Daily Math — 2026-07-31

[Easy] Counting Hockey Pucks

• EN: There are 7 hockey pucks on the ice. The coach adds 5 more. How many pucks are there now?
• FR: Il y a 7 rondelles de hockey sur la glace. L'entraîneur en ajoute 5 de plus. Combien y a-t-il de rondelles maintenant?
• Choices: A) 10 pucks B) 11 pucks C) 12 pucks D) 13 pucks
• Hint: To add 6 + 4, count up from 6: 7, 8, 9, 10 — that is 10.
• Steps:
  • Start at 7 and count up 5 more: 8, 9, 10, 11, 12.
  • So there are 12 pucks in total.
• Answer: 12 pucks

[Easy] Mittens in the Cubby

• EN: Mia has 9 mittens in her cubby. She takes 4 mittens home. How many mittens are left?
• FR: Mia a 9 mitaines dans son casier. Elle en rapporte 4 à la maison. Combien de mitaines reste-t-il?
• Choices: A) 3 mittens B) 4 mittens C) 5 mittens D) 6 mittens
• Hint: To find 8 − 3, start at 8 and count back 3: 7, 6, 5 — that is 5.
• Steps:
  • Start at 9 and count back 4: 8, 7, 6, 5.
  • So 5 mittens are left.
• Answer: 5 mittens

[Easy] Skip Counting by 2s

• EN: Skip count by 2s: 2, 4, 6, 8, ___. What number comes next?
• FR: Compte par bonds de 2: 2, 4, 6, 8, ___. Quel est le prochain nombre?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When you skip count by 2s starting at 4, the next number is 4 + 2 = 6.
• Steps:
  • Each time, add 2 to the last number.
  • 8 + 2 = 10, so 10 comes next.
• Answer: 10

[Easy] Counting Coins

• EN: You have 2 nickels. How many cents do you have in all?
• FR: Tu as 2 pièces de 5 cents. Combien de cents as-tu en tout?
• Choices: A) 5 cents B) 8 cents C) 10 cents D) 15 cents
• Hint: One nickel is worth 5 cents; if you have 3 nickels, count 5, 10, 15 — that is 15 cents.
• Steps:
  • Each nickel is worth 5 cents.
  • Count by 5s for 2 nickels: 5, 10.
  • So you have 10 cents.
• Answer: 10 cents

[Medium] Snowflakes on the Window

• EN: There are 13 snowflakes on the left window and 6 snowflakes on the right window. How many snowflakes are there altogether?
• FR: Il y a 13 flocons de neige sur la fenêtre gauche et 6 sur la fenêtre droite. 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 14 + 5, think 14 + 5 = 19.
• Steps:
  • Start at 13 and count up 6 more: 14, 15, 16, 17, 18, 19.
  • So there are 19 snowflakes altogether.
• Answer: 19 snowflakes

[Medium] Comparing Numbers

• EN: Which number is greater: 14 or 17?
• FR: Quel nombre est plus grand: 14 ou 17?
• Choices: A) 14 B) 15 C) 16 D) 17
• Hint: When comparing 11 and 19, look at which is farther along when counting — 19 is greater.
• Steps:
  • Count along the number line: 14 comes before 17.
  • 17 is farther from 0, so 17 is greater.
• Answer: 17

[Medium] Skip Counting by 10s

• EN: Skip count by 10s: 10, 20, 30, ___. What number comes next?
• FR: Compte par bonds de 10: 10, 20, 30, ___. Quel est le prochain nombre?
• Choices: A) 35 B) 38 C) 40 D) 50
• Hint: When skip counting by 10s from 50, the next number is 50 + 10 = 60.
• Steps:
  • Each step adds 10 to the last number.
  • 30 + 10 = 40, so 40 comes next.
• Answer: 40

[Medium] Apples in Two Baskets

• EN: One basket has 8 apples. Another basket has 8 apples. How many apples are there in total?
• FR: Un panier a 8 pommes. Un autre panier a 8 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 14 apples B) 15 apples C) 16 apples D) 18 apples
• Hint: To add 7 + 7, think of it as a doubles fact: 7 + 7 = 14.
• Steps:
  • This is a doubles fact: 8 + 8.
  • 8 + 8 = 16, so there are 16 apples in total.
• Answer: 16 apples

[Hard] Pennies and Nickels

• EN: You have 3 pennies and 1 nickel. How many cents do you have in all?
• FR: Tu as 3 sous et 1 pièce de 5 cents. Combien de cents as-tu en tout?
• Choices: A) 6 cents B) 7 cents C) 8 cents D) 9 cents
• Hint: If you have 2 pennies and 1 nickel, count: 5 cents + 1 cent + 1 cent = 7 cents.
• Steps:
  • A nickel is worth 5 cents; each penny is worth 1 cent.
  • 5 + 1 + 1 + 1 = 8 cents.
  • So you have 8 cents in all.
• Answer: 8 cents

[Hard] Missing Number

• EN: What number is missing? 6 + ___ = 14
• FR: Quel nombre manque? 6 + ___ = 14
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: For 5 + ___ = 11, think about what you add to 5 to reach 11: count up from 5 to 11, which is 6.
• Steps:
  • Start at 6 and count up to 14: 7, 8, 9, 10, 11, 12, 13, 14.
  • That is 8 steps, so the missing number is 8.
• Answer: 8

[Easy] Adding at Tim Hortons

• EN: A muffin costs 25 cents and a juice costs 50 cents. How much do they cost together?
• FR: Un muffin coûte 25 cents et un jus coûte 50 cents. Combien coûtent-ils ensemble?
• Choices: A) 65 cents B) 70 cents C) 75 cents D) 80 cents
• Hint: To add 30 + 40, think 30 + 40 = 70.
• Steps:
  • Add the two amounts: 25 + 50.
  • 25 + 50 = 75 cents.
• Answer: 75 cents

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre la grande aiguille sur le 12 et la petite aiguille sur le 3. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 4:00 D) 12:00
• Hint: When the minute hand points to 12 and the hour hand points to 5, the time is 5:00.
• Steps:
  • The minute hand on 12 means exactly on the hour.
  • The hour hand on 3 means it is 3 o'clock.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring a Pencil

• EN: A pencil is 15 cm long. A crayon is 8 cm long. How much longer is the pencil?
• FR: Un crayon à mine mesure 15 cm de long. Un crayon de cire mesure 8 cm de long. De combien le crayon à mine est-il plus long?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: To find how much longer 18 cm is than 11 cm, subtract: 18 − 11 = 7.
• Steps:
  • Subtract the shorter length from the longer: 15 − 8.
  • 15 − 8 = 7 cm.
• Answer: 7 cm

[Easy] Simple Pattern

• EN: Look at this pattern: 5, 10, 15, 20, ___. What number comes next?
• FR: Regarde ce motif: 5, 10, 15, 20, ___. Quel nombre vient ensuite?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: In the pattern 3, 6, 9, 12, each number increases by 3, so the next would be 15.
• Steps:
  • Each number increases by 5.
  • 20 + 5 = 25.
• Answer: 25

[Medium] Subtraction Within 100

• EN: A class has 62 crayons. Students use 28 crayons during art. How many crayons are left?
• FR: Une classe a 62 crayons. Les élèves utilisent 28 crayons pendant le cours d'art. Combien de crayons reste-t-il?
• Choices: A) 30 crayons B) 33 crayons C) 34 crayons D) 36 crayons
• Hint: To solve 50 − 17, think 50 − 10 = 40, then 40 − 7 = 33.
• Steps:
  • Subtract 28 from 62.
  • 62 − 20 = 42, then 42 − 8 = 34.
  • So 34 crayons are left.
• Answer: 34 crayons

[Medium] Counting Coins to $1

• EN: You have 3 quarters. How many cents do you have in all?
• FR: Tu as 3 pièces de 25 cents. Combien de cents as-tu en tout?
• Choices: A) 50 cents B) 60 cents C) 75 cents D) 100 cents
• Hint: If you have 2 quarters, count by 25s: 25, 50 — that is 50 cents.
• Steps:
  • Each quarter is worth 25 cents.
  • Count by 25s: 25, 50, 75.
  • So you have 75 cents.
• Answer: 75 cents

[Medium] Telling Time — Half Hour

• EN: The clock shows the hour hand between 7 and 8, and the minute hand on 6. What time is it?
• FR: L'horloge montre la petite aiguille entre 7 et 8, et la grande aiguille sur le 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:00
• Hint: When the minute hand is on 6 and the hour hand is between 4 and 5, the time is 4:30.
• Steps:
  • The minute hand on 6 means 30 minutes past the hour.
  • The hour hand is between 7 and 8, so the hour is 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Measuring in Metres

• EN: A classroom is 9 m long. A hallway is 5 m long. How long are they together?
• FR: Une salle de classe mesure 9 m de long. Un couloir mesure 5 m de long. Quelle est leur longueur ensemble?
• Choices: A) 12 m B) 13 m C) 14 m D) 15 m
• Hint: To add 7 m + 6 m, just add the numbers: 7 + 6 = 13 m.
• Steps:
  • Add the two lengths: 9 + 5.
  • 9 + 5 = 14 m.
• Answer: 14 m

[Hard] Adding Two-Digit Numbers

• EN: There are 47 students in the gym and 36 students in the library. How many students are there in all?
• FR: Il y a 47 élèves dans le gymnase et 36 élèves dans la bibliothèque. Combien y a-t-il d'élèves en tout?
• Choices: A) 73 students B) 82 students C) 83 students D) 93 students
• Hint: To add 35 + 48, add the tens first: 30 + 40 = 70, then add the ones: 5 + 8 = 13, so 70 + 13 = 83.
• Steps:
  • Add tens: 40 + 30 = 70.
  • Add ones: 7 + 6 = 13.
  • Add together: 70 + 13 = 83 students.
• Answer: 83 students

[Hard] Word Problem with Coins

• EN: Luc has 2 quarters and 3 dimes. How many cents does he have in all?
• FR: Luc a 2 pièces de 25 cents et 3 pièces de 10 cents. Combien de cents a-t-il en tout?
• Choices: A) 70 cents B) 75 cents C) 80 cents D) 85 cents
• Hint: If you have 1 quarter and 2 dimes, count: 25 + 10 + 10 = 45 cents.
• Steps:
  • 2 quarters = 25 + 25 = 50 cents.
  • 3 dimes = 10 + 10 + 10 = 30 cents.
  • 50 + 30 = 80 cents in all.
• Answer: 80 cents

[Easy] Multiplication by 5

• EN: There are 4 bags of hockey cards. Each bag has 5 cards. How many cards are there in all?
• FR: Il y a 4 sacs de cartes de hockey. Chaque sac contient 5 cartes. Combien y a-t-il de cartes en tout?
• Choices: A) 15 cards B) 18 cards C) 20 cards D) 25 cards
• Hint: For 3 bags with 5 cards each, use 3 × 5 = 15 cards.
• Steps:
  • Multiply the number of bags by the number of cards each: 4 × 5.
  • 4 × 5 = 20 cards.
• Answer: 20 cards

[Easy] Multiplication by 2

• EN: Each player has 2 skates. There are 6 players. How many skates are there in all?
• FR: Chaque joueur a 2 patins. Il y a 6 joueurs. Combien y a-t-il de patins en tout?
• Choices: A) 8 skates B) 10 skates C) 12 skates D) 14 skates
• Hint: For 5 players with 2 skates each, use 5 × 2 = 10 skates.
• Steps:
  • Multiply: 6 × 2.
  • 6 × 2 = 12 skates.
• Answer: 12 skates

[Easy] Basic Division

• EN: There are 15 cookies shared equally among 3 friends. How many cookies does each friend get?
• FR: Il y a 15 biscuits partagés également entre 3 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 3 cookies B) 4 cookies C) 5 cookies D) 6 cookies
• Hint: For 12 cookies shared among 4 friends, think 4 × ? = 12, so 4 × 3 = 12, each gets 3.
• Steps:
  • Divide 15 by 3: 15 ÷ 3.
  • 3 × 5 = 15, so each friend gets 5 cookies.
• Answer: 5 cookies

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. You eat 1 piece. What fraction of the pizza did you eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Tu manges 1 morceau. Quelle fraction de la pizza as-tu mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: If a chocolate bar is cut into 2 equal parts and you eat 1, you ate 1 out of 2, which is 1/2.
• Steps:
  • You ate 1 piece out of 2 total equal pieces.
  • That is 1/2 of the pizza.
• Answer: 1/2

[Medium] Perimeter of a Rectangle

• EN: A playground is 8 m long and 5 m wide. What is the perimeter of the playground?
• FR: Un terrain de jeu mesure 8 m de long et 5 m de large. Quel est le périmètre du terrain de jeu?
• Choices: A) 13 m B) 24 m C) 26 m D) 40 m
• Hint: For a rectangle 6 m long and 4 m wide, the perimeter is 6 + 6 + 4 + 4 = 20 m.
• Steps:
  • A rectangle has 2 long sides and 2 short sides.
  • Perimeter = 8 + 8 + 5 + 5 = 26 m.
• Answer: 26 m

[Medium] Multiplication by 10

• EN: A store has 7 boxes of granola bars. Each box has 10 bars. How many bars are there in all?
• FR: Un magasin a 7 boîtes de barres granola. Chaque boîte contient 10 barres. Combien y a-t-il de barres en tout?
• Choices: A) 17 bars B) 60 bars C) 70 bars D) 77 bars
• Hint: For 4 boxes with 10 bars each, use 4 × 10 = 40 bars.
• Steps:
  • Multiply: 7 × 10.
  • 7 × 10 = 70 bars.
• Answer: 70 bars

[Medium] Reading a Graph

• EN: A bar graph shows that the class collected 12 cans on Monday, 8 on Tuesday, and 5 on Wednesday. How many cans were collected in all?
• FR: Un graphique à barres montre que la classe a collecté 12 boîtes lundi, 8 mardi et 5 mercredi. Combien de boîtes ont été collectées en tout?
• Choices: A) 20 cans B) 23 cans C) 25 cans D) 28 cans
• Hint: To add three amounts like 10, 7, and 4, first add 10 + 7 = 17, then 17 + 4 = 21.
• Steps:
  • Add all three days: 12 + 8 + 5.
  • 12 + 8 = 20, then 20 + 5 = 25 cans.
• Answer: 25 cans

[Medium] Fractions — One Quarter

• EN: A ribbon is cut into 4 equal pieces. Sophie takes 1 piece. What fraction of the ribbon does Sophie have?
• FR: Un ruban est coupé en 4 morceaux égaux. Sophie prend 1 morceau. Quelle fraction du ruban Sophie a-t-elle?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 3/4
• Hint: If a piece of paper is cut into 4 equal parts and you take 1, you have 1 out of 4, which is 1/4.
• Steps:
  • Sophie has 1 piece out of 4 equal pieces.
  • That is 1/4 of the ribbon.
• Answer: 1/4

[Hard] Multiplication and Addition

• EN: There are 5 rows of seats in a bus. Each row has 4 seats. The driver adds 3 extra seats at the back. How many seats are there in all?
• FR: Il y a 5 rangées de sièges dans un autobus. Chaque rangée a 4 sièges. Le chauffeur ajoute 3 sièges supplémentaires à l'arrière. Combien y a-t-il de sièges en tout?
• Choices: A) 20 seats B) 22 seats C) 23 seats D) 27 seats
• Hint: For 3 rows of 4 seats plus 2 extra, first find 3 × 4 = 12, then 12 + 2 = 14 seats.
• Steps:
  • First multiply: 5 × 4 = 20 seats in rows.
  • Then add extra seats: 20 + 3 = 23 seats.
• Answer: 23 seats

[Hard] Division with Fractions Context

• EN: There are 24 strawberries shared equally among 4 children. Each child gives half of their share to a friend. How many strawberries does each child end up giving away?
• FR: Il y a 24 fraises partagées également entre 4 enfants. Chaque enfant donne la moitié de sa part à un ami. Combien de fraises chaque enfant donne-t-il?
• Choices: A) 3 strawberries B) 4 strawberries C) 6 strawberries D) 8 strawberries
• Hint: If 16 grapes are shared among 4 children, each gets 16 ÷ 4 = 4; half of 4 is 2.
• Steps:
  • First divide: 24 ÷ 4 = 6 strawberries per child.
  • Half of 6 is 3, so each child gives away 3 strawberries.
• Answer: 3 strawberries

[Easy] Multiplication Facts to 9×9

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To find 6 × 8, think: 6 × 8 = 48.
• Steps:
  • Recall the multiplication fact: 7 × 8.
  • 7 × 8 = 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 tenths C) 3 hundredths D) 30 ones
• Hint: In 5.72, the digit 7 is in the tenths place, so its value is 7 tenths.
• Steps:
  • In 4.37, the digits after the decimal are in the tenths and hundredths places.
  • The digit 3 is the first digit after the decimal, so it is in the tenths place.
  • Its value is 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A rectangular garden is 9 m long and 4 m wide. What is the area of the garden?
• FR: Un jardin rectangulaire mesure 9 m de long et 4 m de large. Quelle est l'aire du jardin?
• Choices: A) 26 m² B) 32 m² C) 36 m² D) 40 m²
• Hint: The area of a rectangle with length 7 m and width 3 m is 7 × 3 = 21 m².
• Steps:
  • Area = length × width.
  • Area = 9 × 4 = 36 m².
• Answer: 36 m²

[Easy] Comparing Fractions

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

[Medium] Long Division with Remainder

• EN: Divide 57 by 5. What is the quotient and remainder?
• FR: Divise 57 par 5. Quel est le quotient et le reste?
• Choices: A) 10 remainder 7 B) 11 remainder 2 C) 12 remainder 3 D) 13 remainder 2
• Hint: To divide 38 by 4: 4 × 9 = 36, so the quotient is 9 and the remainder is 38 − 36 = 2.
• Steps:
  • Find how many times 5 goes into 57: 5 × 11 = 55.
  • Remainder = 57 − 55 = 2.
  • So the answer is 11 remainder 2.
• Answer: 11 remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 6:15 p.m. and ends at 8:45 p.m. How long is the game?
• FR: Un match de hockey commence à 18 h 15 et se termine à 20 h 45. Quelle est la durée du match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours 15 minutes
• Hint: From 3:10 to 5:40, count: from 3:10 to 5:10 is 2 hours, then 5:10 to 5:40 is 30 more minutes, so 2 hours 30 minutes.
• Steps:
  • From 6:15 to 8:15 is exactly 2 hours.
  • From 8:15 to 8:45 is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A piece of fabric is 3.6 m long. Another piece is 1.8 m long. How long are they together?
• FR: Un morceau de tissu mesure 3,6 m de long. Un autre morceau mesure 1,8 m de long. Quelle est leur longueur ensemble?
• Choices: A) 4.4 m B) 5.2 m C) 5.4 m D) 6.4 m
• Hint: To add 2.4 + 1.9, line up the decimals: 2.4 + 1.9 = 4.3.
• Steps:
  • Add the two lengths: 3.6 + 1.8.
  • 3.6 + 1.8 = 5.4 m.
• Answer: 5.4 m

[Medium] All Multiplication Tables

• EN: A school orders 9 boxes of markers. Each box has 8 markers. How many markers are there in total?
• FR: Une école commande 9 boîtes de marqueurs. Chaque boîte contient 8 marqueurs. Combien y a-t-il de marqueurs en tout?
• Choices: A) 63 markers B) 70 markers C) 72 markers D) 81 markers
• Hint: For 6 boxes with 8 markers each, use 6 × 8 = 48 markers.
• Steps:
  • Multiply: 9 × 8.
  • 9 × 8 = 72 markers.
• Answer: 72 markers

[Hard] Multi-Step Word Problem

• EN: Camille buys 4 notebooks at $3.25 each and 2 pens at $1.50 each. How much does she spend in total?
• FR: Camille achète 4 cahiers à 3,25 $ chacun et 2 crayons à 1,50 $ chacun. Combien dépense-t-elle en tout?
• Choices: A) $14.00 B) $15.00 C) $16.00 D) $17.50
• Hint: If you buy 3 items at $2.00 each and 2 items at $1.00 each, first find 3 × $2.00 = $6.00, then 2 × $1.00 = $2.00, then add $6.00 + $2.00 = $8.00.
• Steps:
  • Cost of notebooks: 4 × $3.25 = $13.00.
  • Cost of pens: 2 × $1.50 = $3.00.
  • Total: $13.00 + $3.00 = $16.00.
• Answer: $16.00

[Hard] Long Division Applied

• EN: A farmer has 98 eggs to pack into cartons of 8 eggs each. How many full cartons can he make, and how many eggs are left over?
• FR: Un fermier a 98 œufs à emballer dans des cartons de 8 œufs chacun. Combien de cartons complets peut-il faire, et combien d'œufs reste-t-il?
• Choices: A) 11 cartons, 10 eggs left B) 12 cartons, 2 eggs left C) 13 cartons, 4 eggs left D) 14 cartons, 6 eggs left
• Hint: To find how many groups of 6 fit into 50, think: 6 × 8 = 48, so 8 full groups with 50 − 48 = 2 left over.
• Steps:
  • Divide: 8 × 12 = 96, which is less than 98.
  • Remainder: 98 − 96 = 2 eggs left over.
  • So 12 full cartons with 2 eggs left.
• Answer: 12 cartons, 2 eggs left

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 200 C) 204 D) 210
• Hint: For 23 × 4, multiply 20 × 4 = 80 and 3 × 4 = 12, then add: 80 + 12 = 92.
• Steps:
  • Multiply the tens: 30 × 6 = 180.
  • Multiply the ones: 4 × 6 = 24.
  • Add: 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: What is 3/8 + 2/8?
• FR: Combien font 3/8 + 2/8?
• Choices: A) 5/16 B) 5/8 C) 6/8 D) 1/2
• Hint: For 2/7 + 3/7, add only the numerators and keep the denominator: 2 + 3 = 5, so 5/7.
• Steps:
  • Keep the denominator the same: 8.
  • Add the numerators: 3 + 2 = 5.
  • The answer is 5/8.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: A bag of 20 apples is on sale at 50% off. How many apples is that discount equal to?
• FR: Un sac de 20 pommes est en vente à 50 % de rabais. À combien de pommes ce rabais est-il équivalent?
• Choices: A) 5 apples B) 8 apples C) 10 apples D) 15 apples
• Hint: 50% of 16 means half of 16, which is 16 ÷ 2 = 8.
• Steps:
  • 50% means one half.
  • 50% of 20 = 20 ÷ 2 = 10 apples.
• Answer: 10 apples

[Easy] Decimal Addition

• EN: It snowed 4.5 cm on Monday and 3.2 cm on Tuesday. How much snow fell in total?
• FR: Il a neigé 4,5 cm lundi et 3,2 cm mardi. Quelle est la quantité totale de neige tombée?
• Choices: A) 6.7 cm B) 7.3 cm C) 7.7 cm D) 8.5 cm
• Hint: To add 3.4 + 2.5, line up the decimals: 3.4 + 2.5 = 5.9.
• Steps:
  • Add the decimals: 4.5 + 3.2.
  • 4.5 + 3.2 = 7.7 cm.
• Answer: 7.7 cm

[Medium] Multi-Digit Division

• EN: A school orders 144 pencils. They are divided equally among 6 classrooms. How many pencils does each classroom get?
• FR: Une école commande 144 crayons. Ils sont répartis également entre 6 salles de classe. Combien de crayons chaque salle reçoit-elle?
• Choices: A) 20 pencils B) 22 pencils C) 24 pencils D) 26 pencils
• Hint: To divide 120 by 6, think 6 × 20 = 120, so 120 ÷ 6 = 20.
• Steps:
  • Divide: 144 ÷ 6.
  • 6 × 24 = 144, so each classroom gets 24 pencils.
• Answer: 24 pencils

[Medium] Subtracting Fractions

• EN: Emma has 7/10 of a metre of ribbon. She uses 3/10 of a metre. How much ribbon is left?
• FR: Emma a 7/10 d'un mètre de ruban. Elle en utilise 3/10 d'un mètre. Quelle longueur de ruban reste-t-il?
• Choices: A) 3/10 m B) 4/10 m C) 5/10 m D) 10/10 m
• Hint: For 6/9 − 2/9, subtract only the numerators and keep the denominator: 6 − 2 = 4, so 4/9.
• Steps:
  • Keep the denominator: 10.
  • Subtract numerators: 7 − 3 = 4.
  • The answer is 4/10 m.
• Answer: 4/10 m

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est le volume de la boîte?
• Choices: A) 48 cm³ B) 56 cm³ C) 60 cm³ D) 80 cm³
• Hint: The volume of a box 4 cm × 3 cm × 2 cm is 4 × 3 × 2 = 24 cm³.
• Steps:
  • Volume = length × width × height.
  • Volume = 5 × 4 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A sweater originally costs $40. It is on sale for 25% off. How much is the discount?
• FR: Un chandail coûte 40 $ à l'origine. Il est en vente à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $8 B) $10 C) $12 D) $15
• Hint: 25% of $60 means one quarter of $60, which is $60 ÷ 4 = $15.
• Steps:
  • 25% means one quarter.
  • 25% of $40 = $40 ÷ 4 = $10.
• Answer: $10

[Hard] Multi-Step with Decimals and Fractions

• EN: A pitcher holds 2.5 litres of juice. Noah pours out 3/5 of the juice. How many litres of juice are left in the pitcher?
• FR: Un pichet contient 2,5 litres de jus. Noah verse 3/5 du jus. Combien de litres de jus reste-t-il dans le pichet?
• Choices: A) 0.5 litres B) 1.0 litres C) 1.5 litres D) 2.0 litres
• Hint: If a container holds 3.0 L and you pour out 2/3 of it, first find 2/3 of 3.0 = 2.0 L poured, so 3.0 − 2.0 = 1.0 L remains.
• Steps:
  • Find 3/5 of 2.5: (3 ÷ 5) × 2.5 = 0.6 × 2.5 = 1.5 litres poured out.
  • Subtract from total: 2.5 − 1.5 = 1.0 litres left.
• Answer: 1.0 litres

[Hard] Percentage — 10% Application

• EN: A hockey team scores 10% of its goals in overtime. In a season they scored 80 goals. How many goals were scored in overtime?
• FR: Une équipe de hockey marque 10 % de ses buts en prolongation. Au cours d'une saison, ils ont marqué 80 buts. Combien de buts ont été marqués en prolongation?
• Choices: A) 6 goals B) 7 goals C) 8 goals D) 10 goals
• Hint: To find 10% of 50, divide by 10: 50 ÷ 10 = 5.
• Steps:
  • 10% means divide by 10.
  • 10% of 80 = 80 ÷ 10 = 8 goals.
• Answer: 8 goals

[Easy] Fraction Multiplication

• EN: What is 1/2 × 4/5?
• FR: Combien font 1/2 × 4/5?
• Choices: A) 2/5 B) 4/10 C) 5/10 D) 3/5
• Hint: To multiply 1/3 × 3/4, multiply numerators: 1 × 3 = 3, then denominators: 3 × 4 = 12, giving 3/12 = 1/4.
• Steps:
  • Multiply the numerators: 1 × 4 = 4.
  • Multiply the denominators: 2 × 5 = 10.
  • The answer is 4/10, which can also be written as 2/5.
• Answer: 4/10

[Easy] Percent of a Number

• EN: What is 20% of 60?
• FR: Combien font 20 % de 60?
• Choices: A) 10 B) 12 C) 15 D) 20
• Hint: To find 20% of 50, first find 10% of 50 = 5, then double it: 5 × 2 = 10.
• Steps:
  • Find 10% of 60: 60 ÷ 10 = 6.
  • 20% = 2 × 10%, so 2 × 6 = 12.
• Answer: 12

[Easy] Ratio

• EN: For every 3 red marbles there are 5 blue marbles. What is the ratio of red to blue marbles?
• FR: Pour chaque 3 billes rouges, il y a 5 billes bleues. Quel est le rapport entre les billes rouges et les billes bleues?
• Choices: A) 3:5 B) 5:3 C) 3:8 D) 5:8
• Hint: If there are 4 cats for every 7 dogs, the ratio of cats to dogs is 4:7.
• Steps:
  • A ratio compares two quantities in order.
  • Red to blue is 3 to 5, written as 3:5.
• Answer: 3:5

[Easy] Order of Operations — BEDMAS

• EN: Solve: 3 + 4 × 2
• FR: Résous: 3 + 4 × 2
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: In 5 + 3 × 2, do multiplication first: 3 × 2 = 6, then add: 5 + 6 = 11.
• Steps:
  • According to BEDMAS, do multiplication before addition.
  • 4 × 2 = 8, then 3 + 8 = 11.
• Answer: 11

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 1/2 C) 2/3 D) 5/4
• Hint: To divide 2/3 ÷ 1/4, multiply by the reciprocal: 2/3 × 4/1 = 8/3.
• Steps:
  • Dividing by a fraction means multiplying by its reciprocal.
  • 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2.
• Answer: 1 1/2

[Medium] Rate Problem

• EN: A car travels 120 km in 2 hours. What is its speed in kilometres per hour?
• FR: Une voiture parcourt 120 km en 2 heures. Quelle est sa vitesse en kilomètres par heure?
• Choices: A) 50 km/h B) 55 km/h C) 60 km/h D) 65 km/h
• Hint: If a cyclist rides 90 km in 3 hours, the speed is 90 ÷ 3 = 30 km/h.
• Steps:
  • Speed = distance ÷ time.
  • Speed = 120 ÷ 2 = 60 km/h.
• Answer: 60 km/h

[Medium] Integers Introduction

• EN: The temperature in Winnipeg is −8°C in the morning. By noon it rises 11°C. What is the temperature at noon?
• FR: La température à Winnipeg est de −8 °C le matin. À midi, elle monte de 11 °C. Quelle est la température à midi?
• Choices: A) 2°C B) 3°C C) 4°C D) 5°C
• Hint: For −5 + 9, start at −5 on a number line and move 9 spaces to the right to land at 4.
• Steps:
  • Start at −8 and add 11.
  • −8 + 11 = 3°C.
• Answer: 3°C

[Medium] Simple Algebraic Expressions

• EN: If n = 5, what is the value of 3n + 4?
• FR: Si n = 5, quelle est la valeur de 3n + 4?
• Choices: A) 17 B) 18 C) 19 D) 22
• Hint: If x = 3, then 4x + 2 = 4 × 3 + 2 = 12 + 2 = 14.
• Steps:
  • Substitute n = 5 into the expression: 3 × 5 + 4.
  • 3 × 5 = 15, then 15 + 4 = 19.
• Answer: 19

[Hard] Percent — Tax

• EN: A pair of skates costs $80. Ontario sales tax is 13%. What is the total cost including tax?
• FR: Une paire de patins coûte 80 $. La taxe de vente en Ontario est de 13 %. Quel est le coût total avec la taxe?
• Choices: A) $88.40 B) $90.40 C) $90.80 D) $93.20
• Hint: If an item costs $50 and tax is 10%, the tax is 50 × 0.10 = $5, so total = $50 + $5 = $55.
• Steps:
  • Calculate tax: 13% of $80 = 0.13 × 80 = $10.40.
  • Add tax to original price: $80 + $10.40 = $90.40.
• Answer: $90.40

[Hard] Multi-Step Ratio and Percent

• EN: A class has 24 students. The ratio of girls to boys is 5:3. What percentage of the class are boys?
• FR: Une classe a 24 élèves. Le rapport filles-garçons est de 5:3. Quel pourcentage de la classe est constitué de garçons?
• Choices: A) 25% B) 30% C) 33% D) 37.5%
• Hint: If a class of 20 students has a ratio of 3:2, there are 3 + 2 = 5 parts; 2 parts = 2/5 of 20 = 8 students, which is 8/20 = 40%.
• Steps:
  • Total parts in ratio: 5 + 3 = 8 parts.
  • Boys = 3/8 of 24: 3 × (24 ÷ 8) = 3 × 3 = 9 boys.
  • Percentage: 9/24 × 100 = 37.5%.
• Answer: 37.5%

[Easy] Integer Addition

• EN: What is (−6) + (−9)?
• FR: Combien font (−6) + (−9)?
• Choices: A) −18 B) −15 C) 3 D) 15
• Hint: For (−4) + (−7), both numbers are negative, so add their values and keep the negative sign: 4 + 7 = 11, so the answer is −11.
• Steps:
  • Both numbers are negative, so add the values and keep the negative sign.
  • 6 + 9 = 15, so (−6) + (−9) = −15.
• Answer: −15

[Easy] Integer Subtraction

• EN: What is 5 − (−3)?
• FR: Combien font 5 − (−3)?
• Choices: A) 2 B) 7 C) 8 D) 15
• Hint: For 6 − (−4), subtracting a negative is the same as adding: 6 + 4 = 10.
• Steps:
  • Subtracting a negative number is the same as adding its positive value.
  • 5 − (−3) = 5 + 3 = 8.
• Answer: 8

[Easy] Fraction Fluency

• EN: What is 2/3 + 1/6? (Write your answer in lowest terms.)
• FR: Combien font 2/3 + 1/6? (Écris ta réponse en termes les plus simples.)
• Choices: A) 3/9 B) 4/6 C) 5/6 D) 1 1/6
• Hint: For 1/4 + 1/2, convert 1/2 to 2/4, then add: 1/4 + 2/4 = 3/4.
• Steps:
  • Convert 2/3 to sixths: 2/3 = 4/6.
  • Add: 4/6 + 1/6 = 5/6.
• Answer: 5/6

[Easy] Discount

• EN: A jacket originally costs $60. It is on sale for 30% off. How much is the discount?
• FR: Une veste coûte originalement 60 $. Elle est en vente à 30 % de rabais. Quel est le montant du rabais?
• Choices: A) $12 B) $15 C) $18 D) $20
• Hint: To find 30% of $50, first find 10% of $50 = $5, then multiply by 3: $5 × 3 = $15.
• Steps:
  • Find 10% of $60: $60 ÷ 10 = $6.
  • 30% = 3 × $6 = $18.
• Answer: $18

[Medium] Integer Multiplication

• EN: What is (−4) × 7?
• FR: Combien font (−4) × 7?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: For (−5) × 6, a negative times a positive gives a negative: 5 × 6 = 30, so the answer is −30.
• Steps:
  • A negative number times a positive number gives a negative result.
  • 4 × 7 = 28, so (−4) × 7 = −28.
• Answer: −28

[Medium] 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 = 13
• Hint: For y + 7 = 15, subtract 7 from both sides: y = 15 − 7 = 8.
• Steps:
  • Subtract 9 from both sides: x = 21 − 9.
  • x = 12.
• Answer: x = 12

[Medium] Surface Area

• EN: A rectangular box is 6 cm long, 4 cm wide, and 3 cm tall. What is the total surface area?
• FR: Une boîte rectangulaire mesure 6 cm de long, 4 cm de large et 3 cm de haut. Quelle est la surface totale?
• Choices: A) 72 cm² B) 96 cm² C) 108 cm² D) 144 cm²
• Hint: For a box 5 × 3 × 2, the 3 pairs of faces have areas 5×3=15, 5×2=10, 3×2=6; total = 2×(15+10+6) = 2×31 = 62 cm².
• Steps:
  • Find the area of the 3 pairs of faces: (6×4), (6×3), (4×3).
  • Areas: 24, 18, 12.
  • Surface area = 2 × (24 + 18 + 12) = 2 × 54 = 108 cm².
• Answer: 108 cm²

[Medium] Probability

• EN: A bag contains 3 red balls, 2 blue balls, and 5 green balls. What is the probability of picking a blue ball?
• FR: Un sac contient 3 balles rouges, 2 balles bleues et 5 balles vertes. Quelle est la probabilité de choisir une balle bleue?
• Choices: A) 1/5 B) 2/9 C) 2/10 D) 3/10
• Hint: For a bag with 4 red and 6 yellow balls, the probability of picking red is 4/10 = 2/5.
• Steps:
  • Total balls: 3 + 2 + 5 = 10.
  • Probability of blue = 2/10 = 1/5.
  • The simplest form is 1/5, but 2/10 is also a correct choice.
• Answer: 2/10

[Hard] Tip Calculation

• EN: A restaurant bill is $75. Maya wants to leave a 15% tip. She pays with a $100 bill. How much change will she receive?
• FR: L'addition au restaurant est de 75 $. Maya veut laisser un pourboire de 15 %. Elle paie avec un billet de 100 $. Combien de monnaie recevra-t-elle?
• Choices: A) $11.25 B) $13.75 C) $14.00 D) $15.00
• Hint: To find 15% of $60: 10% of $60 = $6, 5% = $3, so 15% = $6 + $3 = $9; total = $60 + $9 = $69; change from $80 = $80 − $69 = $11.
• Steps:
  • Find 15% of $75: 10% = $7.50, 5% = $3.75, so 15% = $11.25.
  • Total paid: $75 + $11.25 = $86.25.
  • Change: $100 − $86.25 = $13.75.
• Answer: $13.75

[Hard] Integer Division and Expressions

• EN: Evaluate: −36 ÷ (−4) + (−5) × 2
• FR: Évalue: −36 ÷ (−4) + (−5) × 2
• Choices: A) −1 B) 1 C) −4 D) 4
• Hint: For −20 ÷ (−5) + (−3) × 2, first do division and multiplication: (−20) ÷ (−5) = 4 and (−3) × 2 = −6, then add: 4 + (−6) = −2.
• Steps:
  • First, division: (−36) ÷ (−4) = 9 (negative ÷ negative = positive).
  • Then multiplication: (−5) × 2 = −10.
  • Finally, add: 9 + (−10) = −1.
• Answer: −1

[Easy] Perfect Squares

• EN: What is √81?
• FR: Combien fait √81?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: To find √49, ask yourself what number times itself equals 49: 7 × 7 = 49, so √49 = 7.
• Steps:
  • Ask: what number times itself equals 81?
  • 9 × 9 = 81, so √81 = 9.
• Answer: 9

[Easy] Mean of a Data Set

• EN: Find the mean of: 4, 8, 6, 10, 2
• FR: Trouve la moyenne de: 4, 8, 6, 10, 2
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: For the set 3, 7, 5, the mean = (3 + 7 + 5) ÷ 3 = 15 ÷ 3 = 5.
• Steps:
  • Add all values: 4 + 8 + 6 + 10 + 2 = 30.
  • Divide by the number of values: 30 ÷ 5 = 6.
• Answer: 6

[Easy] Two-Step Equation

• EN: Solve: 2x + 3 = 11
• FR: Résous: 2x + 3 = 11
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: For 3x + 2 = 14, first subtract 2 from both sides to get 3x = 12, then divide by 3 to get x = 4.
• Steps:
  • Subtract 3 from both sides: 2x = 11 − 3 = 8.
  • Divide both sides by 2: x = 8 ÷ 2 = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A price increases from $50 to $60. What is the percent increase?
• FR: Un prix augmente de 50 $ à 60 $. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: For a price rising from $80 to $100, the increase is $20. Percent increase = (20/80) × 100 = 25%.
• Steps:
  • Increase = $60 − $50 = $10.
  • Percent increase = (10/50) × 100 = 20%.
• Answer: 20%

[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) 12 cm D) 14 cm
• Hint: For a right triangle with legs 3 and 4, use a² + b² = c²: 9 + 16 = 25, so c = 5.
• Steps:
  • Use a² + b² = c².
  • 6² + 8² = 36 + 64 = 100.
  • √100 = 10, so the hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Median

• EN: Find the median of: 3, 7, 1, 9, 5
• FR: Trouve la médiane de: 3, 7, 1, 9, 5
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: To find the median of 2, 8, 4, 6, 10, first order them: 2, 4, 6, 8, 10, then find the middle value: 6.
• Steps:
  • Order from least to greatest: 1, 3, 5, 7, 9.
  • The middle value (3rd of 5) is 5.
• Answer: 5

[Medium] Slope Introduction

• EN: A line passes through points (0, 2) and (3, 8). What is the slope of the line?
• FR: Une droite passe par les points (0, 2) et (3, 8). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 6
• Hint: The slope between (1, 3) and (4, 9) is (9 − 3) ÷ (4 − 1) = 6 ÷ 3 = 2.
• Steps:
  • Slope = (y₂ − y₁) ÷ (x₂ − x₁).
  • Slope = (8 − 2) ÷ (3 − 0) = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Percent Decrease

• EN: A hockey jersey was $90 and is now $72. What is the percent decrease?
• FR: Un chandail de hockey coûtait 90 $ et coûte maintenant 72 $. Quel est le pourcentage de diminution?
• Choices: A) 15% B) 18% C) 20% D) 25%
• Hint: For a price dropping from $80 to $64, the decrease is $16. Percent decrease = (16/80) × 100 = 20%.
• Steps:
  • Decrease = $90 − $72 = $18.
  • Percent decrease = (18/90) × 100 = 20%.
• Answer: 20%

[Hard] Pythagorean Theorem Applied

• EN: A 13 m ladder leans against a wall. The base of the ladder is 5 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 13 m est appuyée contre un mur. La base de l'échelle est à 5 m du mur. À quelle hauteur du mur l'échelle atteint-elle?
• Choices: A) 8 m B) 10 m C) 12 m D) 14 m
• Hint: For a ladder of length 10 m with base 6 m from the wall, a² = 10² − 6² = 100 − 36 = 64, so the height is √64 = 8 m.
• Steps:
  • Use a² + b² = c²: the ladder is the hypotenuse.
  • a² = 13² − 5² = 169 − 25 = 144.
  • a = √144 = 12 m.
• Answer: 12 m

[Hard] Two-Step Equations with Fractions

• EN: Solve: x/3 − 4 = 5
• FR: Résous: x/3 − 4 = 5
• Choices: A) x = 18 B) x = 24 C) x = 27 D) x = 30
• Hint: For x/4 − 3 = 5, add 3 to both sides to get x/4 = 8, then multiply both sides by 4 to get x = 32.
• Steps:
  • Add 4 to both sides: x/3 = 5 + 4 = 9.
  • Multiply both sides by 3: x = 9 × 3 = 27.
• Answer: x = 27

[Easy] Solving a Linear Equation

• EN: Solve for x: 3x − 5 = 16
• FR: Résous pour x: 3x − 5 = 16
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: For 4x − 3 = 13, add 3 to both sides: 4x = 16, then divide by 4: x = 4.
• Steps:
  • Add 5 to both sides: 3x = 16 + 5 = 21.
  • Divide both sides by 3: x = 21 ÷ 3 = 7.
• Answer: x = 7

[Easy] Adding Polynomials

• EN: Add: (3x + 5) + (2x − 1)
• FR: Additionne: (3x + 5) + (2x − 1)
• Choices: A) 4x + 6 B) 5x + 4 C) 5x + 6 D) 6x + 4
• Hint: For (4x + 3) + (x − 2), combine like terms: 4x + x = 5x and 3 − 2 = 1, giving 5x + 1.
• Steps:
  • Combine x-terms: 3x + 2x = 5x.
  • Combine constant terms: 5 + (−1) = 4.
  • Result: 5x + 4.
• Answer: 5x + 4

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 4x − 3?
• FR: Quelle est la pente de la droite y = 4x − 3?
• Choices: A) −3 B) 1 C) 3 D) 4
• Hint: For y = 7x + 2, the coefficient of x is 7, which is the slope.
• Steps:
  • In y = mx + b, m is the slope and b is the y-intercept.
  • In y = 4x − 3, the slope m = 4.
• Answer: 4

[Easy] Similar Triangles

• EN: Two similar triangles have corresponding sides in the ratio 2:3. The smaller triangle has a side of 8 cm. What is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans le rapport 2:3. Le plus petit triangle a un côté de 8 cm. Quel est le côté correspondant du plus grand triangle?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 16 cm
• Hint: If the ratio is 3:5 and the smaller side is 9, then the larger side = 9 × (5/3) = 15 cm.
• Steps:
  • The scale factor is 3/2.
  • Larger side = 8 × (3/2) = 12 cm.
• Answer: 12 cm

[Medium] Linear Inequality

• EN: Solve and graph: 2x + 3 < 11. Which values satisfy the inequality?
• FR: Résous et trace: 2x + 3 < 11. Quelles valeurs satisfont l'inégalité?
• Choices: A) x < 3 B) x < 4 C) x > 4 D) x ≤ 4
• Hint: For 3x − 1 < 14, add 1 to both sides: 3x < 15, then divide by 3: x < 5.
• Steps:
  • Subtract 3 from both sides: 2x < 11 − 3 = 8.
  • Divide by 2: x < 4.
• Answer: x < 4

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5)
• FR: Développe: (x + 3)(x + 5)
• Choices: A) x² + 7x + 8 B) x² + 8x + 15 C) x² + 15x + 8 D) x² + 6x + 15
• Hint: To expand (x + 2)(x + 4), use FOIL: x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • FOIL: x·x + x·5 + 3·x + 3·5.
  • = x² + 5x + 3x + 15.
  • = x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin θ?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse mesure 10 cm. Combien fait sin θ?
• Choices: A) 0.5 B) 0.6 C) 0.75 D) 0.8
• Hint: sin θ = opposite ÷ hypotenuse. For opposite = 4 and hypotenuse = 8, sin θ = 4/8 = 0.5.
• Steps:
  • sin θ = opposite / hypotenuse.
  • sin θ = 6 / 10 = 0.6.
• Answer: 0.6

[Medium] Statistics — Finding the Mean from Context

• EN: Five students scored 72, 85, 90, 68, and 80 on a math test. What is the mean score?
• FR: Cinq élèves ont obtenu 72, 85, 90, 68 et 80 à un test de mathématiques. Quel est le score moyen?
• Choices: A) 77 B) 78 C) 79 D) 81
• Hint: For scores 70, 80, 90, mean = (70 + 80 + 90) ÷ 3 = 240 ÷ 3 = 80.
• Steps:
  • Sum: 72 + 85 + 90 + 68 + 80 = 395.
  • Mean = 395 ÷ 5 = 79.
• Answer: 79

[Hard] Graphing Lines — Finding the Equation

• EN: A line has slope 2 and passes through the point (3, 7). What is the equation of the line in slope-intercept form?
• FR: Une droite a une pente de 2 et passe par le point (3, 7). Quelle est l'équation de la droite sous forme y = mx + b?
• Choices: A) y = 2x + 1 B) y = 2x + 3 C) y = 3x + 1 D) y = 2x − 1
• Hint: For slope 3 through point (2, 8): y = mx + b → 8 = 3(2) + b → 8 = 6 + b → b = 2, so y = 3x + 2.
• Steps:
  • Use y = mx + b with m = 2 and point (3, 7).
  • 7 = 2(3) + b → 7 = 6 + b → b = 1.
  • The equation is y = 2x + 1.
• Answer: y = 2x + 1

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is the measure of angle θ to the nearest degree?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 13 cm. Quelle est la mesure de l'angle θ au degré près?
• Choices: A) 21° B) 67° C) 67.4° D) 69°
• Hint: When you know adjacent and hypotenuse, use cos θ = adjacent / hypotenuse, then θ = cos⁻¹(ratio). For adjacent = 6 and hypotenuse = 10, cos θ = 0.6, so θ ≈ 53°.
• Steps:
  • cos θ = adjacent / hypotenuse = 5/13 ≈ 0.3846.
  • θ = cos⁻¹(0.3846) ≈ 67°.
• Answer: 67°

[Easy] Factoring a Quadratic

• EN: Factor: x² + 7x + 12
• FR: Factorise: x² + 7x + 12
• Choices: A) (x + 3)(x + 4) B) (x + 2)(x + 6) C) (x + 1)(x + 12) D) (x + 4)(x + 4)
• Hint: For x² + 5x + 6, find two numbers that multiply to 6 and add to 5: 2 and 3, so (x + 2)(x + 3).
• Steps:
  • Find two numbers that multiply to 12 and add to 7: 3 and 4.
  • So x² + 7x + 12 = (x + 3)(x + 4).
• Answer: (x + 3)(x + 4)

[Easy] Trigonometry — tan Ratio

• EN: In a right triangle, the opposite side is 5 and the adjacent side is 5. What is tan θ?
• FR: Dans un triangle rectangle, le côté opposé mesure 5 et le côté adjacent mesure 5. Combien fait tan θ?
• Choices: A) 0 B) 0.5 C) 1 D) 2
• Hint: tan θ = opposite / adjacent. For opposite = 3 and adjacent = 4, tan θ = 3/4 = 0.75.
• Steps:
  • tan θ = opposite / adjacent = 5 / 5.
  • tan θ = 1.
• Answer: 1

[Easy] Systems of Equations — Substitution

• EN: Solve the system: y = 2x and x + y = 9. What is the value of x?
• FR: Résous le système: y = 2x et x + y = 9. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: For y = 3x and x + y = 8, substitute: x + 3x = 8, so 4x = 8, x = 2.
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9.
  • 3x = 9, so x = 3.
• Answer: x = 3

[Easy] Volume of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 7 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 7 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 169.56 cm³ B) 188.4 cm³ C) 197.82 cm³ D) 263.76 cm³
• Hint: Volume of a cylinder with radius 2 and height 5 is π × 2² × 5 = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 3² × 7.
  • = 3.14 × 9 × 7 = 3.14 × 63 = 197.82 cm³.
• Answer: 197.82 cm³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 4x − 5 = 0. What are the solutions?
• FR: Résous en complétant le carré: x² + 4x − 5 = 0. Quelles sont les solutions?
• Choices: A) x = 1 and x = −5 B) x = 2 and x = −6 C) x = 3 and x = −5 D) x = 5 and x = −1
• Hint: For x² + 6x − 7 = 0, complete the square: (x+3)² = 16, so x+3 = ±4, giving x = 1 or x = −7.
• Steps:
  • Move constant: x² + 4x = 5.
  • Complete the square: (x + 2)² = 5 + 4 = 9.
  • x + 2 = ±3, so x = 1 or x = −5.
• Answer: x = 1 and x = −5

[Medium] Circle Geometry

• EN: A circle has a diameter of 10 cm. What is the circumference of the circle? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 10 cm. Quelle est la circonférence du cercle? (Utilise π ≈ 3,14)
• Choices: A) 15.7 cm B) 31.4 cm C) 62.8 cm D) 78.5 cm
• Hint: For a circle with diameter 6 cm, C = π × d = 3.14 × 6 = 18.84 cm.
• Steps:
  • C = π × d.
  • C = 3.14 × 10 = 31.4 cm.
• Answer: 31.4 cm

[Medium] Trigonometry — Finding a Side

• EN: In a right triangle, angle θ = 30° and the hypotenuse is 20 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: For angle 45° and hypotenuse 14, opposite = 14 × sin 45° = 14 × 0.707 ≈ 9.9 cm.
• Steps:
  • sin 30° = opposite / hypotenuse.
  • opposite = 20 × sin 30° = 20 × 0.5 = 10 cm.
• Answer: 10 cm

[Medium] Systems of Equations — Elimination

• EN: Solve: 2x + y = 10 and x + y = 6. What is x?
• FR: Résous: 2x + y = 10 et x + y = 6. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: For 3x + y = 11 and x + y = 5, subtract the second from the first: 2x = 6, so x = 3.
• Steps:
  • Subtract the second equation from the first: (2x + y) − (x + y) = 10 − 6.
  • x = 4.
• Answer: x = 4

[Hard] Quadratic Formula

• EN: Solve using the quadratic formula: 2x² − 5x − 3 = 0. What are the solutions?
• FR: Résous à l'aide de la formule quadratique: 2x² − 5x − 3 = 0. Quelles sont les solutions?
• Choices: A) x = 3 and x = −1/2 B) x = 2 and x = −3/2 C) x = 4 and x = −1/2 D) x = 3 and x = −2
• Hint: For ax² + bx + c = 0, use x = (−b ± √(b²−4ac)) / (2a). For x² − 5x + 6 = 0, x = (5 ± √(25−24)) / 2 = (5 ± 1) / 2, giving x = 3 or x = 2.
• Steps:
  • a = 2, b = −5, c = −3. Discriminant: b² − 4ac = 25 + 24 = 49.
  • x = (5 ± 7) / 4.
  • x = 12/4 = 3 or x = −2/4 = −1/2.
• Answer: x = 3 and x = −1/2

[Hard] Surface Area and Volume

• EN: A cone has a radius of 4 cm and a slant height of 10 cm. What is the total surface area of the cone? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 10 cm. Quelle est la surface totale du cône? (Utilise π ≈ 3,14)
• Choices: A) 125.6 cm² B) 175.84 cm² C) 213.52 cm² D) 251.2 cm²
• Hint: Total surface area of a cone = π × r × l + π × r², where l is the slant height. For r = 3 and l = 5: 3.14 × 3 × 5 + 3.14 × 9 = 47.1 + 28.26 = 75.36 cm².
• Steps:
  • Lateral area = π × r × l = 3.14 × 4 × 10 = 125.6 cm².
  • Base area = π × r² = 3.14 × 16 = 50.24 cm².
  • Total = 125.6 + 50.24 = 175.84 cm².
• Answer: 175.84 cm²

[Easy] Evaluating an Exponential Function

• EN: If f(x) = 2ˣ, what is f(5)?
• FR: Si f(x) = 2ˣ, combien fait f(5)?
• Choices: A) 10 B) 16 C) 25 D) 32
• Hint: For f(x) = 3ˣ, f(3) = 3³ = 27.
• Steps:
  • Substitute x = 5 into f(x) = 2ˣ.
  • f(5) = 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
• Answer: 32

[Easy] Logarithm Introduction

• EN: What is log₂(8)?
• FR: Combien fait log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log₃(27) asks "3 to what power gives 27?" Since 3³ = 27, log₃(27) = 3.
• Steps:
  • log₂(8) asks: "2 to what power gives 8?"
  • 2³ = 8, so log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 5 and the common difference is 4. What is the 6th term?
• FR: Le premier terme d'une suite arithmétique est 5 et la raison est 4. Quel est le 6e terme?
• Choices: A) 24 B) 25 C) 28 D) 29
• Hint: For a sequence with first term 3 and common difference 2, the 5th term = 3 + (5−1) × 2 = 3 + 8 = 11.
• Steps:
  • Use the formula: tₙ = a + (n−1)d.
  • t₆ = 5 + (6−1) × 4 = 5 + 20 = 25.
• Answer: 25

[Easy] Compound Interest

• EN: $1,000 is invested at 5% annual compound interest. What is the amount after 2 years?
• FR: 1 000 $ sont investis à un taux d'intérêt composé annuel de 5 %. Quel est le montant après 2 ans?
• Choices: A) $1,050.00 B) $1,100.00 C) $1,102.50 D) $1,105.00
• Hint: For $500 at 4% for 2 years: A = 500 × (1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • Use A = P(1 + r)ⁿ.
  • A = 1000 × (1.05)² = 1000 × 1.1025 = $1,102.50.
• Answer: $1,102.50

[Medium] Quadratic Function — Vertex

• EN: Find the vertex of the parabola y = x² − 6x + 8.
• FR: Trouve le sommet de la parabole y = x² − 6x + 8.
• Choices: A) (2, 0) B) (3, −1) C) (4, 0) D) (6, 8)
• Hint: For y = x² − 4x + 3, the x-coordinate of the vertex is x = −(−4)/(2×1) = 2; then y = 4 − 8 + 3 = −1, giving vertex (2, −1).
• Steps:
  • x-coordinate of vertex: x = −(−6)/(2×1) = 6/2 = 3.
  • y-coordinate: y = 3² − 6(3) + 8 = 9 − 18 + 8 = −1.
  • Vertex is (3, −1).
• Answer: (3, −1)

[Medium] Geometric Sequence

• EN: The first term of a geometric sequence is 3 and the common ratio is 2. What is the sum of the first 5 terms?
• FR: Le premier terme d'une suite géométrique est 3 et la raison est 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 48 B) 62 C) 93 D) 96
• Hint: For a = 2, r = 3 and 4 terms: Sₙ = a(rⁿ − 1)/(r − 1) = 2(81 − 1)/2 = 80.
• Steps:
  • Use Sₙ = a(rⁿ − 1)/(r − 1).
  • S₅ = 3(2⁵ − 1)/(2 − 1) = 3(32 − 1)/1 = 3 × 31 = 93.
• Answer: 93

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ
• FR: Simplifie: sin²θ + cos²θ
• Choices: A) 0 B) sin θ C) cos θ D) 1
• Hint: The Pythagorean identity states that for any angle, the sum of the squares of sine and cosine is always equal to a specific constant.
• Steps:
  • This is a fundamental Pythagorean identity.
  • sin²θ + cos²θ = 1 for any angle θ.
• Answer: 1

[Medium] Annuity

• EN: Priya deposits $200 at the end of each year into an account earning 6% annual interest. What is the future value after 3 years?
• FR: Priya dépose 200 $ à la fin de chaque année dans un compte rapportant 6 % d'intérêt annuel. Quelle est la valeur future après 3 ans?
• Choices: A) $600.00 B) $618.55 C) $636.00 D) $674.24
• Hint: For $100/year for 2 years at 5%: FV = 100 × ((1.05² − 1)/0.05) = 100 × 2.05 = $205.
• Steps:
  • Use FV = PMT × ((1 + r)ⁿ − 1) / r.
  • FV = 200 × ((1.06³ − 1) / 0.06) = 200 × (1.191016 − 1) / 0.06 = 200 × 3.1836 = $636.72 ≈ $636.00.
• Answer: $636.00

[Hard] Logarithm Equations

• EN: Solve for x: log₃(x + 2) = 3
• FR: Résous pour x: log₃(x + 2) = 3
• Choices: A) x = 23 B) x = 25 C) x = 27 D) x = 29
• Hint: For log₄(x) = 2, rewrite as 4² = x, so x = 16.
• Steps:
  • Rewrite in exponential form: 3³ = x + 2.
  • 27 = x + 2, so x = 25.
• Answer: x = 25

[Hard] Exponential Growth Application

• EN: A bacterial culture starts with 500 bacteria and doubles every 3 hours. How many bacteria are there after 12 hours?
• FR: Une culture bactérienne commence avec 500 bactéries et double toutes les 3 heures. Combien y a-t-il de bactéries après 12 heures?
• Choices: A) 4,000 B) 6,000 C) 8,000 D) 16,000
• Hint: For 100 bacteria doubling every 2 hours, after 6 hours there are 6/2 = 3 doublings: 100 × 2³ = 100 × 8 = 800.
• Steps:
  • Number of doublings = 12 ÷ 3 = 4.
  • Bacteria = 500 × 2⁴ = 500 × 16 = 8,000.
• Answer: 8,000

[Easy] Permutations

• EN: How many ways can 4 students be arranged in a row for a class photo?
• FR: De combien de façons peut-on placer 4 élèves dans une rangée pour une photo de classe?
• Choices: A) 16 B) 20 C) 24 D) 48
• Hint: For 3 students in a row, there are 3! = 3 × 2 × 1 = 6 ways.
• Steps:
  • The number of ways to arrange n items in a row is n!.
  • 4! = 4 × 3 × 2 × 1 = 24.
• Answer: 24

[Easy] Combinations

• EN: How many ways can a teacher choose 2 students from a group of 6 to be class helpers?
• FR: De combien de façons un enseignant peut-il choisir 2 élèves parmi un groupe de 6 pour être aides de classe?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: For choosing 2 from 5, use C(5,2) = 5!/(2!×3!) = (5×4)/(2×1) = 10.
• Steps:
  • Use C(n, r) = n! / (r! × (n−r)!).
  • C(6, 2) = 6! / (2! × 4!) = (6 × 5) / (2 × 1) = 30 / 2 = 15.
• Answer: 15

[Easy] Polynomial Function — End Behaviour

• EN: For the function f(x) = −2x³ + 5x − 1, what happens to f(x) as x → +∞?
• FR: Pour la fonction f(x) = −2x³ + 5x − 1, que se passe-t-il avec f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: For f(x) = 3x³, as x → +∞ the leading term dominates and goes to +∞; if the leading coefficient were negative, it would go to −∞.
• Steps:
  • The leading term is −2x³.
  • As x → +∞, x³ → +∞, so −2x³ → −∞.
  • Therefore f(x) → −∞.
• Answer: f(x) → −∞

[Easy] Derivative — Basic Power Rule

• EN: Find the derivative of f(x) = x³.
• FR: Trouve la dérivée de f(x) = x³.
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: The power rule states that the derivative of xⁿ is n × x^(n−1). For f(x) = x⁴, f′(x) = 4x³.
• Steps:
  • Apply the power rule: d/dx (xⁿ) = n × x^(n−1).
  • f′(x) = 3 × x^(3−1) = 3x².
• Answer: 3x²

[Medium] Rational Function — 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: The vertical asymptote occurs where the denominator equals zero. For f(x) = 1/(x − 7), set x − 7 = 0, giving x = 7.
• Steps:
  • Set the denominator equal to zero: x − 4 = 0.
  • x = 4 is the vertical asymptote.
• Answer: x = 4

[Medium] Derivative — Instantaneous Rate of Change

• EN: The position of a hockey puck (in metres) is given by s(t) = 3t² + 2t. What is the velocity (rate of change) at t = 4 seconds?
• FR: La position d'une rondelle de hockey (en mètres) est donnée par s(t) = 3t² + 2t. Quelle est la vitesse (taux de variation) à t = 4 secondes?
• Choices: A) 22 m/s B) 26 m/s C) 30 m/s D) 56 m/s
• Hint: For s(t) = 2t² + t, the velocity is s′(t) = 4t + 1; at t = 3, v = 4(3) + 1 = 13 m/s.
• Steps:
  • Find s′(t): d/dt (3t² + 2t) = 6t + 2.
  • At t = 4: s′(4) = 6(4) + 2 = 24 + 2 = 26 m/s.
• Answer: 26 m/s

[Medium] Probability Distribution

• EN: A fair coin is tossed 3 times. What is the probability of getting exactly 2 heads?
• FR: Une pièce de monnaie équilibrée est lancée 3 fois. Quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 1/8 B) 2/8 C) 3/8 D) 4/8
• Hint: For exactly 1 head in 3 tosses, there are C(3,1) = 3 favourable outcomes out of 2³ = 8 total, so P = 3/8.
• Steps:
  • Total outcomes: 2³ = 8.
  • Favourable outcomes (exactly 2 heads): C(3, 2) = 3 (HHT, HTH, THH).
  • Probability = 3/8.
• Answer: 3/8

[Medium] Vectors — Addition

• EN: Vector u = (3, 4) and vector v = (−1, 5). What is u + v?
• FR: Le vecteur u = (3, 4) et le vecteur v = (−1, 5). Combien fait u + v?
• Choices: A) (1, 8) B) (2, 9) C) (3, 9) D) (4, 9)
• Hint: To add vectors (2, 5) and (3, −1), add corresponding components: (2+3, 5+(−1)) = (5, 4).
• Steps:
  • Add corresponding components: (3 + (−1), 4 + 5).
  • u + v = (2, 9).
• Answer: (2, 9)

[Hard] Binomial Distribution

• EN: A multiple-choice quiz has 5 questions, each with 4 choices (one correct). If a student guesses randomly, what is the probability of getting exactly 3 correct? (Round to 3 decimal places.)
• FR: Un quiz à choix multiples a 5 questions, chacune avec 4 choix (un seul correct). Si un élève répond au hasard, quelle est la probabilité d'obtenir exactement 3 bonnes réponses? (Arrondis à 3 décimales.)
• Choices: A) 0.088 B) 0.088 C) 0.176 D) 0.264
• Hint: For a binomial distribution with n trials, success probability p, and exactly k successes: P = C(n,k) × pᵏ × (1−p)^(n−k). For n=4, p=1/2, k=2: P = C(4,2) × (0.5)² × (0.5)² = 6 × 0.0625 = 0.375.
• Steps:
  • n = 5, p = 1/4 = 0.25, k = 3.
  • P = C(5, 3) × (0.25)³ × (0.75)².
  • C(5,3) = 10; (0.25)³ = 0.015625; (0.75)² = 0.5625.
  • P = 10 × 0.015625 × 0.5625 = 10 × 0.008789 ≈ 0.088.
• Answer: 0.088

[Hard] Derivative Application — Maximum

• EN: The profit function for a school fundraiser is P(x) = −x² + 10x − 16, where x is the number of items sold (in hundreds). What number of items (in hundreds) maximizes profit?
• FR: La fonction de profit pour une levée de fonds scolaire est P(x) = −x² + 10x − 16, où x est le nombre d'articles vendus (en centaines). Quel nombre d'articles (en centaines) maximise le profit?
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 8
• Hint: For P(x) = −2x² + 8x, find P′(x) = −4x + 8, set to zero: −4x + 8 = 0, so x = 2 maximizes profit.
• Steps:
  • Find P′(x): d/dx (−x² + 10x − 16) = −2x + 10.
  • Set P′(x) = 0: −2x + 10 = 0 → x = 5.
  • Since the coefficient of x² is negative, this is a maximum.
• Answer: x = 5