Daily Math — 2026-08-04

[Easy] Counting Carrots

• EN: Kofi has 7 carrots. He picks 5 more. How many carrots does he have now?
• FR: Kofi a 7 carottes. Il en cueille 5 autres. Combien de carottes a-t-il maintenant?
• Choices: A) 10 carrots B) 11 carrots C) 12 carrots D) 13 carrots
• Hint: To add two numbers, count on from the bigger number (e.g., 6 + 3: start at 6, count 3 more → 9).
• Steps:
  • Start at 7 and count on 5 more.
  • 7 → 8, 9, 10, 11, 12.
  • So Kofi has 12 carrots.
• Answer: 12 carrots

[Easy] Snowballs in a Row

• EN: There are 9 snowballs in a row. A dog knocks over 4 of them. How many are still standing?
• FR: Il y a 9 boules de neige en rangée. Un chien en renverse 4. Combien sont encore debout?
• Choices: A) 4 snowballs B) 6 snowballs C) 5 snowballs D) 3 snowballs
• Hint: To subtract, count back from the bigger number (e.g., 8 − 3: start at 8, count back 3 → 5).
• Steps:
  • Start at 9 and count back 4.
  • 9 → 8, 7, 6, 5.
  • So 5 snowballs are still standing.
• Answer: 5 snowballs

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes after 12, 14, 16, ___?
• FR: Compte par 2. Quel nombre vient après 12, 14, 16, ___?
• Choices: A) 17 B) 18 C) 19 D) 20
• Hint: When you skip count by 2s, add 2 each time (e.g., 6, 8, 10, 12…).
• Steps:
  • The pattern adds 2 each time.
  • 16 + 2 = 18.
  • So the next number is 18.
• Answer: 18

[Easy] Which Is More?

• EN: Which number is bigger: 15 or 19?
• FR: Quel nombre est plus grand : 15 ou 19?
• Choices: A) 15 B) 19 C) They are equal D) 11
• Hint: When comparing two numbers, the one that is farther right on a number line is bigger (e.g., 7 is bigger than 4).
• Steps:
  • Find 15 and 19 on the number line.
  • 19 is farther to the right.
  • So 19 is the bigger number.
• Answer: 19

[Medium] Adding at the Hockey Rink

• EN: The Maple Leafs scored 6 goals in the first period and 8 goals in the second period. How many goals did they score in all?
• FR: Les Maple Leafs ont marqué 6 buts en première période et 8 buts en deuxième période. Combien de buts ont-ils marqué en tout?
• Choices: A) 12 goals B) 13 goals C) 14 goals D) 15 goals
• Hint: Add the two groups together (e.g., 5 + 7 = 12).
• Steps:
  • We need to add 6 + 8.
  • Start at 8 (the bigger number) and count on 6: 9, 10, 11, 12, 13, 14.
  • So the total is 14 goals.
• Answer: 14 goals

[Medium] Penny Count

• EN: Amara has 3 pennies and 2 nickels. How many cents does she have in all?
• FR: Amara a 3 sous et 2 pièces de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 10 cents B) 13 cents C) 15 cents D) 8 cents
• Hint: A penny is worth 1 cent and a nickel is worth 5 cents. Add them up (e.g., 2 pennies + 1 nickel = 2 + 5 = 7 cents).
• Steps:
  • 3 pennies = 3 cents.
  • 2 nickels = 2 × 5 = 10 cents.
  • 3 + 10 = 13 cents.
• Answer: 13 cents

[Medium] Skip Counting by 10s

• EN: Skip count by 10s: 20, 30, 40, ___. What is the missing number?
• FR: Compte par 10 : 20, 30, 40, ___. Quel est le nombre manquant?
• Choices: A) 41 B) 44 C) 50 D) 55
• Hint: Add 10 each time you skip count by 10s (e.g., 10, 20, 30, the next is 40).
• Steps:
  • The pattern adds 10 each time.
  • 40 + 10 = 50.
  • The missing number is 50.
• Answer: 50

[Medium] Subtracting Stickers

• EN: Maya has 18 stickers. She gives 9 to her friend. How many stickers does Maya have left?
• FR: Maya a 18 autocollants. Elle en donne 9 à son amie. Combien d'autocollants Maya a-t-elle?
• Choices: A) 7 stickers B) 8 stickers C) 9 stickers D) 10 stickers
• Hint: To subtract, count back or think of the related addition fact (e.g., 15 − 7: think 7 + ? = 15, so the answer is 8).
• Steps:
  • Start at 18 and subtract 9.
  • Think: 9 + 9 = 18, so 18 − 9 = 9.
  • Maya has 9 stickers left.
• Answer: 9 stickers

[Hard] Counting to 100 — What's Missing?

• EN: Fill in the missing number: 74, 76, 78, ___, 82.
• FR: Trouve le nombre manquant : 74, 76, 78, ___, 82.
• Choices: A) 79 B) 80 C) 81 D) 83
• Hint: When numbers increase by 2 each time, add 2 to the number before the blank (e.g., 4, 6, 8, ___, 12 → 8 + 2 = 10).
• Steps:
  • The pattern adds 2 each time.
  • 78 + 2 = 80.
  • Check: 80 + 2 = 82. Yes, that works!
• Answer: 80

[Hard] Three Groups of Apples

• EN: There are 5 red apples, 6 green apples, and 4 yellow apples in a basket. How many apples are there in all?
• FR: Il y a 5 pommes rouges, 6 pommes vertes et 4 pommes jaunes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 13 apples B) 14 apples C) 15 apples D) 16 apples
• Hint: Add three numbers by first adding two of them, then adding the third (e.g., 3 + 4 + 2: first 3 + 4 = 7, then 7 + 2 = 9).
• Steps:
  • First add 5 + 6 = 11.
  • Then add 11 + 4 = 15.
  • There are 15 apples in all.
• Answer: 15 apples

[Easy] Adding Two-Digit Numbers

• EN: There are 32 students in one class and 25 students in another. How many students are there in all?
• FR: Il y a 32 élèves dans une classe et 25 dans une autre. Combien y a-t-il d'élèves en tout?
• Choices: A) 55 students B) 57 students C) 58 students D) 60 students
• Hint: Add the ones first, then the tens (e.g., 41 + 23: ones 1 + 3 = 4, tens 4 + 2 = 6, so 64).
• Steps:
  • Ones: 2 + 5 = 7.
  • Tens: 3 + 2 = 5.
  • So 32 + 25 = 57 students.
• Answer: 57 students

[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 12 et la petite sur 3. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 12:30
• 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.
  • 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 lengths, subtract the shorter from the longer (e.g., 18 cm − 11 cm = 7 cm).
• Steps:
  • Subtract the shorter length from the longer: 14 − 9.
  • 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Coin Counting

• EN: Leo has 2 dimes and 3 nickels. How much money does he have?
• FR: Leo a 2 pièces de 10 cents et 3 pièces de 5 cents. Combien d'argent a-t-il?
• Choices: A) 25 cents B) 30 cents C) 35 cents D) 40 cents
• Hint: A dime = 10 cents, a nickel = 5 cents. Multiply, then add (e.g., 3 dimes + 2 nickels = 30 + 10 = 40 cents).
• Steps:
  • 2 dimes = 2 × 10 = 20 cents.
  • 3 nickels = 3 × 5 = 15 cents.
  • 20 + 15 = 35 cents.
• Answer: 35 cents

[Medium] Subtracting at the Market

• EN: There were 84 apples at the market. By noon, 47 were sold. How many apples are left?
• FR: Il y avait 84 pommes au marché. À midi, 47 ont été vendues. Combien reste-t-il de pommes?
• Choices: A) 36 apples B) 37 apples C) 38 apples D) 47 apples
• Hint: To subtract two-digit numbers, subtract the ones first (regroup if needed), then the tens (e.g., 63 − 28: borrow to get 13 − 8 = 5, then 5 − 2 = 3, so 35).
• Steps:
  • Ones: 4 − 7, need to regroup. Borrow from tens: 14 − 7 = 7.
  • Tens: 7 − 4 = 3 (after borrowing, 8 becomes 7).
  • So 84 − 47 = 37 apples.
• Answer: 37 apples

[Medium] Half-Hour Time

• EN: School starts at 8:00. Reading class begins 30 minutes later. What time does reading class begin?
• FR: L'école commence à 8 h. La classe de lecture commence 30 minutes plus tard. À quelle heure commence-t-elle?
• Choices: A) 8:03 B) 8:15 C) 8:30 D) 9:00
• Hint: Adding 30 minutes to an o'clock time gives a half-hour time (e.g., 5:00 + 30 minutes = 5:30).
• Steps:
  • Start at 8:00.
  • Add 30 minutes.
  • 8:00 + 30 minutes = 8:30.
• Answer: 8:30

[Medium] Repeating Patterns

• EN: The pattern is: star, circle, circle, star, circle, circle, ___. What shape comes next?
• FR: Le motif est : étoile, cercle, cercle, étoile, cercle, cercle, ___. Quelle forme vient ensuite?
• Choices: A) circle B) star C) triangle D) square
• Hint: Find the repeating unit and figure out where you are in the cycle (e.g., A, B, B, A, B, B → the next is A).
• Steps:
  • The repeating unit is: star, circle, circle.
  • After star, circle, circle, the pattern starts again with star.
  • The next shape is star.
• Answer: star

[Medium] Measuring with Metres

• EN: A hallway is 6 metres long. Another hallway is 8 metres long. How long are they together?
• FR: Un couloir mesure 6 mètres de long. Un autre mesure 8 mètres de long. Quelle est leur longueur totale?
• Choices: A) 12 metres B) 13 metres C) 14 metres D) 15 metres
• Hint: Add both lengths together (e.g., 5 m + 7 m = 12 m).
• Steps:
  • Add 6 + 8.
  • 6 + 8 = 14.
  • The total length is 14 metres.
• Answer: 14 metres

[Hard] Making Change

• EN: Priya buys a muffin for 65 cents. She pays with a dollar (100 cents). How much change does she get back?
• FR: Priya achète un muffin pour 65 cents. Elle paie avec un dollar (100 cents). Combien de monnaie reçoit-elle?
• Choices: A) 25 cents B) 35 cents C) 45 cents D) 55 cents
• Hint: Subtract the price from 100 cents to find the change (e.g., if the price is 70 cents, change = 100 − 70 = 30 cents).
• Steps:
  • Change = 100 − 65.
  • 100 − 65 = 35.
  • Priya gets 35 cents back.
• Answer: 35 cents

[Hard] Two-Step Problem

• EN: Yuki has 50 hockey cards. She buys 18 more, then gives 23 to her brother. How many cards does Yuki have now?
• FR: Yuki a 50 cartes de hockey. Elle en achète 18 autres, puis en donne 23 à son frère. Combien de cartes Yuki a-t-elle maintenant?
• Choices: A) 41 cards B) 43 cards C) 45 cards D) 47 cards
• Hint: For two-step problems, do one operation at a time (e.g., start with 40, add 10 = 50, then subtract 15 = 35).
• Steps:
  • Step 1: 50 + 18 = 68 cards.
  • Step 2: 68 − 23 = 45 cards.
  • Yuki has 45 cards now.
• Answer: 45 cards

[Easy] Multiplication by 2

• EN: There are 6 pairs of mittens in a bin. How many mittens are there in all?
• FR: Il y a 6 paires de mitaines dans un bac. 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 add the number to itself (e.g., 5 pairs = 5 × 2 = 10 mittens).
• Steps:
  • Each pair has 2 mittens.
  • 6 × 2 = 12.
  • There are 12 mittens in all.
• Answer: 12 mittens

[Easy] Basic Division

• EN: There are 20 cookies shared equally among 4 friends. How many cookies does each friend get?
• FR: Il y a 20 biscuits partagés également entre 4 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 4 cookies B) 5 cookies C) 6 cookies D) 8 cookies
• Hint: Division means sharing equally — ask "how many times does the divisor fit?" (e.g., 15 ÷ 3: 3 × 5 = 15, so the answer is 5).
• Steps:
  • We need to find 20 ÷ 4.
  • Ask: 4 × ? = 20. The answer is 5.
  • Each friend gets 5 cookies.
• Answer: 5 cookies

[Easy] Understanding Fractions

• EN: A pizza is cut into 4 equal slices. Emma eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 tranches égales. Emma mange 1 tranche. 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 is parts eaten over total equal parts (e.g., 1 out of 3 equal parts = 1/3).
• Steps:
  • The pizza has 4 equal parts (denominator = 4).
  • Emma ate 1 part (numerator = 1).
  • The fraction is 1/4.
• Answer: 1/4

[Easy] Skip Counting by 5s

• EN: Liam counts his hockey pucks by 5s: 5, 10, 15, ___. What is the next number?
• FR: Liam compte ses rondelles par 5 : 5, 10, 15, ___. Quel est le prochain nombre?
• Choices: A) 18 B) 20 C) 25 D) 30
• Hint: Each time you skip count by 5, add 5 to the last number (e.g., 25 + 5 = 30).
• Steps:
  • The pattern adds 5 each time.
  • 15 + 5 = 20.
  • The next number is 20.
• Answer: 20

[Medium] Multiplication by 4

• EN: A box holds 4 crayons. There are 7 boxes on the shelf. How many crayons are there in all?
• FR: Une boîte contient 4 crayons. Il y a 7 boîtes sur l'étagère. Combien y a-t-il de crayons en tout?
• Choices: A) 24 crayons B) 28 crayons C) 32 crayons D) 36 crayons
• Hint: Multiply the number of groups by the number in each group (e.g., 4 × 6 = 24).
• Steps:
  • Number of boxes × crayons per box.
  • 7 × 4 = 28.
  • There are 28 crayons in all.
• Answer: 28 crayons

[Medium] Perimeter of a Rectangle

• EN: A rectangular garden is 5 m long and 3 m wide. What is its perimeter?
• FR: Un jardin rectangulaire mesure 5 m de long et 3 m de large. Quel est son périmètre?
• Choices: A) 14 m B) 15 m C) 16 m D) 18 m
• Hint: Perimeter of a rectangle = length + length + width + width (e.g., 4 + 4 + 2 + 2 = 12 m).
• Steps:
  • Add all four sides: 5 + 5 + 3 + 3.
  • 5 + 5 = 10; 3 + 3 = 6.
  • 10 + 6 = 16 m.
• Answer: 16 m

[Medium] Reading a Bar Graph

• EN: A bar graph shows that 8 students like hockey, 5 like skating, and 3 like skiing. How many students were surveyed in total?
• FR: Un graphique à barres montre que 8 élèves aiment le hockey, 5 aiment le patinage et 3 aiment le ski. Combien d'élèves ont été sondés en tout?
• Choices: A) 13 students B) 14 students C) 15 students D) 16 students
• Hint: Add all the categories together to find the total (e.g., 6 + 4 + 2 = 12).
• Steps:
  • Add: 8 + 5 + 3.
  • 8 + 5 = 13; 13 + 3 = 16.
  • There were 16 students surveyed in total.
• Answer: 16 students

[Medium] Multiplication by 10

• EN: There are 9 boxes of Tim Hortons Timbits. Each box holds 10 Timbits. How many Timbits are there in all?
• FR: Il y a 9 boîtes de Timbits de Tim Hortons. Chaque boîte contient 10 Timbits. Combien y a-t-il de Timbits en tout?
• Choices: A) 80 Timbits B) 85 Timbits C) 90 Timbits D) 100 Timbits
• Hint: Multiplying by 10 always adds a zero at the end of the number (e.g., 7 × 10 = 70).
• Steps:
  • 9 × 10 = 90.
  • There are 90 Timbits in all.
• Answer: 90 Timbits

[Hard] Comparing Fractions

• EN: Which fraction is larger: 1/2 or 1/3?
• FR: Quelle fraction est plus grande : 1/2 ou 1/3?
• Choices: A) 1/3 B) 1/2 C) They are equal D) 2/3
• Hint: When the numerators are the same (both 1), the bigger fraction has the smaller denominator — fewer pieces means each piece is bigger (e.g., 1/4 vs. 1/5: 1/4 is bigger).
• Steps:
  • Both fractions have 1 part.
  • 1/2 means 1 part out of 2 equal pieces — each piece is big.
  • 1/3 means 1 part out of 3 equal pieces — each piece is smaller.
  • So 1/2 is larger.
• Answer: 1/2

[Hard] Two-Step Multiplication and Subtraction

• EN: A bookshelf has 5 rows with 3 books in each row. The librarian removes 6 books. How many books are left?
• FR: Une bibliothèque a 5 rangées avec 3 livres chacune. La bibliothécaire enlève 6 livres. Combien de livres reste-t-il?
• Choices: A) 7 books B) 8 books C) 9 books D) 11 books
• Hint: First multiply to find the total, then subtract (e.g., 4 rows × 5 books = 20 books; 20 − 7 = 13 books).
• Steps:
  • Step 1: Total books = 5 × 3 = 15 books.
  • Step 2: 15 − 6 = 9 books.
  • There are 9 books left.
• Answer: 9 books

[Easy] Multiplication Facts

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 48
• Hint: Use skip counting or a multiplication pattern (e.g., 6 × 8 = 48, then add one more group of 8 to get 7 × 8).
• Steps:
  • 6 × 8 = 48.
  • Add one more group of 8: 48 + 8 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, what digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre est à la place des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 2
• Hint: In a decimal number, the tenths place is the first digit after the decimal point (e.g., in 5.62, the digit 6 is in the tenths place).
• Steps:
  • The decimal point separates wholes from parts.
  • The first digit after the decimal point is the tenths place.
  • In 3.47, the digit 4 is in the tenths place.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A classroom rug is 6 m long and 4 m wide. What is its area?
• FR: Un tapis de classe mesure 6 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 20 m² B) 22 m² C) 24 m² D) 28 m²
• Hint: Area of a rectangle = length × width (e.g., 5 m × 3 m = 15 m²).
• Steps:
  • Area = length × width.
  • Area = 6 × 4 = 24.
  • The area is 24 m².
• Answer: 24 m²

[Easy] Comparing Fractions

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

[Medium] Long Division with Remainders

• EN: A teacher has 29 pencils to share equally among 4 students. How many pencils does each student get, and how many are left over?
• FR: Un enseignant a 29 crayons à partager également entre 4 élèves. Combien de crayons chaque élève reçoit-il, et combien en reste-t-il?
• Choices: A) 6 remainder 5 B) 7 remainder 1 C) 8 remainder 3 D) 5 remainder 9
• Hint: Divide, then check: (quotient × divisor) + remainder = dividend (e.g., 23 ÷ 5: 5 × 4 = 20, remainder = 23 − 20 = 3, so 4 remainder 3).
• Steps:
  • 4 × 7 = 28, which is the closest multiple of 4 that does not exceed 29.
  • Remainder: 29 − 28 = 1.
  • Each student gets 7 pencils with 1 left over.
• Answer: 7 remainder 1

[Medium] Elapsed Time

• EN: A hockey game starts at 6:15 p.m. and ends at 8:45 p.m. How long did the game last?
• FR: Un match de hockey commence à 18 h 15 et se termine à 20 h 45. Combien de temps a duré le match?
• Choices: A) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours
• Hint: Count up from the start time to the end time in steps (e.g., 4:20 to 6:50: from 4:20 to 6:20 = 2 hours, then 6:20 to 6:50 = 30 minutes, total = 2 hours 30 minutes).
• Steps:
  • From 6:15 to 8:15 = 2 hours.
  • From 8:15 to 8:45 = 30 minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: Nia buys a notebook for $2.35 and a pen for $1.50. How much does she spend in total?
• FR: Nia achète un cahier pour 2,35 $ et un stylo pour 1,50 $. Combien dépense-t-elle en tout?
• Choices: A) $3.75 B) $3.80 C) $3.85 D) $4.00
• Hint: Line up the decimal points when adding decimals (e.g., 3.45 + 2.30: 5 + 0 = 5, 4 + 3 = 7, 3 + 2 = 5, so 5.75).
• Steps:
  • 2.35 + 1.50.
  • Cents: 35 + 50 = 85 cents.
  • Dollars: 2 + 1 = 3 dollars.
  • Total: $3.85.
• Answer: $3.85

[Medium] All Times Tables

• EN: A carton holds 9 eggs. There are 8 cartons in the fridge. How many eggs are there in all?
• FR: Une boîte contient 9 œufs. Il y a 8 boîtes dans le réfrigérateur. Combien y a-t-il d'œufs en tout?
• Choices: A) 63 eggs B) 72 eggs C) 81 eggs D) 54 eggs
• Hint: Multiply the number of groups by the size of each group (e.g., 7 × 9 = 63).
• Steps:
  • 8 × 9 = 72.
  • There are 72 eggs in all.
• Answer: 72 eggs

[Hard] Multi-Step Decimal Problem

• EN: Theo has $10.00. He buys a sandwich for $3.75 and a juice for $1.50. How much money does Theo have left?
• FR: Theo a 10,00 $. Il achète un sandwich pour 3,75 $ et un jus pour 1,50 $. Combien d'argent Theo a-t-il?
• Choices: A) $4.50 B) $4.75 C) $5.25 D) $5.75
• Hint: Add the two purchases together, then subtract from the starting amount (e.g., spend $2.50 + $1.25 = $3.75; $10.00 − $3.75 = $6.25).
• Steps:
  • Total spent: $3.75 + $1.50 = $5.25.
  • Money left: $10.00 − $5.25 = $4.75.
  • Theo has $4.75 left.
• Answer: $4.75

[Hard] Long Division and Area

• EN: A rectangular swimming pool has an area of 56 m². Its length is 8 m. What is its width?
• FR: Une piscine rectangulaire a une aire de 56 m². Sa longueur est de 8 m. Quelle est sa largeur?
• Choices: A) 6 m B) 7 m C) 8 m D) 9 m
• Hint: Area = length × width, so width = area ÷ length (e.g., area = 45 m², length = 9 m, width = 45 ÷ 9 = 5 m).
• Steps:
  • Width = area ÷ length = 56 ÷ 8.
  • 8 × 7 = 56.
  • The width is 7 m.
• Answer: 7 m

[Easy] Multi-Digit Multiplication

• EN: A school orders 24 boxes of markers. Each box has 12 markers. How many markers are there in all?
• FR: Une école commande 24 boîtes de marqueurs. Chaque boîte contient 12 marqueurs. Combien y a-t-il de marqueurs en tout?
• Choices: A) 248 markers B) 268 markers C) 288 markers D) 308 markers
• Hint: Use the standard multiplication algorithm (e.g., 23 × 11: 23 × 1 = 23, 23 × 10 = 230, total = 253).
• Steps:
  • 24 × 12: break it up as 24 × 10 + 24 × 2.
  • 24 × 10 = 240; 24 × 2 = 48.
  • 240 + 48 = 288 markers.
• Answer: 288 markers

[Easy] Adding Fractions with Like Denominators

• EN: Sophie ate 2/8 of a pie and her brother ate 3/8. How much pie did they eat together?
• FR: Sophie a mangé 2/8 d'une tarte et son frère en a mangé 3/8. Quelle fraction de la tarte ont-ils mangée ensemble?
• Choices: A) 5/16 B) 5/8 C) 6/8 D) 4/8
• Hint: When denominators are the same, just add the numerators and keep the denominator (e.g., 3/7 + 2/7 = 5/7).
• Steps:
  • Add the numerators: 2 + 3 = 5.
  • Keep the denominator: 8.
  • They ate 5/8 of the pie together.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: A bag of 40 candies is shared. 50% are given away. How many candies are given away?
• FR: Un sac de 40 bonbons est partagé. 50 % sont donnés. Combien de bonbons sont donnés?
• Choices: A) 10 candies B) 20 candies C) 25 candies D) 40 candies
• Hint: 50% means half of the total (e.g., 50% of 60 = 60 ÷ 2 = 30).
• Steps:
  • 50% = half.
  • 40 ÷ 2 = 20.
  • 20 candies are given away.
• Answer: 20 candies

[Easy] Decimal Subtraction

• EN: Snowfall measured 8.75 cm on Monday and 3.20 cm on Tuesday. How much more snow fell on Monday?
• FR: Il est tombé 8,75 cm de neige lundi et 3,20 cm mardi. Combien de centimètres de plus sont tombés lundi?
• Choices: A) 5.45 cm B) 5.55 cm C) 5.65 cm D) 6.55 cm
• Hint: Line up the decimal points and subtract (e.g., 9.80 − 4.35: hundredths 0 − 5, borrow… → 5.45).
• Steps:
  • 8.75 − 3.20.
  • Hundredths: 5 − 0 = 5. Tenths: 7 − 2 = 5. Ones: 8 − 3 = 5.
  • The difference is 5.55 cm.
• Answer: 5.55 cm

[Medium] Multi-Digit Division

• EN: A farmer packs 312 apples equally into 8 crates. How many apples are in each crate?
• FR: Un fermier emballe 312 pommes également dans 8 caisses. Combien y a-t-il de pommes dans chaque caisse?
• Choices: A) 36 apples B) 38 apples C: 39 apples D) 41 apples
• Hint: Use long division step by step (e.g., 256 ÷ 8: 8 goes into 25 three times giving 24, remainder 1, bring down 6 to get 16, 8 × 2 = 16, so the answer is 32).
• Steps:
  • 8 goes into 31 three times (8 × 3 = 24), remainder 7. Bring down 2 to get 72.
  • Wait — let's redo: 8 into 312. 8 × 3 = 24 (hundreds not quite). Use long division: 8 × 39 = 312.
  • So each crate has 39 apples.
• Answer: 39 apples

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume = length × width × height (e.g., 6 × 2 × 4 = 48 cm³).
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions with Like Denominators

• EN: A jug holds 7/10 of a litre of juice. Marcus drinks 3/10. How much juice is left?
• FR: Une cruche contient 7/10 de litre de jus. Marcus boit 3/10. Combien de jus reste-t-il?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: Subtract the numerators and keep the denominator (e.g., 6/9 − 2/9 = 4/9).
• Steps:
  • Subtract numerators: 7 − 3 = 4.
  • Keep the denominator: 10.
  • There is 4/10 of a litre left.
• Answer: 4/10

[Medium] Percentage — 25% and 10%

• EN: A hockey jersey originally costs $80. It is on sale for 25% off. How much is the discount?
• FR: Un chandail de hockey coûte originalement 80 $. Il est en solde à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $8 B) $16 C) $20 D) $25
• Hint: 25% = one quarter. Divide by 4 to find 25% (e.g., 25% of $60 = $60 ÷ 4 = $15).
• Steps:
  • 25% of $80 = $80 ÷ 4.
  • $80 ÷ 4 = $20.
  • The discount is $20.
• Answer: $20

[Hard] Multi-Step Fraction and Decimal Problem

• EN: A recipe needs 1/4 cup of butter for one batch of cookies. Zara makes 3 batches and has 0.9 cups of butter. After using the butter, how much butter does she have left? (Give your answer as a decimal.)
• FR: Une recette nécessite 1/4 de tasse de beurre pour une fournée de biscuits. Zara fait 3 fournées et a 0,9 tasse de beurre. Après avoir utilisé le beurre, combien en reste-t-il?
• Choices: A) 0.10 cups B) 0.15 cups C) 0.20 cups D) 0.25 cups
• Hint: Find the total butter needed (fractions × whole number), convert to decimal, then subtract (e.g., 3 × 1/3 = 1 cup; 1.5 − 1.0 = 0.5 cups).
• Steps:
  • Butter needed: 3 × 1/4 = 3/4 = 0.75 cups.
  • Butter left: 0.9 − 0.75 = 0.15 cups.
  • She has 0.15 cups of butter left.
• Answer: 0.15 cups

[Hard] Volume and Multi-Digit Division

• EN: A storage room has a volume of 720 m³. It is 12 m long and 6 m wide. How tall is the room?
• FR: Une salle de rangement a un volume de 720 m³. Elle mesure 12 m de long et 6 m de large. Quelle est la hauteur de la pièce?
• Choices: A) 8 m B) 10 m C) 12 m D) 15 m
• Hint: Volume = l × w × h, so h = Volume ÷ (l × w) (e.g., V = 120, l = 5, w = 4: h = 120 ÷ 20 = 6 m).
• Steps:
  • h = 720 ÷ (12 × 6).
  • 12 × 6 = 72.
  • 720 ÷ 72 = 10.
  • The room is 10 m tall.
• Answer: 10 m

[Easy] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2.
• FR: Calcule : 3 + 4 × 2.
• Choices: A) 14 B) 11 C) 10 D) 16
• Hint: In BEDMAS, multiplication is done before addition (e.g., 5 + 2 × 3 = 5 + 6 = 11).
• Steps:
  • Do multiplication first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Percent of a Number

• EN: What is 10% of $60?
• FR: Quel est 10 % de 60 $?
• Choices: A) $5 B) $6 C) $10 D) $16
• Hint: 10% of any number = divide by 10 (e.g., 10% of 90 = 90 ÷ 10 = 9).
• Steps:
  • 10% = divide by 10.
  • $60 ÷ 10 = $6.
  • 10% of $60 is $6.
• Answer: $6

[Easy] Integers — Comparing

• EN: Which integer is greater: −5 or −2?
• FR: Quel entier est le plus grand : −5 ou −2?
• Choices: A) −5 B) −2 C) They are equal D) −7
• Hint: On a number line, the integer farther to the right is greater (e.g., −3 > −8 because −3 is farther right).
• Steps:
  • Place −5 and −2 on a number line.
  • −2 is to the right of −5.
  • So −2 is greater.
• Answer: −2

[Easy] Simple Algebraic Expression

• EN: If n = 5, what is the value of 3n + 4?
• FR: Si n = 5, quelle est la valeur de 3n + 4?
• Choices: A) 17 B) 18 C) 19 D) 22
• Hint: Substitute the value for the variable, then evaluate (e.g., if x = 3, then 4x + 2 = 4(3) + 2 = 14).
• Steps:
  • Replace n with 5: 3(5) + 4.
  • 3 × 5 = 15; 15 + 4 = 19.
  • The value is 19.
• Answer: 19

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Quel est le résultat de 2/3 × 3/4?
• Choices: A) 5/7 B) 6/12 C) 1/2 D) 5/12
• Hint: Multiply numerators together and 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] Ratios and Rates

• EN: A car travels 150 km in 3 hours. What is the car's speed in km per hour?
• FR: Une voiture parcourt 150 km en 3 heures. Quelle est sa vitesse en km par heure?
• Choices: A) 40 km/h B) 45 km/h C) 50 km/h D) 55 km/h
• Hint: To find a unit rate, divide the total by the number of units (e.g., 120 km in 4 hours = 120 ÷ 4 = 30 km/h).
• Steps:
  • Speed = distance ÷ time.
  • 150 ÷ 3 = 50.
  • The car's speed is 50 km/h.
• Answer: 50 km/h

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Quel est le résultat de 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 3/2 C) 1/2 D) 6/4
• Hint: To divide fractions, multiply by the reciprocal of the second fraction (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.
  • Simplify: 6/4 = 3/2.
• Answer: 3/2

[Medium] BEDMAS with Brackets

• EN: Evaluate: (8 + 2) × 3 − 4.
• FR: Calcule : (8 + 2) × 3 − 4.
• Choices: A) 26 B) 28 C) 30 D) 22
• Hint: Always solve what is inside brackets first, then multiply, then add or subtract (e.g., (5 + 1) × 4 − 2 = 6 × 4 − 2 = 24 − 2 = 22).
• Steps:
  • Brackets: 8 + 2 = 10.
  • Multiply: 10 × 3 = 30.
  • Subtract: 30 − 4 = 26.
• Answer: 26

[Hard] Percent of a Number — Multi-Step

• EN: A winter jacket costs $120. The store is offering a 15% discount. What is the sale price?
• FR: Un manteau d'hiver coûte 120 $. Le magasin offre un rabais de 15 %. Quel est le prix de vente?
• Choices: A) $100 B) $102 C) $105 D) $108
• Hint: Find 15% (= 10% + 5%) of the price, then subtract from the original (e.g., 15% of $80: 10% = $8, 5% = $4, total discount = $12, sale price = $80 − $12 = $68).
• Steps:
  • 10% of $120 = $12; 5% of $120 = $6; 15% = $18.
  • Sale price = $120 − $18 = $102.
  • The sale price is $102.
• Answer: $102

[Hard] Integers and Algebraic Expression

• EN: If x = −3, what is the value of 2x² − x + 5?
• FR: Si x = −3, quelle est la valeur de 2x² − x + 5?
• Choices: A) 20 B) 26 C) 28 D) 32
• Hint: Substitute carefully, remembering that squaring a negative gives a positive (e.g., if x = −2: 3x² − x = 3(4) − (−2) = 12 + 2 = 14).
• Steps:
  • x = −3; x² = 9.
  • 2(9) − (−3) + 5 = 18 + 3 + 5.
  • 18 + 3 + 5 = 26.
• Answer: 26

[Easy] Integer Addition

• EN: What is (−8) + 5?
• FR: Quel est le résultat de (−8) + 5?
• Choices: A) −3 B) 3 C) −13 D) 13
• Hint: When adding a positive to a negative, find the difference and use the sign of the bigger absolute value (e.g., (−6) + 4 = −2).
• Steps:
  • |−8| = 8 and |5| = 5; difference = 8 − 5 = 3.
  • The bigger absolute value is 8 (negative), so the answer is negative.
  • (−8) + 5 = −3.
• Answer: −3

[Easy] Percent — Tip Calculation

• EN: A meal at a Canadian diner costs $20. You want to leave a 15% tip. How much is the tip?
• FR: Un repas dans un restaurant canadien coûte 20 $. Tu veux laisser un pourboire de 15 %. Quel est le montant du pourboire?
• Choices: A) $2.50 B) $3.00 C) $3.50 D) $4.00
• Hint: Find 15% by calculating 10% and 5%, then add them (e.g., 15% of $40: 10% = $4, 5% = $2, tip = $6).
• Steps:
  • 10% of $20 = $2.00; 5% of $20 = $1.00.
  • 15% = $2.00 + $1.00 = $3.00.
  • The tip is $3.00.
• Answer: $3.00

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x : x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: Isolate the variable by doing the opposite operation on both sides (e.g., x + 5 = 12 → x = 12 − 5 = 7).
• Steps:
  • Subtract 9 from both sides: x + 9 − 9 = 17 − 9.
  • x = 8.
  • Check: 8 + 9 = 17. Correct!
• Answer: x = 8

[Easy] Integer Subtraction

• EN: What is 4 − (−6)?
• FR: Quel est le résultat de 4 − (−6)?
• Choices: A) −2 B) 2 C) 10 D) 14
• Hint: Subtracting a negative is the same as adding a positive (e.g., 3 − (−5) = 3 + 5 = 8).
• Steps:
  • Change the double negative: 4 − (−6) = 4 + 6.
  • 4 + 6 = 10.
  • The answer is 10.
• Answer: 10

[Medium] Percentage — Discount

• EN: A pair of skates originally costs $160. They are on sale for 20% off. What is the sale price?
• FR: Une paire de patins coûte originalement 160 $. Elle est en solde à 20 % de rabais. Quel est le prix de vente?
• Choices: A) $120 B) $128 C) $132 D) $140
• Hint: Find the discount amount (% × original price), then subtract (e.g., 20% off $50: discount = $10, sale price = $40).
• Steps:
  • Discount: 20% of $160 = 0.20 × 160 = $32.
  • Sale price: $160 − $32 = $128.
  • The sale price is $128.
• Answer: $128

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 5 cm long, 4 cm wide, and 3 cm tall. What is the total surface area of the box?
• FR: Une boîte cadeau mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quelle est l'aire totale de la surface de la boîte?
• Choices: A) 74 cm² B) 78 cm² C) 84 cm² D) 94 cm²
• Hint: SA = 2(lw + lh + wh) (e.g., l=4, w=3, h=2: SA = 2(12 + 8 + 6) = 2 × 26 = 52 cm²).
• Steps:
  • lw = 5 × 4 = 20; lh = 5 × 3 = 15; wh = 4 × 3 = 12.
  • SA = 2(20 + 15 + 12) = 2 × 47 = 94.
  • The surface area is 94 cm².
• Answer: 94 cm²

[Medium] Integer Multiplication

• EN: What is (−7) × (−4)?
• FR: Quel est le résultat de (−7) × (−4)?
• Choices: A) −28 B) 11 C) 28 D) −11
• Hint: When you multiply two negatives, the result is positive (e.g., (−3) × (−5) = 15).
• Steps:
  • Multiply the absolute values: 7 × 4 = 28.
  • Two negatives make a positive.
  • (−7) × (−4) = 28.
• Answer: 28

[Medium] Probability

• EN: A bag has 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of randomly picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 billes bleues et 2 billes vertes. Quelle est la probabilité de tirer au hasard une bille bleue?
• Choices: A) 1/2 B) 5/10 C) 3/10 D) 7/10
• Hint: Probability = (number of favourable outcomes) ÷ (total outcomes) (e.g., P(red) = 4 out of 10 = 4/10 = 2/5).
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Blue marbles: 5.
  • P(blue) = 5/10.
• Answer: 5/10

[Hard] Tax Calculation

• EN: A bicycle costs $250 before tax. Ontario's HST is 13%. What is the total price including tax?
• FR: Un vélo coûte 250 $ avant taxes. La TVH de l'Ontario est de 13 %. Quel est le prix total avec taxes?
• Choices: A) $277.50 B) $280.00 C) $282.50 D) $285.00
• Hint: Total with tax = original price × (1 + tax rate as decimal) (e.g., $200 at 10% tax: $200 × 1.10 = $220).
• Steps:
  • Tax = 13% of $250 = 0.13 × 250 = $32.50.
  • Total = $250 + $32.50 = $282.50.
  • The total price is $282.50.
• Answer: $282.50

[Hard] Two-Step Equation and Integers

• EN: Solve for y: 3y − (−5) = 20.
• FR: Résous pour y : 3y − (−5) = 20.
• Choices: A) y = 4 B) y = 5 C) y = 6 D) y = 7
• Hint: Simplify the double negative first, then isolate the variable (e.g., 2x − (−3) = 11 → 2x + 3 = 11 → 2x = 8 → x = 4).
• Steps:
  • Simplify: 3y − (−5) = 3y + 5 = 20.
  • Subtract 5: 3y = 15.
  • Divide by 3: y = 5.
• Answer: y = 5

[Easy] Perfect Squares

• EN: What is √144?
• FR: Quelle est la valeur de √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: A perfect square root asks "what number times itself equals this?" (e.g., √81 = 9 because 9 × 9 = 81).
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored 72, 85, 90, 68, and 75 on a test. What is the mean score?
• FR: Cinq élèves ont obtenu 72, 85, 90, 68 et 75 à un test. Quelle est la note moyenne?
• Choices: A) 76 B) 78 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: 72 + 85 + 90 + 68 + 75 = 390.
  • Mean: 390 ÷ 5 = 78.
  • The mean score is 78.
• Answer: 78

[Easy] Two-Step 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: Undo addition first, then undo multiplication (e.g., 3x + 5 = 14 → 3x = 9 → x = 3).
• Steps:
  • Subtract 3 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
  • Check: 2(4) + 3 = 11. Correct!
• Answer: x = 4

[Easy] Percent Increase

• EN: A hockey player scored 20 goals last season and 25 goals this season. What is the percent increase?
• FR: Un joueur de hockey a marqué 20 buts la saison dernière et 25 cette saison. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 25% C) 5% D) 50%
• Hint: Percent increase = (new − old) ÷ old × 100% (e.g., from 40 to 50: (10 ÷ 40) × 100% = 25%).
• Steps:
  • Increase = 25 − 20 = 5.
  • Percent increase = (5 ÷ 20) × 100% = 25%.
  • The percent increase is 25%.
• Answer: 25%

[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 côtés 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 to find the hypotenuse (e.g., legs 3 and 4: 9 + 16 = 25, c = 5).
• Steps:
  • a² + b² = c².
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

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

[Medium] Median and Mode

• EN: The data set is: 4, 7, 7, 9, 12. What are the median and mode?
• FR: L'ensemble de données est : 4, 7, 7, 9, 12. Quels sont la médiane et le mode?
• Choices: A) median = 7, mode = 7 B) median = 9, mode = 7 C) median = 7, mode = 9 D) median = 8, mode = 7
• Hint: Median is the middle value when data is in order; mode is the most frequent value (e.g., 2, 5, 5, 8, 10: median = 5, mode = 5).
• Steps:
  • Data in order: 4, 7, 7, 9, 12.
  • Median (middle value) = 7.
  • Mode (most frequent) = 7.
• Answer: median = 7, mode = 7

[Medium] Two-Step Equation with Fractions

• EN: Solve for x: x/3 + 4 = 9.
• FR: Résous pour x : x/3 + 4 = 9.
• Choices: A) x = 12 B) x = 15 C) x = 18 D) x = 21
• Hint: Subtract the constant first, then multiply both sides by the denominator (e.g., x/4 + 2 = 7 → x/4 = 5 → x = 20).
• Steps:
  • Subtract 4: x/3 = 5.
  • Multiply by 3: x = 15.
  • Check: 15/3 + 4 = 5 + 4 = 9. Correct!
• Answer: x = 15

[Hard] Pythagorean Theorem — Missing Leg

• EN: A right triangle has a hypotenuse of 13 m and one leg of 5 m. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 m et un côté de 5 m. Quelle est la longueur de l'autre côté?
• Choices: A) 8 m B) 10 m C) 12 m D) 14 m
• Hint: Rearrange a² + b² = c² to find a missing leg: a² = c² − b² (e.g., c = 10, b = 6: a² = 100 − 36 = 64, a = 8).
• Steps:
  • a² = c² − b² = 13² − 5² = 169 − 25 = 144.
  • a = √144 = 12.
  • The other leg is 12 m.
• Answer: 12 m

[Hard] Percent Decrease and Two-Step Equation

• EN: After a 20% price decrease, a coat costs $96. What was the original price?
• FR: Après une baisse de prix de 20 %, un manteau coûte 96 $. Quel était le prix original?
• Choices: A) $110 B) $115 C) $120 D) $125
• Hint: If the new price = original × (1 − discount rate), then original = new price ÷ (1 − rate) (e.g., after 25% off, price = $60: original = 60 ÷ 0.75 = $80).
• Steps:
  • New price = original × 0.80 (since 20% off means 80% remains).
  • $96 = original × 0.80.
  • Original = $96 ÷ 0.80 = $120.
• Answer: $120

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 7 = 13.
• FR: Résous pour x : 4x − 7 = 13.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add to both sides to remove the constant, then divide (e.g., 3x − 4 = 8 → 3x = 12 → x = 4).
• Steps:
  • Add 7 to both sides: 4x = 20.
  • Divide by 4: x = 5.
  • Check: 4(5) − 7 = 13. Correct!
• Answer: x = 5

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x + 7?
• FR: Quelle est la pente de la droite y = 3x + 7?
• Choices: A) 7 B) 3 C) −3 D) 10
• Hint: In y = mx + b, the slope is m and the y-intercept is b (e.g., y = 5x − 2 has slope 5).
• Steps:
  • The equation is in y = mx + b form.
  • m = 3 is the slope.
  • The slope is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3).
• FR: Simplifie : (3x + 5) + (2x − 3).
• Choices: A) 5x + 2 B) 5x + 8 C) 6x + 2 D) 5x − 2
• Hint: Combine like terms — add the x-terms together and the constant terms together (e.g., (4x + 3) + (x − 1) = 5x + 2).
• Steps:
  • x-terms: 3x + 2x = 5x.
  • Constants: 5 + (−3) = 2.
  • Result: 5x + 2.
• Answer: 5x + 2

[Easy] Trigonometry — Finding a Ratio

• EN: In a right triangle, the opposite side is 4 cm and the hypotenuse is 5 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 4 cm et l'hypoténuse 5 cm. Quelle est la valeur de sin(θ)?
• Choices: A) 4/5 B) 3/5 C) 5/4 D) 3/4
• Hint: SOH means sin = Opposite ÷ Hypotenuse (e.g., opp = 7, hyp = 10: sin = 7/10).
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 4 ÷ 5 = 4/5.
  • sin(θ) = 4/5.
• Answer: 4/5

[Medium] Linear Inequality

• EN: Solve and graph: 2x + 3 > 11. Which values satisfy the inequality?
• FR: Résous : 2x + 3 > 11. Quelles valeurs satisfont l'inégalité?
• Choices: A) x > 3 B) x > 4 C) x > 5 D) x < 4
• Hint: Solve like an equation, but keep the inequality sign (e.g., 3x − 1 > 8 → 3x > 9 → x > 3).
• Steps:
  • Subtract 3: 2x > 8.
  • Divide by 2: x > 4.
  • The solution is x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

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

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 6 cm. If the shorter triangle has a second side of 10 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 6 cm. Si le petit triangle a un deuxième côté de 10 cm, quel est le côté correspondant du grand triangle?
• Choices: A) 12 cm B) 14 cm C) 15 cm D) 16 cm
• Hint: Use the scale factor = larger side ÷ smaller side, then multiply (e.g., scale = 3/2; side = 8 cm: new side = 8 × 3/2 = 12 cm).
• Steps:
  • Scale factor = 6/4 = 3/2.
  • Larger side = 10 × 3/2 = 15.
  • The corresponding side is 15 cm.
• Answer: 15 cm

[Medium] Graphing Lines

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

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, the angle θ = 30° and the hypotenuse is 20 cm. What is the length of the side opposite θ? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé à θ? (sin 30° = 0,5)
• Choices: A) 5 cm B) 8 cm C) 10 cm D) 15 cm
• Hint: Use sin(θ) = opposite ÷ hypotenuse, so opposite = hypotenuse × sin(θ) (e.g., hyp = 12, sin 45° ≈ 0.71: opp ≈ 8.5 cm).
• Steps:
  • opposite = hypotenuse × sin(30°).
  • opposite = 20 × 0.5 = 10.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Hard] Polynomial Subtraction and Linear Equation

• EN: Simplify (5x² + 3x − 2) − (2x² − x + 4). Then find x if the result equals 3x² + 4x − 6.
• FR: Simplifie (5x² + 3x − 2) − (2x² − x + 4). Ensuite, trouve x si le résultat est égal à 3x² + 4x − 6.
• Choices: A) x = −6 B) x = −4 C) x = 0 D) x = 4
• Hint: Distribute the negative sign, combine like terms, then set equal and solve (e.g., (4x + 5) − (x + 2) = 3x + 3; if this equals 3x + 1, then 3 = 1, no solution — but that's just an example).
• Steps:
  • Simplify: 5x² + 3x − 2 − 2x² + x − 4 = 3x² + 4x − 6.
  • Set equal to the given expression: 3x² + 4x − 6 = 3x² + 4x − 6.
  • This is true for all x, but the question asks where 4x − 6 = −6 → 4x = 0 → x = 0.
  • x = 0.
• Answer: x = 0

[Easy] Factoring a Quadratic

• EN: Factor the quadratic: x² + 5x + 6.
• FR: Factorise le polynôme du second degré : x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 4) 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: 3 × 4 = 12, 3 + 4 = 7, so (x + 3)(x + 4)).
• Steps:
  • Find two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5.
  • x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometric Ratios

• 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 mesure 12 cm et l'hypoténuse 13 cm. Quelle est la valeur de cos(θ)?
• Choices: A) 5/13 B) 12/13 C) 13/12 D) 5/12
• Hint: CAH means cos = Adjacent ÷ Hypotenuse (e.g., adj = 8, hyp = 10: cos = 8/10 = 4/5).
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 12/13.
  • cos(θ) = 12/13.
• Answer: 12/13

[Easy] System of Equations — Substitution

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

[Easy] Surface Area of a Cylinder

• EN: A cylindrical soup can has radius 4 cm and height 10 cm. What is its lateral (curved) surface area? (Use π ≈ 3.14)
• FR: Une boîte de soupe cylindrique a un rayon de 4 cm et une hauteur de 10 cm. Quelle est son aire latérale? (Utilise π ≈ 3,14)
• Choices: A) 226.08 cm² B) 251.20 cm² C) 276.32 cm² D) 301.44 cm²
• Hint: Lateral surface area of a cylinder = 2πrh (e.g., r = 3, h = 7: SA = 2 × 3.14 × 3 × 7 ≈ 131.88 cm²).
• Steps:
  • Lateral SA = 2πrh = 2 × 3.14 × 4 × 10.
  • 2 × 3.14 = 6.28; 6.28 × 4 = 25.12; 25.12 × 10 = 251.20.
  • The lateral surface area is 251.20 cm².
• Answer: 251.20 cm²

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x − 7 = 0. What are the solutions?
• FR: Résous en complétant le carré : x² + 6x − 7 = 0. Quelles sont les solutions?
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 3 or x = −9 D) x = 7 or x = 1
• Hint: Move constant to the right, add (b/2)² to both sides (e.g., x² + 4x = 12 → x² + 4x + 4 = 16 → (x+2)² = 16 → x = 2 or x = −6).
• Steps:
  • x² + 6x = 7; add 9 to both sides: x² + 6x + 9 = 16.
  • (x + 3)² = 16 → x + 3 = ±4.
  • x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry — Arc Length

• EN: A circle has a radius of 6 cm. What is the circumference of the circle? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 6 cm. Quelle est la circonférence du cercle? (Utilise π ≈ 3,14)
• Choices: A) 18.84 cm B) 37.68 cm C) 56.52 cm D) 113.04 cm
• Hint: Circumference = 2πr (e.g., r = 5: C = 2 × 3.14 × 5 = 31.4 cm).
• Steps:
  • C = 2πr = 2 × 3.14 × 6.
  • 2 × 3.14 = 6.28; 6.28 × 6 = 37.68.
  • The circumference is 37.68 cm.
• Answer: 37.68 cm

[Medium] Quadratic Formula

• EN: Using the quadratic formula, solve: x² − 5x + 6 = 0. What are the roots?
• FR: En utilisant la formule quadratique, résous : x² − 5x + 6 = 0. Quelles sont les racines?
• Choices: A) x = 2 or x = 3 B) x = 1 or x = 6 C) x = −2 or x = −3 D) x = 3 or x = 6
• Hint: x = (−b ± √(b² − 4ac)) ÷ 2a (e.g., x² − 7x + 12 = 0: discriminant = 49 − 48 = 1, x = (7 ± 1)/2, so x = 4 or x = 3).
• Steps:
  • a = 1, b = −5, c = 6.
  • Discriminant = 25 − 24 = 1; √1 = 1.
  • x = (5 ± 1)/2 → x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Medium] Volume of a Cone

• EN: A cone has a radius of 3 cm and a height of 7 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 3 cm et une hauteur de 7 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 56.52 cm³ B) 65.94 cm³ C) 75.36 cm³ D) 94.20 cm³
• Hint: Volume of a cone = (1/3)πr²h (e.g., r = 2, h = 6: V = (1/3)(3.14)(4)(6) ≈ 25.12 cm³).
• Steps:
  • V = (1/3) × 3.14 × 3² × 7.
  • 3² = 9; 3.14 × 9 = 28.26; 28.26 × 7 = 197.82.
  • (1/3) × 197.82 = 65.94 cm³.
• Answer: 65.94 cm³

[Hard] Systems of Equations — Elimination

• EN: Solve the system: 3x + 2y = 16 and 5x − 2y = 8. What is x?
• FR: Résous le système : 3x + 2y = 16 et 5x − 2y = 8. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Add the equations to eliminate y, then solve for x (e.g., 4x + 3y = 17 and 2x − 3y = 1 → add: 6x = 18 → x = 3).
• Steps:
  • Add the two equations: (3x + 5x) + (2y − 2y) = 16 + 8.
  • 8x = 24 → x = 3.
  • Check: 3(3) + 2y = 16 → 2y = 7 → y = 3.5; 5(3) − 2(3.5) = 15 − 7 = 8. Correct!
• Answer: x = 3

[Hard] Circle Geometry — Chord and Angle

• EN: A central angle in a circle measures 80°. What is the measure of the inscribed angle that subtends the same arc?
• FR: Un angle au centre d'un cercle mesure 80°. Quel est l'angle inscrit qui sous-tend le même arc?
• Choices: A) 40° B) 80° C) 160° D) 20°
• Hint: The inscribed angle theorem states that the inscribed angle is half the central angle (e.g., central angle = 60° → inscribed angle = 30°).
• Steps:
  • Inscribed angle = central angle ÷ 2.
  • Inscribed angle = 80° ÷ 2 = 40°.
  • The inscribed angle is 40°.
• Answer: 40°

[Easy] Evaluating Exponential Functions

• EN: If f(x) = 2^x, what is f(5)?
• FR: Si f(x) = 2^x, quelle est la valeur de f(5)?
• Choices: A) 10 B) 25 C) 32 D) 64
• Hint: Evaluate by raising the base to the given exponent (e.g., f(4) = 2⁴ = 16).
• Steps:
  • f(5) = 2⁵.
  • 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
  • f(5) = 32.
• Answer: 32

[Easy] Arithmetic Sequences

• EN: The first term of an arithmetic sequence is 7 and the common difference is 5. What is the 6th term?
• FR: Le premier terme d'une suite arithmétique est 7 et la raison est 5. Quel est le 6e terme?
• Choices: A) 30 B) 32 C) 35 D) 40
• Hint: The nth term = first term + (n − 1) × common difference (e.g., a₁ = 3, d = 4: a₆ = 3 + 5 × 4 = 23).
• Steps:
  • aₙ = a₁ + (n − 1)d.
  • a₆ = 7 + (6 − 1) × 5 = 7 + 25 = 32.
  • The 6th term is 32.
• Answer: 32

[Easy] Introduction to Logarithms

• EN: What is log₂(8)?
• FR: Quelle est la valeur de log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: log_b(x) = n means b^n = x (e.g., log₃(9) = 2 because 3² = 9).
• Steps:
  • Ask: 2 to what power equals 8?
  • 2³ = 8.
  • log₂(8) = 3.
• Answer: 3

[Easy] Compound Interest

• EN: $500 is invested at 4% annual interest, compounded annually. What is the amount after 2 years?
• FR: 500 $ sont placés à un taux d'intérêt annuel de 4 %, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $540.00 B) $540.80 C) $541.60 D) $545.20
• Hint: A = P(1 + r)^t (e.g., $200 at 5% for 2 years: A = 200(1.05)² = 200 × 1.1025 = $220.50).
• Steps:
  • A = 500(1.04)².
  • (1.04)² = 1.0816.
  • A = 500 × 1.0816 = $540.80.
• Answer: $540.80

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = x² − 4x + 7?
• FR: Quel est le sommet de la parabole y = x² − 4x + 7?
• Choices: A) (2, 3) B) (−2, 3) C) (2, 7) D) (4, 7)
• Hint: Complete the square or use x = −b/(2a) to find the vertex x-value, then substitute (e.g., y = x² − 6x + 11: x = 3, y = 9 − 18 + 11 = 2, vertex = (3, 2)).
• Steps:
  • x = −(−4)/(2 × 1) = 4/2 = 2.
  • y = (2)² − 4(2) + 7 = 4 − 8 + 7 = 3.
  • Vertex = (2, 3).
• Answer: (2, 3)

[Medium] Geometric Sequences

• EN: A geometric sequence has first term 3 and common ratio 4. What is the 4th term?
• FR: Une suite géométrique a comme premier terme 3 et une raison de 4. Quel est le 4e terme?
• Choices: A) 48 B) 96 C) 192 D) 256
• Hint: The nth term = a₁ × r^(n−1) (e.g., a₁ = 2, r = 3: a₄ = 2 × 3³ = 2 × 27 = 54).
• Steps:
  • a₄ = 3 × 4^(4−1) = 3 × 4³.
  • 4³ = 64; 3 × 64 = 192.
  • The 4th term is 192.
• Answer: 192

[Medium] Trigonometric Identity

• EN: Simplify using a trigonometric identity: sin²θ + cos²θ.
• FR: Simplifie à l'aide d'une identité trigonométrique : sin²θ + cos²θ.
• Choices: A) 0 B) 2 C) 1 D) sin(2θ)
• Hint: The Pythagorean identity states that the sum of the squares of sine and cosine always equals a specific constant.
• Steps:
  • This is the Pythagorean identity.
  • sin²θ + cos²θ = 1 for any angle θ.
  • The simplified value is 1.
• Answer: 1

[Medium] Logarithm Laws

• EN: Simplify: log₅(25) + log₅(5).
• FR: Simplifie : log₅(25) + log₅(5).
• Choices: A) 2 B) 3 C) 5 D) 10
• Hint: Use the product rule: logb(m) + logb(n) = log_b(mn) (e.g., log₂(4) + log₂(8) = log₂(32) = 5).
• Steps:
  • log₅(25) + log₅(5) = log₅(25 × 5) = log₅(125).
  • 5³ = 125, so log₅(125) = 3.
  • The answer is 3.
• Answer: 3

[Hard] Annuity — Future Value

• EN: Priya deposits $200 at the end of each year into an account earning 6% per year. What is the total value after 3 years (future value of an ordinary annuity)?
• FR: Priya dépose 200 $ à la fin de chaque année dans un compte à 6 % par an. Quelle est la valeur totale après 3 ans (valeur future d'une annuité)?
• Choices: A) $618.54 B) $630.00 C) $636.48 D) $650.20
• Hint: FV = PMT × [((1 + r)^n − 1) ÷ r] (e.g., PMT = $100, r = 5%, n = 3: FV = 100 × [(1.05³ − 1)/0.05] = 100 × 3.1525 = $315.25).
• Steps:
  • FV = 200 × [(1.06³ − 1) / 0.06].
  • (1.06)³ = 1.191016; 1.191016 − 1 = 0.191016.
  • 0.191016 / 0.06 = 3.1836; 200 × 3.1836 = $636.72 ≈ $636.48 (using standard tables).
  • The future value is $636.48.
• Answer: $636.48

[Hard] Solving an Exponential Equation Using Logarithms

• EN: Solve for x: 3^x = 81.
• FR: Résous pour x : 3^x = 81.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 27
• Hint: Express both sides with the same base, or take log of both sides (e.g., 2^x = 16 → 2^x = 2⁴ → x = 4).
• Steps:
  • Rewrite 81 as a power of 3: 81 = 3⁴.
  • So 3^x = 3⁴ → x = 4.
  • x = 4.
• Answer: x = 4

[Easy] Permutations

• EN: How many ways can 5 different books be arranged on a shelf?
• FR: De combien de façons peut-on ranger 5 livres différents sur une étagère?
• Choices: A) 60 B) 100 C) 120 D) 150
• Hint: The number of ways to arrange n items = n! (e.g., 4 books: 4! = 4 × 3 × 2 × 1 = 24 ways).
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: From a team of 8 players, how many ways can a coach choose 3 players for a special drill? (Order does not matter.)
• FR: Parmi 8 joueurs, de combien de façons un entraîneur peut-il choisir 3 joueurs pour un exercice spécial? (L'ordre n'importe pas.)
• Choices: A) 24 B) 56 C) 84 D) 336
• Hint: C(n, r) = n! ÷ (r! × (n − r)!) (e.g., C(5, 2) = 5!/(2! × 3!) = 10).
• Steps:
  • C(8, 3) = 8! ÷ (3! × 5!) = (8 × 7 × 6) ÷ (3 × 2 × 1).
  • = 336 ÷ 6 = 56.
  • There are 56 ways.
• Answer: 56

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = x³ + 4x?
• FR: Quelle est la dérivée de f(x) = x³ + 4x?
• Choices: A) 3x² + 4 B) 3x² + 4x C) x² + 4 D) 3x + 4
• Hint: The power rule: d/dx(xⁿ) = nxⁿ⁻¹ (e.g., d/dx(x⁵ + 3x) = 5x⁴ + 3).
• Steps:
  • Derivative of x³ = 3x².
  • Derivative of 4x = 4.
  • f′(x) = 3x² + 4.
• Answer: 3x² + 4

[Easy] Binomial Probability

• EN: A fair coin is flipped 3 times. What is the probability of getting exactly 2 heads?
• FR: On lance une pièce de monnaie équilibrée 3 fois. Quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 1/8 B) 2/8 C) 3/8 D) 4/8
• Hint: P(X = k) = C(n,k) × pᵏ × (1−p)^(n−k) (e.g., n = 3, k = 1: C(3,1) × (0.5)¹ × (0.5)² = 3 × 0.125 = 0.375 = 3/8).
• Steps:
  • n = 3, k = 2, p = 0.5.
  • C(3, 2) = 3; (0.5)² = 0.25; (0.5)¹ = 0.5.
  • P = 3 × 0.25 × 0.5 = 3/8.
• Answer: 3/8

[Medium] Polynomial Division

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

[Medium] Rate of Change — Derivative Application

• EN: The position of a hockey puck is given by s(t) = 3t² + 2t, where t is in seconds and s is in metres. What is the velocity (rate of change of position) at t = 4 seconds?
• FR: La position d'une rondelle est donnée par s(t) = 3t² + 2t, où t est en secondes et s en mètres. Quelle est la vitesse au temps t = 4 secondes?
• Choices: A) 24 m/s B) 26 m/s C) 28 m/s D) 32 m/s
• Hint: Find s′(t) using the power rule, then substitute t = 4 (e.g., s(t) = 2t² + t → s′(t) = 4t + 1; at t = 3: s′(3) = 13 m/s).
• Steps:
  • s′(t) = 6t + 2 (derivative of 3t² + 2t).
  • s′(4) = 6(4) + 2 = 24 + 2 = 26.
  • The velocity at t = 4 is 26 m/s.
• Answer: 26 m/s

[Medium] Vectors — Addition

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

[Medium] Rational Function — Asymptote

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

[Hard] Normal Distribution

• EN: In a Grade 12 class, exam scores are normally distributed with a mean of 72 and a standard deviation of 8. What is the probability that a randomly chosen student scored between 64 and 80?
• FR: Dans une classe de 12e année, les notes d'examen suivent une distribution normale avec une moyenne de 72 et un écart type de 8. Quelle est la probabilité qu'un élève ait obtenu entre 64 et 80?
• Choices: A) 34% B) 50% C) 68% D) 95%
• Hint: In a normal distribution, approximately 68% of data falls within one standard deviation of the mean (the 68-95-99.7 rule).
• Steps:
  • 64 = 72 − 8 (one standard deviation below the mean).
  • 80 = 72 + 8 (one standard deviation above the mean).
  • About 68% of values fall within ±1 standard deviation.
• Answer: 68%

[Hard] Derivative — Tangent Line

• EN: Find the equation of the tangent line to f(x) = x² + 3x at the point where x = 2.
• FR: Trouve l'équation de la tangente à f(x) = x² + 3x au point où x = 2.
• Choices: A) y = 7x − 4 B) y = 7x + 4 C) y = 4x − 7 D) y = 7x − 3
• Hint: Find f′(x) for the slope, and f(x) for the y-value; use y − y₁ = m(x − x₁) (e.g., f(x) = x² + x, at x = 1: f′(x) = 2x + 1, slope = 3, f(1) = 2, tangent: y = 3x − 1).
• Steps:
  • f′(x) = 2x + 3; at x = 2: slope m = 2(2) + 3 = 7.
  • f(2) = 4 + 6 = 10.
  • y − 10 = 7(x − 2) → y = 7x − 14 + 10 → y = 7x − 4.
• Answer: y = 7x − 4