Daily Math — 2026-07-13

[Easy] Counting Hockey Pucks

• EN: There are 7 hockey pucks on the ice. 3 more are added. How many pucks are there now?
• FR: Il y a 7 rondelles de hockey sur la glace. On en ajoute 3 de plus. Combien de rondelles y a-t-il maintenant?
• Choices: A) 9 pucks B) 10 pucks C) 11 pucks D) 8 pucks
• Hint: Count on from the bigger number. For 5 + 2, start at 5 and count up 2 more.
• Steps:
  • Start at 7 and count on 3 more.
  • 7 → 8, 9, 10.
  • So there are 10 pucks.
• Answer: 10 pucks

[Easy] Skip Counting by 5s

• EN: Skip count by 5s. What comes after 15?
• FR: Compte par bonds de 5. Quel nombre vient après 15?
• Choices: A) 18 B) 25 C) 20 D) 16
• Hint: When you skip count by 5s, add 5 each time. After 10 comes 15.
• Steps:
  • We are counting by 5s: 5, 10, 15, …
  • Add 5 to 15: 15 + 5 = 20.
  • So the next 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) Both are equal C) 14 D) Neither
• Hint: The number that is farther along on a number line is greater. 6 is greater than 4.
• Steps:
  • Put both numbers on a number line.
  • 14 is to the right of 9, so 14 is greater.
  • The answer is 14.
• Answer: 14

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents in Canada?
• FR: Quelle pièce de monnaie vaut 10 cents au Canada?
• Choices: A) Penny B) Loonie C) Nickel D) Dime
• Hint: Think about the coins you use every day. A nickel is worth 5 cents.
• Steps:
  • A penny is worth 1 cent.
  • A nickel is worth 5 cents.
  • A dime is worth 10 cents.
  • The answer is Dime.
• Answer: Dime

[Medium] Subtraction at the Rink

• EN: There are 12 players on the ice. 5 players skate off. How many players are left?
• FR: Il y a 12 joueurs sur la glace. 5 joueurs partent. Combien de joueurs reste-t-il?
• Choices: A) 8 players B) 6 players C) 7 players D) 17 players
• Hint: To subtract, count back from the bigger number. For 9 – 3, count back 3 from 9.
• Steps:
  • Start at 12 and count back 5.
  • 12 → 11, 10, 9, 8, 7.
  • So 7 players are left.
• Answer: 7 players

[Medium] Skip Counting by 2s

• EN: Emma has 6 mittens in her bag. She skip counts the mittens by 2s. What does she say?
• FR: Emma a 6 mitaines dans son sac. Elle compte ses mitaines par bonds de 2. Que dit-elle?
• Choices: A) 2, 4, 6 B) 2, 4, 8 C) 1, 3, 5 D) 2, 3, 6
• Hint: Skip counting by 2s means adding 2 each time: 2, 4, 6, 8, …
• Steps:
  • Start at 2 and add 2 each time.
  • 2, 4, 6 — that covers 6 mittens.
  • So she says 2, 4, 6.
• Answer: 2, 4, 6

[Medium] Adding Within 20

• EN: Liam scored 8 goals and then scored 6 more. How many goals did he score in all?
• FR: Liam a marqué 8 buts, puis 6 de plus. Combien de buts a-t-il marqués en tout?
• Choices: A) 13 goals B) 15 goals C) 14 goals D) 16 goals
• Hint: Make a ten first. For 8 + 5, take 2 from 5 to make 10, then add the rest: 10 + 3 = 13.
• Steps:
  • Take 2 from 6 to give to 8: 8 + 2 = 10.
  • Leftover: 6 – 2 = 4.
  • 10 + 4 = 14 goals.
• Answer: 14 goals

[Medium] Counting to 100

• EN: What number comes just before 100?
• FR: Quel nombre vient juste avant 100?
• Choices: A) 101 B) 98 C) 99 D) 90
• Hint: The number just before any number is one less. The number before 8 is 7.
• Steps:
  • One less than 100 means we subtract 1.
  • 100 – 1 = 99.
  • So the number just before 100 is 99.
• Answer: 99

[Hard] Adding Three Numbers

• EN: Sofia has 5 red stickers, 4 blue stickers, and 6 yellow stickers. How many stickers does she have in all?
• FR: Sofia a 5 autocollants rouges, 4 bleus et 6 jaunes. Combien d'autocollants a-t-elle en tout?
• Choices: A) 14 stickers B) 16 stickers C) 15 stickers D) 13 stickers
• Hint: Add two numbers first, then add the third. For 3 + 4 + 2: add 3 + 4 = 7, then 7 + 2 = 9.
• Steps:
  • Add the first two: 5 + 4 = 9.
  • Add the third: 9 + 6 = 15.
  • So Sofia has 15 stickers in all.
• Answer: 15 stickers

[Hard] Coin Counting

• EN: Olivia has 2 nickels and 1 dime. How much money does she have in total?
• FR: Olivia a 2 pièces de 5 cents et 1 pièce de 10 cents. Combien d'argent a-t-elle en tout?
• Choices: A) 15 cents B) 25 cents C) 12 cents D) 20 cents
• Hint: A nickel is 5 cents and a dime is 10 cents. For 1 nickel + 1 dime: 5 + 10 = 15 cents.
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 1 dime = 10 cents.
  • 10 + 10 = 20 cents.
• Answer: 20 cents

[Easy] Adding Within 100

• EN: There are 34 students at Tim Hortons. 12 more students arrive. How many students are there now?
• FR: Il y a 34 élèves au Tim Hortons. 12 autres élèves arrivent. Combien y a-t-il d'élèves maintenant?
• Choices: A) 44 students B) 22 students C) 46 students D) 48 students
• Hint: Add the tens first, then the ones. For 21 + 15: 20 + 10 = 30, then 1 + 5 = 6, so 36.
• Steps:
  • Add tens: 30 + 10 = 40.
  • Add ones: 4 + 2 = 6.
  • 40 + 6 = 46 students.
• Answer: 46 students

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre la petite aiguille sur le 3 et la grande aiguille sur le 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 6:00
• Hint: When the minute hand is on 12, it is exactly on the hour. If the hour hand is on 5, it is 5:00.
• 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 and an eraser is 5 cm long. How much longer is the pencil?
• FR: Un crayon mesure 15 cm de long et une gomme mesure 5 cm. De combien le crayon est-il plus long?
• Choices: A) 20 cm B) 5 cm C) 8 cm D) 10 cm
• Hint: To find how much longer, subtract. For 12 cm – 4 cm, the answer is 8 cm.
• Steps:
  • Subtract the shorter length from the longer one.
  • 15 – 5 = 10.
  • The pencil is 10 cm longer.
• Answer: 10 cm

[Easy] Simple Patterns

• EN: Look at this pattern: 2, 4, 6, 8, ___. What is the missing number?
• FR: Regarde ce modèle : 2, 4, 6, 8, ___. Quel est le nombre manquant?
• Choices: A) 9 B) 12 C) 10 D) 11
• Hint: Find the rule by looking at the difference between numbers. In 3, 6, 9, 12, the rule is add 3.
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
  • The missing number is 10.
• Answer: 10

[Medium] Subtraction Within 100

• EN: A bag has 72 crayons. 38 crayons are used. How many crayons are left?
• FR: Un sac contient 72 crayons. On utilise 38 crayons. Combien de crayons reste-t-il?
• Choices: A) 34 crayons B) 44 crayons C) 30 crayons D) 36 crayons
• Hint: Borrow from the tens when the ones digit is too small. For 52 – 27: borrow to get 12 – 7 = 5, and 4 – 2 = 2, so 25.
• Steps:
  • Ones: 2 – 8 is hard, so borrow. 12 – 8 = 4.
  • Tens: 6 – 3 = 3 (after borrowing, 7 becomes 6).
  • So 72 – 38 = 34 crayons.
• Answer: 34 crayons

[Medium] Counting Coins to $1

• EN: Aiden has 3 dimes and 4 nickels. How much money does he have?
• FR: Aiden a 3 pièces de 10 cents et 4 pièces de 5 cents. Combien d'argent a-t-il?
• Choices: A) 60 cents B) 50 cents C) 45 cents D) 70 cents
• Hint: Multiply the number of each coin by its value, then add. For 2 dimes and 3 nickels: 20 + 15 = 35 cents.
• Steps:
  • 3 dimes = 3 × 10 = 30 cents.
  • 4 nickels = 4 × 5 = 20 cents.
  • 30 + 20 = 50 cents.
• Answer: 50 cents

[Medium] Telling Time to the 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'horloge montre la petite aiguille entre le 7 et le 8, et la grande aiguille sur le 6. Quelle heure est-il?
• Choices: A) 7:00 B) 6:30 C) 7:30 D) 8:30
• Hint: When the minute hand is on 6, it is half past the hour. If the hour hand is past 4, it is 4:30.
• Steps:
  • Minute hand on 6 means 30 minutes past.
  • The hour hand just passed 7.
  • So the time is 7:30.
• Answer: 7:30

[Medium] Measuring in Metres

• EN: A hockey rink is about 60 m long. A hallway is 20 m long. How much longer is the rink?
• FR: Une patinoire de hockey mesure environ 60 m de long. Un couloir mesure 20 m de long. De combien la patinoire est-elle plus longue?
• Choices: A) 80 m B) 30 m C) 50 m D) 40 m
• Hint: Subtract to find the difference. For 70 m – 30 m, the answer is 40 m.
• Steps:
  • We need to find 60 – 20.
  • 60 – 20 = 40.
  • The rink is 40 m longer.
• Answer: 40 m

[Hard] Two-Step Word Problem

• EN: Maya had 45 stickers. She gave 18 to her friend and then got 10 more. How many stickers does Maya have now?
• FR: Maya avait 45 autocollants. Elle en a donné 18 à son amie puis en a reçu 10 autres. Combien d'autocollants Maya a-t-elle maintenant?
• Choices: A) 37 stickers B) 27 stickers C) 53 stickers D) 33 stickers
• Hint: Do operations in order. For 30 – 12 + 5: first 30 – 12 = 18, then 18 + 5 = 23.
• Steps:
  • First: 45 – 18 = 27.
  • Then: 27 + 10 = 37.
  • Maya has 37 stickers.
• Answer: 37 stickers

[Hard] Pattern Extension

• EN: The snowfall pattern in cm is: 5, 10, 15, 20, 25, ___. What is the next amount?
• FR: Le modèle de chutes de neige en cm est : 5, 10, 15, 20, 25, ___. Quel est le prochain montant?
• Choices: A) 35 cm B) 26 cm C) 28 cm D) 30 cm
• Hint: Find the rule, then apply it. In the pattern 4, 8, 12, 16, the rule is add 4, so the next is 20.
• Steps:
  • The rule is add 5 each time.
  • 25 + 5 = 30.
  • The next amount is 30 cm.
• Answer: 30 cm

[Easy] Multiplication by 2

• EN: There are 4 pairs of hockey skates. How many skates are there in all?
• FR: Il y a 4 paires de patins à glace. Combien de patins y a-t-il en tout?
• Choices: A) 6 skates B) 4 skates C) 8 skates D) 10 skates
• Hint: Multiply by 2 to find the total in pairs. For 3 pairs: 3 × 2 = 6.
• Steps:
  • Each pair has 2 skates.
  • 4 × 2 = 8.
  • There are 8 skates in all.
• Answer: 8 skates

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. Noah eats 1 piece. What fraction of the pizza did he eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Noah mange 1 morceau. Quelle fraction de la pizza a-t-il mangée?
• Choices: A) 1/4 B) 1/3 C) 2/3 D) 1/2
• Hint: A fraction shows parts of a whole. If a bar is cut into 4 equal parts and you take 1, that is 1/4.
• Steps:
  • The pizza is divided into 2 equal parts.
  • Noah ate 1 of those parts.
  • So he ate 1/2.
• Answer: 1/2

[Easy] Multiplication by 5

• EN: There are 6 bags with 5 apples each. How many apples are there in all?
• FR: Il y a 6 sacs avec 5 pommes chacun. Combien de pommes y a-t-il en tout?
• Choices: A) 25 apples B) 11 apples C) 35 apples D) 30 apples
• Hint: Multiply to find equal groups. For 3 bags of 5: 3 × 5 = 15.
• Steps:
  • 6 groups of 5.
  • 6 × 5 = 30.
  • There are 30 apples in all.
• Answer: 30 apples

[Easy] Reading a Simple Graph

• EN: A bar graph shows that 8 students like hockey, 5 like soccer, and 3 like basketball. How many students were surveyed in all?
• FR: Un diagramme à barres montre que 8 élèves aiment le hockey, 5 le soccer et 3 le basketball. Combien d'élèves ont répondu au sondage en tout?
• Choices: A) 18 students B) 13 students C) 16 students D) 15 students
• Hint: To find the total from a graph, add all the values together. For 4 + 3 + 2, the total is 9.
• Steps:
  • Add all three amounts: 8 + 5 + 3.
  • 8 + 5 = 13, then 13 + 3 = 16.
  • So 16 students were surveyed.
• Answer: 16 students

[Medium] Basic Division

• EN: 24 maple cookies are shared equally among 4 students. How many cookies does each student get?
• FR: 24 biscuits à l'érable sont partagés également entre 4 élèves. Combien de biscuits chaque élève reçoit-il?
• Choices: A) 8 cookies B) 5 cookies C) 6 cookies D) 7 cookies
• Hint: Division splits a total into equal groups. For 15 shared among 3: 15 ÷ 3 = 5.
• Steps:
  • We need 24 ÷ 4.
  • Think: 4 × ? = 24. 4 × 6 = 24.
  • Each student gets 6 cookies.
• Answer: 6 cookies

[Medium] Perimeter of a Rectangle

• EN: A rectangular garden is 7 m long and 3 m wide. What is the perimeter?
• FR: Un jardin rectangulaire mesure 7 m de long et 3 m de large. Quel est son périmètre?
• Choices: A) 21 m B) 10 m C) 24 m D) 20 m
• Hint: The perimeter of a rectangle is all four sides added together. For a 5 m × 2 m rectangle: 5 + 5 + 2 + 2 = 14 m.
• Steps:
  • Add all four sides: 7 + 7 + 3 + 3.
  • 7 + 7 = 14 and 3 + 3 = 6.
  • 14 + 6 = 20 m.
• Answer: 20 m

[Medium] Multiplication by 3

• EN: A hockey team has 3 lines of forwards. Each line has 3 players. How many forwards are there in all?
• FR: Une équipe de hockey a 3 lignes d'attaquants. Chaque ligne a 3 joueurs. Combien d'attaquants y a-t-il en tout?
• Choices: A) 6 forwards B) 12 forwards C) 9 forwards D) 10 forwards
• Hint: Multiply to find the total in equal groups. For 4 lines of 3 players: 4 × 3 = 12.
• Steps:
  • 3 lines with 3 players each.
  • 3 × 3 = 9.
  • There are 9 forwards.
• Answer: 9 forwards

[Medium] Fractions — One Quarter

• EN: A chocolate bar is broken into 4 equal pieces. Chloe eats 1 piece. What fraction is left?
• FR: Une tablette de chocolat est cassée en 4 morceaux égaux. Chloe en mange 1 morceau. Quelle fraction reste-t-il?
• Choices: A) 1/4 B) 1/2 C) 3/4 D) 2/3
• Hint: Subtract the eaten fraction from 1 whole. For a bar in 4 parts, if 2 are eaten, 2/4 are left.
• Steps:
  • The bar has 4 equal parts.
  • 1 part is eaten, so 3 parts remain.
  • 3 out of 4 parts = 3/4.
• Answer: 3/4

[Hard] Two-Step Multiplication Problem

• EN: A store has 5 boxes of pencils. Each box has 4 packs, and each pack has 10 pencils. How many pencils are there in all?
• FR: Un magasin a 5 boîtes de crayons. Chaque boîte contient 4 paquets et chaque paquet contient 10 crayons. Combien de crayons y a-t-il en tout?
• Choices: A) 190 pencils B) 150 pencils C) 200 pencils D) 160 pencils
• Hint: Work step by step. For 3 boxes of 2 packs of 5 pencils: 3 × 2 = 6 packs, then 6 × 5 = 30 pencils.
• Steps:
  • First find packs in total: 5 × 4 = 20 packs.
  • Then: 20 × 10 = 200 pencils.
  • There are 200 pencils in all.
• Answer: 200 pencils

[Hard] Division with Interpretation

• EN: 30 students go on a hockey trip. Each van holds 4 students. How many vans are needed so all students can go?
• FR: 30 élèves font un voyage de hockey. Chaque camionnette peut transporter 4 élèves. Combien de camionnettes sont nécessaires pour que tous les élèves puissent y aller?
• Choices: A) 7 vans B) 9 vans C) 6 vans D) 8 vans
• Hint: Divide and round up if there is a remainder. For 22 students in vans of 5: 22 ÷ 5 = 4 remainder 2, so you need 5 vans.
• Steps:
  • 30 ÷ 4 = 7 remainder 2.
  • Since 2 students still need a ride, we need one more van.
  • 7 + 1 = 8 vans.
• Answer: 8 vans

[Easy] Multiplication Table

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 63 C) 48 D) 56
• Hint: Break into smaller facts. For 6 × 8, think: 5 × 8 = 40, then add 8 more to get 48.
• Steps:
  • Think: 7 × 8 = 7 groups of 8.
  • 7 × 8 = 56.
  • The answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 4.35?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,35?
• Choices: A) 3 ones B) 3 hundredths C) 3 tenths D) 3 tens
• Hint: In a decimal number, the first place after the decimal point is tenths, and the second is hundredths.
• Steps:
  • In 4.35, the digit 3 is the first digit after the decimal point.
  • The first place after the decimal is tenths.
  • So 3 means 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A classroom rug is 5 m long and 3 m wide. What is its area?
• FR: Un tapis de classe mesure 5 m de long et 3 m de large. Quelle est son aire?
• Choices: A) 16 m² B) 18 m² C) 15 m² D) 8 m²
• Hint: Area of a rectangle = length × width. For a 4 m × 6 m room: area = 24 m².
• Steps:
  • Area = length × width.
  • Area = 5 × 3 = 15.
  • The area is 15 m².
• Answer: 15 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater, 3/4 or 1/4?
• FR: Quelle fraction est plus grande, 3/4 ou 1/4?
• Choices: A) 1/4 B) Both are equal C) Neither D) 3/4
• Hint: When fractions have the same denominator, compare the numerators. Bigger numerator means bigger fraction.
• Steps:
  • Both fractions have denominator 4.
  • Compare numerators: 3 > 1.
  • So 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainder

• EN: 47 hockey cards are sorted equally into 5 piles. How many cards are in each pile, and how many are left over?
• FR: 47 cartes de hockey sont réparties également en 5 piles. Combien de cartes y a-t-il dans chaque pile et combien en reste-t-il?
• Choices: A) 10 remainder 3 B) 9 remainder 2 C) 8 remainder 7 D) 11 remainder 2
• Hint: Divide and find what remains. For 23 ÷ 4: 4 × 5 = 20, remainder is 23 – 20 = 3, so 5 remainder 3.
• Steps:
  • 5 × 9 = 45, which is close to 47.
  • 47 – 45 = 2 left over.
  • So 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 2:15 p.m. and ends at 4:45 p.m. How long does the game last?
• FR: Un match de hockey commence à 14 h 15 et se termine à 16 h 45. Combien de temps dure le match?
• Choices: A) 3 hours 30 minutes B) 2 hours C) 2 hours 30 minutes D) 1 hour 45 minutes
• Hint: Count the hours first, then the minutes. From 1:10 to 3:40: 2 hours, then 30 more minutes = 2 hours 30 minutes.
• Steps:
  • From 2:15 to 4:15 is 2 hours.
  • From 4:15 to 4:45 is 30 minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Addition

• EN: A skate costs $12.50 and a helmet costs $9.35. What is the total cost?
• FR: Des patins coûtent 12,50 $ et un casque coûte 9,35 $. Quel est le coût total?
• Choices: A) $20.85 B) $22.85 C) $21.85 D) $23.00
• Hint: Line up the decimal points and add. For $5.25 + $3.40: add cents first (25 + 40 = 65), then dollars (5 + 3 = 8), total $8.65.
• Steps:
  • Add cents: 50 + 35 = 85 cents.
  • Add dollars: 12 + 9 = 21 dollars.
  • Total = $21.85.
• Answer: $21.85

[Medium] Multiplying by 2-Digit Numbers

• EN: A store orders 12 boxes of pens. Each box has 9 pens. How many pens are there in all?
• FR: Un magasin commande 12 boîtes de stylos. Chaque boîte contient 9 stylos. Combien de stylos y a-t-il en tout?
• Choices: A) 118 pens B) 98 pens C) 108 pens D) 110 pens
• Hint: Multiply by splitting. For 11 × 8: (10 × 8) + (1 × 8) = 80 + 8 = 88.
• Steps:
  • 12 × 9 = (10 × 9) + (2 × 9).
  • 90 + 18 = 108.
  • There are 108 pens in all.
• Answer: 108 pens

[Hard] Multi-Step Word Problem

• EN: Sam buys 3 notebooks for $2.75 each and pays with a $10 bill. How much change does he receive?
• FR: Sam achète 3 cahiers à 2,75 $ chacun et paie avec un billet de 10 $. Combien de monnaie reçoit-il?
• Choices: A) $1.75 B) $2.75 C) $1.25 D) $3.25
• Hint: Find the total cost first, then subtract from the amount paid. For 2 items at $3.50, total = $7.00. Change from $10 = $3.00.
• Steps:
  • Total cost: 3 × $2.75 = $8.25.
  • Change: $10.00 – $8.25 = $1.75.
  • Sam receives $1.75 in change.
• Answer: $1.75

[Hard] Comparing Decimals and Fractions

• EN: Arrange in order from least to greatest: 0.5, 3/4, 0.25, 1/2.
• FR: Classe ces nombres en ordre croissant : 0,5, 3/4, 0,25, 1/2.
• Choices: A) 0.25, 1/2, 0.5, 3/4 B) 0.5, 1/2, 0.25, 3/4 C) 0.25, 0.5, 1/2, 3/4 D) 3/4, 1/2, 0.5, 0.25
• Hint: Convert everything to decimals first. 1/2 = 0.5, 3/4 = 0.75. Then order the decimals from smallest to largest.
• Steps:
  • Convert: 3/4 = 0.75, 1/2 = 0.5, 0.5 = 0.5, 0.25 = 0.25.
  • Order: 0.25, 0.5, 0.5, 0.75.
  • In original form: 0.25, 0.5, 1/2, 3/4.
• Answer: 0.25, 0.5, 1/2, 3/4

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 194 B) 216 C) 204 D) 180
• Hint: Multiply each part separately. For 23 × 4: (20 × 4) + (3 × 4) = 80 + 12 = 92.
• Steps:
  • 34 × 6 = (30 × 6) + (4 × 6).
  • 180 + 24 = 204.
  • The answer is 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien font 2/7 + 3/7?
• Choices: A) 5/14 B) 6/7 C) 5/7 D) 1/7
• Hint: Add the numerators and keep the denominator the same. For 1/5 + 2/5 = 3/5.
• Steps:
  • Add numerators: 2 + 3 = 5.
  • Keep the denominator: 7.
  • The answer is 5/7.
• Answer: 5/7

[Easy] Percentage Introduction — 50%

• EN: There are 40 students in a gym class. 50% are wearing red jerseys. How many students are wearing red?
• FR: Il y a 40 élèves dans un cours de gym. 50 % portent des maillots rouges. Combien d'élèves portent du rouge?
• Choices: A) 25 students B) 10 students C) 20 students D) 15 students
• Hint: 50% means half. Find half by dividing by 2. For 60 students, 50% = 30 students.
• Steps:
  • 50% of 40 = 40 ÷ 2.
  • 40 ÷ 2 = 20.
  • 20 students are wearing red.
• Answer: 20 students

[Easy] Decimal Subtraction

• EN: A juice box holds 2.50 L and 0.75 L has been poured out. How much juice is left?
• FR: Une boîte de jus contient 2,50 L et on en a versé 0,75 L. Combien de jus reste-t-il?
• Choices: A) 1.75 L B) 3.25 L C) 2.25 L D) 1.50 L
• Hint: Line up decimal points and subtract. For 3.80 – 1.50: subtract to get 2.30.
• Steps:
  • 2.50 – 0.75.
  • Borrow: 150 – 75 = 75, so 1.75.
  • There is 1.75 L left.
• Answer: 1.75 L

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 64 cm³ C) 60 cm³ D) 54 cm³
• Hint: Volume = length × width × height. For a box 2 × 3 × 4: volume = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A Tim Hortons muffin normally costs $2.00. It is on sale for 25% off. How much is saved?
• FR: Un muffin de Tim Hortons coûte normalement 2,00 $. Il est en solde à 25 % de rabais. Combien économise-t-on?
• Choices: A) $0.75 B) $1.00 C) $0.50 D) $0.25
• Hint: 25% means one quarter. Divide by 4. For 25% of $3.00: $3.00 ÷ 4 = $0.75.
• Steps:
  • 25% of $2.00 = $2.00 ÷ 4.
  • $2.00 ÷ 4 = $0.50.
  • $0.50 is saved.
• Answer: $0.50

[Medium] Subtracting Fractions with Like Denominators

• EN: A ribbon is 7/9 m long. Maya cuts off 2/9 m. How much ribbon is left?
• FR: Un ruban mesure 7/9 m de long. Maya en coupe 2/9 m. Quelle longueur de ruban reste-t-il?
• Choices: A) 9/9 m B) 4/9 m C) 5/9 m D) 6/9 m
• Hint: Subtract the numerators and keep the denominator. For 6/8 – 2/8 = 4/8.
• Steps:
  • 7/9 – 2/9: subtract numerators: 7 – 2 = 5.
  • Keep the denominator: 9.
  • 5/9 m is left.
• Answer: 5/9 m

[Medium] Multi-Digit Division

• EN: 156 pencils are packed equally into 4 boxes. How many pencils are in each box?
• FR: 156 crayons sont emballés également dans 4 boîtes. Combien de crayons y a-t-il dans chaque boîte?
• Choices: A) 48 pencils B) 36 pencils C) 39 pencils D) 42 pencils
• Hint: Divide step by step. For 124 ÷ 4: 4 goes into 12 three times (30), and 4 goes into 4 once (1), so 31.
• Steps:
  • 4 goes into 15 three times (12), remainder 3. Bring down 6 to make 36.
  • 4 goes into 36 nine times.
  • So 156 ÷ 4 = 39 pencils.
• Answer: 39 pencils

[Hard] Multi-Step Problem with Decimals

• EN: Jordan buys 3 hockey cards for $1.45 each and 2 stickers for $0.60 each. He pays with a $10 bill. How much change does he receive?
• FR: Jordan achète 3 cartes de hockey à 1,45 $ chacune et 2 autocollants à 0,60 $ chacun. Il paie avec un billet de 10 $. Combien de monnaie reçoit-il?
• Choices: A) $4.15 B) $5.15 C) $3.95 D) $4.75
• Hint: Calculate each part first, then add them. Subtract from $10.00. For 2 × $2.50 + 1 × $1.00 = $6.00; $10.00 – $6.00 = $4.00.
• Steps:
  • 3 cards: 3 × $1.45 = $4.35.
  • 2 stickers: 2 × $0.60 = $1.20.
  • Total: $4.35 + $1.20 = $5.55. Change: $10.00 – $5.55 = $4.45.
• Answer: $4.45

(Correction: The change is $4.45. Let me verify: 3 × 1.45 = 4.35; 2 × 0.60 = 1.20; total = 5.55; 10.00 – 5.55 = 4.45.)

• Choices: A) $4.15 B) $5.55 C) $4.45 D) $3.95
• Answer: $4.45

[Hard] Percentage — 10%

• EN: A hockey camp costs $250. There is a 10% discount for early registration. What is the discounted price?
• FR: Un camp de hockey coûte 250 $. Il y a un rabais de 10 % pour l'inscription hâtive. Quel est le prix réduit?
• Choices: A) $240 B) $215 C) $225 D) $235
• Hint: 10% of a number means divide by 10. Then subtract from the original. 10% of $400 = $40; discounted price = $360.
• Steps:
  • 10% of $250 = $250 ÷ 10 = $25.
  • Discounted price = $250 – $25 = $225.
  • The discounted price is $225.
• Answer: $225

[Easy] Percent of a Number

• EN: What is 30% of 90?
• FR: Combien font 30 % de 90?
• Choices: A) 30 B) 27 C) 25 D) 32
• Hint: Find 10% first by dividing by 10, then multiply by the desired number of tens. 10% of 80 = 8; 30% = 3 × 8 = 24.
• Steps:
  • 10% of 90 = 9.
  • 30% = 3 × 9 = 27.
  • The answer is 27.
• Answer: 27

[Easy] Order of Operations (BEDMAS)

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

[Easy] Integers Introduction

• EN: The temperature in Winnipeg is −5°C in the morning. It rises 9°C by noon. What is the noon temperature?
• FR: La température à Winnipeg est de −5°C le matin. Elle monte de 9°C à midi. Quelle est la température à midi?
• Choices: A) 14°C B) −4°C C) 5°C D) 4°C
• Hint: Adding a positive number to a negative number: move right on the number line. For −3 + 7 = 4.
• Steps:
  • Start at −5 and add 9.
  • −5 + 9 = 4.
  • The noon temperature is 4°C.
• Answer: 4°C

[Easy] Ratios

• EN: In a bag of marbles, there are 4 red and 6 blue marbles. What is the ratio of red to blue marbles?
• FR: Dans un sac de billes, il y a 4 rouges et 6 bleues. Quel est le rapport des billes rouges aux billes bleues?
• Choices: A) 6:4 B) 4:10 C) 2:3 D) 4:6
• Hint: A ratio compares two amounts. Write them in the order asked, separated by a colon. 3 red and 5 blue = 3:5.
• Steps:
  • Red to blue: 4 to 6.
  • Write as 4:6.
  • The ratio of red to blue is 4:6.
• Answer: 4:6

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 6/7 C) 1/2 D) 5/7
• Hint: Multiply numerator × numerator and denominator × denominator. For 1/2 × 2/3: (1×2)/(2×3) = 2/6 = 1/3.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Fraction Division

• EN: How many 1/3-cup servings are there in 2 cups of oatmeal?
• FR: Combien de portions de 1/3 de tasse y a-t-il dans 2 tasses de gruau?
• Choices: A) 8 B) 5 C) 6 D) 7
• Hint: Dividing by a fraction means multiplying by its reciprocal. For 3 ÷ 1/4: multiply 3 × 4 = 12.
• Steps:
  • 2 ÷ 1/3 = 2 × 3/1 = 6.
  • There are 6 servings.
  • The answer is 6.
• Answer: 6

[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) 12 B) 17 C) 19 D) 20
• Hint: Replace the variable with the given number and calculate. For 2x + 3 when x = 4: 2 × 4 + 3 = 8 + 3 = 11.
• Steps:
  • Replace n with 5: 3(5) + 4.
  • 3 × 5 = 15.
  • 15 + 4 = 19.
• Answer: 19

[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) 70 km/h B) 90 km/h C) 80 km/h D) 100 km/h
• Hint: Rate = total ÷ time. For 150 km in 3 hours: 150 ÷ 3 = 50 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 240 ÷ 3 = 80.
  • The speed is 80 km/h.
• Answer: 80 km/h

[Hard] BEDMAS with Brackets

• EN: Solve: (8 + 2) × 3 − 4 ÷ 2.
• FR: Calcule : (8 + 2) × 3 − 4 ÷ 2.
• Choices: A) 25 B) 30 C) 28 D) 22
• Hint: Brackets first, then multiplication and division left to right, then addition and subtraction. For (3 + 1) × 5 − 2: 4 × 5 − 2 = 20 − 2 = 18.
• Steps:
  • Brackets: (8 + 2) = 10.
  • Multiplication: 10 × 3 = 30.
  • Division: 4 ÷ 2 = 2. Then 30 − 2 = 28.
• Answer: 28

[Hard] Multi-Step Percent Problem

• EN: A jacket originally costs $80. It is discounted by 15% and then a 13% tax is added to the sale price. What is the final price?
• FR: Un manteau coûte 80 $ à l'origine. Il est réduit de 15 %, puis une taxe de 13 % est ajoutée au prix de vente. Quel est le prix final?
• Choices: A) $76.68 B) $82.00 C) $79.44 D) $73.00
• Hint: Find the discount first, subtract it, then add the tax on the new price. For 20% off $50 = $40, then 10% tax on $40 = $4, final price = $44.
• Steps:
  • Discount: 15% of $80 = $12. Sale price = $80 – $12 = $68.
  • Tax: 13% of $68 = $8.84. Final price = $68 + $8.84 = $76.84.
  • The final price is $76.84.

(Let me recalculate: 13% of 68 = 0.13 × 68 = 8.84. 68 + 8.84 = 76.84.)

• Choices: A) $76.84 B) $82.00 C) $79.44 D) $73.00
• Answer: $76.84

[Easy] Integer Addition

• EN: What is (−8) + 5?
• FR: Combien font (−8) + 5?
• Choices: A) 13 B) −3 C) 3 D) −13
• Hint: On a number line, start at the negative number and move right by the positive amount. For (−6) + 4 = −2.
• Steps:
  • Start at −8 on the number line and move 5 to the right.
  • −8 + 5 = −3.
  • The answer is −3.
• Answer: −3

[Easy] Percent Discount

• EN: A pair of skates costs $120. They are 20% off. What is the sale price?
• FR: Une paire de patins coûte 120 $. Ils sont à 20 % de rabais. Quel est le prix de vente?
• Choices: A) $100 B) $104 C) $96 D) $108
• Hint: Find 20% then subtract. 20% of $80 = $16, so sale price = $80 – $16 = $64.
• Steps:
  • 20% of $120 = $120 × 0.20 = $24.
  • Sale price = $120 – $24 = $96.
  • The sale price is $96.
• Answer: $96

[Easy] Integer Subtraction

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

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15.
• FR: Trouve x : x + 9 = 15.
• Choices: A) x = 24 B) x = 5 C) x = 7 D) x = 6
• Hint: To isolate the variable, do the opposite operation to both sides. For x + 3 = 10: subtract 3 from both sides, x = 7.
• Steps:
  • Subtract 9 from both sides: x + 9 − 9 = 15 − 9.
  • x = 6.
  • The answer is x = 6.
• Answer: x = 6

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Combien font (−6) × (−4)?
• Choices: A) −24 B) 10 C) −10 D) 24
• Hint: Negative × negative = positive. For (−3) × (−5) = 15.
• Steps:
  • (−6) × (−4): two negatives multiply to give a positive.
  • 6 × 4 = 24.
  • The answer is 24.
• Answer: 24

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 4 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte cadeau mesure 4 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire totale?
• Choices: A) 52 cm² B) 48 cm² C) 24 cm² D) 56 cm²
• Hint: SA = 2(lw + lh + wh). For a 2 × 3 × 1 box: 2(6 + 2 + 3) = 2(11) = 22 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(4×3 + 4×2 + 3×2).
  • = 2(12 + 8 + 6) = 2(26) = 52.
  • Surface area = 52 cm².
• Answer: 52 cm²

[Medium] Probability

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

[Medium] Percent Tip

• EN: A meal at a Canadian restaurant costs $48.00. If you leave a 15% tip, how much is the tip?
• FR: Un repas dans un restaurant canadien coûte 48,00 $. Si tu laisses un pourboire de 15 %, combien est le pourboire?
• Choices: A) $7.20 B) $9.60 C) $4.80 D) $6.40
• Hint: Find 10% first, then add half of that for 15%. For $60: 10% = $6.00; 15% = $6 + $3 = $9.00.
• Steps:
  • 10% of $48 = $4.80.
  • 5% = $4.80 ÷ 2 = $2.40.
  • 15% = $4.80 + $2.40 = $7.20.
• Answer: $7.20

[Hard] Integer Division and Order of Operations

• EN: Evaluate: (−20) ÷ 4 + (−3) × 2.
• FR: Évalue : (−20) ÷ 4 + (−3) × 2.
• Choices: A) −16 B) 4 C) −11 D) −4
• Hint: Divide and multiply first (left to right), then add. For (−12) ÷ 3 + (−2) × 4: −4 + (−8) = −12.
• Steps:
  • (−20) ÷ 4 = −5.
  • (−3) × 2 = −6.
  • −5 + (−6) = −11.
• Answer: −11

[Hard] Multi-Step Equation Problem

• EN: The sum of three consecutive integers is 48. What is the smallest integer?
• FR: La somme de trois entiers consécutifs est 48. Quel est le plus petit entier?
• Choices: A) 16 B) 14 C) 18 D) 15
• Hint: Let the integers be n, n+1, n+2. Set up and solve: n + (n+1) + (n+2) = some total. For a sum of 30: 3n + 3 = 30, so n = 9.
• Steps:
  • Let the integers be n, n+1, n+2.
  • n + (n+1) + (n+2) = 48 → 3n + 3 = 48.
  • 3n = 45 → n = 15. The smallest integer is 15.
• Answer: 15

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 14 C) 13 D) 12
• Hint: Think: what number times itself equals the value? For √81: 9 × 9 = 81, so √81 = 9.
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: A student scored 70, 80, 90, and 60 on four tests. What is the mean score?
• FR: Un élève a obtenu 70, 80, 90 et 60 à quatre tests. Quelle est la moyenne?
• Choices: A) 80 B) 72 C) 75 D) 70
• Hint: Mean = sum ÷ count. For scores 10, 20, 30: sum = 60, count = 3, mean = 20.
• Steps:
  • Sum: 70 + 80 + 90 + 60 = 300.
  • Divide by 4: 300 ÷ 4 = 75.
  • The mean is 75.
• Answer: 75

[Easy] Percent Increase

• EN: A hockey stick costs $80 and the price increases by 10%. What is the new price?
• FR: Un bâton de hockey coûte 80 $ et le prix augmente de 10 %. Quel est le nouveau prix?
• Choices: A) $90 B) $70 C) $88 D) $86
• Hint: Find the increase amount and add it to the original. For 20% increase on $50: increase = $10, new price = $60.
• Steps:
  • 10% of $80 = $8.
  • New price = $80 + $8 = $88.
  • The new price is $88.
• Answer: $88

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 3 = 11.
• FR: Trouve x : 2x + 3 = 11.
• Choices: A) x = 5 B) x = 3 C) x = 4 D) x = 7
• Hint: Undo operations in reverse order. Subtract the constant first, then divide. For 3x + 2 = 14: 3x = 12, x = 4.
• Steps:
  • Subtract 3 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
  • The answer is x = 4.
• Answer: x = 4

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 14 cm B) 12 cm C) 11 cm D) 10 cm
• Hint: Use a² + b² = c². For legs 3 and 4: 9 + 16 = 25, so c = √25 = 5.
• Steps:
  • a² + b² = c²: 6² + 8² = c².
  • 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through (0, 1) and (3, 7). What is the slope of the line?
• FR: Une droite passe par (0, 1) et (3, 7). Quel est le taux de variation (pente)?
• Choices: A) 3 B) 4 C) 2 D) 5
• Hint: Slope = (change in y) ÷ (change in x). For (0, 2) to (2, 6): slope = (6 – 2) ÷ (2 – 0) = 2.
• Steps:
  • Change in y: 7 – 1 = 6.
  • Change in x: 3 – 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Median of a Data Set

• EN: Find the median of: 3, 7, 9, 2, 5.
• FR: Trouve la médiane de : 3, 7, 9, 2, 5.
• Choices: A) 7 B) 2 C) 9 D) 5
• Hint: Arrange numbers in order from least to greatest, then find the middle value. For 1, 4, 6, 8, 10: the middle is 6.
• Steps:
  • Arrange in order: 2, 3, 5, 7, 9.
  • The middle value (3rd of 5) is 5.
  • The median is 5.
• Answer: 5

[Medium] Percent Decrease

• EN: A coat originally costs $150. It is marked down by 30%. What is the sale price?
• FR: Un manteau coûte 150 $ à l'origine. Il est soldé de 30 %. Quel est le prix de vente?
• Choices: A) $120 B) $95 C) $115 D) $105
• Hint: Find the decrease and subtract from the original. 20% of $200 = $40; sale price = $200 – $40 = $160.
• Steps:
  • 30% of $150 = $45.
  • Sale price = $150 – $45 = $105.
  • The sale price is $105.
• Answer: $105

[Hard] Two-Step Equation with Fractions

• EN: Solve for x: x/3 + 5 = 9.
• FR: Trouve x : x/3 + 5 = 9.
• Choices: A) x = 12 B) x = 21 C) x = 6 D) x = 18
• Hint: Subtract the constant first, then multiply both sides by the denominator. For x/4 + 2 = 5: x/4 = 3, x = 12.
• Steps:
  • Subtract 5 from both sides: x/3 = 4.
  • Multiply both sides by 3: x = 12.
  • The answer is x = 12.
• Answer: x = 12

[Hard] Pythagorean Theorem — Find 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) 14 cm B) 8 cm C) 12 cm D) 11 cm
• Hint: Rearrange a² + b² = c² to find a leg: a² = c² – b². For c = 10, b = 6: a² = 100 – 36 = 64, a = 8.
• Steps:
  • a² = c² – b² = 13² – 5² = 169 – 25 = 144.
  • a = √144 = 12.
  • The other leg is 12 cm.
• Answer: 12 cm

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 3 = 13.
• FR: Trouve x : 4x − 3 = 13.
• Choices: A) x = 5 B) x = 2 C) x = 3 D) x = 4
• Hint: Add the constant to both sides first, then divide. For 3x – 6 = 9: 3x = 15, x = 5.
• Steps:
  • Add 3 to both sides: 4x = 16.
  • Divide by 4: x = 4.
  • The answer is x = 4.
• Answer: x = 4

[Easy] Graphing Lines — y-intercept

• EN: What is the y-intercept of the line y = 3x + 5?
• FR: Quel est l'ordonnée à l'origine de la droite y = 3x + 5?
• Choices: A) 3 B) −5 C) 8 D) 5
• Hint: In y = mx + b, the y-intercept is b. For y = 2x + 7, the y-intercept is 7.
• Steps:
  • The equation is in y = mx + b form.
  • b = 5 is the y-intercept.
  • The y-intercept is 5.
• Answer: 5

[Easy] Adding Polynomials

• EN: Add: (3x + 4) + (5x − 2).
• FR: Additionne : (3x + 4) + (5x − 2).
• Choices: A) 9x + 2 B) 8x + 2 C) 8x − 2 D) 7x + 2
• Hint: Combine like terms. For (2x + 3) + (4x + 1): 2x + 4x = 6x and 3 + 1 = 4, so 6x + 4.
• Steps:
  • Combine x terms: 3x + 5x = 8x.
  • Combine constants: 4 + (−2) = 2.
  • Answer: 8x + 2
• Answer: 8x + 2

[Easy] Similar Triangles

• EN: Two similar triangles have sides in a ratio of 2:3. If a side of the smaller triangle is 8 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans un rapport de 2:3. Si un côté du plus petit triangle mesure 8 cm, quel est le côté correspondant du plus grand?
• Choices: A) 16 cm B) 14 cm C) 11 cm D) 12 cm
• Hint: Use the scale factor. If the ratio is 2:5 and the smaller side is 4, the larger side = 4 × (5/2) = 10.
• Steps:
  • Scale factor from small to large = 3/2.
  • Larger side = 8 × (3/2) = 12.
  • The corresponding side is 12 cm.
• Answer: 12 cm

[Medium] Linear Inequality

• EN: Solve for x: 3x + 4 > 13.
• FR: Résous l'inégalité : 3x + 4 > 13.
• Choices: A) x > 5 B) x > 4 C) x < 3 D) x > 3
• Hint: Solve like an equation, but keep the inequality sign. For 2x + 1 > 9: 2x > 8, x > 4.
• Steps:
  • Subtract 4: 3x > 9.
  • Divide by 3: x > 3.
  • The answer is x > 3.
• Answer: x > 3

[Medium] Multiplying Polynomials

• EN: Expand: 2x(3x − 4).
• FR: Développe : 2x(3x − 4).
• Choices: A) 5x² − 8x B) 6x − 8x C) 6x² − 8x D) 6x² + 8x
• Hint: Distribute the term outside the bracket to each term inside. For 3x(2x + 5): 6x² + 15x.
• Steps:
  • Multiply 2x by 3x: 2x × 3x = 6x².
  • Multiply 2x by −4: 2x × (−4) = −8x.
  • Result: 6x² − 8x.
• Answer: 6x² − 8x

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 and the hypotenuse is 10. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 et l'hypoténuse mesure 10. Combien vaut sin(θ)?
• Choices: A) 10/6 B) 0.75 C) 0.8 D) 0.6
• Hint: SOH: sin = opposite ÷ hypotenuse. For opposite = 4, hypotenuse = 8: sin = 4/8 = 0.5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 6 ÷ 10 = 0.6.
  • The answer is 0.6.
• Answer: 0.6

[Medium] Slope from an Equation

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

[Hard] Systems of Linear Equations by Substitution

• EN: Solve the system: y = 2x + 1 and y = −x + 7.
• FR: Résous le système : y = 2x + 1 et y = −x + 7.
• Choices: A) x = 3, y = 4 B) x = 2, y = 5 C) x = 1, y = 3 D) x = 4, y = 3
• Hint: Set the two equations equal to each other, then solve for x. For y = x + 3 and y = 2x + 1: x + 3 = 2x + 1, x = 2.
• Steps:
  • Set equal: 2x + 1 = −x + 7.
  • 3x = 6, x = 2.
  • y = 2(2) + 1 = 5. So x = 2, y = 5.
• Answer: x = 2, y = 5

[Hard] Statistics — Finding Missing Value from Mean

• EN: The mean of five test scores is 78. Four of the scores are 82, 75, 70, and 80. What is the fifth score?
• FR: La moyenne de cinq résultats de tests est 78. Quatre des résultats sont 82, 75, 70 et 80. Quel est le cinquième résultat?
• Choices: A) 83 B) 79 C) 85 D) 81
• Hint: Total = mean × count. Find the total needed, then subtract the known values. For mean = 10, count = 4, total needed = 40. If three values are 8, 9, and 11, the fourth = 40 – 28 = 12.
• Steps:
  • Total needed: 78 × 5 = 390.
  • Sum of known: 82 + 75 + 70 + 80 = 307.
  • Fifth score = 390 – 307 = 83.
• Answer: 83

[Easy] Factoring a Quadratic

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

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 9 and the hypotenuse is 15. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 9 et l'hypoténuse mesure 15. Combien vaut cos(θ)?
• Choices: A) 0.8 B) 0.5 C) 0.75 D) 0.6
• Hint: CAH: cos = adjacent ÷ hypotenuse. For adjacent = 4, hypotenuse = 5: cos = 0.8.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 9 ÷ 15 = 0.6.
  • The answer is 0.6.
• Answer: 0.6

[Easy] Surface Area of a Cylinder

• EN: A cylindrical can has radius 3 cm and height 10 cm. What is the surface area? Use π ≈ 3.14.
• FR: Une boîte cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quelle est l'aire totale? Utilisez π ≈ 3,14.
• Choices: A) 226.08 cm² B) 188.4 cm² C) 245.0 cm² D) 207.24 cm²
• Hint: SA = 2πr² + 2πrh. For r = 2, h = 5: SA = 2π(4) + 2π(2)(5) = 8π + 20π = 28π ≈ 87.96 cm².
• Steps:
  • SA = 2πr² + 2πrh = 2(3.14)(9) + 2(3.14)(3)(10).
  • = 56.52 + 188.4 = 244.92 ≈ 245.0 cm².
  • The surface area is approximately 245.0 cm².

(Recalculate: 2 × 3.14 × 9 = 56.52; 2 × 3.14 × 3 × 10 = 188.4; total = 244.92. Closest choice should be 244.92, let me round to 244.92.)

• Choices: A) 244.92 cm² B) 188.4 cm² C) 207.24 cm² D) 226.08 cm²
• Answer: 244.92 cm²

[Easy] Systems of Equations

• EN: Solve: x + y = 10 and x − y = 4.
• FR: Résous : x + y = 10 et x − y = 4.
• Choices: A) x = 8, y = 2 B) x = 5, y = 5 C) x = 6, y = 4 D) x = 7, y = 3
• Hint: Add the two equations together to eliminate y. For x + y = 8 and x – y = 2: add to get 2x = 10, x = 5, then y = 3.
• Steps:
  • Add the equations: 2x = 14, so x = 7.
  • Substitute: 7 + y = 10, so y = 3.
  • x = 7, y = 3.
• Answer: x = 7, y = 3

[Medium] Completing the Square

• EN: Complete the square for x² + 6x + 2 = 0 to find the value of x (give exact form).
• FR: Complète le carré pour x² + 6x + 2 = 0 afin de trouver les valeurs de x (donne la forme exacte).
• Choices: A) x = −3 ± √11 B) x = −3 ± √7 C) x = 3 ± √7 D) x = −6 ± √11
• Hint: Add (b/2)² to both sides. For x² + 4x + 1 = 0: (x+2)² = 3, so x = −2 ± √3.
• Steps:
  • x² + 6x = −2. Add (3)² = 9 to both sides: (x+3)² = 7.
  • x + 3 = ±√7.
  • x = −3 ± √7.
• Answer: x = −3 ± √7

[Medium] Circle Geometry — Chord

• EN: A chord is 16 cm long and is 6 cm from the centre of a circle. What is the radius of the circle?
• FR: Une corde mesure 16 cm de long et est à 6 cm du centre d'un cercle. Quel est le rayon du cercle?
• Choices: A) 9 cm B) 11 cm C) 10 cm D) 8 cm
• Hint: The perpendicular from the centre bisects the chord, forming a right triangle. Use Pythagorean theorem with half the chord length and the distance.
• Steps:
  • Half chord = 8 cm. Distance from centre = 6 cm.
  • r² = 8² + 6² = 64 + 36 = 100.
  • r = 10 cm.
• Answer: 10 cm

[Medium] Volume of a Cone

• EN: A cone has radius 4 cm and height 9 cm. What is its volume? Use π ≈ 3.14.
• FR: Un cône a un rayon de 4 cm et une hauteur de 9 cm. Quel est son volume? Utilisez π ≈ 3,14.
• Choices: A) 150.72 cm³ B) 113.04 cm³ C) 200.96 cm³ D) 175.84 cm³
• Hint: V = (1/3)πr²h. For r = 3, h = 4: V = (1/3)(3.14)(9)(4) = 37.68 cm³.
• Steps:
  • V = (1/3)πr²h = (1/3)(3.14)(16)(9).
  • = (1/3)(3.14)(144) = (1/3)(452.16) = 150.72.
  • Volume ≈ 150.72 cm³.
• Answer: 150.72 cm³

[Medium] Quadratic Equation — Factoring

• EN: Solve: x² − 7x + 12 = 0.
• FR: Résous : x² − 7x + 12 = 0.
• Choices: A) x = 4 or x = 3 B) x = −4 or x = −3 C) x = 6 or x = 2 D) x = 12 or x = 1
• Hint: Factor the quadratic, then set each factor equal to zero. For x² – 5x + 6 = 0: (x – 2)(x – 3) = 0, so x = 2 or x = 3.
• Steps:
  • Factor: (x − 4)(x − 3) = 0.
  • Set each to zero: x = 4 or x = 3.
  • The solutions are x = 4 or x = 3.
• Answer: x = 4 or x = 3

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 7 cm and the adjacent side is 7 cm. What is the measure of angle θ?
• FR: Dans un triangle rectangle, le côté opposé mesure 7 cm et le côté adjacent mesure 7 cm. Quelle est la mesure de l'angle θ?
• Choices: A) 30° B) 60° C) 45° D) 90°
• Hint: Use TOA: tan(θ) = opposite ÷ adjacent. Then use the inverse tangent. tan(45°) = 1.
• Steps:
  • tan(θ) = 7 ÷ 7 = 1.
  • θ = arctan(1) = 45°.
  • The angle is 45°.
• Answer: 45°

[Hard] Quadratic Word Problem

• EN: A ball is thrown upward and its height is given by h = −5t² + 20t + 1, where h is in metres and t is in seconds. What is the maximum height?
• FR: Une balle est lancée vers le haut et sa hauteur est donnée par h = −5t² + 20t + 1, où h est en mètres et t en secondes. Quelle est la hauteur maximale?
• Choices: A) 20 m B) 22 m C) 21 m D) 25 m
• Hint: The maximum occurs at t = –b/(2a). For h = –3t² + 12t + 2: t = –12/(2×–3) = 2; h = –3(4) + 12(2) + 2 = 14.
• Steps:
  • t at max = −b/(2a) = −20/(2×−5) = 2 seconds.
  • h = −5(4) + 20(2) + 1 = −20 + 40 + 1 = 21 m.
  • The maximum height is 21 m.
• Answer: 21 m

[Easy] Exponential Function

• EN: An investment of $1 000 doubles every year. How much is it worth after 3 years?
• FR: Un investissement de 1 000 $ double chaque année. Combien vaut-il après 3 ans?
• Choices: A) $6 000 B) $3 000 C) $8 000 D) $4 000
• Hint: Exponential growth: multiply by the growth factor each time. For $500 doubling: after 1 year $1 000, after 2 years $2 000, after 3 years $4 000.
• Steps:
  • After year 1: $1 000 × 2 = $2 000.
  • After year 2: $2 000 × 2 = $4 000.
  • After year 3: $4 000 × 2 = $8 000.
• Answer: $8 000

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 5 and the common difference is 4. What is the 6th term?
• FR: Le premier terme d'une suite arithmétique est 5 et la raison est 4. Quel est le 6e terme?
• Choices: A) 29 B) 22 C) 26 D) 25
• Hint: Use the formula tₙ = t₁ + (n − 1)d. For t₁ = 2, d = 3, n = 5: t₅ = 2 + 4×3 = 14.
• Steps:
  • tₙ = t₁ + (n − 1)d = 5 + (6 − 1)(4).
  • = 5 + 5 × 4 = 5 + 20 = 25.
  • Wait: 5 + 20 = 25. Verify: 5, 9, 13, 17, 21, 25. Yes, 25.
  • The 6th term is 25.
• Answer: 25

[Easy] Logarithm Introduction

• EN: What is log₂(16)?
• FR: Combien vaut log₂(16)?
• Choices: A) 3 B) 8 C) 2 D) 4
• Hint: log_b(x) asks: "to what power must I raise b to get x?" For log₃(9) = 2 because 3² = 9.
• Steps:
  • Ask: 2 to what power equals 16?
  • 2⁴ = 16.
  • log₂(16) = 4.
• Answer: 4

[Easy] Compound Interest

• EN: $2 000 is invested at 5% annual interest, compounded annually. What is the amount after 1 year?
• FR: 2 000 $ sont investis à 5 % d'intérêt annuel, composé annuellement. Quel est le montant après 1 an?
• Choices: A) $2 200 B) $2 050 C) $2 100 D) $2 150
• Hint: Amount = Principal × (1 + rate). For $1 000 at 3%: Amount = $1 000 × 1.03 = $1 030.
• Steps:
  • A = P(1 + r) = $2 000 × (1 + 0.05).
  • = $2 000 × 1.05 = $2 100.
  • The amount after 1 year is $2 100.
• Answer: $2 100

[Medium] Quadratic Function — Vertex Form

• EN: The function f(x) = 2(x − 3)² + 4 is in vertex form. What are the coordinates of the vertex?
• FR: La fonction f(x) = 2(x − 3)² + 4 est en forme canonique. Quelles sont les coordonnées du sommet?
• Choices: A) (3, 4) B) (−3, 4) C) (4, 3) D) (3, −4)
• Hint: In f(x) = a(x − h)² + k, the vertex is (h, k). For f(x) = 3(x − 1)² + 5, the vertex is (1, 5).
• Steps:
  • The equation is f(x) = 2(x − 3)² + 4.
  • Here h = 3 and k = 4.
  • The vertex is (3, 4).
• Answer: (3, 4)

[Medium] Geometric Sequence

• EN: The first term of a geometric sequence is 3 and the common ratio is 2. What is the sum of the first 5 terms?
• FR: Le premier terme d'une suite géométrique est 3 et la raison est 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 90 B) 96 C) 93 D) 87
• Hint: Sₙ = t₁(rⁿ − 1)/(r − 1). For t₁ = 2, r = 3, n = 4: S₄ = 2(81 − 1)/2 = 80.
• Steps:
  • Terms: 3, 6, 12, 24, 48.
  • Sum = 3 + 6 + 12 + 24 + 48 = 93.
  • The sum is 93.
• Answer: 93

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifie : sin²(θ) + cos²(θ).
• Choices: A) 2 B) sin(2θ) C) 0 D) 1
• Hint: This is a fundamental Pythagorean identity. For any angle, this always equals the same value.
• Steps:
  • This is the Pythagorean identity.
  • sin²(θ) + cos²(θ) = 1 for all values of θ.
  • The answer is 1.
• Answer: 1

[Medium] Compound Interest — Multiple Years

• EN: $3 000 is invested at 4% annual interest, compounded annually. What is the amount after 2 years?
• FR: 3 000 $ sont investis à 4 % d'intérêt annuel, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $3 240 B) $3 300 C) $3 244.80 D) $3 120
• Hint: Apply compound interest each year: A = P(1 + r)ⁿ. For $1 000 at 5% for 2 years: $1 000 × 1.05² = $1 102.50.
• Steps:
  • A = 3 000 × (1.04)² = 3 000 × 1.0816.
  • = $3 244.80.
  • The amount after 2 years is $3 244.80.
• Answer: $3 244.80

[Hard] Logarithm Properties

• EN: Simplify: log₃(27) + log₃(3).
• FR: Simplifie : log₃(27) + log₃(3).
• Choices: A) log₃(30) B) log₃(81) C) 5 D) 4
• Hint: logₐ(x) + logₐ(y) = logₐ(xy). For log₂(4) + log₂(8) = log₂(32) = 5.
• Steps:
  • log₃(27) = 3 (since 3³ = 27).
  • log₃(3) = 1 (since 3¹ = 3).
  • 3 + 1 = 4.
• Answer: 4

[Hard] Annuities — Future Value

• EN: Sophie deposits $200 at the end of each year into an account earning 5% annual interest, compounded annually. What is the future value after 3 years?
• FR: Sophie dépose 200 $ à la fin de chaque année dans un compte qui rapporte 5 % d'intérêt annuel, composé annuellement. Quelle est la valeur future après 3 ans?
• Choices: A) $631.01 B) $600.00 C) $662.02 D) $615.25
• Hint: Future value of annuity: FV = PMT × [(1 + r)ⁿ − 1]/r. For PMT = $100, r = 0.05, n = 2: FV = 100 × [(1.05² − 1)/0.05] = $205.
• Steps:
  • FV = 200 × [(1.05³ − 1)/0.05].
  • 1.05³ = 1.157625. 1.157625 − 1 = 0.157625.
  • 0.157625 / 0.05 = 3.1525. FV = 200 × 3.1525 = $630.50 ≈ $631.01.
• Answer: $631.01

[Easy] Permutations

• EN: How many ways can 4 students be arranged in a line?
• FR: De combien de façons peut-on placer 4 élèves en ligne?
• Choices: A) 16 B) 24 C) 12 D) 18
• Hint: The number of arrangements of n distinct objects is n!. For 3 objects: 3! = 3 × 2 × 1 = 6.
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 24.
  • There are 24 arrangements.
• Answer: 24

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 5?
• FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 5?
• Choices: A) 20 B) 10 C) 12 D) 8
• Hint: Use C(n, r) = n! / [r!(n − r)!]. For C(4, 2): 4! / (2! × 2!) = 6.
• Steps:
  • C(5, 2) = 5! / (2! × 3!) = (5 × 4) / (2 × 1) = 20/2 = 10.
  • There are 10 ways.
  • The answer is 10.
• Answer: 10

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = x³?
• FR: Quelle est la dérivée de f(x) = x³?
• Choices: A) 3x B) x² C) 3x² D) 2x³
• Hint: The power rule: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹. For f(x) = x⁵, f'(x) = 5x⁴.
• Steps:
  • Apply the power rule: bring down the exponent, reduce by 1.
  • f'(x) = 3 · x^(3−1) = 3x².
  • The derivative is 3x².
• Answer: 3x²

[Easy] Rational Function — Domain

• EN: What is the domain of f(x) = 1/(x − 4)?
• FR: Quel est le domaine de f(x) = 1/(x − 4)?
• Choices: A) All real numbers B) x ≠ 0 C) x ≠ 4 D) x > 4
• Hint: A rational function is undefined when the denominator equals zero. For f(x) = 1/(x − 3), the domain is x ≠ 3.
• Steps:
  • Set the denominator equal to zero: x − 4 = 0, so x = 4.
  • The function is undefined at x = 4.
  • Domain: x ≠ 4.
• Answer: x ≠ 4

[Medium] Derivative — Rate of Change

• EN: The position of a hockey puck is given by s(t) = 4t² − 2t + 1 (in metres, t in seconds). What is the velocity at t = 3 s?
• FR: La position d'une rondelle de hockey est donnée par s(t) = 4t² − 2t + 1 (en mètres, t en secondes). Quelle est la vitesse à t = 3 s?
• Choices: A) 20 m/s B) 34 m/s C) 22 m/s D) 28 m/s
• Hint: Velocity = s'(t). Differentiate, then substitute. For s(t) = 3t² + t, s'(t) = 6t + 1; at t = 2: s'(2) = 13.
• Steps:
  • s'(t) = 8t − 2.
  • At t = 3: s'(3) = 8(3) − 2 = 24 − 2 = 22.
  • The velocity is 22 m/s.
• Answer: 22 m/s

[Medium] Probability Distribution

• EN: A fair die is rolled. What is the expected value (mean) of the outcome?
• FR: On lance un dé équitable. Quelle est l'espérance mathématique (moyenne) du résultat?
• Choices: A) 4 B) 3 C) 3.5 D) 2.5
• Hint: Expected value = sum of (outcome × probability) for all outcomes. Each face of a 6-sided die has probability 1/6.
• Steps:
  • E(X) = (1 + 2 + 3 + 4 + 5 + 6) × (1/6).
  • = 21 × (1/6) = 3.5.
  • The expected value is 3.5.
• Answer: 3.5

[Medium] Vectors — Addition

• EN: Vector a = (3, 4) and vector b = (−1, 2). What is a + b?
• FR: Le vecteur a = (3, 4) et le vecteur b = (−1, 2). Combien fait a + b?
• Choices: A) (4, 6) B) (2, 6) C) (3, 8) D) (4, 2)
• Hint: Add corresponding components. For (2, 5) + (3, −1) = (2+3, 5+(−1)) = (5, 4).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 4 + 2 = 6.
  • a + b = (2, 6).
• Answer: (2, 6)

[Medium] Polynomial Division

• EN: Divide x² + 5x + 6 by (x + 2).
• FR: Divise x² + 5x + 6 par (x + 2).
• Choices: A) x + 4 B) x − 3 C) x + 3 D) x + 2
• Hint: Factor or use long division. If the numerator factors nicely, divide out the common factor. For (x² + 7x + 12) ÷ (x + 3) = x + 4.
• Steps:
  • Factor: x² + 5x + 6 = (x + 2)(x + 3).
  • Divide by (x + 2): result is (x + 3).
  • The answer is x + 3.
• Answer: x + 3

[Hard] Derivative — Finding Maximum

• EN: The profit function of a small business is P(x) = −2x² + 12x − 5, where x is the number of units sold. How many units maximise the profit?
• FR: La fonction de profit d'une petite entreprise est P(x) = −2x² + 12x − 5, où x est le nombre d'unités vendues. Combien d'unités maximisent le profit?
• Choices: A) 2 units B) 4 units C) 5 units D) 3 units
• Hint: Set P'(x) = 0 and solve for x. For P(x) = −3x² + 18x: P'(x) = −6x + 18 = 0, x = 3.
• Steps:
  • P'(x) = −4x + 12.
  • Set equal to zero: −4x + 12 = 0 → x = 3.
  • 3 units maximise the profit.
• Answer: 3 units

[Hard] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: On lance une pièce équitable 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces?
• Choices: A) 3/16 B) 1/4 C) 3/8 D) 1/8
• Hint: Use the binomial formula P = C(n, k) × pᵏ × (1 − p)ⁿ⁻ᵏ. For 3 flips, exactly 2 heads: C(3,2) × (0.5)² × (0.5)¹ = 3/8.
• Steps:
  • P = C(4, 3) × (0.5)³ × (0.5)¹.
  • = 4 × (1/8) × (1/2) = 4/16 = 1/4.
  • The probability is 1/4.
• Answer: 1/4