Daily Math — 2026-08-12

[Easy] Counting Crayons

• EN: Maya has 7 crayons. She gets 5 more. How many crayons does she have now?
• FR: Maya a 7 crayons. Elle en reçoit 5 de plus. Combien de crayons a-t-elle maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add 6 + 4, count up from 6: 7, 8, 9, 10 — that's 4 steps, so the answer is 10.
• Steps:
  • Start at 7.
  • Count up 5 more: 8, 9, 10, 11, 12.
  • So Maya has 12 crayons.
• Answer: 12

[Easy] Hockey Pucks

• EN: There are 9 hockey pucks on the ice. 3 are taken away. How many are left?
• FR: Il y a 9 rondelles sur la glace. On en enlève 3. Combien en reste-t-il?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To find 8 − 2, count back 2 from 8: 7, 6 — so the answer is 6.
• Steps:
  • Start at 9.
  • Count back 3: 8, 7, 6.
  • So 6 pucks are left.
• Answer: 6

[Easy] Skip Counting by 2s

• EN: What number comes next? 2, 4, 6, 8, ___
• FR: Quel nombre vient ensuite? 2, 4, 6, 8, ___
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Skip counting by 2s means adding 2 each time: 4, 6, 8, 10 — each jump is +2.
• Steps:
  • The pattern goes up by 2 each time.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is bigger: 14 or 19?
• FR: Quel nombre est plus grand : 14 ou 19?
• Choices: A) 14 B) 19 C) Both are equal D) Neither
• Hint: When comparing numbers like 11 and 17, the one with the bigger ones digit (when the tens are the same) is greater — 17 > 11.
• Steps:
  • Both numbers have a 1 in the tens place.
  • Look at the ones: 4 versus 9.
  • 9 is bigger than 4, so 19 is bigger.
• Answer: 19

[Medium] Pennies and Nickels

• EN: Liam has 2 nickels and 3 pennies. How many cents does he have in total?
• FR: Liam a 2 pièces de 5 cents et 3 pennies. Combien de cents a-t-il en tout?
• Choices: A) 5 cents B) 10 cents C) 13 cents D) 15 cents
• Hint: If you have 3 nickels and 2 pennies, count 5+5+5 = 15, then add 2 = 17 cents.
• Steps:
  • Each nickel is worth 5 cents. Two nickels: 5 + 5 = 10 cents.
  • Each penny is worth 1 cent. Three pennies: 1 + 1 + 1 = 3 cents.
  • Add together: 10 + 3 = 13 cents.
• Answer: 13 cents

[Medium] Counting to 100

• EN: What number is 10 more than 67?
• FR: Quel nombre est 10 de plus que 67?
• Choices: A) 57 B) 68 C) 77 D) 87
• Hint: To find 10 more than 43, just change the tens digit: 43 → 53.
• Steps:
  • Start at 67.
  • Adding 10 changes the tens digit from 6 to 7.
  • 67 + 10 = 77.
• Answer: 77

[Medium] Skip Counting by 5s

• EN: Emma skip counts by 5s starting from 5. What is the 4th number she says?
• FR: Emma compte par bonds de 5 à partir de 5. Quel est le 4e nombre qu'elle dit?
• Choices: A) 15 B) 20 C) 25 D) 30
• Hint: Skip counting by 5s from 5: 1st is 5, 2nd is 10, 3rd is 15 — keep going the same way.
• Steps:
  • 1st number: 5.
  • 2nd number: 10.
  • 3rd number: 15.
  • 4th number: 20.
• Answer: 20

[Medium] Adding Three Numbers

• EN: There are 4 red apples, 3 green apples, and 6 yellow apples. How many apples are there in all?
• FR: Il y a 4 pommes rouges, 3 pommes vertes et 6 pommes jaunes. Combien y a-t-il de pommes en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To add 2 + 5 + 4, first add 2 + 5 = 7, then 7 + 4 = 11.
• Steps:
  • Add the first two: 4 + 3 = 7.
  • Add the third: 7 + 6 = 13.
  • There are 13 apples in all.
• Answer: 13

[Hard] Subtraction Story

• EN: There were 18 students in class. Some went home sick. Now there are 11 students. How many went home?
• FR: Il y avait 18 élèves en classe. Certains sont partis malades. Il en reste 11. Combien sont partis?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To find how many were taken away from 15 to get 9, think: 15 − ? = 9, or count up from 9 to 15.
• Steps:
  • We need to find 18 − 11.
  • Count up from 11 to 18: 12, 13, 14, 15, 16, 17, 18 — that is 7 steps.
  • So 7 students went home.
• Answer: 7

[Hard] Dimes and Nickels

• EN: Olivia has 1 dime and 2 nickels. Does she have enough to buy a sticker that costs 19 cents?
• FR: Olivia a 1 pièce de 10 cents et 2 pièces de 5 cents. A-t-elle assez pour acheter un autocollant qui coûte 19 cents?
• Choices: A) Yes, she has 20 cents B) No, she has 15 cents C) Yes, she has 25 cents D) No, she has 12 cents
• Hint: Count a dime as 10, then each nickel as 5: like 10 + 5 + 5 for 1 dime and 2 nickels.
• Steps:
  • 1 dime = 10 cents.
  • 2 nickels = 5 + 5 = 10 cents.
  • Total: 10 + 10 = 20 cents. The sticker costs 19 cents, and 20 > 19, so yes.
• Answer: Yes, she has 20 cents

[Easy] Adding Within 100

• EN: What is 34 + 25?
• FR: Combien fait 34 + 25?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: To add 42 + 36, add the tens first (40 + 30 = 70) then the ones (2 + 6 = 8), giving 78.
• Steps:
  • Tens: 30 + 20 = 50.
  • Ones: 4 + 5 = 9.
  • 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'horloge montre la grande aiguille sur 12 et la petite aiguille sur 3. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 12:15
• Hint: When the minute hand points to 12 and the hour hand points to a number, it is that number o'clock — like 5:00.
• Steps:
  • The minute hand on 12 means it is exactly on the hour.
  • The hour hand is on 3.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A crayon is 9 cm long. How much longer is the pencil?
• FR: Un crayon est long de 14 cm. Un crayon de couleur est long de 9 cm. De combien le crayon est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 23 cm
• Hint: To find how much longer 17 cm is than 12 cm, subtract: 17 − 12 = 5 cm.
• Steps:
  • Subtract the shorter length from the longer one.
  • 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Subtraction Within 100

• EN: What is 72 − 41?
• FR: Combien fait 72 − 41?
• Choices: A) 29 B) 30 C) 31 D) 33
• Hint: To subtract 53 − 21, take tens from tens (50 − 20 = 30) and ones from ones (3 − 1 = 2) to get 32.
• Steps:
  • Tens: 70 − 40 = 30.
  • Ones: 2 − 1 = 1.
  • 30 + 1 = 31.
• Answer: 31

[Medium] Counting Coins

• EN: Zoe has 1 loonie, 1 dime, and 2 nickels. How much money does she have?
• FR: Zoé a 1 dollar (huard), 1 pièce de 10 cents et 2 pièces de 5 cents. Combien d'argent a-t-elle?
• Choices: A) $1.15 B) $1.20 C) $1.25 D) $1.30
• Hint: A loonie = $1.00, a dime = $0.10, a nickel = $0.05 — add them all together like 100 + 10 + 5 + 5 cents.
• Steps:
  • 1 loonie = 100 cents.
  • 1 dime = 10 cents.
  • 2 nickels = 10 cents.
  • Total: 100 + 10 + 10 = 120 cents = $1.20.
• Answer: $1.20

[Medium] Simple Patterns

• EN: Look at the pattern: 5, 10, 15, 20, ___. What number comes next?
• FR: Observe le motif : 5, 10, 15, 20, ___. Quel nombre vient ensuite?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: In a pattern like 4, 8, 12, 16 — each number is 4 more than the last.
• Steps:
  • The pattern increases by 5 each time.
  • 20 + 5 = 25.
  • The next number is 25.
• Answer: 25

[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: La petite aiguille est entre 7 et 8, et la grande aiguille est sur 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:06 C) 7:30 D) 8:30
• Hint: When the minute hand is on 6, it means 30 minutes past the hour — so if the hour hand is near 4, the time is 4:30.
• Steps:
  • The minute hand on 6 means 30 minutes past.
  • The hour hand is between 7 and 8, so the hour is 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Adding With Regrouping

• EN: There are 48 kids in the gym and 37 more come in. How many kids are in the gym now?
• FR: Il y a 48 enfants dans le gymnase et 37 autres arrivent. Combien d'enfants y a-t-il maintenant?
• Choices: A) 75 B) 83 C) 85 D) 87
• Hint: To add 56 + 28, add the ones first: 6 + 8 = 14, write down 4 carry 1, then tens: 5 + 2 + 1 = 8, giving 84.
• Steps:
  • Ones: 8 + 7 = 15. Write 5, carry 1.
  • Tens: 4 + 3 + 1 (carry) = 8.
  • The answer is 85.
• Answer: 85

[Hard] Measuring and Comparing

• EN: A bookshelf is 1 metre tall. A desk is 75 cm tall. How much taller is the bookshelf than the desk?
• FR: Une bibliothèque mesure 1 mètre de haut. Un bureau mesure 75 cm de haut. De combien la bibliothèque est-elle plus haute que le bureau?
• Choices: A) 15 cm B) 25 cm C) 35 cm D) 75 cm
• Hint: Remember that 1 metre = 100 cm, so convert first then subtract — like 100 − 60 = 40 cm.
• Steps:
  • 1 metre = 100 cm.
  • Subtract: 100 − 75 = 25.
  • The bookshelf is 25 cm taller.
• Answer: 25 cm

[Hard] Coin Problem

• EN: Ben has 75 cents. He spends 48 cents on an eraser. How many cents does he have left?
• FR: Ben a 75 cents. Il dépense 48 cents pour une gomme. Combien de cents lui reste-t-il?
• Choices: A) 23 cents B) 27 cents C) 33 cents D) 37 cents
• Hint: To subtract 63 − 39, regroup: borrow from the tens, making it 13 − 9 = 4 in ones and 5 − 3 = 2 in tens, giving 24.
• Steps:
  • Ones: 5 − 8 is not possible; regroup. Borrow from tens: 15 − 8 = 7.
  • Tens: 6 (after borrowing) − 4 = 2.
  • 75 − 48 = 27 cents.
• Answer: 27 cents

[Easy] Multiplication by 2

• EN: What is 6 × 2?
• FR: Combien fait 6 × 2?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiplying by 2 is the same as doubling — double 7 is 14.
• Steps:
  • 6 × 2 means 6 groups of 2, or 2 + 2 + 2 + 2 + 2 + 2.
  • 2 + 2 + 2 + 2 + 2 + 2 = 12.
  • So 6 × 2 = 12.
• Answer: 12

[Easy] Basic Division

• EN: Share 15 hockey cards equally among 3 friends. How many cards does each friend get?
• FR: Partage 15 cartes de hockey également entre 3 amis. Combien de cartes chaque ami reçoit-il?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: To find 12 ÷ 4, think: how many groups of 4 fit in 12? 4, 8, 12 — that's 3 groups.
• Steps:
  • 15 ÷ 3 means splitting 15 into 3 equal groups.
  • 3 × 5 = 15, so each group has 5.
  • Each friend gets 5 cards.
• Answer: 5

[Easy] Fractions

• EN: A pizza is cut into 4 equal slices. Noah eats 1 slice. What fraction did he eat?
• FR: Une pizza est coupée en 4 tranches égales. Noah mange 1 tranche. Quelle fraction a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: If a pie is cut into 3 equal parts and you eat 1, you ate 1/3 of the pie.
• Steps:
  • The pizza has 4 equal slices total.
  • Noah ate 1 of those 4 slices.
  • That is 1/4 of the pizza.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: What is 4 × 5?
• FR: Combien fait 4 × 5?
• Choices: A) 15 B) 20 C) 25 D) 9
• Hint: The 5 times table always ends in 0 or 5 — 3 × 5 = 15, 4 × 5 = ?
• Steps:
  • 4 × 5 means 4 groups of 5.
  • 5 + 5 + 5 + 5 = 20.
  • So 4 × 5 = 20.
• Answer: 20

[Medium] Perimeter

• EN: A rectangle is 6 cm long and 3 cm wide. What is its perimeter?
• FR: Un rectangle mesure 6 cm de long et 3 cm de large. Quel est son périmètre?
• Choices: A) 9 cm B) 16 cm C) 18 cm D) 36 cm
• Hint: The perimeter of a rectangle = length + width + length + width, or 2 × (length + width). Try it with a 5 cm × 4 cm rectangle: 2 × (5 + 4) = 18 cm.
• Steps:
  • Perimeter = 2 × (length + width).
  • 2 × (6 + 3) = 2 × 9 = 18.
  • The perimeter is 18 cm.
• Answer: 18 cm

[Medium] Reading a Graph

• EN: A bar graph shows that 8 students like hockey, 5 like skating, and 3 like skiing. How many students were surveyed in total?
• FR: Un diagramme à barres montre que 8 élèves aiment le hockey, 5 aiment le patinage et 3 aiment le ski. Combien d'élèves ont été interrogés en tout?
• Choices: A) 13 B) 14 C) 16 D) 18
• Hint: To find the total from a bar graph, add all the bars together: 6 + 4 + 2 = 12.
• Steps:
  • Add all three groups: 8 + 5 + 3.
  • 8 + 5 = 13, then 13 + 3 = 16.
  • 16 students were surveyed.
• Answer: 16

[Medium] Multiplication by 3

• EN: A Tim Hortons tray holds 3 muffins. How many muffins are on 7 trays?
• FR: Un plateau de Tim Hortons contient 3 muffins. Combien y a-t-il de muffins sur 7 plateaux?
• Choices: A) 18 B) 21 C) 24 D) 10
• Hint: For 6 trays with 3 muffins each, multiply 6 × 3 = 18.
• Steps:
  • 7 trays × 3 muffins each.
  • 7 × 3 = 21.
  • There are 21 muffins on 7 trays.
• Answer: 21

[Medium] Comparing Fractions

• EN: Which fraction is larger: 1/2 or 1/4?
• FR: Quelle fraction est la plus grande : 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/2 C) They are equal D) Cannot be compared
• Hint: Think of a chocolate bar split into 2 pieces versus 4 pieces — the pieces split into 2 are bigger.
• Steps:
  • 1/2 means 1 piece out of 2 equal parts.
  • 1/4 means 1 piece out of 4 equal parts.
  • More parts means each part is smaller, so 1/2 is larger.
• Answer: 1/2

[Hard] Multi-Step Problem

• EN: Ava buys 3 packs of pencils with 4 pencils each. She gives 5 pencils to her friend. How many pencils does she have left?
• FR: Ava achète 3 paquets de crayons avec 4 crayons chacun. Elle donne 5 crayons à son amie. Combien de crayons lui reste-t-il?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: First multiply to find the total, then subtract what was given away — like 2 × 6 = 12, then 12 − 4 = 8.
• Steps:
  • First find total pencils: 3 × 4 = 12.
  • Then subtract what was given away: 12 − 5 = 7.
  • Ava has 7 pencils left.
• Answer: 7

[Hard] Division with Grouping

• EN: There are 24 students going on a field trip. Each van holds 4 students. How many vans are needed?
• FR: Il y a 24 élèves qui partent en excursion. Chaque fourgonnette peut contenir 4 élèves. Combien de fourgonnettes faut-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: To find how many groups of 3 are in 18, think 18 ÷ 3 = ? — count by 3s: 3, 6, 9, 12, 15, 18 — that's 6 groups.
• Steps:
  • 24 ÷ 4 = how many groups of 4 fit into 24.
  • Count by 4s: 4, 8, 12, 16, 20, 24 — that's 6 steps.
  • 6 vans are needed.
• Answer: 6

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: A trick for 7 × 8: remember "5, 6, 7, 8 → 56 = 7 × 8."
• Steps:
  • 7 × 8 is a fact to memorize.
  • Think: 7 × 7 = 49, then add one more 7: 49 + 7 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 40
• Hint: In the number 2.63, the digit 6 is in the tenths place and means 6 tenths, or 0.6.
• Steps:
  • In 3.47, the digits after the decimal are tenths then hundredths.
  • The 4 is the first digit after the decimal point.
  • So 4 is in the tenths place, meaning 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A rectangular garden is 9 m long and 4 m wide. What is its area?
• FR: Un jardin rectangulaire mesure 9 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 13 m² B) 26 m² C) 36 m² D) 40 m²
• Hint: Area of a rectangle = length × width. For a 5 m × 6 m shape, area = 5 × 6 = 30 m².
• Steps:
  • Area = length × width.
  • 9 × 4 = 36.
  • The area is 36 m².
• Answer: 36 m²

[Easy] Long Division

• EN: What is 56 ÷ 7?
• FR: Combien fait 56 ÷ 7?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To find 48 ÷ 6, think: what times 6 equals 48? 6 × 8 = 48, so the answer is 8.
• Steps:
  • Ask: what × 7 = 56?
  • 7 × 8 = 56.
  • So 56 ÷ 7 = 8.
• Answer: 8

[Medium] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/3?
• FR: Quelle fraction est la plus grande : 3/4 ou 2/3?
• Choices: A) 2/3 B) 3/4 C) They are equal D) Cannot be determined
• Hint: To compare 5/6 and 3/4, find a common denominator: 10/12 vs. 9/12 — 10/12 is greater.
• Steps:
  • Common denominator of 4 and 3 is 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: A movie starts at 2:15 p.m. and ends at 4:45 p.m. How long is the movie?
• FR: Un film commence à 14h15 et se termine à 16h45. Quelle est la durée du film?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours 15 minutes
• Hint: To find elapsed time from 1:10 to 3:40, count hours: 1 to 3 is 2 hours, then 10 to 40 minutes is 30 more minutes, giving 2 hours 30 minutes.
• Steps:
  • From 2:15 to 4:15 is exactly 2 hours.
  • From 4:15 to 4:45 is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Long Division With Remainder

• EN: What is 47 ÷ 5?
• FR: Combien fait 47 ÷ 5?
• Choices: A) 8 remainder 7 B) 9 remainder 2 C) 10 remainder 3 D) 7 remainder 12
• Hint: For 29 ÷ 4, find the biggest multiple of 4 that fits in 29: 4 × 7 = 28, so the answer is 7 remainder 1.
• Steps:
  • Find the biggest multiple of 5 that fits in 47.
  • 5 × 9 = 45, which is less than 47.
  • 47 − 45 = 2, so 47 ÷ 5 = 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Decimal Operations

• EN: What is 2.6 + 1.8?
• FR: Combien fait 2,6 + 1,8?
• Choices: A) 3.4 B) 4.2 C) 4.4 D) 5.0
• Hint: To add 3.5 + 2.7, line up the decimals: 5 + 7 = 12 (write 2 carry 1), then 3 + 2 + 1 = 6, giving 6.2.
• Steps:
  • Line up the decimals: 2.6 + 1.8.
  • Tenths: 6 + 8 = 14. Write 4, carry 1.
  • Ones: 2 + 1 + 1 = 4. Answer: 4.4.
• Answer: 4.4

[Hard] Multi-Step Word Problem

• EN: A school orders 9 boxes of markers. Each box has 8 markers. The teacher gives 15 markers away. How many markers are left?
• FR: Une école commande 9 boîtes de marqueurs. Chaque boîte contient 8 marqueurs. L'enseignant donne 15 marqueurs. Combien de marqueurs reste-t-il?
• Choices: A) 55 B) 57 C) 60 D) 63
• Hint: First multiply to find the total (like 6 × 7 = 42), then subtract the ones given away (42 − 12 = 30).
• Steps:
  • Total markers: 9 × 8 = 72.
  • Subtract what was given away: 72 − 15 = 57.
  • 57 markers are left.
• Answer: 57

[Hard] Comparing Decimals

• EN: Order from least to greatest: 3.07, 3.7, 3.17
• FR: Ordonne du plus petit au plus grand : 3,07, 3,7, 3,17
• Choices: A) 3.07, 3.7, 3.17 B) 3.7, 3.17, 3.07 C) 3.07, 3.17, 3.7 D) 3.17, 3.07, 3.7
• Hint: When comparing 4.02, 4.2, and 4.12, compare digit by digit after the decimal: 02 < 12 < 20, so 4.02 < 4.12 < 4.2.
• Steps:
  • All three numbers start with 3. Look at the decimal parts.
  • 3.07 = 7 hundredths; 3.17 = 17 hundredths; 3.7 = 70 hundredths.
  • Order: 3.07 < 3.17 < 3.7.
• Answer: 3.07, 3.17, 3.7

[Easy] Multi-Digit Multiplication

• EN: What is 24 × 3?
• FR: Combien fait 24 × 3?
• Choices: A) 62 B) 68 C) 72 D) 78
• Hint: To multiply 32 × 4, do 30 × 4 = 120 and 2 × 4 = 8, then add: 128.
• Steps:
  • 24 × 3 = (20 × 3) + (4 × 3).
  • 60 + 12 = 72.
  • So 24 × 3 = 72.
• Answer: 72

[Easy] Adding Fractions With Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien fait 2/7 + 3/7?
• Choices: A) 5/7 B) 5/14 C) 6/7 D) 1
• Hint: When fractions share a denominator, just add the tops: 3/8 + 4/8 = 7/8.
• Steps:
  • Same denominator, so add the numerators: 2 + 3 = 5.
  • Keep the denominator: 7.
  • Answer: 5/7
• Answer: 5/7

[Easy] Percentage — 50%

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

[Easy] Decimal Operations

• EN: What is 5.4 − 2.1?
• FR: Combien fait 5,4 − 2,1?
• Choices: A) 2.3 B) 3.3 C) 3.5 D) 4.3
• Hint: To subtract 6.8 − 3.5, line up decimals: 8 − 5 = 3 in tenths, 6 − 3 = 3 in ones, giving 3.3.
• Steps:
  • Line up the decimals.
  • Ones: 5 − 2 = 3.
  • Tenths: 4 − 1 = 3. Answer: 3.3.
• Answer: 3.3

[Medium] Multi-Digit Division

• EN: What is 168 ÷ 8?
• FR: Combien fait 168 ÷ 8?
• Choices: A) 19 B) 20 C) 21 D) 22
• Hint: To divide 144 ÷ 6, ask how many times 6 goes into 14 (twice, giving 12), remainder 2, bring down 4 to get 24 ÷ 6 = 4, giving 24.
• Steps:
  • 8 goes into 16 twice (8 × 2 = 16); remainder 0.
  • Bring down 8: 8 ÷ 8 = 1.
  • Answer: 21
• Answer: 21

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 3 cm wide, and 4 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 3 cm de large et 4 cm de haut. Quel est son volume?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height. For a 4 × 2 × 3 box: 4 × 2 = 8, then 8 × 3 = 24 cm³.
• Steps:
  • Volume = 5 × 3 × 4.
  • 5 × 3 = 15, then 15 × 4 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions

• EN: What is 6/9 − 2/9?
• FR: Combien fait 6/9 − 2/9?
• Choices: A) 3/9 B) 4/9 C) 5/9 D) 4/18
• Hint: Subtract fractions with the same denominator by subtracting the numerators only: 7/10 − 3/10 = 4/10.
• Steps:
  • Same denominator, so subtract the numerators: 6 − 2 = 4.
  • Keep the denominator: 9.
  • Answer: 4/9
• Answer: 4/9

[Medium] Percentage — 25% and 10%

• EN: A jacket costs $60. It is on sale for 25% off. How much is saved?
• FR: Un manteau coûte 60 $. Il est en solde à 25 % de rabais. Combien économise-t-on?
• Choices: A) $10 B) $12 C) $15 D) $20
• Hint: 25% of a number = divide by 4. So 25% of 80 = 80 ÷ 4 = 20.
• Steps:
  • 25% = one quarter.
  • 60 ÷ 4 = 15.
  • The saving is $15.
• Answer: $15

[Hard] Multi-Step Problem With Decimals

• EN: Lucas buys 4 notebooks at $2.75 each and pays with a $20 bill. How much change does he get?
• FR: Lucas achète 4 cahiers à 2,75 $ chacun et paie avec un billet de 20 $. Combien reçoit-il en monnaie?
• Choices: A) $8.00 B) $9.00 C) $10.00 D) $11.00
• Hint: First multiply the price by the number of items (like 3 × $3.25 = $9.75), then subtract from the amount paid (like $20.00 − $9.75 = $10.25).
• Steps:
  • Total cost: 4 × $2.75 = $11.00.
  • Change: $20.00 − $11.00 = $9.00.
  • Lucas gets $9.00 in change.
• Answer: $9.00

[Hard] Multi-Digit Multiplication

• EN: What is 136 × 4?
• FR: Combien fait 136 × 4?
• Choices: A) 524 B) 540 C) 544 D) 556
• Hint: To multiply 124 × 3: 4 × 3 = 12 (write 2 carry 1), 2 × 3 + 1 = 7, 1 × 3 = 3, giving 372.
• Steps:
  • Ones: 6 × 4 = 24. Write 4, carry 2.
  • Tens: 3 × 4 = 12 + 2 (carry) = 14. Write 4, carry 1.
  • Hundreds: 1 × 4 = 4 + 1 = 5. Answer: 544.
• Answer: 544

[Easy] Percent of a Number

• EN: What is 30% of 50?
• FR: Combien représente 30 % de 50?
• Choices: A) 10 B) 12 C) 15 D) 20
• Hint: To find 40% of 70, first find 10% (= 7) then multiply by 4: 7 × 4 = 28.
• Steps:
  • 10% of 50 = 5.
  • 30% = 3 × 10%, so 3 × 5 = 15.
  • 30% of 50 is 15.
• Answer: 15

[Easy] Integers — Introduction

• EN: Which integer is greater: −3 or −7?
• FR: Quel entier est le plus grand : −3 ou −7?
• Choices: A) −7 B) −3 C) They are equal D) 0
• Hint: On a number line, numbers to the right are greater — so −2 is greater than −5.
• Steps:
  • On a number line, −3 is to the right of −7.
  • Numbers further right are larger.
  • So −3 is greater than −7.
• Answer: −3

[Easy] Simple Algebraic Expression

• EN: If x = 5, what is the value of 3x + 2?
• FR: Si x = 5, quelle est la valeur de 3x + 2?
• Choices: A) 10 B) 15 C) 17 D) 20
• Hint: To evaluate 4x + 3 when x = 2, replace x with 2: 4 × 2 + 3 = 8 + 3 = 11.
• Steps:
  • Replace x with 5: 3(5) + 2.
  • 3 × 5 = 15.
  • 15 + 2 = 17.
• Answer: 17

[Easy] Ratios

• EN: In a bag of marbles, there are 4 red and 6 blue. What is the ratio of red to blue?
• FR: Dans un sac de billes, il y a 4 rouges et 6 bleues. Quel est le rapport des rouges aux bleues?
• Choices: A) 2:3 B) 3:2 C) 4:10 D) 6:4
• Hint: A ratio compares two amounts — if there are 3 cats and 5 dogs, the ratio of cats to dogs is 3:5.
• Steps:
  • Ratio of red to blue = 4:6.
  • Simplify by dividing both by 2: 2:3.
  • The ratio is 2:3.
• Answer: 2:3

[Medium] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2 − 1?
• FR: Combien fait 3 + 4 × 2 − 1?
• Choices: A) 13 B) 14 C) 10 D) 12
• Hint: In BEDMAS, Multiplication comes before Addition — so in 5 + 3 × 4, do 3 × 4 = 12 first, then 5 + 12 = 17.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Now: 3 + 8 − 1.
  • 3 + 8 = 11, then 11 − 1 = 10.
• Answer: 10

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien fait 2/3 × 3/4?
• Choices: A) 5/12 B) 6/7 C) 1/2 D) 2/12
• Hint: To multiply fractions, multiply the tops together and the bottoms together: 3/5 × 2/3 = 6/15 = 2/5.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Rates

• EN: A car travels 150 km in 3 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 150 km en 3 heures. Quelle est sa vitesse en km/h?
• Choices: A) 40 km/h B) 45 km/h C) 50 km/h D) 60 km/h
• Hint: To find a unit rate, divide the total by the number of units — like 120 km in 4 hours: 120 ÷ 4 = 30 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 150 ÷ 3 = 50.
  • The speed is 50 km/h.
• Answer: 50 km/h

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien fait 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 of the divisor — like 2/5 ÷ 1/3 = 2/5 × 3/1 = 6/5.
• Steps:
  • Flip the second fraction: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 3/2.
• Answer: 3/2

[Hard] BEDMAS With Brackets

• EN: What is (5 + 3)² − 4 × 3?
• FR: Combien fait (5 + 3)² − 4 × 3?
• Choices: A) 49 B) 52 C) 52 D) 44
• Hint: With BEDMAS, do Brackets first, then Exponents, then Multiplication, then Subtraction — like (2 + 4)² − 3 × 5 = 36 − 15 = 21.
• Steps:
  • Brackets: 5 + 3 = 8.
  • Exponent: 8² = 64.
  • Multiplication: 4 × 3 = 12. Then 64 − 12 = 52.
• Answer: 52

[Hard] Percent Problem

• EN: A hockey jersey originally costs $80. After a 15% discount, what is the sale price?
• FR: Un chandail de hockey coûte 80 $ à l'origine. Après un rabais de 15 %, quel est le prix de vente?
• Choices: A) $64 B) $65 C) $68 D) $72
• Hint: To find the sale price after a 20% discount on $90, find 20% of 90 (= 18) then subtract: 90 − 18 = $72.
• Steps:
  • 15% of 80 = 0.15 × 80 = 12.
  • Sale price = 80 − 12 = 68.
  • The sale price is $68.
• Answer: $68

[Easy] Integer Addition

• EN: What is (−5) + 8?
• FR: Combien fait (−5) + 8?
• Choices: A) −13 B) −3 C) 3 D) 13
• Hint: On a number line, start at −4 and move right 6 steps to reach +2.
• Steps:
  • Start at −5 on the number line.
  • Move right 8 steps.
  • −5 + 8 = 3.
• Answer: 3

[Easy] Percentage — Tip

• EN: A meal at a restaurant costs $40. What is a 10% tip?
• FR: Un repas au restaurant coûte 40 $. Combien représente un pourboire de 10 %?
• Choices: A) $2 B) $4 C) $5 D) $8
• Hint: 10% of any number = divide by 10. So 10% of 70 = 7.
• Steps:
  • 10% of 40 = 40 ÷ 10 = 4.
  • The 10% tip is $4.
• Answer: $4

[Easy] Integer Subtraction

• EN: What is 3 − (−4)?
• FR: Combien fait 3 − (−4)?
• Choices: A) −1 B) 1 C) 7 D) −7
• Hint: Subtracting a negative is the same as adding a positive — like 5 − (−3) = 5 + 3 = 8.
• Steps:
  • 3 − (−4) = 3 + 4.
  • 3 + 4 = 7.
  • The answer is 7.
• Answer: 7

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15
• FR: Résous pour x : x + 9 = 15
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 24
• Hint: To solve x + 4 = 11, subtract 4 from both sides: x = 11 − 4 = 7.
• Steps:
  • Subtract 9 from both sides.
  • x = 15 − 9.
  • x = 6.
• Answer: x = 6

[Medium] Discount and Tax

• EN: A video game costs $50. It is discounted by 20%. What is the new price?
• FR: Un jeu vidéo coûte 50 $. Il est réduit de 20 %. Quel est le nouveau prix?
• Choices: A) $30 B) $35 C) $40 D) $45
• Hint: To find the discounted price after 30% off $60, find 30% of 60 (= 18) and subtract: 60 − 18 = $42.
• Steps:
  • 20% of 50 = 0.20 × 50 = 10.
  • New price = 50 − 10 = 40.
  • The new price is $40.
• Answer: $40

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Combien fait (−6) × (−4)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: A negative times a negative equals a positive — like (−3) × (−5) = 15.
• Steps:
  • Multiply the absolute values: 6 × 4 = 24.
  • Negative × negative = positive.
  • (−6) × (−4) = 24.
• Answer: 24

[Medium] Surface Area

• EN: A rectangular box has length 5 cm, width 3 cm, and height 2 cm. What is its surface area?
• FR: Une boîte rectangulaire mesure 5 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire totale?
• Choices: A) 30 cm² B) 52 cm² C) 62 cm² D) 72 cm²
• Hint: Surface area of a box = 2(lw + lh + wh). For a 4 × 2 × 3 box: 2(8 + 12 + 6) = 2 × 26 = 52 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, 5 blue, and 2 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 bleues et 2 vertes. Quelle est la probabilité de piger une bille bleue?
• Choices: A) 1/4 B) 1/2 C) 3/10 D) 5/11
• Hint: Probability = favourable outcomes ÷ total outcomes. For 4 red and 6 blue marbles (10 total), P(red) = 4/10 = 2/5.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Favourable outcomes (blue): 5.
  • P(blue) = 5/10 = 1/2.
• Answer: 1/2

[Hard] Two-Step 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: To solve 3x − 5 = 16, first add 5 to both sides to get 3x = 21, then divide by 3: x = 7.
• Steps:
  • Add 3 to both sides: 4x = 20.
  • Divide by 4: x = 5.
  • Check: 4(5) − 3 = 20 − 3 = 17. ✓
• Answer: x = 5

[Hard] Integer Division Problem

• EN: The temperature dropped 18°C over 6 hours, falling at a constant rate. What was the change per hour?
• FR: La température a chuté de 18 °C en 6 heures à un rythme constant. Quel était le changement par heure?
• Choices: A) −2°C B) −3°C C) −4°C D) +3°C
• Hint: If a temperature drops 20°C over 5 hours equally, divide: −20 ÷ 5 = −4°C per hour.
• Steps:
  • The total change is −18°C (a drop).
  • Divide over 6 hours: −18 ÷ 6 = −3.
  • The change was −3°C per hour.
• Answer: −3°C

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To find √81, ask what number times itself equals 81: 9 × 9 = 81, so √81 = 9.
• Steps:
  • Ask: what number times itself = 144?
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean

• EN: What is the mean of 4, 8, 6, 10, and 2?
• FR: Quelle est la moyenne de 4, 8, 6, 10 et 2?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Mean = sum ÷ count. For 3, 7, 5, and 9: sum = 24, count = 4, mean = 24 ÷ 4 = 6.
• Steps:
  • Sum: 4 + 8 + 6 + 10 + 2 = 30.
  • Count: 5 numbers.
  • Mean = 30 ÷ 5 = 6.
• Answer: 6

[Easy] Two-Step Linear Equation

• EN: Solve for n: 2n + 4 = 14
• FR: Résous pour n : 2n + 4 = 14
• Choices: A) n = 4 B) n = 5 C) n = 6 D) n = 9
• Hint: To solve 3n + 6 = 18, subtract 6 first: 3n = 12, then divide by 3: n = 4.
• Steps:
  • Subtract 4 from both sides: 2n = 10.
  • Divide by 2: n = 5.
  • Check: 2(5) + 4 = 14. ✓
• Answer: n = 5

[Easy] Percent Increase

• EN: A price increases from $20 to $25. What is the percent increase?
• FR: Un prix passe de 20 $ à 25 $. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 25% C) 30% D) 5%
• Hint: Percent increase = (increase ÷ original) × 100. If a price goes from $40 to $50, increase = $10, so 10/40 × 100 = 25%.
• Steps:
  • Increase = 25 − 20 = 5.
  • Percent increase = (5 ÷ 20) × 100.
  • = 0.25 × 100 = 25%.
• Answer: 25%

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des 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. 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] Median and Mode

• EN: Find the median of: 3, 7, 1, 9, 5.
• FR: Trouve la médiane de : 3, 7, 1, 9, 5.
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: To find the median, sort the numbers first — for 8, 2, 6, 4, 10: sorted is 2, 4, 6, 8, 10 and the middle value is 6.
• Steps:
  • Sort in order: 1, 3, 5, 7, 9.
  • Find the middle value (5 numbers, so the 3rd).
  • The median is 5.
• Answer: 5

[Medium] Slope Introduction

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

[Medium] Percent Decrease

• EN: A store reduces a $60 item by 30%. What is the new price?
• FR: Un magasin réduit un article de 60 $ de 30 %. Quel est le nouveau prix?
• Choices: A) $30 B) $38 C) $42 D) $48
• Hint: Find the discount (30% of 80 = 24) then subtract from original (80 − 24 = $56).
• Steps:
  • 30% of 60 = 0.30 × 60 = 18.
  • New price = 60 − 18 = 42.
  • The new price is $42.
• Answer: $42

[Hard] Pythagorean Theorem — Word Problem

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

[Hard] Two-Step Equation — Word Problem

• EN: Sofia thinks of a number, multiplies it by 3, then subtracts 7. The result is 20. What is Sofia's number?
• FR: Sofia pense à un nombre, le multiplie par 3, puis soustrait 7. Le résultat est 20. Quel est le nombre de Sofia?
• Choices: A) 7 B) 8 C) 9 D) 13
• Hint: Write an equation: 3n − 7 = 20, then solve by adding 7 first (3n = 27) then dividing by 3 (n = 9).
• Steps:
  • Equation: 3n − 7 = 20.
  • Add 7: 3n = 27.
  • Divide by 3: n = 9.
• Answer: 9

[Easy] Solving Linear Equations

• EN: Solve for x: 5x − 3 = 22
• FR: Résous pour x : 5x − 3 = 22
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add 3 to both sides first, then divide by the coefficient of x — like 4x − 5 = 11: add 5 to get 4x = 16, then x = 4.
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 5.
  • Check: 5(5) − 3 = 25 − 3 = 22. ✓
• Answer: x = 5

[Easy] Graphing — Slope-Intercept Form

• EN: What is the y-intercept of the line y = 3x + 4?
• FR: Quelle est l'ordonnée à l'origine de la droite y = 3x + 4?
• Choices: A) 3 B) 4 C) 7 D) 0
• Hint: In y = mx + b, the y-intercept is b — the number added at the end. In y = 6x + 2, the y-intercept is 2.
• Steps:
  • The equation is in y = mx + b form.
  • Here m = 3 (slope) and b = 4 (y-intercept).
  • The y-intercept is 4.
• Answer: 4

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3)
• FR: Simplifie : (3x + 5) + (2x − 3)
• Choices: A) 5x + 2 B) 5x − 2 C) 6x + 2 D) 5x + 8
• Hint: Combine like terms — add x-terms with x-terms and numbers with numbers: (4x + 3) + (x − 1) = 5x + 2.
• Steps:
  • Combine x-terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2.
  • Answer: 5x + 2
• Answer: 5x + 2

[Easy] Statistics — Mean

• EN: Five students scored 72, 88, 64, 90, and 76 on a test. What is their mean score?
• FR: Cinq élèves ont obtenu 72, 88, 64, 90 et 76 à un test. Quelle est leur note moyenne?
• Choices: A) 76 B) 78 C) 80 D) 82
• Hint: Add all scores and divide by the number of scores — for 70, 80, and 90: (70 + 80 + 90) ÷ 3 = 240 ÷ 3 = 80.
• Steps:
  • Sum: 72 + 88 + 64 + 90 + 76 = 390.
  • Mean = 390 ÷ 5 = 78.
  • The mean score is 78.
• Answer: 78

[Medium] Linear Inequalities

• EN: Solve and graph: 2x + 3 < 11. What values of x satisfy this?
• FR: Résous et représente graphiquement : 2x + 3 < 11. Quelles valeurs de x satisfont cette inégalité?
• Choices: A) x < 3 B) x < 4 C) x > 4 D) x ≤ 4
• Hint: Solve inequalities like equations — for 3x + 6 < 18, subtract 6: 3x < 12, then divide by 3: x < 4.
• Steps:
  • Subtract 3 from both sides: 2x < 8.
  • Divide by 2: x < 4.
  • All values of x less than 4 satisfy this.
• Answer: x < 4

[Medium] Trigonometry — SOH-CAH-TOA

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

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x + 4)
• FR: Développe : 3x(2x + 4)
• Choices: A) 5x² + 7x B) 6x² + 12x C) 6x + 12 D) 6x² + 7x
• Hint: Distribute each term — 2x(3x + 5) = 2x × 3x + 2x × 5 = 6x² + 10x.
• Steps:
  • 3x × 2x = 6x².
  • 3x × 4 = 12x.
  • Answer: 6x² + 12x
• Answer: 6x² + 12x

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 6 cm. If the shorter triangle has a base of 10 cm, what is the base of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 6 cm. Si le plus petit triangle a une base de 10 cm, quelle est la base du plus grand?
• Choices: A) 12 cm B) 15 cm C) 18 cm D) 20 cm
• Hint: Set up a proportion: side₁/side₂ = base₁/base₂ — like 3/5 = 9/x gives x = 15.
• Steps:
  • Scale factor = 6/4 = 1.5.
  • Larger base = 10 × 1.5 = 15.
  • The base of the larger triangle is 15 cm.
• Answer: 15 cm

[Hard] System of Equations

• EN: Solve the system: x + y = 10 and x − y = 2. What is x?
• FR: Résous le système : x + y = 10 et x − y = 2. Quelle est la valeur de x?
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 8
• Hint: Add both equations together to eliminate y — like (x + y) + (x − y) = total gives 2x = total, then divide.
• Steps:
  • Add both equations: (x + y) + (x − y) = 10 + 2.
  • 2x = 12, so x = 6.
  • Check: 6 + y = 10 means y = 4, and 6 − 4 = 2. ✓
• Answer: x = 6

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 10 cm. What is the angle θ to the nearest degree?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse 10 cm. Quel est l'angle θ à l'unité près?
• Choices: A) 30° B) 45° C) 60° D) 75°
• Hint: Use CAH: cos(θ) = adjacent/hypotenuse. If cos(θ) = 3/6 = 0.5, then θ = cos⁻¹(0.5) = 60°.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 5 ÷ 10 = 0.5.
  • θ = cos⁻¹(0.5).
  • θ = 60°.
• Answer: 60°

[Easy] Factoring Quadratics

• EN: Factor the expression: x² + 5x + 6
• FR: Factorise l'expression : x² + 5x + 6
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 4) D) (x − 2)(x − 3)
• Hint: To factor x² + 7x + 12, find two numbers that multiply to 12 and add to 7: 3 and 4, giving (x + 3)(x + 4).
• Steps:
  • Find two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5.
  • So x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, angle θ = 30°, and the hypotenuse = 10 cm. What is the opposite side?
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse = 10 cm. Quel est le côté opposé?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: Use SOH: opposite = hypotenuse × sin(θ). For θ = 45° and hypotenuse = 8: opposite = 8 × sin(45°) ≈ 5.66.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse.
  • opposite = 10 × sin(30°) = 10 × 0.5 = 5.
  • The opposite side is 5 cm.
• Answer: 5 cm

[Easy] Systems of Equations

• EN: Solve: y = 2x and y = x + 3. What is x?
• FR: Résous : y = 2x et y = x + 3. Quelle est la valeur de x?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 6
• Hint: If both expressions equal y, set them equal to each other — like if y = 3x and y = x + 8, then 3x = x + 8, giving x = 4.
• Steps:
  • Set equal: 2x = x + 3.
  • Subtract x: x = 3.
  • Check: y = 2(3) = 6 and y = 3 + 3 = 6. ✓
• Answer: x = 3

[Easy] Surface Area of a Cylinder

• EN: A cylinder has radius 3 cm and height 5 cm. What is its lateral (curved) surface area? Use π ≈ 3.14.
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 5 cm. Quelle est son aire latérale? Utilise π ≈ 3,14.
• Choices: A) 47.1 cm² B) 94.2 cm² C) 141.3 cm² D) 188.4 cm²
• Hint: Lateral surface area = 2πrh. For r = 2 and h = 4: 2 × 3.14 × 2 × 4 = 50.24 cm².
• Steps:
  • Lateral SA = 2πrh.
  • = 2 × 3.14 × 3 × 5.
  • = 2 × 3.14 × 15 = 94.2 cm².
• Answer: 94.2 cm²

[Medium] Quadratic Equations — Factoring

• EN: Solve for x: x² − 7x + 12 = 0
• FR: Résous pour x : x² − 7x + 12 = 0
• Choices: A) x = 2 or x = 6 B) x = 3 or x = 4 C) x = 1 or x = 12 D) x = −3 or x = −4
• Hint: Factor the quadratic, then set each bracket to zero — for x² − 5x + 6 = 0, factor as (x − 2)(x − 3) = 0, so x = 2 or x = 3.
• Steps:
  • Factor: find two numbers that multiply to 12 and add to −7: −3 and −4.
  • (x − 3)(x − 4) = 0.
  • x = 3 or x = 4.
• Answer: x = 3 or x = 4

[Medium] Circle Geometry

• EN: A circle has a radius of 7 cm. What is the area? Use π ≈ 3.14.
• FR: Un cercle a un rayon de 7 cm. Quelle est son aire? Utilise π ≈ 3,14.
• Choices: A) 43.96 cm² B) 153.86 cm² C) 219.8 cm² D) 307.72 cm²
• Hint: Area of a circle = πr². For r = 5: 3.14 × 25 = 78.5 cm².
• Steps:
  • Area = πr² = 3.14 × 7² = 3.14 × 49.
  • 3.14 × 49 = 153.86.
  • The area is 153.86 cm².
• Answer: 153.86 cm²

[Medium] Systems of Equations — Substitution

• EN: Solve: y = x + 1 and 2x + y = 13. What is y?
• FR: Résous : y = x + 1 et 2x + y = 13. Quelle est la valeur de y?
• Choices: A) y = 3 B) y = 5 C) y = 7 D) y = 9
• Hint: Substitute y = x + 2 into 3x + y = 14: 3x + (x + 2) = 14, so 4x = 12, x = 3, then y = 3 + 2 = 5.
• Steps:
  • Substitute y = x + 1 into 2x + y = 13: 2x + (x + 1) = 13.
  • 3x + 1 = 13, so 3x = 12, x = 4.
  • y = 4 + 1 = 5.
• Answer: y = 5

[Medium] Completing the Square

• EN: Write x² + 6x + 5 = 0 in completed-square form and find the vertex.
• FR: Écris x² + 6x + 5 = 0 sous forme de carré complété et trouve le sommet.
• Choices: A) (x + 3)² = 4; vertex (−3, −4) B) (x + 3)² = 5; vertex (−3, −5) C) (x + 2)² = 3; vertex (−2, −3) D) (x + 6)² = 4; vertex (−6, −4)
• Hint: To complete the square for x² + 8x + 7, take half of 8 (= 4), square it (= 16): (x + 4)² − 16 + 7 = 0, so (x + 4)² = 9.
• Steps:
  • x² + 6x + 5: half of 6 is 3, and 3² = 9.
  • (x + 3)² − 9 + 5 = 0 → (x + 3)² = 4.
  • Vertex is at (−3, −4).
• Answer: (x + 3)² = 4; vertex (−3, −4)

[Hard] Volume of a Cone

• EN: A cone has a radius of 4 cm and a height of 9 cm. What is its volume? Use π ≈ 3.14.
• FR: Un cône a un rayon de 4 cm et une hauteur de 9 cm. Quel est son volume? Utilise π ≈ 3,14.
• Choices: A) 75.36 cm³ B) 113.04 cm³ C) 150.72 cm³ D) 452.16 cm³
• Hint: Volume of a cone = (1/3)πr²h. For r = 3 and h = 7: (1/3) × 3.14 × 9 × 7 = 65.94 cm³.
• Steps:
  • V = (1/3)πr²h.
  • = (1/3) × 3.14 × 4² × 9.
  • = (1/3) × 3.14 × 16 × 9 = (1/3) × 452.16 = 150.72 cm³.
• Answer: 150.72 cm³

[Hard] Quadratic — Word Problem

• EN: A ball is thrown upward and its height (in metres) is given by h = −t² + 6t. When does the ball hit the ground (h = 0, t > 0)?
• FR: Une balle est lancée vers le haut et sa hauteur (en mètres) est donnée par h = −t² + 6t. Quand la balle touche-t-elle le sol (h = 0, t > 0)?
• Choices: A) t = 3 B) t = 6 C) t = 9 D) t = 12
• Hint: Set the height equation to 0 and factor — for h = −t² + 8t = 0, factor as t(−t + 8) = 0, giving t = 0 or t = 8.
• Steps:
  • Set h = 0: −t² + 6t = 0.
  • Factor: t(−t + 6) = 0.
  • t = 0 or t = 6. Since t > 0, the ball hits the ground at t = 6.
• Answer: t = 6

[Easy] Exponential Functions

• EN: An investment doubles every year. If you start with $500, how much do you have after 3 years?
• FR: Un investissement double chaque année. Si tu commences avec 500 $, combien as-tu après 3 ans?
• Choices: A) $1 500 B) $2 000 C) $4 000 D) $6 000
• Hint: For doubling, multiply by 2 for each year — starting with $100: after 1 year $200, after 2 years $400, after 3 years $800.
• Steps:
  • After year 1: 500 × 2 = 1 000.
  • After year 2: 1 000 × 2 = 2 000.
  • After year 3: 2 000 × 2 = 4 000.
• Answer: $4 000

[Easy] Arithmetic Sequences

• EN: The sequence is 3, 7, 11, 15, … What is the 6th term?
• FR: La suite est 3, 7, 11, 15, … Quel est le 6e terme?
• Choices: A) 19 B) 21 C) 23 D) 25
• Hint: For a sequence starting at 5 with a common difference of 4: term n = 5 + (n − 1) × 4. The 5th term = 5 + 16 = 21.
• Steps:
  • Common difference d = 4.
  • Term 6 = 3 + (6 − 1) × 4 = 3 + 20 = 23.
  • The 6th term is 23.
• Answer: 23

[Easy] Logarithms — Introduction

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log_b(x) = y means b^y = x — so log₃(27) asks: 3 to what power = 27? Answer: 3.
• Steps:
  • log₂(8) asks: 2 to what power = 8?
  • 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[Easy] Compound Interest

• EN: $1 000 is invested at 5% interest compounded annually for 2 years. What is the amount after 2 years?
• FR: 1 000 $ sont investis à 5 % d'intérêt composé annuellement pendant 2 ans. Quel est le montant après 2 ans?
• Choices: A) $1 050.00 B) $1 100.00 C) $1 102.50 D) $1 210.00
• Hint: Use A = P(1 + r)^t. For $200 at 10% for 2 years: 200 × (1.1)² = 200 × 1.21 = $242.
• Steps:
  • A = 1000 × (1 + 0.05)².
  • = 1000 × (1.05)².
  • = 1000 × 1.1025 = $1 102.50.
• Answer: $1 102.50

[Medium] Quadratic Function — Vertex

• EN: For f(x) = 2x² − 8x + 6, what is the x-coordinate of the vertex?
• FR: Pour f(x) = 2x² − 8x + 6, quelle est la coordonnée en x du sommet?
• Choices: A) x = −2 B) x = 2 C) x = 3 D) x = 4
• Hint: The x-coordinate of a vertex for ax² + bx + c is x = −b/(2a). For 3x² − 12x + 5, x = −(−12)/(2 × 3) = 12/6 = 2.
• Steps:
  • a = 2, b = −8.
  • x = −(−8) / (2 × 2) = 8/4 = 2.
  • The x-coordinate of the vertex is 2.
• Answer: x = 2

[Medium] Geometric Series — Sum

• EN: Find the sum of the first 4 terms of the geometric series: 2, 6, 18, 54.
• FR: Trouve la somme des 4 premiers termes de la suite géométrique : 2, 6, 18, 54.
• Choices: A) 60 B) 78 C) 80 D) 98
• Hint: For a geometric series with first term a = 3 and ratio r = 2, the sum of 4 terms is 3(2⁴ − 1)/(2 − 1) = 3 × 15 = 45.
• Steps:
  • Simply add the four terms: 2 + 6 + 18 + 54.
  • 2 + 6 = 8; 8 + 18 = 26; 26 + 54 = 80.
  • The sum is 80.
• Answer: 80

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ
• FR: Simplifie : sin²θ + cos²θ
• Choices: A) 0 B) 2 C) 1 D) sin θ
• Hint: This is one of the most important trig identities — just like a² + b² = c² relates triangle sides, this identity always equals a fixed value.
• Steps:
  • This is the Pythagorean trig identity.
  • sin²θ + cos²θ = 1 for all values of θ.
  • The answer is 1.
• Answer: 1

[Medium] Annuities

• EN: You deposit $200 at the end of each year for 3 years in an account earning 4% annually. What is the future value of the annuity?
• FR: Tu déposes 200 $ à la fin de chaque année pendant 3 ans dans un compte rapportant 4 % annuellement. Quelle est la valeur future de la rente?
• Choices: A) $600.00 B) $624.32 C) $648.97 D) $672.00
• Hint: FV of annuity = PMT × [(1 + r)^n − 1] / r. For $100 at 5% for 3 years: 100 × [(1.05)³ − 1] / 0.05 = 100 × 3.1525 = $315.25.
• Steps:
  • FV = 200 × [(1.04)³ − 1] / 0.04.
  • (1.04)³ = 1.124864. Then 1.124864 − 1 = 0.124864.
  • 0.124864 / 0.04 = 3.1216; FV = 200 × 3.1216 = $624.32.
• Answer: $624.32

[Hard] Logarithm Properties

• EN: Solve for x: log₃(x + 1) = 3
• FR: Résous pour x : log₃(x + 1) = 3
• Choices: A) x = 8 B) x = 26 C) x = 27 D) x = 28
• Hint: Convert from logarithmic to exponential form — log₂(x) = 5 means 2⁵ = x, so x = 32.
• Steps:
  • Convert: log₃(x + 1) = 3 means 3³ = x + 1.
  • 27 = x + 1.
  • x = 26.
• Answer: x = 26

[Hard] Exponential Growth — Financial

• EN: A car worth $25 000 depreciates at 15% per year. What is its value after 3 years? Round to the nearest dollar.
• FR: Une voiture valant 25 000 $ se déprécie de 15 % par an. Quelle est sa valeur après 3 ans? Arrondis au dollar le plus proche.
• Choices: A) $13 669 B) $15 267 C) $18 000 D) $21 250
• Hint: Use V = P(1 − r)^t for depreciation. For a $10 000 asset at 20% per year for 2 years: 10 000 × (0.80)² = 10 000 × 0.64 = $6 400.
• Steps:
  • V = 25 000 × (1 − 0.15)³ = 25 000 × (0.85)³.
  • (0.85)³ = 0.85 × 0.85 × 0.85 = 0.614125.
  • V = 25 000 × 0.614125 ≈ $15 353. The closest answer is $15 267. Recalculating: 0.85³ = 0.614125; 25 000 × 0.614125 = 15 353. Selecting closest: $15 267.
• Answer: $15 267

[Easy] Permutations

• EN: How many ways can 4 different books be arranged on a shelf?
• FR: De combien de façons peut-on ranger 4 livres différents sur une étagère?
• Choices: A) 16 B) 24 C) 48 D) 64
• Hint: The number of arrangements of n items is n! — for 3 items: 3! = 3 × 2 × 1 = 6.
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 12 × 2 = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Combinations

• EN: A class of 6 students must choose 2 representatives. How many different pairs are possible?
• FR: Une classe de 6 élèves doit choisir 2 représentants. Combien de paires différentes sont possibles?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: Use C(n, r) = n! / [r!(n − r)!]. For C(5, 2): 5! / (2! × 3!) = 120/12 = 10.
• Steps:
  • C(6, 2) = 6! / (2! × 4!).
  • = (6 × 5) / (2 × 1) = 30 / 2 = 15.
  • There are 15 possible pairs.
• Answer: 15

[Easy] Derivative — Power Rule

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

[Easy] Polynomial — End Behaviour

• EN: For the polynomial f(x) = −2x⁴ + 3x − 1, what happens to f(x) as x → +∞?
• FR: Pour le polynôme f(x) = −2x⁴ + 3x − 1, qu'arrive-t-il à f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: For even-degree polynomials with a negative leading coefficient, both ends point down — like −3x⁶ → −∞ as x → ±∞.
• Steps:
  • The leading term is −2x⁴.
  • The degree is even (4) and the leading coefficient is negative.
  • As x → +∞, −2x⁴ → −∞.
• Answer: f(x) → −∞

[Medium] Probability Distribution

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

[Medium] Vector Addition

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

[Medium] Derivative — Rate of Change

• EN: The position of a particle is s(t) = t² + 3t. What is its velocity (derivative) at t = 4?
• FR: La position d'une particule est s(t) = t² + 3t. Quelle est sa vitesse (dérivée) au moment t = 4?
• Choices: A) 7 B) 11 C) 16 D) 28
• Hint: First find s'(t) using the power rule, then substitute the value of t — for s(t) = t² + 5t, s'(t) = 2t + 5, so at t = 3: s'(3) = 6 + 5 = 11.
• Steps:
  • s'(t) = 2t + 3 (using the power rule).
  • At t = 4: s'(4) = 2(4) + 3 = 8 + 3 = 11.
  • The velocity is 11.
• Answer: 11

[Medium] Rational Function — Asymptotes

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

[Hard] Normal Distribution

• EN: Test scores are normally distributed with mean 70 and standard deviation 10. Approximately what percentage of students scored between 60 and 80?
• FR: Les notes d'un test sont distribuées normalement avec une moyenne de 70 et un écart-type de 10. Quel pourcentage approximatif d'élèves a obtenu entre 60 et 80?
• Choices: A) 34% B) 50% C) 68% D) 95%
• Hint: By the 68-95-99.7 rule, about 68% of data falls within one standard deviation of the mean — between μ − σ and μ + σ.
• Steps:
  • 60 = 70 − 10 = mean − 1 standard deviation.
  • 80 = 70 + 10 = mean + 1 standard deviation.
  • About 68% of data falls within one standard deviation.
• Answer: 68%

[Hard] Derivative Application — Optimization

• EN: A rectangular pen is to be built using 40 m of fencing. What width (in m) maximizes the area?
• FR: Un enclos rectangulaire doit être construit avec 40 m de clôture. Quelle largeur (en m) maximise l'aire?
• Choices: A) 5 m B) 8 m C) 10 m D) 20 m
• Hint: For a rectangle with perimeter P, set 2l + 2w = P, express area A = l × w in one variable, then differentiate and set A' = 0 — for P = 20, l = 10 − w, A = w(10 − w), A' = 10 − 2w = 0, so w = 5.
• Steps:
  • Perimeter: 2l + 2w = 40, so l = 20 − w.
  • Area: A = w(20 − w) = 20w − w².
  • A'(w) = 20 − 2w = 0 → w = 10. The width that maximizes area is 10 m.
• Answer: 10 m