Daily Math — 2026-09-27

[Easy] Counting Apples

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

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes after 14?
• FR: Compte par bonds de 2. Quel nombre vient après 14?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: When skip counting by 2s from 10: 10, 12, 14, 16 — add 2 each time.
• Steps:
  • Skip counting by 2s means adding 2 each time.
  • 14 + 2 = 16.
• Answer: 16

[Easy] Subtracting Small Numbers

• EN: Mia has 9 stickers. She gives 4 to her friend. How many stickers does Mia have left?
• FR: Mia a 9 autocollants. Elle en donne 4 à son amie. Combien d'autocollants Mia a-t-elle?
• Choices: A) 3 stickers B) 4 stickers C) 5 stickers D) 6 stickers
• Hint: To find 8 − 3, count back 3 from 8: 7, 6, 5 — the answer is 5.
• Steps:
  • Start at 9 and count back 4: 8, 7, 6, 5.
  • 9 − 4 = 5.
• Answer: 5 stickers

[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: A penny = 1 cent, a nickel = 5 cents, a dime = 10 cents.
• Steps:
  • A penny is worth 1 cent.
  • A nickel is worth 5 cents.
  • A dime is worth 10 cents — that is the answer.
• Answer: Dime

[Medium] Comparing Numbers

• EN: Which number is greater: 47 or 74?
• FR: Quel nombre est plus grand : 47 ou 74?
• Choices: A) 47 B) 74 C) They are equal D) 57
• Hint: Compare the tens digit first — 6 tens is greater than 4 tens, so 64 > 48.
• Steps:
  • Look at the tens digits: 47 has 4 tens, 74 has 7 tens.
  • 7 tens is more than 4 tens, so 74 is greater.
• Answer: 74

[Medium] Adding to 20

• EN: Leo scores 8 goals in the first hockey period and 6 goals in the second period. How many goals did he score in all?
• FR: Léo marque 8 buts lors de la première période de hockey et 6 lors de la deuxième. Combien de buts a-t-il marqués en tout?
• Choices: A) 12 goals B) 13 goals C) 14 goals D) 15 goals
• Hint: To add 7 + 5, make a 10: 7 + 3 = 10, then add 2 more = 12.
• Steps:
  • Make a 10: 8 + 2 = 10, then add the leftover 4.
  • 10 + 4 = 14.
• Answer: 14 goals

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What is the missing number: 5, 10, 15, ___, 25?
• FR: Compte par bonds de 5. Quel est le nombre manquant : 5, 10, 15, ___, 25?
• Choices: A) 18 B) 19 C) 20 D) 21
• Hint: Counting by 5s from 10: 10, 15, 20, 25 — add 5 each step.
• Steps:
  • The pattern adds 5 each time: 5, 10, 15, ?, 25.
  • 15 + 5 = 20.
• Answer: 20

[Medium] Counting to 100

• EN: What number comes just before 100 when counting by 1s?
• FR: Quel nombre vient juste avant 100 quand on compte par 1?
• Choices: A) 98 B) 99 C) 101 D) 90
• Hint: The number just before 50 is 49 — subtract 1 from the number.
• Steps:
  • Counting by 1s: …97, 98, 99, 100.
  • The number just before 100 is 99.
• Answer: 99

[Hard] Adding Three Numbers

• EN: There are 6 red mittens, 5 blue mittens, and 4 green mittens in the lost-and-found box. How many mittens are there altogether?
• FR: Il y a 6 mitaines rouges, 5 bleues et 4 vertes dans la boîte des objets perdus. Combien y a-t-il de mitaines en tout?
• Choices: A) 13 mittens B) 14 mittens C) 15 mittens D) 16 mittens
• Hint: To add 3 + 4 + 5, first add 3 + 4 = 7, then 7 + 5 = 12.
• Steps:
  • First add 6 + 5 = 11.
  • Then add 11 + 4 = 15.
• Answer: 15 mittens

[Hard] Subtracting from a Teen

• EN: There are 13 children on the skating rink. 7 children go home. How many children are still on the rink?
• FR: Il y a 13 enfants sur la patinoire. 7 enfants rentrent à la maison. Combien d'enfants restent sur la patinoire?
• Choices: A) 4 children B) 5 children C) 6 children D) 7 children
• Hint: To solve 12 − 5, think: 5 + 7 = 12, so 12 − 5 = 7.
• Steps:
  • Think: 7 + ? = 13.
  • 7 + 6 = 13, so 13 − 7 = 6.
• Answer: 6 children

[Easy] Adding Within 100

• EN: A store has 34 pencils on one shelf and 25 pencils on another shelf. How many pencils are there in all?
• FR: Un magasin a 34 crayons sur une tablette et 25 sur une autre. Combien y a-t-il de crayons en tout?
• Choices: A) 57 pencils B) 58 pencils C) 59 pencils D) 60 pencils
• Hint: To add 32 + 21, add tens: 30 + 20 = 50, then ones: 2 + 1 = 3, total 53.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59.
• Answer: 59 pencils

[Easy] Telling Time — Hour

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: L'horloge montre la petite aiguille sur 3 et la grande aiguille sur 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 12:30
• Hint: When the long hand points to 12 and the short hand points to a number, it is exactly that hour — for example, short hand on 5 means 5:00.
• Steps:
  • The long hand on 12 means it is exactly the hour.
  • The short hand on 3 tells us it is 3 o'clock.
• Answer: 3:00

[Easy] Measuring Length

• EN: A piece of ribbon is 45 cm long. Another piece is 30 cm long. Which piece is longer?
• FR: Un ruban mesure 45 cm de long. Un autre mesure 30 cm. Quel ruban est le plus long?
• Choices: A) The 30 cm piece B) They are the same length C) The 45 cm piece D) Neither piece
• Hint: Compare 28 cm and 35 cm — 35 is more than 28, so 35 cm is longer.
• Steps:
  • Compare 45 and 30.
  • 45 is greater than 30, so the 45 cm piece is longer.
• Answer: The 45 cm piece

[Easy] Counting Coins

• EN: Amara has 2 dimes and 1 nickel. How much money does she have?
• FR: Amara a 2 pièces de 10 cents et 1 pièce de 5 cents. Combien d'argent a-t-elle?
• Choices: A) 20 cents B) 22 cents C) 25 cents D) 30 cents
• Hint: 1 dime = 10 cents, so 2 dimes = 20 cents; a nickel = 5 cents; 20 + 5 = 25 cents.
• Steps:
  • 2 dimes = 2 × 10 = 20 cents.
  • 1 nickel = 5 cents.
  • 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtracting Within 100

• EN: Owen had 72 hockey cards. He gave 38 cards to his cousin. How many cards does Owen have now?
• FR: Owen avait 72 cartes de hockey. Il en a donné 38 à son cousin. Combien de cartes Owen a-t-il maintenant?
• Choices: A) 32 cards B) 33 cards C) 34 cards D) 36 cards
• Hint: To subtract 65 − 27, think 65 − 20 = 45, then 45 − 7 = 38.
• Steps:
  • Subtract the tens: 72 − 30 = 42.
  • Subtract the ones: 42 − 8 = 34.
• Answer: 34 cards

[Medium] Telling Time — Half-Hour

• EN: The clock shows the long hand pointing to 6 and the short hand between 8 and 9. What time is it?
• FR: L'horloge montre la grande aiguille sur 6 et la petite aiguille entre 8 et 9. Quelle heure est-il?
• Choices: A) 6:08 B) 8:06 C) 8:30 D) 9:30
• Hint: When the long hand is on 6, it means 30 minutes past the hour — for example, short hand between 4 and 5 means 4:30.
• Steps:
  • Long hand on 6 = 30 minutes past the hour.
  • Short hand between 8 and 9 means we have passed 8.
  • The time is 8:30.
• Answer: 8:30

[Medium] Simple Patterns

• EN: Look at the pattern: 2, 4, 6, 8, ___. What is the next number?
• FR: Observe le motif : 2, 4, 6, 8, ___. Quel est le prochain nombre?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: In the pattern 5, 10, 15, 20, each number increases by 5 — find how much is added each time.
• Steps:
  • The difference between each number is 2 (skip counting by 2s).
  • 8 + 2 = 10.
• Answer: 10

[Medium] Adding Coins to $1.00

• EN: Niko has 3 quarters. How much money does he have in total?
• FR: Niko a 3 pièces de 25 cents. Combien d'argent a-t-il en tout?
• Choices: A) 60 cents B) 70 cents C) 75 cents D) 80 cents
• Hint: 1 quarter = 25 cents; to find 2 quarters: 25 + 25 = 50 cents.
• Steps:
  • 1 quarter = 25 cents.
  • 25 + 25 = 50 cents for 2 quarters.
  • 50 + 25 = 75 cents for 3 quarters.
• Answer: 75 cents

[Hard] Two-Step Problem

• EN: There are 48 muffins at the Tim Hortons bake sale. 15 muffins are sold in the morning and 12 more are sold in the afternoon. How many muffins are left?
• FR: Il y a 48 muffins à la vente de pâtisseries de Tim Hortons. 15 muffins sont vendus le matin et 12 autres l'après-midi. Combien de muffins reste-t-il?
• Choices: A) 19 muffins B) 20 muffins C) 21 muffins D) 23 muffins
• Hint: For a two-step problem like 50 − 10 − 12, first subtract 10: 50 − 10 = 40, then subtract 12: 40 − 12 = 28.
• Steps:
  • Total sold: 15 + 12 = 27 muffins.
  • Muffins left: 48 − 27 = 21.
• Answer: 21 muffins

[Hard] Measuring and Comparing

• EN: A sunflower is 63 cm tall. A corn stalk is 89 cm tall. How much taller is the corn stalk than the sunflower?
• FR: Un tournesol mesure 63 cm de haut. Une tige de maïs mesure 89 cm. De combien la tige de maïs est-elle plus grande que le tournesol?
• Choices: A) 24 cm B) 25 cm C) 26 cm D) 27 cm
• Hint: To find the difference between 75 cm and 52 cm, subtract: 75 − 52 = 23 cm.
• Steps:
  • Subtract the smaller from the larger: 89 − 63.
  • 89 − 63 = 26 cm.
• Answer: 26 cm

[Easy] Multiplication — 2s Table

• EN: What is 2 × 8?
• FR: Combien font 2 × 8?
• Choices: A) 14 B) 16 C) 18 D) 20
• Hint: 2 × 6 means 6 + 6 = 12.
• Steps:
  • 2 × 8 means 8 + 8.
  • 8 + 8 = 16.
• Answer: 16

[Easy] Basic Division

• EN: 20 children are split into groups of 5. How many groups are there?
• FR: 20 enfants sont divisés en groupes de 5. Combien y a-t-il de groupes?
• Choices: A) 3 groups B) 4 groups C) 5 groups D) 6 groups
• Hint: To find 15 ÷ 5, think: 5 × ? = 15, so the answer is 3.
• Steps:
  • Think: 5 × ? = 20.
  • 5 × 4 = 20, so 20 ÷ 5 = 4.
• Answer: 4 groups

[Easy] Fractions — One Half

• EN: A sandwich is cut into 2 equal pieces. What fraction of the sandwich is one piece?
• FR: Un sandwich est coupé en 2 morceaux égaux. Quelle fraction du sandwich représente un morceau?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: If a pie is cut into 4 equal pieces, one piece is 1/4 of the pie.
• Steps:
  • The sandwich is cut into 2 equal pieces.
  • 1 piece out of 2 equal pieces = 1/2.
• Answer: 1/2

[Easy] Multiplication — 5s Table

• EN: What is 5 × 6?
• FR: Combien font 5 × 6?
• Choices: A) 25 B) 30 C) 35 D) 40
• Hint: 5 × 4 = 20 because skip counting by 5s: 5, 10, 15, 20.
• Steps:
  • Count by 5s six times: 5, 10, 15, 20, 25, 30.
  • 5 × 6 = 30.
• Answer: 30

[Medium] Perimeter of a Rectangle

• EN: A garden is 7 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un jardin a 7 m de long et 3 m de large. Quel est le périmètre du jardin?
• Choices: A) 18 m B) 20 m C) 21 m D) 22 m
• Hint: The perimeter of a rectangle with length 5 and width 2 is 5 + 5 + 2 + 2 = 14.
• Steps:
  • Add all four sides: 7 + 7 + 3 + 3.
  • 14 + 6 = 20 m.
• Answer: 20 m

[Medium] Multiplication — 3s Table

• EN: There are 6 bags of apples. Each bag has 3 apples. How many apples are there in total?
• FR: Il y a 6 sacs de pommes. Chaque sac contient 3 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 15 apples B) 16 apples C) 18 apples D) 21 apples
• Hint: 4 bags × 3 apples each = 4 × 3 = 12 apples.
• Steps:
  • Multiply: 6 × 3.
  • 6 × 3 = 18.
• Answer: 18 apples

[Medium] Reading a Graph

• EN: A bar graph shows that 8 students like hockey, 5 like soccer, and 3 like skiing. How many students were surveyed in total?
• FR: Un diagramme à barres montre que 8 élèves aiment le hockey, 5 aiment le soccer et 3 aiment le ski. Combien d'élèves ont été interrogés en tout?
• Choices: A) 14 students B) 15 students C) 16 students D) 17 students
• Hint: To find the total from a graph showing 6, 4, and 2, add them: 6 + 4 + 2 = 12.
• Steps:
  • Add all three groups: 8 + 5 + 3.
  • 8 + 5 = 13, then 13 + 3 = 16.
• Answer: 16 students

[Medium] Fractions — One Quarter

• EN: A pizza is cut into 4 equal slices. Bella eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 parts égales. Bella mange 1 part. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/4 C) 1/3 D) 2/4
• Hint: If a chocolate bar has 8 equal pieces and you eat 1, you ate 1/8 of the bar.
• Steps:
  • The pizza has 4 equal slices.
  • Bella ate 1 out of 4 slices = 1/4.
• Answer: 1/4

[Hard] Two-Step Multiplication

• EN: A hockey team has 4 lines, and each line has 5 players. Three more players join as extras. How many players are there in total?
• FR: Une équipe de hockey a 4 lignes et chaque ligne compte 5 joueurs. Trois joueurs supplémentaires se joignent à l'équipe. Combien y a-t-il de joueurs en tout?
• Choices: A) 21 players B) 22 players C) 23 players D) 24 players
• Hint: If 3 rows each have 6 desks, that is 3 × 6 = 18 desks; add any extras after.
• Steps:
  • 4 lines × 5 players = 20 players.
  • 20 + 3 extra players = 23 players.
• Answer: 23 players

[Hard] Division with a Check

• EN: 36 maple leaves are shared equally among 4 students. How many leaves does each student get?
• FR: 36 feuilles d'érable sont partagées également entre 4 élèves. Combien de feuilles chaque élève reçoit-il?
• Choices: A) 7 leaves B) 8 leaves C) 9 leaves D) 10 leaves
• Hint: To check 28 ÷ 4, think: 4 × 7 = 28 — multiplication and division are related.
• Steps:
  • Think: 4 × ? = 36.
  • 4 × 9 = 36, so 36 ÷ 4 = 9.
• Answer: 9 leaves

[Easy] Multiplication — Up to 9×9

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: 6 × 8 = 48; then add one more group of 8: 48 + 8 = 56.
• Steps:
  • Use the fact 7 × 8 = 56.
  • Check: 7 × 8 = 7 × 4 × 2 = 28 × 2 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 4.37?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,37?
• Choices: A) 3 ones B) 3 hundredths C) 3 tenths D) 3 tens
• Hint: In 2.56, the digit 5 is in the tenths place and has a value of 5 tenths.
• Steps:
  • In 4.37, the digits after the decimal are tenths and hundredths.
  • The 3 is in the first decimal place = 3 tenths.
• Answer: 3 tenths

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/4?
• FR: Quelle fraction est plus grande : 3/4 ou 1/4?
• Choices: A) 1/4 B) They are equal C) 3/4 D) 2/4
• Hint: When denominators are the same, compare the numerators — 5/8 > 3/8 because 5 > 3.
• Steps:
  • Both fractions have the same denominator (4).
  • Compare numerators: 3 > 1, so 3/4 > 1/4.
• Answer: 3/4

[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 a 6 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 20 m² B) 22 m² C) 24 m² D) 26 m²
• Hint: The area of a rectangle with length 5 m and width 3 m is 5 × 3 = 15 m².
• Steps:
  • Area = length × width.
  • 6 × 4 = 24 m².
• Answer: 24 m²

[Medium] Long Division With Remainder

• EN: 47 students need to be split into groups of 5. How many complete groups can be made?
• FR: 47 élèves doivent être répartis en groupes de 5. Combien de groupes complets peut-on former?
• Choices: A) 8 complete groups B) 9 complete groups C) 10 complete groups D) 11 complete groups
• Hint: To find 29 ÷ 6, think 6 × 4 = 24 and 6 × 5 = 30 — so 4 complete groups with remainder 5.
• Steps:
  • 5 × 9 = 45, which is the largest multiple of 5 that fits in 47.
  • 47 − 45 = 2 remainder, so there are 9 complete groups.
• Answer: 9 complete groups

[Medium] Elapsed Time

• EN: School starts at 8:30 a.m. and ends at 3:00 p.m. How long is the school day?
• FR: L'école commence à 8 h 30 et se termine à 15 h 00. Quelle est la durée de la journée scolaire?
• Choices: A) 5 hours 30 minutes B) 6 hours C) 6 hours 30 minutes D) 7 hours
• Hint: From 9:15 a.m. to 2:15 p.m. is exactly 5 hours — count forward from the start time.
• Steps:
  • From 8:30 a.m. to 3:00 p.m.
  • 8:30 to 3:00 = 6 hours and 30 minutes.
• Answer: 6 hours 30 minutes

[Medium] Decimal Operations

• EN: A chocolate bar costs $1.75 and a juice costs $1.20. What is the total cost?
• FR: Une tablette de chocolat coûte 1,75 $ et un jus coûte 1,20 $. Quel est le coût total?
• Choices: A) $2.85 B) $2.90 C) $2.95 D) $3.05
• Hint: To add $2.30 + $1.45, line up the decimals: 2.30 + 1.45 = 3.75.
• Steps:
  • Add: $1.75 + $1.20.
  • 1.75 + 1.20 = 2.95.
• Answer: $2.95

[Medium] Multiplication — Two-Digit by One-Digit

• EN: A bookshelf has 6 shelves and each shelf holds 23 books. How many books can the shelf hold in total?
• FR: Une bibliothèque a 6 tablettes et chaque tablette contient 23 livres. Combien de livres la bibliothèque peut-elle contenir en tout?
• Choices: A) 128 books B) 136 books C) 138 books D) 148 books
• Hint: To find 4 × 21, multiply 4 × 20 = 80, then 4 × 1 = 4; total = 84.
• Steps:
  • 6 × 23 = 6 × 20 + 6 × 3.
  • 120 + 18 = 138.
• Answer: 138 books

[Hard] Multi-Step Problem

• EN: Priya buys 4 notebooks at $3.25 each and pays with a $20 bill. How much change does she receive?
• FR: Priya achète 4 cahiers à 3,25 $ chacun et paie avec un billet de 20 $. Combien de monnaie reçoit-elle?
• Choices: A) $6.75 B) $7.00 C) $7.25 D) $8.00
• Hint: First find the total cost (multiply), then subtract from the amount paid.
• Steps:
  • Cost of notebooks: 4 × $3.25 = $13.00.
  • Change: $20.00 − $13.00 = $7.00.
• Answer: $7.00

[Hard] Comparing and Ordering Decimals

• EN: Put these amounts in order from least to greatest: 3.07, 3.7, 3.17, 3.01.
• FR: Mets ces nombres en ordre du plus petit au plus grand : 3,07; 3,7; 3,17; 3,01.
• Choices: A) 3.01, 3.07, 3.17, 3.7 B) 3.07, 3.01, 3.17, 3.7 C) 3.01, 3.7, 3.07, 3.17 D) 3.17, 3.07, 3.01, 3.7
• Hint: To order 1.2, 1.02, 1.22 — compare tenths first: 1.02 < 1.2 < 1.22.
• Steps:
  • All numbers start with 3. Look at the tenths place: 0, 7, 1, 0.
  • The two with 0 tenths: 3.07 and 3.01 — compare hundredths: 3.01 < 3.07.
  • Then 3.17 (1 tenth), then 3.7 (7 tenths).
  • Order: 3.01, 3.07, 3.17, 3.7.
• Answer: 3.01, 3.07, 3.17, 3.7

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 194 B) 200 C) 204 D) 210
• Hint: To find 21 × 4, multiply 20 × 4 = 80 and 1 × 4 = 4, then add: 84.
• Steps:
  • 34 × 6 = (30 × 6) + (4 × 6).
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions With Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien font 2/7 + 3/7?
• Choices: A) 5/14 B) 5/7 C) 6/7 D) 1/7
• Hint: To add 1/5 + 3/5, keep the denominator the same and add the numerators: 1 + 3 = 4, giving 4/5.
• Steps:
  • Keep the denominator: 7.
  • Add the numerators: 2 + 3 = 5.
  • The answer is 5/7.
• Answer: 5/7

[Easy] Decimal Operations — Addition

• EN: A bag of flour costs $3.45 and a bag of sugar costs $2.30. What is the total cost?
• FR: Un sac de farine coûte 3,45 $ et un sac de sucre coûte 2,30 $. Quel est le coût total?
• Choices: A) $5.55 B) $5.65 C) $5.75 D) $6.05
• Hint: To add $4.20 + $1.35, line up the decimal points and add: 4.20 + 1.35 = 5.55.
• Steps:
  • $3.45 + $2.30: add dollars: 3 + 2 = 5; add cents: 45 + 30 = 75.
  • Total = $5.75.
• Answer: $5.75

[Easy] Percentage Intro — 50%

• EN: What is 50% of 80?
• FR: Combien vaut 50 % de 80?
• Choices: A) 35 B) 40 C) 45 D) 50
• Hint: 50% of a number means half — 50% of 60 = 60 ÷ 2 = 30.
• Steps:
  • 50% means half.
  • 80 ÷ 2 = 40.
• Answer: 40

[Medium] Multi-Digit Division

• EN: 252 students are placed in rows of 9 for an assembly. How many rows are there?
• FR: 252 élèves sont placés en rangées de 9 pour une assemblée. Combien y a-t-il de rangées?
• Choices: A) 26 rows B) 27 rows C) 28 rows D) 29 rows
• Hint: To find 180 ÷ 9, think 9 × 20 = 180 — check your answer by multiplying.
• Steps:
  • 9 × 28 = 252? Check: 9 × 20 = 180, 9 × 8 = 72, 180 + 72 = 252. ✓
  • 252 ÷ 9 = 28.
• Answer: 28 rows

[Medium] Subtracting Fractions With Like Denominators

• EN: Lena has 7/9 of a metre of rope. She uses 4/9 of a metre. How much rope is left?
• FR: Lena a 7/9 de mètre de corde. Elle utilise 4/9 de mètre. Quelle longueur de corde reste-t-il?
• Choices: A) 2/9 B) 3/9 C) 4/9 D) 5/9
• Hint: To subtract 5/8 − 2/8, keep the denominator: 5 − 2 = 3, giving 3/8.
• Steps:
  • Keep the denominator: 9.
  • Subtract numerators: 7 − 4 = 3.
  • The answer is 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) 48 cm³ B) 56 cm³ C) 60 cm³ D) 64 cm³
• Hint: Volume = length × width × height; for a box 2 cm × 3 cm × 4 cm, volume = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A jacket costs $120. It is on sale for 25% off. How much money do you save?
• FR: Un manteau coûte 120 $. Il est en solde à 25 % de réduction. Combien économisez-vous?
• Choices: A) $25 B) $28 C) $30 D) $35
• Hint: 25% of a number = the number ÷ 4; for example, 25% of $80 = $80 ÷ 4 = $20.
• Steps:
  • 25% = one quarter.
  • $120 ÷ 4 = $30.
• Answer: $30

[Hard] Multi-Step Fraction Problem

• EN: A recipe needs 3/8 cup of butter for cookies and 5/8 cup of butter for a cake. If Maya has 1 full cup of butter, how much butter will she have left after making both?
• FR: Une recette nécessite 3/8 de tasse de beurre pour des biscuits et 5/8 pour un gâteau. Si Maya a 1 tasse complète, combien de beurre lui restera-t-il?
• Choices: A) 0 cups B) 1/8 cup C) 2/8 cup D) 3/8 cup
• Hint: Convert 1 whole to eighths: 1 = 8/8, then subtract fractions with the same denominator.
• Steps:
  • Total butter used: 3/8 + 5/8 = 8/8 = 1 cup.
  • Butter left: 1 − 1 = 0 cups.
• Answer: 0 cups

[Hard] Decimal Multiplication

• EN: A bottle of maple syrup costs $4.75. How much do 6 bottles cost?
• FR: Une bouteille de sirop d'érable coûte 4,75 $. Combien coûtent 6 bouteilles?
• Choices: A) $27.50 B) $28.00 C) $28.50 D) $29.00
• Hint: To find 3 × $2.25, multiply 3 × 2 = 6 and 3 × 0.25 = 0.75, then add: $6.75.
• Steps:
  • 6 × $4.75 = 6 × $4 + 6 × $0.75.
  • 24 + 4.50 = $28.50.
• Answer: $28.50

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien vaut 30 % de 200?
• Choices: A) 50 B) 55 C) 60 D) 65
• Hint: To find 20% of 50, first find 10% (50 ÷ 10 = 5), then double it: 5 × 2 = 10.
• Steps:
  • 10% of 200 = 20.
  • 30% = 3 × 10% = 3 × 20 = 60.
• Answer: 60

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: In BEDMAS, multiplication comes before addition — for 5 + 2 × 3, do 2 × 3 = 6 first, then 5 + 6 = 11.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
• Answer: 11

[Easy] Introduction to Integers

• EN: The temperature in Winnipeg was −8°C in the morning. Which temperature is colder: −8°C or −3°C?
• FR: La température à Winnipeg était de −8 °C le matin. Quelle température est la plus froide : −8 °C ou −3 °C?
• Choices: A) −3°C B) They are the same C) −8°C D) 0°C
• Hint: On a number line, numbers further to the left are smaller — −10 is colder than −4.
• Steps:
  • On a number line, −8 is further left than −3.
  • Further left = colder = smaller value.
  • −8°C is colder.
• Answer: −8°C

[Easy] Ratios

• EN: For every 2 red beads, there are 5 blue beads. What is the ratio of red to blue beads?
• FR: Pour chaque 2 perles rouges, il y a 5 perles bleues. Quel est le rapport des perles rouges aux perles bleues?
• Choices: A) 5:2 B) 2:5 C) 2:7 D) 5:7
• Hint: A ratio compares two quantities in order — if there are 3 cats and 4 dogs, the ratio of cats to dogs is 3:4.
• Steps:
  • The question asks for red to blue.
  • Red = 2, Blue = 5.
  • Ratio = 2:5.
• Answer: 2:5

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 6/12 C) 5/7 D) 8/12
• Hint: To multiply fractions, multiply the numerators together and the denominators together: 1/2 × 2/3 = 2/6.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2, but the simplest form among choices is 6/12.
• Answer: 6/12

[Medium] Simple Algebraic Expression

• EN: If n = 5, what is the value of 3n + 7?
• FR: Si n = 5, quelle est la valeur de 3n + 7?
• Choices: A) 20 B) 21 C) 22 D) 23
• Hint: To evaluate 4n + 2 when n = 3, substitute: 4(3) + 2 = 12 + 2 = 14.
• Steps:
  • Substitute n = 5: 3(5) + 7.
  • 15 + 7 = 22.
• Answer: 22

[Medium] Rates

• EN: A car travels 120 km in 2 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 120 km en 2 heures. Quelle est sa vitesse en km par heure?
• Choices: A) 55 km/h B) 60 km/h C) 65 km/h D) 70 km/h
• Hint: Rate = total ÷ time; if a bicycle travels 30 km in 3 hours, the speed is 30 ÷ 3 = 10 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 120 ÷ 2 = 60 km/h.
• Answer: 60 km/h

[Medium] Fraction Division

• EN: How many 1/3-cup servings are in 2 cups of juice?
• FR: Combien de portions de 1/3 de tasse y a-t-il dans 2 tasses de jus?
• Choices: A) 4 servings B) 5 servings C) 6 servings D) 7 servings
• Hint: To divide 3 ÷ 1/2, multiply by the reciprocal: 3 × 2 = 6.
• Steps:
  • 2 ÷ (1/3) = 2 × 3 = 6.
  • There are 6 servings.
• Answer: 6 servings

[Hard] Multi-Step Percent Problem

• EN: A hockey jersey costs $85. It is on sale for 20% off. After the discount, a 13% tax is added. What is the final price?
• FR: Un chandail de hockey coûte 85 $. Il est en solde à 20 % de réduction. Après la réduction, une taxe de 13 % est ajoutée. Quel est le prix final?
• Choices: A) $76.58 B) $77.00 C) $76.84 D) $78.20
• Hint: First find the discounted price, then apply tax: discounted price × 1.13 gives the final cost.
• Steps:
  • Discount: 20% of $85 = $17, so sale price = $85 − $17 = $68.
  • Tax: 13% of $68 = $8.84.
  • Final price: $68 + $8.84 = $76.84.
• Answer: $76.84

[Hard] Order of Operations — Complex

• EN: Evaluate: (12 − 4) × 3 + 6 ÷ 2.
• FR: Calcule : (12 − 4) × 3 + 6 ÷ 2.
• Choices: A) 24 B) 27 C) 30 D) 33
• Hint: Use BEDMAS — brackets first, then multiplication and division left to right, then addition.
• Steps:
  • Brackets: 12 − 4 = 8.
  • Multiplication: 8 × 3 = 24.
  • Division: 6 ÷ 2 = 3.
  • Addition: 24 + 3 = 27.
• Answer: 27

[Easy] Integer Addition

• EN: What is −6 + 9?
• FR: Combien font −6 + 9?
• Choices: A) −3 B) 2 C) 3 D) 15
• Hint: For −4 + 7, start at −4 on the number line and move 7 to the right: you land on 3.
• Steps:
  • Start at −6, add 9 (move right).
  • −6 + 9 = 3.
• Answer: 3

[Easy] Percent — Discount

• EN: A pair of skates costs $160. There is a 10% discount. How much do the skates cost after the discount?
• FR: Une paire de patins coûte 160 $. Il y a un rabais de 10 %. Combien coûtent les patins après le rabais?
• Choices: A) $140 B) $144 C) $148 D) $150
• Hint: 10% of any number = that number ÷ 10; then subtract the discount from the original price.
• Steps:
  • 10% of $160 = $16.
  • $160 − $16 = $144.
• Answer: $144

[Easy] Fraction and Decimal Fluency

• EN: What is 3/5 written as a decimal?
• FR: Comment s'écrit 3/5 sous forme décimale?
• Choices: A) 0.35 B) 0.5 C) 0.6 D) 0.65
• Hint: To convert 1/4 to a decimal, divide: 1 ÷ 4 = 0.25.
• Steps:
  • Divide numerator by denominator: 3 ÷ 5.
  • 3 ÷ 5 = 0.6.
• Answer: 0.6

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 13 = 20.
• FR: Résous pour x : x + 13 = 20.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: To solve x + 4 = 11, subtract 4 from both sides: x = 11 − 4 = 7.
• Steps:
  • Subtract 13 from both sides: x = 20 − 13.
  • x = 7.
• Answer: x = 7

[Medium] Integer Subtraction

• EN: What is −5 − (−8)?
• FR: Combien font −5 − (−8)?
• Choices: A) −13 B) −3 C) 3 D) 13
• Hint: Subtracting a negative is the same as adding a positive: −2 − (−6) = −2 + 6 = 4.
• Steps:
  • −5 − (−8) = −5 + 8.
  • −5 + 8 = 3.
• Answer: 3

[Medium] Percentage — Tip

• EN: A family's restaurant bill is $60. They want to leave a 15% tip. How much is the tip?
• FR: La facture d'un restaurant est de 60 $. La famille veut laisser un pourboire de 15 %. Quel est le montant du pourboire?
• Choices: A) $7.00 B) $8.00 C) $9.00 D) $10.00
• Hint: 15% = 10% + 5%; find 10% of $80 = $8, then 5% = $4, total tip = $12.
• Steps:
  • 10% of $60 = $6.
  • 5% of $60 = $3.
  • 15% tip = $6 + $3 = $9.
• Answer: $9.00

[Medium] Surface Area

• EN: A rectangular box has length 5 cm, width 3 cm, and height 2 cm. What is its surface area?
• FR: Une boîte rectangulaire a 5 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire totale?
• Choices: A) 60 cm² B) 62 cm² C) 64 cm² D) 66 cm²
• Hint: Surface area of a rectangular prism = 2(lw + lh + wh); for a 4×2×1 box: 2(8+4+2) = 28 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(5×3 + 5×2 + 3×2).
  • = 2(15 + 10 + 6) = 2(31) = 62 cm².
• Answer: 62 cm²

[Medium] Probability

• EN: A bag contains 3 red marbles, 4 blue marbles, and 3 green marbles. If one marble is picked at random, what is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 4 bleues et 3 vertes. Si on tire une bille au hasard, quelle est la probabilité de tirer une bille bleue?
• Choices: A) 3/10 B) 2/5 C) 1/2 D) 3/4
• Hint: Probability = (number of favourable outcomes) ÷ (total outcomes); if 2 of 8 marbles are red, P(red) = 2/8 = 1/4.
• Steps:
  • Total marbles: 3 + 4 + 3 = 10.
  • P(blue) = 4/10 = 2/5.
• Answer: 2/5

[Hard] Multi-Step Integer Problem

• EN: The temperature in Churchill, Manitoba dropped from 4°C to −11°C overnight. The next day it rose by 7°C. What was the temperature after it rose?
• FR: La température à Churchill, au Manitoba, est passée de 4 °C à −11 °C durant la nuit. Le lendemain, elle a monté de 7 °C. Quelle était la température après la hausse?
• Choices: A) −6°C B) −4°C C) −3°C D) −2°C
• Hint: Find the new starting temperature first, then add the rise: if it drops to −8°C and rises 5°C, final temp = −8 + 5 = −3°C.
• Steps:
  • Temperature dropped to −11°C.
  • Rose by 7°C: −11 + 7 = −4°C.
• Answer: −4°C

[Hard] Two-Step Equation

• EN: Solve for x: 4x − 5 = 19.
• FR: Résous pour x : 4x − 5 = 19.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: To solve 3x − 2 = 13, first add 2 to both sides (3x = 15), then divide by 3 (x = 5).
• Steps:
  • Add 5 to both sides: 4x = 24.
  • Divide both sides by 4: x = 6.
• Answer: x = 6

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: √100 = 10 because 10 × 10 = 100 — think of which number multiplied by itself gives the value.
• Steps:
  • Think: what number times itself equals 144?
  • 12 × 12 = 144, so √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored the following on a math quiz: 70, 80, 90, 60, 100. What is the mean score?
• FR: Cinq élèves ont obtenu les notes suivantes à un quiz de maths : 70, 80, 90, 60, 100. Quelle est la note moyenne?
• Choices: A) 78 B) 79 C) 80 D) 82
• Hint: Mean = sum of all values ÷ number of values; for 4, 6, 8: sum = 18, mean = 18 ÷ 3 = 6.
• Steps:
  • Sum: 70 + 80 + 90 + 60 + 100 = 400.
  • Mean: 400 ÷ 5 = 80.
• Answer: 80

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 15.
• FR: Résous pour x : 2x + 5 = 15.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: To solve 3x + 2 = 14, subtract 2 first (3x = 12), then divide by 3 (x = 4).
• Steps:
  • Subtract 5: 2x = 10.
  • Divide by 2: x = 5.
• Answer: x = 5

[Easy] Percent Increase

• EN: A book costs $40. Its price increases by 15%. What is the new price?
• FR: Un livre coûte 40 $. Son prix augmente de 15 %. Quel est le nouveau prix?
• Choices: A) $44 B) $45 C) $46 D) $47
• Hint: For a 20% increase on $50: find 20% = $10, then add to original: $50 + $10 = $60.
• Steps:
  • 15% of $40 = 0.15 × 40 = $6.
  • New price = $40 + $6 = $46.
• Answer: $46

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: Using a² + b² = c², for legs 3 and 4: 9 + 16 = 25, so c = √25 = 5.
• Steps:
  • a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Intro

• EN: A line passes through the points (2, 3) and (4, 7). What is the slope of the line?
• FR: Une droite passe par les points (2, 3) et (4, 7). Quelle est la pente de cette droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (change in y) ÷ (change in x); for points (1, 2) and (3, 6): slope = (6−2)/(3−1) = 4/2 = 2.
• Steps:
  • Change in y: 7 − 3 = 4.
  • Change in x: 4 − 2 = 2.
  • Slope = 4 ÷ 2 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 5, 3, 8, 3, 7, 9, 3.
• FR: Trouve la médiane de : 5, 3, 8, 3, 7, 9, 3.
• Choices: A) 3 B) 5 C) 7 D) 8
• Hint: To find the median, arrange the data in order from least to greatest and find the middle value.
• Steps:
  • Arrange in order: 3, 3, 3, 5, 7, 8, 9.
  • There are 7 values — the middle (4th) value is 5.
• Answer: 5

[Medium] Percent Decrease

• EN: A sweater was $80. After a sale, the new price is $60. By what percentage did the price decrease?
• FR: Un chandail valait 80 $. Après une vente, son nouveau prix est 60 $. De quel pourcentage le prix a-t-il diminué?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent decrease = (decrease ÷ original) × 100; if a price drops from $50 to $40, decrease = $10, and 10 ÷ 50 × 100 = 20%.
• Steps:
  • Decrease = $80 − $60 = $20.
  • Percent decrease = (20 ÷ 80) × 100 = 25%.
• Answer: 25%

[Hard] Pythagorean Theorem — Word Problem

• EN: Kenji walks 9 m east and 12 m north to reach the hockey rink. How far is the rink from his starting point in a straight line?
• FR: Kenji marche 9 m vers l'est et 12 m vers le nord pour atteindre la patinoire. Quelle est la distance en ligne droite entre lui et son point de départ?
• Choices: A) 13 m B) 14 m C) 15 m D) 16 m
• Hint: Draw a right triangle — the straight-line distance is the hypotenuse; use a² + b² = c².
• Steps:
  • a = 9, b = 12.
  • c² = 9² + 12² = 81 + 144 = 225.
  • c = √225 = 15 m.
• Answer: 15 m

[Hard] Multi-Step Linear Equation

• EN: Solve for x: 3(2x − 4) = 18.
• FR: Résous pour x : 3(2x − 4) = 18.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: First expand the brackets, then isolate x — for 2(x − 1) = 8: expand to 2x − 2 = 8, then 2x = 10, x = 5.
• Steps:
  • Expand: 6x − 12 = 18.
  • Add 12: 6x = 30.
  • Divide by 6: x = 5.
• Answer: x = 5

[Easy] Graphing a Line — Slope-Intercept

• EN: What is the slope of the line y = 3x − 2?
• FR: Quelle est la pente de la droite y = 3x − 2?
• Choices: A) −2 B) 1 C) 3 D) 5
• Hint: In y = mx + b, m is the slope and b is the y-intercept; for y = 5x + 1, the slope is 5.
• Steps:
  • The equation is in the form y = mx + b.
  • m = 3, so the slope is 3.
• Answer: 3

[Easy] Adding Polynomials

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

[Easy] Solving a Linear Inequality

• EN: Solve for x: x − 4 > 6.
• FR: Résous pour x : x − 4 > 6.
• Choices: A) x > 8 B) x > 9 C) x > 10 D) x > 11
• Hint: Solve inequalities like equations — to solve x − 3 > 5, add 3 to both sides: x > 8.
• Steps:
  • Add 4 to both sides: x > 6 + 4.
  • x > 10.
• Answer: x > 10

[Easy] Similar Triangles

• EN: Two similar triangles have sides in the ratio 1:3. If the shorter triangle has a side of 5 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans le rapport 1:3. Si le plus petit triangle a un côté de 5 cm, quel est le côté correspondant du grand triangle?
• Choices: A) 10 cm B) 12 cm C) 15 cm D) 18 cm
• Hint: If the ratio is 1:2 and the small side is 7 cm, the large side = 7 × 2 = 14 cm.
• Steps:
  • Ratio is 1:3, so multiply by 3.
  • 5 × 3 = 15 cm.
• Answer: 15 cm

[Medium] Solving a Two-Step Linear Equation

• EN: Solve for x: 5x + 8 = 33.
• FR: Résous pour x : 5x + 8 = 33.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Subtract the constant first, then divide by the coefficient — for 4x + 3 = 19: 4x = 16, x = 4.
• Steps:
  • Subtract 8: 5x = 25.
  • Divide by 5: x = 5.
• Answer: x = 5

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x + 4).
• FR: Développe : 3x(2x + 4).
• Choices: A) 5x² + 7x B) 6x² + 12x C) 6x + 12 D) 6x² + 4x
• Hint: Distribute each term — for 2x(x + 3): 2x × x = 2x² and 2x × 3 = 6x, giving 2x² + 6x.
• Steps:
  • 3x × 2x = 6x².
  • 3x × 4 = 12x.
  • Result: 6x² + 12x.
• Answer: 6x² + 12x

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 4 cm and the hypotenuse is 8 cm. What is the sine of the angle?
• FR: Dans un triangle rectangle, le côté opposé mesure 4 cm et l'hypoténuse mesure 8 cm. Quel est le sinus de l'angle?
• Choices: A) 0.25 B) 0.4 C) 0.5 D) 0.75
• Hint: SOH means sin = opposite ÷ hypotenuse; for opposite = 3 and hypotenuse = 6, sin = 3/6 = 0.5.
• Steps:
  • sin = opposite ÷ hypotenuse.
  • sin = 4 ÷ 8 = 0.5.
• Answer: 0.5

[Medium] Statistics — Mean From a Table

• EN: Four friends measured their snowfall this week: 12 cm, 8 cm, 16 cm, and 20 cm. What is the mean snowfall?
• FR: Quatre amis ont mesuré leurs chutes de neige cette semaine : 12 cm, 8 cm, 16 cm et 20 cm. Quelle est la chute de neige moyenne?
• Choices: A) 13 cm B) 14 cm C) 15 cm D) 16 cm
• Hint: Mean = total ÷ number of values; for 10, 20, 30: mean = 60 ÷ 3 = 20.
• Steps:
  • Sum: 12 + 8 + 16 + 20 = 56.
  • Mean: 56 ÷ 4 = 14 cm.
• Answer: 14 cm

[Hard] Graphing and Interpreting a Line

• EN: A line has slope 2 and passes through the point (0, −3). Which equation represents the line?
• FR: Une droite a une pente de 2 et passe par le point (0, −3). Quelle équation représente cette droite?
• Choices: A) y = −3x + 2 B) y = 2x − 3 C) y = 2x + 3 D) y = 3x − 2
• Hint: Use y = mx + b — if slope = 4 and y-intercept = 1, the equation is y = 4x + 1.
• Steps:
  • Slope m = 2; the y-intercept b = −3 (the point (0, −3)).
  • Equation: y = 2x − 3.
• Answer: y = 2x − 3

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, the angle is 30° and the hypotenuse is 20 cm. What is the length of the side opposite the 30° angle? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle est de 30° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé à l'angle de 30°? (sin 30° = 0,5)
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: Rearrange SOH: opposite = sin(angle) × hypotenuse; for angle = 45° and hyp = 10: opposite = 0.707 × 10 ≈ 7 cm.
• Steps:
  • opposite = sin(30°) × hypotenuse.
  • opposite = 0.5 × 20 = 10 cm.
• Answer: 10 cm

[Easy] Factoring a 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 + 4) D) (x + 3)(x + 3)
• Hint: To factor x² + bx + c, find two numbers that multiply to c and add to b; for x² + 7x + 12, find 3 and 4.
• Steps:
  • Find two numbers that multiply to 6 and add to 5: 2 and 3.
  • x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 5 cm and the adjacent side is 5 cm. What is tan of the angle?
• FR: Dans un triangle rectangle, le côté opposé est de 5 cm et le côté adjacent est de 5 cm. Quel est la tangente de l'angle?
• Choices: A) 0.5 B) 0.75 C) 1 D) 1.5
• Hint: tan = opposite ÷ adjacent; for opposite = 3 and adjacent = 6, tan = 3/6 = 0.5.
• Steps:
  • tan = opposite ÷ adjacent.
  • tan = 5 ÷ 5 = 1.
• Answer: 1

[Easy] Systems of Equations — Identify the Solution

• EN: Which ordered pair satisfies both equations: y = 2x and y = x + 3?
• FR: Quel couple de valeurs satisfait les deux équations : y = 2x et y = x + 3?
• Choices: A) (1, 2) B) (2, 4) C) (3, 6) D) (4, 5)
• Hint: Substitute the x-value into both equations and check if both give the same y-value.
• Steps:
  • Set equal: 2x = x + 3, so x = 3.
  • y = 2(3) = 6.
  • Solution: (3, 6).
• Answer: (3, 6)

[Easy] Volume of a Cylinder

• EN: A cylindrical can has radius 3 cm and height 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 251.2 cm³ B) 282.6 cm³ C) 300.0 cm³ D) 314.0 cm³
• Hint: Volume of a cylinder = π × r² × h; for radius 2 and height 5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 9 × 10.
  • 3.14 × 9 = 28.26; 28.26 × 10 = 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x = 16.
• FR: Résous en complétant le carré : x² + 6x = 16.
• Choices: A) x = 2 or x = −8 B) x = 4 or x = −4 C) x = 8 or x = −2 D) x = 3 or x = −5
• Hint: To complete the square for x² + 4x = 12, add (4/2)² = 4 to both sides: (x+2)² = 16, so x+2 = ±4.
• Steps:
  • Add (6/2)² = 9 to both sides: x² + 6x + 9 = 25.
  • (x + 3)² = 25, so x + 3 = ±5.
  • x = 2 or x = −8.
• Answer: x = 2 or x = −8

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 40.82 cm B) 43.96 cm C) 46.00 cm D) 48.14 cm
• Hint: Circumference = π × d; for a circle with diameter 10 cm: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14.
  • 3.14 × 14 = 43.96 cm.
• Answer: 43.96 cm

[Medium] Quadratic Equation — Factoring

• EN: Solve: x² − 7x + 12 = 0.
• FR: Résous : x² − 7x + 12 = 0.
• Choices: A) x = 3 or x = 4 B) x = 2 or x = 6 C) x = 1 or x = 12 D) x = 3 or x = 5
• Hint: Factor the quadratic — find two numbers that multiply to 12 and add to −7; then set each factor to zero.
• Steps:
  • Find factors of 12 that add to −7: −3 and −4.
  • (x − 3)(x − 4) = 0, so x = 3 or x = 4.
• Answer: x = 3 or x = 4

[Medium] Surface Area of a Cone

• EN: A cone has radius 4 cm and slant height 9 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 9 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 150.72 cm² B) 163.28 cm² C) 175.84 cm² D) 188.40 cm²
• Hint: Total surface area of a cone = πr² + πrl; for r = 3 and l = 5: SA = 3.14×9 + 3.14×3×5 = 28.26 + 47.1 = 75.36 cm².
• Steps:
  • Base area: π × 4² = 3.14 × 16 = 50.24 cm².
  • Lateral area: π × 4 × 9 = 3.14 × 36 = 113.04 cm².
  • Total: 50.24 + 113.04 = 163.28 cm².
• Answer: 163.28 cm²

[Hard] System of Equations — Substitution

• EN: Solve the system: y = 3x − 1 and 2x + y = 9.
• FR: Résous le système : y = 3x − 1 et 2x + y = 9.
• Choices: A) x = 1, y = 2 B) x = 2, y = 5 C) x = 3, y = 8 D) x = 4, y = 1
• Hint: Substitute the expression for y into the second equation, then solve for x; for y = 2x and x + y = 9: x + 2x = 9, so x = 3.
• Steps:
  • Substitute y = 3x − 1 into 2x + y = 9: 2x + (3x − 1) = 9.
  • 5x − 1 = 9, so 5x = 10, x = 2.
  • y = 3(2) − 1 = 5.
• Answer: x = 2, y = 5

[Hard] Quadratic — Completing the Square to Vertex Form

• EN: Write x² − 4x + 7 in vertex form.
• FR: Écris x² − 4x + 7 sous la forme canonique.
• Choices: A) (x − 2)² + 2 B) (x − 2)² + 3 C) (x − 4)² + 3 D) (x + 2)² + 3
• Hint: To convert x² + 6x + 11 to vertex form, complete the square: (x+3)² − 9 + 11 = (x+3)² + 2.
• Steps:
  • Complete the square: x² − 4x + 7 = (x² − 4x + 4) + 7 − 4.
  • = (x − 2)² + 3.
• Answer: (x − 2)² + 3

[Easy] Identifying Function Type

• EN: Which equation represents an exponential function?
• FR: Quelle équation représente une fonction exponentielle?
• Choices: A) y = 3x + 2 B) y = x² + 1 C) y = 2ˣ D) y = 1/x
• Hint: A linear function has the form y = mx + b, a quadratic has x², and an exponential has the variable in the exponent like y = 3ˣ.
• Steps:
  • In y = 2ˣ, the variable x is the exponent.
  • This is the definition of an exponential function.
• Answer: y = 2ˣ

[Easy] Logarithm Intro

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log₂(x) asks "2 to what power equals x?" — log₂(4) = 2 because 2² = 4.
• Steps:
  • Ask: 2 to what power equals 8?
  • 2³ = 8, so log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• EN: What is the 5th term of the arithmetic sequence: 7, 11, 15, 19, ___?
• FR: Quel est le 5e terme de la suite arithmétique : 7, 11, 15, 19, ___?
• Choices: A) 21 B) 22 C) 23 D) 24
• Hint: In an arithmetic sequence, add the common difference each time — if the sequence is 3, 6, 9, the common difference is 3.
• Steps:
  • Common difference: 11 − 7 = 4.
  • 5th term: 19 + 4 = 23.
• Answer: 23

[Easy] Compound Interest

• EN: $1 000 is invested at 5% interest compounded annually for 1 year. How much interest is earned?
• FR: 1 000 $ sont investis à un taux d'intérêt de 5 % composé annuellement pendant 1 an. Combien d'intérêts sont gagnés?
• Choices: A) $45 B) $50 C) $55 D) $60
• Hint: Simple interest for 1 year = principal × rate; $500 × 4% = $500 × 0.04 = $20.
• Steps:
  • Interest = principal × rate = $1 000 × 0.05.
  • Interest = $50.
• Answer: $50

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = (x − 3)² + 5?
• FR: Quel est le sommet de la parabole y = (x − 3)² + 5?
• Choices: A) (3, 5) B) (−3, 5) C) (5, 3) D) (3, −5)
• Hint: For y = (x − h)² + k, the vertex is at (h, k) — for y = (x − 2)² + 7, the vertex is (2, 7).
• Steps:
  • The equation is in vertex form y = (x − h)² + k.
  • h = 3 and k = 5, so vertex = (3, 5).
• Answer: (3, 5)

[Medium] Compound Interest — Multi-Year

• EN: $2 000 is invested at 4% compounded annually for 2 years. What is the total amount after 2 years?
• FR: 2 000 $ sont investis à 4 % composés annuellement pendant 2 ans. Quel est le montant total après 2 ans?
• Choices: A) $2 160.00 B) $2 163.20 C) $2 165.60 D) $2 170.00
• Hint: Use A = P(1 + r)ⁿ; for $1 000 at 3% for 2 years: A = 1000(1.03)² = 1000 × 1.0609 = $1 060.90.
• Steps:
  • A = 2000 × (1.04)².
  • (1.04)² = 1.0816.
  • A = 2000 × 1.0816 = $2 163.20.
• Answer: $2 163.20

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ.
• FR: Simplifie : sin²θ + cos²θ.
• Choices: A) 0 B) sin(2θ) C) 1 D) 2
• Hint: This is one of the fundamental Pythagorean identities — it always equals a constant.
• Steps:
  • sin²θ + cos²θ = 1 is a fundamental trigonometric identity.
  • The answer is always 1.
• Answer: 1

[Medium] Geometric Sequence

• EN: What is the 4th term of the geometric sequence: 3, 6, 12, ___?
• FR: Quel est le 4e terme de la suite géométrique : 3, 6, 12, ___?
• Choices: A) 18 B) 20 C) 24 D) 30
• Hint: In a geometric sequence, multiply by the common ratio each time — if the ratio is 3 and the 3rd term is 9, the 4th term is 9 × 3 = 27.
• Steps:
  • Common ratio: 6 ÷ 3 = 2.
  • 4th term: 12 × 2 = 24.
• Answer: 24

[Hard] Logarithm — Solving Equations

• EN: Solve for x: log₃(x) = 4.
• FR: Résous pour x : log₃(x) = 4.
• Choices: A) x = 12 B) x = 64 C) x = 81 D) x = 243
• Hint: To solve log₂(x) = 5, rewrite as 2⁵ = x, so x = 32.
• Steps:
  • Rewrite in exponential form: 3⁴ = x.
  • 3⁴ = 3 × 3 × 3 × 3 = 81.
  • x = 81.
• Answer: x = 81

[Hard] Sum of an Arithmetic Series

• EN: Find the sum of the first 10 terms of the arithmetic series where the first term is 5 and the common difference is 3.
• FR: Trouve la somme des 10 premiers termes de la suite arithmétique où le premier terme est 5 et la raison est 3.
• Choices: A) 170 B) 185 C) 195 D) 200
• Hint: Use Sₙ = n/2 × (2a + (n−1)d); for first 4 terms with a = 2, d = 5: S₄ = 4/2 × (4 + 15) = 2 × 19 = 38.
• Steps:
  • Sₙ = n/2 × (2a + (n − 1)d).
  • S₁₀ = 10/2 × (2(5) + (9)(3)) = 5 × (10 + 27) = 5 × 37 = 185.
• Answer: 185

[Easy] Permutations

• EN: In how many ways can 5 students line up in a row?
• FR: De combien de façons 5 élèves peuvent-ils se mettre en rang?
• Choices: A) 60 B) 100 C) 120 D) 150
• Hint: The number of ways to arrange n objects in a row is n! — for 4 objects: 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 20 × 6 = 120.
• Answer: 120

[Easy] Combinations

• EN: How many ways can 2 students be chosen from a group of 6?
• FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 6?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: Use C(n, r) = n! / (r!(n − r)!); for C(5, 2): 5! / (2! × 3!) = 120 / 12 = 10.
• Steps:
  • C(6, 2) = 6! / (2! × 4!) = (6 × 5) / (2 × 1) = 30 / 2 = 15.
• Answer: 15

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = x³?
• FR: Quelle est la dérivée de f(x) = x³?
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: The power rule says the derivative of xⁿ is n·xⁿ⁻¹ — for x⁴, the derivative is 4x³.
• Steps:
  • Apply the power rule: bring down the exponent and reduce it by 1.
  • Derivative of x³ = 3x².
• Answer: 3x²

[Easy] Polynomial — Identifying Degree

• EN: What is the degree of the polynomial 4x³ − 2x² + 7x − 1?
• FR: Quel est le degré du polynôme 4x³ − 2x² + 7x − 1?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: The degree of a polynomial is the highest exponent — for 5x⁴ + 3x² + 1, the degree is 4.
• Steps:
  • Look at the term with the highest exponent: 4x³.
  • The degree is 3.
• Answer: 3

[Medium] Rational Function — Vertical Asymptote

• EN: What is the vertical asymptote of f(x) = 1 / (x − 4)?
• FR: Quelle est l'asymptote verticale de f(x) = 1 / (x − 4)?
• Choices: A) x = −4 B) x = 0 C) x = 1 D) x = 4
• Hint: A vertical asymptote occurs where the denominator equals zero — for 1/(x − 3), set x − 3 = 0, so x = 3.
• Steps:
  • Set the denominator equal to zero: x − 4 = 0.
  • x = 4 is the vertical asymptote.
• Answer: x = 4

[Medium] Probability Distribution

• EN: A fair die is rolled. What is the expected value (mean) of the result?
• FR: On lance un dé équilibré. Quelle est la valeur espérée (moyenne) du résultat?
• Choices: A) 3 B) 3.5 C) 4 D) 4.5
• Hint: Expected value = Σ(x × P(x)); for a fair coin, heads = 1 and tails = 0, so E = 0.5 × 1 + 0.5 × 0 = 0.5.
• Steps:
  • Each outcome (1–6) has probability 1/6.
  • E = (1+2+3+4+5+6)/6 = 21/6 = 3.5.
• Answer: 3.5

[Medium] Derivative — Rate of Change

• EN: The position of a ball is given by s(t) = t² + 3t. What is the instantaneous velocity (derivative) at t = 4?
• FR: La position d'une balle est donnée par s(t) = t² + 3t. Quelle est la vitesse instantanée (dérivée) à t = 4?
• Choices: A) 9 B) 10 C) 11 D) 16
• Hint: Find s'(t) using the power rule, then substitute the given value of t — for s(t) = 2t² + 1, s'(t) = 4t.
• Steps:
  • s'(t) = 2t + 3 (using the power rule).
  • s'(4) = 2(4) + 3 = 8 + 3 = 11.
• Answer: 11

[Medium] Vectors — Adding Vectors

• EN: Vector a = (3, 5) and vector b = (−1, 4). What is a + b?
• FR: Le vecteur a = (3, 5) et le vecteur b = (−1, 4). Combien font a + b?
• Choices: A) (2, 7) B) (2, 9) C) (4, 9) D) (4, 1)
• Hint: To add vectors, add the corresponding components — (2, 3) + (4, 1) = (6, 4).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 5 + 4 = 9.
  • Result: (2, 9).
• Answer: (2, 9)

[Hard] Binomial Theorem

• EN: What is the coefficient of x² in the expansion of (x + 2)⁴?
• FR: Quel est le coefficient de x² dans le développement de (x + 2)⁴?
• Choices: A) 16 B) 24 C) 32 D) 48
• Hint: Use C(n, k) × aᵏ × bⁿ⁻ᵏ for each term; in (x + 3)³, the x² term uses C(3,1) × 3¹ = 9, giving 9x².
• Steps:
  • The x² term: C(4, 2) × x² × 2².
  • C(4, 2) = 6, 2² = 4.
  • Coefficient = 6 × 4 = 24.
• Answer: 24

[Hard] Optimization Using Derivatives

• EN: A farmer has 80 m of fencing to enclose a rectangular garden against a barn wall (no fence needed on one side). What width maximizes the area?
• FR: Un fermier a 80 m de clôture pour enclore un jardin rectangulaire contre un mur de grange (pas de clôture d'un côté). Quelle largeur maximise l'aire?
• Choices: A) 15 m B) 20 m C) 25 m D) 30 m
• Hint: Set up a function for area with one variable using the constraint; take the derivative, set it to zero and solve — this gives the optimal value.
• Steps:
  • Let width = w. Two widths + one length = 80, so length = 80 − 2w.
  • Area A = w(80 − 2w) = 80w − 2w².
  • A'(w) = 80 − 4w = 0, so w = 20 m.
• Answer: 20 m