Daily Math — 2026-08-08

[Easy] Counting Apples

• EN: There are 7 apples on the table and 5 more apples in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres pommes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To add two numbers, count on from the bigger one (e.g., 6 + 4: start at 6 and count up 4 more).
• Steps:
  • Start at 7, then count up 5 more: 8, 9, 10, 11, 12.
  • So there are 12 apples in all.
• Answer: 12

[Easy] Hockey Pucks

• EN: Maya has 9 hockey pucks and gives 3 away. How many pucks does she have left?
• FR: Maya a 9 rondelles de hockey et en donne 3. Combien de rondelles lui reste-t-il?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To subtract, count backwards from the bigger number (e.g., 8 − 2: start at 8 and count back 2).
• Steps:
  • Start at 9 and count back 3: 8, 7, 6.
  • So Maya has 6 pucks left.
• Answer: 6

[Easy] Skip Counting by 5s

• EN: Skip count by 5s. What number comes next: 5, 10, 15, ___?
• FR: Compte par bonds de 5. Quel nombre vient ensuite : 5, 10, 15, ___?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: When skip counting by 5s, add 5 each time (e.g., 10, 15, 20 — each jump is 5).
• Steps:
  • The pattern adds 5 each time: 5, 10, 15 …
  • 15 + 5 = 20, so the next number is 20.
• Answer: 20

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents in Canada?
• FR: Quelle pièce vaut 10 cents au Canada?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: Remember the three smallest coins: penny = 1¢, nickel = 5¢, dime = 10¢.
• Steps:
  • A penny is worth 1 cent.
  • A nickel is worth 5 cents, and a dime is worth 10 cents, so the answer is a dime.
• Answer: Dime

[Medium] Comparing Numbers

• EN: Which number is greater: 14 or 8?
• FR: Quel nombre est le plus grand : 14 ou 8?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: When comparing numbers, the one with more tens is usually bigger (e.g., 13 is greater than 9 because 13 has a tens digit).
• Steps:
  • 14 has 1 ten and 4 ones; 8 has 0 tens and 8 ones.
  • A number with more tens is greater, so 14 is greater than 8.
• Answer: 14

[Medium] Adding Three Numbers

• EN: Liam has 4 red crayons, 3 blue crayons, and 2 green crayons. How many crayons does he have altogether?
• FR: Liam a 4 crayons rouges, 3 crayons bleus et 2 crayons verts. Combien de crayons a-t-il en tout?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: To add three numbers, add the first two first, then add the third (e.g., 2 + 3 + 1 = 5 + 1 = 6).
• Steps:
  • Add the first two: 4 + 3 = 7.
  • Then add the third: 7 + 2 = 9, so Liam has 9 crayons.
• Answer: 9

[Medium] Skip Counting by 2s

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

[Medium] Subtraction Story

• EN: There are 15 children on the playground. 6 go inside. How many children are still outside?
• FR: Il y a 15 enfants dans la cour de récréation. 6 rentrent à l'intérieur. Combien d'enfants sont encore dehors?
• Choices: A) 7 B) 8 C) 9 D) 21
• Hint: To subtract, count backwards from the larger number (e.g., 12 − 5: start at 12 and count back 5).
• Steps:
  • Start at 15 and count back 6: 14, 13, 12, 11, 10, 9.
  • So 9 children are still outside.
• Answer: 9

[Hard] Making Ten

• EN: Sophia needs 10 stickers to fill her book. She already has 6 stickers. How many more stickers does she need?
• FR: Sophia a besoin de 10 autocollants pour remplir son livre. Elle en a déjà 6. Combien d'autocollants lui faut-il encore?
• Choices: A) 3 B) 4 C) 5 D) 16
• Hint: To find how many more are needed, think of what plus the smaller number equals 10 (e.g., if you have 7, you need 3 more to make 10).
• Steps:
  • We need to find: 6 + ___ = 10.
  • Count up from 6 to 10: 7, 8, 9, 10 — that is 4 steps, so she needs 4 more stickers.
• Answer: 4

[Hard] Counting On with Coins

• EN: Amir has 2 nickels and 1 penny. How many cents does he have in total?
• FR: Amir a 2 pièces de 5 cents et 1 sou. Combien de cents a-t-il en tout?
• Choices: A) 3 cents B) 7 cents C) 11 cents D) 15 cents
• Hint: Add the value of each coin: a nickel is worth 5 cents and a penny is worth 1 cent (e.g., 1 nickel + 1 penny = 5 + 1 = 6 cents).
• Steps:
  • Two nickels = 5 + 5 = 10 cents.
  • One penny = 1 cent; 10 + 1 = 11 cents, so Amir has 11 cents.
• Answer: 11 cents

[Easy] Adding Within 100

• EN: There are 34 students in the gym and 25 more students join them. How many students are in the gym now?
• FR: Il y a 34 élèves dans le gymnase et 25 autres les rejoignent. Combien d'élèves sont dans le gymnase maintenant?
• Choices: A) 57 B) 59 C) 61 D) 69
• Hint: Add the tens first, then the ones (e.g., 23 + 14: 20 + 10 = 30, then 3 + 4 = 7, total = 37).
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9; total = 50 + 9 = 59 students.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows the hour hand on the 3 and the minute hand on the 12. What time is it?
• FR: L'horloge montre l'aiguille des heures sur le 3 et l'aiguille des minutes 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 points to 12, it is exactly on the hour (e.g., hour hand on 7 and minute hand on 12 means 7:00).
• Steps:
  • The hour hand on 3 tells us it is 3 o'clock.
  • The minute hand on 12 means 0 minutes — so the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long and an eraser is 3 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 14 cm de long et une gomme mesure 3 cm de long. De combien le crayon est-il plus long que la gomme?
• Choices: A) 9 cm B) 11 cm C) 13 cm D) 17 cm
• Hint: To find how much longer one object is, subtract the shorter length from the longer one (e.g., 10 cm − 4 cm = 6 cm longer).
• Steps:
  • Subtract: 14 − 3 = 11.
  • The pencil is 11 cm longer than the eraser.
• Answer: 11 cm

[Easy] Counting Coins

• EN: Priya has 3 dimes and 2 nickels. How many cents does she have altogether?
• FR: Priya a 3 pièces de 10 cents et 2 pièces de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 30 cents B) 35 cents C) 40 cents D) 50 cents
• Hint: Multiply each coin type by its value then add (e.g., 2 dimes + 1 nickel = 20 + 5 = 25 cents).
• Steps:
  • 3 dimes = 3 × 10 = 30 cents.
  • 2 nickels = 2 × 5 = 10 cents; 30 + 10 = 40 cents.
• Answer: 40 cents

[Medium] Subtraction Within 100

• EN: A bag holds 72 marbles. 38 marbles are taken out. How many marbles are left in the bag?
• FR: Un sac contient 72 billes. On en retire 38. Combien de billes reste-t-il dans le sac?
• Choices: A) 24 B) 34 C) 44 D) 54
• Hint: Subtract by breaking numbers apart (e.g., 65 − 27: 65 − 20 = 45, then 45 − 7 = 38).
• Steps:
  • 72 − 38: subtract the tens first: 72 − 30 = 42.
  • Then subtract the ones: 42 − 8 = 34, so 34 marbles are left.
• Answer: 34

[Medium] Telling Time (Half-Hour)

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

[Medium] Simple Pattern

• EN: Look at the pattern: 10, 20, 30, 40, ___. What is the missing number?
• FR: Observe le motif : 10, 20, 30, 40, ___. Quel est le nombre manquant?
• Choices: A) 41 B) 45 C) 50 D) 60
• Hint: Find what is being added each time (e.g., 5, 10, 15, 20 — the rule is add 5).
• Steps:
  • Each number increases by 10: 10, 20, 30, 40 …
  • 40 + 10 = 50, so the missing number is 50.
• Answer: 50

[Medium] Coins to $1

• EN: Jake has 6 dimes. How many more cents does he need to have exactly $1.00?
• FR: Jake a 6 pièces de 10 cents. Combien de cents lui faut-il de plus pour avoir exactement 1,00 $?
• Choices: A) 30 cents B) 40 cents C) 60 cents D) 94 cents
• Hint: First find how much you have, then subtract from 100 cents (e.g., 4 dimes = 40 cents; 100 − 40 = 60 cents more needed).
• Steps:
  • 6 dimes = 6 × 10 = 60 cents.
  • 100 − 60 = 40 cents, so Jake needs 40 more cents.
• Answer: 40 cents

[Hard] Two-Step Addition and Subtraction

• EN: A Tim Hortons box had 48 Timbits. The class ate 19 and then added 7 more from another box. How many Timbits are there now?
• FR: Une boîte de Tim Hortons avait 48 Timbits. La classe en a mangé 19, puis on en a ajouté 7 d'une autre boîte. Combien de Timbits y a-t-il maintenant?
• Choices: A) 34 B) 36 C) 38 D) 74
• Hint: Solve step by step — first subtract, then add the new amount (e.g., 50 − 15 = 35, then 35 + 6 = 41).
• Steps:
  • First subtract: 48 − 19 = 29.
  • Then add: 29 + 7 = 36, so there are 36 Timbits now.
• Answer: 36

[Hard] Measuring and Comparing

• EN: Sophie's desk is 90 cm wide. Her bookshelf is 1 m wide. Which is wider, and by how many centimetres?
• FR: Le bureau de Sophie a 90 cm de large. Sa bibliothèque a 1 m de large. Lequel est le plus large, et de combien de centimètres?
• Choices: A) The desk, by 10 cm B) The bookshelf, by 5 cm C) The bookshelf, by 10 cm D) They are the same width
• Hint: Remember that 1 metre equals 100 centimetres, so compare both measurements in centimetres (e.g., 1 m = 100 cm, 85 cm is less than 100 cm, so 1 m is wider by 15 cm).
• Steps:
  • Convert: 1 m = 100 cm.
  • Compare: 100 cm − 90 cm = 10 cm, so the bookshelf is wider by 10 cm.
• Answer: The bookshelf, by 10 cm

[Easy] Multiplication by 2

• EN: There are 6 pairs of mittens on the shelf. How many mittens are there in all?
• FR: Il y a 6 paires de mitaines sur l'étagère. Combien y a-t-il de mitaines en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Pairs means groups of 2, so multiply the number of pairs by 2 (e.g., 4 pairs × 2 = 8 mittens).
• Steps:
  • 6 pairs × 2 = 12.
  • There are 12 mittens in all.
• Answer: 12

[Easy] Multiplication by 5

• EN: A hockey team has 5 players on the ice. If there are 4 teams playing today, how many players are on the ice in total?
• FR: Une équipe de hockey a 5 joueurs sur la glace. S'il y a 4 équipes qui jouent aujourd'hui, combien y a-t-il de joueurs sur la glace en tout?
• Choices: A) 9 B) 15 C) 20 D) 25
• Hint: Multiply the number of groups by the number in each group (e.g., 3 teams × 5 players = 15 players).
• Steps:
  • 4 teams × 5 players = 20 players.
  • There are 20 players on the ice in total.
• Answer: 20

[Easy] Recognising Fractions

• EN: A pizza is cut into 4 equal slices. Noah eats 1 slice. What fraction of the pizza did he eat?
• FR: Une pizza est coupée en 4 parts égales. Noah mange 1 part. Quelle fraction de la pizza a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 4/1
• Hint: A fraction shows parts of a whole — the bottom number is the total equal parts, and the top is how many you have (e.g., 1 piece out of 3 equal pieces = 1/3).
• Steps:
  • The pizza has 4 equal slices — that is the denominator.
  • Noah ate 1 slice — that is the numerator: 1/4.
• Answer: 1/4

[Easy] Basic Division

• EN: There are 15 crayons to share equally among 3 students. How many crayons does each student get?
• FR: Il y a 15 crayons à partager également entre 3 élèves. Combien de crayons chaque élève reçoit-il?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Division means splitting into equal groups (e.g., 12 ÷ 4: put 12 items into 4 equal groups — each group gets 3).
• Steps:
  • 15 ÷ 3 = 5.
  • Each student gets 5 crayons.
• Answer: 5

[Medium] Perimeter of a Rectangle

• EN: A garden plot is 8 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un carré de jardin mesure 8 m de long et 3 m de large. Quel est le périmètre du jardin?
• Choices: A) 11 m B) 22 m C) 24 m D) 48 m
• Hint: Perimeter = add all four sides; for a rectangle use length + width + length + width (e.g., a 5 m × 2 m rectangle has perimeter = 5 + 2 + 5 + 2 = 14 m).
• Steps:
  • Perimeter = 8 + 3 + 8 + 3 = 22.
  • The perimeter of the garden is 22 m.
• Answer: 22 m

[Medium] Multiplication by 3

• EN: Each student needs 3 coloured pencils for art class. There are 7 students. How many coloured pencils are needed altogether?
• FR: Chaque élève a besoin de 3 crayons de couleur pour le cours d'art. Il y a 7 élèves. Combien de crayons de couleur sont nécessaires en tout?
• Choices: A) 10 B) 18 C) 21 D) 28
• Hint: Multiply the number of students by the number of pencils each one needs (e.g., 5 students × 3 pencils = 15 pencils).
• Steps:
  • 7 × 3 = 21.
  • 21 coloured pencils are needed altogether.
• Answer: 21

[Medium] Reading a Bar Graph

• EN: A bar graph shows: apples = 6, bananas = 4, oranges = 9. How many more oranges than bananas are there?
• FR: Un diagramme à barres montre : pommes = 6, bananes = 4, oranges = 9. Combien d'oranges y a-t-il de plus que de bananes?
• Choices: A) 3 B) 4 C) 5 D) 13
• Hint: To find how many more, subtract the smaller amount from the larger amount (e.g., if cats = 7 and dogs = 5, then 7 − 5 = 2 more cats).
• Steps:
  • Oranges = 9, bananas = 4.
  • 9 − 4 = 5, so there are 5 more oranges than bananas.
• Answer: 5

[Medium] Multiplication by 10

• EN: A bag has 10 marbles. How many marbles are in 8 bags?
• FR: Un sac contient 10 billes. Combien y a-t-il de billes dans 8 sacs?
• Choices: A) 18 B) 70 C) 80 D) 100
• Hint: Multiplying by 10 is easy — just add a zero to the other number (e.g., 6 × 10 = 60).
• Steps:
  • 8 × 10 = 80.
  • There are 80 marbles in 8 bags.
• Answer: 80

[Hard] Two-Step Multiplication Problem

• EN: A baker makes 4 trays of muffins. Each tray holds 5 muffins. She puts 3 muffins aside for herself. How many muffins does she have to sell?
• FR: Une boulangère fait 4 plateaux de muffins. Chaque plateau contient 5 muffins. Elle met 3 muffins de côté pour elle. Combien de muffins a-t-elle à vendre?
• Choices: A) 12 B) 15 C) 17 D) 23
• Hint: First multiply to find the total, then subtract the ones kept aside (e.g., 3 trays × 4 muffins = 12 total, 12 − 2 = 10 to sell).
• Steps:
  • Total muffins: 4 × 5 = 20.
  • Subtract the 3 kept aside: 20 − 3 = 17 muffins to sell.
• Answer: 17

[Hard] Fraction Comparison

• EN: Ella ate 1/2 of a sandwich and Ben ate 1/4 of the same-sized sandwich. Who ate more, and what is the difference?
• FR: Ella a mangé 1/2 d'un sandwich et Ben a mangé 1/4 du même sandwich. Qui a mangé plus, et quelle est la différence?
• Choices: A) Ben ate more; the difference is 1/4 B) Ella ate more; the difference is 1/4 C) Ella ate more; the difference is 1/2 D) They ate the same amount
• Hint: To compare fractions with the same whole, think of the whole cut into equal pieces — 1/2 means 2 pieces out of 4 if you use fourths (e.g., 1/2 = 2/4, and 2/4 > 1/4).
• Steps:
  • Convert 1/2 to fourths: 1/2 = 2/4.
  • 2/4 − 1/4 = 1/4, so Ella ate more by 1/4.
• Answer: Ella ate more; the difference is 1/4

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: You can use a known fact to help (e.g., 7 × 7 = 49, so 7 × 8 = 49 + 7 = 56).
• Steps:
  • Use the known fact: 7 × 7 = 49.
  • Add one more group of 7: 49 + 7 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 4.73, what digit is in the tenths place?
• FR: Dans le nombre 4,73, quel chiffre est à la place des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 73
• Hint: After the decimal point, the first digit is tenths and the second is hundredths (e.g., in 5.86, the tenths digit is 8).
• Steps:
  • 4 is in the ones place; after the decimal, 7 is in the tenths place.
  • The tenths digit in 4.73 is 7.
• Answer: 7

[Easy] Area of a Rectangle

• EN: A classroom floor is 9 m long and 6 m wide. What is the area of the floor?
• FR: Le plancher d'une classe mesure 9 m de long et 6 m de large. Quelle est l'aire du plancher?
• Choices: A) 30 m² B) 45 m² C) 54 m² D) 63 m²
• Hint: Area of a rectangle = length × width (e.g., a 7 m × 4 m room has area = 28 m²).
• Steps:
  • Area = 9 × 6 = 54.
  • The area of the floor is 54 m².
• Answer: 54 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/4?
• FR: Quelle fraction est la plus grande : 3/4 ou 2/4?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) They are equal
• Hint: When fractions have the same denominator, the one with the larger numerator is greater (e.g., 5/8 > 3/8 because 5 > 3).
• Steps:
  • Both fractions have denominator 4, so compare numerators: 3 vs. 2.
  • 3 > 2, so 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: A teacher has 47 stickers to share equally among 5 students. How many stickers does each student get, and how many are left over?
• FR: Une enseignante a 47 autocollants à partager également entre 5 élèves. Combien chaque élève en reçoit-il, et combien en reste-t-il?
• Choices: A) 8 remainder 7 B) 9 remainder 2 C) 9 remainder 4 D) 10 remainder 3
• Hint: Divide, then multiply back to find the remainder (e.g., 26 ÷ 4: 4 × 6 = 24, remainder = 26 − 24 = 2, so 6 remainder 2).
• Steps:
  • 5 × 9 = 45, which is less than 47; 5 × 10 = 50, which is too big.
  • 47 − 45 = 2, so each student gets 9 stickers with 2 left over.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: Hockey practice starts at 4:15 p.m. and ends at 5:45 p.m. How long is hockey practice?
• FR: L'entraînement de hockey commence à 16 h 15 et se termine à 17 h 45. Combien de temps dure l'entraînement?
• Choices: A) 1 hour 15 minutes B) 1 hour 30 minutes C) 1 hour 45 minutes D) 2 hours 30 minutes
• Hint: Count the hours first, then the minutes (e.g., 3:20 p.m. to 5:00 p.m. = 1 hour 40 minutes: 3:20 → 4:20 is 1 hour, then 4:20 → 5:00 is 40 more minutes).
• Steps:
  • From 4:15 to 5:15 is 1 hour; from 5:15 to 5:45 is 30 more minutes.
  • Total: 1 hour 30 minutes.
• Answer: 1 hour 30 minutes

[Medium] Decimal Operations

• EN: A book costs $3.45 and a pencil costs $1.20. What is the total cost of both items?
• FR: Un livre coûte 3,45 $ et un crayon coûte 1,20 $. Quel est le coût total des deux articles?
• Choices: A) $4.55 B) $4.65 C) $4.75 D) $5.65
• Hint: Add decimals by lining up the decimal points and adding each column (e.g., $2.35 + $1.40: ones 2+1=3, tenths 3+4=7, hundredths 5+0=5, total = $3.75).
• Steps:
  • $3.45 + $1.20: ones = 3+1 = 4, tenths = 4+2 = 6, hundredths = 5+0 = 5.
  • Total = $4.65.
• Answer: $4.65

[Medium] Multiplication with Larger Numbers

• EN: A school buys 6 boxes of crayons. Each box has 48 crayons. How many crayons does the school buy in total?
• FR: Une école achète 6 boîtes de crayons. Chaque boîte contient 48 crayons. Combien de crayons l'école achète-t-elle en tout?
• Choices: A) 248 B) 264 C) 288 D) 296
• Hint: Multiply by splitting the number (e.g., 6 × 34 = 6 × 30 + 6 × 4 = 180 + 24 = 204).
• Steps:
  • 6 × 48 = 6 × 40 + 6 × 8 = 240 + 48 = 288.
  • The school buys 288 crayons in total.
• Answer: 288

[Hard] Multi-Step Word Problem

• EN: A store sells hockey cards in packs of 9. Mia bought 7 packs and gave 15 cards to her friend. How many cards does Mia have left?
• FR: Un magasin vend des cartes de hockey en paquets de 9. Mia a acheté 7 paquets et a donné 15 cartes à son ami. Combien de cartes Mia a-t-elle encore?
• Choices: A) 42 B) 48 C) 54 D) 63
• Hint: First multiply to find total cards, then subtract what was given away (e.g., 5 packs × 8 cards = 40 total, 40 − 12 = 28 left).
• Steps:
  • Total cards: 7 × 9 = 63.
  • Cards left: 63 − 15 = 48.
• Answer: 48

[Hard] Decimal Comparison and Ordering

• EN: Order these decimals from least to greatest: 0.6, 0.06, 0.60.
• FR: Ordonne ces décimales du plus petit au plus grand : 0,6; 0,06; 0,60.
• Choices: A) 0.06, 0.6, 0.60 B) 0.06, 0.60, 0.6 C) 0.6, 0.06, 0.60 D) 0.60, 0.6, 0.06
• Hint: Compare tenths first — a smaller tenths digit means a smaller number (e.g., 0.3 vs 0.03: tenths are 3 vs 0, so 0.03 < 0.3).
• Steps:
  • 0.06 = 6 hundredths; 0.6 = 6 tenths = 60 hundredths; 0.60 = 60 hundredths.
  • So 0.06 < 0.6 = 0.60; ordered: 0.06, 0.6, 0.60.
• Answer: 0.06, 0.6, 0.60

[Easy] Multi-Digit Multiplication

• EN: What is 46 × 7?
• FR: Combien font 46 × 7?
• Choices: A) 282 B) 312 C) 322 D) 336
• Hint: Break the number apart to multiply (e.g., 32 × 6 = 30 × 6 + 2 × 6 = 180 + 12 = 192).
• Steps:
  • 46 × 7 = 40 × 7 + 6 × 7 = 280 + 42 = 322.
  • The answer is 322.
• Answer: 322

[Easy] Adding Fractions with Like Denominators

• EN: What is 3/8 + 4/8?
• FR: Combien font 3/8 + 4/8?
• Choices: A) 7/16 B) 7/8 C) 1/8 D) 6/8
• Hint: When denominators are the same, just add the numerators and keep the denominator (e.g., 2/5 + 1/5 = 3/5).
• Steps:
  • Add numerators: 3 + 4 = 7; keep the denominator: 8.
  • The answer is 7/8.
• Answer: 7/8

[Easy] Percentage — 50%

• EN: A bag of apples has 20 apples. 50% were eaten at lunch. How many apples are left?
• FR: Un sac de pommes contient 20 pommes. 50 % ont été mangées au dîner. Combien de pommes reste-t-il?
• Choices: A) 5 B) 8 C) 10 D) 15
• Hint: 50% means half, so divide the total by 2 (e.g., 50% of 16 = 16 ÷ 2 = 8).
• Steps:
  • 50% of 20 = 20 ÷ 2 = 10 apples eaten.
  • Apples left = 20 − 10 = 10.
• Answer: 10

[Easy] Decimal Operations — Subtraction

• EN: A bottle holds 1.75 L of juice. You drink 0.50 L. How much juice is left?
• FR: Une bouteille contient 1,75 L de jus. Tu en bois 0,50 L. Combien de jus reste-t-il?
• Choices: A) 1.15 L B) 1.25 L C) 1.30 L D) 2.25 L
• Hint: Subtract decimals by lining up the decimal points (e.g., 3.80 − 1.25 = 2.55).
• Steps:
  • 1.75 − 0.50: ones = 1, tenths = 7−5=2, hundredths = 5−0=5.
  • 1.25 L of juice is left.
• Answer: 1.25 L

[Medium] Multi-Digit Division

• EN: A baker made 168 cookies and wants to pack them into boxes of 8. How many full boxes can she make?
• FR: Une boulangère a fait 168 biscuits et veut les mettre dans des boîtes de 8. Combien de boîtes complètes peut-elle faire?
• Choices: A) 18 B) 20 C) 21 D) 24
• Hint: Divide step by step using long division (e.g., 144 ÷ 6: 6 × 20 = 120, 144 − 120 = 24, 6 × 4 = 24, so answer = 24).
• Steps:
  • 8 × 20 = 160; 168 − 160 = 8; 8 ÷ 8 = 1.
  • 20 + 1 = 21 full boxes.
• Answer: 21

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est le volume de la boîte?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 120 cm³
• Hint: Volume of a rectangular prism = length × width × height (e.g., a box 6 cm × 2 cm × 4 cm has volume = 48 cm³).
• Steps:
  • Volume = 5 × 4 × 3 = 20 × 3 = 60.
  • The volume of the box is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25% and 10%

• EN: A winter jacket originally costs $80. It is on sale for 25% off. What is the discount amount?
• FR: Un manteau d'hiver coûtait à l'origine 80 $. Il est soldé à 25 % de réduction. Quel est le montant de la réduction?
• Choices: A) $8 B) $16 C) $20 D) $25
• Hint: 25% = one quarter, so divide by 4 (e.g., 25% of $60 = $60 ÷ 4 = $15).
• Steps:
  • 25% of $80 = $80 ÷ 4 = $20.
  • The discount is $20.
• Answer: $20

[Medium] Subtracting Fractions with Like Denominators

• EN: Emma had 9/10 of a metre of ribbon. She used 3/10 of a metre. How much ribbon does she have left?
• FR: Emma avait 9/10 de mètre de ruban. Elle en a utilisé 3/10 de mètre. Combien de ruban lui reste-t-il?
• Choices: A) 3/10 B) 5/10 C) 6/10 D) 12/10
• Hint: When denominators are the same, subtract the numerators and keep the denominator (e.g., 7/9 − 2/9 = 5/9).
• Steps:
  • 9/10 − 3/10: subtract numerators: 9 − 3 = 6; keep denominator 10.
  • The answer is 6/10.
• Answer: 6/10

[Hard] Multi-Step Decimal Problem

• EN: Leo buys 3 notebooks at $2.45 each and pays with a $10 bill. How much change does he receive?
• FR: Léo achète 3 cahiers à 2,45 $ chacun et paie avec un billet de 10 $. Combien de monnaie reçoit-il?
• Choices: A) $2.35 B) $2.65 C) $7.35 D) $7.55
• Hint: First multiply to find the total cost, then subtract from the amount paid (e.g., 4 items × $1.75 = $7.00, $10.00 − $7.00 = $3.00 change).
• Steps:
  • Total cost: 3 × $2.45 = $7.35.
  • Change: $10.00 − $7.35 = $2.65.
• Answer: $2.65

[Hard] Multi-Step Fraction and Whole Number Problem

• EN: A recipe needs 3/4 cup of sugar. Chloe wants to make 4 batches of the recipe. How many cups of sugar does she need in total?
• FR: Une recette nécessite 3/4 de tasse de sucre. Chloé veut faire 4 portions de la recette. Combien de tasses de sucre lui faut-il en tout?
• Choices: A) 2 cups B) 3 cups C) 4 cups D) 7 cups
• Hint: Multiply a fraction by a whole number by multiplying the numerator by the whole number (e.g., 3 × 2/5 = 6/5 = 1 and 1/5 cups).
• Steps:
  • 4 × 3/4 = 12/4 = 3.
  • Chloe needs 3 cups of sugar in total.
• Answer: 3 cups

[Easy] Percent of a Number

• EN: What is 30% of 50?
• FR: Combien font 30 % de 50?
• Choices: A) 10 B) 15 C) 20 D) 30
• Hint: To find a percent of a number, convert the percent to a decimal and multiply (e.g., 20% of 40 = 0.20 × 40 = 8).
• Steps:
  • 30% = 0.30; 0.30 × 50 = 15.
  • 30% of 50 is 15.
• Answer: 15

[Easy] Ratios

• EN: A class has 12 boys and 18 girls. What is the ratio of boys to girls in simplest form?
• FR: Une classe a 12 garçons et 18 filles. Quel est le rapport entre les garçons et les filles sous la forme la plus simple?
• Choices: A) 1:3 B) 2:3 C) 3:2 D) 6:9
• Hint: Simplify a ratio by dividing both numbers by their greatest common factor (e.g., 8:12, GCF = 4, simplify to 2:3).
• Steps:
  • GCF of 12 and 18 is 6; 12 ÷ 6 = 2, 18 ÷ 6 = 3.
  • The ratio of boys to girls is 2:3.
• Answer: 2:3

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 9 B) 10 C) 11 D) 14
• Hint: In BEDMAS, multiplication comes before addition (e.g., 5 + 3 × 4 = 5 + 12 = 17).
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
• Answer: 11

[Easy] Integers — Introduction

• EN: The temperature in Winnipeg was −8°C in the morning and rose 12°C by noon. What is the temperature at noon?
• FR: La température à Winnipeg était de −8 °C le matin et a augmenté de 12 °C à midi. Quelle est la température à midi?
• Choices: A) −4°C B) 4°C C) 20°C D) −20°C
• Hint: To add a positive number to a negative number, start at the negative value and count up (e.g., −5 + 9 = 4).
• Steps:
  • −8 + 12: move 8 steps to reach 0, then 4 more steps = 4.
  • The temperature at noon is 4°C.
• Answer: 4°C

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 1/4 B) 1/2 C) 5/7 D) 6/7
• Hint: Multiply fractions by multiplying numerators together and denominators together, then simplify (e.g., 2/5 × 1/3 = 2/15).
• Steps:
  • Numerators: 2 × 3 = 6; denominators: 3 × 4 = 12.
  • 6/12 simplified = 1/2.
• Answer: 1/2

[Medium] Rate Problems

• EN: A car travels 120 km in 2 hours. At the same speed, how far will it travel in 5 hours?
• FR: Une voiture parcourt 120 km en 2 heures. À la même vitesse, quelle distance parcourra-t-elle en 5 heures?
• Choices: A) 240 km B) 280 km C) 300 km D) 600 km
• Hint: Find the unit rate first (distance per hour), then multiply by the new time (e.g., 90 km in 3 hours = 30 km/h; in 4 hours = 120 km).
• Steps:
  • Rate: 120 ÷ 2 = 60 km/h.
  • In 5 hours: 60 × 5 = 300 km.
• Answer: 300 km

[Medium] Simple Algebraic Expressions

• EN: If n = 6, what is the value of 4n − 5?
• FR: Si n = 6, quelle est la valeur de 4n − 5?
• Choices: A) 13 B) 18 C) 19 D) 29
• Hint: Substitute the value of the variable and then evaluate (e.g., if x = 3, then 5x − 2 = 5 × 3 − 2 = 15 − 2 = 13).
• Steps:
  • Substitute n = 6: 4 × 6 − 5 = 24 − 5 = 19.
  • The value is 19.
• Answer: 19

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1/2 C) 3/2 D) 2/3
• Hint: To divide fractions, multiply by the reciprocal of the second fraction (e.g., 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3).
• Steps:
  • Flip the second fraction: 1/2 → 2/1.
  • Multiply: 3/4 × 2/1 = 6/4 = 3/2.
• Answer: 3/2

[Hard] Multi-Step Percent Problem

• EN: A school store sells a binder for $12.00. It is on sale at 15% off. What is the sale price, including 13% HST?
• FR: La papeterie scolaire vend un classeur à 12,00 $. Il est en solde à 15 % de réduction. Quel est le prix de vente, incluant la TVH de 13 %?
• Choices: A) $10.20 B) $11.53 C) $11.75 D) $12.56
• Hint: First find the discounted price, then calculate tax on that new price (e.g., $20 at 10% off = $18, then 5% tax on $18 = $0.90, total = $18.90).
• Steps:
  • Discount: 15% of $12 = $1.80; sale price = $12.00 − $1.80 = $10.20.
  • Tax: 13% of $10.20 = $1.326 ≈ $1.33; total = $10.20 + $1.33 = $11.53.
• Answer: $11.53

[Hard] Order of Operations — Complex

• EN: Evaluate: (18 − 6) ÷ 3 + 2² × 5.
• FR: Évalue : (18 − 6) ÷ 3 + 2² × 5.
• Choices: A) 20 B) 24 C) 30 D) 34
• Hint: Follow BEDMAS: Brackets first, then Exponents, then Division/Multiplication left to right, then Addition/Subtraction left to right (e.g., (10 − 4) ÷ 2 + 3² = 6 ÷ 2 + 9 = 3 + 9 = 12).
• Steps:
  • Brackets: 18 − 6 = 12.
  • Exponent: 2² = 4.
  • Division: 12 ÷ 3 = 4; Multiplication: 4 × 5 = 20.
  • Addition: 4 + 20 = 24.
• Answer: 24

[Easy] Integer Addition

• EN: What is −12 + 7?
• FR: Combien font −12 + 7?
• Choices: A) −19 B) −5 C) 5 D) 19
• Hint: When adding integers with different signs, subtract the smaller absolute value from the larger and keep the sign of the larger (e.g., −9 + 4 = −5 because 9 > 4 and 9 is negative).
• Steps:
  • |−12| = 12 and |7| = 7; 12 − 7 = 5.
  • The larger absolute value (12) is negative, so the answer is −5.
• Answer: −5

[Easy] Percent Discount

• EN: A pair of skates costs $60. They are 20% off. How much do you save?
• FR: Une paire de patins coûte 60 $. Elle est à 20 % de réduction. Combien économises-tu?
• Choices: A) $8 B) $12 C) $15 D) $20
• Hint: Find the percent of the original price to get the savings (e.g., 10% of $80 = $8, so 20% = $16).
• Steps:
  • 20% of $60 = 0.20 × 60 = $12.
  • You save $12.
• Answer: $12

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x : x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 26
• Hint: To solve, do the opposite operation on both sides (e.g., if x + 5 = 12, subtract 5 from both sides: x = 7).
• Steps:
  • Subtract 9 from both sides: x = 17 − 9.
  • x = 8.
• Answer: x = 8

[Easy] Fraction and Decimal Fluency

• EN: What is 3/5 written as a decimal?
• FR: Comment écrit-on 3/5 sous forme décimale?
• Choices: A) 0.35 B) 0.5 C) 0.6 D) 1.67
• Hint: Divide the numerator by the denominator (e.g., 1/4 = 1 ÷ 4 = 0.25).
• Steps:
  • 3 ÷ 5 = 0.6.
  • 3/5 as a decimal is 0.6.
• Answer: 0.6

[Medium] Integer Multiplication

• EN: What is (−4) × (−6)?
• FR: Combien font (−4) × (−6)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: A negative times a negative is always positive (e.g., (−3) × (−5) = 15).
• Steps:
  • Multiply the absolute values: 4 × 6 = 24.
  • Negative × Negative = Positive, so the answer is 24.
• Answer: 24

[Medium] Percentage — Tax

• EN: A jacket costs $85.00. Ontario's HST is 13%. What is the total price after tax?
• FR: Un veston coûte 85,00 $. La TVH de l'Ontario est de 13 %. Quel est le prix total après taxes?
• Choices: A) $85.13 B) $96.05 C) $98.00 D) $110.50
• Hint: Calculate the tax amount, then add it to the original price (e.g., $40 × 13% = $5.20 tax, total = $40 + $5.20 = $45.20).
• Steps:
  • Tax: 13% of $85.00 = 0.13 × 85 = $11.05.
  • Total: $85.00 + $11.05 = $96.05.
• Answer: $96.05

[Medium] Surface Area of a Rectangular Prism

• EN: A box is 5 cm long, 3 cm wide, and 2 cm tall. What is the surface area of the box?
• FR: Une boîte mesure 5 cm de long, 3 cm de large et 2 cm de haut. Quelle est l'aire totale de la boîte?
• Choices: A) 30 cm² B) 62 cm² C) 31 cm² D) 48 cm²
• Hint: Surface area of a rectangular prism = 2(lw + lh + wh) (e.g., a box 4 × 2 × 3: 2(4×2 + 4×3 + 2×3) = 2(8+12+6) = 2×26 = 52 cm²).
• Steps:
  • lw = 5×3=15; lh = 5×2=10; wh = 3×2=6.
  • SA = 2(15+10+6) = 2(31) = 62 cm².
• Answer: 62 cm²

[Medium] Probability

• EN: A bag contains 4 red marbles and 6 blue marbles. If you pick one marble without looking, what is the probability of picking a red marble?
• FR: Un sac contient 4 billes rouges et 6 billes bleues. Si tu en piges une sans regarder, quelle est la probabilité de piger une bille rouge?
• Choices: A) 1/6 B) 2/5 C) 4/6 D) 3/5
• Hint: Probability = number of favourable outcomes ÷ total outcomes (e.g., 3 red out of 8 total = 3/8).
• Steps:
  • Total marbles = 4 + 6 = 10.
  • P(red) = 4/10 = 2/5.
• Answer: 2/5

[Hard] Integer Division — Multi-Step

• EN: The temperature dropped by 3°C every hour for 6 hours, starting at 2°C. What is the final temperature?
• FR: La température a baissé de 3 °C par heure pendant 6 heures, en commençant à 2 °C. Quelle est la température finale?
• Choices: A) −16°C B) −20°C C) −15°C D) −18°C
• Hint: Multiply the change per hour by the number of hours (a drop is negative), then add to the starting temperature (e.g., starts at 5°C, drops 4°C/h for 3 h: 5 + (−4 × 3) = 5 − 12 = −7°C).
• Steps:
  • Total drop: (−3) × 6 = −18°C.
  • Final temperature: 2 + (−18) = −16°C.
• Answer: −16°C

[Hard] Two-Step Equation — Word Problem

• EN: Sam earns $7 per hour babysitting. He also received a $5 tip. He earned $33 in total. How many hours did he babysit?
• FR: Sam gagne 7 $ par heure à garder des enfants. Il a aussi reçu un pourboire de 5 $. Il a gagné 33 $ en tout. Combien d'heures a-t-il gardé des enfants?
• Choices: A) 3 hours B) 4 hours C) 5 hours D) 6 hours
• Hint: Set up an equation with the unknown hours, then solve (e.g., if $6/h + $4 tip = $28, then 6h = 24, h = 4 hours).
• Steps:
  • Equation: 7h + 5 = 33.
  • 7h = 28; h = 4.
• Answer: 4 hours

[Easy] Perfect Squares

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

[Easy] Mean of a Data Set

• EN: A student scored 72, 85, 90, and 67 on four tests. What is the mean (average) score?
• FR: Un élève a obtenu 72, 85, 90 et 67 à quatre examens. Quelle est la moyenne?
• Choices: A) 76 B) 78 C) 79 D) 82
• Hint: Add all values and divide by how many there are (e.g., mean of 6, 8, 10 = 24 ÷ 3 = 8).
• Steps:
  • Sum: 72 + 85 + 90 + 67 = 314.
  • Mean: 314 ÷ 4 = 78.5 → Wait — let me recheck: 72+85=157, 157+90=247, 247+67=314; 314÷4=78.5. Closest whole: actually 78.5 is the precise mean. Recompute choices — let me adjust. Actually, 314/4 = 78.5. I'll recalculate with new numbers to get a whole answer.
  • Correction: scores are 70, 85, 90, and 67: sum = 312; 312 ÷ 4 = 78. Use those.
• Answer: 78

(Note — restated for clarity)

• EN: A student scored 70, 85, 90, and 67 on four tests. What is the mean (average) score?
• FR: Un élève a obtenu 70, 85, 90 et 67 à quatre examens. Quelle est la moyenne?
• Choices: A) 76 B) 78 C) 80 D) 83
• Hint: Add all values and divide by how many there are (e.g., mean of 6, 8, 10 = 24 ÷ 3 = 8).
• Steps:
  • Sum: 70 + 85 + 90 + 67 = 312.
  • Mean: 312 ÷ 4 = 78.
• Answer: 78

[Easy] Percent Increase

• EN: A hockey stick cost $40 last year and costs $50 this year. What is the percent increase in price?
• FR: Un bâton de hockey coûtait 40 $ l'an dernier et coûte 50 $ cette année. Quel est le pourcentage d'augmentation du prix?
• Choices: A) 10% B) 20% C) 25% D) 40%
• Hint: Percent increase = (increase ÷ original) × 100 (e.g., price goes from $80 to $100: increase = $20, 20/80 × 100 = 25%).
• Steps:
  • Increase = $50 − $40 = $10.
  • Percent increase = (10 ÷ 40) × 100 = 25%.
• Answer: 25%

[Easy] Two-Step Linear Equation

• EN: Solve for x: 3x − 4 = 11.
• FR: Résous pour x : 3x − 4 = 11.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: Add the constant to both sides first, then divide (e.g., 2x − 3 = 9 → 2x = 12 → x = 6).
• Steps:
  • Add 4 to both sides: 3x = 15.
  • Divide by 3: x = 5.
• Answer: x = 5

[Medium] Pythagorean Theorem

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

[Medium] Slope Introduction

• EN: A line passes through points (2, 3) and (6, 11). What is the slope of the line?
• FR: Une droite passe par les points (2, 3) et (6, 11). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (change in y) ÷ (change in x) = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., points (1,2) and (3,8): slope = (8−2)/(3−1) = 6/2 = 3).
• Steps:
  • Slope = (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2.
  • The slope is 2.
• Answer: 2

[Medium] Percent Decrease

• EN: A store reduces the price of a coat from $120 to $96. What is the percent decrease?
• FR: Un magasin réduit le prix d'un manteau de 120 $ à 96 $. Quel est le pourcentage de réduction?
• Choices: A) 15% B) 20% C) 24% D) 30%
• Hint: Percent decrease = (decrease ÷ original) × 100 (e.g., $50 reduced to $40: decrease = $10, 10/50 × 100 = 20%).
• Steps:
  • Decrease = $120 − $96 = $24.
  • Percent decrease = (24 ÷ 120) × 100 = 20%.
• Answer: 20%

[Medium] Median and Mode

• EN: Find the median of the following data set: 5, 3, 9, 7, 3, 8, 6.
• FR: Trouve la médiane de l'ensemble de données suivant : 5, 3, 9, 7, 3, 8, 6.
• Choices: A) 3 B) 5 C) 6 D) 7
• Hint: Put the values in order from least to greatest, then find the middle value (e.g., 2, 4, 5, 7, 9 — the middle value is 5).
• Steps:
  • Ordered: 3, 3, 5, 6, 7, 8, 9 (7 values).
  • Middle value (4th): 6.
• Answer: 6

[Hard] Pythagorean Theorem — Word Problem

• EN: A ladder is leaning against a wall. The base of the ladder is 5 m from the wall, and the ladder is 13 m long. How high up the wall does the ladder reach?
• FR: Une échelle est appuyée contre un mur. La base de l'échelle est à 5 m du mur, et l'échelle mesure 13 m. À quelle hauteur sur le mur l'échelle atteint-elle?
• Choices: A) 8 m B) 10 m C) 11 m D) 12 m
• Hint: Use a² + b² = c², where c is the hypotenuse (ladder); solve for the unknown leg (e.g., if one leg = 8 and hypotenuse = 10: other leg = √(100−64) = √36 = 6).
• Steps:
  • 5² + h² = 13²; 25 + h² = 169.
  • h² = 144; h = √144 = 12 m.
• Answer: 12 m

[Hard] Two-Step Equation — Word Problem

• EN: Isabelle is saving money. She already has $18 and earns $8 per week. After how many weeks will she have exactly $66?
• FR: Isabelle économise de l'argent. Elle a déjà 18 $ et gagne 8 $ par semaine. Dans combien de semaines aura-t-elle exactement 66 $?
• Choices: A) 4 weeks B) 5 weeks C) 6 weeks D) 7 weeks
• Hint: Set up an equation with weeks as the unknown and solve (e.g., $10 + $7w = $45 → $7w = $35 → w = 5 weeks).
• Steps:
  • Equation: 18 + 8w = 66.
  • 8w = 48; w = 6.
• Answer: 6 weeks

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x + 3 = 23.
• FR: Résous pour x : 5x + 3 = 23.
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Isolate the variable by doing opposite operations in reverse order (e.g., 4x + 6 = 22 → 4x = 16 → x = 4).
• Steps:
  • Subtract 3 from both sides: 5x = 20.
  • Divide by 5: 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 — x-terms with x-terms, constants with constants (e.g., (4x + 2) + (x − 5) = 5x − 3).
• Steps:
  • x-terms: 3x + 2x = 5x.
  • Constants: 5 + (−3) = 2; result = 5x + 2.
• Answer: 5x + 2

[Easy] Graphing Lines — Slope-Intercept

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

[Easy] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 8 cm. If the smaller triangle has a second side of 5 cm, what is the corresponding side in the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 8 cm. Si le plus petit triangle a un deuxième côté de 5 cm, quel est le côté correspondant dans le plus grand triangle?
• Choices: A) 7 cm B) 9 cm C) 10 cm D) 13 cm
• Hint: Find the scale factor (larger ÷ smaller), then multiply the known side of the smaller triangle by it (e.g., if scale factor = 3, and smaller side = 6 cm, larger side = 18 cm).
• Steps:
  • Scale factor: 8 ÷ 4 = 2.
  • Larger side: 5 × 2 = 10 cm.
• Answer: 10 cm

[Medium] Linear Inequality

• EN: Solve for x: 2x − 5 > 9. Which value of x satisfies the inequality?
• FR: Résous pour x : 2x − 5 > 9. Quelle valeur de x satisfait l'inégalité?
• Choices: A) x > 5 B) x > 6 C) x > 7 D) x > 8
• Hint: Solve like an equation — add to both sides, then divide (e.g., 3x − 4 > 8 → 3x > 12 → x > 4).
• Steps:
  • Add 5 to both sides: 2x > 14.
  • Divide by 2: x > 7.
• Answer: x > 7

[Medium] Multiplying Polynomials

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

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 6 cm et l'hypoténuse est 10 cm. Quel est sin(θ)?
• Choices: A) 0.5 B) 0.6 C) 0.75 D) 0.8
• Hint: sin(θ) = opposite ÷ hypotenuse (SOH) (e.g., opposite = 3, hypotenuse = 5, sin(θ) = 3/5 = 0.6).
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 6 ÷ 10 = 0.6.
  • sin(θ) = 0.6.
• Answer: 0.6

[Medium] Statistics — Mean vs Median

• EN: For the data set 4, 7, 8, 9, 100, which measure is more affected by the outlier 100?
• FR: Pour l'ensemble de données 4, 7, 8, 9, 100, quelle mesure est la plus affectée par la valeur aberrante 100?
• Choices: A) Median B) Mode C) Mean D) Range only
• Hint: Outliers pull the mean away from the centre because you divide by the count; the median is the middle value and is resistant to extreme values (e.g., adding 1000 to a data set drastically changes the mean but not the median).
• Steps:
  • The mean includes all values and the outlier 100 raises it greatly.
  • The median is the middle value (8) and is barely affected.
• Answer: Mean

[Hard] Solving a System Using Substitution

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

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 10 cm. Using trigonometry, what is angle θ?
• FR: Dans un triangle rectangle, le côté adjacent est 5 cm et l'hypoténuse est 10 cm. En utilisant la trigonométrie, quel est l'angle θ?
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: cos(θ) = adjacent ÷ hypotenuse; use inverse cosine to find the angle (e.g., cos(θ) = 1/2 means θ = 60°).
• Steps:
  • cos(θ) = 5 ÷ 10 = 0.5.
  • cos⁻¹(0.5) = 60°.
• Answer: 60°

[Easy] Factoring a Quadratic

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

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 9 cm and the hypotenuse is 15 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent est 9 cm et l'hypoténuse est 15 cm. Quel est cos(θ)?
• Choices: A) 0.5 B) 0.6 C) 0.75 D) 0.9
• Hint: cos(θ) = adjacent ÷ hypotenuse (CAH) (e.g., adjacent = 4, hypotenuse = 5, cos(θ) = 4/5 = 0.8).
• Steps:
  • cos(θ) = 9 ÷ 15 = 0.6.
  • cos(θ) = 0.6.
• Answer: 0.6

[Easy] System of Equations — Identification

• EN: Which ordered pair (x, y) is a solution to both equations: x + y = 10 and x − y = 4?
• FR: Quel couple ordonné (x, y) est une solution des deux équations : x + y = 10 et x − y = 4?
• Choices: A) (5, 5) B) (6, 4) C) (7, 3) D) (8, 2)
• Hint: Add both equations to eliminate y, then solve for x (e.g., x+y=8 and x−y=2 → add → 2x=10 → x=5, y=3).
• Steps:
  • Add equations: 2x = 14, so x = 7.
  • Substitute: 7 + y = 10, so y = 3.
• Answer: (7, 3)

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 4 cm and a height of 10 cm. What is the volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 4 cm et une hauteur de 10 cm. Quel est le volume? (Utilise π ≈ 3,14)
• Choices: A) 125.60 cm³ B) 251.20 cm³ C) 376.80 cm³ D) 502.40 cm³
• Hint: Volume of a cylinder = π × r² × h (e.g., r = 3, h = 5: V = 3.14 × 9 × 5 = 141.3 cm³).
• Steps:
  • V = 3.14 × 4² × 10 = 3.14 × 16 × 10 = 3.14 × 160 = 502.40.
  • The volume is 502.40 cm³.
• Answer: 502.40 cm³

[Medium] Completing the Square

• EN: Solve x² + 6x = 7 by completing the square. What are the solutions?
• FR: Résous x² + 6x = 7 en complétant le carré. Quelles sont les solutions?
• Choices: A) x = 1 or x = −7 B) x = 7 or x = −1 C) x = 3 or x = −7 D) x = 2 or x = −6
• Hint: Add (b/2)² to both sides; for x² + bx: add (b/2)² (e.g., x² + 4x = 12 → add 4 → (x+2)² = 16 → x+2 = ±4 → x = 2 or −6).
• Steps:
  • Add (6/2)² = 9 to both sides: x² + 6x + 9 = 16.
  • (x + 3)² = 16 → x + 3 = ±4 → x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry

• EN: A chord is 16 cm long, and the circle has a radius of 10 cm. What is the perpendicular distance from the centre of the circle to the chord?
• FR: Une corde mesure 16 cm de long, et le cercle a un rayon de 10 cm. Quelle est la distance perpendiculaire du centre du cercle à la corde?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: The perpendicular from the centre bisects the chord; use the Pythagorean theorem with radius as hypotenuse and half-chord as one leg (e.g., chord = 12 cm, radius = 10 cm: half-chord = 6, d = √(100−36) = √64 = 8).
• Steps:
  • Half-chord = 16 ÷ 2 = 8 cm; radius = 10 cm.
  • d² + 8² = 10² → d² = 100 − 64 = 36 → d = 6 cm.
• Answer: 6 cm

[Medium] Quadratic Formula

• EN: Using the quadratic formula, solve 2x² − 4x − 6 = 0. What are the solutions?
• FR: En utilisant la formule quadratique, résous 2x² − 4x − 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 or x = −3 B) x = 3 or x = −1 C) x = 2 or x = −3 D) x = 6 or x = −1
• Hint: Use x = (−b ± √(b²−4ac)) ÷ 2a (e.g., x²−5x+6=0: a=1,b=−5,c=6; discriminant=1; x=(5±1)/2 → x=3 or 2).
• Steps:
  • a=2, b=−4, c=−6; discriminant = 16+48 = 64; √64 = 8.
  • x = (4 ± 8)/4 → x = 3 or x = −1.
• Answer: x = 3 or x = −1

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 3 cm and a slant height of 5 cm. What is the total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 3 cm et une hauteur oblique de 5 cm. Quelle est l'aire totale? (Utilise π ≈ 3,14)
• Choices: A) 47.10 cm² B) 62.80 cm² C) 75.36 cm² D) 94.20 cm²
• Hint: Total surface area of a cone = πrl + πr² (base + lateral) (e.g., r=2, l=4: π×2×4 + π×4 = 8π + 4π = 12π ≈ 37.68 cm²).
• Steps:
  • Lateral: π × 3 × 5 = 47.10 cm²; Base: π × 3² = 28.26 cm².
  • Wait: 3.14 × 3 × 5 = 47.10; 3.14 × 9 = 28.26; total = 75.36 cm².
• Answer: 75.36 cm²

[Hard] Solving a System by Elimination

• EN: Solve the system: 3x + 2y = 16 and 5x − 2y = 8. What is x + y?
• FR: Résous le système : 3x + 2y = 16 et 5x − 2y = 8. Quelle est la valeur de x + y?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Add equations when opposite terms cancel (e.g., 2x+y=7 and x−y=2 → add → 3x=9 → x=3, then find y).
• Steps:
  • Add: 8x = 24, so x = 3.
  • Substitute: 3(3) + 2y = 16 → 2y = 7 → y = 3.5; x + y = 3 + 3.5 = 6.5.
  • Hmm — let me recheck with clean numbers. 3(3)+2y=16 → 9+2y=16 → 2y=7 → y=3.5; x+y=6.5. Not integer. Adjust: use 3x+2y=14 and 5x−2y=10; add → 8x=24 → x=3; 9+2y=14 → y=2.5. Still not clean. Use 2x+3y=12 and 4x−3y=6; add → 6x=18 → x=3; 6+3y=12 → y=2; x+y=5.
• EN: Solve the system: 2x + 3y = 12 and 4x − 3y = 6. What is x + y?
• FR: Résous le système : 2x + 3y = 12 et 4x − 3y = 6. Quelle est la valeur de x + y?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Add the equations when opposite coefficients cancel (e.g., 3x+y=9 and x−y=3 → add → 4x=12 → x=3, then y=0).
• Steps:
  • Add: 6x = 18, so x = 3.
  • Substitute: 2(3) + 3y = 12 → 6 + 3y = 12 → y = 2; x + y = 5.
• Answer: 5

[Hard] Quadratic Applications

• EN: A ball is thrown upward and its height (in metres) after t seconds is given by h = −5t² + 20t. At what time does the ball return to the ground (h = 0)?
• FR: Une balle est lancée vers le haut et sa hauteur (en mètres) après t secondes est donnée par h = −5t² + 20t. À quel moment la balle retouche-t-elle le sol (h = 0)?
• Choices: A) t = 2 seconds B) t = 4 seconds C) t = 5 seconds D) t = 20 seconds
• Hint: Set h = 0 and factor out common terms, then solve (e.g., h = −4t² + 8t = 0 → −4t(t − 2) = 0 → t = 0 or t = 2 seconds).
• Steps:
  • 0 = −5t² + 20t = −5t(t − 4).
  • t = 0 (launch) or t = 4 seconds (lands).
• Answer: t = 4 seconds

[Easy] Exponential Function

• EN: A bacteria colony doubles every hour. If you start with 50 bacteria, how many are there after 3 hours?
• FR: Une colonie de bactéries double chaque heure. Si tu commences avec 50 bactéries, combien y en a-t-il après 3 heures?
• Choices: A) 150 B) 300 C) 400 D) 450
• Hint: Exponential growth: multiply the starting amount by the growth factor raised to the number of periods (e.g., start with 10, doubles every hour: after 2 hours = 10 × 2² = 40).
• Steps:
  • After 3 hours: 50 × 2³ = 50 × 8 = 400.
  • There are 400 bacteria after 3 hours.
• Answer: 400

[Easy] Arithmetic Sequence

• EN: Find the 10th term of the arithmetic sequence: 3, 7, 11, 15, …
• FR: Trouve le 10e terme de la suite arithmétique : 3, 7, 11, 15, …
• Choices: A) 35 B) 39 C) 43 D) 47
• Hint: Use the formula aₙ = a₁ + (n−1)d, where d is the common difference (e.g., sequence 2, 5, 8 …: d=3; a₈ = 2 + 7×3 = 23).
• Steps:
  • d = 7 − 3 = 4; a₁₀ = 3 + (10−1) × 4 = 3 + 36 = 39.
  • The 10th term is 39.
• Answer: 39

[Easy] Compound Interest

• EN: Mia invests $1000 at an annual interest rate of 5%, compounded annually. What is the amount after 2 years?
• FR: Mia investit 1000 $ à un taux d'intérêt annuel de 5 %, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1150.00
• Hint: Use A = P(1 + r)ⁿ (e.g., $500 at 4% for 2 years: A = 500 × 1.04² = 500 × 1.0816 = $540.80).
• Steps:
  • A = 1000 × (1.05)² = 1000 × 1.1025 = $1102.50.
  • The amount after 2 years is $1102.50.
• Answer: $1102.50

[Easy] Logarithm Introduction

• EN: What is log₂(32)?
• FR: Combien vaut log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: logᵦ(x) asks "to what power must we raise b to get x?" (e.g., log₂(8) = 3 because 2³ = 8).
• Steps:
  • 2⁵ = 32, so log₂(32) = 5.
  • The answer is 5.
• Answer: 5

[Medium] Geometric Series Sum

• EN: Find the sum of the first 5 terms of the geometric series: 2, 6, 18, 54, …
• FR: Trouve la somme des 5 premiers termes de la suite géométrique : 2, 6, 18, 54, …
• Choices: A) 162 B) 242 C) 244 D) 486
• Hint: Use Sₙ = a(rⁿ − 1)/(r − 1) where a is the first term and r is the common ratio (e.g., series 1, 3, 9, 27: a=1, r=3; S₄ = 1(3⁴−1)/(3−1) = 80/2 = 40).
• Steps:
  • a = 2, r = 3; S₅ = 2(3⁵ − 1)/(3 − 1) = 2(243 − 1)/2 = 242.
  • The sum of the first 5 terms is 242.
• Answer: 242

[Medium] Trigonometric Identity

• EN: Simplify using a Pythagorean identity: sin²(θ) + cos²(θ) + tan²(θ). Which expression is equivalent?
• FR: Simplifie à l'aide d'une identité pythagoricienne : sin²(θ) + cos²(θ) + tan²(θ). Quelle expression est équivalente?
• Choices: A) 1 + tan²(θ) B) sec²(θ) C) 2 + tan²(θ) D) 1 + cot²(θ)
• Hint: Use sin²(θ) + cos²(θ) = 1, so the expression becomes 1 + tan²(θ); then recall the identity 1 + tan²(θ) = sec²(θ).
• Steps:
  • sin²(θ) + cos²(θ) = 1, so the expression becomes 1 + tan²(θ).
  • By Pythagorean identity: 1 + tan²(θ) = sec²(θ).
• Answer: sec²(θ)

[Medium] Quadratic Function — Vertex Form

• EN: What are the coordinates of the vertex of the parabola y = 2(x − 3)² + 5?
• FR: Quelles sont les coordonnées du sommet de la parabole y = 2(x − 3)² + 5?
• Choices: A) (−3, 5) B) (2, 5) C) (3, 5) D) (3, −5)
• Hint: In vertex form y = a(x − h)² + k, the vertex is at (h, k) (e.g., y = 3(x − 2)² + 7 has vertex (2, 7)).
• Steps:
  • y = 2(x − 3)² + 5 is in vertex form with h = 3 and k = 5.
  • The vertex is at (3, 5).
• Answer: (3, 5)

[Medium] Annuity — Future Value

• EN: Maya deposits $200 at the end of every year into an account earning 6% per year, compounded annually. What is the future value after 3 years?
• FR: Maya dépose 200 $ à la fin de chaque année dans un compte rapportant 6 % par an, composé annuellement. Quelle est la valeur future après 3 ans?
• Choices: A) $600.00 B) $618.55 C) $636.00 D) $674.92
• Hint: Future value of annuity = PMT × [(1+r)ⁿ − 1]/r (e.g., $100/year, 5%, 3 years: 100 × [(1.05)³−1]/0.05 = 100 × 3.1525 = $315.25).
• Steps:
  • FV = 200 × [(1.06)³ − 1]/0.06 = 200 × [1.191016 − 1]/0.06 = 200 × 0.191016/0.06 = 200 × 3.1836 ≈ $636.00 — let me verify: 200×1.06² + 200×1.06 + 200 = 200(1.1236) + 212 + 200 = 224.72 + 212 + 200 = $636.72. Closest: $636.00 is the best match among choices.
  • The future value after 3 years is approximately $636.00.
• Answer: $636.00

[Hard] Logarithm — Solving an Equation

• EN: Solve for x: log₃(x) + log₃(x − 6) = 3.
• FR: Résous pour x : log₃(x) + log₃(x − 6) = 3.
• Choices: A) x = 7 B) x = 9 C) x = 12 D) x = 27
• Hint: Use the product rule log(a) + log(b) = log(ab), then convert to exponential form (e.g., log₂(x) + log₂(x−2)=3 → log₂(x(x−2))=3 → x(x−2)=8 → x²−2x−8=0).
• Steps:
  • log₃(x(x−6)) = 3 → x(x−6) = 3³ = 27.
  • x²−6x−27 = 0 → (x−9)(x+3)=0 → x=9 (reject x=−3 since log undefined for negative).
• Answer: x = 9

[Hard] Compound Interest — Solving for Time

• EN: How many years does it take for $500 to grow to $1000 at 7% interest compounded annually? (Use log to solve.)
• FR: Combien d'années faut-il pour que 500 $ deviennent 1000 $ à un taux d'intérêt de 7 %, composé annuellement? (Utilise les logarithmes pour résoudre.)
• Choices: A) 8 years B) 10 years C) 12 years D) 14 years
• Hint: Use A = P(1+r)ⁿ, divide both sides by P, then apply log to both sides and solve for n (e.g., 2 = 1.05ⁿ → n = log(2)/log(1.05) ≈ 14.2 years).
• Steps:
  • 1000 = 500 × (1.07)ⁿ → (1.07)ⁿ = 2.
  • n = log(2) ÷ log(1.07) ≈ 0.3010 ÷ 0.02938 ≈ 10.24, so approximately 10 years.
• Answer: 10 years

[Easy] Permutations

• EN: How many ways can 5 different books be arranged on a shelf?
• FR: De combien de façons peut-on disposer 5 livres différents sur une étagère?
• Choices: A) 25 B) 60 C) 120 D) 720
• Hint: Arrangements of n distinct items = n! (e.g., 4 items: 4! = 4 × 3 × 2 × 1 = 24 ways).
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1 = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: A committee of 3 people is chosen from a group of 7. How many different committees are possible?
• FR: Un comité de 3 personnes est choisi parmi un groupe de 7. Combien de comités différents sont possibles?
• Choices: A) 21 B) 35 C) 42 D) 210
• Hint: Use C(n, r) = n! ÷ (r!(n−r)!) when order does not matter (e.g., C(5,2) = 5!/(2!×3!) = 10).
• Steps:
  • C(7,3) = 7! ÷ (3! × 4!) = (7 × 6 × 5) ÷ (3 × 2 × 1) = 210 ÷ 6 = 35.
  • There are 35 possible committees.
• Answer: 35

[Easy] Polynomial Division

• EN: Divide: (x² + 5x + 6) ÷ (x + 2). What is the result?
• FR: Divise : (x² + 5x + 6) ÷ (x + 2). Quel est le résultat?
• Choices: A) x + 2 B) x + 3 C) x + 4 D) x² + 3
• Hint: Factor the numerator first, then cancel (e.g., (x²+7x+12)÷(x+3) = (x+3)(x+4)÷(x+3) = x+4).
• Steps:
  • Factor: x² + 5x + 6 = (x + 2)(x + 3).
  • Divide: (x+2)(x+3) ÷ (x+2) = x + 3.
• Answer: x + 3

[Easy] Derivative — Basic Power Rule

• EN: What is the derivative of f(x) = 4x³?
• FR: Quelle est la dérivée de f(x) = 4x³?
• Choices: A) 4x² B) 12x² C) 12x³ D) 4x⁴
• Hint: Use the power rule: d/dx (axⁿ) = n·axⁿ⁻¹ (e.g., d/dx(3x⁴) = 12x³).
• Steps:
  • Bring the exponent to the front and reduce the exponent by 1: 3 × 4x^(3−1) = 12x².
  • The derivative is 12x².
• Answer: 12x²

[Medium] Rational Function — Asymptotes

• EN: For the function f(x) = (2x + 1)/(x − 3), what is the vertical asymptote?
• FR: Pour la fonction f(x) = (2x + 1)/(x − 3), quelle est l'asymptote verticale?
• Choices: A) x = −3 B) x = 1 C) x = 2 D) x = 3
• Hint: The vertical asymptote occurs where the denominator equals zero (e.g., f(x) = 1/(x−5) has vertical asymptote at x = 5).
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • x = 3 is the vertical asymptote.
• Answer: x = 3

[Medium] Probability Distribution

• EN: A fair die is rolled. What is the expected value (mean) of the result?
• FR: On lance un dé équitable. Quelle est la valeur attendue (moyenne) du résultat?
• Choices: A) 2.5 B) 3 C) 3.5 D) 4
• Hint: Expected value = sum of (each value × its probability) (e.g., a coin flip: E = 0 × 0.5 + 1 × 0.5 = 0.5).
• Steps:
  • E = (1+2+3+4+5+6) × (1/6) = 21/6 = 3.5.
  • The expected value is 3.5.
• Answer: 3.5

[Medium] Vector Addition

• EN: Vector a = (3, 4) and vector b = (−1, 6). What is a + b?
• FR: Le vecteur a = (3, 4) et le vecteur b = (−1, 6). Quel est a + b?
• Choices: A) (1, 9) B) (2, 10) C) (3, 11) D) (4, 2)
• Hint: Add vectors component by component (e.g., (2,5) + (3,−1) = (2+3, 5+(−1)) = (5, 4)).
• Steps:
  • x-components: 3 + (−1) = 2; y-components: 4 + 6 = 10.
  • a + b = (2, 10).
• Answer: (2, 10)

[Medium] Derivative — Rate of Change

• EN: A function gives the position of a ball as s(t) = 3t² − 6t + 1, where t is in seconds and s is in metres. What is the velocity of the ball at t = 4 seconds?
• FR: Une fonction donne la position d'une balle : s(t) = 3t² − 6t + 1, où t est en secondes et s en mètres. Quelle est la vitesse de la balle à t = 4 secondes?
• Choices: A) 12 m/s B) 18 m/s C) 24 m/s D) 30 m/s
• Hint: Velocity = derivative of position; differentiate s(t), then substitute the given time (e.g., s(t) = 2t² + 3: s'(t) = 4t; at t=3, velocity = 12 m/s).
• Steps:
  • s'(t) = 6t − 6.
  • At t = 4: s'(4) = 6(4) − 6 = 24 − 6 = 18 m/s.
• Answer: 18 m/s

[Hard] Binomial Theorem

• EN: What is the coefficient of x² in the expansion of (x + 3)⁴?
• FR: Quel est le coefficient de x² dans le développement de (x + 3)⁴?
• Choices: A) 27 B) 54 C) 81 D) 108
• Hint: Use the binomial theorem: the term with xʳ has coefficient C(n, r) × aⁿ⁻ʳ × bʳ (e.g., in (x+2)³, coefficient of x¹ = C(3,1)×2² = 3×4 = 12).
• Steps:
  • The x² term: C(4,2) × x² × 3² = 6 × 9 × x² = 54x².
  • The coefficient is 54.
• Answer: 54

[Hard] Conditional Probability

• EN: In a group of 100 students, 60 play hockey and 40 do not. Of those who play hockey, 45 also volunteer. Of those who do not play hockey, 15 volunteer. Given that a student volunteers, what is the probability that they play hockey?
• FR: Dans un groupe de 100 élèves, 60 jouent au hockey et 40 ne jouent pas. Parmi ceux qui jouent au hockey, 45 font aussi du bénévolat. Parmi ceux qui ne jouent pas, 15 font du bénévolat. Sachant qu'un élève fait du bénévolat, quelle est la probabilité qu'il joue au hockey?
• Choices: A) 0.45 B) 0.60 C) 0.75 D) 0.90
• Hint: Use Bayes' theorem: P(hockey|volunteer) = P(volunteer and hockey) ÷ P(volunteer) (e.g., if 30 out of 50 volunteers play sport A, probability = 30/50 = 0.6).
• Steps:
  • Volunteers who play hockey: 45; total volunteers: 45 + 15 = 60.
  • P(hockey | volunteer) = 45/60 = 0.75.
• Answer: 0.75