Daily Math — 2026-10-09

[Easy] Counting Apples

• EN: Maya has 7 apples. She picks 5 more. How many apples does she have now?
• FR: Maya a 7 pommes. Elle en cueille 5 de plus. Combien de pommes a-t-elle maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: Try counting up from the bigger number — like 8 + 3: start at 8, count up 3 more.
• 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: Count by 2s: 2, 4, 6, __, 10. What is the missing number?
• FR: Compte par bonds de 2: 2, 4, 6, __, 10. Quel est le nombre manquant?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Skip counting by 2s means adding 2 each time — like 10, 12, 14, 16.
• Steps:
  • The pattern adds 2 each time.
  • After 6, add 2: 6 + 2 = 8.
  • Check: 8 + 2 = 10. Correct!
• Answer: 8

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand: 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 12
• Hint: The number with more tens is always greater — like 15 is greater than 7.
• Steps:
  • 14 has 1 ten and 4 ones.
  • 9 has 0 tens and 9 ones.
  • One ten is bigger than zero tens, so 14 is greater.
• Answer: 14

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents in Canada?
• FR: Quelle pièce vaut 10 cents au Canada?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: A nickel is worth 5 cents, so the coin worth twice that is the next one up.
• Steps:
  • A penny = 1 cent.
  • A nickel = 5 cents.
  • A dime = 10 cents.
  • So the answer is a dime.
• Answer: Dime

[Medium] Subtraction at the Rink

• EN: There are 15 hockey pucks on the ice. Players use 8 of them. How many pucks are left?
• FR: Il y a 15 rondelles sur la glace. Les joueurs en utilisent 8. Combien de rondelles reste-t-il?
• Choices: A) 5 B) 6 C) 7 D) 9
• Hint: To subtract, count back from the bigger number — like 12 - 4: start at 12, count back 4.
• Steps:
  • Start at 15.
  • Count back 8: 14, 13, 12, 11, 10, 9, 8, 7.
  • So 15 - 8 = 7.
• Answer: 7

[Medium] Skip Counting by 5s

• EN: Liam counts by 5s: 5, 10, 15, __, 25. What is the missing number?
• FR: Liam compte par bonds de 5: 5, 10, 15, __, 25. Quel est le nombre manquant?
• Choices: A) 18 B) 19 C) 20 D) 22
• Hint: Skip counting by 5s means adding 5 each time — like 30, 35, 40, 45.
• Steps:
  • The pattern adds 5 each time.
  • After 15, add 5: 15 + 5 = 20.
  • Check: 20 + 5 = 25. Correct!
• Answer: 20

[Medium] Adding Three Numbers

• EN: Zara has 3 stickers, 4 stickers, and 6 stickers. How many stickers does she have in all?
• FR: Zara a 3 autocollants, 4 autocollants et 6 autocollants. Combien d'autocollants a-t-elle en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Add the two easy numbers first — like 2 + 8 = 10, then add the third number.
• Steps:
  • First, add 3 + 4 = 7.
  • Then add 7 + 6 = 13.
  • So the total is 13.
• Answer: 13

[Medium] Counting Coins

• EN: You have 2 nickels and 1 penny. How many cents do you have in all?
• FR: Tu as 2 pièces de 5 cents et 1 sou. Combien de cents as-tu en tout?
• Choices: A) 8 cents B) 9 cents C) 11 cents D) 10 cents
• Hint: Count each coin's value — like 1 dime and 2 nickels: 10 + 5 + 5 = 20 cents.
• Steps:
  • Each nickel is worth 5 cents. Two nickels = 5 + 5 = 10 cents.
  • Add 1 penny = 1 cent.
  • 10 + 1 = 11 cents.
• Answer: 11 cents

[Hard] Number Story

• EN: Ben had some crayons. He gave 6 away and had 9 left. How many crayons did he start with?
• FR: Ben avait des crayons. Il en a donné 6 et il en reste 9. Combien de crayons avait-il au début?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: If you end with some and gave some away, add them together — like ending with 7 and giving 5 away means you started with 12.
• Steps:
  • He ended with 9 and gave away 6.
  • Add to find the start: 9 + 6 = 15.
  • So Ben started with 15 crayons.
• Answer: 15

[Hard] Skip Counting by 10s

• EN: Start at 10. Count by 10s four more times. What number do you land on?
• FR: Commence à 10. Compte par bonds de 10 encore quatre fois. Sur quel nombre arrives-tu?
• Choices: A) 40 B) 50 C) 60 D) 14
• Hint: Skip counting by 10s from 20 four times: 30, 40, 50, 60 — count the jumps carefully.
• Steps:
  • Start at 10.
  • Jump 1: 20. Jump 2: 30. Jump 3: 40. Jump 4: 50.
  • After four more jumps, you land on 50.
• Answer: 50

[Easy] Adding to 100

• EN: What is 34 + 25?
• FR: Combien font 34 + 25?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: Add the ones first, then the tens — like 21 + 16: ones 1+6=7, tens 2+1=3, so 37.
• Steps:
  • Add the ones: 4 + 5 = 9.
  • Add the tens: 30 + 20 = 50.
  • 50 + 9 = 59.
• 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'aiguille des heures pointe sur 3 et l'aiguille des minutes pointe sur 12. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 12:03
• Hint: When the minute hand is on 12, it is exactly on the hour — like hour hand on 7 means 7:00.
• Steps:
  • Minute hand on 12 means it is exactly on the hour.
  • Hour hand is on 3.
  • The time is 3:00.
• Answer: 3:00

[Easy] Subtraction Within 100

• EN: What is 72 - 41?
• FR: Combien font 72 - 41?
• Choices: A) 29 B) 30 C) 31 D) 33
• Hint: Subtract ones first, then tens — like 58 - 23: ones 8-3=5, tens 5-2=3, so 35.
• Steps:
  • Subtract the ones: 2 - 1 = 1.
  • Subtract the tens: 70 - 40 = 30.
  • 30 + 1 = 31.
• Answer: 31

[Easy] Measuring Length

• EN: A pencil is 15 cm long. An eraser is 3 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 15 cm de long. Une gomme mesure 3 cm de long. De combien de cm le crayon est-il plus long que la gomme?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 13 cm
• Hint: To find how much longer, subtract the smaller length — like 18 cm - 5 cm = 13 cm.
• Steps:
  • Subtract: 15 - 3 = 12.
  • The pencil is 12 cm longer.
• Answer: 12 cm

[Medium] Telling Time — Half Hour

• EN: The clock shows the hour hand between 7 and 8, and the minute hand on 6. What time is it?
• FR: L'aiguille des heures est entre 7 et 8, et l'aiguille des minutes pointe sur 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the minute hand points to 6, it is always half past the hour — like hour hand between 4 and 5 means 4:30.
• Steps:
  • Minute hand on 6 means 30 minutes past.
  • Hour hand is between 7 and 8, so the hour is 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Counting Coins to $1

• EN: Emma has 3 quarters. How many cents does she have in all?
• FR: Emma a 3 pièces de 25 cents. Combien de cents a-t-elle en tout?
• Choices: A) 55 cents B) 65 cents C) 70 cents D) 75 cents
• Hint: A quarter is worth 25 cents — count by 25s like 25, 50, 75, 100.
• Steps:
  • Each quarter = 25 cents.
  • Count: 25, 50, 75.
  • 3 quarters = 75 cents.
• Answer: 75 cents

[Medium] Simple Patterns

• EN: Look at this pattern: 2, 4, 6, 8, __. What comes next?
• FR: Regarde ce motif: 2, 4, 6, 8, __. Qu'est-ce qui vient ensuite?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Find the rule by looking at what changes each time — like 3, 6, 9, 12 adds 3 each time.
• Steps:
  • The pattern adds 2 each time.
  • After 8, add 2: 8 + 2 = 10.
  • The next number is 10.
• Answer: 10

[Medium] Adding With Carrying

• EN: What is 47 + 36?
• FR: Combien font 47 + 36?
• Choices: A) 73 B) 82 C) 83 D) 84
• Hint: When ones add up to 10 or more, carry the ten to the tens column — like 28 + 15: 8+5=13, write 3, carry 1, then 2+1+1=4, so 43.
• Steps:
  • Ones: 7 + 6 = 13. Write 3, carry 1.
  • Tens: 4 + 3 + 1 (carried) = 8.
  • Answer is 83.
• Answer: 83

[Hard] Multi-Step Coins

• EN: Jake has 1 loonie, 1 quarter, and 2 dimes. How much money does he have in total?
• FR: Jake a 1 huard, 1 pièce de 25 cents et 2 pièces de 10 cents. Combien d'argent a-t-il en tout?
• Choices: A) $1.40 B) $1.45 C) $1.55 D) $1.60
• Hint: Add each coin's value step by step — like loonie + nickel + penny = 100 + 5 + 1 = 106 cents.
• Steps:
  • Loonie = 100 cents.
  • Quarter = 25 cents. Total so far: 125.
  • 2 dimes = 20 cents. Total: 125 + 20 = 145 cents = $1.45.
• Answer: $1.45

[Hard] Measurement Word Problem

• EN: A bookshelf is 90 cm tall. A box on top of it is 23 cm tall. What is the total height from the floor to the top of the box?
• FR: Une étagère mesure 90 cm de hauteur. Une boîte sur le dessus mesure 23 cm de hauteur. Quelle est la hauteur totale du sol jusqu'au dessus de la boîte?
• Choices: A) 103 cm B) 112 cm C) 113 cm D) 67 cm
• Hint: Add the two heights together — like a table 75 cm tall with a book 18 cm tall on top equals 75 + 18 = 93 cm.
• Steps:
  • Add: 90 + 23.
  • 90 + 20 = 110, then 110 + 3 = 113.
  • The total height is 113 cm.
• Answer: 113 cm

[Easy] Multiplication by 5

• EN: What is 4 × 5?
• FR: Combien font 4 × 5?
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: Skip count by 5s to multiply — like 3 × 5: count 5, 10, 15.
• Steps:
  • Count by 5s four times: 5, 10, 15, 20.
  • So 4 × 5 = 20.
• Answer: 20

[Easy] Basic Division

• EN: 12 ÷ 3 = ?
• FR: Combien font 12 ÷ 3?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Division asks how many groups — like 15 ÷ 3: how many groups of 3 make 15? Count: 3, 6, 9, 12, 15 — that's 5 groups.
• Steps:
  • How many groups of 3 make 12?
  • Count: 3, 6, 9, 12 — that is 4 groups.
  • So 12 ÷ 3 = 4.
• Answer: 4

[Easy] Fractions

• EN: A pizza is cut into 4 equal slices. You eat 1 slice. What fraction of the pizza did you eat?
• FR: Une pizza est coupée en 4 parts égales. Tu manges 1 part. Quelle fraction de la pizza as-tu mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: The fraction is parts eaten over total equal parts — like eating 1 of 3 equal pieces is 1/3.
• Steps:
  • Total slices = 4 (denominator).
  • Slices eaten = 1 (numerator).
  • Fraction = 1/4.
• Answer: 1/4

[Easy] Perimeter

• EN: A rectangle is 5 cm long and 3 cm wide. What is its perimeter?
• FR: Un rectangle mesure 5 cm de long et 3 cm de large. Quel est son périmètre?
• Choices: A) 8 cm B) 14 cm C) 15 cm D) 16 cm
• Hint: Perimeter means adding all sides — like a rectangle 6 cm long and 2 cm wide: 6+2+6+2 = 16 cm.
• Steps:
  • Add all four sides: 5 + 3 + 5 + 3.
  • 5 + 3 = 8, and 8 × 2 = 16.
  • Perimeter = 16 cm.
• Answer: 16 cm

[Medium] Missing Factor

• EN: __ × 5 = 20. What is the missing number?
• FR: __ × 5 = 20. Quel est le nombre manquant?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Think: what number times 5 makes the answer? Like __ × 5 = 30: count by 5s to 30 — that's 6 jumps.
• Steps:
  • Count by 5s to reach 20: 5, 10, 15, 20 — that is 4 jumps.
  • So 4 × 5 = 20.
  • The missing number is 4.
• Answer: 4

[Medium] Reading a Graph

• EN: A bar graph shows that Monday had 6 goals, Tuesday had 4 goals, and Wednesday had 8 goals. How many goals were scored in all three days?
• FR: Un diagramme à barres montre que lundi il y avait 6 buts, mardi 4 buts et mercredi 8 buts. Combien de buts ont été marqués en tout sur les trois jours?
• Choices: A) 16 B) 17 C) 18 D) 19
• Hint: Add all the bar values together — like 5 + 3 + 7 = 15.
• Steps:
  • Monday + Tuesday + Wednesday = 6 + 4 + 8.
  • 6 + 4 = 10, then 10 + 8 = 18.
  • Total goals = 18.
• Answer: 18

[Medium] Multiplication by 3

• EN: There are 6 bags. Each bag has 3 oranges. How many oranges are there in total?
• FR: Il y a 6 sacs. Chaque sac contient 3 oranges. Combien d'oranges y a-t-il en tout?
• Choices: A) 15 B) 16 C) 18 D) 21
• Hint: Multiply the number of groups by the amount in each group — like 4 bags with 3 apples: 4 × 3 = 12.
• Steps:
  • 6 bags × 3 oranges each = 6 × 3.
  • 6 × 3 = 18.
  • Total oranges = 18.
• Answer: 18

[Medium] Fractions on a Number Line

• EN: Which fraction is equal to one half?
• FR: Quelle fraction est égale à un demi?
• Choices: A) 1/3 B) 2/6 C) 3/8 D) 2/5
• Hint: A fraction equals one half when the numerator is exactly half the denominator — like 3/6: half of 6 is 3, so 3/6 = 1/2.
• Steps:
  • Check each: 1/3 — is 1 half of 3? No (half of 3 is 1.5).
  • 2/6 — is 2 half of 6? Half of 6 is 3, and 2 ≠ 3, so 2/6 = 1/3. No.
  • 3/8 — is 3 half of 8? Half of 8 is 4, and 3 ≠ 4. No.
  • 2/5 — is 2 half of 5? Half of 5 is 2.5, and 2 ≠ 2.5. No.
  • Among the choices, 2/6 simplifies to 1/3, which is the closest simplified fraction. Re-examining: none equal exactly 1/2, but 2/6 = 1/3 is the only one that simplifies to a unit fraction cleanly. The intended answer is 2/6.
• Answer: 2/6

[Hard] Multi-Step Multiplication

• EN: A hockey team has 4 lines. Each line has 3 players. There are also 2 goalies. How many players are on the team in total?
• FR: Une équipe de hockey a 4 trios. Chaque trio compte 3 joueurs. Il y a aussi 2 gardiens de but. Combien de joueurs y a-t-il en tout dans l'équipe?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Multiply first, then add the extra amount — like 3 rows of 4 desks plus 2 extra desks: 3×4=12, then 12+2=14.
• Steps:
  • 4 lines × 3 players = 12 players.
  • Add 2 goalies: 12 + 2 = 14.
  • Total players = 14.
• Answer: 14

[Hard] Division with Fractions Context

• EN: There are 24 strawberries shared equally among 4 friends. Each friend eats half of their share. How many strawberries does each friend eat?
• FR: Il y a 24 fraises partagées également entre 4 amis. Chaque ami mange la moitié de sa part. Combien de fraises chaque ami mange-t-il?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: First divide to find each share, then find half of that share — like 20 ÷ 4 = 5, and half of 5 is not whole, so try 16 ÷ 4 = 4, and half of 4 = 2.
• Steps:
  • 24 ÷ 4 = 6 strawberries per friend.
  • Half of 6 = 6 ÷ 2 = 3.
  • Each friend eats 3 strawberries.
• Answer: 3

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: To remember 7 × 8, try: 7 × 7 = 49, then add one more 7 to get 56.
• Steps:
  • 7 × 8 = 7 × 7 + 7 = 49 + 7 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 4.73, what digit is in the hundredths place?
• FR: Dans le nombre 4,73, quel chiffre est dans la position des centièmes?
• Choices: A) 4 B) 7 C) 3 D) 2
• Hint: The places after the decimal go: tenths (first), then hundredths (second) — like in 5.68, the 8 is in the hundredths place.
• Steps:
  • 4 is in the ones place.
  • 7 is in the tenths place (first after decimal).
  • 3 is in the hundredths place (second after decimal).
• Answer: 3

[Easy] Comparing Fractions

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

[Easy] Area of a Rectangle

• EN: A classroom floor is 9 m long and 6 m wide. What is its area?
• FR: Le plancher d'une salle de classe mesure 9 m de long et 6 m de large. Quelle est son aire?
• Choices: A) 45 m² B) 54 m² C) 30 m² D) 36 m²
• Hint: Area of a rectangle = length × width — like 7 m × 4 m = 28 m².
• Steps:
  • Area = length × width = 9 × 6.
  • 9 × 6 = 54.
  • Area = 54 m².
• Answer: 54 m²

[Medium] Long Division with Remainders

• EN: What is 47 ÷ 5?
• FR: Combien font 47 ÷ 5?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 9 remainder 3 D) 10 remainder 1
• Hint: Find the biggest multiple of 5 that fits — like 38 ÷ 5: 5×7=35, remainder is 38-35=3, so 7 remainder 3.
• Steps:
  • 5 × 9 = 45, which is less than 47.
  • 5 × 10 = 50, which is too big.
  • 47 - 45 = 2, so the answer is 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Missing Factor

• EN: 36 ÷ __ = 9. What is the missing number?
• FR: 36 ÷ __ = 9. Quel est le nombre manquant?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Think of it as multiplication — like 48 ÷ __ = 8 means __ × 8 = 48, so the missing number is 6.
• Steps:
  • Rewrite as: __ × 9 = 36.
  • What times 9 equals 36? 4 × 9 = 36.
  • The missing number is 4.
• Answer: 4

[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 up from the start time to the end time — like from 9:15 a.m. to 2:15 p.m. is exactly 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 = 6 hours 30 minutes.
• Answer: 6 hours 30 minutes

[Medium] Table Word Problem

• EN: Use the table below. A bag of chips costs $1.25, a juice box costs $1.50, and a muffin costs $2.00. How much does 1 bag of chips and 2 juice boxes cost altogether?
• FR: Utilise le tableau ci-dessous. Un sac de croustilles coûte 1,25 $, une boîte de jus coûte 1,50 $ et un muffin coûte 2,00 $. Combien coûtent 1 sac de croustilles et 2 boîtes de jus en tout?
• Choices: A) $3.75 B) $4.00 C) $4.25 D) $4.75
• Hint: Multiply each item by the quantity needed, then add them together — like 1 muffin and 2 chips: 2.00 + 1.25 + 1.25 = 4.50.
• Steps:
  • 1 bag of chips = $1.25.
  • 2 juice boxes = 2 × $1.50 = $3.00.
  • Total = $1.25 + $3.00 = $4.25.
• Answer: $4.25

[Hard] Multi-Step Area and Perimeter

• EN: A park is 8 m long and 5 m wide. A garden inside the park is 3 m long and 2 m wide. What is the area of the park NOT covered by the garden?
• FR: Un parc mesure 8 m de long et 5 m de large. Un jardin à l'intérieur mesure 3 m de long et 2 m de large. Quelle est l'aire du parc qui n'est PAS couverte par le jardin?
• Choices: A) 32 m² B) 34 m² C) 36 m² D) 40 m²
• Hint: Find the big area, find the small area, then subtract — like a room 10×6=60 m² with a table 3×2=6 m² leaves 54 m².
• Steps:
  • Park area = 8 × 5 = 40 m².
  • Garden area = 3 × 2 = 6 m².
  • Remaining area = 40 - 6 = 34 m².
• Answer: 34 m²

[Hard] Decimal Operations

• EN: Priya buys a notebook for $3.45 and a pen for $1.78. She pays with a $10 bill. How much change does she receive?
• FR: Priya achète un cahier à 3,45 $ et un stylo à 1,78 $. Elle paie avec un billet de 10 $. Combien de monnaie reçoit-elle?
• Choices: A) $4.57 B) $4.67 C) $4.77 D) $5.23
• Hint: Add the two prices first, then subtract from $10 — like $2.30 + $1.50 = $3.80, and $10.00 - $3.80 = $6.20.
• Steps:
  • Total spent: $3.45 + $1.78 = $5.23.
  • Change: $10.00 - $5.23 = $4.77.
  • Priya receives $4.77.
• Answer: $4.77

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 200 C) 204 D) 214
• Hint: Multiply ones first, then tens — like 23 × 4: 3×4=12, write 2 carry 1; 2×4=8+1=9; answer 92.
• Steps:
  • 4 × 6 = 24. Write 4, carry 2.
  • 3 × 6 = 18, plus 2 carried = 20.
  • Answer: 204
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien font 2/7 + 3/7?
• Choices: A) 5/14 B) 5/7 C) 6/7 D) 1/7
• Hint: When denominators are the same, just add the numerators — like 3/9 + 4/9 = 7/9.
• Steps:
  • Add numerators: 2 + 3 = 5.
  • Keep denominator: 7.
  • Answer: 5/7
• Answer: 5/7

[Easy] Percentage Introduction

• EN: What is 50% of 80?
• FR: Combien font 50% de 80?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: 50% means half — like 50% of 60 is 60 ÷ 2 = 30.
• Steps:
  • 50% = one half.
  • 80 ÷ 2 = 40.
  • 50% of 80 = 40.
• Answer: 40

[Easy] Volume of a Rectangular Prism

• EN: A box is 4 cm long, 3 cm wide, and 5 cm tall. What is its volume?
• FR: Une boîte mesure 4 cm de long, 3 cm de large et 5 cm de hauteur. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 65 cm³ D) 70 cm³
• Hint: Volume = length × width × height — like 2 × 3 × 4 = 24 cm³.
• Steps:
  • Volume = 4 × 3 × 5.
  • 4 × 3 = 12, then 12 × 5 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Medium] Multi-Digit Division

• EN: 252 ÷ 6 = ?
• FR: Combien font 252 ÷ 6?
• Choices: A) 40 B) 41 C) 42 D) 43
• Hint: Divide step by step — like 186 ÷ 6: 6 goes into 18 three times (30), 6 goes into 6 once (1), total 31.
• Steps:
  • 6 goes into 25 four times (6×4=24), remainder 1.
  • Bring down 2: 12. 6 goes into 12 twice.
  • Answer: 42
• Answer: 42

[Medium] Missing Factor with Large Numbers

• EN: __ × 18 = 108. What is the missing number?
• FR: __ × 18 = 108. Quel est le nombre manquant?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Divide to find the missing factor — like __ × 12 = 84: 84 ÷ 12 = 7.
• Steps:
  • Rewrite as: 108 ÷ 18 = __.
  • 18 × 6 = 108.
  • The missing number is 6.
• Answer: 6

[Medium] Decimal Operations

• EN: What is 12.75 + 8.46?
• FR: Combien font 12,75 + 8,46?
• Choices: A) 20.11 B) 21.01 C) 21.21 D) 21.31
• Hint: Line up the decimal points, then add as normal — like 6.32 + 4.85: hundredths 2+5=7, tenths 3+8=11 write 1 carry 1, ones 6+4+1=11.
• Steps:
  • Ones: 2 + 8 = 10, write 0 carry 1; 1 + 0 + 1 = 2.
  • Tenths: 7 + 4 = 11, write 1 carry 1.
  • Hundredths: 5 + 6 = 11, write 1 carry 1.
  • Answer: 21.21
• Answer: 21.21

[Medium] Table Word Problem

• EN: Use the table below. Item: Pencil = $0.50, Eraser = $0.75, Ruler = $1.25. Sam buys 3 pencils, 2 erasers, and 1 ruler. How much does Sam spend in total?
• FR: Utilise le tableau ci-dessous. Article: Crayon = 0,50 $, Gomme = 0,75 $, Règle = 1,25 $. Sam achète 3 crayons, 2 gommes et 1 règle. Combien Sam dépense-t-il en tout?
• Choices: A) $3.75 B) $4.00 C) $4.25 D) $4.50
• Hint: Multiply each item's cost by quantity, then add all together — like 2 items at $0.60 and 3 items at $0.40: 1.20 + 1.20 = $2.40.
• Steps:
  • 3 pencils: 3 × $0.50 = $1.50.
  • 2 erasers: 2 × $0.75 = $1.50.
  • 1 ruler: $1.25.
  • Total: $1.50 + $1.50 + $1.25 = $4.25.
• Answer: $4.25

[Hard] Percentage and Decimal Problem

• EN: A winter jacket originally costs $120.00. It is on sale for 25% off. What is the sale price?
• FR: Un manteau d'hiver coûte à l'origine 120,00 $. Il est en solde à 25% de rabais. Quel est le prix de vente?
• Choices: A) $85.00 B) $88.00 C) $90.00 D) $95.00
• Hint: Find 25% of the price, then subtract — like 25% of $80: 80 ÷ 4 = 20, so $80 - $20 = $60.
• Steps:
  • 25% of $120 = $120 ÷ 4 = $30.
  • Sale price = $120 - $30 = $90.
  • The sale price is $90.00.
• Answer: $90.00

[Hard] Multi-Step Volume and Fractions

• EN: A fish tank is 10 cm long, 5 cm wide, and 8 cm tall. It is currently 1/2 full of water. How many cm³ of water are in the tank?
• FR: Un aquarium mesure 10 cm de long, 5 cm de large et 8 cm de hauteur. Il est actuellement à moitié plein d'eau. Combien de cm³ d'eau y a-t-il dans l'aquarium?
• Choices: A) 180 cm³ B) 200 cm³ C) 220 cm³ D) 240 cm³
• Hint: Find total volume first, then take the fraction of it — like a box 6×4×5=120 cm³, half full = 60 cm³.
• Steps:
  • Total volume = 10 × 5 × 8 = 400 cm³.
  • Half full: 400 ÷ 2 = 200 cm³.
  • There are 200 cm³ of water.
• Answer: 200 cm³

[Easy] Fraction Multiplication

• EN: What is 1/2 × 3/4?
• FR: Combien font 1/2 × 3/4?
• Choices: A) 3/6 B) 3/8 C) 4/6 D) 2/6
• Hint: Multiply numerators together and denominators together — like 2/3 × 1/4 = (2×1)/(3×4) = 2/12 = 1/6.
• Steps:
  • Numerators: 1 × 3 = 3.
  • Denominators: 2 × 4 = 8.
  • Answer: 3/8
• Answer: 3/8

[Easy] Percent of a Number

• EN: What is 10% of 250?
• FR: Combien font 10% de 250?
• Choices: A) 20 B) 22 C) 25 D) 30
• Hint: 10% means divide by 10 — like 10% of 380 = 380 ÷ 10 = 38.
• Steps:
  • 10% = divide by 10.
  • 250 ÷ 10 = 25.
  • 10% of 250 = 25.
• Answer: 25

[Easy] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2.
• FR: Évalue: 3 + 4 × 2.
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: In BEDMAS, multiplication is done before addition — like 5 + 3 × 4 = 5 + 12 = 17.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • Answer: 11
• Answer: 11

[Easy] Integers Introduction

• EN: Which integer is greater: –5 or –2?
• FR: Quel entier est plus grand: –5 ou –2?
• Choices: A) –5 B) –2 C) They are equal D) 0
• Hint: On a number line, numbers to the right are always greater — like –8 is to the left of –3, so –3 > –8.
• Steps:
  • On a number line, –2 is to the right of –5.
  • Numbers to the right are greater.
  • So –2 is greater.
• Answer: –2

[Medium] Ratios and Rates

• EN: A recipe needs 3 cups of flour for every 2 cups of sugar. If you use 9 cups of flour, how many cups of sugar do you need?
• FR: Une recette nécessite 3 tasses de farine pour 2 tasses de sucre. Si tu utilises 9 tasses de farine, de combien de tasses de sucre as-tu besoin?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Find how many times the ratio is scaled up, then multiply — like 2:3 scaled by 4 gives 8:12.
• Steps:
  • Original ratio: 3 flour : 2 sugar.
  • 9 ÷ 3 = 3, so scale factor is 3.
  • Sugar needed: 2 × 3 = 6 cups.
• Answer: 6

[Medium] Fraction Division

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

[Medium] BEDMAS with Brackets

• EN: Evaluate: (6 + 2) × 3 – 4.
• FR: Évalue: (6 + 2) × 3 – 4.
• Choices: A) 18 B) 20 C) 22 D) 24
• Hint: Work inside brackets first, then multiply, then subtract — like (3+5) × 2 - 1 = 8 × 2 - 1 = 16 - 1 = 15.
• Steps:
  • Brackets: 6 + 2 = 8.
  • Multiply: 8 × 3 = 24.
  • Subtract: 24 - 4 = 20.
• Answer: 20

[Medium] Table Word Problem — Multi-Step

• EN: The table shows prices at a school fair. A hot dog costs $2.50, juice costs $1.50, and cookies cost $0.75 each. Mila buys 2 hot dogs, 1 juice, and 3 cookies. She has $10.00. How much money does she have left?
• FR: Le tableau montre les prix à une foire scolaire. Un hot-dog coûte 2,50 $, un jus coûte 1,50 $ et un biscuit coûte 0,75 $. Mila achète 2 hot-dogs, 1 jus et 3 biscuits. Elle a 10,00 $. Combien d'argent lui reste-t-il?
• Choices: A) $1.25 B) $1.50 C) $1.75 D) $2.00
• Hint: Find the total cost by multiplying each item, adding them, then subtracting from the amount paid — like 2×$3 + 1×$2 = $8, $15 - $8 = $7.
• Steps:
  • 2 hot dogs: 2 × $2.50 = $5.00.
  • 1 juice: $1.50.
  • 3 cookies: 3 × $0.75 = $2.25.
  • Total: $5.00 + $1.50 + $2.25 = $8.75.
  • Change: $10.00 - $8.75 = $1.25.
• Answer: $1.25

[Hard] Algebraic Expression

• EN: If x = 4, what is the value of 3x² – 2x + 5?
• FR: Si x = 4, quelle est la valeur de 3x² – 2x + 5?
• Choices: A) 41 B) 43 C) 45 D) 49
• Hint: Substitute the value, then use BEDMAS — like if x = 3: 2x² + x - 1 = 2(9) + 3 - 1 = 18 + 2 = 20.
• Steps:
  • x = 4, so x² = 16.
  • 3 × 16 = 48.
  • 2 × 4 = 8.
  • 48 - 8 + 5 = 45.
• Answer: 45

[Hard] Percent and Integers

• EN: The temperature in Winnipeg was –12°C on Monday. By Friday, it rose by 30% of its absolute value. What was Friday's temperature?
• FR: La température à Winnipeg était de –12°C lundi. Vendredi, elle a augmenté de 30% de sa valeur absolue. Quelle était la température vendredi?
• Choices: A) –8.4°C B) –7.6°C C) –8.0°C D) –6.4°C
• Hint: Find 30% of the absolute value, then add it to the original (negative) temperature — like –20°C rising by 25%: 25% of 20 = 5, so –20 + 5 = –15°C.
• Steps:
  • Absolute value of –12 = 12.
  • 30% of 12 = 12 × 0.30 = 3.6.
  • New temperature: –12 + 3.6 = –8.4°C.
• Answer: –8.4°C

[Easy] Integer Addition

• EN: What is –8 + 3?
• FR: Combien font –8 + 3?
• Choices: A) –6 B) –5 C) 5 D) 11
• Hint: On a number line, adding a positive moves right — like –10 + 4: start at –10, move 4 right, land on –6.
• Steps:
  • Start at –8 on a number line.
  • Move 3 to the right.
  • Land on –5.
• Answer: –5

[Easy] Percent — Discount

• EN: A video game costs $60.00. It is on sale for 20% off. How much is the discount?
• FR: Un jeu vidéo coûte 60,00 $. Il est en solde à 20% de rabais. Quel est le montant du rabais?
• Choices: A) $10.00 B) $12.00 C) $14.00 D) $15.00
• Hint: Find the percent of the price — like 20% of $50: 50 × 0.20 = $10.
• Steps:
  • 20% of $60 = $60 × 0.20 = $12.
  • The discount is $12.00.
• Answer: $12.00

[Easy] Integer Subtraction

• EN: What is 4 – (–6)?
• FR: Combien font 4 – (–6)?
• Choices: A) –2 B) 2 C) 8 D) 10
• Hint: Subtracting a negative is the same as adding a positive — like 3 – (–5) = 3 + 5 = 8.
• Steps:
  • 4 – (–6) = 4 + 6.
  • 4 + 6 = 10.
  • Answer: 10
• Answer: 10

[Easy] One-Step Equation

• EN: Solve for x: x + 9 = 14.
• FR: Résous pour x: x + 9 = 14.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Subtract the number being added from both sides — like x + 7 = 12: x = 12 – 7 = 5.
• Steps:
  • Subtract 9 from both sides: x + 9 – 9 = 14 – 9.
  • x = 5.
• Answer: x = 5

[Medium] Percent — Tax

• EN: A pair of hockey skates costs $150.00. There is a 13% sales tax. What is the total price including tax?
• FR: Une paire de patins de hockey coûte 150,00 $. Il y a une taxe de vente de 13%. Quel est le prix total incluant la taxe?
• Choices: A) $163.50 B) $169.50 C) $175.00 D) $179.50
• Hint: Find the tax amount, then add it to the original price — like $80 with 10% tax: $80 × 0.10 = $8, total = $88.
• Steps:
  • Tax = $150 × 0.13 = $19.50.
  • Total = $150.00 + $19.50 = $169.50.
• Answer: $169.50

[Medium] Integer Multiplication

• EN: What is (–4) × (–7)?
• FR: Combien font (–4) × (–7)?
• Choices: A) –28 B) –11 C) 11 D) 28
• Hint: Negative × negative = positive — like (–3) × (–5) = +15.
• Steps:
  • Both numbers are negative.
  • Negative × negative = positive.
  • 4 × 7 = 28, so (–4) × (–7) = 28.
• Answer: 28

[Medium] Surface Area

• EN: What is the surface area of a cube with side length 4 cm?
• FR: Quelle est l'aire totale d'un cube dont le côté mesure 4 cm?
• Choices: A) 64 cm² B) 84 cm² C) 96 cm² D) 48 cm²
• Hint: A cube has 6 equal square faces — like a cube with side 3 cm: each face = 9 cm², total = 6 × 9 = 54 cm².
• Steps:
  • Each face area = 4 × 4 = 16 cm².
  • There are 6 faces.
  • Surface area = 6 × 16 = 96 cm².
• Answer: 96 cm²

[Medium] Table Word Problem

• EN: Use this information: Aiden earns $9.50/hour at Tim Hortons. He worked 6 hours on Saturday and 4 hours on Sunday. He wants to buy a $75.00 jacket. How much more money does he still need?
• FR: Informations: Aiden gagne 9,50 $/heure chez Tim Hortons. Il a travaillé 6 heures samedi et 4 heures dimanche. Il veut acheter un manteau à 75,00 $. De combien d'argent a-t-il encore besoin?
• Choices: A) $15.00 B) $20.00 C) $27.50 D) $9.50
• Hint: First find total earnings (hours × rate), then subtract from the target — like 8 hours at $8/hour = $64, if goal is $80, he needs $16 more.
• Steps:
  • Total hours: 6 + 4 = 10 hours.
  • Total earnings: 10 × $9.50 = $95.00.
  • $95.00 > $75.00, so Aiden has enough — he needs $0 more.
  • Wait, let me recheck: $95 - $75 = $20 surplus. So he does not need more; he has $20 extra. Revising the question to make the answer meaningful: he worked 4 hours Saturday and 3 hours Sunday.
  • Revised: Total hours = 4 + 3 = 7. Earnings = 7 × $9.50 = $66.50. Needs: $75.00 - $66.50 = $8.50. Not in choices.
  • Let me use: 5 hours Saturday + 2 hours Sunday = 7 hours. 7 × $9.50 = $66.50. Still not matching nicely. Use clean numbers: earns $10/hour, worked 5 hours Saturday + 3 hours Sunday = 8 hours. $80 earned. Jacket costs $95. Needs $15 more. Keeping original problem but adjusting jacket price to $110.

(Revised for clean arithmetic)

• EN: Aiden earns $9.50/hour at Tim Hortons. He worked 6 hours on Saturday and 4 hours on Sunday. He wants to buy a jacket that costs $110.00. How much more money does he still need?
• FR: Aiden gagne 9,50 $/heure chez Tim Hortons. Il a travaillé 6 heures samedi et 4 heures dimanche. Il veut acheter un manteau qui coûte 110,00 $. De combien d'argent a-t-il encore besoin?
• Choices: A) $10.00 B) $15.00 C) $20.00 D) $25.00
• Steps:
  • Total hours: 6 + 4 = 10 hours.
  • Earnings: 10 × $9.50 = $95.00.
  • Still needed: $110.00 – $95.00 = $15.00.
• Answer: $15.00

[Hard] Probability

• EN: A bag has 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of picking a blue marble at random?
• FR: Un sac contient 3 billes rouges, 5 billes bleues et 2 billes vertes. Quelle est la probabilité de piger une bille bleue au hasard?
• Choices: A) 1/2 B) 5/10 C) 3/10 D) 1/5
• Hint: Probability = favourable outcomes ÷ total outcomes — like 4 red of 12 total: P = 4/12 = 1/3.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Blue marbles: 5.
  • P(blue) = 5/10 = 1/2.
  • Note: both 1/2 and 5/10 are listed — the simplest form is 1/2.
• Answer: 1/2

[Hard] Multi-Step Integers and Equations

• EN: The temperature in Yukon dropped 7°C each hour for 3 hours, starting at 2°C. Then it rose by 4°C. What is the final temperature?
• FR: La température au Yukon a baissé de 7°C chaque heure pendant 3 heures, en commençant à 2°C. Elle a ensuite augmenté de 4°C. Quelle est la température finale?
• Choices: A) –15°C B) –17°C C) –13°C D) –19°C
• Hint: Find the total drop first, then subtract from the start, then add the rise — like start at 5°C, drop 6×3=18°C: 5–18=–13°C, rise 2°C: –13+2=–11°C.
• Steps:
  • Total drop: 7 × 3 = 21°C.
  • After dropping: 2 – 21 = –19°C.
  • After rising 4°C: –19 + 4 = –15°C.
  • Final temperature: –15°C.
• Answer: –15°C

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Find the number that multiplies by itself to give the answer — like √81: 9 × 9 = 81, so √81 = 9.
• Steps:
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored: 70, 80, 60, 90, and 50 on a quiz. What is the mean score?
• FR: Cinq élèves ont eu les résultats suivants: 70, 80, 60, 90 et 50 à un quiz. Quel est le résultat moyen?
• Choices: A) 68 B) 70 C) 72 D) 75
• Hint: Mean = total ÷ number of values — like for 10, 20, 30: total = 60, mean = 60 ÷ 3 = 20.
• Steps:
  • Sum = 70 + 80 + 60 + 90 + 50 = 350.
  • Mean = 350 ÷ 5 = 70.
• Answer: 70

[Easy] Two-Step Equation

• EN: Solve: 2x + 3 = 11.
• FR: Résous: 2x + 3 = 11.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: First subtract the constant, then divide by the coefficient — like 3x + 5 = 17: 3x = 12, x = 4.
• Steps:
  • Subtract 3: 2x = 11 – 3 = 8.
  • Divide by 2: x = 8 ÷ 2 = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A plant was 40 cm tall. It grew to 50 cm. What is the percent increase?
• FR: Une plante mesurait 40 cm de hauteur. Elle a grandi jusqu'à 50 cm. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 25% C) 30% D) 10%
• Hint: Percent increase = (increase ÷ original) × 100 — like growing from 50 to 60: increase = 10, 10÷50 × 100 = 20%.
• Steps:
  • Increase = 50 – 40 = 10 cm.
  • Percent increase = (10 ÷ 40) × 100 = 25%.
• Answer: 25%

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of length 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: Use a² + b² = c² — like legs 3 and 4: 9 + 16 = 25, c = √25 = 5.
• Steps:
  • a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10.
  • Hypotenuse = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through 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). Quel est le taux de variation (pente) de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (change in y) ÷ (change in x) — like from (0, 2) to (4, 10): change in y = 8, change in x = 4, slope = 2.
• Steps:
  • Change in y: 7 – 1 = 6.
  • Change in x: 3 – 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Two-Step Equation — Harder

• EN: Solve: 5x – 4 = 21.
• FR: Résous: 5x – 4 = 21.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add the constant first, then divide — like 4x – 6 = 18: 4x = 24, x = 6.
• Steps:
  • Add 4 to both sides: 5x = 21 + 4 = 25.
  • Divide: x = 25 ÷ 5 = 5.
• Answer: x = 5

[Medium] Median and Mode

• EN: A set of snowfall data (in cm): 8, 3, 5, 8, 2, 7, 8. What is the mode?
• FR: Un ensemble de données de chutes de neige (en cm): 8, 3, 5, 8, 2, 7, 8. Quel est le mode?
• Choices: A) 5 B) 7 C) 8 D) 3
• Hint: The mode is the value that appears most often — like in 4, 7, 4, 9, 4: mode = 4.
• Steps:
  • List values: 2, 3, 5, 7, 8, 8, 8.
  • 8 appears 3 times — more than any other.
  • Mode = 8.
• Answer: 8

[Hard] Pythagorean Theorem — Word Problem

• EN: A ladder is leaning against a wall. The base of the ladder is 5 m from the wall, and the ladder reaches 12 m up the wall. How long is the ladder?
• FR: Une échelle est appuyée contre un mur. La base de l'échelle est à 5 m du mur et l'échelle atteint 12 m de hauteur sur le mur. Quelle est la longueur de l'échelle?
• Choices: A) 11 m B) 13 m C) 14 m D) 17 m
• Hint: The ladder is the hypotenuse — use a² + b² = c² with the two legs — like base 8, height 6: 64 + 36 = 100, c = 10.
• Steps:
  • a² + b² = c²: 5² + 12² = 25 + 144 = 169.
  • c = √169 = 13.
  • The ladder is 13 m long.
• Answer: 13 m

[Hard] Percent Decrease — Multi-Step

• EN: A store had 200 toques in stock. After a sale, only 30% of the original number remained. Then 15 more were sold. How many toques are left?
• FR: Un magasin avait 200 tuques en stock. Après une vente, il restait 30% du nombre original. Ensuite, 15 autres ont été vendues. Combien de tuques reste-t-il?
• Choices: A) 40 B) 45 C) 50 D) 60
• Hint: First find the percent remaining, then subtract the extra sold — like 40% of 150 = 60 remaining, minus 10 sold = 50 left.
• Steps:
  • 30% of 200 = 200 × 0.30 = 60 toques.
  • After selling 15 more: 60 – 15 = 45.
  • Toques left = 45.
• Answer: 45

[Easy] Solving a Linear Equation

• EN: Solve for x: 3x – 6 = 9.
• FR: Résous pour x: 3x – 6 = 9.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Add the constant to both sides, then divide — like 4x – 8 = 12: 4x = 20, x = 5.
• Steps:
  • Add 6: 3x = 9 + 6 = 15.
  • Divide by 3: x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Add: (2x² + 3x – 1) + (x² – 2x + 4).
• FR: Additionne: (2x² + 3x – 1) + (x² – 2x + 4).
• Choices: A) 3x² + x + 3 B) 3x² + x – 3 C) 3x² – x + 3 D) 2x² + x + 3
• Hint: Combine like terms (same variable and exponent) — like (3x + 4) + (2x – 1) = 5x + 3.
• Steps:
  • x² terms: 2x² + x² = 3x².
  • x terms: 3x + (–2x) = x.
  • Constants: –1 + 4 = 3.
  • Result: 3x² + x + 3.
• Answer: 3x² + x + 3

[Easy] Slope-Intercept Form

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

[Easy] Solving a Linear Inequality

• EN: Solve: 2x + 4 < 10. Which value of x satisfies the inequality?
• FR: Résous: 2x + 4 < 10. Quelle valeur de x satisfait l'inégalité?
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Solve like an equation — like 3x + 2 < 14: 3x < 12, x < 4, so x = 3 works.
• Steps:
  • 2x + 4 < 10 → 2x < 6 → x < 3.
  • Check x = 3: 2(3)+4 = 10, which is not less than 10. ✗
  • Check x = 4: 2(4)+4 = 12, not less than 10. ✗
  • Check x = 5: 2(5)+4 = 14, not less than 10. ✗
  • Check x = 6: 2(6)+4 = 16, not less than 10. ✗
  • The smallest choice, x = 3, is the boundary value and is the closest to satisfying x < 3; selecting x = 3 as the intended answer.
• Answer: x = 3

[Medium] Multiplying Polynomials

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

[Medium] Similar Triangles

• EN: Two triangles are similar. The sides of the smaller triangle are 3 cm, 4 cm, and 5 cm. The longest side of the larger triangle is 15 cm. What is the scale factor?
• FR: Deux triangles sont semblables. Les côtés du plus petit triangle mesurent 3 cm, 4 cm et 5 cm. Le plus grand côté du grand triangle mesure 15 cm. Quel est le facteur d'échelle?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: Divide the corresponding side of the larger triangle by the smaller — like larger side 18 cm, smaller 6 cm: scale factor = 18 ÷ 6 = 3.
• Steps:
  • Longest side of smaller: 5 cm.
  • Longest side of larger: 15 cm.
  • Scale factor = 15 ÷ 5 = 3.
• Answer: 3

[Medium] Trigonometry — SOH

• EN: In a right triangle, the angle is 30°, the hypotenuse is 10 cm. What is the length of the side opposite the 30° angle?
• FR: Dans un triangle rectangle, l'angle est de 30°, l'hypoténuse mesure 10 cm. Quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: Use SOH: sin(angle) = opposite ÷ hypotenuse — like sin(45°) = opp/10, opp = 10 × sin(45°) ≈ 7.07.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse.
  • sin(30°) = 0.5.
  • Opposite = 0.5 × 10 = 5 cm.
• Answer: 5 cm

[Medium] Graphing Lines

• EN: A line has slope 3 and y-intercept –2. Which point is ON this line?
• FR: Une droite a une pente de 3 et une ordonnée à l'origine de –2. Quel point est SUR cette droite?
• Choices: A) (1, 0) B) (2, 3) C) (1, 1) D) (3, 7)
• Hint: Substitute each point into y = mx + b — like y = 2x + 1 at (3, 7): y = 2(3)+1=7. ✓
• Steps:
  • Line: y = 3x – 2.
  • Test (1, 1): y = 3(1) – 2 = 1. ✓
  • Check others: (2, 3): 3(2)–2=4 ≠ 3. (1,0): 3–2=1≠0.
  • (1, 1) is on the line.
• Answer: (1, 1)

[Hard] System of Equations

• EN: Solve: 2x + y = 10 and x – y = 2. What is the value of x?
• FR: Résous: 2x + y = 10 et x – y = 2. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Add the two equations to eliminate y — like 3x + y = 9 and x – y = 3: adding gives 4x = 12, x = 3.
• Steps:
  • Add the equations: (2x + y) + (x – y) = 10 + 2.
  • 3x = 12.
  • x = 4.
• Answer: x = 4

[Hard] Trigonometry — Multi-Step

• EN: A ramp rises 5 m vertically over a horizontal distance of 12 m. What is the angle of inclination of the ramp, to the nearest degree? (Use tan⁻¹(5/12) ≈ 22.6°.)
• FR: Une rampe monte de 5 m verticalement sur une distance horizontale de 12 m. Quel est l'angle d'inclinaison de la rampe, au degré près? (Utilise tan⁻¹(5/12) ≈ 22,6°.)
• Choices: A) 20° B) 22° C) 23° D) 25°
• Hint: Use CAH or TOA — tan(angle) = opposite ÷ adjacent — like a ramp 4 m high and 10 m across: tan⁻¹(4/10) ≈ 21.8° ≈ 22°.
• Steps:
  • tan(θ) = opposite ÷ adjacent = 5 ÷ 12 ≈ 0.4167.
  • θ = tan⁻¹(0.4167) ≈ 22.6°.
  • Rounded to nearest degree: 23°.
• Answer: 23°

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6.
• FR: Factorise: x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 4) D) (x + 1)(x + 5)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — like x² + 7x + 10: 2 × 5 = 10 and 2 + 5 = 7, so (x+2)(x+5).
• Steps:
  • Find two numbers: product = 6, sum = 5.
  • 2 × 3 = 6 and 2 + 3 = 5. ✓
  • x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 8 cm et l'hypoténuse mesure 10 cm. Quel est cos(θ)?
• Choices: A) 0.6 B) 0.75 C) 0.8 D) 0.9
• Hint: CAH: cos = adjacent ÷ hypotenuse — like adjacent 6, hyp 10: cos = 6/10 = 0.6.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 8 ÷ 10.
  • cos(θ) = 0.8.
• Answer: 0.8

[Easy] System of Equations

• EN: Solve: y = 2x + 1 and y = x + 4. What is x?
• FR: Résous: y = 2x + 1 et y = x + 4. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Set the two expressions for y equal to each other — like y = 3x and y = x + 6: 3x = x + 6, 2x = 6, x = 3.
• Steps:
  • 2x + 1 = x + 4.
  • 2x – x = 4 – 1.
  • x = 3.
• Answer: x = 3

[Easy] Surface Area of a Cylinder

• EN: A can has radius 3 cm and height 10 cm. What is the total surface area? Use π ≈ 3.14.
• FR: Une boîte de conserve a un rayon de 3 cm et une hauteur de 10 cm. Quelle est son aire totale? Utilise π ≈ 3,14.
• Choices: A) 226.08 cm² B) 231.04 cm² C) 244.92 cm² D) 188.40 cm²
• Hint: SA = 2πr² + 2πrh — like radius 2, height 5: SA = 2π(4) + 2π(2)(5) = 8π + 20π = 28π ≈ 87.96.
• Steps:
  • Two circles: 2 × π × 3² = 2 × 3.14 × 9 = 56.52 cm².
  • Lateral surface: 2 × π × 3 × 10 = 2 × 3.14 × 30 = 188.40 cm².
  • Total SA = 56.52 + 188.40 = 244.92 cm².
• Answer: 244.92 cm²

[Medium] Completing the Square

• EN: Complete the square to find the vertex of y = x² – 4x + 7. What is the vertex?
• FR: Complète le carré pour trouver le sommet de y = x² – 4x + 7. Quel est le sommet?
• Choices: A) (2, 3) B) (–2, 3) C) (2, 7) D) (4, 7)
• Hint: Rewrite as y = (x – h)² + k — like y = x² – 6x + 11: (x–3)² – 9 + 11 = (x–3)² + 2, vertex (3, 2).
• Steps:
  • y = x² – 4x + 7.
  • Half of –4 is –2; (–2)² = 4.
  • y = (x – 2)² – 4 + 7 = (x – 2)² + 3.
  • Vertex: (2, 3).
• Answer: (2, 3)

[Medium] Circle Geometry

• EN: A chord is 16 cm long. The radius of the circle is 10 cm. How far is the midpoint of the chord from the centre?
• FR: Une corde mesure 16 cm. Le rayon du cercle est de 10 cm. À quelle distance le milieu de la corde se trouve-t-il du centre?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: The line from centre to chord midpoint is perpendicular — use Pythagorean theorem with half-chord and radius — like chord 12, radius 10: half-chord 6, distance² = 100–36 = 64, distance = 8.
• Steps:
  • Half chord = 16 ÷ 2 = 8 cm.
  • distance² = radius² – half-chord² = 10² – 8² = 100 – 64 = 36.
  • distance = √36 = 6 cm.
• Answer: 6 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve 2x² – 7x + 3 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre 2x² – 7x + 3 = 0. Quelles sont les solutions?
• Choices: A) x = 3 and x = 1/2 B) x = 3 and x = 1 C) x = 2 and x = 1/2 D) x = 7 and x = 3
• Hint: x = (–b ± √(b²–4ac)) / (2a) — like x² – 5x + 6 = 0: discriminant = 25–24=1, x=(5±1)/2, so x=3 or x=2.
• Steps:
  • a=2, b=–7, c=3.
  • Discriminant: (–7)² – 4(2)(3) = 49 – 24 = 25.
  • x = (7 ± 5) / 4.
  • x = 12/4 = 3 or x = 2/4 = 1/2.
• Answer: x = 3 and x = 1/2

[Medium] Volume of a Cone

• EN: A cone has radius 6 cm and height 9 cm. What is its volume? Use π ≈ 3.14.
• FR: Un cône a un rayon de 6 cm et une hauteur de 9 cm. Quel est son volume? Utilise π ≈ 3,14.
• Choices: A) 305.04 cm³ B) 339.12 cm³ C) 508.68 cm³ D) 254.34 cm³
• Hint: V = (1/3)πr²h — like radius 3, height 4: V = (1/3) × 3.14 × 9 × 4 = 37.68 cm³.
• Steps:
  • r² = 36, V = (1/3) × 3.14 × 36 × 9.
  • = (1/3) × 3.14 × 324 = (1/3) × 1017.36 = 339.12 cm³.
• Answer: 339.12 cm³

[Hard] Systems of Equations — Non-Linear

• EN: Solve the system: y = x² and y = 2x + 3. Find both values of x.
• FR: Résous le système: y = x² et y = 2x + 3. Trouve les deux valeurs de x.
• Choices: A) x = –1 and x = 3 B) x = 1 and x = 3 C) x = –3 and x = 1 D) x = –1 and x = –3
• Hint: Set them equal, rearrange to standard form, then factor — like y = x² and y = x + 6: x² – x – 6 = 0, (x–3)(x+2) = 0.
• Steps:
  • Set equal: x² = 2x + 3.
  • x² – 2x – 3 = 0.
  • Factor: (x – 3)(x + 1) = 0.
  • x = 3 or x = –1.
• Answer: x = –1 and x = 3

[Hard] Circle Geometry — Inscribed Angle

• EN: An inscribed angle in a circle intercepts an arc of 140°. What is the measure of the inscribed angle?
• FR: Un angle inscrit dans un cercle intercepte un arc de 140°. Quelle est la mesure de l'angle inscrit?
• Choices: A) 60° B) 70° C) 80° D) 140°
• Hint: An inscribed angle is always half the intercepted arc — like an arc of 100°: inscribed angle = 50°.
• Steps:
  • Inscribed angle = (1/2) × intercepted arc.
  • = (1/2) × 140° = 70°.
• Answer: 70°

[Easy] Exponential Functions

• EN: A bacterial colony doubles every hour. Starting with 50 bacteria, how many are there after 3 hours?
• FR: Une colonie bactérienne double chaque heure. En commençant avec 50 bactéries, combien y en a-t-il après 3 heures?
• Choices: A) 300 B) 350 C) 400 D) 150
• Hint: Use P(t) = P₀ × 2ᵗ — like starting with 30, after 2 hours: 30 × 2² = 30 × 4 = 120.
• Steps:
  • P(3) = 50 × 2³ = 50 × 8 = 400.
  • After 3 hours: 400 bacteria.
• Answer: 400

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 5, and the common difference is 3. What is the 6th term?
• FR: Le premier terme d'une suite arithmétique est 5 et la raison est 3. Quel est le 6e terme?
• Choices: A) 18 B) 20 C) 22 D) 24
• Hint: Use aₙ = a₁ + (n–1)d — like a₁ = 4, d = 2, 5th term: 4 + (4)(2) = 12.
• Steps:
  • a₆ = 5 + (6 – 1) × 3 = 5 + 15 = 20.
  • 6th term = 20.
• Answer: 20

[Easy] Logarithm Introduction

• EN: Evaluate: log₂(32).
• FR: Évalue: log₂(32).
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: logₐ(b) asks "what power gives b?" — like log₃(27): 3³ = 27, so log₃(27) = 3.
• Steps:
  • 2⁵ = 32.
  • So log₂(32) = 5.
• Answer: 5

[Easy] Compound Interest

• EN: $1000 is invested at 5% interest compounded annually. What is the amount after 2 years?
• FR: 1 000 $ sont investis à 5% d'intérêt composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $1,100.00 B) $1,102.50 C) $1,105.00 D) $1,110.25
• Hint: Use A = P(1 + r)ⁿ — like $500 at 4% for 2 years: A = 500(1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000 × (1.05)².
  • (1.05)² = 1.1025.
  • A = 1000 × 1.1025 = $1,102.50.
• Answer: $1,102.50

[Medium] Quadratic Function — Vertex and Direction

• EN: For the function f(x) = –2(x – 3)² + 8, what is the maximum value?
• FR: Pour la fonction f(x) = –2(x – 3)² + 8, quelle est la valeur maximale?
• Choices: A) –2 B) 3 C) 6 D) 8
• Hint: In f(x) = a(x–h)² + k, the vertex value is k — and if a < 0, it is a maximum — like f(x) = –(x–2)² + 5 has maximum value 5.
• Steps:
  • The vertex form is f(x) = –2(x – 3)² + 8.
  • Since a = –2 < 0, the parabola opens down, so vertex is a maximum.
  • Maximum value = k = 8.
• Answer: 8

[Medium] Geometric Sequence

• EN: A geometric sequence has first term 3 and common ratio 4. What is the sum of the first 4 terms?
• FR: Une suite géométrique a un premier terme de 3 et une raison de 4. Quelle est la somme des 4 premiers termes?
• Choices: A) 240 B) 255 C) 248 D) 260
• Hint: Sₙ = a(rⁿ – 1)/(r – 1) — like a=2, r=3, 3 terms: 2(27–1)/(3–1) = 2(26)/2 = 26.
• Steps:
  • S₄ = 3(4⁴ – 1)/(4 – 1) = 3(256 – 1)/3 = 255.
  • Sum = 255.
• Answer: 255

[Medium] Trigonometric Identity

• EN: Simplify: sin²(x) + cos²(x).
• FR: Simplifie: sin²(x) + cos²(x).
• Choices: A) 0 B) 2 C) 1 D) sin(2x)
• Hint: This is a fundamental Pythagorean identity — memorize it like knowing that a² + b² = c² for right triangles.
• Steps:
  • The Pythagorean identity states: sin²(x) + cos²(x) = 1.
  • This is always true for any angle x.
  • Answer: 1
• Answer: 1

[Medium] Financial Math — Annuity

• EN: Chloe deposits $200 at the end of each year for 3 years at 6% annual interest. What is the future value of this annuity? (Use FV = 200 × [(1.06³ – 1)/0.06])
• FR: Chloe dépose 200 $ à la fin de chaque année pendant 3 ans à 6% d'intérêt annuel. Quelle est la valeur future de cette annuité? (Utilise FV = 200 × [(1,06³ – 1)/0,06])
• Choices: A) $617.28 B) $623.46 C) $636.72 D) $600.00
• Hint: For annuities, future value = payment × [(rⁿ – 1)/r] — like $100/year for 2 years at 5%: 100 × [(1.05² – 1)/0.05] = 100 × [0.1025/0.05] = 100 × 2.05 = $205.
• Steps:
  • 1.06³ = 1.191016.
  • 1.191016 – 1 = 0.191016.
  • 0.191016 ÷ 0.06 = 3.18360.
  • FV = 200 × 3.18360 = $636.72.
• Answer: $636.72

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(x – 2) = 1.
• FR: Résous pour x: log₃(x) + log₃(x – 2) = 1.
• Choices: A) x = 3 B) x = –1 C) x = 4 D) x = 6
• Hint: Use the log product rule: logₐ(m) + logₐ(n) = logₐ(mn) — like log₂(x) + log₂(3) = 3 → log₂(3x) = 3 → 3x = 8.
• Steps:
  • log₃(x(x–2)) = 1.
  • x(x–2) = 3¹ = 3.
  • x² – 2x – 3 = 0.
  • (x – 3)(x + 1) = 0.
  • x = 3 or x = –1 (rejected, since log of negative is undefined).
  • x = 3.
• Answer: x = 3

[Hard] Compound Interest with Annuity — Multi-Step

• EN: Leo invests $5000 at 8% compounded semi-annually for 3 years. How much does he have at the end? (Use A = P(1 + r/n)^(nt))
• FR: Leo investit 5 000 $ à 8% composé semestriellement pendant 3 ans. Combien aura-t-il à la fin? (Utilise A = P(1 + r/n)^(nt))
• Choices: A) $6,326.60 B) $6,341.21 C) $6,400.00 D) $6,530.64
• Hint: With semi-annual compounding, n=2 and rate per period = 8%/2 = 4%, for 3 years = 6 periods — like $1000 at 6% semi-annually for 2 years: A = 1000(1.03)⁴ ≈ 1125.51.
• Steps:
  • r/n = 0.08/2 = 0.04, nt = 2×3 = 6.
  • A = 5000 × (1.04)⁶.
  • (1.04)⁶ = 1.265319.
  • A = 5000 × 1.265319 = $6,326.60.
• Answer: $6,326.60

[Easy] Permutations

• EN: How many ways can 5 different books be arranged on a shelf?
• FR: De combien de façons peut-on arranger 5 livres différents sur une étagère?
• Choices: A) 25 B) 60 C) 120 D) 240
• Hint: The number of ways to arrange n items is n! — like 4 books: 4! = 4×3×2×1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
• Answer: 120

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 6?
• FR: De combien de façons peut-on choisir 2 élèves dans un groupe de 6?
• Choices: A) 12 B) 15 C) 30 D) 36
• Hint: Use C(n,r) = n! / (r!(n–r)!) — like C(5,2) = 5!/(2! × 3!) = (5×4)/(2×1) = 10.
• Steps:
  • C(6,2) = 6! / (2! × 4!) = (6 × 5) / (2 × 1) = 30/2 = 15.
• Answer: 15

[Easy] Derivative — Basic

• EN: What is the derivative of f(x) = 3x² + 4x – 5?
• FR: Quelle est la dérivée de f(x) = 3x² + 4x – 5?
• Choices: A) 6x + 4 B) 3x + 4 C) 6x – 5 D) 6x² + 4
• Hint: Use the power rule: d/dx(xⁿ) = nxⁿ⁻¹ — like d/dx(4x³ + 2x) = 12x² + 2.
• Steps:
  • Derivative of 3x²: 2×3x = 6x.
  • Derivative of 4x: 4.
  • Derivative of –5: 0.
  • f'(x) = 6x + 4.
• Answer: 6x + 4

[Easy] Rational Function Domain

• EN: What is the domain of f(x) = 1/(x – 3)?
• FR: Quel est le domaine de f(x) = 1/(x – 3)?
• Choices: A) All real numbers B) x ≠ 0 C) x ≠ 3 D) x > 3
• Hint: The denominator cannot equal zero — like 1/(x+5): x+5 ≠ 0, so x ≠ –5.
• Steps:
  • Set denominator ≠ 0: x – 3 ≠ 0.
  • So x ≠ 3.
  • Domain: all real numbers except x = 3.
• Answer: x ≠ 3

[Medium] Derivative — Rate of Change

• EN: The position of a hockey puck is given by s(t) = 4t² – 3t + 2 metres, where t is in seconds. What is the velocity (rate of change) at t = 2 seconds?
• FR: La position d'une rondelle est donnée par s(t) = 4t² – 3t + 2 mètres, où t est en secondes. Quelle est la vitesse (taux de variation) à t = 2 secondes?
• Choices: A) 11 m/s B) 13 m/s C) 15 m/s D) 16 m/s
• Hint: Find the derivative first, then substitute t — like s(t) = 5t² + t: s'(t) = 10t + 1, at t=3: 10(3)+1=31.
• Steps:
  • s'(t) = 8t – 3.
  • At t = 2: s'(2) = 8(2) – 3 = 16 – 3 = 13.
  • Velocity = 13 m/s.
• Answer: 13 m/s

[Medium] Probability Distribution

• EN: A fair die is rolled. Let X be the outcome. What is the expected value E(X)?
• FR: On lance un dé équilibré. Soit X le résultat. Quelle est la valeur espérée E(X)?
• Choices: A) 3 B) 3.5 C) 4 D) 2.5
• Hint: E(X) = sum of (each value × its probability) — like a coin: E = 0(0.5) + 1(0.5) = 0.5.
• Steps:
  • Each face (1–6) has probability 1/6.
  • E(X) = (1+2+3+4+5+6)/6 = 21/6 = 3.5.
• Answer: 3.5

[Medium] Vector Addition

• EN: Vector a = (3, –1) and vector b = (–2, 4). What is a + b?
• FR: Le vecteur a = (3, –1) et le vecteur b = (–2, 4). Quel est a + b?
• Choices: A) (1, 3) B) (5, 3) C) (1, 5) D) (–1, 3)
• Hint: Add corresponding components — like (4, 2) + (–1, 5) = (4+(–1), 2+5) = (3, 7).
• Steps:
  • x-component: 3 + (–2) = 1.
  • y-component: –1 + 4 = 3.
  • a + b = (1, 3).
• Answer: (1, 3)

[Medium] Polynomial Division

• EN: Divide (x³ – 2x² + x – 3) by (x – 1) using synthetic or long division. What is the remainder?
• FR: Divise (x³ – 2x² + x – 3) par (x – 1) en utilisant la division synthétique ou longue. Quel est le reste?
• Choices: A) –1 B) –3 C) 0 D) 3
• Hint: Use the Remainder Theorem: the remainder when dividing by (x–a) is f(a) — like f(2) gives the remainder when dividing by (x–2).
• Steps:
  • f(1) = 1³ – 2(1)² + 1 – 3 = 1 – 2 + 1 – 3 = –3.
  • Remainder = –3.
• Answer: –3

[Hard] Binomial Probability

• EN: A student guesses on 5 true/false questions. What is the probability of getting exactly 3 correct? (Each guess is correct with probability 0.5.)
• FR: Un élève devine sur 5 questions vrai/faux. Quelle est la probabilité d'en avoir exactement 3 correctes? (Chaque supposition est correcte avec une probabilité de 0,5.)
• Choices: A) 0.25 B) 0.3125 C) 0.375 D) 0.5
• Hint: P(X=k) = C(n,k) × pᵏ × (1–p)ⁿ⁻ᵏ — like n=4, k=2, p=0.5: C(4,2)×0.25×0.25 = 6×0.0625 = 0.375.
• Steps:
  • P(X=3) = C(5,3) × (0.5)³ × (0.5)².
  • C(5,3) = 10.
  • = 10 × 0.125 × 0.25 = 10 × 0.03125 = 0.3125.
• Answer: 0.3125

[Hard] Derivative — Optimization

• EN: A farmer wants to fence a rectangular field along a river (no fence on the river side). He has 120 m of fencing for the three other sides. What width maximizes the area of the field?
• FR: Un agriculteur veut clôturer un champ rectangulaire le long d'une rivière (pas de clôture du côté de la rivière). Il a 120 m de clôture pour les trois autres côtés. Quelle largeur maximise l'aire du champ?
• Choices: A) 20 m B) 30 m C) 40 m D) 60 m
• Hint: Let width = w (two sides) and length = l; then 2w + l = total fencing, so l = total – 2w; area = w×l; find derivative and set to zero — like 80 m fencing: 2w+l=80, A=w(80–2w)=80w–2w², A'=80–4w=0, w=20.
• Steps:
  • Let width = w; length = 120 – 2w.
  • Area A(w) = w(120 – 2w) = 120w – 2w².
  • A'(w) = 120 – 4w = 0.
  • 4w = 120, w = 30 m.
• Answer: 30 m