Daily Math — 2026-09-16

[Easy] Counting Mittens

• EN: Liam has 7 red mittens and 5 blue mittens. How many mittens does he have in all?
• FR: Liam a 7 mitaines rouges et 5 mitaines bleues. Combien de mitaines a-t-il en tout?
• Choices: A) 10 mittens B) 11 mittens C) 12 mittens D) 13 mittens
• Hint: To add 4 + 3, count on from the bigger number: 4 → 5, 6, 7.
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • So Liam has 12 mittens in all.
• Answer: 12 mittens

[Easy] Apples on a Tree

• EN: There are 15 apples on a tree. 6 apples fall off. How many apples are left?
• FR: Il y a 15 pommes dans un arbre. 6 pommes tombent. Combien de pommes reste-t-il?
• Choices: A) 7 apples B) 8 apples C) 9 apples D) 11 apples
• Hint: To subtract 12 − 4, count back from 12: 11, 10, 9, 8.
• Steps:
  • Start at 15 and count back 6: 14, 13, 12, 11, 10, 9.
  • So 9 apples are left on the tree.
• Answer: 9 apples

[Easy] Skip Counting by 5s

• EN: Emma skip-counts by 5s. She says 5, 10, 15, ___. What number comes next?
• FR: Emma compte par bonds de 5. Elle dit 5, 10, 15, ___. Quel nombre vient ensuite?
• Choices: A) 18 B) 20 C) 22 D) 25
• Hint: When skip-counting by 5s, add 5 each time: 10 + 5 = 15, then 15 + 5 = ?
• Steps:
  • The pattern adds 5 each time.
  • 15 + 5 = 20.
• Answer: 20

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents in Canada?
• FR: Quelle pièce de monnaie vaut 10 cents au Canada?
• Choices: A) A penny B) A nickel C) A dime D) A quarter
• Hint: Think about the three smallest coins: 1 cent, 5 cents, and 10 cents.
• Steps:
  • A penny = 1 cent, a nickel = 5 cents, a dime = 10 cents.
  • The dime is worth 10 cents.
• Answer: A dime

[Medium] Hockey Cards

• EN: Noah has 13 hockey cards. He gives 4 to his friend. Then he gets 3 more cards. How many cards does Noah have now?
• FR: Noah a 13 cartes de hockey. Il en donne 4 à son ami. Puis il reçoit 3 autres cartes. Combien de cartes Noah a-t-il maintenant?
• Choices: A) 10 cards B) 11 cards C) 12 cards D) 14 cards
• Hint: Try 10 − 3 + 2: first subtract, then add.
• Steps:
  • Start with 13 cards. Subtract 4: 13 − 4 = 9.
  • Then add 3: 9 + 3 = 12.
• Answer: 12 cards

[Medium] Comparing Numbers

• EN: Which number is greater: 47 or 74?
• FR: Quel nombre est le plus grand : 47 ou 74?
• Choices: A) 47 B) 74 C) Both are equal D) Neither
• Hint: Compare the tens digit first: 3 tens is less than 6 tens.
• Steps:
  • Look at the tens digit: 47 has 4 tens, 74 has 7 tens.
  • 7 tens is more than 4 tens, so 74 is greater.
• Answer: 74

[Medium] Nickels

• EN: Sophia has 3 nickels. How many cents does she have in total?
• FR: Sophia a 3 pièces de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: Count by 5s for each nickel: 5, 10, … how many times?
• Steps:
  • Each nickel = 5 cents. Skip-count by 5s three times: 5, 10, 15.
  • Sophia has 15 cents in total.
• Answer: 15 cents

[Medium] Number Line Jump

• EN: On a number line, start at 8. Jump forward 6 spaces. Where do you land?
• FR: Sur une droite numérique, commence à 8. Avance de 6 espaces. Où arrives-tu?
• Choices: A) 12 B) 13 C) 14 D) 16
• Hint: Starting at 5, jumping 4 spaces lands on 5 + 4 = 9.
• Steps:
  • Start at 8. Count forward 6: 9, 10, 11, 12, 13, 14.
  • You land on 14.
• Answer: 14

[Hard] Two-Step Snowball Story

• EN: Maya made 9 snowballs in the morning and 8 snowballs in the afternoon. She threw 11 snowballs at a target. How many snowballs does she have left?
• FR: Maya a fait 9 boules de neige le matin et 8 boules de neige l'après-midi. Elle en a lancé 11 sur une cible. Combien de boules de neige lui reste-t-il?
• Choices: A) 4 snowballs B) 5 snowballs C) 6 snowballs D) 7 snowballs
• Hint: Try 6 + 5 = 11 total, then 11 − 8 = 3 left.
• Steps:
  • Add the morning and afternoon: 9 + 8 = 17 snowballs.
  • Subtract the ones she threw: 17 − 11 = 6.
• Answer: 6 snowballs

[Hard] Skip Counting Puzzle

• EN: Aiden skip-counts by 2s starting at 2. What is the 9th number he says?
• FR: Aiden compte par bonds de 2 en commençant à 2. Quel est le 9e nombre qu'il dit?
• Choices: A) 16 B) 17 C) 18 D) 19
• Hint: Skip-count by 2s: 2, 4, 6, 8 — the 4th number is 8. Keep going!
• Steps:
  • Count by 2s: 2(1), 4(2), 6(3), 8(4), 10(5), 12(6), 14(7), 16(8), 18(9).
  • The 9th number is 18.
• Answer: 18

[Easy] Adding to 100

• EN: There are 34 students in a school gym and 25 more arrive. How many students are in the gym now?
• FR: Il y a 34 élèves dans le gymnase de l'école et 25 autres arrivent. Combien d'élèves y a-t-il maintenant dans le gymnase?
• Choices: A) 57 students B) 59 students C) 61 students D) 69 students
• Hint: Add the tens first, then the ones: 20 + 30 = 50, then 5 + 4 = 9.
• Steps:
  • Add tens: 30 + 20 = 50.
  • Add ones: 4 + 5 = 9. Total: 50 + 9 = 59 students.
• Answer: 59 students

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre l'aiguille des heures sur le 3 et l'aiguille des minutes sur le 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 6:15
• Hint: When the minute hand points to 12, it is exactly on the hour.
• Steps:
  • The minute hand on 12 means it is exactly the hour.
  • The hour hand is on 3, so the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 14 cm de long. Un crayon de couleur mesure 9 cm. De combien le crayon à mine est-il plus long que le crayon de couleur?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find the difference, subtract: 12 − 7 = 5.
• Steps:
  • Subtract the shorter from the longer: 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Counting Coins

• EN: Zara has 2 dimes and 1 nickel. How much money does she have?
• FR: Zara a 2 pièces de 10 cents et 1 pièce de 5 cents. Combien d'argent a-t-elle?
• Choices: A) 20 cents B) 22 cents C) 25 cents D) 30 cents
• Hint: Count each coin: 10 + 10 = 20, then add the nickel (5 cents).
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • Add 1 nickel: 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtraction Within 100

• EN: A baker made 82 muffins. He sold 47 muffins at the market. How many muffins are left?
• FR: Un boulanger a fait 82 muffins. Il en a vendu 47 au marché. Combien de muffins reste-t-il?
• Choices: A) 35 muffins B) 36 muffins C) 38 muffins D) 45 muffins
• Hint: Try 73 − 38: borrow from the tens → 13 − 8 = 5, then 6 − 3 = 3, giving 35.
• Steps:
  • Subtract ones: 2 − 7 needs borrowing. Borrow 1 ten: 12 − 7 = 5.
  • Subtract tens: 7 − 4 = 3. So 82 − 47 = 35 muffins.
• Answer: 35 muffins

[Medium] Telling Time — Half Hour

• EN: The clock shows the hour hand between 6 and 7, and the minute hand on 6. What time does the clock show?
• FR: L'horloge montre l'aiguille des heures entre 6 et 7, et l'aiguille des minutes sur le 6. Quelle heure l'horloge indique-t-elle?
• Choices: A) 6:00 B) 6:30 C) 7:00 D) 7:30
• Hint: When the minute hand is on 6, it means 30 minutes past the hour.
• Steps:
  • The minute hand on 6 = 30 minutes past.
  • The hour hand is just past 6, so the time is 6:30.
• Answer: 6:30

[Medium] Pattern Recognition

• EN: Look at this pattern: 3, 6, 9, 12, ___. What is the missing number?
• FR: Observe ce motif : 3, 6, 9, 12, ___. Quel est le nombre manquant?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Find how much is added each time: 8, 12, 16, 20 — the rule is +4.
• Steps:
  • The pattern adds 3 each time: 3, 6, 9, 12.
  • 12 + 3 = 15.
• Answer: 15

[Medium] Coin Combinations

• EN: Tyler wants to buy a sticker that costs 75 cents. He has 3 quarters. Does he have enough money?
• FR: Tyler veut acheter un autocollant qui coûte 75 cents. Il a 3 pièces de 25 cents. A-t-il assez d'argent?
• Choices: A) No, he has 50 cents B) No, he has 60 cents C) Yes, he has exactly 75 cents D) Yes, he has 90 cents
• Hint: Count quarters: 25 + 25 = 50, then 50 + 25 = 75.
• Steps:
  • 1 quarter = 25 cents. 3 quarters = 25 + 25 + 25 = 75 cents.
  • The sticker costs 75 cents, so he has exactly enough.
• Answer: Yes, he has exactly 75 cents

[Hard] Two-Part Problem

• EN: A class collects 56 cans on Monday and 38 cans on Tuesday. They give away 29 cans to a food bank. How many cans do they have left?
• FR: Une classe recueille 56 boîtes lundi et 38 boîtes mardi. Elle en donne 29 à une banque alimentaire. Combien de boîtes lui reste-t-il?
• Choices: A) 63 cans B) 65 cans C) 67 cans D) 69 cans
• Hint: First add the two amounts, then subtract: (40 + 30) − 15 = 55.
• Steps:
  • Add Monday and Tuesday: 56 + 38 = 94 cans.
  • Subtract what was given away: 94 − 29 = 65 cans.
• Answer: 65 cans

[Hard] Measuring and Comparing

• EN: A bookshelf is 95 cm tall. A desk is 78 cm tall. How much taller is the bookshelf than the desk?
• FR: Une étagère mesure 95 cm de hauteur. Un bureau mesure 78 cm. De combien l'étagère est-elle plus haute que le bureau?
• Choices: A) 13 cm B) 15 cm C) 17 cm D) 19 cm
• Hint: Subtract to compare: 84 − 67 = 17. Borrow from the tens if needed.
• Steps:
  • Subtract: 95 − 78. Borrow: 15 − 8 = 7 ones, then 8 − 7 = 1 ten.
  • 95 − 78 = 17 cm.
• Answer: 17 cm

[Easy] Multiplication by 5

• EN: There are 6 bags of apples. Each bag has 5 apples. How many apples are there in all?
• FR: Il y a 6 sacs de pommes. Chaque sac contient 5 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 25 apples B) 30 apples C) 35 apples D) 36 apples
• Hint: 4 × 5 = 20; just remember the 5 times table pattern (always ends in 0 or 5).
• Steps:
  • Multiply: 6 × 5 = 30.
  • There are 30 apples in all.
• Answer: 30 apples

[Easy] Basic Fractions

• EN: A pizza is cut into 4 equal slices. Chloe eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 parts égales. Chloé mange 1 part. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: Fraction = parts eaten / total equal parts. If there are 8 parts and you eat 1, that's 1/8.
• Steps:
  • Total equal slices = 4. Chloe ate 1.
  • Fraction eaten = 1 out of 4 = 1/4.
• Answer: 1/4

[Easy] Multiplication by 2

• EN: A hockey team has 8 players. Each player has 2 gloves. How many gloves are there in total?
• FR: Une équipe de hockey a 8 joueurs. Chaque joueur a 2 gants. Combien y a-t-il de gants au total?
• Choices: A) 10 gloves B) 14 gloves C) 16 gloves D) 18 gloves
• Hint: 5 × 2 = 10; multiply the number of groups by 2.
• Steps:
  • Multiply: 8 × 2 = 16.
  • There are 16 gloves in total.
• Answer: 16 gloves

[Easy] Perimeter of a Rectangle

• EN: A garden is 5 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un jardin mesure 5 m de long et 3 m de large. Quel est le périmètre du jardin?
• Choices: A) 8 m B) 15 m C) 16 m D) 18 m
• Hint: Perimeter of a rectangle = add all 4 sides: 4 + 2 + 4 + 2 = 12.
• Steps:
  • Add all four sides: 5 + 3 + 5 + 3 = 16.
  • The perimeter is 16 m.
• Answer: 16 m

[Medium] Division

• EN: A teacher has 24 crayons to share equally among 4 students. How many crayons does each student get?
• FR: Un enseignant a 24 crayons à partager également entre 4 élèves. Combien de crayons chaque élève reçoit-il?
• Choices: A) 4 crayons B) 5 crayons C) 6 crayons D) 8 crayons
• Hint: Think: what times 4 equals 20? → 5 × 4 = 20.
• Steps:
  • Divide: 24 ÷ 4 = 6. (Because 4 × 6 = 24.)
  • Each student gets 6 crayons.
• Answer: 6 crayons

[Medium] Reading a Graph

• EN: A bar graph shows: apples = 8, bananas = 5, oranges = 7. How many more apples than bananas are shown?
• FR: Un diagramme à bandes montre : pommes = 8, bananes = 5, oranges = 7. Combien y a-t-il plus de pommes que de bananes?
• Choices: A) 1 more B) 2 more C) 3 more D) 4 more
• Hint: Find the difference: 10 − 6 = 4 more.
• Steps:
  • Subtract bananas from apples: 8 − 5 = 3.
  • There are 3 more apples than bananas.
• Answer: 3 more

[Medium] Multiplication by 10

• EN: There are 7 boxes. Each box holds 10 books. How many books are there altogether?
• FR: Il y a 7 boîtes. Chaque boîte contient 10 livres. Combien y a-t-il de livres en tout?
• Choices: A) 17 books B) 60 books C) 70 books D) 77 books
• Hint: Any number times 10 just adds a zero: 5 × 10 = 50.
• Steps:
  • Multiply: 7 × 10 = 70.
  • There are 70 books altogether.
• Answer: 70 books

[Medium] Comparing Fractions

• EN: Which fraction is larger: 1/2 or 1/4?
• FR: Quelle fraction est la plus grande : 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/2 C) They are equal D) Cannot be compared
• Hint: Imagine cutting a pie into 2 pieces vs. 4 pieces — bigger pieces when fewer cuts.
• Steps:
  • With the same whole, more parts = smaller pieces.
  • 1/2 means 1 of 2 equal parts, which is bigger than 1 of 4 equal parts.
• Answer: 1/2

[Hard] Multi-Step Multiplication

• EN: A store sells 3 packs of hockey cards. Each pack has 9 cards. The store also sells 4 single cards. How many cards are for sale in total?
• FR: Un magasin vend 3 paquets de cartes de hockey. Chaque paquet contient 9 cartes. Le magasin vend aussi 4 cartes individuelles. Combien de cartes y a-t-il en vente au total?
• Choices: A) 27 cards B) 29 cards C) 31 cards D) 36 cards
• Hint: First multiply (2 × 8 = 16), then add the extra items (16 + 3 = 19).
• Steps:
  • Multiply: 3 × 9 = 27 cards in packs.
  • Add single cards: 27 + 4 = 31 cards in total.
• Answer: 31 cards

[Hard] Perimeter Word Problem

• EN: A square playground has a perimeter of 36 m. What is the length of one side of the playground?
• FR: Une cour de jeu carrée a un périmètre de 36 m. Quelle est la longueur d'un côté de la cour?
• Choices: A) 6 m B) 8 m C) 9 m D) 12 m
• Hint: A square has 4 equal sides. If the perimeter is 20, each side = 20 ÷ 4 = 5.
• Steps:
  • A square has 4 equal sides. Divide: 36 ÷ 4 = 9.
  • Each side is 9 m long.
• Answer: 9 m

[Easy] Multiplication Table

• EN: What is 8 × 7?
• FR: Combien font 8 × 7?
• Choices: A) 48 B) 54 C) 56 D) 64
• Hint: Think of 8 × 6 = 48, then add one more group of 8: 48 + 8 = 56.
• Steps:
  • 8 × 7: recall or build up from 8 × 6 = 48.
  • 48 + 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, what digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre est à la position des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 47
• Hint: In 5.82, the digit 8 is in the tenths place (first digit after the decimal).
• Steps:
  • In 3.47: 3 is ones, 4 is tenths, 7 is hundredths.
  • The digit in the tenths place is 4.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A rectangular rug is 6 m long and 4 m wide. What is the area of the rug?
• FR: Un tapis rectangulaire mesure 6 m de long et 4 m de large. Quelle est l'aire du tapis?
• Choices: A) 10 m² B) 20 m² C) 24 m² D) 28 m²
• Hint: Area of a rectangle = length × width. For 5 m × 3 m, area = 15 m².
• Steps:
  • Area = length × width = 6 × 4 = 24.
  • The area of the rug is 24 m².
• Answer: 24 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/4?
• FR: Quelle fraction est la plus grande : 3/4 ou 2/4?
• Choices: A) 2/4 B) 3/4 C) They are equal D) Cannot be determined
• Hint: When denominators are the same, compare numerators: 5/8 > 3/8.
• Steps:
  • Both fractions have denominator 4. Compare numerators: 3 > 2.
  • So 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: A bag has 58 marbles shared equally among 7 children. How many marbles does each child get, and how many are left over?
• FR: Un sac contient 58 billes partagées également entre 7 enfants. Combien de billes chaque enfant reçoit-il et combien en reste-t-il?
• Choices: A) 7 remainder 9 B) 8 remainder 2 C) 8 remainder 4 D) 9 remainder 1
• Hint: Try 45 ÷ 6: 6 × 7 = 42, remainder = 45 − 42 = 3, so answer is 7 remainder 3.
• Steps:
  • 7 × 8 = 56. 58 − 56 = 2 remainder.
  • Each child gets 8 marbles with 2 left over.
• Answer: 8 remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 PM and ends at 3:45 PM. How long does the game last?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps dure le match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: From 2:10 to 4:40 — count hours first (2 hours), then minutes (30 min) = 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 = 2 hours.
  • From 3:15 to 3:45 = 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A ribbon is 4.6 m long. Another ribbon is 2.3 m long. What is their total length?
• FR: Un ruban mesure 4,6 m de long. Un autre ruban mesure 2,3 m. Quelle est leur longueur totale?
• Choices: A) 6.3 m B) 6.9 m C) 7.0 m D) 7.3 m
• Hint: Line up decimal points, then add like whole numbers: 3.2 + 1.5 = 4.7.
• Steps:
  • Add: 4.6 + 2.3. Ones: 4 + 2 = 6. Tenths: 6 + 3 = 9.
  • Total length = 6.9 m.
• Answer: 6.9 m

[Medium] Multiplication — Two Digits

• EN: A Tim Hortons sells 23 boxes of doughnuts per hour. How many boxes are sold in 4 hours?
• FR: Un Tim Hortons vend 23 boîtes de beignes par heure. Combien de boîtes sont vendues en 4 heures?
• Choices: A) 82 boxes B) 88 boxes C) 92 boxes D) 96 boxes
• Hint: For 32 × 3: multiply ones first (2 × 3 = 6) then tens (30 × 3 = 90) → total 96.
• Steps:
  • 23 × 4: ones: 3 × 4 = 12 (write 2, carry 1). Tens: 2 × 4 = 8 + 1 = 9.
  • Answer is 92 boxes.
• Answer: 92 boxes

[Hard] Multi-Step Area Problem

• EN: A classroom floor is 9 m long and 8 m wide. A carpet covers a section that is 4 m long and 3 m wide. What area of the floor is NOT covered by the carpet?
• FR: Le sol d'une salle de classe mesure 9 m de long et 8 m de large. Un tapis couvre une section de 4 m de long et 3 m de large. Quelle superficie du sol n'est PAS couverte par le tapis?
• Choices: A) 56 m² B) 60 m² C) 64 m² D) 72 m²
• Hint: Find the total area first (6 × 5 = 30), then subtract the rug area (2 × 3 = 6): 30 − 6 = 24.
• Steps:
  • Total floor area: 9 × 8 = 72 m².
  • Carpet area: 4 × 3 = 12 m².
  • Uncovered area: 72 − 12 = 60 m².
• Answer: 60 m²

[Hard] Long Division Challenge

• EN: A school orders 175 pencils for 7 classrooms, shared equally. How many pencils does each classroom receive?
• FR: Une école commande 175 crayons pour 7 classes à parts égales. Combien de crayons chaque classe reçoit-elle?
• Choices: A) 23 pencils B) 24 pencils C) 25 pencils D) 26 pencils
• Hint: For 144 ÷ 6: 6 × 20 = 120, 144 − 120 = 24, 6 × 4 = 24, so answer = 24.
• Steps:
  • 7 × 20 = 140. 175 − 140 = 35. 7 × 5 = 35.
  • 175 ÷ 7 = 25 pencils per classroom.
• Answer: 25 pencils

[Easy] Multi-Digit Multiplication

• EN: A school buys 24 boxes of markers. Each box has 12 markers. How many markers are there in total?
• FR: Une école achète 24 boîtes de marqueurs. Chaque boîte contient 12 marqueurs. Combien y a-t-il de marqueurs au total?
• Choices: A) 248 markers B) 268 markers C) 288 markers D) 296 markers
• Hint: For 22 × 13: 22 × 10 = 220 and 22 × 3 = 66, then 220 + 66 = 286.
• Steps:
  • 24 × 12 = 24 × 10 + 24 × 2 = 240 + 48 = 288.
  • There are 288 markers in total.
• Answer: 288 markers

[Easy] Percentage — 50%

• EN: A hockey jersey normally costs $40. It is on sale for 50% off. How much do you save?
• FR: Un chandail de hockey coûte normalement 40 $. Il est en solde à 50 % de rabais. Combien économises-tu?
• Choices: A) $10 B) $15 C) $20 D) $25
• Hint: 50% means half. Half of $60 = $30.
• Steps:
  • 50% of $40 = $40 ÷ 2 = $20.
  • You save $20.
• Answer: $20

[Easy] Adding Fractions with Like Denominators

• EN: Mia ate 2/8 of a sandwich and her brother ate 3/8. What fraction of the sandwich did they eat together?
• FR: Mia a mangé 2/8 d'un sandwich et son frère en a mangé 3/8. Quelle fraction du sandwich ont-ils mangée ensemble?
• Choices: A) 5/16 B) 4/8 C) 5/8 D) 6/8
• Hint: When denominators match, just add the numerators: 1/5 + 2/5 = 3/5.
• Steps:
  • Same denominator (8): add numerators: 2 + 3 = 5.
  • They ate 5/8 of the sandwich together.
• Answer: 5/8

[Easy] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de hauteur. Quel est son volume?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 80 cm³
• Hint: Volume = length × width × height. For 4 × 3 × 2: 4 × 3 = 12, then 12 × 2 = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3 = 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Multi-Digit Division

• EN: A fundraiser collected $672. The money is shared equally among 8 charities. How much does each charity receive?
• FR: Une levée de fonds a recueilli 672 $. L'argent est partagé également entre 8 organismes de bienfaisance. Combien chaque organisme reçoit-il?
• Choices: A) $74 B) $82 C) $84 D) $96
• Hint: For 480 ÷ 6: 6 × 80 = 480, so the answer is 80.
• Steps:
  • 8 × 80 = 640. 672 − 640 = 32. 8 × 4 = 32.
  • $672 ÷ 8 = $84.
• Answer: $84

[Medium] Decimal Operations

• EN: Jake buys a notebook for $3.75 and a pen for $1.49. How much does he spend altogether?
• FR: Jake achète un cahier pour 3,75 $ et un stylo pour 1,49 $. Combien dépense-t-il en tout?
• Choices: A) $4.24 B) $5.14 C) $5.24 D) $6.14
• Hint: Line up decimals: 2.50 + 1.75 → 3 + 1 = 4, 50 + 75 = 125 cents → $5.25.
• Steps:
  • $3.75 + $1.49: cents: 75 + 49 = 124 → 24 cents, carry $1.
  • Dollars: 3 + 1 + 1 = $5. Total = $5.24.
• Answer: $5.24

[Medium] Percentage — 25%

• EN: A bag of apples weighs 8 kg. 25% of the bag is bruised apples. How many kilograms of apples are bruised?
• FR: Un sac de pommes pèse 8 kg. 25 % du sac contient des pommes meurtries. Combien de kilogrammes de pommes sont meurtries?
• Choices: A) 1 kg B) 2 kg C) 3 kg D) 4 kg
• Hint: 25% = 1/4. Find 1/4 of 12: 12 ÷ 4 = 3.
• Steps:
  • 25% = one quarter. 8 ÷ 4 = 2.
  • 2 kg of apples are bruised.
• Answer: 2 kg

[Medium] Subtracting Fractions

• EN: A pitcher holds 7/10 L of juice. Priya pours out 3/10 L. How much juice is left?
• FR: Un pichet contient 7/10 L de jus. Priya en verse 3/10 L. Combien de jus reste-t-il?
• Choices: A) 3/10 L B) 4/10 L C) 5/10 L D) 6/10 L
• Hint: Same denominator — subtract numerators: 6/9 − 2/9 = 4/9.
• Steps:
  • Subtract numerators: 7 − 3 = 4. Keep denominator: 10.
  • 4/10 L of juice is left.
• Answer: 4/10 L

[Hard] Multi-Step Word Problem

• EN: A snowfall of 14.8 cm fell on Saturday. On Sunday, 9.35 cm more snow fell. On Monday, 6.5 cm of snow melted. What is the total depth of snow after Monday?
• FR: Il est tombé 14,8 cm de neige samedi. Dimanche, il en est tombé 9,35 cm de plus. Lundi, 6,5 cm de neige ont fondu. Quelle est la profondeur totale de neige après lundi?
• Choices: A) 16.65 cm B) 17.65 cm C) 18.15 cm D) 19.65 cm
• Hint: Try 10.2 + 5.6 − 3.4: first add (15.8), then subtract (12.4).
• Steps:
  • Add Saturday and Sunday: 14.80 + 9.35 = 24.15 cm.
  • Subtract Monday's melt: 24.15 − 6.50 = 17.65 cm.
• Answer: 17.65 cm

[Hard] Percentage Challenge

• EN: A winter coat costs $120. It is discounted by 10%, and then there is an additional 25% off the sale price. What is the final price?
• FR: Un manteau d'hiver coûte 120 $. Il est réduit de 10 %, puis il y a un rabais supplémentaire de 25 % sur le prix de vente. Quel est le prix final?
• Choices: A) $78 B) $81 C) $90 D) $96
• Hint: Apply one percent at a time: for $80 reduced by 10%: $80 − $8 = $72, then 25% off $72 = $18 off = $54.
• Steps:
  • 10% of $120 = $12. Sale price: $120 − $12 = $108.
  • 25% of $108 = $27. Final price: $108 − $27 = $81.
• Answer: $81

[Easy] Fraction Multiplication

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

[Easy] Percent of a Number

• EN: What is 20% of 60?
• FR: Combien font 20 % de 60?
• Choices: A) 10 B) 12 C) 14 D) 20
• Hint: 10% of 50 = 5; 20% = double that = 10.
• Steps:
  • 10% of 60 = 6. 20% = 6 × 2 = 12.
  • 20% of 60 is 12.
• Answer: 12

[Easy] Integers Introduction

• EN: The temperature is −3°C in the morning. It rises by 8°C. What is the temperature now?
• FR: La température est de −3 °C le matin. Elle monte de 8 °C. Quelle est la température maintenant?
• Choices: A) −11°C B) −5°C C) 5°C D) 11°C
• Hint: Starting at −5 and going up 7: −5 + 7 = 2.
• Steps:
  • −3 + 8 = 5.
  • The temperature is now 5°C.
• Answer: 5°C

[Easy] Rate and Ratio

• EN: A car travels 90 km in 1 hour. How far does it travel in 3 hours at the same speed?
• FR: Une voiture parcourt 90 km en 1 heure. Quelle distance parcourt-elle en 3 heures à la même vitesse?
• Choices: A) 180 km B) 240 km C) 270 km D) 300 km
• Hint: Multiply the rate by the number of hours: 60 km/h × 4 h = 240 km.
• Steps:
  • Rate = 90 km per hour. Time = 3 hours.
  • Distance = 90 × 3 = 270 km.
• Answer: 270 km

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1.
• FR: Évalue : 3 + 4 × 2 − 1.
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: In 5 + 3 × 2 − 1, do multiplication first: 5 + 6 − 1 = 10.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add and subtract left to right: 3 + 8 − 1 = 10.
• Answer: 10

[Medium] 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) 18 C) 20 D) 22
• Hint: Substitute the value: if x = 4, then 2x + 3 = 2(4) + 3 = 11.
• Steps:
  • Replace n with 5: 3(5) + 7 = 15 + 7 = 22.
  • The value is 22.
• Answer: 22

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1/2 C) 1 and 1/4 D) 3/2
• Hint: Dividing by a fraction means multiplying by its reciprocal: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
• Steps:
  • Multiply by the reciprocal of 1/2, which is 2/1: 3/4 × 2/1 = 6/4 = 3/2.
  • 3/2 = 1 and 1/2. Wait — recalculate: 6/4 = 1 and 2/4 = 1 and 1/2. But checking choices, 3/2 is a listed answer.
  • 3/4 ÷ 1/2 = 3/4 × 2 = 6/4 = 3/2.
• Answer: 3/2

[Medium] Ratio Problem

• EN: In a Grade 6 class, the ratio of boys to girls is 3:4. If there are 12 boys, how many girls are there?
• FR: Dans une classe de 6e année, le rapport entre les garçons et les filles est de 3:4. S'il y a 12 garçons, combien y a-t-il de filles?
• Choices: A) 9 girls B) 14 girls C) 16 girls D) 18 girls
• Hint: If ratio is 2:5 and there are 10 of the first group: 10 ÷ 2 = 5 (scale), 5 × 5 = 25 of the second.
• Steps:
  • Scale factor: 12 ÷ 3 = 4.
  • Girls = 4 × 4 = 16 girls.
• Answer: 16 girls

[Hard] BEDMAS with Brackets

• EN: Evaluate: (12 − 4) × 3 + 2² ÷ 2.
• FR: Évalue : (12 − 4) × 3 + 2² ÷ 2.
• Choices: A) 24 B) 26 C) 28 D) 32
• Hint: For (6 − 2) × 5 + 3² ÷ 3: brackets (4), then exponent (9), then multiply (20), divide (3), then add: 20 + 3 = 23.
• Steps:
  • Brackets: 12 − 4 = 8. Exponent: 2² = 4.
  • Multiply: 8 × 3 = 24. Divide: 4 ÷ 2 = 2.
  • Add: 24 + 2 = 26.
• Answer: 26

[Hard] Multi-Step Percent Problem

• EN: A pair of skates costs $160. They are on sale at 15% off. After the discount, a tax of 10% is added. What is the final price?
• FR: Une paire de patins coûte 160 $. Elle est en solde à 15 % de rabais. Après le rabais, une taxe de 10 % est ajoutée. Quel est le prix final?
• Choices: A) $136.00 B) $148.40 C) $149.60 D) $152.00
• Hint: For $200 at 20% off: $200 − $40 = $160 sale price. Then 10% tax: $160 + $16 = $176.
• Steps:
  • 15% of $160 = $24. Sale price: $160 − $24 = $136.
  • 10% tax on $136 = $13.60. Final price: $136 + $13.60 = $149.60.
• Answer: $149.60

[Easy] Integer Addition

• EN: What is −8 + 15?
• FR: Combien font −8 + 15?
• Choices: A) −23 B) −7 C) 7 D) 23
• Hint: Think of a number line: start at −5, move right 9 spaces: −5 + 9 = 4.
• Steps:
  • Starting at −8, add 15: move 15 places right.
  • −8 + 15 = 7.
• Answer: 7

[Easy] Percent Discount

• EN: A book normally costs $24. It is on sale at 25% off. What is the sale price?
• FR: Un livre coûte normalement 24 $. Il est en solde à 25 % de rabais. Quel est le prix de vente?
• Choices: A) $6 B) $12 C) $16 D) $18
• Hint: 25% off $40: find 25% ($10) then subtract: $40 − $10 = $30.
• Steps:
  • 25% of $24 = $24 ÷ 4 = $6.
  • Sale price = $24 − $6 = $18.
• Answer: $18

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x : x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 26
• Hint: To solve n + 4 = 10, subtract 4 from both sides: n = 6.
• Steps:
  • Subtract 9 from both sides: x = 17 − 9.
  • x = 8.
• Answer: x = 8

[Easy] Integer Subtraction

• EN: What is 3 − (−5)?
• FR: Combien font 3 − (−5)?
• Choices: A) −8 B) −2 C) 2 D) 8
• Hint: Subtracting a negative is the same as adding: 6 − (−2) = 6 + 2 = 8.
• Steps:
  • 3 − (−5) = 3 + 5 = 8.
  • The answer is 8.
• Answer: 8

[Medium] Tip Calculation

• EN: A family's restaurant bill is $85. They want to leave a 15% tip. How much is the tip?
• FR: La facture de restaurant d'une famille est de 85 $. Ils veulent laisser un pourboire de 15 %. Quel est le montant du pourboire?
• Choices: A) $10.50 B) $12.00 C) $12.75 D) $13.50
• Hint: 15% = 10% + 5%. For $60: 10% = $6, 5% = $3, total tip = $9.
• Steps:
  • 10% of $85 = $8.50. 5% of $85 = $4.25.
  • Tip = $8.50 + $4.25 = $12.75.
• Answer: $12.75

[Medium] Surface Area

• EN: A rectangular box is 5 cm long, 4 cm wide, and 3 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 5 cm de long, 4 cm de large et 3 cm de hauteur. Quelle est son aire totale?
• Choices: A) 60 cm² B) 70 cm² C) 74 cm² D) 94 cm²
• Hint: Surface area of a box = 2(lw + lh + wh). For 3 × 2 × 1: 2(6 + 3 + 2) = 2(11) = 22 cm².
• Steps:
  • lw = 5 × 4 = 20; lh = 5 × 3 = 15; wh = 4 × 3 = 12.
  • Surface area = 2(20 + 15 + 12) = 2(47) = 94 cm².
• Answer: 94 cm²

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Combien font (−6) × (−4)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: Negative × negative = positive: (−3) × (−7) = 21.
• Steps:
  • Two negative signs: the product is positive.
  • (−6) × (−4) = 24.
• Answer: 24

[Medium] Probability

• EN: A bag contains 3 red, 5 blue, and 2 green marbles. If one marble is picked at random, what is the probability it is blue?
• FR: Un sac contient 3 billes rouges, 5 bleues et 2 vertes. Si on tire une bille au hasard, quelle est la probabilité qu'elle soit bleue?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 5/10
• Hint: Probability = favourable outcomes / total outcomes. For 4 blue out of 12 total: 4/12 = 1/3.
• Steps:
  • Total marbles = 3 + 5 + 2 = 10. Blue = 5.
  • Probability = 5/10 = 1/2.
• Answer: 1/2

[Hard] Multi-Step Integer Problem

• EN: The temperature in Winnipeg was −14°C. It fell by 7°C overnight, then rose by 19°C by noon. What was the temperature at noon?
• FR: La température à Winnipeg était de −14 °C. Elle a baissé de 7 °C pendant la nuit, puis a monté de 19 °C jusqu'à midi. Quelle était la température à midi?
• Choices: A) −4°C B) −2°C C) 2°C D) 4°C
• Hint: Start at −10, subtract 5, add 20: −10 − 5 = −15, then −15 + 20 = 5.
• Steps:
  • Start: −14. Fall by 7: −14 − 7 = −21.
  • Rise by 19: −21 + 19 = −2. Temperature at noon is −2°C.
• Answer: −2°C

[Hard] Tax and Total

• EN: Alexia buys a pair of headphones for $65 and a phone case for $18. Ontario's HST is 13%. What is the total amount she pays including tax?
• FR: Alexia achète des écouteurs à 65 $ et un étui de téléphone à 18 $. La TVH de l'Ontario est de 13 %. Quel est le montant total qu'elle paie, taxes incluses?
• Choices: A) $83.00 B) $87.19 C) $93.79 D) $95.00
• Hint: Add items first, then find 13% and add it: for $50 + $30 = $80 × 0.13 = $10.40, total = $90.40.
• Steps:
  • Total before tax: $65 + $18 = $83.
  • Tax: 13% of $83 = $10.79. Total: $83 + $10.79 = $93.79.
• Answer: $93.79

[Easy] Square Roots

• EN: What is √144?
• FR: Combien font √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think: what number times itself equals 100? 10 × 10 = 100, so √100 = 10.
• Steps:
  • Ask: what number multiplied by itself gives 144?
  • 12 × 12 = 144, so √144 = 12.
• Answer: 12

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 5 = 17.
• FR: Résous pour x : 2x + 5 = 17.
• Choices: A) x = 4 B) x = 6 C) x = 8 D) x = 11
• Hint: For 3y + 2 = 14: subtract 2 first (3y = 12), then divide by 3 (y = 4).
• Steps:
  • Subtract 5 from both sides: 2x = 12.
  • Divide by 2: x = 6.
• Answer: x = 6

[Easy] Percent Increase

• EN: A jacket costs $80. The price increases by 15%. What is the new price?
• FR: Un manteau coûte 80 $. Le prix augmente de 15 %. Quel est le nouveau prix?
• Choices: A) $88 B) $90 C) $92 D) $96
• Hint: 10% of $60 = $6, 5% = $3, total increase = $9, new price = $69.
• Steps:
  • 15% of $80 = $12. New price = $80 + $12 = $92.
  • The new price is $92.
• Answer: $92

[Easy] Mean

• EN: Find the mean of these test scores: 72, 85, 90, 63, 80.
• FR: Trouve la moyenne de ces résultats d'examen : 72, 85, 90, 63, 80.
• Choices: A) 76 B) 78 C) 80 D) 85
• Hint: Mean = sum ÷ count. For 10, 20, 30: sum = 60, count = 3, mean = 20.
• Steps:
  • Sum: 72 + 85 + 90 + 63 + 80 = 390.
  • Mean = 390 ÷ 5 = 78.
• Answer: 78

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: For legs of 3 and 4: 3² + 4² = 9 + 16 = 25, √25 = 5.
• Steps:
  • a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation (Negative)

• EN: Solve for x: 3x − 7 = 14.
• FR: Résous pour x : 3x − 7 = 14.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: For 4m − 3 = 13: add 3 (4m = 16), then divide by 4 (m = 4).
• Steps:
  • Add 7 to both sides: 3x = 21.
  • Divide by 3: x = 7.
• Answer: x = 7

[Medium] Slope Introduction

• EN: A line passes through points (2, 3) and (6, 11). What is the slope of the line?
• FR: Une droite passe par les points (2, 3) et (6, 11). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). For (1,2) and (3,8): (8−2)/(3−1) = 6/2 = 3.
• Steps:
  • Rise = 11 − 3 = 8. Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 14, 7, 21, 14, 9, 3, 18.
• FR: Trouve la médiane de : 14, 7, 21, 14, 9, 3, 18.
• Choices: A) 9 B) 12 C) 14 D) 18
• Hint: First sort the data: for 5, 2, 8, 1, 7 → sorted: 1, 2, 5, 7, 8. Median = 5 (middle value).
• Steps:
  • Sort: 3, 7, 9, 14, 14, 18, 21. Seven values → middle is the 4th.
  • The median is 14.
• Answer: 14

[Hard] Pythagorean — Find a Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 8 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: Use a² + b² = c². If c = 10 and a = 6: b² = 100 − 36 = 64, b = 8.
• Steps:
  • b² = c² − a² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12 cm.
• Answer: 12 cm

[Hard] Percent Decrease

• EN: A store's revenue was $4,500 in July and $3,600 in August. What is the percent decrease in revenue?
• FR: Le chiffre d'affaires d'un magasin était de 4 500 $ en juillet et de 3 600 $ en août. Quel est le pourcentage de diminution du chiffre d'affaires?
• Choices: A) 15% B) 18% C) 20% D) 25%
• Hint: Percent decrease = (decrease ÷ original) × 100. If it drops from 500 to 400: decrease = 100, 100/500 × 100 = 20%.
• Steps:
  • Decrease = $4,500 − $3,600 = $900.
  • Percent decrease = (900 ÷ 4500) × 100 = 20%.
• Answer: 20%

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 3 = 13.
• FR: Résous pour x : 4x − 3 = 13.
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: For 5n − 2 = 18: add 2 to both sides (5n = 20), then divide by 5 (n = 4).
• Steps:
  • Add 3 to both sides: 4x = 16.
  • Divide by 4: x = 4.
• Answer: x = 4

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x − 7?
• FR: Quelle est la pente de la droite y = 3x − 7?
• Choices: A) −7 B) −3 C) 3 D) 7
• Hint: In y = mx + b, m is the slope and b is the y-intercept. In y = 5x + 2, slope = 5.
• Steps:
  • The equation is in y = mx + b form. m = 3.
  • The slope is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3).
• FR: Simplifie : (3x + 5) + (2x − 3).
• Choices: A) 5x − 2 B) 5x + 2 C) 6x + 2 D) 5x + 8
• Hint: Combine like terms: (4a + 7) + (3a − 2) = 7a + 5.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2. Result: 5x + 2.
• Answer: 5x + 2

[Easy] Linear Inequality

• EN: Solve for x: x − 4 > 10.
• FR: Résous pour x : x − 4 > 10.
• Choices: A) x > 6 B) x > 8 C) x > 14 D) x > 40
• Hint: For n − 3 > 7, add 3 to both sides: n > 10.
• Steps:
  • Add 4 to both sides: x > 14.
  • The solution is x > 14.
• Answer: x > 14

[Medium] Graphing — y-intercept

• EN: What is the y-intercept of the line y = −2x + 9?
• FR: Quel est l'ordonnée à l'origine de la droite y = −2x + 9?
• Choices: A) (0, −2) B) (0, 2) C) (0, 9) D) (9, 0)
• Hint: The y-intercept is where x = 0. In y = 4x + 6, plug in x = 0: y = 6, so y-intercept is (0, 6).
• Steps:
  • Set x = 0: y = −2(0) + 9 = 9.
  • The y-intercept is (0, 9).
• Answer: (0, 9)

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x − 5).
• FR: Développe : 3x(2x − 5).
• Choices: A) 5x² − 8x B) 6x² − 15x C) 6x − 15x D) 6x² + 15x
• Hint: Distribute: 4y(3y − 2) = 4y × 3y − 4y × 2 = 12y² − 8y.
• Steps:
  • 3x × 2x = 6x². 3x × (−5) = −15x.
  • Result: 6x² − 15x.
• Answer: 6x² − 15x

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in a ratio of 3:5. If the shorter triangle has a side of 12 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans un rapport de 3:5. Si le plus petit triangle a un côté de 12 cm, quel est le côté correspondant du plus grand triangle?
• Choices: A) 15 cm B) 18 cm C) 20 cm D) 25 cm
• Hint: Scale factor from 2:7 — if small side = 6, scale = 6/2 = 3, large side = 3 × 7 = 21.
• Steps:
  • Scale factor: 12 ÷ 3 = 4. Multiply by 5: 4 × 5 = 20 cm.
  • The larger triangle's side is 20 cm.
• Answer: 20 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 9 cm and the hypotenuse is 15 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 9 cm et l'hypoténuse mesure 15 cm. Combien fait sin(θ)?
• Choices: A) 3/4 B) 3/5 C) 4/5 D) 9/15 simplified to 5/3
• Hint: SOH: sin = opposite ÷ hypotenuse. If opposite = 4 and hypotenuse = 8, sin = 4/8 = 1/2.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 9 ÷ 15 = 3/5.
  • sin(θ) = 3/5.
• Answer: 3/5

[Hard] System of Equations

• EN: Solve the system: y = 2x + 1 and y = −x + 7.
• FR: Résous le système : y = 2x + 1 et y = −x + 7.
• Choices: A) x = 1, y = 3 B) x = 2, y = 5 C) x = 3, y = 4 D) x = 4, y = 3
• Hint: Set both expressions equal: 3n + 1 = −n + 9 → 4n = 8 → n = 2.
• Steps:
  • Set equal: 2x + 1 = −x + 7. Add x: 3x + 1 = 7. Subtract 1: 3x = 6. x = 2.
  • y = 2(2) + 1 = 5. Solution: x = 2, y = 5.
• Answer: x = 2, y = 5

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 10 cm. What is the angle θ (in degrees) using CAH?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 10 cm. Quel est l'angle θ (en degrés) avec CAH?
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: CAH: cos(θ) = adjacent ÷ hypotenuse. If cos(θ) = 1/2, then θ = 60°.
• Steps:
  • cos(θ) = 5 ÷ 10 = 0.5 = 1/2.
  • cos⁻¹(1/2) = 60°.
• Answer: 60°

[Easy] Factoring a Quadratic

• EN: Factor: x² + 7x + 12.
• FR: Factorise : x² + 7x + 12.
• Choices: A) (x + 2)(x + 6) B) (x + 3)(x + 4) C) (x + 1)(x + 12) D) (x + 4)(x + 8)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient: for x² + 5x + 6, find 2 × 3 = 6 and 2 + 3 = 5.
• Steps:
  • Find two numbers that multiply to 12 and add to 7: 3 × 4 = 12 and 3 + 4 = 7.
  • Factored form: (x + 3)(x + 4).
• Answer: (x + 3)(x + 4)

[Easy] Trigonometry — TOA

• EN: In a right triangle, the opposite side is 8 cm and the adjacent side is 6 cm. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 8 cm et le côté adjacent mesure 6 cm. Combien fait tan(θ)?
• Choices: A) 3/4 B) 4/3 C) 3/5 D) 5/3
• Hint: TOA: tan = opposite ÷ adjacent. If opposite = 3 and adjacent = 9, tan = 3/9 = 1/3.
• Steps:
  • tan(θ) = opposite ÷ adjacent = 8 ÷ 6 = 4/3.
  • tan(θ) = 4/3.
• Answer: 4/3

[Easy] System of Equations

• EN: Solve the system: x + y = 10 and x − y = 4.
• FR: Résous le système : x + y = 10 et x − y = 4.
• Choices: A) x = 6, y = 4 B) x = 7, y = 3 C) x = 8, y = 2 D) x = 5, y = 5
• Hint: Add the equations to eliminate y: (a + b) + (a − b) = 2a, then solve for a.
• Steps:
  • Add: (x + y) + (x − y) = 10 + 4 → 2x = 14 → x = 7.
  • Substitute: 7 + y = 10 → y = 3.
• Answer: x = 7, y = 3

[Easy] Volume of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 188.4 cm³ B) 282.6 cm³ C) 314 cm³ D) 94.2 cm³
• Hint: V = π × r² × h. For r = 2 and h = 5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 9 × 10 = 3.14 × 90.
  • V = 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x − 7 = 0.
• FR: Résous en complétant le carré : x² + 6x − 7 = 0.
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 2 or x = −8 D) x = 3 or x = −9
• Hint: For x² + 4x − 5 = 0: (x + 2)² = 9 → x + 2 = ±3 → x = 1 or x = −5.
• Steps:
  • x² + 6x = 7. Add (3)² = 9: x² + 6x + 9 = 16.
  • (x + 3)² = 16 → x + 3 = ±4 → x = 1 or x = −7.
• Answer: x = 1 or x = −7

[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: C = π × d. For d = 10: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14 = 43.96 cm.
  • The circumference is 43.96 cm.
• Answer: 43.96 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve: x² − 5x + 6 = 0.
• FR: Utilise la formule quadratique pour résoudre : x² − 5x + 6 = 0.
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = −2 or x = −3 D) x = 3 or x = −2
• Hint: For x² − 7x + 10 = 0, factor to find (x − 2)(x − 5) = 0, giving x = 2 or x = 5.
• Steps:
  • Discriminant: b² − 4ac = 25 − 24 = 1. √1 = 1.
  • x = (5 ± 1) ÷ 2 → x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 7 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur de l'apothème de 7 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 87.92 cm² B) 113.04 cm² C) 138.16 cm² D) 175.84 cm²
• Hint: Total SA of cone = πrl + πr². For r = 3, l = 5: 3.14×3×5 + 3.14×9 = 47.1 + 28.26 = 75.36 cm².
• Steps:
  • Lateral area: π × r × l = 3.14 × 4 × 7 = 87.92 cm².
  • Base area: π × r² = 3.14 × 16 = 50.24 cm².
  • Total: 87.92 + 50.24 = 138.16 cm².
• Answer: 138.16 cm²

[Hard] Completing the Square — Vertex Form

• EN: Write y = x² − 8x + 11 in vertex form. What is the vertex?
• FR: Écris y = x² − 8x + 11 sous la forme canonique. Quel est le sommet?
• Choices: A) (4, −5) B) (−4, 5) C) (4, 5) D) (−4, −5)
• Hint: For y = x² − 6x + 2: complete the square → (x − 3)² − 7, vertex = (3, −7).
• Steps:
  • y = (x² − 8x + 16) − 16 + 11 = (x − 4)² − 5.
  • Vertex is at (4, −5).
• Answer: (4, −5)

[Hard] Circle Geometry — Chord and Radius

• EN: A chord of a circle is 16 cm long. The radius of the circle is 10 cm. What is the perpendicular distance from the centre to the chord?
• FR: Une corde d'un cercle mesure 16 cm. Le rayon du cercle est de 10 cm. Quelle est la distance perpendiculaire du centre à la corde?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: The perpendicular from centre bisects the chord. Use Pythagoras: r² = d² + (half chord)². For r = 5 and half chord = 3: d² = 25 − 9 = 16, d = 4.
• Steps:
  • Half chord = 16 ÷ 2 = 8 cm.
  • d² = r² − 8² = 100 − 64 = 36. d = √36 = 6 cm.
• Answer: 6 cm

[Easy] Exponential Function

• EN: A bacteria culture starts with 50 cells and doubles every hour. How many cells are there after 3 hours?
• FR: Une culture bactérienne commence avec 50 cellules et double chaque heure. Combien de cellules y a-t-il après 3 heures?
• Choices: A) 150 cells B) 200 cells C) 350 cells D) 400 cells
• Hint: Doubling: if you start with 10 and double 3 times: 10 → 20 → 40 → 80.
• Steps:
  • After 1 h: 50 × 2 = 100. After 2 h: 200. After 3 h: 400.
  • There are 400 cells.
• Answer: 400 cells

[Easy] Logarithm Introduction

• EN: What is log₂(32)?
• FR: Combien vaut log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log₂(8) asks "2 to what power gives 8?" → 2³ = 8, so log₂(8) = 3.
• Steps:
  • Ask: 2 to what power = 32? 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32.
  • log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequence

• EN: An arithmetic sequence starts at 7 with a common difference of 6. What is the 5th term?
• FR: Une suite arithmétique commence à 7 avec une raison de 6. Quel est le 5e terme?
• Choices: A) 28 B) 31 C) 34 D) 37
• Hint: The nth term formula is: aₙ = a₁ + (n − 1)d. For a₁ = 3 and d = 5: a₄ = 3 + 3(5) = 18.
• Steps:
  • aₙ = 7 + (n − 1) × 6. For n = 5: a₅ = 7 + 4 × 6 = 7 + 24 = 31.
  • The 5th term is 31.
• Answer: 31

[Easy] Compound Interest

• EN: Nico invests $1,000 at an annual interest rate of 5%, compounded annually. How much does he have after 2 years?
• FR: Nico investit 1 000 $ à un taux d'intérêt annuel de 5 %, composé annuellement. Combien a-t-il après 2 ans?
• Choices: A) $1,050.00 B) $1,100.00 C) $1,102.50 D) $1,105.00
• Hint: A = P(1 + r)ⁿ. For $500 at 4% for 2 years: A = 500(1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000 × (1.05)² = 1000 × 1.1025 = $1,102.50.
  • Nico has $1,102.50 after 2 years.
• Answer: $1,102.50

[Medium] Quadratic Function — Vertex

• EN: For the quadratic function f(x) = −2(x − 3)² + 8, what is the maximum value and where does it occur?
• FR: Pour la fonction quadratique f(x) = −2(x − 3)² + 8, quelle est la valeur maximale et où se produit-elle?
• Choices: A) Maximum of 3 at x = 8 B) Maximum of 8 at x = 3 C) Minimum of 8 at x = 3 D) Maximum of 8 at x = −3
• Hint: In f(x) = a(x − h)² + k, the vertex is at (h, k). If a < 0, it is a maximum.
• Steps:
  • Vertex form: (h, k) = (3, 8). Since a = −2 < 0, the parabola opens downward.
  • Maximum value is 8, occurring at x = 3.
• Answer: Maximum of 8 at x = 3

[Medium] Geometric Series Sum

• EN: Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.
• FR: Trouve la somme des 5 premiers termes de la série géométrique avec premier terme 2 et raison 3.
• Choices: A) 182 B) 222 C) 242 D) 262
• Hint: Sₙ = a(rⁿ − 1)/(r − 1). For a = 1, r = 2, n = 4: S₄ = 1(16 − 1)/(2 − 1) = 15.
• Steps:
  • S₅ = 2(3⁵ − 1)/(3 − 1) = 2(243 − 1)/2 = 2 × 242/2 = 242.
  • The sum is 242.
• Answer: 242

[Medium] Logarithm Property

• EN: Simplify: log₃(81) − log₃(9).
• FR: Simplifie : log₃(81) − log₃(9).
• Choices: A) log₃(2) B) 1 C) 2 D) 3
• Hint: log(a) − log(b) = log(a/b). For log₂(16) − log₂(4) = log₂(4) = 2.
• Steps:
  • log₃(81) = 4 (since 3⁴ = 81). log₃(9) = 2 (since 3² = 9).
  • 4 − 2 = 2.
• Answer: 2

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifie : sin²(θ) + cos²(θ).
• Choices: A) 0 B) 1 C) 2 D) sin(2θ)
• Hint: This is the most fundamental Pythagorean identity in trigonometry — it holds for any angle.
• Steps:
  • The Pythagorean identity states: sin²(θ) + cos²(θ) = 1 for all angles θ.
  • The simplified value is 1.
• Answer: 1

[Hard] Annuity Calculation

• EN: Mika deposits $200 at the end of each month into an account earning 6% per year, compounded monthly. What is the total after 3 months?
• FR: Mika dépose 200 $ à la fin de chaque mois dans un compte qui rapporte 6 % par an, composé mensuellement. Quel est le total après 3 mois?
• Choices: A) $600.00 B) $603.01 C) $606.04 D) $612.08
• Hint: Monthly rate = 6%/12 = 0.5%. Each deposit earns interest for remaining months. For 2 months at 0.5%: deposit 1 earns 2 periods, deposit 2 earns 1, deposit 3 none.
• Steps:
  • Monthly rate = 0.5% = 0.005.
  • Month 1 deposit: $200 × (1.005)² = $200 × 1.010025 = $202.005.
  • Month 2 deposit: $200 × (1.005)¹ = $200 × 1.005 = $201.00.
  • Month 3 deposit: $200 × (1.005)⁰ = $200.
  • Total ≈ $202.005 + $201.00 + $200 = $603.005 ≈ $603.01.
• Answer: $603.01

[Hard] Exponential and Logarithm Equation

• EN: Solve for x: 2^(3x) = 64.
• FR: Résous pour x : 2^(3x) = 64.
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 6
• Hint: Express both sides as powers of the same base: if 3^n = 27, then 3^n = 3³, so n = 3.
• Steps:
  • 64 = 2⁶. So 2^(3x) = 2⁶.
  • Therefore 3x = 6, and x = 2.
• Answer: x = 2

[Easy] Combinations

• EN: In how many ways can 3 students be chosen from a group of 7 to form a committee?
• FR: De combien de façons peut-on choisir 3 élèves parmi un groupe de 7 pour former un comité?
• Choices: A) 21 B) 35 C) 42 D) 210
• Hint: C(n, r) = n! ÷ (r! × (n − r)!). For C(5,2): 5!/(2! × 3!) = (5×4)/(2×1) = 10.
• Steps:
  • C(7, 3) = 7! ÷ (3! × 4!) = (7 × 6 × 5) ÷ (3 × 2 × 1) = 210 ÷ 6 = 35.
  • There are 35 ways.
• Answer: 35

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = 4x³.
• FR: Trouve la dérivée de f(x) = 4x³.
• Choices: A) 4x² B) 12x C) 12x² D) 4x⁴
• Hint: Power rule: d/dx(axⁿ) = a × n × x^(n−1). For 5x²: derivative = 5 × 2 × x¹ = 10x.
• Steps:
  • Bring down the exponent and multiply: 4 × 3 = 12.
  • Reduce exponent by 1: x^(3−1) = x².
  • Derivative = 12x².
• Answer: 12x²

[Easy] Permutations

• EN: In how many ways can 4 books be arranged on a shelf?
• FR: De combien de façons peut-on ranger 4 livres sur une étagère?
• Choices: A) 16 B) 24 C) 48 D) 256
• Hint: Arranging 3 items: 3! = 3 × 2 × 1 = 6 ways.
• Steps:
  • P(4) = 4! = 4 × 3 × 2 × 1 = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Rational Function — Asymptote

• EN: What is the vertical asymptote of the function f(x) = 1/(x − 5)?
• FR: Quelle est l'asymptote verticale de la fonction f(x) = 1/(x − 5)?
• Choices: A) x = −5 B) x = 0 C) x = 1 D) x = 5
• Hint: A vertical asymptote occurs where the denominator = 0. For 1/(x + 3), set x + 3 = 0, giving x = −3.
• Steps:
  • Set the denominator to zero: x − 5 = 0.
  • x = 5 is the vertical asymptote.
• Answer: x = 5

[Medium] Derivative — Rate of Change

• EN: A ball is thrown upward. Its height in metres is h(t) = −5t² + 20t + 2, where t is in seconds. What is the velocity (rate of change) of the ball at t = 2 s?
• FR: Une balle est lancée vers le haut. Sa hauteur en mètres est h(t) = −5t² + 20t + 2, où t est en secondes. Quelle est la vitesse (taux de variation) de la balle à t = 2 s?
• Choices: A) −2 m/s B) 0 m/s C) 2 m/s D) 20 m/s
• Hint: Find h'(t) using the power rule, then substitute t. For h(t) = −4t² + 12t: h'(t) = −8t + 12, and h'(2) = −4.
• Steps:
  • h'(t) = −10t + 20. At t = 2: h'(2) = −10(2) + 20 = −20 + 20 = 0.
  • The velocity at t = 2 s is 0 m/s (at the peak).
• Answer: 0 m/s

[Medium] Polynomial Function

• EN: What are the zeros of the polynomial f(x) = x³ − 4x?
• FR: Quels sont les zéros du polynôme f(x) = x³ − 4x?
• Choices: A) x = 0, x = 2, x = −2 B) x = 0, x = 4 C) x = 2, x = −2 D) x = 0, x = 2, x = 4
• Hint: Factor out common terms first: for x³ − 9x, factor out x: x(x² − 9) = x(x − 3)(x + 3).
• Steps:
  • Factor: x³ − 4x = x(x² − 4) = x(x − 2)(x + 2).
  • Set each factor to zero: x = 0, x = 2, x = −2.
• Answer: x = 0, x = 2, x = −2

[Medium] Probability Distribution

• EN: A fair six-sided die is rolled twice. What is the probability of getting a sum of exactly 9?
• FR: On lance un dé équilibré à six faces deux fois. Quelle est la probabilité d'obtenir une somme de 9?
• Choices: A) 1/12 B) 1/9 C) 1/8 D) 1/6
• Hint: Count the favourable outcomes (ordered pairs), then divide by total outcomes (6 × 6 = 36). For sum = 7: pairs are (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6 pairs, P = 6/36 = 1/6.
• Steps:
  • Pairs summing to 9: (3,6),(4,5),(5,4),(6,3) = 4 pairs.
  • P = 4/36 = 1/9.
• Answer: 1/9

[Medium] Vectors — Addition

• EN: Vector u = (3, −2) and vector v = (−1, 5). What is u + v?
• FR: Le vecteur u = (3, −2) et le vecteur v = (−1, 5). Combien font u + v?
• Choices: A) (1, 2) B) (2, 3) C) (4, 3) D) (3, −7)
• Hint: Add corresponding components: (a, b) + (c, d) = (a + c, b + d). For (4,1) + (−2,3) = (2, 4).
• Steps:
  • x-component: 3 + (−1) = 2. y-component: −2 + 5 = 3.
  • u + v = (2, 3).
• Answer: (2, 3)

[Hard] Derivative Application — Maximum

• EN: The profit function for a small Canadian business is P(x) = −2x² + 80x − 300, where x is the number of items sold. How many items should be sold to maximize profit?
• FR: La fonction de profit d'une petite entreprise canadienne est P(x) = −2x² + 80x − 300, où x est le nombre d'articles vendus. Combien d'articles faut-il vendre pour maximiser le profit?
• Choices: A) 10 items B) 20 items C) 30 items D) 40 items
• Hint: Find the critical point by setting P'(x) = 0. For P(x) = −3x² + 60x: P'(x) = −6x + 60 = 0 → x = 10.
• Steps:
  • P'(x) = −4x + 80. Set to zero: −4x + 80 = 0.
  • 4x = 80, so x = 20 items.
• Answer: 20 items

[Hard] Binomial Probability

• EN: In a multiple-choice test, each question has 4 options. If a student guesses randomly on 5 questions, what is the probability of getting exactly 2 correct?
• FR: Dans un test à choix multiples, chaque question a 4 options. Si un élève répond au hasard à 5 questions, quelle est la probabilité d'obtenir exactement 2 bonnes réponses?
• Choices: A) 135/512 B) 270/1024 C) 135/1024 D) 270/512
• Hint: Binomial probability: P = C(n, k) × p^k × (1 − p)^(n − k). For n = 4, k = 2, p = 1/2: P = C(4,2) × (1/2)² × (1/2)² = 6/16 = 3/8.
• Steps:
  • p = 1/4, n = 5, k = 2. C(5,2) = 10.
  • P = 10 × (1/4)² × (3/4)³ = 10 × 1/16 × 27/64 = 270/1024 = 135/512.
• Answer: 135/512