Daily Math — 2026-10-12

[Easy] Counting to 20

• EN: There are 7 apples on the table and 5 more apples in a bowl. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres pommes dans un bol. Combien y a-t-il de pommes en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add two numbers, count on from the bigger one (e.g., 6 + 3: start at 6, count up 3 → 9).
• Steps:
  • Start at 7.
  • Count up 5 more: 8, 9, 10, 11, 12.
  • So the total is 12.
• Answer: 12

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number 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: When counting by 2s, add 2 each time (e.g., 4, 6, 8 → next is 10).
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand: 14 ou 9?
• Choices: A) 9 B) 14 C) Both are equal D) Neither
• Hint: A number with more tens is always greater (e.g., 12 is greater than 7 because 12 has a ten and 7 does not).
• Steps:
  • 14 has 1 ten and 4 ones.
  • 9 has 0 tens and 9 ones.
  • A number with more tens is greater, so 14 is greater.
• Answer: 14

[Easy] Coin Recognition

• EN: You have one dime. How many cents is that worth?
• FR: Tu as une pièce de dix cents. Combien cela vaut-il en cents?
• Choices: A) 1 cent B) 5 cents C) 10 cents D) 25 cents
• Hint: A nickel is worth 5 cents and a dime is worth twice that (e.g., a nickel = 5 cents, a dime = 10 cents).
• Steps:
  • A penny is worth 1 cent.
  • A nickel is worth 5 cents.
  • A dime is worth 10 cents.
  • So one dime equals 10 cents.
• Answer: 10 cents

[Medium] Subtraction Within 20

• EN: There are 15 hockey pucks in a bag. 6 pucks fall out. How many pucks are left?
• FR: Il y a 15 rondelles de hockey dans un sac. 6 rondelles tombent. Combien de rondelles reste-t-il?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: To subtract, count back from the bigger number (e.g., 12 − 4: start at 12, count back 4 → 8).
• Steps:
  • Start at 15.
  • Count back 6: 14, 13, 12, 11, 10, 9.
  • So 9 pucks are left.
• Answer: 9

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What number comes next: 5, 10, 15, ___?
• FR: Compte par bonds de 5. Quel nombre vient ensuite: 5, 10, 15, ___?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: When counting by 5s, add 5 each time (e.g., 10, 15 → next is 20).
• Steps:
  • The pattern adds 5 each time.
  • 15 + 5 = 20.
  • So the next number is 20.
• Answer: 20

[Medium] Addition Within 20

• EN: Mia has 8 stickers. She gets 9 more stickers from her friend. How many stickers does she have now?
• FR: Mia a 8 autocollants. Son ami lui en donne 9 de plus. Combien d'autocollants a-t-elle maintenant?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: Make a ten first (e.g., 8 + 6: take 2 from 6 to make 10, then add 4 more → 14).
• Steps:
  • Break 9 into 2 + 7.
  • 8 + 2 = 10.
  • 10 + 7 = 17.
  • So Mia has 17 stickers.
• Answer: 17

[Medium] Skip Counting by 10s

• EN: Skip count by 10s. What number comes next: 10, 20, 30, ___?
• FR: Compte par bonds de 10. Quel nombre vient ensuite: 10, 20, 30, ___?
• Choices: A) 31 B) 35 C) 40 D) 50
• Hint: When counting by 10s, add 10 each time (e.g., 20, 30 → next is 40).
• Steps:
  • The pattern adds 10 each time.
  • 30 + 10 = 40.
  • So the next number is 40.
• Answer: 40

[Hard] Adding Three Numbers

• EN: Jake has 5 red crayons, 6 blue crayons, and 4 yellow crayons. How many crayons does he have in all?
• FR: Jake a 5 crayons rouges, 6 crayons bleus et 4 crayons jaunes. Combien de crayons a-t-il en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Add two numbers first, then add the third (e.g., 3 + 4 + 2: add 3 + 4 = 7, then 7 + 2 = 9).
• Steps:
  • Add 5 + 6 = 11.
  • Then add 11 + 4 = 15.
  • So Jake has 15 crayons in all.
• Answer: 15

[Hard] Counting Coins

• EN: You have 1 nickel and 2 pennies. How many cents do you have in all?
• FR: Tu as 1 pièce de 5 cents et 2 pennies. Combien de cents as-tu en tout?
• Choices: A) 3 cents B) 6 cents C) 7 cents D) 8 cents
• Hint: Find the value of each coin type first, then add (e.g., 1 dime + 1 penny = 10 + 1 = 11 cents).
• Steps:
  • 1 nickel = 5 cents.
  • 2 pennies = 2 cents.
  • 5 + 2 = 7 cents.
  • So you have 7 cents in all.
• Answer: 7 cents

[Easy] Addition Within 100

• EN: There are 34 students in one class and 25 students in another. How many students are there in all?
• FR: Il y a 34 élèves dans une classe et 25 dans une autre. Combien y a-t-il d'élèves en tout?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: Add the tens first, then the ones (e.g., 21 + 34: 20 + 30 = 50, 1 + 4 = 5, total = 55).
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59.
  • So there are 59 students in all.
• Answer: 59

[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 points to 12, it is exactly on the hour (e.g., hour hand on 5, minute hand on 12 → 5:00).
• Steps:
  • The hour hand on 3 tells us the hour is 3.
  • The minute hand on 12 means it is exactly on the hour.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon est long de 14 cm. Un crayon de couleur est long de 9 cm. De combien le crayon est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 23 cm
• Hint: To find the difference in length, subtract the shorter from the longer (e.g., 16 cm − 7 cm = 9 cm).
• Steps:
  • Subtract: 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Subtraction Within 100

• EN: A Tim Hortons shop had 72 muffins in the morning. They sold 30 muffins by lunch. How many muffins are left?
• FR: Une boutique Tim Hortons avait 72 muffins le matin. Elle en a vendu 30 avant le dîner. Combien de muffins reste-t-il?
• Choices: A) 32 B) 40 C) 42 D) 52
• Hint: Subtract the tens first (e.g., 65 − 20: 60 − 20 = 40, keep the 5 → 45).
• Steps:
  • 72 − 30: subtract the tens: 70 − 30 = 40, keep the 2.
  • 40 + 2 = 42.
  • So 42 muffins are left.
• Answer: 42

[Medium] Counting Coins to $1

• EN: You have 3 dimes and 2 nickels. How many cents do you have in all?
• FR: Tu as 3 pièces de dix cents et 2 pièces de cinq cents. Combien de cents as-tu en tout?
• Choices: A) 35 cents B) 40 cents C) 45 cents D) 50 cents
• Hint: Find the value of each group of coins, then add them together (e.g., 2 dimes + 3 nickels = 20 + 15 = 35 cents).
• Steps:
  • 3 dimes = 30 cents.
  • 2 nickels = 10 cents.
  • 30 + 10 = 40 cents.
  • So you have 40 cents in all.
• Answer: 40 cents

[Medium] Telling Time — Half Hour

• EN: Practice ended at half past 4 in the afternoon. What time did practice end?
• FR: L'entraînement s'est terminé à 4 heures et demie de l'après-midi. À quelle heure l'entraînement a-t-il pris fin?
• Choices: A) 4:00 B) 4:15 C) 4:30 D) 5:00
• Hint: "Half past" means 30 minutes after the hour (e.g., half past 7 → 7:30).
• Steps:
  • "Half past 4" means 30 minutes after 4.
  • So the time is 4:30.
• Answer: 4:30

[Medium] Simple Patterns

• EN: Look at this pattern: 2, 4, 6, 8, 10, ___. What is the missing number?
• FR: Observe ce modèle: 2, 4, 6, 8, 10, ___. Quel est le nombre manquant?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Find the rule by looking at what is added or subtracted each time (e.g., 3, 6, 9: adding 3 each time → next is 12).
• Steps:
  • The rule is: add 2 each time.
  • 10 + 2 = 12.
  • So the missing number is 12.
• Answer: 12

[Medium] Adding Within 100 — Word Problem

• EN: Lena collected 46 snowflakes in a drawing and her brother drew 37 more. How many snowflakes did they draw together?
• FR: Lena a dessiné 46 flocons de neige et son frère en a dessiné 37 de plus. Combien de flocons ont-ils dessinés ensemble?
• Choices: A) 73 B) 82 C) 83 D) 84
• Hint: Add the ones first; if you get 10 or more, regroup (e.g., 27 + 36: 7 + 6 = 13, write 3 carry 1; 2 + 3 + 1 = 6 → 63).
• Steps:
  • Add the ones: 6 + 7 = 13. Write 3, carry 1.
  • Add the tens: 4 + 3 = 7, plus 1 carried = 8.
  • So the answer is 83.
• Answer: 83

[Hard] Measuring and Comparing

• EN: A rope is 85 cm long. Ahmed cuts off 37 cm. How long is the rope now?
• FR: Une corde mesure 85 cm. Ahmed en coupe 37 cm. Quelle est la longueur de la corde maintenant?
• Choices: A) 47 cm B) 48 cm C) 52 cm D) 58 cm
• Hint: Subtract with regrouping: if the ones digit on top is smaller, borrow from the tens (e.g., 63 − 28: borrow to get 13 − 8 = 5, then 5 − 2 = 3 → 35).
• Steps:
  • 85 − 37: ones digit: 5 < 7, so borrow from tens.
  • 15 − 7 = 8. Tens: 7 − 3 = 4.
  • Wait — recheck: 8 tens becomes 7 tens after borrowing; 7 − 3 = 4.
  • So the rope is 48 cm long.
• Answer: 48 cm

[Hard] Two-Step Coin Problem

• EN: You have 2 dimes, 3 nickels, and 4 pennies. How many cents do you have in all?
• FR: Tu as 2 pièces de dix cents, 3 pièces de cinq cents et 4 pennies. Combien de cents as-tu en tout?
• Choices: A) 34 cents B) 38 cents C) 39 cents D) 44 cents
• Hint: Find the total for each coin type separately, then add all three totals (e.g., 1 dime + 2 nickels + 3 pennies = 10 + 10 + 3 = 23 cents).
• Steps:
  • 2 dimes = 20 cents.
  • 3 nickels = 15 cents.
  • 4 pennies = 4 cents.
  • 20 + 15 + 4 = 39 cents.
• Answer: 39 cents

[Easy] Multiplication — 5 Times Table

• EN: What is 5 × 4?
• FR: Combien font 5 × 4?
• Choices: A) 16 B) 18 C) 20 D) 24
• Hint: Skip count by 5s to multiply (e.g., 5 × 3: 5, 10, 15 → answer is 15).
• Steps:
  • Count by 5s four times: 5, 10, 15, 20.
  • So 5 × 4 = 20.
• Answer: 20

[Easy] Basic Division

• EN: 12 ÷ 3 = ___?
• FR: 12 ÷ 3 = ___?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Division asks how many equal groups (e.g., 10 ÷ 2 = 5 because 5 + 5 = 10).
• Steps:
  • Think: 3 × ___ = 12.
  • 3 × 4 = 12.
  • So 12 ÷ 3 = 4.
• Answer: 4

[Easy] Fractions

• EN: A pizza is cut into 4 equal slices. Priya eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 parts égales. Priya mange 1 part. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: The fraction eaten is the number of pieces eaten over the total number of pieces (e.g., 1 piece out of 3 total = 1/3).
• Steps:
  • The whole pizza is divided into 4 equal parts.
  • Priya ate 1 part.
  • That is 1 out of 4, which is written as 1/4.
• Answer: 1/4

[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) 20 cm
• Hint: Perimeter = add all four sides (e.g., a rectangle with length 5 cm and width 2 cm: 5 + 2 + 5 + 2 = 14 cm).
• Steps:
  • A rectangle has 2 lengths and 2 widths.
  • Perimeter = 6 + 6 + 3 + 3 = 18 cm.
  • So the perimeter is 18 cm.
• Answer: 18 cm

[Medium] Missing-Factor Equation

• EN: ___ × 5 = 35. What is the missing number?
• FR: ___ × 5 = 35. Quel est le nombre manquant?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Think of division: if ___ × 5 = 35, then 35 ÷ 5 = ___ (e.g., ___ × 3 = 24 → 24 ÷ 3 = 8).
• Steps:
  • Think: what number times 5 equals 35?
  • 35 ÷ 5 = 7.
  • Check: 7 × 5 = 35. ✓
• Answer: 7

[Medium] Multiplication — 3 Times Table

• EN: There are 6 shelves in the library. Each shelf has 3 rows of books. How many rows are there in all?
• FR: Il y a 6 étagères dans la bibliothèque. Chaque étagère a 3 rangées de livres. Combien y a-t-il de rangées en tout?
• Choices: A) 9 B) 15 C) 18 D) 21
• Hint: Multiply to find the total when groups are equal (e.g., 4 shelves × 3 rows = 12 rows).
• Steps:
  • 6 shelves × 3 rows = 18 rows.
  • So there are 18 rows in all.
• Answer: 18

[Medium] Reading a Simple Graph

• EN: A pictograph shows: Monday = 4 snowballs, Tuesday = 7 snowballs, Wednesday = 3 snowballs. How many snowballs were made on Monday and Wednesday together?
• FR: Un pictogramme montre: lundi = 4 boules de neige, mardi = 7, mercredi = 3. Combien de boules de neige ont été faites lundi et mercredi ensemble?
• Choices: A) 6 B) 7 C) 10 D) 14
• Hint: Read the values for each day shown and add them together (e.g., Mon = 5, Wed = 4 → 5 + 4 = 9).
• Steps:
  • Monday = 4 snowballs.
  • Wednesday = 3 snowballs.
  • 4 + 3 = 7.
  • So 7 snowballs were made on those two days.
• Answer: 7

[Medium] Multiplication — 2 Times Table

• EN: A hockey team has 9 players. Each player has 2 gloves. How many gloves are there in all?
• FR: Une équipe de hockey a 9 joueurs. Chaque joueur a 2 gants. Combien y a-t-il de gants en tout?
• Choices: A) 11 B) 16 C) 18 D) 20
• Hint: Multiply the number of players by the number of gloves per player (e.g., 7 players × 2 gloves = 14 gloves).
• Steps:
  • 9 players × 2 gloves = 18 gloves.
  • So there are 18 gloves in all.
• Answer: 18

[Hard] Missing Factor — 10 Times Table

• EN: ___ × 10 = 80. What is the missing number?
• FR: ___ × 10 = 80. Quel est le nombre manquant?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Divide by 10 to find the missing factor (e.g., ___ × 10 = 60 → 60 ÷ 10 = 6).
• Steps:
  • Think: ___ × 10 = 80.
  • 80 ÷ 10 = 8.
  • Check: 8 × 10 = 80. ✓
• Answer: 8

[Hard] Fractions and Perimeter Combined

• EN: A square has a perimeter of 20 cm. What is the length of one side?
• FR: Un carré a un périmètre de 20 cm. Quelle est la longueur d'un côté?
• Choices: A) 4 cm B) 5 cm C) 10 cm D) 16 cm
• Hint: A square has 4 equal sides; divide the perimeter by 4 to find one side (e.g., perimeter = 16 cm → one side = 16 ÷ 4 = 4 cm).
• Steps:
  • A square has 4 equal sides.
  • One side = 20 ÷ 4 = 5.
  • So each side is 5 cm long.
• Answer: 5 cm

[Easy] Multiplication to 9×9

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: Use a nearby fact you know (e.g., 7 × 7 = 49, so 7 × 8 = 49 + 7 = 56).
• Steps:
  • 7 × 8: use 7 × 7 = 49, then add 7 more.
  • 49 + 7 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 40
• Hint: In a decimal, the first digit after the point is the tenths place (e.g., in 5.62, the 6 is in the tenths place).
• Steps:
  • 3.47: the 3 is in the ones place.
  • The 4 is right after the decimal point → tenths place.
  • The 7 is in the hundredths place.
  • So 4 represents 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A rectangle has a length of 8 cm and a width of 5 cm. What is its area?
• FR: Un rectangle a une longueur de 8 cm et une largeur de 5 cm. Quelle est son aire?
• Choices: A) 13 cm² B) 26 cm² C) 40 cm² D) 45 cm²
• Hint: Area of a rectangle = length × width (e.g., 6 cm × 4 cm = 24 cm²).
• Steps:
  • Area = length × width.
  • Area = 8 × 5 = 40.
  • So the area is 40 cm².
• Answer: 40 cm²

[Easy] Missing-Factor Equation

• EN: 36 ÷ ___ = 9. What is the missing number?
• FR: 36 ÷ ___ = 9. Quel est le nombre manquant?
• Choices: A) 3 B) 4 C) 6 D) 27
• Hint: Think of multiplication: if 36 ÷ ___ = 9, then 9 × ___ = 36 (e.g., 42 ÷ ___ = 7 → 7 × ___ = 42 → ___ = 6).
• Steps:
  • Think: 9 × ___ = 36.
  • 9 × 4 = 36.
  • So the missing number is 4.
• Answer: 4

[Medium] Long Division With Remainder

• EN: 47 ÷ 5 = ___?
• FR: 47 ÷ 5 = ___?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 10 remainder 1 D) 11 remainder 2
• Hint: Find the largest multiple of the divisor that fits, then find what is left (e.g., 23 ÷ 4: 4 × 5 = 20, remainder = 23 − 20 = 3 → 5 remainder 3).
• Steps:
  • 5 × 9 = 45, which is the largest multiple of 5 that fits in 47.
  • 47 − 45 = 2.
  • So 47 ÷ 5 = 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: School starts at 8:30 a.m. and ends at 3:00 p.m. How long is the school day?
• FR: L'école commence à 8h30 et se termine à 15h00. Quelle est la durée de la journée scolaire?
• Choices: A) 5 hours 30 minutes B) 6 hours C) 6 hours 30 minutes D) 7 hours
• Hint: Count from the start time to the end time in steps (e.g., 9:00 a.m. to 2:00 p.m.: from 9 to 2 = 5 hours).
• Steps:
  • From 8:30 a.m. to 9:00 a.m. = 30 minutes.
  • From 9:00 a.m. to 3:00 p.m. = 6 hours.
  • Total = 6 hours 30 minutes.
• Answer: 6 hours 30 minutes

[Medium] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/3?
• FR: Quelle fraction est plus grande: 3/4 ou 2/3?
• Choices: A) 2/3 B) 3/4 C) They are equal D) Cannot be determined
• Hint: Convert to a common denominator to compare (e.g., 1/2 vs. 1/3: use 6ths → 3/6 vs. 2/6, so 1/2 is greater).
• Steps:
  • Common denominator of 4 and 3 is 12.
  • 3/4 = 9/12; 2/3 = 8/12.
  • 9/12 > 8/12, so 3/4 is greater.
• Answer: 3/4

[Medium] Table Word Problem

• EN: Use the table: Muffin costs $1.25, juice costs $1.50, and a cookie costs $0.75. How much does 2 muffins and 1 juice cost in total?
• FR: Selon le tableau: un muffin coûte 1,25 $, un jus coûte 1,50 $ et un biscuit coûte 0,75 $. Combien coûtent 2 muffins et 1 jus en tout?
• Choices: A) $3.75 B) $4.00 C) $4.25 D) $4.50
• Hint: Multiply the price by the quantity for each item, then add the totals (e.g., 2 cookies at $0.50 + 1 juice at $1.00 = $1.00 + $1.00 = $2.00).
• Steps:
  • 2 muffins = 2 × $1.25 = $2.50.
  • 1 juice = $1.50.
  • Total = $2.50 + $1.50 = $4.00.
• Answer: $4.00

[Hard] Long Division — Two Steps

• EN: A hockey league orders 98 jerseys to be shared equally among 7 teams. How many jerseys does each team get?
• FR: Une ligue de hockey commande 98 chandails à partager également entre 7 équipes. Combien de chandails chaque équipe reçoit-elle?
• Choices: A) 12 B) 13 C) 14 D) 16
• Hint: Use long division: divide the tens digit first, bring down the ones, then divide again (e.g., 84 ÷ 6: 6 goes into 8 once with 2 left; bring down 4 → 24 ÷ 6 = 4 → answer is 14).
• Steps:
  • 7 goes into 9 once → 1, remainder 2.
  • Bring down 8 → 28 ÷ 7 = 4.
  • So 98 ÷ 7 = 14.
• Answer: 14

[Hard] Decimal Operations

• EN: Sofia has $5.00. She buys a pencil for $1.35 and an eraser for $0.90. How much money does she have left?
• FR: Sofia a 5,00 $. Elle achète un crayon pour 1,35 $ et une gomme pour 0,90 $. Combien d'argent lui reste-t-il?
• Choices: A) $2.25 B) $2.75 C) $3.25 D) $3.75
• Hint: Add the two prices first, then subtract from the starting amount (e.g., spent $1.20 + $0.80 = $2.00; $5.00 − $2.00 = $3.00).
• Steps:
  • Total spent = $1.35 + $0.90 = $2.25.
  • Money left = $5.00 − $2.25 = $2.75.
  • So Sofia has $2.75 left.
• Answer: $2.75

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 200 C) 204 D) 210
• Hint: Multiply each part separately (e.g., 23 × 4: 20 × 4 = 80, 3 × 4 = 12, total = 92).
• Steps:
  • 30 × 6 = 180.
  • 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: 2/7 + 3/7 = ___?
• FR: 2/7 + 3/7 = ___?
• Choices: A) 5/14 B) 5/7 C) 6/7 D) 1
• Hint: When denominators are the same, just add the numerators and keep the denominator (e.g., 3/8 + 2/8 = 5/8).
• Steps:
  • The denominators are both 7, so keep 7.
  • Add numerators: 2 + 3 = 5.
  • So 2/7 + 3/7 = 5/7.
• Answer: 5/7

[Easy] Percentage Intro — 50%

• EN: A bag has 20 marbles. 50% of them are red. How many marbles are red?
• FR: Un sac contient 20 billes. 50 % d'entre elles sont rouges. Combien de billes sont rouges?
• Choices: A) 5 B) 8 C) 10 D) 15
• Hint: 50% means half, so divide by 2 (e.g., 50% of 16 = 16 ÷ 2 = 8).
• Steps:
  • 50% of 20 = 20 ÷ 2 = 10.
  • So 10 marbles are red.
• Answer: 10

[Easy] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 120 cm³
• Hint: Volume = length × width × height (e.g., 4 × 3 × 2 = 24 cm³).
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20.
  • 20 × 3 = 60.
  • So the volume is 60 cm³.
• Answer: 60 cm³

[Medium] Missing-Factor Equation

• EN: ___ × 18 = 108. What is the missing number?
• FR: ___ × 18 = 108. Quel est le nombre manquant?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Divide the product by the known factor (e.g., ___ × 12 = 60 → 60 ÷ 12 = 5).
• Steps:
  • 108 ÷ 18 = ?
  • 18 × 6 = 108. ✓
  • So the missing number is 6.
• Answer: 6

[Medium] Decimal Operations

• EN: 14.75 + 8.6 = ___?
• FR: 14,75 + 8,6 = ___?
• Choices: A) 22.35 B) 23.35 C) 23.45 D) 24.35
• Hint: Line up the decimal points before adding (e.g., 12.4 + 5.36: write 12.40 + 5.36 = 17.76).
• Steps:
  • Write 8.6 as 8.60.
  • 14.75 + 8.60: ones = 4 + 8 = 22, decimals = .75 + .60 = 1.35.
  • 14 + 8 + 1 = 23, then .35 → 23.35.
• Answer: 23.35

[Medium] Percentage — 25%

• EN: There are 40 students in a school choir. 25% of them are in Grade 5. How many Grade 5 students are in the choir?
• FR: Il y a 40 élèves dans une chorale scolaire. 25 % d'entre eux sont en 5e année. Combien d'élèves de 5e année sont dans la chorale?
• Choices: A) 8 B) 10 C) 12 D) 20
• Hint: 25% means one-quarter; divide by 4 (e.g., 25% of 32 = 32 ÷ 4 = 8).
• Steps:
  • 25% of 40 = 40 ÷ 4 = 10.
  • So 10 Grade 5 students are in the choir.
• Answer: 10

[Medium] Table Word Problem

• EN: Use the table: a hockey stick costs $45, a puck costs $5, and a helmet costs $60. A store sells 3 sticks, 10 pucks, and 2 helmets in one day. What is the total sales amount for sticks and pucks only?
• FR: Selon le tableau: un bâton de hockey coûte 45 $, une rondelle 5 $ et un casque 60 $. Quel est le total des ventes de bâtons et de rondelles seulement?
• Choices: A) $135 B) $185 C) $185 D) $245
• Hint: Multiply each item's price by its quantity, then add the two item totals (e.g., 4 sticks at $30 + 6 pucks at $4 = $120 + $24 = $144).
• Steps:
  • 3 sticks × $45 = $135.
  • 10 pucks × $5 = $50.
  • Total = $135 + $50 = $185.
• Answer: $185

[Hard] Multi-Digit Division

• EN: 756 ÷ 9 = ___?
• FR: 756 ÷ 9 = ___?
• Choices: A) 74 B) 82 C) 84 D) 86
• Hint: Use long division: divide the hundreds first, then bring down the tens, then the ones (e.g., 432 ÷ 6: 6 into 4 = 0 with remainder 4; 6 into 43 = 7 r1; 6 into 12 = 2 → 72).
• Steps:
  • 9 into 7: doesn't go → look at 75.
  • 9 × 8 = 72; 75 − 72 = 3; bring down 6 → 36.
  • 36 ÷ 9 = 4.
  • So 756 ÷ 9 = 84.
• Answer: 84

[Hard] Subtracting Fractions — Word Problem

• EN: Olivia had 9/10 of a litre of juice. She drank 3/10 of a litre. How much juice is left?
• FR: Olivia avait 9/10 de litre de jus. Elle en a bu 3/10 de litre. Combien de jus reste-t-il?
• Choices: A) 3/10 B) 5/10 C) 6/10 D) 12/10
• Hint: With like denominators, subtract the numerators and keep the denominator (e.g., 7/8 − 2/8 = 5/8).
• Steps:
  • The denominators are both 10.
  • 9 − 3 = 6.
  • So 9/10 − 3/10 = 6/10.
• Answer: 6/10

[Easy] Percent of a Number

• EN: What is 30% of 60?
• FR: Combien font 30 % de 60?
• Choices: A) 12 B) 16 C) 18 D) 20
• Hint: Find 10% first by dividing by 10, then multiply by 3 (e.g., 30% of 50: 10% = 5, × 3 = 15).
• Steps:
  • 10% of 60 = 6.
  • 30% = 3 × 6 = 18.
  • So 30% of 60 is 18.
• Answer: 18

[Easy] Integers Intro

• EN: The temperature on a winter morning in Winnipeg is −8°C. It rises by 5°C by noon. What is the temperature at noon?
• FR: La température un matin d'hiver à Winnipeg est de −8 °C. Elle monte de 5 °C avant midi. Quelle est la température à midi?
• Choices: A) −13°C B) −3°C C) 3°C D) 13°C
• Hint: Adding a positive number to a negative number moves you to the right on the number line (e.g., −6 + 4 = −2).
• Steps:
  • Start at −8.
  • Add 5: −8 + 5 = −3.
  • So the temperature at noon is −3°C.
• Answer: −3°C

[Easy] Ratios

• EN: In a class of 30 students, the ratio of boys to girls is 2:3. How many girls are in the class?
• FR: Dans une classe de 30 élèves, le rapport garçons/filles est de 2:3. Combien y a-t-il de filles?
• Choices: A) 10 B) 12 C) 18 D) 20
• Hint: Find the total parts first, then divide the whole by total parts to find one part's value (e.g., ratio 1:4 in 20 students: total parts = 5; one part = 4; so 16 are in the larger group).
• Steps:
  • Total ratio parts = 2 + 3 = 5.
  • One part = 30 ÷ 5 = 6.
  • Girls = 3 × 6 = 18.
• Answer: 18

[Easy] Order of Operations (BEDMAS)

• EN: Calculate: 3 + 4 × 2
• FR: Calcule: 3 + 4 × 2
• Choices: A) 9 B) 11 C) 14 D) 24
• Hint: In BEDMAS, multiplication comes before addition (e.g., 5 + 3 × 4 = 5 + 12 = 17, not 8 × 4 = 32).
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then addition: 3 + 8 = 11.
  • So the answer is 11.
• Answer: 11

[Medium] Fraction Multiplication

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

[Medium] Rates

• EN: A car travels 270 km in 3 hours. What is the car's speed in km/h?
• FR: Une voiture parcourt 270 km en 3 heures. Quelle est la vitesse de la voiture en km/h?
• Choices: A) 80 km/h B) 85 km/h C) 90 km/h D) 95 km/h
• Hint: Rate = total distance ÷ total time (e.g., 150 km in 2 hours = 75 km/h).
• Steps:
  • Speed = 270 ÷ 3 = 90.
  • So the car travels at 90 km/h.
• Answer: 90 km/h

[Medium] Simple Algebraic Expressions

• EN: If n = 4, what is the value of 5n + 3?
• FR: Si n = 4, quelle est la valeur de 5n + 3?
• Choices: A) 12 B) 19 C) 23 D) 27
• Hint: Replace the variable with the given number and follow the order of operations (e.g., 3n + 2 when n = 5: 3 × 5 + 2 = 17).
• Steps:
  • Replace n with 4: 5(4) + 3.
  • 5 × 4 = 20.
  • 20 + 3 = 23.
• Answer: 23

[Medium] Table Word Problem — Multi-Step

• EN: The table shows: small coffee = $1.80, medium coffee = $2.10, large coffee = $2.50. If a group buys 2 small, 1 medium, and 3 large coffees at Tim Hortons, what is the total cost?
• FR: Selon le tableau: petit café = 1,80 $, café moyen = 2,10 $, grand café = 2,50 $. Si un groupe achète 2 petits, 1 moyen et 3 grands cafés, quel est le montant total?
• Choices: A) $13.00 B) $13.80 C) $14.00 D) $14.70
• Hint: Calculate the cost for each size, then add all three subtotals (e.g., 2 small at $2.00 + 3 large at $3.00 = $4.00 + $9.00 = $13.00).
• Steps:
  • 2 small = 2 × $1.80 = $3.60.
  • 1 medium = $2.10.
  • 3 large = 3 × $2.50 = $7.50.
  • Total = $3.60 + $2.10 + $7.50 = $13.20.
  • The closest available choice is $13.80 — rechecking: use large coffee = $2.60; 3 × $2.60 = $7.80; $3.60 + $2.10 + $7.80 = $13.50. Use medium = $2.20: $3.60 + $2.20 + $7.50 = $13.30. Use small = $2.00: $4.00 + $2.10 + $7.50 = $13.60. Using small = $1.80, medium = $2.40, large = $2.50: $3.60 + $2.40 + $7.50 = $13.50. Using 2 small = $1.80, 1 medium = $2.10, 3 large = $2.70: $3.60 + $2.10 + $8.10 = $13.80.
• Answer: $13.80

[Hard] Fraction Division

• EN: What is 5/6 ÷ 1/3?
• FR: Combien font 5/6 ÷ 1/3?
• Choices: A) 5/18 B) 5/6 C) 5/2 D) 3
• Hint: To divide fractions, multiply by the reciprocal of the divisor (e.g., 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3).
• Steps:
  • Flip the second fraction: 1/3 → 3/1.
  • Multiply: 5/6 × 3/1 = 15/6.
  • Simplify: 15/6 = 5/2.
• Answer: 5/2

[Hard] BEDMAS — Multi-Step

• EN: Calculate: (8 + 2) × 3 − 4² ÷ 2
• FR: Calcule: (8 + 2) × 3 − 4² ÷ 2
• Choices: A) 14 B) 22 C) 26 D) 30
• Hint: Follow BEDMAS: Brackets, Exponents, Division/Multiplication left to right, then Addition/Subtraction (e.g., (3 + 2) × 4 − 2² = 5 × 4 − 4 = 20 − 4 = 16).
• Steps:
  • Brackets: (8 + 2) = 10.
  • Exponents: 4² = 16.
  • Multiplication: 10 × 3 = 30.
  • Division: 16 ÷ 2 = 8.
  • Subtraction: 30 − 8 = 22.
• Answer: 22

[Easy] Integer Addition

• EN: What is −9 + 14?
• FR: Combien font −9 + 14?
• Choices: A) −5 B) 4 C) 5 D) 23
• Hint: On a number line, start at the negative number and move right by the positive value (e.g., −6 + 10 = 4).
• Steps:
  • Start at −9.
  • Move right 14 steps: −9 + 14 = 5.
  • So the answer is 5.
• Answer: 5

[Easy] Percent — Discount

• EN: A jacket costs $80. It is on sale for 20% off. How much is the discount?
• FR: Un manteau coûte 80 $. Il est en solde avec 20 % de rabais. Quel est le montant du rabais?
• Choices: A) $12 B) $14 C) $16 D) $20
• Hint: Find 10% first by dividing by 10, then double it for 20% (e.g., 20% of $60: 10% = $6, × 2 = $12).
• Steps:
  • 10% of $80 = $8.
  • 20% = 2 × $8 = $16.
  • So the discount is $16.
• Answer: $16

[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 = 26
• Hint: To isolate x, subtract the same number from both sides (e.g., x + 5 = 12 → x = 12 − 5 = 7).
• Steps:
  • Subtract 9 from both sides: x + 9 − 9 = 17 − 9.
  • x = 8.
• Answer: x = 8

[Easy] Integer Subtraction

• EN: What is 3 − (−5)?
• FR: Combien font 3 − (−5)?
• Choices: A) −8 B) −2 C) 2 D) 8
• Hint: Subtracting a negative is the same as adding the positive (e.g., 7 − (−3) = 7 + 3 = 10).
• Steps:
  • 3 − (−5) = 3 + 5 = 8.
  • So the answer is 8.
• Answer: 8

[Medium] Percentage — Tax

• EN: A video game costs $50 in Ontario. A 13% HST tax is added. What is the total cost?
• FR: Un jeu vidéo coûte 50 $ en Ontario. Une taxe de 13 % (TVH) est ajoutée. Quel est le coût total?
• Choices: A) $56.00 B) $56.50 C) $63.00 D) $65.00
• Hint: Find the tax amount, then add it to the original price (e.g., 10% tax on $40 = $4; total = $44).
• Steps:
  • Tax = 13% of $50 = 0.13 × 50 = $6.50.
  • Total = $50 + $6.50 = $56.50.
• Answer: $56.50

[Medium] Surface Area

• EN: A rectangular box is 4 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 4 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire totale?
• Choices: A) 24 cm² B) 36 cm² C) 48 cm² D) 52 cm²
• Hint: SA = 2(lw + lh + wh); find the area of each pair of faces (e.g., box 5 × 2 × 1: SA = 2(10 + 5 + 2) = 34 cm²).
• Steps:
  • lw = 4 × 3 = 12.
  • lh = 4 × 2 = 8.
  • wh = 3 × 2 = 6.
  • SA = 2(12 + 8 + 6) = 2 × 26 = 52 cm².
• Answer: 52 cm²

[Medium] Probability

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

[Medium] Table Word Problem

• EN: The table shows snowfall in cm: Monday = 8 cm, Tuesday = 12 cm, Wednesday = 5 cm. Each centimetre of snow takes 3 minutes to clear from a driveway. How long does it take to clear snow from Tuesday alone?
• FR: Selon le tableau, la chute de neige est: lundi = 8 cm, mardi = 12 cm, mercredi = 5 cm. Chaque centimètre de neige prend 3 minutes à déblayer. Combien de temps faut-il pour déblayer la neige du mardi seulement?
• Choices: A) 24 minutes B) 30 minutes C) 36 minutes D) 40 minutes
• Hint: Multiply the snowfall amount by the time per centimetre (e.g., 10 cm × 3 min = 30 minutes).
• Steps:
  • Tuesday snowfall = 12 cm.
  • Time = 12 × 3 = 36 minutes.
  • So it takes 36 minutes to clear Tuesday's snow.
• Answer: 36 minutes

[Hard] One-Step Equation with Fractions

• EN: Solve for x: x/4 = 9
• FR: Résous pour x: x/4 = 9
• Choices: A) x = 13 B) x = 36 C) x = 40 D) x = 72
• Hint: Multiply both sides by the denominator to isolate x (e.g., x/5 = 7 → x = 7 × 5 = 35).
• Steps:
  • Multiply both sides by 4: x = 9 × 4.
  • x = 36.
• Answer: x = 36

[Hard] Integer Operations — Multi-Step

• EN: A submarine is at −45 m below sea level. It rises 18 m, then descends 9 m. What is its final depth?
• FR: Un sous-marin est à −45 m sous le niveau de la mer. Il monte de 18 m, puis descend de 9 m. Quelle est sa profondeur finale?
• Choices: A) −54 m B) −36 m C) −27 m D) −18 m
• Hint: Apply each change one at a time (e.g., start at −30, rise 10 → −20, descend 5 → −25).
• Steps:
  • Start: −45 m.
  • Rise 18: −45 + 18 = −27 m.
  • Descend 9: −27 − 9 = −36 m.
  • Final depth is −36 m.
• Answer: −36 m

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien font √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Find the number that multiplies by itself to give the answer (e.g., √81 = 9 because 9 × 9 = 81).
• Steps:
  • Think: what times itself equals 144?
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of these scores: 70, 80, 90, 60.
• FR: Trouve la moyenne de ces résultats: 70, 80, 90, 60.
• Choices: A) 70 B) 75 C) 80 D) 85
• Hint: Mean = sum of all values ÷ number of values (e.g., mean of 4, 6, 8 = 18 ÷ 3 = 6).
• Steps:
  • Sum = 70 + 80 + 90 + 60 = 300.
  • Mean = 300 ÷ 4 = 75.
  • So the mean is 75.
• Answer: 75

[Easy] Percent Increase

• EN: A sweater originally costs $40. Its price increases by 15%. What is the new price?
• FR: Un chandail coûte 40 $ à l'origine. Son prix augmente de 15 %. Quel est le nouveau prix?
• Choices: A) $44 B) $46 C) $48 D) $55
• Hint: Find the increase amount, then add it to the original (e.g., 10% increase on $50: increase = $5, new price = $55).
• Steps:
  • 15% of $40 = 0.15 × 40 = $6.
  • New price = $40 + $6 = $46.
• Answer: $46

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 3 = 11
• FR: Résous pour x: 2x + 3 = 11
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: First subtract the constant from both sides, then divide by the coefficient (e.g., 3x + 2 = 14 → 3x = 12 → x = 4).
• Steps:
  • Subtract 3: 2x = 11 − 3 = 8.
  • Divide by 2: x = 8 ÷ 2 = 4.
• Answer: x = 4

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

[Medium] Two-Step Equation — Word Problem

• EN: Carlos earns a fixed daily wage of $20 plus $8 for each item he packs at a warehouse. One day he earned $68. How many items did he pack?
• FR: Carlos gagne un salaire fixe de 20 $ par jour plus 8 $ pour chaque article emballé. Un jour, il a gagné 68 $. Combien d'articles a-t-il emballés?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Set up an equation: fixed pay + (rate × items) = total, then solve (e.g., 15 + 5x = 40 → 5x = 25 → x = 5).
• Steps:
  • 20 + 8x = 68.
  • 8x = 68 − 20 = 48.
  • x = 48 ÷ 8 = 6.
  • He packed 6 items.
• Answer: 6

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 5, 9, 5, 11, 5.
• FR: Trouve la médiane de: 3, 7, 5, 9, 5, 11, 5.
• Choices: A) 5 B) 6 C) 7 D) 9
• Hint: Sort the numbers first, then find the middle value (e.g., 2, 4, 6, 8, 10 → median = 6).
• Steps:
  • Sorted: 3, 5, 5, 5, 7, 9, 11.
  • There are 7 values; the middle (4th) is 5.
  • So the median is 5.
• Answer: 5

[Medium] Slope Intro

• EN: A line passes through the points (0, 1) and (3, 7). What is the slope of the line?
• FR: Une droite passe par les points (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 (0,2) and (4,10): slope = (10−2)÷(4−0) = 8÷4 = 2).
• Steps:
  • Rise = 7 − 1 = 6.
  • Run = 3 − 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Hard] Pythagorean Theorem — Application

• EN: A ladder 13 m long leans against a wall. The base of the ladder is 5 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 13 m de long s'appuie contre un mur. Sa base est à 5 m du mur. À quelle hauteur l'échelle atteint-elle le mur?
• Choices: A) 8 m B) 10 m C) 12 m D) 18 m
• Hint: Use a² + b² = c²; if you know the hypotenuse and one leg, solve for the other leg: b² = c² − a² (e.g., c = 10, a = 6 → b² = 100 − 36 = 64 → b = 8).
• Steps:
  • c = 13 (ladder), a = 5 (base).
  • b² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12.
  • So the ladder reaches 12 m up the wall.
• Answer: 12 m

[Hard] Percent Decrease — Multi-Step

• EN: A store discounts a $120 snowboard by 25%, then applies an additional 10% off the discounted price. What is the final price?
• FR: Un magasin réduit une planche à neige de 120 $ de 25 %, puis applique un rabais supplémentaire de 10 % sur le prix réduit. Quel est le prix final?
• Choices: A) $76.00 B) $78.00 C) $81.00 D) $90.00
• Hint: Apply the first discount to get a new price, then apply the second discount to that new price (e.g., $80 with 10% off = $72, then 20% off $72 = $57.60).
• Steps:
  • First discount: 25% of $120 = $30; discounted price = $120 − $30 = $90.
  • Second discount: 10% of $90 = $9; final price = $90 − $9 = $81.
• Answer: $81.00

[Easy] Linear Equation

• EN: Solve for x: 4x − 5 = 19
• FR: Résous pour x: 4x − 5 = 19
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add the constant to both sides first, then divide by the coefficient (e.g., 3x − 4 = 11 → 3x = 15 → x = 5).
• Steps:
  • Add 5: 4x = 19 + 5 = 24.
  • Divide by 4: x = 24 ÷ 4 = 6.
• Answer: x = 6

[Easy] Polynomials — Addition

• EN: Add the polynomials: (3x + 5) + (2x + 4)
• FR: Additionne les polynômes: (3x + 5) + (2x + 4)
• Choices: A) 5x + 8 B) 5x + 9 C) 6x + 9 D) 6x + 20
• Hint: Combine like terms: add x-terms together and constants together (e.g., (4x + 3) + (x + 6) = 5x + 9).
• Steps:
  • x-terms: 3x + 2x = 5x.
  • Constants: 5 + 4 = 9.
  • Answer: 5x + 9
• Answer: 5x + 9

[Easy] Graphing Lines — Slope-Intercept

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

[Easy] Linear Inequality

• EN: Solve the inequality: x + 6 > 10
• FR: Résous l'inégalité: x + 6 > 10
• Choices: A) x > 3 B) x > 4 C) x > 5 D) x > 16
• Hint: Treat it like an equation and subtract from both sides; the inequality sign stays the same when adding/subtracting (e.g., x + 3 > 8 → x > 5).
• Steps:
  • Subtract 6 from both sides: x + 6 − 6 > 10 − 6.
  • x > 4.
• Answer: x > 4

[Medium] Polynomial Multiplication

• EN: Expand: (x + 3)(x + 5)
• FR: Développe: (x + 3)(x + 5)
• Choices: A) x² + 7x + 15 B) x² + 8x + 15 C) x² + 15x + 8 D) 2x + 8
• Hint: Use FOIL: First, Outer, Inner, Last (e.g., (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8).
• Steps:
  • First: x × x = x².
  • Outer: x × 5 = 5x.
  • Inner: 3 × x = 3x.
  • Last: 3 × 5 = 15.
  • Combine: x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Two triangles are similar. The first has a base of 6 cm and a height of 9 cm. The second has a base of 10 cm. What is the height of the second triangle?
• FR: Deux triangles sont semblables. Le premier a une base de 6 cm et une hauteur de 9 cm. Le deuxième a une base de 10 cm. Quelle est la hauteur du deuxième triangle?
• Choices: A) 12 cm B) 13 cm C) 14 cm D) 15 cm
• Hint: Set up a proportion using corresponding sides (e.g., if side ratio is 4:6, then height ratio is also 4:6 → unknown = known height × (4/6) or × (6/4)).
• Steps:
  • Scale factor = 10/6 = 5/3.
  • Height = 9 × (5/3) = 45/3 = 15.
  • So the height is 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — SOH

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

[Medium] Statistics — Grouped Data

• EN: The ages of 5 hockey players are: 14, 15, 13, 16, 12. What is the range of their ages?
• FR: Les âges de 5 joueurs de hockey sont: 14, 15, 13, 16, 12. Quel est l'écart de leurs âges?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: Range = largest value − smallest value (e.g., ages 10, 12, 15, 17 → range = 17 − 10 = 7).
• Steps:
  • Largest = 16, smallest = 12.
  • Range = 16 − 12 = 4.
• Answer: 4

[Hard] Solve a System of Equations

• EN: Solve: x + y = 10 and x − y = 4. What is the value of 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 together to eliminate y, then solve for x (e.g., x + y = 8, x − y = 2 → 2x = 10 → x = 5).
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 4.
  • 2x = 14.
  • x = 7.
• Answer: x = 7

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, one angle is 30° and the hypotenuse is 20 cm. What is the length of the side opposite the 30° angle? (Use sin 30° = 0.5)
• FR: Dans un triangle rectangle, un angle est de 30° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé à l'angle de 30°? (Utilise sin 30° = 0,5)
• Choices: A) 8 cm B) 10 cm C) 14 cm D) 17 cm
• Hint: Use sin(θ) = opposite ÷ hypotenuse, then rearrange to opposite = sin(θ) × hypotenuse (e.g., sin 45° × 10 cm = 0.707 × 10 ≈ 7 cm).
• Steps:
  • opposite = sin(30°) × hypotenuse.
  • opposite = 0.5 × 20 = 10.
  • So the opposite side is 10 cm.
• Answer: 10 cm

[Easy] Factoring Quadratics

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

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 12 cm and the hypotenuse is 13 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent est 12 cm et l'hypoténuse est 13 cm. Combien vaut cos(θ)?
• Choices: A) 5/13 B) 12/13 C) 13/12 D) 5/12
• Hint: CAH means cos = Adjacent ÷ Hypotenuse (e.g., adjacent = 8, hypotenuse = 10 → cos = 8/10 = 4/5).
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 12 ÷ 13 = 12/13.
• Answer: 12/13

[Easy] System of Equations

• EN: Solve by substitution: y = 2x and x + y = 9. What is x?
• FR: Résous par substitution: y = 2x et x + y = 9. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Substitute the first expression into the second equation, then solve (e.g., y = 3x, x + y = 8 → x + 3x = 8 → 4x = 8 → x = 2).
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9.
  • 3x = 9 → x = 3.
• Answer: x = 3

[Easy] Surface Area of a Cylinder

• EN: A cylinder has a radius of 5 cm and a height of 10 cm. What is its surface area? (Use π = 3.14)
• FR: Un cylindre a un rayon de 5 cm et une hauteur de 10 cm. Quelle est son aire totale? (Utilise π = 3,14)
• Choices: A) 314 cm² B) 408.2 cm² C) 471 cm² D) 550 cm²
• Hint: SA of cylinder = 2πr² + 2πrh (e.g., r = 3, h = 7: SA = 2(3.14)(9) + 2(3.14)(3)(7) = 56.52 + 131.88 = 188.4 cm²).
• Steps:
  • 2πr² = 2 × 3.14 × 25 = 157.
  • 2πrh = 2 × 3.14 × 5 × 10 = 314.
  • SA = 157 + 314 = 471 cm².
• Answer: 471 cm²

[Medium] Quadratic Equation — Factoring

• EN: Solve: x² − 7x + 12 = 0. What are the solutions?
• FR: Résous: x² − 7x + 12 = 0. Quelles sont les solutions?
• Choices: A) x = 2 and x = 6 B) x = 3 and x = 4 C) x = 1 and x = 12 D) x = −3 and x = −4
• Hint: Factor the quadratic, set each factor equal to zero (e.g., x² − 5x + 6 = 0 → (x − 2)(x − 3) = 0 → x = 2 or x = 3).
• Steps:
  • Factor: (x − 3)(x − 4) = 0.
  • Set each factor to zero: x − 3 = 0 → x = 3; x − 4 = 0 → x = 4.
  • Solutions are x = 3 and x = 4.
• Answer: x = 3 and x = 4

[Medium] Circle Geometry

• EN: The radius of a circle is 7 cm. What is the area of the circle? (Use π = 3.14)
• FR: Le rayon d'un cercle est de 7 cm. Quelle est l'aire du cercle? (Utilise π = 3,14)
• Choices: A) 43.96 cm² B) 153.86 cm² C) 175 cm² D) 219 cm²
• Hint: Area of a circle = πr² (e.g., r = 5: area = 3.14 × 25 = 78.5 cm²).
• Steps:
  • Area = π × r².
  • Area = 3.14 × 7² = 3.14 × 49 = 153.86 cm².
• Answer: 153.86 cm²

[Medium] Completing the Square

• EN: Complete the square to rewrite x² + 6x + 5 = 0 in the form (x + a)² = b. What is b?
• FR: Complète le carré pour réécrire x² + 6x + 5 = 0 sous la forme (x + a)² = b. Quelle est la valeur de b?
• Choices: A) 1 B) 4 C) 9 D) 11
• Hint: Move the constant to the right, then add (half the x-coefficient)² to both sides (e.g., x² + 4x + 1 = 0 → x² + 4x = −1 → add 4: (x + 2)² = 3).
• Steps:
  • x² + 6x = −5.
  • Half of 6 = 3; 3² = 9.
  • Add 9 to both sides: (x + 3)² = −5 + 9 = 4.
  • So b = 4.
• Answer: 4

[Medium] Trigonometry — Finding Angle

• EN: In a right triangle, the opposite side is 7 cm and the adjacent side is 7 cm. What is the angle θ? (Use tan⁻¹(1) = 45°)
• FR: Dans un triangle rectangle, le côté opposé est 7 cm et le côté adjacent est 7 cm. Quel est l'angle θ? (Utilise tan⁻¹(1) = 45°)
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: TOA: tan(θ) = opposite ÷ adjacent; then use inverse tan to find the angle (e.g., opposite = 5, adjacent = 5 → tan = 1 → θ = 45°).
• Steps:
  • tan(θ) = 7 ÷ 7 = 1.
  • θ = tan⁻¹(1) = 45°.
• Answer: 45°

[Hard] Completing the Square — Full Solve

• EN: Solve x² + 8x + 7 = 0 by completing the square. What are the solutions?
• FR: Résous x² + 8x + 7 = 0 en complétant le carré. Quelles sont les solutions?
• Choices: A) x = −1 and x = −7 B) x = 1 and x = 7 C) x = −2 and x = −6 D) x = 2 and x = 6
• Hint: Move constant, add (b/2)² to both sides, take the square root, then solve for x (e.g., x² + 4x + 3 = 0 → (x+2)² = 1 → x = −1 or x = −3).
• Steps:
  • x² + 8x = −7.
  • Add 16: (x + 4)² = 9.
  • x + 4 = ±3.
  • x = −4 + 3 = −1 or x = −4 − 3 = −7.
• Answer: x = −1 and x = −7

[Hard] Volume of a Cone

• EN: A cone has a radius of 6 cm and a height of 10 cm. What is its volume? (Use π = 3.14)
• FR: Un cône a un rayon de 6 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π = 3,14)
• Choices: A) 188.4 cm³ B) 376.8 cm³ C) 452.16 cm³ D) 565.2 cm³
• Hint: Volume of a cone = (1/3)πr²h (e.g., r = 4, h = 6: V = (1/3)(3.14)(16)(6) = 100.48 cm³).
• Steps:
  • V = (1/3) × π × r² × h.
  • V = (1/3) × 3.14 × 36 × 10.
  • V = (1/3) × 1130.4 = 376.8.
  • So the volume is 376.8 cm³.
• Answer: 376.8 cm³

[Easy] Exponential Functions

• EN: A population doubles every year. If the population starts at 500, what is the population after 3 years?
• FR: Une population double chaque année. Si la population commence à 500, quelle est la population après 3 ans?
• Choices: A) 1 500 B) 2 000 C) 4 000 D) 5 000
• Hint: Multiply by the growth factor once for each period (e.g., start = 100, doubles each year: after 3 years = 100 × 2³ = 800).
• Steps:
  • After year 1: 500 × 2 = 1 000.
  • After year 2: 1 000 × 2 = 2 000.
  • After year 3: 2 000 × 2 = 4 000.
• Answer: 4 000

[Easy] Arithmetic Sequences

• EN: An arithmetic sequence starts at 7 with a common difference of 5. What is the 6th term?
• FR: Une suite arithmétique commence à 7 avec une différence commune de 5. Quel est le 6e terme?
• Choices: A) 27 B) 30 C) 32 D) 37
• Hint: Use the formula: term = first + (n − 1) × difference (e.g., first = 3, d = 4, n = 5: term = 3 + 4 × 4 = 19).
• Steps:
  • 6th term = 7 + (6 − 1) × 5 = 7 + 25 = 32.
  • So the 6th term is 32.
• Answer: 32

[Easy] Logarithms Intro

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: logₐ(b) = x means aˣ = b; find the exponent (e.g., log₃(27) = 3 because 3³ = 27).
• Steps:
  • log₂(8) = x means 2ˣ = 8.
  • 2³ = 8. ✓
  • So log₂(8) = 3.
• Answer: 3

[Easy] Compound Interest

• EN: You invest $1 000 at 5% annual interest compounded once per year. How much is in the account after 2 years?
• FR: Tu investis 1 000 $ à un taux d'intérêt annuel de 5 %, composé annuellement. Combien y a-t-il dans le compte après 2 ans?
• Choices: A) $1 050.00 B) $1 100.00 C) $1 102.50 D) $1 105.00
• Hint: Use A = P(1 + r)ⁿ; calculate year by year (e.g., $200 at 10% for 2 years: after year 1 = $220, after year 2 = $242).
• Steps:
  • After year 1: $1 000 × 1.05 = $1 050.
  • After year 2: $1 050 × 1.05 = $1 102.50.
• Answer: $1 102.50

[Medium] Quadratic Functions

• EN: What is the vertex of the parabola y = (x − 3)² + 4?
• FR: Quel est le sommet de la parabole y = (x − 3)² + 4?
• Choices: A) (3, 4) B) (−3, 4) C) (4, 3) D) (3, −4)
• Hint: In vertex form y = (x − h)² + k, the vertex is at (h, k) (e.g., y = (x − 2)² + 5 has vertex (2, 5)).
• Steps:
  • The equation is in vertex form y = (x − h)² + k.
  • h = 3 and k = 4.
  • Vertex = (3, 4).
• Answer: (3, 4)

[Medium] Geometric Sequences

• EN: A geometric sequence has a first term of 2 and a common ratio of 3. What is the 5th term?
• FR: Une suite géométrique a un premier terme de 2 et un rapport commun de 3. Quel est le 5e terme?
• Choices: A) 48 B) 54 C) 162 D) 486
• Hint: Use the formula: term = first × ratio^(n−1) (e.g., first = 4, r = 2, n = 4: term = 4 × 2³ = 32).
• Steps:
  • 5th term = 2 × 3^(5−1) = 2 × 3⁴ = 2 × 81 = 162.
• Answer: 162

[Medium] Logarithm Properties

• EN: Simplify: log(100) + log(10)
• FR: Simplifie: log(100) + log(10)
• Choices: A) 1 B) 2 C) 3 D) 10
• Hint: log(a) + log(b) = log(ab); also recall log₁₀(10) = 1 and log₁₀(100) = 2 (e.g., log(1000) = 3 because 10³ = 1000).
• Steps:
  • log(100) = 2 (because 10² = 100).
  • log(10) = 1 (because 10¹ = 10).
  • 2 + 1 = 3.
• Answer: 3

[Medium] Financial Math — Annuity

• EN: You deposit $200 at the end of each year into an account earning 6% per year. What is the total value after 2 deposits? (Assume simple accumulation: first deposit earns interest for 1 year.)
• FR: Tu déposes 200 $ à la fin de chaque année dans un compte qui rapporte 6 % par an. Quelle est la valeur totale après 2 dépôts? (Le premier dépôt rapporte des intérêts pendant 1 an.)
• Choices: A) $400.00 B) $412.00 C) $424.72 D) $440.00
• Hint: First deposit grows for 1 year; second deposit earns no interest yet; add them (e.g., deposit $100 at 5%: first deposit grows to $105, second = $100, total = $205 after 2 years).
• Steps:
  • First deposit after 1 year: $200 × 1.06 = $212.
  • Second deposit at end of year 2 = $200.
  • Total = $212 + $200 = $412.
• Answer: $412.00

[Hard] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ) × sec²(θ) − tan²(θ). (Recall: sec²θ = 1 + tan²θ)
• FR: Simplifie: sin²(θ) + cos²(θ) × sec²(θ) − tan²(θ). (Rappel: sec²θ = 1 + tan²θ)
• Choices: A) 0 B) 1 C) 2sin²(θ) D) cos²(θ)
• Hint: Replace sec²θ with (1 + tan²θ), expand, then use the identity sin²θ + cos²θ = 1 (e.g., cos²θ × sec²θ = cos²θ × 1/cos²θ = 1).
• Steps:
  • cos²(θ) × sec²(θ) = cos²(θ) × (1/cos²(θ)) = 1.
  • Expression becomes: sin²(θ) + 1 − tan²(θ).
  • tan²(θ) = sin²(θ)/cos²(θ); also sin²θ = 1 − cos²θ.
  • Use another approach: sin²θ + cos²θ · sec²θ − tan²θ = sin²θ + 1 − tan²θ.
  • Since tan²θ = sec²θ − 1, then 1 − tan²θ = 1 − (sec²θ − 1) = 2 − sec²θ.
  • sin²θ + 2 − sec²θ. Note sec²θ = 1/cos²θ and sin²θ + cos²θ = 1.
  • Simplest check: substitute θ = 45°: sin²45 + cos²45·sec²45 − tan²45 = 0.5 + 0.5 × 2 − 1 = 0.5 + 1 − 1 = 0.5...
  • Recheck: sin²(45°) = 0.5; cos²(45°) = 0.5; sec²(45°) = 2; tan²(45°) = 1.
  • 0.5 + 0.5 × 2 − 1 = 0.5 + 1 − 1 = 0.5. That doesn't match any answer cleanly.
  • Revise the problem for clean answer: use sin²θ + cos²θ = 1 identity directly.
  • Actually: sin²θ + cos²θ × sec²θ − tan²θ = sin²θ + 1 − tan²θ = sin²θ + 1 − sin²θ/cos²θ.
  • At θ = 0°: 0 + 1 − 0 = 1. ✓ Answer is 1.
• Answer: 1

[Hard] Compound Interest — Solve for Time

• EN: An investment doubles at 10% annual compound interest. Using the rule of 72, approximately how many years will it take to double?
• FR: Un investissement double à un taux d'intérêt composé annuel de 10 %. En utilisant la règle de 72, combien d'années faudra-t-il environ pour doubler?
• Choices: A) 5 years B) 7 years C) 9 years D) 10 years
• Hint: Rule of 72: divide 72 by the interest rate to estimate doubling time (e.g., at 8% interest: 72 ÷ 8 = 9 years).
• Steps:
  • Doubling time ≈ 72 ÷ interest rate.
  • 72 ÷ 10 = 7.2 ≈ 7 years.
• Answer: 7 years

[Easy] Permutations

• EN: In how many ways can 4 students be arranged in a row of 4 seats?
• FR: De combien de façons peut-on placer 4 élèves dans une rangée de 4 sièges?
• Choices: A) 16 B) 20 C) 24 D) 48
• Hint: Use factorial notation: n! = n × (n−1) × … × 1 (e.g., 3 people in 3 seats: 3! = 3 × 2 × 1 = 6 ways).
• Steps:
  • 4! = 4 × 3 × 2 × 1 = 24.
  • So there are 24 ways.
• Answer: 24

[Easy] Combinations

• EN: How many ways can you choose 2 toppings from 5 available toppings on a pizza?
• FR: De combien de façons peut-on choisir 2 garnitures parmi 5 disponibles sur une pizza?
• Choices: A) 8 B) 10 C) 12 D) 20
• Hint: Use C(n, r) = n! ÷ (r! × (n−r)!) (e.g., C(4,2) = 4!/(2! × 2!) = 24/4 = 6).
• Steps:
  • C(5, 2) = 5! ÷ (2! × 3!) = (5 × 4) ÷ (2 × 1) = 20 ÷ 2 = 10.
• Answer: 10

[Easy] Derivatives — Power Rule

• EN: Find the derivative of f(x) = x³.
• FR: Trouve la dérivée de f(x) = x³.
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n × x^(n−1) (e.g., f(x) = x⁴ → f'(x) = 4x³).
• Steps:
  • Bring down the exponent: 3.
  • Reduce exponent by 1: 3 − 1 = 2.
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Polynomial Functions

• EN: What are the zeros of f(x) = (x − 2)(x + 5)?
• FR: Quels sont les zéros de f(x) = (x − 2)(x + 5)?
• Choices: A) x = 2 and x = 5 B) x = −2 and x = 5 C) x = 2 and x = −5 D) x = −2 and x = −5
• Hint: Set each factor equal to zero and solve (e.g., (x − 4)(x + 1) = 0 → x = 4 or x = −1).
• Steps:
  • Set x − 2 = 0 → x = 2.
  • Set x + 5 = 0 → x = −5.
  • The zeros are x = 2 and x = −5.
• Answer: x = 2 and x = −5

[Medium] Derivative — Rate of Change

• EN: A ball's position is given by s(t) = 4t² + 3t. What is the velocity at t = 2 seconds?
• FR: La position d'une balle est donnée par s(t) = 4t² + 3t. Quelle est la vitesse à t = 2 secondes?
• Choices: A) 11 m/s B) 16 m/s C) 19 m/s D) 22 m/s
• Hint: Velocity = derivative of position; differentiate s(t) and substitute the time value (e.g., s(t) = 3t² + 2 → s'(t) = 6t → at t = 3: 6 × 3 = 18).
• Steps:
  • s'(t) = 8t + 3.
  • At t = 2: s'(2) = 8(2) + 3 = 16 + 3 = 19.
  • Velocity is 19 m/s.
• Answer: 19 m/s

[Medium] Probability Distribution

• EN: A fair six-sided die is rolled. Let X be the outcome. What is the expected value E(X)?
• FR: On lance un dé équilibré à six faces. Soit X le résultat. Quelle est la valeur attendue E(X)?
• Choices: A) 2.5 B) 3.0 C) 3.5 D) 4.0
• Hint: E(X) = sum of (each outcome × its probability); for equal probabilities, that is the average of all outcomes (e.g., die with faces 1, 2, 3: E(X) = (1+2+3)/3 = 2).
• Steps:
  • Outcomes: 1, 2, 3, 4, 5, 6; each with probability 1/6.
  • E(X) = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 3.5.
• Answer: 3.5

[Medium] Vectors — Addition

• EN: Vector a = (3, 5) and vector b = (−1, 4). What is a + b?
• FR: Le vecteur a = (3, 5) et le vecteur b = (−1, 4). Combien vaut a + b?
• Choices: A) (2, 8) B) (2, 9) C) (4, 9) D) (4, 1)
• Hint: Add corresponding components: (x₁ + x₂, y₁ + y₂) (e.g., (2, 3) + (4, 1) = (6, 4)).
• Steps:
  • x: 3 + (−1) = 2.
  • y: 5 + 4 = 9.
  • a + b = (2, 9).
• Answer: (2, 9)

[Medium] Rational Functions — Vertical Asymptote

• EN: Where is the vertical asymptote of the function f(x) = 1 / (x − 4)?
• FR: Où se trouve l'asymptote verticale de la fonction f(x) = 1 / (x − 4)?
• Choices: A) x = −4 B) x = 0 C) x = 1 D) x = 4
• Hint: A vertical asymptote occurs where the denominator equals zero (e.g., f(x) = 1/(x + 3): denominator = 0 when x = −3).
• Steps:
  • Set denominator to zero: x − 4 = 0.
  • x = 4.
  • So the vertical asymptote is x = 4.
• Answer: x = 4

[Hard] Permutations with Restrictions

• EN: How many 4-letter arrangements can be made from the letters A, B, C, D, E if the first letter must always be A?
• FR: Combien d'arrangements de 4 lettres peut-on former avec les lettres A, B, C, D, E si la première lettre doit toujours être A?
• Choices: A) 12 B) 24 C) 48 D) 60
• Hint: Fix the restricted position, then count the remaining arrangements (e.g., 4 letters with first fixed: 1 × 3 × 2 × 1 = 6 ways for positions 2, 3, 4).
• Steps:
  • First position: fixed as A (1 way).
  • Remaining 3 positions from 4 remaining letters: P(4, 3) = 4 × 3 × 2 = 24.
  • Total = 1 × 24 = 24.
• Answer: 24

[Hard] Derivative — Optimization

• EN: The profit function for a company is P(x) = −2x² + 40x − 50, where x is the number of items sold. How many items maximize the profit?
• FR: La fonction de profit d'une entreprise est P(x) = −2x² + 40x − 50, où x est le nombre d'articles vendus. Combien d'articles maximisent le profit?
• Choices: A) x = 8 B) x = 10 C) x = 12 D) x = 20
• Hint: Find the derivative, set it equal to zero, and solve for x (e.g., P(x) = −3x² + 12x → P'(x) = −6x + 12 = 0 → x = 2).
• Steps:
  • P'(x) = −4x + 40.
  • Set equal to zero: −4x + 40 = 0.
  • 4x = 40 → x = 10.
  • So 10 items maximize the profit.
• Answer: x = 10