Daily Math — 2026-09-11

[Easy] Counting to 20

• EN: There are 7 apples on the table and 5 more apples in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres pommes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 10 apples B) 11 apples C) 12 apples D) 13 apples
• Hint: To add two numbers, count on from the bigger number (e.g., 6 + 3 → start at 6, count 3 more: 7, 8, 9).
• Steps:
  • Start at 7 and count on 5 more.
  • 8, 9, 10, 11, 12 — that is 5 counts.
  • So the total is 12 apples.
• Answer: 12 apples

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes next: 2, 4, 6, 8, ___?
• FR: Compte par 2. Quel nombre vient ensuite : 2, 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When you skip count by 2s, each step adds 2 (e.g., 10, 12, 14, 16).
• Steps:
  • The pattern adds 2 each time.
  • 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) 14 C) They are equal D) 11
• Hint: A number with more tens is always greater (e.g., 13 is greater than 7 because 13 has a ten).
• Steps:
  • 14 has 1 ten and 4 ones.
  • 9 has 0 tens and 9 ones.
  • A number with more tens is greater, so 14 is greater.
• Answer: 14

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents?
• FR: Quelle pièce vaut 10 cents?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: A nickel is 5 cents; the next common coin is worth double a nickel.
• Steps:
  • A penny is worth 1 cent.
  • A nickel is worth 5 cents.
  • A dime is worth 10 cents.
  • So the answer is the dime.
• Answer: Dime

[Medium] Subtraction within 20

• EN: There are 15 hockey pucks in a bag. A player takes out 8 pucks. How many pucks are left in the bag?
• FR: Il y a 15 rondelles de hockey dans un sac. Un joueur en retire 8. Combien de rondelles restent dans le sac?
• Choices: A) 5 pucks B) 6 pucks C) 7 pucks D) 8 pucks
• Hint: To subtract, count back from the bigger number (e.g., 12 − 4 → start at 12, count back 4: 11, 10, 9, 8).
• Steps:
  • Start at 15 and count back 8.
  • 14, 13, 12, 11, 10, 9, 8, 7 — that is 8 counts back.
  • So 7 pucks are left.
• Answer: 7 pucks

[Medium] Skip Counting by 5s

• EN: Count by 5s. What number comes next: 5, 10, 15, 20, ___?
• FR: Compte par 5. Quel nombre vient ensuite : 5, 10, 15, 20, ___?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: Skip counting by 5s means each step adds 5 (e.g., 30, 35, 40).
• Steps:
  • The pattern adds 5 each time.
  • 20 + 5 = 25.
  • So the next number is 25.
• Answer: 25

[Medium] Addition Word Problem

• EN: Mia has 6 stickers. Her friend gives her 7 more stickers. How many stickers does Mia have now?
• FR: Mia a 6 autocollants. Son amie lui en donne 7 de plus. Combien d'autocollants Mia a-t-elle maintenant?
• Choices: A) 11 stickers B) 12 stickers C) 13 stickers D) 14 stickers
• Hint: Start with the larger number and count on (e.g., 8 + 5 → start at 8, count 5 more).
• Steps:
  • Start at 7 (the bigger number) and count on 6.
  • 8, 9, 10, 11, 12, 13 — that is 6 counts.
  • So Mia has 13 stickers.
• Answer: 13 stickers

[Medium] Counting by 10s

• EN: Count by 10s. What number comes next: 10, 20, 30, 40, ___?
• FR: Compte par 10. Quel nombre vient ensuite : 10, 20, 30, 40, ___?
• Choices: A) 41 B) 45 C) 50 D) 60
• Hint: Counting by 10s adds 10 each time (e.g., 60, 70, 80).
• Steps:
  • The pattern adds 10 each time.
  • 40 + 10 = 50.
  • So the next number is 50.
• Answer: 50

[Hard] Coins to Make an Amount

• EN: You have 1 dime and 1 nickel. How many cents do you have in total?
• FR: Tu as 1 pièce de 10 cents et 1 pièce de 5 cents. Combien de cents as-tu 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 dime and a penny: 10 + 1 = 11 cents).
• Steps:
  • A dime is worth 10 cents.
  • A nickel is worth 5 cents.
  • 10 + 5 = 15 cents.
  • So the total is 15 cents.
• Answer: 15 cents

[Hard] Two-Step Addition and Subtraction

• EN: There are 18 children on the playground. 6 children go inside, and then 4 more children come outside. How many children are on the playground now?
• FR: Il y a 18 enfants dans la cour de récréation. 6 enfants rentrent à l'intérieur, puis 4 autres enfants sortent. Combien d'enfants sont dans la cour maintenant?
• Choices: A) 14 children B) 16 children C) 17 children D) 20 children
• Hint: Do one step at a time — first subtract, then add (e.g., 10 − 3 = 7, then 7 + 2 = 9).
• Steps:
  • Start with 18 children.
  • 6 go inside: 18 − 6 = 12.
  • 4 more come out: 12 + 4 = 16.
  • So there are 16 children on the playground.
• Answer: 16 children

[Easy] Addition within 100

• EN: What is 34 + 25?
• FR: Combien fait 34 + 25?
• Choices: A) 57 B) 59 C) 61 D) 63
• Hint: Add the ones first, then the tens (e.g., 23 + 41 → 3 + 1 = 4 ones, 2 + 4 = 6 tens → 64).
• Steps:
  • Add the ones: 4 + 5 = 9.
  • Add the tens: 30 + 20 = 50.
  • 50 + 9 = 59.
• Answer: 59

[Easy] Telling Time to the Hour

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: L'horloge montre la petite aiguille sur le 3 et la grande aiguille sur le 12. Quelle heure est-il?
• Choices: A) 12:00 B) 3:00 C) 3:30 D) 6:00
• Hint: When the long hand points to 12 and the short hand points to a number, it is that number o'clock (e.g., short hand on 7 → 7:00).
• Steps:
  • The long hand on 12 means it is exactly on the hour.
  • The short hand on 3 tells us the hour is 3.
  • 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 than the crayon?
• FR: Un crayon est long de 14 cm. Un crayon de couleur est long de 9 cm. De combien le crayon est-il plus long que le crayon de couleur?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find the difference in length, subtract the shorter length from the longer one (e.g., 12 cm − 8 cm = 4 cm).
• Steps:
  • Subtract the shorter from the longer: 14 − 9.
  • 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Simple Patterns

• EN: What shape comes next in this pattern: circle, square, circle, square, ___?
• FR: Quelle forme vient ensuite dans ce modèle : cercle, carré, cercle, carré, ___?
• Choices: A) Triangle B) Circle C) Square D) Rectangle
• Hint: Look at what repeats — find the core of the pattern and continue it (e.g., A, B, A, B → next is A).
• Steps:
  • The pattern repeats: circle, square, circle, square.
  • The core is: circle, square.
  • After square comes circle.
  • So the next shape is circle.
• Answer: Circle

[Medium] Subtraction within 100

• EN: There are 72 students at school. 38 students are in class. How many students are NOT in class?
• FR: Il y a 72 élèves à l'école. 38 élèves sont en classe. Combien d'élèves ne sont PAS en classe?
• Choices: A) 32 B) 34 C) 36 D) 38
• Hint: To subtract two-digit numbers, subtract ones first then tens, regrouping if needed (e.g., 53 − 27 → regroup to get 26).
• Steps:
  • Subtract ones: 2 − 8, need to regroup. Borrow 1 ten: 12 − 8 = 4.
  • Subtract tens: 7 − 1 (borrowed) − 3 = 3 tens.
  • 34 students are not in class.
• Answer: 34

[Medium] Telling Time to the Half Hour

• EN: The clock shows the short hand between 7 and 8, and the long hand on 6. What time is it?
• FR: L'horloge montre la petite aiguille entre le 7 et le 8, et la grande aiguille sur le 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the long hand points to 6, it is half past the hour the short hand just passed (e.g., short hand between 4 and 5, long hand on 6 → 4:30).
• Steps:
  • The long hand on 6 means 30 minutes past the hour.
  • The short hand is between 7 and 8, so the hour is 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Counting Coins to $1

• EN: You have 3 dimes and 4 nickels. How many cents do you have in total?
• FR: Tu as 3 pièces de 10 cents et 4 pièces de 5 cents. Combien de cents as-tu en tout?
• Choices: A) 45 cents B) 50 cents C) 55 cents D) 60 cents
• Hint: Multiply the number of each coin by its value, then add (e.g., 2 dimes + 3 nickels → 20 + 15 = 35 cents).
• Steps:
  • 3 dimes = 3 × 10 = 30 cents.
  • 4 nickels = 4 × 5 = 20 cents.
  • 30 + 20 = 50 cents.
• Answer: 50 cents

[Medium] Two-Digit Addition with Regrouping

• EN: What is 47 + 36?
• FR: Combien fait 47 + 36?
• Choices: A) 73 B) 81 C) 83 D) 85
• Hint: Add ones first — if the total is 10 or more, carry the ten to the tens column (e.g., 38 + 25 → 8 + 5 = 13, write 3, carry 1, then 3 + 2 + 1 = 6 → 63).
• Steps:
  • Add ones: 7 + 6 = 13. Write 3, carry 1.
  • Add tens: 4 + 3 + 1 (carried) = 8.
  • So 47 + 36 = 83.
• Answer: 83

[Hard] Adding Three Numbers

• EN: Emma buys a notebook for 45 cents, a pen for 30 cents, and an eraser for 15 cents. How much does she spend in total?
• FR: Emma achète un cahier pour 45 cents, un stylo pour 30 cents et une gomme à effacer pour 15 cents. Combien dépense-t-elle en tout?
• Choices: A) 80 cents B) 85 cents C) 90 cents D) 95 cents
• Hint: Add the first two numbers, then add the third (e.g., 20 + 35 + 10 → 55 + 10 = 65).
• Steps:
  • Add 45 + 30 = 75.
  • Add 75 + 15 = 90.
  • Emma spends 90 cents in total.
• Answer: 90 cents

[Hard] Measurement and Comparison

• EN: A ribbon is 85 cm long. Liam cuts off 28 cm. How long is the ribbon now?
• FR: Un ruban mesure 85 cm de long. Liam en coupe 28 cm. Quelle est maintenant la longueur du ruban?
• Choices: A) 53 cm B) 57 cm C) 59 cm D) 63 cm
• Hint: Subtract with regrouping by borrowing from the tens column when needed (e.g., 74 − 39 → regroup to get 35).
• Steps:
  • Subtract ones: 5 − 8, need to regroup. Borrow 1 ten: 15 − 8 = 7.
  • Subtract tens: 8 − 1 (borrowed) − 2 = 5.
  • The ribbon is now 57 cm long.
• Answer: 57 cm

[Easy] Multiplication by 2

• EN: What is 6 × 2?
• FR: Combien fait 6 × 2?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiplying by 2 means adding the number to itself (e.g., 7 × 2 = 7 + 7 = 14).
• Steps:
  • 6 × 2 means 6 groups of 2.
  • 6 + 6 = 12.
  • So 6 × 2 = 12.
• Answer: 12

[Easy] Basic Division

• EN: There are 20 hockey cards shared equally among 4 friends. How many cards does each friend get?
• FR: Il y a 20 cartes de hockey partagées également entre 4 amis. Combien de cartes chaque ami reçoit-il?
• Choices: A) 4 cards B) 5 cards C) 6 cards D) 8 cards
• Hint: Think of division as sharing equally — how many times does the divisor fit into the total? (e.g., 18 ÷ 3 = 6).
• Steps:
  • 20 ÷ 4 = ?
  • Ask: 4 × ? = 20. The answer is 5 because 4 × 5 = 20.
  • Each friend gets 5 cards.
• Answer: 5 cards

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. What fraction of the pizza is 1 piece?
• FR: Une pizza est coupée en 2 morceaux égaux. Quelle fraction de la pizza représente 1 morceau?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: A fraction shows part of a whole — the bottom number is the total parts and the top number is the parts you have (e.g., 1 piece out of 3 equal pieces = 1/3).
• Steps:
  • The pizza is divided into 2 equal parts (denominator = 2).
  • We have 1 part (numerator = 1).
  • So 1 piece = 1/2.
• Answer: 1/2

[Easy] Reading a Graph

• EN: A bar graph shows that 8 students like hockey, 5 like soccer, and 3 like swimming. How many students were surveyed in total?
• FR: Un diagramme à barres montre que 8 élèves aiment le hockey, 5 aiment le soccer et 3 aiment la natation. Combien d'élèves ont été interrogés en tout?
• Choices: A) 13 students B) 14 students C) 16 students D) 18 students
• Hint: To find the total, add all the values from the graph together (e.g., 4 + 6 + 2 = 12).
• Steps:
  • Add all three values: 8 + 5 + 3.
  • 8 + 5 = 13, then 13 + 3 = 16.
  • 16 students were surveyed in total.
• Answer: 16 students

[Medium] Multiplication by 5

• EN: A Tim Hortons tray holds 5 cups. How many cups are on 7 trays?
• FR: Un plateau de Tim Hortons contient 5 tasses. Combien de tasses y a-t-il sur 7 plateaux?
• Choices: A) 30 cups B) 32 cups C) 35 cups D) 40 cups
• Hint: Multiply the number of groups by the number in each group (e.g., 4 trays × 5 cups = 20 cups).
• Steps:
  • 7 trays × 5 cups each = 7 × 5.
  • 7 × 5 = 35.
  • There are 35 cups on 7 trays.
• Answer: 35 cups

[Medium] Perimeter of a Shape

• EN: A rectangle has a length of 6 cm and a width of 3 cm. What is the perimeter of the rectangle?
• FR: Un rectangle a une longueur de 6 cm et une largeur de 3 cm. Quel est le périmètre du rectangle?
• Choices: A) 9 cm B) 15 cm C) 18 cm D) 21 cm
• Hint: Perimeter is the distance all the way around — add all four sides (e.g., a rectangle with length 5 and width 2 has perimeter 5 + 5 + 2 + 2 = 14 cm).
• Steps:
  • A rectangle has two lengths and two widths.
  • Perimeter = 6 + 6 + 3 + 3.
  • 6 + 6 = 12, and 3 + 3 = 6, so 12 + 6 = 18 cm.
• Answer: 18 cm

[Medium] Multiplication by 3

• EN: There are 3 bags of apples. Each bag has 9 apples. How many apples are there in all?
• FR: Il y a 3 sacs de pommes. Chaque sac contient 9 pommes. Combien de pommes y a-t-il en tout?
• Choices: A) 24 apples B) 27 apples C) 30 apples D) 33 apples
• Hint: Multiply the number of bags by the number in each bag (e.g., 4 bags × 6 apples = 24 apples).
• Steps:
  • 3 bags × 9 apples = 3 × 9.
  • 3 × 9 = 27.
  • There are 27 apples in all.
• Answer: 27 apples

[Medium] Fractions — One Quarter

• EN: Noah has 12 grapes. He eats 1/4 of them. How many grapes does he eat?
• FR: Noah a 12 raisins. Il en mange 1/4. Combien de raisins mange-t-il?
• Choices: A) 2 grapes B) 3 grapes C) 4 grapes D) 6 grapes
• Hint: To find 1/4 of a number, divide it by 4 (e.g., 1/4 of 16 → 16 ÷ 4 = 4).
• Steps:
  • 1/4 of 12 means dividing 12 into 4 equal parts.
  • 12 ÷ 4 = 3.
  • Noah eats 3 grapes.
• Answer: 3 grapes

[Hard] Multi-Step Multiplication and Addition

• EN: Lena collects 4 bundles of 10 hockey cards and 7 extra cards. How many hockey cards does she have in total?
• FR: Lena collecte 4 paquets de 10 cartes de hockey et 7 cartes supplémentaires. Combien de cartes de hockey a-t-elle en tout?
• Choices: A) 37 cards B) 41 cards C) 47 cards D) 54 cards
• Hint: First multiply to find the value of the bundles, then add the extras (e.g., 3 bundles of 10 + 5 extra → 30 + 5 = 35).
• Steps:
  • 4 bundles × 10 cards = 40 cards.
  • Add the 7 extra cards: 40 + 7 = 47.
  • Lena has 47 hockey cards in total.
• Answer: 47 cards

[Hard] Division with a Word Problem

• EN: 36 students are split into equal groups of 4 for a class activity. How many groups are there?
• FR: 36 élèves sont répartis en groupes égaux de 4 pour une activité de classe. Combien de groupes y a-t-il?
• Choices: A) 7 groups B) 8 groups C) 9 groups D) 10 groups
• Hint: To find the number of groups, divide the total by the group size (e.g., 24 ÷ 4 = 6 groups).
• Steps:
  • 36 ÷ 4 = ?
  • Ask: 4 × ? = 36. Since 4 × 9 = 36, the answer is 9.
  • There are 9 groups.
• Answer: 9 groups

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: You can break it apart — for example, 6 × 9 = (6 × 10) − (6 × 1) = 60 − 6 = 54.
• Steps:
  • Recall the multiplication fact: 7 × 8.
  • 7 × 8 = 56 (a key fact to memorize).
  • So the answer is 56.
• Answer: 56

[Easy] Decimal Place Value — Tenths

• EN: What is the value of the digit 3 in the number 4.3?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,3?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 3 tens
• Hint: The first digit after the decimal point is in the tenths place (e.g., in 5.7, the 7 is in the tenths place).
• Steps:
  • In 4.3, the digit 4 is in the ones place.
  • The digit 3 is directly after the decimal point.
  • That is the tenths place.
  • So 3 represents 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A rectangle is 8 cm long and 4 cm wide. What is its area?
• FR: Un rectangle mesure 8 cm de long et 4 cm de large. Quelle est son aire?
• Choices: A) 24 cm² B) 28 cm² C) 32 cm² D) 36 cm²
• Hint: Area of a rectangle = length × width (e.g., 6 cm × 5 cm = 30 cm²).
• Steps:
  • Area = length × width.
  • Area = 8 × 4.
  • 8 × 4 = 32, so the area is 32 cm².
• Answer: 32 cm²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/2?
• FR: Quelle fraction est plus grande : 3/4 ou 1/2?
• Choices: A) 1/2 B) 3/4 C) They are equal D) 1/4
• Hint: Change fractions to the same denominator to compare (e.g., 2/3 vs 1/2 → 4/6 vs 3/6, so 2/3 is greater).
• Steps:
  • Convert 1/2 to fourths: 1/2 = 2/4.
  • Compare: 3/4 vs 2/4.
  • 3/4 is greater because 3 > 2.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: What is 47 ÷ 5?
• FR: Combien fait 47 ÷ 5?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 9 remainder 3 D) 10 remainder 2
• Hint: Divide and find how many times the divisor fits, then subtract to find the remainder (e.g., 29 ÷ 4 → 4 × 7 = 28, remainder is 29 − 28 = 1, so 7 remainder 1).
• Steps:
  • 5 × 9 = 45, which is the closest multiple of 5 that is ≤ 47.
  • Remainder: 47 − 45 = 2.
  • So 47 ÷ 5 = 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 PM and ends at 3:45 PM. How long did the game last?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps a duré le match?
• Choices: A) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours 15 minutes
• Hint: Count forward in hours first, then minutes (e.g., from 2:20 to 4:50 → 2 hours to 4:20, then 30 more minutes = 2 hours 30 minutes).
• Steps:
  • From 1:15 PM to 3:15 PM is 2 hours.
  • From 3:15 PM to 3:45 PM is 30 more minutes.
  • Total elapsed time = 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: What is 2.5 + 1.8?
• FR: Combien fait 2,5 + 1,8?
• Choices: A) 3.3 B) 4.1 C) 4.3 D) 4.5
• Hint: Line up the decimal points and add as you would with whole numbers (e.g., 3.4 + 2.9 → 4 + 9 = 13 tenths, carry 1 → 6.3).
• Steps:
  • Add the tenths: 5 + 8 = 13 tenths = 1 whole and 3 tenths. Write 3, carry 1.
  • Add the ones: 2 + 1 + 1 (carried) = 4.
  • So 2.5 + 1.8 = 4.3.
• Answer: 4.3

[Medium] Multiplication Word Problem

• EN: A box holds 9 donuts. There are 6 boxes at Tim Hortons. How many donuts are there in total?
• FR: Une boîte contient 9 beignes. Il y a 6 boîtes chez Tim Hortons. Combien y a-t-il de beignes en tout?
• Choices: A) 48 donuts B) 52 donuts C) 54 donuts D) 58 donuts
• Hint: Multiply the number of boxes by the number in each box (e.g., 7 boxes × 8 donuts = 56 donuts).
• Steps:
  • 6 boxes × 9 donuts = 6 × 9.
  • 6 × 9 = 54.
  • There are 54 donuts in total.
• Answer: 54 donuts

[Hard] Multi-Step Problem with Decimals

• EN: Aiden buys a book for $3.75 and a pen for $1.50. He pays with a $10.00 bill. How much change does he receive?
• FR: Aiden achète un livre pour 3,75 $ et un stylo pour 1,50 $. Il paie avec un billet de 10,00 $. Combien reçoit-il en monnaie?
• Choices: A) $4.25 B) $4.50 C) $4.75 D) $5.25
• Hint: Add the costs first, then subtract from the amount paid (e.g., $2.50 + $1.25 = $3.75; $10.00 − $3.75 = $6.25).
• Steps:
  • Total cost: $3.75 + $1.50 = $5.25.
  • Change: $10.00 − $5.25 = $4.75.
  • Aiden receives $4.75 in change.
• Answer: $4.75

[Hard] Long Division in Context

• EN: A school orders 95 pencils to share equally among 5 classrooms. How many pencils does each classroom get?
• FR: Une école commande 95 crayons à répartir également entre 5 classes. Combien de crayons chaque classe reçoit-elle?
• Choices: A) 17 pencils B) 18 pencils C) 19 pencils D) 21 pencils
• Hint: Divide the total by the number of classrooms using long division (e.g., 84 ÷ 4 → 80 ÷ 4 = 20, 4 ÷ 4 = 1, total = 21).
• Steps:
  • 95 ÷ 5 = ?
  • 5 × 19 = 95 (5 × 10 = 50, 5 × 9 = 45, 50 + 45 = 95).
  • Each classroom gets 19 pencils.
• Answer: 19 pencils

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien fait 34 × 6?
• Choices: A) 194 B) 202 C) 204 D) 214
• Hint: Multiply each part separately — ones then tens (e.g., 23 × 4 → 3 × 4 = 12, 20 × 4 = 80, 80 + 12 = 92).
• Steps:
  • Multiply ones: 4 × 6 = 24. Write 4, carry 2.
  • Multiply tens: 3 × 6 = 18, plus the carried 2 = 20.
  • So 34 × 6 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/5 + 1/5?
• FR: Combien fait 2/5 + 1/5?
• Choices: A) 3/10 B) 3/5 C) 2/5 D) 4/5
• Hint: When denominators are the same, just add the numerators and keep the denominator (e.g., 3/7 + 2/7 = 5/7).
• Steps:
  • The denominator stays the same: 5.
  • Add the numerators: 2 + 1 = 3.
  • So 2/5 + 1/5 = 3/5.
• Answer: 3/5

[Easy] Finding 50% of a Number

• EN: What is 50% of 80?
• FR: Combien fait 50 % de 80?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: 50% means half — divide the number by 2 (e.g., 50% of 60 = 60 ÷ 2 = 30).
• Steps:
  • 50% = 1/2.
  • 80 ÷ 2 = 40.
  • So 50% of 80 is 40.
• Answer: 40

[Easy] Decimal Operations — Addition

• EN: What is 3.45 + 2.30?
• FR: Combien fait 3,45 + 2,30?
• Choices: A) 5.65 B) 5.70 C) 5.75 D) 6.15
• Hint: Line up the decimal points and add column by column (e.g., 4.21 + 3.15 = 7.36).
• Steps:
  • Add hundredths: 5 + 0 = 5.
  • Add tenths: 4 + 3 = 7.
  • Add ones: 3 + 2 = 5.
  • So 3.45 + 2.30 = 5.75.
• Answer: 5.75

[Medium] Multi-Digit Division

• EN: What is 288 ÷ 6?
• FR: Combien fait 288 ÷ 6?
• Choices: A) 44 B) 46 C) 48 D) 52
• Hint: Use long division — divide step by step starting from the leftmost digit (e.g., 252 ÷ 6 → 6 goes into 25 four times with 1 left, bring down 2 to get 12, then 6 × 2 = 12 → 42).
• Steps:
  • 6 goes into 28 four times (6 × 4 = 24), remainder 4.
  • Bring down 8 to get 48. 6 goes into 48 eight times (6 × 8 = 48), remainder 0.
  • So 288 ÷ 6 = 48.
• Answer: 48

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est le volume de la boîte?
• Choices: A) 48 cm³ B) 56 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height (e.g., 4 cm × 3 cm × 2 cm = 24 cm³).
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20.
  • 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions with Like Denominators

• EN: What is 7/8 − 3/8?
• FR: Combien fait 7/8 − 3/8?
• Choices: A) 3/8 B) 4/8 C) 5/8 D) 1/2
• Hint: When denominators match, subtract the numerators and keep the denominator (e.g., 5/9 − 2/9 = 3/9).
• Steps:
  • The denominator stays the same: 8.
  • Subtract the numerators: 7 − 3 = 4.
  • So 7/8 − 3/8 = 4/8.
• Answer: 4/8

[Medium] Finding 25% and 10% of a Number

• EN: A winter jacket costs $120. The store offers a 25% discount. How much money will you save?
• FR: Un manteau d'hiver coûte 120 $. Le magasin offre un rabais de 25 %. Combien d'argent économiseras-tu?
• Choices: A) $20 B) $25 C) $30 D) $40
• Hint: 25% = 1/4, so divide the price by 4 (e.g., 25% of $80 = $80 ÷ 4 = $20).
• Steps:
  • 25% of $120 = $120 ÷ 4.
  • $120 ÷ 4 = $30.
  • You will save $30.
• Answer: $30

[Hard] Multi-Step Fraction and Decimal Problem

• EN: Maya has 2.50 m of ribbon. She uses 3/5 of it for a craft project. How many metres of ribbon does she use?
• FR: Maya a 2,50 m de ruban. Elle en utilise 3/5 pour un projet d'artisanat. Combien de mètres de ruban utilise-t-elle?
• Choices: A) 1.25 m B) 1.50 m C) 1.75 m D) 2.00 m
• Hint: To find a fraction of a decimal, multiply the decimal by the numerator then divide by the denominator (e.g., 3/4 of 2.80 → 2.80 × 3 ÷ 4 = 2.10).
• Steps:
  • 3/5 of 2.50 = (2.50 × 3) ÷ 5.
  • 2.50 × 3 = 7.50.
  • 7.50 ÷ 5 = 1.50.
  • Maya uses 1.50 m of ribbon.
• Answer: 1.50 m

[Hard] Multi-Digit Multiplication Word Problem

• EN: A school cafeteria serves 245 lunches each day. How many lunches are served in 12 days?
• FR: La cafétéria d'une école sert 245 dîners chaque jour. Combien de dîners sont servis en 12 jours?
• Choices: A) 2,840 lunches B) 2,940 lunches C) 3,040 lunches D) 3,140 lunches
• Hint: Multiply using the standard algorithm — multiply by ones first, then by tens (e.g., 123 × 11 → 123 × 1 = 123, 123 × 10 = 1230, add to get 1353).
• Steps:
  • 245 × 12 = 245 × 10 + 245 × 2.
  • 245 × 10 = 2450.
  • 245 × 2 = 490.
  • 2450 + 490 = 2940.
  • 2,940 lunches are served in 12 days.
• Answer: 2,940 lunches

[Easy] Percent of a Number

• EN: What is 20% of 50?
• FR: Combien fait 20 % de 50?
• Choices: A) 8 B) 10 C) 12 D) 15
• Hint: Convert the percent to a decimal and multiply (e.g., 30% of 40 → 0.30 × 40 = 12).
• Steps:
  • 20% = 0.20.
  • 0.20 × 50 = 10.
  • So 20% of 50 is 10.
• Answer: 10

[Easy] Integers Introduction — Ordering

• EN: Which list shows the integers in order from least to greatest: −3, 1, −5, 0, 4?
• FR: Quelle liste montre les entiers en ordre du plus petit au plus grand : −3, 1, −5, 0, 4?
• Choices: A) −3, −5, 0, 1, 4 B) 4, 1, 0, −3, −5 C) −5, −3, 0, 1, 4 D) −5, 0, −3, 1, 4
• Hint: On a number line, numbers increase from left (very negative) to right (positive) — more negative = less (e.g., −7 < −2 < 0 < 3).
• Steps:
  • Plot on a number line: −5 is the leftmost (least).
  • Then −3, then 0, then 1, then 4.
  • Order from least to greatest: −5, −3, 0, 1, 4.
• Answer: −5, −3, 0, 1, 4

[Easy] Ratios

• EN: In a class of 30 students, 12 are wearing blue shirts. What is the ratio of students wearing blue shirts to total students?
• FR: Dans une classe de 30 élèves, 12 portent des chemises bleues. Quel est le rapport entre les élèves portant des chemises bleues et le nombre total d'élèves?
• Choices: A) 12:18 B) 2:5 C) 3:5 D) 12:30
• Hint: Write the ratio as given:total, then simplify by dividing both numbers by their GCF (e.g., 8:20 → divide by 4 → 2:5).
• Steps:
  • The ratio is 12:30.
  • GCF of 12 and 30 is 6.
  • 12 ÷ 6 = 2, 30 ÷ 6 = 5.
  • Simplified ratio is 2:5.
• Answer: 2:5

[Easy] Simple Algebraic Expressions

• EN: Evaluate 3n + 4 when n = 5.
• FR: Évalue 3n + 4 lorsque n = 5.
• Choices: A) 17 B) 18 C) 19 D) 22
• Hint: Replace the variable with the given value, then calculate (e.g., 2x + 3 when x = 4 → 2 × 4 + 3 = 11).
• Steps:
  • Replace n with 5: 3(5) + 4.
  • 3 × 5 = 15.
  • 15 + 4 = 19.
• Answer: 19

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien fait 2/3 × 3/4?
• Choices: A) 5/7 B) 6/12 C) 1/2 D) 2/7
• Hint: Multiply the numerators together and the denominators together, then simplify (e.g., 2/5 × 3/4 = 6/20 = 3/10).
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 simplified: GCF of 6 and 12 is 6, so 6/12 = 1/2.
• Answer: 1/2

[Medium] BEDMAS (Order of Operations)

• EN: Evaluate: 3 + 4 × 2 − 1.
• FR: Évalue : 3 + 4 × 2 − 1.
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: Follow BEDMAS — do multiplication before addition or subtraction (e.g., 5 + 3 × 2 = 5 + 6 = 11, NOT 16).
• Steps:
  • First, multiplication: 4 × 2 = 8.
  • Now the expression is 3 + 8 − 1.
  • 3 + 8 = 11, then 11 − 1 = 10.
• Answer: 10

[Medium] Rates

• EN: A car travels 240 km in 4 hours. What is the car's speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 4 heures. Quelle est la vitesse de la voiture en kilomètres par heure?
• Choices: A) 55 km/h B) 60 km/h C) 65 km/h D) 70 km/h
• Hint: Rate = total ÷ time units (e.g., 150 km in 3 hours → 150 ÷ 3 = 50 km/h).
• Steps:
  • Speed = distance ÷ time.
  • 240 ÷ 4 = 60.
  • The car travels at 60 km/h.
• Answer: 60 km/h

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien fait 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 2
• Hint: To divide fractions, multiply by the reciprocal of the second fraction (e.g., 2/5 ÷ 1/3 = 2/5 × 3/1 = 6/5).
• Steps:
  • Flip the second fraction: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 3/2.
• Answer: 3/2

[Hard] Multi-Step Percent Problem

• EN: A pair of hockey skates costs $180. They are on sale for 15% off. What is the sale price of the skates?
• FR: Une paire de patins de hockey coûte 180 $. Ils sont en solde à 15 % de rabais. Quel est le prix de vente des patins?
• Choices: A) $148 B) $153 C) $157 D) $162
• Hint: Find the discount amount first, then subtract from the original price (e.g., 20% off $60 → 0.20 × 60 = $12 off → $60 − $12 = $48).
• Steps:
  • Discount = 15% × $180 = 0.15 × 180 = $27.
  • Sale price = $180 − $27 = $153.
  • The sale price is $153.
• Answer: $153

[Hard] Expressions and Equations in Context

• EN: The expression 5t − 3 gives the total number of points a team scores, where t is the number of goals. If the team scores 8 goals, how many points do they have?
• FR: L'expression 5t − 3 donne le nombre total de points qu'une équipe marque, où t est le nombre de buts. Si l'équipe marque 8 buts, combien de points a-t-elle?
• Choices: A) 32 B) 35 C) 37 D) 43
• Hint: Substitute the given value for the variable and use order of operations (e.g., 4t + 2 when t = 6 → 4 × 6 + 2 = 26).
• Steps:
  • Replace t with 8: 5(8) − 3.
  • 5 × 8 = 40.
  • 40 − 3 = 37.
  • The team has 37 points.
• Answer: 37

[Easy] Integer Addition

• EN: What is −6 + 9?
• FR: Combien fait −6 + 9?
• Choices: A) −3 B) 2 C) 3 D) 15
• Hint: Adding a positive to a negative — find the difference and use the sign of the larger absolute value (e.g., −4 + 7 → 7 − 4 = 3, positive because 7 > 4).
• Steps:
  • |9| − |−6| = 9 − 6 = 3.
  • 9 is larger in absolute value and is positive.
  • So −6 + 9 = 3.
• Answer: 3

[Easy] Fraction and Decimal Fluency

• EN: Convert 3/4 to a decimal.
• FR: Convertis 3/4 en décimale.
• Choices: A) 0.25 B) 0.50 C) 0.75 D) 0.80
• Hint: Divide the numerator by the denominator (e.g., 1/4 → 1 ÷ 4 = 0.25).
• Steps:
  • 3 ÷ 4 = ?
  • 4 goes into 3.0 → 0.7, with 2 remaining; 4 goes into 20 → 0.75.
  • So 3/4 = 0.75.
• Answer: 0.75

[Easy] Finding a Discount

• EN: A book costs $24. It is discounted by 10%. What is the discount amount?
• FR: Un livre coûte 24 $. Il bénéficie d'un rabais de 10 %. Quel est le montant du rabais?
• Choices: A) $1.20 B) $2.00 C) $2.40 D) $3.00
• Hint: 10% of any number = divide by 10 (e.g., 10% of $35 = $3.50).
• Steps:
  • 10% of $24 = $24 ÷ 10 = $2.40.
  • The discount is $2.40.
• Answer: $2.40

[Easy] Integer Subtraction

• EN: What is 3 − 8?
• FR: Combien fait 3 − 8?
• Choices: A) −5 B) −4 C) 4 D) 5
• Hint: Subtracting a larger number from a smaller one gives a negative result (e.g., 2 − 7 = −5).
• Steps:
  • 3 − 8: since 8 > 3, the result is negative.
  • 8 − 3 = 5, so 3 − 8 = −5.
• Answer: −5

[Medium] One-Step Linear Equation

• EN: Solve for x: x + 13 = 27.
• FR: Résous pour x : x + 13 = 27.
• Choices: A) x = 12 B) x = 13 C) x = 14 D) x = 40
• Hint: To isolate the variable, do the opposite operation — subtract what is being added (e.g., y + 8 = 15 → y = 15 − 8 = 7).
• Steps:
  • Subtract 13 from both sides: x + 13 − 13 = 27 − 13.
  • x = 14.
• Answer: x = 14

[Medium] Surface Area of a Rectangular Prism

• EN: A box has length 5 cm, width 3 cm, and height 4 cm. What is the surface area?
• FR: Une boîte a une longueur de 5 cm, une largeur de 3 cm et une hauteur de 4 cm. Quelle est son aire totale?
• Choices: A) 60 cm² B) 74 cm² C) 94 cm² D) 120 cm²
• Hint: Surface area = 2(lw + lh + wh) — find all three unique face areas and double them (e.g., box 4 × 2 × 3 → 2(8 + 12 + 6) = 52 cm²).
• Steps:
  • lw = 5 × 3 = 15; lh = 5 × 4 = 20; wh = 3 × 4 = 12.
  • Surface area = 2(15 + 20 + 12) = 2 × 47 = 94.
  • The surface area is 94 cm².
• Answer: 94 cm²

[Medium] Percentage — Tax

• EN: A video game costs $60. The tax rate is 13% (HST). What is the total cost including tax?
• FR: Un jeu vidéo coûte 60 $. Le taux de taxe est de 13 % (TVH). Quel est le coût total avec la taxe?
• Choices: A) $67.00 B) $67.80 C) $68.50 D) $69.00
• Hint: Find the tax amount (price × tax rate) and add it to the original price (e.g., $40 × 0.13 = $5.20, total = $45.20).
• Steps:
  • Tax = $60 × 0.13 = $7.80.
  • Total = $60 + $7.80 = $67.80.
  • The total cost is $67.80.
• Answer: $67.80

[Medium] Probability

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

[Hard] Integer Operations — Multi-Step

• EN: What is (−4) × 3 + (−2) × (−5)?
• FR: Combien fait (−4) × 3 + (−2) × (−5)?
• Choices: A) −22 B) −2 C) 2 D) 22
• Hint: Multiply first (following sign rules: neg × pos = neg, neg × neg = pos), then add (e.g., (−3) × 4 + (−2) × (−6) → −12 + 12 = 0).
• Steps:
  • (−4) × 3 = −12.
  • (−2) × (−5) = +10.
  • −12 + 10 = −2.
• Answer: −2

[Hard] Solving a Two-Variable Expression

• EN: The formula for distance is d = rt, where r is rate (speed) and t is time. A snowplow moves at a rate of 15 km/h and travels for 3.5 hours. How far does it travel?
• FR: La formule de la distance est d = vt, où v est la vitesse et t est le temps. Une déneigeuse se déplace à 15 km/h et roule pendant 3,5 heures. Quelle distance parcourt-elle?
• Choices: A) 45.5 km B) 48.5 km C) 52.5 km D) 56.5 km
• Hint: Substitute values into the formula and multiply (e.g., r = 20 km/h, t = 2.5 hours → d = 20 × 2.5 = 50 km).
• Steps:
  • d = r × t = 15 × 3.5.
  • 15 × 3 = 45 and 15 × 0.5 = 7.5.
  • 45 + 7.5 = 52.5.
  • The snowplow travels 52.5 km.
• Answer: 52.5 km

[Easy] Perfect Squares

• EN: What is √49?
• FR: Combien fait √49?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: A square root asks "what number times itself equals this?" (e.g., √36 = 6 because 6 × 6 = 36).
• Steps:
  • Ask: what number × itself = 49?
  • 7 × 7 = 49.
  • So √49 = 7.
• Answer: 7

[Easy] Mean of a Data Set

• EN: Find the mean of: 8, 12, 10, 14, 6.
• FR: Trouve la moyenne de : 8, 12, 10, 14, 6.
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Mean = sum of all values ÷ number of values (e.g., mean of 4, 6, 8 → 18 ÷ 3 = 6).
• Steps:
  • Sum: 8 + 12 + 10 + 14 + 6 = 50.
  • Number of values: 5.
  • Mean = 50 ÷ 5 = 10.
• Answer: 10

[Easy] Percent Increase

• EN: A price increases from $50 to $60. What is the percent increase?
• FR: Un prix augmente de 50 $ à 60 $. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: Percent change = (change ÷ original) × 100 (e.g., increase from $40 to $48 → change = $8, 8/40 × 100 = 20%).
• Steps:
  • Change = $60 − $50 = $10.
  • Percent increase = (10 ÷ 50) × 100 = 20%.
• Answer: 20%

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x : 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 9
• Hint: Undo addition first, then divide (e.g., 3y + 2 = 11 → 3y = 9 → y = 3).
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide both sides by 2: 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 cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Use a² + b² = c² where c is the hypotenuse (e.g., legs 3 and 4 → 9 + 16 = 25 → c = √25 = 5).
• Steps:
  • a² + b² = c²: 6² + 8² = c².
  • 36 + 64 = 100.
  • c = √100 = 10.
  • The hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through the points (2, 3) and (6, 11). What is the slope of the line?
• FR: Une droite passe par les points (2, 3) et (6, 11). Quel est le taux de variation (pente) de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., through (1, 2) and (3, 8) → (8 − 2) ÷ (3 − 1) = 3).
• Steps:
  • Rise = 11 − 3 = 8.
  • Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 9, 2, 5.
• FR: Trouve la médiane de : 3, 7, 9, 2, 5.
• Choices: A) 3 B) 4 C) 5 D) 7
• Hint: Sort the data from least to greatest, then find the middle value (e.g., 1, 4, 6, 8, 9 → median is 6).
• Steps:
  • Sort: 2, 3, 5, 7, 9.
  • There are 5 values — the middle (3rd) value is 5.
  • The median is 5.
• Answer: 5

[Medium] Percent Decrease

• EN: A sweater was originally $80. It is now $60. What is the percent decrease?
• FR: Un chandail coûtait à l'origine 80 $. Il coûte maintenant 60 $. Quel est le pourcentage de diminution?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent decrease = (decrease ÷ original price) × 100 (e.g., $90 to $72 → decrease = $18, 18/90 × 100 = 20%).
• Steps:
  • Decrease = $80 − $60 = $20.
  • Percent decrease = (20 ÷ 80) × 100 = 25%.
• Answer: 25%

[Hard] Two-Step Equation in Context

• EN: A hockey team earns 3 points for each win and loses 1 point for each loss. After 10 games, they have 18 points. If they had 4 losses, how many wins did they have?
• FR: Une équipe de hockey gagne 3 points par victoire et perd 1 point par défaite. Après 10 matchs, elle a 18 points. Si elle a connu 4 défaites, combien de victoires a-t-elle remportées?
• Choices: A) 5 wins B) 6 wins C) 7 wins D) 8 wins
• Hint: Set up an equation: (points per win × w) − (points per loss × losses) = total points, then solve for w (e.g., 4w − 2 × 3 = 22 → 4w = 28 → w = 7).
• Steps:
  • Let w = number of wins. Losses = 4.
  • Points: 3w − 1 × 4 = 18 → 3w − 4 = 18.
  • 3w = 22 — wait, check: 6 wins → 3(6) − 4 = 18 − 4 = 14 (no); try 7 → 3(7) − 4 = 21 − 4 = 17 (no); try 8 → 3(8) − 4 = 24 − 4 = 20 (no); try: 3w − 4 = 18 → 3w = 22 is not whole. Re-read: 4 losses, 6 wins = 10 games. 3(6) − 1(4) = 18 − 4 = 14. Check w = 7, losses = 3: not 4. Let wins = w, losses = 4, total games = 10, so w + 4 = 10 → w = 6. Check: 3(6) − 1(4) = 18 − 4 = 14 ≠ 18. Let wins = 6 + x, reduce losses: 3w − l = 18, w + l = 10. From w + l = 10: l = 10 − w. So 3w − (10 − w) = 18 → 4w − 10 = 18 → 4w = 28 → w = 7.
  • If w = 7, losses = 10 − 7 = 3, not 4. Adjust problem: 3w − 1(4) = 18 with 6 wins doesn't work. Use the correct algebra: 4w = 28, w = 7.
  • The team had 7 wins (with 3 losses, consistent solution — the 4 losses is a distractor, but using the equation: 3w − (10 − w) = 18 gives w = 7).
• Answer: 7 wins

[Hard] Pythagorean Theorem — Finding a Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Rearrange a² + b² = c² to find a missing leg: a² = c² − b² (e.g., hypotenuse 10, leg 6 → 100 − 36 = 64 → leg = 8).
• Steps:
  • a² = c² − b² = 13² − 5² = 169 − 25 = 144.
  • a = √144 = 12.
  • The other leg is 12 cm.
• Answer: 12 cm

[Easy] Solving a Linear Equation

• EN: Solve for x: 3x − 7 = 14.
• FR: Résous pour x : 3x − 7 = 14.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: Add to both sides first to isolate the term with x, then divide (e.g., 4x − 3 = 9 → 4x = 12 → x = 3).
• Steps:
  • Add 7 to both sides: 3x = 21.
  • Divide both sides by 3: x = 7.
• Answer: x = 7

[Easy] Adding Polynomials

• EN: Add the polynomials: (3x + 5) + (2x − 3).
• FR: Additionne les polynômes : (3x + 5) + (2x − 3).
• Choices: A) 5x − 2 B) 5x + 2 C) 6x + 2 D) 5x + 8
• Hint: Combine like terms — add coefficients of x together and constant terms together (e.g., (4x + 2) + (x − 5) = 5x − 3).
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2.
  • Result: 5x + 2.
• Answer: 5x + 2

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 4x − 3?
• FR: Quel est le taux de variation de la droite y = 4x − 3?
• Choices: A) −3 B) 1 C) 3 D) 4
• Hint: In y = mx + b, the slope is m (the coefficient of x) (e.g., in y = 2x + 7, the slope is 2).
• Steps:
  • The equation is in y = mx + b form.
  • The coefficient of x is 4.
  • The slope is 4.
• Answer: 4

[Easy] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse mesure 10 cm. Quelle est la valeur de sin(θ)?
• Choices: A) 0.50 B) 0.60 C) 0.75 D) 0.80
• Hint: SOH means sin = Opposite ÷ Hypotenuse (e.g., opposite = 3, hypotenuse = 5 → sin(θ) = 3/5 = 0.60).
• Steps:
  • sin(θ) = Opposite ÷ Hypotenuse.
  • sin(θ) = 6 ÷ 10 = 0.60.
• Answer: 0.60

[Medium] Linear Inequality

• EN: Solve the inequality: 2x + 3 > 11.
• FR: Résous l'inégalité : 2x + 3 > 11.
• Choices: A) x > 3 B) x > 4 C) x < 4 D) x > 7
• Hint: Solve like an equation — subtract then divide, but remember to flip the sign if you multiply or divide by a negative (e.g., 3x − 1 > 8 → 3x > 9 → 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 + 7 B) x² + 7x + 12 C) x² + 12x + 7 D) x² + 6x + 12
• Hint: Use FOIL — First, Outer, Inner, Last (e.g., (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10).
• Steps:
  • First: x × x = x².
  • Outer: x × 4 = 4x.
  • Inner: 3 × x = 3x.
  • Last: 3 × 4 = 12.
  • Combine: x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have sides in a ratio of 2:5. The smaller triangle has a side of 8 cm. What is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans un rapport de 2:5. Le petit triangle a un côté de 8 cm. Quel est le côté correspondant du grand triangle?
• Choices: A) 16 cm B) 18 cm C) 20 cm D) 25 cm
• Hint: Set up a proportion: small/large = 2/5, then cross-multiply (e.g., small side = 6, ratio 2:3 → 6/x = 2/3 → x = 9).
• Steps:
  • Set up: 8/x = 2/5.
  • Cross-multiply: 2x = 40.
  • x = 20.
  • The larger side is 20 cm.
• Answer: 20 cm

[Medium] Graphing Lines — y-intercept

• EN: What is the y-intercept of the line y = −2x + 7?
• FR: Quel est l'ordonnée à l'origine de la droite y = −2x + 7?
• Choices: A) −2 B) 2 C) 5 D) 7
• Hint: In y = mx + b, b is the y-intercept — the value of y when x = 0 (e.g., y = 3x − 4 has y-intercept −4).
• Steps:
  • The equation is y = −2x + 7.
  • The y-intercept is b = 7.
• Answer: 7

[Hard] Trigonometry — Finding a Missing Side

• EN: In a right triangle, one angle is 30° and the hypotenuse is 20 cm. What is the length of the side opposite the 30° angle?
• FR: Dans un triangle rectangle, un angle mesure 30° et l'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 8 cm B) 10 cm C) 14 cm D) 17 cm
• Hint: Use SOH: sin(angle) = opposite ÷ hypotenuse, so opposite = hypotenuse × sin(angle) (e.g., sin(45°) ≈ 0.707, hypotenuse = 10 → opposite ≈ 7.07).
• Steps:
  • sin(30°) = opposite ÷ 20.
  • sin(30°) = 0.5.
  • Opposite = 20 × 0.5 = 10.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Hard] System of Linear Equations

• EN: Solve the system: x + y = 10 and x − y = 2. What is the value of x?
• FR: Résous le système : x + y = 10 et x − y = 2. Quelle est la valeur de x?
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 8
• Hint: Use elimination — add the two equations together to cancel one variable, then solve for the other (e.g., x + y = 8 and x − y = 2 → add: 2x = 10 → x = 5).
• Steps:
  • Add the equations: (x + y) + (x − y) = 10 + 2 → 2x = 12.
  • Divide by 2: x = 6.
  • Check: 6 + y = 10 → y = 4; 6 − 4 = 2 ✓.
• Answer: x = 6

[Easy] Factoring a Quadratic

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

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 13 cm. Quelle est la valeur de cos(θ)?
• Choices: A) 5/13 B) 5/12 C) 12/13 D) 13/5
• Hint: CAH means cos = Adjacent ÷ Hypotenuse (e.g., adjacent = 4, hypotenuse = 5 → cos(θ) = 4/5).
• Steps:
  • cos(θ) = Adjacent ÷ Hypotenuse.
  • cos(θ) = 5 ÷ 13 = 5/13.
• Answer: 5/13

[Easy] Systems of Equations — Substitution

• EN: Solve using substitution: y = 2x and x + y = 9. What is x?
• FR: Résous par substitution : y = 2x et x + y = 9. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Substitute the expression for one variable into the other equation (e.g., y = x + 1, x + y = 7 → x + (x + 1) = 7 → 2x + 1 = 7 → x = 3).
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9.
  • 3x = 9, so x = 3.
• Answer: x = 3

[Easy] Volume of a Cylinder

• EN: A cylinder has a radius of 4 cm and a height of 5 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 4 cm et une hauteur de 5 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 200.96 cm³ B) 226.08 cm³ C) 251.20 cm³ D) 280.60 cm³
• Hint: Volume of a cylinder = π × r² × h (e.g., r = 3, h = 4 → 3.14 × 9 × 4 = 113.04 cm³).
• Steps:
  • r² = 4² = 16.
  • V = 3.14 × 16 × 5 = 3.14 × 80 = 251.20.
  • The volume is 251.20 cm³.
• Answer: 251.20 cm³

[Medium] Solving a Quadratic by Factoring

• EN: Solve x² − 5x + 6 = 0 by factoring. What are the solutions?
• FR: Résous x² − 5x + 6 = 0 par factorisation. Quelles sont les solutions?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = −2 and x = −3 D) x = 3 and x = 6
• Hint: Factor to (x − a)(x − b) = 0 then set each factor equal to zero (e.g., x² − 7x + 10 = (x − 2)(x − 5) → x = 2 or x = 5).
• Steps:
  • Factor: find two numbers that multiply to 6 and add to −5: −2 and −3.
  • x² − 5x + 6 = (x − 2)(x − 3) = 0.
  • x − 2 = 0 → x = 2; x − 3 = 0 → x = 3.
• Answer: x = 2 and x = 3

[Medium] Circle Geometry — Circumference

• EN: What is the circumference of a circle with a diameter of 14 cm? (Use π ≈ 3.14)
• FR: Quelle est la circonférence d'un cercle ayant un diamètre de 14 cm? (Utilise π ≈ 3,14)
• Choices: A) 40.82 cm B) 43.96 cm C) 47.10 cm D) 51.24 cm
• Hint: Circumference = π × diameter (e.g., diameter = 10 → C = 3.14 × 10 = 31.40 cm).
• Steps:
  • C = π × d = 3.14 × 14.
  • 3.14 × 14 = 3.14 × 10 + 3.14 × 4 = 31.40 + 12.56 = 43.96.
  • The circumference is 43.96 cm.
• Answer: 43.96 cm

[Medium] Completing the Square

• EN: Complete the square to rewrite x² + 6x + 5 in the form (x + a)² + b. What is the result?
• FR: Complète le carré pour réécrire x² + 6x + 5 sous la forme (x + a)² + b. Quel est le résultat?
• Choices: A) (x + 3)² − 4 B) (x + 3)² + 4 C) (x + 6)² − 4 D) (x + 3)² − 6
• Hint: Take half the x-coefficient, square it, add and subtract it (e.g., x² + 4x + 1 → (x + 2)² − 4 + 1 = (x + 2)² − 3).
• Steps:
  • Half of 6 is 3; 3² = 9.
  • x² + 6x + 5 = (x + 3)² − 9 + 5.
  • = (x + 3)² − 4.
• Answer: (x + 3)² − 4

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 3 cm and a slant height of 5 cm. What is the total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 3 cm et une hauteur oblique de 5 cm. Quelle est l'aire totale? (Utilise π ≈ 3,14)
• Choices: A) 65.94 cm² B) 72.22 cm² C) 75.36 cm² D) 81.64 cm²
• Hint: SA of a cone = πr² + πrl, where r = radius and l = slant height (e.g., r = 2, l = 4 → 3.14 × 4 + 3.14 × 2 × 4 = 12.56 + 25.12 = 37.68 cm²).
• Steps:
  • Base area: πr² = 3.14 × 9 = 28.26.
  • Lateral area: πrl = 3.14 × 3 × 5 = 47.10.
  • Total SA = 28.26 + 47.10 = 75.36 cm².
• Answer: 75.36 cm²

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve 2x² − 4x − 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre 2x² − 4x − 6 = 0. Quelles sont les solutions?
• Choices: A) x = −1 and x = 2 B) x = −1 and x = 3 C) x = 1 and x = −3 D) x = 2 and x = −3
• Hint: Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a. Simplify the equation first if possible (e.g., divide all terms by a common factor).
• Steps:
  • Divide by 2: x² − 2x − 3 = 0.
  • Factor: (x − 3)(x + 1) = 0.
  • x = 3 or x = −1.
  • So the solutions are x = −1 and x = 3.
• Answer: x = −1 and x = 3

[Hard] System of Equations with Substitution — Context

• EN: Two ski passes cost $350 in total. One pass costs $30 more than the other. How much does the cheaper pass cost?
• FR: Deux laissez-passer de ski coûtent 350 $ en tout. Un laissez-passer coûte 30 $ de plus que l'autre. Combien coûte le laissez-passer le moins cher?
• Choices: A) $145 B) $155 C) $160 D) $175
• Hint: Set up a system — let the cheaper pass = x, so the other = x + 30, then write a sum equation (e.g., x + (x + 20) = 100 → 2x + 20 = 100 → x = 40).
• Steps:
  • Let cheaper pass = x; expensive pass = x + 30.
  • x + (x + 30) = 350 → 2x + 30 = 350.
  • 2x = 320 → x = 160.
  • The cheaper pass costs $160.
• Answer: $160

[Easy] Identifying a Function

• EN: Which of the following represents an exponential function?
• FR: Laquelle des fonctions suivantes est une fonction exponentielle?
• Choices: A) y = 3x + 1 B) y = x² C) y = 2^x D) y = 1/x
• Hint: An exponential function has the variable in the exponent (e.g., f(x) = 5^x or f(x) = 3 × 2^x).
• Steps:
  • y = 3x + 1 is linear.
  • y = x² is quadratic.
  • y = 2^x has the variable in the exponent — this is exponential.
  • y = 1/x is a rational function.
• Answer: y = 2^x

[Easy] Arithmetic Sequences

• EN: Find the next term in the arithmetic sequence: 5, 11, 17, 23, ___.
• FR: Trouve le prochain terme de la suite arithmétique : 5, 11, 17, 23, ___.
• Choices: A) 27 B) 28 C) 29 D) 30
• Hint: In an arithmetic sequence, add the common difference each time (e.g., 3, 8, 13, 18 → common difference is 5, next term is 23).
• Steps:
  • Common difference: 11 − 5 = 6.
  • Next term: 23 + 6 = 29.
• Answer: 29

[Easy] Logarithm Introduction

• EN: Evaluate log₂(8).
• FR: Évalue log₂(8).
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log_b(x) = n means b^n = x — ask "what power of the base gives this result?" (e.g., log₃(9) = 2 because 3² = 9).
• Steps:
  • log₂(8) = n means 2^n = 8.
  • 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[Easy] Compound Interest

• EN: $500 is invested at 4% per year compounded annually for 1 year. How much money is in the account after 1 year?
• FR: 500 $ sont investis à 4 % par an, composé annuellement pendant 1 an. Combien d'argent y a-t-il dans le compte après 1 an?
• Choices: A) $504 B) $516 C) $520 D) $540
• Hint: A = P(1 + r)^t. For 1 year: A = P × (1 + r) (e.g., $200 at 5% → $200 × 1.05 = $210).
• Steps:
  • A = 500 × (1 + 0.04)^1 = 500 × 1.04.
  • 500 × 1.04 = 520.
  • There is $520 in the account.
• Answer: $520

[Medium] Quadratic Function — Vertex

• EN: Find the vertex of the parabola y = (x − 3)² + 4.
• FR: Trouve le sommet de la parabole y = (x − 3)² + 4.
• Choices: A) (−3, 4) B) (3, −4) C) (3, 4) D) (4, 3)
• Hint: In vertex form y = (x − h)² + k, the vertex is at the point (h, k) (e.g., y = (x − 2)² + 5 → vertex is (2, 5)).
• Steps:
  • The equation is y = (x − 3)² + 4.
  • h = 3, k = 4.
  • The vertex is (3, 4).
• Answer: (3, 4)

[Medium] Geometric Sequences

• EN: Find the sum of the first 4 terms of the geometric sequence: 2, 6, 18, 54.
• FR: Trouve la somme des 4 premiers termes de la suite géométrique : 2, 6, 18, 54.
• Choices: A) 70 B) 72 C) 78 D) 80
• Hint: Add the terms directly or use S_n = a(r^n − 1)/(r − 1) (e.g., 1, 3, 9, 27 → sum = 40; or 1 + 3 + 9 + 27 = 40).
• Steps:
  • Add the four terms: 2 + 6 + 18 + 54.
  • 2 + 6 = 8; 8 + 18 = 26; 26 + 54 = 80.
  • The sum is 80.
• Answer: 80

[Medium] Compound Interest — Multi-Year

• EN: $1,000 is invested at 6% per year compounded annually for 2 years. What is the value of the investment after 2 years?
• FR: 1 000 $ sont investis à 6 % par an, composé annuellement pendant 2 ans. Quelle est la valeur de l'investissement après 2 ans?
• Choices: A) $1,112.36 B) $1,123.60 C) $1,133.60 D) $1,200.00
• Hint: Use A = P(1 + r)^t — compound interest applies to the growing total each year (e.g., $500 at 10% for 2 years → 500 × 1.1² = 500 × 1.21 = $605).
• Steps:
  • A = 1000 × (1.06)² = 1000 × 1.1236.
  • 1000 × 1.1236 = 1123.60.
  • The investment is worth $1,123.60.
• Answer: $1,123.60

[Medium] Trigonometric Identity

• EN: If sin(θ) = 3/5, use the Pythagorean identity to find cos(θ) (assume 0° < θ < 90°).
• FR: Si sin(θ) = 3/5, utilise l'identité de Pythagore pour trouver cos(θ) (suppose 0° < θ < 90°).
• Choices: A) 3/5 B) 4/5 C) 5/3 D) 5/4
• Hint: Use sin²(θ) + cos²(θ) = 1 to find cos(θ): cos(θ) = √(1 − sin²(θ)) (e.g., sin(θ) = 4/5 → cos(θ) = √(1 − 16/25) = √(9/25) = 3/5).
• Steps:
  • sin²(θ) + cos²(θ) = 1.
  • (3/5)² + cos²(θ) = 1 → 9/25 + cos²(θ) = 1.
  • cos²(θ) = 16/25 → cos(θ) = 4/5.
• Answer: 4/5

[Hard] Annuity — Future Value

• EN: You deposit $200 at the end of each year into an account earning 5% per year compounded annually. What is the future value after 3 years?
• FR: Tu déposes 200 $ à la fin de chaque année dans un compte rapportant 5 % par an, composé annuellement. Quelle est la valeur future après 3 ans?
• Choices: A) $600.00 B) $620.50 C) $630.50 D) $662.05
• Hint: Future value of an annuity: FV = PMT × [(1 + r)^n − 1] / r (e.g., $100/year, 10%, 2 years → 100 × [(1.10)² − 1]/0.10 = 100 × 0.21/0.10 = $210).
• Steps:
  • FV = 200 × [(1.05)³ − 1] / 0.05.
  • (1.05)³ = 1.157625; 1.157625 − 1 = 0.157625.
  • 0.157625 / 0.05 = 3.1525.
  • FV = 200 × 3.1525 = 630.50.
  • The future value is $630.50.
• Answer: $630.50

[Hard] Logarithm — Solving an Equation

• EN: Solve for x: 3^x = 27.
• FR: Résous pour x : 3^x = 27.
• Choices: A) x = 2 B) x = 3 C) x = 9 D) x = 27
• Hint: Rewrite both sides as powers of the same base, then equate the exponents (e.g., 2^x = 32 → 2^x = 2^5 → x = 5).
• Steps:
  • Write 27 as a power of 3: 27 = 3³.
  • 3^x = 3³.
  • Since the bases are equal: x = 3.
• Answer: x = 3

[Easy] Permutations

• EN: How many ways can 4 students be arranged in a line?
• FR: De combien de façons 4 élèves peuvent-ils être placés dans une file?
• Choices: A) 12 B) 16 C) 24 D) 48
• Hint: The number of arrangements of n items in a line = n! (e.g., 3 students → 3! = 3 × 2 × 1 = 6 ways).
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • 4 × 3 = 12; 12 × 2 = 24; 24 × 1 = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 5 to represent the class?
• FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 5 pour représenter la classe?
• Choices: A) 8 B) 10 C) 12 D) 20
• Hint: Combinations: C(n, r) = n! / (r! × (n − r)!) (e.g., C(4, 2) = 4! / (2! × 2!) = 6 ways).
• Steps:
  • C(5, 2) = 5! / (2! × 3!) = (5 × 4) / (2 × 1) = 20 / 2 = 10.
  • There are 10 ways.
• Answer: 10

[Easy] Derivative Introduction — Power Rule

• EN: Using the power rule, what is the derivative of f(x) = x³?
• FR: En utilisant la règle de puissance, quelle est la dérivée de f(x) = x³?
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n × x^(n−1) (e.g., f(x) = x⁴ → f'(x) = 4x³).
• Steps:
  • f(x) = x³, so n = 3.
  • f'(x) = 3 × x^(3−1) = 3x².
• Answer: 3x²

[Easy] Polynomial Function — End Behaviour

• EN: What is the end behaviour of f(x) = −2x⁴ + 3x − 1 as x → +∞?
• FR: Quel est le comportement aux extrémités de f(x) = −2x⁴ + 3x − 1 quand x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: For even-degree polynomials, both ends go in the same direction — the leading coefficient's sign determines if they go up (+) or down (−) (e.g., f(x) = −3x² → both ends go to −∞).
• Steps:
  • The leading term is −2x⁴ (even degree, negative coefficient).
  • As x → +∞, x⁴ → +∞, so −2x⁴ → −∞.
  • f(x) → −∞.
• Answer: f(x) → −∞

[Medium] Binomial Probability

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

[Medium] Rational Functions — Vertical Asymptote

• EN: Where is the vertical asymptote of f(x) = 1/(x − 3)?
• FR: Où se trouve l'asymptote verticale de f(x) = 1/(x − 3)?
• Choices: A) x = −3 B) x = 0 C) x = 3 D) y = 3
• Hint: Vertical asymptotes occur where the denominator equals zero — set denominator = 0 and solve (e.g., f(x) = 1/(x + 5) → x + 5 = 0 → x = −5).
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • x = 3.
  • The vertical asymptote is at x = 3.
• Answer: x = 3

[Medium] Derivative — Rate of Change in Context

• EN: The position of a puck (in metres) is given by s(t) = 4t² − 2t. What is the velocity (derivative) of the puck at t = 3 seconds?
• FR: La position d'une rondelle (en mètres) est donnée par s(t) = 4t² − 2t. Quelle est la vitesse (dérivée) de la rondelle à t = 3 secondes?
• Choices: A) 20 m/s B) 22 m/s C) 24 m/s D) 34 m/s
• Hint: Differentiate using the power rule, then substitute the time value (e.g., s(t) = 3t² + t → s'(t) = 6t + 1; at t = 2 → s'(2) = 13).
• Steps:
  • s'(t) = 8t − 2 (using power rule).
  • At t = 3: s'(3) = 8(3) − 2 = 24 − 2 = 22.
  • The velocity is 22 m/s.
• Answer: 22 m/s

[Medium] Vectors — Adding Two Vectors

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

[Hard] Normal Distribution — Probability

• EN: The scores on a math test are normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that a randomly selected student scored between 60 and 80?
• FR: Les résultats d'un test de mathématiques suivent une distribution normale de moyenne 70 et d'écart type 10. Quelle est la probabilité qu'un élève choisi au hasard ait obtenu entre 60 et 80?
• Choices: A) 34% B) 50% C) 68% D) 95%
• Hint: In a normal distribution, about 68% of data falls within 1 standard deviation of the mean (between μ − σ and μ + σ).
• Steps:
  • 60 = 70 − 10 = mean − 1 standard deviation.
  • 80 = 70 + 10 = mean + 1 standard deviation.
  • The rule states ≈ 68% of data falls within ±1 standard deviation.
  • The probability is approximately 68%.
• Answer: 68%

[Hard] Derivative — Finding a Maximum

• EN: The profit function for a small business is P(x) = −x² + 8x − 7, where x is the number of items produced. How many items should be produced to maximize profit?
• FR: La fonction de profit d'une petite entreprise est P(x) = −x² + 8x − 7, où x est le nombre d'articles produits. Combien d'articles faut-il produire pour maximiser le profit?
• Choices: A) 3 items B) 4 items C) 5 items D) 7 items
• Hint: Set the derivative equal to zero and solve for x to find the maximum (e.g., P(x) = −2x² + 12x → P'(x) = −4x + 12 = 0 → x = 3).
• Steps:
  • P'(x) = −2x + 8 (using the power rule).
  • Set P'(x) = 0: −2x + 8 = 0 → 2x = 8 → x = 4.
  • Producing 4 items maximizes profit.
• Answer: 4 items