Daily Math — 2026-08-03

[Easy] Counting Hockey Pucks

• EN: There are 7 pucks on the ice. 3 more are added. How many pucks are there now?
• FR: Il y a 7 rondelles sur la glace. On en ajoute 3. Combien de rondelles y a-t-il maintenant?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Count on from the bigger number — if you have 5 and add 2, count 6, 7.
• Steps:
  • Start at 7.
  • Count on 3 more: 8, 9, 10.
  • So there are 10 pucks in total.
• Answer: 10

[Easy] Mittens in a Basket

• EN: A basket has 15 mittens. A child takes out 4. How many mittens are left?
• FR: Un panier contient 15 mitaines. Un enfant en prend 4. Combien de mitaines reste-t-il?
• Choices: A) 10 B) 11 C) 13 D) 19
• Hint: To subtract, count backwards — 8 take away 2 means count back 2 from 8: 7, 6.
• Steps:
  • Start at 15.
  • Count back 4: 14, 13, 12, 11.
  • So 11 mittens are left.
• Answer: 11

[Easy] Skip Counting by 5s

• EN: Skip count by 5s. What number comes after 15?
• FR: Compte par bonds de 5. Quel nombre vient après 15?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: When skip counting by 5s, add 5 each time — 5, 10, 15, then add 5 more.
• Steps:
  • The pattern is 5, 10, 15, …
  • Add 5 to 15: 15 + 5 = 20.
  • The next number is 20.
• Answer: 20

[Easy] Which Number is Bigger?

• EN: Which number is greater: 13 or 18?
• FR: Quel nombre est le plus grand : 13 ou 18?
• Choices: A) 13 B) 18 C) They are equal D) Neither number
• Hint: Compare the tens first — if tens are the same, look at the ones digit.
• Steps:
  • Both numbers have 1 ten.
  • Compare the ones: 3 ones vs 8 ones.
  • 8 ones is more, so 18 is greater.
• Answer: 18

[Medium] Coins at the Store

• EN: Anika has 2 nickels and 3 pennies. How many cents does she have in total?
• FR: Anika a 2 pièces de 5 cents et 3 pièces de 1 cent. Combien de cents a-t-elle au total?
• Choices: A) 5 cents B) 8 cents C) 13 cents D) 15 cents
• Hint: Each nickel is worth 5 cents — if you have 3 nickels, that is 15 cents, then add any pennies.
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 3 pennies = 3 cents.
  • 10 + 3 = 13 cents.
• Answer: 13 cents

[Medium] Snowflakes on a Window

• EN: There are 8 snowflakes on one side of a window and 6 on the other side. How many snowflakes are there altogether?
• FR: Il y a 8 flocons de neige d'un côté d'une fenêtre et 6 de l'autre côté. Combien y a-t-il de flocons en tout?
• Choices: A) 12 B) 14 C) 16 D) 18
• Hint: Use doubles plus one — if you know 7 + 7 = 14, then 8 + 6 is close to that.
• Steps:
  • 8 + 6: think of 8 + 2 = 10, then add the remaining 4.
  • 10 + 4 = 14.
  • There are 14 snowflakes altogether.
• Answer: 14

[Medium] Skip Counting by 2s

• EN: Omar counted by 2s starting at 2. What is the 6th number he said?
• FR: Omar comptait par bonds de 2 en commençant à 2. Quel est le 6e nombre qu'il a dit?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Write the pattern — 2, 4, 6, 8 — and count which position each number is in.
• Steps:
  • 1st: 2, 2nd: 4, 3rd: 6, 4th: 8, 5th: 10, 6th: 12.
  • The 6th number is 12.
• Answer: 12

[Medium] Apples in Two Bags

• EN: One bag has 9 apples and another bag has 9 apples. How many apples are there in all?
• FR: Un sac contient 9 pommes et un autre sac en contient 9. Combien y a-t-il de pommes en tout?
• Choices: A) 16 B) 17 C) 18 D) 19
• Hint: Doubles are quick to learn — 6 + 6 = 12, 7 + 7 = 14, so 9 + 9 = ?
• Steps:
  • This is a doubles fact: 9 + 9.
  • 9 + 9 = 18.
  • There are 18 apples in all.
• Answer: 18

[Hard] How Many Are Left?

• EN: There are 20 students in a class. 7 go to the library and 4 go to gym. How many students stay in the classroom?
• FR: Il y a 20 élèves dans une classe. 7 vont à la bibliothèque et 4 vont au gymnase. Combien d'élèves restent dans la classe?
• Choices: A) 7 B) 9 C) 11 D) 13
• Hint: Subtract one group at a time — start with the total and take away each group.
• Steps:
  • Start with 20 students.
  • Take away 7: 20 − 7 = 13.
  • Take away 4 more: 13 − 4 = 9.
• Answer: 9

[Hard] Mystery Number

• EN: I am a number less than 20. If you add 8 to me, you get 17. What number am I?
• FR: Je suis un nombre inférieur à 20. Si tu m'ajoutes 8, tu obtiens 17. Quel nombre suis-je?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Think of it as a missing addend — if 3 + ? = 10, count up from 3 to 10.
• Steps:
  • We need a number that, when added to 8, gives 17.
  • Count up from 8 to 17: 8 + 9 = 17.
  • The mystery number is 9.
• Answer: 9

[Easy] Adding Two-Digit Numbers

• EN: There are 23 red crayons and 14 blue crayons in a box. How many crayons are there in all?
• FR: Il y a 23 crayons rouges et 14 crayons bleus dans une boîte. Combien y a-t-il de crayons en tout?
• Choices: A) 35 B) 36 C) 37 D) 38
• Hint: Add the ones first, then the tens — for 32 + 15, add 2 + 5 = 7 ones, then 3 + 1 = 4 tens.
• Steps:
  • Ones: 3 + 4 = 7.
  • Tens: 2 + 1 = 3.
  • 23 + 14 = 37 crayons.
• Answer: 37

[Easy] Telling Time

• EN: The clock shows the hour hand on 4 and the minute hand on 12. What time does it show?
• FR: L'horloge montre la petite aiguille sur le 4 et la grande aiguille sur le 12. Quelle heure indique-t-elle?
• Choices: A) 3:00 B) 4:00 C) 4:30 D) 12:00
• Hint: When the minute hand is on 12, it is exactly on the hour — look at the hour hand to find the hour.
• Steps:
  • Minute hand on 12 means it is exactly on the hour.
  • Hour hand is on 4.
  • The time is 4:00.
• Answer: 4:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon est long de 14 cm. Un crayon de couleur est long de 9 cm. De combien le crayon est-il plus long que le crayon de couleur?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find the difference in length, subtract the shorter from the longer — 12 − 7 = 5.
• Steps:
  • Subtract: 14 − 9.
  • 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Subtraction within 100

• EN: A box had 50 stickers. Maya gave away 23 stickers. How many stickers does she have left?
• FR: Une boîte contenait 50 autocollants. Maya en a donné 23. Combien d'autocollants lui reste-t-il?
• Choices: A) 23 B) 25 C) 27 D) 33
• Hint: Subtract the ones first, then the tens — for 50 − 21, do 0 − 1 (regroup if needed), then tens.
• Steps:
  • 50 − 23: borrow from the tens. 10 − 3 = 7 ones.
  • Tens: 4 − 2 = 2 tens.
  • 50 − 23 = 27 stickers.
• Answer: 27

[Medium] Counting Coins

• EN: Liam has 1 dime, 2 nickels, and 3 pennies. How much money does he have?
• FR: Liam a 1 pièce de 10 cents, 2 pièces de 5 cents et 3 pièces de 1 cent. Combien d'argent a-t-il?
• Choices: A) 16 cents B) 18 cents C) 20 cents D) 23 cents
• Hint: Add the biggest coins first — 1 dime = 10 cents, 1 nickel = 5 cents, 1 penny = 1 cent.
• Steps:
  • 1 dime = 10 cents.
  • 2 nickels = 10 cents.
  • 3 pennies = 3 cents. Total: 10 + 10 + 3 = 23 cents.
• Answer: 23 cents

[Medium] Telling Time — Half Hour

• EN: Zara started reading at 2:00. She read for half an hour. What time did she finish?
• FR: Zara a commencé à lire à 2 h. Elle a lu pendant une demi-heure. À quelle heure a-t-elle fini?
• Choices: A) 2:15 B) 2:30 C) 3:00 D) 3:30
• Hint: Half an hour is 30 minutes — if you start at 1:00 and add 30 minutes, you finish at 1:30.
• Steps:
  • Start time: 2:00.
  • Add 30 minutes (half an hour).
  • 2:00 + 30 minutes = 2:30.
• Answer: 2:30

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, ___. What is the missing number?
• FR: Observe ce patron : 5, 10, 15, 20, ___. Quel est le nombre manquant?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: Find the rule by looking at what is added each time — 2, 4, 6, 8 increases by 2 each step.
• Steps:
  • Each number increases by 5.
  • 20 + 5 = 25.
  • The missing number is 25.
• Answer: 25

[Medium] Measuring with Metres

• EN: A hallway is 8 metres long. A classroom is 6 metres long. How long are both rooms together?
• FR: Un couloir mesure 8 mètres. Une salle de classe mesure 6 mètres. Quelle est la longueur totale des deux pièces?
• Choices: A) 12 m B) 13 m C) 14 m D) 16 m
• Hint: Adding lengths works just like adding numbers — 5 m + 4 m = 9 m.
• Steps:
  • 8 metres + 6 metres.
  • 8 + 6 = 14.
  • Together they are 14 m long.
• Answer: 14 m

[Hard] Coins to One Dollar

• EN: Priya wants to buy a Tim Hortons Timbit for 75 cents. She has 2 dimes, 4 nickels, and 7 pennies. Does she have enough money, and how much more or less does she need?
• FR: Priya veut acheter un Timbit de Tim Hortons pour 75 cents. Elle a 2 pièces de 10 cents, 4 pièces de 5 cents et 7 pièces de 1 cent. A-t-elle assez d'argent, et de combien manque-t-il ou a-t-elle de trop?
• Choices: A) She has enough, with 2 cents extra B) She needs 28 more cents C) She needs 28 more cents D) She is short by 22 cents
• Hint: Count your coins total first, then compare to the price — if total is less, subtract to find how short you are.
• Steps:
  • 2 dimes = 20 cents, 4 nickels = 20 cents, 7 pennies = 7 cents.
  • Total = 20 + 20 + 7 = 47 cents.
  • 75 − 47 = 28 cents short. She needs 28 more cents.
• Answer: She needs 28 more cents

[Hard] Two-Step Subtraction

• EN: A bag had 80 marbles. Ben took out 35 marbles on Monday and 18 marbles on Tuesday. How many marbles are left in the bag?
• FR: Un sac contenait 80 billes. Ben en a pris 35 le lundi et 18 le mardi. Combien de billes restent dans le sac?
• Choices: A) 27 B) 29 C) 45 D) 62
• Hint: Solve in two steps — subtract the first amount, then subtract the second amount from what is left.
• Steps:
  • Start: 80 marbles. Subtract Monday: 80 − 35 = 45.
  • Subtract Tuesday: 45 − 18 = 27.
  • There are 27 marbles left.
• Answer: 27

[Easy] Multiplication by 2

• EN: A hockey team has 6 players on the ice. Each player has 2 gloves. How many gloves are there in all?
• FR: Une équipe de hockey a 6 joueurs sur la glace. Chaque joueur a 2 gants. Combien y a-t-il de gants en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiply by 2 by doubling — 7 × 2 = 14 because 7 + 7 = 14.
• Steps:
  • 6 players × 2 gloves each.
  • 6 × 2 = 12.
  • There are 12 gloves in all.
• Answer: 12

[Easy] Identifying Fractions

• EN: A pizza is cut into 4 equal slices. Emma eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 parts égales. Emma mange 1 part. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: The fraction has the number of pieces eaten on top and the total pieces on the bottom.
• Steps:
  • Total slices = 4 (denominator).
  • Emma ate 1 slice (numerator).
  • The fraction is 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: There are 4 bags of apples with 5 apples in each bag. How many apples are there altogether?
• FR: Il y a 4 sacs de pommes avec 5 pommes dans chaque sac. Combien y a-t-il de pommes en tout?
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: Multiples of 5 always end in 0 or 5 — count by 5s to check: 5, 10, 15, 20.
• Steps:
  • 4 bags × 5 apples = ?
  • 4 × 5 = 20.
  • There are 20 apples altogether.
• Answer: 20

[Easy] Perimeter of a Rectangle

• EN: A rectangle is 5 cm long and 3 cm wide. What is its perimeter?
• FR: Un rectangle mesure 5 cm de long et 3 cm de large. Quel est son périmètre?
• Choices: A) 8 cm B) 13 cm C) 15 cm D) 16 cm
• Hint: Perimeter is the total distance around — add all four sides, or use 2 × (length + width).
• Steps:
  • Add all four sides: 5 + 3 + 5 + 3.
  • 5 + 3 = 8, then 8 + 8 = 16.
  • The perimeter is 16 cm.
• Answer: 16 cm

[Medium] Basic Division

• EN: There are 24 cookies to share equally among 4 friends. How many cookies does each friend get?
• FR: Il y a 24 biscuits à partager également entre 4 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Division is the opposite of multiplication — think "4 × ? = 24" to find the answer.
• Steps:
  • 24 ÷ 4 = ?
  • Think: 4 × 6 = 24.
  • Each friend gets 6 cookies.
• Answer: 6

[Medium] Reading a Bar Graph

• EN: A bar graph shows: Monday = 8 books returned, Tuesday = 5 books returned, Wednesday = 7 books returned. How many books were returned in all three days?
• FR: Un diagramme à bandes montre : lundi = 8 livres retournés, mardi = 5 livres retournés, mercredi = 7 livres retournés. Combien de livres ont été retournés en tout au cours de ces trois jours?
• Choices: A) 18 B) 19 C) 20 D) 21
• Hint: To find the total from a graph, add up all the bars — 4 + 6 + 3 = 13.
• Steps:
  • Add: 8 + 5 + 7.
  • 8 + 5 = 13, then 13 + 7 = 20.
  • A total of 20 books were returned.
• Answer: 20

[Medium] Multiplication by 10

• EN: A school orders 7 boxes of pencils with 10 pencils in each box. How many pencils are ordered in total?
• FR: Une école commande 7 boîtes de crayons avec 10 crayons dans chaque boîte. Combien de crayons sont commandés en tout?
• Choices: A) 17 B) 60 C) 70 D) 77
• Hint: Multiplying by 10 is easy — just add a zero to the other number: 6 × 10 = 60.
• Steps:
  • 7 × 10 = ?
  • When you multiply by 10, write the number followed by a zero.
  • 7 × 10 = 70 pencils.
• Answer: 70

[Medium] Fractions of a Group

• EN: There are 12 students in a group. One quarter (1/4) of them are wearing hats. How many students are wearing hats?
• FR: Il y a 12 élèves dans un groupe. Un quart (1/4) d'entre eux portent un chapeau. Combien d'élèves portent un chapeau?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: To find 1/4 of a group, divide the total by 4 — 1/4 of 8 is 8 ÷ 4 = 2.
• Steps:
  • 1/4 of 12 means 12 ÷ 4.
  • 12 ÷ 4 = 3.
  • Three students are wearing hats.
• Answer: 3

[Hard] Multiplication and Addition Together

• EN: Noah buys 3 packs of hockey cards with 9 cards each, and then finds 5 loose cards in his drawer. How many hockey cards does he have in total?
• FR: Noah achète 3 paquets de cartes de hockey avec 9 cartes chacun, puis trouve 5 cartes en vrac dans son tiroir. Combien de cartes de hockey a-t-il au total?
• Choices: A) 27 B) 30 C) 32 D) 36
• Hint: Do the multiplication first, then add the extra amount — 4 packs of 6 cards plus 3 loose cards: 24 + 3 = 27.
• Steps:
  • 3 packs × 9 cards = 27 cards.
  • Add 5 loose cards: 27 + 5 = 32.
  • Noah has 32 hockey cards in total.
• Answer: 32

[Hard] Perimeter Problem

• EN: A triangle has sides of 8 cm, 8 cm, and 6 cm. What is its perimeter?
• FR: Un triangle a des côtés de 8 cm, 8 cm et 6 cm. Quel est son périmètre?
• Choices: A) 14 cm B) 16 cm C) 20 cm D) 22 cm
• Hint: Add all the sides together to find the perimeter — for a triangle with sides 5, 5, and 4, the perimeter is 5 + 5 + 4 = 14.
• Steps:
  • Add all three sides: 8 + 8 + 6.
  • 8 + 8 = 16, then 16 + 6 = 22.
  • The perimeter is 22 cm.
• Answer: 22 cm

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Break it apart — 7 × 8 is the same as 7 × 4 × 2, or think of 7 × 7 = 49, then add one more 7.
• Steps:
  • 7 × 7 = 49.
  • Add one more group of 7: 49 + 7 = 56.
  • 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, which digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre se trouve à la position des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 47
• Hint: After the decimal point, the first digit is tenths and the second digit is hundredths.
• Steps:
  • 3 is in the ones place.
  • 4 is in the tenths place (first digit after the decimal).
  • 7 is in the hundredths place.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A rectangular garden is 9 m long and 4 m wide. What is its area?
• FR: Un jardin rectangulaire mesure 9 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 13 m² B) 26 m² C) 36 m² D) 40 m²
• Hint: Area of a rectangle = length × width — for a 6 m × 3 m room, area = 18 m².
• Steps:
  • Area = length × width.
  • 9 × 4 = 36.
  • The area is 36 m².
• Answer: 36 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/4?
• FR: Quelle fraction est la plus grande : 3/4 ou 1/4?
• Choices: A) 1/4 B) 3/4 C) They are equal D) Neither can be compared
• Hint: When fractions have the same denominator, the one with the bigger numerator is greater.
• Steps:
  • Both fractions have denominator 4.
  • Compare numerators: 3 vs 1.
  • 3 > 1, so 3/4 > 1/4.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: A teacher has 37 stickers to share equally among 5 students. How many stickers does each student get, and how many are left over?
• FR: Une enseignante a 37 autocollants à partager également entre 5 élèves. Combien d'autocollants chaque élève reçoit-il et combien en reste-t-il?
• Choices: A) 6 remainder 7 B) 7 remainder 2 C) 7 remainder 5 D) 8 remainder 3
• Hint: Divide and check — 5 × 7 = 35, so if you have 37, subtract 35 to find the remainder.
• Steps:
  • 37 ÷ 5: 5 × 7 = 35.
  • Remainder: 37 − 35 = 2.
  • Each student gets 7 stickers with 2 left over.
• Answer: 7 remainder 2

[Medium] Elapsed Time

• EN: A hockey game started at 6:15 PM and ended at 8:45 PM. How long did the game last?
• FR: Un match de hockey a commencé à 18 h 15 et s'est terminé à 20 h 45. Combien de temps a duré le match?
• Choices: A) 1 hour 30 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours 15 minutes
• Hint: Count the hours first, then the minutes — from 3:10 to 5:40 is 2 hours and 30 minutes.
• Steps:
  • From 6:15 to 8:15 is exactly 2 hours.
  • From 8:15 to 8:45 is 30 minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: Sophia bought a notebook for $2.35 and a pen for $1.50. How much did she spend in total?
• FR: Sophia a acheté un cahier pour 2,35 $ et un stylo pour 1,50 $. Combien a-t-elle dépensé en tout?
• Choices: A) $3.75 B) $3.85 C) $4.05 D) $4.85
• Hint: Line up the decimal points and add — $1.25 + $2.30: add hundredths, tenths, then ones.
• Steps:
  • $2.35 + $1.50: add hundredths 5 + 0 = 5.
  • Add tenths: 3 + 5 = 8.
  • Add ones: 2 + 1 = 3. Total = $3.85.
• Answer: $3.85

[Medium] All Multiplication Tables

• EN: A baker bakes 9 trays of muffins with 9 muffins on each tray. How many muffins are there in all?
• FR: Un boulanger fait cuire 9 plateaux de muffins avec 9 muffins sur chaque plateau. Combien y a-t-il de muffins en tout?
• Choices: A) 72 B) 78 C) 81 D) 90
• Hint: 9 × 9 is a great fact to memorize — think of 10 × 9 = 90, then subtract one group of 9.
• Steps:
  • 9 × 9: use 10 × 9 = 90, subtract 9.
  • 90 − 9 = 81.
  • There are 81 muffins in all.
• Answer: 81

[Hard] Multi-Step Area and Perimeter

• EN: A rectangular schoolyard is 12 m long and 8 m wide. The principal wants to put a fence around it and also know its area. What is the perimeter of the schoolyard?
• FR: Une cour d'école rectangulaire mesure 12 m de long et 8 m de large. La directrice veut y poser une clôture et connaître aussi son aire. Quel est le périmètre de la cour?
• Choices: A) 20 m B) 40 m C) 96 m² D) 96 m
• Hint: Perimeter uses addition around all sides; area uses multiplication — do not mix them up.
• Steps:
  • Perimeter = 2 × (length + width).
  • 2 × (12 + 8) = 2 × 20 = 40.
  • The perimeter is 40 m.
• Answer: 40 m

[Hard] Long Division and Decimals

• EN: A store has 96 granola bars to pack into boxes of 8. How many full boxes can be packed?
• FR: Un magasin a 96 barres de céréales à emballer dans des boîtes de 8. Combien de boîtes pleines peut-on emballer?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: Use long division — divide and check by multiplying your answer back: 8 × 12 = 96.
• Steps:
  • 96 ÷ 8 = ?
  • 8 × 12 = 96 (check: 8 × 10 = 80, 8 × 2 = 16, 80 + 16 = 96). ✓
  • Exactly 12 full boxes can be packed.
• Answer: 12

[Easy] Multi-Digit Multiplication

• EN: A store sells 125 boxes of crayons. Each box has 8 crayons. How many crayons are there in total?
• FR: Un magasin vend 125 boîtes de crayons. Chaque boîte contient 8 crayons. Combien y a-t-il de crayons en tout?
• Choices: A) 800 B) 900 C) 1 000 D) 1 250
• Hint: Multiply by ones digit first, then by tens, then hundreds — just like 124 × 3: 3×4, 3×20, 3×100.
• Steps:
  • 125 × 8: 8 × 5 = 40, write 0 carry 4.
  • 8 × 2 = 16 + 4 = 20, write 0 carry 2.
  • 8 × 1 = 8 + 2 = 10. Result: 1 000.
• Answer: 1 000

[Easy] Adding Fractions with Like Denominators

• EN: Jake ate 2/8 of a pie and his sister ate 3/8 of the same pie. How much pie did they eat together?
• FR: Jake a mangé 2/8 d'une tarte et sa sœur en a mangé 3/8. Quelle fraction de la tarte ont-ils mangée ensemble?
• Choices: A) 5/16 B) 5/8 C) 6/8 D) 1/2
• Hint: When denominators are the same, just add the numerators and keep the denominator — 1/5 + 2/5 = 3/5.
• Steps:
  • Same denominator (8), so add numerators: 2 + 3 = 5.
  • Keep the denominator: 5/8.
  • They ate 5/8 of the pie together.
• Answer: 5/8

[Easy] Percentage Introduction

• EN: A sweater costs $40. It is on sale for 25% off. How much money do you save?
• FR: Un chandail coûte 40 $. Il est en solde à 25 % de rabais. Combien d'argent économises-tu?
• Choices: A) $4 B) $8 C) $10 D) $12
• Hint: 25% means one quarter — to find 25% of any number, divide it by 4.
• Steps:
  • 25% of $40 = $40 ÷ 4.
  • $40 ÷ 4 = $10.
  • You save $10.
• Answer: $10

[Easy] Volume of a Rectangular Prism

• EN: A box is 4 cm long, 3 cm wide, and 2 cm tall. What is its volume?
• FR: Une boîte mesure 4 cm de long, 3 cm de large et 2 cm de haut. Quel est son volume?
• Choices: A) 9 cm³ B) 18 cm³ C) 24 cm³ D) 26 cm³
• Hint: Volume = length × width × height — for a 5 × 2 × 3 box, volume = 30 cm³.
• Steps:
  • Volume = 4 × 3 × 2.
  • 4 × 3 = 12, then 12 × 2 = 24.
  • The volume is 24 cm³.
• Answer: 24 cm³

[Medium] Multi-Digit Division

• EN: A school orders 576 pencils to share equally among 24 classrooms. How many pencils does each classroom receive?
• FR: Une école commande 576 crayons à partager également entre 24 classes. Combien de crayons chaque classe reçoit-elle?
• Choices: A) 20 B) 23 C) 24 D) 28
• Hint: Try dividing step by step — 24 × 20 = 480, then see how many are left to divide.
• Steps:
  • 576 ÷ 24: 24 × 20 = 480, remainder 576 − 480 = 96.
  • 24 × 4 = 96.
  • 576 ÷ 24 = 24 pencils per classroom.
• Answer: 24

[Medium] Decimal Operations

• EN: Snowfall on Monday was 3.8 cm and on Tuesday it was 5.65 cm. What was the total snowfall over both days?
• FR: Les chutes de neige de lundi étaient de 3,8 cm et de mardi de 5,65 cm. Quelle était la chute de neige totale sur ces deux jours?
• Choices: A) 8.35 cm B) 9.35 cm C) 9.45 cm D) 9.55 cm
• Hint: Line up the decimal points and add zeros as placeholders — 3.80 + 5.65.
• Steps:
  • Write 3.8 as 3.80.
  • 3.80 + 5.65: hundredths 0 + 5 = 5, tenths 8 + 6 = 14 (carry 1), ones 3 + 5 + 1 = 9.
  • Total = 9.45 cm.
• Answer: 9.45 cm

[Medium] Subtracting Fractions

• EN: A loaf of bread was cut into 10 equal slices. The family ate 7 slices. What fraction of the loaf is left?
• FR: Un pain a été coupé en 10 tranches égales. La famille en a mangé 7. Quelle fraction du pain reste-t-il?
• Choices: A) 2/10 B) 3/10 C) 7/10 D) 3/5
• Hint: Subtract the numerators when denominators match — 9/10 − 5/10 = 4/10.
• Steps:
  • Total: 10/10. Eaten: 7/10.
  • 10/10 − 7/10 = 3/10.
  • 3/10 of the loaf is left.
• Answer: 3/10

[Medium] 10% Percentage

• EN: A restaurant bill is $60. If you leave a 10% tip, how much is the tip?
• FR: Une addition au restaurant est de 60 $. Si tu laisses un pourboire de 10 %, quel est le montant du pourboire?
• Choices: A) $5 B) $6 C) $10 D) $16
• Hint: To find 10% of a number, just move the decimal point one place to the left — 10% of $80 = $8.
• Steps:
  • 10% of $60: move decimal left one place.
  • $60 → $6.0 = $6.
  • The tip is $6.
• Answer: $6

[Hard] Combined Fraction and Decimal

• EN: A runner completed 3/4 of a 12 km race. She then ran an extra 0.5 km to warm down. How many kilometres did she run in total?
• FR: Une coureuse a complété 3/4 d'une course de 12 km. Elle a ensuite couru 0,5 km supplémentaire pour récupérer. Combien de kilomètres a-t-elle couru au total?
• Choices: A) 8.5 km B) 9 km C) 9.5 km D) 10.5 km
• Hint: Find the fraction of the race first, then add the extra distance — find 3/4 of 12 by dividing 12 by 4 and multiplying by 3.
• Steps:
  • 3/4 of 12 km: 12 ÷ 4 = 3, then 3 × 3 = 9 km.
  • Add 0.5 km: 9 + 0.5 = 9.5 km.
  • She ran 9.5 km in total.
• Answer: 9.5 km

[Hard] Volume and Cost

• EN: A storage container is 5 m long, 4 m wide, and 3 m tall. It costs $2 per cubic metre to fill it with sand. What is the total cost to fill it completely?
• FR: Un conteneur de stockage mesure 5 m de long, 4 m de large et 3 m de haut. Il coûte 2 $ par mètre cube pour le remplir de sable. Quel est le coût total pour le remplir complètement?
• Choices: A) $24 B) $60 C) $120 D) $240
• Hint: Find the volume first using length × width × height, then multiply volume by the cost per cubic metre.
• Steps:
  • Volume = 5 × 4 × 3 = 60 m³.
  • Cost = 60 m³ × $2 = $120.
  • The total cost is $120.
• Answer: $120

[Easy] Percent of a Number

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

[Easy] Simple Algebraic Expressions

• EN: Evaluate the expression 4x + 3 when x = 5.
• FR: Évalue l'expression 4x + 3 lorsque x = 5.
• Choices: A) 12 B) 20 C) 23 D) 27
• Hint: Replace the variable with the given number and calculate — for 3x + 2 when x = 4: 3(4) + 2 = 14.
• Steps:
  • Replace x with 5: 4(5) + 3.
  • 4 × 5 = 20.
  • 20 + 3 = 23.
• Answer: 23

[Easy] Ratio Basics

• EN: In a class of 20 students, 8 are wearing blue shirts. What is the ratio of blue-shirt students to the total number of students?
• FR: Dans une classe de 20 élèves, 8 portent des chemises bleues. Quel est le rapport entre les élèves en chemise bleue et le nombre total d'élèves?
• Choices: A) 2:5 B) 3:5 C) 8:20 D) 12:20
• Hint: Write a ratio as part-to-whole and simplify if possible — 6 out of 15 simplifies to 2:5.
• Steps:
  • Ratio = 8 to 20.
  • Simplify: 8 ÷ 4 = 2, 20 ÷ 4 = 5.
  • The simplified ratio is 2:5.
• Answer: 2:5

[Easy] Integer Introduction

• EN: The temperature in Winnipeg was −8°C in the morning and rose by 11°C by the afternoon. What was the afternoon temperature?
• FR: La température à Winnipeg était de −8 °C le matin et a augmenté de 11 °C dans l'après-midi. Quelle était la température l'après-midi?
• Choices: A) −3°C B) 2°C C) 3°C D) 19°C
• Hint: Adding a positive number to a negative number — start on the number line at the negative number and move right.
• Steps:
  • −8 + 11.
  • Move 11 steps right from −8: −8 + 8 = 0, then 0 + 3 = 3.
  • The afternoon temperature was 3°C.
• Answer: 3°C

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1.
• FR: Évalue : 3 + 4 × 2 − 1.
• Choices: A) 10 B) 13 C) 14 D) 15
• Hint: Use BEDMAS — do multiplication before addition and subtraction: 5 + 3 × 2 = 5 + 6 = 11.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Now: 3 + 8 − 1.
  • 3 + 8 = 11, then 11 − 1 = 10.
• Answer: 10

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien vaut 2/3 × 3/4?
• Choices: A) 5/12 B) 5/7 C) 1/2 D) 6/7
• Hint: Multiply numerators together and denominators together — then simplify: 2/5 × 3/4 = 6/20 = 3/10.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Rate Problems

• EN: A car travels at 80 km per hour. How far will it travel in 3 hours?
• FR: Une voiture roule à 80 km à l'heure. Quelle distance parcourra-t-elle en 3 heures?
• Choices: A) 83 km B) 160 km C) 240 km D) 320 km
• Hint: Distance = rate × time — if a bike goes 15 km/h for 2 hours, it travels 30 km.
• Steps:
  • Distance = 80 km/h × 3 h.
  • 80 × 3 = 240.
  • The car will travel 240 km.
• Answer: 240 km

[Medium] Fraction Division

• EN: How many 1/4-cup servings are there in 3 cups of juice?
• FR: Combien de portions de 1/4 de tasse y a-t-il dans 3 tasses de jus?
• Choices: A) 6 B) 9 C) 12 D) 16
• Hint: Dividing by a fraction is the same as multiplying by its reciprocal — 2 ÷ 1/3 = 2 × 3 = 6.
• Steps:
  • 3 ÷ 1/4 = 3 × 4 (flip the fraction).
  • 3 × 4 = 12.
  • There are 12 servings.
• Answer: 12

[Hard] Multi-Step Percent

• EN: A jacket originally costs $120. It is on sale for 15% off. After the discount, there is an additional 10% tax on the sale price. What is the final price?
• FR: Une veste coûte 120 $ à l'origine. Elle est en solde à 15 % de rabais. Après le rabais, une taxe supplémentaire de 10 % est appliquée sur le prix soldé. Quel est le prix final?
• Choices: A) $99.00 B) $102.00 C) $111.00 D) $114.00
• Hint: Apply discounts and taxes one step at a time — first find the sale price, then apply tax to that new price.
• Steps:
  • 15% of $120 = $18 discount. Sale price: $120 − $18 = $102.
  • Tax: 10% of $102 = $10.20.
  • Final price: $102 + $10.20 = $112.20. Wait — recheck: 10% of 102 = 10.20; 102 + 10.20 = $112.20.
• Answer: $112.20

[Hard] BEDMAS with Integers

• EN: Evaluate: (−3) × 4 + 20 ÷ (−5).
• FR: Évalue : (−3) × 4 + 20 ÷ (−5).
• Choices: A) −16 B) −8 C) 8 D) 16
• Hint: Apply BEDMAS — do all multiplication and division first (left to right), then addition and subtraction.
• Steps:
  • (−3) × 4 = −12.
  • 20 ÷ (−5) = −4.
  • −12 + (−4) = −16.
• Answer: −16

[Easy] Integer Addition

• EN: What is (−9) + 14?
• FR: Combien vaut (−9) + 14?
• Choices: A) −5 B) 3 C) 5 D) 23
• Hint: On a number line, start at the negative number and move right by the positive amount.
• Steps:
  • Start at −9 on the number line.
  • Move 14 steps to the right.
  • −9 + 14 = 5.
• Answer: 5

[Easy] Percent Discount

• EN: A pair of skates costs $80. They are on sale for 20% off. What is the sale price?
• FR: Une paire de patins coûte 80 $. Elle est en solde à 20 % de rabais. Quel est le prix de vente?
• Choices: A) $16 B) $60 C) $64 D) $75
• Hint: Find the discount amount first, then subtract from the original — 20% of $50 = $10, so sale price = $40.
• Steps:
  • 20% of $80: 0.20 × 80 = $16.
  • Sale price: $80 − $16 = $64.
  • The sale price is $64.
• Answer: $64

[Easy] One-Step Linear Equation

• EN: Solve for n: n + 12 = 25.
• FR: Résous pour n : n + 12 = 25.
• Choices: A) n = 7 B) n = 11 C) n = 13 D) n = 37
• Hint: To isolate the variable, do the opposite operation on both sides — if x + 5 = 12, subtract 5 from both sides.
• Steps:
  • n + 12 = 25.
  • Subtract 12 from both sides: n = 25 − 12.
  • n = 13.
• Answer: n = 13

[Easy] Integer Subtraction

• EN: What is 3 − (−7)?
• FR: Combien vaut 3 − (−7)?
• Choices: A) −4 B) 4 C) 10 D) −10
• Hint: Subtracting a negative is the same as adding a positive — 5 − (−3) = 5 + 3 = 8.
• Steps:
  • 3 − (−7) = 3 + 7.
  • 3 + 7 = 10.
  • The answer is 10.
• Answer: 10

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 6 cm long, 4 cm wide, and 3 cm tall. What is the total surface area of the box?
• FR: Une boîte cadeau mesure 6 cm de long, 4 cm de large et 3 cm de haut. Quelle est l'aire totale de la surface de la boîte?
• Choices: A) 72 cm² B) 84 cm² C) 96 cm² D) 108 cm²
• Hint: Surface area = 2(lw + lh + wh) — for a 5 × 3 × 2 box: 2(15 + 10 + 6) = 2(31) = 62 cm².
• Steps:
  • lw = 6 × 4 = 24, lh = 6 × 3 = 18, wh = 4 × 3 = 12.
  • Sum: 24 + 18 + 12 = 54.
  • SA = 2 × 54 = 108 cm².
• Answer: 108 cm²

[Medium] Percentage — Tax

• EN: A meal at a restaurant costs $45. The sales tax is 13% (HST). What is the total cost including tax?
• FR: Un repas au restaurant coûte 45 $. La taxe de vente est de 13 % (TVH). Quel est le coût total incluant la taxe?
• Choices: A) $45.13 B) $50.85 C) $55.45 D) $58.85
• Hint: Find the tax amount (price × tax rate) and add it to the original price — 10% of $60 = $6, so total with 10% tax = $66.
• Steps:
  • Tax = 13% of $45 = 0.13 × 45 = $5.85.
  • Total = $45 + $5.85 = $50.85.
  • The total cost is $50.85.
• Answer: $50.85

[Medium] Integer Multiplication and Division

• EN: What is (−6) × (−4) ÷ 8?
• FR: Combien vaut (−6) × (−4) ÷ 8?
• Choices: A) −3 B) 3 C) −24 D) 24
• Hint: Negative × negative = positive — then divide the positive result: (−5) × (−2) = 10, and 10 ÷ 5 = 2.
• Steps:
  • (−6) × (−4) = 24 (negative × negative = positive).
  • 24 ÷ 8 = 3.
  • The answer is 3.
• Answer: 3

[Medium] Probability

• EN: A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of picking a blue marble at random?
• FR: Un sac contient 3 billes rouges, 5 bleues et 2 vertes. Quelle est la probabilité de piger une bille bleue au hasard?
• Choices: A) 1/5 B) 1/2 C) 5/10 D) 3/10
• Hint: Probability = favourable outcomes ÷ total outcomes — if 4 out of 12 marbles are red, P(red) = 4/12 = 1/3.
• Steps:
  • Total marbles = 3 + 5 + 2 = 10.
  • Blue marbles = 5.
  • P(blue) = 5/10 = 1/2.
• Answer: 1/2

[Hard] Two-Step Equation

• EN: Solve for x: 3x − 7 = 14.
• FR: Résous pour x : 3x − 7 = 14.
• Choices: A) x = 5 B) x = 7 C) x = 9 D) x = 21
• Hint: Undo the operations in reverse order — add or subtract first, then multiply or divide: for 2x + 4 = 12, subtract 4, then divide by 2.
• Steps:
  • Add 7 to both sides: 3x = 14 + 7 = 21.
  • Divide both sides by 3: x = 21 ÷ 3 = 7.
  • x = 7.
• Answer: x = 7

[Hard] Tip Calculation and Total

• EN: Four friends share a restaurant bill of $96. They want to leave a 15% tip. If they split the total cost (bill + tip) equally, how much does each person pay?
• FR: Quatre amis partagent une addition de restaurant de 96 $. Ils veulent laisser un pourboire de 15 %. S'ils partagent le coût total (addition + pourboire) également, combien chaque personne paie-t-elle?
• Choices: A) $24.00 B) $25.80 C) $27.60 D) $28.80
• Hint: Find the total bill with tip first, then divide by the number of people.
• Steps:
  • Tip: 15% of $96 = 0.15 × 96 = $14.40.
  • Total: $96 + $14.40 = $110.40.
  • Each person pays: $110.40 ÷ 4 = $27.60.
• Answer: $27.60

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of which number times itself gives you the result — 10 × 10 = 100, 12 × 12 = 144.
• Steps:
  • Ask: which number squared equals 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored these marks on a quiz: 70, 80, 90, 60, 100. What is the mean score?
• FR: Cinq élèves ont obtenu ces résultats à un quiz : 70, 80, 90, 60, 100. Quelle est la note moyenne?
• Choices: A) 76 B) 80 C) 85 D) 90
• Hint: To find the mean, add all values and divide by how many there are — for 4, 6, 8: sum = 18, mean = 18 ÷ 3 = 6.
• Steps:
  • Sum = 70 + 80 + 90 + 60 + 100 = 400.
  • Mean = 400 ÷ 5 = 80.
  • The mean score is 80.
• Answer: 80

[Easy] Two-Step Linear Equation

• EN: Solve for y: 2y + 5 = 13.
• FR: Résous pour y : 2y + 5 = 13.
• Choices: A) y = 3 B) y = 4 C) y = 6 D) y = 9
• Hint: Subtract the constant from both sides first, then divide by the coefficient — for 3y + 2 = 11, subtract 2, then divide by 3.
• Steps:
  • 2y + 5 = 13. Subtract 5: 2y = 8.
  • Divide by 2: y = 4.
  • y = 4.
• Answer: y = 4

[Easy] Percent Increase

• EN: A hockey player scored 20 goals last season and 25 goals this season. What is the percent increase?
• FR: Un joueur de hockey a compté 20 buts la saison passée et 25 buts cette saison. Quel est le pourcentage d'augmentation?
• Choices: A) 5% B) 20% C) 25% D) 80%
• Hint: Percent increase = (increase ÷ original) × 100 — if something goes from 10 to 13, increase = 3, percent = 30%.
• Steps:
  • Increase = 25 − 20 = 5.
  • Percent increase = (5 ÷ 20) × 100 = 25%.
  • The percent increase is 25%.
• Answer: 25%

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et de 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 14 cm
• Hint: Use a² + b² = c² — for legs 3 and 4, c² = 9 + 16 = 25, so c = 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 the points (0, 2) and (4, 10). What is the slope of the line?
• FR: Une droite passe par les points (0, 2) et (4, 10). Quelle est la pente de cette droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) — for points (1, 3) and (3, 7): slope = (7−3) ÷ (3−1) = 2.
• Steps:
  • Rise = 10 − 2 = 8.
  • Run = 4 − 0 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of these numbers: 4, 7, 2, 9, 5, 7, 3.
• FR: Trouve la médiane de ces nombres : 4, 7, 2, 9, 5, 7, 3.
• Choices: A) 4 B) 5 C) 7 D) 9
• Hint: Sort the numbers in order first, then find the middle value — for an odd count, the median is the centre number.
• Steps:
  • Sort: 2, 3, 4, 5, 7, 7, 9.
  • There are 7 values; the middle (4th) value is 5.
  • The median is 5.
• Answer: 5

[Medium] Percent Decrease

• EN: A video game originally cost $60. It now costs $45. What is the percent decrease in price?
• FR: Un jeu vidéo coûtait 60 $ à l'origine. Il coûte maintenant 45 $. Quel est le pourcentage de diminution du prix?
• Choices: A) 15% B) 20% C) 25% D) 33%
• Hint: Percent decrease = (decrease ÷ original price) × 100 — if a price drops from $80 to $60, decrease = $20, percent = 25%.
• Steps:
  • Decrease = $60 − $45 = $15.
  • Percent decrease = ($15 ÷ $60) × 100 = 25%.
  • The price decreased by 25%.
• Answer: 25%

[Hard] Pythagorean Theorem — Missing Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 18 cm
• Hint: Rearrange the Pythagorean theorem to find a missing leg: b² = c² − a² — for c = 10 and a = 6, b² = 100 − 36 = 64, b = 8.
• Steps:
  • b² = c² − a² = 13² − 5².
  • 169 − 25 = 144.
  • b = √144 = 12 cm.
• Answer: 12 cm

[Hard] Multi-Step Equation

• EN: Solve for x: 5(x − 3) = 2x + 6.
• FR: Résous pour x : 5(x − 3) = 2x + 6.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: Expand the brackets first, then move all x terms to one side and constants to the other.
• Steps:
  • Expand: 5x − 15 = 2x + 6.
  • Move x terms: 5x − 2x = 6 + 15, so 3x = 21.
  • x = 7.
• Answer: x = 7

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x + 3 = 19.
• FR: Résous pour x : 4x + 3 = 19.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Isolate the variable — subtract the constant from both sides, then divide by the coefficient.
• Steps:
  • 4x + 3 = 19. Subtract 3: 4x = 16.
  • Divide by 4: x = 4.
  • x = 4.
• Answer: x = 4

[Easy] Adding Polynomials

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

[Easy] Slope-Intercept Form

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

[Easy] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse mesure 10 cm. Combien vaut sin(θ)?
• Choices: A) 0.4 B) 0.6 C) 0.75 D) 1.67
• Hint: SOH means sin = opposite ÷ hypotenuse — for opposite = 4 and hypotenuse = 5, sin = 4/5 = 0.8.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 6 ÷ 10 = 0.6.
  • sin(θ) = 0.6.
• Answer: 0.6

[Medium] Linear Inequality

• EN: Solve for x: 2x − 5 > 9.
• FR: Résous pour x : 2x − 5 > 9.
• Choices: A) x > 2 B) x > 5 C) x > 7 D) x > 14
• Hint: Solve an inequality like an equation, but remember: if you divide by a negative number, flip the inequality sign.
• Steps:
  • Add 5 to both sides: 2x > 14.
  • Divide by 2: x > 7.
  • The solution is x > 7.
• Answer: x > 7

[Medium] Multiplying Polynomials

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

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 10 cm. If a side of the first triangle is 6 cm, what is the corresponding side in the second triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 10 cm. Si un côté du premier triangle est de 6 cm, quel est le côté correspondant dans le deuxième triangle?
• Choices: A) 12 cm B) 14 cm C) 15 cm D) 24 cm
• Hint: Set up a proportion — if the scale factor is 4:10, then for any side: (4)/(10) = (known side)/(unknown side).
• Steps:
  • Scale factor: 10 ÷ 4 = 2.5.
  • Corresponding side: 6 × 2.5 = 15.
  • The corresponding side is 15 cm.
• Answer: 15 cm

[Medium] Graphing Lines

• EN: A line has the equation y = −2x + 6. What is the y-intercept of this line?
• FR: Une droite a l'équation y = −2x + 6. Quelle est l'ordonnée à l'origine de cette droite?
• Choices: A) −2 B) 2 C) 6 D) −6
• Hint: In y = mx + b, the y-intercept is b — it is where the line crosses the y-axis (when x = 0).
• Steps:
  • The equation is y = −2x + 6.
  • In y = mx + b form, b = 6.
  • The y-intercept is 6.
• Answer: 6

[Hard] Trigonometry — Find the Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is the angle θ to the nearest degree? (Use cos⁻¹)
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 13 cm. Quelle est la valeur de l'angle θ au degré près? (Utilise cos⁻¹)
• Choices: A) 23° B) 53° C) 67° D) 77°
• Hint: CAH means cos = adjacent ÷ hypotenuse, then use the inverse cosine function to find the angle.
• Steps:
  • cos(θ) = 5 ÷ 13 ≈ 0.3846.
  • θ = cos⁻¹(0.3846) ≈ 67°.
  • The angle is approximately 67°.
• Answer: 67°

[Hard] System of Equations

• EN: Solve this system of equations: y = 2x + 1 and y = −x + 7. What is the value of x?
• FR: Résous ce système d'équations : 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 when both equal y — then solve for x.
• Steps:
  • Set equal: 2x + 1 = −x + 7.
  • Add x to both sides: 3x + 1 = 7. Subtract 1: 3x = 6.
  • x = 2.
• Answer: x = 2

[Easy] Factoring Quadratics

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

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, angle θ = 30° and the hypotenuse = 20 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse = 20 cm. Quelle est la longueur du côté opposé?
• Choices: A) 8 cm B) 10 cm C) 14 cm D) 17 cm
• Hint: Use sin θ = opposite ÷ hypotenuse, so opposite = hypotenuse × sin θ — sin(30°) = 0.5.
• Steps:
  • sin(30°) = 0.5.
  • Opposite = 20 × 0.5 = 10 cm.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Easy] Systems of Equations

• EN: Solve the system: x + y = 10 and x − y = 4. What is x?
• FR: Résous le système : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the two equations together to eliminate y — then solve for x.
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 4.
  • 2x = 14, so x = 7.
  • x = 7.
• Answer: x = 7

[Easy] Surface Area of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 8 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 8 cm. Quelle est son aire totale de surface? (Utilise π ≈ 3,14)
• Choices: A) 75.36 cm² B) 103.62 cm² C) 207.24 cm² D) 226.08 cm²
• Hint: SA of cylinder = 2πr² + 2πrh — for r = 2, h = 5: SA = 2(3.14)(4) + 2(3.14)(2)(5) = 25.12 + 62.8.
• Steps:
  • SA = 2πr² + 2πrh.
  • 2 × 3.14 × 9 = 56.52 (two circles).
  • 2 × 3.14 × 3 × 8 = 150.72 (curved surface). Total = 207.24 cm².
• Answer: 207.24 cm²

[Medium] Completing the Square

• EN: Solve x² + 6x − 7 = 0 by factoring.
• FR: Résous x² + 6x − 7 = 0 en factorisant.
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 7 or x = 1 D) x = 3 or x = −7
• Hint: Factor the quadratic by finding two numbers that multiply to −7 and add to 6.
• Steps:
  • Need two numbers: multiply to −7 and add to 6. Try 7 and −1: 7 × (−1) = −7, 7 + (−1) = 6. ✓
  • (x + 7)(x − 1) = 0.
  • x = −7 or x = 1.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is the 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 = π × d, where d is the diameter — for d = 10, C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d.
  • C = 3.14 × 14 = 43.96 cm.
  • The circumference is 43.96 cm.
• Answer: 43.96 cm

[Medium] Volume of a Cone

• EN: A cone has a radius of 6 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 6 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 188.4 cm³ B) 376.8 cm³ C) 565.2 cm³ D) 1130.4 cm³
• Hint: Volume of a cone = (1/3)πr²h — for r = 3 and h = 7: V = (1/3)(3.14)(9)(7) ≈ 65.94 cm³.
• Steps:
  • V = (1/3) × 3.14 × 6² × 10.
  • 3.14 × 36 = 113.04, then 113.04 × 10 = 1130.4.
  • V = 1130.4 ÷ 3 = 376.8 cm³.
• Answer: 376.8 cm³

[Medium] Systems of Equations — Substitution

• EN: Solve: y = 3x − 2 and 2x + y = 13. What is the value of y?
• FR: Résous : y = 3x − 2 et 2x + y = 13. Quelle est la valeur de y?
• Choices: A) y = 7 B) y = 9 C) y = 10 D) y = 13
• Hint: Substitute the first equation into the second — replace y with (3x − 2) and solve for x, then find y.
• Steps:
  • Substitute: 2x + (3x − 2) = 13. So 5x − 2 = 13, 5x = 15, x = 3.
  • y = 3(3) − 2 = 9 − 2 = 7.
  • y = 7.
• Answer: y = 7

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve: 2x² − 7x + 3 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre : 2x² − 7x + 3 = 0. Quelles sont les solutions?
• Choices: A) x = 3 or x = 1/2 B) x = 7 or x = 1 C) x = −3 or x = −1/2 D) x = 2 or x = 3/2
• Hint: Use x = [−b ± √(b² − 4ac)] ÷ 2a with a = 2, b = −7, c = 3 — first find the discriminant b² − 4ac.
• Steps:
  • Discriminant: (−7)² − 4(2)(3) = 49 − 24 = 25.
  • x = (7 ± 5) ÷ 4. So x = 12/4 = 3 or x = 2/4 = 1/2.
  • Solutions: x = 3 or x = 1/2.
• Answer: x = 3 or x = 1/2

[Hard] Circle Geometry — Chord and Radius

• EN: A chord of a circle is 16 cm long. The radius of the circle is 10 cm. How far is the centre of the circle from the chord? (Hint: use the Pythagorean theorem.)
• FR: Une corde d'un cercle mesure 16 cm. Le rayon du cercle est de 10 cm. À quelle distance le centre du cercle est-il de la corde? (Indice : utilise le théorème de Pythagore.)
• Choices: A) 4 cm B) 6 cm C) 8 cm D) 12 cm
• Hint: The perpendicular from the centre bisects the chord — form a right triangle with the radius as hypotenuse and half the chord as one leg.
• Steps:
  • Half the chord = 8 cm. Radius = 10 cm.
  • d² + 8² = 10²: d² + 64 = 100. d² = 36.
  • d = 6 cm.
• Answer: 6 cm

[Easy] Exponential Function

• EN: A population doubles every year. If there are 200 bacteria now, how many will there be after 3 years?
• FR: Une population double chaque année. S'il y a 200 bactéries maintenant, combien y en aura-t-il après 3 ans?
• Choices: A) 600 B) 800 C) 1 200 D) 1 600
• Hint: For exponential growth doubling, use P = P₀ × 2ⁿ where n is the number of periods.
• Steps:
  • P = 200 × 2³.
  • 2³ = 8.
  • P = 200 × 8 = 1 600.
• Answer: 1 600

[Easy] Arithmetic Sequence

• EN: An arithmetic sequence begins: 5, 11, 17, 23, … What is the 6th term?
• FR: Une suite arithmétique commence : 5, 11, 17, 23, … Quel est le 6e terme?
• Choices: A) 29 B) 33 C) 35 D) 41
• Hint: The nth term of an arithmetic sequence is a₁ + (n − 1) × d — for 3, 7, 11, …, d = 4, so term 5 = 3 + (4)(4) = 19.
• Steps:
  • Common difference d = 6.
  • 6th term = 5 + (6 − 1) × 6 = 5 + 30 = 35.
  • The 6th term is 35.
• Answer: 35

[Easy] Compound Interest

• EN: Sofia invests $1 000 at 4% interest compounded annually. What is the total amount after 2 years?
• FR: Sofia investit 1 000 $ à un taux d'intérêt de 4 % composé annuellement. Quel est le montant total après 2 ans?
• Choices: A) $1 040.00 B) $1 080.00 C) $1 081.60 D) $1 120.00
• Hint: Use A = P(1 + r)ⁿ — for $500 at 3% for 2 years: A = 500(1.03)² = 500 × 1.0609 = $530.45.
• Steps:
  • A = 1000(1 + 0.04)².
  • (1.04)² = 1.0816.
  • A = 1000 × 1.0816 = $1 081.60.
• Answer: $1 081.60

[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) = n means bⁿ = x — ask yourself: "2 to the power of what equals 32?"
• Steps:
  • Ask: 2? = 32.
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32.
  • log₂(32) = 5.
• Answer: 5

[Medium] Geometric Series Sum

• EN: Find the sum of the first 5 terms of the geometric series: 3, 6, 12, 24, 48, …
• FR: Calcule la somme des 5 premiers termes de la suite géométrique : 3, 6, 12, 24, 48, …
• Choices: A) 63 B) 93 C) 93 D) 96
• Hint: Use Sₙ = a₁(rⁿ − 1) ÷ (r − 1) — for 2, 6, 18 with r = 3: S₃ = 2(3³ − 1) ÷ 2 = 26.
• Steps:
  • a₁ = 3, r = 2, n = 5.
  • S₅ = 3(2⁵ − 1) ÷ (2 − 1) = 3(32 − 1) ÷ 1 = 3 × 31 = 93.
  • The sum is 93.
• Answer: 93

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ + tan²θ − sec²θ + 1.
• FR: Simplifie : sin²θ + cos²θ + tan²θ − sec²θ + 1.
• Choices: A) 0 B) 1 C) 2 D) sin²θ
• Hint: Use the Pythagorean identities — sin²θ + cos²θ = 1 and 1 + tan²θ = sec²θ.
• Steps:
  • sin²θ + cos²θ = 1.
  • tan²θ − sec²θ = −1 (from identity 1 + tan²θ = sec²θ → tan²θ − sec²θ = −1).
  • 1 + (−1) + 1 = 1.
• Answer: 1

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = x² − 4x + 7?
• FR: Quel est le sommet de la parabole y = x² − 4x + 7?
• Choices: A) (2, 3) B) (4, 7) C) (−2, 19) D) (2, 7)
• Hint: Complete the square to find the vertex — for y = x² − 6x + 11, complete the square to get y = (x − 3)² + 2, vertex (3, 2).
• Steps:
  • x of vertex = −b ÷ (2a) = 4 ÷ 2 = 2.
  • y = (2)² − 4(2) + 7 = 4 − 8 + 7 = 3.
  • Vertex is (2, 3).
• Answer: (2, 3)

[Medium] Logarithm Laws

• EN: Simplify: log(100) + log(10).
• FR: Simplifie : log(100) + log(10).
• Choices: A) log(110) B) log(1 000) C) 3 D) 4
• Hint: The product law says log(a) + log(b) = log(a × b) — then evaluate the resulting log base 10.
• Steps:
  • log(100) + log(10) = log(100 × 10) = log(1 000).
  • log₁₀(1 000) = 3 because 10³ = 1 000.
  • The answer is 3.
• Answer: 3

[Hard] Annuity Calculation

• EN: Ethan deposits $200 at the end of each year into an account earning 5% per year compounded annually. What is the total value after 3 years?
• FR: Ethan dépose 200 $ à la fin de chaque année dans un compte rapportant 5 % par an composé annuellement. Quelle est la valeur totale après 3 ans?
• Choices: A) $600.00 B) $630.00 C) $630.50 D) $662.05
• Hint: For an ordinary annuity, future value = PMT × [(1 + r)ⁿ − 1] ÷ r — add each deposit with its compound growth separately.
• Steps:
  • Year 1 deposit: $200 × (1.05)² = $200 × 1.1025 = $220.50.
  • Year 2 deposit: $200 × (1.05)¹ = $200 × 1.05 = $210.00.
  • Year 3 deposit: $200 × (1.05)⁰ = $200. Total = $220.50 + $210.00 + $200.00 = $630.50.
• Answer: $630.50

[Hard] Exponential Equation

• EN: Solve for x: 3^(2x − 1) = 27.
• FR: Résous pour x : 3^(2x − 1) = 27.
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Write both sides as powers of the same base — 27 = 3³, so the exponents must be equal.
• Steps:
  • 27 = 3³, so 3^(2x − 1) = 3³.
  • Set exponents equal: 2x − 1 = 3.
  • 2x = 4, x = 2.
• Answer: x = 2

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = x⁴?
• FR: Quelle est la dérivée de f(x) = x⁴?
• Choices: A) 4x B) 4x³ C) x³ D) 4x⁵
• Hint: The power rule says d/dx [xⁿ] = n·xⁿ⁻¹ — bring the exponent down and reduce it by one: d/dx [x⁵] = 5x⁴.
• Steps:
  • f(x) = x⁴.
  • Bring down the exponent: 4 × x^(4−1).
  • f'(x) = 4x³.
• Answer: 4x³

[Easy] Permutations

• EN: In how many ways can 5 different books be arranged on a shelf?
• FR: De combien de façons peut-on ranger 5 livres différents sur une étagère?
• Choices: A) 25 B) 60 C) 120 D) 240
• Hint: The number of ways to arrange n objects is n! (n factorial) — 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 20 × 6 = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: A student must choose 3 elective courses from 7 available options. How many different combinations are possible?
• FR: Un élève doit choisir 3 cours optionnels parmi 7 options disponibles. Combien de combinaisons différentes sont possibles?
• Choices: A) 21 B) 35 C) 42 D) 210
• Hint: Use C(n, r) = n! ÷ [r!(n − r)!] — for choosing 2 from 5: C(5,2) = 120 ÷ (2 × 6) = 10.
• Steps:
  • C(7, 3) = 7! ÷ (3! × 4!) = 5040 ÷ (6 × 24) = 5040 ÷ 144 = 35.
  • There are 35 possible combinations.
• Answer: 35

[Easy] Rational Function — Vertical Asymptote

• EN: What is the vertical asymptote of the function f(x) = 1/(x − 5)?
• FR: Quelle est l'asymptote verticale de la fonction f(x) = 1/(x − 5)?
• Choices: A) x = −5 B) x = 0 C) x = 5 D) y = 5
• Hint: A vertical asymptote occurs where the denominator equals zero — set the denominator equal to zero and solve.
• Steps:
  • Set denominator to zero: x − 5 = 0.
  • x = 5.
  • The vertical asymptote is at x = 5.
• Answer: x = 5

[Medium] Derivative — Chain Rule

• EN: Find the derivative of f(x) = (3x + 2)⁴.
• FR: Trouve la dérivée de f(x) = (3x + 2)⁴.
• Choices: A) 4(3x + 2)³ B) 12(3x + 2)³ C) 3(3x + 2)⁴ D) 12(3x + 2)⁴
• Hint: Use the chain rule: d/dx [u(x)]ⁿ = n·u^(n−1) × u'(x) — for (2x + 1)³, derivative = 3(2x+1)² × 2 = 6(2x+1)².
• Steps:
  • Outer function: bring down 4, reduce power: 4(3x + 2)³.
  • Inner derivative: d/dx [3x + 2] = 3.
  • f'(x) = 4 × 3 × (3x + 2)³ = 12(3x + 2)³.
• Answer: 12(3x + 2)³

[Medium] Probability Distribution

• EN: A fair six-sided die is rolled twice. What is the probability that both rolls show a number greater than 4?
• FR: On lance un dé équilibré à six faces deux fois. Quelle est la probabilité que les deux lancers affichent un nombre supérieur à 4?
• Choices: A) 1/6 B) 1/9 C) 2/6 D) 1/3
• Hint: Multiply independent probabilities — P(A and B) = P(A) × P(B) for independent events.
• Steps:
  • P(>4 on one roll) = 2/6 = 1/3 (numbers 5 and 6).
  • P(both > 4) = 1/3 × 1/3 = 1/9.
  • The probability is 1/9.
• Answer: 1/9

[Medium] Vectors

• EN: Vector u = (3, −1) and vector v = (−2, 5). What is u + v?
• FR: Le vecteur u = (3, −1) et le vecteur v = (−2, 5). Combien vaut u + v?
• Choices: A) (1, 4) B) (5, 6) C) (−1, 4) D) (1, −6)
• Hint: Add vectors component by component — (a, b) + (c, d) = (a + c, b + d).
• Steps:
  • x-component: 3 + (−2) = 1.
  • y-component: −1 + 5 = 4.
  • u + v = (1, 4).
• Answer: (1, 4)

[Medium] Polynomial Long Division

• EN: Divide (x³ + 3x² − x − 3) ÷ (x − 1). What is the quotient?
• FR: Divise (x³ + 3x² − x − 3) ÷ (x − 1). Quel est le quotient?
• Choices: A) x² + 2x + 3 B) x² + 4x + 3 C) x² − 4x + 3 D) x² + 2x − 3
• Hint: Use polynomial long division or synthetic division — verify by multiplying quotient × divisor back.
• Steps:
  • Using synthetic division with root 1: coefficients 1, 3, −1, −3.
  • Bring down 1. 1×1=1, 3+1=4. 1×4=4, −1+4=3. 1×3=3, −3+3=0. ✓
  • Quotient: x² + 4x + 3.
• Answer: x² + 4x + 3

[Hard] Rate of Change — Derivative Application

• EN: The position of a particle is given by s(t) = t³ − 6t² + 9t. At what time t > 0 is the particle at rest (velocity = 0)?
• FR: La position d'une particule est donnée par s(t) = t³ − 6t² + 9t. À quel instant t > 0 la particule est-elle au repos (vitesse = 0)?
• Choices: A) t = 1 and t = 3 B) t = 2 and t = 4 C) t = 3 only D) t = 6 only
• Hint: Find velocity by differentiating s(t), then set v(t) = 0 and factor the quadratic.
• Steps:
  • v(t) = s'(t) = 3t² − 12t + 9.
  • Set equal to zero: 3t² − 12t + 9 = 0 → t² − 4t + 3 = 0 → (t − 1)(t − 3) = 0.
  • t = 1 and t = 3.
• Answer: t = 1 and t = 3

[Hard] Binomial Probability

• EN: A biased coin has P(heads) = 0.4. If the coin is flipped 4 times, what is the probability of getting exactly 2 heads?
• FR: Une pièce biaisée a P(face) = 0,4. Si on lance la pièce 4 fois, quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 0.1296 B) 0.2304 C) 0.3456 D) 0.4096
• Hint: Use the binomial formula P = C(n,k) × p^k × (1−p)^(n−k) — find C(4,2) first, then multiply.
• Steps:
  • C(4, 2) = 6.
  • P = 6 × (0.4)² × (0.6)² = 6 × 0.16 × 0.36.
  • P = 6 × 0.0576 = 0.3456.
• Answer: 0.3456