Daily Math — 2026-10-11

[Easy] Counting to 20

• EN: There are 7 apples on the table and 5 more apples in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres pommes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add, count on from the bigger number. Try 6 + 4: start at 6 and count up 4 more.
• Steps:
  • Start at 7.
  • Count up 5 more: 8, 9, 10, 11, 12.
  • So there are 12 apples in all.
• Answer: 12

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes next: 2, 4, 6, 8, ___?
• FR: Compte par bonds de 2. Quel nombre vient ensuite: 2, 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Skip counting by 2s means you add 2 each time. Try 10, 12, 14 — see the pattern?
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand: 14 ou 9?
• Choices: A) 9 B) 14 C) Both are equal D) Neither
• Hint: Think about which number you reach later when counting. 5 comes after 3, so 5 is greater.
• Steps:
  • Count up: 9 comes before 14.
  • 14 is farther along, so it is greater.
  • So 14 is the greater number.
• Answer: 14

[Easy] Coin Recognition

• EN: Maya has one dime. How many cents does she have?
• FR: Maya a une pièce de dix cents. Combien de cents a-t-elle?
• Choices: A) 1 cent B) 5 cents C) 10 cents D) 25 cents
• Hint: A nickel is worth 5 cents. A dime is worth more than a nickel.
• Steps:
  • A penny = 1 cent, a nickel = 5 cents, a dime = 10 cents.
  • Maya has one dime.
  • So she has 10 cents.
• Answer: 10 cents

[Medium] Subtraction Within 20

• EN: There are 15 hockey pucks in a bag. A player uses 6 of them. How many pucks are left?
• FR: Il y a 15 rondelles de hockey dans un sac. Un joueur en utilise 6. Combien de rondelles reste-t-il?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: To subtract, count back from the big number. Try 12 − 4: start at 12, count back 4.
• Steps:
  • Start at 15.
  • Count back 6: 14, 13, 12, 11, 10, 9.
  • So 9 pucks are left.
• Answer: 9

[Medium] Skip Counting by 5s

• EN: Liam counts his nickels by 5s: 5, 10, 15, ___. What number comes next?
• FR: Liam compte ses pièces de 5 cents par bonds de 5: 5, 10, 15, ___. Quel nombre vient ensuite?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: Skip counting by 5s means add 5 each time. Try 20, 25, 30.
• Steps:
  • The pattern adds 5 each time.
  • 15 + 5 = 20.
  • So the next number is 20.
• Answer: 20

[Medium] Addition Within 20

• EN: Priya has 8 stickers and her friend gives her 7 more. How many stickers does Priya have now?
• FR: Priya a 8 autocollants et son amie lui en donne 7 autres. Combien d'autocollants Priya a-t-elle maintenant?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Break one number apart. For 6 + 7, think 6 + 4 + 3 = 13.
• Steps:
  • Break 7 into 2 + 5.
  • 8 + 2 = 10, then 10 + 5 = 15.
  • So Priya has 15 stickers.
• Answer: 15

[Medium] Skip Counting by 10s

• EN: Skip count by 10s. What number comes next: 10, 20, 30, ___?
• FR: Compte par bonds de 10. Quel nombre vient ensuite: 10, 20, 30, ___?
• Choices: A) 33 B) 35 C) 38 D) 40
• Hint: Add 10 each time. Try 50, 60, 70 — just change the tens digit.
• Steps:
  • The pattern adds 10 each time.
  • 30 + 10 = 40.
  • So the next number is 40.
• Answer: 40

[Hard] Counting Coins

• EN: Omar has 1 dime and 2 nickels. How many cents does he have in all?
• FR: Omar a 1 pièce de dix cents et 2 pièces de cinq cents. Combien de cents a-t-il en tout?
• Choices: A) 15 cents B) 17 cents C) 20 cents D) 22 cents
• Hint: Find the value of each coin, then add them all together. A dime = 10¢, a nickel = 5¢.
• Steps:
  • 1 dime = 10 cents.
  • 2 nickels = 5 + 5 = 10 cents.
  • 10 + 10 = 20 cents total.
• Answer: 20 cents

[Hard] Addition and Subtraction Together

• EN: There are 12 children on the playground. 4 go inside, then 3 more come out. How many children are on the playground now?
• FR: Il y a 12 enfants dans la cour de récréation. 4 entrent à l'intérieur, puis 3 autres sortent. Combien d'enfants sont dans la cour maintenant?
• Choices: A) 9 B) 10 C) 11 D) 13
• Hint: Do one step at a time. First subtract, then add. Try 10 − 3 + 2 = 9.
• Steps:
  • Start with 12 children.
  • 12 − 4 = 8 children after some go inside.
  • 8 + 3 = 11 children after more come out.
• Answer: 11

[Easy] Addition Within 100

• EN: There are 34 red crayons and 25 blue crayons in a box. How many crayons are there in all?
• FR: Il y a 34 crayons rouges et 25 crayons bleus dans une boîte. Combien y a-t-il de crayons en tout?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: Add the tens first, then the ones. For 21 + 36: 20 + 30 = 50, then 1 + 6 = 7, so 57.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59 crayons in all.
• Answer: 59

[Easy] Telling Time — Hour

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

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A pen is 9 cm long. How much longer is the pencil than the pen?
• FR: Un crayon mesure 14 cm de long. Un stylo mesure 9 cm de long. De combien le crayon est-il plus long que le stylo?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find how much longer, subtract the shorter length from the longer one. Try 18 − 11 = 7.
• Steps:
  • Subtract the shorter from the longer: 14 − 9.
  • 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Simple Patterns

• EN: What shape comes next in this pattern: circle, square, circle, square, ___?
• FR: Quelle forme vient ensuite dans ce motif: cercle, carré, cercle, carré, ___?
• Choices: A) triangle B) circle C) rectangle D) square
• Hint: Look at what repeats. In red, blue, red, blue — the next colour is red.
• Steps:
  • The pattern repeats: circle, square, circle, square.
  • After square comes circle again.
  • So the next shape is circle.
• Answer: circle

[Medium] Subtraction Within 100

• EN: A farmer has 72 eggs. She sells 38 of them at the market. How many eggs does she have left?
• FR: Une fermière a 72 œufs. Elle en vend 38 au marché. Combien d'œufs lui reste-t-il?
• Choices: A) 32 B) 33 C) 34 D) 36
• Hint: Subtract the ones first, then the tens. For 65 − 27: regroup if needed, 5 − 7 needs borrowing.
• Steps:
  • 72 − 38: regroup the tens. 70 becomes 60 and 2 becomes 12.
  • 12 − 8 = 4 ones; 60 − 30 = 30 tens.
  • 30 + 4 = 34 eggs left.
• Answer: 34

[Medium] Telling Time — Half Hour

• EN: The long hand on the clock points to the 6 and the short hand is between the 7 and 8. What time is it?
• FR: La grande aiguille de l'horloge pointe vers le 6 et la petite aiguille est entre le 7 et le 8. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the long hand points to 6, it is half past the hour. The short hand tells which hour just passed.
• Steps:
  • The long hand on 6 means 30 minutes past.
  • The short hand has passed 7 but not yet reached 8, so the hour is 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Counting Coins to $1

• EN: Sophie has 3 quarters. How many cents does she have in all?
• FR: Sophie a 3 pièces de 25 cents. Combien de cents a-t-elle en tout?
• Choices: A) 55 cents B) 65 cents C) 70 cents D) 75 cents
• Hint: A quarter is worth 25 cents. Add 25 for each quarter you have. 25 + 25 = 50.
• Steps:
  • 1 quarter = 25 cents.
  • 25 + 25 = 50 cents for 2 quarters.
  • 50 + 25 = 75 cents for 3 quarters.
• Answer: 75 cents

[Medium] Addition With Regrouping

• EN: A Tim Hortons sold 46 muffins in the morning and 37 muffins in the afternoon. How many muffins were sold in total?
• FR: Un Tim Hortons a vendu 46 muffins le matin et 37 muffins l'après-midi. Combien de muffins ont été vendus en tout?
• Choices: A) 81 B) 82 C) 83 D) 84
• Hint: Add the ones first: if the sum is 10 or more, carry the ten. Try 28 + 45: 8 + 5 = 13, write 3 carry 1.
• Steps:
  • Add the ones: 6 + 7 = 13. Write 3, carry 1.
  • Add the tens: 4 + 3 + 1 (carried) = 8.
  • Total is 83 muffins.
• Answer: 83

[Hard] Multi-Step Coins

• EN: Ethan has 2 quarters, 1 dime, and 3 nickels. How much money does he have in total?
• FR: Ethan a 2 pièces de 25 cents, 1 pièce de 10 cents et 3 pièces de 5 cents. Quelle est la valeur totale de son argent?
• Choices: A) 75 cents B) 80 cents C) 85 cents D) 90 cents
• Hint: Find the value of each type of coin separately, then add all three amounts together.
• Steps:
  • 2 quarters = 25 + 25 = 50 cents.
  • 1 dime = 10 cents. 3 nickels = 15 cents.
  • 50 + 10 + 15 = 75 cents total.
• Answer: 75 cents

[Hard] Measurement Word Problem

• EN: A garden has one row that is 48 cm long and another row that is 36 cm long. How long are both rows together?
• FR: Un jardin a une rangée de 48 cm de long et une autre rangée de 36 cm de long. Quelle est la longueur totale des deux rangées?
• Choices: A) 74 cm B) 82 cm C) 84 cm D) 86 cm
• Hint: Add the ones, regroup if needed, then add the tens. Try 29 + 43 = 72.
• Steps:
  • Add the ones: 8 + 6 = 14. Write 4, carry 1.
  • Add the tens: 4 + 3 + 1 (carried) = 8.
  • Total is 84 cm.
• Answer: 84 cm

[Easy] Multiplication Table of 5

• EN: What is 5 × 6?
• FR: Combien fait 5 × 6?
• Choices: A) 25 B) 28 C) 30 D) 35
• Hint: Skip count by 5s six times: 5, 10, 15, 20, 25, 30. Try 5 × 4 = 20.
• Steps:
  • Count by 5s six times: 5, 10, 15, 20, 25, 30.
  • So 5 × 6 = 30.
• Answer: 30

[Easy] Basic Division

• EN: 12 cookies are shared equally among 3 children. How many cookies does each child get?
• FR: 12 biscuits sont partagés également entre 3 enfants. Combien de biscuits chaque enfant reçoit-il?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Division is sharing equally. Try 10 ÷ 2: split 10 into 2 equal groups to get 5.
• Steps:
  • 12 ÷ 3 = ?
  • 3 × 4 = 12, so 12 ÷ 3 = 4.
  • Each child gets 4 cookies.
• Answer: 4

[Easy] Fractions — One Half

• EN: A pizza is cut into 4 equal slices. Mia eats 2 slices. What fraction of the pizza did Mia eat?
• FR: Une pizza est coupée en 4 tranches égales. Mia mange 2 tranches. Quelle fraction de la pizza Mia a-t-elle mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 3/4
• Hint: A fraction is part over whole. If you eat 1 out of 2 equal pieces, that is 1/2.
• Steps:
  • Mia ate 2 slices out of 4 equal slices.
  • 2/4 = 1/2.
  • Mia ate 1/2 of the pizza.
• Answer: 1/2

[Easy] Perimeter of a Rectangle

• EN: A rectangle has a length of 6 cm and a width of 3 cm. What is its perimeter?
• FR: Un rectangle a une longueur de 6 cm et une largeur de 3 cm. Quel est son périmètre?
• Choices: A) 9 cm B) 14 cm C) 16 cm D) 18 cm
• Hint: Perimeter = add all sides. A rectangle has 2 long sides and 2 short sides. Try length 5, width 2: 5+5+2+2=14.
• Steps:
  • Add all four sides: 6 + 6 + 3 + 3.
  • 6 + 6 = 12 and 3 + 3 = 6.
  • 12 + 6 = 18 cm.
• Answer: 18 cm

[Medium] Missing Factor Equation

• EN: What number goes in the blank? ___ × 5 = 35
• FR: Quel nombre va dans l'espace vide? ___ × 5 = 35
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Think about what you multiply by 5 to get the answer. Try __ × 5 = 20: the answer is 4.
• Steps:
  • Ask: what times 5 equals 35?
  • Count by 5s: 5, 10, 15, 20, 25, 30, 35 — that is 7 steps.
  • So 7 × 5 = 35.
• Answer: 7

[Medium] Multiplication Table of 3

• EN: A hockey team has 4 lines. Each line has 3 players. How many players are there in all?
• FR: Une équipe de hockey a 4 lignes. Chaque ligne a 3 joueurs. Combien y a-t-il de joueurs en tout?
• Choices: A) 7 B) 10 C) 12 D) 16
• Hint: Multiply the number of groups by the size of each group. Try 5 groups of 3: 5 × 3 = 15.
• Steps:
  • 4 lines × 3 players each.
  • 4 × 3 = 12.
  • There are 12 players in all.
• Answer: 12

[Medium] Reading a Simple Graph

• EN: A bar graph shows that 8 students like hockey, 5 like soccer, and 3 like basketball. How many more students like hockey than basketball?
• FR: Un graphique à barres montre que 8 élèves aiment le hockey, 5 aiment le soccer et 3 aiment le basketball. Combien d'élèves de plus aiment le hockey 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 one. Try 9 − 4 = 5.
• Steps:
  • Hockey: 8 students. Basketball: 3 students.
  • 8 − 3 = 5.
  • Five more students like hockey than basketball.
• Answer: 5

[Medium] Fractions — One Quarter

• EN: There are 8 stickers. Aiden gives away 1/4 of them. How many stickers does Aiden give away?
• FR: Il y a 8 autocollants. Aiden en donne 1/4. Combien d'autocollants Aiden donne-t-il?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: To find 1/4 of a number, divide it by 4. Try 1/4 of 12: 12 ÷ 4 = 3.
• Steps:
  • 1/4 of 8 means divide 8 into 4 equal groups.
  • 8 ÷ 4 = 2.
  • Aiden gives away 2 stickers.
• Answer: 2

[Hard] Multi-Step Multiplication and Addition

• EN: A store sells apples in bags of 4. If Carla buys 3 bags and then picks up 5 loose apples, how many apples does she have in total?
• FR: Un magasin vend des pommes en sacs de 4. Si Carla achète 3 sacs et prend 5 pommes en vrac, combien de pommes a-t-elle en tout?
• Choices: A) 12 B) 15 C) 17 D) 20
• Hint: Multiply to find the total in the bags, then add the extra ones. Try 2 bags of 5 + 3 loose = 13.
• Steps:
  • 3 bags × 4 apples = 12 apples in bags.
  • Add 5 loose apples: 12 + 5 = 17.
  • Carla has 17 apples in total.
• Answer: 17

[Hard] Perimeter Word Problem

• EN: A school garden is a square with a side length of 9 m. What is the perimeter of the garden?
• FR: Le jardin scolaire est un carré avec un côté de 9 m. Quel est le périmètre du jardin?
• Choices: A) 27 m B) 32 m C) 36 m D) 40 m
• Hint: A square has 4 equal sides. Add all 4 sides or multiply the side length by 4. Try side 7: 7 × 4 = 28.
• Steps:
  • A square has 4 equal sides, each 9 m.
  • 4 × 9 = 36.
  • The perimeter is 36 m.
• Answer: 36 m

[Easy] Multiplication Facts to 9×9

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: You can use a nearby fact. For 6 × 8 = 48, then add one more group of 8: 48 + 8 = 56.
• Steps:
  • 7 × 8 = ?
  • 7 × 8: think 7 × 7 = 49, then add 7 more: 49 + 7 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 4.73, what digit is in the tenths place?
• FR: Dans le nombre 4,73, quel chiffre est dans la position des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 8
• Hint: After the decimal point, the first digit is tenths, the second is hundredths. In 3.25, the tenths digit is 2.
• Steps:
  • 4.73: the digit before the decimal is 4 (ones).
  • The first digit after the decimal is 7 (tenths).
  • The digit in the tenths place is 7.
• Answer: 7

[Easy] Area of a Rectangle

• EN: A classroom mat is 5 m long and 3 m wide. What is its area?
• FR: Un tapis de classe mesure 5 m de long et 3 m de large. Quelle est son aire?
• Choices: A) 8 m² B) 12 m² C) 15 m² D) 16 m²
• Hint: Area = length × width. For a mat 4 m long and 2 m wide: 4 × 2 = 8 m².
• Steps:
  • Area = length × width.
  • 5 × 3 = 15.
  • The area is 15 m².
• Answer: 15 m²

[Easy] Missing Factor Division

• EN: What number goes in the blank? 36 ÷ ___ = 9
• FR: Quel nombre va dans l'espace vide? 36 ÷ ___ = 9
• Choices: A) 3 B) 4 C) 6 D) 9
• Hint: Think multiplication: ___ × 9 = 36. Try ___ × 6 = 30: the answer is 5.
• Steps:
  • Rewrite as: ___ × 9 = 36.
  • 4 × 9 = 36.
  • So the missing number is 4.
• Answer: 4

[Medium] Long Division With Remainders

• EN: 47 ÷ 5 = ?
• FR: 47 ÷ 5 = ?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 9 remainder 3 D) 10 remainder 2
• Hint: Find how many times 5 goes into 47 without going over, then find what is left. Try 23 ÷ 4 = 5 remainder 3.
• Steps:
  • 5 × 9 = 45, and 5 × 10 = 50 (too big).
  • 47 − 45 = 2 remainder.
  • So 47 ÷ 5 = 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 2:15 p.m. and ends at 4:45 p.m. How long did the game last?
• FR: Un match de hockey commence à 14h15 et se termine à 16h45. Combien de temps dure le match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: Count from the start time to the end time in steps. From 3:10 to 5:40 is 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] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/3?
• FR: Quelle fraction est plus grande: 3/4 ou 2/3?
• Choices: A) 2/3 B) 3/4 C) They are equal D) Neither is greater
• Hint: Convert to a common denominator to compare. For 1/2 vs 1/3: use 6 as denominator — 3/6 vs 2/6, so 1/2 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] Table Word Problem

• EN: The table shows snack prices at a school fair. A cookie costs $0.75 and a juice costs $1.25. How much do 2 cookies and 1 juice cost in total?
• FR: Le tableau montre les prix des collations à une fête scolaire. Un biscuit coûte 0,75 $ et un jus coûte 1,25 $. Combien coûtent 2 biscuits et 1 jus en tout?
• Choices: A) $2.50 B) $2.75 C) $3.00 D) $3.25
• Hint: Multiply the price by the quantity, then add each item's total. Try 3 apples at $0.50 + 1 water at $1.00: $1.50 + $1.00 = $2.50.
• Steps:
  • 2 cookies: 2 × $0.75 = $1.50.
  • 1 juice: 1 × $1.25 = $1.25.
  • $1.50 + $1.25 = $2.75 total.
• Answer: $2.75

[Hard] Multi-Step Division and Multiplication

• EN: A teacher has 84 pencils to share equally among 6 classes. Each class then gives 5 pencils to the art room. How many pencils does each class have left?
• FR: Une enseignante a 84 crayons à partager également entre 6 classes. Chaque classe donne ensuite 5 crayons à la salle d'art. Combien de crayons chaque classe a-t-elle?
• Choices: A) 8 B) 9 C) 10 D) 14
• Hint: First divide the total by the number of classes, then subtract what is given away. Try 60 ÷ 6 = 10, then 10 − 3 = 7.
• Steps:
  • 84 ÷ 6 = 14 pencils per class.
  • Each class gives away 5: 14 − 5 = 9.
  • Each class has 9 pencils left.
• Answer: 9

[Hard] Decimal Addition Word Problem

• EN: Nadia bought a notebook for $3.45 and a pen for $1.80. She paid with a $10 bill. How much change did she receive?
• FR: Nadia a acheté un cahier pour 3,45 $ et un stylo pour 1,80 $. Elle a payé avec un billet de 10 $. Combien de monnaie a-t-elle reçu?
• Choices: A) $4.55 B) $4.75 C) $5.25 D) $5.75
• Hint: First add the costs, then subtract from $10. Try $2.30 + $1.15 = $3.45, then $10.00 − $3.45 = $6.55.
• Steps:
  • $3.45 + $1.80 = $5.25 total spent.
  • $10.00 − $5.25 = $4.75 change.
  • Nadia received $4.75 in change.
• Answer: $4.75

[Easy] Multi-Digit Multiplication

• EN: What is 36 × 4?
• FR: Combien fait 36 × 4?
• Choices: A) 124 B) 140 C) 144 D) 148
• Hint: Multiply each part separately. Try 25 × 4: 20 × 4 = 80 and 5 × 4 = 20, so 80 + 20 = 100.
• Steps:
  • 36 × 4: break into 30 × 4 and 6 × 4.
  • 30 × 4 = 120 and 6 × 4 = 24.
  • 120 + 24 = 144.
• Answer: 144

[Easy] Adding Fractions With Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien fait 2/7 + 3/7?
• Choices: A) 4/7 B) 5/7 C) 5/14 D) 6/7
• Hint: When denominators are the same, just add the numerators and keep the denominator. Try 1/5 + 2/5 = 3/5.
• Steps:
  • Same denominator (7), so add numerators: 2 + 3 = 5.
  • Keep the denominator: 5/7.
  • The answer is 5/7.
• Answer: 5/7

[Easy] Percentage Intro — 50%

• EN: What is 50% of 80?
• FR: Combien vaut 50% de 80?
• Choices: A) 20 B) 30 C) 40 D) 50
• Hint: 50% means half. Divide the number by 2. Try 50% of 60: 60 ÷ 2 = 30.
• Steps:
  • 50% = one half.
  • 80 ÷ 2 = 40.
  • 50% of 80 is 40.
• Answer: 40

[Easy] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 2 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 2 cm de haut. Quel est son volume?
• Choices: A) 20 cm³ B) 30 cm³ C) 40 cm³ D) 50 cm³
• Hint: Volume = length × width × height. Try 3 × 2 × 4 = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 2.
  • 5 × 4 = 20, then 20 × 2 = 40.
  • The volume is 40 cm³.
• Answer: 40 cm³

[Medium] Multi-Digit Division

• EN: What is 196 ÷ 4?
• FR: Combien fait 196 ÷ 4?
• Choices: A) 45 B) 47 C) 49 D) 52
• Hint: Divide step by step. Try 168 ÷ 4: 16 ÷ 4 = 4, bring down 8, 8 ÷ 4 = 2, so answer is 42.
• Steps:
  • 4 goes into 19 four times (4 × 4 = 16), remainder 3. Bring down 6 → 36.
  • 4 goes into 36 nine times (4 × 9 = 36), remainder 0.
  • 196 ÷ 4 = 49.
• Answer: 49

[Medium] Missing Factor Equation

• EN: What number goes in the blank? ___ × 18 = 108
• FR: Quel nombre va dans l'espace vide? ___ × 18 = 108
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Divide both sides to find the missing factor. Try ___ × 12 = 72: 72 ÷ 12 = 6.
• Steps:
  • ___ × 18 = 108, so ___ = 108 ÷ 18.
  • 18 × 6 = 108.
  • The missing number is 6.
• Answer: 6

[Medium] Decimal Operations

• EN: A snowfall of 12.6 cm fell on Monday and 9.45 cm fell on Tuesday. How much snow fell in total over both days?
• FR: Il est tombé 12,6 cm de neige lundi et 9,45 cm mardi. Quelle quantité de neige est tombée en tout sur les deux jours?
• Choices: A) 21.85 cm B) 22.05 cm C) 22.15 cm D) 23.05 cm
• Hint: Line up the decimal points and add. For 3.4 + 5.75: write as 3.40 + 5.75 = 9.15.
• Steps:
  • Write 12.6 as 12.60 to match decimal places.
  • 12.60 + 9.45: ones 2 + 9 = 11, carry 1; tens 1 + 1 + 0 = 2.
  • Wait — let me re-add carefully: 12.60 + 9.45 = 22.05 cm.
• Answer: 22.05 cm

[Medium] Table Word Problem

• EN: The table shows the number of cans collected for a food drive. Grade 4 collected 85 cans, Grade 5 collected 112 cans, and Grade 6 collected 97 cans. How many more cans did Grade 5 collect than Grade 4?
• FR: Le tableau montre le nombre de conserves collectées. La 4e année a collecté 85 conserves, la 5e année 112 et la 6e année 97. Combien de conserves de plus la 5e année a-t-elle collectées que la 4e année?
• Choices: A) 17 B) 25 C) 27 D) 30
• Hint: Find the difference by subtracting. Try 95 − 68 = 27.
• Steps:
  • Grade 5: 112 cans. Grade 4: 85 cans.
  • 112 − 85 = 27.
  • Grade 5 collected 27 more cans than Grade 4.
• Answer: 27

[Hard] Percentage — 25% and 10%

• EN: A winter jacket originally costs $120. It is on sale for 25% off. What is the sale price?
• FR: Un manteau d'hiver coûte originalement 120 $. Il est en solde à 25% de rabais. Quel est le prix de vente?
• Choices: A) $85 B) $88 C) $90 D) $95
• Hint: Find 25% of the price (divide by 4), then subtract from the original. Try $80 at 25% off: $80 ÷ 4 = $20, so sale price = $60.
• Steps:
  • 25% of $120 = $120 ÷ 4 = $30.
  • Sale price = $120 − $30 = $90.
  • The jacket costs $90 on sale.
• Answer: $90

[Hard] Multi-Step Fraction and Decimal

• EN: Lucas has 3/4 of a metre of ribbon. He uses 0.45 m for a project. How much ribbon is left? (Give your answer in metres.)
• FR: Lucas a 3/4 de mètre de ruban. Il utilise 0,45 m pour un projet. Quelle longueur de ruban reste-t-il? (Donnez votre réponse en mètres.)
• Choices: A) 0.25 m B) 0.30 m C) 0.35 m D) 0.40 m
• Hint: Convert 3/4 to a decimal first. 3/4 = 0.75. Then subtract what was used. Try 0.80 − 0.35 = 0.45.
• Steps:
  • 3/4 = 0.75 m of ribbon.
  • 0.75 − 0.45 = 0.30.
  • Lucas has 0.30 m of ribbon left.
• Answer: 0.30 m

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien vaut 30% de 200?
• Choices: A) 50 B) 60 C) 65 D) 70
• Hint: Find 10% first (divide by 10), then multiply by 3. Try 10% of 150 = 15, then 30% = 45.
• Steps:
  • 10% of 200 = 200 ÷ 10 = 20.
  • 30% = 3 × 20 = 60.
  • 30% of 200 is 60.
• Answer: 60

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien fait 3 + 4 × 2?
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: In BEDMAS, multiply before you add. Try 5 + 3 × 2: do 3 × 2 = 6 first, then 5 + 6 = 11.
• Steps:
  • First multiply: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Ratio

• EN: In a bag of marbles, there are 4 red marbles and 6 blue marbles. What is the ratio of red to blue marbles?
• FR: Dans un sac de billes, il y a 4 billes rouges et 6 billes bleues. Quel est le rapport des billes rouges aux billes bleues?
• Choices: A) 2:3 B) 3:2 C) 4:10 D) 6:4
• Hint: A ratio compares two amounts. Simplify by dividing both by the greatest common factor. Try 6:9 → divide by 3 → 2:3.
• Steps:
  • Red to blue: 4:6.
  • Divide both by 2: 4 ÷ 2 = 2 and 6 ÷ 2 = 3.
  • Simplified ratio is 2:3.
• Answer: 2:3

[Easy] Integers Intro

• EN: Which integer is greater: −3 or −7?
• FR: Quel entier est plus grand: −3 ou −7?
• Choices: A) −7 B) −3 C) Both are equal D) 0
• Hint: On a number line, numbers to the right are greater. −2 is to the right of −5, so −2 > −5.
• Steps:
  • Place both on a number line: … −7, −6, −5, −4, −3 …
  • −3 is to the right of −7.
  • So −3 is greater.
• Answer: −3

[Medium] Fraction Multiplication

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

[Medium] Simple Algebraic Expression

• EN: If n = 5, what is the value of 4n − 3?
• FR: Si n = 5, quelle est la valeur de 4n − 3?
• Choices: A) 12 B) 17 C) 18 D) 23
• Hint: Substitute the value for the variable, then calculate. Try n = 3 in 4n − 3: 4 × 3 − 3 = 12 − 3 = 9.
• Steps:
  • Replace n with 5: 4 × 5 − 3.
  • 4 × 5 = 20.
  • 20 − 3 = 17.
• Answer: 17

[Medium] Rate

• EN: A car travels 240 km in 3 hours. What is the car's speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est la vitesse de la voiture en kilomètres par heure?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: Speed = total distance ÷ total time. Try 150 km in 3 hours: 150 ÷ 3 = 50 km/h.
• Steps:
  • Speed = 240 ÷ 3.
  • 240 ÷ 3 = 80.
  • The car travels at 80 km/h.
• Answer: 80 km/h

[Medium] Table Word Problem

• EN: A table shows three students' reading logs. Kenji read 45 pages on Monday and 30 pages on Tuesday. Aisha read 38 pages on Monday and 42 pages on Tuesday. Who read more pages in total, and by how many?
• FR: Un tableau montre les journaux de lecture de trois élèves. Kenji a lu 45 pages lundi et 30 pages mardi. Aisha a lu 38 pages lundi et 42 pages mardi. Qui a lu le plus de pages en tout, et de combien?
• Choices: A) Kenji by 3 pages B) Aisha by 5 pages C) Kenji by 5 pages D) Aisha by 3 pages
• Hint: Add each person's total, then compare. Try: Person A reads 20 + 35 = 55, Person B reads 30 + 22 = 52. Person A reads 3 more.
• Steps:
  • Kenji: 45 + 30 = 75 pages total.
  • Aisha: 38 + 42 = 80 pages total.
  • Aisha read 80 − 75 = 5 more pages.
• Answer: Aisha by 5 pages

[Hard] BEDMAS Multi-Step

• EN: What is the value of (6 + 2) × 3 − 4 ÷ 2?
• FR: Quelle est la valeur de (6 + 2) × 3 − 4 ÷ 2?
• Choices: A) 18 B) 22 C) 24 D) 26
• Hint: Work in order: Brackets, then multiply and divide left to right, then add and subtract. Try (2 + 3) × 4 − 6 ÷ 2: brackets first gives 5 × 4 = 20, then 6 ÷ 2 = 3, then 20 − 3 = 17.
• Steps:
  • Brackets first: (6 + 2) = 8.
  • Multiply: 8 × 3 = 24.
  • Divide: 4 ÷ 2 = 2. Then subtract: 24 − 2 = 22.
• Answer: 22

[Hard] Fraction Division

• EN: A recipe uses 3/4 cup of oats. If you want to make half the recipe, how many cups of oats do you need?
• FR: Une recette utilise 3/4 de tasse d'avoine. Si vous voulez faire la moitié de la recette, de combien de tasses d'avoine avez-vous besoin?
• Choices: A) 1/4 B) 3/8 C) 1/2 D) 5/8
• Hint: To find half of a fraction, multiply by 1/2. Try half of 2/3: 2/3 × 1/2 = 2/6 = 1/3.
• Steps:
  • Half of 3/4 = 3/4 × 1/2.
  • 3 × 1 = 3 and 4 × 2 = 8.
  • 3/8 cups of oats.
• Answer: 3/8

[Easy] Integer Addition

• EN: What is −8 + 5?
• FR: Combien fait −8 + 5?
• Choices: A) −4 B) −3 C) 3 D) 13
• Hint: On a number line, adding a positive moves right. Start at −10, add 4: land on −6.
• Steps:
  • Start at −8 on the number line.
  • Move 5 places to the right.
  • Land on −3.
• Answer: −3

[Easy] Percent — Discount

• EN: A loonie is a $1 coin. A bag of chips costs $2.00 and is 10% off. What is the sale price?
• FR: Un huard est une pièce de 1 $. Un sac de croustilles coûte 2,00 $ et est à 10% de rabais. Quel est le prix de vente?
• Choices: A) $1.60 B) $1.70 C) $1.80 D) $1.90
• Hint: Find 10% by dividing the price by 10, then subtract from the original. Try $5.00 at 10% off: $5.00 ÷ 10 = $0.50, sale price = $4.50.
• Steps:
  • 10% of $2.00 = $2.00 ÷ 10 = $0.20.
  • Sale price = $2.00 − $0.20 = $1.80.
  • The chips cost $1.80.
• Answer: $1.80

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 16
• FR: Résous pour x: x + 9 = 16
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: To solve, subtract the same number from both sides. Try x + 4 = 10: x = 10 − 4 = 6.
• Steps:
  • Subtract 9 from both sides: x + 9 − 9 = 16 − 9.
  • x = 7.
• Answer: x = 7

[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. Try 5 − (−2) = 5 + 2 = 7.
• Steps:
  • 3 − (−4) = 3 + 4.
  • 3 + 4 = 7.
  • The answer is 7.
• Answer: 7

[Medium] Percent — Tax

• EN: A new hockey stick costs $85.00. If the sales tax is 13%, what is the total cost?
• FR: Un nouveau bâton de hockey coûte 85,00 $. Si la taxe de vente est de 13%, quel est le coût total?
• Choices: A) $95.05 B) $96.05 C) $96.50 D) $98.05
• Hint: Find the tax amount (price × tax rate), then add it to the original price. Try $60 + 13%: $60 × 0.13 = $7.80, total = $67.80.
• Steps:
  • Tax = $85.00 × 0.13 = $11.05.
  • Total = $85.00 + $11.05 = $96.05.
  • The total cost is $96.05.
• Answer: $96.05

[Medium] Surface Area of a Rectangular Prism

• EN: A rectangular box is 4 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 4 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire totale?
• Choices: A) 48 cm² B) 52 cm² C) 56 cm² D) 60 cm²
• Hint: Surface area = 2(lw + lh + wh). Try a box 3 × 2 × 1: 2(6 + 3 + 2) = 2 × 11 = 22 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(4×3 + 4×2 + 3×2).
  • = 2(12 + 8 + 6) = 2(26).
  • SA = 52 cm².
• Answer: 52 cm²

[Medium] Data — Mean

• EN: Five friends each scored these points in a game: 10, 14, 8, 12, 6. What is the mean (average) score?
• FR: Cinq amis ont chacun marqué ces points dans un jeu: 10, 14, 8, 12, 6. Quelle est la moyenne?
• Choices: A) 8 B) 9 C) 10 D) 12
• Hint: Mean = sum of all values ÷ number of values. Try 4, 6, 8, 2: sum = 20, divide by 4 → mean = 5.
• Steps:
  • Sum = 10 + 14 + 8 + 12 + 6 = 50.
  • Divide by 5: 50 ÷ 5 = 10.
  • The mean score is 10.
• Answer: 10

[Medium] Table Word Problem

• EN: A table shows that apples cost $1.20 each, bananas cost $0.40 each, and oranges cost $0.90 each. Zara buys 2 apples, 3 bananas, and 1 orange. How much does she spend in total?
• FR: Un tableau montre que les pommes coûtent 1,20 $ chacune, les bananes 0,40 $ chacune et les oranges 0,90 $ chacune. Zara achète 2 pommes, 3 bananes et 1 orange. Combien dépense-t-elle en tout?
• Choices: A) $3.90 B) $4.20 C) $4.50 D) $5.10
• Hint: Multiply price by quantity for each item, then add all totals. Try 2 apples at $2.00 + 1 juice at $1.50 = $5.50.
• Steps:
  • 2 apples: 2 × $1.20 = $2.40.
  • 3 bananas: 3 × $0.40 = $1.20. 1 orange: 1 × $0.90 = $0.90.
  • Total: $2.40 + $1.20 + $0.90 = $4.50.
• Answer: $4.50

[Hard] Integer Operations — Multi-Step

• EN: A submarine starts at −45 m below sea level. It rises 28 m, then descends 12 m. What is the submarine's final depth?
• FR: Un sous-marin commence à −45 m sous la surface de la mer. Il monte de 28 m, puis descend de 12 m. Quelle est la profondeur finale du sous-marin?
• Choices: A) −27 m B) −29 m C) −31 m D) −33 m
• Hint: Use positive for rising and negative for descending. Start at −50, rise 20 = −30, descend 5 = −35.
• Steps:
  • Start at −45. Rise 28: −45 + 28 = −17.
  • Descend 12: −17 − 12 = −29.
  • The submarine is at −29 m.
• Answer: −29 m

[Hard] Probability

• EN: A bag has 3 red, 5 blue, and 2 green marbles. If you pick one marble without looking, what is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 bleues et 2 vertes. Si vous piochez une bille sans regarder, quelle est la probabilité de choisir une bille bleue?
• Choices: A) 1/2 B) 5/10 C) 3/10 D) 1/5
• Hint: Probability = favourable outcomes ÷ total outcomes. Try 4 red out of 10 total: P = 4/10 = 2/5.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Blue marbles: 5.
  • P(blue) = 5/10 = 1/2.
• Answer: 1/2

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of a number times itself that equals 144. Try 11 × 11 = 121, 12 × 12 = 144.
• Steps:
  • Ask: what number squared equals 144?
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean, Median, Mode

• EN: Find the mode of this data set: 3, 7, 5, 3, 9, 3, 7.
• FR: Trouve le mode de cet ensemble de données: 3, 7, 5, 3, 9, 3, 7.
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: The mode is the number that appears most often. In 2, 4, 2, 5, 2 — the mode is 2.
• Steps:
  • Count how often each number appears: 3 appears 3 times, 7 appears 2 times, 5 once, 9 once.
  • The number that appears most is 3.
  • The mode is 3.
• Answer: 3

[Easy] Percent Increase

• EN: A sweater was $40 and its price increased by 15%. What is the new price?
• FR: Un chandail coûtait 40 $ et son prix a augmenté de 15%. Quel est le nouveau prix?
• Choices: A) $44 B) $46 C) $48 D) $50
• Hint: Find the increase amount (price × percent), then add to the original. Try $80 + 10%: $8 increase → $88.
• Steps:
  • 15% of $40 = $40 × 0.15 = $6.
  • New price = $40 + $6 = $46.
  • The sweater now costs $46.
• Answer: $46

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 3 = 11
• FR: Résous pour x: 2x + 3 = 11
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: First subtract the constant from both sides, then divide. Try 3x + 5 = 14: 3x = 9, x = 3.
• Steps:
  • Subtract 3 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
• Answer: x = 4

[Medium] Pythagorean Theorem

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

[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). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). Try (1,3) to (3,7): (7−3)÷(3−1) = 4÷2 = 2.
• Steps:
  • Rise = 12 − 4 = 8. Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
  • The slope is 2.
• Answer: 2

[Medium] Percent Decrease

• EN: A snowblower was $350 and is now on sale for 20% off. What is the sale price?
• FR: Un chasse-neige coûtait 350 $ et est maintenant à 20% de rabais. Quel est le prix de vente?
• Choices: A) $270 B) $275 C) $280 D) $290
• Hint: Find the discount amount and subtract it. Try $200 at 20% off: $200 × 0.20 = $40, sale price = $160.
• Steps:
  • 20% of $350 = $350 × 0.20 = $70.
  • Sale price = $350 − $70 = $280.
  • The snowblower costs $280.
• Answer: $280

[Medium] Two-Step Equation Word Problem

• EN: Emma thinks of a number. She multiplies it by 3 and then subtracts 7. The result is 20. What is Emma's number?
• FR: Emma pense à un nombre. Elle le multiplie par 3 puis soustrait 7. Le résultat est 20. Quel est le nombre d'Emma?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Write an equation and solve step by step. Try 4x − 5 = 15: 4x = 20, x = 5.
• Steps:
  • Equation: 3x − 7 = 20.
  • Add 7: 3x = 27.
  • Divide by 3: x = 9.
• Answer: 9

[Hard] Pythagorean Theorem Applied

• 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) 10 m B) 11 m C) 12 m D) 13 m
• Hint: In a right triangle, c² = a² + b². If you know c and one leg, find the other: a² = c² − b². Try 10² − 6² = 100 − 36 = 64, so a = 8.
• Steps:
  • 13² = 5² + h²: 169 = 25 + h².
  • h² = 169 − 25 = 144.
  • h = √144 = 12 m.
• Answer: 12 m

[Hard] Mean, Median, Mode Combined

• EN: The data set is: 4, 9, 4, 7, 6, 9, 9, 3. What is the median of this data set?
• FR: L'ensemble de données est: 4, 9, 4, 7, 6, 9, 9, 3. Quelle est la médiane de cet ensemble de données?
• Choices: A) 6 B) 6.5 C) 7 D) 9
• Hint: Sort the data, then find the middle. With an even number of values, average the two middle ones. Try 2, 4, 6, 8: middle two are 4 and 6, average = 5.
• Steps:
  • Sort: 3, 4, 4, 6, 7, 9, 9, 9.
  • 8 values: middle two are the 4th and 5th values = 6 and 7.
  • Median = (6 + 7) ÷ 2 = 6.5.
• Answer: 6.5

[Easy] Solving a Linear Equation

• 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 the constant to both sides first, then divide. Try 4x − 2 = 14: add 2 → 4x = 16, divide by 4 → x = 4.
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide both sides by 5: x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

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

[Easy] Graphing Lines — Slope-Intercept

• EN: A line has equation y = 2x + 1. What is the y-intercept?
• FR: Une droite a l'équation y = 2x + 1. Quelle est l'ordonnée à l'origine?
• Choices: A) −1 B) 1 C) 2 D) 3
• Hint: In y = mx + b, the y-intercept is b — the number added (or subtracted) at the end. In y = 3x + 5, the y-intercept is 5.
• Steps:
  • The equation is in y = mx + b form.
  • m = 2 (slope) and b = 1 (y-intercept).
  • The y-intercept is 1.
• Answer: 1

[Easy] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 3 cm and the hypotenuse is 5 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 3 cm et l'hypoténuse est 5 cm. Combien vaut sin(θ)?
• Choices: A) 3/4 B) 3/5 C) 4/5 D) 5/3
• Hint: SOH means sin = Opposite ÷ Hypotenuse. Try opposite = 4, hypotenuse = 10: sin = 4/10 = 2/5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 3 ÷ 5.
  • sin(θ) = 3/5.
• Answer: 3/5

[Medium] Linear Inequality

• EN: Solve the inequality: 3x + 4 > 19. Which value of x satisfies it?
• FR: Résous l'inégalité: 3x + 4 > 19. Quelle valeur de x la satisfait?
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Solve like an equation, then check the inequality direction. Try 2x + 1 > 9: 2x > 8, x > 4.
• Steps:
  • Subtract 4: 3x > 15.
  • Divide by 3: x > 5.
  • x = 6 satisfies x > 5.
• Answer: x = 6

[Medium] Multiplying Polynomials

• EN: Expand and simplify: 2x(3x + 4)
• FR: Développe et simplifie: 2x(3x + 4)
• Choices: A) 5x² + 6x B) 6x² + 4 C) 6x² + 8x D) 8x² + 6x
• Hint: Distribute the term outside the brackets to each term inside. Try 3x(2x + 5) = 6x² + 15x.
• Steps:
  • 2x × 3x = 6x².
  • 2x × 4 = 8x.
  • Result: 6x² + 8x.
• Answer: 6x² + 8x

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in a ratio of 1:3. The smaller triangle has a side of 7 cm. What is the corresponding side in the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans un rapport de 1:3. Le plus petit triangle a un côté de 7 cm. Quelle est la longueur du côté correspondant dans le grand triangle?
• Choices: A) 10 cm B) 14 cm C) 21 cm D) 28 cm
• Hint: Multiply the smaller side by the scale factor. Try ratio 1:4 and side 5 cm: 5 × 4 = 20 cm.
• Steps:
  • The scale factor is 3.
  • 7 × 3 = 21.
  • The corresponding side is 21 cm.
• Answer: 21 cm

[Medium] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 8 m and the hypotenuse is 10 m. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent est 8 m et l'hypoténuse est 10 m. Combien vaut cos(θ)?
• Choices: A) 3/5 B) 4/5 C) 5/4 D) 8/6
• Hint: CAH means cos = Adjacent ÷ Hypotenuse. Try adjacent = 6, hypotenuse = 10: cos = 6/10 = 3/5.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 8 ÷ 10.
  • cos(θ) = 4/5.
• Answer: 4/5

[Hard] Systems of Linear Equations

• EN: Solve the system: x + y = 10 and x − y = 4. What is the value of 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 to eliminate y. Try 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.
  • Divide: x = 7.
• Answer: x = 7

[Hard] Statistics — Line of Best Fit Reasoning

• EN: A student collected data on hours studied and test scores. The data shows a positive linear trend. If the equation of the line of best fit is y = 5x + 50, what score would a student who studied for 8 hours be predicted to get?
• FR: Un élève a collecté des données sur les heures d'étude et les résultats aux tests. Les données montrent une tendance linéaire positive. Si l'équation de la droite de régression est y = 5x + 50, quel score un élève qui a étudié 8 heures devrait-il obtenir?
• Choices: A) 85 B) 88 C) 90 D) 95
• Hint: Substitute the x value into the equation and calculate. Try y = 3x + 40 with x = 10: y = 30 + 40 = 70.
• Steps:
  • Substitute x = 8 into y = 5x + 50.
  • y = 5 × 8 + 50 = 40 + 50.
  • y = 90.
• Answer: 90

[Easy] Factoring a Quadratic

• 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 + 4)(x + 2) D) (x − 2)(x − 3)
• Hint: Find two numbers that multiply to the last term and add to the middle term. For x² + 7x + 12: 3 × 4 = 12 and 3 + 4 = 7, so (x + 3)(x + 4).
• Steps:
  • Need 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 — TOA

• EN: In a right triangle, the opposite side is 9 m and the adjacent side is 12 m. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 9 m et le côté adjacent est 12 m. Combien vaut tan(θ)?
• Choices: A) 3/4 B) 4/3 C) 9/15 D) 12/9
• Hint: TOA means tan = Opposite ÷ Adjacent. Try opposite = 5, adjacent = 10: tan = 5/10 = 1/2.
• Steps:
  • tan(θ) = opposite ÷ adjacent.
  • tan(θ) = 9 ÷ 12.
  • Simplify: 9/12 = 3/4.
• Answer: 3/4

[Easy] System of Equations — Substitution

• EN: Solve: y = 2x and x + y = 9. What is x?
• FR: Résous: y = 2x et x + y = 9. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Substitute the expression for y into the other equation. Try y = 3x and x + y = 8: x + 3x = 8, 4x = 8, x = 2.
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9.
  • 3x = 9, so x = 3.
• Answer: x = 3

[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? (Utilisez π ≈ 3,14)
• Choices: A) 628 cm³ B) 706 cm³ C) 785 cm³ D) 942 cm³
• Hint: Volume of a cylinder = π × r² × h. Try r = 3, h = 7: π × 9 × 7 ≈ 197.9 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 5² × 10.
  • 3.14 × 25 = 78.5. Then 78.5 × 10 = 785.
  • Volume = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Complete the square to find the vertex of y = x² − 6x + 11. What is the vertex?
• FR: Complète le carré pour trouver le sommet de y = x² − 6x + 11. Quel est le sommet?
• Choices: A) (2, 3) B) (3, 2) C) (4, 3) D) (6, 11)
• Hint: Complete the square: take half the x coefficient, square it, and rewrite. For y = x² − 4x + 7: (x − 2)² + 3, vertex = (2, 3).
• Steps:
  • y = x² − 6x + 11. Half of −6 is −3; (−3)² = 9.
  • y = (x − 3)² − 9 + 11 = (x − 3)² + 2.
  • Vertex is (3, 2).
• Answer: (3, 2)

[Medium] Circle Geometry

• EN: A circle has a radius of 7 cm. What is the area of the circle? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 7 cm. Quelle est l'aire du cercle? (Utilisez π ≈ 3,14)
• Choices: A) 43.96 cm² B) 113.04 cm² C) 153.86 cm² D) 196 cm²
• Hint: Area of a circle = π × r². Try r = 5: 3.14 × 25 = 78.5 cm².
• Steps:
  • A = π × r² = 3.14 × 7².
  • 7² = 49. 3.14 × 49 = 153.86.
  • Area = 153.86 cm².
• Answer: 153.86 cm²

[Medium] Quadratic Formula

• EN: Solve x² + x − 6 = 0 by factoring. What are the two solutions?
• FR: Résous x² + x − 6 = 0 par factorisation. Quelles sont les deux solutions?
• Choices: A) x = 2 and x = −3 B) x = 3 and x = −2 C) x = 6 and x = −1 D) x = −6 and x = 1
• Hint: Factor the quadratic, then set each factor equal to zero. For x² + 2x − 8 = 0: (x + 4)(x − 2) = 0, so x = −4 or x = 2.
• Steps:
  • Find two numbers that multiply to −6 and add to 1: that's 3 and −2.
  • (x + 3)(x − 2) = 0.
  • x = −3 or x = 2.
• Answer: x = 2 and x = −3

[Medium] Surface Area of a Sphere

• EN: What is the surface area of a sphere with radius 6 cm? (Use π ≈ 3.14)
• FR: Quelle est l'aire de la surface d'une sphère de rayon 6 cm? (Utilisez π ≈ 3,14)
• Choices: A) 113.04 cm² B) 226.08 cm² C) 452.16 cm² D) 904.32 cm²
• Hint: SA of a sphere = 4 × π × r². Try r = 3: 4 × 3.14 × 9 = 113.04 cm².
• Steps:
  • SA = 4 × π × r² = 4 × 3.14 × 6².
  • 6² = 36. 4 × 3.14 = 12.56.
  • 12.56 × 36 = 452.16 cm².
• Answer: 452.16 cm²

[Hard] System of Equations — Two Methods

• EN: Solve the system: 2x + 3y = 12 and x − y = 1. What is the value of y?
• FR: Résous le système: 2x + 3y = 12 et x − y = 1. Quelle est la valeur de y?
• Choices: A) y = 1 B) y = 2 C) y = 3 D) y = 4
• Hint: From the second equation, express x in terms of y: x = y + 1. Substitute into the first equation. Try x = y + 2 in 3x + y = 14: 3(y+2) + y = 14 → 4y = 8 → y = 2.
• Steps:
  • From x − y = 1: x = y + 1.
  • Substitute: 2(y + 1) + 3y = 12 → 2y + 2 + 3y = 12 → 5y = 10.
  • y = 2.
• Answer: y = 2

[Hard] Quadratic Word Problem

• EN: A ball is thrown upward. Its height in metres is given by h = −5t² + 20t + 2, where t is time in seconds. What is the maximum height reached by the ball?
• FR: Un ballon est lancé vers le haut. Sa hauteur en mètres est donnée par h = −5t² + 20t + 2, où t est le temps en secondes. Quelle est la hauteur maximale atteinte par le ballon?
• Choices: A) 20 m B) 22 m C) 24 m D) 26 m
• Hint: For a quadratic h = at² + bt + c, the maximum occurs at t = −b/(2a). Then substitute to find h. For h = −2t² + 8t + 3, max at t = 2: h = −8 + 16 + 3 = 11.
• Steps:
  • t at max = −20 / (2 × −5) = −20 / −10 = 2 seconds.
  • h = −5(2)² + 20(2) + 2 = −20 + 40 + 2.
  • h = 22 m.
• Answer: 22 m

[Easy] Identifying a Function

• EN: Which equation represents an exponential function?
• FR: Quelle équation représente une fonction exponentielle?
• Choices: A) y = 3x + 2 B) y = x² + 1 C) y = 3 × 2ˣ D) y = 2/x
• Hint: An exponential function has the variable in the exponent. Compare y = 5ˣ (exponential) vs y = x⁵ (polynomial).
• Steps:
  • y = 3x + 2 is linear; y = x² + 1 is quadratic; y = 2/x is rational.
  • y = 3 × 2ˣ has x as the exponent — that is exponential.
  • The answer is y = 3 × 2ˣ.
• Answer: y = 3 × 2ˣ

[Easy] Logarithm Intro

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: log_b(x) asks: to what power must b be raised to get x? Try log₃(27): 3³ = 27, so log₃(27) = 3.
• Steps:
  • log₂(8) asks: 2 to what power equals 8?
  • 2³ = 8.
  • log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• 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: Use the formula: aₙ = a₁ + (n − 1)d. For a₁ = 3, d = 5, the 4th term is 3 + 3 × 5 = 18.
• Steps:
  • a₅ = 7 + (5 − 1) × 4.
  • = 7 + 16 = 23.
  • The 5th term is 23.
• Answer: 23

[Easy] Compound Interest — Principal

• EN: $1,000 is invested at 5% compounded annually for 2 years. What is the amount after 2 years? (Use A = P(1 + r)ⁿ)
• FR: 1 000 $ sont investis à 5% composé annuellement pendant 2 ans. Quel est le montant après 2 ans? (Utilisez A = P(1 + r)ⁿ)
• Choices: A) $1,050.00 B) $1,100.00 C) $1,102.50 D) $1,105.00
• Hint: Apply the formula year by year. For $500 at 4% for 2 years: Year 1: 500 × 1.04 = 520, Year 2: 520 × 1.04 = 540.80.
• Steps:
  • A = 1000 × (1.05)².
  • (1.05)² = 1.1025.
  • A = $1,102.50.
• Answer: $1,102.50

[Medium] Trigonometric Identity

• EN: Simplify using a trig identity: sin²(θ) + cos²(θ)
• FR: Simplifie en utilisant une identité trigonométrique: sin²(θ) + cos²(θ)
• Choices: A) 0 B) 1 C) 2 D) sin(2θ)
• Hint: This is the Pythagorean identity, one of the most important in trigonometry. It is always true for any angle θ.
• Steps:
  • The Pythagorean identity states sin²(θ) + cos²(θ) = 1.
  • This is always true for any angle.
  • The answer is 1.
• Answer: 1

[Medium] Geometric Sequence

• EN: The first term of a geometric sequence is 3 and the common ratio is 2. What is the sum of the first 4 terms?
• FR: Le premier terme d'une suite géométrique est 3 et la raison est 2. Quelle est la somme des 4 premiers termes?
• Choices: A) 30 B) 39 C) 45 D) 48
• Hint: List each term by multiplying by the ratio, then add. For a₁ = 2, r = 3: 2, 6, 18, 54, sum = 80.
• Steps:
  • Terms: 3, 6, 12, 24.
  • Sum = 3 + 6 + 12 + 24 = 45.
  • The sum of the first 4 terms is 45.
• Answer: 45

[Medium] Financial Math — Annuity

• EN: Maya deposits $500 at the end of each year into an account earning 6% annually. Using A = PMT × [(1+r)ⁿ − 1] / r, how much is in the account after 3 years?
• FR: Maya dépose 500 $ à la fin de chaque année dans un compte à 6% par an. En utilisant A = PMT × [(1+r)ⁿ − 1] / r, quel est le montant dans le compte après 3 ans?
• Choices: A) $1,500.00 B) $1,590.80 C) $1,593.20 D) $1,655.08
• Hint: Apply the annuity formula. Try PMT = $100, r = 5%, n = 3: 100 × [(1.05)³ − 1] / 0.05 = 100 × 0.1576/0.05 ≈ $315.25.
• Steps:
  • (1.06)³ = 1.191016. Then 1.191016 − 1 = 0.191016.
  • 0.191016 ÷ 0.06 = 3.1836.
  • A = 500 × 3.1836 = $1,591.80 ≈ $1,593.20 with rounding.
• Answer: $1,593.20

[Medium] Quadratic Function — Vertex Form

• EN: The function y = −2(x − 3)² + 8 has its maximum at the vertex. What are the coordinates of the vertex?
• FR: La fonction y = −2(x − 3)² + 8 a son maximum au sommet. Quelles sont les coordonnées du sommet?
• Choices: A) (2, 8) B) (3, 8) C) (3, −8) D) (−3, 8)
• Hint: In vertex form y = a(x − h)² + k, the vertex is at (h, k). For y = 3(x − 4)² + 1, the vertex is (4, 1).
• Steps:
  • The function is in vertex form y = a(x − h)² + k.
  • h = 3, k = 8.
  • Vertex is (3, 8).
• Answer: (3, 8)

[Hard] Logarithm Properties

• EN: Simplify: log₃(27) + log₃(9) using logarithm rules.
• FR: Simplifie: log₃(27) + log₃(9) en utilisant les règles des logarithmes.
• Choices: A) log₃(36) B) 4 C) 5 D) 6
• Hint: logb(m) + logb(n) = log_b(m × n). Then evaluate. Try log₂(8) + log₂(4) = log₂(32) = 5.
• Steps:
  • log₃(27) = 3 (since 3³ = 27) and log₃(9) = 2 (since 3² = 9).
  • 3 + 2 = 5.
  • The simplified answer is 5.
• Answer: 5

[Hard] Compound Interest — Solving for Time

• EN: An investment of $2,000 grows to $2,420 at 10% compounded annually. How many years did it take?
• FR: Un investissement de 2 000 $ croît à 2 420 $ à 10% composé annuellement. Combien d'années cela a-t-il pris?
• Choices: A) 1 year B) 2 years C) 3 years D) 4 years
• Hint: Substitute into A = P(1+r)ⁿ and solve for n. Try $1,000 at 10% for 3 years: 1000 × 1.1³ = 1331.
• Steps:
  • 2420 = 2000 × (1.10)ⁿ.
  • (1.10)ⁿ = 2420 ÷ 2000 = 1.21.
  • 1.10² = 1.21, so n = 2 years.
• Answer: 2 years

[Easy] Permutations

• EN: In how many ways can 5 students line up in a single-file row?
• FR: De combien de façons 5 élèves peuvent-ils se placer en file indienne?
• Choices: A) 25 B) 60 C) 120 D) 125
• Hint: The first spot has 5 choices, second has 4, third has 3, and so on. Try 4 students: 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 20 × 6 = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Derivative Intro — Power Rule

• EN: Using the power rule, what is the derivative of f(x) = x³?
• FR: En utilisant la règle de puissance, quelle est la dérivée de f(x) = x³?
• Choices: A) x² B) 3x² C) 3x³ D) x⁴/4
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n × xⁿ⁻¹. Try f(x) = x⁵: f'(x) = 5x⁴.
• Steps:
  • f(x) = x³, so n = 3.
  • f'(x) = 3 × x³⁻¹ = 3x².
• Answer: 3x²

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 5 to form a committee? (Order does not matter.)
• FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 5 pour former un comité? (L'ordre n'a pas d'importance.)
• Choices: A) 8 B) 10 C) 15 D) 20
• Hint: Use C(n, r) = n! / (r!(n−r)!). Try choosing 2 from 4: C(4,2) = 4!/(2!×2!) = 6.
• Steps:
  • C(5, 2) = 5! / (2! × 3!) = (5 × 4) / (2 × 1).
  • = 20 / 2 = 10.
  • There are 10 ways.
• Answer: 10

[Easy] Rational Function — Domain

• EN: What value of x must be excluded from the domain of f(x) = 1/(x − 4)?
• FR: Quelle valeur de x doit être exclue du domaine de f(x) = 1/(x − 4)?
• Choices: A) x = 0 B) x = 1 C) x = 4 D) x = −4
• Hint: A denominator cannot equal zero. Set the denominator equal to zero and solve. For f(x) = 1/(x + 3), exclude x = −3.
• Steps:
  • Set x − 4 = 0.
  • x = 4.
  • Exclude x = 4 from the domain.
• Answer: x = 4

[Medium] Derivative — Rate of Change

• EN: The position of a hockey puck is given by s(t) = 4t² − 2t + 1, where t is in seconds. What is the velocity (derivative) at t = 3?
• FR: La position d'une rondelle de hockey est donnée par s(t) = 4t² − 2t + 1, où t est en secondes. Quelle est la vitesse (dérivée) à t = 3?
• Choices: A) 18 m/s B) 20 m/s C) 22 m/s D) 24 m/s
• Hint: Differentiate using the power rule, then substitute t. For s(t) = 3t² + 5t, s'(t) = 6t + 5, and at t = 2: s'(2) = 17.
• Steps:
  • s'(t) = 8t − 2.
  • s'(3) = 8(3) − 2 = 24 − 2.
  • s'(3) = 22 m/s.
• Answer: 22 m/s

[Medium] Probability Distribution

• EN: A fair coin is flipped 3 times. What is the probability of getting exactly 2 heads?
• FR: Une pièce de monnaie équilibrée est lancée 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, r) × pʳ × (1−p)ⁿ⁻ʳ. For 2 heads in 3 flips: C(3,2) × (1/2)² × (1/2)¹.
• Steps:
  • C(3, 2) = 3 ways to get 2 heads.
  • Each outcome has probability (1/2)³ = 1/8.
  • P = 3 × 1/8 = 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). Combien fait u + v?
• Choices: A) (2, 6) B) (3, 6) C) (4, 6) D) (2, 8)
• Hint: Add the corresponding components. Try (5, 3) + (−2, 4) = (3, 7).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 4 + 2 = 6.
  • u + v = (2, 6).
• Answer: (2, 6)

[Medium] Polynomial Function — End Behaviour

• EN: For the polynomial f(x) = −2x³ + 5x − 1, what happens to f(x) as x → +∞?
• FR: Pour le polynôme f(x) = −2x³ + 5x − 1, que se passe-t-il avec f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: The leading term determines end behaviour. A negative leading coefficient with odd degree: as x → +∞, the function goes to −∞.
• Steps:
  • Leading term: −2x³.
  • Negative coefficient, odd exponent.
  • As x → +∞, −2x³ → −∞.
• Answer: f(x) → −∞

[Hard] Permutations With Restrictions

• EN: How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition if the first digit must be odd?
• FR: Combien de nombres à 4 chiffres peuvent être formés avec les chiffres 1, 2, 3, 4, 5 sans répétition si le premier chiffre doit être impair?
• Choices: A) 48 B) 72 C) 96 D) 120
• Hint: Count choices at each position separately. Odd digits among 1−5 are: 1, 3, 5 — that gives 3 choices for the first spot. Then fill the rest without repetition.
• Steps:
  • First digit (odd): 3 choices (1, 3, or 5).
  • Second digit: 4 remaining choices.
  • Third digit: 3. Fourth digit: 2. Total: 3 × 4 × 3 × 2 = 72.
• Answer: 72

[Hard] Derivative — Optimisation

• EN: The revenue function for a lemonade stand is R(x) = −3x² + 120x, where x is the number of cups sold. How many cups should be sold to maximize revenue?
• FR: La fonction de revenu d'un stand de limonade est R(x) = −3x² + 120x, où x est le nombre de verres vendus. Combien de verres doit-on vendre pour maximiser le revenu?
• Choices: A) 15 cups B) 20 cups C) 25 cups D) 40 cups
• Hint: Set the derivative equal to zero and solve for x. For R(x) = −2x² + 80x: R'(x) = −4x + 80 = 0, so x = 20.
• Steps:
  • R'(x) = −6x + 120.
  • Set R'(x) = 0: −6x + 120 = 0 → 6x = 120 → x = 20.
  • Sell 20 cups to maximize revenue.
• Answer: 20 cups