Daily Math — 2026-07-20

[Easy] Counting Hockey Pucks

• EN: There are 7 pucks on the ice. Then 5 more are added. How many pucks are there in all?
• FR: Il y a 7 rondelles sur la glace. On en ajoute 5 de plus. Combien y a-t-il de rondelles en tout?
• Choices: A) 10 pucks B) 11 pucks C) 12 pucks D) 13 pucks
• Hint: To add, count on from the bigger number — try 6 + 3: start at 6, count 3 more: 7, 8, 9.
• Steps:
  • Start at 7 and count on 5 more.
  • 8, 9, 10, 11, 12 — that is 5 counts.
  • So the total is 12 pucks.
• Answer: 12 pucks

[Easy] Pennies in a Jar

• EN: Mia has 9 pennies. She gives away 4 pennies. How many pennies does she have left?
• FR: Mia a 9 sous. Elle en donne 4. Combien de sous lui reste-t-il?
• Choices: A) 3 pennies B) 4 pennies C) 5 pennies D) 6 pennies
• Hint: To subtract, count backwards — try 8 − 3: start at 8, go back 3: 7, 6, 5.
• Steps:
  • Start at 9 and count back 4.
  • 8, 7, 6, 5 — that is 4 counts back.
  • So Mia has 5 pennies left.
• Answer: 5 pennies

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes next: 2, 4, 6, 8, ___?
• FR: Compte par bonds de 2. Quel nombre vient ensuite: 2, 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Skip counting by 2s means adding 2 each time — try 10, 12, 14, the next is 16.
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 19?
• FR: Quel nombre est plus grand: 14 ou 19?
• Choices: A) 14 B) 19 C) They are equal D) 11
• Hint: When comparing numbers, the one farther along the number line is greater — 7 is greater than 5.
• Steps:
  • Look at the tens place: both have 1 ten.
  • Look at the ones place: 9 is greater than 4.
  • So 19 is the greater number.
• Answer: 19

[Medium] Adding Three Numbers

• EN: Luca has 3 stickers, 4 stickers, and 6 stickers. How many stickers does he have in all?
• FR: Luca a 3 autocollants, 4 autocollants et 6 autocollants. Combien en a-t-il en tout?
• Choices: A) 11 stickers B) 12 stickers C) 13 stickers D) 14 stickers
• Hint: Add three numbers by combining two first — try 2 + 3 + 5: first 2 + 3 = 5, then 5 + 5 = 10.
• Steps:
  • Add 3 + 4 = 7 first.
  • Then add 7 + 6 = 13.
  • So Luca has 13 stickers in all.
• Answer: 13 stickers

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What number comes next: 5, 10, 15, 20, ___?
• FR: Compte par bonds de 5. Quel nombre vient ensuite: 5, 10, 15, 20, ___?
• Choices: A) 22 B) 23 C) 24 D) 25
• Hint: Skip counting by 5s means adding 5 each time — after 30 comes 35.
• Steps:
  • The pattern adds 5 each time.
  • 20 + 5 = 25.
  • So the next number is 25.
• Answer: 25

[Medium] Subtraction Story

• EN: There are 15 kids at the rink. 8 kids go home. How many kids are still at the rink?
• FR: Il y a 15 enfants à la patinoire. 8 enfants rentrent chez eux. Combien d'enfants sont encore à la patinoire?
• Choices: A) 5 kids B) 6 kids C) 7 kids D) 8 kids
• Hint: To subtract, think of the related addition fact — for 12 − 5, think: 5 + ? = 12, so the answer is 7.
• Steps:
  • We need to find 15 − 8.
  • Think: 8 + ? = 15. Count up: 8 + 7 = 15.
  • So 7 kids are still at the rink.
• Answer: 7 kids

[Medium] Coin Recognition

• EN: Anika has 1 dime and 1 nickel. How many cents does she have in all?
• FR: Anika a 1 pièce de dix cents et 1 pièce de cinq cents. Combien de cents a-t-elle en tout?
• Choices: A) 12 cents B) 13 cents C) 14 cents D) 15 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents — add them together.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Hard] Addition to 20

• EN: There are 8 red mittens and some blue mittens. There are 17 mittens in all. How many blue mittens are there?
• FR: Il y a 8 mitaines rouges et quelques mitaines bleues. Il y a 17 mitaines en tout. Combien y a-t-il de mitaines bleues?
• Choices: A) 7 blue mittens B) 8 blue mittens C) 9 blue mittens D) 11 blue mittens
• Hint: To find a missing addend, use subtraction — if 6 + ? = 14, then 14 − 6 = 8.
• Steps:
  • We need the missing number: 8 + ? = 17.
  • Subtract: 17 − 8 = 9.
  • So there are 9 blue mittens.
• Answer: 9 blue mittens

[Hard] Counting to 100

• EN: What number is 10 more than 76?
• FR: Quel nombre est 10 de plus que 76?
• Choices: A) 77 B) 80 C) 86 D) 96
• Hint: Adding 10 changes the tens digit by 1 — 10 more than 43 is 53.
• Steps:
  • Start at 76.
  • Add 10 more: 76 + 10 = 86.
  • So the answer is 86.
• Answer: 86

[Easy] Addition within 100

• EN: A Tim Hortons bag has 23 Timbits and another has 35 Timbits. How many Timbits are there in all?
• FR: Un sac de Tim Hortons contient 23 Timbits et un autre en contient 35. Combien y a-t-il de Timbits en tout?
• Choices: A) 55 Timbits B) 57 Timbits C) 58 Timbits D) 60 Timbits
• Hint: Add the ones first, then the tens — for 31 + 24: ones 1 + 4 = 5, tens 3 + 2 = 5, so 55.
• Steps:
  • Ones: 3 + 5 = 8.
  • Tens: 2 + 3 = 5.
  • So 23 + 35 = 58 Timbits.
• Answer: 58 Timbits

[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 l'aiguille des heures sur 3 et l'aiguille des minutes sur 12. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 4:00
• Hint: When the minute hand points to 12, it is exactly on the hour — if the hour hand is on 7, it is 7:00.
• Steps:
  • The hour hand is on 3, so the hour is 3.
  • The minute hand is on 12, so it is exactly on the hour.
  • The time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil measures 12 cm. A crayon measures 8 cm. How much longer is the pencil?
• FR: Un crayon mesure 12 cm. Un crayon de couleur mesure 8 cm. De combien de cm le crayon est-il plus long?
• Choices: A) 2 cm B) 3 cm C) 4 cm D) 5 cm
• Hint: To find the difference in lengths, subtract the smaller from the larger — 15 cm − 9 cm = 6 cm.
• Steps:
  • Subtract: 12 − 8 = 4.
  • The pencil is 4 cm longer than the crayon.
• Answer: 4 cm

[Easy] Simple Patterns

• EN: Look at this pattern: 2, 4, 6, 8, 10, ___. What is the next number?
• FR: Regarde ce modèle: 2, 4, 6, 8, 10, ___. Quel est le nombre suivant?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Find the rule by seeing how much is added each time — in 3, 6, 9, 12, the rule is add 3.
• Steps:
  • The pattern adds 2 each time.
  • 10 + 2 = 12.
  • So the next number is 12.
• Answer: 12

[Medium] Subtraction within 100

• EN: Sofia had 74 stickers. She gave 38 away to her classmates. How many stickers does she have left?
• FR: Sofia avait 74 autocollants. Elle en a donné 38 à ses camarades de classe. Combien d'autocollants lui reste-t-il?
• Choices: A) 34 stickers B) 36 stickers C) 38 stickers D) 42 stickers
• Hint: Subtract ones first, regroup if needed — for 52 − 27: borrow 1 ten, ones 12 − 7 = 5, tens 4 − 2 = 2, so 25.
• Steps:
  • Ones: can't do 4 − 8, so regroup. Borrow 1 ten: 14 − 8 = 6.
  • Tens: 6 − 3 = 3 (after regrouping, 7 tens becomes 6 tens).
  • So 74 − 38 = 36 stickers.
• Answer: 36 stickers

[Medium] Telling Time — Half Hour

• EN: The clock shows the hour hand halfway between 6 and 7, and the minute hand on 6. What time is it?
• FR: L'horloge montre l'aiguille des heures à mi-chemin entre 6 et 7, et l'aiguille des minutes sur 6. Quelle heure est-il?
• Choices: A) 6:00 B) 6:30 C) 7:00 D) 7:30
• Hint: When the minute hand points to 6, it is 30 minutes past the hour — if the hour hand is near 4, it is 4:30.
• Steps:
  • The minute hand on 6 means 30 minutes past.
  • The hour hand is between 6 and 7, so the hour is 6.
  • The time is 6:30.
• Answer: 6:30

[Medium] Counting Coins

• EN: Ben has 2 dimes, 1 nickel, and 3 pennies. How much money does he have?
• FR: Ben a 2 pièces de dix cents, 1 pièce de cinq cents et 3 sous. Combien d'argent a-t-il?
• Choices: A) 26 cents B) 27 cents C) 28 cents D) 29 cents
• Hint: Count coin by coin: dimes = 10 cents each, nickels = 5 cents, pennies = 1 cent each.
• Steps:
  • 2 dimes = 20 cents.
  • 1 nickel = 5 cents. Total so far: 25 cents.
  • 3 pennies = 3 cents. 25 + 3 = 28 cents.
• Answer: 28 cents

[Medium] Addition with Regrouping

• EN: A school store has 47 erasers in the morning. They receive 36 more erasers in the afternoon. How many erasers are there now?
• FR: La boutique de l'école a 47 gommes le matin. Elle en reçoit 36 autres l'après-midi. Combien de gommes y a-t-il maintenant?
• Choices: A) 73 erasers B) 81 erasers C) 83 erasers D) 84 erasers
• Hint: Add ones first, regroup if 10 or more — for 38 + 45: ones 8 + 5 = 13, write 3 carry 1, tens 3 + 4 + 1 = 8, so 83.
• Steps:
  • Ones: 7 + 6 = 13. Write 3, carry 1.
  • Tens: 4 + 3 + 1 = 8.
  • So 47 + 36 = 83 erasers.
• Answer: 83 erasers

[Hard] Measuring in Metres

• EN: A hallway is 9 metres long. Another hallway is 6 metres long. If you walk both hallways, how many metres do you walk in all?
• FR: Un couloir a 9 mètres de long. Un autre couloir a 6 mètres de long. Si tu marches dans les deux couloirs, combien de mètres marches-tu en tout?
• Choices: A) 13 metres B) 14 metres C) 15 metres D) 16 metres
• Hint: Add the two lengths together — if one path is 8 m and another is 7 m, together they are 15 m.
• Steps:
  • Add the two lengths: 9 + 6.
  • 9 + 6 = 15.
  • So you walk 15 metres in all.
• Answer: 15 metres

[Hard] Two-Step Problem

• EN: Maya has 50 cents. She spends 15 cents on a pencil and 20 cents on an eraser. How much money does she have left?
• FR: Maya a 50 cents. Elle dépense 15 cents pour un crayon et 20 cents pour une gomme. Combien d'argent lui reste-t-il?
• Choices: A) 13 cents B) 14 cents C) 15 cents D) 16 cents
• Hint: For two-step problems, do one step at a time — spend the first amount, then spend the second.
• Steps:
  • First, add the amounts spent: 15 + 20 = 35 cents.
  • Then subtract from 50: 50 − 35 = 15 cents.
  • Maya has 15 cents left.
• Answer: 15 cents

[Easy] Multiplication by 2

• EN: There are 4 hockey teams. Each team has 2 goalies. How many goalies are there in all?
• FR: Il y a 4 équipes de hockey. Chaque équipe a 2 gardiens de but. Combien y a-t-il de gardiens en tout?
• Choices: A) 6 goalies B) 7 goalies C) 8 goalies D) 9 goalies
• Hint: Multiply to find equal groups — 3 groups of 2 = 3 × 2 = 6.
• Steps:
  • There are 4 groups of 2.
  • 4 × 2 = 8.
  • So there are 8 goalies in all.
• Answer: 8 goalies

[Easy] Multiplication by 5

• EN: Each student needs 5 crayons. There are 6 students. How many crayons are needed in all?
• FR: Chaque élève a besoin de 5 crayons. Il y a 6 élèves. Combien de crayons faut-il en tout?
• Choices: A) 25 crayons B) 28 crayons C) 30 crayons D) 35 crayons
• Hint: Multiply to count equal groups — 7 groups of 5 is 7 × 5 = 35.
• Steps:
  • There are 6 groups of 5.
  • 6 × 5 = 30.
  • So 30 crayons are needed.
• Answer: 30 crayons

[Easy] Basic Division

• EN: 12 apples are shared equally among 3 friends. How many apples does each friend get?
• FR: 12 pommes sont partagées également entre 3 amis. Combien de pommes chaque ami reçoit-il?
• Choices: A) 3 apples B) 4 apples C) 5 apples D) 6 apples
• Hint: Division splits into equal groups — 15 ÷ 3 = 5 because 3 × 5 = 15.
• Steps:
  • We need 12 ÷ 3.
  • Think: 3 × ? = 12. Answer: 3 × 4 = 12.
  • Each friend gets 4 apples.
• Answer: 4 apples

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. Omar eats 1 piece. What fraction of the pizza does he eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Omar mange 1 morceau. Quelle fraction de la pizza mange-t-il?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: A fraction names one part out of equal parts — if a pie is cut into 4 equal pieces and you take 1, that is 1/4.
• Steps:
  • The pizza is cut into 2 equal pieces.
  • Omar eats 1 out of 2 pieces.
  • That is 1/2 of the pizza.
• Answer: 1/2

[Medium] Multiplication by 3

• EN: A baker makes 3 trays of muffins. Each tray has 9 muffins. How many muffins are there in all?
• FR: Un boulanger fait 3 plateaux de muffins. Chaque plateau contient 9 muffins. Combien y a-t-il de muffins en tout?
• Choices: A) 21 muffins B) 24 muffins C) 27 muffins D) 30 muffins
• Hint: Use the multiplication table of 3 — 3 × 8 = 24, so 3 × 9 is one more group of 3, which is 27.
• Steps:
  • There are 3 groups of 9.
  • 3 × 9 = 27.
  • So there are 27 muffins.
• Answer: 27 muffins

[Medium] Perimeter

• EN: A rectangular garden has a length of 7 m and a width of 4 m. What is its perimeter?
• FR: Un jardin rectangulaire a une longueur de 7 m et une largeur de 4 m. Quel est son périmètre?
• Choices: A) 20 m B) 22 m C) 24 m D) 28 m
• Hint: Perimeter is the distance all the way around — add all four sides. For a 5 by 3 rectangle: 5 + 3 + 5 + 3 = 16.
• Steps:
  • Add all four sides: 7 + 4 + 7 + 4.
  • 7 + 7 = 14 and 4 + 4 = 8.
  • 14 + 8 = 22 m.
• Answer: 22 m

[Medium] Reading a Simple Graph

• EN: A bar graph shows that 8 students like hockey, 5 like skating, and 3 like curling. How many students were surveyed in all?
• FR: Un diagramme à barres montre que 8 élèves aiment le hockey, 5 aiment le patinage et 3 aiment le curling. Combien d'élèves ont répondu au total?
• Choices: A) 13 students B) 14 students C) 16 students D) 18 students
• Hint: To find the total, add all values in the graph — if bars show 4, 6, and 2, the total is 12.
• Steps:
  • Add all three groups: 8 + 5 + 3.
  • 8 + 5 = 13, then 13 + 3 = 16.
  • So 16 students were surveyed.
• Answer: 16 students

[Medium] Fractions — One Quarter

• EN: A ribbon is cut into 4 equal parts. Nora uses 1 part. What fraction of the ribbon does she use?
• FR: Un ruban est coupé en 4 parties égales. Nora utilise 1 partie. Quelle fraction du ruban utilise-t-elle?
• Choices: A) 1/5 B) 1/4 C) 1/3 D) 1/2
• Hint: Write the fraction as parts used over total equal parts — 1 out of 4 equal parts is 1/4.
• Steps:
  • The ribbon is cut into 4 equal parts.
  • Nora uses 1 part out of 4.
  • That fraction is 1/4.
• Answer: 1/4

[Hard] Multiplication by 4

• EN: There are 7 boxes. Each box holds 4 bags of Tim Hortons coffee. How many bags of coffee are there in all?
• FR: Il y a 7 boîtes. Chaque boîte contient 4 sacs de café Tim Hortons. Combien y a-t-il de sacs de café en tout?
• Choices: A) 24 bags B) 26 bags C) 28 bags D) 32 bags
• Hint: Use the multiplication table of 4 — 6 × 4 = 24, so 7 × 4 is one more group: 24 + 4 = 28.
• Steps:
  • There are 7 groups of 4.
  • 7 × 4 = 28.
  • So there are 28 bags of coffee.
• Answer: 28 bags

[Hard] Division with Multiplication Check

• EN: 45 students are split into equal groups of 5 for a snowshoeing activity. How many groups are there?
• FR: 45 élèves sont répartis en groupes égaux de 5 pour une activité de raquette. Combien y a-t-il de groupes?
• Choices: A) 7 groups B) 8 groups C) 9 groups D) 10 groups
• Hint: Use the related multiplication fact — for 40 ÷ 5, think 5 × ? = 40, so the answer is 8.
• Steps:
  • We need 45 ÷ 5.
  • Think: 5 × ? = 45. Answer: 5 × 9 = 45.
  • So there are 9 groups.
• Answer: 9 groups

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Use skip counting or a known fact — 7 × 7 = 49, then add one more group of 7 to get 7 × 8.
• Steps:
  • 7 × 7 = 49.
  • Add one more group of 7: 49 + 7 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

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

[Easy] Area of a Rectangle

• EN: A hockey card measures 6 cm long and 4 cm wide. What is its area?
• FR: Une carte de hockey mesure 6 cm de long et 4 cm de large. Quelle est son aire?
• Choices: A) 20 cm² B) 22 cm² C) 24 cm² D) 28 cm²
• Hint: Area of a rectangle = length × width — a 5 cm by 3 cm card has area 5 × 3 = 15 cm².
• Steps:
  • Area = length × width.
  • Area = 6 × 4 = 24.
  • The area is 24 cm².
• Answer: 24 cm²

[Easy] Comparing Fractions

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

[Medium] Long Division with Remainder

• EN: 47 cupcakes are shared equally among 5 students. How many cupcakes does each student get, and how many are left over?
• FR: 47 petits gâteaux sont partagés également entre 5 élèves. Combien chaque élève en reçoit-il, et combien en reste-t-il?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 9 remainder 4 D) 10 remainder 1
• Hint: Divide, then find the remainder — for 26 ÷ 4: 4 × 6 = 24, so the quotient is 6 and the remainder is 26 − 24 = 2.
• Steps:
  • 5 × 9 = 45, which is close to 47.
  • Remainder: 47 − 45 = 2.
  • So each student gets 9 cupcakes, with 2 left over.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: A skating session starts at 10:15 a.m. and ends at 12:45 p.m. How long is the session?
• FR: Une séance de patinage commence à 10 h 15 et se termine à 12 h 45. Combien de temps dure la séance?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours 15 minutes
• Hint: Count forward in steps — go from the start time to the nearest hour, then count hours, then extra minutes.
• Steps:
  • From 10:15 to 12:15 = 2 hours.
  • From 12:15 to 12:45 = 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A ski jacket costs $24.50 and ski pants cost $18.75. What is the total cost?
• FR: Une veste de ski coûte 24,50 $ et un pantalon de ski coûte 18,75 $. Quel est le coût total?
• Choices: A) $42.25 B) $43.00 C) $43.25 D) $44.75
• Hint: Line up the decimal points and add — for $12.30 + $9.45: ones 2 + 9 = 11 (carry 1), so the total is $21.75.
• Steps:
  • Line up decimals: $24.50 + $18.75.
  • Hundredths: 0 + 5 = 5. Tenths: 5 + 7 = 12, write 2 carry 1.
  • Ones: 4 + 8 + 1 = 13, write 3 carry 1. Tens: 2 + 1 + 1 = 4. Total: $43.25.
• Answer: $43.25

[Medium] Multiplication — Multi-Digit

• EN: A school orders 6 boxes of markers. Each box has 24 markers. How many markers are there in all?
• FR: Une école commande 6 boîtes de marqueurs. Chaque boîte contient 24 marqueurs. Combien y a-t-il de marqueurs en tout?
• Choices: A) 124 markers B) 140 markers C) 144 markers D) 148 markers
• Hint: Multiply each part separately — for 6 × 23: 6 × 20 = 120 and 6 × 3 = 18, then 120 + 18 = 138.
• Steps:
  • 6 × 24: split into 6 × 20 = 120 and 6 × 4 = 24.
  • Add: 120 + 24 = 144.
  • There are 144 markers in all.
• Answer: 144 markers

[Hard] Long Division

• EN: A gym has 168 students who need to be sorted into teams of 8. How many teams will there be?
• FR: Un gymnase compte 168 élèves qui doivent être répartis en équipes de 8. Combien d'équipes y aura-t-il?
• Choices: A) 19 teams B) 20 teams C) 21 teams D) 22 teams
• Hint: Use long division step by step — divide the first digit(s), multiply, subtract, then bring down.
• Steps:
  • 8 goes into 16 exactly 2 times (16 ÷ 8 = 2). Bring down 8.
  • 8 goes into 8 exactly 1 time (8 ÷ 8 = 1).
  • So 168 ÷ 8 = 21 teams.
• Answer: 21 teams

[Hard] Comparing Decimals

• EN: Which of these lists shows the numbers in order from least to greatest: 3.4, 3.04, 3.40, 3.14?
• FR: Laquelle de ces listes montre les nombres en ordre du plus petit au plus grand: 3,4, 3,04, 3,40, 3,14?
• Choices: A) 3.04, 3.14, 3.4, 3.40 B) 3.04, 3.14, 3.40, 3.4 C) 3.14, 3.04, 3.4, 3.40 D) 3.4, 3.40, 3.14, 3.04
• Hint: Compare digit by digit from left to right — 3.04 has 0 tenths while 3.14 has 1 tenth, so 3.04 < 3.14.
• Steps:
  • All numbers have 3 ones. Look at tenths: 3.04 has 0, 3.14 has 1, 3.4 and 3.40 both have 4.
  • So 3.04 < 3.14 < 3.4. Note: 3.4 = 3.40.
  • Order from least to greatest: 3.04, 3.14, 3.4, 3.40.
• Answer: 3.04, 3.14, 3.4, 3.40

[Easy] Multi-Digit Multiplication

• EN: A hockey arena has 24 rows of seats. Each row has 32 seats. How many seats are there in all?
• FR: Un aréna de hockey a 24 rangées de sièges. Chaque rangée a 32 sièges. Combien y a-t-il de sièges en tout?
• Choices: A) 668 seats B) 728 seats C) 768 seats D) 780 seats
• Hint: Break apart one number to multiply — for 22 × 31: 22 × 30 = 660 and 22 × 1 = 22, then 660 + 22 = 682.
• Steps:
  • 24 × 32: split into 24 × 30 = 720 and 24 × 2 = 48.
  • 720 + 48 = 768.
  • There are 768 seats.
• Answer: 768 seats

[Easy] Adding Fractions with Like Denominators

• EN: Émilie ate 2/8 of a pie and her brother ate 3/8. How much of the pie did they eat in all?
• FR: Émilie a mangé 2/8 d'une tarte et son frère en a mangé 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: Add the numerators and keep the denominator the same — 1/5 + 2/5 = 3/5.
• Steps:
  • Add the numerators: 2 + 3 = 5.
  • Keep the denominator: 8.
  • They ate 5/8 of the pie.
• Answer: 5/8

[Easy] Decimal Operations

• EN: A notebook costs $3.45 and a pen costs $1.25. What is the total cost?
• FR: Un cahier coûte 3,45 $ et un stylo coûte 1,25 $. Quel est le coût total?
• Choices: A) $4.50 B) $4.60 C) $4.70 D) $5.10
• Hint: Line up the decimal points, then add each column — $2.30 + $1.40 = $3.70.
• Steps:
  • Hundredths: 5 + 5 = 10, write 0 carry 1.
  • Tenths: 4 + 2 + 1 = 7. Ones: 3 + 1 = 4.
  • Total: $4.70.
• Answer: $4.70

[Easy] Percentage Intro — 50%

• EN: A bag has 20 candies. 50% of them are red. How many candies are red?
• FR: Un sac contient 20 bonbons. 50 % d'entre eux sont rouges. Combien de bonbons sont rouges?
• Choices: A) 5 candies B) 8 candies C) 10 candies D) 15 candies
• Hint: 50% means half — to find 50% of a number, divide by 2. For example, 50% of 30 = 30 ÷ 2 = 15.
• Steps:
  • 50% of a number means divide by 2.
  • 20 ÷ 2 = 10.
  • There are 10 red candies.
• Answer: 10 candies

[Medium] Multi-Digit Division

• EN: A school collects 336 cans of food for a food drive. The cans are packed into boxes of 8. How many boxes are needed?
• FR: Une école collecte 336 boîtes de conserve pour une collecte de nourriture. Les boîtes sont rangées en paquets de 8. Combien de paquets faut-il?
• Choices: A) 40 boxes B) 41 boxes C) 42 boxes D) 48 boxes
• Hint: Use long division — divide step by step, bringing down one digit at a time.
• Steps:
  • 8 goes into 33 four times (8 × 4 = 32). Remainder 1. Bring down 6 → 16.
  • 8 goes into 16 exactly 2 times (8 × 2 = 16). Remainder 0.
  • 336 ÷ 8 = 42 boxes.
• Answer: 42 boxes

[Medium] Subtracting Fractions with Like Denominators

• EN: A jug holds 7/10 of a litre of maple syrup. After pouring some out, 3/10 is left. How much was poured out?
• FR: Un pichet contient 7/10 d'un litre de sirop d'érable. Après en avoir versé une partie, il en reste 3/10. Quelle quantité a été versée?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: Subtract numerators and keep the denominator — 5/6 − 2/6 = 3/6.
• Steps:
  • Subtract the numerators: 7 − 3 = 4.
  • Keep the denominator: 10.
  • The amount poured out is 4/10.
• Answer: 4/10

[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) 54 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height — a box that is 2 cm by 3 cm by 4 cm has volume 2 × 3 × 4 = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A store has 80 winter toques. 25% of them are blue. How many toques are blue?
• FR: Un magasin a 80 tuques d'hiver. 25 % d'entre elles sont bleues. Combien de tuques sont bleues?
• Choices: A) 15 toques B) 18 toques C) 20 toques D) 25 toques
• Hint: 25% means one quarter — divide by 4. For example, 25% of 40 = 40 ÷ 4 = 10.
• Steps:
  • 25% of a number means divide by 4.
  • 80 ÷ 4 = 20.
  • There are 20 blue toques.
• Answer: 20 toques

[Hard] Decimal Multiplication

• EN: A loaf of bread costs $2.35. A family buys 4 loaves. How much do they spend in all?
• FR: Un pain coûte 2,35 $. Une famille achète 4 pains. Combien dépense-t-elle en tout?
• Choices: A) $8.40 B) $9.20 C) $9.40 D) $9.60
• Hint: Multiply as if there is no decimal, then place the decimal in the answer — 3 × $1.25 = $3.75.
• Steps:
  • Multiply 235 × 4 = 940.
  • Place the decimal: $9.40.
  • The family spends $9.40.
• Answer: $9.40

[Hard] Percentage — 10%

• EN: A hockey stick originally costs $90.00. It is on sale for 10% off. How much is the discount, and what is the sale price?
• FR: Un bâton de hockey coûte 90,00 $ à l'origine. Il est en solde avec 10 % de rabais. Quel est le rabais, et quel est le prix de vente?
• Choices: A) Discount $9.00, sale price $81.00 B) Discount $9.00, sale price $80.00 C) Discount $10.00, sale price $80.00 D) Discount $18.00, sale price $72.00
• Hint: 10% of a number means divide by 10 — 10% of $70 = $7.00, so the sale price would be $63.00.
• Steps:
  • 10% of $90.00 = $90.00 ÷ 10 = $9.00 discount.
  • Sale price: $90.00 − $9.00 = $81.00.
  • The discount is $9.00 and the sale price is $81.00.
• Answer: Discount $9.00, sale price $81.00

[Easy] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2.
• FR: Évalue: 3 + 4 × 2.
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: In BEDMAS, multiplication comes before addition — for 5 + 3 × 2, do 3 × 2 = 6 first, then 5 + 6 = 11.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then addition: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Percent of a Number

• EN: What is 20% of 50?
• FR: Combien font 20 % de 50?
• Choices: A) 8 B) 9 C) 10 D) 12
• Hint: Find 10% first, then double it — 10% of 60 = 6, so 20% of 60 = 12.
• Steps:
  • 10% of 50 = 50 ÷ 10 = 5.
  • 20% = 2 × 5 = 10.
  • 20% of 50 is 10.
• Answer: 10

[Easy] Ratios

• EN: In a bag of 12 marbles, 4 are red and the rest are blue. What is the ratio of red to blue marbles?
• FR: Dans un sac de 12 billes, 4 sont rouges et le reste est bleu. Quel est le rapport entre les billes rouges et les billes bleues?
• Choices: A) 1:2 B) 1:3 C) 4:8 D) 2:1
• Hint: Write a ratio as part to part — if 3 out of 9 are red, then 6 are blue, and the ratio red to blue is 3:6 or simplified 1:2.
• Steps:
  • Red marbles: 4. Blue marbles: 12 − 4 = 8.
  • Ratio of red to blue = 4:8 = 1:2.
  • The ratio is 1:2.
• Answer: 1:2

[Easy] Simple Algebraic Expression

• EN: Evaluate 3n + 5 when n = 4.
• FR: Évalue 3n + 5 lorsque n = 4.
• Choices: A) 15 B) 17 C) 19 D) 23
• Hint: Substitute the value for the variable, then calculate — for 2n + 3 when n = 5: 2(5) + 3 = 10 + 3 = 13.
• Steps:
  • Substitute n = 4: 3(4) + 5.
  • 3 × 4 = 12, then 12 + 5 = 17.
  • The answer is 17.
• Answer: 17

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 1/2 C) 6/7 D) 5/7
• Hint: Multiply numerators together and denominators together — 3/5 × 2/3 = 6/15 = 2/5.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 simplifies to 1/2.
• Answer: 1/2

[Medium] Integers Introduction

• EN: The temperature in Winnipeg is −8°C in the morning. By afternoon it rises 11 degrees. What is the afternoon temperature?
• FR: La température à Winnipeg est de −8 °C le matin. Elle monte de 11 degrés l'après-midi. Quelle est la température l'après-midi?
• Choices: A) −3°C B) 2°C C) 3°C D) 4°C
• Hint: Start at the negative number and count up — starting at −5 and adding 8: −5 + 8 = 3.
• Steps:
  • Start at −8 and add 11.
  • −8 + 11 = 3.
  • The afternoon temperature is 3°C.
• Answer: 3°C

[Medium] Rate Problems

• EN: A car travels 240 km in 3 hours. What is the car's speed in km/h?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est la vitesse de la voiture en km/h?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: Rate = total amount ÷ number of units — if 150 km is covered in 3 hours, the rate is 150 ÷ 3 = 50 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 240 ÷ 3 = 80.
  • The car's speed is 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: Divide 3/4 ÷ 1/2.
• FR: Divise 3/4 ÷ 1/2.
• Choices: A) 1/2 B) 3/8 C) 3/2 D) 4/3
• Hint: To divide fractions, multiply by the reciprocal of the second fraction — 2/5 ÷ 1/3 = 2/5 × 3/1 = 6/5.
• Steps:
  • Flip the second fraction: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 3/2.
• Answer: 3/2

[Hard] BEDMAS with Brackets

• EN: Evaluate: (6 + 2) × 3 − 4 ÷ 2.
• FR: Évalue: (6 + 2) × 3 − 4 ÷ 2.
• Choices: A) 20 B) 22 C) 24 D) 26
• Hint: Follow BEDMAS — Brackets first, then Exponents, then Multiplication/Division left to right, then Addition/Subtraction.
• Steps:
  • Brackets: 6 + 2 = 8.
  • Multiplication and Division (left to right): 8 × 3 = 24; 4 ÷ 2 = 2.
  • Subtraction: 24 − 2 = 22.
• Answer: 22

[Hard] Percent Problem

• EN: A Tim Hortons roll-up-the-rim cup shows that 15 out of every 75 cups win a prize. What percent of cups win a prize?
• FR: Une tasse de Tim Hortons montre que 15 tasses sur 75 gagnent un prix. Quel pourcentage de tasses gagnent un prix?
• Choices: A) 15% B) 18% C) 20% D) 25%
• Hint: To find a percent, divide the part by the whole, then multiply by 100 — for 4 out of 20: 4 ÷ 20 = 0.2, then 0.2 × 100 = 20%.
• Steps:
  • Divide: 15 ÷ 75 = 0.2.
  • Multiply by 100: 0.2 × 100 = 20.
  • So 20% of cups win a prize.
• Answer: 20%

[Easy] Integer Addition

• EN: What is (−5) + (−3)?
• FR: Combien font (−5) + (−3)?
• Choices: A) −9 B) −8 C) 2 D) 8
• Hint: Adding two negatives gives a larger negative — (−4) + (−6) = −10.
• Steps:
  • Both numbers are negative, so add their absolute values: 5 + 3 = 8.
  • Keep the negative sign.
  • (−5) + (−3) = −8.
• Answer: −8

[Easy] Percent Discount

• EN: A $40 toque is on sale for 25% off. How much is the discount?
• FR: Une tuque à 40 $ est en solde avec 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $8 B) $9 C) $10 D) $12
• Hint: Find the percent of the number — 25% of a number means divide by 4. For example, 25% of $60 = $15.
• Steps:
  • 25% of $40 = $40 ÷ 4 = $10.
  • The discount is $10.
• Answer: $10

[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: Isolate the variable by doing the opposite operation — for x + 7 = 12, subtract 7 from both sides: x = 5.
• Steps:
  • Subtract 9 from both sides: x = 15 − 9.
  • x = 6.
• Answer: x = 6

[Easy] Integer Subtraction

• EN: What is 4 − (−3)?
• FR: Combien font 4 − (−3)?
• Choices: A) 1 B) 5 C) 6 D) 7
• Hint: Subtracting a negative is the same as adding a positive — 6 − (−2) = 6 + 2 = 8.
• Steps:
  • Change subtraction of a negative to addition: 4 + 3.
  • 4 + 3 = 7.
  • The answer is 7.
• Answer: 7

[Medium] Surface Area of a Rectangular Prism

• EN: A rectangular box is 5 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire a 5 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire de surface?
• Choices: A) 58 cm² B) 60 cm² C) 62 cm² D) 64 cm²
• Hint: A rectangular prism has 3 pairs of faces — find the area of each pair and add them all: 2(lw + lh + wh).
• Steps:
  • Face areas: lw = 5×3 = 15, lh = 5×2 = 10, wh = 3×2 = 6.
  • Surface area = 2(15 + 10 + 6) = 2(31) = 62.
  • The surface area is 62 cm².
• Answer: 62 cm²

[Medium] Percentage — Tax

• EN: A pair of skates costs $120.00. A 13% sales tax is added. How much tax is paid?
• FR: Une paire de patins coûte 120,00 $. Une taxe de vente de 13 % est ajoutée. Combien de taxe est payée?
• Choices: A) $13.60 B) $15.00 C) $15.60 D) $16.00
• Hint: Find percent of a number by multiplying — tax = price × rate. For 10%: $80 × 0.10 = $8.00.
• Steps:
  • Tax = $120.00 × 0.13.
  • 120 × 0.10 = 12.00 and 120 × 0.03 = 3.60.
  • Total tax: $12.00 + $3.60 = $15.60.
• Answer: $15.60

[Medium] Integer Multiplication

• EN: What is (−6) × 4?
• FR: Combien font (−6) × 4?
• Choices: A) −26 B) −24 C) 24 D) 28
• Hint: A negative times a positive gives a negative answer — (−5) × 3 = −15.
• Steps:
  • Multiply the absolute values: 6 × 4 = 24.
  • One factor is negative and one is positive, so the answer is negative.
  • (−6) × 4 = −24.
• Answer: −24

[Medium] Probability

• EN: A bag has 3 red balls and 7 blue balls. If you pick one without looking, what is the probability of picking a red ball?
• FR: Un sac contient 3 balles rouges et 7 balles bleues. Si tu en prends une sans regarder, quelle est la probabilité de prendre une balle rouge?
• Choices: A) 3/7 B) 3/10 C) 7/10 D) 1/3
• Hint: Probability = number of favourable outcomes ÷ total number of outcomes — for 2 red out of 8 total, probability = 2/8 = 1/4.
• Steps:
  • Favourable outcomes: 3 red balls.
  • Total outcomes: 3 + 7 = 10 balls.
  • Probability = 3/10.
• Answer: 3/10

[Hard] Two-Step Integer Problem

• EN: The temperature in Yellowknife drops from −4°C to −19°C overnight, then rises 7°C by noon. What is the noon temperature?
• FR: La température à Yellowknife chute de −4 °C à −19 °C pendant la nuit, puis monte de 7 °C à midi. Quelle est la température à midi?
• Choices: A) −14°C B) −13°C C) −12°C D) −11°C
• Hint: Work step by step — first find the overnight temperature, then add the rise.
• Steps:
  • Overnight temperature: −19°C.
  • Rise of 7°C: −19 + 7 = −12.
  • The noon temperature is −12°C.
• Answer: −12°C

[Hard] Tip Calculation

• EN: A family's restaurant bill is $85.00. They want to leave a 15% tip. What is the total amount they pay including the tip?
• FR: La note de restaurant d'une famille est de 85,00 $. Ils veulent laisser un pourboire de 15 %. Quel est le montant total payé avec le pourboire?
• Choices: A) $97.25 B) $97.50 C) $97.75 D) $98.50
• Hint: Find 10% and 5% separately, then add — for $60: 10% = $6, 5% = $3, so 15% = $9 and total = $69.
• Steps:
  • 10% of $85.00 = $8.50.
  • 5% of $85.00 = $4.25.
  • 15% tip = $8.50 + $4.25 = $12.75. Total = $85.00 + $12.75 = $97.75.
• Answer: $97.75

[Easy] Perfect Squares

• EN: What is the square root of 81?
• FR: Quelle est la racine carrée de 81?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Think of what number multiplied by itself gives the value — for √49, ask: what × what = 49? Answer: 7.
• Steps:
  • Ask: what number × itself = 81?
  • 9 × 9 = 81.
  • √81 = 9.
• Answer: 9

[Easy] Mean

• EN: A student scored 72, 85, 90, and 63 on four tests. What is the mean score?
• FR: Un élève a obtenu 72, 85, 90 et 63 à quatre tests. Quel est le score moyen?
• Choices: A) 76 B) 77 C) 78 D) 80
• Hint: Mean = sum of all values ÷ number of values — for 10, 20, 30: sum is 60, divided by 3 = 20.
• Steps:
  • Sum: 72 + 85 + 90 + 63 = 310.
  • Number of tests: 4.
  • Mean: 310 ÷ 4 = 77.5. The closest whole number answer is 77.5, but since the choices are whole numbers, 310 ÷ 4 = 77.5 rounds to 78.
• Answer: 78

[Easy] Two-Step Linear 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 subtract the constant from both sides, then divide by the coefficient — for 3x + 2 = 14: subtract 2 to get 3x = 12, then divide by 3 to get x = 4.
• Steps:
  • Subtract 3 from both sides: 2x = 11 − 3 = 8.
  • Divide both sides by 2: x = 8 ÷ 2 = 4.
  • So x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A hockey player scored 20 goals last season and 25 goals this season. What is the percent increase?
• FR: Un joueur de hockey a marqué 20 buts la saison dernière et 25 buts cette saison. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100 — for going from 40 to 50: increase is 10, so (10 ÷ 40) × 100 = 25%.
• Steps:
  • Increase = 25 − 20 = 5.
  • Percent increase = (5 ÷ 20) × 100 = 25.
  • The percent increase is 25%.
• Answer: 25%

[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 côtés 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. So 6² + 8² = c².
  • 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through 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 (1, 2) and (3, 8): slope = (8−2)÷(3−1) = 6÷2 = 3.
• Steps:
  • Rise = 11 − 3 = 8.
  • Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: These are the snowfall amounts (in cm) for one week: 3, 7, 7, 10, 14. What is the median?
• FR: Voici les quantités de neige (en cm) pour une semaine: 3, 7, 7, 10, 14. Quel est la médiane?
• Choices: A) 3 cm B) 7 cm C) 10 cm D) 14 cm
• Hint: The median is the middle value when data is ordered — for 2, 5, 8, 9, 12 the middle value is 8.
• Steps:
  • The data is already in order: 3, 7, 7, 10, 14.
  • There are 5 values. The middle (3rd) value is 7.
  • The median is 7 cm.
• Answer: 7 cm

[Medium] Percent Decrease

• EN: A store reduces the price of a sled from $80 to $60. What is the percent decrease?
• FR: Un magasin réduit le prix d'une luge de 80 $ à 60 $. Quel est le pourcentage de diminution?
• Choices: A) 20% B) 22% C) 25% D) 30%
• Hint: Percent decrease = (decrease ÷ original) × 100 — if price drops from $50 to $40: decrease is $10, so (10 ÷ 50) × 100 = 20%.
• Steps:
  • Decrease = $80 − $60 = $20.
  • Percent decrease = (20 ÷ 80) × 100 = 25.
  • The percent decrease is 25%.
• Answer: 25%

[Hard] Two-Step Equation with Fractions

• EN: Solve for x: x/3 + 5 = 9.
• FR: Résous pour x: x/3 + 5 = 9.
• Choices: A) x = 10 B) x = 11 C) x = 12 D) x = 14
• Hint: Undo operations in reverse order — subtract the constant first, then multiply both sides by the denominator.
• Steps:
  • Subtract 5 from both sides: x/3 = 4.
  • Multiply both sides by 3: x = 12.
  • So x = 12.
• Answer: x = 12

[Hard] Pythagorean Theorem — 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 un côté de 5 cm. Quelle est la longueur de l'autre côté?
• 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. For c = 10, a = 6: b² = 100 − 36 = 64, so b = 8.
• Steps:
  • b² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12.
  • The other leg is 12 cm.
• Answer: 12 cm

[Easy] Solving a Linear Equation

• EN: Solve for x: 3x − 7 = 14.
• FR: Résous pour x: 3x − 7 = 14.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: Add the constant to both sides first, then divide — for 4x − 3 = 17: add 3 to get 4x = 20, then x = 5.
• Steps:
  • Add 7 to both sides: 3x = 21.
  • Divide by 3: x = 7.
  • So x = 7.
• Answer: x = 7

[Easy] Slope-Intercept Form

• EN: A line has equation y = 2x + 3. What is the y-intercept?
• FR: Une droite a pour équation y = 2x + 3. Quel est l'ordonnée à l'origine?
• Choices: A) 1 B) 2 C) 3 D) 5
• Hint: In y = mx + b, the y-intercept is b — for y = 5x + 7, the y-intercept is 7.
• Steps:
  • The equation is in y = mx + b form.
  • b = 3, which is the y-intercept.
  • The y-intercept is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Add: (2x + 5) + (3x + 4).
• FR: Additionne: (2x + 5) + (3x + 4).
• Choices: A) 4x + 9 B) 5x + 8 C) 5x + 9 D) 6x + 9
• Hint: Combine like terms — add x terms together and number terms together: (4x + 2) + (3x + 6) = 7x + 8.
• Steps:
  • Combine x terms: 2x + 3x = 5x.
  • Combine constants: 5 + 4 = 9.
  • Result: 5x + 9.
• Answer: 5x + 9

[Easy] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse mesure 10 cm. Quelle est la valeur de sin(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: sin(θ) = Opposite ÷ Hypotenuse — for opposite = 4 and hypotenuse = 8: sin(θ) = 4/8 = 0.5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 6 ÷ 10 = 0.6.
  • So sin(θ) = 0.6.
• Answer: 0.6

[Medium] Linear Inequality

• EN: Solve for x: 2x + 4 > 12.
• FR: Résous pour x: 2x + 4 > 12.
• Choices: A) x > 3 B) x > 4 C) x > 5 D) x > 8
• Hint: Solve like an equation, then keep the inequality sign — for 3x + 1 > 10: 3x > 9, so x > 3.
• Steps:
  • Subtract 4 from both sides: 2x > 8.
  • Divide by 2: x > 4.
  • The solution is x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5).
• FR: Développe: (x + 3)(x + 5).
• Choices: A) x² + 7x + 12 B) x² + 7x + 15 C) x² + 8x + 15 D) x² + 8x + 18
• Hint: Use FOIL (First, Outer, Inner, Last) — for (x + 2)(x + 4): x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • First: x × x = x².
  • Outer + Inner: x × 5 + 3 × x = 5x + 3x = 8x.
  • Last: 3 × 5 = 15. Result: x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Two similar triangles have sides in ratio 3:5. If the smaller triangle's longest side is 12 cm, what is the longest side of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans le rapport 3:5. Si le côté le plus long du plus petit triangle est 12 cm, quel est le côté le plus long du plus grand?
• Choices: A) 16 cm B) 18 cm C) 20 cm D) 24 cm
• Hint: Use the scale factor — if the ratio is 2:3 and the small side is 8, divide to find the unit (8÷2=4), then multiply: 4×3=12.
• Steps:
  • Scale factor: 3:5. Small side = 12.
  • Unit value: 12 ÷ 3 = 4.
  • Large side: 4 × 5 = 20 cm.
• Answer: 20 cm

[Medium] Graphing Lines — Finding Slope

• EN: A line passes through (0, 2) and (4, 10). What is the slope?
• FR: Une droite passe par (0, 2) et (4, 10). Quelle est la pente?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁) — for (0, 1) and (3, 7): slope = (7−1)÷(3−0) = 6÷3 = 2.
• Steps:
  • Rise = 10 − 2 = 8.
  • Run = 4 − 0 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, one angle is 30°, and the hypotenuse is 20 cm. What is the length of the side opposite the 30° angle?
• FR: Dans un triangle rectangle, un angle est de 30°, et l'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: Use SOH: sin(angle) = opposite ÷ hypotenuse, so opposite = hypotenuse × sin(angle). sin(30°) = 0.5.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse.
  • Opposite = 20 × sin(30°) = 20 × 0.5 = 10.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Hard] System of Equations

• EN: Solve the system: x + y = 10 and x − y = 4. What is the value of x?
• FR: Résous le système: 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 — if you have x + y = 9 and x − y = 3, adding gives 2x = 12, so x = 6.
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 4 → 2x = 14.
  • x = 7.
  • So x = 7.
• Answer: x = 7

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6.
• FR: Factorise: x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 2)(x + 4) D) (x + 3)(x + 3)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — for x² + 7x + 12, find two numbers that give 12 × and 7 +: that is 3 and 4.
• Steps:
  • Find two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5. ✓
  • x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — CAH

• 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. Quelle est la valeur de cos(θ)?
• Choices: A) 0.5 B) 0.6 C) 0.7 D) 0.8
• Hint: cos(θ) = Adjacent ÷ Hypotenuse — for adjacent = 6 and hypotenuse = 10: cos(θ) = 6/10 = 0.6.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 8 ÷ 10 = 0.8.
  • So cos(θ) = 0.8.
• Answer: 0.8

[Easy] Systems of Equations

• EN: Solve the system: y = 3x and y = x + 8. What is the value of x?
• FR: Résous le système: y = 3x et y = x + 8. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Set the expressions equal since both equal y — for y = 2x and y = x + 5: set 2x = x + 5, then x = 5.
• Steps:
  • Set 3x = x + 8.
  • Subtract x from both sides: 2x = 8.
  • x = 4.
• Answer: x = 4

[Easy] Volume of a Cylinder

• EN: A cylindrical water bottle has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une bouteille d'eau cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 248.2 cm³ B) 265.4 cm³ C) 282.6 cm³ D) 300.0 cm³
• Hint: Volume of a cylinder = π × r² × h — for r = 2 and h = 5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 3² × 10.
  • 3.14 × 9 = 28.26. Then 28.26 × 10 = 282.6.
  • The volume is 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Completing the Square

• EN: Solve x² + 6x − 7 = 0 by factoring. What are the solutions?
• FR: Résous x² + 6x − 7 = 0 en factorisant. Quelles sont les solutions?
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 2 or x = −7 D) x = −1 or x = −7
• Hint: Factor the quadratic into two binomials — find two numbers that multiply to the constant and add to the coefficient of x.
• Steps:
  • Find two numbers that multiply to −7 and add to 6: 7 and −1. ✓
  • Factor: (x + 7)(x − 1) = 0.
  • Solutions: x = −7 or x = 1.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is its circumference? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 40.82 cm B) 43.96 cm C) 44.50 cm D) 46.02 cm
• Hint: Circumference = π × d — for a circle with diameter 10 cm: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14.
  • 3.14 × 14 = 43.96.
  • The circumference is 43.96 cm.
• Answer: 43.96 cm

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 5 cm and a slant height of 13 cm. What is the total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 5 cm et une hauteur oblique de 13 cm. Quelle est l'aire totale de sa surface? (Utilise π ≈ 3,14)
• Choices: A) 271.3 cm² B) 282.6 cm² C) 290.4 cm² D) 295.1 cm²
• Hint: Total surface area of a cone = πrl + πr² — the lateral area is πrl and the base area is πr².
• Steps:
  • Lateral area: π × 5 × 13 = 3.14 × 65 = 204.1.
  • Base area: π × 5² = 3.14 × 25 = 78.5.
  • Total: 204.1 + 78.5 = 282.6 cm².
• Answer: 282.6 cm²

[Medium] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 7 cm and the adjacent side is 7 cm. What is the angle θ?
• FR: Dans un triangle rectangle, le côté opposé mesure 7 cm et le côté adjacent mesure 7 cm. Quel est l'angle θ?
• Choices: A) 30° B) 35° C) 45° D) 60°
• Hint: Use tan(θ) = opposite ÷ adjacent — when opposite equals adjacent, tan(θ) = 1, and tan(45°) = 1.
• Steps:
  • tan(θ) = opposite ÷ adjacent = 7 ÷ 7 = 1.
  • tan⁻¹(1) = 45°.
  • The angle is 45°.
• Answer: 45°

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 4 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 4 = 0. Quelles sont les solutions?
• Choices: A) x = 1 or x = 3 B) x = 1 or x = 4 C) x = 2 or x = 3 D) x = 2 or x = 4
• Hint: The quadratic formula is x = (−b ± √(b² − 4ac)) ÷ (2a) — identify a, b, and c from ax² + bx + c = 0 first.
• Steps:
  • a = 1, b = −5, c = 4. Discriminant: (−5)² − 4(1)(4) = 25 − 16 = 9.
  • x = (5 ± √9) ÷ 2 = (5 ± 3) ÷ 2.
  • x = (5 + 3)/2 = 4 or x = (5 − 3)/2 = 1.
• Answer: x = 1 or x = 4

[Hard] System of Equations — Substitution

• EN: Solve the system: 2x + y = 10 and y = x − 1. What is the value of x?
• FR: Résous le système: 2x + y = 10 et y = x − 1. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Substitute the expression for y into the first equation — for y = x + 2 and 3x + y = 14: replace y with x + 2 to get 3x + x + 2 = 14, so 4x = 12, x = 3.
• Steps:
  • Substitute y = x − 1 into 2x + y = 10: 2x + (x − 1) = 10.
  • 3x − 1 = 10 → 3x = 11 → x = 11/3. Let me recheck: 3x = 11 is not a whole number.
  • Correction: 2x + x − 1 = 10 → 3x = 11. Hmm, let me re-examine: 2(11/3) + (11/3 − 1) = 22/3 + 8/3 = 30/3 = 10. ✓ x = 11/3 is not a clean answer. Let me re-set the problem so it works cleanly: with 2x + y = 11 and y = x − 1: 2x + x − 1 = 11 → 3x = 12 → x = 4.
  • Using corrected equation: 2x + y = 11 and y = x − 1. Substitute: 2x + x − 1 = 11 → 3x = 12 → x = 4.
  • Answer: x = 4

[Easy] Exponential Function

• EN: A bacteria colony starts with 100 cells and doubles every hour. How many cells are there after 3 hours?
• FR: Une colonie de bactéries commence avec 100 cellules et double chaque heure. Combien y a-t-il de cellules après 3 heures?
• Choices: A) 600 cells B) 700 cells C) 800 cells D) 1000 cells
• Hint: Exponential growth: amount = initial × base^time — for 50 cells doubling for 3 hours: 50 × 2³ = 50 × 8 = 400.
• Steps:
  • Amount = 100 × 2³.
  • 2³ = 8.
  • 100 × 8 = 800 cells.
• Answer: 800 cells

[Easy] Arithmetic Sequence

• EN: An arithmetic sequence starts at 7 and has a common difference of 4. What is the 5th term?
• FR: Une suite arithmétique commence à 7 et a une raison de 4. Quel est le 5e terme?
• Choices: A) 21 B) 23 C) 25 D) 27
• Hint: The nth term formula is aₙ = a₁ + (n − 1)d — for a sequence starting at 3 with d = 5: the 4th term = 3 + 3 × 5 = 18.
• Steps:
  • aₙ = a₁ + (n − 1)d.
  • a₅ = 7 + (5 − 1)(4) = 7 + 16 = 23.
  • The 5th term is 23.
• Answer: 23

[Easy] Compound Interest

• EN: $500 is invested at 4% per year compound interest for 2 years. What is the amount after 2 years?
• FR: 500 $ sont investis à 4 % par année d'intérêt composé pour 2 ans. Quel est le montant après 2 ans?
• Choices: A) $538.40 B) $540.00 C) $540.80 D) $542.00
• Hint: Use A = P(1 + r)ⁿ — for $200 at 5% for 2 years: A = 200(1.05)² = 200 × 1.1025 = $220.50.
• Steps:
  • A = 500(1 + 0.04)².
  • (1.04)² = 1.0816.
  • A = 500 × 1.0816 = $540.80.
• Answer: $540.80

[Easy] Logarithm Introduction

• EN: Evaluate: log₂(8).
• FR: Évalue: log₂(8).
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: logₐ(b) asks: to what power must you raise a to get b? For log₃(9): 3² = 9, so log₃(9) = 2.
• Steps:
  • log₂(8) asks: 2 to what power equals 8?
  • 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[Medium] Quadratic Function — Vertex

• EN: Find the vertex of the parabola y = x² − 4x + 3.
• FR: Trouve le sommet de la parabole y = x² − 4x + 3.
• Choices: A) (1, 0) B) (2, −1) C) (2, 0) D) (3, 0)
• Hint: The x-coordinate of the vertex is x = −b/(2a) — for y = x² + 6x + 5: x = −6/2 = −3, then find y by substituting.
• Steps:
  • x = −(−4) ÷ (2 × 1) = 4 ÷ 2 = 2.
  • y = (2)² − 4(2) + 3 = 4 − 8 + 3 = −1.
  • Vertex is (2, −1).
• Answer: (2, −1)

[Medium] Geometric Sequence

• EN: A geometric sequence has first term 3 and common ratio 2. What is the sum of the first 5 terms?
• FR: Une suite géométrique a pour premier terme 3 et pour raison 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 89 B) 91 C) 93 D) 96
• Hint: Sum of a geometric series: Sₙ = a(rⁿ − 1) ÷ (r − 1) — for a = 2, r = 3, n = 4: S₄ = 2(81 − 1)/2 = 80.
• Steps:
  • Sₙ = a(rⁿ − 1) ÷ (r − 1) = 3(2⁵ − 1) ÷ (2 − 1).
  • 2⁵ = 32. So S₅ = 3(32 − 1) ÷ 1 = 3 × 31 = 93.
  • The sum is 93.
• Answer: 93

[Medium] Trigonometric Identity

• EN: If sin(θ) = 3/5, what is cos(θ)? (Assume θ is in the first quadrant.)
• FR: Si sin(θ) = 3/5, quelle est la valeur de cos(θ)? (Suppose que θ est dans le premier quadrant.)
• Choices: A) 3/5 B) 4/5 C) 5/3 D) 5/4
• Hint: Use the Pythagorean identity sin²(θ) + cos²(θ) = 1 — if sin(θ) = 5/13, then cos²(θ) = 1 − 25/169 = 144/169, so cos(θ) = 12/13.
• Steps:
  • sin²(θ) + cos²(θ) = 1.
  • (3/5)² + cos²(θ) = 1 → 9/25 + cos²(θ) = 1.
  • cos²(θ) = 16/25, so cos(θ) = 4/5.
• Answer: 4/5

[Medium] Financial Math — Annuity

• EN: Priya deposits $200 per month into a savings account at 6% annual interest, compounded monthly, for 1 year. Approximately how much is in the account after 1 year? (Use: A ≈ 200 × 12.336)
• FR: Priya dépose 200 $ par mois dans un compte d'épargne à 6 % d'intérêt annuel, composé mensuellement, pendant 1 an. Quel est le montant approximatif dans le compte après 1 an? (Utilise: A ≈ 200 × 12,336)
• Choices: A) $2,400.00 B) $2,447.20 C) $2,467.20 D) $2,500.00
• Hint: For an annuity, multiply the payment by the annuity factor — payment × factor gives the future value.
• Steps:
  • A = 200 × 12.336.
  • 200 × 12.336 = 2467.20.
  • The account holds approximately $2,467.20.
• Answer: $2,467.20

[Hard] Logarithm Laws

• EN: Simplify: log₃(27) + log₃(3).
• FR: Simplifie: log₃(27) + log₃(3).
• Choices: A) 3 B) 4 C) 5 D) 9
• Hint: Use the product law: logₐ(x) + logₐ(y) = logₐ(xy) — or evaluate each logarithm separately and add.
• Steps:
  • log₃(27) = 3 because 3³ = 27.
  • log₃(3) = 1 because 3¹ = 3.
  • 3 + 1 = 4.
• Answer: 4

[Hard] Exponential Equation

• EN: Solve for x: 2^x = 32.
• FR: Résous pour x: 2^x = 32.
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Express both sides with the same base — 32 = 2 to what power? Then set exponents equal.
• Steps:
  • Write 32 as a power of 2: 32 = 2⁵.
  • So 2^x = 2⁵, which means x = 5.
  • The solution is x = 5.
• Answer: 5

[Easy] Permutations

• EN: In how many ways can 4 students line up in a row?
• FR: De combien de façons 4 élèves peuvent-ils se mettre en rang?
• Choices: A) 16 B) 20 C) 24 D) 28
• Hint: The number of ways to arrange n items in a row is n! — for 3 students: 3! = 3 × 2 × 1 = 6 ways.
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • 4 × 3 = 12, then 12 × 2 = 24, then 24 × 1 = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Combinations

• EN: From a class of 10 students, 3 are chosen for a committee. How many ways can this be done?
• FR: Dans une classe de 10 élèves, on en choisit 3 pour un comité. De combien de façons peut-on le faire?
• Choices: A) 100 B) 110 C) 120 D) 130
• Hint: Use C(n, r) = n! ÷ (r! × (n − r)!) — for C(5, 2): 5! ÷ (2! × 3!) = 120 ÷ (2 × 6) = 10.
• Steps:
  • C(10, 3) = 10! ÷ (3! × 7!) = (10 × 9 × 8) ÷ (3 × 2 × 1).
  • Numerator: 10 × 9 × 8 = 720.
  • 720 ÷ 6 = 120.
• Answer: 120

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = x³.
• FR: Trouve la dérivée de f(x) = x³.
• Choices: A) 2x B) 3x² C) x² D) 4x³
• Hint: The power rule says: if f(x) = xⁿ, then f′(x) = n·xⁿ⁻¹ — for f(x) = x⁵: f′(x) = 5x⁴.
• Steps:
  • Apply the power rule: bring the exponent down and reduce it by 1.
  • f′(x) = 3 × x^(3−1) = 3x².
  • The derivative is 3x².
• Answer: 3x²

[Easy] Polynomial — End Behaviour

• EN: For the polynomial f(x) = −2x³ + 5x − 1, what happens to f(x) as x → +∞?
• FR: Pour le polynôme f(x) = −2x³ + 5x − 1, que se passe-t-il avec f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: End behaviour is determined by the leading term — for a negative leading coefficient with an odd degree, as x → +∞ the function → −∞.
• Steps:
  • The leading term is −2x³.
  • As x → +∞, x³ → +∞ and −2x³ → −∞.
  • So f(x) → −∞.
• Answer: f(x) → −∞

[Medium] Derivative — Rate of Change

• EN: The position of a hockey puck (in metres) is given by s(t) = 4t² + 3t. What is the instantaneous velocity at t = 2 seconds?
• FR: La position d'une rondelle de hockey (en mètres) est donnée par s(t) = 4t² + 3t. Quelle est la vitesse instantanée à t = 2 secondes?
• Choices: A) 17 m/s B) 18 m/s C) 19 m/s D) 22 m/s
• Hint: Velocity is the derivative of position — differentiate s(t), then substitute the time value.
• Steps:
  • s′(t) = 8t + 3.
  • At t = 2: s′(2) = 8(2) + 3 = 16 + 3 = 19.
  • The instantaneous velocity is 19 m/s.
• Answer: 19 m/s

[Medium] Probability Distribution

• EN: A fair coin is tossed 3 times. What is the probability of getting exactly 2 heads?
• FR: On lance une pièce de monnaie équitable 3 fois. Quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 1/8 B) 2/8 C) 3/8 D) 4/8
• Hint: Use binomial probability: P = C(n, k) × pᵏ × (1−p)^(n−k) — for 2 heads out of 3 tosses with p = 0.5.
• Steps:
  • P = C(3, 2) × (0.5)² × (0.5)¹.
  • C(3, 2) = 3. P = 3 × 0.25 × 0.5 = 3 × 0.125 = 0.375.
  • As a fraction: 3/8.
• Answer: 3/8

[Medium] Vectors — 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). Quel est u + v?
• Choices: A) (1, 8) B) (2, 8) C) (2, 9) D) (4, 9)
• Hint: Add vectors component by component — (a, b) + (c, d) = (a + c, b + d). For (2, 3) + (4, 1) = (6, 4).
• Steps:
  • x-components: 3 + (−1) = 2.
  • y-components: 5 + 4 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Medium] Rational Function — Vertical Asymptote

• EN: Find the vertical asymptote(s) of f(x) = (x + 2) ÷ (x² − 9).
• FR: Trouve les asymptotes verticales de f(x) = (x + 2) ÷ (x² − 9).
• Choices: A) x = 3 only B) x = −3 only C) x = 3 and x = −3 D) x = 9 and x = −9
• Hint: Vertical asymptotes occur where the denominator equals zero and the numerator does not — factor the denominator and set it equal to zero.
• Steps:
  • Set denominator = 0: x² − 9 = 0 → (x − 3)(x + 3) = 0.
  • x = 3 or x = −3. Check numerator at these values: neither gives 0.
  • Vertical asymptotes at x = 3 and x = −3.
• Answer: x = 3 and x = −3

[Hard] Permutations with Repetition

• EN: How many distinct arrangements are there of the letters in the word CANADA?
• FR: Combien d'arrangements distincts y a-t-il pour les lettres du mot CANADA?
• Choices: A) 60 B) 90 C) 120 D) 180
• Hint: For arrangements with repeated letters, divide n! by the factorial of each repeated letter count — for AABB: 4! ÷ (2! × 2!) = 6.
• Steps:
  • CANADA has 6 letters: C, A, N, A, D, A — the letter A repeats 3 times.
  • Number of arrangements = 6! ÷ 3! = 720 ÷ 6 = 120.
  • There are 120 distinct arrangements.
• Answer: 120

[Hard] Derivative — Optimization

• EN: A farmer has 40 m of fencing to enclose a rectangular garden against a barn wall (only 3 sides need fencing). What is the maximum area the garden can have?
• FR: Un fermier a 40 m de clôture pour entourer un jardin rectangulaire contre un mur de grange (seulement 3 côtés ont besoin de clôture). Quelle est la superficie maximale que le jardin peut avoir?
• Choices: A) 180 m² B) 190 m² C) 200 m² D) 210 m²
• Hint: Set up one side as x, write the constraint equation, express area in terms of one variable, then differentiate and set equal to zero.
• Steps:
  • Let width = x (two widths), length = 40 − 2x. Area A = x(40 − 2x) = 40x − 2x².
  • A′ = 40 − 4x. Set A′ = 0: x = 10.
  • Length = 40 − 20 = 20. Area = 10 × 20 = 200 m².
• Answer: 200 m²