Daily Math — 2026-09-18

[Easy] Counting Apples

• EN: Léa has 7 apples. She picks 5 more. How many apples does she have in all?
• FR: Léa a 7 pommes. Elle en cueille 5 de plus. Combien de pommes a-t-elle en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add two numbers, count on from the bigger one (e.g., 6 + 3: start at 6, count 3 more → 9).
• Steps:
  • Start at 7.
  • Count on 5 more: 8, 9, 10, 11, 12.
  • So Léa has 12 apples.
• Answer: 12

[Easy] Counting by 5s

• EN: Skip count by 5s. Fill in the blank: 5, 10, 15, ___, 25.
• FR: Compte par bonds de 5. Complète le blanc: 5, 10, 15, ___, 25.
• Choices: A) 18 B) 19 C) 20 D) 21
• Hint: When you skip count by 5s, add 5 each time (e.g., 10, 15, 20 → each jump is +5).
• Steps:
  • The pattern adds 5 each time.
  • 15 + 5 = 20.
  • So the missing number is 20.
• Answer: 20

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand: 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 13
• Hint: The number with more tens is usually greater (e.g., 12 has 1 ten, 8 has 0 tens, so 12 is greater).
• Steps:
  • 14 has 1 ten and 4 ones.
  • 9 has 0 tens and 9 ones.
  • 1 ten is more than 0 tens, so 14 is greater.
• Answer: 14

[Easy] Coin Recognition

• EN: Mia has one dime. How many cents does she have?
• FR: Mia a une pièce de dix cents. Combien de sous a-t-elle?
• Choices: A) 1 cent B) 5 cents C) 10 cents D) 25 cents
• Hint: Remember: a penny = 1¢, a nickel = 5¢, a dime = 10¢.
• Steps:
  • A dime is worth 10 cents.
  • Mia has one dime.
  • So she has 10 cents.
• Answer: 10 cents

[Medium] Subtraction Story

• EN: There are 15 students on the playground. 6 go inside. How many students are left outside?
• FR: Il y a 15 élèves dans la cour. 6 rentrent à l'intérieur. Combien d'élèves restent dehors?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: To subtract, count back from the bigger number (e.g., 12 − 4: start at 12, count back 4 → 8).
• Steps:
  • Start at 15.
  • Count back 6: 14, 13, 12, 11, 10, 9.
  • So 9 students are left outside.
• Answer: 9

[Medium] Skip Counting by 2s

• EN: Skip count by 2s. What comes next: 10, 12, 14, ___?
• FR: Compte par bonds de 2. Quel nombre vient après: 10, 12, 14, ___?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: When you skip count by 2s, add 2 each time (e.g., 6, 8, 10 → each jump is +2).
• Steps:
  • The pattern adds 2 each time.
  • 14 + 2 = 16.
  • So the next number is 16.
• Answer: 16

[Medium] Adding Three Numbers

• EN: Noah has 3 red stickers, 4 blue stickers, and 2 yellow stickers. How many stickers does he have altogether?
• FR: Noah a 3 autocollants rouges, 4 bleus et 2 jaunes. Combien d'autocollants a-t-il en tout?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Add all three numbers one step at a time (e.g., 2 + 3 + 4: first 2 + 3 = 5, then 5 + 4 = 9).
• Steps:
  • Add the first two: 3 + 4 = 7.
  • Add the third: 7 + 2 = 9.
  • So Noah has 9 stickers.
• Answer: 9

[Medium] Counting to 100

• EN: What number comes just before 100?
• FR: Quel nombre vient juste avant 100?
• Choices: A) 90 B) 98 C) 99 D) 101
• Hint: "Just before" means one less (e.g., the number just before 50 is 49).
• Steps:
  • One less than 100 is 99.
  • Count: …98, 99, 100.
  • So the number just before 100 is 99.
• Answer: 99

[Hard] Two-Step Addition

• EN: There are 8 books on a shelf. Priya adds 5 more books, then takes away 4. How many books are on the shelf now?
• FR: Il y a 8 livres sur une étagère. Priya en ajoute 5, puis en enlève 4. Combien de livres y a-t-il maintenant?
• Choices: A) 7 B) 8 C) 9 D) 13
• Hint: Do the problem in two steps (e.g., 6 + 3 = 9, then 9 − 2 = 7).
• Steps:
  • Start with 8 books.
  • Add 5: 8 + 5 = 13.
  • Subtract 4: 13 − 4 = 9.
  • So there are 9 books on the shelf.
• Answer: 9

[Hard] Skip Counting by 10s

• EN: Skip count by 10s starting at 20. What is the 5th number in the pattern?
• FR: Compte par bonds de 10 en commençant à 20. Quel est le 5e nombre dans la suite?
• Choices: A) 50 B) 60 C) 70 D) 80
• Hint: When skip counting by 10s from a starting number, multiply the jump count by 10 and add the start (e.g., starting at 30, the 3rd number is 30, 40, 50 → the 3rd is 50).
• Steps:
  • Start at 20. That is the 1st number.
  • 2nd: 30, 3rd: 40, 4th: 50, 5th: 60.
  • So the 5th number is 60.
• Answer: 60

[Easy] Addition Within 100

• EN: What is 34 + 25?
• FR: Combien font 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 → 37).
• Steps:
  • Ones: 4 + 5 = 9.
  • Tens: 3 + 2 = 5.
  • So 34 + 25 = 59.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows 7 o'clock. What time is it?
• FR: L'horloge montre 7 heures. Quelle heure est-il?
• Choices: A) 6:00 B) 7:00 C) 7:30 D) 8:00
• Hint: When the minute hand points to 12 and the hour hand points to a number, it is exactly that hour (e.g., hour hand on 3 → 3:00).
• Steps:
  • The hour hand points to 7.
  • The minute hand points to 12 (o'clock means exactly on the hour).
  • So the time is 7:00.
• Answer: 7:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long and an eraser is 3 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 15 cm et une gomme mesure 3 cm. De combien le crayon est-il plus long?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 18 cm
• Hint: "How much longer" means subtract (e.g., a ruler is 30 cm, a stick is 10 cm → 30 − 10 = 20 cm longer).
• Steps:
  • Subtract: 15 − 3 = 12.
  • The pencil is 12 cm longer than the eraser.
• Answer: 12 cm

[Easy] Counting Coins

• EN: Amir has 2 dimes and 1 nickel. How much money does he have?
• FR: Amir a 2 pièces de dix cents et 1 pièce de cinq cents. Combien d'argent a-t-il?
• Choices: A) 20 cents B) 23 cents C) 25 cents D) 30 cents
• Hint: Count each coin's value: dime = 10¢, nickel = 5¢ (e.g., 1 dime + 2 nickels = 10 + 5 + 5 = 20¢).
• Steps:
  • 2 dimes: 10 + 10 = 20 cents.
  • 1 nickel: 5 cents.
  • Total: 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtraction Within 100

• EN: There are 72 seats in the gym. 38 are filled. How many seats are empty?
• FR: Il y a 72 sièges dans le gymnase. 38 sont occupés. Combien de sièges sont vides?
• Choices: A) 33 B) 34 C) 35 D) 36
• Hint: To subtract with borrowing, break the top number apart (e.g., 53 − 27: borrow from tens → 13 − 7 = 6 ones, 4 − 2 = 2 tens → 26).
• Steps:
  • Ones: 2 − 8, need to borrow. 12 − 8 = 4.
  • Tens: 6 − 3 (after borrowing) = 3.
  • So 72 − 38 = 34.
• Answer: 34

[Medium] Telling Time — Half Hour

• EN: Sam starts reading at 2:00 and reads for half an hour. What time does he finish?
• FR: Sam commence à lire à 2 h et lit pendant une demi-heure. À quelle heure finit-il?
• Choices: A) 2:15 B) 2:30 C) 3:00 D) 3:30
• Hint: Half an hour is 30 minutes, so add 30 minutes to the start time (e.g., 4:00 + 30 min = 4:30).
• Steps:
  • Start time: 2:00.
  • Add 30 minutes: 2:00 + 30 minutes = 2:30.
  • So Sam finishes at 2:30.
• Answer: 2:30

[Medium] Simple Patterns

• EN: What comes next in the pattern: 2, 4, 6, 8, ___?
• FR: Quel nombre vient ensuite dans la suite: 2, 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Find the rule by subtracting one term from the next (e.g., 3, 6, 9 → add 3 each time).
• Steps:
  • Each number increases by 2.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Medium] Counting Coins to $1

• EN: Chloe has 3 quarters. How many cents does she have?
• FR: Chloe a 3 pièces de vingt-cinq cents. Combien de sous a-t-elle?
• Choices: A) 60 cents B) 70 cents C) 75 cents D) 80 cents
• Hint: A quarter is worth 25 cents. Multiply or skip count by 25 (e.g., 2 quarters: 25 + 25 = 50 cents).
• Steps:
  • Each quarter = 25 cents.
  • 3 × 25: 25 + 25 = 50, then 50 + 25 = 75.
  • So Chloe has 75 cents.
• Answer: 75 cents

[Hard] Two-Step Problem

• EN: Ben has 45 hockey cards. He gives 12 to his friend and then buys 20 more. How many cards does Ben have now?
• FR: Ben a 45 cartes de hockey. Il en donne 12 à son ami, puis en achète 20 autres. Combien de cartes Ben a-t-il maintenant?
• Choices: A) 51 B) 53 C) 57 D) 77
• Hint: Solve in two steps: subtract first, then add (e.g., 30 − 5 = 25, then 25 + 10 = 35).
• Steps:
  • After giving away 12: 45 − 12 = 33.
  • After buying 20 more: 33 + 20 = 53.
  • So Ben has 53 cards.
• Answer: 53

[Hard] Measuring and Comparing

• EN: A green ribbon is 48 cm long. A blue ribbon is 19 cm long. What is the total length of both ribbons?
• FR: Un ruban vert mesure 48 cm. Un ruban bleu mesure 19 cm. Quelle est la longueur totale des deux rubans?
• Choices: A) 57 cm B) 65 cm C) 67 cm D) 68 cm
• Hint: Add the lengths together, being careful to regroup ones if needed (e.g., 36 cm + 25 cm: 6 + 5 = 11, write 1 carry 1; 3 + 2 + 1 = 6 → 61 cm).
• Steps:
  • Add ones: 8 + 9 = 17, write 7, carry 1.
  • Add tens: 4 + 1 + 1 (carried) = 6.
  • So 48 + 19 = 67 cm.
• Answer: 67 cm

[Easy] Multiplication by 2

• EN: What is 6 × 2?
• FR: Combien font 6 × 2?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiplying by 2 is the same as doubling (e.g., 5 × 2 = 5 + 5 = 10).
• Steps:
  • 6 × 2 means 6 added twice: 6 + 6 = 12.
  • So 6 × 2 = 12.
• Answer: 12

[Easy] Basic Division

• EN: Share 20 stickers equally among 4 friends. How many stickers does each friend get?
• FR: Partage 20 autocollants également entre 4 amis. Combien chaque ami reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Division is the opposite of multiplication (e.g., 15 ÷ 3 → think 3 × ? = 15 → 5).
• Steps:
  • 20 ÷ 4 = ?
  • Think: 4 × 5 = 20.
  • So each friend gets 5 stickers.
• Answer: 5

[Easy] Fractions

• EN: A pizza is cut into 4 equal pieces. Tariq eats 1 piece. What fraction of the pizza did he eat?
• FR: Une pizza est coupée en 4 parts égales. Tariq mange 1 part. Quelle fraction de la pizza a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: A fraction is written as (parts eaten) ÷ (total equal parts). If you eat 1 of 3 equal pieces, you ate 1/3.
• Steps:
  • Total pieces: 4. Pieces eaten: 1.
  • Fraction = 1/4.
  • Tariq ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Reading a Graph

• EN: A bar graph shows that 8 students like hockey and 5 students like soccer. How many more students like hockey than soccer?
• FR: Un diagramme à barres montre que 8 élèves aiment le hockey et 5 aiment le soccer. Combien d'élèves de plus aiment le hockey?
• Choices: A) 2 B) 3 C) 4 D) 13
• Hint: "How many more" means subtract the smaller bar from the larger bar (e.g., 9 − 4 = 5 more).
• Steps:
  • Hockey: 8 students. Soccer: 5 students.
  • Difference: 8 − 5 = 3.
  • So 3 more students like hockey.
• Answer: 3

[Medium] Multiplication by 5

• EN: A hockey team has 5 players on the ice. There are 7 teams in the tournament. How many players are on the ice in all?
• FR: Une équipe de hockey a 5 joueurs sur la glace. Il y a 7 équipes dans le tournoi. Combien de joueurs y a-t-il en tout sur la glace?
• Choices: A) 30 B) 32 C) 35 D) 40
• Hint: Multiply the number of groups by the number in each group (e.g., 5 teams × 4 players = 20 players).
• Steps:
  • 7 teams × 5 players each = 7 × 5.
  • 7 × 5 = 35.
  • So there are 35 players on the ice in all.
• Answer: 35

[Medium] Perimeter

• EN: A rectangular garden is 6 m long and 4 m wide. What is its perimeter?
• FR: Un jardin rectangulaire a 6 m de long et 4 m de large. Quel est son périmètre?
• Choices: A) 10 m B) 20 m C) 24 m D) 28 m
• Hint: Perimeter of a rectangle = length + width + length + width (e.g., 3 m × 2 m: 3 + 2 + 3 + 2 = 10 m).
• Steps:
  • Add all four sides: 6 + 4 + 6 + 4 = 20.
  • The perimeter is 20 m.
• Answer: 20 m

[Medium] Multiplication by 3

• EN: Each box holds 3 muffins. If there are 8 boxes, how many muffins are there in total?
• FR: Chaque boîte contient 3 muffins. S'il y a 8 boîtes, combien de muffins y a-t-il en tout?
• Choices: A) 11 B) 21 C) 24 D) 27
• Hint: Multiply the number of boxes by the number of items in each box (e.g., 4 boxes × 3 muffins = 12 muffins).
• Steps:
  • 8 × 3 = ?
  • 8 × 3 = 24.
  • So there are 24 muffins in total.
• Answer: 24

[Medium] Comparing Fractions

• EN: Which fraction is greater: 1/2 or 1/4?
• FR: Quelle fraction est plus grande: 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/4
• Hint: When the top number (numerator) is the same, the fraction with the smaller bottom number (denominator) is larger (e.g., 1/2 vs. 1/3 → 1/2 is larger because halves are bigger pieces).
• Steps:
  • Both fractions have 1 on top.
  • 2 is smaller than 4, so each half is bigger than each quarter.
  • So 1/2 is greater.
• Answer: 1/2

[Hard] Multi-Step Multiplication

• EN: A school bakes 9 trays of cookies. Each tray has 10 cookies. The principal gives 15 cookies to the office staff. How many cookies are left?
• FR: L'école fait cuire 9 plateaux de biscuits. Chaque plateau contient 10 biscuits. La directrice donne 15 biscuits au personnel. Combien de biscuits reste-t-il?
• Choices: A) 70 B) 75 C) 80 D) 85
• Hint: Find the total first (multiply), then subtract (e.g., 4 trays × 5 cookies = 20, then 20 − 3 = 17).
• Steps:
  • Total cookies: 9 × 10 = 90.
  • Subtract: 90 − 15 = 75.
  • So 75 cookies are left.
• Answer: 75

[Hard] Fractions of a Group

• EN: There are 12 students in a group. One-third of them are wearing red shirts. How many students are wearing red shirts?
• FR: Il y a 12 élèves dans un groupe. Un tiers d'entre eux portent des chemises rouges. Combien portent des chemises rouges?
• Choices: A) 3 B) 4 C) 6 D) 9
• Hint: To find a fraction of a group, divide the total by the denominator (e.g., 1/4 of 16: 16 ÷ 4 = 4).
• Steps:
  • 1/3 of 12 means divide 12 by 3.
  • 12 ÷ 3 = 4.
  • So 4 students are wearing red shirts.
• Answer: 4

[Easy] Multiplication Tables

• EN: What is 8 × 7?
• FR: Combien font 8 × 7?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: You can break it apart: 8 × 7 = 8 × 5 + 8 × 2 (e.g., try 6 × 7 = 6 × 5 + 6 × 2 = 30 + 12 = 42).
• Steps:
  • 8 × 7: use the times table.
  • 8 × 5 = 40, 8 × 2 = 16, so 8 × 7 = 56.
  • So 8 × 7 = 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) 4 C) 7 D) 47
• Hint: Place values after the decimal: tenths (1st), hundredths (2nd) (e.g., in 5.82, the tenths digit is 8).
• Steps:
  • 3.47: the digits after the decimal point are 4 (tenths) and 7 (hundredths).
  • The tenths digit is 4.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A classroom rug is 5 m long and 3 m wide. What is the area of the rug?
• FR: Un tapis de classe a 5 m de long et 3 m de large. Quelle est l'aire du tapis?
• Choices: A) 8 m² B) 12 m² C) 15 m² D) 16 m²
• Hint: Area of a rectangle = length × width (e.g., a rug 4 m × 2 m has area 4 × 2 = 8 m²).
• Steps:
  • Area = 5 × 3 = 15.
  • The area of the rug is 15 m².
• Answer: 15 m²

[Easy] Comparing Fractions

• EN: Which fraction is smaller: 3/4 or 2/4?
• FR: Quelle fraction est plus petite: 3/4 ou 2/4?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) 4/4
• Hint: When denominators are the same, compare the numerators — a smaller numerator means a smaller fraction (e.g., 2/5 < 4/5 because 2 < 4).
• Steps:
  • Both fractions have 4 as the denominator.
  • Compare numerators: 2 < 3.
  • So 2/4 is smaller.
• Answer: 2/4

[Medium] Long Division with Remainders

• EN: What is 47 ÷ 5?
• FR: Combien font 47 ÷ 5?
• Choices: A) 8 remainder 7 B) 9 remainder 2 C) 9 remainder 3 D) 10 remainder 2
• Hint: Divide, then multiply back to find the remainder (e.g., 23 ÷ 4: 4 × 5 = 20, remainder = 23 − 20 = 3 → 5 remainder 3).
• Steps:
  • 5 × 9 = 45, which is close to 47.
  • Remainder: 47 − 45 = 2.
  • So 47 ÷ 5 = 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 PM and ends at 3:45 PM. How long is the game?
• FR: Une partie de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps dure la partie?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: Count the hours first, then the minutes (e.g., 2:10 to 4:40 → 2 hours + 30 minutes = 2 hours 30 minutes).
• Steps:
  • From 1:15 to 3:15 is exactly 2 hours.
  • From 3:15 to 3:45 is 30 minutes.
  • Total: 2 hours + 30 minutes = 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: Lena buys a notebook for $2.45 and a pen for $1.30. How much does she spend in total?
• FR: Léna achète un cahier à 2,45 $ et un stylo à 1,30 $. Combien dépense-t-elle en tout?
• Choices: A) $3.55 B) $3.65 C) $3.75 D) $4.75
• Hint: Line up the decimal points and add (e.g., $3.20 + $1.15: 20 + 15 = 35 cents, 3 + 1 = 4 dollars → $4.35).
• Steps:
  • $2.45 + $1.30: cents 45 + 30 = 75, dollars 2 + 1 = 3.
  • Total = $3.75.
• Answer: $3.75

[Medium] Multi-Digit Multiplication

• EN: A box holds 24 crayons. There are 4 boxes. How many crayons are there altogether?
• FR: Une boîte contient 24 crayons. Il y a 4 boîtes. Combien de crayons y a-t-il en tout?
• Choices: A) 84 B) 88 C) 92 D) 96
• Hint: Multiply each digit separately, then add (e.g., 13 × 4: 3 × 4 = 12, write 2 carry 1; 1 × 4 + 1 = 5 → 52).
• Steps:
  • 24 × 4: ones 4 × 4 = 16, write 6 carry 1.
  • Tens: 2 × 4 = 8, plus 1 carried = 9.
  • So 24 × 4 = 96.
• Answer: 96

[Hard] Long Division — Two-Step

• EN: A teacher has 95 stickers to give equally to 5 classes. How many stickers does each class get, and how many are left over?
• FR: Une enseignante a 95 autocollants à distribuer également à 5 classes. Combien chaque classe reçoit-elle, et combien en reste-t-il?
• Choices: A) 18 remainder 5 B) 19 remainder 0 C) 20 remainder 5 D) 21 remainder 0
• Hint: Divide digit by digit from left to right (e.g., 76 ÷ 4: 7 ÷ 4 = 1 remainder 3; bring down 6 → 36 ÷ 4 = 9 → answer 19).
• Steps:
  • 9 ÷ 5 = 1 remainder 4. Bring down 5 → 45.
  • 45 ÷ 5 = 9 remainder 0.
  • So 95 ÷ 5 = 19 remainder 0.
• Answer: 19 remainder 0

[Hard] Fraction and Decimal Connection

• EN: Which decimal is equal to 3/4?
• FR: Quel nombre décimal est égal à 3/4?
• Choices: A) 0.34 B) 0.57 C) 0.75 D) 1.33
• Hint: Divide the numerator by the denominator to convert a fraction to a decimal (e.g., 1/2: 1 ÷ 2 = 0.5).
• Steps:
  • 3/4 means 3 ÷ 4.
  • 4 goes into 3.00: 4 × 7 = 28, so first decimal digit is 7; remainder 2 → 20 ÷ 4 = 5.
  • So 3/4 = 0.75.
• Answer: 0.75

[Easy] Multi-Digit Multiplication

• EN: What is 36 × 12?
• FR: Combien font 36 × 12?
• Choices: A) 362 B) 382 C) 412 D) 432
• Hint: Break 12 into 10 + 2, multiply each, then add (e.g., 25 × 12 = 25 × 10 + 25 × 2 = 250 + 50 = 300).
• Steps:
  • 36 × 10 = 360.
  • 36 × 2 = 72.
  • 360 + 72 = 432.
• Answer: 432

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/8 + 3/8?
• FR: Combien font 2/8 + 3/8?
• Choices: A) 5/8 B) 5/16 C) 6/8 D) 1/2
• Hint: When denominators are the same, add only the numerators and keep the denominator (e.g., 1/5 + 3/5 = 4/5).
• Steps:
  • Denominators are the same (8), so add numerators: 2 + 3 = 5.
  • Keep the denominator: 5/8.
  • So 2/8 + 3/8 = 5/8.
• Answer: 5/8

[Easy] Percentage — 50%

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

[Easy] Decimal Addition

• EN: What is 4.6 + 2.3?
• FR: Combien font 4,6 + 2,3?
• Choices: A) 6.7 B) 6.8 C) 6.9 D) 7.1
• Hint: Line up decimal points and add each column (e.g., 3.2 + 1.5: tenths 2 + 5 = 7, ones 3 + 1 = 4 → 4.7).
• Steps:
  • Tenths: 6 + 3 = 9.
  • Ones: 4 + 2 = 6.
  • So 4.6 + 2.3 = 6.9.
• Answer: 6.9

[Medium] Multi-Digit Division

• EN: A school orders 252 juice boxes to be split equally among 6 classes. How many juice boxes does each class get?
• FR: Une école commande 252 boîtes de jus à répartir également entre 6 classes. Combien chaque classe reçoit-elle de boîtes de jus?
• Choices: A) 38 B) 40 C) 42 D) 46
• Hint: Use long division: divide from left to right (e.g., 168 ÷ 6: 6 goes into 16 twice (12), remainder 4; bring down 8 → 48 ÷ 6 = 8 → 28).
• Steps:
  • 25 ÷ 6 = 4 remainder 1. Bring down 2 → 12.
  • 12 ÷ 6 = 2.
  • So 252 ÷ 6 = 42.
• Answer: 42

[Medium] Subtracting Fractions

• EN: What is 7/10 − 3/10?
• FR: Combien font 7/10 − 3/10?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: When denominators match, subtract numerators and keep the denominator (e.g., 5/7 − 2/7 = 3/7).
• Steps:
  • Subtract numerators: 7 − 3 = 4.
  • Keep the denominator: 4/10.
  • So 7/10 − 3/10 = 4/10.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A fish tank is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Un aquarium a 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 120 cm³
• Hint: Volume of a rectangular prism = length × width × height (e.g., 2 × 3 × 4 = 24 cm³).
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • So the volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25% and 10%

• EN: A Tim Hortons muffin costs $2.00. If there is a 25% discount, how much is the discount?
• FR: Un muffin de Tim Hortons coûte 2,00 $. S'il y a un rabais de 25%, quel est le montant du rabais?
• Choices: A) $0.25 B) $0.40 C) $0.50 D) $0.75
• Hint: 25% is one quarter of the amount; divide by 4 (e.g., 25% of $4.00 = $4.00 ÷ 4 = $1.00).
• Steps:
  • 25% of $2.00 = $2.00 ÷ 4 = $0.50.
  • The discount is $0.50.
• Answer: $0.50

[Hard] Multi-Step Decimal Problem

• EN: Maya buys 3 notebooks at $2.75 each and pays with a $10.00 bill. How much change does she receive?
• FR: Maya achète 3 cahiers à 2,75 $ chacun et paie avec un billet de 10,00 $. Combien de monnaie reçoit-elle?
• Choices: A) $1.75 B) $2.25 C) $2.75 D) $7.25
• Hint: Multiply the price by quantity, then subtract from what was paid (e.g., 2 items at $3.50 each paid with $10: 2 × $3.50 = $7.00; $10.00 − $7.00 = $3.00 change).
• Steps:
  • Cost: 3 × $2.75 = $8.25.
  • Change: $10.00 − $8.25 = $1.75.
  • So Maya receives $1.75 in change.
• Answer: $1.75

[Hard] Fraction and Decimal Connection — Multi-Step

• EN: A recipe uses 3/4 cup of sugar and 1/4 cup of brown sugar. What is the total amount of sugar, written as a decimal?
• FR: Une recette utilise 3/4 de tasse de sucre et 1/4 de tasse de cassonade. Quelle est la quantité totale de sucre, écrite en décimal?
• Choices: A) 0.75 B) 0.80 C) 1.00 D) 1.25
• Hint: Add the fractions first, then convert to a decimal (e.g., 1/4 + 2/4 = 3/4; 3 ÷ 4 = 0.75).
• Steps:
  • 3/4 + 1/4 = 4/4 = 1 whole cup.
  • 1 whole = 1.00.
  • So the total is 1.00 cup of sugar.
• Answer: 1.00

[Easy] Fraction Multiplication

• EN: What is 1/2 × 4/5?
• FR: Combien font 1/2 × 4/5?
• Choices: A) 2/5 B) 4/10 C) 5/10 D) 2/7
• Hint: Multiply numerators together and denominators together (e.g., 2/3 × 1/4 = 2/12 = 1/6).
• Steps:
  • Numerators: 1 × 4 = 4.
  • Denominators: 2 × 5 = 10.
  • So 1/2 × 4/5 = 4/10.
• Answer: 4/10

[Easy] Percent of a Number

• EN: What is 30% of 60?
• FR: Combien représente 30% de 60?
• Choices: A) 12 B) 16 C) 18 D) 20
• Hint: Change the percent to a decimal, then multiply (e.g., 20% of 50 = 0.20 × 50 = 10).
• Steps:
  • 30% = 0.30.
  • 0.30 × 60 = 18.
  • So 30% of 60 is 18.
• Answer: 18

[Easy] Ratio

• EN: In a class, the ratio of boys to girls is 3:5. If there are 15 boys, how many girls are there?
• FR: Dans une classe, le rapport garçons:filles est 3:5. S'il y a 15 garçons, combien y a-t-il de filles?
• Choices: A) 20 B) 25 C) 30 D) 45
• Hint: Find the scale factor, then multiply (e.g., ratio 2:3, and there are 8 items for "2" → scale factor is 4 → "3" side has 12).
• Steps:
  • 3 parts = 15 boys → 1 part = 5.
  • Girls: 5 parts × 5 = 25.
  • So there are 25 girls.
• Answer: 25

[Easy] Integers Introduction

• EN: The temperature in Winnipeg is −5°C in the morning and rises 8 degrees by noon. What is the noon temperature?
• FR: La température à Winnipeg est de −5°C le matin et monte de 8 degrés à midi. Quelle est la température à midi?
• Choices: A) −3°C B) 2°C C) 3°C D) 13°C
• Hint: Adding a positive number to a negative number: move right on the number line (e.g., −4 + 6 = 2).
• Steps:
  • −5 + 8 = 3.
  • The noon temperature is 3°C.
• Answer: 3°C

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1.
• FR: Calcule: 3 + 4 × 2 − 1.
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: BEDMAS: do multiplication before addition and subtraction (e.g., 5 + 2 × 3 = 5 + 6 = 11, not 7 × 3 = 21).
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Now: 3 + 8 − 1 = 11 − 1 = 10.
  • So the answer is 10.
• Answer: 10

[Medium] Fraction Division

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

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km par heure?
• Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: Rate = total amount ÷ number of units (e.g., 150 km in 2 hours: 150 ÷ 2 = 75 km/h).
• Steps:
  • Speed = 240 km ÷ 3 hours = 80 km/h.
  • The car travels at 80 km/h.
• Answer: 80 km/h

[Medium] Simple Algebraic Expressions

• EN: Evaluate the expression 5n − 3 when n = 4.
• FR: Évalue l'expression 5n − 3 quand n = 4.
• Choices: A) 15 B) 17 C) 20 D) 22
• Hint: Substitute the value in for the variable, then follow BEDMAS (e.g., 3x + 2 when x = 5: 3 × 5 + 2 = 15 + 2 = 17).
• Steps:
  • Substitute n = 4: 5 × 4 − 3.
  • 5 × 4 = 20. Then 20 − 3 = 17.
  • So 5n − 3 = 17 when n = 4.
• Answer: 17

[Hard] Multi-Step Percent

• EN: A jacket costs $120. It is on sale for 15% off. What is the sale price of the jacket?
• FR: Un manteau coûte 120 $. Il est soldé à 15% de rabais. Quel est le prix de vente du manteau?
• Choices: A) $18 B) $96 C) $102 D) $108
• Hint: Find the discount first, then subtract from the original price (e.g., 10% off $80 = $8 off → sale price = $72).
• Steps:
  • 15% of $120 = 0.15 × 120 = $18.
  • Sale price: $120 − $18 = $102.
  • The sale price is $102.
• Answer: $102

[Hard] Order of Operations — Complex

• EN: Evaluate: (12 − 4)² ÷ 4 + 3 × 2.
• FR: Calcule: (12 − 4)² ÷ 4 + 3 × 2.
• Choices: A) 20 B) 22 C) 24 D) 28
• Hint: BEDMAS order: Brackets, Exponents, Division/Multiplication (left to right), Addition/Subtraction (e.g., (3 + 1)² ÷ 2 = 16 ÷ 2 = 8).
• Steps:
  • Brackets: 12 − 4 = 8.
  • Exponent: 8² = 64.
  • Division: 64 ÷ 4 = 16.
  • Multiplication: 3 × 2 = 6.
  • Addition: 16 + 6 = 22.
• Answer: 22

[Easy] Integer Addition

• EN: What is (−8) + 5?
• FR: Combien font (−8) + 5?
• Choices: A) −13 B) −4 C) −3 D) 3
• Hint: On a number line, start at the negative number and move right for positive (e.g., −6 + 4: start at −6, move 4 right → −2).
• Steps:
  • Start at −8 on the number line.
  • Move 5 steps to the right: −8, −7, −6, −5, −4, −3.
  • So (−8) + 5 = −3.
• Answer: −3

[Easy] Integer Subtraction

• EN: What is 4 − (−6)?
• FR: Combien font 4 − (−6)?
• Choices: A) −2 B) 2 C) 8 D) 10
• Hint: Subtracting a negative is the same as adding a positive (e.g., 3 − (−5) = 3 + 5 = 8).
• Steps:
  • 4 − (−6) = 4 + 6 = 10.
  • So 4 − (−6) = 10.
• Answer: 10

[Easy] Percent Discount

• EN: A pair of skates costs $80. There is a 10% discount. How much money do you save?
• FR: Une paire de patins coûte 80 $. Il y a un rabais de 10%. Combien d'argent économises-tu?
• Choices: A) $6 B) $7 C) $8 D) $10
• Hint: 10% of a number = divide by 10 (e.g., 10% of $50 = $50 ÷ 10 = $5).
• Steps:
  • 10% of $80 = $80 ÷ 10 = $8.
  • You save $8.
• Answer: $8

[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: To isolate x, subtract the same number from both sides (e.g., x + 4 = 11 → x = 11 − 4 = 7).
• Steps:
  • x + 9 = 15.
  • Subtract 9 from both sides: x = 15 − 9 = 6.
  • So x = 6.
• Answer: x = 6

[Medium] Integer Multiplication

• EN: What is (−4) × (−7)?
• FR: Combien font (−4) × (−7)?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: A negative times a negative is positive (e.g., (−3) × (−5) = 15).
• Steps:
  • Multiply the values: 4 × 7 = 28.
  • Both numbers are negative, so the product is positive.
  • So (−4) × (−7) = 28.
• Answer: 28

[Medium] Tip Calculation

• EN: A family eats at a restaurant in Ottawa. The bill is $60. They leave a 15% tip. How much is the tip?
• FR: Une famille dîne dans un restaurant à Ottawa. La facture est de 60 $. Ils laissent un pourboire de 15%. Quel est le montant du pourboire?
• Choices: A) $7.50 B) $8.00 C) $9.00 D) $10.50
• Hint: Find 10%, then add half of that for 15% (e.g., 15% of $40: 10% = $4, half = $2, total = $6).
• Steps:
  • 10% of $60 = $6.
  • 5% = $6 ÷ 2 = $3.
  • 15% tip = $6 + $3 = $9.00.
• Answer: $9.00

[Medium] Surface Area

• EN: A rectangular box is 4 cm long, 3 cm wide, and 2 cm tall. What is the total surface area?
• FR: Une boîte rectangulaire a 4 cm de long, 3 cm de large et 2 cm de haut. Quelle est l'aire totale de sa surface?
• Choices: A) 24 cm² B) 40 cm² C) 48 cm² D) 52 cm²
• Hint: Surface area = 2(lw + lh + wh) (e.g., box 2 × 3 × 4: 2(6 + 8 + 12) = 2 × 26 = 52 cm²).
• Steps:
  • lw = 4 × 3 = 12, lh = 4 × 2 = 8, wh = 3 × 2 = 6.
  • Total = 2(12 + 8 + 6) = 2 × 26 = 52 cm².
  • The surface area is 52 cm².
• Answer: 52 cm²

[Medium] Probability

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

[Hard] Two-Step Integer Problem

• EN: The temperature in Churchill, Manitoba is −12°C. It drops 7 degrees, then rises 4 degrees. What is the final temperature?
• FR: La température à Churchill, Manitoba est de −12°C. Elle baisse de 7 degrés, puis monte de 4 degrés. Quelle est la température finale?
• Choices: A) −17°C B) −16°C C) −15°C D) −14°C
• Hint: Apply each change one step at a time (e.g., start −10, drop 5 → −15, rise 3 → −12).
• Steps:
  • Start: −12°C.
  • Drop 7: −12 − 7 = −19.
  • Rise 4: −19 + 4 = −15.
  • The final temperature is −15°C.
• Answer: −15°C

[Hard] Percent Increase

• EN: Last year, a school had 340 students. This year, there are 391 students. What is the percent increase in enrolment?
• FR: L'année dernière, une école avait 340 élèves. Cette année, il y en a 391. Quel est le pourcentage d'augmentation des inscriptions?
• Choices: A) 12% B) 13% C) 15% D) 17%
• Hint: Percent increase = (new − original) ÷ original × 100 (e.g., 60 to 72: (72 − 60) ÷ 60 × 100 = 12 ÷ 60 × 100 = 20%).
• Steps:
  • Increase: 391 − 340 = 51.
  • Percent: 51 ÷ 340 × 100 = 0.15 × 100 = 15%.
  • The enrolment increased by 15%.
• Answer: 15%

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: A perfect square's root is the number that, multiplied by itself, gives that value (e.g., √81 = 9 because 9 × 9 = 81).
• Steps:
  • Think: what number × itself = 144?
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Five students scored 70, 85, 90, 75, and 80 on a test. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 85, 90, 75 et 80 à un test. Quelle est la note moyenne?
• Choices: A) 78 B) 80 C) 82 D) 85
• Hint: Mean = sum of all values ÷ number of values (e.g., mean of 10, 20, 30 = 60 ÷ 3 = 20).
• Steps:
  • Sum: 70 + 85 + 90 + 75 + 80 = 400.
  • Mean: 400 ÷ 5 = 80.
  • So the mean score is 80.
• Answer: 80

[Easy] Percent Decrease

• EN: A video game was $60 and is now on sale for $45. What is the percent decrease?
• FR: Un jeu vidéo coûtait 60 $ et est maintenant à 45 $. Quel est le pourcentage de réduction?
• Choices: A) 15% B) 20% C) 25% D) 30%
• Hint: Percent decrease = (original − new) ÷ original × 100 (e.g., $80 to $64: (80 − 64) ÷ 80 × 100 = 20%).
• Steps:
  • Decrease: 60 − 45 = 15.
  • Percent: 15 ÷ 60 × 100 = 25%.
  • The percent decrease is 25%.
• Answer: 25%

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 4 = 14.
• FR: Résous pour x: 2x + 4 = 14.
• Choices: A) x = 4 B) x = 5 C) x = 7 D) x = 9
• Hint: Undo addition first, then division (e.g., 3x + 2 = 11 → subtract 2: 3x = 9 → divide by 3: x = 3).
• Steps:
  • Subtract 4: 2x = 14 − 4 = 10.
  • Divide by 2: x = 10 ÷ 2 = 5.
  • So x = 5.
• Answer: x = 5

[Medium] Pythagorean Theorem

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

[Medium] Slope Introduction

• EN: A line passes through the points (2, 3) and (6, 7). What is the slope of the line?
• FR: Une droite passe par les points (2, 3) et (6, 7). Quelle est la pente de la droite?
• Choices: A) 1/2 B) 1 C) 2 D) 4
• Hint: Slope = (rise) ÷ (run) = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., points (1, 2) and (3, 6): (6−2)÷(3−1) = 4÷2 = 2).
• Steps:
  • Rise: 7 − 3 = 4.
  • Run: 6 − 2 = 4.
  • Slope = 4 ÷ 4 = 1.
• Answer: 1

[Medium] Median

• EN: Find the median of the data set: 12, 7, 15, 9, 11.
• FR: Trouve la médiane de l'ensemble de données: 12, 7, 15, 9, 11.
• Choices: A) 7 B) 9 C) 11 D) 12
• Hint: Order the data from least to greatest, then find the middle value (e.g., for 3, 7, 9, 12, 15, the median is 9).
• Steps:
  • Order the data: 7, 9, 11, 12, 15.
  • The middle value (3rd of 5) is 11.
  • The median is 11.
• Answer: 11

[Medium] Two-Step Equation — Harder

• 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 − 3 = 13 → add 3: 4x = 16 → x = 4).
• Steps:
  • Add 7 to both sides: 3x = 14 + 7 = 21.
  • Divide by 3: x = 21 ÷ 3 = 7.
  • So x = 7.
• Answer: x = 7

[Hard] Pythagorean Theorem — Missing 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 une cathète de 5 m. Quelle est la longueur de l'autre cathète?
• Choices: A) 8 m B) 10 m C) 12 m D) 14 m
• Hint: Rearrange a² + b² = c² to find a missing leg: a² = c² − b² (e.g., hyp = 10, one leg = 6: a² = 100 − 36 = 64 → a = 8).
• Steps:
  • a² + 5² = 13².
  • a² = 169 − 25 = 144.
  • a = √144 = 12 m.
• Answer: 12 m

[Hard] Percent Increase — Multi-Step

• EN: A store buys a hockey stick for $80 and sells it at a 35% markup. What is the selling price?
• FR: Un magasin achète un bâton de hockey à 80 $ et le vend avec une majoration de 35%. Quel est le prix de vente?
• Choices: A) $100 B) $104 C) $108 D) $116
• Hint: Find the markup amount, then add it to the original cost (e.g., 20% markup on $50: 0.20 × 50 = $10; selling price = $60).
• Steps:
  • Markup: 35% of $80 = 0.35 × 80 = $28.
  • Selling price: $80 + $28 = $108.
  • The selling price is $108.
• Answer: $108

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 8 = 20.
• FR: Résous pour x: 4x − 8 = 20.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add first, then divide (e.g., 5x − 10 = 15 → add 10: 5x = 25 → x = 5).
• Steps:
  • Add 8: 4x = 28.
  • Divide by 4: x = 7.
  • So x = 7.
• Answer: x = 7

[Easy] Graphing Lines — Slope-Intercept

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

[Easy] Adding Polynomials

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

[Easy] Similar Triangles

• EN: Two triangles are similar. The shorter triangle has sides 3 cm and 5 cm. The longer triangle has a corresponding side of 9 cm. What is the length of the other corresponding side?
• FR: Deux triangles sont semblables. Le plus petit a des côtés de 3 cm et 5 cm. Le plus grand a un côté correspondant de 9 cm. Quelle est la longueur de l'autre côté correspondant?
• Choices: A) 12 cm B) 13 cm C) 15 cm D) 18 cm
• Hint: Similar triangles have proportional sides; find the scale factor first (e.g., sides 4 and 6 scale to 8: 8 ÷ 4 = 2, so partner side = 6 × 2 = 12).
• Steps:
  • Scale factor: 9 ÷ 3 = 3.
  • Other side: 5 × 3 = 15 cm.
  • So the corresponding side is 15 cm.
• Answer: 15 cm

[Medium] Linear Inequality

• EN: Solve and describe the solution: 2x + 3 > 11.
• FR: Résous et décris la solution: 2x + 3 > 11.
• Choices: A) x > 2 B) x > 3 C) x > 4 D) x > 7
• Hint: Solve like an equation, then keep the inequality sign (e.g., 3x + 1 > 10 → 3x > 9 → x > 3).
• Steps:
  • Subtract 3: 2x > 8.
  • Divide by 2: x > 4.
  • The solution is x > 4.
• Answer: x > 4

[Medium] Trigonometry — SOH

• EN: In a right triangle, the angle is 30°, the hypotenuse is 10 cm. What is the length of the side opposite the angle? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle est de 30°, et l'hypoténuse est de 10 cm. Quelle est la longueur du côté opposé à l'angle? (sin 30° = 0,5)
• Choices: A) 3 cm B) 4 cm C) 5 cm D) 8 cm
• Hint: sin(angle) = opposite ÷ hypotenuse → opposite = sin(angle) × hypotenuse (e.g., sin 45° × 8 cm = 0.707 × 8 ≈ 5.7 cm).
• Steps:
  • sin(30°) = opposite ÷ 10.
  • Opposite = 0.5 × 10 = 5 cm.
  • The opposite side is 5 cm.
• Answer: 5 cm

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x + 4).
• FR: Développe: 3x(2x + 4).
• Choices: A) 5x + 7 B) 6x + 12 C) 6x² + 12x D) 6x² + 4
• Hint: Distribute the term outside the brackets to each term inside (e.g., 2x(3x + 5) = 6x² + 10x).
• Steps:
  • 3x × 2x = 6x².
  • 3x × 4 = 12x.
  • So 3x(2x + 4) = 6x² + 12x.
• Answer: 6x² + 12x

[Medium] Statistics — Mean and Outlier

• EN: Six students ran 5 km, 6 km, 7 km, 5 km, 6 km, and 25 km. Which value is an outlier?
• FR: Six élèves ont couru 5 km, 6 km, 7 km, 5 km, 6 km et 25 km. Quelle valeur est une valeur aberrante?
• Choices: A) 5 km B) 6 km C) 7 km D) 25 km
• Hint: An outlier is a value that is far away from the rest of the data (e.g., in 3, 4, 5, 4, 30, the outlier is 30).
• Steps:
  • Most values cluster between 5 and 7.
  • 25 km is far from the rest.
  • So 25 km is the outlier.
• Answer: 25 km

[Hard] System of 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 + 8 → 2x = 6 → x = 3).
• Steps:
  • Set equal: 2x + 1 = −x + 7.
  • Add x: 3x + 1 = 7.
  • Subtract 1: 3x = 6 → x = 2.
• Answer: x = 2

[Hard] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 8 m and the hypotenuse is 10 m. What is the measure of the angle? (cos 36.87° ≈ 0.8)
• FR: Dans un triangle rectangle, le côté adjacent est de 8 m et l'hypoténuse est de 10 m. Quelle est la mesure de l'angle? (cos 36,87° ≈ 0,8)
• Choices: A) 30° B) 36.87° C) 45° D) 53.13°
• Hint: cos(θ) = adjacent ÷ hypotenuse → find the angle using cos⁻¹ (e.g., adj = 6, hyp = 10 → cos θ = 0.6 → θ = cos⁻¹(0.6)).
• Steps:
  • cos(θ) = 8 ÷ 10 = 0.8.
  • θ = cos⁻¹(0.8) ≈ 36.87°.
  • The angle is approximately 36.87°.
• Answer: 36.87°

[Easy] Factoring a Simple 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 + 4)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient (e.g., x² + 7x + 10 → 2 × 5 = 10, 2 + 5 = 7 → (x + 2)(x + 5)).
• Steps:
  • Need two numbers: product = 6, sum = 5.
  • 2 × 3 = 6 and 2 + 3 = 5. ✓
  • So x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Tangent

• EN: In a right triangle, the opposite side is 9 cm and the adjacent side is 12 cm. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé est de 9 cm et le côté adjacent est de 12 cm. Combien vaut tan(θ)?
• Choices: A) 3/5 B) 3/4 C) 4/3 D) 5/4
• Hint: tan(θ) = opposite ÷ adjacent (e.g., opposite = 7, adjacent = 14 → tan θ = 7/14 = 1/2).
• Steps:
  • tan(θ) = 9 ÷ 12 = 3/4.
  • So tan(θ) = 3/4.
• Answer: 3/4

[Easy] Systems of Equations — Substitution

• EN: Solve: y = x + 2 and 2x + y = 11. What is x?
• FR: Résous: y = x + 2 et 2x + y = 11. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Substitute the first equation into the second (e.g., y = x + 1; 3x + y = 13 → 3x + x + 1 = 13 → 4x = 12 → x = 3).
• Steps:
  • Substitute y = x + 2 into 2x + y = 11.
  • 2x + (x + 2) = 11 → 3x + 2 = 11 → 3x = 9 → x = 3.
  • So x = 3.
• Answer: x = 3

[Easy] Volume of a Cylinder

• EN: A cylindrical soup can has a radius of 4 cm and a height of 10 cm. What is its volume? Use π ≈ 3.14.
• FR: Une boîte de soupe cylindrique a un rayon de 4 cm et une hauteur de 10 cm. Quel est son volume? Utilise π ≈ 3,14.
• Choices: A) 125.6 cm³ B) 251.2 cm³ C) 401.9 cm³ D) 502.4 cm³
• Hint: V = πr²h (e.g., radius 3 cm, height 5 cm: V = 3.14 × 9 × 5 = 141.3 cm³).
• Steps:
  • V = π × r² × h = 3.14 × 16 × 10.
  • 3.14 × 16 = 50.24; 50.24 × 10 = 502.4.
  • The volume is 502.4 cm³.
• Answer: 502.4 cm³

[Medium] Completing the Square

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

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is its circumference? Use π ≈ 3.14.
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence? Utilise π ≈ 3,14.
• Choices: A) 21.98 cm B) 43.96 cm C) 87.92 cm D) 153.86 cm
• Hint: Circumference = πd (e.g., diameter = 10 cm: C = 3.14 × 10 = 31.4 cm).
• Steps:
  • C = π × d = 3.14 × 14 = 43.96 cm.
  • The circumference is 43.96 cm.
• Answer: 43.96 cm

[Medium] Quadratic Formula

• EN: Using the quadratic formula, solve x² − 5x + 6 = 0. What are the two solutions?
• FR: En utilisant la formule quadratique, résous x² − 5x + 6 = 0. Quelles sont les deux solutions?
• Choices: A) x = 2 and x = 3 B) x = −2 and x = −3 C) x = 1 and x = 6 D) x = 3 and x = 4
• Hint: Factor or use x = [−b ± √(b² − 4ac)] ÷ 2a (e.g., x² − 5x + 4 = 0 → (x−1)(x−4) = 0 → x = 1 or x = 4).
• Steps:
  • Factor: (x − 2)(x − 3) = 0.
  • x − 2 = 0 → x = 2; x − 3 = 0 → x = 3.
  • So x = 2 and x = 3.
• Answer: x = 2 and x = 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 3 cm and a slant height of 5 cm. What is its total surface area? Use π ≈ 3.14.
• FR: Un cône a un rayon de 3 cm et une hauteur oblique de 5 cm. Quelle est son aire totale? Utilise π ≈ 3,14.
• Choices: A) 37.68 cm² B) 47.10 cm² C) 56.52 cm² D) 75.36 cm²
• Hint: Surface area of cone = πr² + πrl (base + lateral) (e.g., r = 2, l = 4: SA = 3.14 × 4 + 3.14 × 2 × 4 = 12.56 + 25.12 = 37.68 cm²).
• Steps:
  • Base: π × 3² = 3.14 × 9 = 28.26 cm².
  • Lateral: π × 3 × 5 = 3.14 × 15 = 47.10 cm².
  • Total: 28.26 + 47.10 = 75.36 cm².
• Answer: 75.36 cm²

[Hard] Completing the Square — Vertex Form

• EN: Write y = x² + 8x + 7 in vertex form. What is the vertex?
• FR: Écris y = x² + 8x + 7 sous forme canonique. Quel est le sommet?
• Choices: A) (−4, −9) B) (4, 9) C) (−8, 7) D) (−4, 9)
• Hint: Complete the square: take half the x-coefficient, square it, add/subtract inside the equation (e.g., x² + 6x + 2 → (x + 3)² − 9 + 2 → vertex (−3, −7)).
• Steps:
  • Half of 8 is 4; 4² = 16.
  • y = (x² + 8x + 16) − 16 + 7 = (x + 4)² − 9.
  • Vertex form: y = (x + 4)² − 9 → vertex is (−4, −9).
• Answer: (−4, −9)

[Hard] Systems of Equations — Elimination

• EN: Solve the system using elimination: 2x + 3y = 12 and 4x − 3y = 6. What is the value of x?
• FR: Résous le système par addition: 2x + 3y = 12 et 4x − 3y = 6. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Add the equations to eliminate one variable when coefficients are opposites (e.g., 3x + y = 10 and x − y = 2: add → 4x = 12 → x = 3).
• Steps:
  • Add both equations: (2x + 3y) + (4x − 3y) = 12 + 6 → 6x = 18.
  • x = 18 ÷ 6 = 3.
  • So x = 3.
• Answer: x = 3

[Easy] Evaluating a Function

• EN: If f(x) = 2x² − 3, find f(4).
• FR: Si f(x) = 2x² − 3, trouve f(4).
• Choices: A) 26 B) 27 C) 29 D) 32
• Hint: Substitute the input value for x and simplify (e.g., f(x) = x² + 1; f(3) = 9 + 1 = 10).
• Steps:
  • f(4) = 2(4²) − 3 = 2 × 16 − 3 = 32 − 3 = 29.
  • So f(4) = 29.
• Answer: 29

[Easy] Exponential Function

• EN: A population of bacteria doubles every hour. If there are 50 bacteria at the start, how many are there after 3 hours?
• FR: Une population de bactéries double chaque heure. S'il y en a 50 au départ, combien y en a-t-il après 3 heures?
• Choices: A) 150 B) 250 C) 400 D) 450
• Hint: Use the formula: amount = start × 2ⁿ where n = number of hours (e.g., 10 × 2³ = 10 × 8 = 80).
• Steps:
  • After 3 hours: 50 × 2³ = 50 × 8 = 400.
  • So there are 400 bacteria.
• Answer: 400

[Easy] Logarithm Introduction

• EN: What is log₂(32)?
• FR: Combien vaut log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log_b(x) asks "to what power must I raise b to get x?" (e.g., log₂(8) = 3 because 2³ = 8).
• Steps:
  • log₂(32): what power of 2 gives 32?
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32.
  • So log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 7 and the common difference is 4. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 7 et la raison est 4. Quel est le 5e terme?
• Choices: A) 20 B) 23 C) 24 D) 27
• Hint: Use tₙ = t₁ + (n − 1) × d (e.g., t₁ = 3, d = 5, n = 4: t₄ = 3 + 3 × 5 = 18).
• Steps:
  • t₅ = 7 + (5 − 1) × 4 = 7 + 16 = 23.
  • The 5th term is 23.
• Answer: 23

[Medium] Compound Interest

• EN: Aisha deposits $1000 in a savings account at 5% interest, compounded annually for 2 years. How much is in her account at the end?
• FR: Aisha dépose 1000 $ dans un compte d'épargne à 5% d'intérêt, composé annuellement pendant 2 ans. Combien y a-t-il dans son compte à la fin?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1200.00
• Hint: Use A = P(1 + r)ⁿ (e.g., $500 at 4% for 2 years: 500 × 1.04² = 500 × 1.0816 = $540.80).
• Steps:
  • A = 1000 × (1 + 0.05)² = 1000 × 1.1025 = $1102.50.
  • So Aisha has $1102.50.
• Answer: $1102.50

[Medium] Geometric Sequence

• EN: A geometric sequence has a first term of 3 and a common ratio of 2. What is the sum of the first 5 terms?
• FR: Une suite géométrique a un premier terme de 3 et une raison de 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 45 B) 63 C) 93 D) 96
• Hint: Sum of geometric series: Sₙ = t₁(rⁿ − 1)/(r − 1) (e.g., t₁ = 2, r = 3, n = 4: S = 2(81 − 1)/2 = 80).
• Steps:
  • S₅ = 3(2⁵ − 1)/(2 − 1) = 3(32 − 1)/1 = 3 × 31 = 93.
  • The sum of the first 5 terms is 93.
• Answer: 93

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifie: sin²(θ) + cos²(θ).
• Choices: A) 0 B) 1 C) 2 D) sin(2θ)
• Hint: This is the most fundamental Pythagorean identity — memorize it! (It always equals the same value for any angle θ.)
• Steps:
  • The Pythagorean identity states: sin²(θ) + cos²(θ) = 1.
  • This is true for all values of θ.
  • So sin²(θ) + cos²(θ) = 1.
• Answer: 1

[Medium] Annuities

• EN: Omar saves $200 at the end of each year for 3 years at 4% annual interest. What is the future value of this annuity?
• FR: Omar épargne 200 $ à la fin de chaque année pendant 3 ans à un taux d'intérêt annuel de 4%. Quelle est la valeur future de cette rente?
• Choices: A) $600.00 B) $624.32 C) $648.48 D) $672.00
• Hint: FV = PMT × [(1 + r)ⁿ − 1] / r (e.g., $100/yr, 5%, 2 yrs: 100 × [(1.05² − 1)/0.05] = 100 × 2.05 = $205).
• Steps:
  • FV = 200 × [(1.04)³ − 1] / 0.04.
  • (1.04)³ = 1.124864; 1.124864 − 1 = 0.124864.
  • FV = 200 × 0.124864 / 0.04 = 200 × 3.1216 = $624.32.
• Answer: $624.32

[Hard] Solving a Logarithmic Equation

• EN: Solve for x: log₃(x) + log₃(3) = 4.
• FR: Résous pour x: log₃(x) + log₃(3) = 4.
• Choices: A) x = 9 B) x = 18 C) x = 27 D) x = 81
• Hint: Use the product rule: logb(m) + logb(n) = log_b(mn), then convert to exponential form (e.g., log₂(x) + log₂(2) = 3 → log₂(2x) = 3 → 2x = 8 → x = 4).
• Steps:
  • log₃(x) + log₃(3) = log₃(3x) = 4.
  • Convert: 3x = 3⁴ = 81.
  • x = 81 ÷ 3 = 27.
• Answer: x = 27

[Hard] Quadratic and Exponential Functions — Intersection

• EN: At what x-value do y = x² and y = 2x intersect (besides x = 0)? Hint: solve x² = 2x.
• FR: Pour quelle valeur de x les courbes y = x² et y = 2x se croisent-elles (autre que x = 0)? Indice: résous x² = 2x.
• Choices: A) x = 1 B) x = 2 C) x = 4 D) x = 8
• Hint: Set the two expressions equal, factor, and solve — but ignore x = 0 (e.g., x² = 3x → x² − 3x = 0 → x(x − 3) = 0 → x = 0 or x = 3).
• Steps:
  • x² = 2x → x² − 2x = 0.
  • Factor: x(x − 2) = 0.
  • x = 0 or x = 2. The non-zero answer is x = 2.
• Answer: x = 2

[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) 8 B) 16 C) 24 D) 48
• Hint: n! = n × (n−1) × (n−2) × … × 1 (e.g., 3 students: 3! = 3 × 2 × 1 = 6 ways).
• Steps:
  • 4! = 4 × 3 × 2 × 1 = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Derivative — Power Rule

• EN: If f(x) = x³, what is f′(x)?
• FR: Si f(x) = x³, combien vaut f′(x)?
• Choices: A) x² B) 3x C) 3x² D) 4x³
• Hint: Power rule: bring the exponent down and reduce it by 1 (e.g., f(x) = x⁵ → f′(x) = 5x⁴).
• Steps:
  • Bring down the exponent: 3.
  • Reduce the power: x³ → x².
  • f′(x) = 3x².
• Answer: 3x²

[Easy] Combinations

• EN: How many ways can you choose 2 toppings from a menu of 5 toppings?
• FR: De combien de façons peut-on choisir 2 garnitures parmi 5?
• Choices: A) 8 B) 10 C) 15 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!) = 120 / (2 × 6) = 120 / 12 = 10.
  • There are 10 ways.
• Answer: 10

[Easy] Polynomial End Behaviour

• EN: What is the end behaviour of y = −2x⁴ + x − 5 as x → +∞?
• FR: Quel est le comportement final de y = −2x⁴ + x − 5 quand x → +∞?
• Choices: A) y → +∞ B) y → −∞ C) y → 0 D) y → 5
• Hint: The leading term determines end behaviour. Negative even degree → both ends go to −∞ (e.g., y = −x² → as x → ±∞, y → −∞).
• Steps:
  • Leading term: −2x⁴ (even degree, negative coefficient).
  • As x → +∞: −2x⁴ → −∞.
  • So y → −∞.
• Answer: y → −∞

[Medium] Rate of Change — Derivative Application

• EN: A ball's position is given by s(t) = 4t² − 3t + 1 (in metres, where t is in seconds). What is the ball's velocity at t = 2 seconds?
• FR: La position d'une balle est donnée par s(t) = 4t² − 3t + 1 (en mètres, t en secondes). Quelle est la vitesse de la balle à t = 2 secondes?
• Choices: A) 9 m/s B) 11 m/s C) 13 m/s D) 16 m/s
• Hint: Velocity = s′(t); use the power rule to differentiate, then substitute t (e.g., s(t) = 3t² + 2 → s′(t) = 6t; at t = 1: s′(1) = 6 m/s).
• Steps:
  • s′(t) = 8t − 3.
  • At t = 2: s′(2) = 8(2) − 3 = 16 − 3 = 13.
  • The velocity is 13 m/s.
• Answer: 13 m/s

[Medium] Rational Functions — Asymptote

• EN: What is the vertical asymptote of f(x) = (3x + 1) / (x − 4)?
• FR: Quelle est l'asymptote verticale de f(x) = (3x + 1) / (x − 4)?
• Choices: A) x = −4 B) x = 1 C) x = 3 D) x = 4
• Hint: Vertical asymptotes occur where the denominator equals zero (e.g., f(x) = 1/(x − 2) → vertical asymptote at x = 2).
• Steps:
  • Set denominator equal to zero: x − 4 = 0.
  • x = 4.
  • The vertical asymptote is x = 4.
• Answer: x = 4

[Medium] Probability Distribution

• EN: A fair die is rolled twice. What is the probability of getting a sum of 8?
• FR: On lance un dé équitable deux fois. Quelle est la probabilité d'obtenir une somme de 8?
• Choices: A) 3/36 B) 4/36 C) 5/36 D) 6/36
• Hint: List all favourable outcomes, then divide by the total number of outcomes (6 × 6 = 36) (e.g., sum of 4: (1,3), (2,2), (3,1) → 3/36).
• Steps:
  • Pairs summing to 8: (2,6), (3,5), (4,4), (5,3), (6,2) → 5 outcomes.
  • Probability = 5/36.
• Answer: 5/36

[Medium] Vector Addition

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

[Hard] Binomial Theorem

• EN: Using the binomial theorem, find the coefficient of x² in the expansion of (x + 3)⁴.
• FR: En utilisant le théorème binomial, trouve le coefficient de x² dans le développement de (x + 3)⁴.
• Choices: A) 54 B) 81 C) 108 D) 216
• Hint: The term with x² uses C(4, 2) × x² × 3²: C(n, r) × aⁿ⁻ʳ × bʳ (e.g., in (x + 2)⁴, coefficient of x² is C(4,2) × 2² = 6 × 4 = 24).
• Steps:
  • Term with x²: C(4, 2) × x² × 3² = 6 × x² × 9 = 54x².
  • The coefficient of x² is 54.
• Answer: 54

[Hard] Derivative — Chain Rule Introduction

• EN: If f(x) = (2x + 1)³, what is f′(x) evaluated at x = 1?
• FR: Si f(x) = (2x + 1)³, combien vaut f′(x) quand x = 1?
• Choices: A) 27 B) 54 C) 81 D) 108
• Hint: Chain rule: f′(x) = n × (inner function)ⁿ⁻¹ × (derivative of inner function) (e.g., (3x + 2)² → 2(3x + 2) × 3 = 6(3x + 2)).
• Steps:
  • f′(x) = 3(2x + 1)² × 2 = 6(2x + 1)².
  • At x = 1: f′(1) = 6(2 + 1)² = 6 × 9 = 54.
  • So f′(1) = 54.
• Answer: 54