Daily Math — 2026-10-01

[Easy] Counting Skates

• EN: There are 7 skates on the bench. 3 more skates are added. How many skates are there now?
• FR: Il y a 7 patins sur le banc. On en ajoute 3 de plus. Combien y a-t-il de patins maintenant?
• Choices: A) 9 skates B) 10 skates C) 11 skates D) 8 skates
• Hint: To add two numbers, count on from the bigger one (e.g., 5 + 2 = start at 5, count up 2).
• Steps:
  • Start at 7 and count up 3 more.
  • 7 → 8, 9, 10.
  • So the total is 10 skates.
• Answer: 10 skates

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents?
• FR: Quelle pièce vaut 10 cents?
• Choices: A) Penny B) Nickel C) Dime D) Toonie
• Hint: Think about the three smallest coins — penny is 1 cent, nickel is 5 cents, and the next one is 10 cents.
• 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

[Easy] Skip Counting by 5s

• EN: Count by 5s: 5, 10, 15, ___. What number comes next?
• FR: Compte par 5 : 5, 10, 15, ___. Quel nombre vient ensuite?
• Choices: A) 18 B) 25 C) 22 D) 20
• Hint: When skip counting by 5s, add 5 each time (e.g., 10, 15, 20, 25).
• Steps:
  • Start at 15.
  • Add 5 to get the next number.
  • 15 + 5 = 20.
  • So the next number is 20.
• Answer: 20

[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) Both are equal D) 12
• Hint: When comparing two numbers, the one with more tens is greater (e.g., 12 is greater than 7).
• Steps:
  • 14 has a 1 in the tens place.
  • 9 has a 0 in the tens place.
  • A number with more tens is greater.
  • So 14 is greater than 9.
• Answer: 14

[Medium] Hockey Goals

• EN: Luca scored 8 goals this season. He scored 5 more goals last season. How many goals did he score in all?
• FR: Luca a marqué 8 buts cette saison. Il a marqué 5 buts de plus la saison dernière. Combien de buts a-t-il marqués en tout?
• Choices: A) 11 goals B) 14 goals C) 13 goals D) 12 goals
• Hint: To find the total, add both amounts together (e.g., 6 + 4 = 10).
• Steps:
  • Luca scored 8 goals this season and 5 goals last season.
  • Add 8 + 5.
  • 8 + 5 = 13.
  • So he scored 13 goals in all.
• Answer: 13 goals

[Medium] Subtracting Mittens

• EN: There are 15 mittens in a box. 6 mittens are taken out. How many mittens are left?
• FR: Il y a 15 mitaines dans une boîte. On en enlève 6. Combien de mitaines reste-t-il?
• Choices: A) 8 mittens B) 10 mittens C) 9 mittens D) 7 mittens
• Hint: To subtract, count back from the bigger number (e.g., 12 − 4: start at 12, count back 4).
• Steps:
  • Start at 15 and count back 6.
  • 15 → 14, 13, 12, 11, 10, 9.
  • So there are 9 mittens left.
• Answer: 9 mittens

[Medium] Skip Counting by 2s

• EN: Count by 2s: 2, 4, 6, 8, ___. What number comes next?
• FR: Compte par 2 : 2, 4, 6, 8, ___. Quel nombre vient ensuite?
• Choices: A) 11 B) 12 C) 9 D) 10
• Hint: When skip counting by 2s, add 2 each time (e.g., 6, 8, 10, 12).
• Steps:
  • Start at 8.
  • Add 2 to get the next number.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Medium] Pennies and Nickels

• EN: Maya has 2 nickels and 3 pennies. How many cents does she have in all?
• FR: Maya a 2 pièces de 5 cents et 3 pièces de 1 cent. Combien de cents a-t-elle en tout?
• Choices: A) 11 cents B) 8 cents C) 13 cents D) 15 cents
• Hint: Multiply the number of each coin by its value, then add (e.g., 3 nickels + 2 pennies = 15 + 2 = 17 cents).
• Steps:
  • Each nickel is worth 5 cents. 2 nickels = 2 × 5 = 10 cents.
  • Each penny is worth 1 cent. 3 pennies = 3 × 1 = 3 cents.
  • Add them together: 10 + 3 = 13 cents.
  • So Maya has 13 cents.
• Answer: 13 cents

[Hard] Number Story

• EN: There were 18 children at a skating rink. Some children went home. Now there are 11 children. How many children went home?
• FR: Il y avait 18 enfants à la patinoire. Certains enfants sont rentrés chez eux. Maintenant il y en a 11. Combien d'enfants sont rentrés chez eux?
• Choices: A) 6 children B) 8 children C) 7 children D) 9 children
• Hint: To find how many left, subtract the amount that remains from the total (e.g., 14 − 8 = 6).
• Steps:
  • Start with 18 children total.
  • 11 children are still there.
  • Subtract: 18 − 11 = 7.
  • So 7 children went home.
• Answer: 7 children

[Hard] Counting to 100

• EN: What is the number that comes just before 100?
• FR: Quel est le nombre qui vient juste avant 100?
• Choices: A) 101 B) 98 C) 99 D) 90
• Hint: The number just before any number is one less (e.g., the number just before 50 is 49).
• Steps:
  • Think about what is one less than 100.
  • 100 − 1 = 99.
  • So the number just before 100 is 99.
• Answer: 99

[Easy] Adding Two-Digit Numbers

• EN: There are 23 apples in one basket and 14 apples in another. How many apples are there altogether?
• FR: Il y a 23 pommes dans un panier et 14 dans un autre. Combien y a-t-il de pommes en tout?
• Choices: A) 38 apples B) 36 apples C) 37 apples D) 39 apples
• Hint: Add the ones first, then the tens (e.g., 31 + 12: ones 1+2=3, tens 3+1=4, total 43).
• Steps:
  • Add the ones: 3 + 4 = 7.
  • Add the tens: 20 + 10 = 30.
  • Combine: 30 + 7 = 37.
  • So there are 37 apples altogether.
• Answer: 37 apples

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre l'aiguille des heures sur le 3 et l'aiguille des minutes sur le 12. Quelle heure est-il?
• Choices: A) 12:00 B) 3:30 C) 3:00 D) 6:00
• Hint: When the minute hand is on the 12, it means it is exactly on the hour (e.g., hour hand on 7 = 7:00).
• Steps:
  • The hour hand points to 3.
  • The minute hand points to 12, meaning zero minutes.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 12 cm long. An eraser is 3 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 12 cm. Une gomme mesure 3 cm. De combien le crayon est-il plus long que la gomme?
• Choices: A) 10 cm B) 8 cm C) 15 cm D) 9 cm
• Hint: To find how much longer, subtract the shorter length from the longer one (e.g., 14 cm − 6 cm = 8 cm).
• Steps:
  • Subtract the eraser length from the pencil length.
  • 12 − 3 = 9.
  • So the pencil is 9 cm longer than the eraser.
• Answer: 9 cm

[Easy] Simple Patterns

• EN: Look at this pattern: 2, 4, 6, 8, ___. What number comes next?
• FR: Regarde ce motif : 2, 4, 6, 8, ___. Quel nombre vient ensuite?
• Choices: A) 11 B) 12 C) 9 D) 10
• Hint: Find the rule by looking at how much each number increases (e.g., 3, 6, 9, 12 — add 3 each time).
• Steps:
  • Look at the differences: 4−2=2, 6−4=2, 8−6=2.
  • The rule is add 2 each time.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Medium] Counting Coins

• EN: Noah has 1 dime, 2 nickels, and 3 pennies. How much money does he have?
• FR: Noah a 1 pièce de 10 cents, 2 pièces de 5 cents et 3 pièces de 1 cent. Combien d'argent a-t-il?
• Choices: A) 20 cents B) 23 cents C) 25 cents D) 18 cents
• Hint: Multiply each coin by its value, then add all together (e.g., 1 dime + 1 nickel + 2 pennies = 10+5+2 = 17 cents).
• Steps:
  • 1 dime = 10 cents.
  • 2 nickels = 2 × 5 = 10 cents.
  • 3 pennies = 3 × 1 = 3 cents.
  • Total: 10 + 10 + 3 = 23 cents.
• Answer: 23 cents

[Medium] Subtracting Two-Digit Numbers

• EN: A bag had 56 hockey cards. Sam gave away 24 cards. How many cards does Sam have left?
• FR: Un sac contenait 56 cartes de hockey. Sam en a donné 24. Combien de cartes lui reste-t-il?
• Choices: A) 30 cards B) 33 cards C) 32 cards D) 28 cards
• Hint: Subtract the ones first, then the tens (e.g., 48 − 15: ones 8−5=3, tens 40−10=30, total 33).
• Steps:
  • Subtract the ones: 6 − 4 = 2.
  • Subtract the tens: 50 − 20 = 30.
  • Combine: 30 + 2 = 32.
  • So Sam has 32 cards left.
• Answer: 32 cards

[Medium] Telling Time — Half Hour

• EN: The clock shows the hour hand between 6 and 7, and the minute hand on 6. What time is it?
• FR: L'horloge montre l'aiguille des heures entre le 6 et le 7, et l'aiguille des minutes sur le 6. Quelle heure est-il?
• Choices: A) 6:00 B) 7:30 C) 7:00 D) 6:30
• Hint: When the minute hand is on the 6, it means 30 minutes past the hour (e.g., hour hand between 4 and 5 = 4:30).
• Steps:
  • The minute hand on 6 means 30 minutes.
  • The hour hand is between 6 and 7, so it is past 6.
  • The time is 6:30.
• Answer: 6:30

[Medium] Measuring in Metres

• EN: A hallway is 8 m long. A classroom is 5 m long. How long are they together?
• FR: Un couloir mesure 8 m de long. Une salle de classe mesure 5 m de long. Quelle est leur longueur totale?
• Choices: A) 14 m B) 12 m C) 11 m D) 13 m
• Hint: To find the combined length, add both measurements (e.g., 6 m + 7 m = 13 m).
• Steps:
  • Add the two lengths together.
  • 8 + 5 = 13.
  • So together they are 13 m long.
• Answer: 13 m

[Hard] Two-Step Money Problem

• EN: Ava has 75 cents. She spends 30 cents on a sticker and 20 cents on a pencil. How much money does she have left?
• FR: Ava a 75 cents. Elle dépense 30 cents pour un autocollant et 20 cents pour un crayon. Combien d'argent lui reste-t-il?
• Choices: A) 30 cents B) 25 cents C) 45 cents D) 35 cents
• Hint: First add what was spent, then subtract from the total (e.g., 50 cents − 15 cents − 10 cents = 25 cents).
• Steps:
  • Add what she spent: 30 + 20 = 50 cents.
  • Subtract from her total: 75 − 50 = 25 cents.
  • So Ava has 25 cents left.
• Answer: 25 cents

[Hard] Adding Three Numbers

• EN: A Grade 2 class collected 34 cans, 25 cans, and 13 cans for a food drive. How many cans did they collect in all?
• FR: Une classe de 2e année a recueilli 34 boîtes, 25 boîtes et 13 boîtes pour une collecte alimentaire. Combien de boîtes ont-ils recueilli en tout?
• Choices: A) 70 cans B) 73 cans C) 72 cans D) 68 cans
• Hint: Add the first two numbers, then add the third to the result (e.g., 21 + 14 + 12 = 35 + 12 = 47).
• Steps:
  • Add the first two: 34 + 25 = 59.
  • Add the third: 59 + 13 = 72.
  • So they collected 72 cans in all.
• Answer: 72 cans

[Easy] Multiplication by 2

• EN: There are 6 pairs of hockey gloves. Each pair has 2 gloves. How many gloves are there in all?
• FR: Il y a 6 paires de gants de hockey. Chaque paire a 2 gants. Combien y a-t-il de gants en tout?
• Choices: A) 10 gloves B) 14 gloves C) 8 gloves D) 12 gloves
• Hint: Multiply the number of groups by the number in each group (e.g., 4 pairs × 2 = 8).
• Steps:
  • There are 6 pairs, each with 2 gloves.
  • Multiply: 6 × 2 = 12.
  • So there are 12 gloves in all.
• Answer: 12 gloves

[Easy] Basic Division

• EN: 20 cookies are shared equally among 4 friends. How many cookies does each friend get?
• FR: 20 biscuits sont partagés également entre 4 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 6 cookies B) 4 cookies C) 5 cookies D) 8 cookies
• Hint: Division is the opposite of multiplication (e.g., 18 ÷ 3 = 6 because 3 × 6 = 18).
• Steps:
  • Think: 4 × ? = 20.
  • 4 × 5 = 20.
  • So each friend gets 5 cookies.
• Answer: 5 cookies

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. Emma eats 1 piece. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Emma mange 1 morceau. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/4 B) 2/3 C) 1/2 D) 1/3
• Hint: A fraction shows parts out of a whole — the bottom number is how many total pieces, the top is how many you have (e.g., 1 piece out of 3 = 1/3).
• Steps:
  • The pizza has 2 equal pieces total.
  • Emma ate 1 piece.
  • So she ate 1 out of 2 = 1/2.
• Answer: 1/2

[Easy] Multiplication by 5

• EN: Each student has 5 crayons. There are 4 students. How many crayons are there altogether?
• FR: Chaque élève a 5 crayons. Il y a 4 élèves. Combien y a-t-il de crayons en tout?
• Choices: A) 25 crayons B) 20 crayons C) 18 crayons D) 22 crayons
• Hint: Use the 5 times table (e.g., 5 × 3 = 15, 5 × 5 = 25).
• Steps:
  • 4 students × 5 crayons each.
  • 4 × 5 = 20.
  • So there are 20 crayons altogether.
• Answer: 20 crayons

[Medium] Perimeter of a Rectangle

• EN: A rectangular garden is 6 m long and 3 m wide. What is its perimeter?
• FR: Un jardin rectangulaire mesure 6 m de long et 3 m de large. Quel est son périmètre?
• Choices: A) 20 m B) 16 m C) 18 m D) 24 m
• Hint: Perimeter of a rectangle = add all four sides (e.g., a shape 5 m long and 2 m wide: 5+5+2+2 = 14 m).
• Steps:
  • A rectangle has two lengths and two widths.
  • Add all sides: 6 + 6 + 3 + 3.
  • 6 + 6 = 12, and 3 + 3 = 6.
  • 12 + 6 = 18 m.
• Answer: 18 m

[Medium] Multiplication by 3

• EN: A Tim Hortons order has 3 muffins per box. There are 7 boxes. How many muffins are there in total?
• FR: Une commande de Tim Hortons contient 3 muffins par boîte. Il y a 7 boîtes. Combien y a-t-il de muffins au total?
• Choices: A) 24 muffins B) 18 muffins C) 28 muffins D) 21 muffins
• Hint: Use the 3 times table (e.g., 3 × 6 = 18, 3 × 8 = 24).
• Steps:
  • 7 boxes × 3 muffins each.
  • 7 × 3 = 21.
  • So there are 21 muffins in total.
• Answer: 21 muffins

[Medium] Reading a Simple Bar Graph

• EN: A bar graph shows: Monday 4 goals, Tuesday 6 goals, Wednesday 2 goals. How many goals were scored in all three days?
• FR: Un diagramme à barres montre : lundi 4 buts, mardi 6 buts, mercredi 2 buts. Combien de buts ont été marqués en tout sur les trois jours?
• Choices: A) 10 goals B) 14 goals C) 11 goals D) 12 goals
• Hint: To find the total from a graph, add all the values shown (e.g., 3 + 5 + 4 = 12).
• Steps:
  • Monday: 4 goals.
  • Tuesday: 6 goals.
  • Wednesday: 2 goals.
  • Add: 4 + 6 + 2 = 12 goals.
• Answer: 12 goals

[Medium] Fractions — One Quarter

• EN: A chocolate bar has 4 equal pieces. Leo eats 1 piece. What fraction does he eat?
• FR: Une barre de chocolat a 4 morceaux égaux. Léo mange 1 morceau. Quelle fraction mange-t-il?
• Choices: A) 1/3 B) 2/4 C) 1/2 D) 1/4
• Hint: Write the fraction as pieces eaten over total pieces (e.g., 1 piece out of 3 total = 1/3).
• Steps:
  • The bar has 4 equal pieces total.
  • Leo eats 1 piece.
  • So he eats 1 out of 4 = 1/4.
• Answer: 1/4

[Hard] Multiplication by 4 — Two-Step

• EN: There are 4 shelves in a library. Each shelf has 9 books. 8 books are removed. How many books remain?
• FR: Il y a 4 étagères dans une bibliothèque. Chaque étagère a 9 livres. On enlève 8 livres. Combien de livres reste-t-il?
• Choices: A) 36 books B) 26 books C) 28 books D) 30 books
• Hint: First find the total using multiplication, then subtract the amount removed (e.g., 3 × 6 = 18, then 18 − 4 = 14).
• Steps:
  • Find total books: 4 × 9 = 36.
  • Subtract the removed books: 36 − 8 = 28.
  • So 28 books remain.
• Answer: 28 books

[Hard] Perimeter and Fractions

• EN: A square playground has sides of 10 m each. A path covers 1/4 of the perimeter. How long is the path?
• FR: Un terrain de jeux carré a des côtés de 10 m chacun. Un chemin couvre 1/4 du périmètre. Quelle est la longueur du chemin?
• Choices: A) 8 m B) 12 m C) 10 m D) 15 m
• Hint: First find the perimeter, then divide by 4 to find one quarter (e.g., perimeter of 24 m, 1/4 = 24 ÷ 4 = 6 m).
• Steps:
  • Perimeter of a square = 4 × side length.
  • 4 × 10 = 40 m.
  • 1/4 of 40 = 40 ÷ 4 = 10 m.
  • So the path is 10 m long.
• Answer: 10 m

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 54 B) 63 C) 56 D) 48
• Hint: Use a familiar fact to get close (e.g., 7 × 7 = 49, then add one more group of 7).
• Steps:
  • 7 × 7 = 49.
  • Add one more group of 7: 49 + 7 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 4 tens
• Hint: In a decimal, the first digit after the point is in the tenths place (e.g., in 2.56, the 5 is in the tenths place).
• Steps:
  • The number is 3.47.
  • The digit 3 is in the ones place.
  • The digit 4 is right after the decimal point — that is the tenths place.
  • So 4 is worth 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A rectangular carpet is 5 m long and 4 m wide. What is its area?
• FR: Un tapis rectangulaire mesure 5 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 18 m² B) 22 m² C) 20 m² D) 24 m²
• Hint: Area of a rectangle = length × width (e.g., 6 m × 3 m = 18 m²).
• Steps:
  • Area = length × width.
  • Area = 5 × 4 = 20.
  • So the area is 20 m².
• Answer: 20 m²

[Easy] Long Division — No Remainder

• EN: 48 ÷ 6 = ?
• FR: 48 ÷ 6 = ?
• Choices: A) 9 B) 7 C) 8 D) 6
• Hint: Think: 6 × ? = 48 (e.g., for 35 ÷ 5, ask: 5 × ? = 35, which is 7).
• Steps:
  • Ask: 6 × ? = 48.
  • 6 × 8 = 48.
  • So 48 ÷ 6 = 8.
• Answer: 8

[Medium] Long Division with Remainder

• EN: 50 stickers are shared equally among 7 students. How many stickers does each student get, and how many are left over?
• FR: 50 autocollants sont partagés également entre 7 élèves. Combien d'autocollants chaque élève reçoit-il et combien en reste-t-il?
• Choices: A) 7 remainder 2 B) 6 remainder 9 C) 7 remainder 1 D) 8 remainder 1
• Hint: Divide and find the largest multiple of the divisor that fits, then subtract to find the remainder (e.g., 25 ÷ 4: 4×6=24, remainder 25−24=1, so 6 remainder 1).
• Steps:
  • 7 × 7 = 49, which is close to 50.
  • 50 − 49 = 1 left over.
  • So each student gets 7 stickers with 1 remainder.
• Answer: 7 remainder 1

[Medium] 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) They are equal C) 3/4 D) 1/4
• Hint: When denominators are the same, the fraction with the bigger numerator is greater (e.g., 4/5 > 2/5).
• Steps:
  • Both fractions have the same denominator (4).
  • Compare numerators: 3 > 2.
  • So 3/4 is greater than 2/4.
• Answer: 3/4

[Medium] Elapsed Time

• EN: A hockey game started at 2:15 and ended at 4:45. How long did the game last?
• FR: Un match de hockey a commencé à 14 h 15 et s'est terminé à 16 h 45. Combien de temps le match a-t-il duré?
• Choices: A) 2 hours 45 minutes B) 2 hours 30 minutes C) 3 hours 15 minutes D) 1 hour 30 minutes
• Hint: Count up from the start time to the end time in hours and minutes (e.g., 1:10 to 3:40 = 2 hours 30 minutes).
• Steps:
  • From 2:15 to 4:15 is exactly 2 hours.
  • From 4:15 to 4:45 is 30 more minutes.
  • Total: 2 hours + 30 minutes = 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A store sells a notebook for $3.25 and a pen for $1.50. What is the total cost?
• FR: Un magasin vend un cahier à 3,25 $ et un stylo à 1,50 $. Quel est le coût total?
• Choices: A) $5.25 B) $4.50 C) $4.75 D) $5.00
• Hint: Line up the decimal points and add as you would with whole numbers (e.g., $2.40 + $1.35 = $3.75).
• Steps:
  • Add $3.25 + $1.50.
  • Ones: 3 + 1 = 4. Tenths: 2 + 5 = 7. Hundredths: 5 + 0 = 5.
  • Total = $4.75.
• Answer: $4.75

[Hard] Multi-Step Area Problem

• EN: A classroom floor is 9 m long and 6 m wide. A reading rug inside is 3 m long and 2 m wide. How much floor space is NOT covered by the rug?
• FR: Le plancher d'une salle de classe est 9 m de long et 6 m de large. Un tapis de lecture à l'intérieur est 3 m de long et 2 m de large. Quelle surface du plancher n'est PAS couverte par le tapis?
• Choices: A) 54 m² B) 48 m² C) 42 m² D) 50 m²
• Hint: Find the area of each rectangle, then subtract the smaller from the larger (e.g., 8×5=40, rug 2×3=6, uncovered = 40−6=34 m²).
• Steps:
  • Classroom area: 9 × 6 = 54 m².
  • Rug area: 3 × 2 = 6 m².
  • Uncovered floor: 54 − 6 = 48 m².
• Answer: 48 m²

[Hard] Decimals and Division

• EN: Four friends share the cost of a $13.60 Tim Hortons order equally. How much does each person pay?
• FR: Quatre amis partagent également le coût d'une commande de Tim Hortons de 13,60 $. Combien chaque personne paie-t-elle?
• Choices: A) $3.90 B) $3.40 C) $4.00 D) $2.80
• Hint: Divide the total cost by the number of people (e.g., $8.40 ÷ 4 = $2.10).
• Steps:
  • Divide $13.60 ÷ 4.
  • 13 ÷ 4 = 3 with 1 remaining. Bring down the 6: 16 ÷ 4 = 4. Bring down the 0: 0 ÷ 4 = 0.
  • So $13.60 ÷ 4 = $3.40.
• Answer: $3.40

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien fait 34 × 6?
• Choices: A) 214 B) 204 C) 196 D) 224
• Hint: Break the number apart and multiply each part separately (e.g., 23 × 4: 20×4=80, 3×4=12, total = 92).
• Steps:
  • Split 34 into 30 + 4.
  • 30 × 6 = 180.
  • 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

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

[Easy] Percentage — 50%

• EN: There are 60 students at a school event. 50% of them are wearing red shirts. How many students are wearing red shirts?
• FR: Il y a 60 élèves à un événement scolaire. 50 % d'entre eux portent des chemises rouges. Combien d'élèves portent des chemises rouges?
• Choices: A) 25 B) 35 C) 30 D) 40
• Hint: 50% means one half — divide by 2 (e.g., 50% of 80 = 80 ÷ 2 = 40).
• Steps:
  • 50% = one half.
  • 60 ÷ 2 = 30.
  • So 30 students are wearing red shirts.
• Answer: 30

[Easy] Volume of a Rectangular Prism

• EN: A box is 4 cm long, 3 cm wide, and 2 cm tall. What is its volume?
• FR: Une boîte mesure 4 cm de long, 3 cm de large et 2 cm de haut. Quel est son volume?
• Choices: A) 18 cm³ B) 26 cm³ C) 24 cm³ D) 20 cm³
• Hint: Volume = length × width × height (e.g., 5 × 2 × 3 = 30 cm³).
• Steps:
  • Volume = 4 × 3 × 2.
  • 4 × 3 = 12.
  • 12 × 2 = 24.
  • So the volume is 24 cm³.
• Answer: 24 cm³

[Medium] Multi-Digit Division

• EN: 252 pencils are packed equally into 6 boxes. How many pencils are in each box?
• FR: 252 crayons sont emballés également dans 6 boîtes. Combien y a-t-il de crayons dans chaque boîte?
• Choices: A) 38 B) 44 C) 42 D) 46
• Hint: Divide step by step: first divide the hundreds, then the tens, then the ones (e.g., 186 ÷ 6: 6 goes into 18 three times = 30, then 6 into 6 = 1, total 31).
• Steps:
  • 6 goes into 25 four times (6×4=24), remainder 1.
  • Bring down 2: 12. 6 goes into 12 twice.
  • So 252 ÷ 6 = 42.
• Answer: 42

[Medium] Subtracting Fractions

• EN: What is 7/10 − 3/10?
• FR: Combien fait 7/10 − 3/10?
• Choices: A) 4/20 B) 5/10 C) 3/10 D) 4/10
• Hint: When denominators are the same, subtract the numerators and keep the denominator (e.g., 6/9 − 2/9 = 4/9).
• Steps:
  • Denominators are both 10 — keep 10.
  • Subtract numerators: 7 − 3 = 4.
  • So the answer is 4/10.
• Answer: 4/10

[Medium] Decimal Addition

• EN: A snowfall of 14.6 cm fell on Friday and 8.7 cm fell on Saturday. How much snow fell in total?
• FR: Il est tombé 14,6 cm de neige vendredi et 8,7 cm samedi. Combien de neige est tombée en tout?
• Choices: A) 23.3 cm B) 22.9 cm C) 24.1 cm D) 21.7 cm
• Hint: Line up decimal points and add (e.g., 11.4 + 6.8 = 18.2).
• Steps:
  • 14.6 + 8.7.
  • Tenths: 6 + 7 = 13, write 3 and carry 1.
  • Ones: 4 + 8 + 1 (carry) = 13, write 3 and carry 1.
  • Tens: 1 + 0 + 1 = 2.
  • Total = 23.3 cm.
• Answer: 23.3 cm

[Medium] Percentage — 25%

• EN: A bag of 80 marbles is on sale at 25% off the regular price. How many marbles would represent 25% of the bag?
• FR: Un sac de 80 billes est en solde à 25 % de réduction. Combien de billes représentent 25 % du sac?
• Choices: A) 25 marbles B) 15 marbles C) 20 marbles D) 40 marbles
• Hint: 25% means one quarter — divide by 4 (e.g., 25% of 60 = 60 ÷ 4 = 15).
• Steps:
  • 25% = one quarter = divide by 4.
  • 80 ÷ 4 = 20.
  • So 20 marbles represent 25% of the bag.
• Answer: 20 marbles

[Hard] Multi-Step Decimal Problem

• EN: Priya bought 3 books at $4.85 each and paid with a $20 bill. How much change did she receive?
• FR: Priya a acheté 3 livres à 4,85 $ chacun et a payé avec un billet de 20 $. Combien de monnaie a-t-elle reçu?
• Choices: A) $5.45 B) $4.55 C) $5.55 D) $6.15
• Hint: First find the total cost by multiplying, then subtract from the amount paid (e.g., 4 books at $3.20 = $12.80, change from $20 = $7.20).
• Steps:
  • Total cost: 3 × $4.85 = $14.55.
  • Change: $20.00 − $14.55 = $5.45.
  • So Priya received $5.45 in change.
• Answer: $5.45

[Hard] Volume and Percentage

• EN: A rectangular fish tank is 10 cm long, 5 cm wide, and 8 cm tall. It is currently 50% full of water. How many cubic centimetres of water are in the tank?
• FR: Un aquarium rectangulaire mesure 10 cm de long, 5 cm de large et 8 cm de haut. Il est actuellement rempli à 50 % d'eau. Combien de centimètres cubes d'eau y a-t-il dans l'aquarium?
• Choices: A) 250 cm³ B) 200 cm³ C) 400 cm³ D) 175 cm³
• Hint: Find the total volume first, then take 50% of it (e.g., volume = 6×4×5 = 120 cm³, 50% of 120 = 60 cm³).
• Steps:
  • Total volume: 10 × 5 × 8 = 400 cm³.
  • 50% of 400 = 400 ÷ 2 = 200 cm³.
  • So there are 200 cm³ of water in the tank.
• Answer: 200 cm³

[Easy] Percent of a Number

• EN: What is 30% of 90?
• FR: Combien fait 30 % de 90?
• Choices: A) 30 B) 27 C) 24 D) 33
• Hint: Find 10% first by dividing by 10, then multiply by the number of tens (e.g., 30% of 60: 10% = 6, so 30% = 6 × 3 = 18).
• Steps:
  • 10% of 90 = 90 ÷ 10 = 9.
  • 30% = 3 × 9 = 27.
  • So 30% of 90 is 27.
• Answer: 27

[Easy] Simple Algebraic Expression

• EN: If n = 5, what is the value of 3n + 4?
• FR: Si n = 5, quelle est la valeur de 3n + 4?
• Choices: A) 22 B) 17 C) 12 D) 19
• Hint: Substitute the value for the variable, then follow the order of operations (e.g., if n = 3, then 2n + 1 = 2×3 + 1 = 7).
• Steps:
  • Replace n with 5: 3(5) + 4.
  • Multiply first: 3 × 5 = 15.
  • Then add: 15 + 4 = 19.
  • So the value is 19.
• Answer: 19

[Easy] Ratio

• EN: In a bag of 12 candies, 4 are red and 8 are blue. What is the ratio of red to blue candies?
• FR: Dans un sac de 12 bonbons, 4 sont rouges et 8 sont bleus. Quel est le rapport des bonbons rouges aux bonbons bleus?
• Choices: A) 4:8 B) 1:2 C) 2:1 D) 8:4
• Hint: Simplify ratios by dividing both parts by their greatest common factor (e.g., 6:9 → divide by 3 → 2:3).
• Steps:
  • Red to blue = 4:8.
  • Simplify by dividing both by 4: 4÷4 : 8÷4 = 1:2.
  • So the ratio of red to blue is 1:2.
• Answer: 1:2

[Easy] Integers Introduction

• EN: The temperature is −3°C in the morning and rises by 7 degrees. What is the temperature now?
• FR: La température est de −3 °C le matin et monte de 7 degrés. Quelle est la température maintenant?
• Choices: A) 3°C B) 5°C C) 4°C D) 10°C
• Hint: To add a positive number to a negative number, move that many steps to the right on a number line (e.g., −5 + 8 = 3).
• Steps:
  • Start at −3.
  • Add 7: −3 + 7 = 4.
  • So the temperature is now 4°C.
• Answer: 4°C

[Medium] Order of Operations — BEDMAS

• EN: What is the value of 3 + 4 × 2 − 1?
• FR: Quelle est la valeur de 3 + 4 × 2 − 1?
• Choices: A) 13 B) 14 C) 10 D) 12
• Hint: Use BEDMAS — do multiplication and division before addition and subtraction (e.g., 5 + 3 × 2 = 5 + 6 = 11).
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Replace: 3 + 8 − 1.
  • Left to right: 3 + 8 = 11, then 11 − 1 = 10.
  • So the value is 10.
• Answer: 10

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien fait 2/3 × 3/4?
• Choices: A) 5/12 B) 6/12 C) 1/4 D) 2/4
• Hint: Multiply the numerators together and the denominators together, then simplify (e.g., 1/2 × 2/3 = 2/6 = 1/3).
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • Result: 6/12 = 1/2.
  • So 2/3 × 3/4 = 6/12, which simplifies to 1/2.
• Answer: 6/12

[Medium] Rate

• EN: A car travels 150 km in 3 hours. What is its speed in kilometres per hour?
• FR: Une voiture parcourt 150 km en 3 heures. Quelle est sa vitesse en kilomètres par heure?
• Choices: A) 60 km/h B) 45 km/h C) 50 km/h D) 55 km/h
• Hint: Rate = total distance ÷ total time (e.g., 120 km in 4 hours = 120 ÷ 4 = 30 km/h).
• Steps:
  • Speed = distance ÷ time.
  • 150 ÷ 3 = 50.
  • So the car travels at 50 km/h.
• Answer: 50 km/h

[Medium] Fraction Division

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

[Hard] Multi-Step BEDMAS

• EN: What is (5 + 3)² ÷ 4 − 6?
• FR: Quelle est la valeur de (5 + 3)² ÷ 4 − 6?
• Choices: A) 14 B) 10 C) 8 D) 16
• Hint: Follow BEDMAS — Brackets first, then Exponents, then Division, then Subtraction (e.g., (2+3)² ÷ 5 = 25 ÷ 5 = 5).
• Steps:
  • Brackets: 5 + 3 = 8.
  • Exponent: 8² = 64.
  • Division: 64 ÷ 4 = 16.
  • Subtraction: 16 − 6 = 10.
• Answer: 10

[Hard] Percent Problem — Multi-Step

• EN: A jacket regularly costs $80. It is on sale for 15% off. What is the sale price?
• FR: Un manteau coûte normalement 80 $. Il est en solde à 15 % de rabais. Quel est le prix soldé?
• Choices: A) $72 B) $65 C) $68 D) $76
• Hint: Find the discount amount first, then subtract from the original price (e.g., 20% off $50: discount = $10, sale price = $40).
• Steps:
  • 10% of $80 = $8.
  • 5% of $80 = $4.
  • 15% = $8 + $4 = $12 discount.
  • Sale price: $80 − $12 = $68.
• Answer: $68

[Easy] Integer Addition

• EN: What is −9 + 15?
• FR: Combien fait −9 + 15?
• Choices: A) 4 B) 7 C) 6 D) 8
• Hint: On a number line, adding a positive number moves you to the right (e.g., −4 + 9 = 5).
• Steps:
  • Start at −9 on the number line.
  • Move 15 steps to the right.
  • −9 + 15 = 6.
• Answer: 6

[Easy] Percent Discount

• EN: A loonie-store item costs $4.00. It is on sale for 25% off. What is the sale price?
• FR: Un article de magasin coûte 4,00 $. Il est en solde à 25 % de réduction. Quel est le prix soldé?
• Choices: A) $2.50 B) $3.00 C) $1.50 D) $3.50
• Hint: Find 25% of the price, then subtract it (e.g., 25% of $8 = $2, so sale price = $8 − $2 = $6).
• Steps:
  • 25% of $4.00 = $4.00 ÷ 4 = $1.00.
  • Sale price: $4.00 − $1.00 = $3.00.
  • So the sale price is $3.00.
• Answer: $3.00

[Easy] Integer Subtraction

• EN: What is 3 − 8?
• FR: Combien fait 3 − 8?
• Choices: A) −6 B) 5 C) −5 D) −4
• Hint: Subtracting a larger number from a smaller one gives a negative result (e.g., 2 − 7 = −5).
• Steps:
  • 3 − 8 means we owe 5.
  • 8 − 3 = 5, and since we subtracted a larger number, the answer is negative.
  • 3 − 8 = −5.
• Answer: −5

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 16.
• FR: Résoudre pour x : x + 9 = 16.
• Choices: A) x = 8 B) x = 6 C) x = 7 D) x = 5
• Hint: To solve, subtract the number from both sides (e.g., x + 4 = 11: x = 11 − 4 = 7).
• Steps:
  • x + 9 = 16.
  • Subtract 9 from both sides: x = 16 − 9.
  • x = 7.
• Answer: x = 7

[Medium] Tip Calculation

• EN: A meal at a restaurant costs $24.00. If you leave a 15% tip, how much is the tip?
• FR: Un repas au restaurant coûte 24,00 $. Si vous laissez un pourboire de 15 %, quel est le montant du pourboire?
• Choices: A) $4.80 B) $3.60 C) $2.40 D) $5.20
• Hint: Find 10% first, then add half of that for 5% (e.g., 15% of $40: 10% = $4, 5% = $2, total = $6).
• Steps:
  • 10% of $24.00 = $2.40.
  • 5% of $24.00 = $1.20.
  • 15% = $2.40 + $1.20 = $3.60.
  • So the tip is $3.60.
• Answer: $3.60

[Medium] Integer Multiplication

• EN: What is (−4) × 7?
• FR: Combien fait (−4) × 7?
• Choices: A) −24 B) 28 C) −28 D) −32
• Hint: A negative times a positive is always negative (e.g., (−3) × 5 = −15).
• Steps:
  • Multiply the absolute values: 4 × 7 = 28.
  • One sign is negative, so the answer is negative.
  • (−4) × 7 = −28.
• Answer: −28

[Medium] Surface Area

• EN: A rectangular box is 5 cm long, 4 cm wide, and 3 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quelle est son aire de surface?
• Choices: A) 60 cm² B) 94 cm² C) 72 cm² D) 80 cm²
• Hint: Surface area = 2(lw + lh + wh) (e.g., box 2×3×4: 2(6+8+12) = 2×26 = 52 cm²).
• Steps:
  • lw = 5 × 4 = 20. lh = 5 × 3 = 15. wh = 4 × 3 = 12.
  • Sum: 20 + 15 + 12 = 47.
  • Surface area: 2 × 47 = 94 cm².
• Answer: 94 cm²

[Medium] Probability

• EN: A bag has 3 red marbles, 4 blue marbles, and 3 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 4 billes bleues et 3 billes vertes. Quelle est la probabilité de choisir une bille bleue?
• Choices: A) 3/10 B) 2/5 C) 1/4 D) 4/9
• Hint: Probability = number of favourable outcomes ÷ total outcomes (e.g., 2 red out of 8 total = 2/8 = 1/4).
• Steps:
  • Total marbles: 3 + 4 + 3 = 10.
  • Blue marbles: 4.
  • Probability = 4/10 = 2/5.
• Answer: 2/5

[Hard] Two-Step Integer Problem

• EN: The temperature was −12°C. It rose 8 degrees in the morning and then dropped 5 degrees in the evening. What was the final temperature?
• FR: La température était de −12 °C. Elle a monté de 8 degrés le matin puis a baissé de 5 degrés le soir. Quelle était la température finale?
• Choices: A) −9°C B) −10°C C) −8°C D) −11°C
• Hint: Apply each change step by step on a number line (e.g., −6 + 5 − 3 = −1 − 3 = −4).
• Steps:
  • Start at −12.
  • Rise 8: −12 + 8 = −4.
  • Drop 5: −4 − 5 = −9.
  • The final temperature is −9°C.
• Answer: −9°C

[Hard] Percent Tax

• EN: A pair of hockey skates costs $120 before tax. The tax rate is 13%. What is the total cost including tax?
• FR: Une paire de patins de hockey coûte 120 $ avant taxes. Le taux de taxe est de 13 %. Quel est le coût total avec taxes?
• Choices: A) $135.60 B) $132.00 C) $133.60 D) $139.20
• Hint: Find the tax amount by multiplying price × tax rate, then add to the original price (e.g., $50 × 13% = $6.50, total = $56.50).
• Steps:
  • Tax = $120 × 0.13 = $15.60.
  • Total: $120.00 + $15.60 = $135.60.
  • So the total cost is $135.60.
• Answer: $135.60

[Easy] Perfect Squares

• EN: What is the square root of 64?
• FR: Quelle est la racine carrée de 64?
• Choices: A) 6 B) 9 C) 7 D) 8
• Hint: Think about which number multiplied by itself equals the given number (e.g., √36 = 6 because 6 × 6 = 36).
• Steps:
  • Ask: what number × itself = 64?
  • 8 × 8 = 64.
  • So √64 = 8.
• Answer: 8

[Easy] Mean

• EN: Five students scored 70, 80, 90, 60, and 50 on a quiz. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 80, 90, 60 et 50 à un quiz. Quelle est la moyenne?
• Choices: A) 72 B) 68 C) 70 D) 75
• Hint: Mean = sum of all values ÷ number of values (e.g., scores 10, 20, 30: mean = 60 ÷ 3 = 20).
• Steps:
  • Sum: 70 + 80 + 90 + 60 + 50 = 350.
  • Number of scores: 5.
  • Mean = 350 ÷ 5 = 70.
• Answer: 70

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 3 = 11.
• FR: Résoudre pour x : 2x + 3 = 11.
• Choices: A) x = 5 B) x = 3 C) x = 6 D) x = 4
• Hint: First subtract the constant from both sides, then divide by the coefficient (e.g., 3x + 2 = 14: 3x = 12, x = 4).
• Steps:
  • 2x + 3 = 11.
  • Subtract 3: 2x = 8.
  • Divide by 2: x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A hockey team won 20 games last year and 25 games this year. What is the percent increase in wins?
• FR: Une équipe de hockey a gagné 20 matchs l'an dernier et 25 matchs cette année. Quel est le pourcentage d'augmentation des victoires?
• Choices: A) 30% B) 20% C) 25% D) 15%
• Hint: Percent increase = (increase ÷ original) × 100 (e.g., from 40 to 50: increase = 10, 10/40 × 100 = 25%).
• Steps:
  • Increase = 25 − 20 = 5.
  • Percent increase = (5 ÷ 20) × 100 = 25%.
  • So the percent increase is 25%.
• Answer: 25%

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des côtés de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 12 cm B) 10 cm C) 14 cm D) 11 cm
• Hint: Use a² + b² = c² (e.g., legs 3 and 4: 9 + 16 = 25, so c = 5).
• Steps:
  • a² + b² = c².
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation

• EN: Solve for y: 5y − 7 = 28.
• FR: Résoudre pour y : 5y − 7 = 28.
• Choices: A) y = 8 B) y = 6 C) y = 9 D) y = 7
• Hint: Add the constant to both sides, then divide (e.g., 4y − 3 = 17: 4y = 20, y = 5).
• Steps:
  • 5y − 7 = 28.
  • Add 7: 5y = 35.
  • Divide by 5: y = 7.
• Answer: y = 7

[Medium] Median

• EN: Find the median of the following data set: 12, 7, 3, 15, 9.
• FR: Trouvez la médiane de l'ensemble de données suivant : 12, 7, 3, 15, 9.
• Choices: A) 7 B) 12 C) 10 D) 9
• Hint: Sort the values from smallest to largest, then find the middle value (e.g., 4, 6, 8, 10, 12 → median = 8).
• Steps:
  • Sort: 3, 7, 9, 12, 15.
  • There are 5 values. The middle (3rd) is 9.
  • The median is 9.
• Answer: 9

[Medium] Slope Introduction

• EN: A ramp rises 4 m over a horizontal distance of 8 m. What is the slope of the ramp?
• FR: Une rampe monte de 4 m sur une distance horizontale de 8 m. Quelle est la pente de la rampe?
• Choices: A) 2 B) 1/3 C) 1/2 D) 3/4
• Hint: Slope = rise ÷ run (e.g., rise of 3 m over run of 6 m = 3/6 = 1/2).
• Steps:
  • Slope = rise ÷ run.
  • Slope = 4 ÷ 8 = 1/2.
  • So the slope is 1/2.
• Answer: 1/2

[Hard] Pythagorean Theorem — Applied

• EN: A 10 m ladder leans against a wall. The base of the ladder is 6 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 10 m est appuyée contre un mur. La base de l'échelle est à 6 m du mur. À quelle hauteur sur le mur l'échelle atteint-elle?
• Choices: A) 9 m B) 7 m C) 8 m D) 6 m
• Hint: Use a² + b² = c², where c is the hypotenuse (ladder) (e.g., if hypotenuse = 13, base = 5: 5² + b² = 13², b = 12).
• Steps:
  • Hypotenuse = 10 m, base = 6 m.
  • 6² + b² = 10².
  • 36 + b² = 100.
  • b² = 64, so b = 8 m.
• Answer: 8 m

[Hard] Percent Decrease and Two-Step Equation

• EN: A shirt was reduced in price by 20% and now costs $36. What was the original price?
• FR: Un chandail a été réduit de 20 % et coûte maintenant 36 $. Quel était le prix original?
• Choices: A) $48 B) $42 C) $40 D) $45
• Hint: If the new price is 80% of the original, set up the equation: 0.80 × original = new price, then divide (e.g., 0.75 × p = 30, so p = 40).
• Steps:
  • After a 20% decrease, the item costs 80% of the original.
  • 0.80 × p = $36.
  • p = $36 ÷ 0.80 = $45.
  • So the original price was $45.
• Answer: $45

[Easy] Solving a Linear Equation

• EN: Solve for x: 3x − 5 = 16.
• FR: Résoudre pour x : 3x − 5 = 16.
• Choices: A) x = 7 B) x = 8 C) x = 6 D) x = 9
• Hint: Add the constant to both sides first, then divide by the coefficient (e.g., 4x − 2 = 10: 4x = 12, x = 3).
• Steps:
  • 3x − 5 = 16.
  • Add 5: 3x = 21.
  • Divide by 3: x = 7.
• Answer: x = 7

[Easy] Adding Polynomials

• EN: Simplify: (2x + 5) + (3x − 2).
• FR: Simplifier : (2x + 5) + (3x − 2).
• Choices: A) 5x + 4 B) 6x − 3 C) 5x + 3 D) 4x + 7
• Hint: Combine like terms — add the x-terms together and the constant terms together (e.g., (4x+1)+(2x+3) = 6x+4).
• Steps:
  • Combine x-terms: 2x + 3x = 5x.
  • Combine constants: 5 − 2 = 3.
  • Result: 5x + 3.
• Answer: 5x + 3

[Easy] Slope-Intercept Form

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

[Easy] Linear Inequality

• EN: Solve for x: x + 4 > 10.
• FR: Résoudre pour x : x + 4 > 10.
• Choices: A) x > 5 B) x > 7 C) x > 6 D) x > 8
• Hint: Solve an inequality like an equation — subtract from both sides (e.g., x + 3 > 9: x > 6).
• Steps:
  • x + 4 > 10.
  • Subtract 4 from both sides: x > 6.
  • So x > 6.
• Answer: x > 6

[Medium] Multiplying Polynomials

• EN: Expand and simplify: 3x(x + 4).
• FR: Développer et simplifier : 3x(x + 4).
• Choices: A) 3x² + 12x B) 3x + 12x C) 3x² + 7x D) 6x² + 12x
• Hint: Distribute the term outside the brackets to each term inside (e.g., 2x(x+5) = 2x² + 10x).
• Steps:
  • Multiply 3x by x: 3x × x = 3x².
  • Multiply 3x by 4: 3x × 4 = 12x.
  • Result: 3x² + 12x.
• Answer: 3x² + 12x

[Medium] Similar Triangles

• EN: Two similar triangles have sides in a ratio of 1:3. The smaller triangle has a base of 5 cm. What is the base of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans un rapport de 1:3. Le petit triangle a une base de 5 cm. Quelle est la base du grand triangle?
• Choices: A) 20 cm B) 12 cm C) 18 cm D) 15 cm
• Hint: Multiply the smaller side by the scale factor (e.g., ratio 1:4, small side 6 cm → large side = 6 × 4 = 24 cm).
• Steps:
  • The scale factor is 3.
  • Larger triangle base = 5 × 3 = 15 cm.
  • So the base of the larger triangle is 15 cm.
• Answer: 15 cm

[Medium] 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. Quel est sin(θ)?
• Choices: A) 0.8 B) 0.75 C) 0.5 D) 0.6
• Hint: SOH: sin = opposite ÷ hypotenuse (e.g., opposite = 4, hypotenuse = 5: sin = 4/5 = 0.8).
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 6 ÷ 10 = 0.6.
  • So sin(θ) = 0.6.
• Answer: 0.6

[Medium] Graphing Lines

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

[Hard] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is the angle θ to the nearest degree? (Use cos⁻¹)
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 13 cm. Quel est l'angle θ au degré près? (Utilisez cos⁻¹)
• Choices: A) 62° B) 68° C) 67° D) 70°
• Hint: CAH: cos(θ) = adjacent ÷ hypotenuse, then use the inverse cosine (e.g., adj = 3, hyp = 5: cos(θ) = 0.6, θ = cos⁻¹(0.6) ≈ 53°).
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 5 ÷ 13 ≈ 0.3846.
  • θ = cos⁻¹(0.3846) ≈ 67°.
  • So the angle is approximately 67°.
• Answer: 67°

[Hard] Subtracting Polynomials and Solving

• EN: Solve for x: 4x + 7 = 2x + 19.
• FR: Résoudre pour x : 4x + 7 = 2x + 19.
• Choices: A) x = 7 B) x = 5 C) x = 8 D) x = 6
• Hint: Move the variable terms to one side and the constants to the other (e.g., 5x + 3 = 3x + 11: 2x = 8, x = 4).
• Steps:
  • 4x + 7 = 2x + 19.
  • Subtract 2x: 2x + 7 = 19.
  • Subtract 7: 2x = 12.
  • Divide by 2: x = 6.
• Answer: x = 6

[Easy] Factoring Quadratics

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

[Easy] Trigonometry — TOA

• EN: In a right triangle, the opposite side is 7 cm and the adjacent side is 7 cm. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 7 cm et le côté adjacent mesure 7 cm. Quel est tan(θ)?
• Choices: A) 2 B) 0.5 C) 1 D) 0
• Hint: TOA: tan = opposite ÷ adjacent (e.g., opposite = 4, adjacent = 8: tan = 4/8 = 0.5).
• Steps:
  • tan(θ) = opposite ÷ adjacent.
  • tan(θ) = 7 ÷ 7 = 1.
  • So tan(θ) = 1.
• Answer: 1

[Easy] Systems of Equations — Substitution

• EN: Solve the system: y = 2x and x + y = 9. What is x?
• FR: Résoudre le système : y = 2x et x + y = 9. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 4 C) x = 3 D) x = 5
• Hint: Substitute the expression for one variable into the other equation (e.g., y = 3x, x + y = 8: x + 3x = 8, 4x = 8, x = 2).
• Steps:
  • Substitute y = 2x into x + y = 9.
  • x + 2x = 9 → 3x = 9.
  • x = 3.
• Answer: x = 3

[Easy] Volume of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilisez π ≈ 3,14)
• Choices: A) 282.6 cm³ B) 94.2 cm³ C) 188.4 cm³ D) 314.0 cm³
• Hint: Volume of a cylinder = π × r² × h (e.g., r = 2, h = 5: V = 3.14 × 4 × 5 = 62.8 cm³).
• Steps:
  • V = π × r² × h.
  • V = 3.14 × 3² × 10 = 3.14 × 9 × 10.
  • V = 3.14 × 90 = 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Quadratic Equation — Factoring

• EN: Solve: x² − 7x + 12 = 0.
• FR: Résoudre : x² − 7x + 12 = 0.
• Choices: A) x = 3 or x = 4 B) x = 2 or x = 6 C) x = 1 or x = 12 D) x = 3 or x = 5
• Hint: Factor first, then set each factor equal to zero (e.g., x² − 5x + 6 = 0 → (x−2)(x−3) = 0 → x = 2 or x = 3).
• Steps:
  • Factor: x² − 7x + 12 = (x − 3)(x − 4).
  • Set each factor to zero: x − 3 = 0 or x − 4 = 0.
  • x = 3 or x = 4.
• Answer: x = 3 or x = 4

[Medium] Circle Geometry

• EN: A circle has a radius of 5 cm. What is its area? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 5 cm. Quelle est son aire? (Utilisez π ≈ 3,14)
• Choices: A) 31.4 cm² B) 62.8 cm² C) 78.5 cm² D) 47.1 cm²
• Hint: Area of a circle = π × r² (e.g., r = 4: A = 3.14 × 16 = 50.24 cm²).
• Steps:
  • A = π × r².
  • A = 3.14 × 5² = 3.14 × 25 = 78.5 cm².
  • So the area is 78.5 cm².
• Answer: 78.5 cm²

[Medium] Completing the Square

• EN: Solve x² + 6x − 7 = 0 by factoring.
• FR: Résoudre x² + 6x − 7 = 0 par la factorisation.
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 7 or x = 1 D) x = 2 or x = −8
• Hint: Find two numbers that multiply to −7 and add to 6 (e.g., for x² + 2x − 8: numbers are 4 and −2, giving (x+4)(x−2) = 0).
• Steps:
  • Find two numbers: product = −7, sum = 6. Those are 7 and −1.
  • Factor: (x + 7)(x − 1) = 0.
  • x = −7 or x = 1.
• Answer: x = 1 or x = −7

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 6 cm. What is its lateral surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 6 cm. Quelle est son aire latérale? (Utilisez π ≈ 3,14)
• Choices: A) 100.48 cm² B) 75.36 cm² C) 50.24 cm² D) 87.92 cm²
• Hint: Lateral surface area of a cone = π × r × slant height (e.g., r = 3, slant = 5: 3.14 × 3 × 5 = 47.1 cm²).
• Steps:
  • Lateral SA = π × r × l.
  • = 3.14 × 4 × 6 = 3.14 × 24.
  • = 75.36 cm².
• Answer: 75.36 cm²

[Hard] System of Equations — Two Variables

• EN: Solve: 2x + 3y = 12 and x − y = 1. What is y?
• FR: Résoudre : 2x + 3y = 12 et x − y = 1. Quelle est la valeur de y?
• Choices: A) y = 3 B) y = 1 C) y = 4 D) y = 2
• Hint: From the second equation, express x in terms of y, then substitute into the first (e.g., x = y + 3, plug into 3x + 2y = 19).
• Steps:
  • From x − y = 1: x = y + 1.
  • Substitute into 2x + 3y = 12: 2(y+1) + 3y = 12.
  • 2y + 2 + 3y = 12 → 5y = 10 → y = 2.
• Answer: y = 2

[Hard] Quadratic — Word Problem

• EN: The area of a rectangular field is 60 m². The length is 7 m more than the width. What is the width?
• FR: L'aire d'un champ rectangulaire est de 60 m². La longueur est de 7 m de plus que la largeur. Quelle est la largeur?
• Choices: A) 7 m B) 4 m C) 5 m D) 6 m
• Hint: Let width = w and length = w + 7, then set up w(w + 7) = area and solve the quadratic (e.g., w(w+5) = 36 → w² + 5w − 36 = 0).
• Steps:
  • Let width = w, length = w + 7.
  • w(w + 7) = 60 → w² + 7w − 60 = 0.
  • Factor: (w + 12)(w − 5) = 0.
  • w = 5 m (taking the positive value).
• Answer: 5 m

[Easy] Exponential Function

• EN: The function f(x) = 2^x. What is f(4)?
• FR: La fonction f(x) = 2^x. Quelle est f(4)?
• Choices: A) 8 B) 16 C) 12 D) 32
• Hint: Substitute the value into the exponent (e.g., f(3) = 2³ = 2 × 2 × 2 = 8).
• Steps:
  • f(4) = 2⁴.
  • 2⁴ = 2 × 2 × 2 × 2 = 16.
  • So f(4) = 16.
• Answer: 16

[Easy] Logarithms Introduction

• EN: What is log₂(8)?
• FR: Combien fait log₂(8)?
• Choices: A) 4 B) 2 C) 3 D) 5
• Hint: log₂(n) asks "2 to what power equals n?" (e.g., log₂(16) = 4 because 2⁴ = 16).
• Steps:
  • Ask: 2 to what power equals 8?
  • 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[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) 25 B) 20 C) 21 D) 24
• Hint: Use the formula aₙ = a₁ + (n−1)d (e.g., a₁ = 3, d = 6, term 4: 3 + 3×6 = 21).
• Steps:
  • aₙ = a₁ + (n−1)d.
  • a₅ = 5 + (5−1) × 4 = 5 + 16 = 21.
  • So the 5th term is 21.
• Answer: 21

[Easy] Compound Interest

• EN: $1000 is invested at 5% interest per year, compounded annually. What is the amount after 2 years?
• FR: 1000 $ est investi à 5 % d'intérêt par an, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $1100.25 B) $1102.50 C) $1050.00 D) $1200.00
• Hint: Use A = P(1 + r)ⁿ (e.g., $500 at 4% for 2 years: A = 500 × 1.04² = 500 × 1.0816 = $540.80).
• Steps:
  • A = P(1 + r)ⁿ = 1000 × (1.05)².
  • (1.05)² = 1.1025.
  • A = 1000 × 1.1025 = $1102.50.
• Answer: $1102.50

[Medium] Quadratic Function — Vertex

• EN: Find the vertex of the parabola y = x² − 4x + 7.
• FR: Trouver le sommet de la parabole y = x² − 4x + 7.
• Choices: A) (3, 4) B) (4, 7) C) (2, 3) D) (1, 4)
• Hint: The x-coordinate of the vertex is x = −b/(2a); substitute back to find y (e.g., y = x²−6x+11: x = 3, y = 9−18+11 = 2, vertex (3,2)).
• Steps:
  • a = 1, b = −4. x = −(−4)/(2×1) = 4/2 = 2.
  • y = 2² − 4(2) + 7 = 4 − 8 + 7 = 3.
  • Vertex is (2, 3).
• Answer: (2, 3)

[Medium] Geometric Sequence

• EN: A geometric sequence starts at 3 and has a common ratio of 2. What is the sum of the first 4 terms?
• FR: Une suite géométrique commence à 3 et a une raison commune de 2. Quelle est la somme des 4 premiers termes?
• Choices: A) 48 B) 42 C) 45 D) 36
• Hint: Use Sₙ = a(rⁿ − 1)/(r − 1) (e.g., a=2, r=3, n=3: S = 2(27−1)/2 = 26).
• Steps:
  • Terms: 3, 6, 12, 24.
  • Sum = 3 + 6 + 12 + 24 = 45.
  • So the sum of the first 4 terms is 45.
• Answer: 45

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifier : sin²(θ) + cos²(θ).
• Choices: A) 2 B) 0 C) sin(2θ) D) 1
• Hint: This is the most fundamental Pythagorean identity — it is always true for any angle θ.
• Steps:
  • The Pythagorean identity states: sin²(θ) + cos²(θ) = 1.
  • This is true for all values of θ.
  • So the expression simplifies to 1.
• Answer: 1

[Medium] Annuity — Future Value

• EN: $200 is deposited at the end of each year into an account earning 4% per year. What is the future value after 3 years?
• FR: 200 $ sont déposés à la fin de chaque année dans un compte rapportant 4 % par an. Quelle est la valeur future après 3 ans?
• Choices: A) $649.28 B) $614.00 C) $624.32 D) $600.00
• Hint: Future value of an annuity = PMT × [(1+r)ⁿ − 1]/r (e.g., $100 at 5% for 2 years: 100 × [1.05²−1]/0.05 = 100 × 2.05 = $205).
• Steps:
  • FV = 200 × [(1.04)³ − 1] / 0.04.
  • (1.04)³ = 1.124864. 1.124864 − 1 = 0.124864.
  • 0.124864 / 0.04 = 3.1216.
  • FV = 200 × 3.1216 = $624.32.
• Answer: $624.32

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) = 4.
• FR: Résoudre pour x : log₃(x) = 4.
• Choices: A) x = 64 B) x = 27 C) x = 12 D) x = 81
• Hint: Convert logarithm form to exponential form: logᵦ(x) = n means bⁿ = x (e.g., log₂(x) = 5 → x = 2⁵ = 32).
• Steps:
  • log₃(x) = 4 means 3⁴ = x.
  • 3⁴ = 81.
  • So x = 81.
• Answer: x = 81

[Hard] Compound Interest — Solving for Rate

• EN: An investment of $2000 grows to $2420 in 2 years with annual compounding. What is the annual interest rate?
• FR: Un investissement de 2000 $ passe à 2420 $ en 2 ans avec capitalisation annuelle. Quel est le taux d'intérêt annuel?
• Choices: A) 12% B) 8% C) 15% D) 10%
• Hint: Use A = P(1+r)ⁿ, divide both sides by P, take the square root, then subtract 1 (e.g., $1000 grows to $1210 in 2 years: (1210/1000)^(1/2) = √1.21 = 1.10, r = 10%).
• Steps:
  • 2420 = 2000 × (1 + r)².
  • (1 + r)² = 2420/2000 = 1.21.
  • 1 + r = √1.21 = 1.10.
  • r = 0.10 = 10%.
• Answer: 10%

[Easy] Permutations

• EN: In how many ways can 4 students be arranged in a line?
• FR: De combien de façons peut-on placer 4 élèves en ligne?
• Choices: A) 16 B) 24 C) 12 D) 20
• Hint: The number of arrangements of n items = n! (e.g., 3 items: 3! = 3 × 2 × 1 = 6).
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 12 × 2 = 24.
  • So there are 24 ways.
• 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) 3x² C) 3x D) 2x³
• Hint: Power rule: d/dx(xⁿ) = n·xⁿ⁻¹ (e.g., d/dx(x⁵) = 5x⁴).
• Steps:
  • f(x) = x³.
  • Bring down the exponent: 3.
  • Reduce the exponent by 1: x².
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Combinations

• EN: How many ways can a committee of 2 be chosen from a group of 5 people?
• FR: De combien de façons peut-on choisir un comité de 2 personnes parmi un groupe de 5 personnes?
• Choices: A) 10 B) 20 C) 15 D) 8
• Hint: Use C(n,r) = n! / (r! × (n−r)!) (e.g., C(4,2) = 4!/(2!×2!) = 24/4 = 6).
• Steps:
  • C(5,2) = 5! / (2! × 3!).
  • = 120 / (2 × 6) = 120 / 12 = 10.
  • So there are 10 ways.
• Answer: 10

[Easy] Polynomial Function — Evaluating

• EN: Given f(x) = 2x³ − 3x + 1, what is f(2)?
• FR: Pour f(x) = 2x³ − 3x + 1, quelle est f(2)?
• Choices: A) 10 B) 14 C) 11 D) 9
• Hint: Substitute x = 2 into each term (e.g., f(1) for 3x² − x + 2: 3(1) − 1 + 2 = 4).
• Steps:
  • f(2) = 2(2)³ − 3(2) + 1.
  • = 2(8) − 6 + 1.
  • = 16 − 6 + 1 = 11.
• Answer: 11

[Medium] Rate of Change — Derivative Applied

• EN: A ball's height is given by h(t) = −5t² + 20t. What is the instantaneous velocity at t = 2 seconds?
• FR: La hauteur d'une balle est donnée par h(t) = −5t² + 20t. Quelle est la vitesse instantanée à t = 2 secondes?
• Choices: A) 5 m/s B) 0 m/s C) 10 m/s D) −10 m/s
• Hint: Find h'(t) using the power rule, then substitute t = 2 (e.g., h(t) = −4t² + 16t: h'(t) = −8t + 16, h'(1) = 8 m/s).
• Steps:
  • h'(t) = −10t + 20.
  • At t = 2: h'(2) = −10(2) + 20 = −20 + 20 = 0.
  • The instantaneous velocity at t = 2 s is 0 m/s.
• Answer: 0 m/s

[Medium] Binomial Probability

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

[Medium] Vector Addition

• EN: Vector a = (3, 4) and vector b = (−1, 2). What is a + b?
• FR: Le vecteur a = (3, 4) et le vecteur b = (−1, 2). Quel est a + b?
• Choices: A) (4, 2) B) (1, 8) C) (2, 6) D) (3, 5)
• Hint: Add the corresponding components of each vector (e.g., (5, 2) + (−2, 3) = (3, 5)).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 4 + 2 = 6.
  • a + b = (2, 6).
• Answer: (2, 6)

[Medium] Rational Function — Asymptote

• EN: For the function f(x) = (x + 1)/(x − 3), what is the vertical asymptote?
• FR: Pour la fonction f(x) = (x + 1)/(x − 3), quelle est l'asymptote verticale?
• Choices: A) x = 1 B) x = 3 C) x = −1 D) x = −3
• Hint: The vertical asymptote occurs where the denominator equals zero (e.g., f(x) = 1/(x−5) has vertical asymptote x = 5).
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • x = 3.
  • So the vertical asymptote is x = 3.
• Answer: x = 3

[Hard] Derivative and Optimization

• EN: A farmer wants to fence a rectangular field with 60 m of fencing. One side is along a river and needs no fencing. What is the maximum area?
• FR: Un agriculteur veut clôturer un champ rectangulaire avec 60 m de clôture. Un côté longe une rivière et n'a pas besoin de clôture. Quelle est l'aire maximale?
• Choices: A) 400 m² B) 350 m² C) 500 m² D) 450 m²
• Hint: With constraint 2w + l = 60, write A = w × l, substitute l, differentiate, set to zero (e.g., 2w + l = 40: l = 40−2w, A = w(40−2w), dA/dw = 40−4w = 0, w = 10, A = 200).
• Steps:
  • Let width = w, then length l = 60 − 2w.
  • Area A = w(60 − 2w) = 60w − 2w².
  • dA/dw = 60 − 4w = 0 → w = 15 m.
  • l = 60 − 2(15) = 30 m. A = 15 × 30 = 450 m².
• Answer: 450 m²

[Hard] Permutations with Restrictions

• EN: How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if no digit may be repeated and the number must be greater than 300?
• FR: Combien de nombres à 3 chiffres peut-on former avec les chiffres 1, 2, 3, 4, 5 si aucun chiffre ne peut être répété et que le nombre doit être supérieur à 300?
• Choices: A) 48 B) 36 C) 24 D) 30
• Hint: Count by cases based on the first digit — only certain digits can lead (e.g., numbers > 200 using {1,2,3,4}: first digit is 2, 3, or 4, then arrange remaining 3 from the rest).
• Steps:
  • The hundreds digit must be 3, 4, or 5 (to be greater than 300).
  • For each choice of hundreds digit (3 options), choose 2 digits from the remaining 4: P(4,2) = 4 × 3 = 12.
  • Total: 3 × 12 = 36.
• Answer: 36