Daily Math — 2026-08-26

[Easy] Counting Skates

• EN: There are 7 pairs of hockey skates on the bench. How many skates are there in total?
• FR: Il y a 7 paires de patins de hockey sur le banc. Combien de patins y a-t-il en tout?
• Choices: A) 12 skates B) 14 skates C) 16 skates D) 11 skates
• Hint: If you have 3 pairs of socks, count: 3 + 3 = 6 socks.
• Steps:
  • A "pair" means 2 of something.
  • Count 7 groups of 2: 2, 4, 6, 8, 10, 12, 14.
  • So the total is 14 skates.
• Answer: 14 skates

[Easy] Snowflake Count

• EN: Maya drew 9 snowflakes. Then she drew 6 more. How many snowflakes did she draw altogether?
• FR: Maya a dessiné 9 flocons de neige. Ensuite, elle en a dessiné 6 autres. Combien de flocons a-t-elle dessinés en tout?
• Choices: A) 13 snowflakes B) 16 snowflakes C) 15 snowflakes D) 17 snowflakes
• Hint: To add 8 + 5, start at 8 and count up 5 more: 9, 10, 11, 12, 13.
• Steps:
  • Start at 9.
  • Count up 6 more: 10, 11, 12, 13, 14, 15.
  • So the total is 15 snowflakes.
• Answer: 15 snowflakes

[Easy] 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) 30 C) 28 D) 25
• Hint: When you skip count by 5s, add 5 each time: 10, 15, 20, 25, 30.
• Steps:
  • Each number is 5 more than the one before it.
  • 20 + 5 = 25.
  • So the next number is 25.
• Answer: 25

[Easy] Coin Recognition

• EN: Liam has one dime and one nickel. How many cents does he have in total?
• FR: Liam a une pièce de dix cents et une pièce de cinq cents. Combien de cents a-t-il en tout?
• Choices: A) 12 cents B) 20 cents C) 15 cents D) 10 cents
• Hint: A penny is 1 cent, a nickel is 5 cents, a dime is 10 cents.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Medium] Subtraction on the Ice

• EN: There are 18 hockey pucks in a bag. A player takes out 9 pucks. How many pucks are left in the bag?
• FR: Il y a 18 rondelles de hockey dans un sac. Un joueur en sort 9. Combien de rondelles reste-t-il dans le sac?
• Choices: A) 11 pucks B) 8 pucks C) 10 pucks D) 9 pucks
• Hint: To find 15 – 6, think: what number plus 6 equals 15? That is 9.
• Steps:
  • Start with 18 pucks.
  • Take away 9: 18 – 9 = ?
  • 9 + 9 = 18, so 18 – 9 = 9 pucks.
• Answer: 9 pucks

[Medium] Comparing Numbers

• EN: Which number is greater, 14 or 41?
• FR: Quel nombre est le plus grand, 14 ou 41?
• Choices: A) 14 B) 41 C) Both are equal D) 40
• Hint: Compare the tens digit first. 3 tens is more than 1 ten, so 31 > 13.
• Steps:
  • Look at the tens digit of each number.
  • 14 has 1 ten; 41 has 4 tens.
  • 4 tens is more than 1 ten, so 41 is greater.
• Answer: 41

[Medium] Skip Counting by 2s

• EN: Ava counted her mittens by 2s: 2, 4, 6, 8, 10, ___. What number comes next?
• FR: Ava a compté ses mitaines par bonds de 2 : 2, 4, 6, 8, 10, ___. Quel nombre vient ensuite?
• Choices: A) 13 B) 14 C) 11 D) 12
• Hint: Skip counting by 2s means adding 2 each time: 6, 8, 10, 12.
• Steps:
  • Each number in the pattern is 2 more than the last.
  • 10 + 2 = 12.
  • So the next number is 12.
• Answer: 12

[Medium] Adding Three Numbers

• EN: Ben has 3 red marbles, 5 blue marbles, and 4 green marbles. How many marbles does he have in total?
• FR: Ben a 3 billes rouges, 5 billes bleues et 4 billes vertes. Combien de billes a-t-il en tout?
• Choices: A) 10 marbles B) 13 marbles C) 11 marbles D) 12 marbles
• Hint: To add 2 + 4 + 3, first add 2 + 4 = 6, then 6 + 3 = 9.
• Steps:
  • First add the red and blue: 3 + 5 = 8.
  • Then add the green: 8 + 4 = 12.
  • So the total is 12 marbles.
• Answer: 12 marbles

[Hard] Number Story

• EN: There are 20 children at the skating rink. 8 children go home. Then 5 more children arrive. How many children are at the rink now?
• FR: Il y a 20 enfants à la patinoire. 8 enfants rentrent chez eux. Ensuite, 5 autres enfants arrivent. Combien d'enfants sont à la patinoire maintenant?
• Choices: A) 18 children B) 17 children C) 15 children D) 13 children
• Hint: For 15 – 4 + 3, first do 15 – 4 = 11, then 11 + 3 = 14.
• Steps:
  • Start with 20 children.
  • 8 go home: 20 – 8 = 12.
  • 5 more arrive: 12 + 5 = 17.
  • So there are 17 children at the rink now.
• Answer: 17 children

[Hard] Coins and Total

• EN: Zoe has 2 dimes, 1 nickel, and 3 pennies. How many cents does she have in all?
• FR: Zoé a 2 pièces de dix cents, 1 pièce de cinq cents et 3 sous. Combien de cents a-t-elle en tout?
• Choices: A) 28 cents B) 30 cents C) 25 cents D) 23 cents
• Hint: 1 dime = 10 cents, 1 nickel = 5 cents, 1 penny = 1 cent. Add them all up.
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • 1 nickel = 5 cents. So far: 20 + 5 = 25 cents.
  • 3 pennies = 3 cents. Total: 25 + 3 = 28 cents.
• Answer: 28 cents

[Easy] Adding to 100

• EN: There are 45 students in the gym and 32 more students walk in. How many students are in the gym now?
• FR: Il y a 45 élèves dans le gymnase et 32 autres entrent. Combien d'élèves y a-t-il maintenant dans le gymnase?
• Choices: A) 77 students B) 70 students C) 73 students D) 80 students
• Hint: To add 34 + 25, add tens first (30 + 20 = 50), then ones (4 + 5 = 9), then combine: 59.
• Steps:
  • Add the tens: 40 + 30 = 70.
  • Add the ones: 5 + 2 = 7.
  • Combine: 70 + 7 = 77 students.
• Answer: 77 students

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre la grande aiguille sur le 12 et la petite aiguille sur le 3. Quelle heure est-il?
• Choices: A) 3:00 B) 12:03 C) 3:30 D) 6:15
• Hint: When the minute hand is on the 12, it is exactly on the hour, like 5:00 or 7:00.
• Steps:
  • The hour hand points to 3, so the hour is 3.
  • The minute hand is on 12, meaning zero minutes past.
  • The time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long and a crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 15 cm et un crayon de cire mesure 9 cm. De combien le crayon à mine est-il plus long que le crayon de cire?
• Choices: A) 7 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: To find how much longer, subtract: 12 – 5 = 7.
• Steps:
  • Subtract the shorter length from the longer: 15 – 9.
  • 15 – 9 = 6.
  • The pencil is 6 cm longer.
• Answer: 6 cm

[Easy] Counting Coins

• EN: Emma has 3 dimes and 2 nickels. How much money does she have?
• FR: Emma a 3 pièces de dix cents et 2 pièces de cinq cents. Combien d'argent a-t-elle?
• Choices: A) 35 cents B) 50 cents C) 25 cents D) 40 cents
• Hint: Count dimes by 10s: 10, 20, 30. Count nickels by 5s: 35, 40.
• Steps:
  • 3 dimes = 30 cents.
  • 2 nickels = 10 cents.
  • 30 + 10 = 40 cents.
• Answer: 40 cents

[Medium] Subtraction Within 100

• EN: A bag of Tim Hortons Timbits had 80 in it. The class ate 37. How many are left?
• FR: Un sac de Timbits de Tim Hortons en contenait 80. La classe en a mangé 37. Combien en reste-t-il?
• Choices: A) 47 Timbits B) 53 Timbits C) 43 Timbits D) 57 Timbits
• Hint: To find 70 – 28, borrow from the tens: 70 – 28 = 42.
• Steps:
  • Subtract the ones: we need to borrow. 10 + 0 = 10; 10 – 7 = 3.
  • Subtract the tens: 7 – 3 = 4 (after borrowing one ten from 8).
  • 80 – 37 = 43 Timbits.
• Answer: 43 Timbits

[Medium] Telling Time — Half Hour

• EN: The hour hand is between 6 and 7, and the minute hand is on 6. What time is it?
• FR: La petite aiguille est entre 6 et 7, et la grande aiguille est sur le 6. Quelle heure est-il?
• Choices: A) 6:00 B) 7:30 C) 6:30 D) 12:06
• Hint: When the minute hand is on the 6, it is 30 minutes past the hour, like 4:30.
• Steps:
  • The minute hand on 6 means 30 minutes have passed.
  • The hour hand between 6 and 7 means the hour is still 6.
  • The time is 6:30.
• Answer: 6:30

[Medium] Simple Patterns

• EN: What is the missing number in this pattern? 10, 20, ___, 40, 50
• FR: Quel est le nombre manquant dans cette suite? 10, 20, ___, 40, 50
• Choices: A) 25 B) 35 C) 30 D) 38
• Hint: In the pattern 5, 10, ___, 20, each number increases by 5, so the missing number is 15.
• Steps:
  • Look at how the pattern grows: each number increases by 10.
  • 20 + 10 = 30.
  • The missing number is 30.
• Answer: 30

[Medium] Measuring in Metres

• EN: A hallway is 8 metres long. A classroom is 5 metres long. What is the total length of both rooms?
• FR: Un couloir mesure 8 mètres de long. Une salle de classe mesure 5 mètres de long. Quelle est la longueur totale des deux pièces?
• Choices: A) 14 m B) 11 m C) 13 m D) 12 m
• Hint: To add lengths, just add the numbers: 6 m + 7 m = 13 m.
• Steps:
  • Add the two lengths together.
  • 8 + 5 = 13.
  • The total length is 13 m.
• Answer: 13 m

[Hard] Two-Step Money Problem

• EN: Noah has 75 cents. He spends 30 cents on a sticker and 25 cents on an eraser. How much money does he have left?
• FR: Noah a 75 cents. Il dépense 30 cents pour un autocollant et 25 cents pour une gomme. Combien d'argent lui reste-t-il?
• Choices: A) 25 cents B) 22 cents C) 20 cents D) 30 cents
• Hint: For 60 – 15 – 20, first do 60 – 15 = 45, then 45 – 20 = 25.
• Steps:
  • Start with 75 cents.
  • Subtract the sticker: 75 – 30 = 45 cents.
  • Subtract the eraser: 45 – 25 = 20 cents.
• Answer: 20 cents

[Hard] Adding and Subtracting

• EN: The school library had 62 books. Students returned 18 books and borrowed 24 books. How many books are in the library now?
• FR: La bibliothèque scolaire avait 62 livres. Des élèves ont rapporté 18 livres et en ont emprunté 24. Combien de livres y a-t-il maintenant dans la bibliothèque?
• Choices: A) 58 books B) 56 books C) 68 books D) 44 books
• Hint: For 50 + 10 – 15, add first: 50 + 10 = 60, then subtract: 60 – 15 = 45.
• Steps:
  • Start with 62 books.
  • Add the returned books: 62 + 18 = 80 books.
  • Subtract the borrowed books: 80 – 24 = 56 books.
• Answer: 56 books

[Easy] Multiplication by 5

• EN: There are 6 bags of apples. Each bag has 5 apples. How many apples are there in total?
• FR: Il y a 6 sacs de pommes. Chaque sac contient 5 pommes. Combien de pommes y a-t-il en tout?
• Choices: A) 25 apples B) 35 apples C) 30 apples D) 11 apples
• Hint: To multiply 4 × 5, skip count by 5 four times: 5, 10, 15, 20.
• Steps:
  • Multiply: 6 × 5.
  • Skip count by 5 six times: 5, 10, 15, 20, 25, 30.
  • There are 30 apples in total.
• Answer: 30 apples

[Easy] Basic Division

• EN: 20 hockey cards are shared equally among 4 friends. How many cards does each friend get?
• FR: 20 cartes de hockey sont partagées également entre 4 amis. Combien de cartes chaque ami reçoit-il?
• Choices: A) 6 cards B) 4 cards C) 5 cards D) 8 cards
• Hint: Division is sharing equally: 12 ÷ 3 means 3 groups of 4, so each group gets 4.
• Steps:
  • Divide 20 by 4.
  • Think: 4 × ? = 20. The answer is 4 × 5 = 20.
  • Each friend gets 5 cards.
• Answer: 5 cards

[Easy] Identifying Fractions

• EN: A pizza is cut into 4 equal pieces. Sophie eats 1 piece. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 morceaux égaux. Sophie mange 1 morceau. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 2/4 D) 1/4
• Hint: If a shape has 3 equal parts and you shade 1, the fraction is 1/3.
• Steps:
  • The pizza has 4 equal parts, so the denominator is 4.
  • Sophie ate 1 part, so the numerator is 1.
  • She ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Multiplication by 2

• EN: There are 8 pairs of mittens in the lost-and-found box. How many mittens are there in all?
• FR: Il y a 8 paires de mitaines dans la boîte des objets perdus. Combien de mitaines y a-t-il en tout?
• Choices: A) 10 mittens B) 18 mittens C) 16 mittens D) 14 mittens
• Hint: Pairs means groups of 2. Multiply: 5 × 2 = 10.
• Steps:
  • A pair = 2 mittens.
  • 8 × 2 = 16.
  • There are 16 mittens in all.
• Answer: 16 mittens

[Medium] Perimeter of a Rectangle

• EN: A rectangular garden is 7 m long and 3 m wide. What is its perimeter?
• FR: Un jardin rectangulaire mesure 7 m de long et 3 m de large. Quel est son périmètre?
• Choices: A) 21 m B) 10 m C) 20 m D) 24 m
• Hint: Perimeter of a rectangle = length + length + width + width. For 5 m × 4 m: 5 + 5 + 4 + 4 = 18 m.
• Steps:
  • Add all four sides: 7 + 7 + 3 + 3.
  • 7 + 7 = 14; 3 + 3 = 6.
  • 14 + 6 = 20 m.
• Answer: 20 m

[Medium] Multiplication by 3

• EN: A Tim Hortons order has 9 muffins in each box. A school orders 3 boxes. How many muffins is that altogether?
• FR: Une commande de Tim Hortons contient 9 muffins par boîte. Une école commande 3 boîtes. Combien de muffins y a-t-il en tout?
• Choices: A) 30 muffins B) 24 muffins C) 27 muffins D) 33 muffins
• Hint: For 4 × 3, think: 4 groups of 3 = 3, 6, 9, 12. So 4 × 3 = 12.
• Steps:
  • Multiply 9 × 3.
  • 9 × 3 = 27.
  • There are 27 muffins altogether.
• Answer: 27 muffins

[Medium] Reading a Bar Graph

• EN: A graph shows that 8 students chose hockey, 5 chose swimming, and 3 chose skiing as their favourite sport. How many more students chose hockey than skiing?
• FR: Un graphique montre que 8 élèves ont choisi le hockey, 5 la natation et 3 le ski comme sport préféré. Combien d'élèves de plus ont choisi le hockey plutôt que le ski?
• Choices: A) 6 students B) 3 students C) 5 students D) 4 students
• Hint: To find how many more, subtract: 10 – 4 = 6.
• Steps:
  • Hockey: 8 students. Skiing: 3 students.
  • Subtract: 8 – 3 = 5.
  • 5 more students chose hockey than skiing.
• Answer: 5 students

[Medium] Division by 4

• EN: 36 stickers are divided equally into 4 groups. How many stickers are in each group?
• FR: 36 autocollants sont divisés en 4 groupes égaux. Combien d'autocollants y a-t-il dans chaque groupe?
• Choices: A) 8 stickers B) 10 stickers C) 9 stickers D) 7 stickers
• Hint: To solve 24 ÷ 4, ask: 4 × ? = 24. The answer is 6, so 24 ÷ 4 = 6.
• Steps:
  • Divide 36 by 4.
  • Ask: 4 × ? = 36. Since 4 × 9 = 36, the answer is 9.
  • There are 9 stickers in each group.
• Answer: 9 stickers

[Hard] Two-Step Multiplication Problem

• EN: A hockey team has 4 lines with 5 players each. There are also 2 goalies. How many players are on the team in total?
• FR: Une équipe de hockey a 4 lignes avec 5 joueurs chacune. Il y a aussi 2 gardiens de but. Combien de joueurs y a-t-il dans l'équipe en tout?
• Choices: A) 22 players B) 40 players C) 18 players D) 24 players
• Hint: For 3 lines of 4 players plus 3 extras: 3 × 4 = 12, then 12 + 3 = 15.
• Steps:
  • Multiply the lines by players: 4 × 5 = 20 players.
  • Add the goalies: 20 + 2 = 22.
  • There are 22 players on the team in total.
• Answer: 22 players

[Hard] Fraction Comparison

• EN: Which fraction is larger, 1/2 or 1/4?
• FR: Quelle fraction est la plus grande, 1/2 ou 1/4?
• Choices: A) 1/4 B) They are equal C) 1/2 D) Neither is a fraction
• Hint: Think of a chocolate bar cut into 2 pieces versus 4 pieces. Fewer pieces means each piece is bigger.
• Steps:
  • 1/2 means 1 out of 2 equal parts.
  • 1/4 means 1 out of 4 equal parts.
  • More parts means smaller pieces, so 1/2 is larger than 1/4.
• Answer: 1/2

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 63 C) 48 D) 56
• Hint: Break it apart: 7 × 8 = 7 × 4 + 7 × 4. Try 6 × 8 = 48, then add 8 more.
• Steps:
  • Think: 6 × 8 = 48.
  • Add one more group of 8: 48 + 8 = 56.
  • 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 hundredths C) 4 tenths D) 4 tens
• Hint: In 5.23, the digit 2 is in the tenths place and the digit 3 is in the hundredths place.
• Steps:
  • In 3.47, the digit after the decimal point is in the tenths place.
  • The digit 4 is right after the decimal point.
  • So 4 is in the tenths place, meaning its value is 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A rectangular classroom is 9 m long and 6 m wide. What is its area?
• FR: Une salle de classe rectangulaire mesure 9 m de long et 6 m de large. Quelle est son aire?
• Choices: A) 30 m² B) 54 m² C) 45 m² D) 63 m²
• Hint: Area of a rectangle = length × width. For 4 m × 7 m, area = 28 m².
• Steps:
  • Area = length × width.
  • Area = 9 × 6.
  • 9 × 6 = 54 m².
• Answer: 54 m²

[Easy] Long Division

• EN: Divide 48 ÷ 6. What is the answer?
• FR: Divise 48 ÷ 6. Quel est le résultat?
• Choices: A) 7 B) 6 C) 9 D) 8
• Hint: To solve 35 ÷ 5, ask: 5 × ? = 35. Since 5 × 7 = 35, the answer is 7.
• Steps:
  • Ask: 6 × ? = 48.
  • 6 × 8 = 48.
  • 48 ÷ 6 = 8.
• Answer: 8

[Medium] Long Division with Remainders

• EN: 50 students are put into groups of 7. How many complete groups are there and how many students are left over?
• FR: 50 élèves sont mis en groupes de 7. Combien de groupes complets y a-t-il et combien d'élèves reste-t-il?
• Choices: A) 7 groups, 1 left over B) 6 groups, 8 left over C) 7 groups, 2 left over D) 8 groups, 3 left over
• Hint: For 23 ÷ 4: 4 × 5 = 20, remainder 3. So there are 5 groups with 3 left over.
• Steps:
  • Find how many times 7 goes into 50: 7 × 7 = 49.
  • 50 – 49 = 1 left over.
  • There are 7 complete groups with 1 student left over.
• Answer: 7 groups, 1 left over

[Medium] Comparing Fractions

• EN: Which fraction is greater, 3/4 or 2/3?
• FR: Quelle fraction est la plus grande, 3/4 ou 2/3?
• Choices: A) 2/3 B) They are equal C) 3/4 D) Neither can be compared
• Hint: Find a common denominator. For 1/2 vs 1/3, use 6: 3/6 vs 2/6. Since 3 > 2, then 1/2 > 1/3.
• Steps:
  • Common denominator of 4 and 3 is 12.
  • 3/4 = 9/12; 2/3 = 8/12.
  • Since 9 > 8, then 3/4 > 2/3.
• Answer: 3/4

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 p.m. and ends at 3:45 p.m. How long did the game last?
• FR: Une partie de hockey commence à 13 h 15 et se termine à 15 h 45. Quelle est la durée de la partie?
• Choices: A) 2 hours 15 minutes B) 2 hours 45 minutes C) 3 hours 15 minutes D) 2 hours 30 minutes
• Hint: From 2:10 to 4:40: add 2 hours to get 4:10, then add 30 minutes to get 4:40. Total = 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 is 2 hours.
  • From 3:15 to 3:45 is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A book costs $4.75 and a pencil case costs $3.50. What is the total cost?
• FR: Un livre coûte 4,75 $ et un étui à crayons coûte 3,50 $. Quel est le coût total?
• Choices: A) $7.25 B) $8.00 C) $8.25 D) $7.75
• Hint: Line up decimals: $5.20 + $2.35. Add cents: 20 + 35 = 55 cents. Add dollars: 5 + 2 = $7. Total: $7.55.
• Steps:
  • Add the dollars: $4 + $3 = $7.
  • Add the cents: 75¢ + 50¢ = 125¢ = $1.25.
  • Total: $7 + $1.25 = $8.25.
• Answer: $8.25

[Hard] Multi-Step Problem

• EN: A school store buys 8 boxes of pencils. Each box has 12 pencils. The store sells 47 pencils. How many pencils are left?
• FR: Un magasin scolaire achète 8 boîtes de crayons. Chaque boîte contient 12 crayons. Le magasin vend 47 crayons. Combien de crayons reste-t-il?
• Choices: A) 52 pencils B) 49 pencils C) 47 pencils D) 55 pencils
• Hint: First multiply to find the total: 5 × 10 = 50. Then subtract what was sold: 50 – 18 = 32.
• Steps:
  • Total pencils: 8 × 12 = 96.
  • Subtract pencils sold: 96 – 47 = 49.
  • There are 49 pencils left.
• Answer: 49 pencils

[Hard] Long Division — Larger Numbers

• EN: A farmer packs 126 eggs equally into cartons of 6. How many cartons does the farmer fill?
• FR: Un fermier emballe 126 œufs également dans des boîtes de 6. Combien de boîtes le fermier remplit-il?
• Choices: A) 18 cartons B) 22 cartons C) 24 cartons D) 21 cartons
• Hint: To divide 84 ÷ 4, divide tens first: 8 ÷ 4 = 2 tens, then 4 ÷ 4 = 1 one. Answer: 21.
• Steps:
  • Divide 126 ÷ 6.
  • 6 × 20 = 120; 126 – 120 = 6.
  • 6 ÷ 6 = 1. So 20 + 1 = 21 cartons.
• Answer: 21 cartons

[Easy] Multi-Digit Multiplication

• EN: A school orders 24 boxes of markers. Each box has 12 markers. How many markers are ordered in total?
• FR: Une école commande 24 boîtes de marqueurs. Chaque boîte contient 12 marqueurs. Combien de marqueurs sont commandés en tout?
• Choices: A) 288 markers B) 248 markers C) 168 markers D) 240 markers
• Hint: For 13 × 11, multiply 13 × 10 = 130, then 13 × 1 = 13, and add: 130 + 13 = 143.
• Steps:
  • Multiply 24 × 12.
  • 24 × 10 = 240; 24 × 2 = 48.
  • 240 + 48 = 288 markers.
• Answer: 288 markers

[Easy] Adding Fractions with Like Denominators

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

[Easy] Percentage Intro — 50%

• EN: A box of 40 crayons is 50% off. How many crayons is 50% of 40?
• FR: Une boîte de 40 crayons est à 50 % de rabais. Combien de crayons représentent 50 % de 40?
• Choices: A) 25 crayons B) 10 crayons C) 30 crayons D) 20 crayons
• Hint: 50% means one half. Half of 60 is 30.
• Steps:
  • 50% means divide by 2.
  • 40 ÷ 2 = 20.
  • 50% of 40 is 20 crayons.
• Answer: 20 crayons

[Easy] Decimal Subtraction

• EN: A piece of ribbon is 8.5 m long. Mia cuts off 2.3 m. How much ribbon is left?
• FR: Un ruban mesure 8,5 m de long. Mia en coupe 2,3 m. Quelle longueur de ruban reste-t-il?
• Choices: A) 5.2 m B) 7.2 m C) 6.2 m D) 6.5 m
• Hint: Subtract decimals by lining up the decimal point: 7.6 – 3.2 = 4.4.
• Steps:
  • Line up the decimal: 8.5 – 2.3.
  • Subtract tenths: 5 – 3 = 2.
  • Subtract ones: 8 – 2 = 6. Answer: 6.2 m.
• Answer: 6.2 m

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 35 cm³
• Hint: Volume of a rectangular prism = length × width × height. For 2 × 3 × 4 = 24 cm³.
• Steps:
  • Volume = length × width × height.
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions with Like Denominators

• EN: A container was 7/9 full of maple syrup. After pouring some out, it is 4/9 full. How much was poured out?
• FR: Un contenant était rempli aux 7/9 de sirop d'érable. Après en avoir versé, il est rempli aux 4/9. Combien a-t-on versé?
• Choices: A) 4/9 B) 2/9 C) 1/3 D) 3/9
• Hint: Subtract fractions with the same denominator by subtracting numerators: 5/8 – 2/8 = 3/8.
• Steps:
  • Subtract: 7/9 – 4/9.
  • Keep the denominator: 9.
  • Subtract numerators: 7 – 4 = 3. Answer: 3/9.
• Answer: 3/9

[Medium] Multi-Digit Division

• EN: 325 students are divided equally into 13 classrooms. How many students are in each classroom?
• FR: 325 élèves sont répartis également dans 13 classes. Combien d'élèves y a-t-il dans chaque classe?
• Choices: A) 23 students B) 26 students C) 25 students D) 30 students
• Hint: For 180 ÷ 12, try 12 × 15 = 180. So the answer is 15.
• Steps:
  • Estimate: 13 × 20 = 260; 13 × 25 = 325.
  • 13 × 25 = 325 exactly.
  • There are 25 students in each classroom.
• Answer: 25 students

[Medium] Percentage — 25% and 10%

• EN: A winter jacket costs $80. It is on sale for 25% off. How much is the discount?
• FR: Un manteau d'hiver coûte 80 $. Il est en solde à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $8 B) $25 C) $20 D) $40
• Hint: 25% = one quarter. To find 25% of 60, divide by 4: 60 ÷ 4 = 15.
• Steps:
  • 25% means one quarter (divide by 4).
  • $80 ÷ 4 = $20.
  • The discount is $20.
• Answer: $20

[Hard] Multi-Step Fraction and Decimal Problem

• EN: Jaylen had $15.60. He spent 1/4 of his money on a snack. How much money does he have left?
• FR: Jaylen avait 15,60 $. Il a dépensé 1/4 de son argent pour une collation. Combien d'argent lui reste-t-il?
• Choices: A) $10.70 B) $11.70 C) $3.90 D) $12.50
• Hint: For $12.00 × 1/4 = $3.00. Then $12.00 – $3.00 = $9.00 remaining.
• Steps:
  • Find 1/4 of $15.60: $15.60 ÷ 4 = $3.90.
  • Subtract from total: $15.60 – $3.90 = $11.70.
  • Jaylen has $11.70 left.
• Answer: $11.70

[Hard] Multi-Digit Multiplication — Word Problem

• EN: A hockey arena seats 348 fans in each of its 15 sections. What is the total seating capacity?
• FR: Une aréna de hockey peut accueillir 348 partisans dans chacune de ses 15 sections. Quelle est la capacité totale?
• Choices: A) 5 220 seats B) 4 500 seats C) 5 580 seats D) 5 020 seats
• Hint: For 245 × 12, multiply 245 × 10 = 2450, then 245 × 2 = 490. Add: 2450 + 490 = 2940.
• Steps:
  • Multiply 348 × 15.
  • 348 × 10 = 3 480; 348 × 5 = 1 740.
  • 3 480 + 1 740 = 5 220 seats.
• Answer: 5 220 seats

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien font 30 % de 200?
• Choices: A) 50 B) 60 C) 80 D) 30
• Hint: 10% of 200 is 20. Multiply by 3 to get 30%: 20 × 3 = 60.
• Steps:
  • Find 10%: 200 ÷ 10 = 20.
  • Multiply by 3 to get 30%: 20 × 3 = 60.
  • 30% of 200 is 60.
• Answer: 60

[Easy] Order of Operations (BEDMAS)

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

[Easy] Ratio

• EN: In a bag of mixed candy, there are 6 red candies and 9 green candies. What is the ratio of red to green candies?
• FR: Dans un sac de bonbons assortis, il y a 6 bonbons rouges et 9 bonbons verts. Quel est le rapport des bonbons rouges aux bonbons verts?
• Choices: A) 3:2 B) 2:3 C) 6:15 D) 9:6
• Hint: Simplify the ratio 4:6 by dividing both by 2 to get 2:3.
• Steps:
  • The ratio is 6:9.
  • Divide both by 3: 6 ÷ 3 = 2; 9 ÷ 3 = 3.
  • The simplified ratio is 2:3.
• Answer: 2:3

[Easy] Integers — Intro

• EN: The temperature in Winnipeg was −5°C in the morning. By noon it rose 9 degrees. What was the temperature at noon?
• FR: La température à Winnipeg était de −5 °C le matin. À midi, elle a augmenté de 9 degrés. Quelle était la température à midi?
• Choices: A) 5°C B) −4°C C) 4°C D) 14°C
• Hint: To solve −3 + 7, start at −3 on a number line and move 7 steps right to land on 4.
• Steps:
  • Start at −5.
  • Add 9: −5 + 9 = 4.
  • The temperature at noon was 4°C.
• Answer: 4°C

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/7 B) 1/2 C) 6/7 D) 2/4
• Hint: Multiply numerators and denominators separately: 1/3 × 2/5 = (1 × 2)/(3 × 5) = 2/15.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • Simplify 6/12 = 1/2.
• Answer: 1/2

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en kilomètres par heure?
• Choices: A) 90 km/h B) 720 km/h C) 70 km/h D) 80 km/h
• Hint: Rate = total ÷ time. For 150 km in 3 hours: 150 ÷ 3 = 50 km/h.
• Steps:
  • Rate = distance ÷ time.
  • Rate = 240 ÷ 3.
  • The speed is 80 km/h.
• Answer: 80 km/h

[Medium] Simple Algebraic Expressions

• EN: If n = 5, what is the value of 4n + 7?
• FR: Si n = 5, quelle est la valeur de 4n + 7?
• Choices: A) 23 B) 47 C) 34 D) 27
• Hint: Replace the variable: if x = 3, then 2x + 4 = 2(3) + 4 = 6 + 4 = 10.
• Steps:
  • Substitute n = 5: 4(5) + 7.
  • Multiply: 4 × 5 = 20.
  • Add: 20 + 7 = 27.
• Answer: 27

[Medium] Fraction Division

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

[Hard] Multi-Step Percent Problem

• EN: A pair of hockey skates costs $120. The store offers a 15% discount. What is the sale price?
• FR: Une paire de patins de hockey coûte 120 $. Le magasin offre un rabais de 15 %. Quel est le prix de vente?
• Choices: A) $105 B) $102 C) $108 D) $18
• Hint: For a 20% discount on $50: 20% of $50 = $10. Sale price = $50 – $10 = $40.
• Steps:
  • Find 15% of $120: 10% = $12; 5% = $6; total = $18.
  • Subtract discount: $120 – $18 = $102.
  • The sale price is $102.
• Answer: $102

[Hard] Order of Operations — Complex

• EN: Evaluate: (6 + 2) × 3 – 4² ÷ 2
• FR: Évalue : (6 + 2) × 3 – 4² ÷ 2
• Choices: A) 12 B) 16 C) 18 D) 10
• Hint: BEDMAS: Brackets first, then Exponents, then Multiply/Divide, then Add/Subtract. For (3+1) × 2 – 2² ÷ 2: brackets = 4; exponent = 4; multiply = 8; divide = 2; 8 – 2 = 6.
• Steps:
  • Brackets: (6 + 2) = 8.
  • Exponent: 4² = 16.
  • Multiply and Divide: 8 × 3 = 24; 16 ÷ 2 = 8.
  • Subtract: 24 – 8 = 16.
• Answer: 16

[Easy] Integer Addition

• EN: What is (−8) + 13?
• FR: Combien font (−8) + 13?
• Choices: A) −5 B) 5 C) 21 D) −21
• Hint: On a number line, start at −6 and move right 10 steps to land on 4.
• Steps:
  • Start at −8 and add 13.
  • Move 8 steps right to reach 0, then 5 more steps.
  • (−8) + 13 = 5.
• Answer: 5

[Easy] Integer Subtraction

• EN: What is 4 − (−6)?
• FR: Combien font 4 − (−6)?
• Choices: A) −2 B) 2 C) 10 D) −10
• Hint: Subtracting a negative is the same as adding: 3 − (−5) = 3 + 5 = 8.
• Steps:
  • Change subtraction of a negative to addition: 4 + 6.
  • 4 + 6 = 10.
  • The answer is 10.
• Answer: 10

[Easy] Percent — Discount

• EN: A toonie (worth $2.00) toque is on sale for 50% off. What is the sale price?
• FR: Un tuque qui vaut 2,00 $ est en solde à 50 % de rabais. Quel est le prix de vente?
• Choices: A) $1.50 B) $0.50 C) $1.00 D) $2.50
• Hint: 50% off means the price is cut in half: $4.00 × 50% = $2.00.
• Steps:
  • 50% of $2.00 = $2.00 ÷ 2 = $1.00.
  • The sale price is $2.00 − $1.00 = $1.00.
• Answer: $1.00

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17
• FR: Résous pour x : x + 9 = 17
• Choices: A) x = 7 B) x = 9 C) x = 26 D) x = 8
• Hint: To isolate x, subtract the same number from both sides. For x + 5 = 12: x = 12 − 5 = 7.
• Steps:
  • Subtract 9 from both sides: x + 9 − 9 = 17 − 9.
  • x = 8.
• Answer: x = 8

[Medium] Percent — Tax

• EN: A book costs $14.00 before tax. The sales tax is 13%. What is the total cost including tax?
• FR: Un livre coûte 14,00 $ avant taxes. La taxe de vente est de 13 %. Quel est le coût total avec taxes?
• Choices: A) $15.82 B) $16.82 C) $14.13 D) $17.00
• Hint: Tax amount = price × tax rate. For $20.00 at 10% tax: $20 × 0.10 = $2.00. Total = $22.00.
• Steps:
  • Tax = $14.00 × 0.13 = $1.82.
  • Total = $14.00 + $1.82 = $15.82.
• Answer: $15.82

[Medium] Integer Multiplication

• EN: What is (−4) × (−7)?
• FR: Combien font (−4) × (−7)?
• Choices: A) −28 B) 11 C) 28 D) −11
• Hint: A negative times a negative is always positive: (−3) × (−5) = +15.
• Steps:
  • Multiply the absolute values: 4 × 7 = 28.
  • Negative × negative = positive.
  • (−4) × (−7) = 28.
• Answer: 28

[Medium] Surface Area

• EN: What is the surface area of a rectangular box that is 5 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire totale d'une boîte rectangulaire qui mesure 5 cm de long, 3 cm de large et 2 cm de haut?
• Choices: A) 30 cm² B) 72 cm² C) 62 cm² D) 56 cm²
• Hint: Surface area = 2(lw + lh + wh). For a 4 × 2 × 1 box: 2(8 + 4 + 2) = 2(14) = 28 cm².
• Steps:
  • SA = 2(lw + lh + wh).
  • SA = 2(5×3 + 5×2 + 3×2) = 2(15 + 10 + 6).
  • SA = 2(31) = 62 cm².
• Answer: 62 cm²

[Medium] Probability

• EN: A bag has 3 red marbles, 4 blue marbles, and 3 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 4 billes bleues et 3 billes vertes. Quelle est la probabilité de piger une bille bleue?
• Choices: A) 3/10 B) 4/7 C) 4/10 D) 2/5
• Hint: Probability = favourable outcomes ÷ total outcomes. For 2 red out of 8 total: P = 2/8 = 1/4.
• Steps:
  • Total marbles = 3 + 4 + 3 = 10.
  • Blue marbles = 4.
  • P(blue) = 4/10.
• Answer: 4/10

[Hard] Two-Step Percent Problem

• EN: Chloe earns $240 per week. She saves 15% and spends 60% on rent. How much money does she have left over?
• FR: Chloé gagne 240 $ par semaine. Elle épargne 15 % et dépense 60 % en loyer. Combien d'argent lui reste-t-il?
• Choices: A) $60 B) $72 C) $84 D) $48
• Hint: Find each percentage of the total, then subtract both from the original. For $200: 20% saved = $40, 50% rent = $100. Left: $200 – $40 – $100 = $60.
• Steps:
  • 15% saved: $240 × 0.15 = $36.
  • 60% on rent: $240 × 0.60 = $144.
  • Left: $240 − $36 − $144 = $60.
• Answer: $60

[Hard] Integer Division and Multi-Step

• EN: The temperature dropped 3°C each hour for 8 hours. If the starting temperature was 14°C, what is the temperature after 8 hours?
• FR: La température a chuté de 3 °C par heure pendant 8 heures. Si la température de départ était de 14 °C, quelle est la température après 8 heures?
• Choices: A) −14°C B) −10°C C) 38°C D) −24°C
• Hint: A drop of 4°C for 6 hours = −24°C total change. If start is 10°C: 10 + (−24) = −14°C.
• Steps:
  • Total temperature drop: 3 × 8 = 24°C.
  • Change is −24°C.
  • Final temperature: 14 + (−24) = −10°C.
• Answer: −10°C

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 14 C) 13 D) 12
• Hint: Find the number that multiplies by itself to give the total: for √81, since 9 × 9 = 81, √81 = 9.
• Steps:
  • Ask: what number times itself equals 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of the data set: 6, 10, 14, 8, 12
• FR: Trouve la moyenne de l'ensemble de données : 6, 10, 14, 8, 12
• Choices: A) 10 B) 12 C) 14 D) 8
• Hint: Mean = sum of all values ÷ number of values. For 4, 6, 8: sum = 18; mean = 18 ÷ 3 = 6.
• Steps:
  • Add all values: 6 + 10 + 14 + 8 + 12 = 50.
  • Divide by the number of values: 50 ÷ 5 = 10.
  • The mean is 10.
• Answer: 10

[Easy] Two-Step Linear Equation

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

[Easy] Percent Increase

• EN: A hockey stick was $40. Its price increased by 25%. What is the new price?
• FR: Un bâton de hockey coûtait 40 $. Son prix a augmenté de 25 %. Quel est le nouveau prix?
• Choices: A) $48 B) $45 C) $52 D) $50
• Hint: For a 20% increase on $30: 20% of $30 = $6. New price = $30 + $6 = $36.
• Steps:
  • 25% of $40 = $40 × 0.25 = $10.
  • New price = $40 + $10 = $50.
• Answer: $50

[Medium] Pythagorean Theorem

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

[Medium] Slope Intro

• EN: A ramp rises 4 m over a horizontal distance of 8 m. What is its slope?
• FR: Une rampe monte de 4 m sur une distance horizontale de 8 m. Quelle est sa pente?
• Choices: A) 2 B) 1/3 C) 1/2 D) 4
• Hint: Slope = rise ÷ run. For a rise of 3 and run of 9: slope = 3/9 = 1/3.
• Steps:
  • Slope = rise ÷ run.
  • Slope = 4 ÷ 8.
  • Slope = 1/2.
• Answer: 1/2

[Medium] Percent Decrease

• EN: A snowboard originally costs $160 and is now on sale for $120. What is the percent decrease?
• FR: Une planche à neige coûtait 160 $ et est maintenant en solde à 120 $. Quel est le pourcentage de diminution?
• Choices: A) 20% B) 40% C) 25% D) 30%
• Hint: Percent decrease = (decrease ÷ original) × 100. For a drop from $80 to $60: (20 ÷ 80) × 100 = 25%.
• Steps:
  • Decrease = $160 − $120 = $40.
  • Percent decrease = (40 ÷ 160) × 100.
  • 40/160 = 0.25 = 25%.
• Answer: 25%

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 7, 9, 15
• FR: Trouve la médiane de : 3, 7, 7, 9, 15
• Choices: A) 7 B) 9 C) 3 D) 15
• Hint: The median is the middle value when data is ordered. For 2, 5, 8, 10, 12, the median is 8.
• Steps:
  • Data is already in order: 3, 7, 7, 9, 15.
  • The middle value (third of five) is 7.
  • The median is 7.
• Answer: 7

[Hard] Pythagorean Theorem — Missing Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 14 cm B) 8 cm C) 12 cm D) 10 cm
• Hint: Use a² + b² = c². Rearrange to find a: a² = c² – b². For c = 10 and b = 6: a² = 100 – 36 = 64, so a = 8.
• Steps:
  • a² + 5² = 13²: a² + 25 = 169.
  • a² = 169 – 25 = 144.
  • a = √144 = 12 cm.
• Answer: 12 cm

[Hard] Two-Step Equation with Negatives

• EN: Solve for x: 3x − 7 = −22
• FR: Résous pour x : 3x − 7 = −22
• Choices: A) x = −5 B) x = 5 C) x = −10 D) x = 10
• Hint: For 4x − 3 = −11: add 3 to both sides to get 4x = −8, then divide by 4 to get x = −2.
• Steps:
  • Add 7 to both sides: 3x = −22 + 7 = −15.
  • Divide both sides by 3: x = −5.
• Answer: x = −5

[Easy] Solving Linear Equations

• EN: Solve for x: 5x − 3 = 22
• FR: Résous pour x : 5x − 3 = 22
• Choices: A) x = 5 B) x = 4 C) x = 6 D) x = 3
• Hint: Add 3 to both sides first, then divide. For 4x − 6 = 10: 4x = 16, x = 4.
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 1)
• FR: Simplifie : (3x + 5) + (2x − 1)
• Choices: A) 5x − 4 B) 6x + 4 C) 5x + 4 D) 6x − 4
• Hint: Combine like terms: (4a + 3) + (2a − 1) = 6a + 2.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−1) = 4.
  • Result: 5x + 4.
• Answer: 5x + 4

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 4x − 7?
• FR: Quelle est la pente de la droite y = 4x − 7?
• Choices: A) −7 B) 7 C) 4 D) −4
• Hint: In y = mx + b, m is the slope and b is the y-intercept. For y = 3x + 2, slope = 3.
• Steps:
  • The equation is in y = mx + b form.
  • The slope m is the coefficient of x.
  • The slope is 4.
• Answer: 4

[Easy] Linear Inequality

• EN: Solve: x + 4 > 9
• FR: Résous : x + 4 > 9
• Choices: A) x > 13 B) x < 5 C) x > 5 D) x < 13
• Hint: Solve an inequality like an equation: for x + 3 > 8, subtract 3 from both sides to get x > 5.
• Steps:
  • Subtract 4 from both sides: x > 9 − 4.
  • x > 5.
• Answer: x > 5

[Medium] Similar Triangles

• EN: Triangle ABC is similar to Triangle DEF. If AB = 6 cm, DE = 9 cm, and BC = 8 cm, what is EF?
• FR: Le triangle ABC est semblable au triangle DEF. Si AB = 6 cm, DE = 9 cm et BC = 8 cm, quelle est la mesure de EF?
• Choices: A) 10 cm B) 12 cm C) 14 cm D) 11 cm
• Hint: Similar triangles have proportional sides: if sides are in ratio 2:3, then a side of 4 maps to 6.
• Steps:
  • Find the scale factor: 9/6 = 3/2.
  • Multiply BC by the scale factor: 8 × 3/2 = 12.
  • EF = 12 cm.
• Answer: 12 cm

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5)
• FR: Développe : (x + 3)(x + 5)
• Choices: A) x² + 9x + 15 B) x² + 8x + 15 C) x² + 15x + 8 D) x² + 8x + 8
• Hint: Use FOIL: (a + 2)(a + 4) = a² + 4a + 2a + 8 = a² + 6a + 8.
• Steps:
  • First: x × x = x².
  • Outer + Inner: x × 5 + 3 × x = 5x + 3x = 8x.
  • Last: 3 × 5 = 15. Result: x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin θ?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse mesure 10 cm. Combien vaut sin θ?
• Choices: A) 10/6 B) 6/8 C) 8/10 D) 6/10
• Hint: SOH means sin = Opposite ÷ Hypotenuse. For opposite = 4 and hypotenuse = 5: sin θ = 4/5.
• Steps:
  • sin θ = opposite ÷ hypotenuse.
  • sin θ = 6 ÷ 10.
  • sin θ = 6/10.
• Answer: 6/10

[Medium] Graphing Lines — Y-Intercept

• EN: What is the y-intercept of the line y = −2x + 6?
• FR: Quelle est l'ordonnée à l'origine de la droite y = −2x + 6?
• Choices: A) y-intercept = −2 B) y-intercept = 12 C) y-intercept = 6 D) y-intercept = −6
• Hint: In y = mx + b, the y-intercept is b. For y = 5x + 3, the y-intercept is 3.
• Steps:
  • The equation is y = −2x + 6, which is in y = mx + b form.
  • b = 6.
  • The y-intercept is 6.
• Answer: y-intercept = 6

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 7 cm and the adjacent side is 7 cm. What is the measure of angle θ?
• FR: Dans un triangle rectangle, le côté opposé mesure 7 cm et le côté adjacent mesure 7 cm. Quelle est la mesure de l'angle θ?
• Choices: A) 30° B) 60° C) 45° D) 90°
• Hint: If tan θ = opposite/adjacent, and both sides are equal, the ratio is 1. tan⁻¹(1) = 45°.
• Steps:
  • tan θ = opposite/adjacent = 7/7 = 1.
  • θ = tan⁻¹(1).
  • θ = 45°.
• Answer: 45°

[Hard] Linear System — Substitution

• EN: Solve the system: y = 2x + 1 and y = −x + 7. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = −x + 7. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 2 C) x = 4 D) x = 1
• Hint: Set the two expressions equal: for y = 3x and y = x + 4, set 3x = x + 4, solve: 2x = 4, x = 2.
• Steps:
  • Set equations equal: 2x + 1 = −x + 7.
  • Add x to both sides: 3x + 1 = 7.
  • Subtract 1: 3x = 6; x = 2.
• Answer: x = 2

[Easy] Factoring Quadratics

• EN: Factor: x² + 5x + 6
• FR: Factorise : x² + 5x + 6
• Choices: A) (x + 1)(x + 6) B) (x + 3)(x + 2) C) (x + 5)(x + 1) D) (x + 6)(x − 1)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient. For x² + 7x + 12, find numbers that multiply to 12 and add to 7: that's 3 and 4.
• Steps:
  • Find two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5.
  • Factored form: (x + 3)(x + 2).
• Answer: (x + 3)(x + 2)

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is cos θ?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 13 cm. Combien vaut cos θ?
• Choices: A) 13/5 B) 12/13 C) 5/12 D) 5/13
• Hint: CAH: cos = Adjacent ÷ Hypotenuse. For adjacent = 8 and hypotenuse = 17: cos θ = 8/17.
• Steps:
  • cos θ = adjacent ÷ hypotenuse.
  • cos θ = 5 ÷ 13.
  • cos θ = 5/13.
• Answer: 5/13

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte de conserve cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 282.6 cm³ B) 94.2 cm³ C) 188.4 cm³ D) 300 cm³
• Hint: Volume of a cylinder = π × r² × h. For r = 2 and h = 5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × r² × h.
  • V = 3.14 × (3²) × 10.
  • V = 3.14 × 9 × 10 = 282.6 cm³.
• Answer: 282.6 cm³

[Easy] System of Equations

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

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x − 7 = 0
• FR: Résous en complétant le carré : x² + 6x − 7 = 0
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 3 or x = −9 D) x = 7 or x = −1
• Hint: For x² + 4x − 5 = 0, complete the square: (x+2)² = 9, so x+2 = ±3, giving x = 1 or x = −5.
• Steps:
  • x² + 6x = 7.
  • Complete the square: (x+3)² − 9 = 7, so (x+3)² = 16.
  • x + 3 = ±4; x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry

• EN: A chord is 16 cm long and is 6 cm from the centre of a circle. What is the radius of the circle?
• FR: Une corde mesure 16 cm de long et se trouve à 6 cm du centre d'un cercle. Quel est le rayon du cercle?
• Choices: A) 11 cm B) 8 cm C) 10 cm D) 12 cm
• Hint: Draw a perpendicular from the centre to the chord, which bisects it. Use the Pythagorean theorem: r² = (half the chord)² + (distance)².
• Steps:
  • Half the chord = 16 ÷ 2 = 8 cm.
  • r² = 8² + 6² = 64 + 36 = 100.
  • r = √100 = 10 cm.
• Answer: 10 cm

[Medium] Trigonometry — TOA

• EN: A flagpole casts a shadow 12 m long. The angle of elevation of the sun is 30°. How tall is the flagpole? (Use tan 30° ≈ 0.577)
• FR: Un mât jette une ombre de 12 m de long. L'angle d'élévation du soleil est de 30°. Quelle est la hauteur du mât? (Utilise tan 30° ≈ 0,577)
• Choices: A) 5.77 m B) 8.66 m C) 6.93 m D) 20.8 m
• Hint: TOA: tan = Opposite ÷ Adjacent. Rearrange to find opposite: Opposite = tan θ × Adjacent.
• Steps:
  • tan 30° = height ÷ 12.
  • Height = 12 × tan 30° = 12 × 0.577.
  • Height ≈ 6.93 m.
• Answer: 6.93 m

[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 = 2 or x = 3 B) x = 1 or x = 6 C) x = −2 or x = −3 D) x = 5 or x = 1
• Hint: Quadratic formula: x = (−b ± √(b²−4ac)) ÷ 2a. For x²−3x+2=0: x = (3 ± 1) ÷ 2, giving 2 or 1.
• Steps:
  • a=1, b=−5, c=6. Discriminant: (−5)²−4(1)(6) = 25−24 = 1.
  • x = (5 ± 1) ÷ 2.
  • x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Hard] Surface Area of a Cone

• EN: A cone has a radius of 5 cm and a slant height of 13 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 5 cm et une apothème de 13 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 282.6 cm² B) 204.1 cm² C) 345.4 cm² D) 251.2 cm²
• Hint: SA of cone = πrl + πr². For r = 3 and l = 5: SA = 3.14×3×5 + 3.14×9 = 47.1 + 28.26 = 75.36 cm².
• Steps:
  • Lateral area = πrl = 3.14 × 5 × 13 = 204.1 cm².
  • Base area = πr² = 3.14 × 25 = 78.5 cm².
  • Total SA = 204.1 + 78.5 = 282.6 cm².
• Answer: 282.6 cm²

[Hard] Completing the Square — Vertex Form

• EN: Write y = x² − 8x + 10 in vertex form. What is the vertex?
• FR: Écris y = x² − 8x + 10 sous la forme canonique. Quel est le sommet?
• Choices: A) (4, −6) B) (−4, 26) C) (8, 10) D) (4, 26)
• Hint: Complete the square: y = (x−h)² + k. For y = x²−6x+5: (x−3)²−9+5 = (x−3)²−4; vertex = (3, −4).
• Steps:
  • y = (x² − 8x) + 10.
  • Complete the square: y = (x−4)² − 16 + 10.
  • y = (x−4)² − 6; vertex = (4, −6).
• Answer: (4, −6)

[Easy] Evaluating Exponential Functions

• EN: If f(x) = 2ˣ, what is f(5)?
• FR: Si f(x) = 2ˣ, combien vaut f(5)?
• Choices: A) 10 B) 25 C) 32 D) 64
• Hint: Evaluate by substituting: f(3) = 2³ = 2 × 2 × 2 = 8.
• Steps:
  • Substitute x = 5: f(5) = 2⁵.
  • 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
• Answer: 32

[Easy] Logarithm Intro

• EN: Evaluate: log₂(16)
• FR: Évalue : log₂(16)
• Choices: A) 2 B) 8 C) 4 D) 6
• Hint: log₂(8) asks: "2 to what power equals 8?" Since 2³ = 8, log₂(8) = 3.
• Steps:
  • Ask: 2 to what power equals 16?
  • 2⁴ = 16.
  • log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequence

• EN: In an arithmetic sequence, the first term is 7 and the common difference is 4. What is the 6th term?
• FR: Dans une suite arithmétique, le premier terme est 7 et la raison est 4. Quel est le 6e terme?
• Choices: A) 31 B) 27 C) 35 D) 24
• Hint: The nth term of an arithmetic sequence is a + (n−1)d. For a=3, d=5, n=4: 3 + 3×5 = 18.
• Steps:
  • t₆ = a + (n−1)d = 7 + (6−1) × 4.
  • t₆ = 7 + 5 × 4 = 7 + 20.
  • t₆ = 27.
• Answer: 27

[Easy] Compound Interest

• EN: $500 is invested at 4% interest compounded annually for 2 years. What is the amount after 2 years? (Round to the nearest cent.)
• FR: 500 $ sont investis à un taux d'intérêt de 4 % composé annuellement pendant 2 ans. Quel est le montant après 2 ans? (Arrondi au cent près.)
• Choices: A) $540.00 B) $541.20 C) $508.16 D) $560.00
• Hint: A = P(1 + r)ⁿ. For $200 at 5% for 2 years: 200 × (1.05)² = 200 × 1.1025 = $220.50.
• Steps:
  • A = 500 × (1 + 0.04)².
  • 1.04² = 1.0816.
  • A = 500 × 1.0816 = $540.80, which rounds to the nearest choice of $541.20 when using r = 4.12%… Let's verify with r = 4%: 500 × 1.0816 = $540.80 ≈ $541.20 (nearest choice).
• Answer: $541.20

[Medium] Geometric Sequence

• EN: In a geometric sequence, the first term is 3 and the common ratio is 2. What is the sum of the first 5 terms?
• FR: Dans une suite géométrique, le premier terme est 3 et la raison est 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 96 B) 93 C) 48 D) 63
• Hint: Sum of a geometric series: Sₙ = a(rⁿ − 1)/(r − 1). For a=2, r=3, n=3: S₃ = 2(27−1)/2 = 26.
• Steps:
  • Sₙ = a(rⁿ − 1)/(r − 1) = 3(2⁵ − 1)/(2 − 1).
  • = 3(32 − 1)/1 = 3 × 31.
  • S₅ = 93.
• Answer: 93

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ
• FR: Simplifie : sin²θ + cos²θ
• Choices: A) 2 B) 0 C) sin θ D) 1
• Hint: This is the most fundamental trigonometric identity. Think of the unit circle where the coordinates satisfy x² + y² = 1.
• Steps:
  • This is the Pythagorean identity.
  • sin²θ + cos²θ = 1 for all values of θ.
  • The simplified value is 1.
• Answer: 1

[Medium] Quadratic Function — Vertex

• EN: The function f(x) = −2(x − 3)² + 8 has its vertex at which point?
• FR: La fonction f(x) = −2(x − 3)² + 8 a son sommet à quel point?
• Choices: A) (−3, 8) B) (3, −8) C) (3, 8) D) (−3, −8)
• Hint: In f(x) = a(x−h)² + k, the vertex is at (h, k). For f(x) = (x−4)²+1, vertex = (4, 1).
• Steps:
  • The function is in vertex form: f(x) = a(x−h)² + k.
  • h = 3, k = 8.
  • Vertex is at (3, 8).
• Answer: (3, 8)

[Medium] Annuities — Future Value

• EN: Mia deposits $200 at the end of each month into an account earning 6% per year compounded monthly for 1 year. What is the approximate future value? (Use the formula FV = PMT × [(1 + r)ⁿ − 1] ÷ r, where r = 0.005 and n = 12.)
• FR: Mia dépose 200 $ à la fin de chaque mois dans un compte à 6 % par an, composé mensuellement, pendant 1 an. Quelle est la valeur future approximative? (Utilise FV = PMT × [(1 + r)ⁿ − 1] ÷ r, où r = 0,005 et n = 12.)
• Choices: A) $2 400.00 B) $2 467.50 C) $2 536.20 D) $2 448.00
• Hint: For $100/month at 1% monthly for 3 months: FV = 100 × [(1.01)³ − 1]/0.01 ≈ 100 × 3.030 = $303.
• Steps:
  • FV = 200 × [(1.005)¹² − 1] ÷ 0.005.
  • (1.005)¹² ≈ 1.06168; 1.06168 − 1 = 0.06168.
  • FV = 200 × 0.06168 ÷ 0.005 = 200 × 12.336 ≈ $2 467.50.
• Answer: $2 467.50

[Hard] Logarithm — Solving Equations

• EN: Solve for x: 3ˣ = 81
• FR: Résous pour x : 3ˣ = 81
• Choices: A) x = 4 B) x = 27 C) x = 3 D) x = 9
• Hint: Convert to logarithmic form: if aˣ = b, then x = log_a(b). For 2ˣ = 32: x = log₂(32) = 5.
• Steps:
  • Express 81 as a power of 3: 81 = 3⁴.
  • So 3ˣ = 3⁴.
  • Therefore x = 4.
• Answer: x = 4

[Hard] Compound Interest — Solving for Time

• EN: How many years does it take for $1 000 to grow to $1 331 at 10% interest compounded annually?
• FR: Combien d'années faut-il pour que 1 000 $ croissent à 1 331 $ à un taux d'intérêt de 10 % composé annuellement?
• Choices: A) 4 years B) 2 years C) 5 years D) 3 years
• Hint: Use A = P(1 + r)ⁿ. Rearrange: (A/P) = (1+r)ⁿ. For $1000 to $1210 at 10%: (1.1)ⁿ = 1.21; since 1.1² = 1.21, n = 2.
• Steps:
  • 1000 × (1.1)ⁿ = 1331.
  • (1.1)ⁿ = 1.331.
  • 1.1³ = 1.331, so n = 3 years.
• Answer: 3 years

[Easy] Permutations

• EN: In how many ways can 4 different students line up in a row?
• FR: De combien de façons 4 élèves différents peuvent-ils se placer en rang?
• Choices: A) 16 B) 12 C) 24 D) 48
• Hint: The number of ways to arrange n objects is n!. For 3 objects: 3! = 3 × 2 × 1 = 6.
• Steps:
  • 4 students in a row: 4! = 4 × 3 × 2 × 1.
  • = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 6?
• FR: De combien de façons peut-on choisir 2 élèves dans un groupe de 6?
• Choices: A) 30 B) 12 C) 15 D) 36
• Hint: C(n, r) = n! ÷ (r! × (n−r)!). For C(4, 2): 4! ÷ (2! × 2!) = 24 ÷ 4 = 6.
• Steps:
  • C(6, 2) = 6! ÷ (2! × 4!).
  • = (6 × 5) ÷ (2 × 1) = 30 ÷ 2.
  • = 15.
• Answer: 15

[Easy] Polynomial Division

• EN: Divide: (x² + 5x + 6) ÷ (x + 2)
• FR: Divise : (x² + 5x + 6) ÷ (x + 2)
• Choices: A) x + 4 B) x − 3 C) x + 3 D) x + 5
• Hint: Factor the numerator first. For (x²+7x+12) ÷ (x+3): factor to (x+3)(x+4), then cancel to get x+4.
• Steps:
  • Factor x² + 5x + 6 = (x + 2)(x + 3).
  • Divide by (x + 2): cancel the common factor.
  • Result: x + 3.
• Answer: x + 3

[Easy] Derivative — Basic Rule

• EN: If f(x) = 3x², what is f′(x)?
• FR: Si f(x) = 3x², quel est f′(x)?
• Choices: A) 3x B) 6x² C) 6x D) 3x³
• Hint: Power rule: if f(x) = axⁿ, then f′(x) = n·axⁿ⁻¹. For f(x) = 4x³: f′(x) = 12x².
• Steps:
  • Apply the power rule: bring down the exponent, reduce it by 1.
  • f′(x) = 2 × 3x²⁻¹ = 6x¹.
  • f′(x) = 6x.
• Answer: 6x

[Medium] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: On lance une pièce de monnaie équitable 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces?
• Choices: A) 3/16 B) 1/4 C) 1/2 D) 1/4
• Hint: P(X = k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ. For n=3, k=2, p=0.5: C(3,2) × 0.25 × 0.5 = 3/8.

(Note: two choices are 1/4 — correcting to avoid duplicate starts:)

• Choices: A) 3/16 B) 1/4 C) 5/16 D) 1/8
• Hint: P(X = k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ. For n=3, k=2, p=0.5: C(3,2) × 0.25 × 0.5 = 3/8.
• Steps:
  • P(X = 3) = C(4, 3) × (0.5)³ × (0.5)¹.
  • C(4, 3) = 4; (0.5)⁴ = 1/16.
  • P = 4 × (1/16) = 4/16 = 1/4.
• Answer: 1/4

[Medium] Vectors — Addition

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

[Medium] Rational Function — Asymptote

• EN: What is the vertical asymptote of f(x) = (x + 1) ÷ (x − 3)?
• FR: Quelle est l'asymptote verticale de f(x) = (x + 1) ÷ (x − 3)?
• Choices: A) x = 1 B) x = −3 C) x = 3 D) x = −1
• Hint: A vertical asymptote occurs where the denominator equals zero. For f(x) = 1/(x−5), set x−5=0 to get x=5.
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • x = 3.
  • The vertical asymptote is x = 3.
• Answer: x = 3

[Medium] Rate of Change — Derivative Application

• EN: The position of a ball is given by s(t) = 4t² + 2t. What is its velocity (rate of change) at t = 3?
• FR: La position d'une balle est donnée par s(t) = 4t² + 2t. Quelle est sa vitesse (taux de variation) à t = 3?
• Choices: A) 38 m/s B) 26 m/s C) 14 m/s D) 42 m/s
• Hint: Find the derivative, then substitute the time value. For s(t) = 3t² + t, v(t) = 6t + 1. At t = 2: v = 13.
• Steps:
  • Differentiate: s′(t) = 8t + 2.
  • Substitute t = 3: s′(3) = 8(3) + 2 = 24 + 2.
  • Velocity = 26 m/s.
• Answer: 26 m/s

[Hard] Probability Distribution — Expected Value

• EN: A game gives you $5 with probability 0.3, $2 with probability 0.5, and $0 with probability 0.2. What is the expected value?
• FR: Un jeu te donne 5 $ avec une probabilité de 0,3, 2 $ avec une probabilité de 0,5 et 0 $ avec une probabilité de 0,2. Quelle est l'espérance mathématique?
• Choices: A) $3.50 B) $2.00 C) $1.00 D) $2.50
• Hint: Expected value = Σ(value × probability). For $10 with p=0.4 and $0 with p=0.6: E = 10 × 0.4 + 0 × 0.6 = $4.
• Steps:
  • E = 5 × 0.3 + 2 × 0.5 + 0 × 0.2.
  • E = 1.50 + 1.00 + 0.
  • E = $2.50.
• Answer: $2.50

[Hard] Vectors — Dot Product and Angle

• EN: Find the angle between vectors u = (1, 0) and v = (1, 1). (Use cos θ = (u·v) ÷ (|u||v|))
• FR: Trouve l'angle entre les vecteurs u = (1, 0) et v = (1, 1). (Utilise cos θ = (u·v) ÷ (|u||v|))
• Choices: A) 30° B) 90° C) 60° D) 45°
• Hint: Dot product: u·v = u₁v₁ + u₂v₂. Magnitudes: |u| = √(u₁²+u₂²). Then find the angle using inverse cosine.
• Steps:
  • u·v = (1)(1) + (0)(1) = 1.
  • |u| = √(1+0) = 1; |v| = √(1+1) = √2.
  • cos θ = 1/(1 × √2) = 1/√2; θ = cos⁻¹(1/√2) = 45°.
• Answer: 45°