Daily Math — 2026-07-29

[Easy] Counting to Ten

• EN: There are 7 apples on the table. How many apples are there?
• FR: Il y a 7 pommes sur la table. Combien y a-t-il de pommes?
• Choices: A) 5 B) 7 C) 9 D) 6
• Hint: Count each object one by one, like counting 4 chairs: 1, 2, 3, 4.
• Steps:
  • Count the apples one at a time.
  • 1, 2, 3, 4, 5, 6, 7 — there are 7 apples.
• Answer: 7

[Easy] Adding Small Numbers

• EN: Mia has 3 stickers and gets 4 more. How many stickers does she have now?
• FR: Mia a 3 autocollants et en reçoit 4 de plus. Combien d'autocollants a-t-elle maintenant?
• Choices: A) 6 B) 8 C) 7 D) 5
• Hint: Start with the bigger number and count on, like 5 + 2: start at 5, count 6, 7.
• Steps:
  • Start at 3 and count on 4 more.
  • 4, 5, 6, 7 — Mia has 7 stickers.
• Answer: 7

[Easy] Subtraction Within 10

• EN: There are 9 birds on a fence. 4 fly away. How many birds are left?
• FR: Il y a 9 oiseaux sur une clôture. 4 s'envolent. Combien d'oiseaux reste-t-il?
• Choices: A) 6 B) 4 C) 3 D) 5
• Hint: Take away from a group, like 8 − 3: cross out 3, count what is left — 5.
• Steps:
  • Start with 9 birds.
  • Take away 4: 9 − 4 = 5. There are 5 birds left.
• Answer: 5

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes after 6?
• FR: Compte par 2. Quel nombre vient après 6?
• Choices: A) 9 B) 7 C) 8 D) 10
• Hint: Skip counting by 2s means adding 2 each time: 2, 4, 6, 8, 10.
• Steps:
  • The pattern is 2, 4, 6, then add 2 more.
  • 6 + 2 = 8. The next number is 8.
• Answer: 8

[Medium] Addition Within 20

• EN: Leo scores 8 goals in hockey and then scores 6 more. How many goals did he score in all?
• FR: Léo marque 8 buts au hockey puis en marque 6 de plus. Combien de buts a-t-il marqués en tout?
• Choices: A) 13 B) 15 C) 14 D) 16
• Hint: To add 7 + 5, make a ten: 7 + 3 = 10, then add 2 more = 12.
• Steps:
  • Start with 8 and make a ten: 8 + 2 = 10.
  • There are 4 more left from the 6, so 10 + 4 = 14. Leo scored 14 goals.
• Answer: 14

[Medium] Subtraction Within 20

• EN: There are 15 crayons in a box. A student uses 7 of them. How many crayons are left?
• FR: Il y a 15 crayons dans une boîte. Un élève en utilise 7. Combien de crayons reste-t-il?
• Choices: A) 9 B) 6 C) 8 D) 11
• Hint: To subtract 14 − 6, think of what you add to 6 to get 14: 6 + 8 = 14, so the answer is 8.
• Steps:
  • Think: what plus 7 equals 15?
  • 7 + 8 = 15, so 15 − 7 = 8. There are 8 crayons left.
• Answer: 8

[Medium] Skip Counting by 5s

• EN: Count by 5s. What number comes after 15?
• FR: Compte par 5. Quel nombre vient après 15?
• Choices: A) 16 B) 25 C) 18 D) 20
• Hint: Skip counting by 5s: 5, 10, 15 — add 5 each time.
• Steps:
  • The pattern is 5, 10, 15, then add 5 more.
  • 15 + 5 = 20. The next number is 20.
• Answer: 20

[Medium] Comparing Numbers

• EN: Which number is greater: 13 or 17?
• FR: Quel nombre est plus grand : 13 ou 17?
• Choices: A) 13 B) 17 C) 15 D) 12
• Hint: The number that is farther along the number line is greater, like 8 is greater than 5.
• Steps:
  • Count to find where 13 and 17 are on the number line.
  • 17 comes after 13, so 17 is greater.
• Answer: 17

[Hard] Coin Recognition

• EN: You have 1 dime and 1 nickel. How many cents do you have in all?
• FR: Tu as 1 pièce de 10 cents et 1 pièce de 5 cents. Combien de cents as-tu en tout?
• Choices: A) 10 cents B) 5 cents C) 20 cents D) 15 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents — add them together.
• Steps:
  • A dime = 10 cents. A nickel = 5 cents.
  • 10 + 5 = 15. You have 15 cents.
• Answer: 15 cents

[Hard] Addition and Subtraction Together

• EN: There are 12 children at the park. 5 go home and then 3 more arrive. How many children are at the park now?
• FR: Il y a 12 enfants au parc. 5 rentrent chez eux, puis 3 autres arrivent. Combien d'enfants y a-t-il au parc maintenant?
• Choices: A) 11 B) 9 C) 10 D) 8
• Hint: Do two steps — first subtract, then add, like 10 − 4 = 6, then 6 + 2 = 8.
• Steps:
  • Start with 12. Subtract 5: 12 − 5 = 7.
  • Then add 3: 7 + 3 = 10. There are 10 children at the park.
• Answer: 10

[Easy] Addition Within 100

• EN: A student has 24 crayons and gets 13 more. How many crayons does the student have now?
• FR: Un élève a 24 crayons et en reçoit 13 de plus. Combien de crayons l'élève a-t-il maintenant?
• Choices: A) 38 B) 35 C) 37 D) 40
• Hint: Add the ones first, then the tens: for 32 + 15, add 2 + 5 = 7 and 3 + 1 = 4, giving 47.
• Steps:
  • Add the ones: 4 + 3 = 7.
  • Add the tens: 20 + 10 = 30. So 30 + 7 = 37 crayons.
• Answer: 37

[Easy] Subtraction Within 100

• EN: There are 58 books on a shelf. A student takes 25 books. How many books are left on the shelf?
• FR: Il y a 58 livres sur une étagère. Un élève en prend 25. Combien de livres reste-t-il sur l'étagère?
• Choices: A) 34 B) 33 C) 31 D) 29
• Hint: Subtract the ones first, then the tens: for 67 − 34, do 7 − 4 = 3, then 6 − 3 = 3, giving 33.
• Steps:
  • Subtract the ones: 8 − 5 = 3.
  • Subtract the tens: 50 − 20 = 30. So 30 + 3 = 33 books.
• Answer: 33

[Easy] Telling Time — Hour

• EN: The clock shows the hour hand pointing to 4 and the minute hand pointing to 12. What time does the clock show?
• FR: L'aiguille des heures pointe vers 4 et l'aiguille des minutes pointe vers 12. Quelle heure indique l'horloge?
• Choices: A) 3:00 B) 5:00 C) 4:00 D) 12:00
• Hint: When the minute hand points to 12, it is exactly the hour shown by the hour hand, like hour hand at 7 means 7:00.
• Steps:
  • The minute hand at 12 means it is exactly on the hour.
  • The hour hand points to 4, so the time is 4:00.
• Answer: 4:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A crayon is 9 cm long. Which one is longer?
• FR: Un crayon est long de 14 cm. Un crayon de couleur est long de 9 cm. Lequel est le plus long?
• Choices: A) The crayon B) They are the same C) The pencil D) Neither one
• Hint: The object with the bigger number of centimetres is longer, like 20 cm is longer than 12 cm.
• Steps:
  • Compare 14 cm and 9 cm.
  • 14 is greater than 9, so the pencil is longer.
• Answer: The pencil

[Medium] Addition with Regrouping

• EN: A baker made 47 muffins in the morning and 36 muffins in the afternoon. How many muffins did the baker make in all?
• FR: Un boulanger a fait 47 muffins le matin et 36 muffins l'après-midi. Combien de muffins a-t-il faits en tout?
• Choices: A) 81 B) 73 C) 83 D) 78
• Hint: When the ones add up to more than 9, regroup: for 38 + 45, 8 + 5 = 13, write 3 carry 1, then 3 + 4 + 1 = 8, giving 83.
• Steps:
  • Add the ones: 7 + 6 = 13. Write 3, carry the 1.
  • Add the tens: 4 + 3 + 1 (carried) = 8. So the answer is 83 muffins.
• Answer: 83

[Medium] Counting Coins

• EN: Emma has 2 quarters, 1 dime, and 1 nickel. How much money does she have?
• FR: Emma a 2 pièces de 25 cents, 1 pièce de 10 cents et 1 pièce de 5 cents. Combien d'argent a-t-elle?
• Choices: A) 55 cents B) 70 cents C) 60 cents D) 65 cents
• Hint: Count up the value of each coin: 2 dimes + 1 nickel = 20 + 5 = 25 cents.
• Steps:
  • 2 quarters = 25 + 25 = 50 cents. 1 dime = 10 cents. 1 nickel = 5 cents.
  • 50 + 10 + 5 = 65 cents.
• Answer: 65 cents

[Medium] Telling Time — Half Hour

• EN: The minute hand points to 6 and the hour hand is between 2 and 3. What time does the clock show?
• FR: L'aiguille des minutes pointe vers 6 et l'aiguille des heures est entre 2 et 3. Quelle heure indique l'horloge?
• Choices: A) 2:30 B) 3:30 C) 6:00 D) 2:00
• Hint: When the minute hand points to 6, it is half past the hour — if the hour hand has just passed 5, the time is 5:30.
• Steps:
  • The minute hand at 6 means 30 minutes past the hour.
  • The hour hand has just passed 2, so the time is 2:30.
• Answer: 2:30

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, ___. What number comes next?
• FR: Regarde ce motif : 5, 10, 15, 20, ___. Quel nombre vient ensuite?
• Choices: A) 22 B) 30 C) 23 D) 25
• Hint: Find the rule by looking at how much is added each time: if the pattern is 3, 6, 9, the rule is +3.
• Steps:
  • Each number goes up by 5: 5, 10, 15, 20.
  • 20 + 5 = 25. The next number is 25.
• Answer: 25

[Hard] Subtraction with Regrouping

• EN: A school had 72 students on a field trip. 38 students went home early. How many students were still on the trip?
• FR: Une école avait 72 élèves lors d'une sortie scolaire. 38 élèves sont rentrés tôt. Combien d'élèves étaient encore en sortie?
• Choices: A) 36 B) 44 C) 34 D) 40
• Hint: When you cannot subtract the ones, regroup a ten: for 53 − 27, borrow from the 5 to get 4 tens and 13 ones, then 13 − 7 = 6 and 4 − 2 = 2, giving 26.
• Steps:
  • Cannot do 2 − 8, so regroup: 72 becomes 6 tens and 12 ones.
  • 12 − 8 = 4, and 6 − 3 = 3. So 72 − 38 = 34 students.
• Answer: 34

[Hard] Two-Step Problem

• EN: Owen has 45 hockey cards. He gives 12 to his friend and then buys 8 more. How many cards does Owen have now?
• FR: Owen a 45 cartes de hockey. Il en donne 12 à son ami, puis en achète 8 autres. Combien de cartes Owen a-t-il maintenant?
• Choices: A) 39 B) 43 C) 37 D) 41
• Hint: Do two steps — subtract first, then add, like 30 − 6 = 24, then 24 + 5 = 29.
• Steps:
  • First, subtract: 45 − 12 = 33.
  • Then add: 33 + 8 = 41. Owen has 41 cards.
• Answer: 41

[Easy] Multiplication by 2

• EN: There are 6 pairs of mittens in the lost-and-found box. How many mittens are there in all?
• FR: Il y a 6 paires de mitaines dans la boîte des objets trouvés. Combien y a-t-il de mitaines en tout?
• Choices: A) 8 B) 14 C) 12 D) 10
• Hint: Multiplying by 2 is like doubling: 2 × 7 = 7 + 7 = 14.
• Steps:
  • Each pair has 2 mittens. There are 6 pairs.
  • 2 × 6 = 12. There are 12 mittens in all.
• Answer: 12

[Easy] Multiplication by 5

• EN: A Tim Hortons tray holds 5 cups. How many cups do 4 trays hold?
• FR: Un plateau de Tim Hortons peut contenir 5 tasses. Combien de tasses 4 plateaux peuvent-ils contenir?
• Choices: A) 20 B) 9 C) 15 D) 25
• Hint: Skip count by 5s for each group: 5, 10, 15, so 5 × 3 = 15.
• Steps:
  • Each tray holds 5 cups. There are 4 trays.
  • 5 × 4 = 20. Four trays hold 20 cups.
• Answer: 20

[Easy] Basic Division

• EN: 18 apples are shared equally among 3 friends. How many apples does each friend get?
• FR: 18 pommes sont partagées également entre 3 amis. Combien de pommes chaque ami reçoit-il?
• Choices: A) 5 B) 8 C) 6 D) 4
• Hint: Division is sharing equally — think of what times the divisor equals the total: 3 × ? = 18, so 18 ÷ 3 = 6.
• Steps:
  • Think: 3 × ? = 18.
  • 3 × 6 = 18, so each friend gets 6 apples.
• Answer: 6

[Easy] Understanding Fractions

• EN: A pizza is cut into 4 equal slices. Zara eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 tranches égales. Zara mange 1 tranche. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/4 C) 1/3 D) 2/4
• Hint: A fraction shows parts of a whole — if a bar is cut into 3 equal parts and you colour 1 part, the fraction is 1/3.
• Steps:
  • The pizza has 4 equal slices. Zara ate 1 of them.
  • 1 out of 4 equal parts = 1/4.
• Answer: 1/4

[Medium] Multiplication by 3

• EN: A hockey team has 3 lines of 4 players. How many players are on the team in all?
• FR: Une équipe de hockey a 3 trios de 4 joueurs. Combien de joueurs y a-t-il dans l'équipe en tout?
• Choices: A) 16 B) 14 C) 12 D) 10
• Hint: Multiply to find the total in equal groups: 3 × 5 = 15.
• Steps:
  • There are 3 lines with 4 players each.
  • 3 × 4 = 12. There are 12 players on the team.
• Answer: 12

[Medium] Perimeter of a Rectangle

• EN: A garden is 5 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un jardin mesure 5 m de longueur et 3 m de largeur. Quel est le périmètre du jardin?
• Choices: A) 15 m B) 14 m C) 16 m D) 18 m
• Hint: Perimeter of a rectangle = add all four sides: if length = 6 m and width = 2 m, perimeter = 6 + 6 + 2 + 2 = 16 m.
• Steps:
  • Add all four sides: 5 + 5 + 3 + 3.
  • 10 + 6 = 16 m. The perimeter is 16 m.
• Answer: 16 m

[Medium] Reading a Simple Graph

• EN: A bar graph shows that 8 students like hockey, 5 like soccer, and 4 like basketball. How many more students like hockey than basketball?
• FR: Un diagramme à barres montre que 8 élèves aiment le hockey, 5 aiment le soccer et 4 aiment le basketball. Combien d'élèves de plus aiment le hockey que le basketball?
• Choices: A) 5 B) 3 C) 6 D) 4
• Hint: To find how many more, subtract the smaller number from the larger: if 9 students like reading and 4 like drawing, 9 − 4 = 5 more.
• Steps:
  • Hockey: 8. Basketball: 4.
  • 8 − 4 = 4. Four more students like hockey than basketball.
• Answer: 4

[Medium] Multiplication by 10

• EN: There are 10 bags of marbles. Each bag has 7 marbles. How many marbles are there in all?
• FR: Il y a 10 sacs de billes. Chaque sac contient 7 billes. Combien y a-t-il de billes en tout?
• Choices: A) 17 B) 80 C) 70 D) 65
• Hint: Multiplying by 10 just puts a zero at the end of the number: 10 × 6 = 60.
• Steps:
  • 10 × 7 = 70.
  • There are 70 marbles in all.
• Answer: 70

[Hard] Division with a Multiplication Check

• EN: A teacher has 35 pencils to put equally into 5 boxes. How many pencils go in each box?
• FR: Un enseignant a 35 crayons à mettre également dans 5 boîtes. Combien de crayons va dans chaque boîte?
• Choices: A) 6 B) 8 C) 9 D) 7
• Hint: Think of the related multiplication fact: 5 × ? = 28 means 28 ÷ 5 = the missing number.
• Steps:
  • Think: 5 × ? = 35.
  • 5 × 7 = 35, so each box gets 7 pencils.
• Answer: 7

[Hard] Comparing Fractions

• EN: Which fraction is larger: 1/2 or 1/3?
• FR: Quelle fraction est la plus grande : 1/2 ou 1/3?
• Choices: A) 1/3 B) They are equal C) 1/2 D) Neither is larger
• Hint: When the top number (numerator) is the same, the fraction with the smaller bottom number (denominator) is larger — 1/4 is larger than 1/6.
• Steps:
  • Both fractions have a numerator of 1.
  • Splitting something into 2 pieces gives bigger pieces than splitting into 3, so 1/2 is larger than 1/3.
• Answer: 1/2

[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 pattern you know: 7 × 7 = 49, so 7 × 8 is just 7 more than that.
• 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 3 in the number 4.35?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,35?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 3 tens
• Hint: In a decimal number, the digit right after the decimal point is in the tenths place — in 2.71, the 7 is in the tenths place.
• Steps:
  • In 4.35, the digits after the decimal are 3 (tenths) and 5 (hundredths).
  • The 3 is in the tenths place, so its value is 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A classroom rug is 6 m long and 4 m wide. What is the area of the rug?
• FR: Un tapis de classe mesure 6 m de longueur et 4 m de largeur. Quelle est l'aire du tapis?
• Choices: A) 20 m² B) 28 m² C) 24 m² D) 18 m²
• Hint: Area of a rectangle = length × width: if a room is 5 m × 3 m, area = 15 m².
• Steps:
  • Area = length × width = 6 × 4.
  • 6 × 4 = 24. The area of the rug is 24 m².
• Answer: 24 m²

[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) They are equal C) 3/4 D) Neither is greater
• Hint: When the denominators are the same, compare the numerators — 5/8 is greater than 3/8 because 5 > 3.
• Steps:
  • Both fractions have a denominator of 4.
  • Compare the numerators: 3 > 2, so 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: 47 students are put into groups of 5. How many complete groups are there, and how many students are left over?
• FR: 47 élèves sont répartis en groupes de 5. Combien de groupes complets y a-t-il et combien d'élèves reste-t-il?
• Choices: A) 8 groups, remainder 7 B) 9 groups, remainder 2 C) 10 groups, remainder 3 D) 7 groups, remainder 4
• Hint: Divide and find the remainder: for 29 ÷ 4, 4 × 7 = 28 with 1 left over, so 7 remainder 1.
• Steps:
  • 5 × 9 = 45, which is close to 47.
  • 47 − 45 = 2. There are 9 complete groups with 2 students left over.
• Answer: 9 groups, remainder 2

[Medium] Elapsed Time

• EN: School starts at 8:30 a.m. and ends at 3:00 p.m. How long is the school day?
• FR: L'école commence à 8 h 30 et se termine à 15 h. Quelle est la durée de la journée scolaire?
• Choices: A) 7 hours 30 minutes B) 6 hours 30 minutes C) 8 hours D) 7 hours
• Hint: Count forward from the start time to the end time: from 9:15 to 11:45 is 2 hours 30 minutes.
• Steps:
  • From 8:30 to 3:00: from 8:30 to 9:00 is 30 minutes, then from 9:00 to 3:00 is 6 hours.
  • 6 hours + 30 minutes = 6 hours 30 minutes.
• Answer: 6 hours 30 minutes

[Medium] Decimal Operations

• EN: A juice box costs $1.25 and a muffin costs $1.50. How much do they cost together?
• FR: Une boîte de jus coûte 1,25 $ et un muffin coûte 1,50 $. Combien coûtent-ils ensemble?
• Choices: A) $2.85 B) $2.65 C) $2.75 D) $3.00
• Hint: Line up the decimal points and add as usual: $2.30 + $1.45 = $3.75.
• Steps:
  • $1.25 + $1.50: add cents first: 25 + 50 = 75 cents.
  • Add dollars: $1 + $1 = $2. Total = $2.75.
• Answer: $2.75

[Medium] Multiplication — Two-Step Problem

• EN: A bookstore has 8 shelves. Each shelf holds 9 books. The store sells 15 books on Monday. How many books are left?
• FR: Une librairie a 8 étagères. Chaque étagère contient 9 livres. Le magasin vend 15 livres lundi. Combien de livres reste-t-il?
• Choices: A) 57 B) 63 C) 58 D) 72
• Hint: First multiply to find the total, then subtract: if a store has 7 shelves × 6 books = 42 books, then sells 10, 42 − 10 = 32.
• Steps:
  • Total books: 8 × 9 = 72.
  • Books left: 72 − 15 = 57.
• Answer: 57

[Hard] Long Division

• EN: A camp buys 96 water bottles to give equally to 6 cabins. How many water bottles does each cabin get?
• FR: Un camp achète 96 bouteilles d'eau à distribuer également dans 6 cabanes. Combien de bouteilles d'eau chaque cabane reçoit-elle?
• Choices: A) 14 B) 18 C) 16 D) 12
• Hint: Divide by working through each digit: for 84 ÷ 4, think 4 × 2 = 8 for the first digit, then 4 ÷ 4 = 1 for the second, giving 21.
• Steps:
  • 96 ÷ 6: 6 × 1 = 6 (goes into 9 once remainder 3), bring down 6 to get 36.
  • 36 ÷ 6 = 6. So 96 ÷ 6 = 16. Each cabin gets 16 bottles.
• Answer: 16

[Hard] Comparing Decimals

• EN: Order these numbers from smallest to largest: 2.4, 2.04, 2.40.
• FR: Classe ces nombres du plus petit au plus grand : 2,4, 2,04, 2,40.
• Choices: A) 2.04, 2.40, 2.4 B) 2.04, 2.4, 2.40 C) 2.4, 2.04, 2.40 D) 2.40, 2.4, 2.04
• Hint: Compare decimal digits from left to right — 3.07 is less than 3.70 because 0 tenths < 7 tenths.
• Steps:
  • Compare tenths: 2.04 has 0 tenths, while 2.4 has 4 tenths. So 2.04 is smallest.
  • 2.4 and 2.40 are equal (2.40 = 2.4), so the order is 2.04, 2.4, 2.40.
• Answer: 2.04, 2.4, 2.40

[Easy] Multi-Digit Multiplication

• EN: A school orders 24 boxes of pencils. Each box has 12 pencils. How many pencils are there in all?
• FR: Une école commande 24 boîtes de crayons. Chaque boîte contient 12 crayons. Combien y a-t-il de crayons en tout?
• Choices: A) 288 B) 256 C) 300 D) 248
• Hint: Multiply by breaking the problem apart: for 22 × 13, do 22 × 10 = 220 and 22 × 3 = 66, then add: 220 + 66 = 286.
• Steps:
  • 24 × 12: 24 × 10 = 240 and 24 × 2 = 48.
  • 240 + 48 = 288. There are 288 pencils in all.
• Answer: 288

[Easy] Adding Fractions with Like Denominators

• EN: A recipe needs 2/8 cup of oil and 3/8 cup of butter. How much fat is needed in total?
• FR: Une recette nécessite 2/8 de tasse d'huile et 3/8 de tasse de beurre. Quelle quantité de matière grasse faut-il en tout?
• 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: 1/6 + 3/6 = 4/6.
• Steps:
  • Same denominator (8), so add the numerators: 2 + 3 = 5.
  • The total is 5/8 cup.
• Answer: 5/8

[Easy] Decimal Operations — Addition

• EN: Nina ran 3.6 km on Saturday and 2.4 km on Sunday. How far did she run in total?
• FR: Nina a couru 3,6 km samedi et 2,4 km dimanche. Quelle distance a-t-elle parcourue en tout?
• Choices: A) 5.8 km B) 7.0 km C) 6.0 km D) 6.2 km
• Hint: Line up decimal points before adding: 4.5 + 1.3 = 5.8.
• Steps:
  • Line up the decimals: 3.6 + 2.4.
  • 6 + 4 = 10 (write 0, carry 1), then 3 + 2 + 1 = 6. Total = 6.0 km.
• Answer: 6.0 km

[Easy] Percentage Intro — 50%

• EN: A bag has 20 marbles. 50% of them are red. How many red marbles are there?
• FR: Un sac contient 20 billes. 50 % d'entre elles sont rouges. Combien y a-t-il de billes rouges?
• Choices: A) 5 B) 15 C) 10 D) 8
• Hint: 50% means half — to find 50% of a number, divide by 2: 50% of 16 = 8.
• Steps:
  • 50% means half. Half of 20 = 20 ÷ 2.
  • 20 ÷ 2 = 10. There are 10 red marbles.
• Answer: 10

[Medium] Multi-Digit Division

• EN: A warehouse has 432 cans of soup to pack into boxes of 9. How many boxes are needed?
• FR: Un entrepôt a 432 boîtes de soupe à emballer dans des boîtes de 9. Combien de boîtes faut-il?
• Choices: A) 52 B) 48 C) 56 D) 44
• Hint: Divide step by step: for 360 ÷ 9, think 9 × 4 = 36 for the hundreds, then 0 ÷ 9 = 0 for the tens, giving 40.
• Steps:
  • 432 ÷ 9: 9 × 4 = 36, so 43 ÷ 9 = 4 remainder 7. Bring down 2 to get 72.
  • 72 ÷ 9 = 8. So 432 ÷ 9 = 48. The answer is 48 boxes.
• Answer: 48

[Medium] Volume of a Rectangular Prism

• EN: A storage box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte de rangement mesure 5 cm de longueur, 4 cm de largeur et 3 cm de hauteur. Quel est son volume?
• Choices: A) 48 cm³ B) 70 cm³ C) 60 cm³ D) 56 cm³
• Hint: Volume of a rectangular prism = length × width × height: 2 × 3 × 4 = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60. The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions with Like Denominators

• EN: A jug holds 7/10 L of juice. Priya pours out 3/10 L. How much juice is left in the jug?
• FR: Une cruche contient 7/10 L de jus. Priya en verse 3/10 L. Quelle quantité de jus reste-t-il dans la cruche?
• Choices: A) 4/10 B) 3/10 C) 5/10 D) 2/10
• Hint: When denominators are the same, subtract the numerators and keep the denominator: 5/7 − 2/7 = 3/7.
• Steps:
  • Same denominator (10), so subtract numerators: 7 − 3 = 4.
  • The amount left is 4/10 L.
• Answer: 4/10

[Medium] Percentage Intro — 25%

• EN: A hockey team played 40 games this season. They won 25% of the games. How many games did they win?
• FR: Une équipe de hockey a joué 40 matchs cette saison. Elle a gagné 25 % des matchs. Combien de matchs ont-ils gagnés?
• Choices: A) 8 B) 12 C) 10 D) 15
• Hint: 25% means one quarter — to find 25% of a number, divide by 4: 25% of 20 = 5.
• Steps:
  • 25% = 1/4. Find 1/4 of 40: 40 ÷ 4 = 10.
  • The team won 10 games.
• Answer: 10

[Hard] Decimal Multiplication

• EN: A notebook costs $3.25. A student buys 4 notebooks. How much do they cost in total?
• FR: Un cahier coûte 3,25 $. Un élève en achète 4. Combien coûtent-ils en tout?
• Choices: A) $13.00 B) $12.00 C) $14.00 D) $12.50
• Hint: Multiply as if there is no decimal point, then place the decimal: 2.50 × 3 = 7.50.
• Steps:
  • $3.25 × 4: 3 × 4 = 12 and 0.25 × 4 = 1.00.
  • 12 + 1 = $13.00. Four notebooks cost $13.00.
• Answer: $13.00

[Hard] Multi-Step Fraction and Percentage Problem

• EN: A bag has 30 candies. 1/3 of them are chocolate and 10% of the remaining candies are mint. How many mint candies are there?
• FR: Un sac contient 30 bonbons. 1/3 d'entre eux sont au chocolat et 10 % des bonbons restants sont à la menthe. Combien de bonbons à la menthe y a-t-il?
• Choices: A) 3 B) 5 C) 4 D) 2
• Hint: Work step by step — find the first fraction, subtract, then find the percentage of what remains, like 1/4 of 20 = 5, leaving 15, and 10% of 15 = 1.5.
• Steps:
  • 1/3 of 30 = 10 chocolate candies. Remaining: 30 − 10 = 20.
  • 10% of 20 = 20 ÷ 10 = 2. There are 2 mint candies.
• Answer: 2

[Easy] Percent of a Number

• EN: What is 30% of 60?
• FR: Combien font 30 % de 60?
• Choices: A) 20 B) 30 C) 18 D) 24
• Hint: Find 10% first (divide by 10), then multiply by the number of tens: 10% of 50 = 5, so 30% of 50 = 15.
• Steps:
  • 10% of 60 = 6.
  • 30% = 3 × 6 = 18.
• Answer: 18

[Easy] Integers Intro

• EN: The temperature on a winter morning in Winnipeg is −8°C. By noon it rises 11°C. What is the temperature at noon?
• FR: La température un matin d'hiver à Winnipeg est de −8 °C. À midi, elle monte de 11 °C. Quelle est la température à midi?
• Choices: A) 4°C B) 2°C C) 3°C D) 5°C
• Hint: Adding a positive number to a negative number — move right on a number line: −5 + 8 = 3.
• Steps:
  • Start at −8 and add 11.
  • −8 + 11 = 3. The temperature at noon is 3°C.
• Answer: 3°C

[Easy] Ratios and Rates

• EN: A car travels 120 km in 2 hours. What is the speed in kilometres per hour?
• FR: Une voiture parcourt 120 km en 2 heures. Quelle est sa vitesse en kilomètres par heure?
• Choices: A) 50 km/h B) 70 km/h C) 60 km/h D) 80 km/h
• Hint: To find a unit rate, divide the total amount by the number of units: 90 km ÷ 3 hours = 30 km/h.
• Steps:
  • Rate = distance ÷ time = 120 ÷ 2.
  • 120 ÷ 2 = 60 km/h.
• Answer: 60 km/h

[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) 19 D) 15
• Hint: Substitute the value and follow the order of operations: if x = 3, then 2x + 5 = 2(3) + 5 = 6 + 5 = 11.
• Steps:
  • Substitute n = 5: 3(5) + 4.
  • 15 + 4 = 19. The value is 19.
• Answer: 19

[Medium] Fraction Multiplication

• EN: A recipe calls for 3/4 cup of flour. Sunita wants to make 2/3 of the recipe. How much flour does she need?
• FR: Une recette demande 3/4 de tasse de farine. Sunita veut faire 2/3 de la recette. De quelle quantité de farine a-t-elle besoin?
• Choices: A) 5/12 B) 1/2 C) 2/7 D) 5/7
• Hint: Multiply fractions by multiplying the numerators and multiplying the denominators: 2/3 × 3/5 = 6/15 = 2/5.
• Steps:
  • 3/4 × 2/3 = (3 × 2) / (4 × 3) = 6/12.
  • Simplify: 6/12 = 1/2. Sunita needs 1/2 cup of flour.
• Answer: 1/2

[Medium] BEDMAS — Order of Operations

• EN: Evaluate: 4 + 3 × (8 − 2) ÷ 6.
• FR: Évalue : 4 + 3 × (8 − 2) ÷ 6.
• Choices: A) 11 B) 9 C) 8 D) 7
• Hint: Follow BEDMAS — Brackets first, then Exponents, then Multiplication/Division left to right, then Addition/Subtraction: 2 + 4 × (6 − 4) = 2 + 4 × 2 = 2 + 8 = 10.
• Steps:
  • Brackets first: (8 − 2) = 6. Expression: 4 + 3 × 6 ÷ 6.
  • Multiply and divide left to right: 3 × 6 = 18, then 18 ÷ 6 = 3. Then 4 + 3 = 7.
• Answer: 7

[Medium] Ratio Problem

• EN: In a class, the ratio of boys to girls is 3:4. There are 28 students in total. How many are girls?
• FR: Dans une classe, le rapport garçons-filles est de 3:4. Il y a 28 élèves en tout. Combien sont des filles?
• Choices: A) 12 B) 14 C) 16 D) 18
• Hint: Find the total parts of the ratio, then find one part by dividing: if ratio is 2:3 and total is 25, one part = 25 ÷ 5 = 5, so 3 parts = 15.
• Steps:
  • Total parts: 3 + 4 = 7 parts. One part = 28 ÷ 7 = 4 students.
  • Girls = 4 parts × 4 = 16 girls.
• Answer: 16

[Medium] Fraction Division

• EN: How many 1/4-cup servings can you get from 3 cups of trail mix?
• FR: Combien de portions de 1/4 de tasse peut-on obtenir à partir de 3 tasses de mélange de noix?
• Choices: A) 9 B) 16 C) 12 D) 15
• Hint: Dividing by a fraction means multiplying by its reciprocal: 4 ÷ 1/2 = 4 × 2 = 8.
• Steps:
  • 3 ÷ 1/4 = 3 × 4 = 12.
  • You can get 12 servings.
• Answer: 12

[Hard] Percent Problem — Discount

• EN: A pair of hockey skates costs $120. They are on sale for 15% off. What is the sale price?
• FR: Une paire de patins de hockey coûte 120 $. Ils sont en solde à 15 % de rabais. Quel est le prix de vente?
• Choices: A) $100.00 B) $104.00 C) $102.00 D) $108.00
• Hint: Find the discount amount by multiplying price by the percent, then subtract: 10% of $80 = $8, 5% = $4, so 15% = $12, and $80 − $12 = $68.
• Steps:
  • 10% of $120 = $12. 5% of $120 = $6. So 15% = $12 + $6 = $18.
  • Sale price = $120 − $18 = $102.00.
• Answer: $102.00

[Hard] Integer Operations and Expression Evaluation

• EN: Evaluate: (−4) × 3 + (−2) × (−5).
• FR: Évalue : (−4) × 3 + (−2) × (−5).
• Choices: A) −22 B) −2 C) 2 D) 22
• Hint: Multiply first, then add — remember a negative times a negative is positive: (−3) × (−4) = 12.
• Steps:
  • (−4) × 3 = −12. (−2) × (−5) = +10.
  • −12 + 10 = −2.
• Answer: −2

[Easy] Integer Addition

• EN: What is (−6) + 9?
• FR: Combien fait (−6) + 9?
• Choices: A) −3 B) 15 C) 3 D) −15
• Hint: Use a number line — start at −6 and jump 9 to the right: starting at −4 and adding 7 lands at 3.
• Steps:
  • Start at −6 on the number line. Add 9 by moving right.
  • −6 + 9 = 3.
• Answer: 3

[Easy] Percent — Discount

• EN: A $40 backpack is 20% off. How much do you save?
• FR: Un sac à dos à 40 $ est en rabais de 20 %. Combien économises-tu?
• Choices: A) $6 B) $10 C) $8 D) $12
• Hint: 20% = 2 × 10%, and 10% of a number is found by dividing by 10: 10% of $60 = $6, so 20% = $12.
• Steps:
  • 10% of $40 = $4. 20% = 2 × $4 = $8.
  • You save $8.
• Answer: $8

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 13 = 20.
• FR: Résous pour x : x + 13 = 20.
• Choices: A) x = 6 B) x = 33 C) x = 7 D) x = 9
• Hint: To solve an addition equation, subtract the same number from both sides: if x + 5 = 12, then x = 12 − 5 = 7.
• Steps:
  • Subtract 13 from both sides: x = 20 − 13.
  • x = 7.
• Answer: x = 7

[Easy] Integer Subtraction

• EN: What is 4 − (−3)?
• FR: Combien fait 4 − (−3)?
• Choices: A) 1 B) −7 C) 7 D) −1
• Hint: Subtracting a negative is the same as adding a positive: 6 − (−2) = 6 + 2 = 8.
• Steps:
  • 4 − (−3) = 4 + 3.
  • 4 + 3 = 7.
• Answer: 7

[Medium] Percent — Tax

• EN: A video game costs $55. Ontario's HST is 13%. What is the total cost including tax?
• FR: Un jeu vidéo coûte 55 $. La TVH en Ontario est de 13 %. Quel est le prix total avec les taxes?
• Choices: A) $62.15 B) $60.50 C) $63.05 D) $58.65
• Hint: Find the tax amount and add it to the original price: 10% of $40 = $4.00 and 3% of $40 = $1.20, so 13% tax = $5.20, total = $45.20.
• Steps:
  • Tax: 10% of $55 = $5.50; 3% of $55 = $1.65. Tax = $5.50 + $1.65 = $7.15.
  • Total = $55.00 + $7.15 = $62.15.
• Answer: $62.15

[Medium] Integer Multiplication and Division

• EN: What is (−36) ÷ (−4)?
• FR: Combien fait (−36) ÷ (−4)?
• Choices: A) −9 B) −40 C) 9 D) 40
• Hint: A negative divided by a negative is positive: (−20) ÷ (−5) = +4.
• Steps:
  • Two negatives divided give a positive result.
  • 36 ÷ 4 = 9, so (−36) ÷ (−4) = 9.
• Answer: 9

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 10 cm long, 6 cm wide, and 4 cm tall. What is its surface area?
• FR: Une boîte cadeau mesure 10 cm de longueur, 6 cm de largeur et 4 cm de hauteur. Quelle est son aire totale?
• Choices: A) 240 cm² B) 248 cm² C) 256 cm² D) 280 cm²
• Hint: Surface area of a rectangular prism = 2(lw + lh + wh): for a 5 × 3 × 2 box, SA = 2(15 + 10 + 6) = 2(31) = 62 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(10×6 + 10×4 + 6×4) = 2(60 + 40 + 24).
  • 2 × 124 = 248 cm².
• Answer: 248 cm²

[Medium] Fraction and Decimal Fluency

• EN: Express 5/8 as a decimal.
• FR: Exprime 5/8 sous forme décimale.
• Choices: A) 0.58 B) 0.75 C) 0.625 D) 0.60
• Hint: Divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75.
• Steps:
  • Divide 5 by 8: 5.000 ÷ 8.
  • 8 goes into 50 six times (48), remainder 2; 8 goes into 20 twice (16), remainder 4; 8 goes into 40 five times. Result: 0.625.
• Answer: 0.625

[Hard] Probability

• EN: A bag contains 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of randomly picking a blue marble?
• FR: Un sac contient 3 billes rouges, 4 billes bleues et 5 billes vertes. Quelle est la probabilité de choisir au hasard une bille bleue?
• Choices: A) 1/3 B) 4/11 C) 1/4 D) 3/12
• Hint: Probability = favourable outcomes ÷ total outcomes: if a bag has 2 red and 3 blue marbles, P(red) = 2/5.
• Steps:
  • Total marbles: 3 + 4 + 5 = 12.
  • P(blue) = 4/12 = 1/3.
• Answer: 1/3

[Hard] Multi-Step Percent Problem

• EN: A store marks up a $80 item by 25%, then offers a 10% discount on the marked-up price. What is the final price?
• FR: Un magasin majore un article de 80 $ de 25 %, puis offre un rabais de 10 % sur le prix majoré. Quel est le prix final?
• Choices: A) $92 B) $88 C) $90 D) $94
• Hint: Do two separate percent calculations — apply the markup first, then apply the discount to the new price.
• Steps:
  • Marked-up price: $80 + 25% of $80 = $80 + $20 = $100.
  • Discount: 10% of $100 = $10. Final price: $100 − $10 = $90.
• Answer: $90

[Easy] Perfect Squares

• EN: What is the square root of 144?
• FR: Quelle est la racine carrée de 144?
• Choices: A) 11 B) 14 C) 12 D) 13
• Hint: Think of which number multiplied by itself equals the number: √81 = 9 because 9 × 9 = 81.
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144, so √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored 70, 80, 90, 60, and 100 on a test. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 80, 90, 60 et 100 à un test. Quelle est la note moyenne?
• Choices: A) 80 B) 85 C) 75 D) 90
• Hint: The mean = sum of all values ÷ number of values: mean of 4, 6, 8 = 18 ÷ 3 = 6.
• Steps:
  • Sum: 70 + 80 + 90 + 60 + 100 = 400.
  • Mean = 400 ÷ 5 = 80.
• Answer: 80

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x : 2x + 5 = 13.
• Choices: A) x = 9 B) x = 3 C) x = 4 D) x = 6
• Hint: Undo the addition first, then undo the multiplication: for 3x + 2 = 11, subtract 2 to get 3x = 9, then divide by 3 to get x = 3.
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A hockey stick costs $50. Its price increases by 20%. What is the new price?
• FR: Un bâton de hockey coûte 50 $. Son prix augmente de 20 %. Quel est le nouveau prix?
• Choices: A) $65 B) $55 C) $70 D) $60
• Hint: Find the increase amount and add it to the original: 10% of $80 = $8, so 20% = $16, new price = $80 + $16 = $96.
• Steps:
  • 20% of $50 = $10.
  • New price = $50 + $10 = $60.
• Answer: $60

[Medium] Two-Step Equation with Negatives

• EN: Solve for x: 3x − 7 = 11.
• FR: Résous pour x : 3x − 7 = 11.
• Choices: A) x = 5 B) x = 9 C) x = 7 D) x = 6
• Hint: Add to both sides first to isolate the variable term, then divide: for 4x − 3 = 9, add 3 to get 4x = 12, then x = 3.
• Steps:
  • Add 7 to both sides: 3x = 18.
  • Divide by 3: x = 6.
• Answer: x = 6

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 12 cm B) 11 cm C) 14 cm D) 10 cm
• Hint: Use a² + b² = c²: for legs 3 and 4, 3² + 4² = 9 + 16 = 25, and √25 = 5.
• Steps:
  • a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

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

[Medium] Median and Mode

• EN: The data set is: 4, 7, 7, 9, 11, 13, 15. What is the median?
• FR: L'ensemble de données est : 4, 7, 7, 9, 11, 13, 15. Quelle est la médiane?
• Choices: A) 7 B) 11 C) 13 D) 9
• Hint: The median is the middle value when numbers are ordered — for 2, 5, 8, 9, 12, the middle value is 8.
• Steps:
  • Count the values: there are 7. The middle value is the 4th.
  • The ordered list is 4, 7, 7, 9, 11, 13, 15. The 4th value is 9.
• Answer: 9

[Hard] Percent Decrease

• EN: A ski jacket was originally priced at $240. It is now sold for $180. What is the percent decrease in price?
• FR: Une veste de ski était originalement à 240 $. Elle est maintenant vendue à 180 $. Quel est le pourcentage de réduction?
• Choices: A) 20% B) 33% C) 25% D) 30%
• Hint: Percent decrease = (amount of decrease ÷ original price) × 100: if a $60 item drops to $45, decrease = $15, percent = (15 ÷ 60) × 100 = 25%.
• Steps:
  • Decrease: $240 − $180 = $60.
  • Percent decrease = (60 ÷ 240) × 100 = 25%.
• Answer: 25%

[Hard] Pythagorean Theorem — Real World

• EN: A ladder is 13 m long and leans against a wall. The bottom of the ladder is 5 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 13 m de long est appuyée contre un mur. Le bas de l'échelle est à 5 m du mur. À quelle hauteur sur le mur l'échelle arrive-t-elle?
• Choices: A) 10 m B) 14 m C) 11 m D) 12 m
• Hint: Use a² + b² = c², where c is the ladder (hypotenuse): rearrange to find a = √(c² − b²).
• Steps:
  • 13² − 5² = 169 − 25 = 144.
  • √144 = 12. The ladder reaches 12 m up the wall.
• Answer: 12 m

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 3 = 22.
• FR: Résous pour x : 5x − 3 = 22.
• Choices: A) x = 4 B) x = 6 C) x = 7 D) x = 5
• Hint: Add to both sides first, then divide: for 4x − 5 = 11, add 5 to get 4x = 16, then x = 4.
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Add (3x² + 2x + 1) + (x² − x + 4).
• FR: Additionne (3x² + 2x + 1) + (x² − x + 4).
• Choices: A) 4x² + x + 5 B) 3x² + 3x + 5 C) 4x² + 3x + 5 D) 2x² + x + 5
• Hint: Combine like terms — add coefficients of the same type: (2a² + 3a) + (a² − a) = 3a² + 2a.
• Steps:
  • Combine x² terms: 3x² + x² = 4x².
  • Combine x terms: 2x − x = x. Combine constants: 1 + 4 = 5. Result: 4x² + x + 5.
• Answer: 4x² + x + 5

[Easy] Graphing Lines — Slope-Intercept Form

• EN: What is the slope of the line y = 4x − 3?
• FR: Quelle est la pente de la droite y = 4x − 3?
• Choices: A) −3 B) 4 C) 3 D) 7
• Hint: In the form y = mx + b, m is the slope and b is the y-intercept: for y = 2x + 5, the slope is 2.
• Steps:
  • The equation is in y = mx + b form.
  • m = 4, so the slope is 4.
• Answer: 4

[Easy] Linear Inequality

• EN: Solve the inequality: 2x + 4 > 10.
• FR: Résous l'inégalité : 2x + 4 > 10.
• Choices: A) x > 5 B) x < 3 C) x > 3 D) x < 7
• Hint: Solve like an equation but keep the inequality sign: for 3x + 6 > 15, subtract 6 to get 3x > 9, then divide to get x > 3.
• Steps:
  • Subtract 4 from both sides: 2x > 6.
  • Divide by 2: x > 3.
• Answer: x > 3

[Medium] Multiplying Polynomials

• EN: Expand and simplify: (x + 3)(x + 5).
• FR: Développe et simplifie : (x + 3)(x + 5).
• Choices: A) x² + 9x + 15 B) x² + 8x + 15 C) x² + 7x + 8 D) x² + 15x + 8
• Hint: Use the FOIL method — multiply First, Outer, Inner, Last terms: (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • F: x × x = x². O: x × 5 = 5x. I: 3 × x = 3x. L: 3 × 5 = 15.
  • Combine: x² + 5x + 3x + 15 = x² + 8x + 15.
• Answer: x² + 8x + 15

[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 un rapport de 2:5. Le plus petit triangle a un côté de 6 cm. Quel est le côté correspondant du plus grand triangle?
• Choices: A) 18 cm B) 12 cm C) 20 cm D) 15 cm
• Hint: Set up a proportion and cross-multiply: if ratio is 3:7 and the smaller side is 9 cm, then 3/7 = 9/x so x = 21 cm.
• Steps:
  • Ratio 2:5, smaller side is 6 cm.
  • Scale factor: 6 ÷ 2 = 3. Larger side = 5 × 3 = 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 5 cm and the hypotenuse is 13 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 5 cm et l'hypoténuse mesure 13 cm. Combien vaut sin(θ)?
• Choices: A) 13/5 B) 12/13 C) 5/12 D) 5/13
• Hint: SOH: sin = opposite ÷ hypotenuse — if opposite = 3 and hypotenuse = 5, then sin(θ) = 3/5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 5 ÷ 13.
  • sin(θ) = 5/13.
• Answer: 5/13

[Medium] Subtracting Polynomials

• EN: Subtract: (4x² + 5x − 2) − (x² − 3x + 4).
• FR: Soustrait : (4x² + 5x − 2) − (x² − 3x + 4).
• Choices: A) 3x² + 8x − 6 B) 5x² + 2x − 6 C) 3x² + 2x + 2 D) 3x² + 8x + 2
• Hint: Distribute the negative sign to all terms in the second bracket, then combine like terms: (3x + 5) − (x − 2) = 3x + 5 − x + 2 = 2x + 7.
• Steps:
  • Distribute the negative: 4x² + 5x − 2 − x² + 3x − 4.
  • Combine: (4x² − x²) + (5x + 3x) + (−2 − 4) = 3x² + 8x − 6.
• Answer: 3x² + 8x − 6

[Hard] Finding the Equation of a Line

• EN: A line passes through (−1, 2) and (3, 10). What is the equation of the line in slope-intercept form?
• FR: Une droite passe par (−1, 2) et (3, 10). Quelle est l'équation de la droite en forme pente-ordonnée à l'origine?
• Choices: A) y = 3x + 5 B) y = 3x − 5 C) y = 2x + 4 D) y = 2x + 5
• Hint: Find slope with m = (y₂ − y₁) ÷ (x₂ − x₁), then substitute one point into y = mx + b to find b.
• Steps:
  • Slope: m = (10 − 2) ÷ (3 − (−1)) = 8 ÷ 4 = 2.
  • Using (3, 10): 10 = 2(3) + b → b = 4. Equation: y = 2x + 4.
• Answer: y = 2x + 4

[Hard] Trigonometry — Find the Missing Side

• EN: In a right triangle, angle θ = 30° and the hypotenuse is 20 cm. What is the length of the side opposite to θ? (Use sin 30° = 0.5.)
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé à θ? (Utilise sin 30° = 0,5.)
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 15 cm
• Hint: Rearrange SOH — opposite = sin(θ) × hypotenuse: if sin(45°) ≈ 0.707 and hypotenuse = 10, opposite ≈ 7.07 cm.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse → opposite = sin(30°) × 20.
  • Opposite = 0.5 × 20 = 10 cm.
• Answer: 10 cm

[Easy] Factoring a Trinomial

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

[Easy] Trigonometry — Finding an Angle

• EN: In a right triangle, tan(θ) = 1. What is the value of angle θ?
• FR: Dans un triangle rectangle, tan(θ) = 1. Quelle est la valeur de l'angle θ?
• Choices: A) 60° B) 30° C) 45° D) 90°
• Hint: tan(θ) = opposite ÷ adjacent — recall exact values: tan(30°) = 1/√3, tan(45°) = 1, tan(60°) = √3.
• Steps:
  • tan(θ) = 1 means opposite = adjacent.
  • This occurs at θ = 45°.
• Answer: 45°

[Easy] Solving a Quadratic by Factoring

• EN: Solve: x² − 5x + 6 = 0.
• FR: Résous : x² − 5x + 6 = 0.
• Choices: A) x = 2 and x = 3 B) x = 1 and x = 6 C) x = −2 and x = −3 D) x = 3 and x = 6
• Hint: Factor the trinomial, then set each factor to zero: (x − 1)(x − 4) = 0 gives x = 1 or x = 4.
• Steps:
  • Factor: (x − 2)(x − 3) = 0.
  • Set each factor to zero: x − 2 = 0 → x = 2; x − 3 = 0 → x = 3.
• Answer: x = 2 and x = 3

[Easy] Volume of a Cylinder

• EN: A can of soup has a radius of 4 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14.)
• FR: Une boîte de soupe a un rayon de 4 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14.)
• Choices: A) 502.4 cm³ B) 452.2 cm³ C) 326.4 cm³ D) 412.0 cm³
• Hint: Volume of a cylinder = π × r² × h: for r = 3 and h = 5, V = 3.14 × 9 × 5 = 141.3 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 4² × 10 = 3.14 × 16 × 10.
  • 3.14 × 160 = 502.4 cm³.
• Answer: 502.4 cm³

[Medium] System of Equations

• EN: Solve the system: 2x + y = 10 and x − y = 2.
• FR: Résous le système : 2x + y = 10 et x − y = 2.
• Choices: A) x = 5, y = 1 B) x = 3, y = 4 C) x = 4, y = 2 D) x = 6, y = 3
• Hint: Use elimination — add the equations if they have opposite terms: for 3x + y = 9 and x − y = 3, add to get 4x = 12, so x = 3.
• Steps:
  • Add the equations: (2x + y) + (x − y) = 10 + 2 → 3x = 12 → x = 4.
  • Substitute x = 4 into x − y = 2: 4 − y = 2 → y = 2.
• Answer: x = 4, y = 2

[Medium] Completing the Square

• EN: Rewrite x² + 6x + 2 in completed-square form.
• FR: Réécris x² + 6x + 2 sous forme canonique.
• Choices: A) (x + 3)² + 7 B) (x + 3)² − 7 C) (x + 6)² − 34 D) (x + 2)² − 3
• Hint: Take half the x-coefficient, square it, add and subtract: x² + 4x + 1 = (x + 2)² − 4 + 1 = (x + 2)² − 3.
• Steps:
  • Half of 6 is 3; 3² = 9. Add and subtract 9: (x² + 6x + 9) − 9 + 2.
  • = (x + 3)² − 7.
• Answer: (x + 3)² − 7

[Medium] Circle Geometry — Chord and Radius

• EN: A chord in a circle is 16 cm long. The perpendicular distance from the centre to the chord is 6 cm. What is the radius of the circle?
• FR: Une corde dans un cercle mesure 16 cm. La distance perpendiculaire du centre à la corde est de 6 cm. Quel est le rayon du cercle?
• Choices: A) 9 cm B) 11 cm C) 8 cm D) 10 cm
• Hint: The perpendicular from the centre bisects the chord — form a right triangle with half the chord, the perpendicular distance, and the radius as hypotenuse.
• Steps:
  • Half the chord = 16 ÷ 2 = 8 cm. The right triangle has legs 8 cm and 6 cm.
  • r² = 8² + 6² = 64 + 36 = 100, so r = √100 = 10 cm.
• Answer: 10 cm

[Medium] Surface Area of a Cone

• EN: A party hat is a cone with radius 5 cm and slant height 13 cm. What is its lateral surface area? (Use π ≈ 3.14.)
• FR: Un chapeau de fête est un cône avec un rayon de 5 cm et une hauteur oblique de 13 cm. Quelle est son aire latérale? (Utilise π ≈ 3,14.)
• Choices: A) 204.1 cm² B) 220.0 cm² C) 186.2 cm² D) 198.5 cm²
• Hint: Lateral surface area of a cone = π × r × slant height: for r = 3, slant = 5, SA = 3.14 × 3 × 5 = 47.1 cm².
• Steps:
  • SA = π × r × l = 3.14 × 5 × 13.
  • 3.14 × 65 = 204.1 cm².
• Answer: 204.1 cm²

[Hard] Quadratic Formula

• EN: Solve using the quadratic formula: 2x² − 4x − 6 = 0.
• FR: Résous à l'aide de la formule quadratique : 2x² − 4x − 6 = 0.
• Choices: A) x = 3 and x = −1 B) x = 3 and x = 1 C) x = −3 and x = 1 D) x = 6 and x = −2
• Hint: Use x = [−b ± √(b² − 4ac)] ÷ (2a): for x² − 5x + 6 = 0, discriminant = 25 − 24 = 1, so x = (5 ± 1)/2 → x = 3 or x = 2.
• Steps:
  • a = 2, b = −4, c = −6. Discriminant: (−4)² − 4(2)(−6) = 16 + 48 = 64. √64 = 8.
  • x = (4 ± 8) ÷ 4. So x = 12/4 = 3 or x = −4/4 = −1.
• Answer: x = 3 and x = −1

[Hard] System of Equations — Non-Linear Context

• EN: Two numbers have a sum of 20 and their product is 96. What are the two numbers?
• FR: Deux nombres ont une somme de 20 et leur produit est 96. Quels sont ces deux nombres?
• Choices: A) 10 and 10 B) 6 and 16 C) 8 and 12 D) 4 and 18
• Hint: Set up x + y = sum and x × y = product, then use substitution or try factor pairs of the product: factor pairs of 48 that add to 14 would be 6 and 8.
• Steps:
  • Try factor pairs of 96 that add to 20: 8 × 12 = 96 and 8 + 12 = 20. ✓
  • The two numbers are 8 and 12.
• Answer: 8 and 12

[Easy] Evaluating a Function

• EN: If f(x) = 3x² − 2x + 1, what is f(2)?
• FR: Si f(x) = 3x² − 2x + 1, combien vaut f(2)?
• Choices: A) 7 B) 9 C) 11 D) 13
• Hint: Substitute the value into every x in the function: f(3) = 2(3)² − 3 + 4 = 18 − 3 + 4 = 19.
• Steps:
  • f(2) = 3(2)² − 2(2) + 1 = 3(4) − 4 + 1.
  • 12 − 4 + 1 = 9.
• Answer: 9

[Easy] Logarithm Introduction

• EN: Evaluate: log₂(16).
• FR: Évalue : log₂(16).
• Choices: A) 2 B) 8 C) 6 D) 4
• Hint: log_b(x) asks "to what power must b be raised to get x?" — log₃(27) = 3 because 3³ = 27.
• Steps:
  • Ask: 2 to what power equals 16?
  • 2⁴ = 16, so log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 5 and the common difference is 7. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 5 et la raison est 7. Quel est le 5e terme?
• Choices: A) 35 B) 33 C) 38 D) 40
• Hint: Use the formula aₙ = a₁ + (n − 1)d: for a₁ = 3, d = 4, the 4th term = 3 + (3)(4) = 15.
• Steps:
  • a₅ = 5 + (5 − 1)(7) = 5 + 4 × 7 = 5 + 28.
  • a₅ = 33.
• Answer: 33

[Easy] Compound Interest

• EN: Ahmed invests $1000 at an annual interest rate of 5% compounded annually. How much does he have after 2 years?
• FR: Ahmed investit 1000 $ à un taux d'intérêt annuel de 5 % composé annuellement. Combien a-t-il après 2 ans?
• Choices: A) $1102.50 B) $1100.00 C) $1050.00 D) $1200.00
• Hint: Use A = P(1 + r)ⁿ: for $500 at 4% for 2 years, A = 500(1.04)² = 500(1.0816) = $540.80.
• Steps:
  • A = 1000(1 + 0.05)² = 1000(1.05)².
  • (1.05)² = 1.1025. A = 1000 × 1.1025 = $1102.50.
• Answer: $1102.50

[Medium] Exponential Function

• EN: A bacterial colony doubles every hour. It starts with 50 bacteria. How many bacteria are there after 4 hours?
• FR: Une colonie bactérienne double chaque heure. Elle commence avec 50 bactéries. Combien y en a-t-il après 4 heures?
• Choices: A) 600 B) 800 C) 900 D) 500
• Hint: Use the formula A = a(2)ⁿ where a is the initial amount and n is the number of doublings: 30 bacteria doubling 3 times = 30(2)³ = 240.
• Steps:
  • A = 50 × 2⁴ = 50 × 16.
  • A = 800 bacteria.
• Answer: 800

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifie : sin²(θ) + cos²(θ).
• Choices: A) sin(2θ) B) 0 C) 2 D) 1
• Hint: This is one of the fundamental Pythagorean identities — it always equals the same constant value regardless of θ.
• Steps:
  • The Pythagorean identity states sin²(θ) + cos²(θ) = 1 for all angles θ.
  • The answer is 1.
• Answer: 1

[Medium] Geometric Sequence

• EN: A geometric sequence has first term 3 and common ratio 4. What is the sum of the first 3 terms?
• FR: Une suite géométrique a comme premier terme 3 et comme raison 4. Quelle est la somme des 3 premiers termes?
• Choices: A) 60 B) 63 C) 48 D) 57
• Hint: List the terms and add: a₁, a₁r, a₁r² — for first term 2 and ratio 3, terms are 2, 6, 18; sum = 26.
• Steps:
  • Terms: 3, 3×4 = 12, 12×4 = 48.
  • Sum = 3 + 12 + 48 = 63.
• Answer: 63

[Medium] Annuity Calculation

• EN: Isabelle deposits $200 at the end of each month into an account earning 6% annual interest compounded monthly. How much is in the account after 3 months? (Assume monthly rate = 0.5%.)
• FR: Isabelle dépose 200 $ à la fin de chaque mois dans un compte à 6 % d'intérêt annuel composé mensuellement. Combien y a-t-il dans le compte après 3 mois? (Taux mensuel = 0,5 %.)
• Choices: A) $603.01 B) $650.00 C) $580.00 D) $600.00
• Hint: Each deposit earns interest for a different number of months — add each deposit with its earned interest: the first $200 grows for 2 months, the second for 1, the third earns nothing yet.
• Steps:
  • First deposit after month 1, grows for 2 months: 200(1.005)² ≈ $202.01. Second deposit grows for 1 month: 200(1.005)¹ ≈ $201.00. Third deposit: $200.00.
  • Total ≈ 202.01 + 201.00 + 200.00 = $603.01.
• Answer: $603.01

[Hard] Logarithm Laws

• EN: Simplify: log₃(81) − log₃(9).
• FR: Simplifie : log₃(81) − log₃(9).
• Choices: A) log₃(72) B) 1 C) 3 D) 2
• Hint: Use the logarithm quotient law — logb(M) − logb(N) = log_b(M/N): log₄(64) − log₄(4) = log₄(16) = 2.
• Steps:
  • log₃(81) − log₃(9) = log₃(81/9) = log₃(9).
  • 3² = 9, so log₃(9) = 2.
• Answer: 2

[Hard] Quadratic Function — Vertex and Applications

• EN: A ball is thrown upward with height h = −5t² + 20t + 1 (in metres, t in seconds). What is the maximum height the ball reaches?
• FR: Une balle est lancée vers le haut avec une hauteur h = −5t² + 20t + 1 (en mètres, t en secondes). Quelle est la hauteur maximale atteinte par la balle?
• Choices: A) 25 m B) 20 m C) 22 m D) 21 m
• Hint: The maximum occurs at the vertex — find t using t = −b/(2a), then substitute back: for h = −2t² + 8t + 3, t = 8/(2×2) = 2, then h = −8 + 16 + 3 = 11.
• Steps:
  • t at vertex = −20 / (2 × −5) = −20 / −10 = 2 seconds.
  • h = −5(4) + 20(2) + 1 = −20 + 40 + 1 = 21 m.
• Answer: 21 m

[Easy] Permutations

• EN: In how many ways can 4 different students be arranged in a row of 4 seats?
• FR: De combien de façons 4 élèves différents peuvent-ils être placés dans une rangée de 4 sièges?
• Choices: A) 16 B) 24 C) 12 D) 32
• Hint: The number of arrangements of n different items is n! — for 3 items: 3! = 3 × 2 × 1 = 6.
• Steps:
  • 4 choices for the first seat, 3 for the second, 2 for the third, 1 for the fourth.
  • 4! = 4 × 3 × 2 × 1 = 24.
• Answer: 24

[Easy] Combinations

• EN: How many ways can a student choose 2 clubs from 5 available clubs?
• FR: De combien de façons un élève peut-il choisir 2 clubs parmi 5 clubs disponibles?
• Choices: A) 20 B) 8 C) 10 D) 15
• Hint: Use C(n,r) = n! ÷ (r! × (n−r)!): C(4,2) = 4! ÷ (2! × 2!) = 24 ÷ 4 = 6.
• Steps:
  • C(5,2) = 5! ÷ (2! × 3!) = (5 × 4) ÷ (2 × 1).
  • 20 ÷ 2 = 10.
• Answer: 10

[Easy] Derivative — Basic Power Rule

• EN: If f(x) = x³, what is f'(x)?
• FR: Si f(x) = x³, combien vaut f'(x)?
• Choices: A) x² B) 3x C) 3x² D) 3x⁴
• Hint: The power rule states d/dx(xⁿ) = n × xⁿ⁻¹: for f(x) = x⁵, f'(x) = 5x⁴.
• Steps:
  • Apply the power rule: bring down the exponent and subtract 1.
  • f'(x) = 3x³⁻¹ = 3x².
• Answer: 3x²

[Easy] Polynomial Division

• EN: Divide: (x² + 5x + 6) ÷ (x + 2).
• FR: Divise : (x² + 5x + 6) ÷ (x + 2).
• Choices: A) x + 4 B) x + 2 C) x + 3 D) x + 5
• Hint: Factor the numerator if possible, then cancel the common factor: (x² + 6x + 8) ÷ (x + 2) = (x + 4)(x + 2) ÷ (x + 2) = x + 4.
• Steps:
  • Factor x² + 5x + 6 = (x + 2)(x + 3).
  • Divide by (x + 2): (x + 2)(x + 3) ÷ (x + 2) = x + 3.
• Answer: x + 3

[Medium] Rate of Change — Derivative Application

• EN: The position of a car is given by s(t) = 4t² + 3t. What is the velocity of the car at t = 2 seconds?
• FR: La position d'une voiture est donnée par s(t) = 4t² + 3t. Quelle est la vitesse de la voiture à t = 2 secondes?
• Choices: A) 16 m/s B) 22 m/s C) 19 m/s D) 25 m/s
• Hint: Velocity is the derivative of position — differentiate s(t) to get v(t), then substitute t: for s(t) = 3t² + 2t, v(t) = 6t + 2, so v(1) = 8.
• Steps:
  • Differentiate: v(t) = s'(t) = 8t + 3.
  • At t = 2: v(2) = 8(2) + 3 = 16 + 3 = 19 m/s.
• Answer: 19 m/s

[Medium] Binomial Probability Distribution

• EN: A hockey player has a 60% chance of scoring on any penalty shot. If she takes 3 penalty shots, what is the probability she scores exactly 2 goals? (Round to the nearest hundredth.)
• FR: Une joueuse de hockey a 60 % de chances de marquer sur un tir de pénalité. Si elle prend 3 tirs de pénalité, quelle est la probabilité qu'elle marque exactement 2 buts? (Arrondi au centième.)
• Choices: A) 0.36 B) 0.28 C) 0.43 D) 0.50
• Hint: Use P(X = k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ: for n = 4, k = 2, p = 0.5, P = C(4,2) × 0.5² × 0.5² = 6 × 0.0625 = 0.375.
• Steps:
  • P(X = 2) = C(3,2) × (0.6)² × (0.4)¹.
  • C(3,2) = 3; (0.6)² = 0.36; 0.36 × 0.4 = 0.144. So P = 3 × 0.144 = 0.432 ≈ 0.43.
• Answer: 0.43

[Medium] Vector Addition

• EN: Vector a = (3, −1) and vector b = (−2, 5). What is a + b?
• FR: Le vecteur a = (3, −1) et le vecteur b = (−2, 5). Combien fait a + b?
• Choices: A) (5, 4) B) (1, 4) C) (1, 6) D) (−1, 4)
• Hint: Add vectors component by component: (2, 3) + (4, −1) = (6, 2).
• Steps:
  • Add x-components: 3 + (−2) = 1.
  • Add y-components: −1 + 5 = 4. Result: (1, 4).
• Answer: (1, 4)

[Medium] Rational Function — Finding Asymptotes

• EN: What is the vertical asymptote of f(x) = (x + 3) / (x − 5)?
• FR: Quelle est l'asymptote verticale de f(x) = (x + 3) / (x − 5)?
• Choices: A) x = 3 B) x = −3 C) x = 5 D) x = −5
• Hint: A vertical asymptote occurs where the denominator equals zero — for f(x) = 1/(x − 4), the vertical asymptote is x = 4.
• Steps:
  • Set the denominator equal to zero: x − 5 = 0.
  • x = 5. The vertical asymptote is x = 5.
• Answer: x = 5

[Hard] Derivative — Finding a Maximum

• EN: The profit of a company (in thousands of dollars) is modelled by P(x) = −2x² + 12x − 10, where x is the number of units (in thousands). How many units maximize the profit?
• FR: Le profit d'une entreprise (en milliers de dollars) est modélisé par P(x) = −2x² + 12x − 10, où x est le nombre d'unités (en milliers). Combien d'unités maximisent le profit?
• Choices: A) 4 thousand units B) 5 thousand units C) 3 thousand units D) 6 thousand units
• Hint: Differentiate P(x), set P'(x) = 0, and solve for x to find the critical point: for P(x) = −x² + 6x, P'(x) = −2x + 6 = 0 gives x = 3.
• Steps:
  • P'(x) = −4x + 12. Set equal to zero: −4x + 12 = 0.
  • 4x = 12, so x = 3 thousand units.
• Answer: 3 thousand units

[Hard] Permutations with Restriction

• EN: In how many ways can 5 students line up for a class photo if two specific students (Maya and Noah) must NOT stand next to each other?
• FR: De combien de façons 5 élèves peuvent-ils se mettre en ligne pour une photo de classe si deux élèves en particulier (Maya et Noah) ne doivent PAS être côte à côte?
• Choices: A) 48 B) 120 C) 72 D) 96
• Hint: Use complementary counting — total arrangements minus the arrangements where the restricted pair IS together (treat them as one unit): for 4 students with 2 always together, restricted = 3! × 2! = 12; total = 4! = 24; result = 24 − 12 = 12.
• Steps:
  • Total arrangements of 5 students: 5! = 120.
  • Arrangements where Maya and Noah ARE together: treat them as 1 unit → 4 units arranged in 4! = 24 ways × 2 (Maya and Noah can swap) = 48.
  • Answer: 120 − 48 = 72.
• Answer: 72