Daily Math — 2026-10-02

[Easy] Counting Apples

• EN: There are 7 apples on the table. You add 5 more. How many apples are there now?
• FR: Il y a 7 pommes sur la table. Tu en ajoutes 5 de plus. Combien y a-t-il de pommes maintenant?
• Choices: A) 10 apples B) 11 apples C) 12 apples D) 13 apples
• Hint: Start at the bigger number and count up (e.g., 6 + 3: start at 6, count up 3 → 7, 8, 9).
• Steps:
  • Start at 7 and count up 5 more.
  • 8, 9, 10, 11, 12 — that is 5 steps up from 7.
  • So the total is 12 apples.
• Answer: 12 apples

[Easy] Counting Back

• EN: You have 15 stickers. You give away 6. How many stickers do you have left?
• FR: Tu as 15 autocollants. Tu en donnes 6. Combien t'en reste-t-il?
• Choices: A) 7 stickers B) 8 stickers C) 9 stickers D) 11 stickers
• Hint: Start at the bigger number and count back (e.g., 10 − 4: start at 10, count back 4 → 9, 8, 7, 6).
• Steps:
  • Start at 15 and count back 6.
  • 14, 13, 12, 11, 10, 9 — that is 6 steps back.
  • So 15 − 6 = 9 stickers.
• Answer: 9 stickers

[Easy] Skip Counting by 5s

• EN: Skip count by 5s. What comes after 20, 25, 30?
• FR: Compte par bonds de 5. Quel nombre vient après 20, 25, 30?
• Choices: A) 32 B) 33 C) 35 D) 40
• Hint: Each jump adds 5 (e.g., 10, 15, 20 — each time you add 5).
• Steps:
  • The pattern adds 5 each time: 20, 25, 30…
  • 30 + 5 = 35.
  • The next number is 35.
• Answer: 35

[Easy] Comparing Numbers

• EN: Which number is bigger: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 18
• Hint: The number with more tens is bigger (e.g., 13 has 1 ten and 3 ones, so it is bigger than 8).
• Steps:
  • 14 has 1 ten and 4 ones.
  • 9 has 0 tens and 9 ones.
  • 1 ten is more than 0 tens, so 14 is bigger.
• Answer: 14

[Medium] Coin Recognition — Pennies and Nickels

• EN: You have 3 nickels. How many cents do you have in total?
• FR: Tu as 3 pièces de 5 cents. Combien de cents as-tu en tout?
• Choices: A) 3 cents B) 10 cents C) 15 cents D) 20 cents
• Hint: Each nickel is worth 5 cents. Add 5 for each nickel you have (e.g., 2 nickels = 5 + 5 = 10 cents).
• Steps:
  • Each nickel = 5 cents.
  • 3 nickels: 5 + 5 + 5.
  • 5 + 5 = 10, then 10 + 5 = 15 cents.
• Answer: 15 cents

[Medium] Addition Within 20

• EN: There are 8 kids on the ice rink. Then 9 more kids arrive. How many kids are on the ice rink now?
• FR: Il y a 8 enfants sur la patinoire. Puis 9 autres enfants arrivent. Combien y a-t-il d'enfants sur la patinoire maintenant?
• Choices: A) 14 kids B) 16 kids C) 17 kids D) 18 kids
• Hint: Make a 10 first to add easily (e.g., 7 + 6: take 3 from 6 to make 7 into 10, then 10 + 3 = 13).
• Steps:
  • Take 2 from 9 to make 8 into 10: 8 + 2 = 10.
  • 9 − 2 = 7 left to add: 10 + 7 = 17.
  • So 8 + 9 = 17 kids.
• Answer: 17 kids

[Medium] Skip Counting by 2s

• EN: Count by 2s starting at 2. What is the 6th number you say?
• FR: Compte par bonds de 2 en commençant à 2. Quel est le 6e nombre que tu dis?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Write out each step (e.g., counting by 2s from 2: 2, 4, 6 — the 3rd number is 6).
• Steps:
  • 1st: 2, 2nd: 4, 3rd: 6, 4th: 8, 5th: 10, 6th: 12.
  • The 6th number is 12.
• Answer: 12

[Medium] Subtraction Story

• EN: There are 18 crayons in a box. You use 9 of them. How many crayons are still in the box?
• FR: Il y a 18 crayons dans une boîte. Tu en utilises 9. Combien de crayons reste-t-il dans la boîte?
• Choices: A) 7 crayons B) 9 crayons C) 11 crayons D) 13 crayons
• Hint: Think of doubles (e.g., 16 − 8 = 8 because 8 + 8 = 16).
• Steps:
  • 9 + 9 = 18, so 18 − 9 = 9.
  • There are 9 crayons left in the box.
• Answer: 9 crayons

[Hard] Two-Step Addition

• EN: In the morning, 6 kids get on the school bus. At the next stop, 7 more kids get on. At another stop, 4 more get on. How many kids are on the bus altogether?
• FR: Le matin, 6 enfants montent dans l'autobus scolaire. Au prochain arrêt, 7 autres montent. À un autre arrêt, 4 de plus montent. Combien y a-t-il d'enfants dans l'autobus en tout?
• Choices: A) 13 kids B) 15 kids C) 17 kids D) 19 kids
• Hint: Add two numbers first, then add the third (e.g., 3 + 5 + 4: do 3 + 5 = 8, then 8 + 4 = 12).
• Steps:
  • Add the first two groups: 6 + 7 = 13.
  • Then add the third group: 13 + 4 = 17.
  • So there are 17 kids on the bus altogether.
• Answer: 17 kids

[Hard] Counting to 100

• EN: What is the number that is 10 more than 73?
• FR: Quel est le nombre qui est 10 de plus que 73?
• Choices: A) 63 B) 74 C) 83 D) 93
• Hint: Adding 10 always changes the tens digit by 1 (e.g., 10 more than 45 is 55 — the tens go from 4 to 5).
• Steps:
  • 73 has 7 tens and 3 ones.
  • Adding 10 more gives 8 tens and 3 ones.
  • 8 tens and 3 ones = 83.
• Answer: 83

[Easy] Addition Within 100

• EN: A bookshelf has 34 books on it. You add 25 more books. How many books are on the shelf now?
• FR: Une étagère a 34 livres. Tu en ajoutes 25 de plus. Combien de livres y a-t-il sur l'étagère maintenant?
• Choices: A) 49 books B) 57 books C) 59 books D) 61 books
• Hint: Add the tens first, then the ones (e.g., 21 + 36: 20 + 30 = 50, 1 + 6 = 7, so 57).
• Steps:
  • Tens: 30 + 20 = 50.
  • Ones: 4 + 5 = 9.
  • 50 + 9 = 59 books.
• Answer: 59 books

[Easy] Subtraction Within 100

• EN: A school has 87 students. 32 of them go outside for recess. How many students are still inside?
• FR: Une école a 87 élèves. 32 d'entre eux vont dehors pour la récréation. Combien d'élèves sont encore à l'intérieur?
• Choices: A) 45 students B) 55 students C) 57 students D) 65 students
• Hint: Subtract the tens, then the ones (e.g., 79 − 43: 70 − 40 = 30, 9 − 3 = 6, so 36).
• Steps:
  • Tens: 80 − 30 = 50.
  • Ones: 7 − 2 = 5.
  • 50 + 5 = 55 students.
• Answer: 55 students

[Easy] Telling Time — Hour

• EN: The clock shows the short hand on 4 and the long hand on 12. What time is it?
• FR: L'aiguille courte de l'horloge est sur le 4 et la grande aiguille est sur le 12. Quelle heure est-il?
• Choices: A) 3:00 B) 4:00 C) 4:30 D) 12:00
• Hint: When the long hand points to 12, it is exactly on the hour (e.g., short hand on 7, long hand on 12 → 7:00).
• Steps:
  • The long hand on 12 means it is exactly on the hour.
  • The short hand is on 4.
  • So the time is 4:00.
• Answer: 4:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A marker is 9 cm long. How much longer is the pencil than the marker?
• FR: Un crayon mesure 14 cm de long. Un marqueur mesure 9 cm de long. De combien le crayon est-il plus long que le marqueur?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 23 cm
• Hint: Subtract the shorter length from the longer length (e.g., 18 cm − 11 cm = 7 cm longer).
• Steps:
  • Subtract: 14 − 9.
  • 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Medium] Counting Coins

• EN: You have 2 dimes, 1 nickel, and 3 pennies. How many cents do you have in total?
• FR: Tu as 2 pièces de 10 cents, 1 pièce de 5 cents et 3 pennies. Combien de cents as-tu en tout?
• Choices: A) 18 cents B) 24 cents C) 28 cents D) 33 cents
• Hint: Find each coin's value first, then add all together (e.g., 1 dime + 2 nickels + 1 penny = 10 + 10 + 1 = 21 cents).
• Steps:
  • 2 dimes = 20 cents.
  • 1 nickel = 5 cents.
  • 3 pennies = 3 cents.
  • 20 + 5 + 3 = 28 cents.
• Answer: 28 cents

[Medium] Telling Time — Half-Hour

• EN: Hockey practice starts when the clock shows 3:30. The short hand is between 3 and 4, and the long hand is on 6. What time does practice start?
• FR: L'entraînement de hockey commence quand l'horloge indique 3h30. L'aiguille courte est entre 3 et 4 et la grande aiguille est sur le 6. À quelle heure l'entraînement commence-t-il?
• Choices: A) 3:00 B) 3:30 C) 4:00 D) 6:30
• Hint: When the long hand is on 6, it is half-past the hour (e.g., short hand between 7 and 8, long hand on 6 → 7:30).
• Steps:
  • Long hand on 6 means 30 minutes past the hour.
  • Short hand is between 3 and 4, so the hour is 3.
  • The time is 3:30.
• Answer: 3:30

[Medium] Patterns

• EN: Look at this pattern: 5, 10, 15, 20, ___. What number comes next?
• FR: Regarde ce modèle : 5, 10, 15, 20, ___. Quel nombre vient ensuite?
• Choices: A) 21 B) 22 C) 24 D) 25
• Hint: Find the rule by looking at how much you add each time (e.g., 3, 6, 9, 12 — the rule is add 3).
• Steps:
  • 10 − 5 = 5, so the rule is add 5 each time.
  • 20 + 5 = 25.
  • The next number is 25.
• Answer: 25

[Medium] Addition with Regrouping

• EN: A Tim Hortons sells 47 muffins in the morning and 36 muffins in the afternoon. How many muffins did they sell in total?
• FR: Un Tim Hortons vend 47 muffins le matin et 36 muffins l'après-midi. Combien de muffins ont-ils vendus en tout?
• Choices: A) 73 muffins B) 81 muffins C) 83 muffins D) 91 muffins
• Hint: Add the ones first; if they make 10 or more, carry 1 to the tens (e.g., 38 + 25: 8 + 5 = 13, write 3 carry 1, then 3 + 2 + 1 = 6, so 63).
• Steps:
  • Ones: 7 + 6 = 13. Write 3, carry 1.
  • Tens: 4 + 3 + 1 (carried) = 8.
  • Total is 83 muffins.
• Answer: 83 muffins

[Hard] Two-Step Word Problem

• EN: Lena has 65 stickers. She gives 28 to her friend and then gets 14 more as a gift. How many stickers does Lena have now?
• FR: Lena a 65 autocollants. Elle en donne 28 à son amie et en reçoit ensuite 14 en cadeau. Combien d'autocollants Lena a-t-elle maintenant?
• Choices: A) 41 stickers B) 51 stickers C) 61 stickers D) 79 stickers
• Hint: Do one step at a time — subtract first, then add (e.g., 50 − 20 = 30, then 30 + 10 = 40).
• Steps:
  • First, subtract the stickers she gave away: 65 − 28 = 37.
  • Then add the stickers she received: 37 + 14 = 51.
  • Lena has 51 stickers now.
• Answer: 51 stickers

[Hard] Measuring and Comparing

• EN: A red ribbon is 62 cm long. A blue ribbon is 29 cm long. If you put them end to end, how long are they together?
• FR: Un ruban rouge mesure 62 cm de long. Un ruban bleu mesure 29 cm de long. Si tu les mets bout à bout, quelle est leur longueur totale?
• Choices: A) 81 cm B) 89 cm C) 91 cm D) 99 cm
• Hint: Add both lengths together and regroup the ones if needed (e.g., 45 cm + 38 cm: 5 + 8 = 13, carry 1, 4 + 3 + 1 = 8, so 83 cm).
• Steps:
  • Ones: 2 + 9 = 11. Write 1, carry 1.
  • Tens: 6 + 2 + 1 (carried) = 9.
  • 62 + 29 = 91 cm.
• Answer: 91 cm

[Easy] Multiplication by 2

• EN: A hockey team has 2 lines of 6 players each on the ice. How many players are there in total?
• FR: Une équipe de hockey a 2 lignes de 6 joueurs chacune sur la glace. Combien y a-t-il de joueurs en tout?
• Choices: A) 8 players B) 10 players C) 12 players D) 14 players
• Hint: Multiplication is repeated addition (e.g., 2 × 4 means 4 + 4 = 8).
• Steps:
  • 2 × 6 means 6 + 6.
  • 6 + 6 = 12.
  • There are 12 players in total.
• Answer: 12 players

[Easy] Multiplication by 5

• EN: There are 5 bags of marbles. Each bag has 4 marbles. How many marbles are there altogether?
• FR: Il y a 5 sacs de billes. Chaque sac contient 4 billes. Combien y a-t-il de billes en tout?
• Choices: A) 9 marbles B) 16 marbles C) 20 marbles D) 25 marbles
• Hint: Multiply the number of groups by the number in each group (e.g., 5 × 3 = 15 because 5 groups of 3).
• Steps:
  • 5 × 4 = 20.
  • Think: 5, 10, 15, 20 — skip counting by 5 four times.
  • There are 20 marbles altogether.
• Answer: 20 marbles

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. You eat 1 piece. What fraction of the pizza did you eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Tu manges 1 morceau. Quelle fraction de la pizza as-tu mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: A fraction tells how many parts you have out of the total equal parts (e.g., 1 piece out of 4 equal pieces is 1/4).
• Steps:
  • The pizza is cut into 2 equal parts (denominator = 2).
  • You ate 1 part (numerator = 1).
  • So you ate 1/2 of the pizza.
• Answer: 1/2

[Easy] Basic Division

• EN: You have 20 stickers to share equally among 4 friends. How many stickers does each friend get?
• FR: Tu as 20 autocollants à partager également entre 4 amis. Combien d'autocollants chaque ami reçoit-il?
• Choices: A) 4 stickers B) 5 stickers C) 6 stickers D) 8 stickers
• Hint: Division asks how many in each group (e.g., 15 ÷ 3: think 3 × ? = 15, so 3 × 5 = 15, answer is 5).
• Steps:
  • 20 ÷ 4 = ?
  • Think: 4 × 5 = 20.
  • Each friend gets 5 stickers.
• Answer: 5 stickers

[Medium] Multiplication by 3

• EN: A classroom has 7 rows of desks with 3 desks in each row. How many desks are there altogether?
• FR: Une salle de classe a 7 rangées de pupitres avec 3 pupitres dans chaque rangée. Combien y a-t-il de pupitres en tout?
• Choices: A) 10 desks B) 18 desks C) 21 desks D) 24 desks
• Hint: Use skip counting by 3s to multiply (e.g., 3 × 4: count 3, 6, 9, 12 — four jumps of 3).
• Steps:
  • 7 × 3: count by 3s seven times.
  • 3, 6, 9, 12, 15, 18, 21.
  • There are 21 desks altogether.
• Answer: 21 desks

[Medium] Perimeter

• EN: A garden is shaped like a rectangle. It is 8 m long and 4 m wide. What is its perimeter?
• FR: Un jardin est en forme de rectangle. Il mesure 8 m de long et 4 m de large. Quel est son périmètre?
• Choices: A) 20 m B) 24 m C) 28 m D) 32 m
• Hint: Add all four sides of the shape (e.g., a rectangle that is 5 m long and 3 m wide: 5 + 3 + 5 + 3 = 16 m).
• Steps:
  • A rectangle has two long sides and two short sides.
  • 8 + 4 + 8 + 4 = 24.
  • The perimeter is 24 m.
• Answer: 24 m

[Medium] Reading a Graph

• EN: A bar graph shows that 9 students like hockey and 6 students like swimming. How many more students like hockey than swimming?
• FR: Un diagramme à barres montre que 9 élèves aiment le hockey et 6 élèves aiment la natation. Combien d'élèves de plus aiment le hockey que la natation?
• Choices: A) 2 students B) 3 students C) 4 students D) 15 students
• Hint: To find "how many more," subtract the smaller number from the larger (e.g., 12 like soccer, 7 like basketball: 12 − 7 = 5 more).
• Steps:
  • Hockey: 9 students. Swimming: 6 students.
  • 9 − 6 = 3.
  • Three more students like hockey than swimming.
• Answer: 3 students

[Medium] Multiplication by 10

• EN: There are 10 boxes of crayons. Each box holds 8 crayons. How many crayons are there in total?
• FR: Il y a 10 boîtes de crayons. Chaque boîte contient 8 crayons. Combien y a-t-il de crayons en tout?
• Choices: A) 18 crayons B) 70 crayons C) 80 crayons D) 90 crayons
• Hint: Multiplying by 10 always puts a 0 at the end of the number (e.g., 10 × 6 = 60).
• Steps:
  • 10 × 8: add a zero to 8.
  • 10 × 8 = 80.
  • There are 80 crayons in total.
• Answer: 80 crayons

[Hard] Fractions and Division Combined

• EN: There are 24 students in a class. One quarter (1/4) of them are wearing red shirts. How many students are wearing red shirts?
• FR: Il y a 24 élèves dans une classe. Un quart (1/4) d'entre eux portent des chemises rouges. Combien d'élèves portent des chemises rouges?
• Choices: A) 4 students B) 5 students C) 6 students D) 8 students
• Hint: To find 1/4 of a number, divide it by 4 (e.g., 1/4 of 20: 20 ÷ 4 = 5).
• Steps:
  • 1/4 of 24 means divide 24 by 4.
  • 24 ÷ 4 = 6.
  • Six students are wearing red shirts.
• Answer: 6 students

[Hard] Multi-Step Multiplication and Addition

• EN: There are 4 shelves in a library. Each shelf holds 9 books. The librarian adds 8 more books to one shelf. How many books are there in total?
• FR: Il y a 4 étagères dans une bibliothèque. Chaque étagère contient 9 livres. La bibliothécaire ajoute 8 livres de plus sur une étagère. Combien y a-t-il de livres en tout?
• Choices: A) 36 books B) 40 books C) 44 books D) 48 books
• Hint: Multiply first to find the starting total, then add the extra (e.g., 3 shelves × 5 books = 15, then 15 + 4 = 19 books).
• Steps:
  • 4 × 9 = 36 books to start.
  • Add the 8 extra books: 36 + 8 = 44.
  • There are 44 books in total.
• Answer: 44 books

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 49 B) 54 C) 56 D) 64
• Hint: Use a fact you know (e.g., 7 × 7 = 49, so 7 × 8 is one more group of 7: 49 + 7 = 56).
• Steps:
  • 7 × 8: think of 7 × 7 = 49.
  • Add one more 7: 49 + 7 = 56.
  • 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 5.37?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 5,37?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 30 ones
• Hint: After the decimal point, the first place is tenths and the second place is hundredths (e.g., in 2.46, the 4 is in the tenths place).
• Steps:
  • 5.37: the 5 is in the ones place.
  • The 3 is right after the decimal — that is the tenths place.
  • The value of 3 is 3 tenths.
• Answer: 3 tenths

[Easy] Long Division

• EN: What is 72 ÷ 8?
• FR: Combien font 72 ÷ 8?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Think of what number times 8 gives you the dividend (e.g., 48 ÷ 8: think 8 × 6 = 48, so the answer is 6).
• Steps:
  • Think: 8 × ? = 72.
  • 8 × 9 = 72.
  • So 72 ÷ 8 = 9.
• Answer: 9

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 1/2?
• FR: Quelle fraction est plus grande : 3/4 ou 1/2?
• Choices: A) 1/2 B) 1/4 C) 3/4 D) 2/3
• Hint: Change fractions to the same denominator to compare (e.g., 2/3 vs 1/2: change to 4/6 vs 3/6 — so 2/3 is bigger).
• Steps:
  • Write 1/2 as 2/4 so both fractions have the same denominator.
  • Compare 3/4 and 2/4 — 3/4 is larger.
  • So 3/4 is the larger fraction.
• Answer: 3/4

[Medium] Area of a Rectangle

• EN: A classroom floor is 9 m long and 6 m wide. What is the area of the floor?
• FR: Le plancher d'une salle de classe mesure 9 m de long et 6 m de large. Quelle est l'aire du plancher?
• Choices: A) 30 m² B) 45 m² C) 54 m² D) 63 m²
• Hint: Area of a rectangle = length × width (e.g., a room 7 m × 4 m has an area of 28 m²).
• Steps:
  • Area = length × width.
  • 9 × 6 = 54.
  • The area is 54 m².
• Answer: 54 m²

[Medium] Long Division with Remainders

• EN: A baker has 47 cookies to pack equally into boxes of 5. How many full boxes can be made, and how many cookies are left over?
• FR: Un boulanger a 47 biscuits à mettre en boîtes de 5. Combien de boîtes pleines peut-il faire, et combien de biscuits reste-t-il?
• Choices: A) 8 boxes, 7 left over B) 9 boxes, 2 left over C) 10 boxes, 3 left over D) 7 boxes, 4 left over
• Hint: Divide and find the remainder: divide the number by the group size and see what is left (e.g., 23 ÷ 4: 4 × 5 = 20, remainder 3 → 5 boxes, 3 left over).
• Steps:
  • 5 × 9 = 45, which is close to 47.
  • 47 − 45 = 2 left over.
  • 9 full boxes with 2 cookies left over.
• Answer: 9 boxes, 2 left over

[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 00. Combien de temps dure la journée scolaire?
• Choices: A) 5 hours 30 minutes B) 6 hours C) 6 hours 30 minutes D) 7 hours
• Hint: Count up from the start time to the end time in steps (e.g., from 9:15 a.m. to 12:15 p.m. is 3 hours).
• Steps:
  • From 8:30 to 9:00 is 30 minutes.
  • From 9:00 to 3:00 is 6 hours.
  • Total: 6 hours + 30 minutes = 6 hours 30 minutes.
• Answer: 6 hours 30 minutes

[Medium] Decimal Operations

• EN: Maya buys a drink for $1.75 and a muffin for $2.50 at Tim Hortons. How much does she spend in total?
• FR: Maya achète une boisson à 1,75 $ et un muffin à 2,50 $ au Tim Hortons. Combien dépense-t-elle en tout?
• Choices: A) $3.25 B) $4.00 C) $4.25 D) $5.25
• Hint: Line up the decimal points and add just like whole numbers (e.g., $1.20 + $2.35 = $3.55).
• Steps:
  • $1.75 + $2.50.
  • 75 cents + 50 cents = 125 cents = $1.25.
  • $1 + $2 + $1.25 = $4.25.
• Answer: $4.25

[Hard] Multi-Step Problem with Division and Fractions

• EN: There are 36 students going on a field trip. One third (1/3) of them ride in van A. The rest are split equally into 3 other vans. How many students are in each of the other vans?
• FR: 36 élèves partent en excursion. Un tiers (1/3) d'entre eux montent dans la fourgonnette A. Les autres sont répartis également dans 3 autres fourgonnettes. Combien d'élèves y a-t-il dans chacune des autres fourgonnettes?
• Choices: A) 6 students B) 7 students C) 8 students D) 12 students
• Hint: First find 1/3 of the total, then subtract to find the rest, then divide the rest equally (e.g., 24 students, 1/3 = 8, rest = 16, split into 2 vans: 16 ÷ 2 = 8 each).
• Steps:
  • 1/3 of 36 = 36 ÷ 3 = 12 students in van A.
  • Remaining: 36 − 12 = 24 students.
  • 24 ÷ 3 = 8 students in each of the other vans.
• Answer: 8 students

[Hard] Long Multiplication

• EN: A sports store receives 24 boxes of hockey pucks. Each box contains 36 pucks. How many pucks does the store receive in total?
• FR: Un magasin de sport reçoit 24 boîtes de rondelles de hockey. Chaque boîte contient 36 rondelles. Combien de rondelles le magasin reçoit-il en tout?
• Choices: A) 720 pucks B) 756 pucks C) 800 pucks D) 864 pucks
• Hint: Break the multiplication into parts (e.g., 23 × 12: 20 × 12 = 240, 3 × 12 = 36, add them: 276).
• Steps:
  • 24 × 36: split into 20 × 36 and 4 × 36.
  • 20 × 36 = 720.
  • 4 × 36 = 144.
  • 720 + 144 = 864 pucks.
• Answer: 864 pucks

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 200 C) 204 D) 244
• Hint: Break the number apart (e.g., 23 × 4: 20 × 4 = 80, 3 × 4 = 12, total = 92).
• Steps:
  • 34 × 6: split into 30 × 6 and 4 × 6.
  • 30 × 6 = 180.
  • 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: A recipe needs 2/8 cup of sugar and 3/8 cup of flour. What is the total amount of these two ingredients?
• FR: Une recette nécessite 2/8 de tasse de sucre et 3/8 de tasse de farine. Quelle est la quantité totale de ces deux ingrédients?
• Choices: A) 5/16 B) 4/8 C) 5/8 D) 6/8
• Hint: Add only the numerators; keep the denominator the same (e.g., 1/5 + 2/5 = 3/5).
• Steps:
  • 2/8 + 3/8: add the numerators.
  • 2 + 3 = 5, denominator stays 8.
  • Total is 5/8.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: A hockey jersey costs $40. It is on sale for 50% off. How much is the discount?
• FR: Un chandail de hockey coûte 40 $. Il est en solde à 50 % de rabais. Quel est le montant du rabais?
• Choices: A) $10 B) $15 C) $20 D) $25
• Hint: 50% means half (e.g., 50% of $60 = $60 ÷ 2 = $30).
• Steps:
  • 50% of $40 = $40 ÷ 2.
  • $40 ÷ 2 = $20.
  • The discount is $20.
• Answer: $20

[Easy] Decimal Operations

• EN: A snowfall of 12.5 cm fell on Monday and 8.3 cm fell on Tuesday. What was the total snowfall?
• FR: Il est tombé 12,5 cm de neige lundi et 8,3 cm mardi. Quelle était la chute de neige totale?
• Choices: A) 19.8 cm B) 20.2 cm C) 20.8 cm D) 21.5 cm
• Hint: Line up the decimal points and add (e.g., 5.6 + 3.7: 6 + 7 = 13, carry 1, 5 + 3 + 1 = 9, so 9.3).
• Steps:
  • Line up: 12.5 + 8.3.
  • Tenths: 5 + 3 = 8.
  • Ones: 12 + 8 = 20.
  • Total: 20.8 cm.
• Answer: 20.8 cm

[Medium] Multi-Digit Division

• EN: A school orders 325 pencils to be shared equally among 5 classrooms. How many pencils does each classroom get?
• FR: Une école commande 325 crayons à partager également entre 5 classes. Combien de crayons chaque classe reçoit-elle?
• Choices: A) 55 pencils B) 60 pencils C) 65 pencils D) 75 pencils
• Hint: Divide step by step using long division (e.g., 246 ÷ 3: 2 ÷ 3 = 0 r2, 24 ÷ 3 = 8, 6 ÷ 3 = 2, so 82).
• Steps:
  • 325 ÷ 5.
  • 300 ÷ 5 = 60. 25 ÷ 5 = 5.
  • 60 + 5 = 65 pencils.
• Answer: 65 pencils

[Medium] Subtracting Fractions

• EN: Ethan has 7/10 of a metre of ribbon. He uses 3/10 of a metre for a project. How much ribbon is left?
• FR: Ethan a 7/10 de mètre de ruban. Il utilise 3/10 de mètre pour un projet. Combien de ruban lui reste-t-il?
• Choices: A) 2/10 B) 3/10 C) 4/10 D) 10/10
• Hint: Subtract only the numerators; keep the denominator (e.g., 6/9 − 2/9 = 4/9).
• Steps:
  • 7/10 − 3/10: subtract numerators.
  • 7 − 3 = 4, denominator stays 10.
  • 4/10 of a metre is left.
• Answer: 4/10

[Medium] Percentage — 25% and 10%

• EN: A backpack costs $80. What is 25% of $80?
• FR: Un sac à dos coûte 80 $. Combien représente 25 % de 80 $?
• Choices: A) $8 B) $16 C) $20 D) $40
• Hint: 25% is one quarter — divide by 4 (e.g., 25% of $60 = $60 ÷ 4 = $15).
• Steps:
  • 25% of $80 = $80 ÷ 4.
  • $80 ÷ 4 = $20.
  • 25% of $80 is $20.
• Answer: $20

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 80 cm³
• Hint: Volume = length × width × height (e.g., a box 6 cm × 2 cm × 4 cm has volume 48 cm³).
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20.
  • 20 × 3 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Hard] Multi-Step with Decimals and Percents

• EN: Sofia buys school supplies for $24.00. She gets a 25% discount. Then she pays 10% tax on the discounted price. How much does she pay in total?
• FR: Sofia achète des fournitures scolaires pour 24,00 $. Elle obtient un rabais de 25 %. Ensuite, elle paie 10 % de taxe sur le prix réduit. Combien paie-t-elle en tout?
• Choices: A) $16.20 B) $18.00 C) $19.80 D) $21.60
• Hint: First find the discount, subtract it, then find the tax on the new price and add it (e.g., $40 with 50% off = $20, then 10% tax = $2, total = $22).
• Steps:
  • 25% of $24.00 = $24 ÷ 4 = $6.00 discount.
  • Discounted price: $24.00 − $6.00 = $18.00.
  • 10% of $18.00 = $1.80 tax.
  • Total: $18.00 + $1.80 = $19.80.
• Answer: $19.80

[Hard] Multi-Digit Multiplication and Division

• EN: A gym teacher orders 16 packs of basketballs. Each pack has 12 balls. She wants to divide all the balls equally among 8 teams. How many balls does each team get?
• FR: Un enseignant d'éducation physique commande 16 paquets de ballons de basket. Chaque paquet contient 12 ballons. Il veut répartir tous les ballons également entre 8 équipes. Combien de ballons chaque équipe reçoit-elle?
• Choices: A) 20 balls B) 22 balls C) 24 balls D) 28 balls
• Hint: First multiply to find the total, then divide equally (e.g., 3 packs × 10 balls = 30 balls, ÷ 5 teams = 6 balls each).
• Steps:
  • Total balls: 16 × 12 = 192.
  • 192 ÷ 8 = 24.
  • Each team gets 24 balls.
• Answer: 24 balls

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien représente 30 % de 200?
• Choices: A) 30 B) 60 C) 90 D) 120
• Hint: Find 10% first by dividing by 10, then multiply (e.g., 30% of 50: 10% = 5, so 30% = 5 × 3 = 15).
• Steps:
  • 10% of 200 = 200 ÷ 10 = 20.
  • 30% = 3 × 20 = 60.
  • 30% of 200 is 60.
• Answer: 60

[Easy] Order of Operations — BEDMAS

• EN: Evaluate: 3 + 4 × 2
• FR: Évalue : 3 + 4 × 2
• Choices: A) 11 B) 14 C) 16 D) 24
• Hint: In BEDMAS, multiplication comes before addition (e.g., 5 + 2 × 3 = 5 + 6 = 11, not 7 × 3).
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Ratios

• EN: In a bag, there are 4 red marbles and 6 blue marbles. What is the ratio of red marbles to blue marbles?
• FR: Dans un sac, il y a 4 billes rouges et 6 billes bleues. Quel est le rapport entre les billes rouges et les billes bleues?
• Choices: A) 2:3 B) 3:2 C) 4:10 D) 6:4
• Hint: Write the ratio in simplest form by dividing both numbers by their common factor (e.g., 6:9 → divide both by 3 → 2:3).
• Steps:
  • Red to blue: 4:6.
  • Both 4 and 6 are divisible by 2: 4 ÷ 2 = 2, 6 ÷ 2 = 3.
  • Simplified ratio is 2:3.
• Answer: 2:3

[Easy] Integers — Introduction

• EN: The temperature in Winnipeg is −8°C. It drops by 5 more degrees overnight. What is the new temperature?
• FR: La température à Winnipeg est de −8 °C. Elle baisse encore de 5 degrés pendant la nuit. Quelle est la nouvelle température?
• Choices: A) −3°C B) −13°C C) 3°C D) 13°C
• Hint: On a number line, dropping means moving further left into negative numbers (e.g., −4 − 3 = −7, not −1).
• Steps:
  • Start at −8°C.
  • Drop 5 more degrees: −8 − 5 = −13.
  • The new temperature is −13°C.
• Answer: −13°C

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 5/7 C) 6/7 D) 1/2
• Hint: Multiply numerators together and denominators together (e.g., 2/5 × 3/4 = 6/20 = 3/10).
• Steps:
  • Numerators: 2 × 3 = 6.
  • Denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en kilomètres par heure?
• Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: Speed = distance ÷ time (e.g., 180 km in 3 hours: 180 ÷ 3 = 60 km/h).
• Steps:
  • Speed = 240 ÷ 3.
  • 240 ÷ 3 = 80.
  • The car travels at 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: How many pieces of 1/4 metre can you cut from a ribbon that is 3 metres long?
• FR: Combien de morceaux de 1/4 de mètre peut-on couper dans un ruban de 3 mètres de long?
• Choices: A) 8 pieces B) 10 pieces C) 12 pieces D) 16 pieces
• Hint: Dividing by a fraction means multiplying by its reciprocal (e.g., 2 ÷ 1/3 = 2 × 3 = 6).
• Steps:
  • 3 ÷ 1/4 = 3 × 4.
  • 3 × 4 = 12.
  • You can cut 12 pieces.
• Answer: 12 pieces

[Medium] Algebraic Expressions

• EN: What is the value of 3x + 5 when x = 4?
• FR: Quelle est la valeur de 3x + 5 quand x = 4?
• Choices: A) 12 B) 14 C) 17 D) 32
• Hint: Substitute the value and then follow the order of operations (e.g., 2x + 3 when x = 5: 2 × 5 + 3 = 10 + 3 = 13).
• Steps:
  • Replace x with 4: 3(4) + 5.
  • 3 × 4 = 12.
  • 12 + 5 = 17.
• Answer: 17

[Hard] BEDMAS with Multiple Operations

• EN: Evaluate: (18 − 6) ÷ 3 + 2 × 5
• FR: Évalue : (18 − 6) ÷ 3 + 2 × 5
• Choices: A) 10 B) 14 C) 20 D) 34
• Hint: Use BEDMAS order — Brackets first, then Division and Multiplication left to right, then Addition (e.g., (10 − 4) ÷ 2 + 3 × 2: bracket = 6, 6 ÷ 2 = 3, 3 × 2 = 6, 3 + 6 = 9).
• Steps:
  • Brackets first: 18 − 6 = 12.
  • Division: 12 ÷ 3 = 4.
  • Multiplication: 2 × 5 = 10.
  • Addition: 4 + 10 = 14.
• Answer: 14

[Hard] Multi-Step Percent and Ratio Problem

• EN: In a class of 30 students, the ratio of boys to girls is 2:3. What percent of the class are girls?
• FR: Dans une classe de 30 élèves, le rapport garçons:filles est de 2:3. Quel pourcentage de la classe sont des filles?
• Choices: A) 40% B) 50% C) 60% D) 67%
• Hint: Use the ratio to find the number of girls, then divide by the total and multiply by 100 (e.g., ratio 1:4 in a class of 20: girls = 16, 16/20 × 100 = 80%).
• Steps:
  • Total ratio parts: 2 + 3 = 5.
  • Girls' share: 3/5 of 30 = 18 girls.
  • Percent: 18 ÷ 30 × 100 = 60%.
• Answer: 60%

[Easy] Integer Addition

• EN: What is −9 + 15?
• FR: Combien font −9 + 15?
• Choices: A) −6 B) 6 C) 24 D) −24
• Hint: On a number line, adding a positive moves right (e.g., −5 + 8: start at −5, move 8 right → +3).
• Steps:
  • Start at −9 and move 15 steps right.
  • 15 − 9 = 6.
  • −9 + 15 = 6.
• Answer: 6

[Easy] Percent — Discount

• EN: A jacket costs $120. It is on sale at 20% off. How much do you save?
• FR: Un manteau coûte 120 $. Il est en solde à 20 % de rabais. Combien économises-tu?
• Choices: A) $20 B) $24 C) $30 D) $96
• Hint: Find 10% first, then double it for 20% (e.g., 20% of $80: 10% = $8, 20% = $16).
• Steps:
  • 10% of $120 = $12.
  • 20% = 2 × $12 = $24.
  • You save $24.
• Answer: $24

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 14 = 23
• FR: Résous pour x : x + 14 = 23
• Choices: A) x = 7 B) x = 8 C) x = 9 D) x = 37
• Hint: Subtract the same number from both sides to isolate x (e.g., x + 7 = 15 → x = 15 − 7 = 8).
• Steps:
  • x + 14 = 23.
  • Subtract 14 from both sides: x = 23 − 14.
  • x = 9.
• Answer: x = 9

[Easy] Integer Subtraction

• EN: What is 5 − (−3)?
• FR: Combien font 5 − (−3)?
• Choices: A) 2 B) −2 C) 8 D) −8
• Hint: Subtracting a negative is the same as adding a positive (e.g., 4 − (−2) = 4 + 2 = 6).
• Steps:
  • 5 − (−3) = 5 + 3.
  • 5 + 3 = 8.
  • The answer is 8.
• Answer: 8

[Medium] Percent — Tax

• EN: A video game costs $65. HST is 13%. What is the total price including tax?
• FR: Un jeu vidéo coûte 65 $. La TVH est de 13 %. Quel est le prix total incluant la taxe?
• Choices: A) $70.45 B) $73.45 C) $74.45 D) $78.00
• Hint: Find the tax by multiplying the cost by the tax rate, then add to the original price (e.g., $50 at 10% tax: $50 × 0.10 = $5, total = $55).
• Steps:
  • Tax = $65 × 0.13 = $8.45.
  • Total = $65.00 + $8.45 = $73.45.
  • The total price is $73.45.
• Answer: $73.45

[Medium] Surface Area

• EN: What is the surface area of a rectangular box that is 5 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire totale d'une boîte rectangulaire de 5 cm de long, 3 cm de large et 2 cm de haut?
• Choices: A) 30 cm² B) 47 cm² C) 62 cm² D) 71 cm²
• Hint: A box has 6 faces in 3 pairs; find the area of each pair and add them (e.g., a box 4×3×2: 2(4×3) + 2(4×2) + 2(3×2) = 24 + 16 + 12 = 52 cm²).
• Steps:
  • Top and bottom: 2 × (5 × 3) = 2 × 15 = 30 cm².
  • Front and back: 2 × (5 × 2) = 2 × 10 = 20 cm².
  • Left and right: 2 × (3 × 2) = 2 × 6 = 12 cm².
  • Total: 30 + 20 + 12 = 62 cm².
• Answer: 62 cm²

[Medium] Probability

• EN: A bag has 3 yellow balls, 4 green balls, and 5 red balls. If you pick one without looking, what is the probability of picking a red ball?
• FR: Un sac contient 3 balles jaunes, 4 balles vertes et 5 balles rouges. Si tu en piges une sans regarder, quelle est la probabilité de piger une balle rouge?
• Choices: A) 1/4 B) 5/7 C) 5/12 D) 7/12
• Hint: Probability = (number of favourable outcomes) ÷ (total outcomes) (e.g., 2 red out of 8 total = 2/8 = 1/4).
• Steps:
  • Total balls: 3 + 4 + 5 = 12.
  • Red balls: 5.
  • P(red) = 5/12.
• Answer: 5/12

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Combien font (−6) × (−4)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: Negative × negative = positive (e.g., (−3) × (−5) = +15).
• Steps:
  • Two negatives multiplied give a positive.
  • 6 × 4 = 24.
  • (−6) × (−4) = 24.
• Answer: 24

[Hard] Two-Step Equation and Percent

• EN: A store marks up a price by 40%, making the new price $98. What was the original price?
• FR: Un magasin augmente un prix de 40 %, ce qui donne un nouveau prix de 98 $. Quel était le prix original?
• Choices: A) $58.80 B) $65.00 C) $70.00 D) $78.00
• Hint: If the new price is 140% of the original, divide the new price by 1.40 to find the original (e.g., new price $66 = 110%: original = 66 ÷ 1.10 = $60).
• Steps:
  • New price = original × 1.40 = $98.
  • Original = $98 ÷ 1.40.
  • $98 ÷ 1.40 = $70.00.
• Answer: $70.00

[Hard] Data — Mean and Range

• EN: The number of goals scored by a hockey player in 5 games were: 2, 4, 1, 3, and 5. What is the mean number of goals per game?
• FR: Le nombre de buts marqués par un joueur de hockey dans 5 matchs était : 2, 4, 1, 3 et 5. Quel est le nombre moyen de buts par match?
• Choices: A) 2 goals B) 3 goals C) 4 goals D) 5 goals
• Hint: Mean = sum of all values ÷ number of values (e.g., data: 6, 2, 4 → sum = 12, mean = 12 ÷ 3 = 4).
• Steps:
  • Sum: 2 + 4 + 1 + 3 + 5 = 15.
  • Number of games: 5.
  • Mean: 15 ÷ 5 = 3 goals per game.
• Answer: 3 goals

[Easy] Perfect Squares

• EN: What is √144?
• FR: Quelle est la valeur de √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of which number times itself gives the value under the root sign (e.g., √81: 9 × 9 = 81, so √81 = 9).
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Percent Increase

• EN: A sweater was $50. Its price increased by 20%. What is the new price?
• FR: Un chandail coûtait 50 $. Son prix a augmenté de 20 %. Quel est le nouveau prix?
• Choices: A) $55 B) $58 C) $60 D) $70
• Hint: Find the increase and add it to the original (e.g., 10% increase on $80: increase = $8, new price = $88).
• Steps:
  • 20% of $50 = $10.
  • New price: $50 + $10 = $60.
  • The new price is $60.
• Answer: $60

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 17
• FR: Résous pour x : 2x + 5 = 17
• Choices: A) x = 4 B) x = 6 C) x = 7 D) x = 11
• Hint: First subtract the constant from both sides, then divide by the coefficient (e.g., 3x + 2 = 11 → 3x = 9 → x = 3).
• Steps:
  • 2x + 5 = 17 → subtract 5: 2x = 12.
  • Divide by 2: x = 6.
  • x = 6.
• Answer: x = 6

[Easy] Mean

• EN: Find the mean of: 8, 12, 5, 15, and 10.
• FR: Trouve la moyenne de : 8, 12, 5, 15 et 10.
• Choices: A) 8 B) 10 C) 12 D) 15
• Hint: Add all the numbers and divide by how many there are (e.g., mean of 4, 6, 8: sum = 18, count = 3, mean = 6).
• Steps:
  • Sum: 8 + 12 + 5 + 15 + 10 = 50.
  • Count: 5 numbers.
  • Mean = 50 ÷ 5 = 10.
• Answer: 10

[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) 7 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Use a² + b² = c² where c is the hypotenuse (e.g., legs 3 and 4: 9 + 16 = 25, c = √25 = 5).
• Steps:
  • a² + b² = c²: 6² + 8² = c².
  • 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Percent Decrease

• EN: A store reduces the price of a hockey stick from $80 to $64. What is the percent decrease?
• FR: Un magasin réduit le prix d'un bâton de hockey de 80 $ à 64 $. Quel est le pourcentage de réduction?
• Choices: A) 16% B) 20% C) 25% D) 80%
• Hint: Percent decrease = (decrease ÷ original price) × 100 (e.g., from $50 to $40: decrease = $10, 10 ÷ 50 × 100 = 20%).
• Steps:
  • Decrease: $80 − $64 = $16.
  • Percent decrease: (16 ÷ 80) × 100 = 20%.
  • The price decreased by 20%.
• Answer: 20%

[Medium] Slope Introduction

• EN: A ramp rises 4 m for every 8 m it runs horizontally. What is the slope of the ramp?
• FR: Une rampe monte de 4 m pour chaque 8 m de course horizontale. Quelle est la pente de la rampe?
• Choices: A) 1/4 B) 1/2 C) 2 D) 4
• Hint: Slope = rise ÷ run (e.g., rise of 3, run of 6: slope = 3/6 = 1/2).
• Steps:
  • Slope = rise ÷ run.
  • Slope = 4 ÷ 8 = 1/2.
  • The slope is 1/2.
• Answer: 1/2

[Medium] Two-Step Equation with Negatives

• EN: Solve for x: 3x − 7 = 14
• FR: Résous pour x : 3x − 7 = 14
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: Add the constant to both sides first, then divide (e.g., 4x − 3 = 17 → 4x = 20 → x = 5).
• Steps:
  • 3x − 7 = 14 → add 7: 3x = 21.
  • Divide by 3: x = 7.
  • x = 7.
• Answer: x = 7

[Hard] Pythagorean Theorem — Applied

• EN: A 15 m ladder leans against a wall. The base of the ladder is 9 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 15 m est appuyée contre un mur. La base de l'échelle est à 9 m du mur. À quelle hauteur du mur l'échelle atteint-elle?
• Choices: A) 10 m B) 12 m C) 13 m D) 24 m
• Hint: The ladder is the hypotenuse; rearrange a² + b² = c² to find the missing leg: a² = c² − b² (e.g., hypotenuse 13, base 5: leg = √(169 − 25) = √144 = 12).
• Steps:
  • c = 15, b = 9. Find a: a² = 15² − 9².
  • 225 − 81 = 144.
  • a = √144 = 12 m.
• Answer: 12 m

[Hard] Median and Mode

• EN: The ages of players on a hockey team are: 14, 16, 15, 14, 17, 16, 14, 15. What is the mode of the ages?
• FR: Les âges des joueurs d'une équipe de hockey sont : 14, 16, 15, 14, 17, 16, 14, 15. Quel est le mode des âges?
• Choices: A) 15 B) 16 C) 14 D) 17
• Hint: The mode is the value that appears most often in the data set (e.g., in 3, 5, 5, 7, 9, the mode is 5).
• Steps:
  • Count each age: 14 appears 3 times, 15 appears 2 times, 16 appears 2 times, 17 appears 1 time.
  • 14 appears most often.
  • The mode is 14.
• Answer: 14

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 3 = 22
• FR: Résous pour x : 5x − 3 = 22
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add the constant first, then divide by the coefficient (e.g., 4x − 6 = 18 → 4x = 24 → x = 6).
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 5.
  • x = 5.
• Answer: x = 5

[Easy] Graphing Lines — Slope-Intercept

• EN: What is the slope of the line y = 3x − 7?
• FR: Quelle est la pente de la droite y = 3x − 7?
• Choices: A) −7 B) 3 C) 7 D) −3
• Hint: In y = mx + b, the slope is m (the coefficient of x) (e.g., y = 4x + 2 has slope 4).
• Steps:
  • The equation is y = 3x − 7.
  • Written as y = mx + b, the slope m = 3.
  • The slope is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x + 4)
• FR: Simplifie : (3x + 5) + (2x + 4)
• Choices: A) 5x + 8 B) 5x + 9 C) 6x + 9 D) 6x + 8
• Hint: Combine like terms — add the x terms together and add the constants together (e.g., (4x + 2) + (x + 5) = 5x + 7).
• Steps:
  • x terms: 3x + 2x = 5x.
  • Constants: 5 + 4 = 9.
  • Result: 5x + 9.
• Answer: 5x + 9

[Easy] Linear Inequality

• EN: Solve the inequality: x + 6 > 10
• FR: Résous l'inégalité : x + 6 > 10
• Choices: A) x > 3 B) x > 4 C) x < 4 D) x > 16
• Hint: Solve like an equation but keep the inequality sign (e.g., x + 3 > 9 → x > 9 − 3 → x > 6).
• Steps:
  • x + 6 > 10.
  • Subtract 6 from both sides: x > 10 − 6.
  • x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

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

[Medium] Similar Triangles

• EN: Two triangles are similar. The sides of the smaller triangle are 4 cm, 6 cm, and 8 cm. If the longest side of the larger triangle is 20 cm, what is the shortest side of the larger triangle?
• FR: Deux triangles sont semblables. Les côtés du petit triangle sont 4 cm, 6 cm et 8 cm. Si le plus grand côté du grand triangle est 20 cm, quel est son côté le plus court?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 15 cm
• Hint: Find the scale factor by dividing matching sides, then multiply (e.g., small side 3, large matching side 9: scale = 3, so small side 5 becomes 15).
• Steps:
  • Scale factor: 20 ÷ 8 = 2.5.
  • Shortest side: 4 × 2.5 = 10 cm.
  • The shortest side of the larger triangle is 10 cm.
• Answer: 10 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the angle θ = 30°. The hypotenuse is 20 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, l'angle θ = 30°. L'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé?
• Choices: A) 8 cm B) 10 cm C) 14 cm D) 17 cm
• Hint: sin(θ) = opposite ÷ hypotenuse, so opposite = hypotenuse × sin(θ). sin(30°) = 0.5 (e.g., hypotenuse 14, sin(30°) = 0.5: opposite = 14 × 0.5 = 7).
• Steps:
  • sin(30°) = 0.5.
  • Opposite = hypotenuse × sin(30°) = 20 × 0.5.
  • Opposite = 10 cm.
• Answer: 10 cm

[Medium] Statistics — Interpreting Data

• EN: The test scores of 5 students are: 72, 85, 90, 68, and 75. What is the median score?
• FR: Les notes de 5 élèves à un test sont : 72, 85, 90, 68 et 75. Quelle est la médiane?
• Choices: A) 72 B) 75 C) 85 D) 90
• Hint: Arrange numbers in order from least to greatest, then find the middle value (e.g., 4, 7, 9, 11, 13 — the median is 9).
• Steps:
  • Order: 68, 72, 75, 85, 90.
  • The middle value (3rd of 5) is 75.
  • The median is 75.
• Answer: 75

[Hard] Solving a Linear Inequality with Negative Coefficient

• EN: Solve: −3x + 9 ≥ 0
• FR: Résous : −3x + 9 ≥ 0
• Choices: A) x ≤ 3 B) x ≥ 3 C) x ≤ −3 D) x ≥ −3
• Hint: When you divide or multiply both sides by a negative number, flip the inequality sign (e.g., −2x > 8 → x < −4).
• Steps:
  • −3x + 9 ≥ 0 → subtract 9: −3x ≥ −9.
  • Divide by −3 and flip the sign: x ≤ 3.
  • x ≤ 3.
• Answer: x ≤ 3

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 10 cm. What is the angle θ using CAH?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 10 cm. Quel est l'angle θ en utilisant CAH?
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: cos(θ) = adjacent ÷ hypotenuse; find the angle whose cosine matches (e.g., cos(θ) = 1 → θ = 0°).
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 5 ÷ 10 = 0.5.
  • cos⁻¹(0.5) = 60°.
  • θ = 60°.
• Answer: 60°

[Easy] Factoring a Quadratic

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

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, angle θ = 45°, and the adjacent side is 7 cm. What is the hypotenuse? (cos 45° ≈ 0.707)
• FR: Dans un triangle rectangle, l'angle θ = 45° et le côté adjacent mesure 7 cm. Quelle est l'hypoténuse? (cos 45° ≈ 0,707)
• Choices: A) 4.9 cm B) 7.0 cm C) 9.9 cm D) 14.0 cm
• Hint: cos(θ) = adjacent ÷ hypotenuse, so hypotenuse = adjacent ÷ cos(θ) (e.g., adjacent 6, cos(60°) = 0.5: hypotenuse = 6 ÷ 0.5 = 12).
• Steps:
  • cos(45°) = adjacent ÷ hypotenuse.
  • Hypotenuse = 7 ÷ 0.707 ≈ 9.9 cm.
  • The hypotenuse is approximately 9.9 cm.
• Answer: 9.9 cm

[Easy] System of Equations

• EN: Solve the system: y = 2x + 1 and y = x + 4. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = x + 4. Quelle est la valeur de x?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 5
• Hint: Set the two expressions equal to each other and solve for x (e.g., y = 3x and y = x + 6 → 3x = x + 6 → 2x = 6 → x = 3).
• Steps:
  • Set equal: 2x + 1 = x + 4.
  • 2x − x = 4 − 1 → x = 3.
  • x = 3.
• Answer: x = 3

[Easy] Volume of a Cylinder

• EN: What is the volume of a cylinder with radius 5 cm and height 10 cm? (Use π ≈ 3.14)
• FR: Quel est le volume d'un cylindre ayant un rayon de 5 cm et une hauteur de 10 cm? (Utilisez π ≈ 3,14)
• Choices: A) 157 cm³ B) 314 cm³ C) 785 cm³ D) 1570 cm³
• Hint: Volume of a cylinder = π × r² × h (e.g., r = 3, h = 7: V = 3.14 × 9 × 7 = 197.82 cm³).
• Steps:
  • V = π × r² × h = 3.14 × 5² × 10.
  • 5² = 25; 3.14 × 25 = 78.5.
  • 78.5 × 10 = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x = 7
• FR: Résous en complétant le carré : x² + 6x = 7
• Choices: A) x = 1 or x = −7 B) x = 2 or x = −5 C) x = 3 or x = −7 D) x = −1 or x = 7
• Hint: Add (b/2)² to both sides (e.g., x² + 4x = 5: add 4, get (x+2)² = 9, x+2 = ±3, x = 1 or −5).
• Steps:
  • x² + 6x = 7; add (6/2)² = 9 to both sides.
  • (x + 3)² = 16.
  • x + 3 = ±4 → x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry — Arc Length

• EN: A circle has a radius of 6 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 6 cm. Quelle est sa circonférence? (Utilisez π ≈ 3,14)
• Choices: A) 18.84 cm B) 37.68 cm C) 56.52 cm D) 113.04 cm
• Hint: Circumference = 2 × π × r (e.g., r = 4: C = 2 × 3.14 × 4 = 25.12 cm).
• Steps:
  • C = 2 × π × r = 2 × 3.14 × 6.
  • 2 × 6 = 12; 12 × 3.14 = 37.68.
  • Circumference = 37.68 cm.
• Answer: 37.68 cm

[Medium] System of Equations — Substitution

• EN: Solve the system: x + y = 10 and x − y = 4. What is the value of y?
• FR: Résous le système : x + y = 10 et x − y = 4. Quelle est la valeur de y?
• Choices: A) y = 2 B) y = 3 C) y = 5 D) y = 7
• Hint: Add the two equations to eliminate y (or subtract to eliminate x), then solve (e.g., x + y = 8 and x − y = 2: add → 2x = 10 → x = 5, then y = 3).
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 4 → 2x = 14 → x = 7.
  • Substitute: 7 + y = 10 → y = 3.
  • y = 3.
• Answer: y = 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 9 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 9 cm. Quelle est son aire totale? (Utilisez π ≈ 3,14)
• Choices: A) 113.04 cm² B) 163.28 cm² C) 188.40 cm² D) 226.08 cm²
• Hint: Total surface area = πrl + πr² where l is slant height (e.g., r = 3, l = 5: 3.14 × 3 × 5 + 3.14 × 9 = 47.1 + 28.26 = 75.36 cm²).
• Steps:
  • Lateral area: π × r × l = 3.14 × 4 × 9 = 113.04 cm².
  • Base area: π × r² = 3.14 × 16 = 50.24 cm².
  • Total: 113.04 + 50.24 = 163.28 cm².
• Answer: 163.28 cm²

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve: x² − 5x + 4 = 0
• FR: Utilise la formule quadratique pour résoudre : x² − 5x + 4 = 0
• Choices: A) x = 1 or x = 4 B) x = 2 or x = 3 C) x = −1 or x = −4 D) x = 4 or x = 5
• Hint: Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a (e.g., x² − 7x + 12 = 0: discriminant = 49 − 48 = 1, x = (7 ± 1)/2 → x = 4 or 3).
• Steps:
  • a = 1, b = −5, c = 4.
  • Discriminant: (−5)² − 4(1)(4) = 25 − 16 = 9.
  • x = (5 ± 3) / 2 → x = 4 or x = 1.
• Answer: x = 1 or x = 4

[Hard] Circle Geometry — Chord and Radius

• EN: A chord is 16 cm long in a circle with radius 10 cm. What is the perpendicular distance from the centre to the chord?
• FR: Une corde mesure 16 cm de long dans un cercle de rayon 10 cm. Quelle est la distance perpendiculaire du centre à la corde?
• Choices: A) 4 cm B) 6 cm C) 8 cm D) 12 cm
• Hint: The perpendicular from the centre bisects the chord; use the Pythagorean theorem with the radius, half the chord, and the distance (e.g., radius 13, half-chord 5: distance = √(169 − 25) = 12).
• Steps:
  • Half chord = 16 ÷ 2 = 8 cm.
  • Use Pythagorean theorem: d² + 8² = 10².
  • d² = 100 − 64 = 36 → d = 6 cm.
• Answer: 6 cm

[Easy] Exponential Functions

• EN: Evaluate f(x) = 2^x when x = 5.
• FR: Évalue f(x) = 2^x quand x = 5.
• Choices: A) 10 B) 16 C) 25 D) 32
• Hint: Raise the base to the given power (e.g., 2^4 = 2 × 2 × 2 × 2 = 16).
• Steps:
  • 2^5 = 2 × 2 × 2 × 2 × 2.
  • 2 × 2 = 4, × 2 = 8, × 2 = 16, × 2 = 32.
  • f(5) = 32.
• Answer: 32

[Easy] Logarithms — Introduction

• EN: What is log₂(32)?
• FR: Quelle est la valeur de log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log_b(x) = n means b^n = x (e.g., log₃(27): 3^? = 27, 3^3 = 27, so log₃(27) = 3).
• Steps:
  • log₂(32) = n means 2^n = 32.
  • 2^5 = 32.
  • log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequences

• EN: The first term of an arithmetic sequence is 7 and the common difference is 4. What is the 6th term?
• FR: Le premier terme d'une suite arithmétique est 7 et la raison est 4. Quel est le 6e terme?
• Choices: A) 24 B) 27 C) 28 D) 31
• Hint: Use the formula: aₙ = a₁ + (n − 1)d (e.g., a₁ = 3, d = 5, find a₄: 3 + (4−1) × 5 = 3 + 15 = 18).
• Steps:
  • a₆ = 7 + (6 − 1) × 4.
  • (6 − 1) × 4 = 5 × 4 = 20.
  • a₆ = 7 + 20 = 27.
• Answer: 27

[Easy] Compound Interest

• EN: You invest $500 at 4% annual interest, compounded annually for 2 years. How much interest do you earn in total?
• FR: Tu investis 500 $ à un taux d'intérêt annuel de 4 %, composé annuellement pendant 2 ans. Combien d'intérêts gagnes-tu en tout?
• Choices: A) $40.00 B) $40.80 C) $41.60 D) $80.00
• Hint: Use A = P(1 + r)^t and subtract P (e.g., $200 at 5% for 2 years: A = 200 × 1.05² = $220.50, interest = $20.50).
• Steps:
  • A = 500 × (1.04)² = 500 × 1.0816 = $540.80.
  • Interest = $540.80 − $500.00 = $40.80.
  • Total interest earned is $40.80.
• Answer: $40.80

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = x² − 4x + 7?
• FR: Quel est le sommet de la parabole y = x² − 4x + 7?
• Choices: A) (2, 3) B) (−2, 3) C) (2, 7) D) (4, 7)
• Hint: The x-coordinate of the vertex is x = −b/(2a); substitute back to find y (e.g., y = x² − 6x + 5: x = 3, y = 9 − 18 + 5 = −4, vertex (3, −4)).
• Steps:
  • x = −(−4) / (2 × 1) = 4/2 = 2.
  • y = (2)² − 4(2) + 7 = 4 − 8 + 7 = 3.
  • Vertex is (2, 3).
• Answer: (2, 3)

[Medium] Geometric Sequences

• EN: A geometric sequence has first term 3 and common ratio 2. What is the sum of the first 5 terms?
• FR: Une suite géométrique a pour premier terme 3 et pour raison 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 45 B) 63 C) 93 D) 96
• Hint: Sum = a(rⁿ − 1)/(r − 1) (e.g., a = 2, r = 3, n = 4: S = 2(3⁴ − 1)/(3 − 1) = 2(80)/2 = 80).
• Steps:
  • S = 3 × (2⁵ − 1) / (2 − 1).
  • 2⁵ = 32; 32 − 1 = 31.
  • S = 3 × 31 / 1 = 93.
• Answer: 93

[Medium] Trigonometric Identity

• EN: Verify which expression equals sin²(θ) + cos²(θ).
• FR: Vérifie quelle expression est égale à sin²(θ) + cos²(θ).
• Choices: A) 0 B) 2 C) sin(2θ) D) 1
• Hint: This is the Pythagorean identity — it is always true for any angle θ (e.g., try θ = 0°: sin²(0) + cos²(0) = 0 + 1 = 1).
• Steps:
  • The Pythagorean identity states sin²(θ) + cos²(θ) = 1.
  • This is true for all values of θ.
  • The answer is 1.
• Answer: 1

[Medium] Financial Math — Annuity

• EN: You deposit $200 at the end of each year for 3 years at 5% annual interest compounded annually. What is the total future value? (Use FV = PMT × [((1+r)^n − 1)/r])
• FR: Tu déposes 200 $ à la fin de chaque année pendant 3 ans à un taux d'intérêt annuel de 5 %. Quelle est la valeur future totale?
• Choices: A) $600.00 B) $630.50 C) $662.05 D) $700.00
• Hint: Apply the annuity formula step by step (e.g., $100/year, 10%, 3 years: FV = 100 × [(1.10³ − 1)/0.10] = 100 × 3.31 = $331).
• Steps:
  • FV = 200 × [(1.05³ − 1) / 0.05].
  • 1.05³ = 1.157625; 1.157625 − 1 = 0.157625.
  • 0.157625 / 0.05 = 3.1525; FV = 200 × 3.1525 = $630.50.
• Answer: $630.50

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(x − 2) = log₃(8)
• FR: Résous pour x : log₃(x) + log₃(x − 2) = log₃(8)
• Choices: A) x = 2 B) x = 4 C) x = 6 D) x = 8
• Hint: Use the product rule of logarithms: logₐ(m) + logₐ(n) = logₐ(mn), then set arguments equal (e.g., log₂(x) + log₂(x + 2) = log₂(8) → x(x+2) = 8 → x = 2).
• Steps:
  • log₃(x(x − 2)) = log₃(8).
  • x(x − 2) = 8 → x² − 2x − 8 = 0.
  • Factor: (x − 4)(x + 2) = 0 → x = 4 (x must be positive).
• Answer: x = 4

[Hard] Exponential Growth and Decay

• EN: A population of bacteria doubles every 3 hours. Starting with 200 bacteria, how many are there after 9 hours?
• FR: Une population de bactéries double toutes les 3 heures. En partant de 200 bactéries, combien y en a-t-il après 9 heures?
• Choices: A) 800 B) 1200 C) 1600 D) 2000
• Hint: Find how many doubling periods fit in the total time, then multiply by 2 that many times (e.g., start 100, doubles every 2 hours, after 6 hours: 3 periods → 100 × 2³ = 800).
• Steps:
  • Number of doubling periods: 9 ÷ 3 = 3.
  • Population = 200 × 2³ = 200 × 8.
  • 200 × 8 = 1600 bacteria.
• Answer: 1600

[Easy] Permutations

• EN: How many ways can 5 students line up in a row?
• FR: De combien de façons 5 élèves peuvent-ils se mettre en file?
• Choices: A) 25 B) 60 C) 100 D) 120
• Hint: Multiply the number of choices for each position (e.g., 4 students: 4 × 3 × 2 × 1 = 24 ways).
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • 5 × 4 = 20, × 3 = 60, × 2 = 120, × 1 = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = 4x³.
• FR: Trouve la dérivée de f(x) = 4x³.
• Choices: A) 4x² B) 12x C) 12x² D) 16x²
• Hint: Power rule: d/dx(axⁿ) = n·axⁿ⁻¹ (e.g., f(x) = 3x⁴ → f'(x) = 12x³).
• Steps:
  • Bring the exponent down and multiply: 3 × 4 = 12.
  • Reduce the exponent by 1: x³⁻¹ = x².
  • f'(x) = 12x².
• Answer: 12x²

[Easy] Combinations

• EN: A pizza shop offers 8 toppings. How many ways can you choose 2 toppings?
• FR: Une pizzeria offre 8 garnitures. De combien de façons peut-on choisir 2 garnitures?
• Choices: A) 16 B) 28 C) 56 D) 64
• Hint: Use C(n,r) = n! / (r! × (n−r)!) (e.g., C(5,2) = 5! / (2! × 3!) = 120/12 = 10).
• Steps:
  • C(8,2) = 8! / (2! × 6!) = (8 × 7) / (2 × 1).
  • 8 × 7 = 56; 56 / 2 = 28.
  • There are 28 ways.
• Answer: 28

[Easy] Polynomial Function — End Behaviour

• EN: For the function f(x) = −2x⁴ + 3x − 1, what happens to f(x) as x → +∞?
• FR: Pour la fonction f(x) = −2x⁴ + 3x − 1, que se passe-t-il pour f(x) quand x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: The leading term determines end behaviour; negative leading coefficient with even degree → both ends go down (e.g., −3x² → goes to −∞ on both sides).
• Steps:
  • Leading term is −2x⁴ (negative, even degree).
  • As x → +∞, x⁴ → +∞ and −2x⁴ → −∞.
  • f(x) → −∞.
• Answer: f(x) → −∞

[Medium] Derivative — Rate of Change

• EN: A ball's position is given by s(t) = 3t² + 2t. What is the instantaneous velocity at t = 4 seconds?
• FR: La position d'une balle est donnée par s(t) = 3t² + 2t. Quelle est la vitesse instantanée à t = 4 secondes?
• Choices: A) 14 m/s B) 26 m/s C) 48 m/s D) 56 m/s
• Hint: Find the derivative (velocity function), then substitute t (e.g., s(t) = 2t² + t → v(t) = 4t + 1; at t = 3: v = 13).
• Steps:
  • v(t) = s'(t) = 6t + 2 (using power rule).
  • v(4) = 6(4) + 2 = 24 + 2 = 26.
  • Instantaneous velocity is 26 m/s.
• Answer: 26 m/s

[Medium] Probability Distribution — Expected Value

• EN: A spinner has outcomes 1, 2, 3, and 4, each equally likely. What is the expected value?
• FR: Une roulette a les résultats 1, 2, 3 et 4, tous également probables. Quelle est la valeur espérée?
• Choices: A) 1.5 B) 2.0 C) 2.5 D) 3.0
• Hint: Expected value = sum of (each value × its probability) (e.g., outcomes 1 and 3 each with prob. 1/2: E = 1×0.5 + 3×0.5 = 2).
• Steps:
  • Each outcome has probability 1/4.
  • E = 1(1/4) + 2(1/4) + 3(1/4) + 4(1/4).
  • E = (1 + 2 + 3 + 4)/4 = 10/4 = 2.5.
• Answer: 2.5

[Medium] Vectors — Addition

• EN: Vector a = (3, 5) and vector b = (−1, 4). What is a + b?
• FR: Le vecteur a = (3, 5) et le vecteur b = (−1, 4). Quelle est la valeur de a + b?
• Choices: A) (2, 1) B) (4, 9) C) (2, 9) D) (4, 1)
• Hint: Add corresponding components (e.g., (2, 7) + (3, −1) = (2+3, 7+(−1)) = (5, 6)).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: 5 + 4 = 9.
  • a + b = (2, 9).
• Answer: (2, 9)

[Medium] Rational Function — Vertical Asymptote

• EN: What is the vertical asymptote of f(x) = (x + 2) / (x − 5)?
• FR: Quelle est l'asymptote verticale de f(x) = (x + 2) / (x − 5)?
• Choices: A) x = −2 B) x = 2 C) x = 5 D) x = −5
• Hint: Vertical asymptotes occur where the denominator equals zero (e.g., f(x) = 1/(x − 3) has vertical asymptote x = 3).
• Steps:
  • Set the denominator equal to zero: x − 5 = 0.
  • x = 5.
  • Vertical asymptote is at x = 5.
• Answer: x = 5

[Hard] Binomial Theorem

• EN: What is the coefficient of x² in the expansion of (x + 3)⁴?
• FR: Quel est le coefficient de x² dans le développement de (x + 3)⁴?
• Choices: A) 54 B) 81 C) 108 D) 216
• Hint: Use the binomial theorem: the term with x^k is C(n,k) × x^k × 3^(n−k); for x², k = 2 (e.g., (x + 2)³: x² term is C(3,2) × x² × 2¹ = 6x²).
• Steps:
  • The x² term: C(4,2) × x² × 3^(4−2).
  • C(4,2) = 6; 3² = 9.
  • Coefficient = 6 × 9 = 54.
• Answer: 54

[Hard] Derivative Application — Optimisation

• EN: A farmer has 60 m of fencing to enclose a rectangular garden against a barn wall (the barn forms one side, so only 3 sides need fencing). What width (in metres) maximises the area?
• FR: Un fermier a 60 m de clôture pour entourer un jardin rectangulaire contre un mur de grange (la grange forme un côté, donc seulement 3 côtés ont besoin de clôture). Quelle largeur (en mètres) maximise l'aire?
• Choices: A) 10 m B) 15 m C) 20 m D) 30 m
• Hint: Write the area as a function of one variable, take the derivative, set it to zero and solve (e.g., fencing = 40 m, one long side free: L + 2W = 40, A = W(40 − 2W), A' = 40 − 4W = 0, W = 10).
• Steps:
  • Let W = width. Then length L = 60 − 2W.
  • Area A = W(60 − 2W) = 60W − 2W².
  • A'(W) = 60 − 4W = 0 → W = 15 m.
• Answer: 15 m