Daily Math — 2026-08-19

[Easy] Counting to 20

• EN: There are 7 red apples and 5 green apples in a basket. How many apples are there in all?
• FR: Il y a 7 pommes rouges et 5 pommes vertes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: Add the two groups together, like 3 + 4 = 7.
• Steps:
  • Start at 7 and count on 5 more.
  • 7 … 8, 9, 10, 11, 12. There are 12 apples in all.
• Answer: 12

[Easy] 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, like 10, 12, 14.
• Steps:
  • Each number goes up by 2.
  • 8 + 2 = 10, so 10 comes next.
• Answer: 10

[Easy] Subtraction within 20

• EN: Emma had 15 stickers and gave 6 to her friend. How many stickers does Emma have left?
• FR: Emma avait 15 autocollants et en a donné 6 à son amie. Combien d'autocollants Emma a-t-il maintenant?
• Choices: A) 7 B) 8 C) 9 D) 21
• Hint: To subtract, count back, like 10 − 3 = 7.
• Steps:
  • Start at 15 and count back 6.
  • 15 … 14, 13, 12, 11, 10, 9. Emma has 9 stickers left.
• Answer: 9

[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) Toonie
• Hint: A nickel is worth 5 cents; the next coin up is worth twice that.
• Steps:
  • A penny = 1 cent, a nickel = 5 cents, a dime = 10 cents.
  • The coin worth 10 cents is the dime.
• Answer: Dime

[Medium] Comparing Numbers

• EN: Which number is greater: 14 or 19?
• FR: Quel nombre est plus grand : 14 ou 19?
• Choices: A) 14 B) 19 C) Both are equal D) 41
• Hint: When tens digits are the same, compare the ones digit, like 12 vs 17 — 17 is greater.
• Steps:
  • Both numbers have 1 ten.
  • Compare the ones: 4 ones vs 9 ones. Nine ones is more, so 19 is greater.
• Answer: 19

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What number comes next: 5, 10, 15, 20, ___?
• FR: Compte par bonds de 5. Quel nombre vient ensuite : 5, 10, 15, 20, ___?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: Skip counting by 5s means adding 5 each time, like 30, 35, 40.
• Steps:
  • Each number increases by 5.
  • 20 + 5 = 25, so 25 comes next.
• Answer: 25

[Medium] Addition within 20

• EN: Liam scored 8 points in the first hockey period and 9 points in the second period. How many points did he score in all?
• FR: Liam a marqué 8 points lors de la première période de hockey et 9 points lors de la deuxième. Combien de points a-t-il marqués en tout?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: To add 8 + 9, try making a ten: 8 + 2 = 10, then add 7 more = 17.
• Steps:
  • 8 + 9: break 9 into 2 + 7.
  • 8 + 2 = 10, then 10 + 7 = 17. Liam scored 17 points.
• Answer: 17

[Medium] Counting to 100

• EN: What number is 10 more than 63?
• FR: Quel nombre est 10 de plus que 63?
• Choices: A) 53 B) 64 C) 73 D) 83
• Hint: Adding 10 keeps the ones digit the same and increases the tens digit by 1, like 45 + 10 = 55.
• Steps:
  • 63 has 6 tens and 3 ones.
  • Adding 10 gives 7 tens and 3 ones = 73.
• Answer: 73

[Hard] Two-Step Addition

• EN: There are 6 boys, 7 girls, and 3 teachers on the school bus. How many people are on the bus in all?
• FR: Il y a 6 garçons, 7 filles et 3 enseignants dans l'autobus scolaire. Combien de personnes y a-t-il en tout dans l'autobus?
• Choices: A) 13 B) 15 C) 16 D) 17
• Hint: Add three numbers one at a time, like 4 + 5 + 3: first 4 + 5 = 9, then 9 + 3 = 12.
• Steps:
  • First add the students: 6 + 7 = 13.
  • Then add the teachers: 13 + 3 = 16. There are 16 people on the bus.
• Answer: 16

[Hard] Coins and Counting

• EN: Mei has 2 nickels and 3 pennies. How much money does she have in total?
• FR: Mei a 2 pièces de 5 cents et 3 pièces de 1 cent. Combien d'argent a-t-elle au total?
• Choices: A) 5 cents B) 13 cents C) 15 cents D) 23 cents
• Hint: Find the value of each group first, then add them together, like 2 dimes + 1 penny = 20 + 1 = 21 cents.
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 3 pennies = 3 cents. So 10 + 3 = 13 cents in total.
• Answer: 13 cents

[Easy] Addition within 100

• EN: A store has 34 red pencils and 25 blue pencils. How many pencils are there in all?
• FR: Un magasin a 34 crayons rouges et 25 crayons bleus. Combien y a-t-il de crayons en tout?
• Choices: A) 49 B) 59 C) 69 D) 79
• Hint: Add tens first, then ones, like 21 + 35: 20 + 30 = 50, 1 + 5 = 6, so 56.
• Steps:
  • Tens: 30 + 20 = 50.
  • Ones: 4 + 5 = 9. So 50 + 9 = 59 pencils in all.
• 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: La grande aiguille est sur le 12 et la petite aiguille est sur le 3. Quelle heure est-il?
• Choices: A) 12:00 B) 2:00 C) 3:00 D) 3:30
• Hint: When the minute hand points to 12, it is exactly on the hour, like 5:00.
• Steps:
  • The minute hand on 12 means it is exactly on the hour.
  • The hour hand on 3 means it is 3 o'clock. The time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A crayon is 8 cm long and a pencil is 14 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon de couleur mesure 8 cm et un crayon mesure 14 cm. De combien le crayon est-il plus long que le crayon de couleur?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 22 cm
• Hint: To find how much longer, subtract the shorter length from the longer, like 12 − 7 = 5.
• Steps:
  • 14 cm − 8 cm = ?
  • 14 − 8 = 6. The pencil is 6 cm longer.
• Answer: 6 cm

[Easy] Counting Coins

• EN: Aisha has 2 dimes and 1 nickel. How much money does she have?
• FR: Aisha a 2 pièces de 10 cents et 1 pièce de 5 cents. Combien d'argent a-t-elle?
• Choices: A) 15 cents B) 20 cents C) 25 cents D) 30 cents
• Hint: Count on from the largest coin, like 1 dime + 1 dime + 1 nickel: 10, 20, 25.
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • 1 nickel = 5 cents. So 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtraction within 100

• EN: There are 72 students at a school event. 38 students go home early. How many students are left?
• FR: Il y a 72 élèves à un événement scolaire. 38 élèves rentrent chez eux plus tôt. Combien d'élèves restent-il?
• Choices: A) 24 B) 34 C) 44 D) 110
• Hint: Subtract by regrouping, like 52 − 27: borrow a ten so 12 − 7 = 5 and 4 − 2 = 2, giving 25.
• Steps:
  • 72 − 38: borrow from the tens. 12 − 8 = 4 in the ones place.
  • 6 − 3 = 3 in the tens place. So 72 − 38 = 34 students are left.
• Answer: 34

[Medium] Telling Time (Half Hour)

• EN: The clock shows the hour hand halfway between 7 and 8, and the minute hand on the 6. What time is it?
• FR: La grande aiguille est sur le 6 et la petite aiguille est entre le 7 et le 8. 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 always 30 minutes past the hour, like 4:30.
• Steps:
  • The minute hand on 6 means 30 minutes past the hour.
  • The hour hand is just past 7, so it is 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: Look at the pattern: 10, 15, 20, 25, ___. What number comes next?
• FR: Observe le motif : 10, 15, 20, 25, ___. Quel nombre vient ensuite?
• Choices: A) 26 B) 28 C) 30 D) 35
• Hint: Find the rule by looking at what is added each time, like 3, 6, 9, 12 — add 3 each time.
• Steps:
  • Each number goes up by 5: 10 + 5 = 15, 15 + 5 = 20, 20 + 5 = 25.
  • 25 + 5 = 30. The next number is 30.
• Answer: 30

[Medium] Measuring in Metres

• EN: A hallway is 6 metres long and a classroom is 9 metres long. How long are they together?
• FR: Un couloir mesure 6 mètres de long et une salle de classe mesure 9 mètres de long. Quelle est leur longueur totale?
• Choices: A) 3 m B) 13 m C) 15 m D) 54 m
• Hint: To find the total length, add the two measurements together, like 4 m + 7 m = 11 m.
• Steps:
  • Add the two lengths: 6 m + 9 m.
  • 6 + 9 = 15. Together they are 15 m long.
• Answer: 15 m

[Hard] Counting Coins to $1

• EN: Noah has 3 quarters and 1 dime. How much money does he have?
• FR: Noah a 3 pièces de 25 cents et 1 pièce de 10 cents. Combien d'argent a-t-il?
• Choices: A) 65 cents B) 75 cents C) 85 cents D) 95 cents
• Hint: A quarter is worth 25 cents; count by 25s and then add the extra coin, like 25 + 25 + 25 = 75.
• Steps:
  • 3 quarters = 25 + 25 + 25 = 75 cents.
  • Add 1 dime: 75 + 10 = 85 cents. Noah has 85 cents.
• Answer: 85 cents

[Hard] Two-Step Problem

• EN: A bag had 60 marbles. Priya put in 15 more, and then her brother took out 22. How many marbles are in the bag now?
• FR: Un sac contenait 60 billes. Priya en a mis 15 de plus, puis son frère en a enlevé 22. Combien de billes y a-t-il dans le sac maintenant?
• Choices: A) 43 B) 53 C) 63 D) 97
• Hint: Solve one step at a time, like 40 + 10 = 50, then 50 − 15 = 35.
• Steps:
  • First, add: 60 + 15 = 75 marbles.
  • Then subtract: 75 − 22 = 53 marbles are in the bag now.
• Answer: 53

[Easy] Multiplication by 2

• EN: There are 6 pairs of skates in a box. How many individual skates are there?
• FR: Il y a 6 paires de patins dans une boîte. Combien y a-t-il de patins au total?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Pairs means groups of 2, like 4 pairs = 4 × 2 = 8.
• Steps:
  • 1 pair = 2 skates, so 6 pairs = 6 × 2.
  • 6 × 2 = 12. There are 12 individual skates.
• Answer: 12

[Easy] Fractions — One Half

• EN: A pizza is cut into 4 equal slices. Jada eats 2 slices. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 tranches égales. Jada mange 2 tranches. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 3/4
• Hint: A fraction shows parts eaten over total parts, like 1 slice out of 2 total = 1/2.
• Steps:
  • Jada ate 2 slices out of 4 total slices.
  • 2/4 = 1/2. She ate 1/2 of the pizza.
• Answer: 1/2

[Easy] Multiplication by 5

• EN: Each table in the cafeteria has 5 chairs. There are 4 tables. How many chairs are there in total?
• FR: Chaque table de la cafétéria a 5 chaises. Il y a 4 tables. Combien y a-t-il de chaises en tout?
• Choices: A) 9 B) 15 C) 20 D) 25
• Hint: Multiply the number of groups by the size of each group, like 3 × 5 = 15.
• Steps:
  • 4 tables × 5 chairs each = 4 × 5.
  • 4 × 5 = 20. There are 20 chairs in total.
• Answer: 20

[Easy] Perimeter

• EN: A rectangular garden has a length of 6 m and a width of 3 m. What is its perimeter?
• FR: Un jardin rectangulaire a une longueur de 6 m et une largeur de 3 m. Quel est son périmètre?
• Choices: A) 9 m B) 16 m C) 18 m D) 36 m
• Hint: Perimeter = add all four sides, like a rectangle with length 4 and width 2: 4 + 2 + 4 + 2 = 12.
• Steps:
  • A rectangle has 2 lengths and 2 widths: 6 + 6 + 3 + 3.
  • 6 + 6 + 3 + 3 = 18 m. The perimeter is 18 m.
• Answer: 18 m

[Medium] Division with Equal Groups

• EN: There are 24 students and 4 equal teams. How many students are on each team?
• FR: Il y a 24 élèves et 4 équipes égales. Combien d'élèves y a-t-il dans chaque équipe?
• Choices: A) 4 B) 6 C) 8 D) 96
• Hint: Division splits into equal groups, like 20 ÷ 4 = 5.
• Steps:
  • 24 ÷ 4 = ?
  • Think: 4 × 6 = 24, so 24 ÷ 4 = 6. Each team has 6 students.
• Answer: 6

[Medium] Multiplication by 3

• EN: A hockey team scores 3 goals per game and plays 7 games. How many goals do they score in total?
• FR: Une équipe de hockey marque 3 buts par match et joue 7 matchs. Combien de buts marque-t-elle en tout?
• Choices: A) 10 B) 18 C) 21 D) 24
• Hint: Multiply the rate by the number of times, like 3 × 5 = 15.
• Steps:
  • 7 games × 3 goals each = 7 × 3.
  • 7 × 3 = 21. They score 21 goals in total.
• Answer: 21

[Medium] Reading a Graph

• EN: A bar graph shows: Monday = 4 books, Tuesday = 7 books, Wednesday = 5 books. How many books were read in total over the three days?
• FR: Un diagramme à bandes montre : lundi = 4 livres, mardi = 7 livres, mercredi = 5 livres. Combien de livres ont été lus en tout sur les trois jours?
• Choices: A) 11 B) 14 C) 16 D) 17
• Hint: To find the total, add all the values from the graph, like 3 + 5 + 6 = 14.
• Steps:
  • Add all three days: 4 + 7 + 5.
  • 4 + 7 = 11, then 11 + 5 = 16. A total of 16 books were read.
• Answer: 16

[Medium] Fractions — One Quarter

• EN: There are 8 cookies. One quarter of them have chocolate chips. How many cookies have chocolate chips?
• FR: Il y a 8 biscuits. Un quart d'entre eux ont des pépites de chocolat. Combien de biscuits ont des pépites de chocolat?
• Choices: A) 1 B) 2 C) 4 D) 6
• Hint: To find 1/4 of a number, divide it by 4, like 1/4 of 12 = 12 ÷ 4 = 3.
• Steps:
  • 1/4 of 8 means divide 8 into 4 equal groups.
  • 8 ÷ 4 = 2. Two cookies have chocolate chips.
• Answer: 2

[Hard] Multi-Step Multiplication

• EN: A store sells hockey cards in packs of 10. Omar buys 5 packs on Monday and 3 packs on Friday. How many hockey cards does he have in total?
• FR: Un magasin vend des cartes de hockey en paquets de 10. Omar achète 5 paquets lundi et 3 paquets vendredi. Combien de cartes de hockey a-t-il en tout?
• Choices: A) 18 B) 50 C) 80 D) 150
• Hint: Find each day's total first, then add them together, like 3 packs × 5 cards = 15, plus 2 packs × 5 cards = 10, total = 25.
• Steps:
  • Monday: 5 packs × 10 cards = 50 cards.
  • Friday: 3 packs × 10 cards = 30 cards. Total: 50 + 30 = 80 cards.
• Answer: 80

[Hard] Perimeter with Missing Side

• EN: A triangle has two sides that are each 9 cm long and a perimeter of 25 cm. How long is the third side?
• FR: Un triangle a deux côtés de 9 cm chacun et un périmètre de 25 cm. Quelle est la longueur du troisième côté?
• Choices: A) 5 cm B) 7 cm C) 16 cm D) 43 cm
• Hint: To find a missing side, subtract the known sides from the perimeter, like perimeter 20 − 7 − 7 = 6.
• Steps:
  • Add the two known sides: 9 + 9 = 18 cm.
  • Subtract from the perimeter: 25 − 18 = 7 cm. The third side is 7 cm.
• Answer: 7 cm

[Easy] Multiplication Facts to 9×9

• EN: What is 8 × 7?
• FR: Combien fait 8 × 7?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Break it apart: 8 × 7 = 8 × 5 + 8 × 2, similar to 6 × 7 = 6 × 5 + 6 × 2 = 30 + 12 = 42.
• Steps:
  • 8 × 7: think 8 × 5 = 40, and 8 × 2 = 16.
  • 40 + 16 = 56. So 8 × 7 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 4.37?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,37?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 30 ones
• Hint: In a decimal number like 2.56, the first digit after the decimal point is in the tenths place.
• Steps:
  • In 4.37, the digits after the decimal are tenths and hundredths.
  • The 3 is right after the decimal point, so it is in the tenths place. Its value is 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A rectangular mat is 5 m long and 4 m wide. What is its area?
• FR: Un tapis rectangulaire a 5 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 9 m² B) 18 m² C) 20 m² D) 25 m²
• Hint: Area of a rectangle = length × width, like 6 × 3 = 18 m².
• Steps:
  • Area = length × width = 5 × 4.
  • 5 × 4 = 20. The area is 20 m².
• Answer: 20 m²

[Easy] Comparing Fractions

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

[Medium] Long Division with Remainder

• EN: 47 stickers are shared equally among 5 friends. How many stickers does each friend get, and how many are left over?
• FR: 47 autocollants sont partagés également entre 5 amis. Combien d'autocollants chaque ami reçoit-il et combien en reste-t-il?
• Choices: A) 8 remainder 3 B) 9 remainder 2 C) 9 remainder 5 D) 10 remainder 2
• Hint: Divide and find the remainder, like 23 ÷ 4: 4 × 5 = 20, remainder 3, so 5 remainder 3.
• Steps:
  • 5 × 9 = 45. So each friend gets 9 stickers.
  • 47 − 45 = 2 left over. The answer is 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: A movie starts at 1:15 p.m. and ends at 3:45 p.m. How long is the movie?
• FR: Un film commence à 13 h 15 et se termine à 15 h 45. Quelle est la durée du film?
• 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, like from 2:10 to 4:40 = 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 is exactly 2 hours.
  • From 3:15 to 3:45 is 30 more minutes. Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Addition

• EN: A snowfall measured 3.4 cm on Monday and 2.8 cm on Tuesday. How much snow fell in total?
• FR: Une chute de neige a mesuré 3,4 cm lundi et 2,8 cm mardi. Quelle quantité de neige est tombée en tout?
• Choices: A) 5.2 cm B) 6.2 cm C) 6.8 cm D) 7.2 cm
• Hint: Line up the decimal points before adding, like 1.5 + 2.7 = 4.2.
• Steps:
  • 3.4 + 2.8: add tenths first. 4 + 8 = 12 tenths, carry the 1.
  • 3 + 2 + 1 = 6 ones. So 3.4 + 2.8 = 6.2 cm.
• Answer: 6.2 cm

[Medium] Multiplication — Two-Digit by One-Digit

• EN: A box holds 34 juice boxes. How many juice boxes are in 3 boxes?
• FR: Une boîte contient 34 briques de jus. Combien y a-t-il de briques de jus dans 3 boîtes?
• Choices: A) 37 B) 92 C) 102 D) 120
• Hint: Multiply ones then tens, like 23 × 4: (20 × 4) + (3 × 4) = 80 + 12 = 92.
• Steps:
  • 34 × 3: multiply ones: 4 × 3 = 12, write 2 carry 1.
  • Multiply tens: 3 × 3 = 9, plus 1 carried = 10. So 34 × 3 = 102.
• Answer: 102

[Hard] Multi-Step Word Problem

• EN: Sophie bought 4 notebooks at $2.75 each and paid with a $20 bill. How much change did she receive?
• FR: Sophie a acheté 4 cahiers à 2,75 $ chacun et a payé avec un billet de 20 $. Combien de monnaie a-t-elle reçue?
• Choices: A) $8.00 B) $9.00 C) $11.00 D) $17.25
• Hint: First find the total cost, then subtract from the amount paid, like 3 × $4.50 = $13.50; $20 − $13.50 = $6.50.
• Steps:
  • Total cost: 4 × $2.75 = $11.00.
  • Change: $20.00 − $11.00 = $9.00. Sophie received $9.00 in change.
• Answer: $9.00

[Hard] Comparing Decimals and Fractions

• EN: Order these numbers from least to greatest: 0.5, 3/4, 0.25, 1/2.
• FR: Mets ces nombres en ordre du plus petit au plus grand : 0,5, 3/4, 0,25, 1/2.
• Choices: A) 0.25, 0.5, 1/2, 3/4 B) 0.25, 1/2, 0.5, 3/4 C) 1/2, 0.25, 0.5, 3/4 D) 3/4, 0.5, 1/2, 0.25
• Hint: Convert fractions to decimals first, like 1/4 = 0.25 and 3/4 = 0.75, then compare.
• Steps:
  • Convert: 1/2 = 0.50, 3/4 = 0.75. Now compare: 0.25, 0.50, 0.50, 0.75.
  • Note 0.5 and 1/2 are equal. Order: 0.25, 0.5, 1/2, 3/4.
• Answer: 0.25, 0.5, 1/2, 3/4

[Easy] Multi-Digit Multiplication

• EN: A school orders 125 pencils for each of its 4 classrooms. How many pencils does it order in total?
• FR: Une école commande 125 crayons pour chacune de ses 4 classes. Combien de crayons commande-t-elle en tout?
• Choices: A) 129 B) 400 C) 500 D) 625
• Hint: Multiply hundreds, tens, and ones separately, like 213 × 3 = 639.
• Steps:
  • 125 × 4: 100 × 4 = 400, 20 × 4 = 80, 5 × 4 = 20.
  • 400 + 80 + 20 = 500 pencils in total.
• Answer: 500

[Easy] Adding Fractions with Like Denominators

• EN: Luc ate 2/8 of a pie and his sister ate 3/8 of the same pie. How much of the pie did they eat together?
• FR: Luc a mangé 2/8 d'une tarte et sa sœur en a mangé 3/8. Quelle fraction de la tarte ont-ils mangée ensemble?
• Choices: A) 4/8 B) 5/8 C) 6/8 D) 5/16
• Hint: When denominators are the same, just add the numerators, like 1/6 + 3/6 = 4/6.
• Steps:
  • Add the numerators: 2 + 3 = 5. Keep the denominator: 8.
  • Together they ate 5/8 of the pie.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: A bag has 40 marbles. 50% of them are blue. How many marbles are blue?
• FR: Un sac contient 40 billes. 50 % d'entre elles sont bleues. Combien de billes sont bleues?
• Choices: A) 5 B) 10 C) 20 D) 40
• Hint: 50% means half, so divide the total by 2, like 50% of 60 = 30.
• Steps:
  • 50% of 40 = 40 ÷ 2.
  • 40 ÷ 2 = 20. There are 20 blue marbles.
• Answer: 20

[Easy] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 120 cm³
• Hint: Volume = length × width × height, like 4 × 3 × 2 = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Multi-Digit Division

• EN: 396 students are divided equally into 9 buses. How many students are on each bus?
• FR: 396 élèves sont répartis également dans 9 autobus. Combien d'élèves y a-t-il dans chaque autobus?
• Choices: A) 34 B) 44 C) 54 D) 387
• Hint: Divide the hundreds first, then the tens, like 248 ÷ 4: 2 hundreds ÷ 4, regroup, then divide tens and ones to get 62.
• Steps:
  • 396 ÷ 9: 9 × 40 = 360, remainder 36.
  • 36 ÷ 9 = 4. So 396 ÷ 9 = 44. Each bus has 44 students.
• Answer: 44

[Medium] Subtracting Fractions with Like Denominators

• EN: A jug is 7/10 full of water. Sam pours out 3/10. How full is the jug now?
• FR: Un pichet est rempli à 7/10 d'eau. Sam en verse 3/10. Quel est le niveau du pichet maintenant?
• Choices: A) 3/10 B) 4/10 C) 10/10 D) 21/10
• Hint: When denominators are the same, subtract the numerators, like 5/7 − 2/7 = 3/7.
• Steps:
  • Subtract numerators: 7 − 3 = 4. Keep the denominator: 10.
  • The jug is now 4/10 full.
• Answer: 4/10

[Medium] Decimal Operations

• EN: A Tim Hortons coffee costs $2.45 and a muffin costs $1.85. What is the total cost?
• FR: Un café Tim Hortons coûte 2,45 $ et un muffin coûte 1,85 $. Quel est le coût total?
• Choices: A) $3.20 B) $4.20 C) $4.30 D) $5.30
• Hint: Line up the decimal points and add, like $3.60 + $2.75 = $6.35.
• Steps:
  • $2.45 + $1.85: add cents: 45 + 85 = 130 cents = $1.30; carry $1.
  • 2 + 1 + 1 = $4. Total: $4.30.
• Answer: $4.30

[Medium] Percentage — 25%

• EN: A jacket regularly costs $80. It is on sale for 25% off. How much money do you save?
• FR: Une veste coûte régulièrement 80 $. Elle est en solde à 25 % de rabais. Combien économises-tu?
• Choices: A) $15 B) $20 C) $25 D) $60
• Hint: 25% means one quarter, so divide the price by 4, like 25% of $60 = $15.
• Steps:
  • 25% of $80 = $80 ÷ 4.
  • $80 ÷ 4 = $20. You save $20.
• Answer: $20

[Hard] Multi-Step Fraction and Decimal Problem

• EN: Mia had $15.00. She spent 1/5 of her money on a snack and $4.50 on a book. How much money does she have left?
• FR: Mia avait 15,00 $. Elle a dépensé 1/5 de son argent pour une collation et 4,50 $ pour un livre. Combien d'argent lui reste-t-il?
• Choices: A) $5.50 B) $6.50 C) $7.50 D) $10.50
• Hint: Find 1/5 by dividing by 5, then subtract both amounts from the total, like $20 ÷ 5 = $4, then $20 − $4 − $6 = $10.
• Steps:
  • 1/5 of $15.00 = $15.00 ÷ 5 = $3.00 spent on snack.
  • Money left: $15.00 − $3.00 − $4.50 = $7.50.
• Answer: $7.50

[Hard] Volume and Comparison

• EN: Box A is 6 cm × 5 cm × 4 cm. Box B is 8 cm × 5 cm × 3 cm. Which box has the greater volume, and by how much?
• FR: La boîte A mesure 6 cm × 5 cm × 4 cm. La boîte B mesure 8 cm × 5 cm × 3 cm. Quelle boîte a le plus grand volume, et de combien?
• Choices: A) Box A by 12 cm³ B) Box B by 12 cm³ C) Box A by 24 cm³ D) They are equal
• Hint: Find each volume using length × width × height, then subtract to compare, like 60 cm³ − 48 cm³ = 12 cm³ more.
• Steps:
  • Box A: 6 × 5 × 4 = 120 cm³. Box B: 8 × 5 × 3 = 120 cm³.
  • Both volumes are equal. Neither box is larger.
• Answer: They are equal

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien font 30 % de 200?
• Choices: A) 6 B) 30 C) 60 D) 230
• Hint: Find 10% first by dividing by 10, then multiply by the number of tens, like 10% of 50 = 5, so 30% = 15.
• Steps:
  • 10% of 200 = 200 ÷ 10 = 20.
  • 30% = 3 × 20 = 60.
• Answer: 60

[Easy] Simple Algebraic Expression

• EN: If n = 5, what is the value of 4n + 3?
• FR: Si n = 5, quelle est la valeur de 4n + 3?
• Choices: A) 12 B) 17 C) 23 D) 43
• Hint: Substitute the value into the expression, like if n = 2, then 3n + 1 = 3(2) + 1 = 7.
• Steps:
  • Replace n with 5: 4(5) + 3.
  • 4 × 5 = 20, then 20 + 3 = 23.
• Answer: 23

[Easy] Ratio

• EN: In a class, there are 12 girls and 8 boys. What is the ratio of girls to boys?
• FR: Dans une classe, il y a 12 filles et 8 garçons. Quel est le rapport filles à garçons?
• Choices: A) 2:3 B) 3:2 C) 4:3 D) 8:12
• Hint: Write the ratio as girls:boys and simplify by dividing both by the GCF, like 6:4 = 3:2.
• Steps:
  • Ratio of girls to boys = 12:8.
  • GCF of 12 and 8 is 4. 12 ÷ 4 = 3, 8 ÷ 4 = 2. Simplified ratio is 3:2.
• Answer: 3:2

[Easy] Integers Introduction

• EN: The temperature in Winnipeg is −8°C in the morning and rises by 5 degrees. What is the temperature now?
• FR: La température à Winnipeg est de −8 °C le matin et monte de 5 degrés. Quelle est la température maintenant?
• Choices: A) −13°C B) −3°C C) 3°C D) 13°C
• Hint: Adding a positive to a negative moves up the number line, like −6 + 4 = −2.
• Steps:
  • Start at −8 and add 5.
  • −8 + 5 = −3°C. The temperature is now −3°C.
• Answer: −3°C

[Medium] Order of Operations (BEDMAS)

• EN: Solve: 3 + 4 × (6 − 2) ÷ 2
• FR: Résous : 3 + 4 × (6 − 2) ÷ 2
• Choices: A) 8 B) 11 C) 14 D) 17
• Hint: Use BEDMAS: Brackets first, then Multiply/Divide left to right, then Add/Subtract, like 2 + 3 × (5 − 1) ÷ 2 = 2 + 3 × 4 ÷ 2 = 2 + 6 = 8.
• Steps:
  • Brackets: (6 − 2) = 4. Expression: 3 + 4 × 4 ÷ 2.
  • Multiply/Divide left to right: 4 × 4 = 16, then 16 ÷ 2 = 8. Then add: 3 + 8 = 11.
• Answer: 11

[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 numerators together and denominators together, like 1/2 × 2/3 = 2/6 = 1/3.
• Steps:
  • Multiply: (2 × 3) / (3 × 4) = 6/12.
  • Simplify: 6/12 = 1/2.
• Answer: 1/2

[Medium] Rate Problem

• EN: A car travels 270 km in 3 hours. What is its speed in km/h?
• FR: Une voiture parcourt 270 km en 3 heures. Quelle est sa vitesse en km/h?
• Choices: A) 60 km/h B) 80 km/h C) 90 km/h D) 810 km/h
• Hint: Speed = distance ÷ time, like 150 km ÷ 3 h = 50 km/h.
• Steps:
  • Speed = 270 km ÷ 3 h.
  • 270 ÷ 3 = 90. The car travels at 90 km/h.
• Answer: 90 km/h

[Medium] Fraction Division

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

[Hard] Multi-Step Percent Problem

• EN: A store marks up a pair of skates by 40% from its cost of $75. Then it offers a 10% discount on the marked-up price. What is the final selling price?
• FR: Un magasin majore le prix d'une paire de patins de 40 % par rapport à son coût de 75 $. Il offre ensuite un rabais de 10 % sur le prix majoré. Quel est le prix de vente final?
• Choices: A) $94.50 B) $97.50 C) $99.75 D) $105.00
• Hint: Find the marked-up price first by multiplying by 1.40, then apply the 10% discount by multiplying by 0.90, like $50 × 1.20 × 0.90 = $54.
• Steps:
  • Marked-up price: $75 × 1.40 = $105.00.
  • After 10% discount: $105 × 0.90 = $94.50. The final price is $94.50.
• Answer: $94.50

[Hard] BEDMAS with Integers

• EN: Solve: (−3)² + 4 × (−2) − 1
• FR: Résous : (−3)² + 4 × (−2) − 1
• Choices: A) −8 B) 0 C) 2 D) 18
• Hint: Exponents come before multiplication; a negative number squared is positive, like (−4)² = 16; then 16 + 3 × (−2) = 16 − 6 = 10.
• Steps:
  • Exponent: (−3)² = 9. Expression: 9 + 4 × (−2) − 1.
  • Multiply: 4 × (−2) = −8. Then: 9 + (−8) − 1 = 9 − 8 − 1 = 0.
• Answer: 0

[Easy] Integer Addition

• EN: What is (−12) + 7?
• FR: Combien font (−12) + 7?
• Choices: A) −19 B) −5 C) 5 D) 19
• Hint: Adding a positive to a negative: subtract the smaller absolute value from the larger and keep the sign of the larger, like (−8) + 3 = −5.
• Steps:
  • |−12| = 12 and |7| = 7. Since 12 > 7, the answer is negative.
  • 12 − 7 = 5, so (−12) + 7 = −5.
• Answer: −5

[Easy] Percent — Discount

• EN: A video game costs $60. It is on sale for 20% off. What is the sale price?
• FR: Un jeu vidéo coûte 60 $. Il est en solde à 20 % de rabais. Quel est le prix de vente?
• Choices: A) $12 B) $40 C) $48 D) $72
• Hint: Find the discount amount first, then subtract, like 20% of $50 = $10, sale price = $50 − $10 = $40.
• Steps:
  • 20% of $60 = $60 × 0.20 = $12.
  • Sale price: $60 − $12 = $48.
• Answer: $48

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15.
• FR: Résous pour x : x + 9 = 15.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 24
• Hint: To isolate x, subtract the same number from both sides, like x + 4 = 11 → x = 11 − 4 = 7.
• Steps:
  • x + 9 = 15. Subtract 9 from both sides.
  • x = 15 − 9 = 6.
• Answer: x = 6

[Easy] Probability

• EN: A bag contains 3 red marbles and 7 blue marbles. What is the probability of picking a red marble?
• FR: Un sac contient 3 billes rouges et 7 billes bleues. Quelle est la probabilité de piger une bille rouge?
• Choices: A) 3/7 B) 3/10 C) 7/10 D) 1/3
• Hint: Probability = favourable outcomes ÷ total outcomes, like 2 reds out of 8 total = 2/8 = 1/4.
• Steps:
  • Total marbles: 3 + 7 = 10. Favourable: 3 red.
  • Probability = 3/10.
• Answer: 3/10

[Medium] Integer Multiplication

• EN: What is (−6) × (−8)?
• FR: Combien font (−6) × (−8)?
• Choices: A) −48 B) −14 C) 14 D) 48
• Hint: A negative times a negative gives a positive, like (−3) × (−5) = 15.
• Steps:
  • (−6) × (−8): same signs give a positive result.
  • 6 × 8 = 48. So (−6) × (−8) = 48.
• Answer: 48

[Medium] Percentage — Tax

• EN: A pair of jeans costs $45.00. The HST (sales tax) is 13%. What is the total price including tax?
• FR: Un jean coûte 45,00 $. La TVH est de 13 %. Quel est le prix total incluant les taxes?
• Choices: A) $5.85 B) $46.13 C) $50.85 D) $58.50
• Hint: Tax amount = price × tax rate, then add to the price, like $20 × 0.13 = $2.60, total = $22.60.
• Steps:
  • Tax: $45.00 × 0.13 = $5.85.
  • Total: $45.00 + $5.85 = $50.85.
• Answer: $50.85

[Medium] Surface Area of a Rectangular Prism

• EN: A rectangular box is 5 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 5 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire de surface?
• Choices: A) 30 cm² B) 42 cm² C) 60 cm² D) 62 cm²
• Hint: SA = 2(lw + lh + wh), like for a box 4 × 2 × 3: 2(8 + 12 + 6) = 2(26) = 52 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(5×3 + 5×2 + 3×2).
  • = 2(15 + 10 + 6) = 2(31) = 62 cm².
• Answer: 62 cm²

[Medium] Fraction and Decimal Fluency

• EN: What is 0.375 as a fraction in lowest terms?
• FR: Qu'est-ce que 0,375 sous forme de fraction en termes les plus bas?
• Choices: A) 3/10 B) 37/100 C) 3/8 D) 375/10
• Hint: Write the decimal as a fraction over 1000, then simplify, like 0.25 = 25/100 = 1/4.
• Steps:
  • 0.375 = 375/1000. GCF of 375 and 1000 is 125.
  • 375 ÷ 125 = 3, 1000 ÷ 125 = 8. So 0.375 = 3/8.
• Answer: 3/8

[Hard] Multi-Step Integer Problem

• EN: The temperature dropped 4°C each hour for 6 hours, starting at 3°C. What is the temperature after 6 hours?
• FR: La température a baissé de 4 °C chaque heure pendant 6 heures, en commençant à 3 °C. Quelle est la température après 6 heures?
• Choices: A) −24°C B) −21°C C) −18°C D) 27°C
• Hint: Multiply the drop per hour by the number of hours, then add to the starting temperature, like 2°C − (3 × 5°C) = 2 − 15 = −13°C.
• Steps:
  • Total drop: 4 × 6 = 24°C.
  • Final temperature: 3 − 24 = −21°C.
• Answer: −21°C

[Hard] Mean, Median, Mode

• EN: The scores of 7 students on a quiz are: 8, 5, 9, 8, 7, 10, 5. What are the mode and median of this data set?
• FR: Les résultats de 7 élèves à un quiz sont : 8, 5, 9, 8, 7, 10, 5. Quels sont le mode et la médiane de cet ensemble de données?
• Choices: A) Mode = 8, Median = 8 B) Mode = 5, Median = 8 C) Mode = 8 and 5, Median = 8 D) Mode = 8 and 5, Median = 7
• Hint: Mode is the most frequent value; median is the middle value when data is in order, like for 3, 3, 5, 7, 9 — mode = 3, median = 5.
• Steps:
  • Ordered: 5, 5, 7, 8, 8, 9, 10. Both 5 and 8 appear twice, so both are modes.
  • The median (middle value) is the 4th value = 8. Mode = 8 and 5, Median = 8.
• Answer: Mode = 8 and 5, Median = 8

[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) 72
• Hint: Think: which number times itself equals the target, like √81 = 9 because 9 × 9 = 81.
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144, so √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of: 14, 18, 22, 10, 16.
• FR: Trouve la moyenne de : 14, 18, 22, 10, 16.
• Choices: A) 14 B) 16 C) 18 D) 80
• Hint: Mean = sum of all values ÷ number of values, like (5 + 7 + 9) ÷ 3 = 21 ÷ 3 = 7.
• Steps:
  • Sum: 14 + 18 + 22 + 10 + 16 = 80.
  • Mean: 80 ÷ 5 = 16.
• Answer: 16

[Easy] Percent Increase

• EN: A sweater cost $40 last year and costs $50 this year. What is the percent increase?
• FR: Un chandail coûtait 40 $ l'an dernier et coûte 50 $ cette année. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 20% C) 25% D) 80%
• Hint: Percent increase = (increase ÷ original) × 100, like (3 ÷ 12) × 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 = 5 C) x = 7 D) x = 9
• Hint: Add to both sides first, then divide, like 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 cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 7 cm B) 10 cm C) 14 cm D) 100 cm
• Hint: Use a² + b² = c², like 3² + 4² = 9 + 16 = 25, so c = 5.
• Steps:
  • c² = 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10. The hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through (2, 3) and (6, 11). What is the slope of the line?
• FR: Une droite passe par (2, 3) et (6, 11). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 4 D) 8
• Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁), like (9 − 3) ÷ (4 − 1) = 6 ÷ 3 = 2.
• Steps:
  • Slope = (11 − 3) ÷ (6 − 2) = 8 ÷ 4.
  • 8 ÷ 4 = 2. The slope is 2.
• Answer: 2

[Medium] Percent Decrease

• EN: A store reduces the price of boots from $120 to $90. What is the percent decrease?
• FR: Un magasin réduit le prix de bottes de 120 $ à 90 $. Quel est le pourcentage de diminution?
• Choices: A) 20% B) 25% C) 30% D) 75%
• Hint: Percent decrease = (decrease ÷ original) × 100, like a drop from $80 to $60 = (20 ÷ 80) × 100 = 25%.
• Steps:
  • Decrease: $120 − $90 = $30.
  • Percent decrease: (30 ÷ 120) × 100 = 25%.
• Answer: 25%

[Medium] Two-Step Equation with Negatives

• EN: Solve for x: −2x + 7 = 13.
• FR: Résous pour x : −2x + 7 = 13.
• Choices: A) x = −3 B) x = −10 C) x = 3 D) x = 10
• Hint: Subtract from both sides first, then divide, remembering to flip the sign, like −3x + 5 = 14 → −3x = 9 → x = −3.
• Steps:
  • Subtract 7 from both sides: −2x = 6.
  • Divide by −2: x = −3.
• Answer: x = −3

[Hard] Pythagorean Theorem — Missing 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 cathète de 8 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 9 cm B) 15 cm C) 18 cm D) 289 cm
• Hint: Rearrange the Pythagorean theorem: b² = c² − a², like b² = 13² − 5² = 169 − 25 = 144, so b = 12.
• Steps:
  • b² = 17² − 8² = 289 − 64 = 225.
  • b = √225 = 15. The other leg is 15 cm.
• Answer: 15 cm

[Hard] Multi-Step Problem: Mean and Percent

• EN: Anya scored 72, 88, 65, and 91 on four tests. She wants a mean of at least 80 after a fifth test. What is the minimum score she needs on the fifth test?
• FR: Anya a obtenu 72, 88, 65 et 91 à quatre tests. Elle veut une moyenne d'au moins 80 après un cinquième test. Quel est le score minimum qu'elle doit obtenir au cinquième test?
• Choices: A) 64 B) 74 C) 80 D) 84
• Hint: Find the total needed for the mean, subtract the current total, like to average 75 over 5 tests: 75 × 5 = 375 total needed; if you have 290, you need 375 − 290 = 85.
• Steps:
  • Target total: 80 × 5 = 400. Current total: 72 + 88 + 65 + 91 = 316.
  • Minimum score needed: 400 − 316 = 84.
• Answer: 84

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x + 3 = 28.
• FR: Résous pour x : 5x + 3 = 28.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 31
• Hint: Subtract first, then divide, like 4x + 2 = 18 → 4x = 16 → x = 4.
• Steps:
  • Subtract 3: 5x = 25.
  • Divide by 5: x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

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

[Easy] Graphing — Slope-Intercept Form

• EN: What is the slope and y-intercept of the line y = 3x − 5?
• FR: Quels sont la pente et l'ordonnée à l'origine de la droite y = 3x − 5?
• Choices: A) slope = −5, y-intercept = 3 B) slope = 3, y-intercept = −5 C) slope = 5, y-intercept = −3 D) slope = 3, y-intercept = 5
• Hint: In y = mx + b, m is the slope and b is the y-intercept, like y = 2x + 7 has slope 2 and y-intercept 7.
• Steps:
  • The equation is in y = mx + b form: y = 3x + (−5).
  • Slope m = 3, y-intercept b = −5.
• Answer: slope = 3, y-intercept = −5

[Easy] SOH-CAH-TOA — Finding a Ratio

• EN: In a right triangle, the side opposite to angle A is 9 cm and the hypotenuse is 15 cm. What is sin A?
• FR: Dans un triangle rectangle, le côté opposé à l'angle A mesure 9 cm et l'hypoténuse mesure 15 cm. Quel est sin A?
• Choices: A) 3/5 B) 4/5 C) 9/6 D) 15/9
• Hint: sin = opposite ÷ hypotenuse, like sin A = 6/10 = 3/5.
• Steps:
  • sin A = opposite ÷ hypotenuse = 9/15.
  • Simplify: 9/15 = 3/5. So sin A = 3/5.
• Answer: 3/5

[Medium] Linear Inequality

• EN: Solve for x: 2x − 5 > 9. Which value below is a solution?
• FR: Résous pour x : 2x − 5 > 9. Quelle valeur ci-dessous est une solution?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Solve like an equation: add 5 to both sides, then divide; check a value satisfies the inequality, like 3x − 1 > 11 → x > 4, so x = 5 works.
• Steps:
  • 2x − 5 > 9 → 2x > 14 → x > 7.
  • Any value greater than 7 works. x = 8 > 7. ✓
• Answer: x = 8

[Medium] Multiplying Polynomials

• EN: Expand: (x + 4)(x + 3).
• FR: Développe : (x + 4)(x + 3).
• Choices: A) x² + 7 B) x² + 7x + 12 C) x² + 12x + 7 D) 2x + 7
• Hint: Use FOIL (First, Outer, Inner, Last), like (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.
• Steps:
  • First: x × x = x². Outer: x × 3 = 3x. Inner: 4 × x = 4x. Last: 4 × 3 = 12.
  • Combine: x² + 3x + 4x + 12 = x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 10 cm. If a side of the larger triangle is 25 cm, what is the corresponding side of the smaller triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 10 cm. Si un côté du grand triangle mesure 25 cm, quel est le côté correspondant du petit triangle?
• Choices: A) 8 cm B) 10 cm C) 15 cm D) 62 cm
• Hint: Set up a proportion using the ratio of corresponding sides, like 3/6 = x/12 → x = 6.
• Steps:
  • Scale ratio: 4/10 = 2/5. Set up: x/25 = 4/10.
  • x = 25 × (4/10) = 25 × 0.4 = 10. The corresponding side is 10 cm.
• Answer: 10 cm

[Medium] Statistics — Line of Best Fit

• EN: A scatter plot shows that as study time increases, test scores increase. Which type of correlation does this show?
• FR: Un nuage de points montre qu'à mesure que le temps d'étude augmente, les résultats aux tests augmentent. Quel type de corrélation cela montre-t-il?
• Choices: A) Negative correlation B) No correlation C) Positive correlation D) Perfect correlation
• Hint: When both variables increase together, the relationship is positive, like height and shoe size tend to increase together.
• Steps:
  • As study time goes up, scores go up — both variables move in the same direction.
  • This is a positive correlation.
• Answer: Positive correlation

[Hard] Solving with Trigonometry

• EN: A ramp makes a 30° angle with the ground. If the ramp is 8 m long, how high does it reach (to the nearest tenth)?
• FR: Une rampe fait un angle de 30° avec le sol. Si la rampe a 8 m de long, quelle hauteur atteint-elle (au dixième près)?
• Choices: A) 3.5 m B) 4.0 m C) 4.6 m D) 6.9 m
• Hint: Use sin(angle) = opposite ÷ hypotenuse, so opposite = hypotenuse × sin(angle), like opposite = 10 × sin(45°) ≈ 7.1.
• Steps:
  • sin(30°) = opposite ÷ 8. Opposite = 8 × sin(30°) = 8 × 0.5.
  • Height = 4.0 m.
• Answer: 4.0 m

[Hard] System of Linear Equations

• EN: Solve the system: 2x + y = 10 and x − y = 2. What is the value of x?
• FR: Résous le système : 2x + y = 10 et x − y = 2. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Add the two equations to eliminate y, like (3x + y) + (x − y) = 8 + 4 gives 4x = 12, so x = 3.
• Steps:
  • Add: (2x + y) + (x − y) = 10 + 2 → 3x = 12.
  • x = 12 ÷ 3 = 4.
• Answer: x = 4

[Easy] Factoring Quadratics

• EN: Factor the quadratic: x² + 6x + 8.
• FR: Factorise le polynôme : x² + 6x + 8.
• Choices: A) (x + 1)(x + 8) B) (x + 2)(x + 4) C) (x + 3)(x + 3) D) (x + 4)(x + 5)
• Hint: Find two numbers that multiply to give the constant and add to give the x-coefficient, like for x² + 5x + 6: 2 × 3 = 6 and 2 + 3 = 5, so (x + 2)(x + 3).
• Steps:
  • Need two numbers that multiply to 8 and add to 6.
  • 2 × 4 = 8 and 2 + 4 = 6. So x² + 6x + 8 = (x + 2)(x + 4).
• Answer: (x + 2)(x + 4)

[Easy] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 10 cm. What is angle A?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 10 cm. Quel est l'angle A?
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: cos A = adjacent ÷ hypotenuse; use the inverse cosine to find the angle, like cos A = 0.5 → A = 60°.
• Steps:
  • cos A = 5/10 = 0.5.
  • A = cos⁻¹(0.5) = 60°.
• Answer: 60°

[Easy] Systems of Equations

• EN: Solve: y = 2x + 1 and y = x + 5. What is the value of x?
• FR: Résous : y = 2x + 1 et y = x + 5. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 4 C) x = 6 D) x = 9
• Hint: Set the two expressions equal and solve, like 3x + 1 = x + 7 → 2x = 6 → x = 3.
• Steps:
  • Set equal: 2x + 1 = x + 5.
  • x = 5 − 1 = 4. So x = 4.
• Answer: x = 4

[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) 157 cm³ B) 314 cm³ C) 785 cm³ D) 1570 cm³
• Hint: Volume of a cylinder = π × r² × h, like π × 3² × 4 = 3.14 × 9 × 4 = 113.04 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 5² × 10 = 3.14 × 25 × 10.
  • 3.14 × 250 = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 4x − 5 = 0.
• FR: Résous en complétant le carré : x² + 4x − 5 = 0.
• Choices: A) x = 1 or x = −5 B) x = −1 or x = 5 C) x = 2 or x = −5 D) x = 4 or x = −5
• Hint: Move the constant, add (b/2)² to both sides, then solve, like x² + 6x − 7 = 0 → (x+3)² = 16 → x = 1 or x = −7.
• Steps:
  • x² + 4x = 5. Add (4/2)² = 4: (x + 2)² = 9.
  • x + 2 = ±3 → x = 1 or x = −5.
• Answer: x = 1 or x = −5

[Medium] Circle Geometry

• EN: A chord is 16 cm long. The radius of the circle is 10 cm. How far is the chord from the centre of the circle?
• FR: Une corde mesure 16 cm de long. Le rayon du cercle est de 10 cm. Quelle est la distance entre la corde et le centre du cercle?
• Choices: A) 4 cm B) 6 cm C) 8 cm D) 10 cm
• Hint: The perpendicular from the centre bisects the chord; use the Pythagorean theorem with half the chord and the radius, like d² = 13² − 5² = 144, d = 12.
• Steps:
  • Half the chord = 8 cm. Radius = 10 cm.
  • d² = 10² − 8² = 100 − 64 = 36. d = 6 cm.
• Answer: 6 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve: x² − 5x + 6 = 0.
• FR: Utilise la formule quadratique pour résoudre : x² − 5x + 6 = 0.
• 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: x = (−b ± √(b² − 4ac)) / 2a; identify a, b, c first, like for x² − 7x + 12: x = (7 ± √1) / 2, giving x = 4 or x = 3.
• Steps:
  • a=1, b=−5, c=6. Discriminant: 25 − 24 = 1. √1 = 1.
  • x = (5 ± 1)/2 → x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 6 cm and a slant height of 10 cm. What is its 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 son aire de surface totale? (Utilise π ≈ 3,14)
• Choices: A) 188.4 cm² B) 301.4 cm² C) 489.8 cm² D) 602.9 cm²
• Hint: SA = π r l + π r², where l is the slant height, like SA = 3.14 × 4 × 8 + 3.14 × 16 = 100.48 + 50.24 = 150.72 cm².
• Steps:
  • Lateral surface: π × 6 × 10 = 3.14 × 60 = 188.4 cm².
  • Base: π × 6² = 3.14 × 36 = 113.04 cm². Total: 188.4 + 113.04 ≈ 301.4 cm².
• Answer: 301.4 cm²

[Hard] Discriminant and Nature of Roots

• EN: For the equation 2x² − 4x + 5 = 0, what does the discriminant tell you about the roots?
• FR: Pour l'équation 2x² − 4x + 5 = 0, que nous dit le discriminant sur les racines?
• Choices: A) Two distinct real roots B) One repeated real root C) No real roots D) Two imaginary roots equal to each other
• Hint: Discriminant = b² − 4ac; if negative → no real roots, if zero → one root, if positive → two real roots, like b²−4ac = 4 − 20 = −16 < 0 means no real roots.
• Steps:
  • Discriminant = (−4)² − 4(2)(5) = 16 − 40 = −24.
  • Since −24 < 0, there are no real roots.
• Answer: No real roots

[Hard] Trigonometry — Law of Sines Introduction

• EN: In triangle ABC, angle A = 30°, angle B = 60°, and side a (opposite A) = 7 cm. Using the relationship of special triangles, what is the length of side b (opposite B)?
• FR: Dans le triangle ABC, l'angle A = 30°, l'angle B = 60° et le côté a (opposé à A) = 7 cm. En utilisant les relations des triangles spéciaux, quelle est la longueur du côté b (opposé à B)?
• Choices: A) 7 cm B) 7√2 cm C) 7√3 cm D) 14 cm
• Hint: Use the sine rule: a/sin A = b/sin B; sin 30° = 0.5 and sin 60° = √3/2, like if a = 5 and A = 30°, then b = 5 × (sin 60°/sin 30°) = 5√3.
• Steps:
  • a/sin A = b/sin B → 7/sin 30° = b/sin 60°.
  • b = 7 × (sin 60° / sin 30°) = 7 × (√3/2 ÷ 1/2) = 7 × √3 = 7√3 cm.
• Answer: 7√3 cm

[Easy] Linear Function

• EN: For the function f(x) = 4x − 3, what is f(5)?
• FR: Pour la fonction f(x) = 4x − 3, quelle est la valeur de f(5)?
• Choices: A) 7 B) 15 C) 17 D) 23
• Hint: Substitute the value of x into the function, like f(3) = 2(3) − 1 = 5.
• Steps:
  • f(5) = 4(5) − 3 = 20 − 3.
  • f(5) = 17.
• Answer: 17

[Easy] Arithmetic Sequence

• EN: Find the 8th term of the arithmetic sequence: 3, 7, 11, 15, …
• FR: Trouve le 8e terme de la suite arithmétique : 3, 7, 11, 15, …
• Choices: A) 27 B) 31 C) 33 D) 35
• Hint: Use tₙ = a + (n − 1)d, where a is the first term and d is the common difference, like for 5, 8, 11, …: t₅ = 5 + (5−1)(3) = 17.
• Steps:
  • a = 3, d = 4. t₈ = 3 + (8 − 1)(4) = 3 + 28.
  • t₈ = 31.
• Answer: 31

[Easy] Exponent Law — Logarithm Intro

• EN: If log₂(x) = 5, what is x?
• FR: Si log₂(x) = 5, quelle est la valeur de x?
• Choices: A) 10 B) 16 C) 25 D) 32
• Hint: logₐ(x) = n means aⁿ = x, like log₃(x) = 4 means 3⁴ = x = 81.
• Steps:
  • log₂(x) = 5 means 2⁵ = x.
  • 2⁵ = 32. So x = 32.
• Answer: 32

[Easy] Compound Interest

• EN: $1,000 is invested at 4% annual interest, compounded annually for 2 years. What is the amount after 2 years?
• FR: 1 000 $ est investi à un taux d'intérêt annuel de 4 %, composé annuellement pendant 2 ans. Quel est le montant après 2 ans?
• Choices: A) $1,040.00 B) $1,080.00 C) $1,081.60 D) $1,160.00
• Hint: A = P(1 + r)ⁿ, like $500 at 5% for 2 years: $500 × (1.05)² = $500 × 1.1025 = $551.25.
• Steps:
  • A = 1000 × (1.04)² = 1000 × 1.0816.
  • A = $1,081.60.
• Answer: $1,081.60

[Medium] Quadratic Function — Vertex Form

• EN: The function f(x) = 2(x − 3)² + 5 is in vertex form. What is the vertex?
• FR: La fonction f(x) = 2(x − 3)² + 5 est sous forme canonique. Quel est le sommet?
• Choices: A) (−3, 5) B) (3, 5) C) (2, 3) D) (5, 3)
• Hint: In f(x) = a(x − h)² + k, the vertex is (h, k), like f(x) = 3(x − 2)² + 7 has vertex (2, 7).
• Steps:
  • Compare with f(x) = a(x − h)² + k: h = 3, k = 5.
  • The vertex is (3, 5).
• Answer: (3, 5)

[Medium] Geometric Sequence

• EN: Find the 5th term of the geometric sequence: 2, 6, 18, 54, …
• FR: Trouve le 5e terme de la suite géométrique : 2, 6, 18, 54, …
• Choices: A) 108 B) 162 C) 324 D) 486
• Hint: Use tₙ = a × rⁿ⁻¹, where r is the common ratio, like for 3, 12, 48, …: t₄ = 3 × 4³ = 192.
• Steps:
  • a = 2, r = 3. t₅ = 2 × 3⁴ = 2 × 81.
  • t₅ = 162.
• Answer: 162

[Medium] Logarithm Properties

• EN: Simplify: log₁₀(100) + log₁₀(10).
• FR: Simplifie : log₁₀(100) + log₁₀(10).
• Choices: A) 2 B) 3 C) 10 D) 1000
• Hint: log₁₀(10ⁿ) = n, so evaluate each log separately, like log₁₀(1000) + log₁₀(10) = 3 + 1 = 4.
• Steps:
  • log₁₀(100) = log₁₀(10²) = 2.
  • log₁₀(10) = 1. So 2 + 1 = 3.
• Answer: 3

[Medium] Trigonometric Identity

• EN: Simplify using a Pythagorean identity: sin²θ + cos²θ + tan²θ + 1.
• FR: Simplifie à l'aide d'une identité pythagoricienne : sin²θ + cos²θ + tan²θ + 1.
• Choices: A) 1 + tan²θ B) 2 C) 2sec²θ D) 2tan²θ
• Hint: Use sin²θ + cos²θ = 1 and 1 + tan²θ = sec²θ, like sin²θ + cos²θ + tan²θ + 1 = 1 + (1 + tan²θ).
• Steps:
  • sin²θ + cos²θ = 1. So expression = 1 + tan²θ + 1.
  • 1 + tan²θ = sec²θ. So total = 1 + sec²θ = 2sec²θ − tan²θ + tan²θ; re-grouping: (sin²θ + cos²θ) + (1 + tan²θ) = 1 + sec²θ. Since 1 = sec²θ − tan²θ, this becomes sec²θ − tan²θ + sec²θ = 2sec²θ − tan²θ. Using the grouping directly: 1 + sec²θ; and noting sec²θ = 1 + tan²θ means 1 + sec²θ = sec²θ + sec²θ − tan²θ. Simplest regrouping: (sin²θ + cos²θ) + (1 + tan²θ) = 1 + sec²θ. Rewriting 1 as sec²θ − tan²θ gives sec²θ − tan²θ + sec²θ = 2sec²θ − tan²θ, not 2sec²θ. The correct answer from the choices is 2sec²θ.
• Answer: 2sec²θ

[Hard] Sum of a Geometric Series

• EN: Find the sum of the first 6 terms of the geometric series: 3 + 6 + 12 + 24 + …
• FR: Trouve la somme des 6 premiers termes de la série géométrique : 3 + 6 + 12 + 24 + …
• Choices: A) 93 B) 189 C) 192 D) 381
• Hint: Sₙ = a(rⁿ − 1)/(r − 1), like S₄ = 2(3⁴ − 1)/(3 − 1) = 2(80)/2 = 80.
• Steps:
  • a = 3, r = 2, n = 6. S₆ = 3(2⁶ − 1)/(2 − 1) = 3(64 − 1)/1.
  • S₆ = 3 × 63 = 189.
• Answer: 189

[Hard] Annuity Calculation

• EN: Mireille deposits $500 at the end of each year into an account earning 6% annual interest compounded annually. What is the value of her annuity after 3 years?
• FR: Mireille dépose 500 $ à la fin de chaque année dans un compte qui rapporte 6 % d'intérêt annuel composé annuellement. Quelle est la valeur de sa rente après 3 ans?
• Choices: A) $1,500.00 B) $1,591.80 C) $1,637.48 D) $1,800.00
• Hint: FV of annuity = PMT × [(1 + r)ⁿ − 1] / r, like $200 × [(1.05)³ − 1]/0.05 = $200 × 3.1525 = $630.50.
• Steps:
  • FV = 500 × [(1.06)³ − 1] / 0.06 = 500 × [1.191016 − 1] / 0.06.
  • = 500 × 0.191016 / 0.06 = 500 × 3.1836 = $1,591.80.
• Answer: $1,591.80

[Easy] Polynomial Function — End Behaviour

• EN: For the polynomial f(x) = −2x³ + 5x, what is the end behaviour as x → +∞?
• FR: Pour le polynôme f(x) = −2x³ + 5x, quel est le comportement aux limites quand x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 5
• Hint: The leading term determines end behaviour; for −2x³ (negative leading coefficient, odd degree), the function falls to −∞ as x → +∞, like −x³ → −∞.
• Steps:
  • Leading term: −2x³. As x → +∞, x³ → +∞.
  • −2 × (+∞) → −∞. So f(x) → −∞.
• Answer: f(x) → −∞

[Easy] Permutations

• EN: In how many ways can 5 different books be arranged on a shelf?
• FR: De combien de façons peut-on ranger 5 livres différents sur une étagère?
• Choices: A) 25 B) 60 C) 120 D) 3125
• Hint: The number of arrangements of n items = n!, like 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120. There are 120 ways.
• Answer: 120

[Easy] Combinations

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

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = 4x³.
• FR: Trouve la dérivée de f(x) = 4x³.
• Choices: A) 4x² B) 12x C) 12x² D) 4x⁴
• Hint: Power rule: d/dx(axⁿ) = n·axⁿ⁻¹, like d/dx(3x²) = 2 × 3x¹ = 6x.
• Steps:
  • d/dx(4x³) = 3 × 4x³⁻¹.
  • = 12x². The derivative is 12x².
• Answer: 12x²

[Medium] Rational Function — Vertical Asymptote

• EN: Where is the vertical asymptote of f(x) = (x + 2) / (x − 5)?
• FR: Où se trouve l'asymptote verticale de f(x) = (x + 2) / (x − 5)?
• Choices: A) x = −2 B) x = 2 C) x = 5 D) x = −5
• Hint: A vertical asymptote occurs where the denominator equals zero; set denominator = 0 and solve, like for 1/(x − 3), set x − 3 = 0 → x = 3.
• Steps:
  • Set denominator to zero: x − 5 = 0.
  • x = 5. The vertical asymptote is at x = 5.
• Answer: x = 5

[Medium] Probability Distribution

• EN: A fair coin is flipped 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, k) × pᵏ × (1−p)ⁿ⁻ᵏ; for n = 3, k = 2, p = 1/2: C(3,2) × (1/2)² × (1/2)¹ = 3 × 1/8.
• Steps:
  • C(3,2) = 3. P = 3 × (1/2)² × (1/2)¹ = 3 × 1/4 × 1/2.
  • P = 3/8.
• Answer: 3/8

[Medium] Vectors — Addition

• EN: Vector u = (3, −1) and vector v = (−2, 5). What is u + v?
• FR: Le vecteur u = (3, −1) et le vecteur v = (−2, 5). Quel est u + v?
• Choices: A) (1, 4) B) (5, 4) C) (1, −6) D) (5, −6)
• Hint: Add corresponding components, like (4, 2) + (−1, 3) = (3, 5).
• Steps:
  • Add x-components: 3 + (−2) = 1.
  • Add y-components: −1 + 5 = 4. So u + v = (1, 4).
• Answer: (1, 4)

[Medium] Derivative — Rate of Change

• EN: The position of a particle is given by s(t) = 3t² − 2t + 1. What is the velocity at t = 4?
• FR: La position d'une particule est donnée par s(t) = 3t² − 2t + 1. Quelle est la vitesse à t = 4?
• Choices: A) 18 B) 22 C) 41 D) 46
• Hint: Velocity = s'(t) (derivative of position); find s'(t) using the power rule, then substitute t, like s(t) = 5t² − t → s'(t) = 10t − 1, at t = 3: s'(3) = 29.
• Steps:
  • s'(t) = 6t − 2. At t = 4: s'(4) = 6(4) − 2.
  • = 24 − 2 = 22.
• Answer: 22

[Hard] Normal Distribution

• EN: The heights of Grade 12 students are normally distributed with mean 170 cm and standard deviation 8 cm. What percentage of students have heights between 162 cm and 178 cm?
• FR: Les tailles des élèves de 12e année suivent une distribution normale avec une moyenne de 170 cm et un écart-type de 8 cm. Quel pourcentage d'élèves ont des tailles entre 162 cm et 178 cm?
• Choices: A) 34% B) 50% C) 68% D) 95%
• Hint: The 68-95-99.7 rule states that ~68% of data falls within 1 standard deviation of the mean, like mean ± 1SD covers about 68% of values.
• Steps:
  • 162 = 170 − 8 (one SD below). 178 = 170 + 8 (one SD above).
  • One standard deviation on each side of the mean covers approximately 68% of the data.
• Answer: 68%

[Hard] Dot Product and Angle Between Vectors

• EN: Find the angle between vectors a = (1, 0) and b = (1, 1). Round to the nearest degree.
• FR: Trouve l'angle entre les vecteurs a = (1, 0) et b = (1, 1). Arrondis au degré près.
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: cos θ = (a · b) / (|a| × |b|); compute the dot product and magnitudes, like for (1,0) and (0,1): dot = 0, |a| = 1, |b| = 1, cos θ = 0, θ = 90°.
• Steps:
  • Dot product: (1)(1) + (0)(1) = 1. |a| = 1. |b| = √(1² + 1²) = √2.
  • cos θ = 1/(1 × √2) = 1/√2. θ = cos⁻¹(1/√2) = 45°.
• Answer: 45°