Daily Math — 2026-07-17

[Easy] Counting Crayons

• EN: Lily has 7 crayons. She finds 5 more. How many crayons does she have now?
• FR: Lily a 7 crayons. Elle en trouve 5 de plus. Combien de crayons a-t-elle maintenant?
• Choices: A) 10 crayons B) 11 crayons C) 12 crayons D) 13 crayons
• Hint: To add, count on from the bigger number (e.g., 6 + 3: start at 6, count 3 more → 9).
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • So Lily has 12 crayons.
• Answer: 12 crayons

[Easy] Apples on a Tree

• EN: There are 9 apples on a tree. 4 fall off. How many apples are left on the tree?
• FR: Il y a 9 pommes dans un arbre. 4 tombent. Combien de pommes reste-t-il dans l'arbre?
• Choices: A) 4 apples B) 6 apples C) 5 apples D) 3 apples
• Hint: To subtract, count back from the bigger number (e.g., 8 − 3: start at 8, count back 3 → 5).
• Steps:
  • Start at 9 and count back 4: 8, 7, 6, 5.
  • So 5 apples are left on the tree.
• Answer: 5 apples

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes after 12, 14, 16, ___?
• FR: Compte par bonds de 2. Quel nombre vient après 12, 14, 16, ___?
• Choices: A) 19 B) 17 C) 20 D) 18
• Hint: Skip counting by 2s means you always add 2 (e.g., 4, 6, 8, 10 → the next is 12).
• Steps:
  • Each number goes up by 2: 12, 14, 16, …
  • 16 + 2 = 18.
• Answer: 18

[Easy] Penny Count

• EN: You have 3 pennies. How many cents do you have?
• FR: Tu as 3 sous (pennies). Combien de cents as-tu?
• Choices: A) 5 cents B) 4 cents C) 3 cents D) 6 cents
• Hint: Each penny is worth 1 cent, so count them one by one (e.g., 2 pennies = 2 cents).
• Steps:
  • Each penny = 1 cent.
  • 3 pennies = 3 cents.
• Answer: 3 cents

[Medium] Hockey Cards

• EN: Omar has 15 hockey cards. He gives 8 to his friend. How many cards does Omar have left?
• FR: Omar a 15 cartes de hockey. Il en donne 8 à son ami. Combien de cartes Omar a-t-il?
• Choices: A) 8 cards B) 6 cards C) 7 cards D) 9 cards
• Hint: To subtract bigger numbers, count back step by step (e.g., 14 − 6: start at 14, count back 6 → 8).
• Steps:
  • Start at 15 and count back 8: 14, 13, 12, 11, 10, 9, 8, 7.
  • So Omar has 7 cards left.
• Answer: 7 cards

[Medium] Comparing Numbers

• EN: Which number is greater: 13 or 17?
• FR: Quel nombre est plus grand : 13 ou 17?
• Choices: A) 17 B) 15 C) 13 D) 11
• Hint: The number that comes later when you count is greater (e.g., 8 comes after 5, so 8 is greater).
• Steps:
  • Count up: …13, 14, 15, 16, 17.
  • 17 comes after 13, so 17 is greater.
• Answer: 17

[Medium] Skip Count by 5s

• EN: Skip count by 5s. What is the missing number: 5, 10, 15, ___, 25?
• FR: Compte par bonds de 5. Quel est le nombre manquant : 5, 10, 15, ___, 25?
• Choices: A) 18 B) 22 C) 20 D) 16
• Hint: When skip counting by 5s, add 5 each time (e.g., 10, 15, 20, 25, 30).
• Steps:
  • 15 + 5 = 20.
  • The missing number is 20.
• Answer: 20

[Medium] Snowflakes

• EN: There are 11 snowflakes on one mitten and 6 snowflakes on another. How many snowflakes are there in all?
• FR: Il y a 11 flocons de neige sur une mitaine et 6 sur une autre. Combien y a-t-il de flocons au total?
• Choices: A) 16 snowflakes B) 18 snowflakes C) 17 snowflakes D) 15 snowflakes
• Hint: Add both groups together (e.g., 10 + 4 = 14 total).
• Steps:
  • 11 + 6 = 17.
  • There are 17 snowflakes in all.
• Answer: 17 snowflakes

[Hard] Nickels

• EN: You have 3 nickels. How many cents do you have in total?
• FR: Tu as 3 pièces de 5 cents (nickels). Combien de cents as-tu en tout?
• Choices: A) 10 cents B) 20 cents C) 15 cents D) 12 cents
• Hint: Each nickel is worth 5 cents; skip count by 5s (e.g., 2 nickels = 5, 10 → 10 cents).
• Steps:
  • 1 nickel = 5 cents.
  • Skip count: 5, 10, 15.
  • So 3 nickels = 15 cents.
• Answer: 15 cents

[Hard] Number Story

• EN: There are 20 children in the class. 9 are outside. How many children are still inside?
• FR: Il y a 20 enfants dans la classe. 9 sont dehors. Combien d'enfants sont encore à l'intérieur?
• Choices: A) 10 children B) 12 children C) 9 children D) 11 children
• Hint: Subtract the ones who left from the total (e.g., 16 − 7 = 9 children stay).
• Steps:
  • Start at 20, count back 9: 19, 18, 17, 16, 15, 14, 13, 12, 11.
  • So 11 children are still inside.
• Answer: 11 children

[Easy] Adding to 100

• EN: What is 34 + 25?
• FR: Combien font 34 + 25?
• Choices: A) 57 B) 61 C) 59 D) 55
• Hint: Add the ones first, then the tens (e.g., 22 + 13: 2 + 3 = 5 ones, 2 + 1 = 3 tens → 35).
• Steps:
  • Ones: 4 + 5 = 9.
  • Tens: 30 + 20 = 50.
  • 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: La grande aiguille est sur 12 et la petite est sur 3. Quelle heure est-il?
• Choices: A) 3:30 B) 12:03 C) 3:00 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:
  • Minute hand on 12 means it is exactly on the hour.
  • Hour hand on 3, so the time is 3:00.
• Answer: 3:00

[Easy] Subtracting within 100

• EN: What is 78 − 43?
• FR: Combien font 78 − 43?
• Choices: A) 38 B) 30 C) 45 D) 35
• Hint: Subtract the ones first, then the tens (e.g., 59 − 24: 9 − 4 = 5 ones, 5 − 2 = 3 tens → 35).
• Steps:
  • Ones: 8 − 3 = 5.
  • Tens: 70 − 40 = 30.
  • 30 + 5 = 35.
• Answer: 35

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A pen is 17 cm long. How much longer is the pen?
• FR: Un crayon mesure 14 cm et un stylo mesure 17 cm. De combien le stylo est-il plus long?
• Choices: A) 4 cm B) 2 cm C) 5 cm D) 3 cm
• Hint: To find the difference in length, subtract the shorter from the longer (e.g., 10 cm − 7 cm = 3 cm longer).
• Steps:
  • 17 − 14 = 3.
  • The pen is 3 cm longer.
• Answer: 3 cm

[Medium] Counting Coins

• EN: You have 2 dimes and 3 nickels. How many cents do you have?
• FR: Tu as 2 pièces de 10 cents et 3 pièces de 5 cents. Combien de cents as-tu?
• Choices: A) 40 cents B) 25 cents C) 30 cents D) 35 cents
• Hint: A dime = 10 cents, a nickel = 5 cents; add each group (e.g., 1 dime + 2 nickels = 10 + 10 = 20 cents).
• Steps:
  • 2 dimes = 20 cents.
  • 3 nickels = 15 cents.
  • 20 + 15 = 35 cents.
• Answer: 35 cents

[Medium] Telling Time (Half Hour)

• EN: The clock shows the hour hand between 7 and 8, and the minute hand on 6. What time is it?
• FR: La petite aiguille est entre 7 et 8, et la grande aiguille est sur 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 8:30 D) 7:30
• Hint: When the minute hand is on 6, it is half past the hour (e.g., hour hand between 4 and 5 → 4:30).
• Steps:
  • Minute hand on 6 = 30 minutes past.
  • Hour hand is just past 7, so it is 7:30.
• Answer: 7:30

[Medium] Patterns

• EN: What is the next number in this pattern: 4, 8, 12, 16, ___?
• FR: Quel est le prochain nombre dans ce patron : 4, 8, 12, 16, ___?
• Choices: A) 18 B) 22 C) 17 D) 20
• Hint: Find the rule by looking at how much the number increases each time (e.g., 3, 6, 9, 12 → add 3 each time).
• Steps:
  • Each number increases by 4: 4, 8, 12, 16, …
  • 16 + 4 = 20.
• Answer: 20

[Medium] Adding with Regrouping

• EN: What is 47 + 36?
• FR: Combien font 47 + 36?
• Choices: A) 71 B) 73 C) 83 D) 76
• Hint: When the ones add up to more than 9, carry 1 to the tens (e.g., 28 + 15: 8 + 5 = 13, write 3 carry 1, then 2 + 1 + 1 = 4 → 43).
• Steps:
  • Ones: 7 + 6 = 13, write 3 carry 1.
  • Tens: 4 + 3 + 1 = 8.
  • Answer is 83.
• Answer: 83

[Hard] Word Problem with Coins

• EN: Mei has 1 loonie (100 cents). She spends 65 cents on a snack. How many cents does she have left?
• FR: Mei a 1 huard (100 cents). Elle dépense 65 cents pour une collation. Combien de cents lui reste-t-il?
• Choices: A) 40 cents B) 25 cents C) 35 cents D) 45 cents
• Hint: Subtract the amount spent from 100 cents (e.g., 100 − 30 = 70 cents left).
• Steps:
  • 100 − 65 = 35.
  • Mei has 35 cents left.
• Answer: 35 cents

[Hard] Two-Step Problem

• EN: A shelf has 25 books. 12 books are returned and then 7 books are borrowed. How many books are on the shelf now?
• FR: Une étagère a 25 livres. On en retourne 12, puis 7 sont empruntés. Combien de livres y a-t-il sur l'étagère maintenant?
• Choices: A) 28 books B) 31 books C) 30 books D) 26 books
• Hint: Do the operations one at a time in order (e.g., 20 + 5 = 25, then 25 − 3 = 22).
• Steps:
  • Start with 25, add 12: 25 + 12 = 37.
  • Then subtract 7: 37 − 7 = 30.
  • There are 30 books on the shelf.
• Answer: 30 books

[Easy] Multiplication by 2

• EN: What is 6 × 2?
• FR: Combien font 6 × 2?
• Choices: A) 14 B) 10 C) 12 D) 8
• Hint: Multiplying by 2 is the same as doubling the number (e.g., 4 × 2 = 4 + 4 = 8).
• Steps:
  • 6 × 2 means 6 + 6.
  • 6 + 6 = 12.
• Answer: 12

[Easy] Fractions

• EN: A pizza is cut into 4 equal pieces. You eat 1 piece. What fraction did you eat?
• FR: Une pizza est coupée en 4 parts égales. Tu en manges 1. Quelle fraction as-tu mangée?
• Choices: A) 1/2 B) 4/1 C) 1/4 D) 2/4
• Hint: A fraction is written as parts eaten over total parts (e.g., 1 piece out of 3 = 1/3).
• Steps:
  • Total pieces = 4, pieces eaten = 1.
  • Fraction eaten = 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: What is 4 × 5?
• FR: Combien font 4 × 5?
• Choices: A) 25 B) 24 C) 20 D) 15
• Hint: Multiplying by 5 is like skip counting by 5s (e.g., 3 × 5: count 5, 10, 15 → 15).
• Steps:
  • Skip count by 5, four times: 5, 10, 15, 20.
  • 4 × 5 = 20.
• Answer: 20

[Easy] Perimeter

• EN: A rectangle is 3 cm long and 2 cm wide. What is its perimeter?
• FR: Un rectangle a 3 cm de long et 2 cm de large. Quel est son périmètre?
• Choices: A) 6 cm B) 8 cm C) 12 cm D) 10 cm
• Hint: Perimeter = add all four sides (e.g., a rectangle 5 cm × 4 cm: 5 + 4 + 5 + 4 = 18 cm).
• Steps:
  • Add all sides: 3 + 2 + 3 + 2 = 10.
  • The perimeter is 10 cm.
• Answer: 10 cm

[Medium] Division

• EN: There are 15 stickers to share equally among 3 friends. How many stickers does each friend get?
• FR: Il y a 15 autocollants à partager également entre 3 amis. Combien chacun en reçoit-il?
• Choices: A) 4 stickers B) 6 stickers C) 5 stickers D) 3 stickers
• Hint: Division means splitting into equal groups (e.g., 12 ÷ 4 = 3 because 3 × 4 = 12).
• Steps:
  • 15 ÷ 3 = ?
  • Think: 3 × 5 = 15, so each friend gets 5 stickers.
• Answer: 5 stickers

[Medium] Multiplication by 3

• EN: The hockey team has 7 players on the ice. Each player has 3 pucks. How many pucks are there in total?
• FR: L'équipe de hockey a 7 joueurs sur la glace. Chaque joueur a 3 rondelles. Combien y a-t-il de rondelles en tout?
• Choices: A) 24 pucks B) 18 pucks C) 21 pucks D) 28 pucks
• Hint: Multiply the number of players by the number of items each has (e.g., 5 players × 4 pucks = 20 pucks).
• Steps:
  • 7 × 3 = 21.
  • There are 21 pucks in total.
• Answer: 21 pucks

[Medium] Reading a Bar Graph

• EN: A bar graph shows: Monday = 8 lunches sold, Tuesday = 5 lunches sold. How many more lunches were sold on Monday than Tuesday?
• FR: Un diagramme à barres montre : lundi = 8 repas vendus, mardi = 5 repas vendus. Combien de repas de plus ont été vendus lundi que mardi?
• Choices: A) 2 lunches B) 4 lunches C) 3 lunches D) 13 lunches
• Hint: To find "how many more," subtract the smaller value from the larger (e.g., 10 − 6 = 4 more).
• Steps:
  • Subtract: 8 − 5 = 3.
  • 3 more lunches were sold on Monday.
• Answer: 3 lunches

[Medium] Multiplication by 10

• EN: What is 9 × 10?
• FR: Combien font 9 × 10?
• Choices: A) 90 B) 19 C) 80 D) 99
• Hint: When you multiply any number by 10, just put a zero on the end (e.g., 6 × 10 = 60).
• Steps:
  • 9 × 10: put a zero after 9.
  • 9 × 10 = 90.
• Answer: 90

[Hard] Perimeter Problem

• EN: A park has the shape of a triangle with sides 12 m, 9 m, and 15 m. What is the perimeter?
• FR: Un parc a la forme d'un triangle avec des côtés de 12 m, 9 m et 15 m. Quel est son périmètre?
• Choices: A) 34 m B) 38 m C) 36 m D) 40 m
• Hint: Perimeter of a triangle = add all three sides (e.g., 4 m + 6 m + 5 m = 15 m).
• Steps:
  • Add all three sides: 12 + 9 + 15.
  • 12 + 9 = 21, then 21 + 15 = 36.
  • The perimeter is 36 m.
• Answer: 36 m

[Hard] Fraction Comparison

• 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) They are equal C) 1/2 D) 2/4 is smaller than 1/4
• Hint: When the top number (numerator) is the same, the fraction with the smaller bottom number (denominator) is larger (e.g., 1/3 is larger than 1/5).
• Steps:
  • Both fractions have 1 on top.
  • The smaller the denominator, the bigger the piece: halves are bigger than quarters.
  • So 1/2 is larger than 1/4.
• Answer: 1/2

[Easy] Multiplication Facts

• EN: What is 8 × 7?
• FR: Combien font 8 × 7?
• Choices: A) 54 B) 63 C) 56 D) 48
• Hint: Use a fact you know to help (e.g., 8 × 6 = 48, so 8 × 7 = 48 + 8 = 56).
• Steps:
  • 8 × 7: think of 8 × 6 = 48, then add one more group of 8.
  • 48 + 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in 4.37?
• FR: Quelle est la valeur du chiffre 3 dans 4,37?
• Choices: A) 3 ones B) 3 hundredths C) 3 tens D) 3 tenths
• Hint: The first digit after the decimal point is the tenths place (e.g., in 5.62, the 6 is in the tenths place).
• Steps:
  • In 4.37: 4 is ones, 3 is tenths, 7 is hundredths.
  • The digit 3 is in the tenths place.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A rectangle is 6 cm long and 4 cm wide. What is its area?
• FR: Un rectangle a 6 cm de long et 4 cm de large. Quelle est son aire?
• Choices: A) 20 cm² B) 24 cm² C) 10 cm² D) 28 cm²
• Hint: Area of a rectangle = length × width (e.g., 5 cm × 3 cm = 15 cm²).
• Steps:
  • Area = length × width = 6 × 4.
  • 6 × 4 = 24 cm².
• Answer: 24 cm²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/4?
• FR: Quelle fraction est plus grande : 3/4 ou 2/4?
• Choices: A) 2/4 B) 3/4 C) They are equal D) 1/4
• Hint: When fractions have the same denominator, the one with the larger numerator is greater (e.g., 5/8 > 3/8).
• Steps:
  • Both have denominator 4.
  • 3 > 2, so 3/4 > 2/4.
• Answer: 3/4

[Medium] Long Division

• EN: What is 84 ÷ 4?
• FR: Combien font 84 ÷ 4?
• Choices: A) 22 B) 18 C) 24 D) 21
• Hint: Divide one digit at a time (e.g., 96 ÷ 4: 4 goes into 9 twice (8), remainder 1; bring down 6 to get 16; 4 goes into 16 four times → 24).
• Steps:
  • 4 goes into 8 twice: write 2.
  • 4 goes into 4 once: write 1.
  • Wait — re-check: 84 ÷ 4: 4 × 20 = 80; 84 − 80 = 4; 4 ÷ 4 = 1; so 20 + 1 = 21.
• Answer: 21

[Medium] Elapsed Time

• EN: A hockey game starts at 2:15 and ends at 4:45. How long does the game last?
• FR: Un match de hockey commence à 14 h 15 et se termine à 16 h 45. Combien de temps dure le match?
• Choices: A) 2 hours 15 minutes B) 3 hours 30 minutes C) 2 hours 45 minutes D) 2 hours 30 minutes
• Hint: Count from the start time to the end time in hours then minutes (e.g., 1:10 to 3:40 = 2 hours 30 minutes).
• Steps:
  • From 2:15 to 4:15 = 2 hours.
  • From 4:15 to 4:45 = 30 minutes.
  • Total = 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Addition

• EN: A juice box costs $1.25 and a granola bar costs $0.75. What is the total cost?
• FR: Une boîte de jus coûte 1,25 $ et une barre granola coûte 0,75 $. Quel est le coût total?
• Choices: A) $1.75 B) $2.25 C) $2.00 D) $1.90
• Hint: Line up the decimal points when adding decimals (e.g., $2.30 + $0.50 = $2.80).
• Steps:
  • $1.25 + $0.75: ones 1 + 0 = 1; hundredths 5 + 5 = 10, write 0 carry 1; tenths 2 + 7 + 1 = 10, write 0 carry 1; ones becomes 2.
  • Total = $2.00.
• Answer: $2.00

[Medium] Long Division with Remainder

• EN: What is 53 ÷ 5? Write the answer as quotient with remainder.
• FR: Combien font 53 ÷ 5? Écris la réponse avec le quotient et le reste.
• Choices: A) 11 remainder 3 B) 9 remainder 3 C) 10 remainder 4 D) 10 remainder 3
• Hint: Divide to find how many times the divisor fits, then subtract to find the remainder (e.g., 27 ÷ 4: 4 × 6 = 24, remainder = 27 − 24 = 3 → 6 remainder 3).
• Steps:
  • 5 × 10 = 50, which is the largest multiple of 5 not exceeding 53.
  • 53 − 50 = 3.
  • So 53 ÷ 5 = 10 remainder 3.
• Answer: 10 remainder 3

[Hard] Multi-Step Area

• EN: A room is 8 m long and 5 m wide. A rug covers an area of 6 m². What is the area of the floor NOT covered by the rug?
• FR: Une pièce a 8 m de long et 5 m de large. Un tapis couvre une superficie de 6 m². Quelle est la superficie du plancher non couverte par le tapis?
• Choices: A) 42 m² B) 46 m² C) 34 m² D) 38 m²
• Hint: Find the total area first, then subtract the rug area (e.g., room 7 × 4 = 28 m², minus rug 5 m² = 23 m² uncovered).
• Steps:
  • Total area = 8 × 5 = 40 m².
  • Subtract rug: 40 − 6 = 34 m².
  • The uncovered area is 34 m².
• Answer: 34 m²

[Hard] Fraction Problem

• EN: Maya has $2.40 in dimes. How many dimes does she have?
• FR: Maya a 2,40 $ en pièces de 10 cents. Combien de pièces de 10 cents a-t-elle?
• Choices: A) 20 dimes B) 24 dimes C) 12 dimes D) 16 dimes
• Hint: Divide the total amount in cents by the value of one dime (e.g., $1.50 ÷ $0.10 = 150 ÷ 10 = 15 dimes).
• Steps:
  • $2.40 = 240 cents.
  • Each dime = 10 cents.
  • 240 ÷ 10 = 24 dimes.
• Answer: 24 dimes

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 196 B) 204 C) 184 D) 216
• Hint: Multiply the ones first, then the tens, carrying when needed (e.g., 23 × 4: 3 × 4 = 12, write 2 carry 1; 2 × 4 + 1 = 9 → 92).
• Steps:
  • Ones: 4 × 6 = 24, write 4 carry 2.
  • Tens: 3 × 6 = 18, plus 2 = 20.
  • 34 × 6 = 204.
• Answer: 204

[Easy] Adding Fractions (Like Denominators)

• EN: What is 2/7 + 3/7?
• FR: Combien font 2/7 + 3/7?
• Choices: A) 5/14 B) 6/7 C) 5/7 D) 4/7
• Hint: When denominators are the same, just add the numerators and keep the denominator (e.g., 1/5 + 2/5 = 3/5).
• Steps:
  • 2/7 + 3/7: add the numerators: 2 + 3 = 5.
  • Keep the denominator: 5/7.
• Answer: 5/7

[Easy] Decimal Operations

• EN: What is 3.6 + 2.8?
• FR: Combien font 3,6 + 2,8?
• Choices: A) 6.2 B) 5.4 C) 6.4 D) 7.2
• Hint: Line up the decimals and add tenths first, then ones, carrying if needed (e.g., 1.7 + 2.5: 7 + 5 = 12, write 2 carry 1; 1 + 2 + 1 = 4 → 4.2).
• Steps:
  • Tenths: 6 + 8 = 14, write 4 carry 1.
  • Ones: 3 + 2 + 1 = 6.
  • 3.6 + 2.8 = 6.4.
• Answer: 6.4

[Easy] Percentage Intro — 50%

• EN: What is 50% of 80?
• FR: Combien font 50% de 80?
• Choices: A) 50 B) 30 C) 40 D) 45
• Hint: 50% means half, so divide by 2 (e.g., 50% of 60 = 60 ÷ 2 = 30).
• Steps:
  • 50% = half.
  • 80 ÷ 2 = 40.
• Answer: 40

[Medium] Multi-Digit Division

• EN: What is 252 ÷ 6?
• FR: Combien font 252 ÷ 6?
• Choices: A) 40 B) 42 C) 48 D) 36
• Hint: Divide step by step: how many times does 6 go into the first digit(s)? (e.g., 168 ÷ 6: 6 into 16 = 2, remainder 4; bring down 8 → 48 ÷ 6 = 8 → 28).
• Steps:
  • 6 into 25 = 4 (since 6 × 4 = 24), remainder 1.
  • Bring down 2: 12 ÷ 6 = 2.
  • 252 ÷ 6 = 42.
• Answer: 42

[Medium] Subtracting Fractions

• EN: What is 6/9 − 2/9?
• FR: Combien font 6/9 − 2/9?
• Choices: A) 3/9 B) 5/9 C) 4/9 D) 8/18
• Hint: Subtract the numerators and keep the same denominator (e.g., 5/8 − 3/8 = 2/8).
• Steps:
  • 6/9 − 2/9: subtract numerators 6 − 2 = 4.
  • Keep denominator: 4/9.
• Answer: 4/9

[Medium] Volume of Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte a 5 cm de long, 4 cm de large et 3 cm de hauteur. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 50 cm³
• Hint: Volume = length × width × height (e.g., 2 cm × 3 cm × 4 cm = 24 cm³).
• Steps:
  • V = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25% and 10%

• EN: A Tim Hortons muffin costs $2.00. It is on sale for 25% off. How much do you save?
• FR: Un muffin de Tim Hortons coûte 2,00 $. Il est en solde à 25 % de rabais. Combien économises-tu?
• Choices: A) $0.75 B) $0.25 C) $1.00 D) $0.50
• Hint: 25% = one quarter, so divide the price by 4 (e.g., 25% of $4.00 = $4.00 ÷ 4 = $1.00).
• Steps:
  • 25% of $2.00 = $2.00 ÷ 4 = $0.50.
  • You save $0.50.
• Answer: $0.50

[Hard] Multi-Step Fraction Problem

• EN: A bag of trail mix is 3/8 peanuts and 2/8 raisins. What fraction of the bag is NOT peanuts or raisins?
• FR: Un sac de mélange de randonnée contient 3/8 d'arachides et 2/8 de raisins. Quelle fraction du sac n'est ni des arachides ni des raisins?
• Choices: A) 2/8 B) 5/8 C) 3/8 D) 1/8
• Hint: Add the two fractions first, then subtract from the whole (e.g., 2/6 + 1/6 = 3/6; 1 whole − 3/6 = 3/6 remaining).
• Steps:
  • Peanuts + raisins = 3/8 + 2/8 = 5/8.
  • Remaining = 8/8 − 5/8 = 3/8.
• Answer: 3/8

[Hard] Decimal Word Problem

• EN: Jake earns $12.50 per hour shovelling snow. He works for 3 hours. How much does he earn in total?
• FR: Jake gagne 12,50 $ de l'heure en pelletant de la neige. Il travaille pendant 3 heures. Combien gagne-t-il au total?
• Choices: A) $36.50 B) $37.50 C) $38.00 D) $35.50
• Hint: Multiply the hourly rate by the number of hours (e.g., $10.25 × 4 = $41.00).
• Steps:
  • $12.50 × 3: $12.00 × 3 = $36.00; $0.50 × 3 = $1.50.
  • $36.00 + $1.50 = $37.50.
• Answer: $37.50

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien font 30% de 200?
• Choices: A) 50 B) 60 C) 40 D) 70
• Hint: Find 10% first by dividing by 10, then multiply (e.g., 30% of 500: 500 ÷ 10 = 50, then 50 × 3 = 150).
• Steps:
  • 10% of 200 = 200 ÷ 10 = 20.
  • 30% = 20 × 3 = 60.
• Answer: 60

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 14 B) 10 C) 11 D) 16
• Hint: Multiplication comes before addition in BEDMAS (e.g., 5 + 2 × 3: do 2 × 3 = 6 first, then 5 + 6 = 11).
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then addition: 3 + 8 = 11.
• Answer: 11

[Easy] Ratio

• EN: In a bag of marbles, there are 4 red and 6 blue marbles. What is the ratio of red to blue?
• FR: Dans un sac de billes, il y a 4 rouges et 6 bleues. Quel est le rapport des rouges aux bleues?
• Choices: A) 6:4 B) 4:10 C) 4:6 D) 2:3
• Hint: A ratio compares two quantities in order (e.g., 3 cats and 5 dogs → ratio of cats to dogs is 3:5).
• Steps:
  • Red : Blue = 4 : 6.
  • The ratio of red to blue is 4:6.
• Answer: 4:6

[Easy] Integers Introduction

• EN: On a winter day, the temperature is −3°C. It drops by 4 degrees. What is the new temperature?
• FR: Par une journée d'hiver, la température est de −3 °C. Elle baisse de 4 degrés. Quelle est la nouvelle température?
• Choices: A) −8°C B) 1°C C) −7°C D) −6°C
• Hint: Dropping below zero means going further negative (e.g., −2°C dropping 3 degrees → −2 − 3 = −5°C).
• Steps:
  • −3 − 4 = −7.
  • The new temperature is −7°C.
• Answer: −7°C

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 6/7 C) 1/2 D) 2/7
• Hint: Multiply numerators together and denominators together (e.g., 1/2 × 2/5 = 2/10 = 1/5).
• Steps:
  • Numerators: 2 × 3 = 6.
  • Denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] BEDMAS with Brackets

• EN: What is (5 + 3) × 2 − 4?
• FR: Combien font (5 + 3) × 2 − 4?
• Choices: A) 10 B) 14 C) 12 D) 16
• Hint: Solve brackets first, then multiply, then subtract (e.g., (2 + 4) × 3 − 5 = 6 × 3 − 5 = 18 − 5 = 13).
• Steps:
  • Brackets: 5 + 3 = 8.
  • Multiply: 8 × 2 = 16.
  • Subtract: 16 − 4 = 12.
• Answer: 12

[Medium] Rate Problem

• EN: A car travels 120 km in 2 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 120 km en 2 heures. Quelle est sa vitesse en km/h?
• Choices: A) 50 km/h B) 70 km/h C) 60 km/h D) 80 km/h
• Hint: Divide the total distance by the number of hours to find the rate (e.g., 90 km in 3 hours = 90 ÷ 3 = 30 km/h).
• Steps:
  • Speed = distance ÷ time = 120 ÷ 2.
  • 120 ÷ 2 = 60 km/h.
• Answer: 60 km/h

[Medium] Simple Algebraic Expression

• EN: If n = 5, what is the value of 3n + 7?
• FR: Si n = 5, quelle est la valeur de 3n + 7?
• Choices: A) 20 B) 25 C) 22 D) 18
• Hint: Replace the variable with the given number and then calculate (e.g., if x = 3, then 4x + 2 = 4 × 3 + 2 = 14).
• Steps:
  • Replace n with 5: 3 × 5 + 7.
  • 3 × 5 = 15; 15 + 7 = 22.
• Answer: 22

[Hard] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 2/3 C) 1 1/2 D) 4/3
• 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 = 3/2.
  • 3/2 = 1 1/2.
• Answer: 1 1/2

[Hard] Percent Problem

• EN: There are 40 students in a class. 35% of them play hockey. How many students play hockey?
• FR: Il y a 40 élèves dans une classe. 35% d'entre eux jouent au hockey. Combien d'élèves jouent au hockey?
• Choices: A) 16 students B) 12 students C) 14 students D) 18 students
• Hint: Find 10% first, then multiply to get 35% (e.g., 10% of 60 = 6; 35% = 3 × 10% + 5% = 3 × 6 + 3 = 21).
• Steps:
  • 10% of 40 = 4.
  • 35% = 3 × 4 + (5% = 2) = 12 + 2 = 14.
  • 14 students play hockey.
• Answer: 14 students

[Easy] Integer Addition

• EN: What is (−5) + 9?
• FR: Combien font (−5) + 9?
• Choices: A) −14 B) 3 C) 4 D) −4
• Hint: When adding integers with different signs, subtract the smaller absolute value from the larger (e.g., (−3) + 7 = 4 because 7 − 3 = 4, and 7 is positive).
• Steps:
  • |9| > |−5|, so the answer is positive.
  • 9 − 5 = 4.
• Answer: 4

[Easy] Percent — Discount

• EN: A jacket costs $80. It is 20% off. How much is the discount?
• FR: Une veste coûte 80 $. Elle est à 20 % de rabais. Quel est le montant du rabais?
• Choices: A) $18 B) $20 C) $16 D) $14
• Hint: Find 10% by dividing by 10, then double it for 20% (e.g., 20% of $60 = $6 × 2 = $12).
• Steps:
  • 10% of $80 = $8.
  • 20% = $8 × 2 = $16.
  • The discount is $16.
• Answer: $16

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15.
• FR: Résous pour x : x + 9 = 15.
• Choices: A) x = 5 B) x = 7 C) x = 6 D) x = 24
• Hint: To isolate x, do the opposite operation on both sides (e.g., x + 4 = 10 → x = 10 − 4 = 6).
• Steps:
  • Subtract 9 from both sides: x = 15 − 9.
  • x = 6.
• Answer: x = 6

[Easy] Integer Subtraction

• EN: What is 3 − (−4)?
• FR: Combien font 3 − (−4)?
• Choices: A) −1 B) 8 C) −7 D) 7
• Hint: Subtracting a negative is the same as adding a positive (e.g., 5 − (−2) = 5 + 2 = 7).
• Steps:
  • 3 − (−4) = 3 + 4 = 7.
• Answer: 7

[Medium] Percentage — Tax

• EN: A book costs $15.00. Ontario's HST is 13%. How much tax is added?
• FR: Un livre coûte 15,00 $. La TVH en Ontario est de 13 %. Combien de taxe est ajoutée?
• Choices: A) $1.50 B) $2.25 C) $1.95 D) $2.60
• Hint: Find 10% then 3% separately and add (e.g., 13% of $20: 10% = $2.00, 3% = $0.60, total tax = $2.60).
• Steps:
  • 10% of $15 = $1.50.
  • 3% of $15 = $0.45.
  • Tax = $1.50 + $0.45 = $1.95.
• Answer: $1.95

[Medium] Integer Multiplication

• EN: What is (−6) × (−3)?
• FR: Combien font (−6) × (−3)?
• Choices: A) −18 B) 14 C) 18 D) −9
• Hint: A negative times a negative equals a positive (e.g., (−4) × (−5) = +20).
• Steps:
  • Negative × negative = positive.
  • 6 × 3 = 18.
  • (−6) × (−3) = 18.
• Answer: 18

[Medium] Surface Area

• EN: What is the surface area of a rectangular prism that is 5 cm × 4 cm × 3 cm?
• FR: Quelle est l'aire de la surface d'un prisme rectangulaire de 5 cm × 4 cm × 3 cm?
• Choices: A) 60 cm² B) 94 cm² C) 120 cm² D) 74 cm²
• Hint: Surface area = 2(lw + lh + wh) (e.g., for a 2 × 3 × 4 box: 2(6 + 8 + 12) = 2 × 26 = 52 cm²).
• Steps:
  • lw = 5 × 4 = 20; lh = 5 × 3 = 15; wh = 4 × 3 = 12.
  • SA = 2(20 + 15 + 12) = 2(47) = 94 cm².
• Answer: 94 cm²

[Medium] Probability

• EN: A bag has 3 red, 4 blue, and 3 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 4 bleues et 3 vertes. Quelle est la probabilité de piger une bille bleue?
• Choices: A) 3/10 B) 4/7 C) 2/5 D) 4/10
• Hint: Probability = favourable outcomes ÷ total outcomes (e.g., 2 red out of 8 total = 2/8).
• Steps:
  • Total marbles = 3 + 4 + 3 = 10.
  • Blue marbles = 4.
  • Probability = 4/10.
• Answer: 4/10

[Hard] Two-Step Equation Preview

• EN: Solve for n: 3n − 5 = 16.
• FR: Résous pour n : 3n − 5 = 16.
• Choices: A) n = 8 B) n = 9 C) n = 7 D) n = 11
• Hint: Add 5 to both sides first, then divide (e.g., 4x − 3 = 13 → 4x = 16 → x = 4).
• Steps:
  • Add 5 to both sides: 3n = 21.
  • Divide both sides by 3: n = 7.
• Answer: n = 7

[Hard] Percent Increase

• EN: A store raises the price of skates from $60 to $75. What is the percent increase?
• FR: Un magasin augmente le prix des patins de 60 $ à 75 $. Quel est le pourcentage d'augmentation?
• Choices: A) 15% B) 20% C) 25% D) 18%
• Hint: Percent increase = (increase ÷ original) × 100 (e.g., price goes from $40 to $50: increase = $10; 10 ÷ 40 × 100 = 25%).
• Steps:
  • Increase = $75 − $60 = $15.
  • Percent increase = (15 ÷ 60) × 100 = 0.25 × 100 = 25%.
• Answer: 25%

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144?
• Choices: A) 11 B) 14 C) 13 D) 12
• Hint: A perfect square root asks "what number times itself gives this?" (e.g., √81 = 9 because 9 × 9 = 81).
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of: 4, 8, 6, 10, 12.
• FR: Trouve la moyenne de : 4, 8, 6, 10, 12.
• Choices: A) 8 B) 6 C) 10 D) 9
• Hint: Mean = sum of all values ÷ number of values (e.g., mean of 2, 4, 6 = 12 ÷ 3 = 4).
• Steps:
  • Sum = 4 + 8 + 6 + 10 + 12 = 40.
  • Number of values = 5.
  • Mean = 40 ÷ 5 = 8.
• Answer: 8

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 3 = 11.
• FR: Résous pour x : 2x + 3 = 11.
• Choices: A) x = 5 B) x = 3 C) x = 7 D) x = 4
• Hint: Undo addition first, then division (e.g., 3x + 2 = 14 → 3x = 12 → x = 4).
• Steps:
  • Subtract 3: 2x = 8.
  • Divide by 2: x = 4.
• Answer: x = 4

[Easy] Percent Increase/Decrease

• EN: A $50 sweater is on sale for 10% off. What is the sale price?
• FR: Un chandail de 50 $ est en solde à 10 % de rabais. Quel est le prix de vente?
• Choices: A) $40 B) $45 C) $48 D) $42
• Hint: Find the discount first, then subtract from the original price (e.g., 10% off $80 = $8 off → $72).
• Steps:
  • 10% of $50 = $5.
  • Sale price = $50 − $5 = $45.
• Answer: $45

[Medium] Pythagorean Theorem

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

[Medium] Slope Introduction

• EN: A line passes through (0, 2) and (3, 8). What is the slope?
• FR: Une droite passe par (0, 2) et (3, 8). Quelle est la pente?
• Choices: A) 3 B) 4 C) 2 D) 6
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., (0,1) to (2,5): rise = 4, run = 2, slope = 2).
• Steps:
  • Rise = 8 − 2 = 6.
  • Run = 3 − 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 7, 9, 11.
• FR: Trouve la médiane de : 3, 7, 7, 9, 11.
• Choices: A) 3 B) 9 C) 11 D) 7
• Hint: The median is the middle value when data is ordered (e.g., in 2, 5, 8, 10, 13 the median is 8).
• Steps:
  • Data is already in order: 3, 7, 7, 9, 11.
  • The middle (3rd) value is 7.
• Answer: 7

[Medium] Two-Step Equation (Harder)

• EN: Solve for y: 5y − 8 = 22.
• FR: Résous pour y : 5y − 8 = 22.
• Choices: A) y = 7 B) y = 5 C) y = 9 D) y = 6
• Hint: Add to both sides first, then divide (e.g., 4y − 3 = 17 → 4y = 20 → y = 5).
• Steps:
  • Add 8 to both sides: 5y = 30.
  • Divide by 5: y = 6.
• Answer: y = 6

[Hard] Pythagorean Theorem — Find a Leg

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

[Hard] Percent Change

• EN: A hockey team won 18 games last year and 24 games this year. What is the percent increase in wins?
• FR: Une équipe de hockey a gagné 18 parties l'an dernier et 24 cette année. Quel est le pourcentage d'augmentation?
• Choices: A) 25% B) 35% C) 30% D) 33%
• Hint: Percent change = (change ÷ original) × 100 (e.g., from 20 to 25: change = 5; 5 ÷ 20 × 100 = 25%).
• Steps:
  • Change = 24 − 18 = 6.
  • Percent increase = (6 ÷ 18) × 100 = 0.3333… × 100 ≈ 33%.
  • The percent increase is 33%.
• Answer: 33%

[Easy] Solving Linear Equations

• EN: Solve for x: 4x − 6 = 10.
• FR: Résous pour x : 4x − 6 = 10.
• Choices: A) x = 5 B) x = 3 C) x = 4 D) x = 6
• Hint: Add to both sides, then divide (e.g., 3x − 5 = 7 → 3x = 12 → x = 4).
• Steps:
  • Add 6 to both sides: 4x = 16.
  • Divide by 4: x = 4.
• Answer: x = 4

[Easy] Slope-Intercept Form

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

[Easy] Adding Polynomials

• EN: Simplify: (3x + 4) + (2x − 1).
• FR: Simplifie : (3x + 4) + (2x − 1).
• Choices: A) 6x + 4 B) 5x + 5 C) 5x + 3 D) 4x + 3
• Hint: Combine like terms: add the x-terms together and the number terms together (e.g., (4x + 3) + (x − 2) = 5x + 1).
• Steps:
  • x-terms: 3x + 2x = 5x.
  • Constant terms: 4 + (−1) = 3.
  • Result: 5x + 3.
• Answer: 5x + 3

[Easy] SOH-CAH-TOA Intro

• EN: In a right triangle, the side opposite an angle is 3 cm and the hypotenuse is 5 cm. What is the sine of that angle?
• FR: Dans un triangle rectangle, le côté opposé à un angle mesure 3 cm et l'hypoténuse mesure 5 cm. Quel est le sinus de cet angle?
• Choices: A) 5/3 B) 4/5 C) 3/4 D) 3/5
• Hint: sin(θ) = opposite ÷ hypotenuse (e.g., opposite = 4, hypotenuse = 8 → sin = 4/8 = 1/2).
• Steps:
  • sin(θ) = opposite / hypotenuse = 3/5.
• Answer: 3/5

[Medium] Linear Inequality

• EN: Solve and identify the correct answer: 2x + 3 > 11.
• FR: Résous et identifie la bonne réponse : 2x + 3 > 11.
• Choices: A) x > 3 B) x > 5 C) x > 4 D) x < 4
• Hint: Solve like an equation, but keep the inequality sign (e.g., 3x + 1 > 10 → 3x > 9 → x > 3).
• Steps:
  • Subtract 3: 2x > 8.
  • Divide by 2: x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x + 5).
• FR: Développe : 3x(2x + 5).
• Choices: A) 5x² + 8x B) 6x² + 15x C) 6x + 15 D) 6x² + 8x
• Hint: Distribute by multiplying the term outside to each term inside (e.g., 2x(x + 4) = 2x² + 8x).
• Steps:
  • 3x × 2x = 6x².
  • 3x × 5 = 15x.
  • Result: 6x² + 15x.
• Answer: 6x² + 15x

[Medium] Similar Triangles

• EN: Two similar triangles have sides in ratio 2:5. The shorter triangle has a side of 6 cm. What is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans le rapport 2:5. Le petit triangle a un côté de 6 cm. Quel est le côté correspondant du grand triangle?
• Choices: A) 12 cm B) 18 cm C) 15 cm D) 20 cm
• Hint: Set up a proportion and solve (e.g., ratio 3:7, short side = 9; long side = 9 × 7/3 = 21 cm).
• Steps:
  • Ratio is 2:5; short side = 6.
  • 6 ÷ 2 = 3 (scale factor).
  • Large side = 5 × 3 = 15 cm.
• Answer: 15 cm

[Medium] Graphing Lines

• EN: Which point lies on the line y = 2x + 1?
• FR: Quel point se trouve sur la droite y = 2x + 1?
• Choices: A) (2, 6) B) (3, 8) C) (1, 4) D) (4, 10)
• Hint: Substitute the x-value into the equation and check if y matches (e.g., for y = x + 3, test (2, 5): 2 + 3 = 5 ✓).
• Steps:
  • Test (3, 8): y = 2(3) + 1 = 6 + 1 = 7 ≠ 8.
  • Test (2, 6): y = 2(2) + 1 = 5 ≠ 6.
  • Test (1, 4): y = 2(1) + 1 = 3 ≠ 4.
  • Test (4, 10): y = 2(4) + 1 = 9 ≠ 10.
  • Re-check (3, 8): 2(3)+1 = 7 — re-verify all. Test (4, 9) — not an option. Recheck (2, 5) — not an option. The closest correct answer among options: checking each: (1,4): 2+1=3 no; (2,6): 5 no; (3,8): 7 no; (4,10): 9 no. Let me reselect: correct point on y=2x+1 that matches an option — (3,7) would be correct but not listed. Adjust choice C to (1, 3) — but I must keep all choices as listed. Let me recalculate with a different point selection. The correct answer on y=2x+1: if x=3, y=7. If x=4, y=9. Use (3, 7) as correct choice. Revising choices: A) (2, 6) B) (3, 7) C) (1, 4) D) (4, 10) — correct is B.
• Answer: (3, 7)

(Revised problem — restating cleanly:)

[Medium] Graphing Lines

• EN: Which point lies on the line y = 2x + 1?
• FR: Quel point se trouve sur la droite y = 2x + 1?
• Choices: A) (2, 6) B) (3, 7) C) (1, 4) D) (4, 10)
• Hint: Substitute the x-value into the equation and check if y matches (e.g., for y = x + 3, test (2, 5): 2 + 3 = 5 ✓).
• Steps:
  • Test (3, 7): y = 2(3) + 1 = 6 + 1 = 7 ✓.
  • The point (3, 7) lies on the line.
• Answer: (3, 7)

[Hard] Trigonometry — Find a Side

• EN: In a right triangle, one angle is 30°. The hypotenuse is 10 cm. What is the length of the side opposite the 30° angle?
• FR: Dans un triangle rectangle, un angle mesure 30°. L'hypoténuse est de 10 cm. Quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 8 cm B) 7 cm C) 5 cm D) 6 cm
• Hint: Use sin(θ) = opposite/hypotenuse; opposite = hypotenuse × sin(θ) (e.g., 45° angle, hypotenuse = 8: opposite = 8 × sin(45°) ≈ 5.66 cm).
• Steps:
  • sin(30°) = 0.5.
  • Opposite = 10 × sin(30°) = 10 × 0.5 = 5 cm.
• Answer: 5 cm

[Hard] Systems of Equations Preview

• EN: Solve the system: x + y = 10 and x − y = 4. What is x?
• FR: Résous le système : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 8 B) x = 6 C) x = 9 D) x = 7
• Hint: Add the two equations together to eliminate y (e.g., x + y = 9 and x − y = 3 → 2x = 12 → x = 6).
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 4 → 2x = 14.
  • x = 7.
• Answer: x = 7

[Easy] Factoring Quadratics

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

[Easy] Trigonometry

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 8 cm et l'hypoténuse mesure 10 cm. Quel est cos(θ)?
• Choices: A) 8/6 B) 6/10 C) 10/8 D) 8/10
• Hint: cos(θ) = adjacent ÷ hypotenuse (e.g., adjacent = 5, hypotenuse = 13 → cos = 5/13).
• Steps:
  • cos(θ) = adjacent / hypotenuse = 8/10.
• Answer: 8/10

[Easy] Systems of Equations

• EN: Solve the system: y = 2x and y = x + 5. What is x?
• FR: Résous le système : y = 2x et y = x + 5. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 7 C) x = 4 D) x = 5
• Hint: Set the two expressions equal since both equal y (e.g., y = 3x and y = x + 8 → 3x = x + 8 → x = 4).
• Steps:
  • Set equal: 2x = x + 5.
  • Subtract x: x = 5.
• Answer: x = 5

[Easy] Quadratic Formula — Roots

• EN: What are the roots of (x − 3)(x + 2) = 0?
• FR: Quelles sont les racines de (x − 3)(x + 2) = 0?
• Choices: A) x = 3 or x = 2 B) x = −3 or x = 2 C) x = 3 or x = −2 D) x = −3 or x = −2
• Hint: Set each bracket equal to zero (e.g., (x − 5)(x + 1) = 0 → x = 5 or x = −1).
• Steps:
  • x − 3 = 0 → x = 3.
  • x + 2 = 0 → x = −2.
• Answer: x = 3 or x = −2

[Medium] Completing the Square

• EN: Rewrite x² + 6x + 5 by completing the square. What is the vertex form?
• FR: Réécris x² + 6x + 5 en complétant le carré. Quelle est la forme du sommet?
• Choices: A) (x + 3)² − 5 B) (x + 3)² − 4 C) (x + 6)² − 5 D) (x + 3)² + 4
• Hint: Take half the middle coefficient, square it, add and subtract (e.g., x² + 4x + 1: half of 4 = 2; (x+2)² − 4 + 1 = (x+2)² − 3).
• Steps:
  • Half of 6 = 3; 3² = 9.
  • x² + 6x + 5 = (x + 3)² − 9 + 5 = (x + 3)² − 4.
• Answer: (x + 3)² − 4

[Medium] Circle Geometry

• EN: A circle has a radius of 7 cm. What is the area of the circle? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 7 cm. Quelle est son aire? (Utilise π ≈ 3,14)
• Choices: A) 43.96 cm² B) 153.86 cm² C) 44.00 cm² D) 196.00 cm²
• Hint: Area = πr² (e.g., radius = 5: A = 3.14 × 25 = 78.5 cm²).
• Steps:
  • A = πr² = 3.14 × 7² = 3.14 × 49.
  • 3.14 × 49 = 153.86 cm².
• Answer: 153.86 cm²

[Medium] Volume of a Cylinder

• EN: A cylindrical can has radius 3 cm and height 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 282.60 cm³ B) 94.20 cm³ C) 188.40 cm³ D) 314.00 cm³
• Hint: Volume of cylinder = πr²h (e.g., r = 2, h = 5: V = 3.14 × 4 × 5 = 62.8 cm³).
• Steps:
  • V = πr²h = 3.14 × 3² × 10 = 3.14 × 9 × 10.
  • 3.14 × 90 = 282.60 cm³.
• Answer: 282.60 cm³

[Medium] Solving a Quadratic by Factoring

• EN: Solve for x: x² − 7x + 12 = 0.
• FR: Résous pour x : x² − 7x + 12 = 0.
• Choices: A) x = 4 or x = 3 B) x = 6 or x = 2 C) x = 4 or x = −3 D) x = 12 or x = 1
• Hint: Factor first, then set each bracket to zero (e.g., x² − 5x + 6 = (x−2)(x−3) = 0 → x = 2 or x = 3).
• Steps:
  • Factor: find two numbers with product 12 and sum −7: −3 and −4.
  • x² − 7x + 12 = (x − 3)(x − 4) = 0.
  • x = 3 or x = 4.
• Answer: x = 4 or x = 3

[Hard] Quadratic Word Problem

• EN: A ball is kicked and its height h (in metres) is given by h = −t² + 4t + 5, where t is time in seconds. What is the maximum height?
• FR: Un ballon est botté et sa hauteur h (en mètres) est donnée par h = −t² + 4t + 5, où t est le temps en secondes. Quelle est la hauteur maximale?
• Choices: A) 8 m B) 10 m C) 9 m D) 11 m
• Hint: The maximum height of a parabola is at the vertex; find t = −b/(2a) then substitute (e.g., h = −t² + 6t + 1: t = 3, h = −9 + 18 + 1 = 10 m).
• Steps:
  • t at vertex = −b/(2a) = −4/(2 × −1) = 2 seconds.
  • h = −(2)² + 4(2) + 5 = −4 + 8 + 5 = 9 m.
• Answer: 9 m

[Hard] Systems — Word Problem

• EN: Two friends buy school supplies. Alex buys 3 pencils and 2 erasers for $1.60. Sam buys 1 pencil and 4 erasers for $1.40. What is the cost of one pencil?
• FR: Deux amis achètent des fournitures scolaires. Alex achète 3 crayons et 2 gommes pour 1,60 $. Sam achète 1 crayon et 4 gommes pour 1,40 $. Quel est le coût d'un crayon?
• Choices: A) $0.30 B) $0.40 C) $0.20 D) $0.50
• Hint: Set up two equations and use substitution or elimination (e.g., 2x + y = 5 and x + y = 3 → subtract: x = 2).
• Steps:
  • Let p = pencil, e = eraser: 3p + 2e = 1.60 and p + 4e = 1.40.
  • Multiply second by 3: 3p + 12e = 4.20.
  • Subtract first: 10e = 2.60 → e = 0.26.
  • Substitute: p + 4(0.26) = 1.40 → p + 1.04 = 1.40 → p = 0.36. Hmm — let me use cleaner numbers.
  • Revised: Using elimination: multiply eq2 by 3: 3p + 12e = 4.20; subtract eq1: 10e = 2.60 → e = $0.26; p = 1.40 − 4(0.26) = 1.40 − 1.04 = $0.36. This doesn't match choices. Let me re-design.

(Redesigning for clean numbers: 3p + 2e = 1.60 and p + 4e = 1.20)

• Revised problem:

[Hard] Systems — Word Problem

• EN: Alex buys 3 pencils and 2 erasers for $1.60. Sam buys 1 pencil and 2 erasers for $0.80. What is the cost of one pencil?
• FR: Alex achète 3 crayons et 2 gommes pour 1,60 $. Sam achète 1 crayon et 2 gommes pour 0,80 $. Quel est le coût d'un crayon?
• Choices: A) $0.50 B) $0.30 C) $0.40 D) $0.60
• Hint: Subtract one equation from the other to eliminate one variable (e.g., 4x + y = 10 and 2x + y = 6 → subtract: 2x = 4 → x = 2).
• Steps:
  • Equation 1: 3p + 2e = 1.60; Equation 2: p + 2e = 0.80.
  • Subtract eq2 from eq1: 2p = 0.80 → p = $0.40.
• Answer: $0.40

[Easy] Exponential Functions

• EN: An investment doubles every 10 years. If you start with $500, how much will you have after 10 years?
• FR: Un investissement double tous les 10 ans. Si tu commences avec 500 $, combien auras-tu après 10 ans?
• Choices: A) $1500 B) $750 C) $1000 D) $2000
• Hint: "Doubles" means multiply by 2 once for each period (e.g., $200 after one doubling = $200 × 2 = $400).
• Steps:
  • After one doubling period: $500 × 2 = $1000.
• Answer: $1000

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 5 and the common difference is 4. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 5 et la raison est 4. Quel est le 5e terme?
• Choices: A) 20 B) 25 C) 21 D) 16
• Hint: Use the formula aₙ = a₁ + (n − 1)d (e.g., a₁ = 3, d = 2, find a₄: 3 + 3 × 2 = 9).
• Steps:
  • a₅ = 5 + (5 − 1) × 4 = 5 + 16 = 21.
• Answer: 21

[Easy] Logarithm Intro

• EN: What is log₂(8)?
• FR: Combien fait log₂(8)?
• Choices: A) 2 B) 4 C) 3 D) 8
• Hint: log_b(x) asks "to what power must b be raised to get x?" (e.g., log₃(9) = 2 because 3² = 9).
• Steps:
  • 2? = 8: 2¹ = 2, 2² = 4, 2³ = 8.
  • log₂(8) = 3.
• Answer: 3

[Easy] Compound Interest

• EN: $1000 is invested at 5% interest compounded annually for 1 year. How much interest is earned?
• FR: 1 000 $ est investi à 5 % d'intérêt composé annuellement pendant 1 an. Combien d'intérêts sont gagnés?
• Choices: A) $25 B) $100 C) $50 D) $75
• Hint: For one year, interest = principal × rate (e.g., $800 at 4% for 1 year = $800 × 0.04 = $32).
• Steps:
  • Interest = $1000 × 0.05 = $50.
• Answer: $50

[Medium] Quadratic Function — Vertex

• EN: The function f(x) = −2(x − 3)² + 7 has its vertex at which point?
• FR: La fonction f(x) = −2(x − 3)² + 7 a son sommet en quel point?
• Choices: A) (−3, 7) B) (3, −7) C) (3, 7) D) (−3, −7)
• Hint: In f(x) = a(x − h)² + k, the vertex is at (h, k) (e.g., f(x) = 3(x − 1)² + 5 has vertex (1, 5)).
• Steps:
  • h = 3, k = 7.
  • Vertex is at (3, 7).
• Answer: (3, 7)

[Medium] Geometric Sequence

• EN: The first term of a geometric sequence is 2 and the common ratio is 3. What is the 4th term?
• FR: Le premier terme d'une suite géométrique est 2 et la raison est 3. Quel est le 4e terme?
• Choices: A) 54 B) 18 C) 24 D) 36
• Hint: Use aₙ = a₁ × rⁿ⁻¹ (e.g., a₁ = 4, r = 2, find a₃: 4 × 2² = 4 × 4 = 16).
• Steps:
  • a₄ = 2 × 3⁴⁻¹ = 2 × 3³ = 2 × 27 = 54.
• Answer: 54

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifie : sin²(θ) + cos²(θ).
• Choices: A) 0 B) 2 C) sin(2θ) D) 1
• Hint: This is one of the most important identities in trigonometry — it always equals a constant (e.g., for any angle, try θ = 30°: (1/2)² + (√3/2)² = 1/4 + 3/4 = 1).
• Steps:
  • sin²(θ) + cos²(θ) = 1 is the Pythagorean identity.
• Answer: 1

[Medium] Compound Interest Formula

• EN: $2000 is invested at 6% compounded annually for 2 years. What is the amount after 2 years?
• FR: 2 000 $ est investi à 6 % composé annuellement pendant 2 ans. Quel est le montant après 2 ans?
• Choices: A) $2247.20 B) $2240.00 C) $2120.00 D) $2260.00
• Hint: Use A = P(1 + r)ⁿ (e.g., $1000 at 5% for 2 years: A = 1000 × 1.05² = 1000 × 1.1025 = $1102.50).
• Steps:
  • A = 2000 × (1.06)² = 2000 × 1.1236 = $2247.20.
• Answer: $2247.20

[Hard] Sum of Arithmetic Series

• EN: Find the sum of the first 10 terms of the arithmetic series where a₁ = 3 and d = 5.
• FR: Trouve la somme des 10 premiers termes de la série arithmétique où a₁ = 3 et d = 5.
• Choices: A) 255 B) 240 C) 280 D) 255
• Hint: Use Sₙ = n/2 × (2a₁ + (n−1)d) (e.g., a₁ = 1, d = 3, n = 5: S₅ = 5/2 × (2 + 12) = 5/2 × 14 = 35).
• Steps:
  • S₁₀ = 10/2 × (2 × 3 + 9 × 5) = 5 × (6 + 45) = 5 × 51 = 255.

(Note: choices A and D are both 255 — correcting:)

• Choices: A) 255 B) 240 C) 280 D) 300
• Steps:
  • S₁₀ = 10/2 × (2 × 3 + 9 × 5) = 5 × (6 + 45) = 5 × 51 = 255.
• Answer: 255

[Hard] Sum of Arithmetic Series (corrected)

• EN: Find the sum of the first 10 terms of the arithmetic series where a₁ = 3 and d = 5.
• FR: Trouve la somme des 10 premiers termes de la série arithmétique où a₁ = 3 et d = 5.
• Choices: A) 255 B) 240 C) 280 D) 300
• Hint: Use Sₙ = n/2 × (2a₁ + (n−1)d) (e.g., a₁ = 2, d = 4, n = 5: S₅ = 5/2 × (4 + 16) = 50).
• Steps:
  • S₁₀ = 10/2 × (2 × 3 + 9 × 5).
  • = 5 × (6 + 45) = 5 × 51 = 255.
• Answer: 255

[Hard] Exponential Growth

• EN: A bacteria culture starts with 200 cells and triples every hour. How many cells are there after 3 hours?
• FR: Une culture bactérienne commence avec 200 cellules et triple chaque heure. Combien de cellules y a-t-il après 3 heures?
• Choices: A) 1800 cells B) 5400 cells C) 1600 cells D) 2400 cells
• Hint: Use exponential growth: A = a × rⁿ (e.g., 100 cells tripling for 2 hours: 100 × 3² = 900 cells).
• Steps:
  • A = 200 × 3³ = 200 × 27 = 5400.
  • There are 5400 cells after 3 hours.
• Answer: 5400 cells

[Easy] Permutations

• EN: How many ways can you arrange 4 different books on a shelf?
• FR: De combien de façons peut-on placer 4 livres différents sur une étagère?
• Choices: A) 16 B) 24 C) 12 D) 48
• Hint: For n objects in a row, the number of arrangements = n! (e.g., 3 objects: 3! = 3 × 2 × 1 = 6).
• Steps:
  • 4! = 4 × 3 × 2 × 1 = 24.
• Answer: 24

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = x³?
• FR: Quelle est la dérivée de f(x) = x³?
• Choices: A) x² B) 3x C) 3x² D) x⁴
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = nxⁿ⁻¹ (e.g., f(x) = x⁵ → f'(x) = 5x⁴).
• Steps:
  • f(x) = x³; apply power rule: bring down 3, reduce exponent by 1.
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Combinations

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

[Easy] Rational Function — Domain

• EN: What value of x must be excluded from the domain of f(x) = 1/(x − 3)?
• FR: Quelle valeur de x doit être exclue du domaine de f(x) = 1/(x − 3)?
• Choices: A) x = 1 B) x = −3 C) x = 3 D) x = 0
• Hint: A rational function is undefined when the denominator equals zero (e.g., f(x) = 1/(x + 5): set x + 5 = 0 → x = −5 is excluded).
• Steps:
  • Set denominator = 0: x − 3 = 0 → x = 3.
  • x = 3 must be excluded.
• Answer: x = 3

[Medium] Derivative — Rate of Change

• EN: The position of a car (in metres) is given by s(t) = 4t² + 3t. What is the velocity (derivative) at t = 2?
• FR: La position d'une voiture (en mètres) est donnée par s(t) = 4t² + 3t. Quelle est la vitesse (dérivée) à t = 2?
• Choices: A) 16 m/s B) 22 m/s C) 19 m/s D) 25 m/s
• Hint: Differentiate s(t), then substitute t (e.g., s(t) = 3t² + 2t → s'(t) = 6t + 2; at t = 3: s'(3) = 20).
• Steps:
  • s'(t) = 8t + 3.
  • At t = 2: s'(2) = 8(2) + 3 = 16 + 3 = 19 m/s.
• Answer: 19 m/s

[Medium] Normal Distribution — Probability

• EN: In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
• FR: Dans une distribution normale, environ quel pourcentage des données se situe à moins d'un écart type de la moyenne?
• Choices: A) 99.7% B) 95% C) 68% D) 75%
• Hint: Remember the empirical rule: 68% within 1σ, 95% within 2σ, 99.7% within 3σ.
• Steps:
  • The 68-95-99.7 rule states 68% falls within one standard deviation.
• Answer: 68%

[Medium] Polynomial Division

• EN: Divide: (x² + 5x + 6) ÷ (x + 2).
• FR: Divise : (x² + 5x + 6) ÷ (x + 2).
• Choices: A) x + 4 B) x − 3 C) x + 3 D) x + 2
• Hint: Factor the numerator, then cancel common factors (e.g., (x² + 7x + 10) ÷ (x + 2) = (x+5)(x+2)/(x+2) = x + 5).
• Steps:
  • Factor: x² + 5x + 6 = (x + 2)(x + 3).
  • Divide by (x + 2): result is (x + 3).
• Answer: x + 3

[Medium] Vector Addition

• EN: Vector u = (3, 4) and vector v = (−1, 2). What is u + v?
• FR: Le vecteur u = (3, 4) et le vecteur v = (−1, 2). Quel est u + v?
• Choices: A) (4, 2) B) (2, 6) C) (3, 6) D) (4, 6)
• Hint: Add corresponding components (e.g., (5, 1) + (−2, 3) = (3, 4)).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: 4 + 2 = 6.
  • u + v = (2, 6).
• Answer: (2, 6)

[Hard] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: On lance une pièce équitable 4 fois. Quelle est la probabilité d'obtenir exactement 3 têtes?
• Choices: A) 3/16 B) 1/4 C) 1/16 D) 1/2
• Hint: Use P = C(n, k) × pᵏ × (1−p)ⁿ⁻ᵏ (e.g., 3 flips, exactly 2 heads: C(3,2) × (0.5)² × (0.5)¹ = 3 × 0.25 × 0.5 = 3/8).
• Steps:
  • P = C(4, 3) × (0.5)³ × (0.5)¹ = 4 × (1/8) × (1/2) = 4/16 = 1/4.
• Answer: 1/4

[Hard] Derivative — Optimization

• EN: A rectangular pen uses 40 m of fencing on three sides (the fourth side is a wall). What width maximizes the area?
• FR: Un enclos rectangulaire utilise 40 m de clôture pour trois côtés (le quatrième est un mur). Quelle largeur maximise l'aire?
• Choices: A) 8 m B) 15 m C) 10 m D) 20 m
• Hint: Express area in terms of one variable, differentiate, and set equal to zero (e.g., for a 3-sided fence of 30 m with width w and length L: L = 30 − 2w; A = w(30−2w); A' = 30 − 4w = 0 → w = 7.5 m).
• Steps:
  • Let width = w; then the two widths + one length = 40: L = 40 − 2w.
  • Area A = w(40 − 2w) = 40w − 2w².
  • A' = 40 − 4w = 0 → 4w = 40 → w = 10 m.
• Answer: 10 m