Daily Math — 2026-09-13

[Easy] Counting Apples

• EN: There are 7 apples on the table. How many apples are there?
• FR: Il y a 7 pommes sur la table. Combien y a-t-il de pommes?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Count each object one by one — try counting 3 pencils: 1, 2, 3!
• Steps:
  • Start at 1 and count each apple.
  • 1, 2, 3, 4, 5, 6, 7 — there are 7 apples.
• Answer: 7

[Easy] Adding Mittens

• EN: Mia has 4 mittens and finds 3 more. How many mittens does she have in all?
• FR: Mia a 4 mitaines et en trouve 3 autres. Combien de mitaines a-t-elle en tout?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To add 2 + 3, count on from 2: 3, 4, 5 — the answer is 5.
• Steps:
  • Start with 4 mittens.
  • Count on 3 more: 5, 6, 7.
  • So Mia has 7 mittens in all.
• Answer: 7

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What comes after 8?
• FR: Compte par bonds de 2. Quel nombre vient après 8?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: To skip count by 2s from 4, say: 4, 6, 8 — add 2 each time!
• Steps:
  • We skip count by 2s: 2, 4, 6, 8…
  • Add 2 to 8: 8 + 2 = 10.
  • The next number is 10.
• Answer: 10

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents?
• FR: Quelle pièce vaut 10 cents?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: A penny is 1 cent, a nickel is 5 cents — the next one up is worth 10!
• Steps:
  • A penny = 1 cent.
  • A nickel = 5 cents.
  • A dime = 10 cents.
  • So the dime is worth 10 cents.
• Answer: Dime

[Medium] Subtraction at the Rink

• EN: There are 12 hockey pucks on the ice. 5 are taken away. How many are left?
• FR: Il y a 12 rondelles sur la glace. On en enlève 5. Combien en reste-t-il?
• Choices: A) 6 B) 7 C) 8 D) 17
• Hint: To solve 9 − 3, start at 9 and count back 3: 8, 7, 6 — the answer is 6.
• Steps:
  • Start at 12.
  • Count back 5: 11, 10, 9, 8, 7.
  • There are 7 pucks left.
• Answer: 7

[Medium] Comparing Numbers

• EN: Which number is greater: 15 or 9?
• FR: Quel nombre est le plus grand : 15 ou 9?
• Choices: A) 9 B) 15 C) Both are equal D) Neither
• Hint: To compare 12 and 7, think: 12 has 1 ten, 7 has 0 tens — so 12 is greater.
• Steps:
  • 15 has 1 ten and 5 ones.
  • 9 has 0 tens and 9 ones.
  • A number with more tens is greater, so 15 is greater than 9.
• Answer: 15

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What comes after 15?
• FR: Compte par bonds de 5. Quel nombre vient après 15?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: To skip count by 5s from 10, say: 10, 15, 20 — add 5 each time!
• Steps:
  • We skip count by 5s: 5, 10, 15…
  • Add 5 to 15: 15 + 5 = 20.
  • The next number is 20.
• Answer: 20

[Medium] Adding to 20

• EN: Sam has 9 stickers and gets 8 more. How many stickers does Sam have now?
• FR: Sam a 9 autocollants et en reçoit 8 autres. Combien d'autocollants Sam a-t-il maintenant?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: To add 8 + 6, make a 10 first: 8 + 2 = 10, then add 4 more to get 14.
• Steps:
  • Start with 9.
  • Break 8 into 1 + 7: 9 + 1 = 10, then 10 + 7 = 17.
  • Sam has 17 stickers.
• Answer: 17

[Hard] Adding Three Numbers

• EN: There are 5 red blocks, 4 blue blocks, and 6 yellow blocks. How many blocks are there in all?
• FR: Il y a 5 blocs rouges, 4 blocs bleus et 6 blocs jaunes. Combien y a-t-il de blocs en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: To add 3 + 2 + 4, first add 3 + 2 = 5, then add 5 + 4 = 9.
• Steps:
  • First add 5 + 4 = 9.
  • Then add 9 + 6 = 15.
  • There are 15 blocks in all.
• Answer: 15

[Hard] Number Order

• EN: Put these numbers in order from smallest to largest: 14, 3, 9, 17. Which is second?
• FR: Mets ces nombres en ordre du plus petit au plus grand : 14, 3, 9, 17. Quel est le deuxième?
• Choices: A) 3 B) 9 C) 14 D) 17
• Hint: To order 5, 2, 8: smallest first gives 2, 5, 8 — the second number is 5.
• Steps:
  • Order smallest to largest: 3, 9, 14, 17.
  • The second number in that list is 9.
• Answer: 9

[Easy] Adding Within 100

• EN: What is 34 + 25?
• FR: Combien font 34 + 25?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: To add 21 + 13, add the tens: 20 + 10 = 30, then ones: 1 + 3 = 4, so 34.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59.
• Answer: 59

[Easy] Telling Time — Hour

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

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A crayon is 8 cm long. Which is longer?
• FR: Un crayon est long de 15 cm. Un crayon de couleur est long de 8 cm. Lequel est le plus long?
• Choices: A) Crayon B) Pencil C) Both the same D) Neither
• Hint: To compare 12 cm and 9 cm, 12 is greater, so 12 cm is longer.
• Steps:
  • Compare 15 cm and 8 cm.
  • 15 is greater than 8.
  • So the pencil is longer.
• Answer: Pencil

[Easy] Counting Coins

• EN: You have 2 dimes and 1 nickel. How much money do you have?
• FR: Tu as 2 pièces de 10 cents et 1 pièce de 5 cents. Combien d'argent as-tu?
• Choices: A) 20 cents B) 25 cents C) 30 cents D) 15 cents
• Hint: 1 dime = 10 cents, so 3 dimes = 30 cents; a nickel adds 5 more.
• Steps:
  • 2 dimes = 20 cents.
  • 1 nickel = 5 cents.
  • 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtracting Within 100

• EN: A Tim Hortons order costs 47 cents. You pay 80 cents. How much change do you get?
• FR: Une commande à Tim Hortons coûte 47 cents. Tu paies 80 cents. Combien de monnaie reçois-tu?
• Choices: A) 27 cents B) 33 cents C) 43 cents D) 37 cents
• Hint: To find 70 − 42, subtract tens: 70 − 40 = 30, then subtract ones: 30 − 2 = 28.
• Steps:
  • Subtract: 80 − 47.
  • 80 − 40 = 40, then 40 − 7 = 33.
  • You get 33 cents change.
• Answer: 33 cents

[Medium] Telling Time — Half Hour

• EN: The clock shows the long hand on 6 and the short hand between 2 and 3. What time is it?
• FR: La grande aiguille est sur le 6 et la petite est entre 2 et 3. Quelle heure est-il?
• Choices: A) 2:00 B) 3:30 C) 2:30 D) 6:30
• Hint: When the long hand is on 6, it is half past the hour — the short hand shows which hour.
• Steps:
  • Long hand on 6 means half past.
  • Short hand between 2 and 3 means it is past 2.
  • The time is 2:30.
• Answer: 2:30

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, ___. What is the missing number?
• FR: Regarde ce modèle : 5, 10, 15, 20, ___. Quel est le nombre manquant?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: In a pattern like 3, 6, 9, 12, each number increases by 3 — find the rule and add it.
• Steps:
  • The pattern increases by 5 each time.
  • 20 + 5 = 25.
  • The missing number is 25.
• Answer: 25

[Medium] Adding Within 100

• EN: A bookstore has 46 books on one shelf and 38 books on another. How many books are there in all?
• FR: Une librairie a 46 livres sur une étagère et 38 sur une autre. Combien y a-t-il de livres en tout?
• Choices: A) 74 B) 82 C) 84 D) 86
• Hint: To add 23 + 45, add tens: 20 + 40 = 60, add ones: 3 + 5 = 8, so 68.
• Steps:
  • Add the tens: 40 + 30 = 70.
  • Add the ones: 6 + 8 = 14, carry the 1.
  • 70 + 14 = 84. There are 84 books.
• Answer: 84

[Hard] Counting Coins to $1

• EN: You have 3 quarters. How many more cents do you need to make exactly $1.00?
• FR: Tu as 3 pièces de 25 cents. Combien de cents de plus as-tu besoin pour faire exactement 1,00 $?
• Choices: A) 15 cents B) 20 cents C) 25 cents D) 30 cents
• Hint: 2 quarters = 50 cents; $1.00 = 100 cents — find how much more you need.
• Steps:
  • 3 quarters = 75 cents.
  • $1.00 = 100 cents.
  • 100 − 75 = 25 cents more needed.
• Answer: 25 cents

[Hard] Two-Step Problem

• EN: Lena has 55 cm of ribbon. She cuts off 18 cm and then cuts off 12 more cm. How much ribbon is left?
• FR: Lena a 55 cm de ruban. Elle coupe 18 cm, puis encore 12 cm. Combien de ruban reste-t-il?
• Choices: A) 23 cm B) 25 cm C) 27 cm D) 29 cm
• Hint: For 40 − 10 − 8, first do 40 − 10 = 30, then 30 − 8 = 22.
• Steps:
  • Start with 55 cm.
  • After first cut: 55 − 18 = 37 cm.
  • After second cut: 37 − 12 = 25 cm left.
• Answer: 25 cm

[Easy] Multiplication by 2

• EN: What is 6 × 2?
• FR: Combien font 6 × 2?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: To find 4 × 2, skip count by 2 four times: 2, 4, 6, 8.
• Steps:
  • Skip count by 2 six times: 2, 4, 6, 8, 10, 12.
  • 6 × 2 = 12.
• Answer: 12

[Easy] Basic Fractions

• EN: A pizza is cut into 4 equal pieces. Emma eats 1 piece. What fraction did she eat?
• FR: Une pizza est coupée en 4 parts égales. Emma mange 1 part. Quelle fraction a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: If a pie is cut into 3 equal parts and you take 1, you have 1/3 of the pie.
• Steps:
  • The pizza has 4 equal pieces total.
  • Emma ate 1 piece.
  • She ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: There are 4 bags with 5 apples each. How many apples are there in all?
• FR: Il y a 4 sacs avec 5 pommes chacun. Combien y a-t-il de pommes en tout?
• Choices: A) 15 B) 20 C) 25 D) 9
• Hint: To find 3 × 5, skip count by 5 three times: 5, 10, 15.
• Steps:
  • 4 bags × 5 apples each.
  • Skip count by 5 four times: 5, 10, 15, 20.
  • There are 20 apples in all.
• Answer: 20

[Easy] Perimeter

• EN: A rectangle is 5 cm long and 3 cm wide. What is its perimeter?
• FR: Un rectangle est long de 5 cm et large de 3 cm. Quel est son périmètre?
• Choices: A) 8 cm B) 15 cm C) 16 cm D) 12 cm
• Hint: Perimeter of a rectangle with length 4 and width 2: add all sides 4 + 2 + 4 + 2 = 12.
• Steps:
  • Add all four sides: 5 + 3 + 5 + 3.
  • 5 + 3 = 8, and 8 + 8 = 16.
  • The perimeter is 16 cm.
• Answer: 16 cm

[Medium] Basic Division

• EN: There are 24 hockey cards shared equally among 4 friends. How many does each friend get?
• FR: Il y a 24 cartes de hockey partagées également entre 4 amis. Combien chacun en reçoit-il?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To find 15 ÷ 3, think: what times 3 equals 15? 5 × 3 = 15, so the answer is 5.
• Steps:
  • 24 ÷ 4 = ?
  • Think: 4 × 6 = 24.
  • Each friend gets 6 hockey cards.
• Answer: 6

[Medium] Multiplication by 3

• EN: A store has 7 shelves with 3 jars of maple syrup on each shelf. How many jars are there in all?
• FR: Un magasin a 7 étagères avec 3 pots de sirop d'érable sur chaque étagère. Combien y a-t-il de pots en tout?
• Choices: A) 18 B) 21 C) 24 D) 10
• Hint: To find 5 × 3, count by 3 five times: 3, 6, 9, 12, 15.
• Steps:
  • 7 shelves × 3 jars each.
  • Count by 3 seven times: 3, 6, 9, 12, 15, 18, 21.
  • There are 21 jars in all.
• Answer: 21

[Medium] Reading a Simple Graph

• EN: A bar graph shows 8 students like hockey and 5 students like skating. How many more students like hockey than skating?
• FR: Un diagramme à bandes montre que 8 élèves aiment le hockey et 5 aiment le patinage. Combien d'élèves de plus aiment le hockey?
• Choices: A) 2 B) 3 C) 4 D) 13
• Hint: To find how many more 9 is than 6, subtract: 9 − 6 = 3.
• Steps:
  • Hockey: 8 students. Skating: 5 students.
  • Subtract: 8 − 5 = 3.
  • Three more students like hockey than skating.
• Answer: 3

[Medium] Comparing Fractions

• EN: Which fraction is larger: 1/2 or 1/4?
• FR: Quelle fraction est la plus grande : 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/2 C) They are equal D) Neither
• Hint: Think of a pie cut into 2 pieces vs. 4 pieces — bigger pieces come from fewer cuts.
• Steps:
  • 1/2 means 1 out of 2 equal parts.
  • 1/4 means 1 out of 4 equal parts.
  • Fewer pieces means each piece is bigger, so 1/2 is larger.
• Answer: 1/2

[Hard] Multiplication and Perimeter

• EN: A square playground has a side length of 9 m. What is its perimeter?
• FR: Une cour de récréation carrée a un côté de 9 m. Quel est son périmètre?
• Choices: A) 27 m B) 36 m C) 45 m D) 81 m
• Hint: A square has 4 equal sides — to find the perimeter of a square with side 5, do 5 × 4 = 20.
• Steps:
  • A square has 4 equal sides.
  • Each side = 9 m.
  • Perimeter = 9 × 4 = 36 m.
• Answer: 36 m

[Hard] Two-Step Multiplication and Division

• EN: There are 5 boxes with 10 crayons each. The crayons are shared equally among 2 classrooms. How many crayons does each classroom get?
• FR: Il y a 5 boîtes de 10 crayons chacune. Les crayons sont partagés également entre 2 classes. Combien de crayons chaque classe reçoit-elle?
• Choices: A) 20 B) 25 C) 35 D) 50
• Hint: First find the total (e.g., 3 × 4 = 12), then divide (12 ÷ 2 = 6).
• Steps:
  • Total crayons: 5 × 10 = 50.
  • Shared among 2 classrooms: 50 ÷ 2 = 25.
  • Each classroom gets 25 crayons.
• Answer: 25

[Easy] Multiplication Tables

• EN: What is 8 × 7?
• FR: Combien font 8 × 7?
• Choices: A) 54 B) 56 C) 63 D) 48
• Hint: To find 6 × 7, remember: 6 × 7 = 42 — practice your times tables!
• Steps:
  • 8 × 7 can be found using the times table.
  • 8 × 7 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, what digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre est à la position des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 0
• Hint: In 5.82, the digits go: 5 ones, 8 tenths, 2 hundredths.
• Steps:
  • 3.47: 3 is in the ones place.
  • 4 is in the tenths place.
  • 7 is in the hundredths place.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A rectangular garden is 6 m long and 4 m wide. What is its area?
• FR: Un jardin rectangulaire est long de 6 m et large de 4 m. Quelle est son aire?
• Choices: A) 10 m² B) 20 m² C) 24 m² D) 28 m²
• Hint: Area of a rectangle = length × width; for a 3 × 5 rectangle, area = 15 square units.
• Steps:
  • Area = length × width.
  • Area = 6 × 4 = 24.
  • The area is 24 m².
• Answer: 24 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/4?
• FR: Quelle fraction est la plus grande : 3/4 ou 2/4?
• Choices: A) 2/4 B) 3/4 C) They are equal D) Neither
• Hint: When fractions have the same denominator, compare the numerators — 5/8 is more than 3/8.
• Steps:
  • Both fractions have the same denominator (4).
  • Compare numerators: 3 > 2.
  • So 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: Divide 29 by 4. What is the remainder?
• FR: Divise 29 par 4. Quel est le reste?
• Choices: A) 0 B) 1 C) 2 D) 3
• Hint: For 17 ÷ 5, 5 × 3 = 15, so 17 − 15 = 2 remainder.
• Steps:
  • 4 × 7 = 28, which is the largest multiple of 4 less than 29.
  • 29 − 28 = 1.
  • The remainder is 1.
• Answer: 1

[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. Combien de temps dure la journée scolaire?
• Choices: A) 5 hours 30 minutes B) 6 hours 30 minutes C) 7 hours D) 7 hours 30 minutes
• Hint: From 9:00 a.m. to 2:00 p.m. is 5 hours — count the hours between start and end.
• Steps:
  • From 8:30 a.m. to 3:00 p.m.
  • 8:30 to 9:00 = 30 minutes; 9:00 to 3:00 = 6 hours.
  • Total = 6 hours 30 minutes.
• Answer: 6 hours 30 minutes

[Medium] Decimal Operations

• EN: A notebook costs $3.25 and a pen costs $1.50. What is the total cost?
• FR: Un cahier coûte 3,25 $ et un stylo coûte 1,50 $. Quel est le coût total?
• Choices: A) $4.50 B) $4.75 C) $5.25 D) $5.75
• Hint: To add $2.30 + $1.40, add dollars: $3, add cents: 70 cents, total $3.70.
• Steps:
  • Add dollars: $3 + $1 = $4.
  • Add cents: 25¢ + 50¢ = 75¢.
  • Total = $4.75.
• Answer: $4.75

[Medium] Multiplication (Multi-digit)

• EN: A hockey team plays 24 games a season. If there are 6 seasons, how many games are played in total?
• FR: Une équipe de hockey joue 24 parties par saison. S'il y a 6 saisons, combien de parties sont jouées en tout?
• Choices: A) 124 B) 144 C) 154 D) 164
• Hint: To multiply 23 × 4, do 20 × 4 = 80 and 3 × 4 = 12, then add: 80 + 12 = 92.
• Steps:
  • 24 × 6: multiply 20 × 6 = 120.
  • Then 4 × 6 = 24.
  • 120 + 24 = 144 games.
• Answer: 144

[Hard] Long Division

• EN: A school buys 126 pencils to put equally into 9 boxes. How many pencils go in each box?
• FR: Une école achète 126 crayons à répartir également dans 9 boîtes. Combien de crayons y a-t-il dans chaque boîte?
• Choices: A) 12 B) 13 C) 14 D) 15
• Hint: For 84 ÷ 6, think: 6 × 14 = 84 — use multiplication to check your division.
• Steps:
  • 126 ÷ 9 = ?
  • 9 × 14 = 126.
  • Each box gets 14 pencils.
• Answer: 14

[Hard] Multi-Step Problem

• EN: Maya earns $9 per hour raking leaves. She works 7 hours on Saturday and 5 hours on Sunday. How much does she earn in total?
• FR: Maya gagne 9 $ de l'heure en ratissant des feuilles. Elle travaille 7 heures samedi et 5 heures dimanche. Combien gagne-t-elle en tout?
• Choices: A) $99 B) $108 C) $117 D) $126
• Hint: Find total hours first (e.g., 3 + 4 = 7), then multiply by the rate (7 × $8 = $56).
• Steps:
  • Total hours: 7 + 5 = 12 hours.
  • Earnings: 12 × $9 = $108.
  • Maya earns $108 in total.
• Answer: $108

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 194 C) 204 D) 216
• Hint: To find 21 × 4, do 20 × 4 = 80 and 1 × 4 = 4, then add: 80 + 4 = 84.
• Steps:
  • 34 × 6: multiply 30 × 6 = 180.
  • Then 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions (Like Denominators)

• EN: What is 2/5 + 1/5?
• FR: Combien font 2/5 + 1/5?
• Choices: A) 3/10 B) 3/5 C) 2/5 D) 4/5
• Hint: To add 1/6 + 2/6, keep the denominator and add numerators: 1 + 2 = 3, so 3/6.
• Steps:
  • The denominators are the same (5).
  • Add the numerators: 2 + 1 = 3.
  • The answer is 3/5.
• Answer: 3/5

[Easy] Percentage Intro

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

[Easy] Decimal Operations

• EN: What is 5.6 + 2.3?
• FR: Combien font 5,6 + 2,3?
• Choices: A) 7.5 B) 7.9 C) 8.1 D) 8.9
• Hint: To add 3.4 + 1.2, add ones: 3 + 1 = 4 and tenths: 0.4 + 0.2 = 0.6, so 4.6.
• Steps:
  • Add the ones: 5 + 2 = 7.
  • Add the tenths: 0.6 + 0.3 = 0.9.
  • 5.6 + 2.3 = 7.9.
• Answer: 7.9

[Medium] Multi-Digit Division

• EN: A farmer has 256 eggs to pack into cartons of 8. How many cartons does she fill?
• FR: Une fermière a 256 œufs à emballer dans des boîtes de 8. Combien de boîtes remplit-elle?
• Choices: A) 28 B) 32 C) 36 D) 42
• Hint: For 120 ÷ 6, think 6 × 20 = 120 — use known multiplication facts.
• Steps:
  • 256 ÷ 8 = ?
  • 8 × 32 = 256.
  • She fills 32 cartons.
• Answer: 32

[Medium] Subtracting Fractions

• EN: What is 7/8 − 3/8?
• FR: Combien font 7/8 − 3/8?
• Choices: A) 3/8 B) 4/8 C) 5/8 D) 4/0
• Hint: To subtract 5/9 − 2/9, keep the denominator and subtract numerators: 5 − 2 = 3, so 3/9.
• Steps:
  • Denominators are the same (8).
  • Subtract numerators: 7 − 3 = 4.
  • The answer is 4/8.
• Answer: 4/8

[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 est longue de 5 cm, large de 4 cm et haute de 3 cm. Quel est son volume?
• Choices: A) 47 cm³ B) 60 cm³ C) 72 cm³ D) 48 cm³
• Hint: Volume = length × width × height; for a 2 × 3 × 4 box, volume = 24 cubic units.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20.
  • 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage Intro

• EN: A jacket costs $80. It is on sale for 25% off. How much is the discount?
• FR: Une veste coûte 80 $. Elle est soldée à 25% de rabais. Quel est le rabais?
• Choices: A) $15 B) $20 C) $25 D) $40
• Hint: 25% of a number is one quarter of it — so 25% of 40 is 40 ÷ 4 = 10.
• Steps:
  • 25% = 1/4.
  • 1/4 of $80 = $80 ÷ 4 = $20.
  • The discount is $20.
• Answer: $20

[Hard] Multi-Step Decimal Problem

• EN: Lucy buys 3 items at $4.75 each and pays with a $20 bill. How much change does she receive?
• FR: Lucy achète 3 articles à 4,75 $ chacun et paie avec un billet de 20 $. Combien de monnaie reçoit-elle?
• Choices: A) $4.75 B) $5.25 C) $5.75 D) $6.25
• Hint: First find the total cost (e.g., 3 × $2.50 = $7.50), then subtract from the amount paid.
• Steps:
  • Total cost: 3 × $4.75 = $14.25.
  • Change: $20.00 − $14.25 = $5.75.
  • Lucy receives $5.75 in change.
• Answer: $5.75

[Hard] Multi-Step Fractions and Whole Numbers

• EN: A recipe uses 3/4 cup of oats. Jake makes the recipe 6 times. How many cups of oats does he need in total?
• FR: Une recette utilise 3/4 de tasse de flocons d'avoine. Jake fait la recette 6 fois. De combien de tasses de flocons d'avoine a-t-il besoin en tout?
• Choices: A) 3 cups B) 4 cups C) 4 and 1/2 cups D) 5 cups
• Hint: To find 5 × 2/3, multiply the whole number by the numerator: 5 × 2 = 10, so 10/3 = 3 and 1/3.
• Steps:
  • 6 × 3/4 = 18/4.
  • Simplify: 18 ÷ 4 = 4 remainder 2, so 4 and 2/4 = 4 and 1/2 cups.
  • Jake needs 4 and 1/2 cups.
• Answer: 4 and 1/2 cups

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 14 B) 11 C) 10 D) 16
• Hint: BEDMAS says multiply before you add — for 2 + 3 × 4, do 3 × 4 = 12 first, then 2 + 12 = 14.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Percent of a Number

• EN: What is 10% of 90?
• FR: Combien font 10% de 90?
• Choices: A) 7 B) 9 C) 10 D) 19
• Hint: 10% of any number means divide by 10 — so 10% of 70 is 7.
• Steps:
  • 10% means divide by 10.
  • 90 ÷ 10 = 9.
  • 10% of 90 is 9.
• Answer: 9

[Easy] Ratio Introduction

• EN: In a class, there are 12 girls and 8 boys. What is the ratio of girls to boys?
• FR: Dans une classe, il y a 12 filles et 8 garçons. Quel est le rapport filles à garçons?
• Choices: A) 2:3 B) 3:2 C) 4:3 D) 3:4
• Hint: A ratio of 6 to 4 can be simplified by dividing both by 2 to get 3:2.
• Steps:
  • Girls to boys: 12:8.
  • Divide both by 4: 12 ÷ 4 = 3, 8 ÷ 4 = 2.
  • The simplified ratio is 3:2.
• Answer: 3:2

[Easy] Integers Introduction

• EN: A temperature drops from 5°C to −3°C. What is the change in temperature?
• FR: La température passe de 5 °C à −3 °C. Quelle est la variation de température?
• Choices: A) 2°C B) −2°C C) −8°C D) 8°C
• Hint: To find the difference from −2 to 5, count up on the number line: the change is 7.
• Steps:
  • Change = final − initial = −3 − 5.
  • −3 − 5 = −8.
  • The temperature dropped by 8°C.
• Answer: −8°C

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/7 B) 6/12 C) 1/2 D) 2/7
• Hint: To multiply 1/2 × 2/5, multiply the numerators (1 × 2 = 2) and denominators (2 × 5 = 10) to get 2/10 = 1/5.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Simple Algebraic Expression

• 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) 12
• Hint: For 2n + 3 when n = 4, substitute: 2 × 4 + 3 = 8 + 3 = 11.
• Steps:
  • Substitute n = 5 into 3n + 4.
  • 3 × 5 + 4 = 15 + 4 = 19.
  • The value is 19.
• Answer: 19

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 and 1/4 C) 3/2 D) 1 and 1/2
• Hint: To divide by a fraction, multiply by its reciprocal — so 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
• Steps:
  • Flip the second fraction: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 1 and 1/2.
• Answer: 1 and 1/2

[Medium] Rate Problem

• EN: A car travels 120 km in 2 hours. What is its speed in km/h?
• FR: Une voiture parcourt 120 km en 2 heures. Quelle est sa vitesse en km/h?
• Choices: A) 50 km/h B) 55 km/h C) 60 km/h D) 65 km/h
• Hint: Speed = distance ÷ time — if a bike travels 30 km in 3 hours, speed = 30 ÷ 3 = 10 km/h.
• Steps:
  • Speed = distance ÷ time.
  • Speed = 120 ÷ 2 = 60.
  • The car's speed is 60 km/h.
• Answer: 60 km/h

[Hard] Multi-Step BEDMAS

• EN: Calculate: (12 − 4) × 3 + 6 ÷ 2.
• FR: Calcule : (12 − 4) × 3 + 6 ÷ 2.
• Choices: A) 27 B) 30 C) 33 D) 36
• Hint: In (10 − 3) × 2 + 8 ÷ 4, do brackets first: 7; then multiply: 14; then divide: 2; then add: 16.
• Steps:
  • Brackets first: 12 − 4 = 8.
  • Multiply: 8 × 3 = 24.
  • Divide: 6 ÷ 2 = 3.
  • Add: 24 + 3 = 27.
• Answer: 27

[Hard] Percentage Problem

• EN: A pair of skates regularly costs $120. It is on sale for 35% off. What is the sale price?
• FR: Une paire de patins coûte habituellement 120 $. Elle est soldée à 35% de rabais. Quel est le prix de vente?
• Choices: A) $72 B) $78 C) $80 D) $84
• Hint: Find the discount first (e.g., 20% of $50 = $10), then subtract from the original price.
• Steps:
  • 35% of $120 = 0.35 × 120 = $42.
  • Sale price = $120 − $42 = $78.
  • The sale price is $78.
• Answer: $78

[Easy] Integer Addition

• EN: What is (−4) + 7?
• FR: Combien font (−4) + 7?
• Choices: A) −3 B) 3 C) 11 D) −11
• Hint: On a number line, start at −3 and move 5 to the right: you land on 2.
• Steps:
  • Start at −4 on the number line.
  • Move 7 steps to the right.
  • −4 + 7 = 3.
• Answer: 3

[Easy] Percentage — Discount

• EN: A $60 hoodie is 20% off. How much do you save?
• FR: Un chandail à capuchon de 60 $ est à 20% de rabais. Combien économises-tu?
• Choices: A) $10 B) $12 C) $15 D) $20
• Hint: 20% of a number = 2 × (10% of the number); 10% of 80 = 8, so 20% of 80 = 16.
• Steps:
  • 10% of $60 = $6.
  • 20% = 2 × $6 = $12.
  • You save $12.
• Answer: $12

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15.
• FR: Résous pour x : x + 9 = 15.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 24
• Hint: To solve n + 4 = 10, subtract 4 from both sides: n = 10 − 4 = 6.
• Steps:
  • x + 9 = 15.
  • Subtract 9 from both sides: x = 15 − 9.
  • x = 6.
• Answer: x = 6

[Easy] Integer Subtraction

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

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Combien font (−6) × (−4)?
• Choices: A) −24 B) 10 C) 24 D) −10
• Hint: A negative times a negative gives a positive — (−3) × (−5) = +15.
• Steps:
  • (−6) × (−4): negative × negative = positive.
  • 6 × 4 = 24.
  • The answer is 24.
• Answer: 24

[Medium] Percentage — Tax

• EN: A video game costs $45.00 before tax. Ontario's HST is 13%. What is the total price including tax?
• FR: Un jeu vidéo coûte 45,00 $ avant taxes. La TVH en Ontario est de 13%. Quel est le prix total avec taxes?
• Choices: A) $49.35 B) $50.85 C) $51.85 D) $52.35
• Hint: Tax amount = price × tax rate; for $20 at 10% tax, tax = $2.00, total = $22.00.
• Steps:
  • Tax = $45 × 0.13 = $5.85.
  • Total = $45.00 + $5.85 = $50.85.
  • The total price is $50.85.
• Answer: $50.85

[Medium] Surface Area

• EN: A rectangular box is 4 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire est longue de 4 cm, large de 3 cm et haute de 2 cm. Quelle est son aire de surface?
• Choices: A) 48 cm² B) 52 cm² C) 56 cm² D) 24 cm²
• Hint: Surface area = 2(lw + lh + wh); for a 2×3×1 box: 2(6 + 2 + 3) = 2 × 11 = 22 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(4×3 + 4×2 + 3×2).
  • = 2(12 + 8 + 6) = 2 × 26.
  • SA = 52 cm².
• Answer: 52 cm²

[Medium] Data and Probability

• EN: A bag has 3 red, 5 blue, and 2 yellow marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 bleues et 2 jaunes. Quelle est la probabilité de piger une bille bleue?
• Choices: A) 1/2 B) 5/10 C) 1/4 D) 3/10
• Hint: Probability = favourable outcomes ÷ total outcomes; for 2 red out of 8 total: 2/8 = 1/4.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Blue marbles: 5.
  • Probability = 5/10 = 1/2.
• Answer: 1/2

[Hard] Two-Step Equation

• EN: Solve for x: 3x − 7 = 14.
• FR: Résous pour x : 3x − 7 = 14.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: For 2x − 3 = 7, first add 3 to both sides: 2x = 10, then divide by 2: x = 5.
• Steps:
  • Add 7 to both sides: 3x = 21.
  • Divide both sides by 3: x = 7.
  • The answer is x = 7.
• Answer: x = 7

[Hard] Integer Division Multi-Step

• EN: The temperature in Winnipeg drops 3°C every hour. If it starts at 4°C, what is the temperature after 8 hours?
• FR: La température à Winnipeg baisse de 3 °C par heure. Si elle commence à 4 °C, quelle est la température après 8 heures?
• Choices: A) −20°C B) −24°C C) −28°C D) −32°C
• Hint: For a starting temp of 6°C dropping 2°C per hour for 5 hours: 6 + (−2 × 5) = 6 − 10 = −4°C.
• Steps:
  • Total drop = 3 × 8 = 24°C.
  • Final temperature = 4 − 24 = −20°C.
  • The temperature is −20°C.
• Answer: −20°C

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To find √81, ask: what number times itself equals 81? 9 × 9 = 81, so √81 = 9.
• Steps:
  • Ask: what number times itself equals 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of: 8, 12, 10, 14, 6.
• FR: Trouve la moyenne de : 8, 12, 10, 14, 6.
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Mean = sum ÷ count; for 4, 6, 8, the sum is 18, count is 3, so mean = 18 ÷ 3 = 6.
• Steps:
  • Sum: 8 + 12 + 10 + 14 + 6 = 50.
  • Count: 5 values.
  • Mean = 50 ÷ 5 = 10.
• Answer: 10

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x : 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 9
• Hint: For 3x + 2 = 11, subtract 2 first: 3x = 9, then divide by 3: x = 3.
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide by 2: x = 4.
  • The answer is x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A hockey ticket costs $50 and the price increases by 10%. What is the new price?
• FR: Un billet de hockey coûte 50 $ et le prix augmente de 10%. Quel est le nouveau prix?
• Choices: A) $5 B) $45 C) $55 D) $60
• Hint: A 10% increase on $80 means adding $8, so the new price is $88.
• Steps:
  • 10% of $50 = $5.
  • New price = $50 + $5 = $55.
  • The new price is $55.
• Answer: $55

[Medium] Pythagorean Theorem

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

[Medium] Two-Step Equation

• EN: Solve for y: 4y − 3 = 17.
• FR: Résous pour y : 4y − 3 = 17.
• Choices: A) y = 3 B) y = 4 C) y = 5 D) y = 6
• Hint: For 5y − 2 = 13, add 2 first: 5y = 15, then divide by 5: y = 3.
• Steps:
  • Add 3 to both sides: 4y = 20.
  • Divide by 4: y = 5.
  • The answer is y = 5.
• Answer: y = 5

[Medium] Slope Introduction

• EN: A line passes through (0, 2) and (4, 10). What is the slope of the line?
• FR: Une droite passe par (0, 2) et (4, 10). Quel est le taux de variation de cette droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁); for (0,1) and (3,7): slope = 6 ÷ 3 = 2.
• Steps:
  • Rise = 10 − 2 = 8.
  • Run = 4 − 0 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Percent Decrease

• EN: A sweater originally costs $80. It goes on sale for 25% off. What is the sale price?
• FR: Un pull coûte originalement 80 $. Il est soldé à 25% de rabais. Quel est le prix de vente?
• Choices: A) $55 B) $60 C) $65 D) $70
• Hint: 25% off $40 means saving $10, so you pay $30 — find the discount then subtract.
• Steps:
  • 25% of $80 = $20.
  • Sale price = $80 − $20 = $60.
  • The sale price is $60.
• Answer: $60

[Hard] Pythagorean Theorem — Applied

• EN: A ladder is 13 m long and leans against a wall. Its base 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. Sa base est à 5 m du mur. À quelle hauteur la l'échelle atteint-elle le mur?
• Choices: A) 8 m B) 10 m C) 11 m D) 12 m
• Hint: Use a² + b² = c²; if the hypotenuse is 10 and one leg is 6, the other leg is √(100 − 36) = 8.
• Steps:
  • c² = a² + b²: 13² = 5² + h².
  • 169 = 25 + h², so h² = 144.
  • h = √144 = 12 m.
• Answer: 12 m

[Hard] Median and Mode

• EN: Find the median and mode of: 5, 3, 8, 3, 9, 7, 3. What is the median?
• FR: Trouve la médiane et le mode de : 5, 3, 8, 3, 9, 7, 3. Quelle est la médiane?
• Choices: A) 3 B) 5 C) 7 D) 8
• Hint: To find the median of 2, 4, 4, 6, 9, arrange in order — the middle value (4th of 7 is not needed here; middle of 5 values is the 3rd) gives the median.
• Steps:
  • Arrange in order: 3, 3, 3, 5, 7, 8, 9.
  • There are 7 values; the middle (4th) value is 5.
  • The median is 5.
• Answer: 5

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 3 = 22.
• FR: Résous pour x : 5x − 3 = 22.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: For 4x − 2 = 14, add 2: 4x = 16, then divide by 4: x = 4.
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 5.
  • The answer is x = 5.
• Answer: x = 5

[Easy] Graphing Lines — Slope-Intercept

• EN: What is the y-intercept of the line y = 3x + 7?
• FR: Quel est l'ordonnée à l'origine de la droite y = 3x + 7?
• Choices: A) 3 B) 7 C) −3 D) −7
• Hint: In y = mx + b, the y-intercept is b — for y = 2x + 5, the y-intercept is 5.
• Steps:
  • The equation is in the form y = mx + b.
  • Here, m = 3 and b = 7.
  • The y-intercept is 7.
• Answer: 7

[Easy] Adding Polynomials

• EN: Add: (3x + 5) + (2x − 1).
• FR: Additionne : (3x + 5) + (2x − 1).
• Choices: A) 5x + 4 B) 5x + 6 C) 6x + 4 D) 5x − 4
• Hint: To add (4x + 2) + (x + 3), combine like terms: 4x + x = 5x and 2 + 3 = 5, so 5x + 5.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−1) = 4.
  • The answer is 5x + 4.
• Answer: 5x + 4

[Easy] Linear Inequality

• EN: Solve for x: x + 4 > 9.
• FR: Résous pour x : x + 4 > 9.
• Choices: A) x > 4 B) x > 5 C) x < 5 D) x > 13
• Hint: For x + 3 > 7, subtract 3 from both sides: x > 4.
• Steps:
  • Subtract 4 from both sides.
  • x > 9 − 4.
  • x > 5.
• Answer: x > 5

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 4).
• FR: Développe : (x + 3)(x + 4).
• Choices: A) x² + 7x + 12 B) x² + 12x + 7 C) x² + 7x + 7 D) x² + 12
• Hint: To expand (x + 2)(x + 5), use FOIL: x² + 5x + 2x + 10 = x² + 7x + 10.
• Steps:
  • FOIL: x·x = x², x·4 = 4x, 3·x = 3x, 3·4 = 12.
  • Combine: x² + 4x + 3x + 12 = x² + 7x + 12.
  • The answer is x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 6 cm and 9 cm. If the smaller triangle has a second side of 8 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 6 cm et 9 cm. Si le plus petit triangle a un autre côté de 8 cm, quel est le côté correspondant du plus grand triangle?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 14 cm
• Hint: Set up a proportion; if sides are in ratio 2:3 and one side is 4, the other is 4 × (3/2) = 6.
• Steps:
  • Scale factor = 9/6 = 3/2.
  • Corresponding side = 8 × (3/2) = 12.
  • The side is 12 cm.
• Answer: 12 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 5 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 5 cm et l'hypoténuse est 10 cm. Combien fait sin(θ)?
• Choices: A) 0.25 B) 0.5 C) 0.75 D) 2.0
• Hint: SOH means sin = opposite ÷ hypotenuse; for opposite = 3, hypotenuse = 6, sin = 0.5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 5 ÷ 10 = 0.5.
  • sin(θ) = 0.5.
• Answer: 0.5

[Medium] Subtracting Polynomials

• EN: Subtract: (6x² + 4x − 2) − (2x² + x − 5).
• FR: Soustrait : (6x² + 4x − 2) − (2x² + x − 5).
• Choices: A) 4x² + 3x + 3 B) 4x² + 5x − 7 C) 8x² + 3x + 3 D) 4x² + 3x − 7
• Hint: For (5x² + 3x) − (2x² + x), distribute the minus: 5x² − 2x² = 3x² and 3x − x = 2x.
• Steps:
  • Distribute the minus: 6x² + 4x − 2 − 2x² − x + 5.
  • Combine x² terms: 6x² − 2x² = 4x².
  • Combine x terms: 4x − x = 3x; constants: −2 + 5 = 3. Result: 4x² + 3x + 3.
• Answer: 4x² + 3x + 3

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 7 cm and the adjacent side is 7 cm. What is the angle θ (in degrees)?
• FR: Dans un triangle rectangle, le côté opposé est 7 cm et le côté adjacent est 7 cm. Quel est l'angle θ (en degrés)?
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: tan(θ) = opposite ÷ adjacent; if both sides are equal, tan(θ) = 1, and tan(45°) = 1.
• Steps:
  • tan(θ) = opposite ÷ adjacent = 7 ÷ 7 = 1.
  • θ = arctan(1) = 45°.
  • The angle is 45°.
• Answer: 45°

[Hard] Linear Equation — Multi-Step

• EN: Solve for x: 4(x − 2) = 2(x + 6).
• FR: Résous pour x : 4(x − 2) = 2(x + 6).
• Choices: A) x = 8 B) x = 10 C) x = 12 D) x = 14
• Hint: For 3(x − 1) = 2(x + 2), expand: 3x − 3 = 2x + 4, then x = 7.
• Steps:
  • Expand: 4x − 8 = 2x + 12.
  • Subtract 2x: 2x − 8 = 12.
  • Add 8: 2x = 20, so x = 10.
• Answer: x = 10

[Easy] Factoring Quadratics

• 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: For x² + 7x + 12, find two numbers that multiply to 12 and add to 7: 3 and 4 — so (x + 3)(x + 4).
• Steps:
  • Find two numbers that multiply to 6 and add to 5: 2 and 3.
  • So x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 6 cm and the hypotenuse is 10 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent est 6 cm et l'hypoténuse est 10 cm. Combien fait cos(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: CAH means cos = adjacent ÷ hypotenuse; for adjacent = 4 and hypotenuse = 8, cos = 0.5.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 6 ÷ 10 = 0.6.
  • cos(θ) = 0.6.
• Answer: 0.6

[Easy] System of Equations — Substitution

• EN: Solve: y = 2x and x + y = 9. What is the value of x?
• FR: Résous : 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.
  • The value of x is 3.
• Answer: x = 3

[Easy] Volume of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 10 cm. Use π ≈ 3.14. What is its volume?
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 10 cm. Utilise π ≈ 3,14. Quel est son volume?
• Choices: A) 188.4 cm³ B) 282.6 cm³ C) 94.2 cm³ D) 376.8 cm³
• Hint: Volume of a cylinder = π × r² × h; for r = 2 and h = 5: 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 3² × 10.
  • = 3.14 × 9 × 10 = 3.14 × 90.
  • V = 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Completing the Square

• EN: Write x² + 6x + 5 in completed square form. What is the completed square portion?
• FR: Écris x² + 6x + 5 sous forme de carré complété. Quelle est la partie du carré complété?
• Choices: A) (x + 2)² − 3 B) (x + 3)² − 4 C) (x + 3)² − 9 D) (x + 6)² − 5
• Hint: For x² + 4x + 3, half of 4 is 2; (x + 2)² = x² + 4x + 4, so x² + 4x + 3 = (x + 2)² − 1.
• Steps:
  • Half of 6 is 3; (x + 3)² = x² + 6x + 9.
  • x² + 6x + 5 = (x + 3)² − 9 + 5 = (x + 3)² − 4.
  • The completed square form is (x + 3)² − 4.
• Answer: (x + 3)² − 4

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is its circumference? Use π ≈ 3.14.
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence? Utilise π ≈ 3,14.
• Choices: A) 21.98 cm B) 43.96 cm C) 87.92 cm D) 153.86 cm
• Hint: Circumference = π × diameter; for a diameter of 10: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14.
  • 3.14 × 14 = 43.96.
  • The circumference is 43.96 cm.
• Answer: 43.96 cm

[Medium] Quadratic Equation — Factoring

• EN: Solve: x² − 7x + 12 = 0. What are the solutions?
• FR: Résous : x² − 7x + 12 = 0. Quelles sont les solutions?
• Choices: A) x = 2 and x = 6 B) x = 3 and x = 4 C) x = 1 and x = 12 D) x = −3 and x = −4
• Hint: For x² − 5x + 6 = 0, find two numbers that multiply to 6 and add to −5: −2 and −3, so (x − 2)(x − 3) = 0.
• Steps:
  • Find two numbers that multiply to 12 and add to −7: −3 and −4.
  • (x − 3)(x − 4) = 0.
  • x = 3 or x = 4.
• Answer: x = 3 and x = 4

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 5 cm and a slant height of 13 cm. Use π ≈ 3.14. What is its lateral surface area?
• FR: Un cône a un rayon de 5 cm et une hauteur oblique de 13 cm. Utilise π ≈ 3,14. Quelle est son aire latérale?
• Choices: A) 188.4 cm² B) 204.1 cm² C) 245.0 cm² D) 314.0 cm²
• Hint: Lateral surface area of cone = π × r × l; for r = 3 and l = 5: 3.14 × 3 × 5 = 47.1 cm².
• Steps:
  • Lateral SA = π × r × l = 3.14 × 5 × 13.
  • = 3.14 × 65.
  • Lateral SA = 204.1 cm².
• Answer: 204.1 cm²

[Hard] System of Equations — Elimination

• EN: Solve: 2x + 3y = 12 and 4x − y = 10. What is the value of y?
• FR: Résous : 2x + 3y = 12 et 4x − y = 10. Quelle est la valeur de y?
• Choices: A) y = 1 B) y = 2 C) y = 3 D) y = 4
• Hint: To eliminate x from 3x + y = 7 and 3x − 2y = 1, subtract the equations: 3y = 6, so y = 2.
• Steps:
  • Multiply the second equation by 3: 12x − 3y = 30.
  • Add to the first: (2x + 3y) + (12x − 3y) = 12 + 30 → 14x = 42 → x = 3.
  • Substitute x = 3 into 4(3) − y = 10: 12 − y = 10, so y = 2.
• Answer: y = 2

[Hard] Quadratic — Real-World Application

• EN: A ball is thrown upward. Its height in metres is given by h = −5t² + 20t. At what time t (in seconds) does the ball reach the ground again (h = 0, t > 0)?
• FR: Un ballon est lancé vers le haut. Sa hauteur en mètres est h = −5t² + 20t. À quel moment t (en secondes) le ballon touche-t-il de nouveau le sol (h = 0, t > 0)?
• Choices: A) t = 2 seconds B) t = 4 seconds C) t = 5 seconds D) t = 8 seconds
• Hint: Factor −5t² + 20t = 0 as −5t(t − 4) = 0; then t = 0 or t equals the other factor.
• Steps:
  • Set h = 0: −5t² + 20t = 0.
  • Factor: −5t(t − 4) = 0.
  • t = 0 (launch) or t = 4 seconds (lands).
• Answer: t = 4 seconds

[Easy] Exponential Functions

• EN: A bacteria culture doubles every hour. Starting with 50 bacteria, how many are there after 3 hours?
• FR: Une culture de bactéries double chaque heure. En partant de 50 bactéries, combien y en a-t-il après 3 heures?
• Choices: A) 200 B) 300 C) 400 D) 150
• Hint: Doubling 3 times means multiplying by 2³ = 8; if you start with 10, you get 10 × 8 = 80.
• Steps:
  • After 1 hour: 50 × 2 = 100.
  • After 2 hours: 100 × 2 = 200.
  • After 3 hours: 200 × 2 = 400.
• Answer: 400

[Easy] Arithmetic Sequence

• EN: The sequence is 4, 9, 14, 19, … What is the 6th term?
• FR: La suite est 4, 9, 14, 19, … Quel est le 6e terme?
• Choices: A) 24 B) 27 C) 29 D) 34
• Hint: For sequence 3, 7, 11, … with common difference 4, the nth term = 3 + (n−1) × 4.
• Steps:
  • Common difference = 5.
  • 6th term = 4 + (6 − 1) × 5 = 4 + 25 = 29.
  • The 6th term is 29.
• Answer: 29

[Easy] Logarithms — Basic

• EN: What is log₂(8)?
• FR: Combien fait log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: logₐ(b) asks: what power must a be raised to in order to get b? For log₂(16): 2⁴ = 16, so the answer is 4.
• Steps:
  • log₂(8) asks: 2 to what power equals 8?
  • 2³ = 8.
  • log₂(8) = 3.
• Answer: 3

[Easy] Compound Interest — Basic

• EN: $1000 is invested at 5% annual interest, compounded annually. What is the amount after 1 year?
• FR: 1 000 $ est investi à 5% d'intérêt annuel, composé annuellement. Quel est le montant après 1 an?
• Choices: A) $1050 B) $1100 C) $1005 D) $1150
• Hint: For compound interest after 1 year: A = P × (1 + r); for $500 at 4%, A = 500 × 1.04 = $520.
• Steps:
  • A = P(1 + r)ⁿ = 1000 × (1 + 0.05)¹.
  • A = 1000 × 1.05 = $1050.
  • The amount after 1 year is $1050.
• Answer: $1050

[Medium] Quadratic Function — Vertex

• EN: Find the vertex of the parabola y = 2(x − 3)² + 5.
• FR: Trouve le sommet de la parabole y = 2(x − 3)² + 5.
• Choices: A) (3, 5) B) (−3, 5) C) (3, −5) D) (2, 5)
• Hint: For y = a(x − h)² + k, the vertex is at (h, k) — for y = (x − 1)² + 4, the vertex is (1, 4).
• Steps:
  • The equation is in vertex form y = a(x − h)² + k.
  • Here h = 3 and k = 5.
  • The vertex is (3, 5).
• Answer: (3, 5)

[Medium] Geometric Series Sum

• EN: Find the sum of the first 4 terms of the geometric series: 3, 6, 12, 24.
• FR: Trouve la somme des 4 premiers termes de la suite géométrique : 3, 6, 12, 24.
• Choices: A) 42 B) 45 C) 48 D) 51
• Hint: For a geometric series with first term 2 and ratio 3, the sum of 3 terms is 2 + 6 + 18 = 26.
• Steps:
  • Sum = 3 + 6 + 12 + 24.
  • 3 + 6 = 9, 9 + 12 = 21, 21 + 24 = 45.
  • The sum is 45.
• Answer: 45

[Medium] Compound Interest — Multi-Year

• EN: $2000 is invested at 6% compounded annually. What is the amount after 2 years?
• FR: 2 000 $ est investi à 6% composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $2247.20 B) $2240.00 C) $2200.00 D) $2120.00
• Hint: A = P(1 + r)ⁿ; for $1000 at 10% for 2 years: A = 1000 × 1.1² = 1000 × 1.21 = $1210.
• Steps:
  • A = 2000 × (1.06)².
  • 1.06² = 1.1236.
  • A = 2000 × 1.1236 = $2247.20.
• Answer: $2247.20

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifie : sin²(θ) + cos²(θ).
• Choices: A) 0 B) 1 C) 2 D) sin(θ)
• Hint: This is the most fundamental trig identity — think of it as the Pythagorean theorem applied to a unit circle.
• Steps:
  • The Pythagorean identity states: sin²(θ) + cos²(θ) = 1.
  • This is true for all values of θ.
  • The simplified result is 1.
• Answer: 1

[Hard] Logarithm Laws

• EN: Simplify: log₃(27) + log₃(9).
• FR: Simplifie : log₃(27) + log₃(9).
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: log rule: logₐ(m) + logₐ(n) = logₐ(mn); for log₂(4) + log₂(8) = log₂(32) = 5.
• Steps:
  • log₃(27) = 3, because 3³ = 27.
  • log₃(9) = 2, because 3² = 9.
  • Sum = 3 + 2 = 5.
• Answer: 5

[Hard] Annuity Problem

• EN: Priya saves $200 at the end of each month for 3 months at 6% annual interest (0.5% per month). What is the total value of the annuity at the end of 3 months?
• FR: Priya épargne 200 $ à la fin de chaque mois pendant 3 mois à un taux annuel de 6% (0,5% par mois). Quelle est la valeur totale de la rente à la fin de 3 mois?
• Choices: A) $600.00 B) $603.01 C) $606.04 D) $612.08
• Hint: Each payment earns interest for a different number of periods — the last payment earns 0 periods of interest, the first earns 2 periods.
• Steps:
  • Payment 1 (at end of month 1) grows for 2 months: 200 × 1.005² = 200 × 1.010025 = $202.01.
  • Payment 2 (end of month 2) grows for 1 month: 200 × 1.005 = $201.00.
  • Payment 3 (end of month 3) grows for 0 months: $200.00. Total = $202.01 + $201.00 + $200.00 = $603.01.
• Answer: $603.01

[Easy] Permutations

• EN: How many ways can 4 students be arranged in a line?
• FR: De combien de façons peut-on placer 4 élèves en ligne?
• Choices: A) 12 B) 16 C) 24 D) 48
• Hint: To arrange 3 items: 3 × 2 × 1 = 6 ways — this is 3! (3 factorial).
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 12 × 2 = 24.
  • There are 24 arrangements.
• Answer: 24

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 5?
• FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 5?
• Choices: A) 8 B) 10 C) 20 D) 25
• Hint: C(n,r) = n! ÷ (r! × (n−r)!); for C(4,2): 4! ÷ (2! × 2!) = 24 ÷ 4 = 6.
• Steps:
  • C(5,2) = 5! ÷ (2! × 3!) = 120 ÷ (2 × 6) = 120 ÷ 12 = 10.
  • There are 10 ways.
• Answer: 10

[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) 3x C) 3x² D) x⁴
• Hint: The power rule says: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹; for f(x) = x⁴, f'(x) = 4x³.
• Steps:
  • Apply the power rule: f'(x) = 3 × x^(3−1).
  • f'(x) = 3x².
  • The derivative is 3x².
• Answer: 3x²

[Easy] Rational Function — Domain

• EN: What value of x makes the rational function f(x) = 1 ÷ (x − 4) undefined?
• FR: Quelle valeur de x rend la fonction rationnelle f(x) = 1 ÷ (x − 4) indéfinie?
• Choices: A) x = 0 B) x = 1 C) x = 4 D) x = −4
• Hint: A rational function is undefined where its denominator equals zero — for 1/(x − 3), set x − 3 = 0, so x = 3.
• Steps:
  • Set the denominator equal to zero: x − 4 = 0.
  • Solve: x = 4.
  • The function is undefined at x = 4.
• Answer: x = 4

[Medium] Polynomial Function — End Behaviour

• EN: For the polynomial f(x) = −2x⁴ + 3x − 1, what is the end behaviour as x → +∞?
• FR: Pour le polynôme f(x) = −2x⁴ + 3x − 1, quel est le comportement de la fonction lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: For a polynomial with an even degree and negative leading coefficient, both ends go down — like an upside-down parabola.
• Steps:
  • Leading term is −2x⁴ (even degree, negative coefficient).
  • As x → +∞, −2x⁴ → −∞.
  • So f(x) → −∞.
• Answer: f(x) → −∞

[Medium] Derivative — Rate of Change

• EN: The position of a particle is s(t) = 3t² − 2t + 1. What is the velocity at t = 4?
• FR: La position d'une particule est s(t) = 3t² − 2t + 1. Quelle est la vitesse à t = 4?
• Choices: A) 20 B) 22 C) 24 D) 26
• Hint: Velocity = s'(t); differentiate using the power rule: for s(t) = 2t² + t, s'(t) = 4t + 1.
• Steps:
  • s'(t) = 6t − 2.
  • At t = 4: s'(4) = 6(4) − 2 = 24 − 2 = 22.
  • The velocity at t = 4 is 22.
• Answer: 22

[Medium] Probability Distribution

• EN: A fair die is rolled. What is the expected value (mean) of the outcome?
• FR: On lance un dé équitable. Quelle est la valeur attendue (moyenne) du résultat?
• Choices: A) 3 B) 3.5 C) 4 D) 4.5
• Hint: Expected value = sum of (outcome × probability); for a fair coin, E = 0×0.5 + 1×0.5 = 0.5.
• Steps:
  • Outcomes: 1, 2, 3, 4, 5, 6, each with probability 1/6.
  • E = (1 + 2 + 3 + 4 + 5 + 6)/6 = 21/6 = 3.5.
  • The expected value is 3.5.
• Answer: 3.5

[Medium] Vectors — Addition

• EN: Vector a = (3, 4) and vector b = (−1, 2). What is a + b?
• FR: Le vecteur a = (3, 4) et le vecteur b = (−1, 2). Combien font a + b?
• Choices: A) (2, 6) B) (4, 2) C) (2, 8) D) (4, 6)
• Hint: To add vectors (1, 3) and (2, −1), add x-components and y-components separately: (3, 2).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 4 + 2 = 6.
  • a + b = (2, 6).
• Answer: (2, 6)

[Hard] Binomial Probability

• EN: A basketball player makes 70% of free throws. If she takes 5 shots, what is the probability she makes exactly 4 of them? (Round to 3 decimal places.)
• FR: Une joueuse de basketball réussit 70% de ses lancers francs. Si elle prend 5 lancers, quelle est la probabilité qu'elle en réussisse exactement 4? (Arrondis à 3 décimales.)
• Choices: A) 0.240 B) 0.360 C) 0.360 D) 0.168
• Hint: Use P(X = k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ; for n = 4, k = 2, p = 0.5: C(4,2) × 0.25 × 0.25 = 6 × 0.0625 = 0.375.
• Steps:
  • P(X = 4) = C(5,4) × (0.7)⁴ × (0.3)¹.
  • C(5,4) = 5; (0.7)⁴ = 0.2401; (0.3)¹ = 0.3.
  • P = 5 × 0.2401 × 0.3 = 5 × 0.07203 = 0.360.
• Answer: 0.360

[Hard] Derivative — Optimization

• EN: The profit function of a small Canadian business is P(x) = −x² + 10x − 16, where x is the number of items sold (in hundreds). How many items (in hundreds) maximize the profit?
• FR: La fonction de profit d'une petite entreprise canadienne est P(x) = −x² + 10x − 16, où x est le nombre d'articles vendus (en centaines). Combien d'articles (en centaines) maximisent le profit?
• Choices: A) x = 4 hundreds B) x = 5 hundreds C) x = 6 hundreds D) x = 8 hundreds
• Hint: Set P'(x) = 0 to find the maximum; for P(x) = −x² + 8x, P'(x) = −2x + 8 = 0, so x = 4.
• Steps:
  • Find P'(x): P'(x) = −2x + 10.
  • Set equal to zero: −2x + 10 = 0 → x = 5.
  • Maximum profit occurs at x = 5 hundreds.
• Answer: x = 5 hundreds