Daily Math — 2026-09-24

[Easy] Counting Carrots

• EN: Mia has 7 carrots. She picks 5 more. How many carrots does she have now?
• FR: Mia a 7 carottes. Elle en cueille 5 autres. Combien de carottes a-t-elle maintenant?
• Choices: A) 10 carrots B) 11 carrots C) 12 carrots D) 13 carrots
• Hint: To add 3 + 4, count on from 3: 4, 5, 6, 7 — you get 7.
• Steps:
  • Start at 7 and count on 5 more.
  • 8, 9, 10, 11, 12 — that is 5 steps forward.
  • So Mia has 12 carrots.
• Answer: 12 carrots

[Easy] Hockey Pucks

• EN: There are 9 hockey pucks on the ice. 3 slide away. How many are left?
• FR: Il y a 9 rondelles de hockey sur la glace. 3 glissent. Combien en reste-t-il?
• Choices: A) 5 pucks B) 6 pucks C) 7 pucks D) 8 pucks
• Hint: To subtract 5 − 2, count back from 5: 4, 3 — you get 3.
• Steps:
  • Start at 9 and count back 3.
  • 8, 7, 6 — that is 3 steps back.
  • So 6 pucks remain.
• Answer: 6 pucks

[Easy] Skip Counting by 5s

• EN: Count by 5s: 5, 10, 15, ___. What is the missing number?
• FR: Compte par 5: 5, 10, 15, ___. Quel est le nombre manquant?
• Choices: A) 18 B) 19 C) 20 D) 25
• Hint: When counting by 5s, add 5 each time: 2, 7, 12, 17 — always add 5.
• Steps:
  • The pattern adds 5 each time.
  • 15 + 5 = 20.
  • The missing number is 20.
• Answer: 20

[Easy] Coin Recognition

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

[Medium] Snowball Count

• EN: Liam made 12 snowballs in the morning and 6 in the afternoon. How many snowballs did he make altogether?
• FR: Liam a fait 12 boules de neige le matin et 6 l'après-midi. Combien en a-t-il fait en tout?
• Choices: A) 16 snowballs B) 17 snowballs C) 18 snowballs D) 19 snowballs
• Hint: To add 11 + 5, think 11 + 5 = 16. Try the same idea with your numbers.
• Steps:
  • Add the morning and afternoon snowballs together.
  • 12 + 6 = 18.
  • Liam made 18 snowballs altogether.
• Answer: 18 snowballs

[Medium] Comparing Numbers

• EN: Which number is greater: 14 or 17?
• FR: Quel nombre est plus grand: 14 ou 17?
• Choices: A) 14 B) 17 C) They are equal D) 11
• Hint: When comparing 8 and 11, the number farther along the number line is greater.
• Steps:
  • Place 14 and 17 on a number line.
  • 17 comes after 14, so it is greater.
  • The answer is 17.
• Answer: 17

[Medium] Skip Counting by 2s

• EN: Count by 2s starting at 2: 2, 4, 6, 8, ___. What comes next?
• FR: Compte par 2 en commençant à 2: 2, 4, 6, 8, ___. Quel est le prochain nombre?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When counting by 2s, always add 2 to the last number: 4, 6, 8, 10.
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
  • The next number is 10.
• Answer: 10

[Medium] Pennies and Nickels

• EN: Zara has 2 nickels and 3 pennies. How many cents does she have in total?
• FR: Zara a 2 pièces de 5 cents et 3 pennies. Combien de cents a-t-elle en tout?
• Choices: A) 11 cents B) 13 cents C) 15 cents D) 8 cents
• Hint: If you have 3 nickels and 2 pennies, that is 15 + 2 = 17 cents.
• Steps:
  • 2 nickels = 2 × 5 = 10 cents.
  • 3 pennies = 3 × 1 = 3 cents.
  • 10 + 3 = 13 cents.
• Answer: 13 cents

[Hard] Number Puzzle

• EN: I am a number between 15 and 20. You say me when you count by 5s. What number am I?
• FR: Je suis un nombre entre 15 et 20. On me dit quand on compte par 5. Quel nombre suis-je?
• Choices: A) 16 B) 18 C) 19 D) 20
• Hint: Numbers you say when counting by 5s: 5, 10, 15, 20, 25 — which one fits between 15 and 20?
• Steps:
  • Count by 5s: 5, 10, 15, 20, 25.
  • Which of these is between 15 and 20? That is 20 (just after 15).
  • Wait — "between 15 and 20" and also said when counting by 5s means 20.
  • The answer is 20.
• Answer: 20

[Hard] Total Apples

• EN: There are 3 baskets. Each basket has 5 apples. How many apples are there altogether?
• FR: Il y a 3 paniers. Chaque panier a 5 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 8 apples B) 13 apples C) 15 apples D) 16 apples
• Hint: For 2 bags with 4 items each, count: 4, 8 — add 4 twice.
• Steps:
  • Count 5 apples for each of the 3 baskets: 5, 10, 15.
  • That is skip-counting by 5s three times.
  • There are 15 apples altogether.
• Answer: 15 apples

[Easy] Adding to 100

• EN: What is 43 + 25?
• FR: Combien font 43 + 25?
• Choices: A) 60 B) 65 C) 68 D) 72
• Hint: For 31 + 24, add the tens first (30 + 20 = 50) then ones (1 + 4 = 5) to get 55.
• Steps:
  • Add the tens: 40 + 20 = 60.
  • Add the ones: 3 + 5 = 8.
  • 60 + 8 = 68.
• Answer: 68

[Easy] Telling Time

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: L'aiguille courte est sur le 3 et la grande aiguille est sur le 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 6:15
• Hint: When the long hand points to 12, it is exactly on the hour — like 5:00 or 7:00.
• Steps:
  • The long hand on 12 means it is exactly on the hour.
  • The short hand on 3 means it is 3 o'clock.
  • The time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A crayon is 8 cm long. How much longer is the pencil?
• FR: Un crayon est long de 15 cm. Un crayon de couleur est long de 8 cm. De combien le crayon est-il plus long?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 23 cm
• Hint: To find the difference between 12 cm and 5 cm, subtract: 12 − 5 = 7 cm.
• Steps:
  • Subtract the shorter length from the longer: 15 − 8.
  • 15 − 8 = 7.
  • The pencil is 7 cm longer.
• Answer: 7 cm

[Easy] Subtraction within 100

• EN: What is 76 − 34?
• FR: Combien font 76 − 34?
• Choices: A) 32 B) 40 C) 42 D) 44
• Hint: For 58 − 23, subtract tens (50 − 20 = 30) then ones (8 − 3 = 5) to get 35.
• Steps:
  • Subtract the tens: 70 − 30 = 40.
  • Subtract the ones: 6 − 4 = 2.
  • 40 + 2 = 42.
• Answer: 42

[Medium] Counting Coins to $1

• EN: Owen has 3 dimes, 2 nickels, and 4 pennies. How many cents does he have in total?
• FR: Owen a 3 pièces de 10 cents, 2 pièces de 5 cents et 4 pennies. Combien de cents a-t-il en tout?
• Choices: A) 40 cents B) 44 cents C) 45 cents D) 48 cents
• Hint: For 2 dimes, 1 nickel, 2 pennies: 20 + 5 + 2 = 27 cents.
• Steps:
  • 3 dimes = 30 cents.
  • 2 nickels = 10 cents.
  • 4 pennies = 4 cents.
  • 30 + 10 + 4 = 44 cents.
• Answer: 44 cents

[Medium] Simple Patterns

• EN: What comes next in the pattern? 10, 20, 30, 40, ___
• FR: Qu'est-ce qui vient ensuite dans cette suite? 10, 20, 30, 40, ___
• Choices: A) 41 B) 45 C) 50 D) 55
• Hint: In the pattern 3, 6, 9, 12, you add 3 each time — find how much is added in your pattern.
• Steps:
  • Check the pattern: each number increases by 10.
  • 40 + 10 = 50.
  • The next number is 50.
• Answer: 50

[Medium] Telling Time — Half Hour

• EN: The clock shows the short hand between 7 and 8, and the long hand on 6. What time is it?
• FR: L'aiguille courte est entre 7 et 8, et la grande aiguille est sur le 6. Quelle heure est-il?
• Choices: A) 6:07 B) 7:06 C) 7:30 D) 8:30
• Hint: When the long hand points to 6, it is always 30 minutes past the hour — like 2:30.
• Steps:
  • Long hand on 6 = 30 minutes past the hour.
  • Short hand between 7 and 8 = past 7 o'clock.
  • The time is 7:30.
• Answer: 7:30

[Medium] Adding with Regrouping

• EN: There are 47 students in the gym and 38 more join them. How many students are in the gym now?
• FR: Il y a 47 élèves dans le gymnase et 38 autres les rejoignent. Combien y a-t-il d'élèves en tout?
• Choices: A) 75 students B) 80 students C) 85 students D) 87 students
• Hint: For 36 + 29, add ones first (6 + 9 = 15, carry 1), then tens (3 + 2 + 1 = 6), giving 65.
• Steps:
  • Add the ones: 7 + 8 = 15 — write 5, carry 1.
  • Add the tens: 4 + 3 + 1 = 8.
  • The answer is 85 students.
• Answer: 85 students

[Hard] Two-Step Word Problem

• EN: Sofia had 60 stickers. She gave 15 to her friend and then bought 8 more. How many stickers does she have now?
• FR: Sofia avait 60 autocollants. Elle en a donné 15 à son amie et en a acheté 8 autres. Combien en a-t-elle maintenant?
• Choices: A) 37 stickers B) 45 stickers C) 51 stickers D) 53 stickers
• Hint: For 50 − 10 + 6, first subtract (50 − 10 = 40) then add (40 + 6 = 46).
• Steps:
  • Start with 60 stickers.
  • After giving away 15: 60 − 15 = 45.
  • After buying 8 more: 45 + 8 = 53.
• Answer: 53 stickers

[Hard] Length Problem

• EN: A garden path is 1 metre long. A rock is placed 65 cm from one end. How many centimetres from the rock to the other end of the path?
• FR: Un sentier de jardin a 1 mètre de long. Une roche est placée à 65 cm d'un bout. Combien de centimètres y a-t-il entre la roche et l'autre bout du sentier?
• Choices: A) 25 cm B) 30 cm C) 35 cm D) 45 cm
• Hint: Remember 1 metre = 100 cm. To find the remaining part, subtract: 100 − 72 = 28 cm.
• Steps:
  • 1 metre = 100 cm.
  • Subtract the rock's position from the total: 100 − 65 = 35.
  • There are 35 cm from the rock to the other end.
• Answer: 35 cm

[Easy] Multiplication by 2

• EN: What is 6 × 2?
• FR: Combien font 6 × 2?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: 5 × 2 means 5 groups of 2: 2, 4, 6, 8, 10. Try the same idea.
• Steps:
  • 6 groups of 2: 2, 4, 6, 8, 10, 12.
  • Or use the fact: 6 × 2 = 12.
  • The answer is 12.
• Answer: 12

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. Emma eats 1 piece. What fraction did she eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Emma mange 1 morceau. Quelle fraction a-t-elle mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: If a sandwich is cut into 2 equal halves and you eat one, you ate 1 out of 2 parts.
• Steps:
  • The pizza has 2 equal pieces (denominator = 2).
  • Emma ate 1 piece (numerator = 1).
  • The fraction is 1/2.
• Answer: 1/2

[Easy] Multiplication by 5

• EN: What is 4 × 5?
• FR: Combien font 4 × 5?
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: Counting by 5s: 5, 10, 15, 20 — 4 jumps of 5 lands on 20.
• Steps:
  • 4 groups of 5: 5, 10, 15, 20.
  • 4 × 5 = 20.
  • The answer is 20.
• Answer: 20

[Easy] Perimeter

• EN: A square has a side length of 4 cm. What is its perimeter?
• FR: Un carré a un côté de 4 cm. Quel est son périmètre?
• Choices: A) 8 cm B) 12 cm C) 16 cm D) 20 cm
• Hint: A square has 4 equal sides. If each side is 3 cm, perimeter = 3 + 3 + 3 + 3 = 12 cm.
• Steps:
  • A square has 4 sides, each 4 cm long.
  • Perimeter = 4 + 4 + 4 + 4 = 16 cm.
  • The perimeter is 16 cm.
• Answer: 16 cm

[Medium] Basic Division

• EN: 18 cookies are shared equally among 3 friends. How many cookies does each friend get?
• FR: 18 biscuits sont partagés également entre 3 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 4 cookies B) 5 cookies C) 6 cookies D) 7 cookies
• Hint: For 15 ÷ 3, think: how many groups of 3 make 15? 3, 6, 9, 12, 15 — that is 5 groups.
• Steps:
  • Ask: how many groups of 3 fit into 18?
  • 3 × 6 = 18, so each friend gets 6 cookies.
  • The answer is 6 cookies.
• Answer: 6 cookies

[Medium] Multiplication by 3

• EN: At the Tim Hortons hockey camp, each team has 3 players. There are 7 teams. How many players are there in total?
• FR: Au camp de hockey Tim Hortons, chaque équipe a 3 joueurs. Il y a 7 équipes. Combien y a-t-il de joueurs en tout?
• Choices: A) 18 players B) 21 players C) 24 players D) 28 players
• Hint: For 5 teams of 3, use 5 × 3 = 15 players total.
• Steps:
  • Multiply the number of teams by players per team: 7 × 3.
  • 7 × 3 = 21.
  • There are 21 players in total.
• Answer: 21 players

[Medium] Reading a Graph

• EN: A bar graph shows 8 students chose winter and 5 students chose summer as their favourite season. How many more students chose winter?
• FR: Un diagramme à bandes montre que 8 élèves ont choisi l'hiver et 5 ont choisi l'été comme saison préférée. Combien d'élèves de plus ont choisi l'hiver?
• Choices: A) 2 students B) 3 students C) 4 students D) 13 students
• Hint: To find "how many more," subtract the smaller bar from the larger bar.
• Steps:
  • Winter: 8 students. Summer: 5 students.
  • Difference: 8 − 5 = 3.
  • 3 more students chose winter.
• Answer: 3 students

[Medium] Fractions — One Quarter

• EN: A chocolate bar is cut into 4 equal pieces. Ben eats 1 piece. What fraction is left?
• FR: Une barre de chocolat est coupée en 4 morceaux égaux. Ben mange 1 morceau. Quelle fraction reste-t-il?
• Choices: A) 1/4 B) 1/3 C) 2/4 D) 3/4
• Hint: If a bar has 4 equal parts and you eat 1, there are 3 parts left out of 4 total.
• Steps:
  • 4 pieces total, 1 eaten: 4 − 1 = 3 pieces left.
  • Fraction left = 3 out of 4 = 3/4.
  • The answer is 3/4.
• Answer: 3/4

[Hard] Multi-Step Multiplication

• EN: There are 4 boxes of crayons. Each box has 10 crayons. If 8 crayons are given away, how many crayons are left?
• FR: Il y a 4 boîtes de crayons. Chaque boîte contient 10 crayons. Si 8 crayons sont donnés, combien en reste-t-il?
• Choices: A) 30 crayons B) 32 crayons C) 38 crayons D) 42 crayons
• Hint: First find the total using multiplication, then subtract what was given away.
• Steps:
  • Total crayons: 4 × 10 = 40.
  • After giving away 8: 40 − 8 = 32.
  • There are 32 crayons left.
• Answer: 32 crayons

[Hard] Perimeter of a Rectangle

• EN: A rectangular garden is 9 m long and 5 m wide. What is the perimeter of the garden?
• FR: Un jardin rectangulaire est long de 9 m et large de 5 m. Quel est le périmètre du jardin?
• Choices: A) 14 m B) 24 m C) 28 m D) 45 m
• Hint: For a rectangle with length 6 m and width 3 m, perimeter = 6 + 3 + 6 + 3 = 18 m.
• Steps:
  • A rectangle has two lengths and two widths.
  • Perimeter = 9 + 5 + 9 + 5.
  • 9 + 5 = 14, and 14 × 2 = 28 m.
• Answer: 28 m

[Easy] Multiplication Table

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

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 40 ones
• Hint: In the number 2.56, the 5 is in the tenths place and the 6 is in the hundredths place.
• Steps:
  • In 3.47: 3 is in the ones place.
  • 4 is in the tenths place (first digit after the decimal).
  • 7 is in the hundredths place.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A rectangle is 6 cm long and 4 cm wide. What is its area?
• FR: Un rectangle est long de 6 cm et large de 4 cm. Quelle est son aire?
• Choices: A) 10 cm² B) 20 cm² C) 24 cm² D) 28 cm²
• Hint: For a rectangle 5 cm long and 3 cm wide, area = 5 × 3 = 15 cm².
• Steps:
  • Area = length × width.
  • Area = 6 × 4 = 24.
  • The area is 24 cm².
• Answer: 24 cm²

[Easy] Long Division (No Remainder)

• EN: What is 48 ÷ 4?
• FR: Combien font 48 ÷ 4?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: For 36 ÷ 3, think: 3 × 10 = 30, then 3 × 2 = 6, so 36 ÷ 3 = 12.
• Steps:
  • How many times does 4 go into 48?
  • 4 × 12 = 48, so 48 ÷ 4 = 12.
  • The answer is 12.
• Answer: 12

[Medium] Long Division with Remainder

• EN: What is 53 ÷ 5? Express your answer with a remainder.
• FR: Combien font 53 ÷ 5? Exprime ta réponse avec un reste.
• Choices: A) 9 remainder 8 B) 10 remainder 3 C) 11 remainder 2 D) 12 remainder 1
• Hint: For 27 ÷ 4, find the biggest multiple of 4 that fits: 4 × 6 = 24, remainder = 27 − 24 = 3, so answer is 6 remainder 3.
• Steps:
  • Find the biggest multiple of 5 that fits into 53: 5 × 10 = 50.
  • Remainder = 53 − 50 = 3.
  • Answer is 10 remainder 3.
• Answer: 10 remainder 3

[Medium] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/3?
• FR: Quelle fraction est plus grande: 3/4 ou 2/3?
• Choices: A) 2/3 B) 3/4 C) They are equal D) 1/2
• Hint: Convert both to a common denominator: for 1/2 and 2/3, use 6: 3/6 and 4/6 — compare numerators.
• Steps:
  • Find a common denominator for 4 and 3: use 12.
  • 3/4 = 9/12 and 2/3 = 8/12.
  • 9/12 > 8/12, so 3/4 is greater.
• Answer: 3/4

[Medium] Elapsed Time

• EN: The school play starts at 1:15 PM and ends at 3:45 PM. How long is the play?
• FR: La pièce de théâtre commence à 13 h 15 et se termine à 15 h 45. Combien de temps dure-t-elle?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: From 2:10 to 4:40 — count up from 2:10 to 4:10 (2 hours) then 4:10 to 4:40 (30 min) = 2 hours 30 minutes.
• Steps:
  • From 1:15 PM to 3:15 PM is 2 hours.
  • From 3:15 PM to 3:45 PM is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: What is 4.6 + 2.7?
• FR: Combien font 4,6 + 2,7?
• Choices: A) 6.13 B) 6.3 C) 7.3 D) 8.3
• Hint: For 3.4 + 1.9, add the tenths (4 + 9 = 13, write 3, carry 1) then ones (3 + 1 + 1 = 5), giving 5.3.
• Steps:
  • Add the tenths: 6 + 7 = 13 — write 3, carry 1.
  • Add the ones: 4 + 2 + 1 = 7.
  • 4.6 + 2.7 = 7.3.
• Answer: 7.3

[Hard] Multi-Step Problem

• EN: A store sells packs of hockey cards. Each pack has 9 cards and costs $4. If Marco buys 6 packs, how many cards does he get and how much does he spend?
• FR: Un magasin vend des emballages de cartes de hockey. Chaque emballage contient 9 cartes et coûte 4 $. Si Marco achète 6 emballages, combien de cartes obtient-il et combien dépense-t-il?
• Choices: A) 45 cards and $20 B) 54 cards and $24 C) 54 cards and $20 D) 63 cards and $24
• Hint: Find cards: multiply cards per pack × number of packs. Find cost: multiply price per pack × number of packs.
• Steps:
  • Cards: 6 × 9 = 54 cards.
  • Cost: 6 × $4 = $24.
  • Marco gets 54 cards and spends $24.
• Answer: 54 cards and $24

[Hard] Area and Perimeter Combined

• EN: A rectangle has a perimeter of 26 cm and a length of 8 cm. What is its width and area?
• FR: Un rectangle a un périmètre de 26 cm et une longueur de 8 cm. Quelles sont sa largeur et son aire?
• Choices: A) Width 5 cm, Area 40 cm² B) Width 5 cm, Area 45 cm² C) Width 6 cm, Area 48 cm² D) Width 9 cm, Area 72 cm²
• Hint: Perimeter = 2 × (length + width), so length + width = perimeter ÷ 2. Then subtract the length to find the width.
• Steps:
  • Half the perimeter: 26 ÷ 2 = 13.
  • Width = 13 − 8 = 5 cm.
  • Area = 8 × 5 = 40 cm².
• Answer: Width 5 cm, Area 40 cm²

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 200 C) 204 D) 210
• Hint: For 23 × 4, multiply ones first (3 × 4 = 12, write 2, carry 1) then tens (2 × 4 + 1 = 9), giving 92.
• Steps:
  • Multiply ones: 4 × 6 = 24 — write 4, carry 2.
  • Multiply tens: 3 × 6 = 18, plus 2 = 20.
  • 34 × 6 = 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: For 3/8 + 2/8, just add the numerators and keep the denominator: 5/8.
• Steps:
  • The denominators are the same (7), so add the numerators.
  • 2 + 3 = 5.
  • The answer is 5/7.
• Answer: 5/7

[Easy] 50% of a Number

• EN: What is 50% of 80?
• FR: Combien vaut 50% de 80?
• Choices: A) 20 B) 30 C) 40 D) 45
• Hint: 50% means half, so find 50% of 60 by dividing 60 by 2 = 30.
• Steps:
  • 50% means one half.
  • 80 ÷ 2 = 40.
  • 50% of 80 is 40.
• Answer: 40

[Easy] Decimal Operations — Subtraction

• EN: What is 9.8 − 3.5?
• FR: Combien font 9,8 − 3,5?
• Choices: A) 5.3 B) 6.2 C) 6.3 D) 7.3
• Hint: For 7.6 − 2.3, subtract tenths (6 − 3 = 3) then ones (7 − 2 = 5), giving 5.3.
• Steps:
  • Subtract the tenths: 8 − 5 = 3.
  • Subtract the ones: 9 − 3 = 6.
  • 9.8 − 3.5 = 6.3.
• Answer: 6.3

[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 est longue de 5 cm, large de 4 cm et haute de 3 cm. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume = length × width × height. For a box 2 cm × 3 cm × 4 cm, volume = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Multi-Digit Division

• EN: What is 432 ÷ 4?
• FR: Combien font 432 ÷ 4?
• Choices: A) 98 B) 100 C) 108 D) 118
• Hint: For 246 ÷ 3, divide each digit group: 2 ÷ 3 doesn't work, so try 24 ÷ 3 = 8, then 6 ÷ 3 = 2, giving 82.
• Steps:
  • 4 ÷ 4 = 1 (hundreds).
  • 3 ÷ 4 — borrow: 32 ÷ 4 = 8 (tens) with 0 remaining.
  • Wait, let's use long division: 4 goes into 4 once, into 03 zero times, into 32 eight times. So 432 ÷ 4 = 108.
• Answer: 108

[Medium] Subtracting Fractions with Like Denominators

• EN: What is 5/6 − 2/6?
• FR: Combien font 5/6 − 2/6?
• Choices: A) 3/12 B) 3/6 C) 4/6 D) 7/6
• Hint: For 7/9 − 3/9, subtract the numerators and keep the denominator: 4/9.
• Steps:
  • The denominators are the same (6).
  • Subtract the numerators: 5 − 2 = 3.
  • The answer is 3/6.
• Answer: 3/6

[Medium] 25% of a Number

• EN: A jacket costs $60. It is on sale for 25% off. How much money is saved?
• FR: Une veste coûte 60 $. Elle est en solde à 25% de rabais. Combien économise-t-on?
• Choices: A) $10 B) $12 C) $15 D) $20
• Hint: 25% means one quarter. To find 25% of 40, divide 40 by 4 = 10.
• Steps:
  • 25% = 1/4.
  • 60 ÷ 4 = 15.
  • The savings are $15.
• Answer: $15

[Hard] Multi-Step Fraction Problem

• EN: A recipe needs 3/8 cup of sugar and 5/8 cup of flour. If Priya doubles the recipe, how many cups of ingredients does she need in total?
• FR: Une recette nécessite 3/8 de tasse de sucre et 5/8 de tasse de farine. Si Priya double la recette, de combien de tasses d'ingrédients a-t-elle besoin en tout?
• Choices: A) 1 cup B) 2 cups C) 3 cups D) 4 cups
• Hint: First add the fractions, then multiply by 2 to double the recipe.
• Steps:
  • Total for one recipe: 3/8 + 5/8 = 8/8 = 1 cup.
  • Double the recipe: 1 × 2 = 2 cups.
  • Priya needs 2 cups in total.
• Answer: 2 cups

[Hard] Percentage and Decimal Combined

• EN: A hockey stick costs $45.00. The store adds a 10% tax. What is the total price?
• FR: Un bâton de hockey coûte 45,00 $. Le magasin ajoute une taxe de 10 %. Quel est le prix total?
• Choices: A) $4.50 B) $45.10 C) $49.50 D) $50.50
• Hint: 10% of any number = divide by 10. For $30, 10% = $3, so total = $33.
• Steps:
  • 10% of $45.00 = $45.00 ÷ 10 = $4.50.
  • Total = $45.00 + $4.50 = $49.50.
  • The total price is $49.50.
• Answer: $49.50

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: In BEDMAS, multiplication comes before addition. For 5 + 2 × 3, do 2 × 3 = 6 first, then 5 + 6 = 11.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then addition: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Percent of a Number

• EN: What is 30% of 50?
• FR: Combien vaut 30% de 50?
• Choices: A) 10 B) 15 C) 20 D) 30
• Hint: To find 20% of 60: 10% of 60 = 6, so 20% = 6 × 2 = 12.
• Steps:
  • 10% of 50 = 5.
  • 30% = 3 × 5 = 15.
  • 30% of 50 is 15.
• Answer: 15

[Easy] Integer Introduction

• EN: The temperature in Winnipeg was −8°C in the morning and rose by 5°C by noon. What is the noon temperature?
• FR: La température à Winnipeg était de −8°C le matin et a augmenté de 5°C à midi. Quelle est la température à midi?
• Choices: A) −13°C B) −3°C C) 3°C D) 13°C
• Hint: On a number line, starting at −6 and moving right 4 steps brings you to −2.
• Steps:
  • Start at −8 and add 5.
  • −8 + 5 = −3.
  • The noon temperature is −3°C.
• Answer: −3°C

[Easy] Simple Algebraic Expression

• EN: If n = 4, what is the value of 3n + 2?
• FR: Si n = 4, quelle est la valeur de 3n + 2?
• Choices: A) 9 B) 12 C) 14 D) 18
• Hint: For 2n + 5 when n = 3, substitute: 2(3) + 5 = 6 + 5 = 11.
• Steps:
  • Substitute n = 4 into 3n + 2.
  • 3(4) + 2 = 12 + 2 = 14.
  • The value is 14.
• Answer: 14

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/7 B) 6/12 C) 5/12 D) 8/9
• Hint: For 1/2 × 2/5, multiply numerators (1 × 2 = 2) and denominators (2 × 5 = 10) to get 2/10 = 1/5.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 simplifies to 1/2.
• Answer: 6/12

[Medium] Ratio and Rate

• EN: A car travels 150 km in 3 hours. What is the car's speed in kilometres per hour?
• FR: Une voiture parcourt 150 km en 3 heures. Quelle est la vitesse de la voiture en kilomètres par heure?
• Choices: A) 40 km/h B) 45 km/h C) 50 km/h D) 55 km/h
• Hint: Rate = total amount ÷ number of units. For 200 km in 4 hours: 200 ÷ 4 = 50 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 150 ÷ 3 = 50.
  • The car's speed is 50 km/h.
• Answer: 50 km/h

[Medium] BEDMAS with Brackets

• EN: What is (5 + 3) × 2 − 4?
• FR: Combien font (5 + 3) × 2 − 4?
• Choices: A) 10 B) 12 C) 14 D) 16
• Hint: For (2 + 4) × 3 − 5, do brackets first: 6 × 3 = 18, then subtract: 18 − 5 = 13.
• Steps:
  • Brackets first: (5 + 3) = 8.
  • Multiply: 8 × 2 = 16.
  • Subtract: 16 − 4 = 12.
• Answer: 12

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1/2 C) 3/2 D) 5/4
• Hint: To divide fractions, multiply by the reciprocal: 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.
  • The answer is 3/2.
• Answer: 3/2

[Hard] Multi-Step Percent Problem

• EN: A sweater costs $80. It is discounted by 20%, then the sale price has 13% tax added. What is the final price?
• FR: Un chandail coûte 80 $. Il est rabais de 20 %, puis la taxe de 13 % est ajoutée au prix de vente. Quel est le prix final?
• Choices: A) $64.00 B) $70.00 C) $72.32 D) $80.00
• Hint: First find the discount (percent × original price), subtract to get sale price, then add tax (percent × sale price).
• Steps:
  • 20% of $80 = $16. Sale price = $80 − $16 = $64.
  • 13% of $64 = $8.32.
  • Final price = $64 + $8.32 = $72.32.
• Answer: $72.32

[Hard] Algebraic Expression with Ratios

• EN: In a class, the ratio of boys to girls is 3:5. If there are 40 students in total, how many are girls?
• FR: Dans une classe, le rapport garçons/filles est de 3:5. S'il y a 40 élèves en tout, combien y a-t-il de filles?
• Choices: A) 15 girls B) 20 girls C) 25 girls D) 30 girls
• Hint: Find the total ratio parts (3 + 5 = 8), divide total students by 8 to find one part, then multiply by the girls' ratio number.
• Steps:
  • Total parts: 3 + 5 = 8.
  • One part = 40 ÷ 8 = 5 students.
  • Girls = 5 × 5 = 25 girls.
• Answer: 25 girls

[Easy] Integer Addition

• EN: What is −12 + 7?
• FR: Combien font −12 + 7?
• Choices: A) −19 B) −5 C) 5 D) 19
• Hint: On a number line, −10 + 4 means starting at −10 and moving 4 steps right, landing on −6.
• Steps:
  • Start at −12 and move 7 steps to the right.
  • −12 + 7 = −5.
  • The answer is −5.
• Answer: −5

[Easy] Integer Subtraction

• EN: What is 3 − (−6)?
• FR: Combien font 3 − (−6)?
• Choices: A) −9 B) −3 C) 3 D) 9
• Hint: Subtracting a negative is the same as adding a positive: 5 − (−2) = 5 + 2 = 7.
• Steps:
  • 3 − (−6) = 3 + 6.
  • 3 + 6 = 9.
  • The answer is 9.
• Answer: 9

[Easy] Percent — Discount

• EN: A video game costs $60. It is on sale at 15% off. How much is the discount?
• FR: Un jeu vidéo coûte 60 $. Il est en solde à 15 % de rabais. Quel est le montant du rabais?
• Choices: A) $6 B) $9 C) $10 D) $15
• Hint: For 20% of $50: 10% = $5, so 20% = $10.
• Steps:
  • 10% of $60 = $6.
  • 15% = $6 + $3 = $9 (since 5% = $3).
  • The discount is $9.
• Answer: $9

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 20.
• FR: Résous pour x: x + 9 = 20.
• Choices: A) x = 9 B) x = 11 C) x = 20 D) x = 29
• Hint: To solve n + 5 = 13, subtract 5 from both sides: n = 13 − 5 = 8.
• Steps:
  • Subtract 9 from both sides.
  • x = 20 − 9.
  • x = 11.
• Answer: x = 11

[Medium] Integer Multiplication

• EN: What is −4 × (−7)?
• FR: Combien font −4 × (−7)?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: A negative times a negative is always positive: −3 × (−5) = 15.
• Steps:
  • Multiply the absolute values: 4 × 7 = 28.
  • Negative × negative = positive.
  • The answer is 28.
• Answer: 28

[Medium] Percentage — Tip

• EN: A restaurant meal costs $45. A 15% tip is added. What is the total bill?
• FR: Un repas au restaurant coûte 45 $. Un pourboire de 15 % est ajouté. Quel est le montant total?
• Choices: A) $50.75 B) $51.75 C) $52.25 D) $53.25
• Hint: 15% tip = 10% + 5%. For $80: 10% = $8, 5% = $4, tip = $12, total = $92.
• Steps:
  • 10% of $45 = $4.50.
  • 5% of $45 = $2.25.
  • Tip = $4.50 + $2.25 = $6.75. Total = $45 + $6.75 = $51.75.
• Answer: $51.75

[Medium] Surface Area

• EN: A rectangular box is 5 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire est longue de 5 cm, large de 3 cm et haute de 2 cm. Quelle est son aire totale?
• Choices: A) 52 cm² B) 60 cm² C) 62 cm² D) 70 cm²
• Hint: Surface area = 2(lw + lh + wh). For a 4 × 2 × 1 box: 2(8 + 4 + 2) = 2(14) = 28 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(5×3 + 5×2 + 3×2).
  • = 2(15 + 10 + 6) = 2(31).
  • = 62 cm².
• Answer: 62 cm²

[Medium] Probability

• EN: A bag contains 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 bleues et 2 vertes. Quelle est la probabilité de piger au hasard une bille bleue?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 5/10
• Hint: Probability = favourable outcomes ÷ total outcomes. For 4 red and 6 blue balls, P(blue) = 6/10.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Favourable (blue): 5.
  • P(blue) = 5/10.
• Answer: 5/10

[Hard] Integer Division and Multi-Step

• EN: The temperature dropped 3°C every hour for 8 hours, starting at 4°C. What is the temperature after 8 hours?
• FR: La température a chuté de 3°C par heure pendant 8 heures, en commençant à 4°C. Quelle est la température après 8 heures?
• Choices: A) −28°C B) −24°C C) −20°C D) 28°C
• Hint: Total change = rate × time. If temperature drops 2°C/hour for 5 hours starting at 3°C: change = −10°C, final = 3 + (−10) = −7°C.
• Steps:
  • Total temperature drop: 3 × 8 = 24°C drop.
  • Starting at 4°C: 4 + (−24) = 4 − 24 = −20°C.
  • The temperature is −20°C.
• Answer: −20°C

[Hard] One-Step Equations and Fractions

• EN: Solve for y: y/3 + 5 = 14.
• FR: Résous pour y: y/3 + 5 = 14.
• Choices: A) y = 3 B) y = 19 C) y = 27 D) y = 57
• Hint: To solve n/4 + 2 = 6, first subtract 2 from both sides (n/4 = 4), then multiply both sides by 4 (n = 16).
• Steps:
  • Subtract 5 from both sides: y/3 = 9.
  • Multiply both sides by 3: y = 27.
  • The answer is y = 27.
• Answer: y = 27

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think: what number times itself equals the number under the root? For √81, 9 × 9 = 81.
• Steps:
  • Ask: what number squared equals 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x: 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 6 D) x = 9
• Hint: For 3x + 4 = 10, subtract 4 first (3x = 6), then divide by 3 (x = 2).
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
  • The answer is x = 4.
• Answer: x = 4

[Easy] Mean

• EN: Find the mean of: 8, 12, 10, 6, 14.
• FR: Trouve la moyenne de: 8, 12, 10, 6, 14.
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: To find the mean of 4, 6, 8, add them (18), then divide by 3 (how many numbers): 18 ÷ 3 = 6.
• Steps:
  • Add all values: 8 + 12 + 10 + 6 + 14 = 50.
  • Divide by the count: 50 ÷ 5 = 10.
  • The mean is 10.
• Answer: 10

[Easy] Percent Increase

• EN: A shirt costs $40. The price increases by 25%. What is the new price?
• FR: Une chemise coûte 40 $. Le prix augmente de 25 %. Quel est le nouveau prix?
• Choices: A) $45 B) $48 C) $50 D) $55
• Hint: 25% of $60 = $15, so the new price would be $60 + $15 = $75.
• Steps:
  • 25% of $40 = $40 ÷ 4 = $10.
  • New price = $40 + $10 = $50.
  • The new price is $50.
• Answer: $50

[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) 14 cm D) 15 cm
• Hint: Use a² + b² = c². For legs 3 and 4: 9 + 16 = 25, so c = √25 = 5.
• Steps:
  • a² + b² = c².
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation with Negatives

• EN: Solve for x: 3x − 7 = 11.
• FR: Résous pour x: 3x − 7 = 11.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 8
• Hint: For 4x − 3 = 9, add 3 first (4x = 12), then divide by 4 (x = 3).
• Steps:
  • Add 7 to both sides: 3x = 18.
  • Divide both sides by 3: x = 6.
  • The answer is x = 6.
• Answer: x = 6

[Medium] Median

• EN: Find the median of: 3, 9, 1, 7, 5.
• FR: Trouve la médiane de: 3, 9, 1, 7, 5.
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: To find the median, arrange the numbers from least to greatest and find the middle one. For 2, 4, 6, 8, 10 — the middle is 6.
• Steps:
  • Arrange in order: 1, 3, 5, 7, 9.
  • The middle value (3rd out of 5) is 5.
  • The median is 5.
• Answer: 5

[Medium] Slope Introduction

• EN: A line passes through (0, 2) and (3, 8). What is the slope of the line?
• FR: Une droite passe par (0, 2) et (3, 8). Quelle est la pente de cette droite?
• Choices: A) 1 B) 2 C) 3 D) 6
• Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁). For points (0, 1) and (2, 5): slope = (5 − 1) ÷ (2 − 0) = 4 ÷ 2 = 2.
• Steps:
  • Slope = (y₂ − y₁) ÷ (x₂ − x₁).
  • = (8 − 2) ÷ (3 − 0) = 6 ÷ 3.
  • Slope = 2.
• Answer: 2

[Hard] Pythagorean Theorem — Find a Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et un côté de 5 cm. Quelle est la longueur de l'autre côté?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 18 cm
• Hint: Use a² + b² = c², then rearrange to find b: b² = c² − a². For c = 10, a = 6: b² = 100 − 36 = 64, b = 8.
• Steps:
  • b² = c² − a² = 13² − 5².
  • = 169 − 25 = 144.
  • b = √144 = 12 cm.
• Answer: 12 cm

[Hard] Percent Decrease — Multi-Step

• EN: A hockey team won 40 games last season. This season they won 30 games. What is the percent decrease in wins?
• FR: Une équipe de hockey a gagné 40 matchs la saison dernière. Cette saison, elle en a gagné 30. Quel est le pourcentage de diminution?
• Choices: A) 10% B) 20% C) 25% D) 33%
• Hint: Percent decrease = (original − new) ÷ original × 100%. For 50 to 40: (50 − 40) ÷ 50 × 100% = 20%.
• Steps:
  • Decrease = 40 − 30 = 10.
  • Percent decrease = 10 ÷ 40 × 100%.
  • = 0.25 × 100% = 25%.
• Answer: 25%

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 3 = 17.
• FR: Résous pour x: 4x − 3 = 17.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: For 5x − 2 = 13, add 2 first (5x = 15), then divide by 5 (x = 3).
• Steps:
  • Add 3 to both sides: 4x = 20.
  • Divide both sides by 4: x = 5.
  • The answer is x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: What is (3x + 5) + (2x − 1)?
• FR: Combien font (3x + 5) + (2x − 1)?
• Choices: A) 4x + 6 B) 5x + 4 C) 5x + 6 D) 6x + 4
• Hint: Combine like terms: for (4y + 3) + (2y − 1), add y-terms (4y + 2y = 6y) and constants (3 − 1 = 2) to get 6y + 2.
• Steps:
  • Combine x-terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−1) = 4.
  • Answer: 5x + 4
• Answer: 5x + 4

[Easy] Graphing Lines — Y-Intercept

• EN: What is the y-intercept of the line y = 3x + 7?
• FR: Quel est l'ordonnée à l'origine de la droite y = 3x + 7?
• Choices: A) 3 B) 5 C) 7 D) 10
• Hint: In y = mx + b, b is always the y-intercept. For y = 2x + 5, the y-intercept is 5.
• Steps:
  • The equation is in slope-intercept form y = mx + b.
  • The y-intercept is b = 7.
  • The y-intercept is 7.
• Answer: 7

[Easy] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 6 cm et l'hypoténuse est 10 cm. Combien vaut sin(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: SOH: sin = opposite ÷ hypotenuse. For opposite = 4, hypotenuse = 8: sin = 4/8 = 0.5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • = 6 ÷ 10 = 0.6.
  • sin(θ) = 0.6.
• Answer: 0.6

[Medium] Linear Inequality

• EN: Solve for x: 2x + 4 > 10.
• FR: Résous pour x: 2x + 4 > 10.
• Choices: A) x > 2 B) x > 3 C) x < 3 D) x > 7
• Hint: For 3x + 1 > 7, subtract 1 (3x > 6) then divide by 3 (x > 2).
• Steps:
  • Subtract 4 from both sides: 2x > 6.
  • Divide both sides by 2: x > 3.
  • The solution is x > 3.
• Answer: x > 3

[Medium] Multiplying Polynomials

• EN: What is 2x(3x + 5)?
• FR: Combien font 2x(3x + 5)?
• Choices: A) 5x + 10 B) 6x + 10x C) 6x² + 10x D) 8x² + 10x
• Hint: For 3y(2y + 4), distribute: 3y × 2y = 6y², 3y × 4 = 12y, giving 6y² + 12y.
• Steps:
  • Distribute 2x to each term.
  • 2x × 3x = 6x², and 2x × 5 = 10x.
  • Answer: 6x² + 10x
• Answer: 6x² + 10x

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in the ratio 2:5. The smaller triangle has a side of 4 cm. What is the corresponding side in the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans un rapport de 2:5. Le petit triangle a un côté de 4 cm. Quel est le côté correspondant du grand triangle?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: Set up a proportion: small/large = 2/5. If small side = 6, then 6/x = 2/5, so x = 6 × 5/2 = 15.
• Steps:
  • Set up proportion: 4/x = 2/5.
  • Cross-multiply: 2x = 20.
  • x = 10 cm.
• Answer: 10 cm

[Medium] Slope-Intercept Form

• EN: A line has a slope of 3 and passes through the point (0, −2). What is the equation of the line?
• FR: Une droite a une pente de 3 et passe par le point (0, −2). Quelle est l'équation de la droite?
• Choices: A) y = 2x − 3 B) y = 3x − 2 C) y = −2x + 3 D) y = 3x + 2
• Hint: Slope-intercept form is y = mx + b. If slope = 4 and y-intercept = 1, the equation is y = 4x + 1.
• Steps:
  • Use y = mx + b.
  • m = 3 (slope), b = −2 (y-intercept from point (0, −2)).
  • Equation: y = 3x − 2.
• Answer: y = 3x − 2

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is the angle θ (to the nearest degree)?
• FR: Dans un triangle rectangle, le côté adjacent est 5 cm et l'hypoténuse est 13 cm. Quel est l'angle θ (au degré près)?
• Choices: A) 23° B) 67° C) 37° D) 53°
• Hint: CAH: cos(θ) = adjacent ÷ hypotenuse. Then use θ = cos⁻¹(value). For adj = 8, hyp = 10: cos(θ) = 0.8, θ ≈ 37°.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 5 ÷ 13 ≈ 0.385.
  • θ = cos⁻¹(0.385) ≈ 67°.
  • The angle θ is approximately 67°.
• Answer: 67°

[Hard] System Setup from Word Problem

• EN: Two friends collected cans for a food drive. Together they collected 84 cans. One friend collected 12 more cans than the other. How many cans did the friend with fewer cans collect?
• FR: Deux amis ont collecté des conserves pour une banque alimentaire. Ensemble, ils en ont collecté 84. L'un en a collecté 12 de plus que l'autre. Combien de conserves l'ami avec le moins en a-t-il collecté?
• Choices: A) 30 cans B) 36 cans C) 42 cans D) 48 cans
• Hint: If two numbers sum to S and differ by d, the smaller number = (S − d) ÷ 2.
• Steps:
  • Let the smaller amount = x. Then x + (x + 12) = 84.
  • 2x + 12 = 84, so 2x = 72, x = 36.
  • The friend with fewer cans collected 36 cans.
• Answer: 36 cans

[Easy] Factoring Quadratics

• EN: Factor x² + 7x + 12.
• FR: Factorise x² + 7x + 12.
• Choices: A) (x + 2)(x + 6) B) (x + 3)(x + 4) C) (x + 1)(x + 12) D) (x + 4)(x + 3)
• Hint: Find two numbers that multiply to 12 and add to 7. For x² + 5x + 6, those numbers are 2 and 3.
• Steps:
  • Need two numbers that multiply to 12 and add to 7.
  • 3 × 4 = 12 and 3 + 4 = 7. ✓
  • x² + 7x + 12 = (x + 3)(x + 4).
• Answer: (x + 3)(x + 4)

[Easy] Trigonometry — All Ratios

• EN: In a right triangle, the opposite = 8 and adjacent = 6. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé = 8 et le côté adjacent = 6. Combien vaut tan(θ)?
• Choices: A) 3/4 B) 4/3 C) 4/5 D) 3/5
• Hint: TOA: tan = opposite ÷ adjacent. For opposite = 5, adjacent = 10: tan = 5/10 = 1/2.
• Steps:
  • tan(θ) = opposite ÷ adjacent.
  • = 8 ÷ 6 = 4/3.
  • tan(θ) = 4/3.
• Answer: 4/3

[Easy] System of Equations — Substitution

• EN: Solve the system: y = 2x and x + y = 12.
• FR: Résous le système: y = 2x et x + y = 12.
• Choices: A) x = 2, y = 4 B) x = 3, y = 9 C) x = 4, y = 8 D) x = 6, y = 6
• Hint: Substitute the first equation into the second. For y = 3x and x + y = 8: x + 3x = 8, 4x = 8, x = 2, y = 6.
• Steps:
  • Substitute y = 2x into x + y = 12: x + 2x = 12.
  • 3x = 12, so x = 4.
  • y = 2(4) = 8. So x = 4, y = 8.
• Answer: x = 4, y = 8

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 94.2 cm³ B) 188.4 cm³ C) 251.2 cm³ D) 282.6 cm³
• Hint: V = π × r² × h. For r = 2, h = 5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 3² × 10.
  • = 3.14 × 9 × 10 = 3.14 × 90.
  • = 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Completing the Square

• EN: Complete the square to solve: x² + 6x − 7 = 0.
• FR: Complète le carré pour résoudre: x² + 6x − 7 = 0.
• Choices: A) x = 1 or x = −7 B) x = 7 or x = −1 C) x = 2 or x = −8 D) x = 3 or x = −9
• Hint: To complete the square for x² + 4x − 5 = 0: (x+2)² = 9, x + 2 = ±3, x = 1 or x = −5.
• Steps:
  • x² + 6x = 7. Add 9 to both sides: (x + 3)² = 16.
  • x + 3 = ±4. So x = 1 or x = −7.
  • The solutions are 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? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 6 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 18.84 cm B) 37.68 cm C) 56.52 cm D) 113.04 cm
• Hint: Circumference = 2πr. For r = 5: C = 2 × 3.14 × 5 = 31.4 cm.
• Steps:
  • C = 2 × π × r = 2 × 3.14 × 6.
  • = 6.28 × 6 = 37.68 cm.
  • The circumference is 37.68 cm.
• Answer: 37.68 cm

[Medium] Systems of Equations — Elimination

• EN: Solve: 2x + y = 10 and x − y = 2.
• FR: Résous: 2x + y = 10 et x − y = 2.
• Choices: A) x = 3, y = 4 B) x = 4, y = 2 C) x = 5, y = 1 D) x = 6, y = −2
• Hint: Add the two equations to eliminate y. For 3x + y = 9 and x − y = 3: adding gives 4x = 12, x = 3, y = 0.
• Steps:
  • Add the equations: (2x + y) + (x − y) = 10 + 2 → 3x = 12, x = 4.
  • Substitute into x − y = 2: 4 − y = 2, y = 2.
  • x = 4, y = 2.
• Answer: x = 4, y = 2

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 7 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 7 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 87.92 cm² B) 100.48 cm² C) 138.16 cm² D) 175.84 cm²
• Hint: SA of cone = πr² + πrl (base + lateral). For r = 3, l = 5: SA = 3.14(9) + 3.14(3)(5) = 28.26 + 47.1 = 75.36 cm².
• Steps:
  • Base area = π × r² = 3.14 × 16 = 50.24 cm².
  • Lateral area = π × r × l = 3.14 × 4 × 7 = 87.92 cm².
  • Total SA = 50.24 + 87.92 = 138.16 cm².
• Answer: 138.16 cm²

[Hard] Quadratic Formula

• EN: Solve using the quadratic formula: 2x² − 5x − 3 = 0.
• FR: Résous à l'aide de la formule quadratique: 2x² − 5x − 3 = 0.
• Choices: A) x = 3 or x = −1/2 B) x = −3 or x = 1/2 C) x = 5 or x = −2 D) x = 1 or x = −3
• Hint: Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ (2a). Identify a, b, c first, then substitute carefully.
• Steps:
  • a = 2, b = −5, c = −3.
  • Discriminant: (−5)² − 4(2)(−3) = 25 + 24 = 49.
  • x = (5 ± 7) ÷ 4. So x = 12/4 = 3 or x = −2/4 = −1/2.
• Answer: x = 3 or x = −1/2

[Hard] Circle Geometry — Chord and Angle

• EN: A chord is 16 cm long in a circle with a radius of 10 cm. How far (in cm) is the chord from the centre of the circle?
• FR: Une corde de 16 cm se trouve dans un cercle de rayon 10 cm. À quelle distance (en cm) la corde est-elle du centre du cercle?
• Choices: A) 4 cm B) 6 cm C) 8 cm D) 12 cm
• Hint: The perpendicular from the centre to a chord bisects it. Use the Pythagorean theorem with radius, half-chord, and distance as the three sides.
• Steps:
  • The perpendicular bisects the chord: half-chord = 16 ÷ 2 = 8 cm.
  • Use Pythagorean theorem: d² + 8² = 10².
  • d² = 100 − 64 = 36, d = 6 cm.
• Answer: 6 cm

[Easy] Evaluating an Exponential Function

• EN: If f(x) = 2^x, what is f(5)?
• FR: Si f(x) = 2^x, combien vaut f(5)?
• Choices: A) 10 B) 16 C) 32 D) 64
• Hint: For f(x) = 3^x, f(4) = 3 × 3 × 3 × 3 = 81. Multiply the base by itself x times.
• Steps:
  • f(5) = 2^5 = 2 × 2 × 2 × 2 × 2.
  • = 4 × 4 × 2 = 32.
  • The answer is 32.
• Answer: 32

[Easy] Logarithm Introduction

• EN: What is log₂(16)?
• FR: Combien vaut log₂(16)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log₃(27) asks: "3 to what power equals 27?" 3³ = 27, so log₃(27) = 3.
• Steps:
  • log₂(16) asks: "2 to what power equals 16?"
  • 2⁴ = 16.
  • log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequence

• EN: Find the 10th term of the arithmetic sequence: 3, 7, 11, 15, …
• FR: Trouve le 10e terme de la suite arithmétique: 3, 7, 11, 15, …
• Choices: A) 39 B) 41 C) 43 D) 45
• Hint: For a sequence 2, 5, 8, 11: first term a = 2, common difference d = 3. The nth term = a + (n − 1)d.
• Steps:
  • First term a = 3, common difference d = 4.
  • 10th term = 3 + (10 − 1)(4) = 3 + 36 = 39.
  • The 10th term is 39.
• Answer: 39

[Easy] Simple Interest vs. Compound Interest

• EN: $500 is invested at 4% per year simple interest. How much interest is earned in 3 years?
• FR: 500 $ sont investis à 4 % d'intérêt simple par an. Combien d'intérêts sont gagnés en 3 ans?
• Choices: A) $20 B) $40 C) $60 D) $80
• Hint: Simple interest = Principal × Rate × Time. For $200 at 5% for 2 years: I = 200 × 0.05 × 2 = $20.
• Steps:
  • I = P × r × t = 500 × 0.04 × 3.
  • = 500 × 0.12 = 60.
  • Interest earned is $60.
• Answer: $60

[Medium] Geometric Sequence

• EN: Find the sum of the first 5 terms of the geometric series: 2, 6, 18, 54, …
• FR: Trouve la somme des 5 premiers termes de la suite géométrique: 2, 6, 18, 54, …
• Choices: A) 182 B) 240 C) 242 D) 256
• Hint: Sum of a geometric series = a(rⁿ − 1) ÷ (r − 1). For 1, 2, 4, 8, 16: a=1, r=2, n=5, S = 1(2⁵−1)/(2−1) = 31.
• Steps:
  • a = 2, r = 3, n = 5.
  • S = 2(3⁵ − 1) ÷ (3 − 1) = 2(243 − 1) ÷ 2 = 242.
  • The sum is 242.
• Answer: 242

[Medium] Compound Interest

• EN: $1000 is invested at 5% annual interest, compounded annually. What is the amount after 2 years?
• FR: 1 000 $ sont investis à 5 % d'intérêt annuel, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1105.00
• Hint: Compound interest: A = P(1 + r)^t. For $500 at 10% for 2 years: A = 500(1.1)² = 500(1.21) = $605.
• Steps:
  • A = 1000(1 + 0.05)² = 1000(1.05)².
  • 1.05² = 1.1025.
  • A = 1000 × 1.1025 = $1102.50.
• Answer: $1102.50

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifie: sin²(θ) + cos²(θ).
• Choices: A) 0 B) 1 C) 2 D) tan²(θ)
• Hint: This is a fundamental Pythagorean identity that holds for every angle θ — it always equals a specific constant.
• Steps:
  • This is the Pythagorean identity.
  • sin²(θ) + cos²(θ) = 1 for all values of θ.
  • The answer is 1.
• Answer: 1

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = 2(x − 3)² + 5?
• FR: Quel est le sommet de la parabole y = 2(x − 3)² + 5?
• Choices: A) (−3, 5) B) (3, 5) C) (3, −5) D) (5, 3)
• Hint: For y = a(x − h)² + k, the vertex is always the point (h, k). For y = 4(x − 2)² + 7, the vertex is (2, 7).
• Steps:
  • The equation is in vertex form: y = a(x − h)² + k.
  • Here h = 3 and k = 5.
  • The vertex is (3, 5).
• Answer: (3, 5)

[Hard] Annuity — Future Value

• EN: A student deposits $200 at the end of every year into a savings account that earns 6% annual interest compounded annually. What is the total amount (future value) after 3 years?
• FR: Un(e) étudiant(e) dépose 200 $ à la fin de chaque année dans un compte d'épargne qui rapporte 6 % d'intérêt annuel composé. Quel est le montant total (valeur future) après 3 ans?
• Choices: A) $600.00 B) $618.55 C) $636.48 D) $662.35
• Hint: FV = PMT × [(1 + r)^n − 1] ÷ r. For $100/year at 5% for 2 years: FV = 100 × [(1.05)² − 1] ÷ 0.05 = 100 × 2.05 = $205.
• Steps:
  • FV = 200 × [(1.06)³ − 1] ÷ 0.06.
  • (1.06)³ = 1.191016. So (1.191016 − 1) ÷ 0.06 = 0.191016 ÷ 0.06 = 3.1836.
  • FV = 200 × 3.1836 = $636.48 (approximately).
• Answer: $636.48

[Hard] Logarithm Laws — Solving

• EN: Solve for x: log₃(x) + log₃(4) = log₃(36).
• FR: Résous pour x: log₃(x) + log₃(4) = log₃(36).
• Choices: A) x = 6 B) x = 9 C) x = 12 D) x = 32
• Hint: Use the product rule: logₐ(m) + logₐ(n) = logₐ(mn). Then equate the arguments. For log₂(x) + log₂(3) = log₂(12): x × 3 = 12, x = 4.
• Steps:
  • Combine logs: log₃(4x) = log₃(36).
  • Since the bases and results are equal: 4x = 36.
  • x = 36 ÷ 4 = 9.
• Answer: x = 9

[Easy] Permutations

• EN: How many ways can 5 students line up in a row?
• FR: De combien de façons 5 élèves peuvent-ils se placer en rang?
• Choices: A) 25 B) 60 C) 120 D) 240
• Hint: For 4 students in a row: 4 × 3 × 2 × 1 = 24 ways. This is called a factorial.
• Steps:
  • 5 students lining up = 5!
  • 5! = 5 × 4 × 3 × 2 × 1 = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: How many ways can you choose 2 toppings from a list of 5 toppings for a Tim Hortons muffin?
• FR: De combien de façons peut-on choisir 2 garnitures parmi 5 garnitures pour un muffin Tim Hortons?
• Choices: A) 5 B) 10 C) 20 D) 25
• Hint: C(n, r) = n! ÷ (r! × (n − r)!). For C(4, 2): 4! ÷ (2! × 2!) = 24 ÷ 4 = 6.
• Steps:
  • C(5, 2) = 5! ÷ (2! × 3!) = (5 × 4) ÷ (2 × 1).
  • = 20 ÷ 2 = 10.
  • There are 10 ways.
• Answer: 10

[Easy] Polynomial Function — Degree

• EN: What is the degree of the polynomial f(x) = 4x⁵ − 3x³ + 7x − 2?
• FR: Quel est le degré du polynôme f(x) = 4x⁵ − 3x³ + 7x − 2?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: The degree of a polynomial is the highest exponent. For 6x⁴ − 2x² + 1, the degree is 4.
• Steps:
  • Identify the highest power of x.
  • The term 4x⁵ has the highest power: 5.
  • The degree is 5.
• Answer: 5

[Easy] Introduction to Derivatives — Power Rule

• EN: If f(x) = x³, what is f'(x)?
• FR: Si f(x) = x³, combien vaut f'(x)?
• Choices: A) x² B) 3x C) 3x² D) x⁴
• Hint: The power rule: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹. For f(x) = x⁴, f'(x) = 4x³.
• Steps:
  • Apply the power rule: bring down the exponent, reduce the power by 1.
  • f(x) = x³ → f'(x) = 3x².
  • The derivative is 3x².
• Answer: 3x²

[Medium] Binomial Probability

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

[Medium] Rational Function — Vertical Asymptote

• EN: What is the vertical asymptote of f(x) = (2x + 1) ÷ (x − 4)?
• FR: Quelle est l'asymptote verticale de f(x) = (2x + 1) ÷ (x − 4)?
• Choices: A) x = −1/2 B) x = 2 C) x = 4 D) x = −4
• Hint: Vertical asymptotes occur where the denominator equals zero. For f(x) = 1/(x − 3), set x − 3 = 0, so x = 3.
• Steps:
  • Set the denominator equal to zero: x − 4 = 0.
  • x = 4.
  • The vertical asymptote is x = 4.
• Answer: x = 4

[Medium] Vector Addition

• EN: Vector u = (3, 5) and vector v = (−1, 4). What is u + v?
• FR: Le vecteur u = (3, 5) et le vecteur v = (−1, 4). Combien vaut u + v?
• Choices: A) (2, 1) B) (2, 9) C) (4, 9) D) (4, 1)
• Hint: To add vectors, add the corresponding components: (a, b) + (c, d) = (a + c, b + d). For (2, 3) + (4, 1) = (6, 4).
• Steps:
  • Add the x-components: 3 + (−1) = 2.
  • Add the y-components: 5 + 4 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Medium] Derivative — Rate of Change

• EN: The position of a hockey puck is given by s(t) = 3t² + 2t. What is the velocity (derivative) at t = 4 seconds?
• FR: La position d'une rondelle est donnée par s(t) = 3t² + 2t. Quelle est la vitesse (dérivée) à t = 4 secondes?
• Choices: A) 14 m/s B) 24 m/s C) 26 m/s D) 56 m/s
• Hint: Find the derivative using the power rule, then substitute the given t value. For s(t) = 2t² + t, s'(t) = 4t + 1, and at t = 3: s'(3) = 13.
• Steps:
  • s'(t) = 6t + 2 (using the power rule).
  • At t = 4: s'(4) = 6(4) + 2 = 24 + 2.
  • Velocity = 26 m/s.
• Answer: 26 m/s

[Hard] Normal Distribution — Probability

• EN: In a normally distributed dataset, scores have a mean of 70 and a standard deviation of 10. Approximately what percent of students scored between 60 and 80?
• FR: Dans une distribution normale, la moyenne est de 70 et l'écart-type est de 10. Environ quel pourcentage d'élèves a obtenu entre 60 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 (from μ − σ to μ + σ).
• Steps:
  • 60 = 70 − 10 (one standard deviation below the mean).
  • 80 = 70 + 10 (one standard deviation above the mean).
  • By the 68-95-99.7 rule, approximately 68% of data falls within one standard deviation.
• Answer: 68%

[Hard] Permutations with Restrictions

• EN: In how many ways can the letters in the word MAPLE be arranged if the letter M must always be first?
• FR: De combien de façons peut-on arranger les lettres du mot MAPLE si la lettre M doit toujours être en première position?
• Choices: A) 6 B) 12 C) 24 D) 120
• Hint: If one position is fixed, count arrangements for the remaining positions only. For 4 letters with the first fixed: 3! = 6 ways for the remaining 3.
• Steps:
  • Fix M in the first position. There are 4 remaining letters (A, P, L, E).
  • Arrange 4 letters in 4 positions: 4! = 4 × 3 × 2 × 1 = 24.
  • There are 24 ways.
• Answer: 24