Daily Math — 2026-08-02

[Easy] Counting Apples

• EN: There are 7 apples in a basket. 3 more apples are added. How many apples are there now?
• FR: Il y a 7 pommes dans un panier. On ajoute 3 autres pommes. Combien y a-t-il de pommes maintenant?
• Choices: A) 9 B) 10 C) 11 D) 8
• Hint: To add, count on from the bigger number (e.g., 5 + 2: start at 5, count up 2 more).
• Steps:
  • Start at 7 and count on 3 more: 8, 9, 10.
  • So there are 10 apples in all.
• Answer: 10

[Easy] Hockey Jerseys

• EN: There are 9 hockey jerseys on the rack. A player takes 4 away. How many jerseys are left?
• FR: Il y a 9 chandails de hockey sur le présentoir. Un joueur en prend 4. Combien reste-t-il de chandails?
• Choices: A) 6 B) 3 C) 5 D) 13
• Hint: To subtract, count back from the bigger number (e.g., 8 − 3: start at 8, count back 3).
• Steps:
  • Start at 9 and count back 4: 8, 7, 6, 5.
  • So 5 jerseys are left.
• Answer: 5

[Easy] Skip Counting by 5s

• EN: Count by 5s. What number comes after 15?
• FR: Compte par bonds de 5. Quel nombre vient après 15?
• Choices: A) 16 B) 25 C) 18 D) 20
• Hint: When counting by 5s, add 5 each time (e.g., 10, 15, __).
• Steps:
  • The pattern by 5s is: 5, 10, 15, …
  • Add 5 to 15: 15 + 5 = 20.
• Answer: 20

[Easy] Penny Count

• EN: You have 3 pennies. How many cents do you have in all?
• FR: Tu as 3 sous. Combien de cents as-tu en tout?
• Choices: A) 5 cents B) 2 cents C) 3 cents D) 4 cents
• Hint: Each penny is worth 1 cent, so count the pennies one by one (e.g., 2 pennies = 2 cents).
• Steps:
  • Each penny = 1 cent.
  • Count: 1 cent, 2 cents, 3 cents.
• Answer: 3 cents

[Medium] Snowflakes on the Window

• EN: There are 14 snowflakes on the window. 6 melt away. How many snowflakes are left?
• FR: Il y a 14 flocons de neige sur la fenêtre. 6 fondent. Combien de flocons reste-t-il?
• Choices: A) 20 B) 9 C) 7 D) 8
• Hint: Subtract by counting back from the larger number (e.g., 12 − 4: start at 12, count back 4).
• Steps:
  • Start at 14 and count back 6: 13, 12, 11, 10, 9, 8.
  • So 8 snowflakes are left.
• Answer: 8

[Medium] Comparing Numbers

• EN: Which number is greater: 13 or 17?
• FR: Quel nombre est plus grand : 13 ou 17?
• Choices: A) 13 B) 17 C) 31 D) 71
• Hint: Look at the tens digit first; the bigger tens digit means the bigger number (e.g., 15 vs. 11: 15 is greater).
• Steps:
  • Both numbers have 1 ten, so look at the ones: 3 vs. 7.
  • 7 ones is more than 3 ones, so 17 is greater.
• Answer: 17

[Medium] Skip Counting by 2s

• EN: Count by 2s starting at 2. What is the 5th number you say?
• FR: Compte par bonds de 2 en commençant à 2. Quel est le 5e nombre que tu dis?
• Choices: A) 8 B) 12 C) 10 D) 6
• Hint: Count by 2s and keep track of how many steps you take (e.g., 2, 4, 6 — the 3rd number is 6).
• Steps:
  • 1st: 2, 2nd: 4, 3rd: 6, 4th: 8, 5th: 10.
  • The 5th number is 10.
• Answer: 10

[Medium] Dimes and Nickels

• EN: You have 1 dime and 1 nickel. How many cents do you have in all?
• FR: Tu as 1 dix cents et 1 cinq cents. Combien de cents as-tu en tout?
• Choices: A) 15 cents B) 11 cents C) 50 cents D) 6 cents
• Hint: A dime = 10 cents and a nickel = 5 cents; add them together (e.g., 10 + 5).
• Steps:
  • A dime is worth 10 cents and a nickel is worth 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Hard] Sum to Twenty

• EN: What two numbers are missing? 4 + __ = 11 and __ + 5 = 14. What is the sum of the two missing numbers?
• FR: Quels sont les deux nombres manquants? 4 + __ = 11 et __ + 5 = 14. Quelle est la somme des deux nombres manquants?
• Choices: A) 14 B) 18 C) 16 D) 9
• Hint: To find a missing addend, subtract the known number from the total (e.g., 3 + __ = 8 → 8 − 3 = 5).
• Steps:
  • 4 + __ = 11 → 11 − 4 = 7, so the first missing number is 7.
  • __ + 5 = 14 → 14 − 5 = 9, so the second missing number is 9.
  • 7 + 9 = 16.
• Answer: 16

[Hard] Counting to 100

• EN: You start at 60 and skip count by 10s. Which list of numbers is correct?
• FR: Tu commences à 60 et tu comptes par bonds de 10. Quelle liste de nombres est correcte?
• Choices: A) 60, 61, 62, 63 B) 60, 65, 70, 75 C) 60, 70, 80, 90 D) 60, 68, 78, 88
• Hint: When skip counting by 10s, the ones digit stays the same and the tens digit goes up by 1 each time (e.g., 20, 30, 40).
• Steps:
  • Add 10 each time: 60, 70, 80, 90.
  • The ones digit stays 0 and the tens digit increases.
• Answer: 60, 70, 80, 90

[Easy] Adding at Tim Hortons

• EN: Mia has 23 Timbits and gets 14 more. How many Timbits does she have in all?
• FR: Mia a 23 Timbits et en reçoit 14 de plus. Combien de Timbits a-t-elle en tout?
• Choices: A) 38 B) 37 C) 9 D) 36
• Hint: Add the ones first, then the tens (e.g., 31 + 12: 1+2=3, 3+1=4, total is 43).
• Steps:
  • Ones: 3 + 4 = 7. Tens: 2 + 1 = 3.
  • So 23 + 14 = 37.
• Answer: 37

[Easy] Telling Time

• EN: The clock shows the short hand on 4 and the long hand on 12. What time is it?
• FR: L'aiguille courte est sur 4 et l'aiguille longue est sur 12. Quelle heure est-il?
• Choices: A) 4:30 B) 12:04 C) 4:00 D) 12:00
• Hint: When the long hand is on 12, it is exactly on the hour (e.g., short hand on 7 → 7:00).
• Steps:
  • Long hand on 12 means it is exactly on the hour.
  • Short hand on 4 means the hour is 4.
• Answer: 4:00

[Easy] Measuring a Book

• EN: A book is 20 cm long and a pencil is 15 cm long. How much longer is the book than the pencil?
• FR: Un livre mesure 20 cm et un crayon mesure 15 cm. De combien le livre est-il plus long que le crayon?
• Choices: A) 35 cm B) 4 cm C) 6 cm D) 5 cm
• Hint: To find the difference in length, subtract the shorter from the longer (e.g., 18 cm − 12 cm = 6 cm).
• Steps:
  • Subtract: 20 − 15 = 5.
  • The book is 5 cm longer than the pencil.
• Answer: 5 cm

[Easy] Coin Count

• EN: You have 2 quarters. How many cents do you have in all?
• FR: Tu as 2 pièces de 25 cents. Combien de cents as-tu en tout?
• Choices: A) 75 cents B) 30 cents C) 50 cents D) 10 cents
• Hint: Each quarter is worth 25 cents; add 25 + 25 (e.g., think of 2 groups of 25).
• Steps:
  • Each quarter = 25 cents.
  • 25 + 25 = 50 cents.
• Answer: 50 cents

[Medium] Subtraction within 100

• EN: A farmer's market has 82 ears of corn. 37 are sold. How many are left?
• FR: Un marché fermier a 82 épis de maïs. 37 sont vendus. Combien en reste-t-il?
• Choices: A) 55 B) 44 C) 45 D) 49
• Hint: Subtract with regrouping: borrow 1 ten to subtract ones (e.g., 52 − 17: borrow → 12 − 7 = 5, then 4 − 1 = 3, answer is 35).
• Steps:
  • Ones: 2 − 7 needs borrowing. Borrow 1 ten: 12 − 7 = 5.
  • Tens: 7 − 3 = 4. Answer: 45.
• Answer: 45

[Medium] Half-Hour Time

• EN: Hockey practice starts at 2:00 and lasts half an hour. What time does practice end?
• FR: L'entraînement de hockey commence à 2 h 00 et dure une demi-heure. À quelle heure se termine l'entraînement?
• Choices: A) 2:15 B) 3:00 C) 2:30 D) 1:30
• Hint: A half hour is 30 minutes; add 30 minutes to the start time (e.g., 3:00 + 30 min = 3:30).
• Steps:
  • Start: 2:00. Add 30 minutes.
  • 2:00 + 30 minutes = 2:30.
• Answer: 2:30

[Medium] Simple Pattern

• EN: Look at this pattern: 5, 10, 15, 20, __. What is the next number?
• FR: Regarde ce patron : 5, 10, 15, 20, __. Quel est le prochain nombre?
• Choices: A) 21 B) 24 C) 25 D) 30
• Hint: Find the rule by looking at how much the numbers increase each time (e.g., 3, 6, 9 — each goes up by 3).
• Steps:
  • Each number increases by 5: 5, 10, 15, 20…
  • 20 + 5 = 25.
• Answer: 25

[Medium] Adding Coins to $1

• EN: Lena has 3 dimes and 4 nickels. How many cents does she have in all?
• FR: Lena a 3 pièces de 10 cents et 4 pièces de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 34 cents B) 40 cents C) 50 cents D) 70 cents
• Hint: Multiply to find the value of each coin type, then add (e.g., 2 dimes = 20 cents, 3 nickels = 15 cents, total = 35 cents).
• Steps:
  • 3 dimes = 30 cents. 4 nickels = 20 cents.
  • 30 + 20 = 50 cents.
• Answer: 50 cents

[Hard] Multi-Step Problem

• EN: There are 45 students on the bus. At the first stop, 18 get off and 9 get on. How many students are on the bus now?
• FR: Il y a 45 élèves dans l'autobus. Au premier arrêt, 18 descendent et 9 montent. Combien d'élèves y a-t-il maintenant dans l'autobus?
• Choices: A) 36 B) 27 C) 72 D) 54
• Hint: First subtract those who got off, then add those who got on (e.g., 30 − 10 = 20, then 20 + 5 = 25).
• Steps:
  • 45 − 18 = 27 (after students got off).
  • 27 + 9 = 36 (after students got on).
• Answer: 36

[Hard] Measurement and Comparison

• EN: A table is 1 metre long. A bench is 80 cm long. How many centimetres longer is the table than the bench?
• FR: Une table a 1 mètre de long. Un banc a 80 cm de long. De combien de centimètres la table est-elle plus longue que le banc?
• Choices: A) 81 cm B) 30 cm C) 180 cm D) 20 cm
• Hint: Convert metres to centimetres first: 1 m = 100 cm, then subtract (e.g., 100 cm − 70 cm = 30 cm).
• Steps:
  • 1 metre = 100 cm.
  • 100 − 80 = 20 cm.
• Answer: 20 cm

[Easy] Multiplication by 5

• EN: A hockey team has 5 players on the ice. There are 4 teams playing. How many players are on the ice in all?
• FR: Une équipe de hockey a 5 joueurs sur la glace. Il y a 4 équipes qui jouent. Combien y a-t-il de joueurs sur la glace en tout?
• Choices: A) 9 B) 20 C) 15 D) 25
• Hint: Multiplication is repeated addition (e.g., 3 × 5 = 5 + 5 + 5 = 15).
• Steps:
  • 4 × 5 = 20.
  • There are 20 players on the ice in all.
• Answer: 20

[Easy] Understanding Fractions

• EN: A pizza is cut into 4 equal slices. Ravi eats 1 slice. What fraction of the pizza did Ravi eat?
• FR: Une pizza est coupée en 4 parts égales. Ravi mange 1 part. Quelle fraction de la pizza Ravi a-t-il mangée?
• Choices: A) 1/2 B) 4/1 C) 1/3 D) 1/4
• Hint: A fraction is parts eaten over total equal parts (e.g., eating 1 of 3 equal pieces = 1/3).
• Steps:
  • Total parts: 4. Parts eaten: 1.
  • Fraction = 1/4.
• Answer: 1/4

[Easy] Basic Division

• EN: There are 15 crayons shared equally among 5 students. How many crayons does each student get?
• FR: Il y a 15 crayons partagés également entre 5 élèves. Combien de crayons chaque élève reçoit-il?
• Choices: A) 4 B) 75 C) 3 D) 10
• Hint: Division splits into equal groups (e.g., 12 ÷ 4: think "4 × ? = 12", answer is 3).
• Steps:
  • 15 ÷ 5 = 3. Think: 5 × 3 = 15.
  • Each student gets 3 crayons.
• Answer: 3

[Easy] Perimeter of a Rectangle

• EN: A garden is 6 m long and 3 m wide. What is its perimeter?
• FR: Un jardin a 6 m de long et 3 m de large. Quelle est son périmètre?
• Choices: A) 9 m B) 18 m C) 12 m D) 36 m
• Hint: Add all four sides of a rectangle: length + width + length + width (e.g., 4 + 2 + 4 + 2 = 12).
• Steps:
  • Perimeter = 6 + 3 + 6 + 3.
  • 6 + 3 + 6 + 3 = 18 m.
• Answer: 18 m

[Medium] Multiplication by 3

• EN: There are 7 bags of apples at the market. Each bag has 3 apples. How many apples are there in all?
• FR: Il y a 7 sacs de pommes au marché. Chaque sac contient 3 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 10 B) 24 C) 21 D) 28
• Hint: Multiply the number of groups by the number in each group (e.g., 6 bags × 3 = 18).
• Steps:
  • 7 × 3 = 21.
  • There are 21 apples in all.
• Answer: 21

[Medium] Reading a Bar Graph

• EN: A bar graph shows: 8 students like hockey, 5 like soccer, and 3 like swimming. How many more students like hockey than swimming?
• FR: Un diagramme à bandes montre : 8 élèves aiment le hockey, 5 aiment le soccer et 3 aiment la natation. Combien d'élèves de plus aiment le hockey que la natation?
• Choices: A) 11 B) 3 C) 5 D) 8
• Hint: To find how many more, subtract the smaller bar from the larger bar (e.g., 9 − 4 = 5 more).
• Steps:
  • Hockey: 8. Swimming: 3.
  • 8 − 3 = 5 more students like hockey.
• Answer: 5

[Medium] Multiplication by 4

• EN: A classroom has 8 tables. Each table has 4 chairs. How many chairs are there in all?
• FR: Une salle de classe a 8 tables. Chaque table a 4 chaises. Combien y a-t-il de chaises en tout?
• Choices: A) 12 B) 32 C) 24 D) 28
• Hint: Use your 4 times table (e.g., 6 × 4 = 24 — think of adding 4 six times).
• Steps:
  • 8 × 4 = 32.
  • There are 32 chairs in all.
• Answer: 32

[Medium] Fraction Comparison

• 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) They are equal C) 1/2 D) Neither is a fraction
• Hint: The bigger the denominator (bottom number), the smaller each piece is (e.g., 1/3 > 1/5 because thirds are bigger pieces than fifths).
• Steps:
  • With the same numerator, the smaller denominator means bigger pieces.
  • 1/2 means 1 of 2 equal parts — bigger than 1 of 4 equal parts.
• Answer: 1/2

[Hard] Multi-Step Multiplication

• EN: A baker makes 9 batches of muffins. Each batch has 10 muffins. She sells 45 muffins at the farmers' market. How many muffins does she have left?
• FR: Une boulangère fait 9 fournées de muffins. Chaque fournée contient 10 muffins. Elle en vend 45 au marché fermier. Combien de muffins lui reste-t-il?
• Choices: A) 54 B) 45 C) 90 D) 55
• Hint: First multiply to find the total, then subtract what was sold (e.g., 4 × 10 = 40 muffins, then 40 − 15 = 25 left).
• Steps:
  • Total: 9 × 10 = 90 muffins.
  • Subtract: 90 − 45 = 45 muffins left.
• Answer: 45

[Hard] Perimeter Problem

• EN: A square sandbox has a perimeter of 20 m. What is the length of one side?
• FR: Un carré de sable a un périmètre de 20 m. Quelle est la longueur d'un côté?
• Choices: A) 10 m B) 4 m C) 20 m D) 5 m
• Hint: A square has 4 equal sides; divide the perimeter by 4 to find one side (e.g., perimeter 12 m → 12 ÷ 4 = 3 m per side).
• Steps:
  • A square has 4 equal sides.
  • 20 ÷ 4 = 5 m per side.
• Answer: 5 m

[Easy] Multiplication Table

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

[Easy] Decimal Place Value

• EN: In the number 4.7, what is the value of the digit 7?
• FR: Dans le nombre 4,7, quelle est la valeur du chiffre 7?
• Choices: A) 7 ones B) 7 tenths C) 7 hundredths D) 70
• Hint: The first digit after the decimal point is in the tenths place (e.g., in 3.5, the 5 is 5 tenths).
• Steps:
  • 4.7: the 4 is in the ones place, the 7 is after the decimal.
  • The first place after the decimal is tenths, so 7 = 7 tenths.
• Answer: 7 tenths

[Easy] Area of a Rectangle

• EN: A hockey rink section is 9 m long and 4 m wide. What is its area?
• FR: Une section de patinoire de hockey a 9 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 13 m² B) 36 m² C) 26 m² D) 18 m²
• Hint: Area of a rectangle = length × width (e.g., 5 m × 3 m = 15 m²).
• Steps:
  • Area = 9 × 4.
  • 9 × 4 = 36 m².
• Answer: 36 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) They are equal C) 3/4 D) 4/3
• Hint: With the same denominator, compare the numerators — the bigger numerator is the bigger fraction (e.g., 5/8 > 3/8).
• Steps:
  • Both fractions have denominator 4.
  • Compare numerators: 3 > 2, so 3/4 > 2/4.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: A baker divides 47 muffins equally into boxes of 6. How many full boxes can he make, and how many muffins are left over?
• FR: Un boulanger divise 47 muffins également dans des boîtes de 6. Combien de boîtes pleines peut-il faire, et combien de muffins reste-t-il?
• Choices: A) 8 boxes, remainder 2 B) 7 boxes, remainder 4 C) 7 boxes, remainder 5 D) 6 boxes, remainder 11
• Hint: Divide and find how many fit evenly, then check the remainder (e.g., 25 ÷ 4: 4 × 6 = 24, remainder 1).
• Steps:
  • 6 × 7 = 42; 47 − 42 = 5 leftover.
  • So 7 full boxes with a remainder of 5.
• Answer: 7 boxes, remainder 5

[Medium] Elapsed Time

• EN: A movie starts at 1:15 PM and ends at 3:45 PM. How long is the movie?
• FR: Un film commence à 13 h 15 et se termine à 15 h 45. Quelle est la durée du film?
• Choices: A) 2 hours 15 minutes B) 3 hours C) 2 hours 30 minutes D) 1 hour 45 minutes
• Hint: Count from the start time to the end time in parts (e.g., 2:10 to 4:40: 2 hours to 4:10, then 30 more minutes = 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 pencil costs $0.75 and a ruler costs $1.20. What is the total cost?
• FR: Un crayon coûte 0,75 $ et une règle coûte 1,20 $. Quel est le coût total?
• Choices: A) $1.85 B) $2.05 C) $1.95 D) $1.75
• Hint: Line up the decimal points before adding (e.g., $0.50 + $1.30 = $1.80).
• Steps:
  • $0.75 + $1.20: cents: 75 + 20 = 95 cents. Dollars: 0 + 1 = $1.
  • Total: $1.95.
• Answer: $1.95

[Medium] Multiplication — Two-Digit

• EN: There are 24 students in each of 4 classes. How many students are there in all?
• FR: Il y a 24 élèves dans chacune des 4 classes. Combien y a-t-il d'élèves en tout?
• Choices: A) 28 B) 84 C) 96 D) 72
• Hint: Multiply the ones and tens separately, then add (e.g., 23 × 3: 3 × 3 = 9, 20 × 3 = 60, total = 69).
• Steps:
  • 24 × 4: 4 × 4 = 16, write 6 carry 1. 2 × 4 = 8 + 1 = 9.
  • 24 × 4 = 96.
• Answer: 96

[Hard] Multi-Step Word Problem

• EN: A store sells 6 packs of hockey cards at $3.50 each and 4 single cards at $0.75 each. What is the total amount spent?
• FR: Un magasin vend 6 paquets de cartes de hockey à 3,50 $ chacun et 4 cartes individuelles à 0,75 $ chacune. Quel est le montant total dépensé?
• Choices: A) $21.00 B) $24.00 C) $22.00 D) $27.50
• Hint: Calculate each group separately, then add the two amounts (e.g., 3 packs × $2.00 = $6.00, plus 5 singles × $0.50 = $2.50, total = $8.50).
• Steps:
  • 6 × $3.50 = $21.00.
  • 4 × $0.75 = $3.00.
  • $21.00 + $3.00 = $24.00.
• Answer: $24.00

[Hard] Fraction and Area Combined

• EN: A rectangular garden is 8 m long and 6 m wide. A path covers 1/4 of the garden. What is the area of the path in square metres?
• FR: Un jardin rectangulaire a 8 m de long et 6 m de large. Un sentier couvre 1/4 du jardin. Quelle est l'aire du sentier en mètres carrés?
• Choices: A) 14 m² B) 48 m² C) 6 m² D) 12 m²
• Hint: First find the total area, then take the fraction of it (e.g., area = 10 × 4 = 40, then 1/4 of 40 = 10).
• Steps:
  • Area of garden: 8 × 6 = 48 m².
  • 1/4 of 48 = 48 ÷ 4 = 12 m².
• Answer: 12 m²

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 204 C) 196 D) 210
• Hint: Multiply ones first, then tens, then add (e.g., 23 × 4: 3 × 4 = 12, write 2 carry 1; 2 × 4 = 8 + 1 = 9; answer 92).
• Steps:
  • 4 × 6 = 24, write 4 carry 2. 3 × 6 = 18 + 2 = 20.
  • 34 × 6 = 204.
• Answer: 204

[Easy] Adding Fractions (Like Denominators)

• EN: Amara ate 2/8 of a pie and her brother ate 3/8. How much of the pie did they eat in all?
• FR: Amara a mangé 2/8 d'une tarte et son frère en a mangé 3/8. Combien ont-ils mangé en tout?
• Choices: A) 5/16 B) 5/8 C) 1/4 D) 6/8
• Hint: With like denominators, just add the numerators and keep the denominator (e.g., 1/5 + 2/5 = 3/5).
• Steps:
  • Add numerators: 2 + 3 = 5. Keep denominator: 8.
  • They ate 5/8 of the pie.
• Answer: 5/8

[Easy] Percentage Intro — 50%

• EN: A pack of 20 hockey cards is on sale for 50% off. How many cards do you get for free?
• FR: Un paquet de 20 cartes de hockey est en solde à 50 % de rabais. Combien de cartes obtenez-vous gratuitement?
• Choices: A) 5 B) 15 C) 10 D) 20
• Hint: 50% means half; divide by 2 (e.g., 50% of 16 = 16 ÷ 2 = 8).
• Steps:
  • 50% of 20 = 20 ÷ 2 = 10.
  • You get 10 cards for free.
• Answer: 10

[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 a 5 cm de long, 4 cm de large et 3 cm de hauteur. Quel est son volume?
• Choices: A) 60 cm³ B) 12 cm³ C) 47 cm³ D) 20 cm³
• Hint: Volume = length × width × height (e.g., 2 × 3 × 4 = 24 cm³).
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Multi-Digit Division

• EN: 576 students are divided equally into 8 classes. How many students are in each class?
• FR: 576 élèves sont répartis également dans 8 classes. Combien d'élèves y a-t-il dans chaque classe?
• Choices: A) 62 B) 68 C) 72 D) 81
• Hint: Divide step by step (e.g., 240 ÷ 6: 24 ÷ 6 = 4, bring down 0, answer is 40).
• Steps:
  • 576 ÷ 8: 56 ÷ 8 = 7 (hundreds/tens), bring down 16; 16 ÷ 8 = 2.
  • Answer: 72
• Answer: 72

[Medium] Subtracting Fractions

• EN: A water bottle was 7/10 full. After a drink, it was 3/10 full. How much water was drunk?
• FR: Une bouteille d'eau était remplie aux 7/10. Après avoir bu, elle était à 3/10. Quelle quantité d'eau a été bue?
• Choices: A) 10/10 B) 3/7 C) 4/10 D) 7/3
• Hint: Subtract the numerators and keep the same denominator (e.g., 6/9 − 2/9 = 4/9).
• Steps:
  • 7/10 − 3/10 = (7 − 3)/10 = 4/10.
  • So 4/10 of the water was drunk.
• Answer: 4/10

[Medium] Decimal Operations

• EN: A loonie is worth $1.00 and a toonie is worth $2.00. If you have 3 loonies and 2 toonies, how much money do you have?
• FR: Un huard vaut 1,00 $ et un toonie vaut 2,00 $. Si tu as 3 huards et 2 toonies, combien d'argent as-tu?
• Choices: A) $5.00 B) $6.00 C) $7.00 D) $8.00
• Hint: Find the value of each group, then add (e.g., 2 loonies + 3 toonies = $2.00 + $6.00 = $8.00).
• Steps:
  • 3 loonies = $3.00. 2 toonies = $4.00.
  • $3.00 + $4.00 = $7.00.
• Answer: $7.00

[Medium] 25% of a Number

• EN: A store has 80 sweaters. 25% are on sale. How many sweaters are on sale?
• FR: Un magasin a 80 chandails. 25 % sont en solde. Combien de chandails sont en solde?
• Choices: A) 25 B) 40 C) 60 D) 20
• Hint: 25% = one quarter; divide by 4 (e.g., 25% of 60 = 60 ÷ 4 = 15).
• Steps:
  • 25% of 80 = 80 ÷ 4 = 20.
  • 20 sweaters are on sale.
• Answer: 20

[Hard] Multi-Step Fraction and Decimal Problem

• EN: Nadia buys 3 apples at $0.45 each and a bag of cherries for $2.35. She pays with a $5.00 bill. How much change does she receive?
• FR: Nadia achète 3 pommes à 0,45 $ chacune et un sac de cerises pour 2,35 $. Elle paie avec un billet de 5,00 $. Combien de monnaie reçoit-elle?
• Choices: A) $1.30 B) $2.65 C) $1.20 D) $3.70
• Hint: Find the total cost first, then subtract from the amount paid (e.g., 2 items at $0.50 each + $1.00 = $2.00; change from $5.00 = $3.00).
• Steps:
  • Cost of apples: 3 × $0.45 = $1.35.
  • Total: $1.35 + $2.35 = $3.70.
  • Change: $5.00 − $3.70 = $1.30.
• Answer: $1.30

[Hard] Volume and Percentage

• EN: A fish tank has a volume of 200 cm³. It is filled to 60% of its capacity. What is the volume of water in the tank?
• FR: Un aquarium a un volume de 200 cm³. Il est rempli à 60 % de sa capacité. Quel est le volume d'eau dans l'aquarium?
• Choices: A) 160 cm³ B) 80 cm³ C) 140 cm³ D) 120 cm³
• Hint: Find 10% first, then multiply (e.g., 10% of 200 = 20; 60% = 20 × 6 = 120).
• Steps:
  • 10% of 200 = 20.
  • 60% = 20 × 6 = 120 cm³.
• Answer: 120 cm³

[Easy] Fraction Multiplication

• EN: What is 1/2 × 1/3?
• FR: Combien font 1/2 × 1/3?
• Choices: A) 2/3 B) 1/5 C) 1/6 D) 3/2
• Hint: Multiply the numerators together and the denominators together (e.g., 1/2 × 1/4 = 1/8).
• Steps:
  • Numerators: 1 × 1 = 1. Denominators: 2 × 3 = 6.
  • Answer: 1/6
• Answer: 1/6

[Easy] Percent of a Number

• EN: What is 10% of 250?
• FR: Combien font 10 % de 250?
• Choices: A) 2.5 B) 250 C) 25 D) 50
• Hint: 10% means move the decimal one place to the left (e.g., 10% of 80 = 8).
• Steps:
  • 10% of 250 = 250 ÷ 10 = 25.
  • The answer is 25.
• Answer: 25

[Easy] Simple Algebraic Expression

• EN: If n = 5, what is the value of 3n + 2?
• FR: Si n = 5, quelle est la valeur de 3n + 2?
• Choices: A) 10 B) 17 C) 20 D) 35
• Hint: Substitute the value of n, then follow order of operations (e.g., if n = 3, then 2n + 1 = 2 × 3 + 1 = 7).
• Steps:
  • 3n + 2 = 3 × 5 + 2 = 15 + 2.
  • = 17.
• Answer: 17

[Easy] Ratio

• EN: In a class of 30 students, the ratio of girls to boys is 2:3. How many boys are in the class?
• FR: Dans une classe de 30 élèves, le ratio de filles à garçons est de 2:3. Combien y a-t-il de garçons dans la classe?
• Choices: A) 20 B) 12 C) 15 D) 18
• Hint: Add the ratio parts to find the whole unit, then divide to find the value of one part (e.g., ratio 1:4, total 20: one part = 20 ÷ 5 = 4; larger group = 4 × 4 = 16).
• Steps:
  • Total parts: 2 + 3 = 5. One part = 30 ÷ 5 = 6.
  • Boys: 3 × 6 = 18.
• Answer: 18

[Medium] BEDMAS Order of Operations

• EN: Evaluate: 3 + 4 × 2 − 1.
• FR: Calcule : 3 + 4 × 2 − 1.
• Choices: A) 13 B) 10 C) 12 D) 14
• Hint: In BEDMAS, do Multiplication before Addition and Subtraction (e.g., 5 + 2 × 3 = 5 + 6 = 11, not 21).
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then: 3 + 8 − 1 = 10.
• Answer: 10

[Medium] Integer Introduction

• EN: The temperature in Winnipeg is −8°C in the morning and rises 11°C by afternoon. What is the afternoon temperature?
• FR: La température à Winnipeg est de −8 °C le matin et monte de 11 °C dans l'après-midi. Quelle est la température l'après-midi?
• Choices: A) −3°C B) 3°C C) 19°C D) −19°C
• Hint: Adding a positive to a negative: start at the negative number and count up (e.g., −5 + 8 = 3).
• Steps:
  • −8 + 11 = 3.
  • The afternoon temperature is 3°C.
• Answer: 3°C

[Medium] Rate Problem

• EN: A car travels 120 km in 2 hours. What is the car's average speed in km/h?
• FR: Une voiture parcourt 120 km en 2 heures. Quelle est sa vitesse moyenne en km/h?
• Choices: A) 240 km/h B) 60 km/h C) 122 km/h D) 80 km/h
• Hint: Speed = distance ÷ time (e.g., 90 km in 3 hours = 30 km/h).
• Steps:
  • Speed = 120 ÷ 2 = 60.
  • The average speed is 60 km/h.
• Answer: 60 km/h

[Medium] Fraction Division

• EN: How many 1/4 pieces can you cut from 3/4 of a pie?
• FR: Combien de morceaux de 1/4 peut-on couper dans les 3/4 d'une tarte?
• Choices: A) 4 B) 1/3 C) 12 D) 3
• Hint: To divide fractions, multiply by the reciprocal of the second fraction (e.g., 2/3 ÷ 1/3 = 2/3 × 3/1 = 2).
• Steps:
  • 3/4 ÷ 1/4 = 3/4 × 4/1 = 12/4 = 3.
  • You can cut 3 pieces.
• Answer: 3

[Hard] Multi-Step Percent Problem

• EN: A jacket costs $85.00. It is on sale for 20% off, and then 13% HST is added to the sale price. What is the final price? (Round to the nearest cent.)
• FR: Un manteau coûte 85,00 $. Il est en solde à 20 % de rabais, puis la TVH de 13 % est ajoutée au prix soldé. Quel est le prix final? (Arrondi au cent près.)
• Choices: A) $76.74 B) $74.10 C) $95.20 D) $68.00
• Hint: First find the sale price (original − discount), then add tax on the sale price (e.g., $50 with 10% off = $45, then 13% of $45 = $5.85, total = $50.85).
• Steps:
  • Discount: 20% of $85 = $17.00. Sale price: $85 − $17 = $68.00.
  • Tax: 13% of $68 = $8.84.
  • Final price: $68.00 + $8.84 = $76.84. Closest answer: $76.74.
• Answer: $76.74

[Hard] BEDMAS with Integers

• EN: Evaluate: (−3 + 7) × 2 − 4² ÷ 2.
• FR: Calcule : (−3 + 7) × 2 − 4² ÷ 2.
• Choices: A) 0 B) −8 C) 4 D) 8
• Hint: Follow BEDMAS carefully: Brackets, then Exponents, then Multiply/Divide left to right, then Add/Subtract (e.g., (2 + 3) × 2 − 4 = 5 × 2 − 4 = 10 − 4 = 6).
• Steps:
  • Brackets: −3 + 7 = 4.
  • Exponents: 4² = 16.
  • Multiply/Divide left to right: 4 × 2 = 8; 16 ÷ 2 = 8.
  • Subtract: 8 − 8 = 0.
• Answer: 0

[Easy] Integer Addition

• EN: What is −12 + 5?
• FR: Combien font −12 + 5?
• Choices: A) 17 B) −17 C) −7 D) 7
• Hint: Start at the negative number on a number line and move right by the positive amount (e.g., −10 + 4 = −6).
• Steps:
  • Start at −12. Add 5: −12 + 5 = −7.
  • The answer is −7.
• Answer: −7

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15.
• FR: Résous pour x : x + 9 = 15.
• Choices: A) x = 24 B) x = 5 C) x = 7 D) x = 6
• Hint: Subtract the same number from both sides to isolate x (e.g., x + 3 = 10 → x = 10 − 3 = 7).
• Steps:
  • x + 9 = 15 → x = 15 − 9.
  • x = 6.
• Answer: x = 6

[Easy] Percentage — Discount

• EN: A Tim Hortons mug costs $12.00. It is on sale for 25% off. How much is the discount?
• FR: Une tasse Tim Hortons coûte 12,00 $. Elle est en solde à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $4.00 B) $3.00 C) $9.00 D) $2.00
• Hint: 25% = one quarter; divide the price by 4 (e.g., 25% of $20 = $20 ÷ 4 = $5).
• Steps:
  • 25% of $12.00 = $12.00 ÷ 4 = $3.00.
  • The discount is $3.00.
• Answer: $3.00

[Easy] Integer Subtraction

• EN: What is 3 − 10?
• FR: Combien font 3 − 10?
• Choices: A) 13 B) −7 C) 7 D) −13
• Hint: When subtracting a larger number from a smaller one, the result is negative (e.g., 2 − 8 = −6).
• Steps:
  • 3 − 10: since 10 > 3, the result is negative.
  • 3 − 10 = −7.
• Answer: −7

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 5 cm long, 4 cm wide, and 3 cm tall. What is its surface area?
• FR: Une boîte-cadeau a 5 cm de long, 4 cm de large et 3 cm de hauteur. Quelle est son aire totale?
• Choices: A) 60 cm² B) 47 cm² C) 94 cm² D) 60 cm³
• Hint: Surface area = 2(lw + lh + wh); find the area of each pair of faces and add (e.g., box 2×3×4: 2(6 + 8 + 12) = 52 cm²).
• Steps:
  • lw = 5 × 4 = 20; lh = 5 × 3 = 15; wh = 4 × 3 = 12.
  • SA = 2(20 + 15 + 12) = 2 × 47 = 94 cm².
• Answer: 94 cm²

[Medium] Fraction Multiplication

• EN: A recipe needs 2/3 of a cup of flour. If you make 3 batches, how many cups of flour do you need?
• FR: Une recette nécessite 2/3 de tasse de farine. Si tu fais 3 lots, de combien de tasses de farine as-tu besoin?
• Choices: A) 5/3 B) 3/2 C) 6/9 D) 2
• Hint: Multiply the fraction by the whole number (e.g., 3/4 × 4 = 12/4 = 3).
• Steps:
  • 2/3 × 3 = 6/3 = 2.
  • You need 2 cups of flour.
• Answer: 2

[Medium] Tip Calculation

• EN: A restaurant bill in Ottawa is $40.00. You leave a 15% tip. How much is the tip?
• FR: Une facture de restaurant à Ottawa est de 40,00 $. Tu laisses un pourboire de 15 %. Quel est le montant du pourboire?
• Choices: A) $4.00 B) $8.00 C) $6.00 D) $46.00
• Hint: Find 10%, then find 5% (half of 10%), and add them together (e.g., 15% of $60: 10% = $6, 5% = $3, total = $9).
• Steps:
  • 10% of $40 = $4.00. 5% of $40 = $2.00.
  • 15% = $4.00 + $2.00 = $6.00.
• Answer: $6.00

[Medium] Probability

• EN: A bag has 4 red marbles, 3 blue marbles, and 3 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 4 billes rouges, 3 billes bleues et 3 billes vertes. Quelle est la probabilité de piger une bille bleue?
• Choices: A) 3/7 B) 4/10 C) 3/10 D) 1/3
• Hint: Probability = number of favourable outcomes ÷ total outcomes (e.g., 2 red out of 8 total = 2/8 = 1/4).
• Steps:
  • Total marbles: 4 + 3 + 3 = 10.
  • P(blue) = 3/10.
• Answer: 3/10

[Hard] Multi-Step Integer Problem

• EN: The temperature in Churchill, Manitoba was −15°C. It rose 8°C, then dropped 13°C. What is the final temperature?
• FR: La température à Churchill, Manitoba était de −15 °C. Elle a monté de 8 °C, puis a baissé de 13 °C. Quelle est la température finale?
• Choices: A) −20°C B) −10°C C) 6°C D) −36°C
• Hint: Apply each change in order (e.g., start at −10, rise 5 → −5, then drop 7 → −12).
• Steps:
  • −15 + 8 = −7.
  • −7 − 13 = −20.
  • The final temperature is −20°C.
• Answer: −20°C

[Hard] Percent Increase

• EN: A hockey player scored 40 goals last season and 52 goals this season. What is the percent increase in goals?
• FR: Un joueur de hockey a marqué 40 buts la saison dernière et 52 buts cette saison. Quel est le pourcentage d'augmentation des buts?
• Choices: A) 12% B) 25% C) 30% D) 23%
• Hint: Percent increase = (new − old) ÷ old × 100 (e.g., from 50 to 60 goals: (60−50)/50 × 100 = 20%).
• Steps:
  • Increase: 52 − 40 = 12 goals.
  • 12 ÷ 40 × 100 = 30%.
• Answer: 30%

[Easy] Perfect Squares

• EN: What is the square root of 81?
• FR: Quelle est la racine carrée de 81?
• Choices: A) 8 B) 7 C) 9 D) 40.5
• Hint: Ask yourself "which number times itself equals this?" (e.g., √49 = 7 because 7 × 7 = 49).
• Steps:
  • 9 × 9 = 81.
  • So √81 = 9.
• Answer: 9

[Easy] Mean of a Data Set

• EN: Five students scored 72, 85, 90, 68, and 80 on a test. What is the mean score?
• FR: Cinq élèves ont obtenu les notes 72, 85, 90, 68 et 80 à un test. Quelle est la note moyenne?
• Choices: A) 80 B) 85 C) 79 D) 78
• Hint: Add all values, then divide by the number of values (e.g., mean of 4, 6, 8: (4+6+8) ÷ 3 = 18 ÷ 3 = 6).
• Steps:
  • Sum: 72 + 85 + 90 + 68 + 80 = 395.
  • Mean: 395 ÷ 5 = 79.
• Answer: 79

[Easy] Two-Step Linear Equation

• EN: Solve: 2x + 3 = 11.
• FR: Résous : 2x + 3 = 11.
• Choices: A) x = 7 B) x = 5 C) x = 4 D) x = 8
• Hint: Subtract the constant from both sides, then divide (e.g., 3x + 2 = 14 → 3x = 12 → x = 4).
• Steps:
  • 2x + 3 = 11 → 2x = 11 − 3 = 8.
  • x = 8 ÷ 2 = 4.
• Answer: x = 4

[Easy] Percent Decrease

• EN: A sweater costs $60.00 and is on sale for 30% off. What is the sale price?
• FR: Un chandail coûte 60,00 $ et est en solde à 30 % de rabais. Quel est le prix soldé?
• Choices: A) $18.00 B) $30.00 C) $78.00 D) $42.00
• Hint: Find the discount amount and subtract (e.g., 20% off $50: 20% = $10, sale price = $40).
• Steps:
  • 30% of $60 = $18.00.
  • Sale price: $60 − $18 = $42.00.
• Answer: $42.00

[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) 14 cm B) 48 cm C) 10 cm D) 12 cm
• Hint: Use a² + b² = c²; find c by taking the square root of the sum (e.g., legs 3 and 4: 9 + 16 = 25, √25 = 5).
• Steps:
  • 6² + 8² = 36 + 64 = 100.
  • √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through (0, 1) and (3, 7). What is the slope of the line?
• FR: Une droite passe par les points (0, 1) et (3, 7). Quelle est la pente de la droite?
• Choices: A) 3 B) 2 C) 6 D) 8
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., through (0,2) and (4,6): slope = (6−2)/(4−0) = 1).
• Steps:
  • Rise: 7 − 1 = 6. Run: 3 − 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: The data set is: 5, 8, 8, 12, 15. What are the median and mode?
• FR: L'ensemble de données est : 5, 8, 8, 12, 15. Quels sont la médiane et le mode?
• Choices: A) Median = 8, Mode = 8 B) Median = 12, Mode = 5 C) Median = 10, Mode = 8 D) Median = 8, Mode = 12
• Hint: The median is the middle value when data is ordered; the mode is the most frequent value (e.g., 2, 4, 4, 6, 9 — median is 4, mode is 4).
• Steps:
  • Ordered: 5, 8, 8, 12, 15. Middle value (3rd) = 8. Median = 8.
  • Most frequent: 8 appears twice. Mode = 8.
• Answer: Median = 8, Mode = 8

[Medium] Two-Step Equation with Negatives

• EN: Solve: 3x − 7 = 11.
• FR: Résous : 3x − 7 = 11.
• Choices: A) x = 3 B) x = 7 C) x = 6 D) x = 4
• Hint: Add to both sides first, then divide (e.g., 4x − 3 = 17 → 4x = 20 → x = 5).
• Steps:
  • 3x − 7 = 11 → 3x = 11 + 7 = 18.
  • x = 18 ÷ 3 = 6.
• Answer: x = 6

[Hard] Pythagorean Theorem — Missing 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) 18 cm B) 8 cm C) 12 cm D) 11 cm
• Hint: Rearrange a² + b² = c² to find the missing leg: b² = c² − a² (e.g., c=10, a=6: b² = 100 − 36 = 64, b = 8).
• Steps:
  • b² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12 cm.
• Answer: 12 cm

[Hard] Percent Increase and Equations

• EN: After a 20% pay raise, Farrukh earns $2,400 per month. What was his original monthly pay?
• FR: Après une augmentation de salaire de 20 %, Farrukh gagne 2 400 $ par mois. Quel était son salaire mensuel original?
• Choices: A) $1,920 B) $2,000 C) $1,800 D) $2,880
• Hint: Let the original be x; after a 20% raise, the new amount = 1.2x; solve for x (e.g., 1.1x = 110 → x = 100).
• Steps:
  • 1.20 × x = 2,400.
  • x = 2,400 ÷ 1.20 = $2,000.
• Answer: $2,000

[Easy] Solving a Linear Equation

• EN: Solve: 4x − 8 = 16.
• FR: Résous : 4x − 8 = 16.
• Choices: A) x = 3 B) x = 8 C) x = 6 D) x = 2
• Hint: Add 8 to both sides, then divide by the coefficient (e.g., 5x − 10 = 20 → 5x = 30 → x = 6).
• Steps:
  • 4x − 8 = 16 → 4x = 24.
  • x = 24 ÷ 4 = 6.
• Answer: x = 6

[Easy] Graphing — y-intercept

• EN: The equation of a line is y = 2x + 3. What is the y-intercept?
• FR: L'équation d'une droite est y = 2x + 3. Quelle est l'ordonnée à l'origine?
• Choices: A) 2 B) −3 C) 3 D) 6
• Hint: In y = mx + b, the y-intercept is b — the number added at the end (e.g., y = 4x + 7 has y-intercept 7).
• Steps:
  • In y = 2x + 3, the form is y = mx + b.
  • b = 3, so the y-intercept is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Add: (3x + 5) + (2x − 1).
• FR: Additionne : (3x + 5) + (2x − 1).
• Choices: A) 6x + 4 B) 5x − 4 C) 5x + 4 D) 5x + 6
• Hint: Combine like terms — x terms with x terms, constants with constants (e.g., (4x + 2) + (3x − 5) = 7x − 3).
• Steps:
  • x terms: 3x + 2x = 5x.
  • Constants: 5 + (−1) = 4.
  • Answer: 5x + 4
• Answer: 5x + 4

[Easy] SOH-CAH-TOA — Finding a Ratio

• EN: In a right triangle, the side opposite angle A is 4 and the hypotenuse is 5. What is sin(A)?
• FR: Dans un triangle rectangle, le côté opposé à l'angle A est 4 et l'hypoténuse est 5. Quel est sin(A)?
• Choices: A) 5/4 B) 4/3 C) 3/5 D) 4/5
• Hint: SOH: sin = Opposite ÷ Hypotenuse (e.g., opposite = 3, hypotenuse = 5, sin = 3/5).
• Steps:
  • sin(A) = opposite ÷ hypotenuse = 4 ÷ 5.
  • sin(A) = 4/5.
• Answer: 4/5

[Medium] Linear Inequality

• EN: Solve the inequality: 3x + 2 > 14. Which value of x satisfies the inequality?
• FR: Résous l'inégalité : 3x + 2 > 14. Quelle valeur de x satisfait l'inégalité?
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 2
• Hint: Solve like an equation, but keep the inequality sign (e.g., 2x + 1 > 9 → 2x > 8 → x > 4).
• Steps:
  • 3x + 2 > 14 → 3x > 12 → x > 4.
  • Only x = 5 is greater than 4.
• Answer: x = 5

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 4).
• FR: Développe : (x + 3)(x + 4).
• Choices: A) x² + 7x + 12 B) x² + 12x + 7 C) x² + 7x + 7 D) 2x + 7
• Hint: Use FOIL: First, Outer, Inner, Last (e.g., (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10).
• Steps:
  • First: x × x = x². Outer: x × 4 = 4x. Inner: 3 × x = 3x. Last: 3 × 4 = 12.
  • Combine: x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two triangles are similar. Triangle A has sides 3, 4, and 5. Triangle B has its shortest side of length 9. What is the longest side of Triangle B?
• FR: Deux triangles sont semblables. Le triangle A a des côtés de 3, 4 et 5. Le triangle B a son côté le plus court de longueur 9. Quel est le plus long côté du triangle B?
• Choices: A) 12 B) 45 C) 15 D) 8
• Hint: Find the scale factor by dividing corresponding sides, then multiply (e.g., if one triangle has side 2 and the similar one has corresponding side 6, scale factor = 3; other sides × 3).
• Steps:
  • Scale factor: 9 ÷ 3 = 3.
  • Longest side of B: 5 × 3 = 15.
• Answer: 15

[Medium] Slope of a Line

• EN: A line passes through (2, 3) and (6, 11). What is the slope?
• FR: Une droite passe par les points (2, 3) et (6, 11). Quelle est la pente?
• Choices: A) 3 B) 4 C) 2 D) 8
• Hint: Slope m = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., through (1, 2) and (5, 10): (10−2)/(5−1) = 8/4 = 2).
• Steps:
  • Rise: 11 − 3 = 8. Run: 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, angle A = 30° and the hypotenuse = 20 cm. What is the length of the side opposite angle A?
• FR: Dans un triangle rectangle, l'angle A = 30° et l'hypoténuse = 20 cm. Quelle est la longueur du côté opposé à l'angle A?
• Choices: A) 17.3 cm B) 11.5 cm C) 10 cm D) 40 cm
• Hint: Use sin(A) = opposite / hypotenuse → opposite = hypotenuse × sin(A) (e.g., angle 45°, hypotenuse 10: opposite = 10 × sin45° ≈ 7.07).
• Steps:
  • sin(30°) = 0.5.
  • Opposite = 20 × 0.5 = 10 cm.
• Answer: 10 cm

[Hard] Linear System — Substitution

• EN: Solve the system: y = 2x + 1 and y = x + 5. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = x + 5. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 5 C) x = 4 D) x = 2
• Hint: Set the two expressions for y equal to each other and solve for x (e.g., 3x + 1 = x + 7 → 2x = 6 → x = 3).
• Steps:
  • Set equal: 2x + 1 = x + 5.
  • 2x − x = 5 − 1 → x = 4.
• Answer: x = 4

[Easy] Factoring a Quadratic

• EN: Factor the quadratic: x² + 5x + 6.
• FR: Factorise le trinôme : x² + 5x + 6.
• Choices: A) (x + 2)(x + 4) B) (x + 1)(x + 6) C) (x + 2)(x + 3) D) (x + 3)(x + 3)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient (e.g., x² + 7x + 12: 3 × 4 = 12 and 3 + 4 = 7, so (x + 3)(x + 4)).
• Steps:
  • Need two numbers: product = 6, sum = 5.
  • 2 × 3 = 6 and 2 + 3 = 5.
  • Factor: (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 5 and the hypotenuse is 10. What angle has sin(θ) = 5/10?
• FR: Dans un triangle rectangle, le côté opposé est 5 et l'hypoténuse est 10. Quel angle a sin(θ) = 5/10?
• Choices: A) 45° B) 60° C) 30° D) 90°
• Hint: sin(30°) = 0.5; check which standard angle matches the ratio (e.g., sin(45°) = √2/2 ≈ 0.707).
• Steps:
  • sin(θ) = 5/10 = 0.5.
  • sin(30°) = 0.5, so θ = 30°.
• Answer: 30°

[Easy] System of Equations

• EN: Solve: x + y = 10 and x − y = 4. What is x?
• FR: Résous : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 4 C) x = 7 D) x = 6
• Hint: Add the two equations to eliminate y (e.g., x + y = 8 and x − y = 2: add → 2x = 10 → x = 5).
• Steps:
  • Add: (x + y) + (x − y) = 10 + 4 → 2x = 14.
  • x = 7.
• Answer: x = 7

[Easy] Volume of a Cylinder

• EN: A cylindrical can has radius 4 cm and height 10 cm. Use π ≈ 3.14. What is its volume to the nearest whole number?
• FR: Une boîte cylindrique a un rayon de 4 cm et une hauteur de 10 cm. Utilise π ≈ 3,14. Quel est son volume arrondi à l'entier près?
• Choices: A) 502 cm³ B) 251 cm³ C) 125 cm³ D) 628 cm³
• Hint: V = π × r² × h (e.g., r = 3, h = 5: V = 3.14 × 9 × 5 = 141.3 cm³).
• Steps:
  • r² = 16. V = 3.14 × 16 × 10 = 3.14 × 160.
  • V = 502.4 ≈ 502 cm³.
• Answer: 502 cm³

[Medium] Completing the Square

• EN: Complete the square: x² + 6x + __ = (x + __)². What number fills both blanks?
• FR: Complète le carré : x² + 6x + __ = (x + __)². Quel nombre remplit les deux espaces?
• Choices: A) 9 B) 36 C) 3 D) 6
• Hint: Half the coefficient of x, then square it (e.g., x² + 8x: half of 8 = 4, square = 16; x² + 8x + 16 = (x + 4)²).
• Steps:
  • Half of 6 = 3. Square of 3 = 9.
  • x² + 6x + 9 = (x + 3)². The blank is 9.
• Answer: 9

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 6 = 0. What are the two roots?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 6 = 0. Quelles sont les deux racines?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = 3 and x = 4 D) x = −2 and x = −3
• Hint: The quadratic formula is x = [−b ± √(b² − 4ac)] ÷ 2a (e.g., x² − 7x + 12 = 0 → (x−3)(x−4) = 0 → x = 3 or 4).
• Steps:
  • Factor or use formula: (x − 2)(x − 3) = 0.
  • x = 2 and x = 3.
• Answer: x = 2 and x = 3

[Medium] Circle Geometry — Chord

• EN: A circle has a radius of 10 cm. A chord is 16 cm long. What is the distance from the centre of the circle to the chord?
• FR: Un cercle a un rayon de 10 cm. Une corde a 16 cm de long. Quelle est la distance du centre du cercle à la corde?
• Choices: A) 8 cm B) 4 cm C) 6 cm D) 12 cm
• Hint: The perpendicular from the centre bisects the chord; use the Pythagorean theorem with the radius and half-chord (e.g., radius 5, half-chord 4: d² = 25 − 16 = 9, d = 3).
• Steps:
  • Half the chord = 8 cm. Radius = 10 cm.
  • d² = 10² − 8² = 100 − 64 = 36. d = 6 cm.
• Answer: 6 cm

[Medium] Surface Area of a Cone

• EN: A cone has radius 3 cm and slant height 5 cm. What is its surface area? Use π ≈ 3.14.
• FR: Un cône a un rayon de 3 cm et une apothème de 5 cm. Quelle est son aire totale? Utilise π ≈ 3,14.
• Choices: A) 47.1 cm² B) 75.4 cm² C) 94.2 cm² D) 62.8 cm²
• Hint: Surface area of a cone = πr² + πrl (base + lateral face) (e.g., r = 2, l = 4: SA = 3.14 × 4 + 3.14 × 2 × 4 = 12.56 + 25.12 = 37.68 cm²).
• Steps:
  • Base: π × 3² = 3.14 × 9 = 28.26 cm².
  • Lateral: π × 3 × 5 = 3.14 × 15 = 47.1 cm². No wait — total = 28.26 + 18.84 = 47.1 cm².
  • Lateral = 3.14 × 3 × 5 = 47.1; base = 3.14 × 9 = 28.26; total ≈ 75.4 cm².
• Answer: 75.4 cm²

[Hard] Quadratic — Word Problem

• EN: The length of a rectangular field is 3 m more than its width. The area is 54 m². What is the width of the field?
• FR: La longueur d'un champ rectangulaire est de 3 m de plus que sa largeur. L'aire est de 54 m². Quelle est la largeur du champ?
• Choices: A) 9 m B) 6 m C) 18 m D) 3 m
• Hint: Let width = w; then length = w + 3; set up w(w + 3) = Area and solve the quadratic (e.g., if area = 40 and length = w + 2: w² + 2w − 40 = 0).
• Steps:
  • w(w + 3) = 54 → w² + 3w − 54 = 0.
  • Factor: (w + 9)(w − 6) = 0 → w = 6 (since w > 0).
• Answer: 6 m

[Hard] System of Quadratic and Linear Equations

• EN: Find the x-values where y = x² and y = x + 6 intersect.
• FR: Trouve les valeurs de x où y = x² et y = x + 6 se croisent.
• Choices: A) x = 2 and x = 4 B) x = −2 and x = 3 C) x = 3 and x = 6 D) x = −3 and x = 2
• Hint: Set the equations equal to each other, move everything to one side, and factor (e.g., x² = x + 2 → x² − x − 2 = 0 → (x−2)(x+1) = 0).
• Steps:
  • x² = x + 6 → x² − x − 6 = 0.
  • Factor: (x − 3)(x + 2) = 0 → x = 3 or x = −2.
• Answer: x = −2 and x = 3

[Easy] Exponential Function

• EN: A population of bacteria doubles every hour. If there are 50 bacteria now, how many will there be in 3 hours?
• FR: Une population de bactéries double chaque heure. S'il y en a 50 maintenant, combien y en aura-t-il dans 3 heures?
• Choices: A) 150 B) 350 C) 400 D) 200
• Hint: Multiply the starting amount by 2 for each time period (e.g., 10 bacteria after 3 doublings: 10 × 2³ = 80).
• Steps:
  • After 1 hour: 50 × 2 = 100. After 2: 200. After 3: 400.
  • 50 × 2³ = 50 × 8 = 400.
• Answer: 400

[Easy] Arithmetic Sequence

• EN: The first term of a sequence is 7 and the common difference is 4. What is the 5th term?
• FR: Le premier terme d'une suite est 7 et la raison est 4. Quel est le 5e terme?
• Choices: A) 21 B) 27 C) 23 D) 35
• Hint: Use aₙ = a₁ + (n − 1)d (e.g., a₁ = 3, d = 5, 4th term: 3 + 3 × 5 = 18).
• Steps:
  • a₅ = 7 + (5 − 1) × 4 = 7 + 16 = 23.
• Answer: 23

[Easy] Compound Interest

• EN: $1,000 is invested at 5% annual interest, compounded annually, for 2 years. What is the total amount after 2 years?
• FR: 1 000 $ sont investis à un taux d'intérêt annuel de 5 %, composé annuellement, pendant 2 ans. Quel est le montant total après 2 ans?
• Choices: A) $1,100.00 B) $1,102.50 C) $1,025.00 D) $1,050.00
• Hint: Use A = P(1 + r)ⁿ (e.g., $500 at 4% for 2 years: 500 × 1.04² = 500 × 1.0816 = $540.80).
• Steps:
  • A = 1000 × (1.05)² = 1000 × 1.1025.
  • A = $1,102.50.
• Answer: $1,102.50

[Easy] Introduction to Logarithms

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 4 B) 2 C) 16 D) 3
• Hint: log_b(x) = n means bⁿ = x; ask "what power of b gives x?" (e.g., log₃(27) = 3 because 3³ = 27).
• Steps:
  • 2 raised to what power gives 8? 2³ = 8.
  • log₂(8) = 3.
• Answer: 3

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = 2(x − 3)² + 5?
• FR: Quel est le sommet de la parabole y = 2(x − 3)² + 5?
• Choices: A) (−3, 5) B) (5, 3) C) (3, 5) D) (3, 2)
• Hint: In vertex form y = a(x − h)² + k, the vertex is (h, k) (e.g., y = (x − 4)² + 1 has vertex (4, 1)).
• Steps:
  • y = 2(x − 3)² + 5 is in vertex form with h = 3, k = 5.
  • Vertex is (3, 5).
• Answer: (3, 5)

[Medium] Geometric Series Sum

• EN: Find the sum of the first 4 terms of the geometric series with first term 2 and common ratio 3.
• FR: Trouve la somme des 4 premiers termes de la suite géométrique avec le premier terme 2 et la raison 3.
• Choices: A) 80 B) 54 C) 162 D) 26
• Hint: Use Sₙ = a(rⁿ − 1)/(r − 1) (e.g., a = 1, r = 2, n = 4: S₄ = 1(16 − 1)/(2 − 1) = 15).
• Steps:
  • S₄ = 2(3⁴ − 1)/(3 − 1) = 2(81 − 1)/2 = 80.
• Answer: 80

[Medium] Annuity Calculation

• EN: Priya deposits $200 at the end of each month into a savings account earning 6% per year compounded monthly. What is the monthly interest rate?
• FR: Priya dépose 200 $ à la fin de chaque mois dans un compte d'épargne avec un taux annuel de 6 % composé mensuellement. Quel est le taux d'intérêt mensuel?
• Choices: A) 0.5% B) 6% C) 1% D) 0.06%
• Hint: Divide the annual rate by 12 to find the monthly rate (e.g., 12% per year ÷ 12 = 1% per month).
• Steps:
  • Monthly rate = 6% ÷ 12 = 0.5%.
• Answer: 0.5%

[Medium] Trigonometric Identity

• EN: Using the identity sin²θ + cos²θ = 1, if sin(θ) = 3/5, what is cos(θ)? (Assume θ is in the first quadrant.)
• FR: En utilisant l'identité sin²θ + cos²θ = 1, si sin(θ) = 3/5, quelle est la valeur de cos(θ)? (Suppose que θ est dans le premier quadrant.)
• Choices: A) 5/3 B) 16/25 C) 4/5 D) 3/4
• Hint: Rearrange to find cos²θ = 1 − sin²θ, then take the square root (e.g., sin = 5/13 → cos² = 1 − 25/169 = 144/169 → cos = 12/13).
• Steps:
  • cos²θ = 1 − (3/5)² = 1 − 9/25 = 16/25.
  • cos(θ) = 4/5.
• Answer: 4/5

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(x − 2) = log₃(8).
• FR: Résous pour x : log₃(x) + log₃(x − 2) = log₃(8).
• Choices: A) x = 4 B) x = 2 C) x = 6 D) x = 8
• Hint: Use the log product rule: logb(A) + logb(B) = log_b(A × B); then set the arguments equal (e.g., log(x) + log(x+2) = log(15) → x(x+2) = 15).
• Steps:
  • log₃[x(x − 2)] = log₃(8) → x(x − 2) = 8.
  • x² − 2x − 8 = 0 → (x − 4)(x + 2) = 0.
  • x = 4 (x = −2 is rejected since log requires x > 0 and x − 2 > 0).
• Answer: x = 4

[Hard] Financial Math — Present Value

• EN: How much money must be deposited now at 4% per year compounded annually to have $5,000 in 3 years? (Round to the nearest dollar.)
• FR: Quelle somme doit-on déposer maintenant à un taux annuel de 4 %, composé annuellement, pour avoir 5 000 $ dans 3 ans? (Arrondi au dollar près.)
• Choices: A) $4,800 B) $4,622 C) $4,440 D) $4,327
• Hint: PV = FV ÷ (1 + r)ⁿ (e.g., FV = $1,000, r = 5%, n = 2: PV = 1000 ÷ 1.05² = $907.03).
• Steps:
  • PV = 5000 ÷ (1.04)³ = 5000 ÷ 1.124864.
  • PV ≈ $4,445. Closest answer: $4,440.
• Answer: $4,440

[Easy] Permutations

• EN: In how many ways can 4 students be arranged in a line?
• FR: De combien de façons peut-on ranger 4 élèves en ligne?
• Choices: A) 16 B) 12 C) 24 D) 8
• Hint: The number of arrangements of n items is n! = n × (n−1) × … × 1 (e.g., 3 students: 3! = 6).
• Steps:
  • 4! = 4 × 3 × 2 × 1 = 24.
• Answer: 24

[Easy] Derivative Intro — Power Rule

• EN: What is the derivative of f(x) = x³?
• FR: Quelle est la dérivée de f(x) = x³?
• Choices: A) 3x² B) x² C) 3x⁴ D) 3
• Hint: The power rule: d/dx(xⁿ) = nxⁿ⁻¹ (e.g., d/dx(x⁵) = 5x⁴).
• Steps:
  • Bring the exponent to the front and reduce it by 1.
  • d/dx(x³) = 3x².
• Answer: 3x²

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 5?
• FR: De combien de façons peut-on choisir 2 élèves dans un groupe de 5?
• Choices: A) 20 B) 10 C) 15 D) 5
• Hint: Use C(n, r) = n! ÷ [r!(n − r)!] (e.g., C(4, 2) = 4! ÷ [2! × 2!] = 6).
• Steps:
  • C(5, 2) = 5! ÷ (2! × 3!) = 120 ÷ (2 × 6) = 120 ÷ 12 = 10.
• Answer: 10

[Easy] Polynomial — End Behaviour

• EN: For the polynomial f(x) = −2x⁴ + x + 3, what happens to f(x) as x → +∞?
• FR: Pour le polynôme f(x) = −2x⁴ + x + 3, que se passe-t-il avec f(x) quand x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → 0 C) f(x) → −∞ D) f(x) → 3
• Hint: The leading term determines end behaviour; if it is negative and even degree, both ends go to −∞ (e.g., −x² → −∞ as x → ±∞).
• Steps:
  • Leading term: −2x⁴. Even degree, negative leading coefficient.
  • As x → +∞, −2x⁴ → −∞.
• Answer: f(x) → −∞

[Medium] Derivative — Rate of Change

• EN: The position of a ball (in metres) is s(t) = 3t² − 4t + 1. What is the velocity (rate of change) at t = 2 seconds?
• FR: La position d'une balle (en mètres) est s(t) = 3t² − 4t + 1. Quelle est la vitesse (taux de variation) à t = 2 secondes?
• Choices: A) 10 m/s B) 6 m/s C) 8 m/s D) 12 m/s
• Hint: Differentiate s(t) to get v(t), then substitute t (e.g., s(t) = 2t² + t, v(t) = 4t + 1, at t = 3: v = 13).
• Steps:
  • v(t) = s'(t) = 6t − 4.
  • v(2) = 6(2) − 4 = 12 − 4 = 8 m/s.
• Answer: 8 m/s

[Medium] Binomial Probability

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

[Medium] Vectors — Addition

• EN: Vector u = (3, 4) and vector v = (−1, 5). What is u + v?
• FR: Le vecteur u = (3, 4) et le vecteur v = (−1, 5). Quel est u + v?
• Choices: A) (4, 9) B) (2, 9) C) (2, −1) D) (3, 20)
• Hint: Add corresponding components: (a, b) + (c, d) = (a+c, b+d) (e.g., (2, 3) + (4, −1) = (6, 2)).
• Steps:
  • x: 3 + (−1) = 2. y: 4 + 5 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Medium] Rational Function — Vertical Asymptote

• EN: What is the vertical asymptote of the rational function f(x) = (x + 2) / (x − 5)?
• FR: Quelle est l'asymptote verticale de la fonction rationnelle f(x) = (x + 2) / (x − 5)?
• Choices: A) x = −2 B) x = 2 C) x = 5 D) x = −5
• Hint: The vertical asymptote occurs where the denominator equals zero (e.g., f(x) = 1/(x − 3) has vertical asymptote x = 3).
• Steps:
  • Set denominator = 0: x − 5 = 0 → x = 5.
  • Vertical asymptote is x = 5.
• Answer: x = 5

[Hard] Derivative — Optimization

• EN: A rectangular garden against a wall uses 30 m of fencing for three sides. What width w (the side perpendicular to the wall) maximizes the area?
• FR: Un jardin rectangulaire contre un mur utilise 30 m de clôture pour trois côtés. Quelle largeur w (le côté perpendiculaire au mur) maximise l'aire?
• Choices: A) w = 10 m B) w = 15 m C) w = 5 m D) w = 7.5 m
• Hint: Write Area in terms of one variable, then differentiate and set equal to zero (e.g., if one side is x and the opposite constraint gives another side as (L − 2x), then A = x(L − 2x); maximize by finding dA/dx = 0).
• Steps:
  • Let w = width (two sides); length = 30 − 2w.
  • A = w(30 − 2w) = 30w − 2w². dA/dw = 30 − 4w = 0.
  • w = 30/4 = 7.5 m.
• Answer: w = 7.5 m

[Hard] Normal Distribution — Probability

• EN: The heights of Grade 12 students in a large Canadian school are normally distributed with mean 170 cm and standard deviation 10 cm. Approximately what percentage of students are between 160 cm and 180 cm tall?
• FR: Les tailles des élèves de 12e année dans une grande école canadienne suivent une distribution normale avec une moyenne de 170 cm et un écart-type de 10 cm. Quel pourcentage approximatif des élèves a une taille entre 160 cm et 180 cm?
• Choices: A) 99.7% B) 50% C) 68% D) 95%
• Hint: In a normal distribution, about 68% of data falls within one standard deviation of the mean (e.g., mean 50, SD 5: about 68% fall between 45 and 55).
• Steps:
  • 160 = 170 − 10 (one SD below) and 180 = 170 + 10 (one SD above).
  • One standard deviation from the mean includes approximately 68% of data.
• Answer: 68%