Daily Math — 2026-07-24

[Easy] Counting to 20

• EN: There are 7 apples in a basket. 5 more apples are added. How many apples are there in all?
• FR: Il y a 7 pommes dans un panier. On ajoute 5 pommes de plus. Combien de pommes y a-t-il en tout?
• Choices: A) 11 apples B) 12 apples C) 13 apples D) 14 apples
• Hint: To add 6 + 4, start at 6 and count up 4 more: 7, 8, 9, 10.
• Steps:
  • Start at 7 and count up 5 more.
  • 8, 9, 10, 11, 12.
  • So there are 12 apples in all.
• Answer: 12 apples

[Easy] Subtraction Within 20

• EN: There are 15 crayons on the table. A student takes 6 away. How many crayons are left?
• FR: Il y a 15 crayons sur la table. Un élève en prend 6. Combien de crayons reste-t-il?
• Choices: A) 7 crayons B) 8 crayons C) 9 crayons D) 11 crayons
• Hint: To find 14 − 5, count back 5 from 14: 13, 12, 11, 10, 9.
• Steps:
  • Start at 15 and count back 6.
  • 14, 13, 12, 11, 10, 9.
  • So there are 9 crayons left.
• Answer: 9 crayons

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes after 8?
• FR: Compte par 2. Quel nombre vient après 8?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Skip counting by 2s from 4: 4, 6, 8, … the next number is always 2 more.
• Steps:
  • We are skip counting by 2s.
  • Start at 8 and add 2 more.
  • 8 + 2 = 10.
  • So the number after 8 when counting by 2s is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is bigger: 13 or 17?
• FR: Quel nombre est le plus grand: 13 ou 17?
• Choices: A) 13 B) 15 C) 17 D) 19
• Hint: To compare 11 and 16, think of a number line — the number farther right is bigger.
• Steps:
  • Place 13 and 17 on a number line.
  • 17 is farther to the right than 13.
  • So 17 is the bigger number.
• Answer: 17

[Medium] Addition with a Story

• EN: Maya has 9 stickers. Her friend gives her 8 more stickers. How many stickers does Maya have now?
• FR: Maya a 9 autocollants. Son amie lui donne 8 de plus. Combien d'autocollants Maya a-t-elle maintenant?
• Choices: A) 15 stickers B) 16 stickers C) 17 stickers D) 18 stickers
• Hint: To add 8 + 7, think of it as 8 + 2 + 5 = 15; break the second number to make a 10.
• Steps:
  • Start with 9. We need to add 8.
  • Break 8 into 1 + 7 so that 9 + 1 = 10.
  • Then 10 + 7 = 17.
  • So Maya has 17 stickers.
• Answer: 17 stickers

[Medium] Skip Counting by 5s

• EN: Liam counts by 5s starting at 5. What is the fourth number he says?
• FR: Liam compte par 5 en commençant à 5. Quel est le quatrième nombre qu'il dit?
• Choices: A) 15 B) 20 C) 25 D) 30
• Hint: Counting by 5s from 5: 5, 10, 15, … the third number is 15.
• Steps:
  • Start at 5 and count by 5s.
  • First: 5. Second: 10. Third: 15. Fourth: 20.
  • The fourth number is 20.
• Answer: 20

[Medium] Coin Recognition

• EN: Priya has 1 dime and 1 nickel. How many cents does she have in total?
• FR: Priya a 1 pièce de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents; to find 10 + 3, count on from 10.
• Steps:
  • A dime is worth 10 cents.
  • A nickel is worth 5 cents.
  • 10 + 5 = 15 cents.
  • So Priya has 15 cents in total.
• Answer: 15 cents

[Medium] Subtraction Story

• EN: There are 18 kids at the park. 9 kids go home. How many kids are still at the park?
• FR: Il y a 18 enfants au parc. 9 enfants rentrent à la maison. Combien d'enfants sont encore au parc?
• Choices: A) 7 kids B) 8 kids C) 9 kids D) 11 kids
• Hint: To solve 16 − 7, think about what plus 7 equals 16: 9 + 7 = 16, so the answer is 9.
• Steps:
  • Start with 18 kids.
  • 9 kids leave, so we subtract: 18 − 9.
  • Think: 9 + 9 = 18, so 18 − 9 = 9.
  • There are 9 kids still at the park.
• Answer: 9 kids

[Hard] Two-Step Addition and Subtraction

• EN: There are 14 birds on a fence. 5 birds fly away, and then 3 more birds land. How many birds are on the fence now?
• FR: Il y a 14 oiseaux sur une clôture. 5 oiseaux s'envolent, puis 3 autres se posent. Combien d'oiseaux y a-t-il maintenant sur la clôture?
• Choices: A) 10 birds B) 11 birds C) 12 birds D) 13 birds
• Hint: Do two steps: first subtract, then add — like 10 − 3 = 7, then 7 + 2 = 9.
• Steps:
  • Start with 14 birds.
  • Step 1: 5 birds fly away. 14 − 5 = 9.
  • Step 2: 3 more birds land. 9 + 3 = 12.
  • There are 12 birds on the fence now.
• Answer: 12 birds

[Hard] Counting to 100

• EN: What number is 10 more than 73?
• FR: Quel nombre est 10 de plus que 73?
• Choices: A) 63 B) 74 C) 82 D) 83
• Hint: To find 10 more than 45, the ones digit stays the same and the tens digit goes up by 1: 55.
• Steps:
  • Start at 73.
  • Adding 10 means the tens digit goes up by 1.
  • 7 tens + 1 ten = 8 tens, and the ones stay as 3.
  • So 10 more than 73 is 83.
• Answer: 83

[Easy] Addition Within 100

• EN: A store has 34 red pencils and 25 blue pencils. How many pencils are there in all?
• FR: Un magasin a 34 crayons rouges et 25 crayons bleus. Combien de crayons y a-t-il en tout?
• Choices: A) 57 pencils B) 58 pencils C) 59 pencils D) 61 pencils
• Hint: To add 32 + 21, add the tens first: 30 + 20 = 50, then add the ones: 2 + 1 = 3, total 53.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59.
  • There are 59 pencils in all.
• Answer: 59 pencils

[Easy] Subtraction Within 100

• EN: A jar had 76 marbles. Ethan took out 23 marbles. How many marbles are left?
• FR: Un bocal contenait 76 billes. Ethan en a retiré 23. Combien de billes reste-t-il?
• Choices: A) 43 marbles B) 52 marbles C) 53 marbles D) 54 marbles
• Hint: To subtract 85 − 32, take away the tens: 80 − 30 = 50, then ones: 5 − 2 = 3, total 53.
• Steps:
  • Subtract the tens: 70 − 20 = 50.
  • Subtract the ones: 6 − 3 = 3.
  • 50 + 3 = 53.
  • There are 53 marbles left.
• Answer: 53 marbles

[Easy] Telling Time

• EN: The clock shows the hour hand on 4 and the minute hand on 12. What time is it?
• FR: L'horloge montre la petite aiguille sur le 4 et la grande aiguille sur le 12. Quelle heure est-il?
• Choices: A) 3:00 B) 4:00 C) 4:30 D) 5:00
• Hint: When the minute hand points to 12, it is exactly on the hour — like 7:00 or 9:00.
• Steps:
  • The minute hand is on 12, so it is exactly on the hour.
  • The hour hand is on 4.
  • The time is 4:00.
• Answer: 4:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 14 cm de long. Un crayon de couleur mesure 9 cm de long. De combien le crayon à mine est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find the difference between 12 and 7, count up from 7 to 12: that is 5 steps.
• Steps:
  • We need to find 14 − 9.
  • Count up from 9 to 14: 10, 11, 12, 13, 14 — that is 5 steps.
  • The pencil is 5 cm longer than the crayon.
• Answer: 5 cm

[Medium] Counting Coins

• EN: Sofia has 2 dimes, 3 nickels, and 4 pennies. How much money does she have in total?
• FR: Sofia a 2 pièces de 10 cents, 3 pièces de 5 cents et 4 sous. Combien d'argent a-t-elle en tout?
• Choices: A) 37 cents B) 38 cents C) 39 cents D) 41 cents
• Hint: Count each coin type separately: 2 dimes = 20 cents, 2 nickels = 10 cents, 3 pennies = 3 cents, then add all together.
• Steps:
  • 2 dimes = 2 × 10 = 20 cents.
  • 3 nickels = 3 × 5 = 15 cents.
  • 4 pennies = 4 × 1 = 4 cents.
  • 20 + 15 + 4 = 39 cents.
• Answer: 39 cents

[Medium] Telling Time — Half Hour

• EN: Hockey practice starts at 2:00 and lasts half an hour. What time does practice end?
• FR: La pratique de hockey commence à 14 h et dure une demi-heure. À quelle heure la pratique se termine-t-elle?
• Choices: A) 2:15 B) 2:30 C) 3:00 D) 3:30
• Hint: Half an hour after 5:00 is 5:30 — the minute hand moves from 12 to 6.
• Steps:
  • Practice starts at 2:00.
  • Half an hour = 30 minutes.
  • 2:00 + 30 minutes = 2:30.
  • Practice ends at 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: Find the rule first — in 3, 6, 9, 12, the rule is adding 3 each time; the next is 15.
• Steps:
  • Look at the pattern: 5, 10, 15, 20.
  • Each number is 5 more than the one before.
  • 20 + 5 = 25.
  • The missing number is 25.
• Answer: 25

[Medium] Addition with Regrouping

• EN: There are 47 students in the gym and 36 more students join them. How many students are in the gym now?
• FR: Il y a 47 élèves dans le gymnase et 36 autres les rejoignent. Combien d'élèves y a-t-il maintenant dans le gymnase?
• Choices: A) 73 students B) 82 students C) 83 students D) 84 students
• Hint: To add 38 + 24, add ones: 8 + 4 = 12, write 2 carry 1; then tens: 3 + 2 + 1 = 6, giving 62.
• Steps:
  • Add the ones: 7 + 6 = 13. Write 3, carry the 1.
  • Add the tens: 4 + 3 + 1 (carried) = 8.
  • So 47 + 36 = 83.
  • There are 83 students in the gym.
• Answer: 83 students

[Hard] Two-Step Coins Problem

• EN: Noah has 3 dimes and 2 nickels. He spends 27 cents on a sticker. How many cents does he have left?
• FR: Noah a 3 pièces de 10 cents et 2 pièces de 5 cents. Il dépense 27 cents pour un autocollant. Combien de cents lui reste-t-il?
• Choices: A) 13 cents B) 14 cents C) 15 cents D) 17 cents
• Hint: First find the total (e.g., 2 dimes + 3 nickels = 35 cents), then subtract what was spent.
• Steps:
  • 3 dimes = 30 cents. 2 nickels = 10 cents.
  • Total: 30 + 10 = 40 cents.
  • 40 − 27 = 13 cents.
  • Noah has 13 cents left.
• Answer: 13 cents

[Hard] Measuring and Comparing

• EN: A bookshelf is 95 cm tall. A table is 68 cm tall. How much taller is the bookshelf than the table?
• FR: Une bibliothèque mesure 95 cm de haut. Une table mesure 68 cm de haut. De combien la bibliothèque est-elle plus haute que la table?
• Choices: A) 23 cm B) 26 cm C) 27 cm D) 37 cm
• Hint: To subtract 82 − 55, regroup: borrow from the tens — 12 − 5 = 7 ones, 7 − 5 = 2 tens, giving 27.
• Steps:
  • Subtract: 95 − 68.
  • Regroup: borrow 1 ten from 9. Now we have 15 − 8 = 7 ones.
  • Tens: 8 − 6 = 2 tens.
  • 95 − 68 = 27 cm. The bookshelf is 27 cm taller.
• Answer: 27 cm

[Easy] Multiplication — 2s Table

• EN: What is 2 × 8?
• FR: Combien font 2 × 8?
• Choices: A) 14 B) 16 C) 18 D) 20
• Hint: Multiplying by 2 is the same as adding a number to itself — like 2 × 5 = 5 + 5 = 10.
• Steps:
  • 2 × 8 means 8 + 8.
  • 8 + 8 = 16.
  • So 2 × 8 = 16.
• Answer: 16

[Easy] Multiplication — 5s Table

• EN: There are 4 bags of hockey pucks. Each bag has 5 pucks. How many pucks are there in all?
• FR: Il y a 4 sacs de rondelles de hockey. Chaque sac contient 5 rondelles. Combien de rondelles y a-t-il en tout?
• Choices: A) 15 pucks B) 20 pucks C) 25 pucks D) 30 pucks
• Hint: 3 bags of 5 is 3 × 5 = 15; count by 5s: 5, 10, 15.
• Steps:
  • 4 bags × 5 pucks each = 4 × 5.
  • Count by 5s: 5, 10, 15, 20.
  • 4 × 5 = 20 pucks.
• Answer: 20 pucks

[Easy] Basic Fractions

• EN: A pizza is cut into 4 equal pieces. Emma eats 1 piece. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 morceaux égaux. Emma mange 1 morceau. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: A fraction shows parts out of a whole — if you eat 1 out of 3 equal pieces, that is 1/3.
• Steps:
  • The pizza has 4 equal pieces (denominator = 4).
  • Emma eats 1 piece (numerator = 1).
  • The fraction is 1/4.
• Answer: 1/4

[Easy] Reading a Simple Graph

• EN: A bar graph shows that 6 students chose cats and 9 students chose dogs as their favourite pet. How many more students chose dogs than cats?
• FR: Un diagramme à bandes montre que 6 élèves ont choisi le chat et 9 ont choisi le chien comme animal préféré. Combien d'élèves de plus ont choisi le chien?
• Choices: A) 2 students B) 3 students C) 4 students D) 5 students
• Hint: To find "how many more," subtract the smaller number from the larger — like 8 − 5 = 3.
• Steps:
  • Dogs: 9 students. Cats: 6 students.
  • Subtract: 9 − 6 = 3.
  • 3 more students chose dogs than cats.
• Answer: 3 students

[Medium] Division

• EN: There are 24 cookies to share equally among 3 friends. How many cookies does each friend get?
• FR: Il y a 24 biscuits à partager également entre 3 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 6 cookies B) 7 cookies C) 8 cookies D) 9 cookies
• Hint: Division is the opposite of multiplication — to solve 18 ÷ 3, think: 3 × ? = 18, so the answer is 6.
• Steps:
  • We need 24 ÷ 3.
  • Think: 3 × ? = 24.
  • 3 × 8 = 24.
  • Each friend gets 8 cookies.
• Answer: 8 cookies

[Medium] Perimeter of a Rectangle

• EN: A garden has a length of 7 m and a width of 3 m. What is the perimeter of the garden?
• FR: Un jardin a une longueur de 7 m et une largeur de 3 m. Quel est le périmètre du jardin?
• Choices: A) 18 m B) 20 m C) 21 m D) 24 m
• Hint: Perimeter of a rectangle = add all 4 sides; for a 5 m × 2 m rectangle: 5 + 2 + 5 + 2 = 14 m.
• Steps:
  • Perimeter = length + width + length + width.
  • 7 + 3 + 7 + 3 = 20.
  • The perimeter of the garden is 20 m.
• Answer: 20 m

[Medium] Multiplication — 3s Table

• EN: A Tim Hortons box holds 3 muffins. How many muffins are in 6 boxes?
• FR: Une boîte Tim Hortons contient 3 muffins. Combien de muffins y a-t-il dans 6 boîtes?
• Choices: A) 15 muffins B) 16 muffins C) 18 muffins D) 21 muffins
• Hint: To find 4 × 3, count by 3s four times: 3, 6, 9, 12.
• Steps:
  • 6 boxes × 3 muffins each = 6 × 3.
  • Count by 3s: 3, 6, 9, 12, 15, 18.
  • 6 × 3 = 18 muffins.
• Answer: 18 muffins

[Medium] Fractions — Half

• EN: There are 14 students in a class. Half of them wear glasses. How many students wear glasses?
• FR: Il y a 14 élèves dans une classe. La moitié d'entre eux portent des lunettes. Combien d'élèves portent des lunettes?
• Choices: A) 5 students B) 6 students C) 7 students D) 8 students
• Hint: Half of a number means dividing by 2 — half of 10 is 10 ÷ 2 = 5.
• Steps:
  • Half means dividing into 2 equal groups.
  • 14 ÷ 2 = 7.
  • 7 students wear glasses.
• Answer: 7 students

[Hard] Multiplication — 10s Table with Reasoning

• EN: A school orders 10 packs of markers. Each pack has 8 markers. The school gives away 15 markers to the library. How many markers does the school have left?
• FR: Une école commande 10 paquets de marqueurs. Chaque paquet contient 8 marqueurs. L'école donne 15 marqueurs à la bibliothèque. Combien de marqueurs reste-t-il à l'école?
• Choices: A) 65 markers B) 70 markers C) 75 markers D) 80 markers
• Hint: First multiply to find the total, then subtract — like 5 × 4 = 20, then 20 − 3 = 17.
• Steps:
  • Step 1: 10 packs × 8 markers = 10 × 8 = 80 markers.
  • Step 2: Give away 15 markers: 80 − 15 = 65.
  • The school has 65 markers left.
• Answer: 65 markers

[Hard] Perimeter with Missing Side

• EN: A triangle has two sides that are each 9 cm long. The perimeter of the triangle is 25 cm. How long is the third side?
• FR: Un triangle a deux côtés qui mesurent chacun 9 cm. Le périmètre du triangle est de 25 cm. Quelle est la longueur du troisième côté?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: Perimeter is the total of all sides — if you know the total and two sides, subtract to find the third: 20 − 6 − 6 = 8.
• Steps:
  • Perimeter = side 1 + side 2 + side 3.
  • 25 = 9 + 9 + side 3.
  • 25 = 18 + side 3.
  • side 3 = 25 − 18 = 7 cm.
• Answer: 7 cm

[Easy] Multiplication Tables to 9×9

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: You can use 7 × 8 = 7 × 4 × 2 = 28 × 2 = 56, or recall 6 × 8 = 48 and add one more 8.
• Steps:
  • Recall: 7 × 8 is a key fact.
  • 7 × 8 = 56.
  • Double-check: 8 × 7 = 8 + 8 + 8 + 8 + 8 + 8 + 8 = 56. ✓
• Answer: 56

[Easy] Decimal Place Value — Tenths

• EN: What is the value of the digit 3 in the number 5.3?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 5,3?
• Choices: A) 3 ones B) 3 tens C) 3 tenths D) 3 hundredths
• Hint: In the number 4.7, the digit 7 is to the right of the decimal point, so it represents 7 tenths.
• Steps:
  • In 5.3, the digit 3 is in the first position after the decimal point.
  • That position is the tenths place.
  • So the value of 3 in 5.3 is 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A rectangular rug is 6 m long and 4 m wide. What is the area of the rug?
• FR: Un tapis rectangulaire mesure 6 m de long et 4 m de large. Quelle est l'aire du tapis?
• Choices: A) 20 m² B) 22 m² C) 24 m² D) 26 m²
• Hint: Area of a rectangle = length × width — for a 5 m × 3 m rectangle, area = 5 × 3 = 15 m².
• Steps:
  • Area = length × width.
  • Area = 6 × 4 = 24.
  • The area of the rug is 24 m².
• Answer: 24 m²

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 1/2?
• FR: Quelle fraction est la plus grande: 3/4 ou 1/2?
• Choices: A) 1/2 B) 1/4 C) 3/4 D) 2/3
• Hint: Convert to the same denominator — 1/2 = 2/4, and then compare 2/4 and 3/4.
• Steps:
  • Convert 1/2 to fourths: 1/2 = 2/4.
  • Compare 2/4 and 3/4.
  • Since 3 > 2, we know 3/4 > 2/4.
  • So 3/4 is larger.
• Answer: 3/4

[Medium] Long Division with Remainder

• EN: A teacher has 47 pencils to put into boxes. Each box holds 5 pencils. How many full boxes can she make, and how many pencils are left over?
• FR: Une enseignante a 47 crayons à mettre dans des boîtes. Chaque boîte contient 5 crayons. Combien de boîtes pleines peut-elle faire, et combien de crayons restent-il?
• Choices: A) 8 boxes remainder 5 B) 9 boxes remainder 2 C) 9 boxes remainder 3 D) 10 boxes remainder 1
• Hint: To divide 38 ÷ 5, find how many 5s fit in 38: 5 × 7 = 35, so 7 boxes with 3 left over.
• Steps:
  • 47 ÷ 5: find the largest multiple of 5 that is ≤ 47.
  • 5 × 9 = 45. That fits.
  • Remainder: 47 − 45 = 2.
  • She can make 9 full boxes with 2 pencils left over.
• Answer: 9 boxes remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 PM and ends at 3:45 PM. How long is the game?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Quelle est la durée du match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: To find elapsed time from 2:20 to 4:50, count the hours (2) then the minutes (30), total 2 hours 30 minutes.
• Steps:
  • From 1:15 PM to 3:15 PM is exactly 2 hours.
  • From 3:15 PM to 3:45 PM is 30 more minutes.
  • Total: 2 hours + 30 minutes = 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A book costs $4.75 and a pencil case costs $3.20. What is the total cost?
• FR: Un livre coûte 4,75 $ et une trousse coûte 3,20 $. Quel est le coût total?
• Choices: A) $7.85 B) $7.95 C) $8.05 D) $8.15
• Hint: Line up the decimal points to add — like adding $2.40 + $1.30: 2.40 + 1.30 = 3.70.
• Steps:
  • Line up decimals: 4.75 + 3.20.
  • Add hundredths: 5 + 0 = 5.
  • Add tenths: 7 + 2 = 9.
  • Add ones: 4 + 3 = 7. Total: $7.95.
• Answer: $7.95

[Medium] Multiplication — 2-Digit by 1-Digit

• EN: A school bus has 8 rows of seats. Each row holds 6 students. How many students can the bus hold?
• FR: Un autobus scolaire a 8 rangées de sièges. Chaque rangée peut accueillir 6 élèves. Combien d'élèves l'autobus peut-il accueillir?
• Choices: A) 42 students B) 46 students C) 48 students D) 54 students
• Hint: To find 7 × 9, think 7 × 10 = 70 and subtract 7 to get 63.
• Steps:
  • 8 rows × 6 seats each = 8 × 6.
  • 8 × 6 = 48.
  • The bus can hold 48 students.
• Answer: 48 students

[Hard] Multi-Step Problem with Decimals

• EN: Ava has $10.00. She buys a notebook for $3.75 and a pen for $1.50. How much money does she have left?
• FR: Ava a 10,00 $. Elle achète un cahier à 3,75 $ et un stylo à 1,50 $. Combien d'argent lui reste-t-il?
• Choices: A) $4.25 B) $4.50 C) $4.75 D) $5.25
• Hint: Add the two costs first, then subtract from the total — like $10.00 − ($2.00 + $1.50) = $6.50.
• Steps:
  • Add the two purchases: $3.75 + $1.50 = $5.25.
  • Subtract from $10.00: $10.00 − $5.25 = $4.75.
  • Ava has $4.75 left.
• Answer: $4.75

[Hard] Area and Perimeter Combined

• EN: A rectangular park has a perimeter of 36 m. The length of the park is 11 m. What is the area of the park?
• FR: Un parc rectangulaire a un périmètre de 36 m. La longueur du parc est de 11 m. Quelle est l'aire du parc?
• Choices: A) 66 m² B) 70 m² C) 77 m² D) 88 m²
• Hint: Perimeter of a rectangle = 2 × (l + w); use this to find width first, then area = l × w.
• Steps:
  • Perimeter = 2 × (length + width). 36 = 2 × (11 + w).
  • 18 = 11 + w, so w = 7 m.
  • Area = 11 × 7 = 77 m².
  • The area of the park is 77 m².
• Answer: 77 m²

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 198 C) 204 D) 214
• Hint: Break it into parts — 30 × 6 = 180 and 4 × 6 = 24, then add: 180 + 24 = 204.
• Steps:
  • 34 × 6 = (30 + 4) × 6.
  • 30 × 6 = 180.
  • 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/8 + 3/8?
• FR: Combien font 2/8 + 3/8?
• Choices: A) 5/16 B) 5/8 C) 6/8 D) 1/2
• Hint: When denominators are the same, just add the numerators — like 1/5 + 2/5 = 3/5.
• Steps:
  • The denominators are both 8, so they are the same.
  • Add the numerators: 2 + 3 = 5.
  • Keep the denominator: 5/8.
  • The answer is 5/8.
• Answer: 5/8

[Easy] Decimal Operations — Addition

• EN: What is 3.6 + 2.7?
• FR: Combien font 3,6 + 2,7?
• Choices: A) 5.3 B) 6.3 C) 6.13 D) 6.4
• Hint: Line up the decimal points — like 4.5 + 1.8: ones 4 + 1 = 5, tenths 5 + 8 = 13, carry 1, giving 6.3.
• Steps:
  • Line up: 3.6 + 2.7.
  • Tenths: 6 + 7 = 13. Write 3, carry 1.
  • Ones: 3 + 2 + 1 = 6.
  • Answer: 6.3
• Answer: 6.3

[Easy] Percentage Intro — 50%

• 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 any number is that number divided by 2; 50% of 60 = 30.
• Steps:
  • 50% = one half.
  • 80 ÷ 2 = 40.
  • 50% of 80 is 40.
• Answer: 40

[Medium] Multi-Digit Division

• EN: A school orders 168 pencils to be shared equally among 8 classrooms. How many pencils does each classroom get?
• FR: Une école commande 168 crayons à répartir également entre 8 classes. Combien de crayons chaque classe reçoit-elle?
• Choices: A) 19 pencils B) 20 pencils C) 21 pencils D) 22 pencils
• Hint: To divide 144 ÷ 6, think: 6 × 20 = 120, 144 − 120 = 24, 24 ÷ 6 = 4, so answer is 24.
• Steps:
  • 168 ÷ 8. Think: 8 × 20 = 160.
  • 168 − 160 = 8. Then 8 ÷ 8 = 1.
  • 20 + 1 = 21.
  • Each classroom gets 21 pencils.
• Answer: 21 pencils

[Medium] Subtracting Fractions with Like Denominators

• EN: What is 7/10 − 2/10?
• FR: Combien font 7/10 − 2/10?
• Choices: A) 4/10 B) 5/10 C) 5/20 D) 9/10
• Hint: Same denominator — just subtract numerators: 8/9 − 3/9 = 5/9.
• Steps:
  • The denominators are both 10.
  • Subtract the numerators: 7 − 2 = 5.
  • Keep the denominator: 5/10.
  • The answer is 5/10.
• Answer: 5/10

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume of a rectangular prism = length × width × height — like 6 × 2 × 4 = 48 cm³.
• Steps:
  • Volume = l × w × h.
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A winter jacket costs $120. It is on sale for 25% off. How much money will you save?
• FR: Un manteau d'hiver coûte 120 $. Il est en solde avec 25% de rabais. Combien d'argent économiserez-vous?
• Choices: A) $25 B) $28 C) $30 D) $35
• Hint: 25% means one quarter — divide by 4; 25% of $80 = $80 ÷ 4 = $20.
• Steps:
  • 25% = one quarter.
  • $120 ÷ 4 = $30.
  • You will save $30.
• Answer: $30

[Hard] Multi-Step Decimal Problem

• EN: Chloe runs 2.35 km on Monday, 3.6 km on Wednesday, and 1.75 km on Friday. What is the total distance she runs in the three days?
• FR: Chloé court 2,35 km lundi, 3,6 km mercredi et 1,75 km vendredi. Quelle est la distance totale qu'elle parcourt en trois jours?
• Choices: A) 7.50 km B) 7.60 km C) 7.70 km D) 7.80 km
• Hint: Add all three decimals by lining up the decimal points — like 1.20 + 2.50 + 3.10 = 6.80.
• Steps:
  • Line up: 2.35 + 3.60 + 1.75.
  • Hundredths: 5 + 0 + 5 = 10. Write 0, carry 1.
  • Tenths: 3 + 6 + 7 + 1 = 17. Write 7, carry 1.
  • Ones: 2 + 3 + 1 + 1 = 7.
  • Total: 7.70 km.
• Answer: 7.70 km

[Hard] Volume and Percentage Combined

• EN: A fish tank holds 200 litres when full. Right now it is 10% full. How many litres of water are in the tank?
• FR: Un aquarium peut contenir 200 litres quand il est plein. En ce moment, il est rempli à 10%. Combien de litres d'eau contient-il?
• Choices: A) 10 litres B) 15 litres C) 20 litres D) 25 litres
• Hint: 10% of a number = divide by 10; 10% of 150 = 150 ÷ 10 = 15.
• Steps:
  • 10% means divide by 10.
  • 200 ÷ 10 = 20.
  • There are 20 litres of water in the tank.
• Answer: 20 litres

[Easy] Percent of a Number

• EN: What is 20% of 60?
• FR: Combien font 20% de 60?
• Choices: A) 10 B) 12 C) 14 D) 15
• Hint: 20% = 2 × 10%; find 10% first by dividing by 10, then double it — like 10% of 50 = 5, so 20% = 10.
• Steps:
  • 10% of 60 = 60 ÷ 10 = 6.
  • 20% = 2 × 6 = 12.
  • 20% of 60 is 12.
• Answer: 12

[Easy] Simple Algebraic Expressions

• EN: Evaluate 3n + 4 when n = 5.
• FR: Évalue 3n + 4 lorsque n = 5.
• Choices: A) 17 B) 18 C) 19 D) 22
• Hint: Substitute the value into the expression — like 2x + 3 when x = 4: 2 × 4 + 3 = 11.
• Steps:
  • Replace n with 5: 3(5) + 4.
  • 3 × 5 = 15.
  • 15 + 4 = 19.
  • The answer is 19.
• Answer: 19

[Easy] Ratio

• EN: In a bag, there are 3 red marbles and 5 blue marbles. What is the ratio of red to blue marbles?
• FR: Dans un sac, il y a 3 billes rouges et 5 billes bleues. Quel est le rapport des billes rouges aux billes bleues?
• Choices: A) 3:8 B) 5:3 C) 3:5 D) 5:8
• Hint: A ratio compares two quantities in order — if there are 4 cats and 7 dogs, the ratio of cats to dogs is 4:7.
• Steps:
  • Red marbles: 3. Blue marbles: 5.
  • The ratio of red to blue is 3:5.
• Answer: 3:5

[Easy] Integers — Introduction

• EN: Which integer is 3 less than −1?
• FR: Quel entier est 3 de moins que −1?
• Choices: A) −5 B) −4 C) 2 D) 4
• Hint: Going 3 less means moving left on the number line — from −2, move left 3 steps to reach −5.
• Steps:
  • Start at −1 on the number line.
  • Move 3 steps to the left (less than).
  • −1 − 3 = −4.
  • The answer is −4.
• Answer: −4

[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) 5/12
• Hint: Multiply numerators together and denominators together — like 1/2 × 2/3 = 2/6 = 1/3.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2 (simplified).
  • The answer is 1/2.
• Answer: 1/2

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1.
• FR: Évalue: 3 + 4 × 2 − 1.
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: BEDMAS: do multiplication before addition — in 5 + 3 × 2, multiply first: 5 + 6 = 11.
• Steps:
  • Follow BEDMAS: multiplication first.
  • 4 × 2 = 8.
  • Now: 3 + 8 − 1.
  • 3 + 8 = 11, then 11 − 1 = 10.
• Answer: 10

[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/h?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 85 km/h
• Hint: Rate = total ÷ time — if you walk 15 km in 3 hours, your rate is 15 ÷ 3 = 5 km/h.
• Steps:
  • Speed = distance ÷ time.
  • Speed = 240 ÷ 3.
  • 240 ÷ 3 = 80.
  • The car's speed is 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 2
• Hint: To divide by a fraction, multiply by its reciprocal — like 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
• Steps:
  • Keep 3/4, change ÷ to ×, flip 1/2 to 2/1.
  • 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 3/2.
  • The answer is 3/2.
• Answer: 3/2

[Hard] Multi-Step Percent Problem

• EN: A sweater originally costs $80. It is on sale for 30% off. After the discount, there is a 5% tax on the sale price. What is the final price?
• FR: Un chandail coûte originalement 80 $. Il est en solde avec 30% de rabais. Après la réduction, une taxe de 5% s'applique sur le prix réduit. Quel est le prix final?
• Choices: A) $54.60 B) $56.00 C) $58.80 D) $59.50
• Hint: First subtract the discount, then apply tax to the new price — like $100 − 20% = $80, then $80 × 1.10 = $88.
• Steps:
  • Discount: 30% of $80 = $24. Sale price: $80 − $24 = $56.
  • Tax: 5% of $56 = $2.80.
  • Final price: $56 + $2.80 = $58.80.
• Answer: $58.80

[Hard] Order of Operations with Integers

• EN: Evaluate: (−3 + 7) × 2 − 4 ÷ 2.
• FR: Évalue: (−3 + 7) × 2 − 4 ÷ 2.
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: BEDMAS — brackets first, then multiply and divide left to right, then add and subtract.
• Steps:
  • Brackets first: −3 + 7 = 4.
  • Now: 4 × 2 − 4 ÷ 2.
  • Multiply and divide: 4 × 2 = 8; 4 ÷ 2 = 2.
  • Subtract: 8 − 2 = 6.
• Answer: 6

[Easy] Integer Addition

• EN: What is −5 + 9?
• FR: Combien font −5 + 9?
• Choices: A) −4 B) 3 C) 4 D) 14
• Hint: On a number line, start at −3 and move right 8 spaces to land on 5.
• Steps:
  • Start at −5 on the number line.
  • Move right 9 spaces (adding a positive number).
  • −5 + 9 = 4.
• Answer: 4

[Easy] Integer Subtraction

• EN: What is 3 − (−4)?
• FR: Combien font 3 − (−4)?
• Choices: A) −1 B) 1 C) 6 D) 7
• Hint: Subtracting a negative is the same as adding — like 5 − (−2) = 5 + 2 = 7.
• Steps:
  • Change subtraction of a negative to addition: 3 − (−4) = 3 + 4.
  • 3 + 4 = 7.
  • The answer is 7.
• Answer: 7

[Easy] Percentage — Discount

• EN: A $60 video game is discounted by 10%. What is the sale price?
• FR: Un jeu vidéo à 60 $ est réduit de 10%. Quel est le prix de vente?
• Choices: A) $48 B) $50 C) $54 D) $56
• Hint: 10% of any number = divide by 10; then subtract from the original — like 10% of $80 = $8, sale price = $72.
• Steps:
  • 10% of $60 = $60 ÷ 10 = $6.
  • Sale price = $60 − $6 = $54.
  • The sale price is $54.
• Answer: $54

[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 isolate x, do the opposite operation — 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] Integer Multiplication

• EN: What is (−7) × (−4)?
• FR: Combien font (−7) × (−4)?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: Negative × negative = positive — like (−3) × (−5) = +15.
• Steps:
  • A negative times a negative gives a positive result.
  • 7 × 4 = 28.
  • So (−7) × (−4) = +28.
• Answer: 28

[Medium] Surface Area of a Rectangular Prism

• EN: What is the surface area of a box that is 5 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire de la surface d'une boîte qui mesure 5 cm de long, 3 cm de large et 2 cm de haut?
• Choices: A) 54 cm² B) 58 cm² C) 62 cm² D) 66 cm²
• Hint: Surface area = 2(lw + lh + wh) — for a 4 × 2 × 1 box: 2(8 + 4 + 2) = 2 × 14 = 28 cm².
• Steps:
  • SA = 2(lw + lh + wh).
  • = 2(5×3 + 5×2 + 3×2).
  • = 2(15 + 10 + 6).
  • = 2 × 31 = 62 cm².
• Answer: 62 cm²

[Medium] Percentage — Tax

• EN: A pair of skates costs $150. The HST rate is 13%. What is the total price with tax?
• FR: Une paire de patins coûte 150 $. Le taux de TVH est de 13%. Quel est le prix total avec la taxe?
• Choices: A) $165.00 B) $169.50 C) $172.00 D) $175.50
• Hint: To find total with tax, multiply the price by (1 + tax rate) — like $200 × 1.10 = $220 for a 10% tax.
• Steps:
  • Tax = 13% of $150 = 0.13 × 150 = $19.50.
  • Total = $150 + $19.50 = $169.50.
• Answer: $169.50

[Medium] Integer Division

• EN: What is (−36) ÷ 9?
• FR: Combien font (−36) ÷ 9?
• Choices: A) −5 B) −4 C) 4 D) 5
• Hint: A negative divided by a positive gives a negative — like (−20) ÷ 5 = −4.
• Steps:
  • 36 ÷ 9 = 4.
  • Negative ÷ positive = negative.
  • (−36) ÷ 9 = −4.
• Answer: −4

[Hard] Two-Step Linear Equation

• EN: Solve for x: 4x − 3 = 17.
• FR: Résous pour x: 4x − 3 = 17.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: Add 3 to both sides first, then divide both sides by the coefficient — like 3x − 2 = 13: add 2 → 3x = 15 → x = 5.
• Steps:
  • Add 3 to both sides: 4x − 3 + 3 = 17 + 3 → 4x = 20.
  • Divide both sides by 4: x = 20 ÷ 4 = 5.
  • So x = 5.
• Answer: x = 5

[Hard] Probability

• EN: A bag has 4 red chips, 3 blue chips, and 5 green chips. If you pick one chip without looking, what is the probability of picking a blue chip?
• FR: Un sac contient 4 jetons rouges, 3 jetons bleus et 5 jetons verts. Si tu en piges un sans regarder, quelle est la probabilité de piger un jeton bleu?
• Choices: A) 1/4 B) 3/12 C) 1/3 D) 3/4
• Hint: Probability = favourable outcomes ÷ total outcomes — like 2 red out of 8 total = 2/8 = 1/4.
• Steps:
  • Total chips: 4 + 3 + 5 = 12.
  • Blue chips: 3.
  • Probability = 3/12 = 1/4.
  • The probability of picking a blue chip is 1/4.
• Answer: 1/4

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien font √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: A perfect square's root is a whole number — √100 = 10 because 10 × 10 = 100.
• Steps:
  • Ask: what number times itself equals 144?
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored 70, 80, 90, 60, and 100 on a math test. What is the mean (average) score?
• FR: Cinq élèves ont obtenu 70, 80, 90, 60 et 100 à un examen de mathématiques. Quelle est la note moyenne?
• Choices: A) 78 B) 80 C) 82 D) 85
• Hint: Mean = sum of all values ÷ number of values — like (4 + 6 + 8) ÷ 3 = 18 ÷ 3 = 6.
• Steps:
  • Add the scores: 70 + 80 + 90 + 60 + 100 = 400.
  • Divide by 5 (number of scores): 400 ÷ 5 = 80.
  • The mean score is 80.
• Answer: 80

[Easy] Percent Increase

• EN: A shirt costs $40. Its price increases by 15%. What is the new price?
• FR: Une chemise coûte 40 $. Son prix augmente de 15%. Quel est le nouveau prix?
• Choices: A) $44 B) $45 C) $46 D) $47
• Hint: Percent increase: find the increase amount then add to original — like 10% of $50 = $5, new price = $55.
• Steps:
  • 15% of $40 = 0.15 × 40 = $6.
  • New price = $40 + $6 = $46.
• Answer: $46

[Easy] Two-Step Linear Equation

• EN: Solve for x: 3x + 5 = 20.
• FR: Résous pour x: 3x + 5 = 20.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 8
• Hint: Subtract the constant first, then divide — like 2x + 4 = 12: subtract 4 to get 2x = 8, then divide by 2: x = 4.
• Steps:
  • Subtract 5 from both sides: 3x = 20 − 5 = 15.
  • Divide both sides by 3: x = 15 ÷ 3 = 5.
  • So x = 5.
• Answer: x = 5

[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 — for legs of 3 and 4: 9 + 16 = 25, so c = √25 = 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 (0, 2) and (4, 10). What is the slope of the line?
• FR: Une droite passe par les points (0, 2) et (4, 10). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) — like from (0, 1) to (3, 7): (7−1) ÷ (3−0) = 6 ÷ 3 = 2.
• Steps:
  • Slope = (y₂ − y₁) ÷ (x₂ − x₁).
  • = (10 − 2) ÷ (4 − 0).
  • = 8 ÷ 4.
  • = 2.
• Answer: 2

[Medium] Median and Mode

• EN: The snowfall (in cm) over 7 days was: 3, 5, 5, 7, 8, 10, 12. What is the median snowfall?
• FR: Les chutes de neige (en cm) sur 7 jours étaient: 3, 5, 5, 7, 8, 10, 12. Quelle est la médiane?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: The median is the middle value when data is ordered — in 2, 4, 6, 8, 10, the middle (3rd) value is 6.
• Steps:
  • The data is already ordered: 3, 5, 5, 7, 8, 10, 12.
  • There are 7 values, so the middle is the 4th value.
  • The 4th value is 7.
  • The median is 7 cm.
• Answer: 7 cm

[Medium] Percent Decrease

• EN: A pair of boots originally cost $120. After a sale, the price drops by 25%. What is the sale price?
• FR: Une paire de bottes coûtait 120 $. Après une vente, le prix baisse de 25%. Quel est le prix de vente?
• Choices: A) $85 B) $88 C) $90 D) $95
• Hint: Percent decrease: find the decrease then subtract — 25% of $80 = $20, new price = $60.
• Steps:
  • 25% of $120 = 0.25 × 120 = $30.
  • Sale price = $120 − $30 = $90.
• Answer: $90

[Hard] Pythagorean Theorem — Finding 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) 11 cm D) 12 cm
• Hint: Rearrange a² + b² = c² to find a leg: b² = c² − a² — like c = 10, a = 6: b² = 100 − 36 = 64, b = 8.
• Steps:
  • a² + b² = c². We know c = 13 and a = 5.
  • b² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12 cm.
• Answer: 12 cm

[Hard] Two-Step Equation with Fractions

• EN: Solve for x: x/3 + 4 = 9.
• FR: Résous pour x: x/3 + 4 = 9.
• Choices: A) x = 13 B) x = 15 C) x = 18 D) x = 21
• Hint: Subtract the constant first, then multiply both sides by the denominator — like x/4 + 2 = 7: subtract 2 → x/4 = 5 → x = 20.
• Steps:
  • Subtract 4 from both sides: x/3 = 9 − 4 = 5.
  • Multiply both sides by 3: x = 5 × 3 = 15.
  • So x = 15.
• Answer: x = 15

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 7 = 18.
• FR: Résous pour x: 5x − 7 = 18.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add 7 to both sides to isolate the term with x, then divide — like 3x − 4 = 8: add 4 → 3x = 12 → x = 4.
• Steps:
  • Add 7 to both sides: 5x = 18 + 7 = 25.
  • Divide both sides by 5: x = 25 ÷ 5 = 5.
  • So x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Add: (3x + 4) + (2x − 1).
• FR: Additionne: (3x + 4) + (2x − 1).
• Choices: A) 4x + 3 B) 5x + 3 C) 5x − 5 D) 6x + 3
• Hint: Combine like terms — like (4x + 2) + (x + 5): x terms: 4x + x = 5x; constants: 2 + 5 = 7; answer: 5x + 7.
• Steps:
  • Group like terms: (3x + 2x) + (4 − 1).
  • x terms: 3x + 2x = 5x.
  • Constants: 4 − 1 = 3.
  • Answer: 5x + 3
• Answer: 5x + 3

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 4x − 3?
• FR: Quelle est la pente de la droite y = 4x − 3?
• Choices: A) −4 B) −3 C) 3 D) 4
• Hint: In y = mx + b, m is the slope and b is the y-intercept — in y = 6x + 2, the slope is 6.
• Steps:
  • The equation is in y = mx + b form.
  • m is the coefficient of x.
  • In y = 4x − 3, m = 4.
  • The slope is 4.
• Answer: 4

[Easy] SOH-CAH-TOA Introduction

• EN: In a right triangle, the side opposite an angle is 3 cm and the hypotenuse is 5 cm. What is the sine of that angle?
• FR: Dans un triangle rectangle, le côté opposé à un angle mesure 3 cm et l'hypoténuse mesure 5 cm. Quel est le sinus de cet angle?
• Choices: A) 3/4 B) 3/5 C) 4/5 D) 5/3
• Hint: SOH means Sine = Opposite ÷ Hypotenuse — if opposite = 4 and hypotenuse = 8, sin = 4/8 = 1/2.
• Steps:
  • sin(angle) = Opposite ÷ Hypotenuse.
  • = 3 ÷ 5.
  • = 3/5.
• Answer: 3/5

[Medium] Linear Inequality

• EN: Solve for x: 2x + 3 > 11. Which value is in the solution set?
• FR: Résous pour x: 2x + 3 > 11. Quelle valeur fait partie de l'ensemble solution?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Solve like an equation first — for 3x + 2 > 14: subtract 2 → 3x > 12 → x > 4, so x = 5 works.
• Steps:
  • Subtract 3: 2x > 8.
  • Divide by 2: x > 4.
  • Values greater than 4: x = 5 is in the solution set.
• Answer: x = 5

[Medium] Multiplying Polynomials

• EN: Expand and simplify: 3(2x − 4).
• FR: Développe et simplifie: 3(2x − 4).
• Choices: A) 5x − 7 B) 6x − 7 C) 6x − 12 D) 8x − 12
• Hint: Distribute — multiply each term inside the brackets by the number outside: 4(3x − 2) = 12x − 8.
• Steps:
  • Multiply 3 by each term in the brackets.
  • 3 × 2x = 6x.
  • 3 × (−4) = −12.
  • Answer: 6x − 12
• Answer: 6x − 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 6 cm. If the smaller triangle has a second side of 5 cm, how long is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 6 cm. Si le petit triangle a un deuxième côté de 5 cm, quelle est la longueur du côté correspondant du grand triangle?
• Choices: A) 6.5 cm B) 7 cm C) 7.5 cm D) 8 cm
• Hint: The scale factor is the ratio of corresponding sides — if sides are in ratio 2:3, multiply each known side by 3/2 to find the larger triangle's sides.
• Steps:
  • Scale factor = 6 ÷ 4 = 1.5.
  • Larger side = 5 × 1.5 = 7.5 cm.
• Answer: 7.5 cm

[Medium] Graphing Lines — y-intercept

• EN: A line has equation y = −2x + 6. What is the y-intercept?
• FR: Une droite a l'équation y = −2x + 6. Quel est l'ordonnée à l'origine?
• Choices: A) −6 B) −2 C) 2 D) 6
• Hint: In y = mx + b, b is the y-intercept (where the line crosses the y-axis) — in y = 3x + 7, the y-intercept is 7.
• Steps:
  • The equation is y = −2x + 6.
  • In y = mx + b form, b = 6.
  • The y-intercept is 6.
• Answer: 6

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, one angle is 30°. The hypotenuse is 20 cm. Using trigonometry, what is the length of the side opposite the 30° angle?
• FR: Dans un triangle rectangle, un angle est de 30°. L'hypoténuse mesure 20 cm. En utilisant la trigonométrie, quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Use sin(angle) = opposite/hypotenuse and rearrange to opposite = hypotenuse × sin(angle); sin(45°) = 0.707.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse.
  • sin(30°) = 0.5.
  • opposite = 20 × 0.5 = 10 cm.
• Answer: 10 cm

[Hard] Polynomial Subtraction and Evaluation

• EN: Subtract: (5x² + 3x − 2) − (2x² − x + 4). Then evaluate the result when x = 2.
• FR: Soustrait: (5x² + 3x − 2) − (2x² − x + 4). Puis évalue le résultat pour x = 2.
• Choices: A) 14 B) 18 C) 22 D) 26
• Hint: Subtract polynomials by changing signs of the second one, then combine like terms — then substitute the given x value.
• Steps:
  • Subtract: (5x² + 3x − 2) − (2x² − x + 4) = 3x² + 4x − 6.
  • Evaluate at x = 2: 3(4) + 4(2) − 6 = 12 + 8 − 6 = 14.
  • The answer is 14.
• Answer: 14

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6.
• FR: Factorise: x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 3) D) (x − 2)(x + 3)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — for x² + 7x + 10, use 2 and 5: (x + 2)(x + 5).
• Steps:
  • Find two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5. ✓
  • Factor: (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — cos Ratio

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 8 cm et l'hypoténuse mesure 10 cm. Combien vaut cos(θ)?
• Choices: A) 3/5 B) 4/5 C) 5/4 D) 6/10
• Hint: CAH means cosine = adjacent ÷ hypotenuse — like adjacent = 3, hypotenuse = 5: cos = 3/5.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • = 8 ÷ 10.
  • = 4/5.
• Answer: 4/5

[Easy] System of Equations — Substitution

• EN: Solve: y = 2x and x + y = 9. What is 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: Substitute the expression for y into the second equation — like y = x + 1 and x + y = 7: x + (x + 1) = 7 → 2x = 6 → x = 3.
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9.
  • 3x = 9.
  • x = 3.
• Answer: x = 3

[Easy] Surface Area of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 8 cm. What is the area of just the curved surface? Use π ≈ 3.14.
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 8 cm. Quelle est l'aire de la surface courbe seulement? Utilise π ≈ 3,14.
• Choices: A) 125.6 cm² B) 150.72 cm² C) 164.8 cm² D) 188.4 cm²
• Hint: Curved surface area of a cylinder = 2πrh — for r = 2, h = 5: 2 × 3.14 × 2 × 5 = 62.8 cm².
• Steps:
  • Curved SA = 2πrh.
  • = 2 × 3.14 × 3 × 8.
  • = 2 × 3.14 × 24.
  • = 150.72 cm².
• Answer: 150.72 cm²

[Medium] Completing the Square

• EN: Complete the square to find the vertex form of y = x² + 6x + 5.
• FR: Complète le carré pour trouver la forme sommet de y = x² + 6x + 5.
• Choices: A) y = (x + 2)² − 3 B) y = (x + 3)² − 4 C) y = (x + 3)² + 5 D) y = (x + 6)² − 4
• Hint: Take half the x-coefficient, square it, add and subtract inside: x² + 4x + 5 → (x + 2)² − 4 + 5 = (x + 2)² + 1.
• Steps:
  • Half of 6 is 3; 3² = 9.
  • y = (x² + 6x + 9) − 9 + 5.
  • y = (x + 3)² − 4.
• Answer: y = (x + 3)² − 4

[Medium] Circle Geometry — Chord

• EN: A circle has a radius of 10 cm. A chord is 6 cm from the centre. How long is the chord?
• FR: Un cercle a un rayon de 10 cm. Une corde est à 6 cm du centre. Quelle est la longueur de la corde?
• Choices: A) 12 cm B) 14 cm C) 16 cm D) 18 cm
• Hint: The radius, the distance to the chord, and half the chord form a right triangle — use Pythagorean theorem to find half the chord length, then double it.
• Steps:
  • Half-chord² + 6² = 10².
  • Half-chord² = 100 − 36 = 64.
  • Half-chord = 8 cm.
  • Full chord = 2 × 8 = 16 cm.
• Answer: 16 cm

[Medium] Volume of a Cone

• EN: A cone has a radius of 4 cm and a height of 9 cm. What is its volume? Use π ≈ 3.14.
• FR: Un cône a un rayon de 4 cm et une hauteur de 9 cm. Quel est son volume? Utilise π ≈ 3,14.
• Choices: A) 113.04 cm³ B) 150.72 cm³ C) 175.86 cm³ D) 226.08 cm³
• Hint: Volume of a cone = (1/3)πr²h — for r = 3, h = 7: (1/3) × 3.14 × 9 × 7 ≈ 65.94 cm³.
• Steps:
  • V = (1/3)πr²h.
  • = (1/3) × 3.14 × 16 × 9.
  • = (1/3) × 3.14 × 144.
  • = (1/3) × 452.16 = 150.72 cm³.
• Answer: 150.72 cm³

[Medium] Systems of Equations — Elimination

• EN: Solve the system: 2x + y = 10 and x − y = 2. What is y?
• FR: Résous le système: 2x + y = 10 et x − y = 2. Quelle est la valeur de y?
• Choices: A) y = 1 B) y = 2 C) y = 3 D) y = 4
• Hint: Add the two equations to eliminate y, solve for x, then substitute back to find y.
• Steps:
  • Add equations: (2x + y) + (x − y) = 10 + 2 → 3x = 12 → x = 4.
  • Substitute x = 4 into x − y = 2: 4 − y = 2 → y = 2.
• Answer: y = 2

[Hard] Quadratic Formula

• EN: Solve 2x² − 5x − 3 = 0 using the quadratic formula. What are the solutions?
• FR: Résous 2x² − 5x − 3 = 0 à l'aide de la formule quadratique. Quelles sont les solutions?
• Choices: A) x = 3 or x = −1/2 B) x = −3 or x = 1/2 C) x = 3 or x = 1/2 D) x = −3 or x = −1/2
• Hint: Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ (2a) — identify a, b, c first, then substitute carefully.
• Steps:
  • a = 2, b = −5, c = −3. Discriminant: 25 + 24 = 49. √49 = 7.
  • x = (5 + 7) ÷ 4 = 3 or x = (5 − 7) ÷ 4 = −1/2.
  • Solutions: x = 3 or x = −1/2.
• Answer: x = 3 or x = −1/2

[Hard] Trigonometry — Angle of Elevation

• EN: From a point on the ground, the angle of elevation to the top of a tree is 40°. The distance from the point to the base of the tree is 15 m. How tall is the tree? Use tan(40°) ≈ 0.839.
• FR: Depuis un point au sol, l'angle d'élévation vers le sommet d'un arbre est de 40°. La distance du point à la base de l'arbre est de 15 m. Quelle est la hauteur de l'arbre? Utilise tan(40°) ≈ 0,839.
• Choices: A) 11.2 m B) 12.6 m C) 13.8 m D) 17.9 m
• Hint: tan(angle) = opposite ÷ adjacent → opposite = adjacent × tan(angle) — like tan(30°) ≈ 0.577, so height = 20 × 0.577 ≈ 11.5 m.
• Steps:
  • tan(40°) = height ÷ 15.
  • height = 15 × tan(40°) = 15 × 0.839.
  • height = 12.585 ≈ 12.6 m.
• Answer: 12.6 m

[Easy] Evaluating an Exponential Function

• EN: If f(x) = 2^x, what is f(5)?
• FR: Si f(x) = 2^x, combien vaut f(5)?
• Choices: A) 10 B) 16 C) 32 D) 64
• Hint: f(4) = 2⁴ = 2 × 2 × 2 × 2 = 16; each step multiplies by 2 again.
• Steps:
  • f(5) = 2⁵.
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32.
  • f(5) = 32.
• Answer: 32

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 7 and the common difference is 5. What is the 6th term?
• FR: Le premier terme d'une suite arithmétique est 7 et la raison est 5. Quel est le 6e terme?
• Choices: A) 27 B) 30 C) 32 D) 37
• Hint: The nth term = first term + (n − 1) × common difference — for first term 3, difference 4, 5th term = 3 + 4 × 4 = 19.
• Steps:
  • tn = a + (n − 1)d.
  • t6 = 7 + (6 − 1) × 5.
  • t_6 = 7 + 25 = 32.
• Answer: 32

[Easy] Introduction to Logarithms

• EN: Evaluate: log₂(8).
• FR: Évalue: log₂(8).
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: log_b(x) asks "to what power must b be raised to get x?" — log₃(9) = 2 because 3² = 9.
• Steps:
  • log₂(8) asks: 2 to what power equals 8?
  • 2¹ = 2, 2² = 4, 2³ = 8. ✓
  • log₂(8) = 3.
• Answer: 3

[Easy] Simple Interest vs Compound Interest

• EN: $500 is invested at 4% annual simple interest. How much interest is earned after 3 years?
• FR: 500 $ sont investis à 4% d'intérêt simple annuel. Combien d'intérêts sont gagnés après 3 ans?
• Choices: A) $48 B) $55 C) $60 D) $72
• Hint: Simple interest = principal × rate × time — like $200 × 5% × 2 = $200 × 0.05 × 2 = $20.
• Steps:
  • I = P × r × t.
  • I = 500 × 0.04 × 3.
  • I = 500 × 0.12 = $60.
• Answer: $60

[Medium] Compound Interest

• EN: $1000 is invested at 5% per year, compounded annually. What is the amount after 2 years?
• FR: 1000 $ sont investis à 5% par an, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1105.00
• Hint: A = P(1 + r)^n — like $800 at 3% for 2 years: $800 × 1.03² = $800 × 1.0609 = $848.72.
• Steps:
  • A = 1000 × (1 + 0.05)².
  • = 1000 × 1.05².
  • = 1000 × 1.1025.
  • = $1102.50.
• Answer: $1102.50

[Medium] Logarithm — Solving an Equation

• EN: Solve for x: log₃(x) = 4.
• FR: Résous pour x: log₃(x) = 4.
• Choices: A) x = 12 B) x = 64 C) x = 81 D) x = 243
• Hint: If log_b(x) = n, then x = b^n — like log₅(x) = 3 means x = 5³ = 125.
• Steps:
  • log₃(x) = 4 means 3⁴ = x.
  • 3⁴ = 3 × 3 × 3 × 3 = 81.
  • x = 81.
• Answer: x = 81

[Medium] Geometric Series Sum

• EN: Find the sum of the first 4 terms of the geometric series: 2, 6, 18, 54.
• FR: Trouve la somme des 4 premiers termes de la suite géométrique: 2, 6, 18, 54.
• Choices: A) 72 B) 78 C) 80 D) 82
• Hint: Sum of n terms of a geometric series: S = a(r^n − 1) ÷ (r − 1) — for a = 1, r = 3, n = 3: S = 1(27 − 1) ÷ 2 = 13.
• Steps:
  • a = 2, r = 3, n = 4.
  • S = 2(3⁴ − 1) ÷ (3 − 1) = 2(81 − 1) ÷ 2.
  • = 2 × 80 ÷ 2 = 80.
  • OR simply: 2 + 6 + 18 + 54 = 80.
• Answer: 80

[Medium] Trigonometric Identity

• EN: Simplify: sin²(x) + cos²(x).
• FR: Simplifie: sin²(x) + cos²(x).
• Choices: A) 0 B) sin(2x) C) 1 D) 2
• Hint: This is one of the most fundamental trigonometric identities — think of the unit circle where x² + y² = 1.
• Steps:
  • The Pythagorean identity states sin²(x) + cos²(x) = 1 for all values of x.
  • This is always true.
  • The answer is 1.
• Answer: 1

[Hard] Annuity — Future Value

• EN: Olivia deposits $200 at the end of each month into an account earning 6% per year, compounded monthly. What is the approximate future value after 2 years (24 payments)? Use the formula FV = PMT × [(1 + r)^n − 1] ÷ r, where r = 0.005.
• FR: Olivia dépose 200 $ à la fin de chaque mois dans un compte à 6% annuel, composé mensuellement. Quelle est la valeur future approximative après 2 ans (24 versements)? Utilise FV = PMT × [(1 + r)^n − 1] ÷ r, où r = 0,005.
• Choices: A) $4 800.00 B) $5 004.00 C) $5 086.74 D) $5 200.00
• Hint: For FV of an ordinary annuity, first compute (1.005)^24 ≈ 1.1272, subtract 1, divide by 0.005, then multiply by PMT.
• Steps:
  • (1.005)^24 ≈ 1.12716.
  • 1.12716 − 1 = 0.12716.
  • 0.12716 ÷ 0.005 = 25.433.
  • FV = 200 × 25.433 ≈ $5 086.74.
• Answer: $5 086.74

[Hard] Exponential Equation

• EN: Solve for x: 3^(2x) = 81.
• FR: Résous pour x: 3^(2x) = 81.
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Write 81 as a power of 3, then equate exponents — like 2^(3x) = 64 = 2⁶, so 3x = 6 and x = 2.
• Steps:
  • 81 = 3⁴.
  • So 3^(2x) = 3⁴.
  • Therefore 2x = 4.
  • x = 2.
• Answer: x = 2

[Easy] Combinations

• EN: In how many ways can you choose 3 toppings from a menu of 6 toppings at Tim Hortons?
• FR: De combien de façons peut-on choisir 3 garnitures parmi 6 garnitures au menu de Tim Hortons?
• Choices: A) 15 B) 18 C) 20 D) 24
• Hint: Use C(n, r) = n! ÷ (r! × (n − r)!) — like C(5, 2) = 5! ÷ (2! × 3!) = 120 ÷ 12 = 10.
• Steps:
  • C(6, 3) = 6! ÷ (3! × 3!) = 720 ÷ (6 × 6) = 720 ÷ 36 = 20.
  • There are 20 ways to choose 3 toppings.
• Answer: 20

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = x³.
• FR: Trouve la dérivée de f(x) = x³.
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹ — like d/dx(x⁴) = 4x³.
• Steps:
  • Apply the power rule: bring the exponent down and reduce it by 1.
  • f'(x) = 3 · x^(3−1) = 3x².
• Answer: 3x²

[Easy] Permutations

• EN: How many different ways can 4 students line up in a row?
• FR: De combien de façons différentes 4 élèves peuvent-ils se mettre en rang?
• Choices: A) 12 B) 16 C) 20 D) 24
• Hint: P(n, n) = n! — for 3 students lining up: 3! = 3 × 2 × 1 = 6 ways.
• Steps:
  • 4 students in a row: 4! = 4 × 3 × 2 × 1.
  • = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Polynomial Function — End Behaviour

• EN: For the polynomial f(x) = −2x³ + 5x, what happens to f(x) as x → +∞?
• FR: Pour le polynôme f(x) = −2x³ + 5x, que se passe-t-il avec f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → 0 C) f(x) → −∞ D) f(x) → 2
• Hint: End behaviour of polynomials is determined by the leading term — for −3x³, as x grows large positively, the output becomes very large negatively.
• Steps:
  • The leading term is −2x³.
  • As x → +∞, x³ → +∞ and −2x³ → −∞.
  • So f(x) → −∞.
• Answer: f(x) → −∞

[Medium] Rate of Change — Derivative

• EN: The position of a hockey puck is given by s(t) = 3t² + 2t (in metres, t in seconds). What is the velocity of the puck at t = 4 seconds?
• FR: La position d'une rondelle est donnée par s(t) = 3t² + 2t (en mètres, t en secondes). Quelle est la vitesse de la rondelle à t = 4 secondes?
• Choices: A) 24 m/s B) 26 m/s C) 28 m/s D) 30 m/s
• Hint: Velocity = derivative of position; differentiate then substitute t — like s(t) = 2t² + t: v(t) = 4t + 1, at t = 3: v = 13.
• Steps:
  • v(t) = s'(t) = 6t + 2.
  • At t = 4: v(4) = 6(4) + 2 = 24 + 2 = 26.
  • The velocity is 26 m/s.
• Answer: 26 m/s

[Medium] Binomial Distribution

• EN: A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads?
• FR: Une pièce de monnaie équilibrée est lancée 5 fois. Quelle est la probabilité d'obtenir exactement 3 têtes?
• Choices: A) 3/16 B) 5/16 C) 7/32 D) 10/32
• Hint: P(X = k) = C(n, k) × p^k × (1 − p)^(n − k) — for n = 4, k = 2, p = 0.5: C(4,2) × (0.5)⁴ = 6/16.
• Steps:
  • P(X = 3) = C(5, 3) × (0.5)³ × (0.5)².
  • C(5, 3) = 10.
  • = 10 × (1/8) × (1/4) = 10/32.
  • Simplified: 5/16.
• Answer: 5/16

[Medium] Vector Addition

• EN: Vector u = (3, 5) and vector v = (−1, 4). What is u + v?
• FR: Le vecteur u = (3, 5) et le vecteur v = (−1, 4). Combien vaut u + v?
• Choices: A) (2, 8) B) (2, 9) C) (4, 8) D) (4, 9)
• Hint: Add vectors component by component — like (2, 3) + (4, −1) = (2 + 4, 3 + (−1)) = (6, 2).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 5 + 4 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Medium] Rational Function — Vertical Asymptote

• EN: Find the vertical asymptote of f(x) = (x + 2) ÷ (x − 5).
• FR: Trouve l'asymptote verticale de f(x) = (x + 2) ÷ (x − 5).
• Choices: A) x = −5 B) x = −2 C) x = 2 D) x = 5
• Hint: Vertical asymptotes occur where the denominator equals zero — for f(x) = 1/(x + 3), set x + 3 = 0: x = −3.
• Steps:
  • Set the denominator equal to zero: x − 5 = 0.
  • x = 5.
  • The vertical asymptote is at x = 5.
• Answer: x = 5

[Hard] Permutations with Restrictions

• EN: A class of 7 students is choosing a president, vice-president, and treasurer. No student can hold more than one position. In how many ways can these three positions be filled?
• FR: Dans une classe de 7 élèves, on choisit un président, un vice-président et un trésorier. Aucun élève ne peut occuper plus d'un poste. De combien de façons ces trois postes peuvent-ils être pourvus?
• Choices: A) 120 B) 180 C) 210 D) 240
• Hint: This is a permutation — P(n, r) = n! ÷ (n − r)!; for P(6, 3) = 6 × 5 × 4 = 120.
• Steps:
  • P(7, 3) = 7 × 6 × 5.
  • = 42 × 5.
  • = 210.
  • There are 210 ways to fill the three positions.
• Answer: 210

[Hard] Derivative Application — Optimization

• EN: A farmer has 60 m of fencing to enclose a rectangular field against a barn wall (so only 3 sides need fencing). What width (in metres) maximizes the enclosed area?
• FR: Un agriculteur dispose de 60 m de clôture pour enclore un champ rectangulaire contre un mur de grange (seulement 3 côtés nécessitent une clôture). Quelle largeur (en mètres) maximise l'aire enfermée?
• Choices: A) 12 m B) 15 m C) 18 m D) 20 m
• Hint: Write area as A = w × l, where 2w + l = total fencing; express A in terms of one variable, differentiate, and set equal to zero.
• Steps:
  • Let width = w and length = l. Constraint: 2w + l = 60, so l = 60 − 2w.
  • Area: A(w) = w(60 − 2w) = 60w − 2w².
  • Differentiate: A'(w) = 60 − 4w. Set A'(w) = 0: 60 − 4w = 0 → w = 15.
  • The width that maximizes area is 15 m.
• Answer: 15 m