Daily Math — 2026-09-15

[Easy] Counting Mittens

• EN: Mia has 7 mittens on a shelf. Her friend gives her 3 more. How many mittens does Mia have now?
• FR: Mia a 7 mitaines sur une étagère. Son amie lui en donne 3 de plus. Combien de mitaines Mia a-t-elle maintenant?
• Choices: A) 8 B) 9 C) 10 D) 11
• Hint: To add 5 + 4, count on from the bigger number: 5… 6, 7, 8, 9 — that's 9.
• Steps:
  • Start at 7 and count on 3 more.
  • 7… 8, 9, 10 — that is 10 mittens.
• Answer: 10

[Easy] Hockey Pucks

• EN: There are 15 hockey pucks in a bag. A player takes out 5. How many are left in the bag?
• FR: Il y a 15 rondelles de hockey dans un sac. Un joueur en sort 5. Combien en reste-t-il dans le sac?
• Choices: A) 8 B) 10 C) 12 D) 20
• Hint: To subtract 12 − 4, count back from 12: 11, 10, 9, 8 — that's 8.
• Steps:
  • Start at 15 and count back 5.
  • 15… 14, 13, 12, 11, 10 — that is 10 pucks.
• Answer: 10

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes next? 2, 4, 6, 8, ___
• FR: Compte par 2. Quel nombre vient ensuite? 2, 4, 6, 8, ___
• Choices: A) 9 B) 10 C) 12 D) 11
• Hint: When counting by 2s, each number is 2 more than the one before it. After 6 comes 8.
• Steps:
  • Each step goes up by 2: 2, 4, 6, 8…
  • Add 2 more to 8: 8 + 2 = 10.
• Answer: 10

[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: Think about coin values: a penny = 1¢, a nickel = 5¢, a quarter = 25¢.
• 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: Ben made 12 snowballs in the morning and 6 snowballs in the afternoon. How many snowballs did he make in all?
• FR: Ben a fait 12 boules de neige le matin et 6 boules de neige l'après-midi. Combien de boules de neige a-t-il faites en tout?
• Choices: A) 16 B) 18 C) 17 D) 20
• Hint: To add 11 + 5, think 11 + 5 = 16. Use your fingers or count on.
• Steps:
  • Start at the bigger number: 12.
  • Count on 6 more: 13, 14, 15, 16, 17, 18.
  • The answer is 18 snowballs.
• Answer: 18

[Medium] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) Both are equal C) 14 D) 10
• Hint: When comparing 11 and 7, the number with more tens is bigger. 11 has a 1 in the tens place; 7 has no tens.
• Steps:
  • 14 has 1 ten and 4 ones.
  • 9 has 0 tens and 9 ones.
  • A number with more tens is greater, so 14 is greater.
• Answer: 14

[Medium] Skip Counting by 5s

• EN: Count by 5s. What number is missing? 5, 10, ___, 20, 25
• FR: Compte par 5. Quel nombre manque? 5, 10, ___, 20, 25
• Choices: A) 12 B) 14 C) 15 D) 16
• Hint: When counting by 5s, each jump adds 5. After 20 comes 25, so what comes before 20?
• Steps:
  • The pattern goes up by 5 each time: 5, 10, ?, 20, 25.
  • 10 + 5 = 15, and 15 + 5 = 20. The missing number is 15.
• Answer: 15

[Medium] Loonie and Dimes

• EN: Emma has 1 dime and 3 pennies. How many cents does she have in all?
• FR: Emma a 1 pièce de dix cents et 3 sous. Combien de cents a-t-elle en tout?
• Choices: A) 11 cents B) 13 cents C) 14 cents D) 30 cents
• Hint: If you have 1 dime (10¢) and 2 pennies (2¢), you have 10 + 2 = 12¢.
• Steps:
  • A dime is worth 10 cents.
  • 3 pennies are worth 3 cents.
  • 10 + 3 = 13 cents in all.
• Answer: 13 cents

[Hard] Adding Three Numbers

• EN: There are 4 red crayons, 5 blue crayons, and 6 green crayons on a table. How many crayons are there in all?
• FR: Il y a 4 crayons rouges, 5 crayons bleus et 6 crayons verts sur une table. Combien y a-t-il de crayons en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: To add 3 + 4 + 5, first add 3 + 4 = 7, then add 5 more: 7 + 5 = 12.
• Steps:
  • First add 4 + 5 = 9.
  • Then add 9 + 6 = 15.
  • There are 15 crayons in all.
• Answer: 15

[Hard] Counting Back

• EN: There are 18 apples on a tree. Birds eat 9 of them. How many apples are left?
• FR: Il y a 18 pommes dans un arbre. Des oiseaux en mangent 9. Combien reste-t-il de pommes?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: To solve 16 − 8, count back from 16 eight times: 15, 14, 13, 12, 11, 10, 9, 8 — that's 8.
• Steps:
  • Start at 18 and count back 9.
  • 17, 16, 15, 14, 13, 12, 11, 10, 9.
  • There are 9 apples left.
• Answer: 9

[Easy] Adding to 100

• EN: A student has 34 stickers and gets 25 more. How many stickers does the student have now?
• FR: Un élève a 34 autocollants et en reçoit 25 de plus. Combien d'autocollants l'élève a-t-il maintenant?
• Choices: A) 57 B) 59 C) 61 D) 54
• Hint: To add 41 + 23, add the ones first (1 + 3 = 4), then the tens (4 + 2 = 6), giving 64.
• Steps:
  • Add the ones: 4 + 5 = 9.
  • Add the tens: 3 + 2 = 5, meaning 50.
  • 50 + 9 = 59 stickers.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: La petite aiguille est sur le 3 et la grande aiguille est sur le 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:30 C) 3:00 D) 6:15
• Hint: When the long hand points to 12, it is exactly on the hour. The short hand tells you which hour.
• Steps:
  • The long hand on 12 means it is exactly on the hour.
  • The short hand is on 3, so the hour is 3.
  • The time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon est long de 15 cm. Un crayon de cire est long de 9 cm. De combien le crayon est-il plus long que le crayon de cire?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: To find how much longer 18 cm is than 11 cm, subtract: 18 − 11 = 7 cm.
• Steps:
  • Subtract to find the difference: 15 − 9.
  • 15 − 9 = 6.
  • The pencil is 6 cm longer.
• Answer: 6 cm

[Easy] Counting Coins

• EN: Luc has 2 dimes and 1 nickel. How many cents does he have in all?
• FR: Luc a 2 pièces de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 15 cents B) 20 cents C) 25 cents D) 30 cents
• Hint: Two dimes = 20¢ and two nickels = 10¢, so together that is 30¢.
• Steps:
  • Two dimes = 10 + 10 = 20 cents.
  • One nickel = 5 cents.
  • 20 + 5 = 25 cents in all.
• Answer: 25 cents

[Medium] Subtracting within 100

• EN: There are 72 students in a school. 38 go home early. How many students are still at school?
• FR: Il y a 72 élèves dans une école. 38 rentrent tôt à la maison. Combien d'élèves sont encore à l'école?
• Choices: A) 34 B) 36 C) 44 D) 46
• Hint: To subtract 85 − 47, think 85 − 40 = 45, then 45 − 7 = 38.
• Steps:
  • Subtract 72 − 38.
  • 72 − 30 = 42, then 42 − 8 = 34.
  • There are 34 students still at school.
• Answer: 34

[Medium] Telling Time to the Half Hour

• EN: The long hand is on the 6 and the short hand is between 7 and 8. What time does the clock show?
• FR: La grande aiguille est sur le 6 et la petite aiguille est entre 7 et 8. Quelle heure indique l'horloge?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:00
• Hint: When the long hand points to 6, it is half past the hour. The short hand tells you which hour just passed.
• Steps:
  • The long hand on 6 means "half past."
  • The short hand is past 7 (but not yet at 8), so the hour is 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: Look at this pattern: 2, 4, 6, 8, 10, ___. What number comes next?
• FR: Regarde ce motif : 2, 4, 6, 8, 10, ___. Quel nombre vient ensuite?
• Choices: A) 11 B) 12 C) 14 D) 13
• Hint: In the pattern 3, 6, 9, 12, each number goes up by 3. Find the rule, then apply it.
• Steps:
  • The pattern goes up by 2 each time.
  • 10 + 2 = 12.
  • The next number is 12.
• Answer: 12

[Medium] Adding with Regrouping

• EN: A baker made 47 muffins in the morning and 36 more in the afternoon. How many muffins were made in all?
• FR: Un boulanger a fait 47 muffins le matin et 36 de plus l'après-midi. Combien de muffins a-t-il faits en tout?
• Choices: A) 73 B) 81 C) 83 D) 84
• Hint: To add 29 + 54: ones are 9 + 4 = 13, write 3 and carry 1; tens are 2 + 5 + 1 = 8, giving 83.
• Steps:
  • Add the ones: 7 + 6 = 13. Write 3, carry 1.
  • Add the tens: 4 + 3 + 1 (carried) = 8, meaning 80.
  • 80 + 3 = 83 muffins in all.
• Answer: 83

[Hard] Counting Coins to $1

• EN: Zara has 3 quarters. How many cents does she have, and is that more or less than $1.00?
• FR: Zara a 3 pièces de 25 cents. Combien de cents a-t-elle, et est-ce plus ou moins que 1,00 $?
• Choices: A) 65 cents, less than $1.00 B) 75 cents, less than $1.00 C) 85 cents, less than $1.00 D) 75 cents, more than $1.00
• Hint: Two quarters = 50¢. Add one more quarter (25¢) to find the total for three quarters.
• Steps:
  • One quarter = 25 cents.
  • 25 + 25 + 25 = 75 cents.
  • 75 cents is less than 100 cents ($1.00).
• Answer: 75 cents, less than $1.00

[Hard] Measuring and Comparing

• EN: A ribbon is 63 cm long. After cutting off 28 cm, how many centimetres of ribbon are left?
• FR: Un ruban fait 63 cm de long. Après avoir coupé 28 cm, combien de centimètres de ruban reste-t-il?
• Choices: A) 25 cm B) 35 cm C) 37 cm D) 41 cm
• Hint: To solve 75 − 29, think 75 − 30 = 45, then add back 1: 45 + 1 = 46.
• Steps:
  • Subtract 63 − 28.
  • 63 − 30 = 33, then add back 2: 33 + 2 = 35.
  • There are 35 cm of ribbon left.
• Answer: 35 cm

[Easy] Multiplication by 2

• EN: A hockey team has 6 players on the ice. How many skates are there in all?
• FR: Une équipe de hockey a 6 joueurs sur la glace. Combien de patins y a-t-il en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Each player wears 2 skates. To find the total, multiply the number of players by 2: for 4 players, 4 × 2 = 8.
• Steps:
  • Each player has 2 skates.
  • 6 × 2 = 12.
  • There are 12 skates in all.
• Answer: 12

[Easy] Multiplication by 5

• EN: There are 4 bags of apples. Each bag has 5 apples. How many apples are there in all?
• FR: Il y a 4 sacs de pommes. Chaque sac contient 5 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: For 3 bags with 5 apples each, 3 × 5 = 15. Multiply the number of groups by 5.
• Steps:
  • 4 bags, each with 5 apples.
  • 4 × 5 = 20.
  • There are 20 apples in all.
• Answer: 20

[Easy] Basic Fractions

• EN: A pizza is cut into 4 equal pieces. Maya eats 1 piece. What fraction of the pizza did Maya eat?
• FR: Une pizza est coupée en 4 morceaux égaux. Maya mange 1 morceau. Quelle fraction de la pizza Maya a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: If a pie is cut into 8 equal slices and you eat 1, you ate 1/8 of the pie.
• Steps:
  • The pizza is cut into 4 equal parts.
  • Maya ate 1 of those 4 parts.
  • That is 1/4 of the pizza.
• Answer: 1/4

[Easy] Perimeter

• EN: A square has sides that are each 5 cm long. What is the perimeter of the square?
• FR: Un carré a des côtés de 5 cm chacun. Quel est le périmètre du carré?
• Choices: A) 10 cm B) 15 cm C) 20 cm D) 25 cm
• Hint: A square has 4 equal sides. For sides of 3 cm, the perimeter is 3 + 3 + 3 + 3 = 12 cm.
• Steps:
  • A square has 4 sides, each 5 cm.
  • Add all sides: 5 + 5 + 5 + 5 = 20.
  • The perimeter is 20 cm.
• Answer: 20 cm

[Medium] Multiplication by 3

• EN: There are 7 shelves in a library. Each shelf holds 3 books. How many books are there in all?
• FR: Il y a 7 étagères dans une bibliothèque. Chaque étagère contient 3 livres. Combien y a-t-il de livres en tout?
• Choices: A) 18 B) 21 C) 24 D) 27
• Hint: To find 6 × 3, think of it as 6 groups of 3: 3, 6, 9, 12, 15, 18.
• Steps:
  • 7 shelves, each with 3 books.
  • 7 × 3 = 21.
  • There are 21 books in all.
• Answer: 21

[Medium] Basic Division

• EN: 24 students are put into groups of 4. How many groups are there?
• FR: 24 élèves sont mis en groupes de 4. Combien y a-t-il de groupes?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: To find 20 ÷ 4, think: "How many groups of 4 make 20?" Count by 4s: 4, 8, 12, 16, 20 — that's 5 groups.
• Steps:
  • We need to divide 24 into groups of 4.
  • 24 ÷ 4 = 6.
  • There are 6 groups.
• Answer: 6

[Medium] Reading a Graph

• EN: A bar graph shows that 8 students chose hockey, 5 chose soccer, and 3 chose basketball. How many more students chose hockey than basketball?
• FR: Un diagramme à barres montre que 8 élèves ont choisi le hockey, 5 le soccer et 3 le basketball. Combien d'élèves de plus ont choisi le hockey plutôt que le basketball?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: To find how many more, subtract the smaller number from the larger. For 9 and 4: 9 − 4 = 5 more.
• Steps:
  • Hockey: 8 students. Basketball: 3 students.
  • Subtract: 8 − 3 = 5.
  • Five more students chose hockey than basketball.
• Answer: 5

[Medium] Fractions on a Number Line

• EN: A chocolate bar is divided into 3 equal pieces. Theo eats 2 pieces. What fraction of the chocolate bar did Theo eat?
• FR: Une tablette de chocolat est divisée en 3 morceaux égaux. Théo mange 2 morceaux. Quelle fraction de la tablette de chocolat Théo a-t-il mangée?
• Choices: A) 1/3 B) 2/4 C) 2/3 D) 3/4
• Hint: If a bar is cut into 5 equal pieces and you eat 3, you ate 3/5 — the numerator is how many you ate, the denominator is total pieces.
• Steps:
  • The bar is divided into 3 equal pieces (denominator = 3).
  • Theo ate 2 of those pieces (numerator = 2).
  • The fraction is 2/3.
• Answer: 2/3

[Hard] Multiplication by 4 and 10

• EN: A store sells boxes of 10 crayons. A school orders 6 boxes. How many crayons does the school get in all?
• FR: Un magasin vend des boîtes de 10 crayons. Une école commande 6 boîtes. Combien de crayons l'école reçoit-elle en tout?
• Choices: A) 16 B) 40 C) 60 D) 66
• Hint: Multiplying by 10 is easy — just add a zero to the other number. For 4 × 10, the answer is 40.
• Steps:
  • 6 boxes, each with 10 crayons.
  • 6 × 10 = 60.
  • The school gets 60 crayons in all.
• Answer: 60

[Hard] Perimeter of a Rectangle

• EN: A rectangular garden is 8 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un jardin rectangulaire est long de 8 m et large de 3 m. Quel est le périmètre du jardin?
• Choices: A) 11 m B) 22 m C) 24 m D) 32 m
• Hint: A rectangle has 2 long sides and 2 short sides. For a 5 m by 2 m rectangle: 5 + 2 + 5 + 2 = 14 m.
• Steps:
  • Add all four sides: 8 + 3 + 8 + 3.
  • 8 + 8 = 16 and 3 + 3 = 6.
  • 16 + 6 = 22 m is the perimeter.
• Answer: 22 m

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To remember 6 × 8, think: 6 × 8 = 48. Then for 7 × 8, add one more group of 8: 48 + 8 = 56.
• Steps:
  • 7 × 8 means 7 groups of 8.
  • 7 × 8 = 56.
  • The answer is 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 5.29, the 2 is in the tenths place and is worth 2 tenths, and the 9 is in the hundredths place.
• Steps:
  • In 3.47, the digit 3 is in the ones place.
  • The digit 4 is right after the decimal point — that is the tenths place.
  • The value of 4 is 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A classroom floor is 9 m long and 6 m wide. What is the area of the floor?
• FR: Le plancher d'une salle de classe est long de 9 m et large de 6 m. Quelle est l'aire du plancher?
• Choices: A) 15 m² B) 30 m² C) 54 m² D) 56 m²
• Hint: Area = length × width. For a 5 m × 4 m room, area = 5 × 4 = 20 m².
• Steps:
  • Area = length × width.
  • 9 × 6 = 54.
  • The area of the floor is 54 m².
• Answer: 54 m²

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 2/4?
• FR: Quelle fraction est plus grande : 3/4 ou 2/4?
• Choices: A) 2/4 B) They are equal C) 3/4 D) 1/4
• Hint: When fractions have the same denominator, just compare the numerators. For 5/8 and 3/8, since 5 > 3, then 5/8 > 3/8.
• Steps:
  • Both fractions have the same denominator (4).
  • Compare the numerators: 3 vs 2.
  • Since 3 > 2, then 3/4 is larger.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: 47 students are divided into teams of 5. How many full teams are there, and how many students are left over?
• FR: 47 élèves sont divisés en équipes de 5. Combien d'équipes complètes y a-t-il, et combien d'élèves restent-il?
• Choices: A) 8 teams, remainder 7 B) 9 teams, remainder 2 C) 9 teams, remainder 3 D) 10 teams, remainder 1
• Hint: To solve 38 ÷ 5: 5 × 7 = 35, so there are 7 groups with 38 − 35 = 3 left over.
• Steps:
  • 5 × 9 = 45, which is the closest multiple of 5 less than 47.
  • 47 − 45 = 2 students left over.
  • There are 9 full teams with a remainder of 2.
• Answer: 9 teams, remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 p.m. and ends at 3:45 p.m. How long did the game last?
• FR: Une partie de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps a duré la partie?
• Choices: A) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours
• Hint: To find elapsed time from 2:10 to 4:40, count forward: 2:10 → 4:10 is 2 hours, then add 30 more minutes = 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 is 2 hours.
  • From 3:15 to 3:45 is 30 more minutes.
  • The game lasted 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A book costs $4.75 and a pencil case costs $2.50. What is the total cost?
• FR: Un livre coûte 4,75 $ et une trousse coûte 2,50 $. Quel est le coût total?
• Choices: A) $6.25 B) $7.00 C) $7.25 D) $8.50
• Hint: To add $3.60 + $1.80, line up the decimal points and add: 60 + 80 = 140 cents = $1.40, then 3 + 1 = 4, so $4 + $1.40 = $5.40.
• Steps:
  • Add the dollars: $4 + $2 = $6.
  • Add the cents: 75¢ + 50¢ = 125¢ = $1.25.
  • $6 + $1.25 = $7.25 total.
• Answer: $7.25

[Medium] Multi-Digit Multiplication

• EN: A school orders 24 boxes of markers. Each box has 8 markers. How many markers are ordered in all?
• FR: Une école commande 24 boîtes de marqueurs. Chaque boîte contient 8 marqueurs. Combien de marqueurs sont commandés en tout?
• Choices: A) 162 B) 182 C) 192 D) 196
• Hint: To multiply 32 × 6: (30 × 6) + (2 × 6) = 180 + 12 = 192.
• Steps:
  • Break apart 24: 20 × 8 = 160 and 4 × 8 = 32.
  • 160 + 32 = 192.
  • The school ordered 192 markers.
• Answer: 192

[Hard] Long Division

• EN: A farmer packs 156 eggs into cartons of 6. How many full cartons does the farmer fill?
• FR: Un fermier emballe 156 œufs dans des boîtes de 6. Combien de boîtes complètes le fermier remplit-il?
• Choices: A) 24 B) 26 C) 28 D) 32
• Hint: To solve 120 ÷ 6: think 6 × 20 = 120, so the answer is 20.
• Steps:
  • 6 × 20 = 120; 156 − 120 = 36 remaining.
  • 6 × 6 = 36.
  • 20 + 6 = 26 full cartons.
• Answer: 26

[Hard] Comparing Decimals and Fractions

• EN: Order these numbers from least to greatest: 0.5, 3/4, 0.25, 1/2.
• FR: Ordonne ces nombres du plus petit au plus grand : 0,5, 3/4, 0,25, 1/2.
• Choices: A) 0.25, 0.5, 1/2, 3/4 B) 0.25, 1/2, 0.5, 3/4 C) 1/2, 0.25, 0.5, 3/4 D) 0.25, 1/2, 3/4, 0.5
• Hint: Convert fractions to decimals: 1/2 = 0.50 and 3/4 = 0.75. Then compare all numbers as decimals.
• Steps:
  • Convert: 3/4 = 0.75 and 1/2 = 0.50.
  • All values: 0.25, 0.50, 0.50, 0.75.
  • Note 0.5 = 1/2, so: 0.25, 0.5 (same as 1/2), 3/4.
• Answer: 0.25, 1/2, 0.5, 3/4

[Easy] Multi-Digit Multiplication

• EN: A factory makes 125 hockey pucks per hour. How many pucks does it make in 4 hours?
• FR: Une usine fabrique 125 rondelles de hockey par heure. Combien de rondelles fabrique-t-elle en 4 heures?
• Choices: A) 400 B) 450 C) 500 D) 520
• Hint: To multiply 230 × 3: (200 × 3) + (30 × 3) = 600 + 90 = 690.
• Steps:
  • Multiply 125 × 4.
  • 100 × 4 = 400 and 25 × 4 = 100.
  • 400 + 100 = 500 pucks.
• Answer: 500

[Easy] Adding Fractions (Like Denominators)

• EN: Nadia ate 2/8 of a pie at lunch and 3/8 of the same pie at dinner. What fraction of the pie did she eat in all?
• FR: Nadia a mangé 2/8 d'une tarte au dîner et 3/8 de la même tarte au souper. Quelle fraction de la tarte a-t-elle mangée en tout?
• Choices: A) 4/8 B) 5/8 C) 5/16 D) 6/8
• Hint: To add 1/6 + 3/6, keep the denominator the same and just add the numerators: 1 + 3 = 4, so 4/6.
• Steps:
  • The denominators are the same (8), so add the numerators.
  • 2 + 3 = 5.
  • Nadia ate 5/8 of the pie.
• Answer: 5/8

[Easy] Percentages — 50% and 25%

• EN: A jacket costs $80. It is on sale for 25% off. How much is the discount?
• FR: Une veste coûte 80 $. Elle est en solde à 25 % de réduction. Quel est le montant de la réduction?
• Choices: A) $10 B) $15 C) $20 D) $25
• Hint: 25% of a number is the same as dividing by 4. For 25% of $60: 60 ÷ 4 = $15.
• Steps:
  • 25% means one quarter.
  • $80 ÷ 4 = $20.
  • The discount is $20.
• Answer: $20

[Easy] Decimal Subtraction

• EN: A water bottle holds 1.75 L. After drinking 0.50 L, how much water is left?
• FR: Une bouteille d'eau contient 1,75 L. Après avoir bu 0,50 L, quelle quantité d'eau reste-t-il?
• Choices: A) 1.00 L B) 1.15 L C) 1.25 L D) 1.50 L
• Hint: To subtract 2.80 − 0.60, line up the decimals and subtract: 80 − 60 = 20 hundredths, so 2.20.
• Steps:
  • 1.75 − 0.50.
  • Subtract the hundredths: 75 − 50 = 25 hundredths.
  • The answer is 1.25 L.
• Answer: 1.25 L

[Medium] Multi-Digit Division

• EN: 364 cookies are packed into bags of 7. How many bags are filled?
• FR: 364 biscuits sont emballés dans des sacs de 7. Combien de sacs sont remplis?
• Choices: A) 48 B) 52 C) 54 D) 57
• Hint: To solve 252 ÷ 7: 7 × 30 = 210 and 7 × 6 = 42, so 7 × 36 = 252. The answer is 36.
• Steps:
  • 7 × 50 = 350; 364 − 350 = 14 remaining.
  • 14 ÷ 7 = 2.
  • 50 + 2 = 52 bags.
• Answer: 52

[Medium] Subtracting Fractions

• EN: A rope is 7/10 m long. You cut off 3/10 m. How much rope is left?
• FR: Une corde mesure 7/10 m de long. Tu coupes 3/10 m. Quelle longueur de corde reste-t-il?
• Choices: A) 3/10 m B) 4/10 m C) 5/10 m D) 10/10 m
• Hint: To subtract 5/9 − 2/9, keep the denominator and subtract numerators: 5 − 2 = 3, giving 3/9.
• Steps:
  • The denominators are both 10.
  • Subtract the numerators: 7 − 3 = 4.
  • The remaining rope is 4/10 m.
• Answer: 4/10 m

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte est longue de 5 cm, large de 4 cm et haute de 3 cm. Quel est le volume de la boîte?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height. For a box of 2 × 3 × 4: Volume = 2 × 3 × 4 = 24 cm³.
• Steps:
  • Volume = length × width × height.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • The volume of the box is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 10%

• EN: Tim's restaurant bill is $45.00. He wants to leave a 10% tip. How much is the tip?
• FR: La facture de Tim au restaurant est de 45,00 $. Il veut laisser un pourboire de 10 %. Quel est le montant du pourboire?
• Choices: A) $4.00 B) $4.50 C) $5.00 D) $9.00
• Hint: To find 10% of a number, simply divide by 10. For 10% of $70: 70 ÷ 10 = $7.
• Steps:
  • 10% means divide by 10.
  • $45.00 ÷ 10 = $4.50.
  • The tip is $4.50.
• Answer: $4.50

[Hard] Multi-Step Fraction Problem

• EN: A recipe calls for 3/5 cup of sugar. Marco is making 3 batches. He already has 1/5 cup. How much more sugar does Marco need?
• FR: Une recette nécessite 3/5 de tasse de sucre. Marco prépare 3 portions. Il a déjà 1/5 de tasse. De combien de sucre supplémentaire Marco a-t-il besoin?
• Choices: A) 7/5 cups B) 8/5 cups C) 9/5 cups D) 10/5 cups
• Hint: First find total needed (multiply the fraction by 3), then subtract what he has. For 2/7 × 3 = 6/7, minus 1/7 = 5/7.
• Steps:
  • Total sugar needed: 3/5 × 3 = 9/5 cups.
  • He already has 1/5 cup.
  • 9/5 − 1/5 = 8/5 cups more needed.
• Answer: 8/5 cups

[Hard] Decimal Multi-Step Problem

• EN: A bookstore sells notebooks for $3.75 each. Priya buys 4 notebooks and pays with a $20 bill. How much change does she receive?
• FR: Une librairie vend des cahiers 3,75 $ chacun. Priya en achète 4 et paie avec un billet de 20 $. Combien reçoit-elle en monnaie?
• Choices: A) $4.00 B) $5.00 C) $5.50 D) $6.25
• Hint: First multiply to find the total cost, then subtract from the amount paid. For 3 items at $2.50: 3 × $2.50 = $7.50; change from $10 = $10 − $7.50 = $2.50.
• Steps:
  • Cost: 4 × $3.75 = $15.00.
  • Change: $20.00 − $15.00 = $5.00.
  • Priya receives $5.00 in change.
• Answer: $5.00

[Easy] Fraction Multiplication

• EN: What is 1/2 × 3/4?
• FR: Combien font 1/2 × 3/4?
• Choices: A) 4/6 B) 3/8 C) 2/6 D) 1/6
• Hint: To multiply fractions, multiply the top numbers together and the bottom numbers together: 2/3 × 1/4 = (2×1)/(3×4) = 2/12.
• Steps:
  • Multiply the numerators: 1 × 3 = 3.
  • Multiply the denominators: 2 × 4 = 8.
  • The answer is 3/8.
• Answer: 3/8

[Easy] Ratios

• EN: In a bag of 20 marbles, 8 are blue and the rest are red. What is the ratio of blue to red marbles?
• FR: Dans un sac de 20 billes, 8 sont bleues et les autres sont rouges. Quel est le rapport des billes bleues aux billes rouges?
• Choices: A) 8:20 B) 12:8 C) 8:12 D) 8:5
• Hint: First find the number of red marbles by subtracting, then write blue : red. For 5 blue out of 15 total: 15 − 5 = 10 red, ratio is 5:10.
• Steps:
  • Red marbles: 20 − 8 = 12.
  • Ratio of blue to red: 8 to 12.
  • Written as 8:12.
• Answer: 8:12

[Easy] Percent of a Number

• EN: What is 30% of 90?
• FR: Combien font 30 % de 90?
• Choices: A) 27 B) 30 C) 33 D) 60
• Hint: To find 20% of 80: first find 10% (80 ÷ 10 = 8), then multiply by 2: 8 × 2 = 16.
• Steps:
  • 10% of 90 = 9.
  • 30% = 3 × 10% = 3 × 9 = 27.
  • 30% of 90 is 27.
• Answer: 27

[Easy] Integers Introduction

• EN: The temperature in Whitehorse was −8°C in the morning and rose 11°C by afternoon. What was the afternoon temperature?
• FR: La température à Whitehorse était de −8 °C le matin et a augmenté de 11 °C en après-midi. Quelle était la température en après-midi?
• Choices: A) −3°C B) 3°C C) 4°C D) 19°C
• Hint: To add a positive number to a negative, move right on a number line. For −5 + 7: start at −5, move 7 to the right, land on 2.
• Steps:
  • Start at −8 and add 11.
  • −8 + 11 = 3.
  • The afternoon temperature was 3°C.
• Answer: 3°C

[Medium] Fraction Division

• EN: You have 3/4 of a pizza. If you divide it equally among 3 friends, what fraction does each friend get?
• FR: Tu as 3/4 d'une pizza. Si tu la divises en parts égales entre 3 amis, quelle fraction chaque ami reçoit-il?
• Choices: A) 1/4 B) 2/4 C) 3/12 D) 9/4
• Hint: To divide a fraction by a whole number, multiply the denominator by that number. For 2/5 ÷ 2: 2/(5×2) = 2/10 = 1/5.
• Steps:
  • Divide 3/4 by 3: multiply the denominator by 3.
  • 3/(4 × 3) = 3/12 = 1/4.
  • Each friend gets 1/4 of the pizza.
• Answer: 1/4

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1
• FR: Évalue : 3 + 4 × 2 − 1
• Choices: A) 9 B) 10 C) 13 D) 14
• Hint: In BEDMAS, multiply and divide before adding and subtracting. For 5 + 3 × 2: do 3 × 2 = 6 first, then 5 + 6 = 11.
• Steps:
  • First multiply: 4 × 2 = 8.
  • Rewrite the expression: 3 + 8 − 1.
  • 3 + 8 = 11, then 11 − 1 = 10.
• Answer: 10

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km par heure?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: Speed = distance ÷ time. For 180 km in 3 hours: 180 ÷ 3 = 60 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 240 ÷ 3 = 80.
  • The car's speed is 80 km/h.
• Answer: 80 km/h

[Medium] Simple Algebraic Expressions

• EN: If n = 5, what is the value of 3n + 7?
• FR: Si n = 5, quelle est la valeur de 3n + 7?
• Choices: A) 15 B) 20 C) 22 D) 35
• Hint: Replace the variable with the given number. For 2x + 3 when x = 4: 2 × 4 + 3 = 8 + 3 = 11.
• Steps:
  • Substitute n = 5 into 3n + 7.
  • 3 × 5 + 7 = 15 + 7.
  • The value is 22.
• Answer: 22

[Hard] Multi-Step Percent Problem

• EN: A hockey jersey that normally costs $120 is on sale for 35% off. What is the sale price?
• FR: Un chandail de hockey qui coûte normalement 120 $ est en solde à 35 % de réduction. Quel est le prix de vente?
• Choices: A) $42 B) $72 C) $78 D) $85
• Hint: Find the discount (price × percent as decimal), then subtract from original price. For 20% off $50: 50 × 0.20 = $10 discount; $50 − $10 = $40.
• Steps:
  • Discount = 35% of $120 = 0.35 × 120 = $42.
  • Sale price = $120 − $42 = $78.
  • The jersey costs $78 on sale.
• Answer: $78

[Hard] Integer Operations

• EN: Evaluate: (−6) × 4 + (−2) × (−5)
• FR: Évalue : (−6) × 4 + (−2) × (−5)
• Choices: A) −34 B) −14 C) 14 D) 34
• Hint: Remember the sign rules: negative × positive = negative; negative × negative = positive. For (−3) × 2 + (−1) × (−4): −6 + 4 = −2.
• Steps:
  • (−6) × 4 = −24.
  • (−2) × (−5) = +10.
  • −24 + 10 = −14.
• Answer: −14

[Easy] Integer Addition

• EN: A submarine is at −45 m below sea level. It rises 18 m. What is its new depth?
• FR: Un sous-marin est à −45 m sous le niveau de la mer. Il monte de 18 m. Quelle est sa nouvelle profondeur?
• Choices: A) −27 m B) −18 m C) 27 m D) 63 m
• Hint: Adding a positive number to a negative makes it less negative. For −30 + 12, think of 30 − 12 = 18, and keep the negative: −18.
• Steps:
  • Start at −45 and add 18.
  • −45 + 18 = −27.
  • The new depth is −27 m.
• Answer: −27 m

[Easy] Fraction Fluency

• EN: Write 12/8 as a mixed number in simplest form.
• FR: Écris 12/8 sous forme de nombre fractionnaire en termes les plus simples.
• Choices: A) 1 1/2 B) 1 2/8 C) 2 1/4 D) 1 4/8
• Hint: To convert 10/4 to a mixed number: 10 ÷ 4 = 2 remainder 2, so it is 2 and 2/4 = 2 1/2.
• Steps:
  • 12 ÷ 8 = 1 remainder 4.
  • So 12/8 = 1 and 4/8.
  • Simplify 4/8 = 1/2, giving 1 1/2.
• Answer: 1 1/2

[Easy] Percentage — Discount

• EN: A pair of skates costs $160. They are on sale for 20% off. What is the discount amount?
• FR: Une paire de patins coûte 160 $. Elle est en solde à 20 % de réduction. Quel est le montant de la réduction?
• Choices: A) $20 B) $32 C) $40 D) $48
• Hint: 20% = 2 × 10%. Find 10% first (divide by 10), then double it. For 10% of $90 = $9, so 20% = $18.
• Steps:
  • 10% of $160 = $16.
  • 20% = 2 × $16 = $32.
  • The discount is $32.
• Answer: $32

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 14 = 30
• FR: Résous pour x : x + 14 = 30
• Choices: A) x = 14 B) x = 16 C) x = 44 D) x = 15
• Hint: To solve x + 9 = 20, subtract 9 from both sides: x = 20 − 9 = 11.
• Steps:
  • To isolate x, subtract 14 from both sides.
  • x = 30 − 14 = 16.
  • The solution is x = 16.
• Answer: x = 16

[Medium] Integer Multiplication and Division

• EN: Evaluate: (−3) × (−4) ÷ (−6)
• FR: Évalue : (−3) × (−4) ÷ (−6)
• Choices: A) −2 B) 2 C) −8 D) 8
• Hint: Work left to right. For (−2) × (−5) ÷ 10: (−2) × (−5) = 10, then 10 ÷ 10 = 1.
• Steps:
  • (−3) × (−4) = 12 (negative × negative = positive).
  • 12 ÷ (−6) = −2 (positive ÷ negative = negative).
  • The answer is −2.
• Answer: −2

[Medium] Percentage — Tax

• EN: A video game costs $50 before tax. The HST in Ontario is 13%. What is the total price including tax?
• FR: Un jeu vidéo coûte 50 $ avant les taxes. La TVH en Ontario est de 13 %. Quel est le prix total taxes incluses?
• Choices: A) $56.50 B) $57.00 C) $58.00 D) $63.00
• Hint: Tax amount = price × tax rate. Then add to original. For a $40 item with 10% tax: 40 × 0.10 = $4 tax; total = $44.
• Steps:
  • Tax = 13% of $50 = 0.13 × 50 = $6.50.
  • Total = $50 + $6.50 = $56.50.
  • The total price is $56.50.
• Answer: $56.50

[Medium] Surface Area

• EN: A rectangular box is 6 cm long, 4 cm wide, and 2 cm tall. What is the total surface area of the box?
• FR: Une boîte rectangulaire est longue de 6 cm, large de 4 cm et haute de 2 cm. Quelle est l'aire totale de la surface de la boîte?
• Choices: A) 48 cm² B) 64 cm² C) 80 cm² D) 88 cm²
• Hint: Surface area of a rectangular box = 2(lw + lh + wh). For a box of 3 × 2 × 1: 2(6 + 3 + 2) = 2(11) = 22 cm².
• Steps:
  • Compute each pair: lw = 6×4 = 24, lh = 6×2 = 12, wh = 4×2 = 8.
  • Sum: 24 + 12 + 8 = 44.
  • Surface area = 2 × 44 = 88 cm².
• Answer: 88 cm²

[Medium] Probability

• EN: A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 billes bleues et 2 billes vertes. Quelle est la probabilité de piger une bille bleue?
• Choices: A) 1/4 B) 1/2 C) 3/10 D) 2/5
• Hint: Probability = favourable outcomes ÷ total outcomes. For 4 red out of 12 total: 4/12 = 1/3.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Blue marbles: 5.
  • Probability = 5/10 = 1/2.
• Answer: 1/2

[Hard] Multi-Step Percent Problem — Tip, Tax, and Discount

• EN: At a Tim Hortons, a group's bill is $36.00. They get a 15% tip and an 8% tax applied to the original bill. What is the total amount they pay?
• FR: Au Tim Hortons, la facture d'un groupe est de 36,00 $. Ils laissent un pourboire de 15 % et paient une taxe de 8 % sur la facture originale. Quel est le montant total qu'ils paient?
• Choices: A) $46.08 B) $47.52 C) $48.24 D) $50.40
• Hint: Calculate tip and tax separately (both as a percent of the original), then add all three amounts together.
• Steps:
  • Tip = 15% of $36 = 0.15 × 36 = $5.40.
  • Tax = 8% of $36 = 0.08 × 36 = $2.88.
  • Total = $36 + $5.40 + $2.88 = $44.28. Wait — let me recalculate: $36 + $5.40 = $41.40; $41.40 + $2.88 = $44.28.
• Answer: $47.52

(Correction note: Recalculating to match a choice — let me verify the correct choice by recalculating: Tip 15% of $36 = $5.40; Tax 8% of $36 = $2.88; Total = $44.28. None match. Adjusting: tax = 13%: 0.13 × 36 = $4.68; total = $36 + $5.40 + $4.68 = $46.08.)

Revised Problem 9:

[Hard] Multi-Step Percent Problem

• EN: A restaurant bill at a Tim Hortons is $36.00. A 15% tip and a 13% tax are both calculated on the original bill. What is the total amount paid?
• FR: La facture dans un Tim Hortons est de 36,00 $. Un pourboire de 15 % et une taxe de 13 % sont tous deux calculés sur la facture originale. Quel est le montant total payé?
• Choices: A) $43.92 B) $46.08 C) $47.52 D) $50.40
• Hint: Calculate tip and tax separately as percentages of the original, then add all three amounts.
• Steps:
  • Tip = 15% of $36 = 0.15 × 36 = $5.40.
  • Tax = 13% of $36 = 0.13 × 36 = $4.68.
  • Total = $36 + $5.40 + $4.68 = $46.08.
• Answer: $46.08

[Hard] Two-Variable Integer Problem

• EN: A football team gains 7 yards, loses 12 yards, gains 5 yards, and then loses 3 yards. What is their overall change in yards?
• FR: Une équipe de football gagne 7 verges, en perd 12, en gagne 5, puis en perd 3. Quel est leur changement total de verges?
• Choices: A) −5 B) −3 C) 3 D) 5
• Hint: Add all values keeping their signs. For +8, −5, +3: 8 − 5 + 3 = 6.
• Steps:
  • Add the gains and losses: 7 + (−12) + 5 + (−3).
  • 7 − 12 = −5; −5 + 5 = 0; 0 − 3 = −3.
  • The overall change is −3 yards.
• Answer: −3

[Easy] Perfect Squares and Square Roots

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: Think about which number multiplied by itself gives the target. For √81: 9 × 9 = 81, so √81 = 9.
• Steps:
  • Ask: what number times itself equals 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Five students scored 72, 85, 90, 68, and 80 on a test. What is the mean (average) score?
• FR: Cinq élèves ont obtenu 72, 85, 90, 68 et 80 à un test. Quel est le score moyen?
• Choices: A) 79 B) 80 C) 82 D) 85
• Hint: To find the mean of 60, 70, and 80: add them (60+70+80 = 210), then divide by 3 (210÷3 = 70).
• Steps:
  • Sum: 72 + 85 + 90 + 68 + 80 = 395.
  • Divide by the number of scores: 395 ÷ 5 = 79.
  • The mean score is 79.
• Answer: 79

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 17
• FR: Résous pour x : 2x + 5 = 17
• Choices: A) x = 4 B) x = 6 C) x = 7 D) x = 11
• Hint: To solve 3x + 4 = 16: first subtract 4 from both sides (3x = 12), then divide by 3 (x = 4).
• Steps:
  • Subtract 5 from both sides: 2x = 17 − 5 = 12.
  • Divide both sides by 2: x = 12 ÷ 2 = 6.
  • The solution is x = 6.
• Answer: x = 6

[Easy] Percent Increase

• EN: A sweater's price increased from $40 to $50. What is the percent increase?
• FR: Le prix d'un chandail est passé de 40 $ à 50 $. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: Percent increase = (increase ÷ original) × 100. For a price going from $60 to $72: increase = $12; 12 ÷ 60 = 0.20 = 20%.
• Steps:
  • Increase = $50 − $40 = $10.
  • Percent increase = (10 ÷ 40) × 100 = 25%.
  • The price increased by 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 jambes 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 = c².
  • 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation with Fractions

• EN: Solve for x: x/3 − 4 = 2
• FR: Résous pour x : x/3 − 4 = 2
• Choices: A) x = 6 B) x = 12 C) x = 18 D) x = 24
• Hint: To solve x/4 + 1 = 5: first subtract 1 from both sides (x/4 = 4), then multiply both sides by 4 (x = 16).
• Steps:
  • Add 4 to both sides: x/3 = 6.
  • Multiply both sides by 3: x = 18.
  • The solution is x = 18.
• Answer: x = 18

[Medium] Slope Introduction

• EN: A line passes through points (2, 4) and (6, 12). What is the slope of the line?
• FR: Une droite passe par les points (2, 4) et (6, 12). Quel est le taux de variation de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁). For points (1, 3) and (3, 7): slope = (7−3)÷(3−1) = 4÷2 = 2.
• Steps:
  • Rise = 12 − 4 = 8.
  • Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median and mode of this data set: 5, 3, 7, 3, 9, 5, 3.
• FR: Trouve la médiane et le mode de cet ensemble de données : 5, 3, 7, 3, 9, 5, 3.
• Choices: A) Median = 5, Mode = 3 B) Median = 3, Mode = 5 C) Median = 4, Mode = 3 D) Median = 5, Mode = 5
• Hint: To find the median, sort the data and pick the middle value. The mode is the value that appears most often.
• Steps:
  • Sort: 3, 3, 3, 5, 5, 7, 9. The middle (4th) value is 5 → median = 5.
  • The number 3 appears 3 times (more than any other) → mode = 3.
  • Median = 5, Mode = 3.
• Answer: Median = 5, Mode = 3

[Hard] Pythagorean Theorem — Applied

• EN: A ladder is 13 m long and 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 sur le mur l'échelle atteint-elle?
• Choices: A) 8 m B) 10 m C) 12 m D) 14 m
• Hint: The ladder is the hypotenuse. Use a² + b² = c²: rearrange to find a = √(c² − b²). For c = 10, b = 6: a = √(100 − 36) = √64 = 8.
• Steps:
  • 13² = 5² + height².
  • 169 = 25 + height².
  • Height² = 144 → height = √144 = 12 m.
• Answer: 12 m

[Hard] Percent Decrease and Two-Step Equations

• EN: A store reduced the price of a jacket by 30%, and the sale price became $84. What was the original price?
• FR: Un magasin a réduit le prix d'une veste de 30 % et le prix de vente est devenu 84 $. Quel était le prix original?
• Choices: A) $110 B) $115 C) $120 D) $125
• Hint: If price after 20% reduction = $80, then 0.80 × original = 80, so original = 80 ÷ 0.80 = $100.
• Steps:
  • After a 30% reduction, the price is 70% of the original.
  • 0.70 × original = $84.
  • Original = $84 ÷ 0.70 = $120.
• Answer: $120

[Easy] Linear Equations

• EN: Solve for x: 3x − 9 = 18
• FR: Résous pour x : 3x − 9 = 18
• Choices: A) x = 3 B) x = 7 C) x = 9 D) x = 27
• Hint: To solve 4x − 8 = 16: add 8 to both sides (4x = 24), then divide by 4 (x = 6).
• Steps:
  • Add 9 to both sides: 3x = 27.
  • Divide both sides by 3: x = 9.
  • The solution is x = 9.
• Answer: x = 9

[Easy] Adding Polynomials

• EN: Add: (2x + 5) + (3x − 2)
• FR: Additionne : (2x + 5) + (3x − 2)
• Choices: A) 5x + 7 B) 5x + 3 C) 6x − 3 D) 5x − 3
• Hint: Combine like terms: add the x-terms together and the constant terms together. For (3x + 2) + (4x − 5): 3x + 4x = 7x and 2 − 5 = −3, giving 7x − 3.
• Steps:
  • Combine x-terms: 2x + 3x = 5x.
  • Combine constants: 5 + (−2) = 3.
  • Answer: 5x + 3
• Answer: 5x + 3

[Easy] Slope-Intercept Form

• EN: Identify the slope and y-intercept of the line: y = 4x − 3
• FR: Identifie le taux de variation et l'ordonnée à l'origine de la droite : y = 4x − 3
• Choices: A) slope = −3, y-intercept = 4 B) slope = 4, y-intercept = 3 C) slope = 4, y-intercept = −3 D) slope = −4, y-intercept = 3
• Hint: In y = mx + b, m is always the slope and b is always the y-intercept. For y = 2x + 7: slope = 2, y-intercept = 7.
• Steps:
  • The equation is in y = mx + b form.
  • m = 4 (slope) and b = −3 (y-intercept).
  • Slope = 4, y-intercept = −3.
• Answer: slope = 4, y-intercept = −3

[Easy] Similar Triangles

• EN: Two similar triangles have sides in ratio 3:5. If the shorter triangle has a side of 9 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans le rapport 3:5. Si le triangle plus petit a un côté de 9 cm, quelle est la longueur du côté correspondant du triangle plus grand?
• Choices: A) 12 cm B) 13 cm C) 15 cm D) 18 cm
• Hint: Use the proportion: small/large = 3/5. Cross-multiply to find the missing side. For small = 6 and ratio 2:3: 6/x = 2/3, so x = 9.
• Steps:
  • Set up proportion: 9/x = 3/5.
  • Cross-multiply: 3x = 45.
  • x = 15 cm.
• Answer: 15 cm

[Medium] Multiplying Polynomials

• EN: Expand and simplify: (x + 3)(x + 5)
• FR: Développe et simplifie : (x + 3)(x + 5)
• Choices: A) x² + 8x + 15 B) x² + 15x + 8 C) x² + 8x + 8 D) 2x² + 8x + 15
• Hint: Use FOIL: First, Outside, Inside, Last. For (x + 2)(x + 4): x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • First: x × x = x².
  • Outside + Inside: x × 5 + 3 × x = 5x + 3x = 8x.
  • Last: 3 × 5 = 15. Result: x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Linear Inequalities

• EN: Solve the inequality: 2x + 3 < 11
• FR: Résous l'inégalité : 2x + 3 < 11
• Choices: A) x < 3 B) x < 4 C) x < 5 D) x > 4
• Hint: Solve like an equation but keep the inequality sign. For 3x − 1 < 8: add 1 to get 3x < 9, divide by 3 to get x < 3.
• Steps:
  • Subtract 3 from both sides: 2x < 8.
  • Divide both sides by 2: x < 4.
  • The solution is x < 4.
• 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 est de 5 cm et l'hypoténuse est de 13 cm. Combien vaut sin(θ)?
• Choices: A) 5/12 B) 12/13 C) 5/13 D) 13/5
• Hint: SOH means sin = opposite ÷ hypotenuse. For opposite = 3 and hypotenuse = 5: sin = 3/5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 5 ÷ 13.
  • sin(θ) = 5/13.
• Answer: 5/13

[Medium] Graphing Lines

• EN: Which point lies on the line y = 2x + 1?
• FR: Quel point se trouve sur la droite y = 2x + 1?
• Choices: A) (1, 4) B) (2, 5) C) (3, 8) D) (4, 7)
• Hint: Substitute the x-value into the equation and check if you get the y-value. For y = 3x − 1 and point (2, 5): 3(2) − 1 = 5. Yes, it lies on the line.
• Steps:
  • Test (3, 8): y = 2(3) + 1 = 6 + 1 = 7 ≠ 8. No.
  • Test (2, 5): y = 2(2) + 1 = 4 + 1 = 5 ✓.
  • The point (2, 5) is on the line.
• Answer: (2, 5)

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What is the angle θ to the nearest degree? (Use cos θ = 0.8 → θ ≈ 37°)
• FR: Dans un triangle rectangle, le côté adjacent est de 8 cm et l'hypoténuse est de 10 cm. Quel est l'angle θ au degré près? (Utilise cos θ = 0,8 → θ ≈ 37°)
• Choices: A) 30° B) 37° C) 45° D) 53°
• Hint: CAH means cos = adjacent ÷ hypotenuse. Then use the inverse cosine (cos⁻¹) to find the angle. For cos = 0.5, the angle is 60°.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 8 ÷ 10 = 0.8.
  • cos⁻¹(0.8) ≈ 37°.
  • The angle θ is approximately 37°.
• Answer: 37°

[Hard] Systems of Equations — Substitution

• EN: Solve the system: y = 2x − 1 and y = x + 3. What is the value of x?
• FR: Résous le système : y = 2x − 1 et y = x + 3. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Since both expressions equal y, set them equal to each other. For y = 3x and y = x + 6: 3x = x + 6 → 2x = 6 → x = 3.
• Steps:
  • Set the two expressions equal: 2x − 1 = x + 3.
  • Subtract x from both sides: x − 1 = 3.
  • Add 1: x = 4.
• Answer: x = 4

[Easy] Factoring Quadratics

• EN: Factor: x² + 7x + 12
• FR: Factorise : x² + 7x + 12
• Choices: A) (x + 3)(x + 4) B) (x + 2)(x + 6) C) (x + 1)(x + 12) D) (x + 4)(x + 5)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient. For x² + 5x + 6: numbers are 2 and 3 (2×3=6, 2+3=5), giving (x+2)(x+3).
• Steps:
  • Find two numbers that multiply to 12 and add to 7.
  • 3 × 4 = 12 and 3 + 4 = 7.
  • The factored form is (x + 3)(x + 4).
• Answer: (x + 3)(x + 4)

[Easy] Trigonometry

• EN: In a right triangle with an angle of 30°, the hypotenuse is 20 cm. What is the length of the opposite side? (Use sin 30° = 0.5)
• FR: Dans un triangle rectangle avec un angle de 30°, l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé? (Utilise sin 30° = 0,5)
• Choices: A) 5 cm B) 8 cm C) 10 cm D) 14 cm
• Hint: sin = opposite ÷ hypotenuse, so opposite = sin × hypotenuse. For sin 45° ≈ 0.707 with hypotenuse 10: opposite ≈ 7.07.
• Steps:
  • sin(30°) = opposite ÷ 20.
  • Opposite = 0.5 × 20 = 10.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Easy] Systems of Equations

• EN: Solve the system: x + y = 10 and x − y = 4. What is x?
• FR: Résous le système : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the two equations together to eliminate y. For x + y = 8 and x − y = 2: adding gives 2x = 10, so x = 5.
• Steps:
  • Add the equations: (x + y) + (x − y) = 10 + 4 → 2x = 14.
  • x = 7.
  • The value of x is 7.
• Answer: x = 7

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 5 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 392.5 cm³ B) 471 cm³ C) 785 cm³ D) 1570 cm³
• Hint: Volume of a cylinder = π × r² × h. For r = 3 and h = 5: V = 3.14 × 9 × 5 = 141.3 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 5² × 10.
  • 5² = 25; 3.14 × 25 = 78.5.
  • 78.5 × 10 = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Complete the square to find the vertex of y = x² − 6x + 5. What is the vertex?
• FR: Complète le carré pour trouver le sommet de y = x² − 6x + 5. Quel est le sommet?
• Choices: A) (3, −4) B) (−3, −4) C) (3, 4) D) (6, 5)
• Hint: For y = x² − 4x + 7: take half of −4 (= −2), square it (= 4). Rewrite as y = (x−2)² + 3. Vertex is (2, 3).
• Steps:
  • y = x² − 6x + 5; half of −6 is −3, (−3)² = 9.
  • y = (x − 3)² − 9 + 5 = (x − 3)² − 4.
  • Vertex is (3, −4).
• Answer: (3, −4)

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 21.98 cm B) 43.96 cm C) 87.92 cm D) 153.86 cm
• Hint: Circumference = π × diameter. For a circle with diameter 10: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14.
  • 3.14 × 14 = 43.96.
  • The circumference is 43.96 cm.
• Answer: 43.96 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = −2 and x = −3 D) x = 3 and x = 4
• Hint: First try factoring: find two numbers that multiply to 6 and add to −5. For x² − 7x + 12, those numbers are −3 and −4, giving (x−3)(x−4), so x = 3 or 4.
• Steps:
  • Factor: (x − 2)(x − 3) = 0.
  • Set each factor to zero: x − 2 = 0 or x − 3 = 0.
  • x = 2 and x = 3.
• Answer: x = 2 and x = 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 9 cm. What is the lateral surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 9 cm. Quelle est l'aire latérale? (Utilise π ≈ 3,14)
• Choices: A) 78.5 cm² B) 100.5 cm² C) 113.04 cm² D) 150.72 cm²
• Hint: Lateral surface area of a cone = π × r × slant height. For r = 3, slant = 7: 3.14 × 3 × 7 = 65.94 cm².
• Steps:
  • Lateral SA = π × r × l = 3.14 × 4 × 9.
  • 3.14 × 4 = 12.56; 12.56 × 9 = 113.04.
  • The lateral surface area is 113.04 cm².
• Answer: 113.04 cm²

[Hard] Systems with Quadratics

• EN: Find the x-values where y = x² and y = 2x + 3 intersect.
• FR: Trouve les valeurs de x où y = x² et y = 2x + 3 se croisent.
• Choices: A) x = −1 and x = 3 B) x = 1 and x = 3 C) x = −3 and x = 1 D) x = −1 and x = −3
• Hint: Set the two equations equal: x² = 2x + 3, then rearrange to standard form and factor. For x² = x + 6: x² − x − 6 = 0 → (x−3)(x+2) = 0.
• Steps:
  • Set equal: x² = 2x + 3 → x² − 2x − 3 = 0.
  • Factor: (x − 3)(x + 1) = 0.
  • x = 3 and x = −1.
• Answer: x = −1 and x = 3

[Hard] Circle Geometry — Inscribed Angle

• EN: An inscribed angle in a circle intercepts an arc of 110°. What is the measure of the inscribed angle?
• FR: Un angle inscrit dans un cercle intercepte un arc de 110°. Quelle est la mesure de l'angle inscrit?
• Choices: A) 40° B) 55° C) 110° D) 220°
• Hint: The inscribed angle theorem states that an inscribed angle is always half the intercepted arc. For an arc of 80°, the inscribed angle is 40°.
• Steps:
  • The inscribed angle = (intercepted arc) ÷ 2.
  • 110° ÷ 2 = 55°.
  • The inscribed angle is 55°.
• Answer: 55°

[Easy] Evaluating Exponential Functions

• EN: If f(x) = 2ˣ, what is f(4)?
• FR: Si f(x) = 2ˣ, combien vaut f(4)?
• Choices: A) 8 B) 12 C) 16 D) 32
• Hint: For f(x) = 3ˣ, f(3) = 3 × 3 × 3 = 27. Just multiply the base by itself the number of times shown by the exponent.
• Steps:
  • f(4) = 2⁴.
  • 2⁴ = 2 × 2 × 2 × 2 = 16.
  • f(4) = 16.
• Answer: 16

[Easy] Logarithms Introduction

• EN: What is log₂(32)?
• FR: Combien vaut log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log_b(x) asks "b to what power equals x?" For log₃(27): 3³ = 27, so log₃(27) = 3.
• Steps:
  • Ask: 2 to what power equals 32?
  • 2⁵ = 32.
  • log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequences

• EN: The first term of an arithmetic sequence is 7 and the common difference is 4. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 7 et la raison est 4. Quel est le 5e terme?
• Choices: A) 19 B) 23 C) 27 D) 31
• Hint: The nth term formula is: aₙ = a₁ + (n − 1)d. For a₁ = 3 and d = 5, the 4th term is 3 + (3)(5) = 18.
• Steps:
  • a₅ = 7 + (5 − 1) × 4.
  • a₅ = 7 + 4 × 4 = 7 + 16.
  • a₅ = 23.
• Answer: 23

[Easy] Compound Interest

• EN: $1000 is invested at 5% annual interest, compounded annually. What is the amount after 2 years?
• FR: 1000 $ sont investis à un taux d'intérêt annuel de 5 %, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1105.00
• Hint: Use A = P(1 + r)ⁿ. For P = $500, r = 0.10, n = 2: A = 500(1.10)² = 500 × 1.21 = $605.
• Steps:
  • A = 1000 × (1 + 0.05)².
  • (1.05)² = 1.1025.
  • A = 1000 × 1.1025 = $1102.50.
• Answer: $1102.50

[Medium] Quadratic Functions — Vertex and Zeros

• EN: For the function f(x) = −x² + 4x − 3, find the x-intercepts.
• FR: Pour la fonction f(x) = −x² + 4x − 3, trouve les zéros de la fonction.
• Choices: A) x = 1 and x = 3 B) x = −1 and x = 3 C) x = 2 and x = 4 D) x = 1 and x = 4
• Hint: Set f(x) = 0 and factor. Factor out −1 first if needed. For −x² + 2x + 3 = 0: multiply by −1 to get x² − 2x − 3 = 0, then factor.
• Steps:
  • Set −x² + 4x − 3 = 0; multiply by −1: x² − 4x + 3 = 0.
  • Factor: (x − 1)(x − 3) = 0.
  • x = 1 and x = 3.
• Answer: x = 1 and x = 3

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ + tan²θ − sec²θ + 1
• FR: Simplifie : sin²θ + cos²θ + tan²θ − sec²θ + 1
• Choices: A) 0 B) 1 C) 2 D) −1
• Hint: Recall the Pythagorean identities: sin²θ + cos²θ = 1 and sec²θ − tan²θ = 1. Apply them in sequence.
• Steps:
  • sin²θ + cos²θ = 1 (identity 1).
  • tan²θ − sec²θ = −1 (since sec²θ = tan²θ + 1, so tan²θ − sec²θ = −1).
  • 1 + (−1) + 1 = 1.
• Answer: 1

[Medium] Geometric Sequences

• EN: A geometric sequence has a first term of 3 and a common ratio of 2. What is the sum of the first 5 terms?
• FR: Une suite géométrique a un premier terme de 3 et une raison de 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 63 B) 93 C) 96 D) 99
• Hint: The sum of a geometric series is Sₙ = a(rⁿ − 1)/(r − 1). For a = 2, r = 3, n = 4: S₄ = 2(81−1)/(3−1) = 2(80)/2 = 80.
• Steps:
  • S₅ = 3 × (2⁵ − 1)/(2 − 1).
  • 2⁵ = 32; 32 − 1 = 31; 31 ÷ 1 = 31.
  • S₅ = 3 × 31 = 93.
• Answer: 93

[Medium] Financial Math — Annuity

• EN: You deposit $200 at the end of each year for 3 years at 6% annual interest. What is the total future value? (Use: FV = 200 × [(1.06³ − 1)/0.06], where 1.06³ ≈ 1.191)
• FR: Tu déposes 200 $ à la fin de chaque année pendant 3 ans à un taux d'intérêt annuel de 6 %. Quelle est la valeur future totale? (Utilise : FV = 200 × [(1,06³ − 1)/0,06], où 1,06³ ≈ 1,191)
• Choices: A) $600.00 B) $618.00 C) $637.00 D) $651.20
• Hint: For annuity future value, use FV = PMT × [(1+r)ⁿ − 1]/r. Carefully substitute the values step by step.
• Steps:
  • (1.06³ − 1)/0.06 = (1.191 − 1)/0.06 = 0.191/0.06 ≈ 3.185.
  • FV = 200 × 3.185 = $637.00.
  • The future value is $637.00.
• Answer: $637.00

[Hard] Logarithm Properties

• EN: Solve for x: log₃(x) + log₃(x − 6) = 3
• FR: Résous pour x : log₃(x) + log₃(x − 6) = 3
• Choices: A) x = 7 B) x = 9 C) x = 12 D) x = 27
• Hint: Use the log product rule: logₐ(m) + logₐ(n) = logₐ(mn). Then convert from logarithmic to exponential form. For log₂(a) + log₂(b) = 4: ab = 2⁴ = 16.
• Steps:
  • Combine: log₃[x(x − 6)] = 3, so x(x − 6) = 3³ = 27.
  • x² − 6x − 27 = 0 → (x − 9)(x + 3) = 0.
  • x = 9 (reject x = −3, as log of negative is undefined).
• Answer: x = 9

[Hard] Sinusoidal Function

• EN: A sinusoidal function has amplitude 4, period 2π, and is shifted up by 3. Which function matches this description?
• FR: Une fonction sinusoïdale a une amplitude de 4, une période de 2π et est décalée vers le haut de 3. Quelle fonction correspond à cette description?
• Choices: A) y = 3 sin(x) + 4 B) y = 4 sin(x) + 3 C) y = 4 cos(2x) + 3 D) y = 2 sin(4x) + 3
• Hint: The general form is y = A sin(Bx) + D where A = amplitude, period = 2π/B, D = vertical shift. For amplitude 2, period π, shift 5: B = 2π/π = 2, giving y = 2 sin(2x) + 5.
• Steps:
  • Amplitude = 4 → A = 4.
  • Period = 2π → B = 2π/2π = 1.
  • Vertical shift = 3 → D = 3. Function: y = 4 sin(x) + 3.
• Answer: y = 4 sin(x) + 3

[Easy] Polynomial Functions

• EN: What is the degree and leading coefficient of the polynomial f(x) = −3x⁴ + 5x² − x + 7?
• FR: Quel est le degré et le coefficient dominant du polynôme f(x) = −3x⁴ + 5x² − x + 7?
• Choices: A) degree 2, leading coefficient 5 B) degree 4, leading coefficient −3 C) degree 4, leading coefficient 3 D) degree 3, leading coefficient −1
• Hint: The degree is the highest exponent, and the leading coefficient is the number multiplying the highest-degree term. For 7x³ − 2x + 1: degree = 3, leading coefficient = 7.
• Steps:
  • The highest power of x is 4 (the term −3x⁴).
  • The leading coefficient is −3 (the number in front of x⁴).
  • Degree = 4, leading coefficient = −3.
• Answer: degree 4, leading coefficient −3

[Easy] Permutations

• EN: How many ways can 5 different books be arranged in a row on a shelf?
• FR: De combien de façons peut-on ranger 5 livres différents en rangée sur une étagère?
• Choices: A) 25 B) 60 C) 120 D) 720
• Hint: For n distinct objects in a row, the number of arrangements is n! For 4 objects: 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • 5 × 4 = 20; 20 × 3 = 60; 60 × 2 = 120; 120 × 1 = 120.
  • There are 120 arrangements.
• Answer: 120

[Easy] Derivatives — Power Rule

• EN: Find the derivative of f(x) = 3x² + 4x − 7.
• FR: Trouve la dérivée de f(x) = 3x² + 4x − 7.
• Choices: A) 3x + 4 B) 6x + 4 C) 6x − 7 D) 6x² + 4
• Hint: Power rule: the derivative of axⁿ is n × axⁿ⁻¹. For 5x³ + 2x: derivative is 15x² + 2.
• Steps:
  • Derivative of 3x²: 2 × 3x = 6x.
  • Derivative of 4x: 4.
  • Derivative of −7: 0. So f'(x) = 6x + 4.
• Answer: 6x + 4

[Easy] Combinations

• EN: How many ways can a committee of 3 students be chosen from a group of 6 students?
• FR: De combien de façons peut-on choisir un comité de 3 élèves parmi un groupe de 6 élèves?
• Choices: A) 18 B) 20 C) 24 D) 36
• Hint: Use C(n, r) = n! / [r!(n−r)!]. For C(5, 2): 5!/(2! × 3!) = (5×4)/(2×1) = 10.
• Steps:
  • C(6, 3) = 6! / (3! × 3!) = (6 × 5 × 4) / (3 × 2 × 1).
  • Numerator: 6 × 5 × 4 = 120. Denominator: 6.
  • 120 ÷ 6 = 20 ways.
• Answer: 20

[Medium] Rational Functions

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

[Medium] Vectors

• EN: Vector a⃗ = (3, −1) and vector b⃗ = (−2, 4). What is a⃗ + b⃗?
• FR: Le vecteur a⃗ = (3, −1) et le vecteur b⃗ = (−2, 4). Combien vaut a⃗ + b⃗?
• Choices: A) (1, 2) B) (1, 3) C) (5, −5) D) (−1, 3)
• Hint: To add vectors, add the corresponding components. For (4, 2) + (−1, 3): x-components 4 + (−1) = 3; y-components 2 + 3 = 5. Result: (3, 5).
• Steps:
  • x-component: 3 + (−2) = 1.
  • y-component: (−1) + 4 = 3.
  • a⃗ + b⃗ = (1, 3).
• Answer: (1, 3)

[Medium] Probability Distributions

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

[Medium] Derivative — Rate of Change

• EN: A ball's position is given by s(t) = 4t² − 3t + 1. What is the instantaneous velocity (derivative) at t = 2?
• FR: La position d'une balle est donnée par s(t) = 4t² − 3t + 1. Quelle est la vitesse instantanée (dérivée) à t = 2?
• Choices: A) 9 B) 11 C) 13 D) 16
• Hint: First find s'(t) using the power rule, then substitute the given t-value. For s(t) = 3t² + 2, s'(t) = 6t; at t = 3, s'(3) = 18.
• Steps:
  • s'(t) = 8t − 3.
  • At t = 2: s'(2) = 8(2) − 3 = 16 − 3 = 13.
  • The instantaneous velocity is 13.
• Answer: 13

[Hard] Binomial Theorem

• EN: Using the binomial theorem, what is the coefficient of x² in the expansion of (x + 3)⁴?
• FR: En utilisant le théorème binomial, quel est le coefficient de x² dans le développement de (x + 3)⁴?
• Choices: A) 18 B) 54 C) 81 D) 108
• Hint: The term containing xᵏ in (x + a)ⁿ is C(n, k) × xᵏ × aⁿ⁻ᵏ. For x² in (x + 2)⁴: C(4,2) × x² × 2² = 6 × 4 × x² = 24x².
• Steps:
  • The x² term: C(4, 2) × x² × 3⁴⁻².
  • C(4, 2) = 6 and 3² = 9.
  • Coefficient = 6 × 9 = 54.
• Answer: 54

[Hard] Derivatives — Optimization

• EN: A rectangular field is to be enclosed with 60 m of fencing on three sides (the fourth side is a wall). What width w maximizes the area, and what is that maximum area?
• FR: Un champ rectangulaire doit être entouré de 60 m de clôture sur trois côtés (le quatrième côté est un mur). Quelle largeur w maximise l'aire, et quelle est cette aire maximale?
• Choices: A) w = 15 m, Area = 450 m² B) w = 20 m, Area = 400 m² C) w = 15 m, Area = 225 m² D) w = 30 m, Area = 450 m²
• Hint: With two widths (w) and one length (l): 2w + l = total fencing. Express l in terms of w, write Area = l × w, then take the derivative and set it equal to zero.
• Steps:
  • Constraint: 2w + l = 60 → l = 60 − 2w.
  • Area A = w × l = w(60 − 2w) = 60w − 2w².
  • A'(w) = 60 − 4w = 0 → w = 15 m; A = 15 × (60 − 30) = 15 × 30 = 450 m².
• Answer: w = 15 m, Area = 450 m²