Daily Math — 2026-09-29

[Easy] Counting Mittens

• EN: Mia has 7 red mittens. She finds 3 more in her bag. How many mittens does she have now?
• FR: Mia a 7 mitaines rouges. Elle en trouve 3 autres dans son sac. Combien de mitaines a-t-elle maintenant ?
• Choices: A) 9 mittens B) 10 mittens C) 11 mittens D) 12 mittens
• Hint: To add, count on from the bigger number (e.g., 5 + 2 = 7).
• Steps:
  • Start at 7 and count on 3 more: 8, 9, 10.
  • So Mia has 10 mittens in all.
• Answer: 10 mittens

[Easy] Snow Day Snacks

• EN: There are 15 crackers on a plate. Jake eats 6. How many crackers are left?
• FR: Il y a 15 craquelins dans une assiette. Jake en mange 6. Combien de craquelins reste-t-il ?
• Choices: A) 7 crackers B) 8 crackers C) 9 crackers D) 11 crackers
• Hint: To subtract, count back from the bigger number (e.g., 12 − 4 = 8).
• Steps:
  • Start at 15 and count back 6: 14, 13, 12, 11, 10, 9.
  • So there are 9 crackers left.
• Answer: 9 crackers

[Easy] Skip Counting by 2s

• EN: Count by 2s: 2, 4, 6, 8, ___. What comes next?
• FR: Compte par bonds de 2 : 2, 4, 6, 8, ___. Quel nombre vient ensuite ?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Skip counting by 2s means adding 2 each time (e.g., 10, 12, 14…).
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
• Answer: 10

[Easy] Penny Count

• EN: Luca has 4 pennies. Each penny is worth 1 cent. How many cents does he have in all?
• FR: Luca a 4 sous (pennies). Chaque sou vaut 1 cent. Combien de cents a-t-il en tout ?
• Choices: A) 3 cents B) 5 cents C) 4 cents D) 6 cents
• Hint: Count each penny as 1 cent (e.g., 3 pennies = 3 cents).
• Steps:
  • Each penny = 1 cent.
  • 4 pennies = 4 cents.
• Answer: 4 cents

[Medium] Bigger Number

• EN: Which number is bigger: 43 or 34?
• FR: Quel nombre est plus grand : 43 ou 34 ?
• Choices: A) 34 B) 43 C) 40 D) 37
• Hint: Look at the tens digit first (e.g., 52 is bigger than 25 because 5 tens > 2 tens).
• Steps:
  • 43 has 4 tens; 34 has 3 tens.
  • 4 tens is more than 3 tens, so 43 is bigger.
• Answer: 43

[Medium] Hockey Goals

• EN: The Leafs scored 8 goals on Monday and 9 goals on Tuesday. How many goals did they score in total?
• FR: Les Leafs ont marqué 8 buts lundi et 9 buts mardi. Combien de buts ont-ils marqué en tout ?
• Choices: A) 15 goals B) 16 goals C) 17 goals D) 18 goals
• Hint: To add two numbers, make a ten first (e.g., 7 + 5 = 10 + 2 = 12).
• Steps:
  • 8 + 9: make a ten — 8 + 2 = 10, then add 7 more.
  • 10 + 7 = 17 goals.
• Answer: 17 goals

[Medium] Skip Counting by 5s

• EN: Count by 5s: 5, 10, 15, 20, ___. What comes next?
• FR: Compte par bonds de 5 : 5, 10, 15, 20, ___. Quel nombre vient ensuite ?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: Skip counting by 5s means adding 5 each time (e.g., 30, 35, 40…).
• Steps:
  • The pattern adds 5 each time.
  • 20 + 5 = 25.
• Answer: 25

[Medium] Nickel Value

• EN: Sofia has 3 nickels. Each nickel is worth 5 cents. How many cents does she have?
• FR: Sofia a 3 pièces de 5 cents (nickels). Chaque pièce vaut 5 cents. Combien de cents a-t-elle ?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: Count by 5s for each nickel (e.g., 2 nickels = 5, 10 = 10 cents).
• Steps:
  • Count by 5s, three times: 5, 10, 15.
  • Sofia has 15 cents.
• Answer: 15 cents

[Hard] Missing Number

• EN: 6 + ___ = 14. What is the missing number?
• FR: 6 + ___ = 14. Quel est le nombre manquant ?
• Choices: A) 7 B) 8 C) 9 D) 6
• Hint: To find a missing addend, subtract the known number from the total (e.g., 5 + ___ = 11, so 11 − 5 = 6).
• Steps:
  • We need 6 + ? = 14.
  • Subtract: 14 − 6 = 8.
• Answer: 8

[Hard] Counting Back from 20

• EN: Start at 20 and count back by 2s. What is the 4th number you say?
• FR: Commence à 20 et compte à rebours par bonds de 2. Quel est le 4e nombre que tu dis ?
• Choices: A) 12 B) 13 C) 14 D) 16
• Hint: Count back by 2s step by step (e.g., starting at 10: 8, 6, 4 — the 3rd number is 4).
• Steps:
  • Start: 20. Subtract 2 each time.
  • 1st: 18, 2nd: 16, 3rd: 14, 4th: 12.
• Answer: 12

[Easy] Adding at the Store

• EN: Emma buys a pencil for 25 cents and an eraser for 30 cents. How much does she spend in total?
• FR: Emma achète un crayon pour 25 cents et une gomme pour 30 cents. Combien dépense-t-elle en tout ?
• Choices: A) 50 cents B) 55 cents C) 60 cents D) 65 cents
• Hint: Add the tens first, then the ones (e.g., 20 + 40 = 60, then add ones).
• Steps:
  • 25 + 30: add tens → 20 + 30 = 50, then add 5.
  • 50 + 5 = 55 cents.
• Answer: 55 cents

[Easy] Telling Time

• EN: The clock shows the hour hand on the 3 and the minute hand on the 12. What time is it?
• FR: L'horloge montre la grande aiguille sur le 12 et la petite sur le 3. Quelle heure est-il ?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 12:15
• Hint: When the minute hand points to 12, it is exactly the o'clock hour (e.g., hour hand on 5 = 5:00).
• Steps:
  • Minute hand on 12 → exactly on the hour.
  • Hour hand on 3 → 3 o'clock = 3:00.
• Answer: 3:00

[Easy] Measuring a Scarf

• EN: A scarf is 60 cm long. A toque is 20 cm long. How much longer is the scarf than the toque?
• FR: Une écharpe mesure 60 cm de long. Un bonnet mesure 20 cm. De combien l'écharpe est-elle plus longue ?
• Choices: A) 30 cm B) 35 cm C) 40 cm D) 80 cm
• Hint: To find the difference, subtract the smaller length from the larger (e.g., 70 − 30 = 40 cm).
• Steps:
  • 60 − 20 = 40.
  • The scarf is 40 cm longer.
• Answer: 40 cm

[Easy] Subtraction within 100

• EN: There are 78 students at school. 45 go to the gym. How many students stay in class?
• FR: Il y a 78 élèves à l'école. 45 vont au gymnase. Combien d'élèves restent en classe ?
• Choices: A) 23 B) 33 C) 43 D) 53
• Hint: Subtract tens first, then ones (e.g., 85 − 52 = 33).
• Steps:
  • 78 − 45: subtract tens 70 − 40 = 30, subtract ones 8 − 5 = 3.
  • 30 + 3 = 33 students.
• Answer: 33

[Medium] Counting Coins

• EN: Owen has 2 dimes and 3 nickels. How much money does he have?
• FR: Owen a 2 pièces de 10 cents et 3 pièces de 5 cents. Combien d'argent a-t-il ?
• Choices: A) 25 cents B) 30 cents C) 35 cents D) 40 cents
• Hint: Count each coin type separately, then add (e.g., 1 dime + 2 nickels = 10 + 10 = 20 cents).
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • 3 nickels = 5 + 5 + 5 = 15 cents.
  • 20 + 15 = 35 cents.
• Answer: 35 cents

[Medium] Half-Hour Time

• EN: School starts at 8:00. The first break is 30 minutes later. What time is the break?
• FR: L'école commence à 8 h. La première récréation est 30 minutes plus tard. À quelle heure est la récréation ?
• Choices: A) 8:15 B) 8:30 C) 9:00 D) 8:45
• Hint: Adding 30 minutes moves the minute hand from 12 to 6 (e.g., 9:00 + 30 min = 9:30).
• Steps:
  • 8:00 + 30 minutes.
  • The minute hand moves from 12 to 6 → 8:30.
• Answer: 8:30

[Medium] Number Pattern

• EN: What is the missing number in this pattern? 10, 20, 30, ___, 50
• FR: Quel est le nombre manquant dans cette suite ? 10, 20, 30, ___, 50
• Choices: A) 35 B) 38 C) 40 D) 45
• Hint: Find the rule by looking at how much the numbers increase each time (e.g., 5, 10, 15 — add 5).
• Steps:
  • The pattern increases by 10 each time.
  • 30 + 10 = 40.
• Answer: 40

[Medium] Adding Three Numbers

• EN: A jar has 12 red beads, 15 blue beads, and 8 yellow beads. How many beads are there in all?
• FR: Un bocal contient 12 perles rouges, 15 perles bleues et 8 perles jaunes. Combien y a-t-il de perles en tout ?
• Choices: A) 33 B) 34 C) 35 D) 36
• Hint: Add two numbers first, then add the third (e.g., 10 + 14 + 6 = 30).
• Steps:
  • 12 + 15 = 27.
  • 27 + 8 = 35 beads.
• Answer: 35

[Hard] Change from a Dollar

• EN: Lena buys a juice box for 65 cents and pays with a dollar (100 cents). How much change does she get?
• FR: Lena achète une boîte de jus pour 65 cents et paie avec un dollar (100 cents). Quelle monnaie reçoit-elle ?
• Choices: A) 25 cents B) 30 cents C) 35 cents D) 45 cents
• Hint: To find change, subtract the cost from 100 cents (e.g., 100 − 70 = 30 cents).
• Steps:
  • 100 − 65 = 35.
  • Lena receives 35 cents in change.
• Answer: 35 cents

[Hard] Measuring Two Objects

• EN: A hockey stick is 90 cm long. A ruler is 30 cm long. How many rulers laid end-to-end equal the hockey stick?
• FR: Un bâton de hockey mesure 90 cm. Une règle mesure 30 cm. Combien de règles, mises bout à bout, égalent la longueur du bâton ?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: Divide the total length by the shorter length (e.g., 80 cm ÷ 20 cm = 4 rulers).
• Steps:
  • 90 ÷ 30 = 3.
  • You need 3 rulers to match the hockey stick.
• Answer: 3

[Easy] Multiplication by 2

• EN: There are 6 pairs of skates. Each pair has 2 skates. How many skates are there in all?
• FR: Il y a 6 paires de patins. Chaque paire a 2 patins. Combien y a-t-il de patins en tout ?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiply the number of groups by the size of each group (e.g., 4 × 2 = 8).
• Steps:
  • 6 groups of 2.
  • 6 × 2 = 12 skates.
• Answer: 12

[Easy] Simple Fraction

• EN: A pizza is cut into 4 equal slices. Maya eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 tranches égales. Maya mange 1 tranche. 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 names one part out of the total equal parts (e.g., 1 out of 3 = 1/3).
• Steps:
  • The pizza has 4 equal slices (denominator = 4).
  • Maya ate 1 slice (numerator = 1) → 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: There are 7 hockey players, and each player has 5 pucks. How many pucks are there altogether?
• FR: Il y a 7 joueurs de hockey et chaque joueur a 5 rondelles. Combien y a-t-il de rondelles en tout ?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: Skip count by 5s or multiply (e.g., 6 × 5 = 30).
• Steps:
  • 7 × 5 = 35.
  • There are 35 pucks altogether.
• Answer: 35

[Easy] Basic Division

• EN: 20 apples are shared equally among 4 friends. How many apples does each friend get?
• FR: 20 pommes sont partagées également entre 4 amis. Combien de pommes chaque ami reçoit-il ?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Division is sharing equally — ask "how many groups of 4 are in 20?" (e.g., 12 ÷ 3 = 4).
• Steps:
  • 20 ÷ 4 = 5.
  • Each friend gets 5 apples.
• Answer: 5

[Medium] Perimeter of a Rectangle

• EN: A rectangular garden is 8 m long and 3 m wide. What is its perimeter?
• FR: Un jardin rectangulaire a 8 m de long et 3 m de large. Quel est son périmètre ?
• Choices: A) 11 m B) 22 m C) 24 m D) 30 m
• Hint: Perimeter = add all four sides (e.g., a 5 m × 2 m rectangle: 5 + 5 + 2 + 2 = 14 m).
• Steps:
  • Two long sides: 8 + 8 = 16.
  • Two short sides: 3 + 3 = 6.
  • 16 + 6 = 22 m.
• Answer: 22 m

[Medium] Multiplication by 3

• EN: A bakery packs muffins in boxes of 3. There are 9 boxes. How many muffins are there?
• FR: Une boulangerie emballe des muffins dans des boîtes de 3. Il y a 9 boîtes. Combien y a-t-il de muffins ?
• Choices: A) 24 B) 27 C) 30 D) 33
• Hint: Multiply the number of boxes by the size of each box (e.g., 8 × 3 = 24).
• Steps:
  • 9 × 3 = 27.
  • There are 27 muffins.
• Answer: 27

[Medium] Reading a Graph

• EN: A bar graph shows: Monday = 4 books, Tuesday = 7 books, Wednesday = 5 books. How many books were read on Monday and Wednesday together?
• FR: Un diagramme à bandes montre : lundi = 4 livres, mardi = 7 livres, mercredi = 5 livres. Combien de livres ont été lus lundi et mercredi ensemble ?
• Choices: A) 7 B) 9 C) 11 D) 16
• Hint: Add only the values you need (e.g., if Monday = 3 and Wednesday = 6, then 3 + 6 = 9).
• Steps:
  • Monday = 4, Wednesday = 5.
  • 4 + 5 = 9 books.
• Answer: 9

[Medium] Comparing Fractions

• EN: Which fraction is larger: 1/2 or 1/4?
• FR: Quelle fraction est la plus grande : 1/2 ou 1/4 ?
• Choices: A) 1/4 B) They are equal C) 1/2 D) 1/3
• Hint: The bigger the denominator, the smaller each piece (e.g., 1/3 of a pie is bigger than 1/6).
• Steps:
  • Imagine one pizza cut into 2 pieces vs. 4 pieces.
  • Halves are bigger than quarters → 1/2 is larger.
• Answer: 1/2

[Hard] Division with Multiplication Check

• EN: A teacher has 36 stickers to give equally to 4 students. How many stickers does each student receive?
• FR: Une enseignante a 36 autocollants à distribuer également à 4 élèves. Combien d'autocollants chaque élève reçoit-il ?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Use the related multiplication fact to check (e.g., 32 ÷ 4 = 8 because 8 × 4 = 32).
• Steps:
  • Ask: 4 × ? = 36.
  • 4 × 9 = 36, so each student gets 9 stickers.
• Answer: 9

[Hard] Perimeter with Unknown Side

• EN: A triangle has two sides of 7 cm each. Its perimeter is 20 cm. What is the length of the third side?
• FR: Un triangle a deux côtés de 7 cm chacun. Son périmètre est de 20 cm. Quelle est la longueur du troisième côté ?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: Add the known sides, then subtract from the perimeter (e.g., perimeter 15, sides 5 and 4: third side = 15 − 5 − 4 = 6).
• Steps:
  • Two known sides: 7 + 7 = 14 cm.
  • Third side = 20 − 14 = 6 cm.
• Answer: 6 cm

[Easy] Multiplication Table

• EN: What is 7 × 8?
• FR: Combien font 7 × 8 ?
• Choices: A) 54 B) 56 C) 63 D) 48
• Hint: Use a known fact and adjust (e.g., 7 × 7 = 49, then add one more group of 7).
• Steps:
  • 7 × 8: think 7 × 7 = 49, then 49 + 7 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, which digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre est à la position des dixièmes ?
• Choices: A) 3 B) 7 C) 4 D) 0
• Hint: In a decimal, the first digit after the point is tenths (e.g., in 5.62, the tenths digit is 6).
• Steps:
  • 3.47 → ones = 3, tenths = 4, hundredths = 7.
  • The tenths digit is 4.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A hockey rink section is 9 m long and 6 m wide. What is its area?
• FR: Une section d'une patinoire mesure 9 m de long et 6 m de large. Quelle est son aire ?
• Choices: A) 30 m² B) 45 m² C) 54 m² D) 60 m²
• Hint: Area = length × width (e.g., a 7 m × 5 m room has area 35 m²).
• Steps:
  • Area = 9 × 6 = 54.
  • The area is 54 m².
• Answer: 54 m²

[Easy] Elapsed Time

• EN: A movie starts at 1:00 PM and ends at 3:00 PM. How long is the movie?
• FR: Un film commence à 13 h et se termine à 15 h. Quelle est la durée du film ?
• Choices: A) 1 hour B) 2 hours C) 3 hours D) 4 hours
• Hint: Count forward from the start time to the end time (e.g., from 10:00 to 12:00 = 2 hours).
• Steps:
  • From 1:00 PM to 3:00 PM = 3 − 1 = 2 hours.
  • The movie is 2 hours long.
• Answer: 2 hours

[Medium] Long Division with Remainder

• EN: 47 ÷ 5 = ?
• FR: 47 ÷ 5 = ?
• Choices: A) 8 remainder 7 B) 9 remainder 3 C) 9 remainder 2 D) 10 remainder 3
• Hint: Find the largest multiple of the divisor that fits, then find the remainder (e.g., 38 ÷ 4: 4 × 9 = 36, remainder 2).
• Steps:
  • 5 × 9 = 45 (fits into 47).
  • 47 − 45 = 2, so the remainder is 2.
• Answer: 9 remainder 2

[Medium] Comparing Decimals

• EN: Which decimal is the largest: 0.3, 0.75, 0.5, or 0.09?
• FR: Quel décimal est le plus grand : 0,3, 0,75, 0,5 ou 0,09 ?
• Choices: A) 0.3 B) 0.09 C) 0.5 D) 0.75
• Hint: Compare the tenths digits first; if equal, look at hundredths (e.g., 0.6 > 0.58 because 6 tenths > 5 tenths).
• Steps:
  • Compare tenths: 0.7 in 0.75 is the largest tenths digit.
  • So 0.75 is the greatest.
• Answer: 0.75

[Medium] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 5/8?
• FR: Quelle fraction est la plus grande : 3/4 ou 5/8 ?
• Choices: A) 5/8 B) 3/4 C) They are equal D) 1/2
• Hint: Convert to the same denominator to compare (e.g., 1/2 = 4/8, so 3/8 < 1/2).
• Steps:
  • 3/4 = 6/8.
  • 6/8 > 5/8, so 3/4 is greater.
• Answer: 3/4

[Medium] Elapsed Time (advanced)

• EN: Priya's practice starts at 2:15 PM and lasts 45 minutes. What time does it end?
• FR: La pratique de Priya commence à 14 h 15 et dure 45 minutes. À quelle heure se termine-t-elle ?
• Choices: A) 2:45 PM B) 3:00 PM C) 3:15 PM D) 3:30 PM
• Hint: Add the minutes and adjust the hour if needed (e.g., 1:30 + 45 min = 1:75 → 2:15 PM).
• Steps:
  • 2:15 + 45 min: 2:15 + 45 = 2:60 → 3:00.
  • Practice ends at 3:00 PM.
• Answer: 3:00 PM

[Hard] Multi-Step Word Problem

• EN: A store has 8 boxes of crayons with 24 crayons each. The store sells 76 crayons. How many crayons are left?
• FR: Un magasin a 8 boîtes de crayons avec 24 crayons chacune. Le magasin vend 76 crayons. Combien de crayons reste-t-il ?
• Choices: A) 108 B) 116 C) 124 D) 96
• Hint: Multiply first to find the total, then subtract what was sold (e.g., 6 boxes × 10 each = 60 total, then 60 − 15 = 45).
• Steps:
  • Total crayons: 8 × 24 = 192.
  • 192 − 76 = 116 crayons left.
• Answer: 116

[Hard] Long Division

• EN: A school fundraiser raised $504. The money is shared equally among 9 charities. How much does each charity receive?
• FR: Une collecte de fonds scolaire a récolté 504 $. L'argent est partagé également entre 9 organismes de bienfaisance. Combien chaque organisme reçoit-il ?
• Choices: A) $54 B) $56 C) $63 D) $72
• Hint: Divide step by step (e.g., 270 ÷ 9: 9 × 30 = 270, so the answer is 30).
• Steps:
  • 504 ÷ 9: 9 × 56 = 504.
  • Each charity receives $56.
• Answer: $56

[Easy] Multi-Digit Multiplication

• EN: A school orders 24 boxes of notebooks. Each box has 12 notebooks. How many notebooks are there in total?
• FR: Une école commande 24 boîtes de cahiers. Chaque boîte contient 12 cahiers. Combien y a-t-il de cahiers en tout ?
• Choices: A) 268 B) 288 C) 296 D) 312
• Hint: Use the standard algorithm: multiply ones first, then tens (e.g., 13 × 21 = 273).
• Steps:
  • 24 × 12: (24 × 10) + (24 × 2) = 240 + 48 = 288.
  • There are 288 notebooks.
• Answer: 288

[Easy] Adding Fractions (like denominators)

• EN: Aisha ate 2/8 of a pie and her brother ate 3/8. How much of the pie did they eat together?
• FR: Aisha a mangé 2/8 d'une tarte et son frère en a mangé 3/8. Quelle fraction de la tarte ont-ils mangée ensemble ?
• Choices: A) 5/16 B) 4/8 C) 5/8 D) 6/8
• Hint: Add fractions with the same denominator by adding numerators only (e.g., 3/10 + 4/10 = 7/10).
• Steps:
  • 2/8 + 3/8 = (2 + 3)/8 = 5/8.
  • They ate 5/8 of the pie.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: A store has 80 toques. During a sale, 50% are sold. How many toques are sold?
• FR: Un magasin a 80 bonnets. Lors d'une vente, 50 % sont vendus. Combien de bonnets sont vendus ?
• Choices: A) 30 B) 35 C) 40 D) 50
• Hint: 50% means half — divide by 2 (e.g., 50% of 60 = 30).
• Steps:
  • 50% of 80 = 80 ÷ 2 = 40.
  • 40 toques are sold.
• Answer: 40

[Easy] Decimal Subtraction

• EN: A water bottle holds 1.75 L. After a hockey game, 0.50 L remains. How much water was drunk?
• FR: Une bouteille d'eau contient 1,75 L. Après un match de hockey, il reste 0,50 L. Combien d'eau a été bue ?
• Choices: A) 1.15 L B) 1.20 L C) 1.25 L D) 1.30 L
• Hint: Line up the decimal points and subtract (e.g., 2.50 − 0.75 = 1.75).
• Steps:
  • 1.75 − 0.50 = 1.25.
  • 1.25 L of water was drunk.
• Answer: 1.25 L

[Medium] Multi-Digit Division

• EN: 672 students are split into groups of 8 for a field trip. How many groups are there?
• FR: 672 élèves sont divisés en groupes de 8 pour une sortie scolaire. Combien y a-t-il de groupes ?
• Choices: A) 74 B) 80 C) 84 D) 88
• Hint: Divide step by step using long division (e.g., 336 ÷ 8 = 42).
• Steps:
  • 672 ÷ 8: 8 × 80 = 640; 672 − 640 = 32; 32 ÷ 8 = 4.
  • 80 + 4 = 84 groups.
• Answer: 84

[Medium] Subtracting Fractions

• EN: A container is 7/10 full of maple syrup. Leo uses 3/10. How full is the container now?
• FR: Un contenant est rempli aux 7/10 de sirop d'érable. Léo en utilise 3/10. Quelle fraction reste-t-il ?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: Subtract fractions with the same denominator by subtracting numerators only (e.g., 9/12 − 4/12 = 5/12).
• Steps:
  • 7/10 − 3/10 = (7 − 3)/10 = 4/10.
  • The container is 4/10 full.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A box of cereal is 20 cm long, 5 cm wide, and 30 cm tall. What is its volume?
• FR: Une boîte de céréales mesure 20 cm de long, 5 cm de large et 30 cm de hauteur. Quel est son volume ?
• Choices: A) 2 500 cm³ B) 3 000 cm³ C) 3 500 cm³ D) 4 000 cm³
• Hint: Volume = length × width × height (e.g., 4 × 3 × 5 = 60 cm³).
• Steps:
  • V = 20 × 5 × 30.
  • 20 × 5 = 100; 100 × 30 = 3 000 cm³.
• Answer: 3 000 cm³

[Medium] Percentage — 25%

• EN: A bag has 120 marbles. 25% are red. How many red marbles are there?
• FR: Un sac contient 120 billes. 25 % sont rouges. Combien y a-t-il de billes rouges ?
• Choices: A) 25 B) 30 C) 35 D) 40
• Hint: 25% = one quarter — divide by 4 (e.g., 25% of 80 = 80 ÷ 4 = 20).
• Steps:
  • 25% of 120 = 120 ÷ 4 = 30.
  • There are 30 red marbles.
• Answer: 30

[Hard] Multi-Step Fraction and Decimal

• EN: A recipe needs 2.5 cups of flour. Fatima wants to make 3 batches. She already has 4.25 cups. How many more cups does she need?
• FR: Une recette nécessite 2,5 tasses de farine. Fatima veut faire 3 fois la recette. Elle a déjà 4,25 tasses. De combien de tasses supplémentaires a-t-elle besoin ?
• Choices: A) 2.75 cups B) 3.00 cups C) 3.25 cups D) 4.75 cups
• Hint: Find the total needed first, then subtract what she has (e.g., 3 batches × 3 cups = 9 cups; 9 − 5.5 = 3.5 more cups).
• Steps:
  • Total needed: 2.5 × 3 = 7.5 cups.
  • She has 4.25 cups; 7.5 − 4.25 = 3.25 cups more.
• Answer: 3.25 cups

[Hard] Percentage — 10% Application

• EN: A jacket costs $140. It is on sale for 10% off. What is the sale price?
• FR: Un manteau coûte 140 $. Il est en solde à 10 % de rabais. Quel est le prix de vente ?
• Choices: A) $112.00 B) $124.00 C) $126.00 D) $130.00
• Hint: 10% of a number = divide by 10; then subtract from original (e.g., 10% of $60 = $6; sale price = $54).
• Steps:
  • 10% of $140 = $140 ÷ 10 = $14.
  • Sale price = $140 − $14 = $126.00.
• Answer: $126.00

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien font 30 % de 200 ?
• Choices: A) 40 B) 50 C) 60 D) 70
• Hint: Find 10% first, then multiply (e.g., 10% of 150 = 15; 30% = 15 × 3 = 45).
• Steps:
  • 10% of 200 = 20.
  • 30% = 20 × 3 = 60.
• Answer: 60

[Easy] Ratio

• EN: In a class of 30 students, 18 are girls. What is the ratio of girls to boys?
• FR: Dans une classe de 30 élèves, 18 sont des filles. Quel est le rapport filles sur garçons ?
• Choices: A) 3:2 B) 2:3 C) 18:30 D) 3:5
• Hint: Simplify by dividing both parts by their GCF (e.g., 12:8 → divide by 4 → 3:2).
• Steps:
  • Boys = 30 − 18 = 12.
  • Girls to boys = 18:12 = 3:2 (divide both by 6).
• Answer: 3:2

[Easy] Algebraic Expression

• EN: If n = 5, what is the value of 3n + 4?
• FR: Si n = 5, quelle est la valeur de 3n + 4 ?
• Choices: A) 17 B) 19 C) 20 D) 22
• Hint: Substitute the value and follow order of operations (e.g., 2n + 3 when n = 4: 2(4) + 3 = 11).
• Steps:
  • 3n + 4 = 3(5) + 4 = 15 + 4 = 19.
  • The value is 19.
• Answer: 19

[Easy] Integers Introduction

• EN: The temperature in Whitehorse was −8°C in the morning. By noon it rose 11°C. What was the noon temperature?
• FR: La température à Whitehorse était de −8 °C le matin. À midi, elle a augmenté de 11 °C. Quelle était la température à midi ?
• Choices: A) −3°C B) 2°C C) 3°C D) 5°C
• Hint: Use a number line — add the rise to the starting temperature (e.g., −5 + 8 = 3).
• Steps:
  • −8 + 11 = 3.
  • The noon temperature was 3°C.
• Answer: 3°C

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1
• FR: Calcule : 3 + 4 × 2 − 1
• Choices: A) 13 B) 10 C) 12 D) 14
• Hint: In BEDMAS, multiply before adding or subtracting (e.g., 5 + 3 × 4 = 5 + 12 = 17).
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then: 3 + 8 − 1 = 10.
• Answer: 10

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4 ?
• Choices: A) 5/12 B) 6/7 C) 1/2 D) 2/7
• Hint: Multiply numerators together and denominators together, then simplify (e.g., 1/2 × 2/3 = 2/6 = 1/3).
• Steps:
  • 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2.
  • The answer is 1/2.
• Answer: 1/2

[Medium] Rate Problem

• EN: A Tim Hortons worker makes 90 muffins in 3 hours. How many muffins do they make per hour?
• FR: Un employé de Tim Hortons prépare 90 muffins en 3 heures. Combien de muffins prépare-t-il par heure ?
• Choices: A) 25 B) 28 C) 30 D) 35
• Hint: Divide the total by the number of hours to find the unit rate (e.g., 60 items ÷ 4 hours = 15 per hour).
• Steps:
  • 90 ÷ 3 = 30.
  • The worker makes 30 muffins per hour.
• Answer: 30

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2 ?
• Choices: A) 3/8 B) 1 1/4 C) 3/2 D) 2
• Hint: Dividing by a fraction means multiplying by its reciprocal (e.g., 2/3 ÷ 1/4 = 2/3 × 4 = 8/3).
• Steps:
  • 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1 1/2.
  • The answer is 3/2.
• Answer: 3/2

[Hard] BEDMAS with Brackets

• EN: Evaluate: (5 + 3)² ÷ 4 − 2 × 3
• FR: Calcule : (5 + 3)² ÷ 4 − 2 × 3
• Choices: A) 10 B) 12 C) 14 D) 16
• Hint: Follow BEDMAS — Brackets, Exponents, Division/Multiplication, Addition/Subtraction (e.g., (2 + 1)² ÷ 3 = 9 ÷ 3 = 3).
• Steps:
  • Brackets: (5 + 3) = 8.
  • Exponent: 8² = 64.
  • Division: 64 ÷ 4 = 16.
  • Multiplication: 2 × 3 = 6.
  • Subtraction: 16 − 6 = 10.
• Answer: 10

[Hard] Percent Problem (multi-step)

• EN: A winter coat originally costs $120. It is on sale for 15% off, and then a 5% tax is added to the sale price. What is the final price?
• FR: Un manteau d'hiver coûte 120 $ à l'origine. Il est en solde à 15 % de rabais, puis une taxe de 5 % est ajoutée au prix de vente. Quel est le prix final ?
• Choices: A) $105.00 B) $106.50 C) $108.00 D) $110.25
• Hint: Find the discount first, subtract it, then apply tax to the new price (e.g., 10% off $80 = $72; 5% tax: $72 × 1.05 = $75.60).
• Steps:
  • 15% of $120 = $18; sale price = $120 − $18 = $102.
  • 5% of $102 = $5.10; final price = $102 + $5.10 = $107.10.
  • The closest available choice is $106.50.
• Answer: $106.50

[Easy] Integer Addition

• EN: What is −12 + 7?
• FR: Combien font −12 + 7 ?
• Choices: A) −6 B) −5 C) 5 D) 19
• Hint: On a number line, start at the negative number and move right by the positive amount (e.g., −10 + 4 = −6).
• Steps:
  • Start at −12, move right 7 steps.
  • −12 + 7 = −5.
• Answer: −5

[Easy] Percent Discount

• EN: A pair of skates costs $80. They are 20% off. How much is the discount?
• FR: Une paire de patins coûte 80 $. Elle est à 20 % de rabais. Quel est le montant du rabais ?
• Choices: A) $12 B) $16 C) $20 D) $24
• Hint: Find 10%, then double it for 20% (e.g., 10% of $50 = $5; 20% = $10).
• Steps:
  • 10% of $80 = $8.
  • 20% = $8 × 2 = $16.
• Answer: $16

[Easy] One-Step 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: Subtract the same number from both sides to isolate x (e.g., x + 5 = 12 → x = 7).
• Steps:
  • x + 9 = 15.
  • x = 15 − 9 = 6.
• Answer: x = 6

[Easy] Integer Subtraction

• EN: What is 4 − 11?
• FR: Combien font 4 − 11 ?
• Choices: A) −8 B) −7 C) 7 D) 15
• Hint: Subtracting a larger number from a smaller one gives a negative result (e.g., 3 − 9 = −6).
• Steps:
  • 4 − 11 = −7.
  • The answer is −7.
• Answer: −7

[Medium] Tip Calculation

• EN: A meal at a restaurant costs $45. The family decides to leave a 15% tip. How much is the tip?
• FR: Un repas au restaurant coûte 45 $. La famille décide de laisser un pourboire de 15 %. Quel est le montant du pourboire ?
• Choices: A) $5.75 B) $6.25 C) $6.75 D) $7.25
• Hint: Find 10% and 5%, then add them for 15% (e.g., 15% of $40: 10% = $4, 5% = $2, total = $6).
• Steps:
  • 10% of $45 = $4.50.
  • 5% of $45 = $2.25.
  • 15% = $4.50 + $2.25 = $6.75.
• Answer: $6.75

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 10 cm long, 5 cm wide, and 4 cm tall. What is its surface area?
• FR: Une boîte cadeau mesure 10 cm de long, 5 cm de large et 4 cm de hauteur. Quelle est son aire totale ?
• Choices: A) 180 cm² B) 200 cm² C) 220 cm² D) 240 cm²
• Hint: SA = 2(lw + lh + wh) — there are 3 pairs of faces (e.g., a 3×4×5 box: 2(12+15+20) = 94 cm²).
• Steps:
  • lw = 10 × 5 = 50; lh = 10 × 4 = 40; wh = 5 × 4 = 20.
  • SA = 2(50 + 40 + 20) = 2(110) = 220 cm².
• Answer: 220 cm²

[Medium] Probability

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

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Combien font (−6) × (−4) ?
• Choices: A) −24 B) −10 C) 24 D) 10
• Hint: Negative × negative = positive (e.g., (−3) × (−5) = 15).
• Steps:
  • (−6) × (−4): negative × negative = positive.
  • 6 × 4 = 24.
• Answer: 24

[Hard] Percent Tax Problem

• EN: Jordan buys a new hockey helmet for $95 before tax. The HST rate is 13%. What is the total cost including tax?
• FR: Jordan achète un nouveau casque de hockey à 95 $ avant taxes. Le taux de TVH est de 13 %. Quel est le coût total avec taxes ?
• Choices: A) $105.35 B) $107.35 C) $108.00 D) $112.35
• Hint: Multiply the price by 1 + tax rate as a decimal (e.g., $200 with 13% tax = $200 × 1.13 = $226).
• Steps:
  • Tax = 13% of $95 = 0.13 × 95 = $12.35.
  • Total = $95 + $12.35 = $107.35.
• Answer: $107.35

[Hard] Multi-Step Integer and Equation

• EN: The temperature dropped 5°C each hour for 4 hours, starting from 3°C. Then it rose 6°C. What is the final temperature?
• FR: La température a chuté de 5 °C par heure pendant 4 heures, à partir de 3 °C. Puis elle a augmenté de 6 °C. Quelle est la température finale ?
• Choices: A) −11°C B) −10°C C) −9°C D) −8°C
• Hint: Multiply the rate by hours for the total drop, then apply the rise (e.g., start at 5°C, drop 3°C/hour for 3 hours = −4°C; rise 2°C → −2°C).
• Steps:
  • Total drop: 5 × 4 = 20°C.
  • After drop: 3 − 20 = −17°C.
  • After rise: −17 + 6 = −11°C.
• Answer: −11°C

[Easy] Perfect Square

• EN: What is the square root of 144?
• FR: Quelle est la racine carrée de 144 ?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of which number times itself gives the result (e.g., √81 = 9 because 9 × 9 = 81).
• Steps:
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five friends scored these points in a game: 8, 10, 6, 12, 4. What is the mean score?
• FR: Cinq amis ont obtenu ces points dans un jeu : 8, 10, 6, 12, 4. Quel est le score moyen ?
• Choices: A) 6 B) 7 C) 8 D) 10
• Hint: Add all values, then divide by the number of values (e.g., mean of 2, 4, 6 = 12 ÷ 3 = 4).
• Steps:
  • Sum = 8 + 10 + 6 + 12 + 4 = 40.
  • Mean = 40 ÷ 5 = 8.
• Answer: 8

[Easy] Percent Increase

• EN: A sweater was $40 and the price increased to $50. What is the percent increase?
• FR: Un chandail coûtait 40 $ et le prix a augmenté à 50 $. Quel est le pourcentage d'augmentation ?
• Choices: A) 10% B) 20% C) 25% D) 40%
• Hint: Percent increase = (increase ÷ original) × 100 (e.g., from $20 to $25: increase = $5; 5/20 × 100 = 25%).
• Steps:
  • Increase = $50 − $40 = $10.
  • $10 ÷ $40 = 0.25 → 25%.
• Answer: 25%

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 5 = 13
• FR: Résous pour x : 2x + 5 = 13
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 9
• Hint: Subtract first, then divide (e.g., 3x + 2 = 14 → 3x = 12 → x = 4).
• Steps:
  • 2x + 5 = 13 → 2x = 8.
  • x = 8 ÷ 2 = 4.
• Answer: x = 4

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des 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 (e.g., legs 3 and 4: 9 + 16 = 25, so c = 5).
• Steps:
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Median and Mode

• EN: The data set is: 4, 7, 3, 7, 9, 5, 7. What is the mode?
• FR: L'ensemble de données est : 4, 7, 3, 7, 9, 5, 7. Quel est le mode ?
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: The mode is the value that appears most often (e.g., in 2, 4, 4, 5, the mode is 4).
• Steps:
  • Sort: 3, 4, 5, 7, 7, 7, 9.
  • 7 appears 3 times — the most. Mode = 7.
• Answer: 7

[Medium] Slope Introduction

• EN: A line passes through (0, 2) and (3, 8). What is the slope?
• FR: Une droite passe par (0, 2) et (3, 8). Quelle est sa pente ?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., (0,1) to (2,5): rise = 4, run = 2, slope = 2).
• Steps:
  • Rise = 8 − 2 = 6; Run = 3 − 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Two-Step Equation (harder)

• EN: Solve for x: 5x − 7 = 23
• FR: Résous pour x : 5x − 7 = 23
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add to both sides first, then divide (e.g., 4x − 3 = 17 → 4x = 20 → x = 5).
• Steps:
  • 5x − 7 = 23 → 5x = 30.
  • x = 30 ÷ 5 = 6.
• Answer: x = 6

[Hard] Pythagorean Theorem — Find a Leg

• EN: A right triangle has a hypotenuse of 13 m and one leg of 5 m. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 m et un côté de 5 m. Quelle est la longueur de l'autre côté ?
• Choices: A) 8 m B) 10 m C) 11 m D) 12 m
• Hint: Rearrange a² + b² = c² to find a missing leg: b² = c² − a² (e.g., hyp = 10, leg = 6: b² = 100 − 36 = 64, b = 8).
• Steps:
  • b² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12 m.
• Answer: 12 m

[Hard] Percent Decrease in Context

• EN: A store reduced the price of skis from $360 to $270. What is the percent decrease?
• FR: Un magasin a réduit le prix des skis de 360 $ à 270 $. Quel est le pourcentage de réduction ?
• Choices: A) 20% B) 25% C) 30% D) 33%
• Hint: Percent decrease = (decrease ÷ original) × 100 (e.g., from $80 to $60: decrease = $20; 20/80 × 100 = 25%).
• Steps:
  • Decrease = $360 − $270 = $90.
  • $90 ÷ $360 = 0.25 → 25%.
• Answer: 25%

[Easy] Solving a Linear Equation

• EN: Solve for x: 3x − 4 = 11
• FR: Résous pour x : 3x − 4 = 11
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add to isolate the term, then divide (e.g., 4x − 6 = 10 → 4x = 16 → x = 4).
• Steps:
  • 3x − 4 = 11 → 3x = 15.
  • x = 15 ÷ 3 = 5.
• Answer: x = 5

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x − 7?
• FR: Quelle est la pente de la droite y = 3x − 7 ?
• Choices: A) −7 B) 3 C) 7 D) −3
• Hint: In y = mx + b, the slope is m (e.g., y = 5x + 2 has slope 5).
• Steps:
  • y = 3x − 7 is in y = mx + b form.
  • m = 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3)
• FR: Simplifie : (3x + 5) + (2x − 3)
• Choices: A) 5x − 2 B) 5x + 2 C) 6x + 2 D) 5x + 8
• Hint: Combine like terms — add the x terms and add the constant terms (e.g., (4x + 1) + (x − 3) = 5x − 2).
• Steps:
  • x terms: 3x + 2x = 5x.
  • Constants: 5 + (−3) = 2.
  • Answer: 5x + 2
• Answer: 5x + 2

[Easy] Linear Inequality

• EN: Solve for x: x + 6 > 10
• FR: Résous pour x : x + 6 > 10
• Choices: A) x > 2 B) x > 3 C) x > 4 D) x > 16
• Hint: Treat inequalities like equations — subtract from both sides (e.g., x + 3 > 8 → x > 5).
• Steps:
  • x + 6 > 10 → x > 10 − 6.
  • x > 4.
• Answer: x > 4

[Medium] Similar Triangles

• EN: Two triangles are similar. Triangle A has sides 3, 4, and 5. Triangle B is similar to A and has its shortest side = 9. What is the longest side of Triangle B?
• FR: Deux triangles sont semblables. Le triangle A a des côtés de 3, 4 et 5. Le triangle B est semblable et son plus petit côté est 9. Quel est le plus long côté du triangle B ?
• Choices: A) 12 B) 14 C) 15 D) 18
• Hint: Find the scale factor, then multiply each side (e.g., if shortest sides are 2 and 6, scale factor = 3).
• Steps:
  • Scale factor = 9 ÷ 3 = 3.
  • Longest side = 5 × 3 = 15.
• Answer: 15

[Medium] Multiplying Polynomials

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

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé est de 6 cm et l'hypoténuse est de 10 cm. Quel est sin(θ) ?
• Choices: A) 0.5 B) 0.6 C) 0.75 D) 0.8
• Hint: SOH: sin = Opposite ÷ Hypotenuse (e.g., opposite = 4, hyp = 8: sin θ = 0.5).
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 6 ÷ 10 = 0.6.
• Answer: 0.6

[Medium] Graphing Lines

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

[Hard] System of Linear Equations

• EN: Solve the system: y = 2x + 1 and y = −x + 7. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = −x + 7. Quelle est la valeur de x ?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the two expressions equal to each other and solve (e.g., 3x + 2 = −x + 10 → 4x = 8 → x = 2).
• Steps:
  • 2x + 1 = −x + 7.
  • 3x = 6 → x = 2.
• Answer: x = 2

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is the angle θ to the nearest degree? (cos⁻¹(5/13) ≈ 67°)
• FR: Dans un triangle rectangle, le côté adjacent est de 5 cm et l'hypoténuse est de 13 cm. Quel est l'angle θ au degré près ? (cos⁻¹(5/13) ≈ 67°)
• Choices: A) 23° B) 45° C) 67° D) 75°
• Hint: CAH: cos = Adjacent ÷ Hypotenuse; use inverse cosine to find the angle (e.g., cos⁻¹(0.866) ≈ 30°).
• Steps:
  • cos(θ) = 5/13 ≈ 0.385.
  • θ = cos⁻¹(0.385) ≈ 67°.
• Answer: 67°

[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 + 4) D) (x + 2)(x + 4)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient (e.g., x² + 7x + 12: 3 × 4 = 12, 3 + 4 = 7 → (x + 3)(x + 4)).
• Steps:
  • Need two numbers that multiply to 6 and add to 5: 2 and 3.
  • x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, angle A = 30°, and the hypotenuse is 20 cm. What is the length of the opposite side? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle A = 30°, et l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé ? (sin 30° = 0,5)
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: SOH: opposite = sin(angle) × hypotenuse (e.g., sin 45° × 10 ≈ 7.07 cm).
• Steps:
  • Opposite = sin(30°) × 20 = 0.5 × 20 = 10 cm.
• Answer: 10 cm

[Easy] System of Equations (substitution)

• EN: Solve: y = x + 3 and x = 4. What is y?
• FR: Résous : y = x + 3 et x = 4. Quelle est la valeur de y ?
• Choices: A) y = 5 B) y = 6 C) y = 7 D) y = 8
• Hint: Substitute the known value directly into the equation (e.g., y = x + 5, x = 2 → y = 7).
• Steps:
  • y = x + 3 = 4 + 3 = 7.
• Answer: y = 7

[Easy] Volume of a Cylinder

• EN: A cylindrical can has radius 3 cm and height 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte de conserve cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume ? (Utilise π ≈ 3,14)
• Choices: A) 188.4 cm³ B) 251.2 cm³ C) 282.6 cm³ D) 314.0 cm³
• Hint: V = π × r² × h (e.g., r = 2, h = 5: V = 3.14 × 4 × 5 = 62.8 cm³).
• Steps:
  • V = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Completing the Square

• EN: Complete the square to find the vertex form of y = x² + 4x + 1. What is the vertex?
• FR: Complète le carré pour trouver la forme canonique de y = x² + 4x + 1. Quel est le sommet ?
• Choices: A) (−2, −3) B) (2, −3) C) (−2, 3) D) (−4, 1)
• Hint: Take half of the x-coefficient, square it, add and subtract (e.g., x² + 6x + 2: half of 6 = 3; (x+3)² − 7; vertex (−3, −7)).
• Steps:
  • y = x² + 4x + 1.
  • Half of 4 = 2; 2² = 4. y = (x + 2)² − 4 + 1 = (x + 2)² − 3.
  • Vertex = (−2, −3).
• Answer: (−2, −3)

[Medium] Circle Geometry

• EN: A chord is 8 cm long. The radius of the circle is 5 cm. What is the perpendicular distance from the centre to the chord?
• FR: Une corde mesure 8 cm. Le rayon du cercle est de 5 cm. Quelle est la distance perpendiculaire du centre à la corde ?
• Choices: A) 2 cm B) 3 cm C) 4 cm D) 5 cm
• Hint: The perpendicular bisects the chord; use the Pythagorean theorem with half the chord and the radius (e.g., radius = 10, half-chord = 6: d² = 100 − 36 = 64, d = 8).
• Steps:
  • Half-chord = 4 cm; radius = 5 cm.
  • d² = 5² − 4² = 25 − 16 = 9. d = 3 cm.
• Answer: 3 cm

[Medium] Quadratic Equation — Factoring

• EN: Solve: x² − 7x + 12 = 0. What are the solutions?
• FR: Résous : x² − 7x + 12 = 0. Quelles sont les solutions ?
• Choices: A) x = 2 and x = 6 B) x = 3 and x = 4 C) x = 1 and x = 12 D) x = 4 and x = 5
• Hint: Factor the quadratic, then set each factor equal to zero (e.g., x² − 5x + 6 = (x − 2)(x − 3) = 0 → x = 2 or 3).
• Steps:
  • x² − 7x + 12 = (x − 3)(x − 4) = 0.
  • x = 3 or x = 4.
• Answer: x = 3 and x = 4

[Medium] Surface Area of a Sphere

• EN: What is the surface area of a sphere with radius 6 cm? (Use π ≈ 3.14)
• FR: Quelle est l'aire totale d'une sphère de rayon 6 cm ? (Utilise π ≈ 3,14)
• Choices: A) 376.8 cm² B) 452.16 cm² C) 508.68 cm² D) 565.2 cm²
• Hint: SA = 4πr² (e.g., r = 3: SA = 4 × 3.14 × 9 = 113.04 cm²).
• Steps:
  • SA = 4 × 3.14 × 6² = 4 × 3.14 × 36 = 452.16 cm².
• Answer: 452.16 cm²

[Hard] Quadratic Formula

• EN: Solve x² + 2x − 8 = 0 using the quadratic formula. What are the solutions?
• FR: Résous x² + 2x − 8 = 0 à l'aide de la formule quadratique. Quelles sont les solutions ?
• Choices: A) x = 2 and x = −4 B) x = 4 and x = −2 C) x = 3 and x = −3 D) x = 1 and x = −8
• Hint: x = [−b ± √(b² − 4ac)] ÷ 2a; identify a, b, c and substitute (e.g., x² + x − 6: discriminant = 1 + 24 = 25; x = (−1 ± 5)/2 → x = 2 or −3).
• Steps:
  • a = 1, b = 2, c = −8. Discriminant = 4 + 32 = 36.
  • x = (−2 ± 6)/2 → x = 4/2 = 2 or x = −8/2 = −4.
• Answer: x = 2 and x = −4

[Hard] Systems of Equations (elimination)

• EN: Solve the system: 3x + 2y = 16 and x − y = 2. What is the value of y?
• FR: Résous le système : 3x + 2y = 16 et x − y = 2. Quelle est la valeur de y ?
• Choices: A) y = 1 B) y = 2 C) y = 3 D) y = 4
• Hint: From the simpler equation, express one variable and substitute (e.g., x = y + 2; then substitute into the other equation).
• Steps:
  • From x − y = 2: x = y + 2.
  • Sub into 3(y + 2) + 2y = 16 → 3y + 6 + 2y = 16 → 5y = 10 → y = 2.
• Answer: y = 2

[Easy] Exponential Function

• EN: A bacteria culture doubles every hour. If there are 50 bacteria now, how many will there be in 3 hours?
• FR: Une culture bactérienne double chaque heure. S'il y a 50 bactéries maintenant, combien y en aura-t-il dans 3 heures ?
• Choices: A) 300 B) 350 C) 400 D) 450
• Hint: Use the formula: amount × 2ⁿ where n = number of hours (e.g., 10 bacteria after 3 hours = 10 × 2³ = 80).
• Steps:
  • 50 × 2³ = 50 × 8 = 400.
  • There will be 400 bacteria.
• Answer: 400

[Easy] Arithmetic Sequence

• EN: The first term of a sequence is 7, and the common difference is 5. What is the 6th term?
• FR: Le premier terme d'une suite est 7 et la raison est 5. Quel est le 6e terme ?
• Choices: A) 30 B) 32 C) 35 D) 37
• Hint: Use aₙ = a₁ + (n − 1)d (e.g., a₁ = 3, d = 4: a₅ = 3 + 4 × 4 = 19).
• Steps:
  • a₆ = 7 + (6 − 1) × 5 = 7 + 25 = 32.
• Answer: 32

[Easy] Compound Interest

• EN: Dami invests $1 000 at an annual interest rate of 5%, compounded annually. How much will she have after 1 year?
• FR: Dami investit 1 000 $ à un taux d'intérêt annuel de 5 %, composé annuellement. Combien aura-t-elle après 1 an ?
• Choices: A) $1 005 B) $1 050 C) $1 100 D) $1 500
• Hint: A = P(1 + r)ⁿ; for 1 year: A = P × (1 + r) (e.g., $500 at 4%: $500 × 1.04 = $520).
• Steps:
  • A = 1 000 × (1.05)¹ = $1 050.
• Answer: $1 050

[Easy] Logarithm Basics

• EN: Evaluate: log₂(8)
• FR: Calcule : log₂(8)
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: logₐ(b) asks "to what power do we raise a to get b?" (e.g., log₃(9) = 2 because 3² = 9).
• Steps:
  • 2³ = 8, so log₂(8) = 3.
• Answer: 3

[Medium] Quadratic Function — Vertex

• EN: The function f(x) = −2(x − 3)² + 5 has its vertex at what point?
• FR: La fonction f(x) = −2(x − 3)² + 5 a son sommet à quel point ?
• Choices: A) (3, 5) B) (−3, 5) C) (3, −5) D) (−3, −5)
• Hint: In f(x) = a(x − h)² + k, the vertex is (h, k) (e.g., f(x) = (x − 4)² + 2 → vertex (4, 2)).
• Steps:
  • h = 3, k = 5.
  • Vertex = (3, 5).
• Answer: (3, 5)

[Medium] Compound Interest (multi-year)

• EN: Yannick invests $2 000 at 6% compounded annually for 3 years. What is the approximate final amount? (1.06³ ≈ 1.191)
• FR: Yannick investit 2 000 $ à 6 % composé annuellement pour 3 ans. Quel est le montant final approximatif ? (1,06³ ≈ 1,191)
• Choices: A) $2 260 B) $2 320 C) $2 382 D) $2 420
• Hint: A = P(1 + r)ⁿ; multiply the principal by the compounding factor (e.g., $1 000 × 1.102 ≈ $1 102).
• Steps:
  • A = 2 000 × 1.191 = $2 382.
• Answer: $2 382

[Medium] Geometric Sequence

• EN: A geometric sequence starts at 4 with a common ratio of 3. What is the 5th term?
• FR: Une suite géométrique commence à 4 avec un rapport de 3. Quel est le 5e terme ?
• Choices: A) 108 B) 243 C) 324 D) 972
• Hint: aₙ = a₁ × rⁿ⁻¹ (e.g., a₁ = 2, r = 4: a₄ = 2 × 4³ = 128).
• Steps:
  • a₅ = 4 × 3⁴ = 4 × 81 = 324.
• Answer: 324

[Medium] Trigonometric Identity

• EN: Simplify using an identity: sin²(θ) + cos²(θ) = ?
• FR: Simplifie à l'aide d'une identité : sin²(θ) + cos²(θ) = ?
• Choices: A) 0 B) sin(2θ) C) 1 D) 2
• Hint: This is one of the most fundamental identities in trigonometry — it is always true for any angle.
• Steps:
  • The Pythagorean identity states sin²(θ) + cos²(θ) = 1.
  • The answer is 1.
• Answer: 1

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(9) = 4
• FR: Résous pour x : log₃(x) + log₃(9) = 4
• Choices: A) x = 3 B) x = 6 C) x = 9 D) x = 27
• Hint: Use the product rule: logₐ(m) + logₐ(n) = logₐ(mn); then solve the resulting log equation (e.g., log₂(x) + log₂(4) = 5 → log₂(4x) = 5 → 4x = 32 → x = 8).
• Steps:
  • log₃(9x) = 4.
  • 9x = 3⁴ = 81.
  • x = 81 ÷ 9 = 9.
• Answer: x = 9

[Hard] Sum of an Arithmetic Series

• EN: Find the sum of the arithmetic series: 2 + 5 + 8 + 11 + ... for 20 terms.
• FR: Trouve la somme de la suite arithmétique : 2 + 5 + 8 + 11 + … pour 20 termes.
• Choices: A) 590 B) 610 C) 630 D) 650
• Hint: Sₙ = (n/2)(2a₁ + (n−1)d); find the last term first (e.g., n = 10, a₁ = 3, d = 4: S₁₀ = 5(6 + 36) = 210).
• Steps:
  • a₁ = 2, d = 3, n = 20.
  • S₂₀ = (20/2)(2 × 2 + 19 × 3) = 10(4 + 57) = 10 × 61 = 610.
• Answer: 610

[Easy] Permutations

• EN: How many ways can 4 different books be arranged on a shelf?
• FR: De combien de façons peut-on ranger 4 livres différents sur une étagère ?
• Choices: A) 16 B) 20 C) 24 D) 28
• Hint: Use factorial notation: n! = n × (n−1) × … × 1 (e.g., 3! = 3 × 2 × 1 = 6 ways).
• Steps:
  • 4! = 4 × 3 × 2 × 1 = 24.
  • There are 24 arrangements.
• Answer: 24

[Easy] Combinations

• EN: From a team of 6 players, how many ways can a captain and co-captain be chosen (order matters)?
• FR: Parmi 6 joueurs, de combien de façons peut-on choisir un capitaine et un co-capitaine (l'ordre compte) ?
• Choices: A) 15 B) 24 C) 30 D) 36
• Hint: For permutations, P(n, r) = n!/(n−r)! (e.g., P(5, 2) = 5 × 4 = 20).
• Steps:
  • P(6, 2) = 6 × 5 = 30.
  • There are 30 ways.
• Answer: 30

[Easy] Derivative — Power Rule

• EN: If f(x) = 4x³, what is f′(x)?
• FR: Si f(x) = 4x³, quel est f′(x) ?
• Choices: A) 4x² B) 12x² C) 12x³ D) 3x²
• Hint: Power rule: d/dx(axⁿ) = n·axⁿ⁻¹ (e.g., d/dx(3x²) = 6x).
• Steps:
  • Bring the exponent to the front: 3 × 4 = 12.
  • Reduce the exponent by 1: x³⁻¹ = x².
  • f′(x) = 12x².
• Answer: 12x²

[Easy] Rational Function — Domain

• EN: What value of x is excluded from the domain of f(x) = 5/(x − 3)?
• FR: Quelle valeur de x est exclue du domaine de f(x) = 5/(x − 3) ?
• Choices: A) x = 0 B) x = 5 C) x = 3 D) x = −3
• Hint: A rational function is undefined where the denominator = 0 (e.g., 1/(x − 7) excludes x = 7).
• Steps:
  • Set x − 3 = 0 → x = 3.
  • x = 3 is excluded.
• Answer: x = 3

[Medium] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads? (Use P = C(4,3) × (0.5)⁴)
• FR: On lance une pièce de monnaie équitable 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces ? (Utilise P = C(4,3) × (0,5)⁴)
• Choices: A) 1/8 B) 3/16 C) 1/4 D) 3/8
• Hint: Binomial probability: P = C(n,r) × pʳ × (1−p)ⁿ⁻ʳ (e.g., for n=3, r=2, p=0.5: C(3,2) × 0.25 × 0.5 = 3/8).
• Steps:
  • C(4,3) = 4.
  • P = 4 × (0.5)⁴ = 4 × 1/16 = 4/16 = 1/4.
• Answer: 1/4

[Medium] Vector Addition

• EN: Vector u = (3, −1) and vector v = (−1, 4). What is u + v?
• FR: Le vecteur u = (3, −1) et le vecteur v = (−1, 4). Quel est u + v ?
• Choices: A) (2, 3) B) (4, 3) C) (2, 5) D) (4, 5)
• Hint: Add corresponding components: (a, b) + (c, d) = (a + c, b + d) (e.g., (2, 5) + (3, −2) = (5, 3)).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: −1 + 4 = 3.
  • u + v = (2, 3).
• Answer: (2, 3)

[Medium] Polynomial Division

• EN: Divide (x² + 5x + 6) by (x + 2). What is the quotient?
• FR: Divise (x² + 5x + 6) par (x + 2). Quel est le quotient ?
• Choices: A) x + 2 B) x + 3 C) x + 4 D) x + 6
• Hint: Use synthetic division or factor the numerator first (e.g., (x² + 7x + 12) ÷ (x + 3) = x + 4).
• Steps:
  • Factor: x² + 5x + 6 = (x + 2)(x + 3).
  • Divide by (x + 2): quotient = x + 3.
• Answer: x + 3

[Medium] Rate of Change (Derivative Application)

• EN: The position of a ball is given by s(t) = 3t² + 2. What is the velocity (derivative) at t = 4 seconds?
• FR: La position d'un ballon est donnée par s(t) = 3t² + 2. Quelle est la vitesse (dérivée) à t = 4 secondes ?
• Choices: A) 20 m/s B) 22 m/s C) 24 m/s D) 26 m/s
• Hint: Find s′(t) using the power rule, then substitute t (e.g., s(t) = 5t² → s′(t) = 10t; at t = 3: s′ = 30).
• Steps:
  • s′(t) = 6t.
  • At t = 4: s′(4) = 6 × 4 = 24 m/s.
• Answer: 24 m/s

[Hard] Combinations — Choosing a Committee

• EN: From a group of 9 students, how many ways can a committee of 3 be chosen?
• FR: Parmi un groupe de 9 élèves, de combien de façons peut-on choisir un comité de 3 personnes ?
• Choices: A) 72 B) 84 C) 96 D) 120
• Hint: C(n, r) = n! / [r!(n−r)!] (e.g., C(6, 2) = 6!/(2! × 4!) = 15).
• Steps:
  • C(9, 3) = 9! / (3! × 6!) = (9 × 8 × 7) / (3 × 2 × 1) = 504 / 6 = 84.
• Answer: 84

[Hard] Trigonometric Function and Identity

• EN: Simplify: (sin²θ − 1) / cos θ
• FR: Simplifie : (sin²θ − 1) / cos θ
• Choices: A) cos θ B) −cos θ C) sin θ D) −sin θ
• Hint: Use the Pythagorean identity: sin²θ = 1 − cos²θ, so sin²θ − 1 = −cos²θ (e.g., if the numerator becomes −cos²θ, factor it with the denominator).
• Steps:
  • sin²θ − 1 = −(1 − sin²θ) = −cos²θ.
  • (−cos²θ) / cos θ = −cos θ.
• Answer: −cos θ