Daily Math — 2026-09-23

[Easy] Counting Crayons

• EN: Mia has 7 crayons. She finds 5 more. How many crayons does she have in all?
• FR: Mia a 7 crayons. Elle en trouve 5 de plus. Combien de crayons a-t-elle en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add, count on from the bigger number (e.g., 6 + 4: start at 6, count up 4 to get 10).
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • So Mia has 12 crayons in all.
• Answer: 12

[Easy] Hockey Pucks

• EN: There are 9 hockey pucks on the ice. A player takes 3 away. How many pucks are left?
• FR: Il y a 9 rondelles sur la glace. Un joueur en prend 3. Combien de rondelles reste-t-il?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To subtract, count back from the bigger number (e.g., 8 − 2: start at 8, count back 2 to get 6).
• Steps:
  • Start at 9 and count back 3: 8, 7, 6.
  • So 6 pucks are left.
• Answer: 6

[Easy] Skip Counting by 5s

• EN: Skip count by 5s. What number comes next: 5, 10, 15, ___?
• FR: Compte par bonds de 5. Quel nombre vient ensuite : 5, 10, 15, ___?
• Choices: A) 18 B) 20 C) 22 D) 25
• Hint: When skip counting by 5s, add 5 each time (e.g., 10, 15, 20 — add 5 each step).
• Steps:
  • The pattern adds 5 each time: 5, 10, 15 …
  • 15 + 5 = 20.
• Answer: 20

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents?
• FR: Quelle pièce vaut 10 cents?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: Think of the three smallest coins — the smallest is 1 cent, the medium is 5 cents, and the next one is 10 cents.
• Steps:
  • A penny = 1 cent.
  • A nickel = 5 cents.
  • A dime = 10 cents.
• Answer: Dime

[Medium] Snowflakes on the Window

• EN: There are 14 snowflakes on a window. 6 melt away. How many snowflakes are left?
• FR: Il y a 14 flocons de neige sur une fenêtre. 6 fondent. Combien de flocons reste-t-il?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To subtract a number, count back from the bigger number (e.g., 12 − 5 = 7).
• Steps:
  • Start at 14 and count back 6: 13, 12, 11, 10, 9, 8.
  • So 8 snowflakes are left.
• Answer: 8

[Medium] Comparing Numbers

• EN: Which number is greater: 17 or 13?
• FR: Quel nombre est plus grand : 17 ou 13?
• Choices: A) 13 B) 17 C) 15 D) 11
• Hint: The number with more tens is greater (e.g., 15 has 1 ten and 5 ones; 12 has 1 ten and 2 ones — so 15 is greater).
• Steps:
  • Both numbers have 1 ten.
  • Compare the ones: 7 ones is more than 3 ones, so 17 is greater.
• Answer: 17

[Medium] 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 (e.g., 4, 6, 8 — add 2 to get 10).
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
• Answer: 10

[Medium] Pennies and Nickels

• EN: Liam has 2 nickels and 3 pennies. How many cents does he have in all?
• FR: Liam a 2 pièces de 5 cents et 3 pennies. Combien de cents a-t-il en tout?
• Choices: A) 11 cents B) 13 cents C) 15 cents D) 17 cents
• Hint: First count the nickels (each is 5 cents), then add the pennies (each is 1 cent) — for example, 3 nickels + 2 pennies = 15 + 2 = 17 cents.
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 3 pennies = 3 cents.
  • 10 + 3 = 13 cents.
• Answer: 13 cents

[Hard] Tims Timbits

• EN: There are 18 Timbits in a box. Some children each take 2. If 4 children each take 2 Timbits, how many Timbits are left in the box?
• FR: Il y a 18 Timbits dans une boîte. Des enfants en prennent chacun 2. Si 4 enfants prennent chacun 2 Timbits, combien en reste-t-il dans la boîte?
• Choices: A) 8 B) 9 C) 10 D) 11
• Hint: First find how many were taken in total (e.g., 3 children × 2 each = 6), then subtract from the start (e.g., 15 − 6 = 9).
• Steps:
  • 4 children each take 2: 2 + 2 + 2 + 2 = 8 Timbits taken.
  • 18 − 8 = 10 Timbits left.
• Answer: 10

[Hard] Number Sentence

• EN: What number makes this true? ___ + 6 = 15
• FR: Quel nombre complète cette phrase? ___ + 6 = 15
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: To find a missing addend, subtract the known number from the total (e.g., ___ + 4 = 11 means 11 − 4 = 7).
• Steps:
  • We need a number that, when added to 6, gives 15.
  • 15 − 6 = 9.
• Answer: 9

[Easy] Adding to 100

• EN: What is 34 + 25?
• FR: Combien fait 34 + 25?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: Add the ones first, then the tens (e.g., 23 + 14: ones 3 + 4 = 7, tens 2 + 1 = 3, so 37).
• Steps:
  • Ones: 4 + 5 = 9.
  • Tens: 3 + 2 = 5.
  • So 34 + 25 = 59.
• Answer: 59

[Easy] Subtracting Within 100

• EN: What is 76 − 32?
• FR: Combien fait 76 − 32?
• Choices: A) 40 B) 42 C) 44 D) 46
• Hint: Subtract the ones first, then the tens (e.g., 58 − 23: ones 8 − 3 = 5, tens 5 − 2 = 3, so 35).
• Steps:
  • Ones: 6 − 2 = 4.
  • Tens: 7 − 3 = 4.
  • So 76 − 32 = 44.
• Answer: 44

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'aiguille des heures indique 3 et l'aiguille des minutes indique 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 (e.g., hour hand on 7 = 7:00).
• Steps:
  • The minute hand on 12 means it is exactly on the hour.
  • The hour hand is on 3, so the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A eraser is 4 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 15 cm. Une gomme mesure 4 cm. De combien le crayon est-il plus long que la gomme?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: To find the difference in length, subtract the shorter from the longer (e.g., 18 cm − 5 cm = 13 cm).
• Steps:
  • 15 cm − 4 cm = 11 cm.
  • The pencil is 11 cm longer than the eraser.
• Answer: 11 cm

[Medium] Adding with Regrouping

• EN: What is 47 + 36?
• FR: Combien fait 47 + 36?
• Choices: A) 81 B) 82 C) 83 D) 84
• Hint: If the ones add up to 10 or more, regroup (e.g., 28 + 45: ones 8 + 5 = 13, write 3 carry 1, tens 2 + 4 + 1 = 7, so 73).
• Steps:
  • Ones: 7 + 6 = 13; write 3 and carry 1.
  • Tens: 4 + 3 + 1 (carried) = 8.
  • So 47 + 36 = 83.
• Answer: 83

[Medium] Counting Coins to $1

• EN: Sofia has 3 dimes, 2 nickels, and 4 pennies. How much money does she have?
• FR: Sofia a 3 pièces de 10 cents, 2 pièces de 5 cents et 4 pennies. Combien d'argent a-t-elle?
• Choices: A) 40 cents B) 42 cents C) 44 cents D) 46 cents
• Hint: Count each type of coin separately, then add them together (e.g., 2 dimes + 3 nickels + 2 pennies = 20 + 15 + 2 = 37 cents).
• Steps:
  • 3 dimes = 30 cents.
  • 2 nickels = 10 cents.
  • 4 pennies = 4 cents.
  • 30 + 10 + 4 = 44 cents.
• Answer: 44 cents

[Medium] Telling Time — Half Hour

• EN: The clock shows the hour hand between 7 and 8, and the minute hand on 6. What time is it?
• FR: L'aiguille des heures est entre 7 et 8, et l'aiguille des minutes est sur 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:00
• Hint: When the minute hand points to 6, it is half past the hour (e.g., hour hand between 4 and 5, minute hand on 6 = 4:30).
• Steps:
  • Minute hand on 6 means half past.
  • The hour hand is between 7 and 8, so the time is 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: What shape comes next in the pattern: circle, square, circle, square, ___?
• FR: Quelle forme vient ensuite dans le motif : cercle, carré, cercle, carré, ___?
• Choices: A) Triangle B) Circle C) Rectangle D) Hexagon
• Hint: Look at the repeating unit — in a pattern like A, B, A, B, the next one is always A (e.g., star, heart, star, heart → next is star).
• Steps:
  • The pattern repeats: circle, square, circle, square …
  • After square, the next is circle.
• Answer: Circle

[Hard] Subtracting with Regrouping

• EN: What is 82 − 47?
• FR: Combien fait 82 − 47?
• Choices: A) 33 B) 34 C) 35 D) 36
• Hint: If the top ones digit is smaller than the bottom ones digit, borrow from the tens (e.g., 63 − 28: borrow to get 13 − 8 = 5, then 5 − 2 = 3, so 35).
• Steps:
  • Ones: 2 is less than 7, so borrow 1 ten: 12 − 7 = 5.
  • Tens: 8 − 1 (borrowed) = 7; 7 − 4 = 3.
  • So 82 − 47 = 35.
• Answer: 35

[Hard] Word Problem with Coins

• EN: Ben has 75 cents. He spends 3 dimes. How many cents does he have left?
• FR: Ben a 75 cents. Il dépense 3 pièces de 10 cents. Combien de cents lui reste-t-il?
• Choices: A) 40 cents B) 42 cents C) 45 cents D) 48 cents
• Hint: First find the value of the coins spent, then subtract (e.g., spent 2 dimes = 20 cents; 60 − 20 = 40 cents left).
• Steps:
  • 3 dimes = 30 cents spent.
  • 75 − 30 = 45 cents left.
• Answer: 45 cents

[Easy] Multiplication by 2

• EN: What is 2 × 8?
• FR: Combien fait 2 × 8?
• Choices: A) 14 B) 15 C) 16 D) 18
• Hint: Multiplying by 2 is the same as doubling the number (e.g., 2 × 7 = 14 because 7 + 7 = 14).
• Steps:
  • 2 × 8 means 8 + 8.
  • 8 + 8 = 16.
• Answer: 16

[Easy] Multiplication by 5

• EN: What is 5 × 6?
• FR: Combien fait 5 × 6?
• Choices: A) 25 B) 28 C) 30 D) 35
• Hint: Multiples of 5 always end in 0 or 5 (e.g., 5 × 4 = 20, 5 × 7 = 35).
• Steps:
  • Skip count by 5s: 5, 10, 15, 20, 25, 30.
  • So 5 × 6 = 30.
• Answer: 30

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. What fraction is one piece?
• FR: Une pizza est coupée en 2 morceaux égaux. Quelle fraction représente un morceau?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: The fraction name tells you how many equal parts there are in total (e.g., cut into 4 equal parts → each part is 1/4).
• Steps:
  • There are 2 equal pieces in total.
  • One piece out of 2 is written as 1/2.
• Answer: 1/2

[Easy] Basic Division

• EN: 12 ÷ 3 = ?
• FR: 12 ÷ 3 = ?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Division is like sharing equally — think "how many groups of 3 fit into 12?" (e.g., 15 ÷ 3 = 5 because 3 × 5 = 15).
• Steps:
  • Ask: how many groups of 3 make 12?
  • 3 × 4 = 12, so 12 ÷ 3 = 4.
• Answer: 4

[Medium] Perimeter

• EN: A rectangle has a length of 6 cm and a width of 3 cm. What is its perimeter?
• FR: Un rectangle a une longueur de 6 cm et une largeur de 3 cm. Quel est son périmètre?
• Choices: A) 15 cm B) 16 cm C) 17 cm D) 18 cm
• Hint: Perimeter is the distance around the shape — add all four sides (e.g., length 5 cm, width 2 cm: 5 + 2 + 5 + 2 = 14 cm).
• Steps:
  • A rectangle has two lengths and two widths.
  • Perimeter = 6 + 3 + 6 + 3 = 18 cm.
• Answer: 18 cm

[Medium] Multiplication by 4

• EN: There are 4 bags with 7 apples in each. How many apples are there in total?
• FR: Il y a 4 sacs avec 7 pommes dans chacun. Combien y a-t-il de pommes en tout?
• Choices: A) 24 B) 26 C) 28 D) 32
• Hint: To find the total in equal groups, multiply the number of groups by the number in each group (e.g., 4 groups of 6 = 4 × 6 = 24).
• Steps:
  • 4 bags × 7 apples each = 4 × 7.
  • 4 × 7 = 28.
• Answer: 28

[Medium] Reading a Graph

• EN: A bar graph shows that 8 students chose hockey, 5 chose soccer, and 3 chose basketball. How many students were surveyed in total?
• FR: Un diagramme à barres montre que 8 élèves ont choisi le hockey, 5 le soccer et 3 le basketball. Combien d'élèves ont été sondés en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Add all the values from the graph together (e.g., 6 + 4 + 2 = 12).
• Steps:
  • 8 + 5 = 13.
  • 13 + 3 = 16.
• Answer: 16

[Medium] Fractions — One Quarter

• EN: A chocolate bar is broken into 4 equal pieces. Jake eats 1 piece. What fraction did Jake eat?
• FR: Une tablette de chocolat est brisée en 4 morceaux égaux. Jake mange 1 morceau. Quelle fraction Jake a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: Write the number of pieces eaten over the total number of pieces (e.g., 1 piece out of 3 = 1/3).
• Steps:
  • Total pieces = 4; pieces eaten = 1.
  • Fraction eaten = 1/4.
• Answer: 1/4

[Hard] Multi-Step Word Problem

• EN: A teacher has 24 stickers to give equally to 4 groups of students. Each group then shares their stickers equally among 3 students. How many stickers does each student get?
• FR: Un enseignant donne 24 autocollants également à 4 groupes d'élèves. Chaque groupe partage ensuite ses autocollants entre 3 élèves. Combien d'autocollants chaque élève reçoit-il?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: Solve in two steps — first divide into groups, then divide each group again (e.g., 30 ÷ 5 = 6 per group, then 6 ÷ 3 = 2 each).
• Steps:
  • Step 1: 24 ÷ 4 = 6 stickers per group.
  • Step 2: 6 ÷ 3 = 2 stickers per student.
• Answer: 2

[Hard] Multiplication and Perimeter

• EN: A square hockey rink model has a side length of 9 cm. What is the perimeter of the model?
• FR: Un modèle carré de patinoire de hockey a un côté de 9 cm. Quel est le périmètre du modèle?
• Choices: A) 27 cm B) 32 cm C) 36 cm D) 40 cm
• Hint: A square has 4 equal sides — multiply the side length by 4 (e.g., side = 7 cm, perimeter = 7 × 4 = 28 cm).
• Steps:
  • A square has 4 equal sides, each 9 cm.
  • Perimeter = 9 × 4 = 36 cm.
• Answer: 36 cm

[Easy] Multiplication Table

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Break it into smaller parts to check (e.g., 7 × 8 = 7 × 4 + 7 × 4 = 28 + 28 = 56).
• Steps:
  • 7 × 8: use the fact 7 × 4 = 28.
  • 28 + 28 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, what digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre est à la position des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 47
• Hint: The digits after the decimal point are: first is tenths, second is hundredths (e.g., in 5.63 — the tenths digit is 6).
• Steps:
  • 3 is in the ones place.
  • 4 is in the tenths place (first after the decimal).
  • 7 is in the hundredths place.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A rectangle is 8 cm long and 5 cm wide. What is its area?
• FR: Un rectangle mesure 8 cm de long et 5 cm de large. Quelle est son aire?
• Choices: A) 26 cm² B) 36 cm² C) 40 cm² D) 45 cm²
• Hint: Area of a rectangle = length × width (e.g., 6 cm × 4 cm = 24 cm²).
• Steps:
  • Area = length × width = 8 × 5.
  • 8 × 5 = 40 cm².
• Answer: 40 cm²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/2?
• FR: Quelle fraction est la plus grande : 3/4 ou 1/2?
• Choices: A) 1/2 B) 3/4 C) 2/4 D) 1/4
• Hint: Convert to the same denominator to compare (e.g., 1/2 = 2/4, and 3/4 > 2/4, so 3/4 is greater).
• Steps:
  • Convert 1/2 to quarters: 1/2 = 2/4.
  • Compare: 3/4 vs. 2/4 — 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: What is 53 ÷ 6?
• FR: Combien fait 53 ÷ 6?
• Choices: A) 8 remainder 4 B) 8 remainder 5 C) 9 remainder 1 D) 9 remainder 2
• Hint: Find the largest multiple of the divisor that fits (e.g., 38 ÷ 5: 5 × 7 = 35, remainder 38 − 35 = 3, so 7 remainder 3).
• Steps:
  • 6 × 8 = 48; 6 × 9 = 54 (too big).
  • So the quotient is 8; remainder = 53 − 48 = 5.
• Answer: 8 remainder 5

[Medium] Elapsed Time

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

[Medium] Decimal Addition

• EN: What is 2.35 + 1.4?
• FR: Combien fait 2,35 + 1,4?
• Choices: A) 3.65 B) 3.70 C) 3.75 D) 4.05
• Hint: Line up the decimal points before adding (e.g., 3.20 + 1.5 = 3.20 + 1.50 = 4.70).
• Steps:
  • Write 1.4 as 1.40 so both have hundredths.
  • 2.35 + 1.40 = 3.75.
• Answer: 3.75

[Medium] All Multiplication to 9×9

• EN: A bookshelf has 9 shelves and each shelf holds 9 books. How many books are there in total?
• FR: Une bibliothèque a 9 étagères et chaque étagère contient 9 livres. Combien y a-t-il de livres en tout?
• Choices: A) 72 B) 78 C) 81 D) 90
• Hint: Multiply the number of shelves by the number of books per shelf (e.g., 8 shelves × 7 books = 56 books).
• Steps:
  • 9 shelves × 9 books = 9 × 9.
  • 9 × 9 = 81.
• Answer: 81

[Hard] Multi-Step with Decimals

• EN: Maya buys 3 notebooks at $2.45 each. She pays with a $10 bill. How much change does she receive?
• FR: Maya achète 3 cahiers à 2,45 $ chacun. Elle paie avec un billet de 10 $. Combien reçoit-elle en monnaie?
• Choices: A) $2.55 B) $2.65 C) $3.55 D) $7.35
• Hint: First find the total cost (price × quantity), then subtract from the amount paid (e.g., 4 × $1.75 = $7.00; $10.00 − $7.00 = $3.00 change).
• Steps:
  • Total cost: 3 × $2.45 = $7.35.
  • Change: $10.00 − $7.35 = $2.65.
• Answer: $2.65

[Hard] Long Division and Area

• EN: A rectangular garden has an area of 72 m² and a width of 8 m. What is the length of the garden?
• FR: Un jardin rectangulaire a une superficie de 72 m² et une largeur de 8 m. Quelle est la longueur du jardin?
• Choices: A) 7 m B) 8 m C) 9 m D) 11 m
• Hint: Area = length × width, so length = area ÷ width (e.g., area 48 m², width 6 m → length = 48 ÷ 6 = 8 m).
• Steps:
  • Length = area ÷ width = 72 ÷ 8.
  • 72 ÷ 8 = 9 m.
• Answer: 9 m

[Easy] Multi-Digit Multiplication

• EN: What is 23 × 4?
• FR: Combien fait 23 × 4?
• Choices: A) 82 B) 88 C) 92 D) 96
• Hint: Multiply each digit separately and add (e.g., 31 × 3: ones 1 × 3 = 3, tens 3 × 3 = 9, so 93).
• Steps:
  • 23 × 4: ones 3 × 4 = 12, write 2 carry 1.
  • Tens: 2 × 4 = 8, plus 1 carried = 9.
  • So 23 × 4 = 92.
• Answer: 92

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien fait 2/7 + 3/7?
• Choices: A) 4/7 B) 5/7 C) 5/14 D) 6/7
• Hint: When denominators are the same, just add the numerators and keep the denominator (e.g., 1/5 + 3/5 = 4/5).
• Steps:
  • Same denominator (7), so add numerators: 2 + 3 = 5.
  • Answer is 5/7.
• Answer: 5/7

[Easy] Percentage — 50%

• EN: What is 50% of 80?
• FR: Combien vaut 50% de 80?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: 50% means half, so divide the number by 2 (e.g., 50% of 60 = 60 ÷ 2 = 30).
• Steps:
  • 50% = half.
  • 80 ÷ 2 = 40.
• Answer: 40

[Easy] Decimal Operations

• EN: What is 4.6 + 2.3?
• FR: Combien fait 4,6 + 2,3?
• Choices: A) 6.7 B) 6.8 C) 6.9 D) 7.1
• Hint: Line up the decimal points and add each column (e.g., 3.4 + 1.5 = 4.9).
• Steps:
  • Tenths: 6 + 3 = 9.
  • Ones: 4 + 2 = 6.
  • So 4.6 + 2.3 = 6.9.
• Answer: 6.9

[Medium] Multi-Digit Division

• EN: What is 156 ÷ 4?
• FR: Combien fait 156 ÷ 4?
• Choices: A) 37 B) 38 C) 39 D) 41
• Hint: Use long division — divide digit by digit from left to right (e.g., 144 ÷ 4: 14 ÷ 4 = 3 remainder 2, bring down 4, 24 ÷ 4 = 6, so 36).
• Steps:
  • 15 ÷ 4 = 3 remainder 3; bring down 6 to get 36.
  • 36 ÷ 4 = 9.
  • So 156 ÷ 4 = 39.
• Answer: 39

[Medium] Subtracting Fractions

• EN: What is 6/9 − 2/9?
• FR: Combien fait 6/9 − 2/9?
• Choices: A) 3/9 B) 4/9 C) 4/18 D) 5/9
• Hint: Same denominator — just subtract the numerators and keep the denominator (e.g., 5/8 − 2/8 = 3/8).
• Steps:
  • Same denominator (9), so subtract numerators: 6 − 2 = 4.
  • Answer is 4/9.
• Answer: 4/9

[Medium] Percentage — 25%

• EN: There are 60 students at a school event. 25% of them are wearing red jerseys. How many students are wearing red jerseys?
• FR: Il y a 60 élèves à un événement scolaire. 25% d'eux portent des maillots rouges. Combien portent des maillots rouges?
• Choices: A) 12 B) 15 C) 18 D) 20
• Hint: 25% = one quarter, so divide by 4 (e.g., 25% of 40 = 40 ÷ 4 = 10).
• Steps:
  • 25% = 1/4, so divide by 4.
  • 60 ÷ 4 = 15.
• Answer: 15

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 3 cm wide, and 4 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 3 cm de large et 4 cm de hauteur. Quel est son volume?
• Choices: A) 48 cm³ B) 55 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height (e.g., 6 × 2 × 3 = 36 cm³).
• Steps:
  • Volume = 5 × 3 × 4.
  • 5 × 3 = 15; 15 × 4 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Hard] Multi-Step Decimal Problem

• EN: A Tim Hortons coffee costs $2.15 and a muffin costs $1.85. Carla buys 2 coffees and 1 muffin. How much does she spend in total?
• FR: Un café chez Tim Hortons coûte 2,15 $ et un muffin coûte 1,85 $. Carla achète 2 cafés et 1 muffin. Combien dépense-t-elle en tout?
• Choices: A) $5.85 B) $6.05 C) $6.15 D) $6.25
• Hint: Find the cost of each type of item, then add them together (e.g., 2 drinks at $3.50 each = $7.00, plus 1 snack at $2.00 = $9.00).
• Steps:
  • 2 coffees: 2 × $2.15 = $4.30.
  • 1 muffin: $1.85.
  • Total: $4.30 + $1.85 = $6.15.
• Answer: $6.15

[Hard] Percentage — 10% and Multi-Step

• EN: A hockey jersey originally costs $90. It is on sale for 10% off. What is the sale price?
• FR: Un maillot de hockey coûte 90 $ à l'origine. Il est en solde avec 10% de réduction. Quel est le prix de vente?
• Choices: A) $79 B) $81 C) $83 D) $85
• Hint: 10% means one tenth — divide the price by 10 to find the discount, then subtract (e.g., 10% of $70 = $7, sale price = $70 − $7 = $63).
• Steps:
  • 10% of $90 = $90 ÷ 10 = $9.
  • Sale price = $90 − $9 = $81.
• Answer: $81

[Easy] Fraction Multiplication

• EN: What is 1/2 × 1/3?
• FR: Combien fait 1/2 × 1/3?
• Choices: A) 1/5 B) 1/6 C) 2/3 D) 2/5
• Hint: Multiply numerators together and denominators together (e.g., 1/3 × 1/4 = 1/12).
• Steps:
  • Numerators: 1 × 1 = 1.
  • Denominators: 2 × 3 = 6.
  • So 1/2 × 1/3 = 1/6.
• Answer: 1/6

[Easy] Percent of a Number

• EN: What is 30% of 50?
• FR: Combien vaut 30% de 50?
• Choices: A) 12 B) 15 C) 18 D) 20
• Hint: Find 10% first by dividing by 10, then multiply by the number of tens (e.g., 30% of 60: 10% = 6, so 30% = 6 × 3 = 18).
• Steps:
  • 10% of 50 = 5.
  • 30% = 5 × 3 = 15.
• Answer: 15

[Easy] Order of Operations — BEDMAS

• EN: What is 3 + 2 × 4?
• FR: Combien fait 3 + 2 × 4?
• Choices: A) 10 B) 11 C) 14 D) 20
• Hint: In BEDMAS, multiplication comes before addition (e.g., 5 + 3 × 2 = 5 + 6 = 11, not 16).
• Steps:
  • Multiplication first: 2 × 4 = 8.
  • Then add: 3 + 8 = 11.
• Answer: 11

[Easy] Ratios

• EN: In a class, there are 12 boys and 8 girls. What is the ratio of boys to girls?
• FR: Dans une classe, il y a 12 garçons et 8 filles. Quel est le rapport garçons à filles?
• Choices: A) 2:3 B) 3:2 C) 4:3 D) 8:12
• Hint: Simplify ratios by dividing both numbers by their greatest common factor (e.g., 6:9 → divide by 3 → 2:3).
• Steps:
  • Ratio is 12:8.
  • GCF of 12 and 8 is 4; 12 ÷ 4 = 3, 8 ÷ 4 = 2.
  • Simplified ratio = 3:2.
• Answer: 3:2

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien fait 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1/2 C) 3/2 D) 2
• Hint: To divide by a fraction, multiply by its reciprocal — flip the second fraction and multiply (e.g., 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3).
• Steps:
  • Flip 1/2 to get 2/1.
  • 3/4 × 2/1 = 6/4 = 3/2.
• Answer: 3/2

[Medium] Integers — Introduction

• EN: The temperature in Winnipeg was −8°C in the morning and rose 11°C by afternoon. What was the afternoon temperature?
• FR: La température à Winnipeg était de −8 °C le matin et a augmenté de 11 °C l'après-midi. Quelle était la température l'après-midi?
• Choices: A) −3°C B) 2°C C) 3°C D) 4°C
• Hint: Adding a positive number to a negative number — move to the right on the number line (e.g., −5 + 8 = 3).
• Steps:
  • −8 + 11 = 3.
  • The afternoon temperature was 3°C.
• Answer: 3°C

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km/h?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: Rate = total amount ÷ time (e.g., 180 km in 3 hours = 180 ÷ 3 = 60 km/h).
• Steps:
  • Speed = distance ÷ time = 240 ÷ 3.
  • 240 ÷ 3 = 80 km/h.
• Answer: 80 km/h

[Medium] Algebraic Expressions

• EN: If n = 5, what is the value of 3n + 4?
• FR: Si n = 5, quelle est la valeur de 3n + 4?
• Choices: A) 17 B) 18 C) 19 D) 22
• Hint: Substitute the value for the variable, then calculate following BEDMAS (e.g., if x = 3, then 2x + 5 = 2(3) + 5 = 6 + 5 = 11).
• Steps:
  • Substitute n = 5: 3(5) + 4.
  • 3 × 5 = 15; 15 + 4 = 19.
• Answer: 19

[Hard] BEDMAS with Integers

• EN: What is (−3 + 7) × 2 − 5?
• FR: Combien fait (−3 + 7) × 2 − 5?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Work inside brackets first, then multiply, then subtract (e.g., (−2 + 6) × 3 − 4 = 4 × 3 − 4 = 12 − 4 = 8).
• Steps:
  • Brackets first: −3 + 7 = 4.
  • Multiply: 4 × 2 = 8.
  • Subtract: 8 − 5 = 3.
• Answer: 3

[Hard] Percent — Multi-Step

• EN: A pair of skates costs $120. The store offers a 15% discount. After the discount, 13% HST is added. What is the final price? (Round to the nearest cent.)
• FR: Une paire de patins coûte 120 $. Le magasin offre un rabais de 15%. Après le rabais, une TVH de 13% est ajoutée. Quel est le prix final? (Arrondis au cent près.)
• Choices: A) $110.45 B) $115.02 C) $115.82 D) $116.01
• Hint: First apply the discount to get the reduced price, then calculate tax on the reduced price and add it (e.g., $80 with 10% off = $72, then 5% tax = $72 × 1.05 = $75.60).
• Steps:
  • Discount: 15% of $120 = $18; discounted price = $120 − $18 = $102.
  • Tax: 13% of $102 = $13.26.
  • Final price: $102 + $13.26 = $115.26.
  • Rounded to nearest cent: $115.26.
• Answer: $115.02

[Easy] Integer Addition

• EN: What is −5 + 9?
• FR: Combien fait −5 + 9?
• Choices: A) −4 B) 3 C) 4 D) 14
• Hint: On a number line, start at the negative number and move right by the positive number (e.g., −3 + 7 = 4).
• Steps:
  • Start at −5, move 9 steps to the right.
  • −5 + 9 = 4.
• Answer: 4

[Easy] Integer Subtraction

• EN: What is 3 − (−4)?
• FR: Combien fait 3 − (−4)?
• Choices: A) −1 B) 1 C) 6 D) 7
• Hint: Subtracting a negative is the same as adding a positive (e.g., 5 − (−3) = 5 + 3 = 8).
• Steps:
  • 3 − (−4) = 3 + 4.
  • 3 + 4 = 7.
• Answer: 7

[Easy] Percent — Discount

• EN: A book costs $20.00. It is on sale for 20% off. How much is the discount?
• FR: Un livre coûte 20,00 $. Il est en solde avec 20% de réduction. Quel est le montant de la réduction?
• Choices: A) $2.00 B) $4.00 C) $5.00 D) $8.00
• Hint: Find the percent of the price by multiplying (e.g., 10% of $30 = $3, so 20% = $6).
• Steps:
  • 20% of $20 = 0.20 × $20 = $4.00.
  • The discount is $4.00.
• Answer: $4.00

[Easy] One-Step Equation

• EN: Solve for x: x + 9 = 15
• FR: Résous pour x : x + 9 = 15
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 24
• Hint: To isolate the variable, do the opposite operation on both sides (e.g., x + 4 = 10 → x = 10 − 4 = 6).
• Steps:
  • Subtract 9 from both sides: x = 15 − 9.
  • x = 6.
• Answer: x = 6

[Medium] Integer Multiplication

• EN: What is (−6) × (−7)?
• FR: Combien fait (−6) × (−7)?
• Choices: A) −42 B) −13 C) 13 D) 42
• Hint: Negative × Negative = Positive (e.g., (−4) × (−5) = 20).
• Steps:
  • Both factors are negative, so the product is positive.
  • 6 × 7 = 42, so (−6) × (−7) = 42.
• Answer: 42

[Medium] Surface Area of a Rectangular Prism

• EN: A box is 5 cm long, 3 cm wide, and 2 cm tall. What is the total surface area?
• FR: Une boîte mesure 5 cm de long, 3 cm de large et 2 cm de hauteur. Quelle est l'aire totale?
• Choices: A) 58 cm² B) 60 cm² C) 62 cm² D) 64 cm²
• Hint: Surface area = 2(lw + lh + wh) — find the area of each pair of faces and add them all (e.g., l=4, w=2, h=3: 2(8+12+6) = 2(26) = 52 cm²).
• Steps:
  • lw = 5 × 3 = 15; lh = 5 × 2 = 10; wh = 3 × 2 = 6.
  • SA = 2(15 + 10 + 6) = 2(31) = 62 cm².
• Answer: 62 cm²

[Medium] Percentage — Tip

• EN: The Nguyen family's restaurant bill is $48. They leave a 15% tip. How much is the tip?
• FR: La famille Nguyen a une facture de restaurant de 48 $. Ils laissent un pourboire de 15%. Combien est le pourboire?
• Choices: A) $6.20 B) $6.80 C) $7.20 D) $7.60
• Hint: Find 10% first, then 5% (which is half of 10%), and add them (e.g., 15% of $60: 10% = $6, 5% = $3, total = $9).
• Steps:
  • 10% of $48 = $4.80.
  • 5% of $48 = $2.40.
  • 15% = $4.80 + $2.40 = $7.20.
• Answer: $7.20

[Medium] Probability

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

[Hard] Integer Division and Multi-Step

• EN: The temperature in Yellowknife dropped by 4°C each hour for 6 hours, starting at 2°C. What was the final temperature?
• FR: La température à Yellowknife a baissé de 4 °C par heure pendant 6 heures, en partant de 2 °C. Quelle était la température finale?
• Choices: A) −20°C B) −22°C C) −24°C D) −26°C
• Hint: Multiply the change per hour by the number of hours, then add to the starting temperature (e.g., starts at 5°C, drops 3°C per hour for 4 hours: 5 + (−3 × 4) = 5 − 12 = −7°C).
• Steps:
  • Total drop: 4 × 6 = 24°C.
  • Final temperature: 2 − 24 = −22°C.
• Answer: −22°C

[Hard] One-Step Equation with Fractions

• EN: Solve for x: x/4 = 7
• FR: Résous pour x : x/4 = 7
• Choices: A) x = 11 B) x = 21 C) x = 28 D) x = 35
• Hint: To undo dividing by 4, multiply both sides by 4 (e.g., x/3 = 5 → x = 5 × 3 = 15).
• Steps:
  • Multiply both sides by 4: x = 7 × 4.
  • x = 28.
• Answer: x = 28

[Easy] Perfect Squares

• EN: What is √49?
• FR: Combien vaut √49?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: A perfect square has a whole number square root — ask yourself "what number times itself gives this?" (e.g., √36 = 6 because 6 × 6 = 36).
• Steps:
  • Ask: what number × itself = 49?
  • 7 × 7 = 49, so √49 = 7.
• Answer: 7

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 3 = 11
• FR: Résous pour x : 2x + 3 = 11
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: First subtract the constant from both sides, then divide by the coefficient (e.g., 3x + 2 = 11 → 3x = 9 → x = 3).
• Steps:
  • Subtract 3 from both sides: 2x = 8.
  • Divide by 2: x = 4.
• Answer: x = 4

[Easy] Mean

• EN: What is the mean of 6, 8, 10, and 12?
• FR: Quelle est la moyenne de 6, 8, 10 et 12?
• Choices: A) 8 B) 9 C) 10 D) 11
• Hint: Add all values, then divide by how many there are (e.g., mean of 4, 6, 8 = (4+6+8)÷3 = 18÷3 = 6).
• Steps:
  • Sum: 6 + 8 + 10 + 12 = 36.
  • Mean: 36 ÷ 4 = 9.
• Answer: 9

[Easy] Percent Increase

• EN: A price rises from $50 to $60. What is the percent increase?
• FR: Un prix passe de 50 $ à 60 $. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: Percent change = (change ÷ original) × 100 (e.g., goes from $40 to $48: change = $8, 8 ÷ 40 × 100 = 20%).
• Steps:
  • Change = 60 − 50 = 10.
  • Percent increase = (10 ÷ 50) × 100 = 20%.
• Answer: 20%

[Medium] Two-Step Equation — Negative

• 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 to both sides first, then divide (e.g., 4x − 5 = 11 → 4x = 16 → x = 4).
• Steps:
  • Add 7 to both sides: 3x = 21.
  • Divide by 3: x = 7.
• Answer: x = 7

[Medium] Pythagorean Theorem

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

[Medium] Slope

• EN: What is the slope of a line passing through (2, 3) and (6, 11)?
• FR: Quelle est la pente d'une droite passant par (2, 3) et (6, 11)?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., through (1, 2) and (3, 6): slope = (6−2)÷(3−1) = 4÷2 = 2).
• Steps:
  • Rise: 11 − 3 = 8.
  • Run: 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 5, 9, 5, 11, 5
• FR: Trouve la médiane de : 3, 7, 5, 9, 5, 11, 5
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: Arrange values in order from least to greatest, then pick the middle one (e.g., 2, 4, 6, 8, 10 → median = 6).
• Steps:
  • Ordered: 3, 5, 5, 5, 7, 9, 11.
  • The middle value (4th of 7) is 5.
• Answer: 5

[Hard] Pythagorean Theorem — Finding a Leg

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

[Hard] Two-Step Equation — Fractions

• EN: Solve for x: x/3 + 5 = 9
• FR: Résous pour x : x/3 + 5 = 9
• Choices: A) x = 4 B) x = 9 C) x = 12 D) x = 21
• Hint: Subtract the constant first, then multiply both sides by the denominator (e.g., x/2 + 3 = 7 → x/2 = 4 → x = 8).
• Steps:
  • Subtract 5 from both sides: x/3 = 4.
  • Multiply both sides by 3: x = 12.
• Answer: x = 12

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 2 = 14
• FR: Résous pour x : 4x − 2 = 14
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Add to both sides to remove the constant, then divide (e.g., 5x − 3 = 12 → 5x = 15 → x = 3).
• Steps:
  • Add 2 to both sides: 4x = 16.
  • Divide by 4: x = 4.
• Answer: x = 4

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x + 5?
• FR: Quelle est la pente de la droite y = 3x + 5?
• Choices: A) 1 B) 3 C) 5 D) 8
• Hint: In y = mx + b, m is the slope and b is the y-intercept (e.g., y = 7x − 2 has slope 7).
• Steps:
  • The equation is in y = mx + b form.
  • m = 3, so the slope is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Simplify: (3x + 4) + (5x − 2)
• FR: Simplifie : (3x + 4) + (5x − 2)
• Choices: A) 7x + 2 B) 8x + 2 C) 8x + 6 D) 9x − 2
• Hint: Combine like terms — add the x terms together and add the constant terms together (e.g., (2x + 3) + (4x − 1) = 6x + 2).
• Steps:
  • x terms: 3x + 5x = 8x.
  • Constants: 4 + (−2) = 2.
  • Result: 8x + 2.
• Answer: 8x + 2

[Easy] Linear Inequality

• EN: Which value of x satisfies x + 3 > 7?
• FR: Quelle valeur de x satisfait x + 3 > 7?
• Choices: A) x = 1 B) x = 3 C) x = 4 D) x = 5
• Hint: Solve the inequality like an equation, but keep the inequality sign (e.g., x + 2 > 5 → x > 3, so x = 4 works).
• Steps:
  • x + 3 > 7 → x > 4.
  • Only x = 5 satisfies x > 4.
• Answer: x = 5

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 4)
• FR: Développe : (x + 3)(x + 4)
• Choices: A) x² + 6x + 12 B) x² + 7x + 12 C) x² + 7x + 7 D) x² + 12x + 7
• Hint: Use FOIL — First, Outer, Inner, Last (e.g., (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10).
• Steps:
  • First: x × x = x².
  • Outer: x × 4 = 4x.
  • Inner: 3 × x = 3x.
  • Last: 3 × 4 = 12.
  • Combine: x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in the ratio 2:5. If the smaller triangle has a base of 6 cm, what is the base of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans un rapport de 2:5. Si le plus petit triangle a une base de 6 cm, quelle est la base du plus grand?
• Choices: A) 12 cm B) 13 cm C) 15 cm D) 18 cm
• Hint: Set up a proportion using the scale factor (e.g., ratio 3:7, smaller base = 9 cm → 9 ÷ 3 = 3, larger = 3 × 7 = 21 cm).
• Steps:
  • Scale factor: 2:5.
  • 6 ÷ 2 = 3; larger base = 3 × 5 = 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 4 cm and the hypotenuse is 8 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 4 cm et l'hypoténuse mesure 8 cm. Combien vaut sin(θ)?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: SOH: sin = opposite ÷ hypotenuse (e.g., opposite = 3, hypotenuse = 6 → sin = 3/6 = 1/2).
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 4 ÷ 8.
  • sin(θ) = 1/2.
• Answer: 1/2

[Medium] Graphing — y-intercept

• EN: The line y = −2x + 6 crosses the y-axis at which point?
• FR: La droite y = −2x + 6 coupe l'axe des y en quel point?
• Choices: A) (0, −2) B) (0, 3) C) (0, 6) D) (6, 0)
• Hint: The y-intercept is found when x = 0 (e.g., y = 4x − 3: when x = 0, y = −3, so (0, −3)).
• Steps:
  • Set x = 0: y = −2(0) + 6 = 6.
  • The y-intercept is (0, 6).
• Answer: (0, 6)

[Hard] Solving a Linear Inequality

• EN: Solve for x: −3x + 5 ≤ 14. Which graph shows the solution?
• FR: Résous pour x : −3x + 5 ≤ 14. Quelle représentation montre la solution?
• Choices: A) x ≤ −3 B) x ≥ −3 C) x ≤ 3 D) x ≥ 3
• Hint: When you divide or multiply both sides of an inequality by a negative number, flip the inequality sign (e.g., −2x < 6 → x > −3).
• Steps:
  • Subtract 5 from both sides: −3x ≤ 9.
  • Divide by −3 and flip the sign: x ≥ −3.
• Answer: x ≥ −3

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, the angle is 30° and the hypotenuse is 20 cm. What is the length of the side opposite the angle?
• FR: Dans un triangle rectangle, l'angle est de 30° et l'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé à l'angle?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 11 cm
• Hint: Use SOH: opposite = sin(angle) × hypotenuse (e.g., angle 45°, hypotenuse 14: opposite = sin(45°) × 14 ≈ 0.707 × 14 ≈ 9.9 cm).
• Steps:
  • sin(30°) = 0.5.
  • Opposite = sin(30°) × 20 = 0.5 × 20 = 10 cm.
• Answer: 10 cm

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6
• FR: Factorise : x² + 5x + 6
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 3) D) (x − 2)(x − 3)
• Hint: Find two numbers that multiply to the constant and add to the x coefficient (e.g., x² + 7x + 12 → 3 × 4 = 12 and 3 + 4 = 7, so (x + 3)(x + 4)).
• Steps:
  • Need two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5.
  • So x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 6 cm and the hypotenuse is 10 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 6 cm et l'hypoténuse mesure 10 cm. Combien vaut cos(θ)?
• Choices: A) 3/8 B) 3/5 C) 4/5 D) 5/6
• Hint: CAH: cos = adjacent ÷ hypotenuse (e.g., adjacent = 4, hypotenuse = 8 → cos = 4/8 = 1/2).
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 6 ÷ 10.
  • cos(θ) = 3/5.
• Answer: 3/5

[Easy] Systems of Equations — Substitution

• EN: If y = 2x and x = 3, what is y?
• FR: Si y = 2x et x = 3, quelle est la valeur de y?
• Choices: A) 4 B) 5 C) 6 D) 9
• Hint: Substitute the known value directly into the equation (e.g., y = 3x, x = 4 → y = 12).
• Steps:
  • Substitute x = 3 into y = 2x.
  • y = 2 × 3 = 6.
• Answer: 6

[Easy] Volume of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 5 cm. Using π ≈ 3.14, what is its volume? (Round to the nearest whole number.)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 5 cm. En utilisant π ≈ 3,14, quel est son volume? (Arrondis au nombre entier.)
• Choices: A) 127 cm³ B) 134 cm³ C) 141 cm³ D) 148 cm³
• Hint: Volume of cylinder = π × r² × h (e.g., r = 2, h = 7, π ≈ 3.14 → 3.14 × 4 × 7 = 87.92 cm³).
• Steps:
  • V = π × r² × h = 3.14 × 9 × 5.
  • 3.14 × 9 = 28.26; 28.26 × 5 = 141.3 ≈ 141 cm³.
• Answer: 141 cm³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x = 7
• FR: Résous en complétant le carré : x² + 6x = 7
• Choices: A) x = 1 or x = −7 B) x = 2 or x = −8 C) x = 3 or x = −9 D) x = 7 or x = −1
• Hint: Add (b/2)² to both sides, then take the square root (e.g., x² + 4x = 5 → x² + 4x + 4 = 9 → (x+2)² = 9 → x+2 = ±3 → x = 1 or −5).
• Steps:
  • Add (6/2)² = 9 to both sides: x² + 6x + 9 = 16.
  • (x + 3)² = 16 → x + 3 = ±4.
  • x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry

• EN: A circle has a radius of 7 cm. What is the circumference? (Use π ≈ 3.14, round to one decimal place.)
• FR: Un cercle a un rayon de 7 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14, arrondis à un décimal.)
• Choices: A) 40.8 cm B) 43.5 cm C) 44.0 cm D) 45.2 cm
• Hint: Circumference = 2 × π × r (e.g., r = 5: C = 2 × 3.14 × 5 = 31.4 cm).
• Steps:
  • C = 2 × π × r = 2 × 3.14 × 7.
  • 2 × 3.14 = 6.28; 6.28 × 7 = 43.96 ≈ 44.0 cm.
• Answer: 44.0 cm

[Medium] Systems of Equations — Two Equations

• EN: Solve: y = x + 2 and y = 2x − 1. What is x?
• FR: Résous : y = x + 2 et y = 2x − 1. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Set the two expressions equal to each other and solve (e.g., x + 4 = 2x − 1 → 4 + 1 = 2x − x → x = 5).
• Steps:
  • Set equal: x + 2 = 2x − 1.
  • 2 + 1 = 2x − x → 3 = x.
  • x = 3.
• Answer: x = 3

[Medium] Quadratic — Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = 3 and x = 4 D) x = −2 and x = −3
• Hint: The quadratic formula gives x = (−b ± √(b²−4ac)) / 2a (e.g., x² − 7x + 12 = 0 → x = 3 or x = 4).
• Steps:
  • a=1, b=−5, c=6; discriminant = 25 − 24 = 1.
  • x = (5 ± 1) / 2 → x = 3 or x = 2.
• Answer: x = 2 and x = 3

[Hard] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 9 cm. What is the total surface area? (Use π ≈ 3.14, round to the nearest whole number.)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 9 cm. Quelle est l'aire totale? (Utilise π ≈ 3,14, arrondis au nombre entier.)
• Choices: A) 151 cm² B) 163 cm² C) 175 cm² D) 188 cm²
• Hint: Total surface area of cone = π r l + π r² (e.g., r = 3, l = 5: 3.14 × 3 × 5 + 3.14 × 9 = 47.1 + 28.26 = 75.36 cm²).
• Steps:
  • Lateral area: π × 4 × 9 = 3.14 × 36 = 113.04 cm².
  • Base area: π × 4² = 3.14 × 16 = 50.24 cm².
  • Total: 113.04 + 50.24 = 163.28 ≈ 163 cm².
• Answer: 163 cm²

[Hard] Circle Geometry — Angle in a Semicircle

• EN: An inscribed angle in a circle intercepts an arc of 110°. What is the measure of the inscribed angle?
• FR: Un angle inscrit dans un cercle intercepte un arc de 110°. Quelle est la mesure de l'angle inscrit?
• Choices: A) 50° B) 55° C) 60° D) 110°
• Hint: An inscribed angle equals half the intercepted arc (e.g., arc = 80° → inscribed angle = 40°).
• Steps:
  • Inscribed angle = arc ÷ 2.
  • 110° ÷ 2 = 55°.
• Answer: 55°

[Easy] Evaluating a Function

• EN: If f(x) = 2x² − 3, find f(4).
• FR: Si f(x) = 2x² − 3, trouve f(4).
• Choices: A) 27 B) 29 C) 31 D) 35
• Hint: Substitute the value into the function and evaluate (e.g., f(x) = x² + 1, f(3) = 9 + 1 = 10).
• Steps:
  • f(4) = 2(4²) − 3 = 2(16) − 3.
  • 32 − 3 = 29.
• Answer: 29

[Easy] Exponential Function

• EN: A savings account doubles every year. If you start with $200, how much will you have after 3 years?
• FR: Un compte d'épargne double chaque année. Si tu commences avec 200 $, combien auras-tu après 3 ans?
• Choices: A) $1 200 B) $1 400 C) $1 600 D) $1 800
• Hint: Multiply by the growth factor for each time period (e.g., $100 doubled for 2 years: $100 × 2 × 2 = $400).
• Steps:
  • Year 1: $200 × 2 = $400.
  • Year 2: $400 × 2 = $800.
  • Year 3: $800 × 2 = $1 600.
• Answer: $1 600

[Easy] Logarithm — Basic

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: logₐ(b) asks "to what power must a be raised to get b?" (e.g., log₃(9) = 2 because 3² = 9).
• Steps:
  • Ask: 2 to what power = 8?
  • 2¹ = 2, 2² = 4, 2³ = 8.
  • log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• EN: What is the 6th term of the sequence 3, 7, 11, 15, …?
• FR: Quel est le 6e terme de la suite 3, 7, 11, 15, …?
• Choices: A) 19 B) 21 C) 23 D) 25
• Hint: Use the formula aₙ = a₁ + (n − 1)d where d is the common difference (e.g., sequence 2, 5, 8, 11: d = 3, 5th term = 2 + 4×3 = 14).
• Steps:
  • Common difference d = 7 − 3 = 4.
  • 6th term = 3 + (6 − 1)(4) = 3 + 20 = 23.
• Answer: 23

[Medium] Compound Interest

• EN: An investment of $1 000 earns 5% interest compounded annually for 2 years. What is the amount after 2 years?
• FR: Un investissement de 1 000 $ rapporte 5% d'intérêts composés annuellement pendant 2 ans. Quel est le montant après 2 ans?
• Choices: A) $1 100.00 B) $1 102.50 C) $1 105.00 D) $1 110.00
• Hint: Use A = P(1 + r)ⁿ — apply the interest for each compounding period (e.g., $500 at 4% for 2 years: 500 × 1.04² = 500 × 1.0816 = $540.80).
• Steps:
  • A = 1000 × (1.05)².
  • 1.05² = 1.1025.
  • A = $1 102.50.
• Answer: $1 102.50

[Medium] Geometric Sequence

• EN: In the geometric sequence 2, 6, 18, 54, …, what is the 5th term?
• FR: Dans la suite géométrique 2, 6, 18, 54, …, quel est le 5e terme?
• Choices: A) 108 B) 144 C) 162 D) 216
• Hint: Use aₙ = a₁ × rⁿ⁻¹ where r is the common ratio (e.g., sequence 3, 12, 48: r = 4, 4th term = 3 × 4³ = 192).
• Steps:
  • Common ratio r = 6 ÷ 2 = 3.
  • 5th term = 2 × 3⁴ = 2 × 81 = 162.
• Answer: 162

[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, combien vaut cos(θ)? (Suppose que θ est dans le premier quadrant.)
• Choices: A) 3/4 B) 4/5 C) 5/3 D) 5/4
• Hint: Use the identity sin²(θ) + cos²(θ) = 1 (e.g., sin = 5/13 → cos = 12/13 because 5² + 12² = 13²).
• Steps:
  • sin²(θ) + cos²(θ) = 1 → (3/5)² + cos²(θ) = 1.
  • 9/25 + cos²(θ) = 1 → cos²(θ) = 16/25.
  • cos(θ) = 4/5.
• Answer: 4/5

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = (x − 3)² + 4?
• FR: Quel est le sommet de la parabole y = (x − 3)² + 4?
• Choices: A) (−3, 4) B) (3, −4) C) (3, 4) D) (4, 3)
• Hint: In vertex form y = (x − h)² + k, the vertex is at (h, k) — watch the sign of h (e.g., y = (x − 2)² + 5 has vertex (2, 5)).
• Steps:
  • The equation is in vertex form y = (x − h)² + k.
  • h = 3, k = 4, so the vertex is (3, 4).
• Answer: (3, 4)

[Hard] Sum of an Arithmetic Series

• EN: Find the sum of the first 20 terms of the arithmetic series: 4 + 8 + 12 + …
• FR: Trouve la somme des 20 premiers termes de la série arithmétique : 4 + 8 + 12 + …
• Choices: A) 780 B) 820 C) 840 D) 880
• Hint: Use Sₙ = n/2 × (a₁ + aₙ), first finding the last term with aₙ = a₁ + (n−1)d (e.g., first 10 terms of 2 + 5 + 8 …: a₁₀ = 2 + 27 = 29, S₁₀ = 5 × (2+29) = 155).
• Steps:
  • d = 4; a₂₀ = 4 + 19 × 4 = 4 + 76 = 80.
  • S₂₀ = 20/2 × (4 + 80) = 10 × 84 = 840.
• Answer: 840

[Hard] Annuity — Future Value

• EN: Emma deposits $500 at the end of each year into an account earning 6% per year compounded annually. What is the value after 3 years? (Use FV = PMT × [((1+r)ⁿ − 1)/r])
• FR: Emma dépose 500 $ à la fin de chaque année dans un compte à 6% par an composé annuellement. Quelle est la valeur après 3 ans? (Utilise FV = PMT × [((1+r)ⁿ − 1)/r])
• Choices: A) $1 500.00 B) $1 591.80 C) $1 637.40 D) $1 685.00
• Hint: Compute (1.06)³ first, subtract 1, divide by 0.06, then multiply by the payment (e.g., PMT=$200, r=5%, n=3: (1.05³−1)/0.05 = 3.1525, FV = 200 × 3.1525 = $630.50).
• Steps:
  • (1.06)³ = 1.191016.
  • ((1.191016 − 1) / 0.06) = 0.191016 / 0.06 = 3.1836.
  • FV = 500 × 3.1836 = $1 591.80.
• Answer: $1 591.80

[Easy] Permutations

• EN: In how many ways can 4 students be arranged in a line?
• FR: De combien de façons peut-on placer 4 élèves dans une file?
• Choices: A) 16 B) 20 C) 24 D) 32
• Hint: The number of arrangements of n items is n! = n × (n−1) × … × 1 (e.g., 3 students: 3! = 3 × 2 × 1 = 6).
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • 4 × 3 = 12; 12 × 2 = 24; 24 × 1 = 24.
• Answer: 24

[Easy] Combinations

• EN: How many ways can you choose 2 books from a shelf of 5?
• FR: De combien de façons peut-on choisir 2 livres parmi 5?
• Choices: A) 8 B) 10 C) 12 D) 20
• Hint: Use C(n, r) = n! / (r! × (n−r)!) (e.g., C(4,2) = 4!/(2!×2!) = 24/4 = 6).
• Steps:
  • C(5, 2) = 5! / (2! × 3!) = (5 × 4) / (2 × 1).
  • 20 / 2 = 10.
• Answer: 10

[Easy] Derivative — Power Rule

• EN: If f(x) = x³, what is f′(x)?
• FR: Si f(x) = x³, quelle est f′(x)?
• Choices: A) x² B) 3x C) 3x² D) 3x³
• Hint: Power rule: bring the exponent down as a coefficient and reduce the exponent by 1 (e.g., f(x) = x⁴ → f′(x) = 4x³).
• Steps:
  • Bring down the exponent: coefficient = 3.
  • Reduce exponent: 3 − 1 = 2.
  • f′(x) = 3x².
• Answer: 3x²

[Easy] Polynomial Function — 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, qu'arrive-t-il à f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: For end behaviour, only the leading term matters — a negative leading coefficient on an odd-degree polynomial falls to −∞ as x → +∞ (e.g., −3x⁵ → −∞).
• Steps:
  • Leading term: −2x³.
  • Negative × (positive large number) → very negative.
  • So f(x) → −∞.
• Answer: f(x) → −∞

[Medium] Derivative — Rate of Change

• EN: The position of a hockey puck is given by s(t) = 3t² + 2t, where s is in metres and t is in seconds. What is the velocity (in m/s) at t = 4?
• FR: La position d'une rondelle est donnée par s(t) = 3t² + 2t, où s est en mètres et t en secondes. Quelle est la vitesse (en m/s) à t = 4?
• Choices: A) 24 m/s B) 26 m/s C) 28 m/s D) 30 m/s
• Hint: Find the derivative (velocity function), then substitute t (e.g., s(t) = 2t² + 5t → s′(t) = 4t + 5 → at t = 3: 4(3) + 5 = 17).
• Steps:
  • s′(t) = 6t + 2.
  • At t = 4: s′(4) = 6(4) + 2 = 24 + 2 = 26 m/s.
• Answer: 26 m/s

[Medium] Probability Distribution

• EN: A fair six-sided die is rolled twice. What is the probability of getting a sum of 9?
• FR: On lance un dé équilibré à six faces deux fois. Quelle est la probabilité d'obtenir une somme de 9?
• Choices: A) 1/12 B) 1/9 C) 1/6 D) 4/36
• Hint: List the favourable outcomes (pairs that sum to the target) and divide by the total outcomes (36) (e.g., sum of 5: (1,4),(2,3),(3,2),(4,1) = 4 ways → 4/36 = 1/9).
• Steps:
  • Pairs summing to 9: (3,6),(4,5),(5,4),(6,3) = 4 ways.
  • Total outcomes: 6 × 6 = 36.
  • Probability = 4/36 = 1/9.
• Answer: 1/9

[Medium] Vectors — Addition

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

[Medium] Rational Function — Vertical Asymptote

• EN: Find the vertical asymptote of the function f(x) = 1 / (x − 5).
• FR: Trouve l'asymptote verticale de la fonction f(x) = 1 / (x − 5).
• Choices: A) x = −5 B) x = 0 C) x = 1 D) x = 5
• Hint: Set the denominator equal to zero and solve (e.g., f(x) = 1/(x + 3): denominator = 0 when x + 3 = 0, so x = −3).
• Steps:
  • Set denominator = 0: x − 5 = 0.
  • x = 5 is the vertical asymptote.
• Answer: x = 5

[Hard] Binomial Theorem

• EN: What is the coefficient of x² in the expansion of (x + 2)⁴?
• FR: Quel est le coefficient de x² dans le développement de (x + 2)⁴?
• Choices: A) 12 B) 18 C) 24 D) 32
• Hint: Use the Binomial Theorem: the term with xʳ in (x + a)ⁿ is C(n, n−r) × xʳ × aⁿ⁻ʳ (e.g., coefficient of x² in (x+3)³ = C(3,2) × 3¹ = 3 × 3 = 9).
• Steps:
  • We want the x² term: r = 2, n = 4.
  • Term = C(4, 2) × x² × 2² = 6 × x² × 4 = 24x².
  • Coefficient = 24.
• Answer: 24

[Hard] Derivative — Application

• EN: A rectangular garden has a perimeter of 40 m. Let one side be x metres. Express the area A(x) and find the value of x that maximizes the area.
• FR: Un jardin rectangulaire a un périmètre de 40 m. Soit un côté x mètres. Exprime l'aire A(x) et trouve la valeur de x qui maximise l'aire.
• Choices: A) x = 5 m B) x = 8 m C) x = 10 m D) x = 12 m
• Hint: Write the area in terms of one variable, then differentiate, set A′(x) = 0, and solve (e.g., perimeter 24: 2x + 2y = 24, y = 12 − x, A = x(12−x) = 12x − x², A′ = 12 − 2x = 0, x = 6).
• Steps:
  • Perimeter: 2x + 2y = 40, so y = 20 − x.
  • Area: A(x) = x(20 − x) = 20x − x².
  • A′(x) = 20 − 2x; set equal to 0: 20 − 2x = 0 → x = 10.
• Answer: x = 10 m