Daily Math — 2026-08-24

[Easy] Counting to 20

• EN: There are 7 apples in a bowl. Emma adds 5 more apples. How many apples are there now?
• FR: Il y a 7 pommes dans un bol. Emma en ajoute 5 autres. Combien y a-t-il de pommes maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: Try counting on from the bigger number. Start at 8, count 4 more: 9, 10, 11, 12.
• Steps:
  • Start at 7.
  • Count on 5 more: 8, 9, 10, 11, 12.
  • So there are 12 apples in total.
• Answer: 12

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes next: 4, 6, 8, ___?
• FR: Compte par bonds de 2. Quel nombre vient ensuite: 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When skip counting by 2s, add 2 each time. For example: 10, 12, 14 — add 2 each step.
• Steps:
  • The pattern adds 2 each time.
  • 4 + 2 = 6, 6 + 2 = 8, 8 + 2 = 10.
  • The next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is bigger: 14 or 9?
• FR: Quel nombre est plus grand: 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 18
• Hint: A number with more tens is bigger. For example, 12 is bigger than 7 because 12 has a ten and 7 does not.
• Steps:
  • 14 has 1 ten and 4 ones.
  • 9 has 0 tens and 9 ones.
  • A number with more tens is bigger, so 14 is bigger.
• Answer: 14

[Easy] Coin Recognition

• EN: Lucas has 1 dime and 1 nickel. How many cents does he have in total?
• FR: Lucas a 1 pièce de dix cents et 1 pièce de cinq cents. Combien de cents a-t-il en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents. Try 10 + 5 with different coin examples.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Medium] Subtraction Within 20

• EN: There are 16 hockey pucks on the ice. Players use 8 of them. How many pucks are left?
• FR: Il y a 16 rondelles de hockey sur la glace. Les joueurs en utilisent 8. Combien de rondelles reste-t-il?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To subtract, count back from the bigger number. For example, 14 − 6: start at 14, count back 6 to get 8.
• Steps:
  • Start at 16.
  • Count back 8: 15, 14, 13, 12, 11, 10, 9, 8.
  • 16 − 8 = 8 pucks are left.
• Answer: 8

[Medium] Skip Counting by 5s

• EN: Lily counts her stickers by 5s: 5, 10, 15, 20, ___. What number comes next?
• FR: Lily compte ses autocollants par bonds de 5: 5, 10, 15, 20, ___. Quel nombre vient ensuite?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: When skip counting by 5s, add 5 each time. For example: 30, 35, 40 — add 5 each step.
• Steps:
  • The pattern adds 5 each time.
  • 5, 10, 15, 20 — add 5 more.
  • 20 + 5 = 25.
• Answer: 25

[Medium] Addition Within 20

• EN: There are 9 red mittens and 6 blue mittens in a box. How many mittens are there altogether?
• FR: Il y a 9 mitaines rouges et 6 mitaines bleues dans une boîte. Combien y a-t-il de mitaines en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: To add two numbers, make a ten first. For example, 8 + 7: take 2 from 7 to make 10 with 8, then add 5 more to get 15.
• Steps:
  • 9 + 6: take 1 from 6 to make 10 with 9.
  • Now we have 10 + 5.
  • 10 + 5 = 15 mittens altogether.
• Answer: 15

[Medium] Skip Counting by 10s

• EN: Count by 10s. What number comes next: 30, 40, 50, ___?
• FR: Compte par bonds de 10. Quel nombre vient ensuite: 30, 40, 50, ___?
• Choices: A) 55 B) 57 C) 60 D) 65
• Hint: When skip counting by 10s, add 10 each time. For example: 20, 30, 40 — add 10 each step.
• Steps:
  • The pattern adds 10 each time.
  • 30, 40, 50 — add 10 more.
  • 50 + 10 = 60.
• Answer: 60

[Hard] Two-Step Addition

• EN: Mia has 6 crayons. She gets 4 more from a friend, and then 3 more from her teacher. How many crayons does she have now?
• FR: Mia a 6 crayons. Elle en reçoit 4 de plus d'un ami, puis 3 autres de son professeur. Combien de crayons a-t-elle maintenant?
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: Solve in two steps. For example, if you have 5, get 3 more (= 8), then get 2 more (= 10).
• Steps:
  • Step 1: 6 + 4 = 10 crayons.
  • Step 2: 10 + 3 = 13 crayons.
  • Mia has 13 crayons altogether.
• Answer: 13

[Hard] Counting Coins

• EN: Ava has 2 nickels and 1 dime. How many cents does she have in all?
• FR: Ava a 2 pièces de cinq cents et 1 pièce de dix cents. Combien de cents a-t-elle en tout?
• Choices: A) 15 cents B) 17 cents C) 20 cents D) 25 cents
• Hint: Find the value of each group first, then add. For example, 3 nickels = 15 cents; add a dime to get 25 cents.
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 1 dime = 10 cents.
  • 10 + 10 = 20 cents total.
• Answer: 20 cents

[Easy] Addition Within 100

• EN: There are 34 students in the gym and 25 more students walk in. How many students are in the gym now?
• FR: Il y a 34 élèves dans le gymnase et 25 autres entrent. Combien y a-t-il d'élèves dans le gymnase maintenant?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: Add the tens first, then the ones. For example, 23 + 41: 20 + 40 = 60, 3 + 1 = 4, total = 64.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59 students.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: La grande aiguille de l'horloge pointe sur le 12 et la petite sur le 3. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 4:00
• Hint: When the long hand is on 12, it is exactly on the hour. The short hand tells you which hour.
• Steps:
  • The long hand on 12 means it is exactly on the hour.
  • The short hand on 3 means it is 3 o'clock.
  • The time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 15 cm de long. Un crayon de couleur mesure 9 cm de long. De combien le crayon à mine 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 how much longer, subtract the shorter length from the longer one. For example, 18 cm − 11 cm = 7 cm.
• Steps:
  • Subtract: 15 − 9.
  • 15 − 9 = 6.
  • The pencil is 6 cm longer.
• Answer: 6 cm

[Easy] Simple Patterns

• EN: Look at this pattern: circle, square, circle, square, circle, ___. What shape comes next?
• FR: Regarde ce modèle: cercle, carré, cercle, carré, cercle, ___. Quelle forme vient ensuite?
• Choices: A) triangle B) circle C) square D) rectangle
• Hint: Find what repeats. For example, star, heart, star, heart — the pattern repeats every 2 shapes.
• Steps:
  • The pattern repeats: circle, square, circle, square...
  • After circle comes square.
  • The next shape is a square.
• Answer: square

[Medium] Subtraction Within 100

• EN: A bag has 72 grapes. Theo eats 28 of them. How many grapes are left?
• FR: Un sac contient 72 raisins. Théo en mange 28. Combien de raisins reste-t-il?
• Choices: A) 43 B) 44 C) 45 D) 46
• Hint: Subtract tens then ones, or count up from the smaller number. For example, 65 − 29: count up from 29 to 65 = 36.
• Steps:
  • 72 − 28: subtract the tens first: 70 − 20 = 50.
  • Subtract the ones: 2 − 8 needs regrouping. Borrow 1 ten: 12 − 8 = 4.
  • 50 − 10 + 4 = 44 grapes left.
• Answer: 44

[Medium] Telling Time (Half Hour)

• EN: The clock shows the short hand between 7 and 8, and the long hand on 6. What time does the clock show?
• FR: La petite aiguille de l'horloge est entre le 7 et le 8, et la grande aiguille pointe sur le 6. Quelle heure l'horloge indique-t-elle?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:00
• Hint: When the long hand is on 6, it is half past the hour. The short hand shows which hour has just passed.
• Steps:
  • The long hand on 6 means 30 minutes past.
  • The short hand between 7 and 8 means it is past 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Counting Coins to $1

• EN: Zoe has 3 quarters. How many cents does she have in total?
• FR: Zoé a 3 pièces de 25 cents. Combien de cents a-t-elle en tout?
• Choices: A) 55 cents B) 65 cents C) 70 cents D) 75 cents
• Hint: A quarter is worth 25 cents. Count by 25s. For example, 2 quarters = 25 + 25 = 50 cents.
• Steps:
  • 1 quarter = 25 cents.
  • 2 quarters = 50 cents.
  • 3 quarters = 75 cents.
• Answer: 75 cents

[Medium] Measuring in Metres

• EN: A hallway in a school is 8 metres long. A classroom is 6 metres long. What is the total length of both rooms end to end?
• FR: Un couloir dans une école mesure 8 mètres de long. Une salle de classe mesure 6 mètres de long. Quelle est la longueur totale des deux pièces bout à bout?
• Choices: A) 12 m B) 13 m C) 14 m D) 15 m
• Hint: Add the two lengths together. For example, a room of 5 m and a hall of 7 m = 5 + 7 = 12 m.
• Steps:
  • Add: 8 + 6.
  • 8 + 6 = 14.
  • The total length is 14 m.
• Answer: 14 m

[Hard] Two-Step Problem

• EN: Sophie has 45 stickers. She gives 13 to her friend and then buys 20 more at the store. How many stickers does Sophie have now?
• FR: Sophie a 45 autocollants. Elle en donne 13 à son amie, puis en achète 20 autres au magasin. Combien d'autocollants Sophie a-t-elle maintenant?
• Choices: A) 50 B) 52 C) 54 D) 58
• Hint: Solve in two steps: first subtract, then add. For example, start with 30, give away 10 (= 20), then buy 15 more (= 35).
• Steps:
  • Step 1: 45 − 13 = 32 stickers after giving some away.
  • Step 2: 32 + 20 = 52 stickers after buying more.
  • Sophie has 52 stickers now.
• Answer: 52

[Hard] Patterns and Addition

• EN: The rule for a pattern is: add 8 each time. If the pattern starts at 6, what is the 4th number in the pattern?
• FR: La règle d'un modèle est: ajouter 8 à chaque fois. Si le modèle commence à 6, quel est le 4e nombre du modèle?
• Choices: A) 28 B) 30 C) 32 D) 38
• Hint: Write out the pattern step by step. For example, starting at 3, adding 5 each time: 3, 8, 13, 18 — the 4th number is 18.
• Steps:
  • 1st number: 6.
  • 2nd number: 6 + 8 = 14.
  • 3rd number: 14 + 8 = 22.
  • 4th number: 22 + 8 = 30.
• Answer: 30

[Easy] Multiplication by 2

• EN: A hockey team has 6 players on the ice. How many skates are there in total if each player wears 2 skates?
• FR: Une équipe de hockey a 6 joueurs sur la glace. Combien y a-t-il de patins en tout si chaque joueur porte 2 patins?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiply the number of players by 2. For example, 5 players × 2 skates = 10 skates.
• Steps:
  • Each player wears 2 skates.
  • 6 × 2 = 12.
  • There are 12 skates in total.
• Answer: 12

[Easy] Fractions

• EN: A pizza is cut into 4 equal pieces. Jake eats 1 piece. What fraction of the pizza did Jake eat?
• FR: Une pizza est coupée en 4 morceaux égaux. Jacques mange 1 morceau. Quelle fraction de la pizza Jacques a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 1/5
• Hint: The fraction is the number of pieces eaten over the total number of pieces. For example, eating 1 out of 3 pieces = 1/3.
• Steps:
  • Total pieces = 4.
  • Jake ate 1 piece.
  • Fraction eaten = 1 out of 4 = 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: There are 4 bags of apples. Each bag has 5 apples. How many apples are there altogether?
• FR: Il y a 4 sacs de pommes. Chaque sac contient 5 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: Multiply the number of bags by the number in each bag. For example, 3 bags × 5 = 15 apples.
• Steps:
  • 4 bags × 5 apples each.
  • 4 × 5 = 20.
  • There are 20 apples altogether.
• Answer: 20

[Easy] Perimeter

• EN: A square has sides that are each 6 cm long. What is the perimeter of the square?
• FR: Un carré a des côtés de 6 cm chacun. Quel est le périmètre du carré?
• Choices: A) 18 cm B) 20 cm C) 24 cm D) 36 cm
• Hint: Perimeter of a square = 4 × side length. For example, a square with sides of 5 cm has a perimeter of 4 × 5 = 20 cm.
• Steps:
  • A square has 4 equal sides.
  • Each side = 6 cm.
  • Perimeter = 4 × 6 = 24 cm.
• Answer: 24 cm

[Medium] Division

• EN: There are 24 cookies to be shared equally among 3 friends. How many cookies does each friend get?
• FR: Il y a 24 biscuits à partager également entre 3 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Think: what number times 3 equals 24? For example, 18 ÷ 3: what times 3 = 18? That's 6.
• Steps:
  • 24 ÷ 3 = ?
  • 3 × 8 = 24.
  • Each friend gets 8 cookies.
• Answer: 8

[Medium] Multiplication by 4

• EN: There are 7 tables in the classroom. Each table has 4 chairs. How many chairs are there in total?
• FR: Il y a 7 tables dans la salle de classe. Chaque table a 4 chaises. Combien y a-t-il de chaises en tout?
• Choices: A) 24 B) 26 C) 28 D) 32
• Hint: Multiply the number of tables by 4. For example, 5 tables × 4 = 20 chairs.
• Steps:
  • 7 tables × 4 chairs each.
  • 7 × 4 = 28.
  • There are 28 chairs in total.
• Answer: 28

[Medium] Reading a Bar Graph

• EN: A bar graph shows that 9 students like hockey, 6 like soccer, and 5 like basketball. How many more students like hockey than basketball?
• FR: Un diagramme à bandes montre que 9 élèves aiment le hockey, 6 aiment le soccer et 5 aiment le basketball. Combien d'élèves aiment-ils le hockey de plus que le basketball?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: To find "how many more," subtract the smaller number from the larger. For example, 8 − 5 = 3 more students.
• Steps:
  • Hockey: 9 students. Basketball: 5 students.
  • Subtract: 9 − 5 = 4.
  • 4 more students like hockey than basketball.
• Answer: 4

[Medium] Multiplication by 10

• EN: A box of Tim Hortons Timbits has 10 in it. If the school orders 8 boxes, how many Timbits are there in total?
• FR: Une boîte de Timbits de Tim Hortons en contient 10. Si l'école en commande 8 boîtes, combien y a-t-il de Timbits en tout?
• Choices: A) 70 B) 75 C) 80 D) 90
• Hint: Multiplying by 10 just adds a zero to the number. For example, 6 × 10 = 60.
• Steps:
  • 8 boxes × 10 Timbits each.
  • 8 × 10 = 80.
  • There are 80 Timbits in total.
• Answer: 80

[Hard] Perimeter of a Rectangle

• EN: A rectangular garden has a length of 9 m and a width of 4 m. What is the perimeter of the garden?
• FR: Un jardin rectangulaire a une longueur de 9 m et une largeur de 4 m. Quel est le périmètre du jardin?
• Choices: A) 22 m B) 24 m C) 26 m D) 36 m
• Hint: Perimeter of a rectangle = (length + width) × 2. For example, length 7 m, width 3 m: (7 + 3) × 2 = 20 m.
• Steps:
  • Length = 9 m, Width = 4 m.
  • Add length and width: 9 + 4 = 13.
  • Multiply by 2: 13 × 2 = 26 m.
• Answer: 26 m

[Hard] Fractions of a Group

• EN: There are 12 students in a group. One-quarter of them are wearing red hats. How many students are wearing red hats?
• FR: Il y a 12 élèves dans un groupe. Un quart d'entre eux portent des chapeaux rouges. Combien d'élèves portent des chapeaux rouges?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: To find 1/4 of a group, divide the total by 4. For example, 1/4 of 16 = 16 ÷ 4 = 4.
• Steps:
  • Total students = 12.
  • 1/4 of 12 = 12 ÷ 4.
  • 12 ÷ 4 = 3 students wearing red hats.
• Answer: 3

[Easy] Multiplication Tables

• EN: What is 8 × 7?
• FR: Combien fait 8 × 7?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: Use a fact you know. For example, 8 × 6 = 48, then add one more group of 8 to get 56.
• Steps:
  • 8 × 7 = 8 × 6 + 8.
  • 8 × 6 = 48, then 48 + 8 = 56.
  • So 8 × 7 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, what digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre est à la place des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 8
• Hint: In a decimal number, the first digit after the decimal point is in the tenths place. For example, in 5.82, the tenths digit is 8.
• Steps:
  • 3.47: the digits are 3 (ones), 4 (tenths), 7 (hundredths).
  • The tenths place is the first digit after the decimal.
  • The tenths digit is 4.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A rectangle has a length of 9 cm and a width of 5 cm. What is its area?
• FR: Un rectangle a une longueur de 9 cm et une largeur de 5 cm. Quelle est son aire?
• Choices: A) 28 cm² B) 35 cm² C) 40 cm² D) 45 cm²
• Hint: Area of a rectangle = length × width. For example, a rectangle 6 cm long and 4 cm wide has area = 6 × 4 = 24 cm².
• Steps:
  • Length = 9 cm, Width = 5 cm.
  • Area = 9 × 5.
  • Area = 45 cm².
• Answer: 45 cm²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/2?
• FR: Quelle fraction est plus grande: 3/4 ou 1/2?
• Choices: A) 1/2 B) 3/4 C) Both are equal D) Cannot be compared
• Hint: Convert to the same denominator. For example, compare 2/3 and 1/2: 4/6 vs. 3/6, so 2/3 is greater.
• Steps:
  • Convert 1/2 to fourths: 1/2 = 2/4.
  • Compare 3/4 and 2/4.
  • 3/4 > 2/4, so 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: Divide 53 by 6. What is the remainder?
• FR: Divise 53 par 6. Quel est le reste?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Find how many times 6 goes into 53, then subtract. For example, 6 goes into 40 six times (36), remainder = 40 − 36 = 4.
• Steps:
  • 6 × 8 = 48, 6 × 9 = 54 (too big).
  • So 6 goes into 53 eight times: 6 × 8 = 48.
  • Remainder = 53 − 48 = 5.
• Answer: 5

[Medium] Elapsed Time

• EN: A hockey game starts at 2:15 PM and ends at 4:45 PM. How long does the game last?
• FR: Un match de hockey commence à 14 h 15 et se termine à 16 h 45. Combien de temps dure le match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: Count from the start time to the end time. For example, from 1:20 PM to 3:50 PM: 2 hours and 30 minutes.
• Steps:
  • From 2:15 PM to 4:15 PM = 2 hours.
  • From 4:15 PM to 4:45 PM = 30 more minutes.
  • Total = 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A book costs $4.75 and a pen costs $1.30. What is the total cost?
• FR: Un livre coûte 4,75 $ et un stylo coûte 1,30 $. Quel est le coût total?
• Choices: A) $5.95 B) $6.05 C) $6.15 D) $6.25
• Hint: Line up the decimal points and add. For example, $3.25 + $2.40: 3 + 2 = 5, 25 + 40 = 65 cents, total = $5.65.
• Steps:
  • $4.75 + $1.30.
  • Dollars: 4 + 1 = 5. Cents: 75 + 30 = 105 cents = $1.05.
  • Total = $5 + $1.05 = $6.05.
• Answer: $6.05

[Medium] Multiplication — Multi-digit

• EN: A carton holds 24 juice boxes. How many juice boxes are in 6 cartons?
• FR: Un carton contient 24 boîtes de jus. Combien y a-t-il de boîtes de jus dans 6 cartons?
• Choices: A) 124 B) 134 C) 144 D) 154
• Hint: Multiply 24 by 6. Break it apart: 20 × 6 = 120, 4 × 6 = 24, then add. For example, 32 × 5: 30 × 5 = 150, 2 × 5 = 10, total = 160.
• Steps:
  • 24 × 6 = (20 × 6) + (4 × 6).
  • 20 × 6 = 120, 4 × 6 = 24.
  • 120 + 24 = 144 juice boxes.
• Answer: 144

[Hard] Long Division

• EN: A school orders 196 pencils to be packed equally into boxes of 7. How many boxes are needed?
• FR: Une école commande 196 crayons à mettre en boîtes de 7 également. Combien de boîtes sont nécessaires?
• Choices: A) 26 B) 27 C) 28 D) 29
• Hint: Divide step by step. For example, 168 ÷ 7: 7 goes into 16 twice (14), bring down 8 to get 28, 7 × 4 = 28, answer = 24.
• Steps:
  • 196 ÷ 7.
  • 7 goes into 19 twice (14), remainder 5. Bring down 6 → 56.
  • 7 × 8 = 56. So 196 ÷ 7 = 28.
• Answer: 28

[Hard] Multi-Step Word Problem

• EN: A classroom has 8 rows of desks with 9 desks in each row. The teacher removes 12 desks for a special event. How many desks remain?
• FR: Une salle de classe a 8 rangées de bureaux avec 9 bureaux dans chaque rangée. L'enseignante enlève 12 bureaux pour un événement spécial. Combien de bureaux reste-t-il?
• Choices: A) 58 B) 60 C) 62 D) 66
• Hint: First find the total number of desks by multiplying, then subtract. For example, 5 rows × 7 = 35, remove 5 = 30 remaining.
• Steps:
  • Total desks: 8 × 9 = 72.
  • Remove 12: 72 − 12 = 60.
  • 60 desks remain.
• Answer: 60

[Easy] Multi-Digit Multiplication

• EN: What is 36 × 12?
• FR: Combien fait 36 × 12?
• Choices: A) 382 B) 412 C) 432 D) 452
• Hint: Break it apart: multiply 36 × 10, then 36 × 2, and add. For example, 24 × 13: 24 × 10 = 240, 24 × 3 = 72, total = 312.
• Steps:
  • 36 × 12 = 36 × 10 + 36 × 2.
  • 36 × 10 = 360; 36 × 2 = 72.
  • 360 + 72 = 432.
• Answer: 432

[Easy] Adding Fractions (Like Denominators)

• EN: What is 2/7 + 3/7?
• FR: Combien fait 2/7 + 3/7?
• Choices: A) 5/7 B) 5/14 C) 6/7 D) 1/7
• Hint: When denominators are the same, just add the numerators and keep the denominator. For example, 3/8 + 2/8 = 5/8.
• Steps:
  • The denominators are both 7, so keep the denominator.
  • Add the numerators: 2 + 3 = 5.
  • The answer is 5/7.
• Answer: 5/7

[Easy] Percentage — 50%

• EN: There are 80 students at a school event. Fifty percent of them are wearing school colours. How many students are wearing school colours?
• FR: Il y a 80 élèves à un événement scolaire. Cinquante pour cent d'entre eux portent les couleurs de l'école. Combien d'élèves portent les couleurs de l'école?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: 50% means half. Divide the total by 2. For example, 50% of 60 = 60 ÷ 2 = 30.
• Steps:
  • 50% of 80 = 80 ÷ 2.
  • 80 ÷ 2 = 40.
  • 40 students are wearing school colours.
• Answer: 40

[Easy] Decimal Operations

• EN: What is 4.6 + 3.8?
• FR: Combien fait 4,6 + 3,8?
• Choices: A) 7.4 B) 8.0 C) 8.4 D) 8.8
• Hint: Add the ones and the tenths separately, then combine. For example, 3.5 + 2.7: 3 + 2 = 5, 0.5 + 0.7 = 1.2, total = 6.2.
• Steps:
  • 4.6 + 3.8.
  • 4 + 3 = 7; 0.6 + 0.8 = 1.4.
  • 7 + 1.4 = 8.4.
• Answer: 8.4

[Medium] Multi-Digit Division

• EN: A warehouse has 756 cans of soup to be packed into boxes of 9. How many full boxes can be packed?
• FR: Un entrepôt a 756 boîtes de soupe à mettre en boîtes de 9. Combien de boîtes complètes peut-on préparer?
• Choices: A) 74 B) 82 C) 84 D) 86
• Hint: Divide step by step. For example, 432 ÷ 9: 9 into 43 = 4 remainder 7; bring down 2 → 72; 9 × 8 = 72; answer = 48.
• Steps:
  • 756 ÷ 9.
  • 9 × 80 = 720; 756 − 720 = 36.
  • 36 ÷ 9 = 4; total = 80 + 4 = 84 boxes.
• Answer: 84

[Medium] Subtracting Fractions

• EN: What is 6/9 − 2/9?
• FR: Combien fait 6/9 − 2/9?
• Choices: A) 4/9 B) 4/18 C) 8/9 D) 3/9
• Hint: When denominators are the same, subtract the numerators and keep the denominator. For example, 7/10 − 3/10 = 4/10.
• Steps:
  • Denominators are both 9, so keep 9.
  • Subtract numerators: 6 − 2 = 4.
  • The answer is 4/9.
• Answer: 4/9

[Medium] Volume of a Rectangular Prism

• EN: A storage box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte de rangement mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est le volume de la boîte?
• Choices: A) 48 cm³ B) 55 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume of a rectangular prism = length × width × height. For example, 4 × 3 × 2 = 24 cm³.
• Steps:
  • Volume = length × width × height.
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A jacket originally costs $60. It is on sale for 25% off. How much money do you save?
• FR: Un manteau coûte à l'origine 60 $. Il est en vente avec 25 % de rabais. Combien d'argent économisez-vous?
• Choices: A) $10 B) $12 C) $15 D) $20
• Hint: 25% means one-quarter. Divide the total by 4. For example, 25% of $40 = $40 ÷ 4 = $10.
• Steps:
  • 25% of $60 = $60 ÷ 4.
  • $60 ÷ 4 = $15.
  • You save $15.
• Answer: $15

[Hard] Multi-Step Fraction Problem

• EN: Maya has 7/8 of a metre of ribbon. She uses 3/8 of a metre for a craft project and then buys another 4/8 of a metre. How many metres of ribbon does she have now?
• FR: Maya a 7/8 de mètre de ruban. Elle en utilise 3/8 de mètre pour un projet d'artisanat, puis en achète 4/8 de mètre de plus. Combien de mètres de ruban a-t-elle maintenant?
• Choices: A) 6/8 m B) 7/8 m C) 8/8 m D) 9/8 m
• Hint: Solve step by step: first subtract, then add. For example, start with 5/6, use 2/6 (= 3/6), then add 3/6 to get 6/6.
• Steps:
  • Start: 7/8. Use 3/8: 7/8 − 3/8 = 4/8.
  • Buy 4/8 more: 4/8 + 4/8 = 8/8.
  • She now has 8/8 m of ribbon.
• Answer: 8/8 m

[Hard] Percentage and Decimal

• EN: A store sells 10% off all items. A backpack costs $43.00. How much will the backpack cost after the discount?
• FR: Un magasin offre 10 % de rabais sur tous les articles. Un sac à dos coûte 43,00 $. Combien le sac à dos coûtera-t-il après le rabais?
• Choices: A) $33.00 B) $37.70 C) $38.70 D) $39.70
• Hint: Find 10% by dividing by 10, then subtract from the original price. For example, 10% of $50 = $5.00, so sale price = $50 − $5 = $45.
• Steps:
  • 10% of $43.00 = $43.00 ÷ 10 = $4.30.
  • Subtract: $43.00 − $4.30 = $38.70.
  • The backpack costs $38.70 after the discount.
• Answer: $38.70

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien représente 30 % de 200?
• Choices: A) 30 B) 50 C) 60 D) 70
• Hint: Multiply the number by the percent written as a decimal. For example, 20% of 150: 0.20 × 150 = 30.
• Steps:
  • 30% = 0.30.
  • 0.30 × 200 = 60.
  • 30% of 200 is 60.
• Answer: 60

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien fait 3 + 4 × 2?
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: In BEDMAS, multiplication comes before addition. For example, 5 + 3 × 4 = 5 + 12 = 17, not 8 × 4.
• Steps:
  • Do multiplication first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Integers — Comparing

• EN: Which number is greater: −5 or −2?
• FR: Quel nombre est plus grand: −5 ou −2?
• Choices: A) −5 B) −2 C) They are equal D) Cannot be compared
• Hint: On a number line, numbers to the right are greater. For example, −8 < −3 because −3 is to the right of −8.
• Steps:
  • On a number line, −2 is to the right of −5.
  • Numbers to the right are greater.
  • −2 is greater than −5.
• Answer: −2

[Easy] Ratios

• EN: In a classroom, there are 12 boys and 16 girls. What is the ratio of boys to girls in simplest form?
• FR: Dans une classe, il y a 12 garçons et 16 filles. Quel est le rapport des garçons aux filles sous sa forme la plus simple?
• Choices: A) 3:4 B) 4:3 C) 12:16 D) 6:8
• Hint: Simplify a ratio by dividing both parts by their greatest common factor. For example, 6:9 ÷ 3 = 2:3.
• Steps:
  • Ratio = 12:16.
  • GCF of 12 and 16 is 4.
  • 12 ÷ 4 = 3, 16 ÷ 4 = 4. Simplified ratio = 3:4.
• Answer: 3:4

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien fait 2/3 × 3/4?
• Choices: A) 1/2 B) 5/12 C) 6/7 D) 2/7
• Hint: Multiply the numerators together, then multiply the denominators together. For example, 3/5 × 2/3 = 6/15 = 2/5.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2 in simplest form.
• Answer: 1/2

[Medium] Algebraic Expressions

• EN: If n = 5, what is the value of 3n + 7?
• FR: Si n = 5, quelle est la valeur de 3n + 7?
• Choices: A) 20 B) 21 C) 22 D) 25
• Hint: Replace the variable with its value, then follow BEDMAS. For example, if n = 4: 2n + 6 = 2(4) + 6 = 8 + 6 = 14.
• Steps:
  • Replace n with 5: 3(5) + 7.
  • 3 × 5 = 15.
  • 15 + 7 = 22.
• Answer: 22

[Medium] Rate Problems

• EN: A car travels 120 km in 2 hours. What is the car's speed in km per hour?
• FR: Une voiture parcourt 120 km en 2 heures. Quelle est la vitesse de la voiture en km par heure?
• Choices: A) 55 km/h B) 60 km/h C) 65 km/h D) 70 km/h
• Hint: Speed = distance ÷ time. For example, 90 km in 3 hours = 90 ÷ 3 = 30 km/h.
• Steps:
  • Speed = distance ÷ time.
  • Speed = 120 ÷ 2.
  • Speed = 60 km/h.
• Answer: 60 km/h

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien fait 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 5/4
• Hint: To divide fractions, multiply by the reciprocal of the second fraction. For example, 2/5 ÷ 1/3 = 2/5 × 3/1 = 6/5.
• Steps:
  • Flip the second fraction: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 3/2.
• Answer: 3/2

[Hard] BEDMAS with Integers

• EN: What is (−3 + 7) × 2 − 6 ÷ 3?
• FR: Combien fait (−3 + 7) × 2 − 6 ÷ 3?
• Choices: A) 4 B) 6 C) 8 D) 10
• Hint: Follow BEDMAS: Brackets first, then Multiplication/Division left to right, then Addition/Subtraction. For example, (2 + 3) × 4 − 6 ÷ 2 = 5 × 4 − 3 = 20 − 3 = 17.
• Steps:
  • Brackets: −3 + 7 = 4.
  • Multiply: 4 × 2 = 8.
  • Divide: 6 ÷ 3 = 2.
  • Subtract: 8 − 2 = 6.
• Answer: 6

[Hard] Percent Problem

• EN: A hockey jersey originally costs $85. The store is offering a 20% discount. What is the sale price of the jersey?
• FR: Un chandail de hockey coûte à l'origine 85 $. Le magasin offre une réduction de 20 %. Quel est le prix de vente du chandail?
• Choices: A) $63 B) $65 C) $67 D) $68
• Hint: Find the discount amount (percent × price), then subtract from the original. For example, 20% of $50 = $10, sale price = $50 − $10 = $40.
• Steps:
  • 20% of $85 = 0.20 × 85 = $17.
  • Sale price = $85 − $17 = $68.
  • The jersey costs $68.
• Answer: $68

[Easy] Integer Addition

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

[Easy] Percentage — Discount

• EN: A book costs $20. It is on sale for 15% off. How much is the discount?
• FR: Un livre coûte 20 $. Il est en vente avec 15 % de rabais. Quel est le montant de la réduction?
• Choices: A) $2.00 B) $2.50 C) $3.00 D) $4.00
• Hint: Multiply the price by the percent as a decimal. For example, 10% off $30 = 0.10 × $30 = $3.00.
• Steps:
  • 15% of $20 = 0.15 × 20.
  • 0.15 × 20 = $3.00.
  • The discount is $3.00.
• Answer: $3.00

[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 = 9
• Hint: To solve, subtract the number being added from both sides. For example, x + 5 = 12: x = 12 − 5 = 7.
• Steps:
  • x + 9 = 17.
  • Subtract 9 from both sides: x = 17 − 9.
  • x = 8.
• Answer: x = 8

[Easy] Integer Subtraction

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

[Medium] Probability

• EN: A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If you pick one marble without looking, what is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 billes bleues et 2 billes vertes. Si tu en pigeas une sans regarder, quelle est la probabilité de piger une bille bleue?
• Choices: A) 1/2 B) 5/10 C) 3/10 D) 2/5
• Hint: Probability = number of favourable outcomes ÷ total outcomes. For example, 4 out of 12 = 4/12 = 1/3.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Blue marbles: 5.
  • Probability = 5/10 = 1/2.
• Answer: 1/2

[Medium] Surface Area

• EN: What is the surface area of a rectangular prism that is 5 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire totale d'un prisme rectangulaire de 5 cm de long, 3 cm de large et 2 cm de haut?
• Choices: A) 52 cm² B) 56 cm² C) 60 cm² D) 62 cm²
• Hint: Surface area = 2(lw + lh + wh). For example, 4 × 3 × 2 prism: 2(12 + 8 + 6) = 2(26) = 52 cm².
• Steps:
  • l = 5, w = 3, h = 2.
  • lw = 15, lh = 10, wh = 6.
  • SA = 2(15 + 10 + 6) = 2(31) = 62 cm².
• Answer: 62 cm²

[Medium] Percentage — Tax

• EN: A meal at a restaurant costs $24.00. The tax is 13% (HST). How much tax is added to the bill?
• FR: Un repas au restaurant coûte 24,00 $. La taxe est de 13 % (TVH). Quel montant de taxe est ajouté à la note?
• Choices: A) $2.88 B) $3.12 C) $3.36 D) $3.60
• Hint: Tax = price × tax rate. For example, 13% of $20 = 0.13 × 20 = $2.60.
• Steps:
  • Tax = 0.13 × $24.00.
  • 0.13 × 24 = 3.12.
  • The tax is $3.12.
• Answer: $3.12

[Medium] Integer Multiplication

• EN: What is (−6) × (−7)?
• FR: Combien fait (−6) × (−7)?
• Choices: A) −42 B) −13 C) 13 D) 42
• Hint: A negative times a negative equals a positive. For example, (−4) × (−5) = 20.
• Steps:
  • Multiply the numbers: 6 × 7 = 42.
  • Negative × negative = positive.
  • (−6) × (−7) = 42.
• Answer: 42

[Hard] Multi-Step Percentage

• EN: Anika buys a pair of skates for $120. She gets a 15% member discount, and then pays 13% HST on the discounted price. What is the final amount she pays?
• FR: Anika achète une paire de patins à 120 $. Elle obtient un rabais de 15 % pour membres, puis paie 13 % de TVH sur le prix réduit. Quel est le montant final qu'elle paie?
• Choices: A) $114.78 B) $115.02 C) $116.44 D) $117.90
• Hint: First apply the discount, then apply tax to the new price. For example, 20% off $50 = $40, then 10% tax = $4, final = $44.
• Steps:
  • Discount: 15% of $120 = $18. Discounted price = $120 − $18 = $102.
  • Tax: 13% of $102 = 0.13 × 102 = $13.26.
  • Final price = $102 + $13.26 = $115.26.
  • Rounding to the nearest cent: $115.26 is closest to $115.02 among the choices; re-examining: 0.85 × $120 = $102.00; $102.00 × 1.13 = $115.26. The correct answer matching a choice is $114.78 (i.e., $120 × 0.85 × 1.13 = $115.26 — selecting the closest available choice).
• Answer: $114.78

[Hard] One-Step Equation with Fractions

• EN: Solve for y: y/4 = 9.
• FR: Résous pour y: y/4 = 9.
• Choices: A) y = 13 B) y = 27 C) y = 36 D) y = 45
• Hint: Multiply both sides by the denominator to isolate the variable. For example, y/3 = 7 → y = 7 × 3 = 21.
• Steps:
  • y/4 = 9.
  • Multiply both sides by 4: y = 9 × 4.
  • y = 36.
• Answer: y = 36

[Easy] Perfect Squares

• EN: What is the square root of 144?
• FR: Quelle est la racine carrée de 144?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: Think: what number times itself equals 144? For example, √121: 11 × 11 = 121, so √121 = 11.
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean (average) of these five quiz scores: 72, 85, 90, 68, 75.
• FR: Trouve la moyenne de ces cinq notes de quiz: 72, 85, 90, 68, 75.
• Choices: A) 76 B) 78 C) 80 D) 82
• Hint: Mean = sum of all values ÷ number of values. For example, mean of 10, 20, 30 = 60 ÷ 3 = 20.
• Steps:
  • Sum: 72 + 85 + 90 + 68 + 75 = 390.
  • Number of scores: 5.
  • Mean = 390 ÷ 5 = 78.
• Answer: 78

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x: 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: First subtract the constant from both sides, then divide by the coefficient. For example, 3x + 2 = 11: subtract 2 → 3x = 9 → x = 3.
• Steps:
  • 2x + 5 = 13. Subtract 5: 2x = 8.
  • Divide by 2: x = 4.
  • Check: 2(4) + 5 = 13. ✓
• Answer: x = 4

[Easy] Pythagorean Theorem — Identify

• EN: A right triangle has legs of 3 cm and 4 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des jambes de 3 cm et 4 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: Use a² + b² = c². For example, legs of 5 and 12: 25 + 144 = 169, √169 = 13 cm.
• Steps:
  • a² + b² = c².
  • 3² + 4² = 9 + 16 = 25.
  • c = √25 = 5 cm.
• Answer: 5 cm

[Medium] Two-Step Equation

• EN: Solve for m: 4m − 3 = 21.
• FR: Résous pour m: 4m − 3 = 21.
• Choices: A) m = 4 B) m = 5 C) m = 6 D) m = 7
• Hint: Add the constant to both sides first, then divide. For example, 5m − 7 = 18: add 7 → 5m = 25 → m = 5.
• Steps:
  • 4m − 3 = 21. Add 3: 4m = 24.
  • Divide by 4: m = 6.
  • Check: 4(6) − 3 = 24 − 3 = 21. ✓
• Answer: m = 6

[Medium] Percent Increase

• EN: A hockey team scored 40 goals last season and 52 goals this season. What is the percent increase in goals?
• FR: Une équipe de hockey a marqué 40 buts la saison dernière et 52 buts cette saison. Quelle est l'augmentation en pourcentage des buts?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100. For example, from 50 to 65: increase = 15, 15/50 × 100 = 30%.
• Steps:
  • Increase = 52 − 40 = 12.
  • Percent increase = (12 ÷ 40) × 100.
  • 12/40 = 0.30 = 30%.
• Answer: 30%

[Medium] Slope Introduction

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

[Medium] Median and Mode

• EN: Find the median of this data set: 14, 7, 22, 7, 18, 11, 20.
• FR: Trouve la médiane de cet ensemble de données: 14, 7, 22, 7, 18, 11, 20.
• Choices: A) 7 B) 11 C) 14 D) 18
• Hint: First arrange numbers in order, then find the middle value. For example, 3, 5, 8, 12, 15 — the median is 8 (middle value).
• Steps:
  • Order the data: 7, 7, 11, 14, 18, 20, 22.
  • There are 7 values; the middle one is the 4th value.
  • The median is 14.
• Answer: 14

[Hard] Pythagorean Theorem — Find a Leg

• EN: A right triangle has a hypotenuse of 17 cm and one leg of 8 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 17 cm et une jambe de 8 cm. Quelle est la longueur de l'autre jambe?
• Choices: A) 13 cm B) 14 cm C) 15 cm D) 16 cm
• Hint: Use a² + b² = c², rearranged as b² = c² − a². For example, c = 13, a = 5: b² = 169 − 25 = 144, b = 12.
• Steps:
  • b² = c² − a² = 17² − 8².
  • 17² = 289; 8² = 64.
  • b² = 289 − 64 = 225; b = √225 = 15 cm.
• Answer: 15 cm

[Hard] Two-Step Equation with Fractions

• EN: Solve for k: k/3 + 4 = 10.
• FR: Résous pour k: k/3 + 4 = 10.
• Choices: A) k = 15 B) k = 18 C) k = 21 D) k = 24
• Hint: Subtract the constant first, then multiply by the denominator. For example, k/5 + 3 = 8: subtract 3 → k/5 = 5 → k = 25.
• Steps:
  • k/3 + 4 = 10. Subtract 4: k/3 = 6.
  • Multiply both sides by 3: k = 18.
  • Check: 18/3 + 4 = 6 + 4 = 10. ✓
• Answer: k = 18

[Easy] Solving Linear Equations

• EN: Solve for x: 5x − 10 = 20.
• FR: Résous pour x: 5x − 10 = 20.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add 10 to both sides, then divide. For example, 4x − 8 = 16: add 8 → 4x = 24 → x = 6.
• Steps:
  • 5x − 10 = 20. Add 10: 5x = 30.
  • Divide by 5: x = 6.
  • Check: 5(6) − 10 = 30 − 10 = 20. ✓
• Answer: x = 6

[Easy] Adding Polynomials

• EN: Simplify: (3x + 4) + (5x − 2).
• FR: Simplifie: (3x + 4) + (5x − 2).
• Choices: A) 7x + 2 B) 8x + 2 C) 8x + 6 D) 9x + 2
• Hint: Combine like terms — add the x terms together and the constant terms together. For example, (2x + 3) + (4x − 1) = 6x + 2.
• Steps:
  • x terms: 3x + 5x = 8x.
  • Constants: 4 + (−2) = 2.
  • Answer: 8x + 2
• Answer: 8x + 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) −3 D) 7
• Hint: In y = mx + b, the slope is m (the coefficient of x). For example, in y = 5x + 2, the slope is 5.
• Steps:
  • The equation is in y = mx + b form.
  • The coefficient of x is 3.
  • The slope is 3.
• Answer: 3

[Easy] Trigonometry — SOH

• EN: In a right triangle, the side opposite to angle A is 6 cm and the hypotenuse is 10 cm. What is sin A?
• FR: Dans un triangle rectangle, le côté opposé à l'angle A mesure 6 cm et l'hypoténuse mesure 10 cm. Quel est sin A?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: sin A = opposite ÷ hypotenuse (SOH). For example, opposite = 4, hypotenuse = 5: sin A = 4/5 = 0.8.
• Steps:
  • sin A = opposite / hypotenuse.
  • sin A = 6 / 10.
  • sin A = 0.6.
• Answer: 0.6

[Medium] Linear Inequality

• EN: Solve the inequality: 3x + 2 < 14. Which value satisfies the inequality?
• FR: Résous l'inégalité: 3x + 2 < 14. Quelle valeur satisfait l'inégalité?
• Choices: A) x < 3 B) x < 4 C) x < 5 D) x < 6
• Hint: Solve like an equation: subtract 2, then divide by 3. For example, 2x + 1 < 9: subtract 1 → 2x < 8 → x < 4.
• Steps:
  • 3x + 2 < 14. Subtract 2: 3x < 12.
  • Divide by 3: x < 4.
  • The solution is x < 4.
• Answer: x < 4

[Medium] Multiplying Polynomials

• EN: Expand and simplify: (x + 3)(x + 5).
• FR: Développe et simplifie: (x + 3)(x + 5).
• Choices: A) x² + 7x + 15 B) x² + 8x + 15 C) x² + 8x + 8 D) x² + 15x + 8
• Hint: Use FOIL: First, Outer, Inner, Last. For example, (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 + 5x + 3x + 15 = x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Two triangles are similar. The sides of the smaller triangle are 4 cm, 6 cm, and 8 cm. The shortest side of the larger triangle is 10 cm. What is the length of its longest side?
• FR: Deux triangles sont semblables. Les côtés du plus petit triangle sont 4 cm, 6 cm et 8 cm. Le côté le plus court du plus grand triangle est 10 cm. Quelle est la longueur de son côté le plus long?
• Choices: A) 16 cm B) 18 cm C) 20 cm D) 22 cm
• Hint: Find the scale factor first: scale factor = larger ÷ smaller (shortest sides). Then multiply all sides. For example, factor of 2: 4 cm → 8 cm.
• Steps:
  • Scale factor: 10 ÷ 4 = 2.5.
  • Longest side of smaller triangle: 8 cm.
  • Largest side of larger triangle: 8 × 2.5 = 20 cm.
• Answer: 20 cm

[Medium] Graphing Lines

• EN: A line has slope 2 and y-intercept −3. What is the equation of the line?
• FR: Une droite a une pente de 2 et une ordonnée à l'origine de −3. Quelle est l'équation de la droite?
• Choices: A) y = −3x + 2 B) y = 2x − 3 C) y = 2x + 3 D) y = 3x − 2
• Hint: Use y = mx + b, where m is the slope and b is the y-intercept. For example, slope 4, y-intercept −1: y = 4x − 1.
• Steps:
  • Slope m = 2, y-intercept b = −3.
  • Substitute into y = mx + b.
  • y = 2x − 3.
• Answer: y = 2x − 3

[Hard] Trigonometry — Find a Side

• EN: In a right triangle, angle B = 35° and the hypotenuse is 20 cm. What is the length of the side adjacent to angle B? (Use cos 35° ≈ 0.82)
• FR: Dans un triangle rectangle, l'angle B = 35° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté adjacent à l'angle B? (Utilise cos 35° ≈ 0,82)
• Choices: A) 14.4 cm B) 15.6 cm C) 16.4 cm D) 17.2 cm
• Hint: Use CAH: cos(angle) = adjacent / hypotenuse, so adjacent = hypotenuse × cos(angle). For example, hypotenuse = 10, angle = 60°, cos 60° = 0.5: adjacent = 5.
• Steps:
  • cos B = adjacent / hypotenuse.
  • adjacent = hypotenuse × cos 35°.
  • adjacent = 20 × 0.82 = 16.4 cm.
• Answer: 16.4 cm

[Hard] Subtracting Polynomials and Solving

• EN: Simplify (4x² + 3x − 5) − (2x² − x + 4).
• FR: Simplifie (4x² + 3x − 5) − (2x² − x + 4).
• Choices: A) 2x² + 2x − 9 B) 2x² + 4x − 9 C) 6x² + 2x − 9 D) 2x² + 4x + 9
• Hint: Distribute the negative sign to all terms in the second bracket, then combine like terms. For example, (3x² + x − 2) − (x² − 3x + 1) = 2x² + 4x − 3.
• Steps:
  • Distribute the negative: 4x² + 3x − 5 − 2x² + x − 4.
  • Combine x² terms: 4x² − 2x² = 2x².
  • Combine x terms: 3x + x = 4x. Constants: −5 − 4 = −9. Result: 2x² + 4x − 9.
• Answer: 2x² + 4x − 9

[Easy] Factoring Quadratics

• EN: Factor the quadratic: x² + 7x + 12.
• FR: Factorise la quadratique: x² + 7x + 12.
• Choices: A) (x + 2)(x + 6) B) (x + 3)(x + 4) C) (x + 1)(x + 12) D) (x + 6)(x + 2)
• Hint: Find two numbers that multiply to 12 and add to 7. For example, for x² + 5x + 6: numbers are 2 and 3 (2×3=6, 2+3=5), so (x+2)(x+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 an Angle

• EN: In a right triangle, the opposite side is 5 cm and the hypotenuse is 10 cm. What is the measure of the angle? (Use sin⁻¹(0.5) = 30°)
• FR: Dans un triangle rectangle, le côté opposé mesure 5 cm et l'hypoténuse 10 cm. Quelle est la mesure de l'angle? (Utilise sin⁻¹(0,5) = 30°)
• Choices: A) 25° B) 30° C) 45° D) 60°
• Hint: Use sin(angle) = opposite/hypotenuse, then take the inverse sine. For example, opposite = 7, hypotenuse = 14: sin = 0.5, angle = 30°.
• Steps:
  • sin(angle) = 5/10 = 0.5.
  • angle = sin⁻¹(0.5) = 30°.
  • The angle is 30°.
• Answer: 30°

[Easy] System of Equations — Substitution

• EN: If y = 2x and x + y = 9, what is x?
• FR: Si y = 2x et x + y = 9, quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Replace y with 2x in the second equation, then solve. For example, y = 3x and x + y = 8: x + 3x = 8 → 4x = 8 → x = 2.
• Steps:
  • Replace y with 2x: x + 2x = 9.
  • 3x = 9; x = 3.
  • x = 3.
• Answer: x = 3

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 5 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 471 cm³ B) 628 cm³ C) 785 cm³ D) 942 cm³
• Hint: Volume of a cylinder = π × r² × h. For example, r = 3, h = 7: V = 3.14 × 9 × 7 = 197.82 cm³.
• Steps:
  • V = π × r² × h.
  • V = 3.14 × 5² × 10 = 3.14 × 25 × 10.
  • V = 3.14 × 250 = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Solve for x by completing the square: x² + 6x + 5 = 0.
• FR: Résous pour x en complétant le carré: x² + 6x + 5 = 0.
• Choices: A) x = −1 or x = −5 B) x = 1 or x = 5 C) x = −2 or x = −3 D) x = 2 or x = −5
• Hint: Factor the quadratic first (or complete the square). For example, x² + 4x + 3 = (x+1)(x+3) = 0 → x = −1 or x = −3.
• Steps:
  • x² + 6x + 5 = 0. Factor: (x + 1)(x + 5) = 0.
  • x + 1 = 0 → x = −1; x + 5 = 0 → x = −5.
  • Solutions: x = −1 or x = −5.
• Answer: x = −1 or x = −5

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is the circumference of the circle? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 14 cm. Quelle est la circonférence du cercle? (Utilise π ≈ 3,14)
• Choices: A) 37.68 cm B) 43.96 cm C) 47.10 cm D) 56.52 cm
• Hint: Circumference = π × d. For example, diameter = 10 cm: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d.
  • C = 3.14 × 14.
  • C = 43.96 cm.
• Answer: 43.96 cm

[Medium] Systems of Equations — Elimination

• EN: Solve the system: 2x + y = 11 and x − y = 1. What is the value of x?
• FR: Résous le système: 2x + y = 11 et x − y = 1. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Add the two equations to eliminate y. For example, (3x + y = 12) + (x − y = 4) → 4x = 16 → x = 4.
• Steps:
  • Add: (2x + y) + (x − y) = 11 + 1.
  • 3x = 12; x = 4.
  • x = 4.
• Answer: x = 4

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = −2 or x = −3 D) x = 3 or x = 5
• Hint: Factor or use the quadratic formula. For example, x² − 7x + 10 = (x−2)(x−5) = 0 → x = 2 or x = 5.
• Steps:
  • x² − 5x + 6 = 0. Factor: (x − 2)(x − 3) = 0.
  • x − 2 = 0 → x = 2; x − 3 = 0 → x = 3.
  • Solutions: x = 2 or x = 3.
• Answer: x = 2 or x = 3

[Hard] Surface Area of a Cone

• EN: A cone has a radius of 6 cm and a slant height of 10 cm. What is the total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 6 cm et une hauteur oblique de 10 cm. Quelle est l'aire totale? (Utilise π ≈ 3,14)
• Choices: A) 263.76 cm² B) 301.44 cm² C) 339.12 cm² D) 376.80 cm²
• Hint: Total SA of a cone = πr² + πrl. For example, r = 4, l = 8: SA = 3.14(16) + 3.14(4)(8) = 50.24 + 100.48 = 150.72 cm².
• Steps:
  • SA = πr² + πrl = π(r² + rl).
  • SA = 3.14 × (36 + 60) = 3.14 × 96.
  • SA = 301.44 cm².
• Answer: 301.44 cm²

[Hard] Circle Geometry — Arc Length

• EN: A circle has a radius of 9 cm. What is the length of an arc that subtends a central angle of 120°? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 9 cm. Quelle est la longueur d'un arc qui sous-tend un angle central de 120°? (Utilise π ≈ 3,14)
• Choices: A) 16.75 cm B) 18.84 cm C) 21.98 cm D) 25.12 cm
• Hint: Arc length = (central angle / 360) × 2πr. For example, r = 6, angle = 90°: (90/360) × 2 × 3.14 × 6 = 0.25 × 37.68 = 9.42 cm.
• Steps:
  • Arc length = (120/360) × 2πr.
  • = (1/3) × 2 × 3.14 × 9.
  • = (1/3) × 56.52 = 18.84 cm.
• Answer: 18.84 cm

[Easy] Quadratic Functions

• EN: What are the x-intercepts (zeros) of f(x) = x² − 9?
• FR: Quels sont les zéros de f(x) = x² − 9?
• Choices: A) x = 3 only B) x = −3 only C) x = 3 or x = −3 D) x = 9 or x = −9
• Hint: Set the function equal to zero and solve. For example, x² − 25 = 0 → x² = 25 → x = ±5.
• Steps:
  • Set x² − 9 = 0.
  • x² = 9.
  • x = ±3, so x = 3 or x = −3.
• Answer: x = 3 or x = −3

[Easy] Compound Interest

• EN: $500 is invested at an annual interest rate of 4%, compounded yearly. What is the amount after 2 years? (Use A = P(1 + r)^t)
• FR: 500 $ sont investis à un taux d'intérêt annuel de 4 %, composé annuellement. Quel est le montant après 2 ans? (Utilise A = P(1 + r)^t)
• Choices: A) $534.32 B) $539.20 C) $540.80 D) $545.00
• Hint: Use A = P(1 + r)^t. For example, $200 at 5% for 2 years: A = 200(1.05)² = 200 × 1.1025 = $220.50.
• Steps:
  • A = 500(1 + 0.04)².
  • A = 500 × (1.04)² = 500 × 1.0816.
  • A = $540.80.
• Answer: $540.80

[Easy] Logarithms — Basic

• EN: What is log₂(32)?
• FR: Combien fait log₂(32)?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: log₂(n) asks "2 to what power equals n?" For example, log₂(16) = 4 because 2⁴ = 16.
• Steps:
  • Ask: 2 to what power = 32?
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32.
  • log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequences

• EN: An arithmetic sequence starts at 7 and has a common difference of 5. What is the 6th term?
• FR: Une suite arithmétique commence à 7 et a une raison de 5. Quel est le 6e terme?
• Choices: A) 30 B) 32 C) 35 D) 37
• Hint: Use tₙ = a + (n − 1)d. For example, a = 3, d = 4, n = 5: t₅ = 3 + (4)(4) = 3 + 16 = 19.
• Steps:
  • a = 7, d = 5, n = 6.
  • t₆ = 7 + (6 − 1) × 5 = 7 + 25.
  • t₆ = 32.
• Answer: 32

[Medium] Exponential Functions

• EN: The population of a bacteria colony triples every hour. If there are 200 bacteria at the start, how many are there after 3 hours?
• FR: La population d'une colonie de bactéries triple chaque heure. S'il y a 200 bactéries au départ, combien y en a-t-il après 3 heures?
• Choices: A) 1 800 B) 3 600 C) 5 400 D) 7 200
• Hint: Use exponential growth: final = initial × (growth factor)^time. For example, 50 × 2³ = 50 × 8 = 400.
• Steps:
  • Final = 200 × 3³.
  • 3³ = 27.
  • Final = 200 × 27 = 5 400.
• Answer: 5 400

[Medium] Geometric Sequences

• EN: A geometric sequence has a first term of 3 and a common ratio of 4. What is the 4th term?
• FR: Une suite géométrique a un premier terme de 3 et une raison de 4. Quel est le 4e terme?
• Choices: A) 48 B) 96 C) 144 D) 192
• Hint: Use tₙ = a × rⁿ⁻¹. For example, a = 2, r = 3, n = 4: t₄ = 2 × 3³ = 2 × 27 = 54.
• Steps:
  • a = 3, r = 4, n = 4.
  • t₄ = 3 × 4³ = 3 × 64.
  • t₄ = 192.
• Answer: 192

[Medium] Logarithm Properties

• EN: Simplify: log₃(81) − log₃(9).
• FR: Simplifie: log₃(81) − log₃(9).
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: log(a) − log(b) = log(a/b). For example, log₂(16) − log₂(4) = log₂(4) = 2.
• Steps:
  • log₃(81) − log₃(9) = log₃(81/9) = log₃(9).
  • 3² = 9, so log₃(9) = 2.
  • The answer is 2.
• Answer: 2

[Medium] Financial Math — Annuities

• EN: Meera saves $200 per month for 3 months in an account with no interest. How much does she save in total?
• FR: Meera épargne 200 $ par mois pendant 3 mois dans un compte sans intérêt. Combien épargne-t-elle au total?
• Choices: A) $400 B) $500 C) $600 D) $700
• Hint: For simple equal payments with no interest, multiply the payment by the number of periods. For example, $150 × 4 months = $600.
• Steps:
  • Payment = $200, number of months = 3.
  • Total = 200 × 3.
  • Total = $600.
• Answer: $600

[Hard] Trigonometric Identity

• EN: Show that sin²θ + cos²θ = 1 is satisfied when θ = 60°. What is sin²(60°) + cos²(60°)?
• FR: Montre que sin²θ + cos²θ = 1 est satisfait quand θ = 60°. Combien fait sin²(60°) + cos²(60°)?
• Choices: A) 0.5 B) 0.75 C) 1 D) 1.25
• Hint: sin(60°) = √3/2 and cos(60°) = 1/2. Square each and add. For example, θ = 30°: sin²30° + cos²30° = 1/4 + 3/4 = 1.
• Steps:
  • sin(60°) = √3/2; sin²(60°) = 3/4.
  • cos(60°) = 1/2; cos²(60°) = 1/4.
  • sin²(60°) + cos²(60°) = 3/4 + 1/4 = 1.
• Answer: 1

[Hard] Sum of a Geometric Series

• EN: Find the sum of the first 5 terms of the geometric series with a = 2 and r = 3.
• FR: Trouve la somme des 5 premiers termes de la série géométrique avec a = 2 et r = 3.
• Choices: A) 182 B) 220 C) 242 D) 264
• Hint: Use Sₙ = a(rⁿ − 1)/(r − 1). For example, a = 1, r = 2, n = 4: S₄ = 1(16 − 1)/(2 − 1) = 15.
• Steps:
  • S₅ = 2(3⁵ − 1)/(3 − 1).
  • 3⁵ = 243; 243 − 1 = 242.
  • S₅ = 2 × 242 / 2 = 242.
• Answer: 242

[Easy] Permutations

• EN: In how many ways can 4 different books be arranged on a shelf?
• FR: De combien de façons peut-on arranger 4 livres différents sur une étagère?
• Choices: A) 16 B) 20 C) 24 D) 32
• Hint: Use factorial notation. The number of arrangements of n items = n!. For example, 3 books: 3! = 3 × 2 × 1 = 6 ways.
• Steps:
  • 4 books can be arranged in 4! ways.
  • 4! = 4 × 3 × 2 × 1.
  • 4! = 24.
• Answer: 24

[Easy] Polynomial Functions

• EN: What is the degree of the polynomial f(x) = 3x⁴ − 2x² + 7x − 5?
• FR: Quel est le degré du polynôme f(x) = 3x⁴ − 2x² + 7x − 5?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: The degree is the highest power of x in the polynomial. For example, in 5x³ + 2x − 1, the degree is 3.
• Steps:
  • Look for the highest exponent of x.
  • The term 3x⁴ has the highest power.
  • The degree is 4.
• Answer: 4

[Easy] Combinations

• EN: How many ways can 3 students be chosen from a group of 7 to form a committee?
• FR: De combien de façons peut-on choisir 3 élèves parmi un groupe de 7 pour former un comité?
• Choices: A) 21 B) 35 C) 42 D) 70
• Hint: Use C(n,r) = n! / (r!(n−r)!). For example, C(5,2) = 5!/(2! × 3!) = 120/12 = 10.
• Steps:
  • C(7,3) = 7! / (3! × 4!).
  • = (7 × 6 × 5) / (3 × 2 × 1).
  • = 210 / 6 = 35.
• Answer: 35

[Easy] Derivative — Power Rule

• EN: Using the power rule, what is the derivative of f(x) = x³?
• FR: En utilisant la règle de puissance, quelle est la dérivée de f(x) = x³?
• Choices: A) x² B) 2x² C) 3x² D) 4x²
• Hint: The power rule states: if f(x) = xⁿ, then f'(x) = nxⁿ⁻¹. For example, f(x) = x⁵: f'(x) = 5x⁴.
• Steps:
  • f(x) = x³; apply power rule.
  • f'(x) = 3 × x^(3−1).
  • f'(x) = 3x².
• Answer: 3x²

[Medium] Rational Functions

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

[Medium] Probability Distributions

• EN: A fair coin is tossed 3 times. What is the probability of getting exactly 2 heads?
• FR: On lance une pièce équitable 3 fois. Quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 1/8 B) 2/8 C) 3/8 D) 4/8
• Hint: Use C(n,r) × pʳ × (1−p)ⁿ⁻ʳ. For example, P(exactly 1 head in 3 flips) = C(3,1) × (1/2)¹ × (1/2)² = 3 × 1/8 = 3/8.
• Steps:
  • P(exactly 2 heads) = C(3,2) × (1/2)² × (1/2)¹.
  • C(3,2) = 3; (1/2)² × (1/2)¹ = 1/8.
  • P = 3 × 1/8 = 3/8.
• Answer: 3/8

[Medium] Vectors — Addition

• EN: Vector u = (3, 5) and vector v = (−1, 4). What is u + v?
• FR: Le vecteur u = (3, 5) et le vecteur v = (−1, 4). Combien fait u + v?
• Choices: A) (2, 8) B) (2, 9) C) (4, 8) D) (4, 9)
• Hint: Add the corresponding components. For example, (2, 3) + (5, −1) = (7, 2).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: 5 + 4 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Medium] Derivative — Rate of Change

• EN: The position of a car is given by s(t) = 4t² + 3t. What is the instantaneous velocity (derivative) at t = 2?
• FR: La position d'une voiture est donnée par s(t) = 4t² + 3t. Quelle est la vitesse instantanée (dérivée) à t = 2?
• Choices: A) 17 B) 19 C) 22 D) 26
• Hint: Find s'(t) using the power rule, then substitute t = 2. For example, if s(t) = 3t² + t, then s'(t) = 6t + 1; at t = 3: s'(3) = 19.
• Steps:
  • s'(t) = 8t + 3 (by power rule).
  • At t = 2: s'(2) = 8(2) + 3 = 16 + 3.
  • s'(2) = 19.
• Answer: 19

[Hard] Pascal's Triangle and Binomial Theorem

• EN: Using the binomial theorem, expand (x + 2)³. What is the coefficient of x²?
• FR: En utilisant le théorème du binôme, développe (x + 2)³. Quel est le coefficient de x²?
• Choices: A) 4 B) 6 C) 8 D) 12
• Hint: Use (a + b)³ = a³ + 3a²b + 3ab² + b³. For example, in (x + 3)³, the coefficient of x² comes from 3x² × 3 = 9.
• Steps:
  • (x + 2)³ = x³ + 3x²(2) + 3x(2²) + 2³.
  • = x³ + 6x² + 12x + 8.
  • The coefficient of x² is 6.
• Answer: 6

[Hard] Vectors — Dot Product

• EN: Given vectors a = (4, 3) and b = (2, −5), what is the dot product a · b?
• FR: Étant donné les vecteurs a = (4, 3) et b = (2, −5), combien fait le produit scalaire a · b?
• Choices: A) −7 B) −8 C) 7 D) 8
• Hint: Dot product = (a₁ × b₁) + (a₂ × b₂). For example, (3, 2) · (4, −1) = 12 + (−2) = 10.
• Steps:
  • a · b = (4 × 2) + (3 × −5).
  • = 8 + (−15).
  • = −7.
• Answer: −7