Daily Math — 2026-06-29

[Easy] Counting Bears

• EN: Lena has 7 teddy bears. She gets 5 more. How many bears does she have now?
• FR: Lena a 7 oursons en peluche. Elle en reçoit 5 de plus. Combien en a-t-elle maintenant ?
• Choices: A) 10 bears B) 11 bears C) 12 bears D) 13 bears
• Hint: To add, count on from the bigger number (e.g., 6 + 3: start at 6, count on 3 → 7, 8, 9).
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • 7 + 5 = 12.
• Answer: 12 bears

[Easy] Hockey Sticks

• EN: There are 9 hockey sticks on the floor. 4 are taken away. How many are left?
• FR: Il y a 9 bâtons de hockey sur le plancher. On en prend 4. Combien en reste-t-il ?
• Choices: A) 3 sticks B) 4 sticks C) 5 sticks D) 6 sticks
• Hint: To subtract, count back from the bigger number (e.g., 8 − 3: start at 8, count back 3 → 7, 6, 5).
• Steps:
  • Start at 9 and count back 4: 8, 7, 6, 5.
  • 9 − 4 = 5.
• Answer: 5 sticks

[Easy] Skip Counting by 2s

• EN: Count by 2s: 2, 4, 6, ___, 10. What is the missing number?
• FR: Compte par bonds de 2 : 2, 4, 6, ___, 10. Quel est le nombre manquant ?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: When skip counting by 2s, add 2 each time (e.g., 10, 12, 14…).
• Steps:
  • The pattern adds 2 each time: 2, 4, 6, then 6 + 2 = 8.
  • Check: 8 + 2 = 10. ✓
• Answer: 8

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents in Canada?
• FR: Quelle pièce vaut 10 cents au Canada ?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: Remember: penny = 1¢, nickel = 5¢, dime = 10¢, quarter = 25¢.
• Steps:
  • A penny is 1 cent.
  • A nickel is 5 cents.
  • A dime is 10 cents. That is the answer.
• Answer: Dime

[Medium] Snowflakes on the Window

• EN: There are 13 snowflakes on one window and 6 snowflakes on another. How many snowflakes are there in all?
• FR: Il y a 13 flocons de neige sur une fenêtre et 6 sur une autre. Combien y a-t-il de flocons en tout ?
• Choices: A) 17 snowflakes B) 18 snowflakes C) 19 snowflakes D) 20 snowflakes
• Hint: To add a one-digit number to a teen number, count on from the teen (e.g., 14 + 4 = 18).
• Steps:
  • Start at 13 and count on 6: 14, 15, 16, 17, 18, 19.
  • 13 + 6 = 19.
• Answer: 19 snowflakes

[Medium] Comparing Numbers

• EN: Which number is greater: 14 or 18?
• FR: Quel nombre est plus grand : 14 ou 18 ?
• Choices: A) 14 B) 18 C) They are equal D) 12
• Hint: Look at the tens digit first; if the same, compare the ones (e.g., 16 vs. 19 → both have 1 ten, but 9 > 6, so 19 is greater).
• Steps:
  • Both numbers have 1 ten.
  • Compare the ones: 8 > 4, so 18 > 14.
• Answer: 18

[Medium] Skip Counting by 5s

• EN: Count by 5s: 5, 10, 15, ___, 25. What is the missing number?
• FR: Compte par bonds de 5 : 5, 10, 15, ___, 25. Quel est le nombre manquant ?
• Choices: A) 16 B) 18 C) 20 D) 22
• Hint: When skip counting by 5s, add 5 each time (e.g., 20, 25, 30…).
• Steps:
  • 15 + 5 = 20.
  • Check: 20 + 5 = 25. ✓
• Answer: 20

[Medium] Nickels in a Jar

• EN: Mia has 3 nickels. How many cents does she have in all?
• FR: Mia 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 (e.g., 2 nickels = 5, 10 → 10 cents).
• Steps:
  • Each nickel = 5 cents.
  • Count by 5s three times: 5, 10, 15.
• Answer: 15 cents

[Hard] Missing Number

• EN: 8 + ___ = 17. What is the missing number?
• FR: 8 + ___ = 17. Quel est le nombre manquant ?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: To find a missing addend, subtract what you know from the total (e.g., 6 + ___ = 14 → 14 − 6 = 8).
• Steps:
  • We need 17 − 8.
  • Count up from 8 to 17: that is 9 steps. So the missing number is 9.
• Answer: 9

[Hard] Counting to 100

• EN: What number comes just before 100 when counting by 10s from 10? (10, 20, 30, …, ___, 100)
• FR: Quel nombre vient juste avant 100 en comptant par bonds de 10 à partir de 10 ? (10, 20, 30, …, ___, 100)
• Choices: A) 80 B) 85 C) 90 D) 95
• Hint: Count by 10s and the number before 100 is 100 − 10 (e.g., the number before 50 when counting by 10s is 40).
• Steps:
  • Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.
  • The number just before 100 is 90.
• Answer: 90

[Easy] Adding at Tim Hortons

• EN: Tim Hortons sold 34 muffins in the morning and 25 muffins in the afternoon. How many muffins were sold in total?
• FR: Tim Hortons a vendu 34 muffins le matin et 25 l'après-midi. Combien de muffins ont été vendus en tout ?
• Choices: A) 57 muffins B) 58 muffins C) 59 muffins D) 60 muffins
• Hint: Add the ones first, then the tens (e.g., 32 + 21: ones → 2 + 1 = 3, tens → 3 + 2 = 5, answer = 53).
• Steps:
  • Ones: 4 + 5 = 9.
  • Tens: 3 + 2 = 5.
  • Total: 59 muffins.
• Answer: 59 muffins

[Easy] Subtracting Stickers

• EN: Chloe has 82 stickers. She gives away 41. How many stickers does she have left?
• FR: Chloé a 82 autocollants. Elle en donne 41. Combien lui en reste-t-il ?
• Choices: A) 39 stickers B) 40 stickers C) 41 stickers D) 43 stickers
• Hint: Subtract ones first, then tens (e.g., 75 − 23: ones → 5 − 3 = 2, tens → 7 − 2 = 5, answer = 52).
• Steps:
  • Ones: 2 − 1 = 1.
  • Tens: 8 − 4 = 4.
  • Answer: 41 stickers
• Answer: 41 stickers

[Easy] Telling Time

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: L'aiguille courte est sur le 3 et l'aiguille longue est sur le 12. Quelle heure est-il ?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 12:03
• 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 the hour.
  • Short hand on 3 means it is 3 o'clock.
• Answer: 3:00

[Easy] Measuring Length

• EN: A crayon is 9 cm long. A pencil is 15 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon de cire mesure 9 cm. Un crayon à mine mesure 15 cm. De combien le crayon à mine est-il plus long ?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find the difference in length, subtract the shorter from the longer (e.g., 18 cm − 11 cm = 7 cm).
• Steps:
  • 15 − 9 = 6.
  • The pencil is 6 cm longer.
• Answer: 6 cm

[Medium] Counting Coins

• EN: Aiden has 2 quarters, 1 dime, and 1 nickel. How much money does he have?
• FR: Aiden a 2 pièces de 25 cents, 1 de 10 cents et 1 de 5 cents. Combien d'argent a-t-il ?
• Choices: A) 55 cents B) 60 cents C) 65 cents D) 70 cents
• Hint: Add coin values one at a time (e.g., 1 quarter + 1 dime = 25 + 10 = 35 cents).
• Steps:
  • 2 quarters = 50 cents.
  • Add 1 dime: 50 + 10 = 60 cents.
  • Add 1 nickel: 60 + 5 = 65 cents.
• Answer: 65 cents

[Medium] Telling Time (Half-Hour)

• EN: The clock shows the short hand between 7 and 8, and the long hand on 6. What time is it?
• FR: L'aiguille courte est entre le 7 et le 8, et l'aiguille longue est sur le 6. Quelle heure est-il ?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the long hand is on 6, it is half past the hour (e.g., short hand between 4 and 5, long hand on 6 → 4:30).
• Steps:
  • Long hand on 6 means 30 minutes past.
  • Short hand between 7 and 8 means the hour just passed is 7.
  • Time is 7:30.
• Answer: 7:30

[Medium] Number Patterns

• EN: What comes next in the pattern? 10, 15, 20, 25, ___
• FR: Quel est le prochain nombre dans la suite ? 10, 15, 20, 25, ___
• Choices: A) 28 B) 29 C) 30 D) 35
• Hint: Find the rule by seeing what is added each time (e.g., 4, 8, 12, 16 — adding 4 each time, so next is 20).
• Steps:
  • Each number increases by 5: 10, 15, 20, 25.
  • 25 + 5 = 30.
• Answer: 30

[Medium] Subtraction with Regrouping

• EN: There were 63 students at school. 27 went home early. How many students were still at school?
• FR: Il y avait 63 élèves à l'école. 27 sont partis plus tôt. Combien restait-il d'élèves ?
• Choices: A) 34 students B) 36 students C) 38 students D) 40 students
• Hint: Regroup when the top ones digit is smaller than the bottom (e.g., 52 − 18: ones → borrow to get 12 − 8 = 4, tens → 4 − 1 = 3, answer = 34).
• Steps:
  • Ones: 3 < 7, so regroup: 13 − 7 = 6.
  • Tens: 5 − 2 = 3 (after borrowing one ten).
  • Answer: 36 students
• Answer: 36 students

[Hard] Word Problem with Two Steps

• EN: Ella has 45 cents. She earns 30 more cents doing chores, then spends 28 cents on a snack. How much does she have left?
• FR: Ella a 45 cents. Elle gagne 30 cents de plus en faisant des corvées, puis dépense 28 cents pour une collation. Combien lui reste-t-il ?
• Choices: A) 43 cents B) 45 cents C) 47 cents D) 50 cents
• Hint: Do the problem in two steps: first add, then subtract (e.g., start 20¢ + earn 15¢ = 35¢, then spend 10¢ → 35 − 10 = 25¢).
• Steps:
  • Step 1: 45 + 30 = 75 cents.
  • Step 2: 75 − 28 = 47 cents.
• Answer: 47 cents

[Hard] Measuring and Comparing

• EN: A red ribbon is 78 cm long. A blue ribbon is 54 cm long. Together, are they longer or shorter than 1 metre (100 cm)? By how many centimetres?
• FR: Un ruban rouge mesure 78 cm. Un ruban bleu mesure 54 cm. Ensemble, sont-ils plus longs ou plus courts qu'1 mètre (100 cm) ? De combien de centimètres ?
• Choices: A) Longer by 32 cm B) Shorter by 32 cm C) Longer by 22 cm D) Shorter by 22 cm
• Hint: First add the two lengths, then compare to 100 cm (e.g., 60 + 50 = 110 cm, which is 10 cm longer than 100 cm).
• Steps:
  • 78 + 54 = 132 cm.
  • 132 > 100, so they are longer.
  • 132 − 100 = 32 cm longer.
• Answer: Longer by 32 cm

[Easy] Multiplication by 2

• EN: There are 6 pairs of skates. How many skates are there in all?
• FR: Il y a 6 paires de patins. Combien y a-t-il de patins en tout ?
• Choices: A) 8 skates B) 10 skates C) 12 skates D) 14 skates
• Hint: "Pairs" means groups of 2, so multiply by 2 (e.g., 5 pairs = 5 × 2 = 10).
• Steps:
  • 6 pairs × 2 = 12.
  • There are 12 skates.
• Answer: 12 skates

[Easy] Multiplication by 5

• EN: A bag holds 5 apples. How many apples are in 4 bags?
• FR: Un sac contient 5 pommes. Combien y a-t-il de pommes dans 4 sacs ?
• Choices: A) 15 apples B) 20 apples C) 25 apples D) 9 apples
• Hint: Multiply the number of groups by the size of each group (e.g., 3 × 5 = 15).
• Steps:
  • 4 × 5 = 20.
  • There are 20 apples.
• Answer: 20 apples

[Easy] Basic Fractions

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

[Easy] Reading a Simple Graph

• EN: A bar graph shows: Monday = 4 books read, Tuesday = 7 books read. How many more books were read on Tuesday than Monday?
• FR: Un graphique à barres montre : lundi = 4 livres lus, mardi = 7 livres lus. Combien de livres de plus ont été lus le mardi ?
• Choices: A) 2 books B) 3 books C) 4 books D) 11 books
• Hint: To find "how many more," subtract the smaller bar from the larger (e.g., 9 − 5 = 4 more).
• Steps:
  • 7 − 4 = 3.
  • 3 more books were read on Tuesday.
• Answer: 3 books

[Medium] Division

• EN: 24 students are divided equally into 4 groups. How many students are in each group?
• FR: 24 élèves sont divisés en 4 groupes égaux. Combien d'élèves y a-t-il dans chaque groupe ?
• Choices: A) 4 students B) 5 students C) 6 students D) 8 students
• Hint: Division is sharing equally — think of the related multiplication (e.g., 15 ÷ 3: what times 3 = 15? → 5).
• Steps:
  • 4 × ? = 24.
  • 4 × 6 = 24, so 24 ÷ 4 = 6.
• Answer: 6 students

[Medium] Perimeter

• EN: A rectangular garden has a length of 8 m and a width of 3 m. What is its perimeter?
• FR: Un jardin rectangulaire a une longueur de 8 m et une largeur de 3 m. Quel est son périmètre ?
• Choices: A) 11 m B) 22 m C) 24 m D) 24 m²
• Hint: Perimeter of a rectangle = add all 4 sides (e.g., length 5 m, width 2 m → 5 + 5 + 2 + 2 = 14 m).
• Steps:
  • Perimeter = 8 + 8 + 3 + 3.
  • = 16 + 6 = 22 m.
• Answer: 22 m

[Medium] Multiplication by 3

• EN: A hockey team scores 3 goals per game. How many goals do they score in 7 games?
• FR: Une équipe de hockey marque 3 buts par match. Combien de buts marque-t-elle en 7 matchs ?
• Choices: A) 18 goals B) 21 goals C) 24 goals D) 28 goals
• Hint: Multiply the number of games by goals per game (e.g., 4 games × 3 goals = 12 goals).
• Steps:
  • 7 × 3 = 21.
  • They score 21 goals.
• Answer: 21 goals

[Medium] Fractions on a Number Line

• EN: Which fraction is equal to one half?
• FR: Quelle fraction est égale à la moitié ?
• Choices: A) 2/6 B) 2/4 C) 3/8 D) 1/3
• Hint: A fraction equals one half if the numerator is exactly half the denominator (e.g., 3/6 → half of 6 is 3, so 3/6 = 1/2).
• Steps:
  • Check each: 2/6 → half of 6 is 3, not 2. 2/4 → half of 4 is 2. ✓
  • 2/4 = 1/2.
• Answer: 2/4

[Hard] Multi-Step Word Problem

• EN: A store has 5 shelves. Each shelf holds 10 books. The store sells 18 books on Saturday. How many books are left?
• FR: Un magasin a 5 étagères. Chaque étagère contient 10 livres. Le magasin vend 18 livres samedi. Combien de livres reste-t-il ?
• Choices: A) 28 books B) 32 books C) 38 books D) 42 books
• Hint: First find the total using multiplication, then subtract the amount sold (e.g., 3 shelves × 8 books − 5 sold = 24 − 5 = 19).
• Steps:
  • Total books: 5 × 10 = 50.
  • Books left: 50 − 18 = 32.
• Answer: 32 books

[Hard] Multiplication Table Challenge

• EN: What is 7 × 4?
• FR: Combien font 7 × 4 ?
• Choices: A) 24 B) 27 C) 28 D) 32
• Hint: Break it into known facts (e.g., 7 × 4 = 7 × 2 + 7 × 2 = 14 + 14, like how 6 × 4 = 6 × 2 + 6 × 2 = 24).
• Steps:
  • 7 × 4 = 7 × 2 + 7 × 2 = 14 + 14 = 28.
  • Answer: 28
• Answer: 28

[Easy] Multiplication Tables

• EN: What is 8 × 7?
• FR: Combien font 8 × 7 ?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: Use a nearby fact (e.g., 8 × 6 = 48, then add one more group of 8 → 48 + 8 = 56).
• Steps:
  • 8 × 7 = 8 × 6 + 8 = 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 a decimal, the first digit after the decimal point is the tenths place (e.g., in 5.82, the tenths digit is 8).
• Steps:
  • 3.47: the digit after the decimal point is 4.
  • The tenths digit is 4.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A classroom mat is 6 m long and 4 m wide. What is its area?
• FR: Un tapis de classe mesure 6 m de long et 4 m de large. Quelle est son aire ?
• Choices: A) 10 m² B) 20 m² C) 24 m² D) 28 m²
• Hint: Area of a rectangle = length × width (e.g., 5 m × 3 m = 15 m²).
• Steps:
  • Area = 6 × 4 = 24 m².
• Answer: 24 m²

[Easy] Comparing Fractions

• EN: Which fraction is larger: 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) 1/4
• Hint: When the denominators are the same, compare the numerators — bigger numerator means bigger fraction (e.g., 5/8 > 3/8).
• Steps:
  • Both have denominator 4.
  • Compare numerators: 3 > 2.
  • 3/4 is larger.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: 53 ÷ 4 = ? (Give quotient and remainder.)
• FR: 53 ÷ 4 = ? (Donne le quotient et le reste.)
• Choices: A) 12 remainder 5 B) 13 remainder 1 C) 14 remainder 1 D) 13 remainder 3
• Hint: Divide, then multiply to find what was used, then subtract to find the remainder (e.g., 29 ÷ 4: 4 × 7 = 28, remainder = 29 − 28 = 1, so 7 remainder 1).
• Steps:
  • 4 × 13 = 52. 53 − 52 = 1.
  • Answer: 13 remainder 1
• Answer: 13 remainder 1

[Medium] Elapsed Time

• EN: A hockey game starts at 2:15 p.m. and ends at 4:45 p.m. How long does the game last?
• FR: Un match de hockey commence à 14 h 15 et se termine à 16 h 45. Quelle est la durée du match ?
• Choices: A) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours
• Hint: Count up from the start time to the end time (e.g., 1:20 to 3:50 → 2 hours 30 minutes).
• Steps:
  • From 2:15 to 4:15 = 2 hours.
  • From 4:15 to 4:45 = 30 minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A notebook costs $2.45 and a pen costs $1.30. What is the total cost?
• FR: Un cahier coûte 2,45 $ et un stylo coûte 1,30 $. Quel est le coût total ?
• Choices: A) $3.55 B) $3.70 C) $3.75 D) $4.00
• Hint: Line up the decimal points, then add as usual (e.g., $3.20 + $1.15 = $4.35).
• Steps:
  • $2.45 + $1.30: cents → 45 + 30 = 75 cents; dollars → $2 + $1 = $3.
  • Total: $3.75.
• Answer: $3.75

[Medium] Comparing Fractions — Different Denominators

• EN: Which fraction is greater: 1/2 or 3/8?
• FR: Quelle fraction est la plus grande : 1/2 ou 3/8 ?
• Choices: A) 1/2 B) 3/8 C) They are equal D) 4/8
• Hint: Convert 1/2 to eighths by multiplying top and bottom by 4 (e.g., 1/3 vs. 3/9 → 1/3 = 3/9, so equal).
• Steps:
  • 1/2 = 4/8.
  • Compare: 4/8 > 3/8.
  • 1/2 is greater.
• Answer: 1/2

[Hard] Long Division Two-Digit Divisor

• EN: 96 ÷ 8 = ?
• FR: 96 ÷ 8 = ?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: Use the multiplication table for 8 to find the quotient (e.g., 72 ÷ 8 → 8 × 9 = 72, answer = 9).
• Steps:
  • 8 × 12 = 96. Verify: 8 × 10 = 80, 8 × 2 = 16, 80 + 16 = 96. ✓
  • Answer: 12
• Answer: 12

[Hard] Multi-Step Problem

• EN: A school orders 9 boxes of crayons. Each box has 24 crayons. The school gives 36 crayons to the art room. How many crayons remain?
• FR: Une école commande 9 boîtes de crayons. Chaque boîte contient 24 crayons. L'école donne 36 crayons à la salle d'art. Combien reste-t-il de crayons ?
• Choices: A) 180 crayons B) 186 crayons C) 192 crayons D) 198 crayons
• Hint: First multiply to find the total, then subtract (e.g., 4 boxes × 12 crayons = 48, minus 10 given away = 38).
• Steps:
  • Total crayons: 9 × 24 = 216.
  • Remaining: 216 − 36 = 180.
• Answer: 180 crayons

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6 ?
• Choices: A) 184 B) 200 C) 204 D) 214
• Hint: Multiply each part separately (e.g., 23 × 4 = 20 × 4 + 3 × 4 = 80 + 12 = 92).
• Steps:
  • 30 × 6 = 180.
  • 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: 2/7 + 3/7 = ?
• FR: 2/7 + 3/7 = ?
• Choices: A) 5/7 B) 5/14 C) 6/7 D) 1/7
• Hint: When denominators are the same, just add the numerators (e.g., 1/5 + 2/5 = 3/5).
• Steps:
  • Add the numerators: 2 + 3 = 5.
  • Keep the denominator: 5/7.
• Answer: 5/7

[Easy] Percentage Basics

• EN: What is 50% of 80?
• FR: Combien fait 50 % de 80 ?
• Choices: A) 30 B) 40 C) 50 D) 60
• Hint: 50% means half, so divide by 2 (e.g., 50% of 60 = 60 ÷ 2 = 30).
• Steps:
  • 50% = 1/2.
  • 80 ÷ 2 = 40.
• Answer: 40

[Easy] Decimal Operations

• EN: 4.6 + 2.3 = ?
• FR: 4,6 + 2,3 = ?
• Choices: A) 6.7 B) 6.8 C) 6.9 D) 7.0
• Hint: Line up the decimal points and add each column (e.g., 3.2 + 1.5 = 4.7).
• Steps:
  • Tenths: 6 + 3 = 9.
  • Ones: 4 + 2 = 6.
  • Answer: 6.9
• Answer: 6.9

[Medium] Multi-Digit Division

• EN: 336 ÷ 8 = ?
• FR: 336 ÷ 8 = ?
• Choices: A) 40 B) 42 C) 44 D) 48
• Hint: Divide the hundreds, then tens, then ones (e.g., 240 ÷ 6 → 6 × 40 = 240, answer = 40).
• Steps:
  • 8 × 40 = 320. 336 − 320 = 16.
  • 16 ÷ 8 = 2.
  • 40 + 2 = 42.
• Answer: 42

[Medium] Subtracting Fractions

• EN: 5/9 − 2/9 = ?
• FR: 5/9 − 2/9 = ?
• Choices: A) 3/0 B) 3/9 C) 7/9 D) 3/18
• Hint: Subtract numerators, keep the denominator the same (e.g., 6/8 − 2/8 = 4/8).
• Steps:
  • 5 − 2 = 3.
  • Keep denominator: 3/9.
• Answer: 3/9

[Medium] 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 haut. Quel est son volume ?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 80 cm³
• Hint: Volume = length × width × height (e.g., 2 cm × 3 cm × 4 cm = 24 cm³).
• Steps:
  • V = 5 × 4 × 3.
  • = 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage (25%)

• EN: A winter jacket costs $80.00. It is on sale for 25% off. How much is the discount?
• FR: Un manteau d'hiver coûte 80,00 $. Il est en solde avec 25 % de rabais. Quel est le montant du rabais ?
• Choices: A) $15.00 B) $20.00 C) $25.00 D) $40.00
• Hint: 25% = 1/4, so divide the price by 4 (e.g., 25% of $60 = $60 ÷ 4 = $15).
• Steps:
  • 25% = 1/4.
  • $80 ÷ 4 = $20.00 discount.
• Answer: $20.00

[Hard] Multi-Step Fraction and Decimal

• EN: Mia ran 1.8 km on Monday, 2.4 km on Wednesday, and 1.6 km on Friday. How far did she run in total?
• FR: Mia a couru 1,8 km lundi, 2,4 km mercredi et 1,6 km vendredi. Quelle distance a-t-elle parcourue en tout ?
• Choices: A) 5.6 km B) 5.8 km C) 6.0 km D) 6.2 km
• Hint: Add the decimals carefully, column by column, carrying when needed (e.g., 1.5 + 2.7 + 1.3 = 5.5).
• Steps:
  • 1.8 + 2.4 = 4.2 km.
  • 4.2 + 1.6 = 5.8 km.
• Answer: 5.8 km

[Hard] Percentage Multi-Step

• EN: A store sells 120 granola bars. 10% are chocolate chip. How many granola bars are NOT chocolate chip?
• FR: Un magasin vend 120 barres granola. 10 % sont aux pépites de chocolat. Combien de barres granola ne sont PAS aux pépites de chocolat ?
• Choices: A) 12 bars B) 96 bars C) 108 bars D) 110 bars
• Hint: Find 10% first, then subtract from the total (e.g., 10% of 200 = 20, so 200 − 20 = 180 are not that type).
• Steps:
  • 10% of 120 = 120 ÷ 10 = 12 chocolate chip.
  • Not chocolate chip: 120 − 12 = 108.
• Answer: 108 bars

[Easy] Order of Operations (BEDMAS)

• EN: Calculate: 3 + 4 × 2
• FR: Calcule : 3 + 4 × 2
• Choices: A) 9 B) 10 C) 11 D) 14
• Hint: In BEDMAS, multiply before you add (e.g., 5 + 3 × 2 = 5 + 6 = 11, not 16).
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
• Answer: 11

[Easy] Integers Introduction

• EN: It is −8°C in Ottawa. The temperature rises 5°C. What is the new temperature?
• FR: Il fait −8 °C à Ottawa. La température monte de 5 °C. Quelle est la nouvelle température ?
• Choices: A) −13°C B) −3°C C) 3°C D) 13°C
• Hint: Adding a positive to a negative moves you to the right on the number line (e.g., −6 + 4 = −2).
• Steps:
  • −8 + 5 = −3.
  • The new temperature is −3°C.
• Answer: −3°C

[Easy] Percent of a Number

• EN: What is 10% of 250?
• FR: Combien fait 10 % de 250 ?
• Choices: A) 20 B) 25 C) 30 D) 50
• Hint: 10% means divide by 10 (e.g., 10% of 80 = 80 ÷ 10 = 8).
• Steps:
  • 10% of 250 = 250 ÷ 10 = 25.
• Answer: 25

[Easy] Simple Algebraic Expression

• EN: If n = 6, what is the value of 3n + 2?
• FR: Si n = 6, quelle est la valeur de 3n + 2 ?
• Choices: A) 18 B) 20 C) 22 D) 24
• Hint: Substitute the value in, then follow BEDMAS (e.g., if x = 4, then 2x + 1 = 2 × 4 + 1 = 9).
• Steps:
  • 3n + 2 = 3 × 6 + 2 = 18 + 2 = 20.
• Answer: 20

[Medium] Ratios

• EN: In a class, there are 15 girls and 10 boys. What is the ratio of girls to boys?
• FR: Dans une classe, il y a 15 filles et 10 garçons. Quel est le rapport entre les filles et les garçons ?
• Choices: A) 2:3 B) 3:2 C) 1:2 D) 5:3
• Hint: Write the ratio as the first amount to the second, then simplify by dividing both by their GCF (e.g., 6:4 → GCF is 2 → 3:2).
• Steps:
  • Ratio = 15:10.
  • GCF of 15 and 10 = 5.
  • 15 ÷ 5 = 3; 10 ÷ 5 = 2 → ratio is 3:2.
• Answer: 3:2

[Medium] Fraction Division

• EN: 3/4 ÷ 1/2 = ?
• FR: 3/4 ÷ 1/2 = ?
• Choices: A) 3/8 B) 1 C) 3/2 D) 6/4
• Hint: To divide fractions, multiply by the reciprocal (e.g., 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3).
• Steps:
  • 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2.
• Answer: 3/2

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in km/h?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km/h ?
• Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: Speed = distance ÷ time (e.g., 150 km in 3 hours = 150 ÷ 3 = 50 km/h).
• Steps:
  • 240 ÷ 3 = 80 km/h.
• Answer: 80 km/h

[Medium] Percent of a Number (Multi-step)

• EN: A pair of hockey skates costs $140. There is a 15% tax. How much is the tax?
• FR: Une paire de patins de hockey coûte 140 $. Il y a une taxe de 15 %. Quel est le montant de la taxe ?
• Choices: A) $14.00 B) $18.00 C) $21.00 D) $28.00
• Hint: Find 10% first, then 5% (half of 10%), then add them (e.g., 15% of $80 = $8 + $4 = $12).
• Steps:
  • 10% of $140 = $14.
  • 5% of $140 = $7.
  • 15% = $14 + $7 = $21.00.
• Answer: $21.00

[Hard] BEDMAS with Brackets

• EN: Calculate: (5 + 3)² − 4 × 3
• FR: Calcule : (5 + 3)² − 4 × 3
• Choices: A) 48 B) 52 C) 54 D) 58
• Hint: BEDMAS — do Brackets first, then Exponents, then Multiply/Divide, then Add/Subtract (e.g., (2 + 3)² − 1 × 4 = 25 − 4 = 21).
• Steps:
  • Brackets: 5 + 3 = 8.
  • Exponent: 8² = 64.
  • Multiply: 4 × 3 = 12.
  • Subtract: 64 − 12 = 52.
• Answer: 52

[Hard] Integer Word Problem

• EN: The temperature in Winnipeg was −15°C. It dropped 8°C overnight, then rose 12°C the next day. What is the final temperature?
• FR: La température à Winnipeg était de −15 °C. Elle a baissé de 8 °C pendant la nuit, puis a monté de 12 °C le lendemain. Quelle est la température finale ?
• Choices: A) −19°C B) −11°C C) −9°C D) 5°C
• Hint: Do the operations step by step, watching the signs (e.g., −10 − 5 + 8 = −15 + 8 = −7).
• Steps:
  • Start: −15.
  • Drop 8: −15 − 8 = −23.
  • Rise 12: −23 + 12 = −11.
• Answer: −11°C

[Easy] Integer Addition

• EN: (−12) + 7 = ?
• FR: (−12) + 7 = ?
• Choices: A) −19 B) −5 C) 5 D) 19
• Hint: Adding a positive to a negative: subtract the smaller absolute value from the larger, keep the sign of the larger (e.g., −8 + 3 = −5).
• Steps:
  • |−12| = 12 > |7| = 7, so the answer is negative.
  • 12 − 7 = 5 → answer is −5.
• Answer: −5

[Easy] Fraction Fluency

• EN: Write 0.75 as a fraction in lowest terms.
• FR: Écris 0,75 sous forme de fraction réduite.
• Choices: A) 75/100 B) 7/10 C) 3/4 D) 7/5
• Hint: Write the decimal as a fraction over 100, then simplify by dividing top and bottom by the GCF (e.g., 0.50 = 50/100 = 1/2).
• Steps:
  • 0.75 = 75/100.
  • GCF of 75 and 100 = 25.
  • 75 ÷ 25 = 3; 100 ÷ 25 = 4 → 3/4.
• Answer: 3/4

[Easy] Percentage Discount

• EN: A $60 jersey is on sale at 20% off. How much do you save?
• FR: Un chandail de 60 $ est en solde à 20 % de rabais. Combien économises-tu ?
• Choices: A) $10.00 B) $12.00 C) $15.00 D) $20.00
• Hint: To find 20%, find 10% and double it (e.g., 20% of $50 = $5 × 2 = $10).
• Steps:
  • 10% of $60 = $6.
  • 20% = $6 × 2 = $12.00.
• Answer: $12.00

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 21
• FR: Résous pour x : x + 9 = 21
• Choices: A) x = 10 B) x = 11 C) x = 12 D) x = 30
• Hint: Isolate x by doing the opposite operation on both sides (e.g., x + 4 = 10 → x = 10 − 4 = 6).
• Steps:
  • x + 9 = 21.
  • x = 21 − 9 = 12.
• Answer: x = 12

[Medium] Integer Multiplication

• EN: (−6) × (−4) = ?
• FR: (−6) × (−4) = ?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: Negative × Negative = Positive (e.g., (−3) × (−5) = +15).
• Steps:
  • 6 × 4 = 24.
  • Negative × Negative = Positive.
  • Answer: 24
• Answer: 24

[Medium] Surface Area

• EN: A rectangular box has length 5 cm, width 3 cm, and height 2 cm. What is the total surface area?
• FR: Une boîte rectangulaire a une longueur de 5 cm, une largeur de 3 cm et une hauteur de 2 cm. Quelle est l'aire totale de sa surface ?
• Choices: A) 30 cm² B) 54 cm² C) 62 cm² D) 72 cm²
• Hint: Surface area = 2(lw + lh + wh) (e.g., l=4, w=2, h=3 → 2(8 + 12 + 6) = 2(26) = 52 cm²).
• Steps:
  • lw = 5 × 3 = 15; lh = 5 × 2 = 10; wh = 3 × 2 = 6.
  • SA = 2(15 + 10 + 6) = 2(31) = 62 cm².
• Answer: 62 cm²

[Medium] Tax and Total Price

• EN: A video game costs $55.00. The HST is 13%. What is the total price after tax?
• FR: Un jeu vidéo coûte 55,00 $. La TVH est de 13 %. Quel est le prix total avec la taxe ?
• Choices: A) $60.65 B) $62.15 C) $63.00 D) $65.00
• Hint: Find the tax amount first (price × tax rate), then add to the original price (e.g., $40 × 13% = $5.20, total = $45.20).
• Steps:
  • Tax: $55.00 × 0.13 = $7.15.
  • Total: $55.00 + $7.15 = $62.15.
• Answer: $62.15

[Medium] Probability

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

[Hard] Integer Division with Word Problem

• EN: The temperature in Yellowknife changed by −42°C over 6 equal days. What was the change each day?
• FR: La température à Yellowknife a changé de −42 °C en 6 jours égaux. Quel était le changement chaque jour ?
• Choices: A) −5°C B) −6°C C) −7°C D) −8°C
• Hint: Divide the total change by the number of days, keeping the sign (e.g., −30 ÷ 5 = −6).
• Steps:
  • −42 ÷ 6 = −7.
  • Change each day: −7°C.
• Answer: −7°C

[Hard] Two-Step Equation

• EN: Solve for x: 4x − 3 = 17
• FR: Résous pour x : 4x − 3 = 17
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: First add to both sides to remove the constant, then divide (e.g., 3x − 2 = 10 → 3x = 12 → x = 4).
• Steps:
  • 4x − 3 = 17.
  • Add 3: 4x = 20.
  • Divide by 4: x = 5.
• Answer: x = 5

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13
• FR: Résous pour x : 2x + 5 = 13
• Choices: A) x = 3 B) x = 4 C) x = 6 D) x = 9
• Hint: Subtract the constant from both sides first, then divide (e.g., 3x + 1 = 10 → 3x = 9 → x = 3).
• Steps:
  • 2x + 5 = 13 → 2x = 13 − 5 = 8.
  • x = 8 ÷ 2 = 4.
• Answer: x = 4

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144 ?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of which number times itself equals the value (e.g., √81 → 9 × 9 = 81, so √81 = 9).
• Steps:
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Four students scored 72, 85, 90, and 63 on a test. What is the mean (average) score?
• FR: Quatre élèves ont obtenu 72, 85, 90 et 63 à un test. Quelle est la moyenne ?
• Choices: A) 75 B) 77.5 C) 78 D) 80
• Hint: Mean = sum of all values ÷ number of values (e.g., 10, 20, 30 → sum = 60, mean = 60 ÷ 3 = 20).
• Steps:
  • Sum: 72 + 85 + 90 + 63 = 310.
  • Mean: 310 ÷ 4 = 77.5.
• Answer: 77.5

[Easy] Percent Increase

• EN: A hockey player scored 20 goals last season and 25 goals this season. What is the percent increase?
• FR: Un joueur de hockey a marqué 20 buts la saison dernière et 25 cette saison. Quel est le pourcentage d'augmentation ?
• Choices: A) 5% B) 20% C) 25% D) 50%
• Hint: Percent increase = (new − old) ÷ old × 100% (e.g., from 40 to 50: (10 ÷ 40) × 100% = 25%).
• Steps:
  • Increase: 25 − 20 = 5.
  • Percent increase: (5 ÷ 20) × 100% = 25%.
• Answer: 25%

[Medium] Two-Step Equation with Fractions

• EN: Solve for x: x/3 + 4 = 9
• FR: Résous pour x : x/3 + 4 = 9
• Choices: A) x = 5 B) x = 13 C) x = 15 D) x = 21
• Hint: Subtract the constant first, then multiply both sides by the denominator (e.g., x/4 + 2 = 6 → x/4 = 4 → x = 16).
• Steps:
  • x/3 + 4 = 9 → x/3 = 5.
  • x = 5 × 3 = 15.
• Answer: x = 15

[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) 7 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Use a² + b² = c² (e.g., legs 3 and 4: 9 + 16 = 25, c = √25 = 5).
• Steps:
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through (0, 2) and (4, 10). What is the slope?
• FR: Une droite passe par (0, 2) et (4, 10). Quelle est la pente ?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., through (0,1) and (3,7): slope = (7−1)÷(3−0) = 6÷3 = 2).
• Steps:
  • Rise: 10 − 2 = 8.
  • Run: 4 − 0 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 5, 3, 9, 7, 1
• FR: Trouve la médiane de : 5, 3, 9, 7, 1
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: To find the median, order the numbers from least to greatest and pick the middle one (e.g., 2, 4, 6, 8, 10 → middle is 6).
• Steps:
  • Order: 1, 3, 5, 7, 9.
  • Middle value (3rd of 5): 5.
• Answer: 5

[Hard] Pythagorean Theorem — Reverse

• EN: The hypotenuse of a right triangle is 13 cm and one leg is 5 cm. What is the other leg?
• FR: L'hypoténuse d'un triangle rectangle est de 13 cm et une cathète est de 5 cm. Quelle est l'autre cathète ?
• Choices: A) 8 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: Rearrange: 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 Decrease — Word Problem

• EN: A store reduces the price of a $240 snowboard by 35%. What is the sale price?
• FR: Un magasin réduit le prix d'une planche de surf des neiges de 240 $ de 35 %. Quel est le prix de vente ?
• Choices: A) $84.00 B) $156.00 C) $168.00 D) $204.00
• Hint: Find the discount amount (price × percent), then subtract from the original (e.g., $200 at 20% off: $200 × 0.20 = $40, $200 − $40 = $160).
• Steps:
  • Discount: $240 × 0.35 = $84.
  • Sale price: $240 − $84 = $156.00.
• Answer: $156.00

[Easy] Solving a Linear Equation

• 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: Add the constant to both sides, then divide (e.g., 4x − 3 = 13 → 4x = 16 → x = 4).
• Steps:
  • 3x = 14 + 7 = 21.
  • x = 21 ÷ 3 = 7.
• Answer: x = 7

[Easy] Adding Polynomials

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

[Easy] Slope-Intercept Form

• EN: What is the y-intercept of the line y = 4x − 3?
• FR: Quel est l'ordonnée à l'origine de la droite y = 4x − 3 ?
• Choices: A) 4 B) −3 C) 3 D) −4
• Hint: In y = mx + b, b is the y-intercept (e.g., y = 2x + 7 → y-intercept is 7).
• Steps:
  • y = 4x − 3 is in the form y = mx + b.
  • b = −3, so the y-intercept is −3.
• Answer: −3

[Easy] SOH-CAH-TOA

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

[Medium] Linear Inequality

• EN: Solve for x: 2x + 3 > 11
• FR: Résous pour x : 2x + 3 > 11
• Choices: A) x > 3 B) x > 4 C) x > 5 D) x < 4
• Hint: Solve like an equation, but keep the inequality sign (only flip it when dividing by a negative) (e.g., 3x + 1 > 10 → 3x > 9 → x > 3).
• Steps:
  • 2x + 3 > 11 → 2x > 8.
  • x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x − 5)
• FR: Développe : 3x(2x − 5)
• Choices: A) 6x − 15 B) 5x² − 15x C) 6x² − 15x D) 6x² + 15x
• Hint: Distribute the outer term to each term inside the brackets (e.g., 2x(3x + 4) = 6x² + 8x).
• Steps:
  • 3x × 2x = 6x².
  • 3x × (−5) = −15x.
  • Answer: 6x² − 15x
• Answer: 6x² − 15x

[Medium] Similar Triangles

• EN: Two similar triangles have a side ratio of 2:5. If the smaller triangle has a base of 6 cm, what is the base of the larger triangle?
• FR: Deux triangles semblables ont un rapport de côté de 2:5. Si le plus petit triangle a une base de 6 cm, quelle est la base du plus grand ?
• Choices: A) 10 cm B) 12 cm C) 15 cm D) 18 cm
• Hint: Set up a proportion: small/large = 2/5 (e.g., smaller base = 4 cm, ratio 2:3 → 4/x = 2/3 → x = 6).
• Steps:
  • 6/x = 2/5.
  • x = 6 × 5/2 = 30/2 = 15 cm.
• Answer: 15 cm

[Medium] Graphing Lines

• EN: Which equation describes a line with slope −2 and y-intercept 4?
• FR: Quelle équation décrit une droite avec une pente de −2 et un ordonnée à l'origine de 4 ?
• Choices: A) y = 2x + 4 B) y = −2x − 4 C) y = −2x + 4 D) y = 4x − 2
• Hint: Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (e.g., slope = 3, y-int = −1 → y = 3x − 1).
• Steps:
  • m = −2, b = 4.
  • y = −2x + 4.
• Answer: y = −2x + 4

[Hard] Solving a System of Equations

• EN: Solve the system: y = 2x + 1 and y = −x + 7. Find the value of x.
• FR: Résous le système : y = 2x + 1 et y = −x + 7. Trouve la valeur de x.
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the two expressions equal to each other and solve for x (e.g., 3x + 2 = x + 8 → 2x = 6 → x = 3).
• Steps:
  • 2x + 1 = −x + 7.
  • 3x = 6.
  • x = 2.
• Answer: x = 2

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, angle θ = 30° and the hypotenuse is 20 cm. What is the length of the side adjacent to θ? (cos 30° ≈ 0.866)
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté adjacent à θ ? (cos 30° ≈ 0,866)
• Choices: A) 10.0 cm B) 15.0 cm C) 17.3 cm D) 19.3 cm
• Hint: CAH means cos θ = Adjacent ÷ Hypotenuse, so Adjacent = cos θ × Hypotenuse (e.g., θ = 45°, hyp = 10: adj = 0.707 × 10 ≈ 7.07 cm).
• Steps:
  • cos 30° = adjacent/hypotenuse.
  • Adjacent = 0.866 × 20 = 17.32 ≈ 17.3 cm.
• Answer: 17.3 cm

[Easy] Factoring a Simple Quadratic

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

[Easy] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 7 cm and the hypotenuse is 14 cm. What is angle θ? (sin θ = 0.5 → θ = 30°)
• FR: Dans un triangle rectangle, le côté opposé est de 7 cm et l'hypoténuse est de 14 cm. Quel est l'angle θ ? (sin θ = 0,5 → θ = 30°)
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: sin θ = opposite/hypotenuse; then use inverse sin (e.g., opposite = 5, hyp = 10 → sin θ = 0.5 → θ = 30°).
• Steps:
  • sin θ = 7/14 = 0.5.
  • θ = sin⁻¹(0.5) = 30°.
• Answer: 30°

[Easy] Systems of Equations — Substitution

• EN: If y = 3x and y = 12, what is x?
• FR: Si y = 3x et y = 12, quelle est la valeur de x ?
• Choices: A) x = 3 B) x = 4 C) x = 6 D) x = 9
• Hint: Substitute the known y value into the first equation and solve (e.g., y = 2x and y = 10 → 2x = 10 → x = 5).
• Steps:
  • 3x = 12.
  • x = 4.
• Answer: x = 4

[Easy] Surface Area of a Cylinder

• EN: A cylinder has radius 5 cm and height 10 cm. What is the curved surface area? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 5 cm et une hauteur de 10 cm. Quelle est l'aire latérale ? (Utilise π ≈ 3,14)
• Choices: A) 157 cm² B) 314 cm² C) 471 cm² D) 628 cm²
• Hint: Curved surface area = 2πrh (e.g., r = 3, h = 4 → 2 × 3.14 × 3 × 4 ≈ 75.4 cm²).
• Steps:
  • CSA = 2 × 3.14 × 5 × 10 = 2 × 3.14 × 50 = 314 cm².
• Answer: 314 cm²

[Medium] Quadratic by Factoring

• EN: Solve: x² − 7x + 12 = 0
• FR: Résous : x² − 7x + 12 = 0
• Choices: A) x = 2 or x = 6 B) x = 3 or x = 4 C) x = −3 or x = −4 D) x = 1 or x = 12
• Hint: Factor the quadratic, then set each factor equal to zero (e.g., x² − 5x + 6 = (x−2)(x−3) → x = 2 or x = 3).
• Steps:
  • Factor: (x − 3)(x − 4) = 0.
  • x − 3 = 0 → x = 3; x − 4 = 0 → x = 4.
• Answer: x = 3 or x = 4

[Medium] Systems of Equations — Elimination

• EN: Solve: 2x + y = 10 and x + y = 7. What is x?
• FR: Résous : 2x + y = 10 et x + y = 7. Quelle est la valeur de x ?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Subtract one equation from the other to eliminate y (e.g., (3x+y=11) − (x+y=7) → 2x = 4 → x = 2).
• Steps:
  • Subtract: (2x + y) − (x + y) = 10 − 7.
  • x = 3.
• Answer: x = 3

[Medium] Circle Geometry

• EN: The diameter of a circle is 18 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Le diamètre d'un cercle est de 18 cm. Quelle est la circonférence ? (Utilise π ≈ 3,14)
• Choices: A) 28.26 cm B) 56.52 cm C) 113.04 cm D) 254.34 cm
• Hint: Circumference = π × diameter (e.g., d = 10 cm → C = 3.14 × 10 = 31.4 cm).
• Steps:
  • C = π × d = 3.14 × 18 = 56.52 cm.
• Answer: 56.52 cm

[Medium] Volume of a Cone

• EN: A cone has radius 6 cm and height 9 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 6 cm et une hauteur de 9 cm. Quel est son volume ? (Utilise π ≈ 3,14)
• Choices: A) 169.56 cm³ B) 339.12 cm³ C) 508.68 cm³ D) 1017.36 cm³
• Hint: Volume of cone = (1/3)πr²h (e.g., r = 3, h = 4 → (1/3) × 3.14 × 9 × 4 ≈ 37.68 cm³).
• Steps:
  • V = (1/3) × 3.14 × 6² × 9 = (1/3) × 3.14 × 36 × 9.
  • = (1/3) × 1017.36 = 339.12 cm³.
• Answer: 339.12 cm³

[Hard] 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 = 3 or x = −7 D) x = 7 or x = −1
• Hint: Move the constant, complete the square by adding (b/2)² to both sides (e.g., x² + 4x − 5 = 0 → (x+2)² = 9 → x = 1 or x = −5).
• Steps:
  • x² + 6x = 7.
  • Add (6/2)² = 9: (x + 3)² = 16.
  • x + 3 = ±4 → x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Hard] Trigonometry — Law of Sines Setup

• EN: In triangle ABC, angle A = 45°, angle B = 60°, and side a (opposite A) = 10 cm. Using the Law of Sines, which expression gives side b?
• FR: Dans le triangle ABC, l'angle A = 45°, l'angle B = 60° et le côté a (opposé à A) = 10 cm. En utilisant la loi des sinus, quelle expression donne le côté b ?
• Choices: A) b = 10 × sin 45° / sin 60° B) b = 10 × sin 60° / sin 45° C) b = sin 60° / (10 × sin 45°) D) b = 10 / (sin 60° + sin 45°)
• Hint: Law of Sines: a/sin A = b/sin B → b = a × sin B / sin A (e.g., a = 8, A = 30°, B = 45° → b = 8 × sin45°/sin30°).
• Steps:
  • a/sin A = b/sin B → b = a × sin B / sin A.
  • b = 10 × sin 60° / sin 45°.
• Answer: b = 10 × sin 60° / sin 45°

[Easy] Evaluating a Quadratic Function

• EN: If f(x) = 2x² − 3x + 1, what is f(4)?
• FR: Si f(x) = 2x² − 3x + 1, quelle est la valeur de f(4) ?
• Choices: A) 17 B) 21 C) 25 D) 33
• Hint: Substitute the value in for x and follow BEDMAS (e.g., f(3) = 2(9) − 3(3) + 1 = 18 − 9 + 1 = 10).
• Steps:
  • f(4) = 2(16) − 3(4) + 1 = 32 − 12 + 1 = 21.
• Answer: 21

[Easy] Logarithm Basics

• EN: What is log₂(32)?
• FR: Combien fait log₂(32) ?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log_b(x) = n means b^n = x (e.g., log₂(8) → 2^? = 8 → 2³ = 8, so log₂(8) = 3).
• Steps:
  • 2^? = 32.
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32.
  • log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequence

• EN: Find the 8th term of the arithmetic sequence: 3, 7, 11, 15, …
• FR: Trouve le 8e terme de la suite arithmétique : 3, 7, 11, 15, …
• Choices: A) 27 B) 30 C) 31 D) 33
• Hint: Use aₙ = a₁ + (n − 1)d (e.g., a₁ = 2, d = 5, n = 4 → a₄ = 2 + 3 × 5 = 17).
• Steps:
  • a₁ = 3, d = 4, n = 8.
  • a₈ = 3 + (8 − 1) × 4 = 3 + 28 = 31.
• Answer: 31

[Easy] Exponential Function

• EN: A bacteria culture doubles every hour. If you start with 50 bacteria, how many are there after 3 hours?
• FR: Une culture de bactéries double chaque heure. Si vous commencez avec 50 bactéries, combien y en aura-t-il après 3 heures ?
• Choices: A) 150 B) 200 C) 300 D) 400
• Hint: Use the formula: A = A₀ × 2ⁿ (e.g., start 100, after 2 doublings → 100 × 2² = 400).
• Steps:
  • A = 50 × 2³ = 50 × 8 = 400.
• Answer: 400

[Medium] Compound Interest

• EN: $2 000 is invested at 4% per year, compounded annually. What is the amount after 3 years?
• FR: 2 000 $ sont investis à 4 % par an, composé annuellement. Quel est le montant après 3 ans ?
• Choices: A) $2 160.00 B) $2 240.00 C) $2 249.73 D) $2 252.00
• Hint: Use A = P(1 + r)ⁿ (e.g., P = $1000, r = 5%, n = 2 → A = 1000 × 1.05² = $1102.50).
• Steps:
  • A = 2000 × (1.04)³.
  • (1.04)³ = 1.124864.
  • A = 2000 × 1.124864 = $2 249.73.
• Answer: $2 249.73

[Medium] Geometric Series Sum

• EN: Find the sum of the first 4 terms of the geometric series: 3, 6, 12, 24, …
• FR: Trouve la somme des 4 premiers termes de la série géométrique : 3, 6, 12, 24, …
• Choices: A) 42 B) 45 C) 48 D) 51
• Hint: Add the listed terms directly, or use Sₙ = a(rⁿ − 1)/(r − 1) (e.g., first 3 terms of 1, 2, 4 → sum = 7).
• Steps:
  • Sum = 3 + 6 + 12 + 24 = 45.
• Answer: 45

[Medium] Trig Identity

• EN: Simplify: sin²θ + cos²θ
• FR: Simplifie : sin²θ + cos²θ
• Choices: A) 0 B) 1 C) sin θ D) 2
• Hint: This is a fundamental Pythagorean identity — memorize it (e.g., it holds for any angle θ such as 30°: (0.5)² + (0.866)² ≈ 1).
• Steps:
  • This is the Pythagorean identity.
  • sin²θ + cos²θ = 1 for all θ.
• Answer: 1

[Medium] Logarithm Laws

• EN: Simplify: log₃(81) − log₃(9)
• FR: Simplifie : log₃(81) − log₃(9)
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: logb(x) − logb(y) = log_b(x/y) (e.g., log₂(16) − log₂(4) = log₂(4) = 2).
• Steps:
  • log₃(81) − log₃(9) = log₃(81/9) = log₃(9).
  • 3² = 9, so log₃(9) = 2.
• Answer: 2

[Hard] Annuity Problem

• EN: Maya deposits $500 at the end of every year into an account earning 6% per year, compounded annually. What is the total value after 3 years?
• FR: Maya dépose 500 $ à la fin de chaque année dans un compte rapportant 6 % par an, composé annuellement. Quelle est la valeur totale après 3 ans ?
• Choices: A) $1 500.00 B) $1 573.50 C) $1 591.80 D) $1 637.48
• Hint: Future value of annuity: FV = PMT × [(1+r)ⁿ − 1]/r (e.g., $100/yr, 5%, 2 yrs → 100 × [(1.05)²−1]/0.05 = $205).
• Steps:
  • FV = 500 × [(1.06)³ − 1] / 0.06.
  • (1.06)³ = 1.191016.
  • FV = 500 × (0.191016 / 0.06) = 500 × 3.1836 = $1 591.80.
• Answer: $1 591.80

[Hard] Quadratic with Complex Nature of Roots

• EN: Determine the nature of the roots of: x² − 6x + 10 = 0 using the discriminant.
• FR: Détermine la nature des racines de : x² − 6x + 10 = 0 à l'aide du discriminant.
• Choices: A) Two distinct real roots B) One repeated real root C) Two complex (non-real) roots D) No roots exist
• Hint: Discriminant = b² − 4ac; if < 0 → complex roots, = 0 → one real root, > 0 → two real roots (e.g., x²−2x+5: 4−20 = −16 < 0 → complex).
• Steps:
  • a = 1, b = −6, c = 10.
  • Δ = (−6)² − 4(1)(10) = 36 − 40 = −4.
  • Δ < 0, so two complex (non-real) roots.
• Answer: Two complex (non-real) roots

[Easy] Polynomial Function — End Behaviour

• EN: For f(x) = −3x⁴ + x² − 5, what happens to f(x) as x → +∞?
• FR: Pour f(x) = −3x⁴ + x² − 5, que se passe-t-il avec f(x) lorsque x → +∞ ?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 5
• Hint: For even-degree polynomials, the leading coefficient sign determines end behaviour (e.g., −2x⁴ → f(x) → −∞ on both sides).
• Steps:
  • Leading term: −3x⁴ (even degree, negative coefficient).
  • As x → +∞, −3x⁴ → −∞.
• Answer: f(x) → −∞

[Easy] Permutations

• EN: In how many ways can 4 students line up for a photo?
• FR: De combien de façons 4 élèves peuvent-ils se mettre en ligne pour une photo ?
• Choices: A) 12 B) 16 C) 24 D) 48
• Hint: The number of ways to arrange n objects in a line = n! (e.g., 3 students: 3! = 3 × 2 × 1 = 6).
• Steps:
  • 4! = 4 × 3 × 2 × 1 = 24.
• Answer: 24

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = x³.
• FR: Trouve la dérivée de f(x) = x³.
• Choices: A) 3x B) x² C) 3x² D) 3x⁴
• Hint: Power rule: d/dx(xⁿ) = n·xⁿ⁻¹ (e.g., d/dx(x⁴) = 4x³).
• Steps:
  • Bring down the exponent: 3.
  • Reduce the exponent by 1: x².
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Combinations

• EN: A committee of 3 is chosen from 6 students. How many ways can this be done?
• FR: Un comité de 3 personnes est choisi parmi 6 élèves. De combien de façons peut-on le faire ?
• Choices: A) 12 B) 18 C) 20 D) 30
• Hint: C(n, r) = n! / [r!(n − r)!] (e.g., C(5,2) = 5!/(2!×3!) = 10).
• Steps:
  • C(6, 3) = 6! / (3! × 3!) = (6 × 5 × 4) / (3 × 2 × 1) = 120 / 6 = 20.
• Answer: 20

[Medium] Rational Function — Vertical Asymptote

• EN: Where is the vertical asymptote of f(x) = 5 / (x − 3)?
• FR: Où est l'asymptote verticale de f(x) = 5 / (x − 3) ?
• Choices: A) x = 5 B) x = 3 C) x = 0 D) x = −3
• Hint: Vertical asymptote occurs where the denominator equals zero (e.g., f(x) = 1/(x + 2) → asymptote at x = −2).
• Steps:
  • Set denominator equal to zero: x − 3 = 0 → x = 3.
• Answer: x = 3

[Medium] Rate of Change — Derivative

• EN: The position of a ball is s(t) = 3t² + 2t. What is the velocity at t = 4?
• FR: La position d'une balle est s(t) = 3t² + 2t. Quelle est la vitesse à t = 4 ?
• Choices: A) 24 B) 26 C) 28 D) 30
• Hint: Velocity = derivative of position: s'(t) = 6t + 2 (e.g., if s(t) = 2t² + t, then s'(t) = 4t + 1; at t = 3, v = 13).
• Steps:
  • s'(t) = 6t + 2.
  • s'(4) = 6(4) + 2 = 24 + 2 = 26.
• Answer: 26

[Medium] Binomial Probability

• EN: A coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: On lance une pièce de monnaie 4 fois. Quelle est la probabilité d'obtenir exactement 3 fois « face » ?
• Choices: A) 1/4 B) 3/8 C) 1/4 D) 1/2
• Hint: P(X = k) = 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(3 heads) = C(4,3) × (1/2)³ × (1/2)¹ = 4 × 1/8 × 1/2 = 4/16 = 1/4.
• Answer: 1/4

[Medium] Vectors — Adding Vectors

• EN: Vector u = (3, 5) and vector v = (−1, 4). What is u + v?
• FR: Le vecteur u = (3, 5) et le vecteur v = (−1, 4). Quelle est la valeur de u + v ?
• Choices: A) (2, 1) B) (2, 9) C) (4, 9) D) (4, 1)
• Hint: Add the corresponding components (e.g., (2, 3) + (4, −1) = (6, 2)).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: 5 + 4 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Hard] Derivative — Finding a Maximum

• EN: Find the x-value where f(x) = −2x² + 8x − 3 has a maximum.
• FR: Trouve la valeur de x où f(x) = −2x² + 8x − 3 atteint un maximum.
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the derivative equal to zero and solve for x (e.g., f(x) = −x² + 6x → f'(x) = −2x + 6 = 0 → x = 3).
• Steps:
  • f'(x) = −4x + 8.
  • Set equal to zero: −4x + 8 = 0 → x = 2.
• Answer: x = 2

[Hard] Normal Distribution

• EN: Exam scores are normally distributed with mean 75 and standard deviation 10. What percent of students scored between 65 and 85?
• FR: Les résultats d'examen suivent une distribution normale avec une moyenne de 75 et un écart-type de 10. Quel pourcentage d'élèves a obtenu un score entre 65 et 85 ?
• Choices: A) 50% B) 68% C) 90% D) 95%
• Hint: The 68-95-99.7 rule: about 68% of data falls within 1 standard deviation of the mean (e.g., mean 100, SD 15 → 68% between 85 and 115).
• Steps:
  • 65 = 75 − 10 → one SD below the mean.
  • 85 = 75 + 10 → one SD above the mean.
  • Approximately 68% of scores fall within one SD of the mean.
• Answer: 68%