Daily Math — 2026-08-06

[Easy] Counting Pucks

• EN: There are 7 hockey pucks on the ice. 3 more pucks slide over. How many pucks are there now?
• FR: Il y a 7 rondelles de hockey sur la glace. 3 autres rondelles arrivent. Combien y a-t-il de rondelles maintenant?
• Choices: A) 8 pucks B) 9 pucks C) 10 pucks D) 11 pucks
• Hint: To add, count on from the bigger number — for example, 5 + 2: start at 5 and count 2 more.
• Steps:
  • Start at 7 and count on 3 more.
  • 7 → 8, 9, 10.
  • So there are 10 pucks in all.
• Answer: 10 pucks

[Easy] Pennies in a Jar

• EN: Maya has 6 pennies. She finds 4 more pennies. How many pennies does she have in all?
• FR: Maya a 6 sous. Elle trouve 4 autres sous. Combien de sous a-t-elle en tout?
• Choices: A) 8 pennies B) 9 pennies C) 10 pennies D) 11 pennies
• Hint: To add two numbers, count on from the larger one — for example, 8 + 3 means start at 8 and count 3 more.
• Steps:
  • Start at 6, which is the bigger number.
  • Count on 4 more: 7, 8, 9, 10.
  • So Maya has 10 pennies.
• Answer: 10 pennies

[Easy] Skip Counting by 5s

• EN: Count by 5s. What number comes after 15?
• FR: Compte par 5. Quel nombre vient après 15?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: When skip counting by 5s, each number goes up by 5 — for example, after 10 comes 15.
• Steps:
  • The pattern is 5, 10, 15, ...
  • Add 5 to 15: 15 + 5 = 20.
  • The next number is 20.
• Answer: 20

[Easy] Fewer Mittens

• EN: There are 9 mittens on the shelf. 4 mittens fall off. How many mittens are left?
• FR: Il y a 9 mitaines sur l'étagère. 4 mitaines tombent. Combien de mitaines reste-t-il?
• Choices: A) 3 mittens B) 4 mittens C) 5 mittens D) 6 mittens
• Hint: To subtract, count back from the starting number — for example, 8 − 3: start at 8 and count back 3.
• Steps:
  • Start at 9 and count back 4.
  • 9 → 8, 7, 6, 5.
  • So 5 mittens are left.
• Answer: 5 mittens

[Medium] Comparing Numbers

• EN: Which number is greater: 14 or 18?
• FR: Quel nombre est plus grand : 14 ou 18?
• Choices: A) 12 B) 14 C) 16 D) 18
• Hint: On a number line, the number farther to the right is greater — for example, 7 is greater than 4.
• Steps:
  • Place 14 and 18 on a number line.
  • 18 is farther to the right than 14.
  • So 18 is greater.
• Answer: 18

[Medium] Nickels

• EN: Liam has 3 nickels. How many cents does he have in all?
• FR: Liam a 3 pièces de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 3 cents B) 10 cents C) 15 cents D) 20 cents
• Hint: Each nickel is worth 5 cents — skip count by 5s to find the total, for example, 2 nickels = 10 cents.
• Steps:
  • Each nickel = 5 cents.
  • Skip count by 5s for 3 nickels: 5, 10, 15.
  • Liam has 15 cents.
• Answer: 15 cents

[Medium] Tims Muffins

• EN: There are 12 muffins at Tim Hortons. 5 are sold. How many muffins are left?
• FR: Il y a 12 muffins au Tim Hortons. On en vend 5. Combien de muffins reste-t-il?
• Choices: A) 6 muffins B) 7 muffins C) 8 muffins D) 9 muffins
• Hint: To subtract, count back from the starting number — for example, 10 − 4 = 6.
• Steps:
  • Start at 12 and subtract 5.
  • 12 − 5 = 7.
  • So 7 muffins are left.
• Answer: 7 muffins

[Medium] Skip Counting by 2s

• EN: Ava counts by 2s starting at 2. What is the 5th number she says?
• FR: Ava compte par 2 en commençant à 2. Quel est le 5e nombre qu'elle dit?
• Choices: A) 8 B) 9 C) 10 D) 12
• Hint: Skip counting by 2s means adding 2 each time — for example, 2, 4, 6 are the first three numbers.
• Steps:
  • 1st number: 2, 2nd: 4, 3rd: 6, 4th: 8, 5th: 10.
  • The 5th number Ava says is 10.
• Answer: 10

[Hard] Adding Three Numbers

• EN: Noah puts 4 red blocks, 5 blue blocks, and 3 yellow blocks in a bag. How many blocks are in the bag?
• FR: Noah met 4 blocs rouges, 5 blocs bleus et 3 blocs jaunes dans un sac. Combien y a-t-il de blocs en tout?
• Choices: A) 10 blocks B) 11 blocks C) 12 blocks D) 13 blocks
• Hint: To add three numbers, add any two first, then add the third — for example, 3 + 3 + 2 = 6 + 2 = 8.
• Steps:
  • Add 4 + 5 = 9.
  • Then add 9 + 3 = 12.
  • There are 12 blocks in the bag.
• Answer: 12 blocks

[Hard] Numbers to 100

• EN: What number is 10 more than 67?
• FR: Quel nombre est 10 de plus que 67?
• Choices: A) 57 B) 68 C) 76 D) 77
• Hint: Adding 10 to any number just increases the tens digit by 1 — for example, 10 more than 34 is 44.
• Steps:
  • Start at 67.
  • Add 10: the tens digit goes from 6 to 7.
  • 67 + 10 = 77.
• Answer: 77

[Easy] Adding to 100

• EN: There are 34 students at recess and 23 more come outside. How many students are outside now?
• FR: Il y a 34 élèves à la récréation et 23 de plus sortent. Combien d'élèves sont dehors maintenant?
• Choices: A) 55 students B) 57 students C) 58 students D) 61 students
• Hint: To add two-digit numbers, add the tens first then the ones — for example, 21 + 15: 20 + 10 = 30, then 1 + 5 = 6, so 36.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 3 = 7.
  • 50 + 7 = 57 students.
• Answer: 57 students

[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 petite aiguille sur le 3 et la grande aiguille sur le 12. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 12:03
• Hint: When the minute hand is on 12, it is exactly on the hour — for example, hour hand on 7 = 7:00.
• Steps:
  • The minute hand on 12 means it is exactly on the hour.
  • The hour hand is on 3.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Subtracting within 100

• EN: There are 50 crayons in a box. 18 crayons are taken out. How many crayons remain?
• FR: Il y a 50 crayons dans une boîte. On en retire 18. Combien de crayons reste-t-il?
• Choices: A) 28 crayons B) 32 crayons C) 38 crayons D) 42 crayons
• Hint: To subtract, count back or use place value — for example, 40 − 12 = 28.
• Steps:
  • 50 − 18: subtract the ones first.
  • 50 − 10 = 40, then 40 − 8 = 32.
  • 32 crayons remain.
• Answer: 32 crayons

[Easy] Measuring Length

• EN: Zoe measures her pencil and it is 15 cm long. Her eraser is 3 cm long. How much longer is the pencil than the eraser?
• FR: Zoé mesure son crayon et il a 15 cm de long. Sa gomme a 3 cm de long. De combien le crayon est-il plus long que la gomme?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 18 cm
• Hint: To find how much longer, subtract the smaller length from the bigger one — for example, 9 cm − 4 cm = 5 cm.
• Steps:
  • Subtract: 15 cm − 3 cm.
  • 15 − 3 = 12.
  • The pencil is 12 cm longer.
• Answer: 12 cm

[Medium] Counting Coins

• EN: Ben has 2 dimes and 3 nickels. How much money does he have in total?
• FR: Ben a 2 pièces de 10 cents et 3 pièces de 5 cents. Combien d'argent a-t-il en tout?
• Choices: A) 25 cents B) 30 cents C) 35 cents D) 40 cents
• Hint: Count the dimes first (10 cents each), then add the nickels (5 cents each) — for example, 1 dime + 2 nickels = 10 + 10 = 20 cents.
• Steps:
  • 2 dimes = 20 cents.
  • 3 nickels = 15 cents.
  • 20 + 15 = 35 cents.
• Answer: 35 cents

[Medium] Half-Hour Time

• EN: Mia starts reading at 2:00. She reads for half an hour. What time does she finish?
• FR: Mia commence à lire à 2 h. Elle lit pendant une demi-heure. À quelle heure finit-elle?
• Choices: A) 2:15 B) 2:30 C) 3:00 D) 3:30
• Hint: Half an hour is 30 minutes — for example, 4:00 plus half an hour is 4:30.
• Steps:
  • Start at 2:00.
  • Add 30 minutes (half an hour).
  • 2:00 + 30 minutes = 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 patron : 5, 10, 15, 20, ___. Quel est le nombre manquant?
• Choices: A) 22 B) 23 C) 24 D) 25
• Hint: Find the rule by looking at how much the numbers increase each time — for example, 2, 4, 6, 8 increases by 2.
• Steps:
  • Each number increases by 5.
  • 20 + 5 = 25.
  • The missing number is 25.
• Answer: 25

[Medium] Subtraction within 100

• EN: A bag has 73 marbles. 29 marbles are given away. How many marbles are left?
• FR: Un sac contient 73 billes. On en donne 29. Combien de billes reste-t-il?
• Choices: A) 34 marbles B) 44 marbles C) 46 marbles D) 54 marbles
• Hint: To subtract with regrouping, break apart the number — for example, 52 − 28: think 52 − 20 = 32, then 32 − 8 = 24.
• Steps:
  • 73 − 29: subtract 20 first: 73 − 20 = 53.
  • Then subtract 9: 53 − 9 = 44.
  • 44 marbles are left.
• Answer: 44 marbles

[Hard] Measuring and Adding

• EN: A garden path is 48 cm long. Workers add another 35 cm to it. How long is the path now?
• FR: Un chemin de jardin a 48 cm de long. Les ouvriers y ajoutent 35 cm. Quelle est maintenant la longueur du chemin?
• Choices: A) 73 cm B) 80 cm C) 83 cm D) 93 cm
• Hint: Add the tens then the ones, regrouping if needed — for example, 37 + 46: 30 + 40 = 70, 7 + 6 = 13, so 70 + 13 = 83.
• Steps:
  • Add the tens: 40 + 30 = 70.
  • Add the ones: 8 + 5 = 13.
  • 70 + 13 = 83 cm.
• Answer: 83 cm

[Hard] Multi-Step Coins

• EN: Priya has 4 dimes, 2 nickels, and 3 pennies. How much money does she have altogether?
• FR: Priya a 4 pièces de 10 cents, 2 pièces de 5 cents et 3 sous. Combien d'argent a-t-elle en tout?
• Choices: A) 45 cents B) 50 cents C) 53 cents D) 58 cents
• Hint: Find the value of each type of coin, then add all three amounts — for example, 2 dimes + 1 nickel + 2 pennies = 20 + 5 + 2 = 27 cents.
• Steps:
  • 4 dimes = 40 cents; 2 nickels = 10 cents; 3 pennies = 3 cents.
  • 40 + 10 = 50, then 50 + 3 = 53.
  • Priya has 53 cents.
• Answer: 53 cents

[Easy] Multiplication by 5

• EN: There are 4 bags of apples. Each bag has 5 apples. How many apples are there in all?
• FR: Il y a 4 sacs de pommes. Chaque sac contient 5 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 15 apples B) 18 apples C) 20 apples D) 25 apples
• Hint: Multiplication is repeated addition — for example, 3 × 5 means 5 + 5 + 5 = 15.
• Steps:
  • 4 groups of 5: 4 × 5.
  • 4 × 5 = 20.
  • There are 20 apples in all.
• Answer: 20 apples

[Easy] Basic Division

• EN: A teacher has 12 stickers to share equally among 3 students. How many stickers does each student get?
• FR: Une enseignante a 12 autocollants à partager également entre 3 élèves. Combien d'autocollants chaque élève reçoit-il?
• Choices: A) 3 stickers B) 4 stickers C) 5 stickers D) 6 stickers
• Hint: To divide, think of the matching multiplication fact — for example, 10 ÷ 2: ask yourself 2 × ? = 10.
• Steps:
  • 12 ÷ 3: ask 3 × ? = 12.
  • 3 × 4 = 12.
  • Each student gets 4 stickers.
• Answer: 4 stickers

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. Leo eats 1 piece. What fraction of the pizza did he eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Léo mange 1 morceau. Quelle fraction de la pizza a-t-il mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: A fraction shows part of a whole — the bottom number is how many equal parts total, the top is how many you have.
• Steps:
  • The pizza is cut into 2 equal pieces — so the denominator is 2.
  • Leo eats 1 piece — so the numerator is 1.
  • He ate 1/2 of the pizza.
• Answer: 1/2

[Easy] Multiplication by 2

• EN: A hockey team has 6 players on each side. How many players are on the ice in total (both teams)?
• FR: Une équipe de hockey a 6 joueurs de chaque côté. Combien y a-t-il de joueurs sur la glace en tout (les deux équipes)?
• Choices: A) 8 players B) 10 players C) 12 players D) 14 players
• Hint: Multiply by 2 for two equal groups — for example, 2 × 5 = 10.
• Steps:
  • 2 teams × 6 players = 2 × 6.
  • 2 × 6 = 12.
  • There are 12 players on the ice.
• Answer: 12 players

[Medium] Perimeter

• EN: A rectangular garden is 8 m long and 3 m wide. What is its perimeter?
• FR: Un jardin rectangulaire a 8 m de long et 3 m de large. Quel est son périmètre?
• Choices: A) 11 m B) 22 m C) 24 m D) 30 m
• Hint: To find the perimeter of a rectangle, add all four sides — for example, a 5 m × 2 m rectangle: 5 + 2 + 5 + 2 = 14 m.
• Steps:
  • Perimeter = length + width + length + width.
  • 8 + 3 + 8 + 3 = 22.
  • The perimeter is 22 m.
• Answer: 22 m

[Medium] Multiplication by 4

• EN: A shelf holds 4 rows of books with 7 books in each row. How many books are on the shelf?
• FR: Une étagère a 4 rangées de livres avec 7 livres dans chaque rangée. Combien y a-t-il de livres sur l'étagère?
• Choices: A) 24 books B) 27 books C) 28 books D) 32 books
• Hint: Multiply the number of rows by the number in each row — for example, 3 rows of 6 books = 3 × 6 = 18.
• Steps:
  • 4 rows × 7 books = 4 × 7.
  • 4 × 7 = 28.
  • There are 28 books on the shelf.
• Answer: 28 books

[Medium] Reading a Bar Graph

• EN: A bar graph shows that the Maple Leafs scored 6 goals on Monday, 4 on Tuesday, and 3 on Wednesday. How many goals did they score in total?
• FR: Un diagramme à bandes montre que les Maple Leafs ont marqué 6 buts lundi, 4 mardi et 3 mercredi. Combien de buts ont-ils marqué en tout?
• Choices: A) 11 goals B) 12 goals C) 13 goals D) 14 goals
• Hint: To find the total from a graph, add all the values together — for example, 5 + 3 + 4 = 12.
• Steps:
  • Add Monday + Tuesday + Wednesday.
  • 6 + 4 + 3 = 13.
  • They scored 13 goals in total.
• Answer: 13 goals

[Medium] Fractions — One Quarter

• EN: A ribbon is cut into 4 equal pieces. Sara keeps 1 piece. What fraction of the ribbon does Sara have?
• FR: Un ruban est coupé en 4 morceaux égaux. Sara garde 1 morceau. Quelle fraction du ruban Sara possède-t-elle?
• Choices: A) 1/5 B) 1/4 C) 1/3 D) 1/2
• Hint: The denominator is the total number of equal parts — for example, cut into 3 parts means denominator is 3.
• Steps:
  • The ribbon is cut into 4 equal parts — denominator = 4.
  • Sara keeps 1 part — numerator = 1.
  • Sara has 1/4 of the ribbon.
• Answer: 1/4

[Hard] Multi-Step Multiplication

• EN: There are 5 boxes of crayons. Each box has 10 crayons. If 8 crayons are taken out of one box, how many crayons are there in total?
• FR: Il y a 5 boîtes de crayons. Chaque boîte en contient 10. Si on retire 8 crayons d'une boîte, combien y a-t-il de crayons en tout?
• Choices: A) 38 crayons B) 40 crayons C) 42 crayons D) 48 crayons
• Hint: First multiply to find the total, then subtract the ones taken out — for example, 3 boxes of 10 minus 5 = 30 − 5 = 25.
• Steps:
  • 5 × 10 = 50 crayons total.
  • Subtract 8: 50 − 8 = 42.
  • There are 42 crayons in total.
• Answer: 42 crayons

[Hard] Fractions and Division

• EN: There are 24 students in a class. One third of them are wearing red shirts. How many students are wearing red shirts?
• FR: Il y a 24 élèves dans une classe. Le tiers d'entre eux portent des chemises rouges. Combien d'élèves portent des chemises rouges?
• Choices: A) 6 students B) 7 students C) 8 students D) 9 students
• Hint: To find one third of a number, divide it by 3 — for example, 1/3 of 15 = 15 ÷ 3 = 5.
• Steps:
  • One third means divide by 3.
  • 24 ÷ 3 = 8.
  • 8 students are wearing red shirts.
• Answer: 8 students

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To multiply 7 × 8, think of 7 × 7 = 49, then add one more 7 — but practise your times tables up to 9 × 9.
• Steps:
  • 7 × 8 is a multiplication fact.
  • 7 × 8 = 56.
  • The answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 40 tenths
• Hint: In a decimal number, the first digit after the decimal point is in the tenths place — for example, in 5.62, the 6 is in the tenths place.
• Steps:
  • In 3.47, the digit 3 is in the ones place.
  • The digit 4 is immediately after the decimal point — that is the tenths place.
  • The value is 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A floor tile is 6 cm long and 4 cm wide. What is the area of the tile?
• FR: Un carreau de plancher a 6 cm de long et 4 cm de large. Quelle est l'aire du carreau?
• Choices: A) 10 cm² B) 20 cm² C) 24 cm² D) 28 cm²
• Hint: Area of a rectangle = length × width — for example, a 5 cm × 3 cm rectangle has an area of 15 cm².
• Steps:
  • Area = length × width.
  • 6 × 4 = 24.
  • The area is 24 cm².
• Answer: 24 cm²

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 1/4?
• FR: Quelle fraction est la plus grande : 3/4 ou 1/4?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) 4/4
• Hint: When fractions have the same denominator, the one with the bigger numerator is larger — for example, 5/8 > 3/8.
• Steps:
  • Both fractions have denominator 4.
  • Compare numerators: 3 > 1.
  • So 3/4 is the larger fraction.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: There are 29 students going on a field trip. Each van holds 6 students. How many vans are needed to carry all the students?
• FR: 29 élèves partent en excursion. Chaque fourgonnette peut contenir 6 élèves. Combien de fourgonnettes sont nécessaires pour tous les transporter?
• Choices: A) 3 vans B) 4 vans C) 5 vans D) 6 vans
• Hint: Divide and check the remainder — if there is a remainder, you need one more van; for example, 14 ÷ 4 = 3 remainder 2, so you need 4 groups.
• Steps:
  • 29 ÷ 6 = 4 remainder 5.
  • 4 vans carry 24 students; the remaining 5 students need 1 more van.
  • 4 + 1 = 5 vans are needed.
• Answer: 5 vans

[Medium] Elapsed Time

• EN: The hockey game starts at 1:15 p.m. and ends at 3:45 p.m. How long does the game last?
• FR: Le match de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps dure le match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: To find elapsed time, count the hours first then the minutes — for example, from 2:20 to 4:50 is 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 is 2 hours.
  • From 3:15 to 3:45 is 30 minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: Olivia buys a pencil for $0.75 and an eraser for $0.45. How much does she spend in total?
• FR: Olivia achète un crayon pour 0,75 $ et une gomme pour 0,45 $. Combien dépense-t-elle en tout?
• Choices: A) $1.10 B) $1.15 C) $1.20 D) $1.25
• Hint: Line up decimal points and add — for example, $0.60 + $0.55 = $1.15.
• Steps:
  • $0.75 + $0.45.
  • 75 + 45 = 120 cents = $1.20.
  • Olivia spends $1.20.
• Answer: $1.20

[Medium] Multiplication — Two Digit by One Digit

• EN: A bookstore has 6 shelves. Each shelf holds 24 books. How many books are in the store?
• FR: Une librairie a 6 étagères. Chaque étagère contient 24 livres. Combien y a-t-il de livres dans la librairie?
• Choices: A) 124 books B) 134 books C) 140 books D) 144 books
• Hint: Multiply ones first, then tens, then add — for example, 4 × 23: 4 × 3 = 12, 4 × 20 = 80, so 80 + 12 = 92.
• Steps:
  • 6 × 24: multiply 6 × 4 = 24, carry 2.
  • 6 × 20 = 120, plus 20 carried = 140... let me recount: 6 × 20 = 120 + 24 = 144.
  • There are 144 books.
• Answer: 144 books

[Hard] Long Division Multi-Step

• EN: A farmer has 138 eggs to pack into cartons of 6. How many full cartons can she fill?
• FR: Une fermière a 138 œufs à emballer dans des boîtes de 6. Combien de boîtes complètes peut-elle remplir?
• Choices: A) 21 cartons B) 22 cartons C) 23 cartons D) 24 cartons
• Hint: Use long division step by step — for example, 96 ÷ 4: 4 goes into 9 twice (8), remainder 1, bring down 6 to get 16, 16 ÷ 4 = 4, so 24.
• Steps:
  • 138 ÷ 6: 6 goes into 13 twice (12), remainder 1.
  • Bring down 8: 18 ÷ 6 = 3.
  • So 138 ÷ 6 = 23 cartons.
• Answer: 23 cartons

[Hard] Multi-Step Area and Perimeter

• EN: A rectangular room is 9 m long and 5 m wide. What is the difference between the room's perimeter and its area?
• FR: Une pièce rectangulaire a 9 m de long et 5 m de large. Quelle est la différence entre le périmètre et l'aire de la pièce?
• Choices: A) 17 m B) 18 m C) 19 m D) 20 m
• Hint: Find perimeter (add all sides) and area (length × width) separately, then subtract — for example, a 4 × 3 room: perimeter = 14, area = 12, difference = 2.
• Steps:
  • Perimeter = 2 × (9 + 5) = 2 × 14 = 28.
  • Area = 9 × 5 = 45.
  • Difference = 45 − 28 = 17.
• Answer: 17 m

[Easy] Multi-Digit Multiplication

• EN: A school orders 32 boxes of markers. Each box has 12 markers. How many markers are ordered in total?
• FR: Une école commande 32 boîtes de marqueurs. Chaque boîte en contient 12. Combien de marqueurs sont commandés en tout?
• Choices: A) 364 markers B) 374 markers C) 384 markers D) 394 markers
• Hint: To multiply two two-digit numbers, multiply by the ones digit first, then the tens digit, and add — for example, 21 × 13: 21 × 3 = 63, 21 × 10 = 210, total = 273.
• Steps:
  • 32 × 12: 32 × 2 = 64; 32 × 10 = 320.
  • 64 + 320 = 384.
  • 384 markers are ordered.
• Answer: 384 markers

[Easy] Adding Fractions with Like Denominators

• EN: Emma eats 2/8 of a pie and her brother eats 3/8 of the same pie. How much pie have they eaten altogether?
• FR: Emma mange 2/8 d'une tarte et son frère en mange 3/8. Quelle fraction de la tarte ont-ils mangée en tout?
• Choices: A) 4/8 B) 5/8 C) 5/16 D) 6/8
• Hint: When denominators are the same, just add the numerators and keep the denominator — for example, 1/5 + 2/5 = 3/5.
• Steps:
  • Add numerators: 2 + 3 = 5.
  • Keep the denominator: 8.
  • They ate 5/8 of the pie.
• Answer: 5/8

[Easy] 50% of a Number

• EN: A jacket costs $80. It is on sale for 50% off. How much is the discount?
• FR: Un manteau coûte 80 $. Il est en solde à 50 % de rabais. Quel est le montant du rabais?
• Choices: A) $30 B) $35 C) $40 D) $45
• Hint: 50% means half — divide the number by 2; for example, 50% of $60 = $30.
• Steps:
  • 50% of $80 = $80 ÷ 2.
  • $80 ÷ 2 = $40.
  • The discount is $40.
• Answer: $40

[Easy] Decimal Subtraction

• EN: A water bottle holds 1.50 L. After practice, 0.75 L is gone. How much water is left?
• FR: Une bouteille d'eau contient 1,50 L. Après l'entraînement, 0,75 L est bu. Combien d'eau reste-t-il?
• Choices: A) 0.55 L B) 0.65 L C) 0.75 L D) 0.85 L
• Hint: Line up the decimal points and subtract — for example, 2.30 − 1.40 = 0.90.
• Steps:
  • 1.50 − 0.75.
  • 150 − 75 = 75.
  • So 0.75 L of water is left.
• Answer: 0.75 L

[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 a 5 cm de long, 4 cm de large et 3 cm de hauteur. Quel est son volume?
• Choices: A) 47 cm³ B) 57 cm³ C) 60 cm³ D) 75 cm³
• Hint: Volume = length × width × height — for example, a 2 × 3 × 4 box has volume 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] 25% of a Number

• EN: There are 120 students at a school event. 25% of them are wearing toques. How many students are wearing toques?
• FR: Il y a 120 élèves lors d'un événement scolaire. 25 % d'entre eux portent des tuques. Combien d'élèves portent des tuques?
• Choices: A) 25 students B) 30 students C) 35 students D) 40 students
• Hint: 25% means one quarter — divide by 4; for example, 25% of 200 = 200 ÷ 4 = 50.
• Steps:
  • 25% of 120 = 120 ÷ 4.
  • 120 ÷ 4 = 30.
  • 30 students are wearing toques.
• Answer: 30 students

[Medium] Subtracting Fractions with Like Denominators

• EN: A full pitcher holds 7/10 L of lemonade. Carlos drinks 3/10 L. How much lemonade is left in the pitcher?
• FR: Un pichet plein contient 7/10 L de limonade. Carlos en boit 3/10 L. Combien de limonade reste-t-il dans le pichet?
• Choices: A) 3/10 L B) 4/10 L C) 5/10 L D) 10/10 L
• Hint: Subtract the numerators and keep the denominator — for example, 6/7 − 2/7 = 4/7.
• Steps:
  • 7/10 − 3/10: subtract numerators 7 − 3 = 4.
  • Keep the denominator: 10.
  • 4/10 L of lemonade is left.
• Answer: 4/10 L

[Medium] Multi-Digit Division

• EN: A school buys 252 pencils to hand out equally to 9 classrooms. How many pencils does each classroom get?
• FR: Une école achète 252 crayons à distribuer également dans 9 classes. Combien de crayons chaque classe reçoit-elle?
• Choices: A) 24 pencils B) 26 pencils C) 28 pencils D) 32 pencils
• Hint: Use long division — for example, 180 ÷ 9: 9 goes into 18 twice, bring down 0, 9 goes into 0 zero times, so 20.
• Steps:
  • 252 ÷ 9: 9 goes into 25 twice (18), remainder 7.
  • Bring down 2: 72 ÷ 9 = 8.
  • Each classroom gets 28 pencils.
• Answer: 28 pencils

[Hard] 10% Applications

• EN: A restaurant bill is $65.00. The family wants to leave a 10% tip. How much is the tip?
• FR: L'addition au restaurant est de 65,00 $. La famille veut laisser un pourboire de 10 %. Quel est le montant du pourboire?
• Choices: A) $5.50 B) $6.00 C) $6.50 D) $7.50
• Hint: 10% of any number means divide by 10 — for example, 10% of $90 = $9.00.
• Steps:
  • 10% of $65.00 = $65.00 ÷ 10.
  • $65.00 ÷ 10 = $6.50.
  • The tip is $6.50.
• Answer: $6.50

[Hard] Multi-Step Fractions and Volume

• EN: A rectangular fish tank is 8 cm long, 5 cm wide, and 6 cm tall. The tank is 3/4 full of water. What is the volume of water in the tank?
• FR: Un aquarium rectangulaire a 8 cm de long, 5 cm de large et 6 cm de hauteur. Le réservoir est rempli aux 3/4 d'eau. Quel est le volume d'eau dans l'aquarium?
• Choices: A) 150 cm³ B) 160 cm³ C) 175 cm³ D) 180 cm³
• Hint: First find the total volume (l × w × h), then multiply by the fraction — for example, total volume 40 cm³ × 3/4 = 30 cm³.
• Steps:
  • Total volume = 8 × 5 × 6 = 240 cm³.
  • 3/4 of 240 = 240 ÷ 4 × 3 = 60 × 3 = 180.
  • The volume of water is 180 cm³.
• Answer: 180 cm³

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien font 30 % de 200?
• Choices: A) 30 B) 50 C) 60 D) 70
• Hint: To find a percent of a number, multiply the number by the percent written as a decimal — for example, 20% of 150 = 0.20 × 150 = 30.
• Steps:
  • 30% = 0.30.
  • 0.30 × 200 = 60.
  • 30% of 200 is 60.
• Answer: 60

[Easy] Order of Operations — BEDMAS

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: In BEDMAS, multiplication comes before addition — for example, 5 + 3 × 4 = 5 + 12 = 17, not 32.
• Steps:
  • Do the multiplication first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Integers — Introduction

• EN: The temperature in Winnipeg is −8°C in the morning and −3°C in the afternoon. Which temperature is warmer?
• FR: La température à Winnipeg est de −8 °C le matin et de −3 °C l'après-midi. Quelle température est la plus chaude?
• Choices: A) −8°C B) −5°C C) −3°C D) 0°C
• Hint: On a number line, temperatures closer to zero (or above zero) are warmer — for example, −2°C is warmer than −7°C.
• Steps:
  • −3 is closer to 0 than −8.
  • On a number line, −3 > −8.
  • −3°C is warmer.
• Answer: −3°C

[Easy] Ratios

• EN: In a class, there are 12 boys and 8 girls. What is the ratio of boys to girls in simplest form?
• FR: Dans une classe, il y a 12 garçons et 8 filles. Quel est le rapport des garçons aux filles sous la forme la plus simple?
• Choices: A) 2:3 B) 3:2 C) 4:3 D) 12:8
• Hint: To simplify a ratio, divide both numbers by their greatest common factor — for example, 6:4 simplifies to 3:2.
• Steps:
  • GCF of 12 and 8 is 4.
  • 12 ÷ 4 = 3; 8 ÷ 4 = 2.
  • The simplified ratio is 3:2.
• Answer: 3:2

[Medium] Fraction Multiplication

• EN: A recipe needs 3/4 of a cup of flour. Sophie wants to make 2/3 of the recipe. How much flour does she need?
• FR: Une recette nécessite 3/4 de tasse de farine. Sophie veut faire les 2/3 de la recette. De quelle quantité de farine a-t-elle besoin?
• Choices: A) 1/2 cup B) 5/12 cup C) 5/7 cup D) 6/7 cup
• Hint: To multiply fractions, multiply the numerators together and the denominators together — for example, 2/3 × 3/5 = 6/15 = 2/5.
• Steps:
  • 2/3 × 3/4 = (2 × 3) ÷ (3 × 4) = 6/12.
  • Simplify: 6/12 = 1/2.
  • Sophie needs 1/2 cup of flour.
• Answer: 1/2 cup

[Medium] Algebraic Expressions

• EN: If n = 5, what is the value of 3n + 7?
• FR: Si n = 5, quelle est la valeur de 3n + 7?
• Choices: A) 15 B) 20 C) 22 D) 25
• Hint: Substitute the value for the variable and then calculate — for example, if n = 4, then 2n + 3 = 2(4) + 3 = 11.
• Steps:
  • Substitute n = 5: 3(5) + 7.
  • 3 × 5 = 15.
  • 15 + 7 = 22.
• Answer: 22

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km par heure?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: To find a unit rate, divide the total by the number of units — for example, 150 km in 2 hours = 75 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 240 ÷ 3 = 80.
  • The car travels at 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: How many 1/3-cup servings are in 2 cups of orange juice?
• FR: Combien de portions de 1/3 de tasse y a-t-il dans 2 tasses de jus d'orange?
• Choices: A) 3 servings B) 4 servings C) 5 servings D) 6 servings
• Hint: To divide by a fraction, multiply by its reciprocal — for example, 3 ÷ 1/4 = 3 × 4 = 12.
• Steps:
  • 2 ÷ 1/3 = 2 × 3 = 6.
  • There are 6 servings.
• Answer: 6 servings

[Hard] Multi-Step Percent

• EN: A pair of skates costs $120. They are on sale for 15% off. What is the sale price?
• FR: Une paire de patins coûte 120 $. Ils sont en solde à 15 % de rabais. Quel est le prix de vente?
• Choices: A) $96.00 B) $100.00 C) $102.00 D) $105.00
• Hint: Find the discount amount first (percent × price), then subtract from the original price — for example, 20% off $50: discount = $10, sale price = $40.
• Steps:
  • 15% of $120 = 0.15 × 120 = $18.
  • Sale price = $120 − $18 = $102.
  • The skates cost $102.00.
• Answer: $102.00

[Hard] BEDMAS with Brackets and Integers

• EN: What is the value of (3 + 5)² − 4 × 6 + 2?
• FR: Quelle est la valeur de (3 + 5)² − 4 × 6 + 2?
• Choices: A) 38 B) 40 C) 42 D) 44
• Hint: Follow BEDMAS — Brackets, Exponents, Division/Multiplication, Addition/Subtraction; for example, (2 + 3)² − 2 × 4 = 25 − 8 = 17.
• Steps:
  • Brackets: (3 + 5) = 8.
  • Exponent: 8² = 64.
  • Multiply: 4 × 6 = 24.
  • 64 − 24 + 2 = 42.
• Answer: 42

[Easy] Integer Addition

• EN: The temperature in Ottawa drops from 5°C to −7°C overnight. By how many degrees did it drop?
• FR: La température à Ottawa passe de 5 °C à −7 °C pendant la nuit. De combien de degrés a-t-elle baissé?
• Choices: A) 2 degrees B) 9 degrees C) 12 degrees D) 15 degrees
• Hint: To find a change, subtract: end − start, but for a drop, find the distance between the values — for example, from 4 to −6 is a drop of 10 degrees.
• Steps:
  • Drop = 5 − (−7) = 5 + 7 = 12.
  • The temperature dropped by 12 degrees.
• Answer: 12 degrees

[Easy] Percent — Discount

• EN: A toque that normally costs $24 is on sale for 25% off. How much money do you save?
• FR: Une tuque qui coûte normalement 24 $ est en solde à 25 % de rabais. Combien économises-tu?
• Choices: A) $4.00 B) $5.00 C) $6.00 D) $8.00
• Hint: 25% = one quarter — divide the price by 4 to find the savings; for example, 25% of $40 = $10.
• Steps:
  • 25% of $24 = $24 ÷ 4 = $6.
  • You save $6.00.
• Answer: $6.00

[Easy] Integer Subtraction

• EN: What is −3 − 5?
• FR: Combien font −3 − 5?
• Choices: A) −9 B) −8 C) 2 D) 8
• Hint: Subtracting a positive is like moving left on a number line — for example, −2 − 4 = −6.
• Steps:
  • −3 − 5 means move 5 more to the left of −3.
  • −3 − 5 = −8.
  • The answer is −8.
• Answer: −8

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15.
• FR: Résous pour x : x + 9 = 15.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: To solve, do the opposite operation to both sides — for example, if x + 4 = 10, subtract 4 from both sides: x = 6.
• Steps:
  • x + 9 = 15.
  • Subtract 9 from both sides: x = 15 − 9.
  • x = 6.
• Answer: x = 6

[Medium] Probability

• EN: A bag contains 3 red marbles, 4 blue marbles, and 3 green marbles. What is the probability of drawing a blue marble?
• FR: Un sac contient 3 billes rouges, 4 billes bleues et 3 billes vertes. Quelle est la probabilité de tirer une bille bleue?
• Choices: A) 1/5 B) 2/5 C) 3/10 D) 4/10
• Hint: Probability = favourable outcomes ÷ total outcomes — for example, 3 red out of 9 total = 3/9 = 1/3.
• Steps:
  • Total marbles = 3 + 4 + 3 = 10.
  • Blue marbles = 4.
  • Probability = 4/10.
• Answer: 4/10

[Medium] Tax

• EN: A video game costs $45.00. The HST is 13%. What is the total price including tax?
• FR: Un jeu vidéo coûte 45,00 $. La TVH est de 13 %. Quel est le prix total, taxes comprises?
• Choices: A) $49.85 B) $50.35 C) $50.85 D) $51.35
• Hint: Find the tax amount (price × tax rate), then add to the original price — for example, $20 + 13% tax: $20 × 0.13 = $2.60, total = $22.60.
• 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 gift box is 10 cm long, 6 cm wide, and 4 cm tall. What is the surface area of the box?
• FR: Une boîte cadeau rectangulaire a 10 cm de long, 6 cm de large et 4 cm de hauteur. Quelle est l'aire totale de la boîte?
• Choices: A) 208 cm² B) 218 cm² C) 228 cm² D) 248 cm²
• Hint: Surface area of a rectangular prism = 2(lw + lh + wh) — for example, a 3 × 2 × 1 box: 2(6 + 3 + 2) = 2(11) = 22 cm².
• Steps:
  • lw = 10 × 6 = 60; lh = 10 × 4 = 40; wh = 6 × 4 = 24.
  • SA = 2(60 + 40 + 24) = 2(124) = 248.
  • The surface area is 248 cm².
• Answer: 248 cm²

[Medium] Integer Multiplication

• EN: What is (−6) × 7?
• FR: Combien font (−6) × 7?
• Choices: A) −48 B) −42 C) 42 D) 48
• Hint: A negative times a positive gives a negative product — for example, (−5) × 3 = −15.
• Steps:
  • Multiply the absolute values: 6 × 7 = 42.
  • One factor is negative, so the product is negative.
  • (−6) × 7 = −42.
• Answer: −42

[Hard] Multi-Step Percent — Tip and Tax

• EN: A restaurant meal costs $48.00. A 13% HST is added. Then a 15% tip is calculated on the original meal price only. What is the total amount paid?
• FR: Un repas au restaurant coûte 48,00 $. On ajoute 13 % de TVH. Ensuite, un pourboire de 15 % est calculé sur le prix original du repas seulement. Quel est le montant total payé?
• Choices: A) $60.00 B) $61.44 C) $62.64 D) $63.84
• Hint: Calculate tax and tip separately, then add everything — for example, $30 meal: tax = $3.90, tip = $4.50, total = $38.40.
• Steps:
  • Tax = $48 × 0.13 = $6.24.
  • Tip = $48 × 0.15 = $7.20.
  • Total = $48.00 + $6.24 + $7.20 = $61.44.
• Answer: $61.44

[Hard] Solving a Two-Step Equation

• EN: Solve for x: 3x − 4 = 14.
• FR: Résous pour x : 3x − 4 = 14.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: First add or subtract to isolate the term with x, then divide — for example, 2x − 3 = 9: add 3 to get 2x = 12, then x = 6.
• Steps:
  • Add 4 to both sides: 3x = 18.
  • Divide by 3: x = 18 ÷ 3 = 6.
  • x = 6.
• Answer: x = 6

[Easy] Perfect Squares

• EN: What is the square root of 144?
• FR: Quelle est la racine carrée de 144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: The square root of a number asks what times itself equals that number — for example, √81 = 9 because 9 × 9 = 81.
• Steps:
  • Ask: what number times itself equals 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored 70, 80, 85, 90, and 75 on a math test. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 80, 85, 90 et 75 à un test de mathématiques. Quel est le résultat moyen?
• Choices: A) 78 B) 80 C) 82 D) 85
• Hint: To find the mean, add all values and divide by how many there are — for example, mean of 4, 6, 8 is (4 + 6 + 8) ÷ 3 = 6.
• Steps:
  • Sum = 70 + 80 + 85 + 90 + 75 = 400.
  • Divide by 5: 400 ÷ 5 = 80.
  • The mean score is 80.
• Answer: 80

[Easy] Percent Increase

• EN: A hockey player scored 20 goals last year and 25 goals this year. What is the percent increase?
• FR: Un joueur de hockey a marqué 20 buts l'année dernière et 25 buts cette année. Quel est le pourcentage d'augmentation?
• Choices: A) 15% B) 20% C) 25% D) 30%
• Hint: Percent increase = (increase ÷ original) × 100 — for example, from 10 to 12 is (2 ÷ 10) × 100 = 20%.
• Steps:
  • Increase = 25 − 20 = 5.
  • Percent increase = (5 ÷ 20) × 100 = 25%.
  • The percent increase is 25%.
• Answer: 25%

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 3 = 11.
• FR: Résous pour x : 2x + 3 = 11.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: First undo the addition, then undo the multiplication — for example, 3x + 2 = 11: subtract 2 to get 3x = 9, then x = 3.
• Steps:
  • Subtract 3 from both sides: 2x = 8.
  • Divide by 2: x = 4.
  • x = 4.
• Answer: x = 4

[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: Use a² + b² = c² where c is the hypotenuse — for example, legs 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] Slope Introduction

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

[Medium] Percent Decrease

• EN: A pair of boots was $80 and is now $60. What is the percent decrease?
• FR: Une paire de bottes coûtait 80 $ et coûte maintenant 60 $. Quel est le pourcentage de diminution?
• Choices: A) 15% B) 20% C) 25% D) 30%
• Hint: Percent decrease = (decrease ÷ original) × 100 — for example, from 50 to 40 is (10 ÷ 50) × 100 = 20%.
• Steps:
  • Decrease = 80 − 60 = 20.
  • Percent decrease = (20 ÷ 80) × 100 = 25%.
  • The percent decrease is 25%.
• Answer: 25%

[Medium] Median

• EN: Seven test scores are: 55, 72, 68, 90, 61, 85, and 72. What is the median score?
• FR: Sept résultats de tests sont : 55, 72, 68, 90, 61, 85 et 72. Quel est le résultat médian?
• Choices: A) 68 B) 71 C) 72 D) 85
• Hint: To find the median, put the values in order and pick the middle one — for example, 3, 7, 9, 10, 12: the median is 9.
• Steps:
  • In order: 55, 61, 68, 72, 72, 85, 90.
  • The middle (4th) value is 72.
  • The median is 72.
• Answer: 72

[Hard] Pythagorean Theorem — Find a Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Rearrange a² + b² = c² to find the missing leg: b² = c² − a² — for example, c = 10, a = 6: b² = 100 − 36 = 64, b = 8.
• Steps:
  • b² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12.
  • The other leg is 12 cm.
• Answer: 12 cm

[Hard] Multi-Step Linear Equation

• EN: Solve for x: 5(x − 2) = 3x + 8.
• FR: Résous pour x : 5(x − 2) = 3x + 8.
• Choices: A) x = 7 B) x = 8 C) x = 9 D) x = 11
• Hint: Expand the brackets first, then collect like terms — for example, 3(x − 1) = x + 7: 3x − 3 = x + 7, so 2x = 10, x = 5.
• Steps:
  • Expand: 5x − 10 = 3x + 8.
  • Subtract 3x: 2x − 10 = 8.
  • Add 10: 2x = 18, so x = 9.
• Answer: x = 9

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 7 = 17.
• FR: Résous pour x : 4x − 7 = 17.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add or subtract to isolate the x term, then divide — for example, 3x − 5 = 10: add 5 to get 3x = 15, x = 5.
• Steps:
  • Add 7 to both sides: 4x = 24.
  • Divide by 4: x = 6.
  • x = 6.
• Answer: x = 6

[Easy] Adding Polynomials

• EN: What is (3x + 5) + (2x − 3)?
• FR: Que donne (3x + 5) + (2x − 3)?
• Choices: A) 4x + 2 B) 5x + 2 C) 5x + 8 D) 6x + 2
• Hint: Combine like terms — add the x terms together and the constant terms together; for example, (4x + 2) + (x − 5) = 5x − 3.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2.
  • Answer: 5x + 2
• Answer: 5x + 2

[Easy] Slope-Intercept Form

• EN: A line has equation y = 3x + 2. What is the slope of the line?
• FR: Une droite a pour équation y = 3x + 2. Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 5
• Hint: In y = mx + b, the slope is m (the coefficient of x) — for example, y = 5x − 4 has slope 5.
• Steps:
  • The equation is in y = mx + b form.
  • m = 3.
  • The slope is 3.
• Answer: 3

[Easy] Linear Inequality

• EN: Solve the inequality: x − 4 > 6.
• FR: Résous l'inégalité : x − 4 > 6.
• Choices: A) x > 2 B) x > 8 C) x > 10 D) x > 12
• Hint: Solve an inequality like an equation — add or subtract from both sides; for example, x − 3 > 5 means x > 8.
• Steps:
  • Add 4 to both sides: x > 6 + 4.
  • x > 10.
  • The solution is x > 10.
• Answer: x > 10

[Medium] Multiplying Polynomials

• EN: Expand and simplify: 2x(x + 5).
• FR: Développe et simplifie : 2x(x + 5).
• Choices: A) 2x + 10 B) 2x² + 5x C) 2x² + 10x D) 3x² + 10x
• Hint: Multiply each term inside the brackets by the factor outside — for example, 3x(x + 4) = 3x² + 12x.
• Steps:
  • 2x × x = 2x².
  • 2x × 5 = 10x.
  • 2x(x + 5) = 2x² + 10x.
• Answer: 2x² + 10x

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 9 cm and the hypotenuse is 15 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 9 cm et l'hypoténuse est 15 cm. Quel est sin(θ)?
• Choices: A) 3/5 B) 4/5 C) 9/6 D) 15/9
• Hint: SOH means sin = Opposite ÷ Hypotenuse — for example, opposite = 4, hypotenuse = 5, sin(θ) = 4/5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 9 ÷ 15 = 3/5.
  • sin(θ) = 3/5.
• Answer: 3/5

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in the ratio 1:3. The smaller triangle has a side of 7 cm. What is the length of the corresponding side in the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans le rapport 1:3. Le plus petit triangle a un côté de 7 cm. Quelle est la longueur du côté correspondant du plus grand triangle?
• Choices: A) 10 cm B) 14 cm C) 21 cm D) 28 cm
• Hint: Multiply the small side by the scale factor — for example, if scale factor is 1:4 and small side is 5, large side = 20.
• Steps:
  • Scale factor = 3.
  • Corresponding large side = 7 × 3 = 21.
  • The side is 21 cm.
• Answer: 21 cm

[Medium] Graphing Lines

• EN: A line has slope 2 and y-intercept −3. Which equation represents this line?
• FR: Une droite a une pente de 2 et une ordonnée à l'origine de −3. Quelle équation représente cette droite?
• Choices: A) y = 2x + 3 B) y = −3x + 2 C) y = 2x − 3 D) y = 3x − 2
• Hint: Use y = mx + b where m is slope and b is the y-intercept — for example, slope 4, y-intercept −1: y = 4x − 1.
• Steps:
  • m = 2, b = −3.
  • y = mx + b becomes y = 2x − 3.
  • The equation is y = 2x − 3.
• Answer: y = 2x − 3

[Hard] Trigonometry — Find an Angle

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What is the measure of angle θ to the nearest degree?
• FR: Dans un triangle rectangle, le côté adjacent est 8 cm et l'hypoténuse est 10 cm. Quelle est la mesure de l'angle θ au degré près?
• Choices: A) 37° B) 40° C) 53° D) 60°
• Hint: Use CAH: cos(θ) = adjacent ÷ hypotenuse, then use the inverse cosine — for example, cos(θ) = 0.5 means θ = 60°.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 8 ÷ 10 = 0.8.
  • θ = cos⁻¹(0.8) ≈ 37°.
  • Angle θ is approximately 37°.
• Answer: 37°

[Hard] Systems of Equations — Substitution

• EN: Solve the system: y = 2x + 1 and y = 4x − 3. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = 4x − 3. Quelle est la valeur de x?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the two expressions equal and solve — for example, 3x + 2 = x + 8: 2x = 6, x = 3.
• Steps:
  • Set 2x + 1 = 4x − 3.
  • 1 + 3 = 4x − 2x → 4 = 2x.
  • x = 2.
• Answer: x = 2

[Easy] Factoring a Quadratic

• EN: Factor the expression: x² + 7x + 12.
• FR: Factorise l'expression : x² + 7x + 12.
• Choices: A) (x + 2)(x + 6) B) (x + 3)(x + 4) C) (x + 1)(x + 12) D) (x + 6)(x + 2)
• Hint: Find two numbers that multiply to the constant and add to the x-coefficient — for example, x² + 5x + 6: find two numbers multiplying to 6 and adding to 5, which are 2 and 3.
• Steps:
  • Find two numbers that multiply to 12 and add to 7.
  • 3 × 4 = 12 and 3 + 4 = 7.
  • x² + 7x + 12 = (x + 3)(x + 4).
• Answer: (x + 3)(x + 4)

[Easy] Trigonometry — Find 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 est 20 cm. Quelle est la longueur du côté opposé?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: Use SOH: opposite = hypotenuse × sin(θ) — for example, sin(45°) ≈ 0.707; opposite = 10 × 0.707 ≈ 7.07 cm.
• Steps:
  • sin(30°) = 0.5.
  • opposite = 20 × 0.5 = 10.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Easy] System of Equations

• EN: Solve: x + y = 10 and x − y = 4. What is the value of x?
• FR: Résous : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the two equations together to eliminate y — for example, (x + y) + (x − y) = 10 + 4 gives 2x = 14.
• Steps:
  • Add the equations: (x + y) + (x − y) = 10 + 4.
  • 2x = 14, so x = 7.
  • x = 7.
• Answer: x = 7

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 5 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 628 cm³ B) 706 cm³ C) 785 cm³ D) 800 cm³
• Hint: Volume of cylinder = π × r² × h — for example, r = 3, h = 4: V = 3.14 × 9 × 4 = 113.04 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 25 × 10.
  • 3.14 × 25 = 78.5.
  • 78.5 × 10 = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: What is the vertex of the parabola y = x² − 6x + 11?
• FR: Quel est le sommet de la parabole y = x² − 6x + 11?
• Choices: A) (2, 3) B) (3, 2) C) (4, 3) D) (6, 11)
• Hint: Complete the square: y = (x − h)² + k; the vertex is (h, k) — for example, y = x² − 4x + 5 = (x − 2)² + 1, vertex (2, 1).
• Steps:
  • y = x² − 6x + 11 = (x² − 6x + 9) + 2 = (x − 3)² + 2.
  • Vertex = (3, 2).
  • The vertex is (3, 2).
• Answer: (3, 2)

[Medium] Circle Geometry

• EN: A chord in a circle subtends a central angle of 120°. The radius of the circle is 9 cm. What is the length of the arc cut off by the chord?
• FR: Une corde dans un cercle sous-tend un angle central de 120°. Le rayon du cercle est de 9 cm. Quelle est la longueur de l'arc découpé par la corde? (Utilise π ≈ 3.14)
• Choices: A) 16.76 cm B) 18.84 cm C) 20.94 cm D) 22.00 cm
• Hint: Arc length = (angle ÷ 360) × 2πr — for example, 90° arc on a circle with r = 4: (90 ÷ 360) × 2 × 3.14 × 4 = 6.28 cm.
• Steps:
  • Arc length = (120 ÷ 360) × 2 × 3.14 × 9.
  • = (1/3) × 56.52 = 18.84.
  • The arc length is 18.84 cm.
• Answer: 18.84 cm

[Medium] Quadratic Formula

• EN: Solve using the quadratic formula: x² − 5x + 6 = 0. What are the solutions?
• FR: Résous à l'aide de la formule quadratique : x² − 5x + 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = 3 and x = 4 D) x = −2 and x = −3
• Hint: x = [−b ± √(b² − 4ac)] ÷ 2a — identify a, b, c from ax² + bx + c = 0; for example, x² − 3x + 2 = 0 gives x = 1 and x = 2.
• Steps:
  • a = 1, b = −5, c = 6.
  • Discriminant: 25 − 24 = 1; √1 = 1.
  • x = (5 ± 1) ÷ 2: x = 3 and x = 2.
• Answer: x = 2 and x = 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 6 cm and a slant height of 10 cm. What is the total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 6 cm et une hauteur oblique de 10 cm. Quelle est l'aire totale? (Utilise π ≈ 3,14)
• Choices: A) 263.76 cm² B) 289.45 cm² C) 301.44 cm² D) 310.56 cm²
• Hint: Total surface area of a cone = πr² + πrl where l is slant height — for example, r = 3, l = 5: SA = 3.14(9) + 3.14(3)(5) = 28.26 + 47.1 = 75.36 cm².
• Steps:
  • Base: π × 6² = 3.14 × 36 = 113.04.
  • Lateral: π × 6 × 10 = 3.14 × 60 = 188.4.
  • Total = 113.04 + 188.4 = 301.44 cm².
• Answer: 301.44 cm²

[Hard] Quadratic — Word Problem

• EN: A ball is thrown upward from the ground. Its height in metres is given by h = −5t² + 20t. At what time (in seconds) does the ball reach the ground again?
• FR: Un ballon est lancé vers le haut depuis le sol. Sa hauteur en mètres est donnée par h = −5t² + 20t. Au bout de combien de secondes le ballon touche-t-il à nouveau le sol?
• Choices: A) t = 2 seconds B) t = 3 seconds C) t = 4 seconds D) t = 5 seconds
• Hint: Set h = 0 and factor or use the quadratic formula — for example, −4t² + 16t = 0: factor out t, so t(−4t + 16) = 0, giving t = 0 or t = 4.
• Steps:
  • Set h = 0: −5t² + 20t = 0.
  • Factor: t(−5t + 20) = 0.
  • t = 0 (launch) or t = 4 (lands). The ball hits the ground at t = 4 seconds.
• Answer: t = 4 seconds

[Hard] Systems with Quadratics

• EN: Find the x-coordinates of the intersection points of y = x² − 4 and y = x + 2.
• FR: Trouve les coordonnées x des points d'intersection de y = x² − 4 et y = x + 2.
• Choices: A) x = −1 and x = 3 B) x = −2 and x = 3 C) x = 1 and x = −3 D) x = 2 and x = −3
• Hint: Set the two expressions equal and solve the resulting quadratic — for example, x² = x + 6 → x² − x − 6 = 0 → (x − 3)(x + 2) = 0.
• Steps:
  • Set equal: x² − 4 = x + 2.
  • x² − x − 6 = 0.
  • Factor: (x − 3)(x + 2) = 0, so x = 3 or x = −2.
• Answer: x = −2 and x = 3

[Easy] Exponential Function

• EN: A bacteria culture starts with 100 bacteria and doubles every hour. How many bacteria are there after 3 hours?
• FR: Une culture bactérienne commence avec 100 bactéries et double chaque heure. Combien y a-t-il de bactéries après 3 heures?
• Choices: A) 600 bacteria B) 700 bacteria C) 800 bacteria D) 1000 bacteria
• Hint: Use the formula A = P × 2ⁿ where n is the number of periods — for example, 50 bacteria doubling for 2 hours: 50 × 2² = 200.
• Steps:
  • A = 100 × 2³.
  • 2³ = 8.
  • A = 100 × 8 = 800 bacteria.
• Answer: 800 bacteria

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 4 and the common difference is 6. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 4 et la raison est 6. Quel est le 5e terme?
• Choices: A) 24 B) 26 C) 28 D) 30
• Hint: Use tₙ = t₁ + (n − 1)d — for example, t₁ = 2, d = 5, find t₄: 2 + (3)(5) = 17.
• Steps:
  • t₅ = 4 + (5 − 1) × 6 = 4 + 24 = 28.
  • The 5th term is 28.
• Answer: 28

[Easy] Compound Interest

• EN: Emily invests $1000 at an annual interest rate of 5% compounded annually. How much does she have after 2 years?
• FR: Emily investit 1 000 $ à un taux d'intérêt annuel de 5 %, composé annuellement. Combien a-t-elle après 2 ans?
• Choices: A) $1 100.00 B) $1 102.50 C) $1 105.00 D) $1 210.00
• Hint: Use A = P(1 + r)ⁿ — for example, $500 at 4% for 2 years: 500 × (1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000 × (1.05)².
  • (1.05)² = 1.1025.
  • A = 1000 × 1.1025 = $1102.50.
• Answer: $1 102.50

[Easy] Logarithm Basics

• EN: What is log₂(32)?
• FR: Combien vaut log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: logₐ(x) = n means aⁿ = x — for example, log₂(8) = 3 because 2³ = 8.
• Steps:
  • Ask: 2ⁿ = 32.
  • 2⁵ = 32.
  • log₂(32) = 5.
• Answer: 5

[Medium] Geometric Series Sum

• EN: Find the sum of the first 5 terms of a geometric series with first term 2 and common ratio 3.
• FR: Trouve la somme des 5 premiers termes d'une suite géométrique de premier terme 2 et de raison 3.
• Choices: A) 184 B) 212 C) 242 D) 256
• Hint: Use Sₙ = t₁(rⁿ − 1) ÷ (r − 1) — for example, t₁ = 1, r = 2, n = 4: S = 1(16 − 1) ÷ 1 = 15.
• Steps:
  • S₅ = 2(3⁵ − 1) ÷ (3 − 1) = 2(243 − 1) ÷ 2.
  • = 2 × 242 ÷ 2 = 242.
  • The sum is 242.
• Answer: 242

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ + cos²θ.
• FR: Simplifie : sin²θ + cos²θ + cos²θ.
• Choices: A) 1 + sin²θ B) 2 − sin²θ C) 1 + cos²θ D) 2 + cos²θ
• Hint: Use the Pythagorean identity sin²θ + cos²θ = 1, then simplify — for example, sin²θ + cos²θ + sin²θ = 1 + sin²θ.
• Steps:
  • sin²θ + cos²θ = 1 (Pythagorean identity).
  • So the expression = 1 + cos²θ.
  • The simplified form is 1 + cos²θ.
• Answer: 1 + cos²θ

[Medium] Quadratic Function — Vertex Form

• EN: A parabola has equation y = 2(x − 3)² + 5. What is the minimum value of y?
• FR: Une parabole a pour équation y = 2(x − 3)² + 5. Quelle est la valeur minimale de y?
• Choices: A) 2 B) 3 C) 5 D) 7
• Hint: In vertex form y = a(x − h)² + k, the vertex is (h, k); if a > 0, the minimum is k — for example, y = 3(x − 1)² + 4 has a minimum of 4.
• Steps:
  • The equation is in vertex form: a = 2, h = 3, k = 5.
  • Since a = 2 > 0, the parabola opens upward.
  • The minimum value is k = 5.
• Answer: 5

[Medium] Financial Math — Annuity

• EN: Lucas deposits $200 at the end of each month into an account earning 6% per year compounded monthly. How much will he have after 12 months? (Use the formula Sₙ = PMT × [(1 + r)ⁿ − 1] ÷ r, r = 0.005)
• FR: Lucas dépose 200 $ à la fin de chaque mois dans un compte à 6 % par an composé mensuellement. Combien aura-t-il après 12 mois? (Utilise Sₙ = PMT × [(1 + r)ⁿ − 1] ÷ r, r = 0,005)
• Choices: A) $2 400.00 B) $2 456.78 C) $2 467.11 D) $2 544.00
• Hint: Substitute into the annuity formula — for example, PMT = $100, r = 0.01, n = 6: S = 100 × [(1.01)⁶ − 1] ÷ 0.01.
• Steps:
  • S = 200 × [(1.005)¹² − 1] ÷ 0.005.
  • (1.005)¹² ≈ 1.06168; 1.06168 − 1 = 0.06168.
  • S = 200 × 0.06168 ÷ 0.005 = 200 × 12.336 ≈ $2 467.11.
• Answer: $2 467.11

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(x − 2) = log₃(8).
• FR: Résous pour x : log₃(x) + log₃(x − 2) = log₃(8).
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Use the product rule logₐ(m) + logₐ(n) = logₐ(mn), then set the arguments equal — for example, log₂(x) + log₂(3) = log₂(12): x × 3 = 12, x = 4.
• Steps:
  • log₃(x(x − 2)) = log₃(8).
  • x(x − 2) = 8 → x² − 2x − 8 = 0.
  • Factor: (x − 4)(x + 2) = 0; x = 4 (since x must be positive).
• Answer: x = 4

[Hard] Exponential Growth — Compound Interest Challenge

• EN: An investment doubles in value every 8 years. If $3 000 is invested today, how much is the investment worth after 24 years?
• FR: Un investissement double de valeur tous les 8 ans. Si 3 000 $ sont investis aujourd'hui, quelle est la valeur de l'investissement après 24 ans?
• Choices: A) $12 000 B) $18 000 C) $24 000 D) $36 000
• Hint: Find how many doubling periods fit in the total time, then use A = P × 2ⁿ — for example, $500 doubling every 5 years for 15 years: n = 3, A = 500 × 8 = $4 000.
• Steps:
  • Number of doublings = 24 ÷ 8 = 3.
  • A = 3000 × 2³ = 3000 × 8 = 24 000.
  • The investment is worth $24 000.
• Answer: $24 000

[Easy] Permutations

• EN: In how many ways can 5 different hockey trophies be arranged in a row on a shelf?
• FR: De combien de façons peut-on aligner 5 trophées de hockey différents sur une étagère?
• Choices: A) 25 ways B) 60 ways C) 100 ways D) 120 ways
• Hint: The number of ways to arrange n distinct objects is n! — for example, 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
  • There are 120 ways.
• Answer: 120 ways

[Easy] Combinations

• EN: A committee of 3 students is chosen from a group of 7. How many different committees are possible?
• FR: Un comité de 3 élèves est choisi parmi un groupe de 7. Combien de comités différents sont possibles?
• Choices: A) 21 committees B) 35 committees C) 42 committees D) 70 committees
• Hint: Use C(n, r) = n! ÷ [r!(n − r)!] — for example, C(5, 2) = 10.
• Steps:
  • C(7, 3) = 7! ÷ (3! × 4!) = (7 × 6 × 5) ÷ (3 × 2 × 1).
  • = 210 ÷ 6 = 35.
  • There are 35 possible committees.
• Answer: 35 committees

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = 4x³?
• FR: Quelle est la dérivée de f(x) = 4x³?
• Choices: A) 4x² B) 8x² C) 12x² D) 16x²
• Hint: The power rule states that the derivative of axⁿ is n × axⁿ⁻¹ — for example, the derivative of 3x² is 6x.
• Steps:
  • Apply the power rule: bring down the exponent, multiply by coefficient.
  • d/dx(4x³) = 3 × 4 × x² = 12x².
  • The derivative is 12x².
• Answer: 12x²

[Easy] Polynomial Long Division

• EN: Divide: (x² + 5x + 6) ÷ (x + 2). What is the quotient?
• FR: Divise : (x² + 5x + 6) ÷ (x + 2). Quel est le quotient?
• Choices: A) x + 1 B) x + 2 C) x + 3 D) x + 4
• Hint: Factor the numerator first if possible — for example, (x² + 3x + 2) ÷ (x + 1) = x + 2.
• Steps:
  • Factor: x² + 5x + 6 = (x + 2)(x + 3).
  • (x + 2)(x + 3) ÷ (x + 2) = x + 3.
  • The quotient is x + 3.
• Answer: x + 3

[Medium] Binomial Probability

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

[Medium] Derivative — Rate of Change

• EN: The position of a car (in metres) at time t seconds is s(t) = 3t² + 2t. What is the car's velocity at t = 4 seconds?
• FR: La position d'une voiture (en mètres) au temps t secondes est s(t) = 3t² + 2t. Quelle est la vitesse de la voiture à t = 4 secondes?
• Choices: A) 22 m/s B) 24 m/s C) 26 m/s D) 28 m/s
• Hint: Velocity = ds/dt (the derivative of position); find s'(t), then substitute — for example, s(t) = 2t² + t: v(t) = 4t + 1, so v(3) = 13.
• Steps:
  • s'(t) = 6t + 2.
  • At t = 4: s'(4) = 6(4) + 2 = 24 + 2 = 26.
  • The velocity is 26 m/s.
• Answer: 26 m/s

[Medium] Rational Function — Asymptotes

• EN: What is the vertical asymptote of the function f(x) = 3 ÷ (x − 5)?
• FR: Quelle est l'asymptote verticale de la fonction f(x) = 3 ÷ (x − 5)?
• Choices: A) x = −5 B) x = 0 C) x = 3 D) x = 5
• Hint: The vertical asymptote occurs where the denominator equals zero — for example, f(x) = 1 ÷ (x − 3) has a vertical asymptote at x = 3.
• Steps:
  • Set the denominator equal to zero: x − 5 = 0.
  • x = 5.
  • The vertical asymptote is x = 5.
• Answer: x = 5

[Medium] Vector Addition

• EN: Vector a = (3, 4) and vector b = (−1, 5). What is a + b?
• FR: Le vecteur a = (3, 4) et le vecteur b = (−1, 5). Quel est a + b?
• Choices: A) (1, 8) B) (2, 9) C) (3, 8) D) (4, 9)
• Hint: Add corresponding components — for example, (2, 3) + (5, 1) = (7, 4).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 4 + 5 = 9.
  • a + b = (2, 9).
• Answer: (2, 9)

[Hard] Derivatives — Optimization

• EN: A Canadian farmer wants to fence a rectangular area of 144 m² using the least amount of fencing. What is the minimum perimeter?
• FR: Un fermier canadien veut clôturer une aire rectangulaire de 144 m² en utilisant le moins de clôture possible. Quel est le périmètre minimal?
• Choices: A) 36 m B) 40 m C) 44 m D) 48 m
• Hint: For a fixed area, the rectangle with minimum perimeter is a square — find the side length by taking the square root of the area, then calculate the perimeter; for example, area = 36 m²: side = 6, P = 24 m.
• Steps:
  • For minimum perimeter with fixed area, use a square.
  • Side = √144 = 12 m.
  • Perimeter = 4 × 12 = 48 m.
• Answer: 48 m

[Hard] Normal Distribution

• EN: The heights of Grade 12 students at a school are normally distributed with a mean of 170 cm and a standard deviation of 10 cm. Approximately what percentage of students are between 160 cm and 180 cm tall?
• FR: Les tailles des élèves de 12e année dans une école suivent une distribution normale de moyenne 170 cm et d'écart-type 10 cm. Environ quel pourcentage d'élèves mesurent entre 160 cm et 180 cm?
• Choices: A) 50% B) 64% C) 68% D) 95%
• Hint: The empirical rule states that about 68% of data falls within one standard deviation of the mean — for example, mean = 50, SD = 5: about 68% are between 45 and 55.
• Steps:
  • 160 = 170 − 10 (one SD below); 180 = 170 + 10 (one SD above).
  • The range 160–180 is within one standard deviation.
  • By the empirical rule, approximately 68% of students are in this range.
• Answer: 68%