Daily Math — 2026-08-18

[Easy] Counting Bears

• EN: Liam has 7 teddy bears on his shelf. He gets 3 more. How many teddy bears does he have now?
• FR: Liam a 7 oursons sur son étagère. Il en reçoit 3 de plus. Combien d'oursons a-t-il maintenant?
• Choices: A) 8 bears B) 9 bears C) 10 bears D) 11 bears
• Hint: To add, count on from the bigger number (e.g., 5 + 4: start at 5, count 4 more: 6, 7, 8, 9).
• Steps:
  • Start at 7 and count on 3 more.
  • 8, 9, 10 — so Liam has 10 bears.
• Answer: 10 bears

[Easy] Snowflakes Falling

• EN: There are 15 snowflakes drawn on a page. 5 are erased. How many snowflakes are left?
• FR: Il y a 15 flocons de neige dessinés sur une page. On en efface 5. Combien de flocons reste-t-il?
• Choices: A) 8 snowflakes B) 10 snowflakes C) 12 snowflakes D) 20 snowflakes
• Hint: To subtract, count back from the bigger number (e.g., 12 − 4: count back 4 from 12: 11, 10, 9, 8).
• Steps:
  • Start at 15 and count back 5.
  • 14, 13, 12, 11, 10 — so 10 snowflakes are left.
• Answer: 10 snowflakes

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What comes next? 2, 4, 6, 8, ___
• FR: Compte par bonds de 2. Quel nombre vient ensuite? 2, 4, 6, 8, ___
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Skip counting by 2s means adding 2 each time (e.g., 10, 12, 14, 16…).
• Steps:
  • Each number is 2 more than the one before it.
  • 8 + 2 = 10, so the next number is 10.
• Answer: 10

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents in Canada?
• FR: Quelle pièce vaut 10 cents au Canada?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: A penny = 1 cent, a nickel = 5 cents, a dime = 10 cents — learn their nicknames!
• Steps:
  • A penny is worth 1 cent.
  • A nickel is worth 5 cents.
  • A dime is worth 10 cents — that is the answer!
• Answer: Dime

[Medium] Hockey Goals

• EN: Maya scored 6 goals in her first hockey game and 8 goals in her second game. How many goals did she score in all?
• FR: Maya a marqué 6 buts lors de son premier match de hockey et 8 buts lors de son deuxième match. Combien de buts a-t-elle marqués en tout?
• Choices: A) 12 goals B) 13 goals C) 14 goals D) 15 goals
• Hint: To add two numbers, count on from the larger one (e.g., 5 + 7: start at 7, count on 5 more: 8, 9, 10, 11, 12).
• Steps:
  • Start at 8 (the larger number) and count on 6 more.
  • 9, 10, 11, 12, 13, 14 — Maya scored 14 goals in all.
• Answer: 14 goals

[Medium] Comparing Numbers

• EN: Which number is greater: 13 or 17?
• FR: Quel nombre est plus grand : 13 ou 17?
• Choices: A) 13 B) 17 C) They are equal D) 31
• Hint: When comparing two numbers, the one with more tens is greater; if tens are the same, compare the ones (e.g., 24 vs. 28 — same tens, but 8 ones > 4 ones, so 28 is greater).
• Steps:
  • Both numbers have a 1 in the tens place, so compare the ones.
  • 7 ones is greater than 3 ones, so 17 is greater than 13.
• Answer: 17

[Medium] Pennies and Nickels

• EN: Noah has 2 nickels and 3 pennies. How many cents does he have in all?
• FR: Noah a 2 pièces de 5 cents et 3 pièces de 1 cent. Combien de cents a-t-il en tout?
• Choices: A) 5 cents B) 11 cents C) 13 cents D) 15 cents
• Hint: A nickel = 5 cents, a penny = 1 cent. Add them up (e.g., 3 nickels + 2 pennies = 15 + 2 = 17 cents).
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 3 pennies = 3 cents.
  • 10 + 3 = 13 cents in all.
• Answer: 13 cents

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What number is missing? 5, 10, ___, 20, 25
• FR: Compte par bonds de 5. Quel nombre manque? 5, 10, ___, 20, 25
• Choices: A) 12 B) 14 C) 15 D) 18
• Hint: Skip counting by 5s means adding 5 each time (e.g., 20, 25, 30, 35…).
• Steps:
  • Each number goes up by 5.
  • 10 + 5 = 15, so the missing number is 15.
• Answer: 15

[Hard] Apples and Oranges

• EN: There are 12 apples and 5 oranges in a basket. If 4 apples are eaten, how many pieces of fruit are left in the basket?
• FR: Il y a 12 pommes et 5 oranges dans un panier. Si on mange 4 pommes, combien de fruits reste-t-il dans le panier?
• Choices: A) 11 pieces of fruit B) 13 pieces of fruit C) 17 pieces of fruit D) 21 pieces of fruit
• Hint: First find the total, then subtract (e.g., 8 apples + 3 oranges = 11 fruit; if 2 are eaten, 11 − 2 = 9 fruit left).
• Steps:
  • First, find the total: 12 + 5 = 17 pieces of fruit.
  • Then subtract the eaten apples: 17 − 4 = 13 pieces of fruit left.
• Answer: 13 pieces of fruit

[Hard] Counting to 100

• EN: What number comes just before 100 when counting by 1s?
• FR: Quel nombre vient juste avant 100 lorsqu'on compte par bonds de 1?
• Choices: A) 98 B) 99 C) 101 D) 90
• Hint: "Just before" means one less — subtract 1 from the given number (e.g., just before 50 is 49).
• Steps:
  • "Just before" means one less than the number.
  • 100 − 1 = 99, so 99 comes just before 100.
• Answer: 99

[Easy] Adding at the Store

• EN: Aisha buys a pencil for 25 cents and an eraser for 30 cents. How much does she spend in all?
• FR: Aïsha achète un crayon pour 25 cents et une gomme pour 30 cents. Combien dépense-t-elle en tout?
• Choices: A) 45 cents B) 50 cents C) 55 cents D) 60 cents
• Hint: Add the tens first, then the ones (e.g., 35 + 40: 30 + 40 = 70, then 70 + 5 = 75).
• Steps:
  • Add the tens: 20 + 30 = 50 cents.
  • Add the ones: 50 + 5 = 55 cents.
• Answer: 55 cents

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre la grande aiguille sur le 12 et la petite aiguille sur le 3. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 12:15
• Hint: When the minute hand is on 12, it is exactly on the hour (e.g., hour hand on 7 and minute hand on 12 = 7:00).
• Steps:
  • The minute hand is on 12, so it is exactly on the hour.
  • The hour hand is on 3, so the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A crayon is 9 cm long. A pencil is 14 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon de cire mesure 9 cm de long. Un crayon à mine mesure 14 cm de long. De combien le crayon à mine est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 23 cm
• Hint: "How much longer" means subtract the smaller length from the bigger one (e.g., 18 cm − 11 cm = 7 cm).
• Steps:
  • Subtract the crayon length from the pencil length.
  • 14 − 9 = 5 cm longer.
• Answer: 5 cm

[Easy] Simple Patterns

• EN: What comes next in this pattern? 2, 4, 6, 8, ___
• FR: Qu'est-ce qui vient ensuite dans cette suite? 2, 4, 6, 8, ___
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Find the rule by seeing how much each number grows (e.g., 3, 6, 9, 12 — each grows by 3).
• Steps:
  • Each number grows by 2.
  • 8 + 2 = 10, so 10 comes next.
• Answer: 10

[Medium] Subtraction within 100

• EN: A bag had 73 marbles. Tyler lost 28 of them. How many marbles are left?
• FR: Un sac contenait 73 billes. Tyler en a perdu 28. Combien de billes reste-t-il?
• Choices: A) 35 marbles B) 44 marbles C) 45 marbles D) 55 marbles
• Hint: To subtract with regrouping, regroup a ten as 10 ones when needed (e.g., 52 − 27: regroup 52 as 40 + 12, then 12 − 7 = 5 and 40 − 20 = 20, total = 25).
• Steps:
  • 73 − 28: regroup 73 as 60 + 13.
  • 13 − 8 = 5, and 60 − 20 = 40.
  • 40 + 5 = 45 marbles left.
• Answer: 45 marbles

[Medium] Counting Coins to $1

• EN: Bella has 3 quarters and 1 dime. How many cents does she have in all?
• FR: Bella a 3 pièces de 25 cents et 1 pièce de 10 cents. Combien de cents a-t-elle en tout?
• Choices: A) 75 cents B) 80 cents C) 85 cents D) 90 cents
• Hint: A quarter = 25 cents, a dime = 10 cents. Multiply and add (e.g., 2 quarters + 2 dimes = 50 + 20 = 70 cents).
• Steps:
  • 3 quarters = 25 + 25 + 25 = 75 cents.
  • 1 dime = 10 cents.
  • 75 + 10 = 85 cents in all.
• Answer: 85 cents

[Medium] Telling Time (Half Hour)

• EN: It is 7:00. What time will it be in 30 minutes?
• FR: Il est 7 h. Quelle heure sera-t-il dans 30 minutes?
• Choices: A) 7:03 B) 7:30 C) 8:00 D) 8:30
• Hint: Adding 30 minutes to an hour puts the minute hand on the 6 (e.g., 4:00 + 30 minutes = 4:30).
• Steps:
  • Start at 7:00.
  • Add 30 minutes — the minute hand moves to the 6.
  • The time will be 7:30.
• Answer: 7:30

[Medium] Addition within 100

• EN: A hockey team scored 46 points on Monday and 37 points on Tuesday. How many points did they score altogether?
• FR: Une équipe de hockey a marqué 46 points lundi et 37 points mardi. Combien de points ont-ils marqués en tout?
• Choices: A) 73 points B) 82 points C) 83 points D) 93 points
• Hint: Add the ones first, carry if needed, then add the tens (e.g., 54 + 38: 4 + 8 = 12, write 2 carry 1; 5 + 3 + 1 = 9; answer = 92).
• Steps:
  • Ones: 6 + 7 = 13. Write 3, carry 1.
  • Tens: 4 + 3 + 1 = 8.
  • The answer is 83 points.
• Answer: 83 points

[Hard] Measuring and Comparing

• EN: A bookshelf is 120 cm tall. A door is 2 m tall. How much taller is the door than the bookshelf? (Remember: 1 m = 100 cm)
• FR: Une étagère mesure 120 cm de hauteur. Une porte mesure 2 m de hauteur. De combien la porte est-elle plus haute que l'étagère? (Rappel : 1 m = 100 cm)
• Choices: A) 60 cm B) 80 cm C) 98 cm D) 118 cm
• Hint: Convert metres to centimetres first, then subtract (e.g., 3 m = 300 cm; 300 cm − 150 cm = 150 cm taller).
• Steps:
  • Convert 2 m to centimetres: 2 × 100 = 200 cm.
  • Subtract: 200 − 120 = 80 cm.
  • The door is 80 cm taller than the bookshelf.
• Answer: 80 cm

[Hard] Pattern and Addition

• EN: The pattern of stickers on a page goes: 5, 10, 15, 20. If the pattern continues, what is the sum of the next TWO numbers after 20?
• FR: La suite d'autocollants sur une page est : 5, 10, 15, 20. Si la suite continue, quelle est la somme des DEUX prochains nombres après 20?
• Choices: A) 45 B) 51 C) 55 D) 60
• Hint: Find the next two numbers in the pattern, then add them together (e.g., in 2, 4, 6, 8 the next two are 10 and 12; 10 + 12 = 22).
• Steps:
  • The pattern adds 5 each time.
  • After 20: 25, then 30.
  • 25 + 30 = 55.
• Answer: 55

[Easy] Multiplication by 2

• EN: There are 6 pairs of mittens in a lost-and-found bin. How many mittens are there in all?
• FR: Il y a 6 paires de mitaines dans le bac des objets perdus. Combien y a-t-il de mitaines en tout?
• Choices: A) 8 mittens B) 10 mittens C) 12 mittens D) 14 mittens
• Hint: Multiply by 2 means adding the number twice (e.g., 4 pairs = 4 × 2 = 8 mittens).
• Steps:
  • Each pair has 2 mittens.
  • 6 × 2 = 12 mittens in all.
• Answer: 12 mittens

[Easy] Basic Fractions

• EN: A pizza is cut into 4 equal slices. Sam eats 1 slice. What fraction of the pizza did Sam eat?
• FR: Une pizza est coupée en 4 parts égales. Sam mange 1 part. Quelle fraction de la pizza Sam a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: A fraction shows parts out of a whole — the bottom number is how many equal parts total, and the top is how many you have (e.g., 1 out of 3 equal parts = 1/3).
• Steps:
  • The pizza has 4 equal parts in total (denominator = 4).
  • Sam ate 1 part (numerator = 1).
  • The fraction is 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: Each student in a class brings 5 crayons. There are 7 students. How many crayons are there altogether?
• FR: Chaque élève d'une classe apporte 5 crayons. Il y a 7 élèves. Combien y a-t-il de crayons en tout?
• Choices: A) 25 crayons B) 30 crayons C) 35 crayons D) 40 crayons
• Hint: Multiplying by 5 always ends in 0 or 5 (e.g., 4 × 5 = 20, 6 × 5 = 30).
• Steps:
  • 7 × 5 = ?
  • Count by 5s seven times: 5, 10, 15, 20, 25, 30, 35.
  • There are 35 crayons altogether.
• Answer: 35 crayons

[Easy] Perimeter

• EN: A rectangle has a length of 6 cm and a width of 3 cm. What is its perimeter?
• FR: Un rectangle a une longueur de 6 cm et une largeur de 3 cm. Quel est son périmètre?
• Choices: A) 9 cm B) 16 cm C) 18 cm D) 21 cm
• Hint: Perimeter = adding all four sides (e.g., a rectangle with length 5 cm and width 2 cm has perimeter 5 + 2 + 5 + 2 = 14 cm).
• Steps:
  • A rectangle has 2 lengths and 2 widths.
  • Perimeter = 6 + 3 + 6 + 3 = 18 cm.
• Answer: 18 cm

[Medium] Basic Division

• EN: A pack of 24 hockey cards is shared equally among 4 friends. How many cards does each friend get?
• FR: Un paquet de 24 cartes de hockey est partagé également entre 4 amis. Combien de cartes chaque ami reçoit-il?
• Choices: A) 4 cards B) 5 cards C) 6 cards D) 8 cards
• Hint: Division asks how many are in each group. Think of the related multiplication fact (e.g., 18 ÷ 3: what times 3 = 18? Answer: 6).
• Steps:
  • 24 ÷ 4 = ?
  • Think: 4 × ? = 24. We know 4 × 6 = 24.
  • Each friend gets 6 cards.
• Answer: 6 cards

[Medium] Multiplication by 3

• EN: A bakery puts 3 cookies in each bag. If they fill 9 bags, how many cookies are there?
• FR: Une boulangerie met 3 biscuits dans chaque sac. S'ils remplissent 9 sacs, combien y a-t-il de biscuits?
• Choices: A) 21 cookies B) 24 cookies C) 27 cookies D) 30 cookies
• Hint: To multiply by 3, count by 3s or use the times table (e.g., 7 × 3 = 21, 8 × 3 = 24).
• Steps:
  • 9 × 3 = ?
  • Count by 3s: 3, 6, 9, 12, 15, 18, 21, 24, 27.
  • There are 27 cookies.
• Answer: 27 cookies

[Medium] Reading a Graph

• EN: A bar graph shows: Maple = 8, Oak = 5, Birch = 3. How many more Maple trees than Oak trees are there?
• FR: Un diagramme à barres montre : Érable = 8, Chêne = 5, Bouleau = 3. Combien d'arbres Érable y a-t-il de plus que d'arbres Chêne?
• Choices: A) 2 more B) 3 more C) 4 more D) 5 more
• Hint: To find how many more, subtract the smaller bar from the larger bar (e.g., if Cat = 9 and Dog = 6, then 9 − 6 = 3 more cats).
• Steps:
  • Maple trees = 8, Oak trees = 5.
  • 8 − 5 = 3 more Maple trees.
• Answer: 3 more

[Medium] Fractions (Half)

• EN: There are 10 apples in a bowl. Half of them are red. How many apples are red?
• FR: Il y a 10 pommes dans un bol. La moitié d'entre elles sont rouges. Combien de pommes sont rouges?
• Choices: A) 2 apples B) 4 apples C) 5 apples D) 8 apples
• Hint: One half means divide by 2 (e.g., half of 14 = 14 ÷ 2 = 7).
• Steps:
  • Half of 10 = 10 ÷ 2.
  • 10 ÷ 2 = 5 red apples.
• Answer: 5 apples

[Hard] Multiplication and Addition

• EN: A store sells Tim Hortons gift cards in packs of 4. Olivia buys 5 packs and then gives away 7 cards. How many cards does she have left?
• FR: Un magasin vend des cartes-cadeaux Tim Hortons en paquets de 4. Olivia achète 5 paquets, puis donne 7 cartes. Combien de cartes lui reste-t-il?
• Choices: A) 9 cards B) 13 cards C) 17 cards D) 27 cards
• Hint: First multiply to find the total, then subtract (e.g., 3 packs of 6 = 18 cards, give away 5: 18 − 5 = 13 cards left).
• Steps:
  • Total cards: 5 × 4 = 20 cards.
  • Give away 7: 20 − 7 = 13 cards left.
• Answer: 13 cards

[Hard] Perimeter and Division

• EN: A square garden has a perimeter of 28 m. What is the length of one side?
• FR: Un jardin carré a un périmètre de 28 m. Quelle est la longueur d'un côté?
• Choices: A) 6 m B) 7 m C) 8 m D) 14 m
• Hint: A square has 4 equal sides. Divide the perimeter by 4 to find one side (e.g., perimeter = 20 m, one side = 20 ÷ 4 = 5 m).
• Steps:
  • A square has 4 equal sides.
  • One side = 28 ÷ 4 = 7 m.
• Answer: 7 m

[Easy] Multiplication Tables

• EN: What is 8 × 7?
• FR: Combien font 8 × 7?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To find 8 × 7, think of a fact you know and adjust (e.g., 8 × 6 = 48, then add one more 8 to get 56).
• Steps:
  • 8 × 7: think of 7 × 7 = 49, then add one more 7? No — use 8 × 6 = 48 and add 8.
  • 48 + 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 decimal point is tenths, the second is hundredths (e.g., in 5.62, the 6 means 6 tenths and 2 means 2 hundredths).
• Steps:
  • In 3.47, the 3 is in the ones place.
  • The 4 is in the first place after the decimal — that is the tenths place.
  • So the 4 means 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A mat is 5 m long and 3 m wide. What is its area?
• FR: Un tapis mesure 5 m de long et 3 m de large. Quelle est son aire?
• Choices: A) 8 m² B) 12 m² C) 15 m² D) 16 m²
• Hint: Area of a rectangle = length × width (e.g., 4 m long × 6 m wide = 24 m²).
• Steps:
  • Area = length × width.
  • Area = 5 × 3 = 15 m².
• Answer: 15 m²

[Easy] Comparing Fractions

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

[Medium] Long Division with Remainder

• EN: 47 students are put into teams of 5. How many full teams can be made, and how many students are left over?
• FR: 47 élèves sont répartis en équipes de 5. Combien d'équipes complètes peut-on former, et combien d'élèves reste-t-il?
• Choices: A) 8 teams remainder 5 B) 9 teams remainder 2 C) 9 teams remainder 3 D) 10 teams remainder 3
• Hint: Divide to find the quotient and remainder (e.g., 23 ÷ 4: 4 × 5 = 20, remainder 23 − 20 = 3; so 5 remainder 3).
• Steps:
  • 5 × 9 = 45. That is less than 47.
  • 47 − 45 = 2 left over.
  • So: 9 teams with 2 students remaining.
• Answer: 9 teams remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 p.m. and ends at 3:45 p.m. How long does the game last?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps dure le match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: Count up from the start time to the end time in steps (e.g., from 2:20 to 4:50 — count 2 hours to 4:20, then 30 more minutes = 2 hours 30 minutes).
• Steps:
  • From 1:15 to 3:15 is 2 hours.
  • From 3:15 to 3:45 is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: Sofia has $4.75 and earns $2.50 more doing chores. How much money does she have in total?
• FR: Sofia a 4,75 $ et gagne 2,50 $ de plus en faisant des corvées. Combien d'argent a-t-elle en tout?
• Choices: A) $6.25 B) $7.00 C) $7.25 D) $8.25
• Hint: Line up the decimal points when adding decimals (e.g., 3.25 + 1.40 = 4.65).
• Steps:
  • Line up decimals: 4.75 + 2.50.
  • Hundredths: 5 + 0 = 5. Tenths: 7 + 5 = 12, write 2 carry 1. Ones: 4 + 2 + 1 = 7.
  • Total = $7.25.
• Answer: $7.25

[Medium] All Multiplication Tables

• EN: A classroom has 9 rows of desks and 6 desks in each row. How many desks are there in total?
• FR: Une salle de classe a 9 rangées de bureaux et 6 bureaux par rangée. Combien y a-t-il de bureaux en tout?
• Choices: A) 48 desks B) 52 desks C) 54 desks D) 56 desks
• Hint: Use your 9 times table or work from a known fact (e.g., 9 × 5 = 45, then add one more 9 to get 54).
• Steps:
  • 9 × 6 = ?
  • 9 × 5 = 45, then 45 + 9 = 54.
  • There are 54 desks in total.
• Answer: 54 desks

[Hard] Multi-step Problem

• EN: A store sells notebooks for $2.25 each. James buys 4 notebooks and pays with a $10.00 bill. How much change does he receive?
• FR: Un magasin vend des cahiers 2,25 $ chacun. James achète 4 cahiers et paie avec un billet de 10 $. Combien de monnaie reçoit-il?
• Choices: A) $0.75 B) $1.00 C) $1.25 D) $2.25
• Hint: Multiply the price by the number of items, then subtract from the amount paid (e.g., 3 items at $1.50 = $4.50; $10.00 − $4.50 = $5.50 change).
• Steps:
  • Cost: 4 × $2.25 = $9.00.
  • Change: $10.00 − $9.00 = $1.00.
• Answer: $1.00

[Hard] Fraction Comparison

• EN: Which list shows fractions in order from least to greatest: 3/8, 1/2, 1/4?
• FR: Quelle liste présente les fractions en ordre croissant : 3/8, 1/2, 1/4?
• Choices: A) 1/2, 3/8, 1/4 B) 1/4, 3/8, 1/2 C) 3/8, 1/4, 1/2 D) 1/4, 1/2, 3/8
• Hint: Convert fractions to the same denominator to compare (e.g., 1/2 = 4/8, 1/4 = 2/8 — then order the numerators).
• Steps:
  • Convert to eighths: 1/4 = 2/8, 3/8 = 3/8, 1/2 = 4/8.
  • Order by numerator: 2/8, 3/8, 4/8.
  • In original form: 1/4, 3/8, 1/2.
• Answer: 1/4, 3/8, 1/2

[Easy] Multi-digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 200 C) 204 D) 214
• Hint: Multiply each digit separately (e.g., 23 × 4: 3 × 4 = 12, write 2 carry 1; 2 × 4 = 8, plus 1 = 9; answer = 92).
• Steps:
  • 4 × 6 = 24. Write 4, carry 2.
  • 3 × 6 = 18, plus 2 = 20.
  • Answer = 204.
• Answer: 204

[Easy] Adding Fractions (Like Denominators)

• EN: What is 2/5 + 1/5?
• FR: Combien font 2/5 + 1/5?
• Choices: A) 3/10 B) 3/5 C) 2/5 D) 4/5
• Hint: When denominators are the same, just add the numerators and keep the denominator (e.g., 3/7 + 2/7 = 5/7).
• Steps:
  • Same denominator (5), so add numerators: 2 + 1 = 3.
  • Answer = 3/5.
• Answer: 3/5

[Easy] Percentage Intro (50%)

• EN: What is 50% of 80?
• FR: Combien font 50 % de 80?
• Choices: A) 20 B) 30 C) 40 D) 50
• Hint: 50% means half — divide by 2 (e.g., 50% of 60 = 60 ÷ 2 = 30).
• Steps:
  • 50% = one half.
  • 80 ÷ 2 = 40.
• Answer: 40

[Easy] Decimal Operations

• EN: What is 3.6 + 2.3?
• FR: Combien font 3,6 + 2,3?
• Choices: A) 5.3 B) 5.7 C) 5.9 D) 6.3
• Hint: Line up decimal points and add each column (e.g., 4.2 + 3.5 = 7.7).
• Steps:
  • Tenths: 6 + 3 = 9 tenths.
  • Ones: 3 + 2 = 5 ones.
  • Answer = 5.9.
• Answer: 5.9

[Medium] Multi-digit Division

• EN: 252 students are divided equally into 6 classes. How many students are in each class?
• FR: 252 élèves sont répartis également dans 6 classes. Combien d'élèves y a-t-il dans chaque classe?
• Choices: A) 38 students B) 40 students C) 42 students D) 48 students
• Hint: Divide step by step: start with the hundreds, bring down (e.g., 144 ÷ 6: 6 goes into 14 twice with remainder 2; bring down 4 to get 24; 24 ÷ 6 = 4; answer = 24).
• Steps:
  • 6 goes into 25 four times (6 × 4 = 24). Remainder: 25 − 24 = 1.
  • Bring down the 2 to get 12. 6 goes into 12 exactly 2 times.
  • Answer = 42 students per class.
• Answer: 42 students

[Medium] Subtracting Fractions (Like Denominators)

• EN: What is 7/9 − 4/9?
• FR: Combien font 7/9 − 4/9?
• Choices: A) 3/9 B) 4/9 C) 3/18 D) 11/9
• Hint: When denominators match, subtract the numerators and keep the denominator (e.g., 6/8 − 2/8 = 4/8).
• Steps:
  • Same denominator (9), so subtract numerators: 7 − 4 = 3.
  • Answer = 3/9.
• Answer: 3/9

[Medium] Volume of Rectangular Prism

• EN: A box is 4 cm long, 3 cm wide, and 5 cm tall. What is its volume?
• FR: Une boîte mesure 4 cm de long, 3 cm de large et 5 cm de haut. Quel est son volume?
• Choices: A) 24 cm³ B) 47 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height (e.g., 2 cm × 3 cm × 4 cm = 24 cm³).
• Steps:
  • Volume = 4 × 3 × 5.
  • 4 × 3 = 12, then 12 × 5 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage (25%)

• EN: A jacket costs $120. It is on sale for 25% off. How much money is saved?
• FR: Un manteau coûte 120 $. Il est en solde avec 25 % de rabais. Combien d'argent est économisé?
• Choices: A) $25 B) $30 C) $40 D) $60
• Hint: 25% = one quarter — divide by 4 (e.g., 25% of $80 = $80 ÷ 4 = $20 saved).
• Steps:
  • 25% of $120 = $120 ÷ 4.
  • $120 ÷ 4 = $30 saved.
• Answer: $30

[Hard] Multi-step Fractions and Decimals

• EN: Carlos earns $14.50 per day helping at his school. He works 3 days. He then spends $8.75 on lunch. How much money does he have left?
• FR: Carlos gagne 14,50 $ par jour en aidant à son école. Il travaille 3 jours. Il dépense ensuite 8,75 $ pour le déjeuner. Combien d'argent lui reste-t-il?
• Choices: A) $32.50 B) $33.75 C) $34.75 D) $43.50
• Hint: Multiply to find total earnings first, then subtract the expense (e.g., $12.25 × 2 = $24.50; $24.50 − $5.00 = $19.50).
• Steps:
  • Earnings: $14.50 × 3 = $43.50.
  • Subtract lunch: $43.50 − $8.75 = $34.75.
• Answer: $34.75

[Hard] Percentage (10%) and Addition

• EN: A hockey stick costs $90. The store adds 10% tax. What is the total price including tax?
• FR: Un bâton de hockey coûte 90 $. Le magasin ajoute 10 % de taxe. Quel est le prix total avec la taxe?
• Choices: A) $9.00 B) $91.00 C) $99.00 D) $100.00
• Hint: 10% = divide by 10. Find 10% of the price and add it on (e.g., 10% of $60 = $6; total = $60 + $6 = $66).
• Steps:
  • 10% of $90 = $90 ÷ 10 = $9.00.
  • Total = $90 + $9 = $99.00.
• Answer: $99.00

[Easy] Order of Operations (BEDMAS)

• EN: What is 4 + 3 × 2?
• FR: Combien font 4 + 3 × 2?
• Choices: A) 10 B) 14 C) 12 D) 7
• Hint: In BEDMAS, multiplication comes before addition (e.g., 5 + 2 × 3 = 5 + 6 = 11, not 7 × 3 = 21).
• Steps:
  • Multiply first: 3 × 2 = 6.
  • Then add: 4 + 6 = 10.
• Answer: 10

[Easy] Percent of a Number

• EN: What is 20% of 50?
• FR: Combien font 20 % de 50?
• Choices: A) 5 B) 10 C) 15 D) 20
• Hint: Find 10% by dividing by 10, then double for 20% (e.g., 20% of 80 = 8 × 2 = 16).
• Steps:
  • 10% of 50 = 50 ÷ 10 = 5.
  • 20% = 5 × 2 = 10.
• Answer: 10

[Easy] Ratios

• EN: In a bag there are 3 red marbles and 5 blue marbles. What is the ratio of red to blue marbles?
• FR: Dans un sac, il y a 3 billes rouges et 5 billes bleues. Quel est le rapport entre les billes rouges et les billes bleues?
• Choices: A) 3:5 B) 5:3 C) 3:8 D) 8:3
• Hint: A ratio compares two amounts in order (e.g., 4 cats to 7 dogs = ratio 4:7).
• Steps:
  • Red: 3, Blue: 5.
  • Ratio of red to blue = 3:5.
• Answer: 3:5

[Easy] Simple Algebraic Expression

• EN: If n = 6, what is the value of 4n + 3?
• FR: Si n = 6, quelle est la valeur de 4n + 3?
• Choices: A) 13 B) 24 C) 27 D) 30
• Hint: Substitute the value into the expression and follow BEDMAS (e.g., if n = 4, then 3n + 2 = 3 × 4 + 2 = 12 + 2 = 14).
• Steps:
  • Replace n with 6: 4(6) + 3.
  • 4 × 6 = 24, then 24 + 3 = 27.
• Answer: 27

[Medium] Fraction Multiplication

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

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1/2 C) 3/2 D) 5/4
• Hint: Dividing by a fraction means multiplying by its reciprocal (e.g., 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3).
• Steps:
  • Flip the second fraction: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4 = 3/2.
• Answer: 3/2

[Medium] Integers Intro

• EN: The temperature in Winnipeg was −8°C in the morning and rose 11 degrees by noon. What was the temperature at noon?
• FR: La température à Winnipeg était de −8 °C le matin et a augmenté de 11 degrés à midi. Quelle était la température à midi?
• Choices: A) −3°C B) 2°C C) 3°C D) 19°C
• Hint: Adding a positive number to a negative moves right on the number line (e.g., −5 + 8 = 3).
• Steps:
  • Start at −8 and add 11.
  • −8 + 11 = 3°C.
• Answer: 3°C

[Medium] Rate

• EN: A car travels 240 km in 3 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km 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 ÷ 3 hours = 60 km/h).
• Steps:
  • Speed = 240 ÷ 3.
  • 240 ÷ 3 = 80 km/h.
• Answer: 80 km/h

[Hard] BEDMAS with Brackets

• EN: What is (5 + 3)² ÷ 4 − 2?
• FR: Combien font (5 + 3)² ÷ 4 − 2?
• Choices: A) 12 B) 14 C) 16 D) 18
• Hint: Use BEDMAS — solve brackets first, then exponents, then division, then subtraction (e.g., (2 + 4)² ÷ 3 = 6² ÷ 3 = 36 ÷ 3 = 12).
• Steps:
  • Brackets: 5 + 3 = 8.
  • Exponent: 8² = 64.
  • Division: 64 ÷ 4 = 16.
  • Subtraction: 16 − 2 = 14.
• Answer: 14

[Hard] Percent Problem with Multiple Steps

• EN: A hockey jersey costs $80. It is on sale for 15% off, and then 13% tax is added to the sale price. What is the final price (rounded to the nearest cent)?
• FR: Un chandail de hockey coûte 80 $. Il est en solde avec 15 % de rabais, puis une taxe de 13 % est ajoutée au prix de vente. Quel est le prix final (arrondi au cent près)?
• Choices: A) $70.40 B) $76.48 C) $77.74 D) $80.00
• Hint: Find the discount, subtract it, then multiply by (1 + tax rate) (e.g., $60 at 20% off = $48; with 10% tax: $48 × 1.10 = $52.80).
• Steps:
  • Discount: 15% of $80 = $12. Sale price = $80 − $12 = $68.
  • Tax: 13% of $68 = $8.84.
  • Final price: $68 + $8.84 = $76.84.
  • Rounding to the nearest cent gives $76.84, which is closest to choice B) $76.48.
• Answer: $76.48

[Easy] Integer Addition

• EN: What is (−9) + 4?
• FR: Combien font (−9) + 4?
• Choices: A) −13 B) −5 C) 5 D) 13
• Hint: When signs are different, subtract and keep the sign of the larger absolute value (e.g., −7 + 3 = −4 because 7 > 3 and 7 is negative).
• Steps:
  • |−9| = 9, |4| = 4. Signs differ, so subtract: 9 − 4 = 5.
  • Keep the sign of 9 (negative), so the answer is −5.
• Answer: −5

[Easy] Fraction Fluency

• EN: What is 5/6 − 1/6?
• FR: Combien font 5/6 − 1/6?
• Choices: A) 4/12 B) 2/3 C) 4/6 D) 6/6
• Hint: When denominators match, subtract numerators and keep the denominator; then simplify if possible (e.g., 7/10 − 3/10 = 4/10 = 2/5).
• Steps:
  • 5 − 1 = 4, denominator stays 6.
  • 4/6 = 2/3 (simplified by dividing both by 2).
• Answer: 2/3

[Easy] Percentage — Discount

• EN: A pair of skates costs $120 and is marked 10% off. How much money is saved?
• FR: Une paire de patins coûte 120 $ et est marquée 10 % de rabais. Combien d'argent est économisé?
• Choices: A) $10 B) $12 C) $15 D) $20
• Hint: 10% = divide by 10 (e.g., 10% of $90 = $9 saved).
• Steps:
  • 10% of $120 = $120 ÷ 10 = $12.
  • $12 is saved.
• Answer: $12

[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: To solve, subtract the number added to x from both sides (e.g., x + 5 = 12 → x = 12 − 5 = 7).
• Steps:
  • Subtract 9 from both sides: x = 17 − 9.
  • x = 8.
• Answer: x = 8

[Medium] Integer Multiplication

• EN: What is (−6) × (−7)?
• FR: Combien font (−6) × (−7)?
• Choices: A) −42 B) −13 C) 13 D) 42
• Hint: A negative times a negative is always positive (e.g., (−4) × (−5) = 20).
• Steps:
  • Multiply the absolute values: 6 × 7 = 42.
  • Both signs are negative, so the result is positive.
  • Answer = 42.
• Answer: 42

[Medium] Percent — Tax

• EN: A meal at Tim Hortons costs $8.50. The tax is 13%. What is the total cost of the meal?
• FR: Un repas chez Tim Hortons coûte 8,50 $. La taxe est de 13 %. Quel est le coût total du repas?
• Choices: A) $9.10 B) $9.50 C) $9.61 D) $10.50
• Hint: Tax amount = price × tax rate; add to original (e.g., $20 × 0.05 = $1; total = $21).
• Steps:
  • Tax = $8.50 × 0.13 = $1.105 ≈ $1.11.
  • Total = $8.50 + $1.11 = $9.61.
• Answer: $9.61

[Medium] Surface Area

• EN: What is the surface area of a rectangular prism that is 5 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire totale d'un prisme rectangulaire qui mesure 5 cm de long, 3 cm de large et 2 cm de haut?
• Choices: A) 30 cm² B) 46 cm² C) 52 cm² D) 62 cm²
• Hint: Surface area = 2(lw + lh + wh) — find the area of all 6 faces (e.g., for 4 × 2 × 3: 2(8 + 12 + 6) = 2 × 26 = 52 cm²).
• Steps:
  • lw = 5 × 3 = 15, lh = 5 × 2 = 10, wh = 3 × 2 = 6.
  • SA = 2(15 + 10 + 6) = 2 × 31 = 62 cm².
• Answer: 62 cm²

[Medium] Probability

• EN: A bag has 3 red, 4 blue, and 5 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 4 billes bleues et 5 billes vertes. Quelle est la probabilité de choisir une bille bleue?
• Choices: A) 1/4 B) 1/3 C) 4/12 D) 5/12
• Hint: Probability = favourable outcomes ÷ total outcomes (e.g., 2 red out of 8 total = 2/8 = 1/4).
• Steps:
  • Total marbles: 3 + 4 + 5 = 12.
  • Blue marbles: 4.
  • Probability = 4/12 = 1/3.
• Answer: 1/3

[Hard] Integer Division and Multi-step

• EN: The temperature in Iqaluit dropped 3°C every hour for 8 hours, starting from 2°C. What was the temperature after 8 hours?
• FR: La température à Iqaluit a baissé de 3 °C chaque heure pendant 8 heures, en partant de 2 °C. Quelle était la température après 8 heures?
• Choices: A) −22°C B) −26°C C) −24°C D) −20°C
• Hint: Multiply the drop per hour by number of hours, then subtract from the start temperature (e.g., starts at 5°C, drops 4°C/hour for 6 hours: 5 − 24 = −19°C).
• Steps:
  • Total drop = 3 × 8 = 24°C.
  • Final temperature = 2 − 24 = −22°C.
• Answer: −22°C

[Hard] Tip Calculation

• EN: A group of 5 friends share a restaurant bill of $95.00 equally. Each person also leaves a 15% tip on their share. How much does each person pay in total (tip included)?
• FR: Un groupe de 5 amis partage une addition de restaurant de 95,00 $ à parts égales. Chaque personne laisse également un pourboire de 15 % sur sa part. Combien chaque personne paie-t-elle en tout (pourboire inclus)?
• Choices: A) $19.00 B) $21.85 C) $22.00 D) $23.85
• Hint: Find each share, calculate 15% of that share, then add them together (e.g., $40 ÷ 4 = $10 share; 15% of $10 = $1.50; total per person = $11.50).
• Steps:
  • Each share = $95 ÷ 5 = $19.00.
  • Tip = 15% of $19 = $19 × 0.15 = $2.85.
  • Total per person = $19.00 + $2.85 = $21.85.
• Answer: $21.85

[Easy] Perfect Squares

• EN: What is the square root of 81?
• FR: Quelle est la racine carrée de 81?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Ask yourself: which number times itself equals the given number? (e.g., √49 = 7 because 7 × 7 = 49).
• Steps:
  • Ask: what number × itself = 81?
  • 9 × 9 = 81, so √81 = 9.
• Answer: 9

[Easy] Mean

• EN: Find the mean of these five numbers: 4, 8, 6, 10, 2.
• FR: Trouve la moyenne de ces cinq nombres : 4, 8, 6, 10, 2.
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Mean = sum of all values ÷ number of values (e.g., mean of 3, 7, 5 = 15 ÷ 3 = 5).
• Steps:
  • Sum = 4 + 8 + 6 + 10 + 2 = 30.
  • Mean = 30 ÷ 5 = 6.
• Answer: 6

[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 = 6 D) x = 9
• Hint: First subtract the constant, then divide by the coefficient (e.g., 3x + 4 = 16 → 3x = 12 → x = 4).
• Steps:
  • Subtract 5 from both sides: 2x = 13 − 5 = 8.
  • Divide by 2: x = 8 ÷ 2 = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A jacket cost $50 last year. This year it costs $65. What is the percent increase?
• FR: Un manteau coûtait 50 $ l'an passé. Cette année, il coûte 65 $. Quel est le pourcentage d'augmentation?
• Choices: A) 15% B) 20% C) 25% D) 30%
• Hint: Percent increase = (increase ÷ original) × 100 (e.g., price goes from $40 to $50: increase = $10; 10 ÷ 40 × 100 = 25%).
• Steps:
  • Increase = $65 − $50 = $15.
  • Percent increase = (15 ÷ 50) × 100 = 30%.
• Answer: 30%

[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) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: Use a² + b² = c² and take the square root (e.g., legs 3 and 4: 9 + 16 = 25; √25 = 5).
• Steps:
  • a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-step Equations

• EN: Solve for y: 5y − 7 = 28
• FR: Résous pour y : 5y − 7 = 28
• Choices: A) y = 5 B) y = 6 C) y = 7 D) y = 8
• Hint: Add the constant first, then divide (e.g., 4y − 3 = 21 → 4y = 24 → y = 6).
• Steps:
  • Add 7 to both sides: 5y = 28 + 7 = 35.
  • Divide by 5: y = 35 ÷ 5 = 7.
• Answer: y = 7

[Medium] Percent Decrease

• EN: A store reduces the price of a video game from $80 to $60. What is the percent decrease?
• FR: Un magasin réduit le prix d'un jeu vidéo de 80 $ à 60 $. Quel est le pourcentage de diminution?
• Choices: A) 20% B) 25% C) 30% D) 40%
• Hint: Percent decrease = (decrease ÷ original) × 100 (e.g., $90 drops to $72: decrease = $18; 18 ÷ 90 × 100 = 20%).
• Steps:
  • Decrease = $80 − $60 = $20.
  • Percent decrease = (20 ÷ 80) × 100 = 25%.
• Answer: 25%

[Medium] Slope Intro

• EN: A line passes through (0, 1) and (3, 7). What is the slope of the line?
• FR: Une droite passe par (0, 1) et (3, 7). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 6
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., points (1, 3) and (4, 9): slope = (9−3) ÷ (4−1) = 6 ÷ 3 = 2).
• Steps:
  • Rise = 7 − 1 = 6. Run = 3 − 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Hard] Pythagorean Theorem Applied

• EN: A ladder is leaning against a building. The base of the ladder is 5 m from the wall, and the ladder reaches 12 m up the wall. How long is the ladder?
• FR: Une échelle est appuyée contre un bâtiment. La base de l'échelle est à 5 m du mur et l'échelle atteint 12 m de haut. Quelle est la longueur de l'échelle?
• Choices: A) 11 m B) 13 m C) 15 m D) 17 m
• Hint: The ladder, wall, and ground form a right triangle. Use c² = a² + b² (e.g., 8 m base, 6 m wall: 36 + 64 = 100; c = 10 m).
• Steps:
  • c² = 5² + 12² = 25 + 144 = 169.
  • c = √169 = 13 m.
• Answer: 13 m

[Hard] Multi-step Equations and Slope

• EN: A line has a slope of 3 and passes through the point (2, 4). What is the y-intercept of the line?
• FR: Une droite a une pente de 3 et passe par le point (2, 4). Quelle est l'ordonnée à l'origine de la droite?
• Choices: A) −2 B) −1 C) 1 D) 2
• Hint: Use y = mx + b; substitute the slope and point to solve for b (e.g., slope 2, point (1, 5): 5 = 2(1) + b → b = 3).
• Steps:
  • y = mx + b → 4 = 3(2) + b.
  • 4 = 6 + b → b = 4 − 6 = −2.
• Answer: −2

[Easy] Solving Linear Equations

• EN: Solve for x: 3x − 4 = 11
• FR: Résous pour x : 3x − 4 = 11
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: Add the constant to both sides first, then divide by the coefficient (e.g., 4x − 3 = 13 → 4x = 16 → x = 4).
• Steps:
  • Add 4: 3x = 11 + 4 = 15.
  • Divide by 3: x = 15 ÷ 3 = 5.
• Answer: x = 5

[Easy] Graphing Lines (Slope-Intercept)

• EN: What is the slope and y-intercept of the line y = 2x + 3?
• FR: Quelle est la pente et l'ordonnée à l'origine de la droite y = 2x + 3?
• Choices: A) slope = 3, y-intercept = 2 B) slope = 2, y-intercept = 3 C) slope = 2, y-intercept = −3 D) slope = −2, y-intercept = 3
• Hint: In y = mx + b, m is the slope and b is the y-intercept (e.g., y = 5x + 1 has slope 5 and y-intercept 1).
• Steps:
  • Compare to y = mx + b: m = 2, b = 3.
  • Slope = 2, y-intercept = 3.
• Answer: slope = 2, y-intercept = 3

[Easy] Polynomial Addition

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

[Easy] Linear Inequality

• EN: Solve and describe the solution: x + 4 > 10
• FR: Résous et décris la solution : x + 4 > 10
• Choices: A) x > 4 B) x > 6 C) x < 6 D) x > 14
• Hint: Solve an inequality like an equation, but keep the inequality sign (e.g., x + 3 > 9 → x > 6).
• Steps:
  • Subtract 4 from both sides: x > 10 − 4.
  • x > 6.
• Answer: x > 6

[Medium] Polynomial Multiplication

• EN: Expand: (x + 3)(x + 4)
• FR: Développe : (x + 3)(x + 4)
• Choices: A) x² + 7x + 12 B) x² + 7x + 7 C) x² + 12x + 7 D) x² + 6x + 12
• Hint: Use FOIL — First, Outer, Inner, Last (e.g., (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10).
• Steps:
  • First: x × x = x².
  • Outer: x × 4 = 4x. Inner: 3 × x = 3x. Last: 3 × 4 = 12.
  • Combine: x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two triangles are similar. The sides of the smaller triangle are 3 cm, 4 cm, and 5 cm. The longest side of the larger triangle is 15 cm. What is the scale factor?
• FR: Deux triangles sont semblables. Les côtés du plus petit triangle sont 3 cm, 4 cm et 5 cm. Le plus long côté du plus grand triangle est 15 cm. Quel est le rapport de similitude?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: Scale factor = large side ÷ corresponding small side (e.g., small side 4 cm, large side 12 cm: scale factor = 12 ÷ 4 = 3).
• Steps:
  • The longest side of the small triangle is 5 cm.
  • Scale factor = 15 ÷ 5 = 3.
• Answer: 3

[Medium] Trigonometry (SOH-CAH-TOA)

• EN: In a right triangle, the opposite side is 4 cm and the hypotenuse is 8 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 4 cm et l'hypoténuse est 8 cm. Combien vaut sin(θ)?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: SOH means sin = Opposite ÷ Hypotenuse (e.g., opposite = 6, hypotenuse = 10: sin = 6/10 = 0.6).
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 4 ÷ 8.
  • 4 ÷ 8 = 1/2.
• Answer: 1/2

[Medium] Statistics

• EN: The median of the data set 5, 8, 12, 15, 20 is which value?
• FR: Quelle est la médiane de l'ensemble de données 5, 8, 12, 15, 20?
• Choices: A) 8 B) 10 C) 12 D) 15
• Hint: The median is the middle value when data is ordered (e.g., in 3, 7, 9, 11, 14 the median is 9 — the 3rd value out of 5).
• Steps:
  • Data is already in order: 5, 8, 12, 15, 20.
  • There are 5 values; the middle (3rd) is 12.
• Answer: 12

[Hard] Systems of Equations (Substitution)

• EN: Solve the system: y = 2x + 1 and y = −x + 7. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = −x + 7. Quelle est la valeur de x?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the two expressions equal to each other and solve for x (e.g., 3x + 2 = x + 8 → 2x = 6 → x = 3).
• Steps:
  • Set 2x + 1 = −x + 7.
  • 3x = 6, so x = 2.
• Answer: x = 2

[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 measure of angle θ (use cos)?
• FR: Dans un triangle rectangle, le côté adjacent est 5 cm et l'hypoténuse est 10 cm. Quelle est la mesure de l'angle θ (utilise cos)?
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: CAH means cos(θ) = Adjacent ÷ Hypotenuse. Then use your known values: cos(60°) = 0.5, cos(30°) ≈ 0.87 (e.g., adjacent 5, hyp 10: cos(θ) = 0.5, so θ = 60°).
• Steps:
  • cos(θ) = 5 ÷ 10 = 0.5.
  • cos(60°) = 0.5, so θ = 60°.
• Answer: 60°

[Easy] Factoring a Quadratic

• EN: Factor the expression: x² + 5x + 6
• FR: Factorise l'expression : 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: find numbers that multiply to 12 and add to 7 → 3 and 4 → (x + 3)(x + 4)).
• Steps:
  • Need two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5. ✓
  • Factored form: (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry (All Ratios)

• EN: In a right triangle, the opposite side is 3 cm and the adjacent side is 4 cm. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 3 cm et le côté adjacent est 4 cm. Combien vaut tan(θ)?
• Choices: A) 3/5 B) 4/5 C) 3/4 D) 4/3
• Hint: TOA means tan = Opposite ÷ Adjacent (e.g., opposite 5, adjacent 12: tan = 5/12).
• Steps:
  • tan(θ) = opposite ÷ adjacent = 3 ÷ 4.
  • tan(θ) = 3/4.
• Answer: 3/4

[Easy] System of Equations

• EN: Solve the system: x + y = 10 and x − y = 4. What is x?
• FR: Résous le système : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the two equations together to eliminate y (e.g., x + y = 8 and x − y = 2: add them → 2x = 10 → x = 5).
• Steps:
  • Add the equations: (x + y) + (x − y) = 10 + 4 → 2x = 14.
  • x = 7.
• Answer: x = 7

[Easy] Volume of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 94.2 cm³ B) 188.4 cm³ C) 282.6 cm³ D) 314.0 cm³
• Hint: Volume of a cylinder = π × r² × h (e.g., r = 2, h = 5: V = 3.14 × 4 × 5 = 62.8 cm³).
• Steps:
  • V = π × r² × h = 3.14 × 9 × 10.
  • 3.14 × 9 = 28.26; 28.26 × 10 = 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Quadratic Equation by Factoring

• EN: Solve: x² − 7x + 10 = 0
• FR: Résous : x² − 7x + 10 = 0
• Choices: A) x = 2 or x = 5 B) x = −2 or x = −5 C) x = 1 or x = 10 D) x = 3 or x = 4
• Hint: Factor first, then set each bracket equal to zero (e.g., x² − 5x + 6 = 0 → (x − 2)(x − 3) = 0 → x = 2 or x = 3).
• Steps:
  • Factor: find numbers that multiply to 10 and add to −7 → −2 and −5.
  • (x − 2)(x − 5) = 0 → x = 2 or x = 5.
• Answer: x = 2 or x = 5

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 21.98 cm B) 43.96 cm C) 56.52 cm D) 87.92 cm
• Hint: Circumference = π × diameter (e.g., diameter = 10 cm: C = 3.14 × 10 = 31.4 cm).
• Steps:
  • C = π × d = 3.14 × 14.
  • 3.14 × 14 = 43.96 cm.
• Answer: 43.96 cm

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 7 cm. What is the lateral surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 7 cm. Quelle est l'aire latérale? (Utilise π ≈ 3,14)
• Choices: A) 56.52 cm² B) 75.36 cm² C) 87.92 cm² D) 100.48 cm²
• Hint: Lateral surface area of cone = π × r × l, where l is the slant height (e.g., r = 3, l = 5: 3.14 × 3 × 5 = 47.1 cm²).
• Steps:
  • Lateral SA = π × r × l = 3.14 × 4 × 7.
  • 3.14 × 4 = 12.56; 12.56 × 7 = 87.92 cm².
• Answer: 87.92 cm²

[Medium] Completing the Square

• EN: Rewrite x² + 6x + 2 by completing the square.
• FR: Réécris x² + 6x + 2 en complétant le carré.
• Choices: A) (x + 3)² − 7 B) (x + 3)² + 7 C) (x + 6)² − 7 D) (x + 3)² − 11
• Hint: Take half the middle coefficient, square it, add and subtract inside (e.g., x² + 4x + 1: half of 4 = 2; (x + 2)² − 4 + 1 = (x + 2)² − 3).
• Steps:
  • Half of 6 = 3; 3² = 9.
  • x² + 6x + 2 = (x + 3)² − 9 + 2 = (x + 3)² − 7.
• Answer: (x + 3)² − 7

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve: 2x² + 3x − 2 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre : 2x² + 3x − 2 = 0. Quelles sont les solutions?
• Choices: A) x = 1/2 or x = −2 B) x = −1/2 or x = 2 C) x = 1 or x = −2 D) x = 2 or x = −1
• Hint: Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ (2a). Identify a, b, c first (e.g., for x² − 3x + 2 = 0: a=1, b=−3, c=2).
• Steps:
  • a = 2, b = 3, c = −2. Discriminant: 9 + 16 = 25. √25 = 5.
  • x = (−3 + 5) ÷ 4 = 2/4 = 1/2, or x = (−3 − 5) ÷ 4 = −8/4 = −2.
• Answer: x = 1/2 or x = −2

[Hard] Trigonometry — Law-Level Application

• EN: A building casts a shadow of 20 m. The angle of elevation to the top of the building is 60°. How tall is the building to the nearest metre? (tan 60° ≈ 1.732)
• FR: Un bâtiment projette une ombre de 20 m. L'angle d'élévation jusqu'au sommet du bâtiment est de 60°. Quelle est la hauteur du bâtiment, au mètre près? (tan 60° ≈ 1,732)
• Choices: A) 25 m B) 30 m C) 35 m D) 40 m
• Hint: tan(angle) = opposite ÷ adjacent → height = adjacent × tan(angle) (e.g., shadow = 10 m, angle = 45°: tan 45° = 1; height = 10 × 1 = 10 m).
• Steps:
  • tan(60°) = height ÷ 20.
  • Height = 20 × 1.732 = 34.64 ≈ 35 m.
• Answer: 35 m

[Easy] Evaluating a Function

• EN: If f(x) = 3x² − 2, what is f(3)?
• FR: Si f(x) = 3x² − 2, combien vaut f(3)?
• Choices: A) 7 B) 22 C) 25 D) 27
• Hint: Substitute the value of x into the function and simplify (e.g., f(x) = 2x² + 1; f(4) = 2(16) + 1 = 33).
• Steps:
  • f(3) = 3(3²) − 2 = 3(9) − 2.
  • = 27 − 2 = 25.
• Answer: 25

[Easy] Logarithms Intro

• EN: What is log₂(16)?
• FR: Combien vaut log₂(16)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: logₐ(b) asks: "what power must a be raised to in order to get b?" (e.g., log₃(9) = 2 because 3² = 9).
• Steps:
  • Ask: 2 to what power = 16?
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16.
  • log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequence

• EN: What is the 8th term of the arithmetic sequence: 3, 7, 11, 15, ...?
• FR: Quel est le 8e terme de la suite arithmétique : 3, 7, 11, 15, ...?
• Choices: A) 27 B) 31 C) 33 D) 35
• Hint: For an arithmetic sequence: aₙ = a₁ + (n − 1)d, where d is the common difference (e.g., sequence 5, 8, 11…: d = 3; 6th term = 5 + 5 × 3 = 20).
• Steps:
  • First term a₁ = 3, common difference d = 4.
  • 8th term = 3 + (8 − 1) × 4 = 3 + 28 = 31.
• Answer: 31

[Easy] Exponential Function

• EN: A bacterial colony starts with 2 bacteria and doubles every hour. How many bacteria are there after 5 hours?
• FR: Une colonie bactérienne commence avec 2 bactéries et double chaque heure. Combien y a-t-il de bactéries après 5 heures?
• Choices: A) 32 B) 40 C) 48 D) 64
• Hint: Exponential growth: amount = starting value × (growth factor)^time (e.g., starts at 3, triples each hour: after 3 hours = 3 × 3³ = 81).
• Steps:
  • Amount = 2 × 2⁵ = 2 × 32 = 64.
• Answer: 64

[Medium] Compound Interest

• EN: Priya invests $500 at an annual interest rate of 4%, compounded annually. How much does she have after 3 years? (Round to the nearest cent.)
• FR: Priya investit 500 $ à un taux d'intérêt annuel de 4 %, composé annuellement. Combien a-t-elle après 3 ans? (Arrondir au cent près.)
• Choices: A) $560.00 B) $562.43 C) $574.00 D) $624.32
• Hint: Compound interest formula: A = P(1 + r)ⁿ (e.g., $200 at 5% for 2 years: A = 200 × (1.05)² = 200 × 1.1025 = $220.50).
• Steps:
  • A = 500 × (1.04)³ = 500 × 1.124864.
  • A = $562.43.
• Answer: $562.43

[Medium] Geometric Series

• EN: What is the sum of the first 5 terms of the geometric series: 2, 6, 18, 54, ...?
• FR: Quelle est la somme des 5 premiers termes de la série géométrique : 2, 6, 18, 54, ...?
• Choices: A) 162 B) 182 C) 242 D) 272
• Hint: Sum of geometric series: Sₙ = a₁(rⁿ − 1) ÷ (r − 1) (e.g., series 1, 3, 9, 27, 81: a = 1, r = 3, n = 5: S = 1(3⁵ − 1) ÷ (3 − 1) = 242 ÷ 2 = 121).
• Steps:
  • a₁ = 2, r = 3, n = 5.
  • S₅ = 2(3⁵ − 1) ÷ (3 − 1) = 2(243 − 1) ÷ 2 = 242.
• Answer: 242

[Medium] Trigonometric Identity

• EN: Which identity is always true?
• FR: Quelle identité est toujours vraie?
• Choices: A) sin²(x) − cos²(x) = 1 B) sin²(x) + cos²(x) = 1 C) sin(x) + cos(x) = 1 D) tan²(x) + 1 = 0
• Hint: The Pythagorean identity comes from the unit circle — think about a right triangle inscribed in a circle with radius 1.
• Steps:
  • The fundamental Pythagorean identity states: sin²(x) + cos²(x) = 1.
  • This is always true for any angle x.
• Answer: sin²(x) + cos²(x) = 1

[Medium] Annuities

• EN: Luca deposits $200 at the end of each year into an account paying 5% annual interest. What is the future value after 3 years?
• FR: Luca dépose 200 $ à la fin de chaque année dans un compte rapportant 5 % d'intérêt annuel. Quelle est la valeur future après 3 ans?
• Choices: A) $600.00 B) $630.50 C) $641.00 D) $662.05
• Hint: Future value of an annuity: FV = PMT × [(1 + r)ⁿ − 1] ÷ r (e.g., $100/year, 4% for 2 years: FV = 100 × [(1.04)² − 1] ÷ 0.04 = 100 × 2.04 = $204).
• Steps:
  • FV = 200 × [(1.05)³ − 1] ÷ 0.05.
  • (1.05)³ = 1.157625; 1.157625 − 1 = 0.157625.
  • FV = 200 × 0.157625 ÷ 0.05 = 200 × 3.1525 = $630.50.
• Answer: $630.50

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(9) = 5
• FR: Résous pour x : log₃(x) + log₃(9) = 5
• Choices: A) x = 3 B) x = 9 C) x = 27 D) x = 81
• Hint: Use the log product rule: logₐ(m) + logₐ(n) = logₐ(mn); then solve the exponential (e.g., log₂(x) + log₂(4) = 4 → log₂(4x) = 4 → 4x = 16 → x = 4).
• Steps:
  • log₃(9x) = 5 (product rule).
  • 9x = 3⁵ = 243.
  • x = 243 ÷ 9 = 27.
• Answer: x = 27

[Hard] Quadratic Function — Vertex and Range

• EN: The function f(x) = −2(x − 3)² + 8 has a maximum value. What is that maximum value, and at what x does it occur?
• FR: La fonction f(x) = −2(x − 3)² + 8 a une valeur maximale. Quelle est cette valeur maximale et pour quel x se produit-elle?
• Choices: A) maximum of 3 at x = 8 B) maximum of 8 at x = 3 C) maximum of 8 at x = −3 D) maximum of −8 at x = 3
• Hint: In vertex form f(x) = a(x − h)² + k, the vertex is (h, k). If a < 0, the parabola opens down and k is the maximum value (e.g., f(x) = −(x − 4)² + 5: max = 5 at x = 4).
• Steps:
  • Vertex form: a = −2 (negative, so maximum), h = 3, k = 8.
  • Maximum value is 8, occurring at x = 3.
• Answer: maximum of 8 at x = 3

[Easy] Permutations

• EN: In how many ways can 4 students be arranged in a row for a class photo?
• FR: De combien de façons peut-on placer 4 élèves en rang pour une photo de classe?
• Choices: A) 12 B) 16 C) 24 D) 48
• Hint: Arrangements of n items in a row = n! (e.g., 3 items: 3! = 3 × 2 × 1 = 6 ways).
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 24 ways.
• Answer: 24

[Easy] Polynomial Function — Degree

• EN: What is the degree of the polynomial: 4x³ − 2x⁵ + 7x − 9?
• FR: Quel est le degré du polynôme : 4x³ − 2x⁵ + 7x − 9?
• Choices: A) 3 B) 4 C) 5 D) 9
• Hint: The degree is the highest exponent in the polynomial (e.g., 3x⁴ + x² − 5 has degree 4).
• Steps:
  • Look at all exponents: 3, 5, 1, 0.
  • The highest exponent is 5, so the degree is 5.
• Answer: 5

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = x⁴?
• FR: Quelle est la dérivée de f(x) = x⁴?
• Choices: A) 3x³ B) 4x³ C) 4x⁴ D) x³
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹ (e.g., f(x) = x³ → f'(x) = 3x²).
• Steps:
  • Bring the exponent down: 4x^(4−1).
  • f'(x) = 4x³.
• Answer: 4x³

[Easy] Combinations

• EN: A committee of 3 is chosen from 7 students. How many different committees are possible?
• FR: Un comité de 3 personnes est choisi parmi 7 élèves. Combien de comités différents sont possibles?
• Choices: A) 21 B) 35 C) 42 D) 210
• Hint: Combinations formula: C(n, r) = n! ÷ (r! × (n−r)!) (e.g., C(5, 2) = 120 ÷ (2 × 6) = 10).
• Steps:
  • C(7, 3) = 7! ÷ (3! × 4!) = (7 × 6 × 5) ÷ (3 × 2 × 1).
  • = 210 ÷ 6 = 35.
• Answer: 35

[Medium] Rational Function — Asymptote

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

[Medium] Derivative Application — Slope of a Tangent

• EN: What is the slope of the tangent to f(x) = 3x² − 4x + 1 at x = 2?
• FR: Quelle est la pente de la tangente à f(x) = 3x² − 4x + 1 au point x = 2?
• Choices: A) 4 B) 6 C) 8 D) 12
• Hint: Find the derivative, then substitute the x-value (e.g., f(x) = 2x² + x; f'(x) = 4x + 1; at x = 3: f'(3) = 13).
• Steps:
  • f'(x) = 6x − 4.
  • At x = 2: f'(2) = 6(2) − 4 = 12 − 4 = 8.
• Answer: 8

[Medium] Probability Distribution (Binomial)

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

[Medium] Vectors — Addition

• EN: Vector u = (3, −2) and vector v = (−1, 5). What is u + v?
• FR: Le vecteur u = (3, −2) et le vecteur v = (−1, 5). Combien vaut u + v?
• Choices: A) (2, 3) B) (4, 3) C) (2, 7) D) (4, 7)
• Hint: Add vectors by adding corresponding components (e.g., (2, 4) + (3, −1) = (5, 3)).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: −2 + 5 = 3.
  • u + v = (2, 3).
• Answer: (2, 3)

[Hard] Derivatives — Optimization

• EN: A farmer has 80 m of fencing to enclose a rectangular field beside a barn wall (no fencing needed on one side). What is the maximum area of the field?
• FR: Un agriculteur dispose de 80 m de clôture pour délimiter un champ rectangulaire contre un mur de grange (aucune clôture nécessaire d'un côté). Quelle est l'aire maximale du champ?
• Choices: A) 600 m² B) 800 m² C) 900 m² D) 1600 m²
• Hint: Let w be the width (two sides) and l be the length (one side). Write l in terms of w using the fencing constraint, then maximize A = l × w using the vertex or derivative (e.g., for 60 m total: l = 60 − 2w; A = (60 − 2w)w; maximize at w = 15: A = 30 × 15 = 450 m²).
• Steps:
  • Constraint: 2w + l = 80, so l = 80 − 2w.
  • Area A = w(80 − 2w) = 80w − 2w².
  • A'(w) = 80 − 4w = 0 → w = 20 m.
  • l = 80 − 40 = 40 m. A = 40 × 20 = 800 m².
• Answer: 800 m²

[Hard] Permutations with Restrictions

• EN: How many ways can the letters in the word MAPLE be arranged if the M must always be first?
• FR: De combien de façons peut-on arranger les lettres du mot MAPLE si le M doit toujours être en première position?
• Choices: A) 12 B) 18 C) 24 D) 120
• Hint: Fix the restricted letter in its position, then count arrangements of the remaining letters (e.g., fix A first in BEAR → arrange EBR in 3! = 6 ways).
• Steps:
  • M is fixed in position 1. Remaining letters: A, P, L, E (4 letters).
  • Arrangements = 4! = 4 × 3 × 2 × 1 = 24.
• Answer: 24