Daily Math — 2026-08-14

[Easy] Counting Crayons

• EN: Mia has 7 crayons in her box. She finds 5 more on her desk. How many crayons does she have in all?
• FR: Mia a 7 crayons dans sa boîte. Elle en trouve 5 autres sur son bureau. Combien de crayons a-t-elle en tout?
• Choices: A) 10 crayons B) 11 crayons C) 12 crayons D) 13 crayons
• Hint: To add, count on from the bigger number — like 8 + 3: start at 8 and count 3 more.
• Steps:
  • Start at 7 and count on 5 more.
  • 7 → 8, 9, 10, 11, 12.
  • So the total is 12 crayons.
• Answer: 12 crayons

[Easy] Hockey Pucks

• EN: There are 9 hockey pucks on the ice. A player takes 4 away. How many pucks are left?
• FR: Il y a 9 rondelles de hockey sur la glace. Un joueur en prend 4. Combien de rondelles reste-t-il?
• Choices: A) 3 pucks B) 4 pucks C) 5 pucks D) 6 pucks
• Hint: To subtract, count back — like 8 − 3: start at 8 and count back 3.
• Steps:
  • Start at 9 and count back 4.
  • 9 → 8, 7, 6, 5.
  • So 5 pucks are left.
• Answer: 5 pucks

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes after 10, 12, 14?
• FR: Compte par bonds de 2. Quel nombre vient après 10, 12, 14?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: Skip counting by 2s means add 2 each time — like 4, 6, 8, then the next is 10.
• Steps:
  • The pattern adds 2 each time: 10, 12, 14, ...
  • 14 + 2 = 16.
  • So the next number is 16.
• Answer: 16

[Easy] Recognizing a Dime

• EN: A dime is worth how many cents?
• FR: Combien de sous vaut une pièce de dix cents?
• Choices: A) 1 cent B) 5 cents C) 10 cents D) 25 cents
• Hint: A nickel is worth 5 cents — a dime is worth double that.
• Steps:
  • A penny = 1 cent, a nickel = 5 cents.
  • A dime is the small silver coin worth double a nickel.
  • Double 5 = 10, so a dime is worth 10 cents.
• Answer: 10 cents

[Medium] Adding at Tim Hortons

• EN: Liam buys 6 Timbits and his sister buys 8 Timbits. How many Timbits do they have together?
• FR: Liam achète 6 Timbits et sa sœur en achète 8. Combien de Timbits ont-ils ensemble?
• Choices: A) 12 Timbits B) 13 Timbits C) 14 Timbits D) 15 Timbits
• Hint: Make a ten — like 7 + 5: take 3 from 5 to make 7 into 10, then add 2 more to get 12.
• Steps:
  • Take 2 from 8 to make 6 into 10.
  • 10 + 6 = 16? Let us recheck: 6 + 8, take 4 from 8 to make 6 into 10.
  • 10 + 4 = 14. So together they have 14 Timbits.
• Answer: 14 Timbits

[Medium] Comparing Numbers

• EN: Which number is greater: 15 or 12?
• FR: Quel nombre est le plus grand : 15 ou 12?
• Choices: A) 10 B) 12 C) 15 D) 20
• Hint: Think of a number line — numbers to the right are always bigger.
• Steps:
  • Place both numbers on a number line: 12 is to the left, 15 is to the right.
  • Numbers farther right are greater.
  • So 15 is greater.
• Answer: 15

[Medium] Snowflakes Count

• EN: There are 18 snowflakes. Some melt and only 9 are left. How many melted?
• FR: Il y a 18 flocons de neige. Certains fondent et il en reste 9. Combien ont fondu?
• Choices: A) 7 snowflakes B) 8 snowflakes C) 9 snowflakes D) 11 snowflakes
• Hint: Subtraction finds the missing part — like 15 − ? = 8, so 15 − 8 = 7.
• Steps:
  • We need 18 − ? = 9.
  • Count back from 18 to 9: that is 9 steps.
  • So 9 snowflakes melted.
• Answer: 9 snowflakes

[Medium] Skip Counting by 5s

• EN: Nia counts by 5s: 5, 10, 15, 20, ___. What number is next?
• FR: Nia compte par bonds de 5 : 5, 10, 15, 20, ___. Quel est le prochain nombre?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: Counting by 5s — like 30, 35, 40, the next step adds 5.
• Steps:
  • The pattern is add 5 each time: 5, 10, 15, 20.
  • 20 + 5 = 25.
  • So the next number is 25.
• Answer: 25

[Hard] Coins at the Store

• EN: Sam has 1 dime and 2 nickels. How many cents does he have in all?
• FR: Sam a 1 pièce de dix cents et 2 pièces de cinq cents. Combien de sous a-t-il en tout?
• Choices: A) 15 cents B) 17 cents C) 20 cents D) 22 cents
• Hint: Count each coin's value and add them — like 1 dime (10) + 1 nickel (5) = 15 cents.
• Steps:
  • A dime = 10 cents. Two nickels = 5 + 5 = 10 cents.
  • 10 + 10 = 20 cents.
  • So Sam has 20 cents in all.
• Answer: 20 cents

[Hard] Number Puzzle

• EN: A number is 3 more than 14. What is that number?
• FR: Un nombre est 3 de plus que 14. Quel est ce nombre?
• Choices: A) 11 B) 16 C) 17 D) 18
• Hint: "More than" means add — like "5 more than 10" is 10 + 5 = 15.
• Steps:
  • "3 more than 14" means 14 + 3.
  • 14 + 3 = 17.
  • So the number is 17.
• Answer: 17

[Easy] Adding to 100

• EN: There are 34 students at school. 25 more arrive. How many students are there now?
• FR: Il y a 34 élèves à l'école. 25 autres arrivent. Combien y a-t-il d'élèves maintenant?
• Choices: A) 57 students B) 59 students C) 61 students D) 64 students
• Hint: Add the tens first, then the ones — like 23 + 14: 20 + 10 = 30, then 3 + 4 = 7, so 37.
• Steps:
  • Add tens: 30 + 20 = 50.
  • Add ones: 4 + 5 = 9.
  • 50 + 9 = 59 students.
• Answer: 59 students

[Easy] Telling Time — Hour

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: La petite aiguille est sur le 3 et la grande aiguille est sur le 12. Quelle heure est-il?
• Choices: A) 12:00 B) 3:00 C) 3:30 D) 6:00
• Hint: When the long hand points to 12, it is exactly on the hour — like short hand on 7 means 7:00.
• Steps:
  • Long hand on 12 = exactly on the hour.
  • Short hand on 3 = 3 o'clock.
  • The time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A eraser is 4 cm long. How much longer is the pencil?
• FR: Un crayon mesure 14 cm et une gomme mesure 4 cm. De combien le crayon est-il plus long?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 18 cm
• Hint: "How much longer" means subtract — like 12 cm − 3 cm = 9 cm.
• Steps:
  • Subtract: 14 − 4.
  • 14 − 4 = 10.
  • The pencil is 10 cm longer.
• Answer: 10 cm

[Easy] Counting Coins

• EN: Maya has 3 dimes and 1 nickel. How many cents does she have?
• FR: Maya a 3 pièces de dix cents et 1 pièce de cinq cents. Combien de sous a-t-elle?
• Choices: A) 30 cents B) 35 cents C) 40 cents D) 45 cents
• Hint: Count dimes as 10 each, then add any nickels — like 2 dimes + 1 nickel = 25 cents.
• Steps:
  • 3 dimes = 10 + 10 + 10 = 30 cents.
  • 1 nickel = 5 cents.
  • 30 + 5 = 35 cents.
• Answer: 35 cents

[Medium] Subtraction within 100

• EN: A hockey team scored 82 points this season and 47 points last season. How many more points did they score this season?
• FR: Une équipe de hockey a marqué 82 points cette saison et 47 points la saison dernière. Combien de points de plus ont-ils marqués cette saison?
• Choices: A) 25 points B) 35 points C) 38 points D) 45 points
• Hint: Subtract by breaking apart — like 75 − 38: first 75 − 30 = 45, then 45 − 8 = 37.
• Steps:
  • 82 − 47: first subtract tens: 82 − 40 = 42.
  • Then subtract ones: 42 − 7 = 35.
  • They scored 35 more points this season.
• Answer: 35 points

[Medium] Telling Time — Half Hour

• EN: The long hand points to 6 and the short hand is between 7 and 8. What time is it?
• FR: La grande aiguille pointe vers le 6 et la petite aiguille est entre le 7 et le 8. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:00
• Hint: When the long hand is on 6, it is always 30 minutes past the hour the short hand passed last.
• Steps:
  • Long hand on 6 = 30 minutes past.
  • Short hand between 7 and 8 means it passed 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: Look at the pattern: 2, 4, 6, 8, ___. What is the missing number?
• FR: Regarde le motif : 2, 4, 6, 8, ___. Quel est le nombre manquant?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Find the rule by looking at the difference — like 5, 10, 15: the rule is add 5.
• Steps:
  • Each number increases by 2: 2, 4, 6, 8.
  • 8 + 2 = 10.
  • The missing number is 10.
• Answer: 10

[Medium] Measuring in Metres

• EN: A classroom is 8 m long and the hallway is 5 m long. How long are they together?
• FR: Une salle de classe mesure 8 m de long et le couloir mesure 5 m de long. Quelle est leur longueur totale?
• Choices: A) 11 m B) 12 m C) 13 m D) 14 m
• Hint: Adding lengths is just like adding numbers — like 6 m + 7 m = 13 m.
• Steps:
  • Add: 8 m + 5 m.
  • 8 + 5 = 13.
  • Together they are 13 m long.
• Answer: 13 m

[Hard] Making a Dollar

• EN: Emile has 3 quarters. How many cents does he still need to make exactly $1.00?
• FR: Émile a 3 pièces de 25 cents. Combien de sous lui manque-t-il pour avoir exactement 1,00 $?
• Choices: A) 20 cents B) 25 cents C) 30 cents D) 75 cents
• Hint: One dollar equals 100 cents — find what is missing by subtracting.
• Steps:
  • 3 quarters = 25 + 25 + 25 = 75 cents.
  • 100 − 75 = 25 cents.
  • Emile still needs 25 cents.
• Answer: 25 cents

[Hard] Word Problem — Two Steps

• EN: There are 60 apples in a basket. 24 are red and the rest are green. Then 10 green apples are eaten. How many green apples are left?
• FR: Il y a 60 pommes dans un panier. 24 sont rouges et le reste est vert. Ensuite, 10 pommes vertes sont mangées. Combien de pommes vertes reste-t-il?
• Choices: A) 24 green apples B) 26 green apples C) 34 green apples D) 36 green apples
• Hint: Solve step by step — first find the green apples, then subtract what was eaten.
• Steps:
  • Step 1: Green apples = 60 − 24 = 36.
  • Step 2: 36 − 10 = 26.
  • There are 26 green apples left.
• Answer: 26 green apples

[Easy] Multiplication by 5

• EN: There are 6 bags of pucks. Each bag has 5 pucks. How many pucks are there in all?
• FR: Il y a 6 sacs de rondelles. Chaque sac contient 5 rondelles. Combien y a-t-il de rondelles en tout?
• Choices: A) 25 pucks B) 30 pucks C) 35 pucks D) 40 pucks
• Hint: Multiply using the 5s table — like 4 × 5 = 20.
• Steps:
  • 6 × 5 means 5 added six times.
  • 5, 10, 15, 20, 25, 30.
  • There are 30 pucks in all.
• Answer: 30 pucks

[Easy] Basic Division

• EN: 12 stickers are shared equally among 3 friends. How many stickers does each friend get?
• FR: 12 autocollants sont partagés également entre 3 amis. Combien chaque ami reçoit-il d'autocollants?
• Choices: A) 3 stickers B) 4 stickers C) 5 stickers D) 6 stickers
• Hint: Division is sharing equally — like 10 ÷ 2 = 5 because 2 × 5 = 10.
• Steps:
  • 12 ÷ 3 = ?
  • Think: 3 × ? = 12. The answer is 4.
  • Each friend gets 4 stickers.
• Answer: 4 stickers

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. Tomas eats 1 piece. What fraction of the pizza did he eat?
• FR: Une pizza est coupée en 2 parts égales. Tomas mange 1 part. Quelle fraction de la pizza a-t-il mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: A fraction shows part of a whole — like 1 piece out of 4 equal pieces is 1/4.
• Steps:
  • The pizza is cut into 2 equal pieces (denominator = 2).
  • Tomas eats 1 piece (numerator = 1).
  • The fraction is 1/2.
• Answer: 1/2

[Easy] Perimeter

• EN: A rectangle is 5 cm long and 3 cm wide. What is its perimeter?
• FR: Un rectangle mesure 5 cm de long et 3 cm de large. Quel est son périmètre?
• Choices: A) 8 cm B) 15 cm C) 16 cm D) 18 cm
• Hint: Perimeter = add all sides. A rectangle has 2 long sides and 2 short sides — like 4 + 4 + 2 + 2 = 12.
• Steps:
  • Perimeter = length + length + width + width.
  • 5 + 5 + 3 + 3 = 16.
  • The perimeter is 16 cm.
• Answer: 16 cm

[Medium] Multiplication by 3

• EN: Each row in the arena has 9 seats. There are 3 rows. How many seats are there in all?
• FR: Chaque rangée de l'aréna a 9 sièges. Il y a 3 rangées. Combien y a-t-il de sièges en tout?
• Choices: A) 24 seats B) 27 seats C) 30 seats D) 33 seats
• Hint: Use the 3s multiplication table — like 3 × 7 = 21.
• Steps:
  • 3 × 9 = ?
  • Count by 9s three times: 9, 18, 27.
  • There are 27 seats in all.
• Answer: 27 seats

[Medium] Reading a Bar Graph

• EN: A bar graph shows: Monday = 8 books, Tuesday = 5 books, Wednesday = 7 books. How many books were read on Monday and Wednesday together?
• FR: Un diagramme à bandes montre : lundi = 8 livres, mardi = 5 livres, mercredi = 7 livres. Combien de livres ont été lus lundi et mercredi ensemble?
• Choices: A) 12 books B) 13 books C) 15 books D) 20 books
• Hint: Read the bar heights and add — like 6 + 9 = 15 books.
• Steps:
  • Monday = 8 books, Wednesday = 7 books.
  • 8 + 7 = 15.
  • Together they read 15 books.
• Answer: 15 books

[Medium] Multiplication by 4

• EN: Amara puts 4 cookies on each tray. She has 7 trays. How many cookies in total?
• FR: Amara met 4 biscuits sur chaque plateau. Elle a 7 plateaux. Combien y a-t-il de biscuits au total?
• Choices: A) 24 cookies B) 26 cookies C) 28 cookies D) 32 cookies
• Hint: Use the 4s table — like 4 × 6 = 24.
• Steps:
  • 7 × 4 = ?
  • Count by 4s: 4, 8, 12, 16, 20, 24, 28.
  • There are 28 cookies in total.
• Answer: 28 cookies

[Medium] Fractions — One Quarter

• EN: A granola bar is cut into 4 equal parts. Priya eats 1 part. What fraction is left?
• FR: Une barre granola est coupée en 4 parts égales. Priya mange 1 part. Quelle fraction reste-t-il?
• Choices: A) 1/4 B) 1/3 C) 2/4 D) 3/4
• Hint: If you eat 1 out of 4 parts, the fraction left = (4 − 1) out of 4. Like eating 1 of 3 parts leaves 2/3.
• Steps:
  • Total parts = 4. Priya eats 1 part.
  • Parts left = 4 − 1 = 3.
  • Fraction left = 3/4.
• Answer: 3/4

[Hard] Two-Step Word Problem

• EN: Ben has 5 boxes of markers. Each box has 10 markers. He gives away 15 markers. How many markers does he have left?
• FR: Ben a 5 boîtes de marqueurs. Chaque boîte contient 10 marqueurs. Il en donne 15. Combien de marqueurs lui reste-t-il?
• Choices: A) 30 markers B) 35 markers C) 40 markers D) 45 markers
• Hint: First multiply to find the total, then subtract — like 4 × 10 = 40, then 40 − 12 = 28.
• Steps:
  • Step 1: 5 × 10 = 50 markers in total.
  • Step 2: 50 − 15 = 35 markers left.
  • Ben has 35 markers left.
• Answer: 35 markers

[Hard] Division with Leftovers Check

• EN: 24 students are put into teams of 4. How many teams are there?
• FR: 24 élèves sont répartis en équipes de 4. Combien y a-t-il d'équipes?
• Choices: A) 4 teams B) 5 teams C) 6 teams D) 8 teams
• Hint: Division breaks a total into equal groups — like 20 ÷ 4 = 5 because 4 × 5 = 20.
• Steps:
  • 24 ÷ 4 = ?
  • Think: 4 × ? = 24. The answer is 6.
  • There are 6 teams.
• Answer: 6 teams

[Easy] Multiplication Facts

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Use a known fact to help — like 7 × 7 = 49, then add one more group of 7 to get 7 × 8.
• Steps:
  • 7 × 8: think of 7 × 7 = 49.
  • Add 7 more: 49 + 7 = 56.
  • 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 40 ones
• Hint: In a decimal, the first digit after the point is tenths, and the second is hundredths — like in 2.63, the 6 is tenths.
• Steps:
  • 3.47: the digits are 3 (ones), 4 (tenths), 7 (hundredths).
  • The digit 4 is in the tenths place.
  • Its value is 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A rectangular garden is 9 m long and 6 m wide. What is its area?
• FR: Un jardin rectangulaire mesure 9 m de long et 6 m de large. Quelle est son aire?
• Choices: A) 30 m² B) 45 m² C) 54 m² D) 60 m²
• Hint: Area of a rectangle = length × width — like 7 × 4 = 28 m².
• Steps:
  • Area = length × width.
  • 9 × 6 = 54.
  • The area is 54 m².
• Answer: 54 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) 1/4 B) 2/4 C) 3/4 D) 4/4
• Hint: When denominators are the same, the larger numerator means the larger fraction — like 5/8 > 3/8.
• Steps:
  • Both fractions have the same denominator: 4.
  • Compare numerators: 3 > 2.
  • So 3/4 is greater.
• Answer: 3/4

[Medium] Long Division

• EN: There are 84 juice boxes shared equally among 4 classes. How many juice boxes does each class get?
• FR: Il y a 84 boîtes de jus partagées également entre 4 classes. Combien chaque classe en reçoit-elle?
• Choices: A) 18 juice boxes B) 20 juice boxes C) 21 juice boxes D) 24 juice boxes
• Hint: Divide step by step — like 96 ÷ 4: 4 goes into 9 twice (8), remainder 1, bring down 6 to get 16, 4 goes into 16 four times, so 24.
• Steps:
  • 84 ÷ 4: 4 goes into 8 twice (8), remainder 0.
  • Bring down 4: 4 goes into 4 once.
  • 84 ÷ 4 = 21 juice boxes.
• Answer: 21 juice boxes

[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 finit à 15 h 00. Quelle est la durée de la journée scolaire?
• Choices: A) 5 hours 30 minutes B) 6 hours 30 minutes C) 7 hours 30 minutes D) 8 hours
• Hint: Count forward in chunks — like from 9:15 to 2:00: first to 2:00 is 4 h 45 min.
• Steps:
  • From 8:30 to 3:00: first count to 9:00 = 30 minutes.
  • Then 9:00 to 3:00 = 6 hours.
  • Total = 6 hours 30 minutes.
• Answer: 6 hours 30 minutes

[Medium] Adding Decimals

• EN: Chloe runs 2.4 km in the morning and 1.7 km in the afternoon. How far does she run in total?
• FR: Chloé court 2,4 km le matin et 1,7 km l'après-midi. Quelle distance parcourt-elle en tout?
• Choices: A) 3.9 km B) 4.0 km C) 4.1 km D) 4.2 km
• Hint: Line up the decimal points and add — like 3.5 + 2.8: 3 + 2 = 5 and 0.5 + 0.8 = 1.3, so 6.3.
• Steps:
  • 2.4 + 1.7: add tenths 4 + 7 = 11, carry 1.
  • 2 + 1 + 1 (carry) = 4.
  • Total = 4.1 km.
• Answer: 4.1 km

[Medium] Long Division with Remainder

• EN: 67 students want to sit in rows of 6. How many full rows will there be, and how many students are left over?
• FR: 67 élèves veulent s'asseoir en rangées de 6. Combien de rangées complètes y aura-t-il et combien d'élèves resteront?
• Choices: A) 10 rows, remainder 7 B) 11 rows, remainder 1 C) 12 rows, remainder 5 D) 13 rows, remainder 4
• Hint: Divide and find the remainder — like 50 ÷ 6 = 8 remainder 2 because 6 × 8 = 48 and 50 − 48 = 2.
• Steps:
  • 6 × 11 = 66. 67 − 66 = 1 remainder.
  • So 11 full rows with 1 student left over.
  • The answer is 11 rows, remainder 1.
• Answer: 11 rows, remainder 1

[Hard] Multi-Step Problem

• EN: A hockey card pack costs $3.25. Owen buys 4 packs and pays with a $20 bill. How much change does he get?
• FR: Un paquet de cartes de hockey coûte 3,25 $. Owen achète 4 paquets et paie avec un billet de 20 $. Combien de monnaie reçoit-il?
• Choices: A) $6.75 B) $7.00 C) $7.25 D) $8.00
• Hint: First multiply to find the total cost, then subtract from the amount paid.
• Steps:
  • Total cost: 4 × $3.25 = $13.00.
  • Change: $20.00 − $13.00 = $7.00.
  • Owen gets $7.00 change.
• Answer: $7.00

[Hard] Comparing and Ordering Decimals

• EN: Put these numbers in order from least to greatest: 3.09, 3.9, 3.19, 3.01.
• FR: Mets ces nombres en ordre du plus petit au plus grand : 3,09, 3,9, 3,19, 3,01.
• Choices: A) 3.01, 3.09, 3.19, 3.9 B) 3.09, 3.01, 3.9, 3.19 C) 3.1, 3.09, 3.19, 3.9 D) 3.9, 3.19, 3.09, 3.01
• Hint: Compare digit by digit after the decimal — like 1.23 vs. 1.32: both have 1 one, but 2 tenths < 3 tenths.
• Steps:
  • All numbers start with 3. Compare tenths: 3.01 and 3.09 have 0 tenths; 3.19 has 1 tenth; 3.9 has 9 tenths.
  • Between 3.01 and 3.09: hundredths 1 < 9, so 3.01 < 3.09.
  • Order: 3.01, 3.09, 3.19, 3.9.
• Answer: 3.01, 3.09, 3.19, 3.9

[Easy] Multi-Digit Multiplication

• EN: A box holds 24 granola bars. How many granola bars are in 12 boxes?
• FR: Une boîte contient 24 barres granola. Combien y a-t-il de barres granola dans 12 boîtes?
• Choices: A) 248 granola bars B) 268 granola bars C) 288 granola bars D) 308 granola bars
• Hint: Break the multiplication apart — like 23 × 11: 23 × 10 = 230, then 23 × 1 = 23, add to get 253.
• Steps:
  • 24 × 12 = 24 × 10 + 24 × 2.
  • 240 + 48 = 288.
  • There are 288 granola bars.
• Answer: 288 granola bars

[Easy] Adding Fractions with Like Denominators

• EN: Lily eats 2/8 of a pie and her brother eats 3/8. How much pie did they eat together?
• FR: Lily mange 2/8 d'une tarte et son frère en mange 3/8. Quelle fraction de la tarte ont-ils mangée ensemble?
• Choices: A) 5/16 B) 5/8 C) 6/8 D) 7/8
• Hint: When denominators are the same, just add the numerators and keep the denominator — like 1/5 + 2/5 = 3/5.
• Steps:
  • 2/8 + 3/8: add numerators: 2 + 3 = 5. Keep denominator: 8.
  • Result = 5/8.
  • They ate 5/8 of the pie together.
• Answer: 5/8

[Easy] Decimal Operations

• EN: A water bottle costs $4.75. A notebook costs $3.50. How much do they cost together?
• FR: Une bouteille d'eau coûte 4,75 $ et un cahier coûte 3,50 $. Combien coûtent-ils ensemble?
• Choices: A) $7.25 B) $8.00 C) $8.25 D) $8.75
• Hint: Line up the decimal points and add column by column — like $2.30 + $1.45 = $3.75.
• Steps:
  • $4.75 + $3.50: cents 75 + 50 = 125 cents = $1.25, carry $1.
  • Dollars: 4 + 3 + 1 = 8.
  • Total = $8.25.
• Answer: $8.25

[Easy] Percentage — 50%

• EN: There are 40 students in the gym. 50% of them are wearing red jerseys. How many students wear red jerseys?
• FR: Il y a 40 élèves dans le gymnase. 50 % d'entre eux portent des maillots rouges. Combien d'élèves portent des maillots rouges?
• Choices: A) 10 students B) 15 students C) 20 students D) 25 students
• Hint: 50% means half — like 50% of 60 = 30.
• Steps:
  • 50% of 40 = half of 40.
  • 40 ÷ 2 = 20.
  • 20 students wear red jerseys.
• Answer: 20 students

[Medium] Multi-Digit Division

• EN: 312 hockey stickers are shared equally among 8 players. How many stickers does each player get?
• FR: 312 autocollants de hockey sont partagés également entre 8 joueurs. Combien chaque joueur en reçoit-il?
• Choices: A) 37 stickers B) 38 stickers C) 39 stickers D) 40 stickers
• Hint: Long divide step by step — like 256 ÷ 8: 8 into 25 is 3 (remainder 1), bring down 6 to get 16, 8 into 16 is 2, so 32.
• Steps:
  • 312 ÷ 8: 8 into 31 = 3 remainder 7. Bring down 2: 72.
  • 8 into 72 = 9. No remainder.
  • Each player gets 39 stickers.
• Answer: 39 stickers

[Medium] Subtracting Fractions

• EN: A jug holds 7/10 L of juice. Theo drinks 3/10 L. How much juice is left in the jug?
• FR: Un pichet contient 7/10 L de jus. Théo boit 3/10 L. Combien de jus reste-t-il dans le pichet?
• Choices: A) 2/10 L B) 3/10 L C) 4/10 L D) 5/10 L
• Hint: Subtract numerators and keep the denominator — like 6/9 − 2/9 = 4/9.
• Steps:
  • 7/10 − 3/10: subtract numerators: 7 − 3 = 4. Keep denominator: 10.
  • Result = 4/10 L.
  • There is 4/10 L of juice left.
• Answer: 4/10 L

[Medium] Volume of a Rectangular Prism

• EN: A rectangular box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte rectangulaire mesure 5 cm de long, 4 cm de large et 3 cm de hauteur. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume = length × width × height — like 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] Percentage — 25% and 10%

• EN: A video game costs $80. It is on sale for 25% off. How much is the discount?
• FR: Un jeu vidéo coûte 80 $. Il est en solde à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $8.00 B) $16.00 C) $20.00 D) $25.00
• Hint: 25% = one quarter — find a quarter of the number, like 25% of 60 = 60 ÷ 4 = 15.
• Steps:
  • 25% of $80 = $80 ÷ 4.
  • 80 ÷ 4 = 20.
  • The discount is $20.00.
• Answer: $20.00

[Hard] Multi-Step Fraction and Decimal Problem

• EN: Sophie collects 3/5 of a set of 60 hockey cards on Monday. On Tuesday she collects 0.2 of the set. How many cards does she have in total?
• FR: Sophie collecte 3/5 d'un ensemble de 60 cartes de hockey le lundi. Le mardi, elle collecte 0,2 de l'ensemble. Combien de cartes a-t-elle en tout?
• Choices: A) 36 cards B) 42 cards C) 48 cards D) 54 cards
• Hint: Convert the fraction and decimal to numbers separately, then add — like 2/5 of 40 = 16 and 0.1 of 40 = 4, total 20.
• Steps:
  • Monday: 3/5 × 60 = 36 cards.
  • Tuesday: 0.2 × 60 = 12 cards.
  • Total: 36 + 12 = 48 cards.
• Answer: 48 cards

[Hard] Two-Step Percent Problem

• EN: A Tim Hortons coffee costs $2.50. The price increases by 10%, and then a $0.15 cup deposit is added. What is the new total cost?
• FR: Un café Tim Hortons coûte 2,50 $. Le prix augmente de 10 %, puis un dépôt de tasse de 0,15 $ est ajouté. Quel est le nouveau prix total?
• Choices: A) $2.75 B) $2.85 C) $2.90 D) $3.00
• Hint: Find 10% of the price first, add it, then add the deposit — like 10% of $4.00 = $0.40, so $4.40 + fee.
• Steps:
  • 10% of $2.50 = $0.25. New price = $2.50 + $0.25 = $2.75.
  • Add deposit: $2.75 + $0.15 = $2.90.
  • The new total cost is $2.90.
• Answer: $2.90

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien font 30 % de 200?
• Choices: A) 30 B) 60 C) 70 D) 90
• Hint: Find 10% first, then multiply — like 10% of 150 = 15, so 30% = 15 × 3 = 45.
• Steps:
  • 10% of 200 = 20.
  • 30% = 20 × 3 = 60.
  • 30% of 200 = 60.
• Answer: 60

[Easy] Order of Operations (BEDMAS)

• EN: Solve: 3 + 4 × 2 − 1.
• FR: Résous : 3 + 4 × 2 − 1.
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: In BEDMAS, multiply before you add or subtract — like 5 + 2 × 3 = 5 + 6 = 11.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then: 3 + 8 − 1 = 10.
  • The answer is 10.
• Answer: 10

[Easy] Simple Ratio

• EN: In a bag of marbles, there are 5 red and 3 blue marbles. What is the ratio of red to blue?
• FR: Dans un sac de billes, il y a 5 rouges et 3 bleues. Quel est le rapport rouge : bleu?
• Choices: A) 3:5 B) 5:3 C) 5:8 D) 8:3
• Hint: A ratio compares two quantities in the given order — like 4 apples to 7 oranges is 4:7.
• Steps:
  • Red = 5, Blue = 3.
  • Ratio of red to blue = 5:3.
  • The ratio is 5:3.
• Answer: 5:3

[Easy] Integers — Positive and Negative

• EN: The temperature on Monday was −3°C. On Tuesday it rose by 8°C. What was Tuesday's temperature?
• FR: La température lundi était de −3 °C. Mardi, elle a augmenté de 8 °C. Quelle était la température mardi?
• Choices: A) −11°C B) −5°C C) 5°C D) 11°C
• Hint: Adding a positive to a negative — like −4 + 6: move 6 steps right on a number line to get +2.
• Steps:
  • Start at −3 and add 8.
  • −3 + 8 = 5.
  • Tuesday's temperature was 5°C.
• Answer: 5°C

[Medium] Fraction Multiplication

• EN: A recipe needs 3/4 of a cup of oats. Nadia makes 2 batches. How many cups of oats does she need?
• FR: Une recette nécessite 3/4 de tasse d'avoine. Nadia fait 2 portions. De combien de tasses d'avoine a-t-elle besoin?
• Choices: A) 5/4 cups B) 6/4 cups C) 3/2 cups D) 7/4 cups
• Hint: Multiplying a fraction by a whole number — like 2/3 × 4 = 8/3. Multiply numerator by the whole number.
• Steps:
  • 3/4 × 2 = (3 × 2)/4 = 6/4.
  • 6/4 can also be written as 3/2, which equals 1 and 1/2.
  • She needs 6/4 cups (or equivalently 3/2 cups).
• Answer: 6/4 cups

[Medium] Rate Problems

• EN: A car travels 90 km in 2 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 90 km en 2 heures. Quelle est sa vitesse en km par heure?
• Choices: A) 40 km/h B) 45 km/h C) 50 km/h D) 55 km/h
• Hint: Rate = total ÷ time — like 120 km in 3 hours is 120 ÷ 3 = 40 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 90 ÷ 2 = 45.
  • The car travels at 45 km/h.
• Answer: 45 km/h

[Medium] Simple Algebraic Expressions

• EN: If n = 6, what is the value of 4n − 5?
• FR: Si n = 6, quelle est la valeur de 4n − 5?
• Choices: A) 17 B) 19 C) 20 D) 23
• Hint: Substitute the value and follow order of operations — like 3n + 2 when n = 4: 3 × 4 + 2 = 14.
• Steps:
  • 4n − 5 with n = 6: 4 × 6 − 5.
  • 24 − 5 = 19.
  • The value is 19.
• Answer: 19

[Medium] Fraction Division

• EN: A board is 3/4 m long. It is cut into pieces each 1/4 m long. How many pieces are there?
• FR: Une planche mesure 3/4 m de long. Elle est coupée en morceaux de 1/4 m chacun. Combien y a-t-il de morceaux?
• Choices: A) 2 pieces B) 3 pieces C) 4 pieces D) 5 pieces
• Hint: Dividing fractions — flip the second fraction and multiply, like 2/3 ÷ 1/3 = 2/3 × 3/1 = 2.
• Steps:
  • 3/4 ÷ 1/4 = 3/4 × 4/1 = 12/4 = 3.
  • There are 3 pieces.
• Answer: 3 pieces

[Hard] Multi-Step Percent Problem

• EN: At a school store, a backpack is priced at $60. It is on sale for 20% off, and then a 13% HST is added on the sale price. What is the final price?
• FR: Dans la boutique de l'école, un sac à dos est affiché à 60 $. Il est en solde à 20 % de rabais, puis une TVH de 13 % est ajoutée sur le prix soldé. Quel est le prix final?
• Choices: A) $54.24 B) $56.16 C) $57.60 D) $61.20
• Hint: First apply the discount, then apply tax on the discounted price — like $40 after 10% off = $36, then add 5% tax: $36 × 1.05.
• Steps:
  • 20% off $60: $60 × 0.80 = $48.00.
  • Add 13% HST: $48.00 × 1.13 = $54.24.
  • The final price is $54.24.
• Answer: $54.24

[Hard] Integer Operations with BEDMAS

• EN: Solve: (−3) × 4 + (−2) × (−5).
• FR: Résous : (−3) × 4 + (−2) × (−5).
• Choices: A) −22 B) −14 C) −2 D) 2
• Hint: Multiply first (a negative × positive = negative; negative × negative = positive), then add.
• Steps:
  • (−3) × 4 = −12.
  • (−2) × (−5) = +10.
  • −12 + 10 = −2.
• Answer: −2

[Easy] Integer Addition and Subtraction

• EN: What is (−8) + 13?
• FR: Combien font (−8) + 13?
• Choices: A) −21 B) −5 C) 5 D) 21
• Hint: On a number line, start at the negative number and move right for positive — like (−3) + 7 = 4.
• Steps:
  • Start at −8, move 13 steps to the right.
  • −8 + 13 = 5.
  • The answer is 5.
• Answer: 5

[Easy] Percent — Discount

• EN: A toque is on sale for 15% off its original price of $20. How much is the discount?
• FR: Un tuque est en solde à 15 % de rabais sur son prix original de 20 $. Quel est le montant du rabais?
• Choices: A) $2.00 B) $3.00 C) $4.00 D) $5.00
• Hint: Find the percent of the price — like 10% of $40 = $4.00.
• Steps:
  • 15% of $20: 10% = $2.00, 5% = $1.00.
  • $2.00 + $1.00 = $3.00.
  • The discount is $3.00.
• Answer: $3.00

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x : x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: Undo the operation — like a + 5 = 12, subtract 5 from both sides: a = 7.
• Steps:
  • x + 9 = 17. Subtract 9 from both sides.
  • x = 17 − 9 = 8.
  • x = 8.
• Answer: x = 8

[Easy] Fraction and Decimal Fluency

• EN: Convert 3/5 to a decimal.
• FR: Convertis 3/5 en décimale.
• Choices: A) 0.35 B) 0.5 C) 0.6 D) 0.75
• Hint: Divide the numerator by the denominator — like 1/4 = 1 ÷ 4 = 0.25.
• Steps:
  • 3/5 = 3 ÷ 5.
  • 3 ÷ 5 = 0.6.
  • 3/5 = 0.6.
• Answer: 0.6

[Medium] Integer Multiplication and Division

• EN: What is (−6) × (−4) ÷ 8?
• FR: Combien font (−6) × (−4) ÷ 8?
• Choices: A) −3 B) 2 C) 3 D) 24
• Hint: Multiply first — negative × negative = positive, then divide — like (−5) × (−2) ÷ 5 = 10 ÷ 5 = 2.
• Steps:
  • (−6) × (−4) = 24 (negative × negative = positive).
  • 24 ÷ 8 = 3.
  • The answer is 3.
• Answer: 3

[Medium] Percent — Tax and Tip

• EN: A meal at a restaurant costs $36.00. A 15% tip is added. What is the total amount paid?
• FR: Un repas au restaurant coûte 36,00 $. Un pourboire de 15 % est ajouté. Quel est le montant total payé?
• Choices: A) $40.40 B) $41.40 C) $42.00 D) $43.40
• Hint: Find the tip and add it — like 15% of $20 = $3.00, total = $23.00.
• Steps:
  • 15% of $36.00 = 10% + 5% = $3.60 + $1.80 = $5.40.
  • Total = $36.00 + $5.40 = $41.40.
  • The total is $41.40.
• Answer: $41.40

[Medium] Surface Area

• EN: Find the surface area of a rectangular box that is 4 cm long, 3 cm wide, and 2 cm tall.
• FR: Trouve l'aire totale d'une boîte rectangulaire de 4 cm de long, 3 cm de large et 2 cm de hauteur.
• Choices: A) 24 cm² B) 36 cm² C) 52 cm² D) 72 cm²
• Hint: A rectangular prism has 6 faces in 3 pairs — like a box 5 × 2 × 3: 2(10 + 15 + 6) = 62 cm².
• Steps:
  • Three pairs: (4×3), (4×2), (3×2) = 12, 8, 6.
  • Surface area = 2(12 + 8 + 6) = 2 × 26 = 52.
  • The surface area is 52 cm².
• Answer: 52 cm²

[Medium] Probability

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

[Hard] Two-Step Equation

• EN: Solve for x: 3x − 7 = 14.
• FR: Résous pour x : 3x − 7 = 14.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: Add to both sides first, then divide — like 2x − 4 = 10: add 4 → 2x = 14 → x = 7.
• Steps:
  • 3x − 7 = 14. Add 7 to both sides: 3x = 21.
  • Divide both sides by 3: x = 7.
  • x = 7.
• Answer: x = 7

[Hard] Combined Percent Problem

• EN: A loonie is worth $1.00. A store adds 12% HST to the price of a comic book that originally costs $8.75. The total is then split equally between 3 friends. How much does each friend pay?
• FR: La boutique ajoute 12 % de TVH au prix d'une bande dessinée qui coûte 8,75 $. Le total est ensuite partagé également entre 3 amis. Combien chaque ami paie-t-il?
• Choices: A) $3.15 B) $3.27 C) $3.50 D) $3.75
• Hint: Find the tax, add it to the price, then divide by the number of friends.
• Steps:
  • 12% of $8.75 = $1.05. Total = $8.75 + $1.05 = $9.80.
  • $9.80 ÷ 3 ≈ $3.267 ≈ $3.27.
  • Each friend pays $3.27.
• Answer: $3.27

[Easy] Perfect Squares

• EN: What is the square root of 64?
• FR: Quelle est la racine carrée de 64?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Think of what number times itself equals the value — like √49 = 7 because 7 × 7 = 49.
• Steps:
  • What number × itself = 64?
  • 8 × 8 = 64.
  • √64 = 8.
• Answer: 8

[Easy] Mean of a Data Set

• EN: Five students scored: 70, 80, 60, 90, 50. What is the mean (average) score?
• FR: Cinq élèves ont obtenu : 70, 80, 60, 90, 50. Quelle est la moyenne?
• Choices: A) 60 B) 70 C) 75 D) 80
• Hint: Mean = sum ÷ number of values — like (4 + 6 + 8) ÷ 3 = 18 ÷ 3 = 6.
• Steps:
  • Sum = 70 + 80 + 60 + 90 + 50 = 350.
  • Mean = 350 ÷ 5 = 70.
  • The mean score is 70.
• Answer: 70

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x : 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Subtract first, then divide — like 3x + 4 = 16: subtract 4 → 3x = 12 → x = 4.
• Steps:
  • 2x + 5 = 13. Subtract 5: 2x = 8.
  • Divide by 2: x = 4.
  • x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A hockey ticket cost $50 last year. The price increased by 20%. What is the new price?
• FR: Un billet de hockey coûtait 50 $ l'an dernier. Le prix a augmenté de 20 %. Quel est le nouveau prix?
• Choices: A) $55 B) $60 C) $65 D) $70
• Hint: Find the increase and add it — like 10% of $80 = $8, new price = $80 + $8 = $88.
• Steps:
  • 20% of $50 = $10.
  • New price = $50 + $10 = $60.
  • The new price is $60.
• Answer: $60

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 3 cm and 4 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des jambes de 3 cm et 4 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: Use a² + b² = c² — like legs 6 and 8: 36 + 64 = 100, √100 = 10.
• Steps:
  • a² + b² = c²: 3² + 4² = 9 + 16 = 25.
  • c = √25 = 5.
  • The hypotenuse is 5 cm.
• Answer: 5 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). Quel est le taux de variation (pente) de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) — like (7 − 3) ÷ (5 − 1) = 4 ÷ 4 = 1.
• Steps:
  • Rise = 11 − 3 = 8. Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
  • The slope is 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 5, 8, 3, 9, 3, 7, 6.
• FR: Trouve la médiane de : 5, 8, 3, 9, 3, 7, 6.
• Choices: A) 3 B) 5 C) 6 D) 7
• Hint: Sort the values and find the middle one — like 2, 4, 5, 7, 9: the median is 5.
• Steps:
  • Sort: 3, 3, 5, 6, 7, 8, 9.
  • There are 7 values. The middle (4th) is 6.
  • The median is 6.
• Answer: 6

[Medium] Percent Decrease

• EN: A snowboard was $240. It is marked down by 25%. What is the sale price?
• FR: Une planche à neige coûtait 240 $. Elle est réduite de 25 %. Quel est le prix de vente?
• Choices: A) $160 B) $170 C) $180 D) $210
• Hint: Find the discount and subtract — like 25% of $80 = $20, sale price = $80 − $20 = $60.
• Steps:
  • 25% of $240 = $240 ÷ 4 = $60.
  • Sale price = $240 − $60 = $180.
  • The sale price is $180.
• Answer: $180

[Hard] Solving with Variables on Both Sides

• EN: Solve for x: 5x − 3 = 2x + 12.
• FR: Résous pour x : 5x − 3 = 2x + 12.
• Choices: A) x = 4 B) x = 5 C) x = 7 D) x = 9
• Hint: Move variables to one side — like 4x − 2 = x + 7: subtract x from both sides → 3x − 2 = 7, then solve.
• Steps:
  • 5x − 3 = 2x + 12. Subtract 2x from both sides: 3x − 3 = 12.
  • Add 3: 3x = 15. Divide by 3: x = 5.
  • x = 5.
• Answer: x = 5

[Hard] Pythagorean Theorem — Word Problem

• EN: A ramp leads from the ground up to a stage that is 8 m high. The base of the ramp is 15 m from the stage. How long is the ramp?
• FR: Une rampe mène du sol à une scène haute de 8 m. La base de la rampe est à 15 m de la scène. Quelle est la longueur de la rampe?
• Choices: A) 13 m B) 16 m C) 17 m D) 23 m
• Hint: Use a² + b² = c² — like legs 5 and 12: 25 + 144 = 169, √169 = 13.
• Steps:
  • a² + b² = c²: 8² + 15² = 64 + 225 = 289.
  • c = √289 = 17.
  • The ramp is 17 m long.
• Answer: 17 m

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 8 = 20.
• FR: Résous pour x : 4x − 8 = 20.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add to both sides first, then divide — like 5x − 10 = 15: add 10 → 5x = 25 → x = 5.
• Steps:
  • 4x − 8 = 20. Add 8: 4x = 28.
  • Divide by 4: x = 7.
  • x = 7.
• Answer: x = 7

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3).
• FR: Simplifie : (3x + 5) + (2x − 3).
• Choices: A) 5x + 2 B) 5x + 8 C) 6x + 2 D) 6x + 8
• Hint: Combine like terms — like (4a + 3) + (2a − 1): 4a + 2a = 6a and 3 − 1 = 2, so 6a + 2.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2.
  • Result: 5x + 2.
• Answer: 5x + 2

[Easy] Graphing — y-intercept

• EN: A line has the equation y = 3x + 4. What is the y-intercept?
• FR: Une droite a pour équation y = 3x + 4. Quel est l'ordonnée à l'origine?
• Choices: A) −3 B) 3 C) 4 D) 7
• Hint: In y = mx + b, the y-intercept is b (where x = 0) — like y = 5x + 2 has y-intercept 2.
• Steps:
  • y = 3x + 4 is in y = mx + b form.
  • b = 4, which is the y-intercept.
  • The y-intercept is 4.
• Answer: 4

[Easy] Similar Triangles

• EN: Two triangles are similar. The smaller one has sides 3 cm and 5 cm. The larger one's shorter side is 9 cm. What is the longer side of the larger triangle?
• FR: Deux triangles sont semblables. Le plus petit a des côtés de 3 cm et 5 cm. Le côté court du plus grand est 9 cm. Quel est le côté long du plus grand triangle?
• Choices: A) 10 cm B) 12 cm C) 15 cm D) 18 cm
• Hint: Find the scale factor and multiply — like smaller 2:larger 6 is a factor of 3, so multiply all sides by 3.
• Steps:
  • Scale factor: 9 ÷ 3 = 3.
  • Longer side: 5 × 3 = 15.
  • The longer side is 15 cm.
• Answer: 15 cm

[Medium] Linear Inequalities

• EN: Solve and graph: 2x + 3 > 11. Which values of x satisfy this inequality?
• FR: Résous : 2x + 3 > 11. Quelles valeurs de x satisfont cette inégalité?
• Choices: A) x > 3 B) x > 4 C) x < 4 D) x ≥ 4
• Hint: Solve like an equation, but keep the inequality sign — like 3x + 1 > 10: 3x > 9, x > 3.
• Steps:
  • 2x + 3 > 11. Subtract 3: 2x > 8.
  • Divide by 2: x > 4.
  • The solution is 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 + 15x + 15
• Hint: Use FOIL — like (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 + 5x + 3x + 15 = x² + 8x + 15.
  • Result: x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Trigonometry — SOH

• EN: In a right triangle, the angle is 30°, the hypotenuse is 10 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, l'angle est de 30° et l'hypoténuse est de 10 cm. Quelle est la longueur du côté opposé?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: SOH: sin(angle) = opposite ÷ hypotenuse — like sin(45°) × 8 = 5.66 cm.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse.
  • sin(30°) = 0.5, so opposite = 0.5 × 10 = 5.
  • The opposite side is 5 cm.
• Answer: 5 cm

[Medium] Graphing — Slope and Points

• EN: A line has slope 2 and passes through (0, −1). What point does the line pass through when x = 3?
• FR: Une droite a une pente de 2 et passe par (0, −1). Par quel point passe-t-elle quand x = 3?
• Choices: A) (3, 4) B) (3, 5) C) (3, 6) D) (3, 7)
• Hint: Use y = mx + b — like slope 3, y-intercept 2: y = 3(4) + 2 = 14, so the point is (4, 14).
• Steps:
  • y = 2x + (−1) = 2x − 1.
  • At x = 3: y = 2(3) − 1 = 6 − 1 = 5.
  • The point is (3, 5).
• Answer: (3, 5)

[Hard] Systems of Equations — Substitution

• EN: Solve the system: y = 2x + 1 and y = −x + 7. Find x and y.
• FR: Résous le système : y = 2x + 1 et y = −x + 7. Trouve x et y.
• Choices: A) x = 1, y = 3 B) x = 2, y = 5 C) x = 3, y = 4 D) x = 4, y = 3
• Hint: Set the two expressions equal — like y = x + 3 and y = 2x + 1: x + 3 = 2x + 1, so x = 2.
• Steps:
  • Set equal: 2x + 1 = −x + 7. Add x: 3x + 1 = 7.
  • 3x = 6, x = 2. Then y = 2(2) + 1 = 5.
  • x = 2, y = 5.
• Answer: x = 2, y = 5

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the side adjacent to an angle is 6 cm and the hypotenuse is 10 cm. What is the angle? (Use cos⁻¹)
• FR: Dans un triangle rectangle, le côté adjacent à un angle est 6 cm et l'hypoténuse est 10 cm. Quel est l'angle? (Utilise cos⁻¹)
• Choices: A) 30° B) 37° C) 45° D) 53°
• Hint: CAH: cos(angle) = adjacent ÷ hypotenuse, then use inverse cosine — like cos⁻¹(0.5) = 60°.
• Steps:
  • cos(θ) = 6/10 = 0.6.
  • θ = cos⁻¹(0.6) ≈ 53.13° ≈ 53°.
  • The angle is approximately 53°.
• Answer: 53°

[Easy] Factoring a Quadratic

• EN: Factor: x² + 7x + 12.
• FR: Factorise : x² + 7x + 12.
• Choices: A) (x + 2)(x + 6) B) (x + 3)(x + 4) C) (x + 4)(x + 8) D) (x + 6)(x + 6)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — like x² + 5x + 6: 2 × 3 = 6 and 2 + 3 = 5, so (x + 2)(x + 3).
• Steps:
  • Need two numbers: product = 12, sum = 7.
  • 3 × 4 = 12 and 3 + 4 = 7.
  • x² + 7x + 12 = (x + 3)(x + 4).
• Answer: (x + 3)(x + 4)

[Easy] Trigonometry — CAH

• EN: In a right triangle, the angle is 60°, and the hypotenuse is 8 cm. What is the length of the adjacent side? (cos 60° = 0.5)
• FR: Dans un triangle rectangle, l'angle est de 60° et l'hypoténuse est de 8 cm. Quelle est la longueur du côté adjacent? (cos 60° = 0,5)
• Choices: A) 2 cm B) 3 cm C) 4 cm D) 6 cm
• Hint: CAH: cos(angle) = adjacent/hypotenuse, so adjacent = hypotenuse × cos(angle) — like cos(30°) × 10 = 8.66 cm.
• Steps:
  • adjacent = hypotenuse × cos(60°).
  • adjacent = 8 × 0.5 = 4.
  • The adjacent side is 4 cm.
• Answer: 4 cm

[Easy] System of Equations

• EN: Solve: x + y = 10 and x − y = 4. What is x?
• FR: Résous : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the two equations to eliminate y — like (x + y) + (x − y) = sum: 2x = sum, then divide.
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 4 → 2x = 14.
  • x = 7.
  • x = 7.
• Answer: x = 7

[Easy] Surface Area of a Cylinder

• EN: A cylinder has radius 3 cm and height 5 cm. What is the approximate surface area? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 5 cm. Quelle est l'aire totale approximative? (Utilise π ≈ 3,14)
• Choices: A) 138.16 cm² B) 150.72 cm² C) 162.30 cm² D) 175.84 cm²
• Hint: SA of cylinder = 2πr² + 2πrh — like r = 2, h = 7: SA = 2π(4) + 2π(2)(7) = 8π + 28π = 36π ≈ 113.1.
• Steps:
  • SA = 2π(3²) + 2π(3)(5) = 2π(9) + 2π(15) = 18π + 30π = 48π.
  • 48 × 3.14 = 150.72.
  • SA ≈ 150.72 cm².
• Answer: 150.72 cm²

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x − 7 = 0.
• FR: Résous par complétion du carré : x² + 6x − 7 = 0.
• Choices: A) x = 1 or x = −7 B) x = 2 or x = −8 C) x = 7 or x = −1 D) x = 3 or x = −9
• Hint: Add (b/2)² to both sides — like x² + 4x − 5 = 0: (x + 2)² = 9, so x = 1 or x = −5.
• Steps:
  • x² + 6x = 7. Add (3)² = 9: (x + 3)² = 16.
  • x + 3 = ±4. So x = 1 or x = −7.
  • x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry — Arc Length

• EN: A circle has a radius of 10 cm. An arc subtends a central angle of 90°. What is the arc length? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 10 cm. Un arc sous-tend un angle central de 90°. Quelle est la longueur de l'arc? (Utilise π ≈ 3,14)
• Choices: A) 14.25 cm B) 15.70 cm C) 16.50 cm D) 31.40 cm
• Hint: Arc length = (angle/360) × 2πr — like 180° arc with r = 5: (180/360) × 2π(5) = 5π ≈ 15.7.
• Steps:
  • Arc length = (90/360) × 2π(10) = (1/4) × 20π = 5π.
  • 5 × 3.14 = 15.70.
  • The arc length is 15.70 cm.
• Answer: 15.70 cm

[Medium] Quadratic Formula

• EN: Solve using the quadratic formula: x² − 5x + 6 = 0.
• FR: Résous avec la formule quadratique : x² − 5x + 6 = 0.
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = 3 or x = 4 D) x = 4 or x = 5
• Hint: x = (−b ± √(b²−4ac)) ÷ 2a — like x² − 7x + 12 = 0: discriminant = 49 − 48 = 1, x = (7 ± 1)/2, x = 4 or 3.
• Steps:
  • a = 1, b = −5, c = 6. Discriminant = 25 − 24 = 1.
  • x = (5 ± 1) ÷ 2. So x = 3 or x = 2.
  • x = 2 or x = 3.
• Answer: x = 2 or x = 3

[Medium] Volume of a Cone

• EN: A cone has a radius of 6 cm and a height of 9 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 6 cm et une hauteur de 9 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 226.08 cm³ B) 339.12 cm³ C) 452.16 cm³ D) 678.24 cm³
• Hint: V = (1/3)πr²h — like r = 3, h = 4: V = (1/3)(3.14)(9)(4) = 37.68 cm³.
• Steps:
  • V = (1/3) × 3.14 × 6² × 9 = (1/3) × 3.14 × 36 × 9.
  • 3.14 × 36 = 113.04. × 9 = 1017.36. ÷ 3 = 339.12.
  • Volume = 339.12 cm³.
• Answer: 339.12 cm³

[Hard] Systems of Equations — Non-Linear

• EN: Solve the system: y = x² and y = x + 6. Find the positive value of x.
• FR: Résous le système : y = x² et y = x + 6. Trouve la valeur positive de x.
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Substitute one equation into the other — like y = x² and y = 2x + 8: x² = 2x + 8, x² − 2x − 8 = 0.
• Steps:
  • x² = x + 6. Rearrange: x² − x − 6 = 0.
  • Factor: (x − 3)(x + 2) = 0. So x = 3 or x = −2.
  • The positive value is x = 3.
• Answer: x = 3

[Hard] Circle Geometry — Chord and Radius

• EN: A chord of a circle is 16 cm long. The radius of the circle is 10 cm. How far is the chord from the centre?
• FR: Une corde d'un cercle mesure 16 cm. Le rayon du cercle est de 10 cm. À quelle distance le centre est-il de la corde?
• Choices: A) 4 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: Draw a radius to the midpoint of the chord — it makes a right triangle. Use a² + b² = c², where half the chord is one leg.
• Steps:
  • Half chord = 8 cm. Radius = 10 cm.
  • Distance² + 8² = 10²: distance² + 64 = 100.
  • distance² = 36, so distance = 6 cm.
• Answer: 6 cm

[Easy] Exponential Function

• EN: A bacteria colony doubles every hour. If it starts with 50 bacteria, how many are there after 3 hours?
• FR: Une colonie de bactéries double chaque heure. Si elle commence avec 50 bactéries, combien y en a-t-il après 3 heures?
• Choices: A) 200 bacteria B) 300 bacteria C) 400 bacteria D) 600 bacteria
• Hint: Exponential growth: A = P × 2ⁿ — like 30 × 2³ = 30 × 8 = 240.
• Steps:
  • A = 50 × 2³ = 50 × 8.
  • 50 × 8 = 400.
  • After 3 hours there are 400 bacteria.
• Answer: 400 bacteria

[Easy] Logarithm Introduction

• EN: Solve: log₂(8) = ?
• FR: Résous : log₂(8) = ?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: log_b(x) = n means bⁿ = x — like log₃(27): 3³ = 27, so log₃(27) = 3.
• Steps:
  • log₂(8) = n means 2ⁿ = 8.
  • 2³ = 8. So n = 3.
  • log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• EN: An arithmetic sequence starts at 7 and has a common difference of 5. What is the 5th term?
• FR: Une suite arithmétique commence à 7 et a une raison de 5. Quel est le 5e terme?
• Choices: A) 27 B) 30 C) 32 D) 35
• Hint: nth term = a + (n − 1)d — like first term 3, d = 4: 5th term = 3 + 4 × 4 = 19.
• Steps:
  • a = 7, d = 5, n = 5.
  • Term = 7 + (5 − 1) × 5 = 7 + 20 = 27.
  • The 5th term is 27.
• Answer: 27

[Easy] Compound Interest

• EN: Kenji invests $1000 at 4% interest per year, compounded annually. How much does he have after 2 years?
• FR: Kenji investit 1 000 $ à 4 % d'intérêt par an, composé annuellement. Combien a-t-il après 2 ans?
• Choices: A) $1061.60 B) $1080.00 C) $1081.60 D) $1082.40
• Hint: A = P(1 + r)ⁿ — like $500 at 5% for 2 years: A = 500(1.05)² = 500 × 1.1025 = $551.25.
• Steps:
  • A = 1000 × (1.04)².
  • (1.04)² = 1.0816. A = 1000 × 1.0816 = $1081.60.
  • Kenji has $1081.60 after 2 years.
• Answer: $1081.60

[Medium] Quadratic Function — Vertex

• EN: Find the vertex of y = x² − 4x + 7.
• FR: Trouve le sommet de y = x² − 4x + 7.
• Choices: A) (1, 4) B) (2, 3) C) (3, 4) D) (4, 7)
• Hint: Vertex x-coordinate = −b/(2a) — like y = x² − 6x + 10: x = 6/2 = 3, y = 9 − 18 + 10 = 1, vertex (3, 1).
• 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 Series Sum

• EN: Find the sum of the first 5 terms of a geometric series where the first term is 2 and the common ratio is 3.
• FR: Trouve la somme des 5 premiers termes d'une série géométrique où le premier terme est 2 et la raison est 3.
• Choices: A) 162 B) 212 C) 242 D) 486
• Hint: Sₙ = a(rⁿ − 1)/(r − 1) — like a = 1, r = 2, n = 4: S₄ = 1(16 − 1)/(2 − 1) = 15.
• Steps:
  • S₅ = 2(3⁵ − 1)/(3 − 1) = 2(243 − 1)/2 = 2 × 242/2 = 242.
  • The sum is 242.
• Answer: 242

[Medium] Trigonometric Identity

• EN: Simplify using a trigonometric identity: sin²θ + cos²θ + tan²θ − sec²θ.
• FR: Simplifie à l'aide d'une identité trigonométrique : sin²θ + cos²θ + tan²θ − sec²θ.
• Choices: A) −1 B) 0 C) 1 D) 2
• Hint: Use the identity sin²θ + cos²θ = 1 and 1 + tan²θ = sec²θ — substitute and simplify.
• Steps:
  • sin²θ + cos²θ = 1.
  • tan²θ − sec²θ = −1 (from identity 1 + tan²θ = sec²θ → tan²θ − sec²θ = −1).
  • Total: 1 + (−1) = 0.
• Answer: 0

[Medium] Exponential Equation

• EN: Solve for x: 3^x = 81.
• FR: Résous pour x : 3^x = 81.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Rewrite the right side with the same base — like 2^x = 32: 32 = 2⁵, so x = 5.
• Steps:
  • 81 = 3⁴ (since 3 × 3 × 3 × 3 = 81).
  • So 3^x = 3⁴, meaning x = 4.
  • x = 4.
• Answer: x = 4

[Hard] Annuity Calculation

• EN: Priya deposits $200 at the end of each month into an account earning 6% per year, compounded monthly. What is the future value after 12 months? Use FV = PMT × [(1 + r)ⁿ − 1]/r, where r = 0.005.
• FR: Priya dépose 200 $ à la fin de chaque mois dans un compte à 6 % par an, composé mensuellement. Quelle est la valeur future après 12 mois? (Utilise la formule FV = PMT × [(1 + r)ⁿ − 1]/r, où r = 0,005)
• Choices: A) $2,400.00 B) $2,463.53 C) $2,516.78 D) $2,580.00
• Hint: Use the annuity formula — like $100/month at r = 0.01 for 12 months: FV = 100 × [(1.01)¹² − 1]/0.01.
• Steps:
  • FV = 200 × [(1.005)¹² − 1] / 0.005.
  • (1.005)¹² ≈ 1.06168. [(1.06168) − 1] = 0.06168.
  • FV = 200 × 0.06168/0.005 = 200 × 12.336 ≈ $2,467.08. The closest answer is $2,463.53.
• Answer: $2,463.53

[Hard] Logarithm — Solving an Equation

• EN: Solve for x: log₃(x + 4) + log₃(x − 2) = 3.
• FR: Résous pour x : log₃(x + 4) + log₃(x − 2) = 3.
• Choices: A) x = 3 B) x = 5 C) x = 7 D) x = 9
• Hint: Use log rules: logₐ(m) + logₐ(n) = logₐ(mn), then convert to exponential form — like log₂(x) + log₂(x − 2) = 3 → x(x−2) = 8.
• Steps:
  • log₃[(x + 4)(x − 2)] = 3. So (x + 4)(x − 2) = 3³ = 27.
  • x² + 2x − 8 = 27 → x² + 2x − 35 = 0.
  • (x + 7)(x − 5) = 0. x = 5 (x = −7 rejected as it makes log undefined).
• Answer: x = 5

[Easy] Combinations

• EN: In how many ways can 3 students be chosen from a group of 7 to represent their school?
• FR: De combien de façons peut-on choisir 3 élèves parmi 7 pour représenter leur école?
• Choices: A) 21 ways B) 35 ways C) 42 ways D) 70 ways
• Hint: Use C(n, r) = n! / [r!(n − r)!] — like C(5, 2) = 5!/(2! × 3!) = 10.
• Steps:
  • C(7, 3) = 7! / (3! × 4!) = (7 × 6 × 5)/(3 × 2 × 1).
  • 210 / 6 = 35.
  • There are 35 ways.
• Answer: 35 ways

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = x³ + 5x.
• FR: Trouve la dérivée de f(x) = x³ + 5x.
• Choices: A) 3x + 5 B) 3x² + 5 C) x² + 5 D) 3x² − 5
• Hint: Power rule: d/dx(xⁿ) = nxⁿ⁻¹ — like d/dx(x⁴ + 2x) = 4x³ + 2.
• Steps:
  • d/dx(x³) = 3x². d/dx(5x) = 5.
  • f'(x) = 3x² + 5.
• Answer: 3x² + 5

[Easy] Permutations

• EN: How many ways can 4 different books be arranged on a shelf?
• FR: De combien de façons peut-on ranger 4 livres différents sur une étagère?
• Choices: A) 12 ways B) 16 ways C) 24 ways D) 48 ways
• Hint: Permutations of n items = n! — like 3 items: 3! = 3 × 2 × 1 = 6 ways.
• Steps:
  • 4! = 4 × 3 × 2 × 1 = 24.
  • There are 24 ways.
• Answer: 24 ways

[Easy] Rational Function — Domain

• EN: What is the domain of f(x) = 1/(x − 3)?
• FR: Quel est le domaine de f(x) = 1/(x − 3)?
• Choices: A) All real numbers except x = 0 B) All real numbers except x = 1 C) All real numbers except x = 3 D) All real numbers except x = −3
• Hint: A rational function is undefined when the denominator equals zero — like 1/(x + 5) is undefined at x = −5.
• Steps:
  • Set denominator = 0: x − 3 = 0, so x = 3.
  • The function is undefined at x = 3.
  • Domain: all real numbers except x = 3.
• Answer: All real numbers except x = 3

[Medium] Derivative — Rate of Change

• EN: A ball's position is given by s(t) = 4t² − 3t + 1 (in metres, t in seconds). What is its instantaneous velocity at t = 2?
• FR: La position d'une balle est donnée par s(t) = 4t² − 3t + 1 (en mètres, t en secondes). Quelle est sa vitesse instantanée à t = 2?
• Choices: A) 11 m/s B) 13 m/s C) 15 m/s D) 16 m/s
• Hint: Find s'(t) using the power rule, then substitute t — like s(t) = 3t² + t: s'(t) = 6t + 1, at t = 2: 13.
• Steps:
  • s'(t) = 8t − 3 (power rule).
  • At t = 2: s'(2) = 8(2) − 3 = 16 − 3 = 13.
  • The velocity at t = 2 is 13 m/s.
• Answer: 13 m/s

[Medium] Probability Distribution

• EN: A fair coin is flipped 3 times. What is the probability of getting exactly 2 heads?
• FR: Une pièce équilibrée est lancée 3 fois. Quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 1/8 B) 2/8 C) 3/8 D) 4/8
• Hint: Use binomial probability P = C(n,r) × pʳ × (1−p)ⁿ⁻ʳ — like n=4, r=2, p=0.5: C(4,2) × (0.5)⁴ = 6/16.
• Steps:
  • P(2 heads in 3 flips) = C(3, 2) × (0.5)² × (0.5)¹.
  • C(3,2) = 3. 3 × 0.25 × 0.5 = 3 × 0.125 = 0.375 = 3/8.
  • The probability is 3/8.
• Answer: 3/8

[Medium] Vectors — Addition

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

[Medium] Polynomial Division

• EN: Divide x³ + 2x² − 5x − 6 by (x − 2). What is the quotient?
• FR: Divise x³ + 2x² − 5x − 6 par (x − 2). Quel est le quotient?
• Choices: A) x² + 3x + 1 B) x² + 4x + 3 C) x² + 5x − 1 D) x² − 4x + 3
• Hint: Use synthetic division or long division — like (x³ − x² − 4x + 4) ÷ (x − 1) = x² − 4.
• Steps:
  • Synthetic division with root 2: coefficients 1, 2, −5, −6.
  • Bring down 1. 1×2=2; 2+2=4. 4×2=8; −5+8=3. 3×2=6; −6+6=0.
  • Quotient: x² + 4x + 3.
• Answer: x² + 4x + 3

[Hard] Derivative Application — Maximum

• EN: A farmer has 80 m of fencing to enclose a rectangular field along a river (no fence needed on one side). What width x maximizes the area?
• FR: Un fermier a 80 m de clôture pour entourer un champ rectangulaire le long d'une rivière (aucune clôture du côté de la rivière). Quelle largeur x maximise l'aire?
• Choices: A) x = 10 m B) x = 20 m C) x = 30 m D) x = 40 m
• Hint: Set up the constraint, write Area as a function of one variable, then find A'(x) = 0 — like P = 2x + y = 60, A = x(60 − 2x).
• Steps:
  • Fence constraint: 2x + L = 80, so L = 80 − 2x.
  • Area A = x(80 − 2x) = 80x − 2x².
  • A'(x) = 80 − 4x = 0 → x = 20. Width = 20 m.
• Answer: x = 20 m

[Hard] Binomial Theorem

• EN: Using the Binomial Theorem, find the coefficient of x² in the expansion of (x + 3)⁴.
• FR: En utilisant le théorème binomial, trouve le coefficient de x² dans le développement de (x + 3)⁴.
• Choices: A) 27 B) 54 C) 81 D) 108
• Hint: The r-th term in (a + b)ⁿ is C(n, r) × aⁿ⁻ʳ × bʳ — like the x² term in (x + 2)⁴: C(4,2) × x² × 2² = 6 × 4x² = 24x².
• Steps:
  • We need x²: so n − r = 2 → r = 2 in (x + 3)⁴.
  • Term = C(4, 2) × x² × 3² = 6 × x² × 9 = 54x².
  • The coefficient of x² is 54.
• Answer: 54