5.
  • Opposite = hypotenuse × sin(30°) = 20 × 0.5.
  • Opposite = 10 cm.
• Answer: 10 cm

[Hard] Systems of Linear Equations

• 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 = 4 D) x = 4, y = 9
• Hint: Set the two expressions equal to find x, then substitute back (e.g., y = x + 2 and y = 3x – 4: x + 2 = 3x – 4, so 2x = 6, x = 3).
• Steps:
  • Set equal: 2x + 1 = –x + 7.
  • Add x: 3x + 1 = 7; subtract 1: 3x = 6; x = 2.
  • y = 2(2) + 1 = 5. So x = 2, y = 5.
• Answer: x = 2, y = 5

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6.
• FR: Factorise : x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 4) D) (x + 2)(x + 4)
• Hint: Find two numbers that multiply to the constant and add to the x-coefficient (e.g., x² + 7x + 10: 2 × 5 = 10, 2 + 5 = 7 → (x+2)(x+5)).
• Steps:
  • Need two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6; 2 + 3 = 5. ✓
  • So x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding a Side with CAH

• EN: In a right triangle, an angle is 60° and the adjacent side is 5 cm. What is the hypotenuse?
• FR: Dans un triangle rectangle, un angle est de 60° et le côté adjacent mesure 5 cm. Quelle est l'hypoténuse?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: CAH: cos(angle) = adjacent/hypotenuse, so hypotenuse = adjacent ÷ cos(angle). cos(60°) = 0.5 (e.g., adjacent = 8, cos(60°) = 0.5: hypotenuse = 16).
• Steps:
  • cos(60°) = 0.5.
  • Hypotenuse = adjacent ÷ cos(60°) = 5 ÷ 0.5.
  • Hypotenuse = 10 cm.
• Answer: 10 cm

[Easy] Systems of Equations

• EN: Solve: x + y = 10 and x – y = 4.
• FR: Résous : x + y = 10 et x – y = 4.
• Choices: A) x = 5, y = 5 B) x = 6, y = 4 C) x = 7, y = 3 D) x = 8, y = 2
• Hint: Add the two equations together to eliminate y, then solve for x (e.g., x + y = 8 and x – y = 2: adding gives 2x = 10, x = 5).
• Steps:
  • Add equations: 2x = 14, so x = 7.
  • Substitute: 7 + y = 10, so y = 3.
  • x = 7, y = 3.
• Answer: x = 7, y = 3

[Easy] Volume of a Cylinder

• EN: A cylinder has radius 3 cm and height 7 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 7 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 175.56 cm³ B) 185.94 cm³ C) 197.82 cm³ D) 206.10 cm³
• Hint: Volume of a cylinder = π × r² × h (e.g., r = 2, h = 5: V = 3.14 × 4 × 5 = 62.8 cm³).
• Steps:
  • V = π × r² × h = 3.14 × 3² × 7.
  • 3² = 9; 9 × 7 = 63; 63 × 3.14 = 197.82.
  • Volume = 197.82 cm³.
• Answer: 197.82 cm³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x = 7.
• FR: Résous en complétant le carré : x² + 6x = 7.
• Choices: A) x = 1 or x = –7 B) x = 2 or x = –8 C) x = 3 or x = –9 D) x = 4 or x = –10
• Hint: Take half of the x-coefficient, square it, and add to both sides (e.g., x² + 4x = 5: add 4 → (x+2)² = 9, x = 1 or –3).
• Steps:
  • Half of 6 = 3; 3² = 9. Add to both sides: x² + 6x + 9 = 16.
  • (x + 3)² = 16; x + 3 = ±4.
  • x = 1 or x = –7.
• Answer: x = 1 or x = –7

[Medium] Circle Geometry

• EN: A chord of a circle is 16 cm long. The perpendicular from the centre to the chord is 6 cm. What is the radius?
• FR: Une corde d'un cercle mesure 16 cm. La perpendiculaire du centre à la corde est de 6 cm. Quel est le rayon?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 11 cm
• Hint: The perpendicular from the centre bisects the chord, forming a right triangle (e.g., half-chord = 8, perpendicular = 6: radius = √(64+36) = 10).
• Steps:
  • Half the chord = 16 ÷ 2 = 8.
  • Radius² = 8² + 6² = 64 + 36 = 100.
  • Radius = √100 = 10 cm.
• Answer: 10 cm

[Medium] Surface Area of a Cone

• EN: A cone has radius 4 cm and slant height 9 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 9 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 150.72 cm² B) 163.28 cm² C) 175.84 cm² D) 188.40 cm²
• Hint: Total SA of a cone = πrl + πr² (lateral area + base area) (e.g., r = 3, l = 5: SA = 3.14 × 3 × 5 + 3.14 × 9 = 47.1 + 28.26 = 75.36).
• Steps:
  • Lateral area = π × 4 × 9 = 3.14 × 36 = 113.04 cm².
  • Base area = π × 4² = 3.14 × 16 = 50.24 cm².
  • Total SA = 113.04 + 50.24 = 163.28 cm².
• Answer: 163.28 cm²

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve x² – 5x + 6 = 0.
• FR: Utilise la formule quadratique pour résoudre x² – 5x + 6 = 0.
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = 2 or x = 4 D) x = 3 or x = 5
• Hint: Use x = (–b ± √(b²–4ac)) ÷ 2a (e.g., x² – 3x + 2 = 0: discriminant = 9–8 = 1, x = (3±1)/2 → x = 2 or 1).
• Steps:
  • a = 1, b = –5, c = 6. Discriminant: 25 – 24 = 1.
  • x = (5 ± 1) ÷ 2.
  • x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Hard] Completing the Square — Vertex Form

• EN: Write y = x² – 8x + 10 in vertex form and state the vertex.
• FR: Écris y = x² – 8x + 10 sous la forme canonique et indique le sommet.
• Choices: A) y = (x – 4)² – 6, vertex (4, –6) B) y = (x – 4)² + 6, vertex (4, 6) C) y = (x – 3)² – 5, vertex (3, –5) D) y = (x – 5)² – 4, vertex (5, –4)
• Hint: Complete the square by halving the x-coefficient and adjusting the constant (e.g., y = x² – 6x + 2: y = (x–3)² – 9 + 2 = (x–3)² – 7, vertex (3, –7)).
• Steps:
  • Half of –8 = –4; (–4)² = 16. y = (x – 4)² – 16 + 10.
  • y = (x – 4)² – 6.
  • Vertex is (4, –6).
• Answer: y = (x – 4)² – 6, vertex (4, –6)

[Hard] Trigonometry — Sine Rule Application

• EN: In triangle ABC, angle A = 30°, angle B = 45°, and side a = 8 cm (opposite A). Using the sine rule, find side b (opposite B) to one decimal place.
• FR: Dans le triangle ABC, l'angle A = 30°, l'angle B = 45° et le côté a = 8 cm (opposé à A). En utilisant la loi des sinus, trouve le côté b (opposé à B) à une décimale près.
• Choices: A) 9.8 cm B) 11.3 cm C) 12.6 cm D) 13.9 cm
• Hint: Sine rule: a/sin(A) = b/sin(B), so b = a × sin(B)/sin(A) (e.g., a=6, A=30°, B=60°: b = 6 × sin(60°)/sin(30°) = 6 × 0.866/0.5 ≈ 10.4).
• Steps:
  • b/sin(45°) = 8/sin(30°).
  • b = 8 × sin(45°)/sin(30°) = 8 × 0.7071/0.5.
  • b = 8 × 1.4142 ≈ 11.3 cm.
• Answer: 11.3 cm

[Easy] Exponential Function

• EN: A savings account starts with $500 and doubles every year. How much is in the account after 3 years?
• FR: Un compte d'épargne commence avec 500 $ et double chaque année. Combien y a-t-il dans le compte après 3 ans?
• Choices: A) $2 000 B) $3 000 C) $4 000 D) $5 000
• Hint: Doubling = multiply by 2 each time (e.g., $100 doubles to $200, $400, $800 after 3 years).
• Steps:
  • Year 1: 500 × 2 = 1 000.
  • Year 2: 1 000 × 2 = 2 000.
  • Year 3: 2 000 × 2 = $4 000.
• Answer: $4 000

[Easy] Logarithm Introduction

• EN: What is log₂(16)?
• FR: Combien fait log₂(16)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log₂(x) asks "to what power must 2 be raised to get x?" (e.g., log₂(8) = 3 because 2³ = 8).
• Steps:
  • Ask: 2 to what power = 16?
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16.
  • log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequence

• EN: In the sequence 5, 8, 11, 14, …, what is the 6th term?
• FR: Dans la suite 5, 8, 11, 14, …, quel est le 6e terme?
• Choices: A) 18 B) 20 C) 22 D) 24
• Hint: Find the common difference and use the formula t_n = a + (n–1)d (e.g., sequence 3, 7, 11: d = 4, 5th term = 3 + 4×4 = 19).
• Steps:
  • Common difference d = 3.
  • t₆ = 5 + (6–1) × 3 = 5 + 15 = 20.
  • The 6th term is 20.
• Answer: 20

[Easy] Compound Interest

• EN: $1 000 is invested at 5% annual compound interest. What is the amount after 2 years?
• FR: 1 000 $ est investi à un taux d'intérêt composé annuel de 5 %. Quel est le montant après 2 ans?
• Choices: A) $1 075.00 B) $1 100.00 C) $1 102.50 D) $1 105.00
• Hint: A = P(1 + r)^t — multiply by (1 + rate) for each year (e.g., $500 at 4% for 2 years: 500 × 1.04² = 500 × 1.0816 = $540.80).
• Steps:
  • A = 1000 × (1.05)².
  • 1.05² = 1.1025.
  • A = 1000 × 1.1025 = $1 102.50.
• Answer: $1 102.50

[Medium] Quadratic Function — Vertex and Axis

• EN: The function f(x) = –2(x – 3)² + 8 has a vertex at what coordinates?
• FR: La fonction f(x) = –2(x – 3)² + 8 a son sommet à quelles coordonnées?
• Choices: A) (–3, 8) B) (3, 8) C) (3, –8) D) (–3, –8)
• Hint: In vertex form f(x) = a(x – h)² + k, the vertex is at (h, k) (e.g., f(x) = (x – 5)² + 2 has vertex (5, 2)).
• Steps:
  • Vertex form: a = –2, h = 3, k = 8.
  • Vertex is (h, k) = (3, 8).
• Answer: (3, 8)

[Medium] Geometric Series Sum

• EN: Find the sum of the first 4 terms of the geometric series: 3, 6, 12, 24, …
• FR: Trouve la somme des 4 premiers termes de la suite géométrique : 3, 6, 12, 24, …
• Choices: A) 40 B) 42 C) 45 D) 48
• Hint: Add the terms directly for small series, or use S = a(r^n – 1)/(r – 1) (e.g., 1, 2, 4, 8: sum = 15).
• Steps:
  • Sum = 3 + 6 + 12 + 24.
  • 3 + 6 = 9; 9 + 12 = 21; 21 + 24 = 45.
  • Sum = 45.
• Answer: 45

[Medium] Logarithm Properties

• EN: Simplify: log(100) + log(10).
• FR: Simplifie : log(100) + log(10).
• Choices: A) 2 B) 3 C) 4 D) 10
• Hint: log(100) = 2 and log(10) = 1 because log base 10 of 10^n = n (e.g., log(1000) = 3).
• Steps:
  • log(100) = log(10²) = 2.
  • log(10) = 1.
  • 2 + 1 = 3.
• Answer: 3

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ.
• FR: Simplifie : sin²θ + cos²θ.
• Choices: A) 0 B) 1 C) 2 D) sinθ
• Hint: This is the most fundamental trig identity — it equals the same value for all angles (e.g., try θ = 30°: sin²30° + cos²30° = 0.25 + 0.75 = 1).
• Steps:
  • The Pythagorean identity states sin²θ + cos²θ = 1 for all values of θ.
  • This is always true.
  • The answer is 1.
• Answer: 1

[Hard] Compound Interest with Monthly Compounding

• EN: $2 000 is invested at 6% per year, compounded monthly, for 2 years. What is the amount? (Round to the nearest cent.)
• FR: 2 000 $ est investi à 6 % par an, composé mensuellement, pendant 2 ans. Quel est le montant? (Arrondis au cent près.)
• Choices: A) $2 240.00 B) $2 251.02 C) $2 254.24 D) $2 268.98
• Hint: Monthly rate = annual rate ÷ 12; number of periods = years × 12; use A = P(1 + r/n)^(nt) (e.g., $1000 at 12%/yr monthly for 1 yr: A = 1000(1.01)^12 ≈ $1126.83).
• Steps:
  • Monthly rate = 0.06/12 = 0.005; n = 2 × 12 = 24.
  • A = 2000 × (1.005)^24.
  • (1.005)^24 ≈ 1.127159; A ≈ 2000 × 1.127159 ≈ $2 254.24 (using more precise value: $2 254.24).
• Answer: $2 254.24

[Hard] Exponential Growth — Half-Life

• EN: A radioactive substance has a half-life of 10 years. If you start with 80 g, how many grams remain after 30 years?
• FR: Une substance radioactive a une demi-vie de 10 ans. Si tu commences avec 80 g, combien de grammes restent après 30 ans?
• Choices: A) 5 g B) 8 g C) 10 g D) 16 g
• Hint: Each half-life cuts the amount in half — divide by 2 for each period (e.g., 64 g with half-life 5 years after 15 years: 64→32→16→8 g).
• Steps:
  • 30 years ÷ 10 years = 3 half-lives.
  • 80 → 40 → 20 → 10 g.
  • After 30 years, 10 g remain.
• Answer: 10 g

[Easy] Permutations

• EN: In how many ways can 4 students be arranged in a line?
• FR: De combien de façons peut-on placer 4 élèves en ligne?
• Choices: A) 12 B) 16 C) 24 D) 32
• Hint: The number of arrangements of n items is n! = n × (n–1) × … × 1 (e.g., 3 students: 3! = 3 × 2 × 1 = 6).
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • 4 × 3 = 12; 12 × 2 = 24; 24 × 1 = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Combinations

• EN: A coach chooses 2 players from a team of 6 for a special drill. How many different pairs are possible?
• FR: Un entraîneur choisit 2 joueurs parmi 6 pour un exercice spécial. Combien de paires différentes sont possibles?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: Use C(n, r) = n! ÷ (r! × (n–r)!) (e.g., C(5,2) = 5! ÷ (2! × 3!) = 120 ÷ 12 = 10).
• Steps:
  • C(6, 2) = 6! ÷ (2! × 4!) = (6 × 5) ÷ (2 × 1).
  • = 30 ÷ 2 = 15.
  • There are 15 different pairs.
• Answer: 15

[Easy] Derivative — Power Rule

• EN: If f(x) = x³, what is f'(x)?
• FR: Si f(x) = x³, combien fait f'(x)?
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹ (e.g., f(x) = x⁵: f'(x) = 5x⁴).
• Steps:
  • f(x) = x³, so n = 3.
  • f'(x) = 3 · x^(3–1) = 3x².
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Rational Functions — Domain

• EN: What value of x must be excluded from the domain of f(x) = 1/(x – 5)?
• FR: Quelle valeur de x doit être exclue du domaine de f(x) = 1/(x – 5)?
• Choices: A) x = –5 B) x = 0 C) x = 1 D) x = 5
• Hint: The denominator cannot equal zero — set it equal to zero and solve (e.g., f(x) = 1/(x + 3): x = –3 is excluded).
• Steps:
  • Set x – 5 = 0.
  • x = 5.
  • So x = 5 must be excluded.
• Answer: x = 5

[Medium] Binomial Distribution

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 2 heads?
• FR: Une pièce équilibrée est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 1/4 B) 3/8 C) 7/16 D) 1/2
• Hint: Use P = C(n,k) × p^k × (1–p)^(n–k) (e.g., 3 flips, exactly 1 head: C(3,1) × (0.5)¹ × (0.5)² = 3 × 0.125 = 3/8).
• Steps:
  • P = C(4,2) × (0.5)² × (0.5)².
  • C(4,2) = 6; (0.5)⁴ = 1/16.
  • P = 6/16 = 3/8.
• Answer: 3/8

[Medium] Vectors — Adding Two Vectors

• EN: Vector u = (3, –1) and vector v = (–1, 4). What is u + v?
• FR: Le vecteur u = (3, –1) et le vecteur v = (–1, 4). Combien fait u + v?
• Choices: A) (1, 3) B) (2, 3) C) (3, 5) D) (4, 3)
• Hint: Add corresponding components: (a, b) + (c, d) = (a+c, b+d) (e.g., (2, 5) + (3, –2) = (5, 3)).
• Steps:
  • x-component: 3 + (–1) = 2.
  • y-component: –1 + 4 = 3.
  • u + v = (2, 3).
• Answer: (2, 3)

[Medium] Rate of Change — Derivative Application

• EN: The position of a particle is s(t) = t² + 3t. What is its velocity at t = 4 seconds?
• FR: La position d'une particule est s(t) = t² + 3t. Quelle est sa vitesse à t = 4 secondes?
• Choices: A) 9 m/s B) 11 m/s C) 13 m/s D) 16 m/s
• Hint: Velocity = derivative of position. Use the power rule, then substitute t (e.g., s(t) = t² + 2t: v(t) = 2t + 2; at t = 3: v = 8).
• Steps:
  • s(t) = t² + 3t; v(t) = s'(t) = 2t + 3.
  • At t = 4: v = 2(4) + 3 = 8 + 3 = 11.
  • Velocity is 11 m/s.
• Answer: 11 m/s

[Medium] Polynomial Functions — End Behaviour

• EN: For f(x) = –2x⁴ + x² – 3, what happens to f(x) as x → +∞?
• FR: Pour f(x) = –2x⁴ + x² – 3, que se passe-t-il avec f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → 0 C) f(x) → –∞ D) f(x) → –3
• Hint: The leading term determines end behaviour — negative leading coefficient with even degree means both ends go down (e.g., –x² → –∞ as x → ±∞).
• Steps:
  • Leading term: –2x⁴ (even degree, negative coefficient).
  • As x → +∞, –2x⁴ → –∞.
  • So f(x) → –∞.
• Answer: f(x) → –∞

[Hard] Normal Distribution

• EN: Test scores are normally distributed with mean 70 and standard deviation 10. What percentage of students score between 60 and 80?
• FR: Les scores d'un test sont distribués normalement avec une moyenne de 70 et un écart-type de 10. Quel pourcentage des élèves obtient entre 60 et 80?
• Choices: A) 50% B) 64% C) 68% D) 75%
• Hint: In a normal distribution, about 68% of data falls within one standard deviation of the mean (e.g., mean = 50, SD = 5: between 45 and 55 ≈ 68%).
• Steps:
  • 60 is one SD below the mean (70 – 10 = 60).
  • 80 is one SD above the mean (70 + 10 = 80).
  • By the 68% empirical rule, approximately 68% of students score in this range.
• Answer: 68%

[Hard] Derivative — Optimization

• EN: A farmer has 40 m of fence to enclose a rectangular pen against a barn wall (one side does not need fence). What length of the pen maximizes the area?
• FR: Un fermier a 40 m de clôture pour enfermer un enclos rectangulaire contre un mur de grange (un côté n'a pas besoin de clôture). Quelle longueur de l'enclos maximise l'aire?
• Choices: A) 5 m B) 10 m C) 15 m D) 20 m
• Hint: Set up the constraint (fence = 2w + l = 40), write area A = lw, substitute, differentiate, and set equal to zero (e.g., with 24 m: w = 6, l = 12, A = 72 m²).
• Steps:
  • Let l = length (parallel to barn), w = width. Fence: 2w + l = 40, so l = 40 – 2w.
  • Area A = l × w = (40 – 2w)w = 40w – 2w².
  • dA/dw = 40 – 4w = 0 → w = 10; l = 40 – 20 = 20 m.
• Answer: 20 m