Daily Math — 2026-07-19

[Easy] Counting to 20

• EN: There are 7 apples on the table and 5 more apples in the basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres pommes dans le panier. Combien y a-t-il de pommes en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add 4 + 3, count on from the bigger number: 4 … 5, 6, 7. That's 7.
• Steps:
  • Start at 7 and count on 5 more.
  • 7 … 8, 9, 10, 11, 12.
  • So there are 12 apples in all.
• Answer: 12

[Easy] Subtraction Within 20

• EN: There are 14 hockey cards in a box. A student takes out 6 cards. How many cards are left?
• FR: Il y a 14 cartes de hockey dans une boîte. Un élève en retire 6. Combien reste-t-il de cartes?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To solve 10 − 3, count back 3 from 10: 9, 8, 7. The answer is 7.
• Steps:
  • Start at 14 and count back 6.
  • 14 … 13, 12, 11, 10, 9, 8.
  • So 8 cards are left.
• Answer: 8

[Easy] Skip Counting by 5s

• EN: Count by 5s. What number comes after 15?
• FR: Compte par 5. Quel nombre vient après 15?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: Counting by 5s: 5, 10, 15 — the next number is 5 more each time.
• Steps:
  • The pattern is 5, 10, 15, …
  • Add 5 to 15: 15 + 5 = 20.
  • So the next number is 20.
• Answer: 20

[Easy] Comparing Numbers

• EN: Which number is greater: 13 or 17?
• FR: Quel nombre est plus grand : 13 ou 17?
• Choices: A) 13 B) 15 C) 17 D) 19
• Hint: On a number line, numbers to the right are always greater, so 9 is greater than 6.
• Steps:
  • Place 13 and 17 on a number line.
  • 17 is farther to the right than 13.
  • So 17 is the greater number.
• Answer: 17

[Medium] Adding Three Numbers

• EN: Sam has 4 stickers, 3 stickers, and 6 stickers. How many stickers does Sam have altogether?
• FR: Sam a 4 autocollants, 3 autocollants et 6 autocollants. Combien d'autocollants Sam a-t-il en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To add 2 + 5 + 3, first add 2 + 5 = 7, then 7 + 3 = 10.
• Steps:
  • Add the first two numbers: 4 + 3 = 7.
  • Then add the third: 7 + 6 = 13.
  • Sam has 13 stickers altogether.
• Answer: 13

[Medium] Skip Counting by 2s

• EN: Maya counts her mittens by 2s: 2, 4, 6, 8, ___. What number comes next?
• FR: Maya compte ses mitaines par 2 : 2, 4, 6, 8, ___. Quel nombre vient ensuite?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Counting by 2s means adding 2 each time: 4, 6, 8 — so the next is 8 + 2.
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Medium] Coin Recognition

• EN: A nickel is worth 5 cents and a dime is worth 10 cents. How much are one nickel and one dime worth together?
• FR: Un nickel vaut 5 cents et un dime vaut 10 cents. Combien valent ensemble un nickel et un dime?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: A nickel is 5 cents and a penny is 1 cent; together they make 6 cents.
• Steps:
  • A nickel = 5 cents and a dime = 10 cents.
  • Add: 5 + 10 = 15.
  • Together they are worth 15 cents.
• Answer: 15 cents

[Medium] Subtraction Story

• EN: There are 18 children on the playground. 9 children go inside. How many children are still outside?
• FR: Il y a 18 enfants dans la cour. 9 enfants rentrent à l'intérieur. Combien d'enfants sont encore dehors?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: To solve 16 − 8, think: what plus 8 equals 16? That's 8.
• Steps:
  • Start with 18 children.
  • Take away 9: 18 − 9 = 9.
  • So 9 children are still outside.
• Answer: 9

[Hard] Adding and Comparing

• EN: Luca has 8 crayons. He gets 4 more. Mia has 15 crayons. Who has more crayons, and by how many?
• FR: Luca a 8 crayons. Il en reçoit 4 de plus. Mia a 15 crayons. Qui a le plus de crayons, et de combien?
• Choices: A) Luca by 3 B) Mia by 3 C) Mia by 5 D) Luca by 5
• Hint: If Amir has 6 + 2 = 8 and Priya has 11, then Priya has 11 − 8 = 3 more.
• Steps:
  • Find Luca's total: 8 + 4 = 12.
  • Compare: Mia has 15 and Luca has 12.
  • 15 − 12 = 3, so Mia has 3 more crayons.
• Answer: Mia by 3

[Hard] Skip Counting and Adding

• EN: Count by 10s to fill in the blank: 10, 20, 30, ___. Then add 5 to that number. What do you get?
• FR: Compte par 10 pour remplir le blanc : 10, 20, 30, ___. Ensuite, ajoute 5 à ce nombre. Que trouves-tu?
• Choices: A) 35 B) 40 C) 45 D) 50
• Hint: Counting by 10s: 10, 20, 30 — the next is 40. Then add another number to it.
• Steps:
  • Count by 10s: 10, 20, 30, 40. The missing number is 40.
  • Now add 5: 40 + 5 = 45.
  • The answer is 45.
• Answer: 45

[Easy] Adding Within 100

• EN: A student earns 34 points in a reading game and then 25 more points. How many points does the student have in total?
• FR: Un élève gagne 34 points dans un jeu de lecture, puis 25 points de plus. Combien de points l'élève a-t-il en tout?
• Choices: A) 57 B) 58 C) 59 D) 61
• Hint: To add 21 + 36, add the tens first (20 + 30 = 50), then the ones (1 + 6 = 7), giving 57.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59 points in total.
• Answer: 59

[Easy] Subtracting Within 100

• EN: There are 76 snowflakes drawn on a poster. Students erase 23 of them. How many snowflakes are left?
• FR: Il y a 76 flocons de neige dessinés sur une affiche. Les élèves en effacent 23. Combien en reste-t-il?
• Choices: A) 43 B) 53 C) 63 D) 99
• Hint: To subtract 58 − 32, subtract the tens (50 − 30 = 20) then the ones (8 − 2 = 6), giving 26.
• Steps:
  • Subtract the tens: 70 − 20 = 50.
  • Subtract the ones: 6 − 3 = 3.
  • 50 + 3 = 53 snowflakes are left.
• Answer: 53

[Easy] Telling Time to the Hour

• EN: The clock shows the short hand on the 4 and the long hand on the 12. What time does the clock show?
• FR: L'horloge montre la petite aiguille sur le 4 et la grande aiguille sur le 12. Quelle heure l'horloge indique-t-elle?
• Choices: A) 3:00 B) 4:00 C) 4:30 D) 5:00
• Hint: When the long hand points to 12 and the short hand points to a number, it is that number o'clock.
• Steps:
  • The long hand on 12 means it is exactly on the hour.
  • The short hand on 4 tells us the hour is 4.
  • The time is 4:00.
• Answer: 4:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long and an eraser is 4 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 14 cm de long et une gomme mesure 4 cm de long. De combien le crayon est-il plus long que la gomme?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 18 cm
• Hint: To find how much longer one thing is than another, subtract: 12 − 5 = 7 cm.
• Steps:
  • Subtract the shorter length from the longer: 14 − 4 = 10.
  • The pencil is 10 cm longer than the eraser.
• Answer: 10 cm

[Medium] Counting Coins

• EN: Anya has 2 dimes and 3 nickels. How much money does she have in total?
• FR: Anya a 2 dimes et 3 nickels. Combien d'argent a-t-elle en tout?
• Choices: A) 25 cents B) 30 cents C) 35 cents D) 40 cents
• Hint: 1 dime = 10 cents, 1 nickel = 5 cents; for 2 dimes + 1 nickel: 10 + 10 + 5 = 25 cents.
• Steps:
  • 2 dimes = 2 × 10 = 20 cents.
  • 3 nickels = 3 × 5 = 15 cents.
  • 20 + 15 = 35 cents in total.
• Answer: 35 cents

[Medium] Telling Time to the Half-Hour

• EN: Hockey practice starts at 2:30. The clock shows the long hand on the 6. Where is the short hand?
• FR: L'entraînement de hockey commence à 2h30. La grande aiguille est sur le 6. Où est la petite aiguille?
• Choices: A) Between the 1 and 2 B) Between the 2 and 3 C) On the 3 D) On the 6
• Hint: At half past the hour, the long hand is on 6 and the short hand is halfway between two numbers.
• Steps:
  • At 2:30, it is half past 2.
  • The long hand is on 6 (half-hour mark).
  • The short hand is halfway between 2 and 3.
• Answer: Between the 2 and 3

[Medium] Simple Patterns

• EN: Look at the pattern: 5, 10, 15, 20, ___. What number comes next?
• FR: Observe le motif : 5, 10, 15, 20, ___. Quel nombre vient ensuite?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: In the pattern 3, 6, 9, 12, each number is 3 more than the last; so 12 + 3 = 15 comes next.
• Steps:
  • Each number in the pattern is 5 more than the previous one.
  • 20 + 5 = 25.
  • The next number is 25.
• Answer: 25

[Medium] Adding With Regrouping

• EN: There are 47 students at one school and 38 students at another school going on a field trip together. How many students are there in all?
• FR: Il y a 47 élèves dans une école et 38 élèves dans une autre école qui partent en sortie ensemble. Combien y a-t-il d'élèves en tout?
• Choices: A) 75 B) 84 C) 85 D) 86
• Hint: To add 29 + 43, add ones first: 9 + 3 = 12, write 2 and carry 1; then tens: 2 + 4 + 1 = 7; answer is 72.
• Steps:
  • Add the ones: 7 + 8 = 15. Write 5, carry 1.
  • Add the tens: 4 + 3 + 1 = 8.
  • The total is 85 students.
• Answer: 85

[Hard] Measuring and Comparing

• EN: A blue ribbon is 45 cm long. A red ribbon is 28 cm long. If you put them end to end, how long are they together?
• FR: Un ruban bleu mesure 45 cm de long. Un ruban rouge mesure 28 cm de long. Si tu les mets bout à bout, quelle est leur longueur totale?
• Choices: A) 63 cm B) 71 cm C) 73 cm D) 83 cm
• Hint: To add 36 + 25, add ones: 6 + 5 = 11 (write 1, carry 1); tens: 3 + 2 + 1 = 6; answer is 61 cm.
• Steps:
  • Add ones: 5 + 8 = 13. Write 3, carry 1.
  • Add tens: 4 + 2 + 1 = 7.
  • Together they are 73 cm long.
• Answer: 73 cm

[Hard] Multi-Step Coins

• EN: Omar has 3 dimes, 2 nickels, and 4 pennies. He spends 27 cents at the school store. How many cents does he have left?
• FR: Omar a 3 dimes, 2 nickels et 4 pennies. Il dépense 27 cents à la boutique de l'école. Combien de cents lui reste-t-il?
• Choices: A) 17 cents B) 21 cents C) 23 cents D) 27 cents
• Hint: Count coins: 2 dimes + 1 nickel + 3 pennies = 20 + 5 + 3 = 28 cents; then subtract what was spent.
• Steps:
  • Count Omar's coins: 3 × 10 + 2 × 5 + 4 × 1 = 30 + 10 + 4 = 44 cents.
  • Subtract what he spent: 44 − 27 = 17.
  • Omar has 17 cents left.
• Answer: 17 cents

[Easy] Multiplication by 2

• EN: There are 6 pairs of mittens in a box. How many mittens are there altogether?
• FR: Il y a 6 paires de mitaines dans une boîte. Combien y a-t-il de mitaines en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Pairs means groups of 2; for 4 pairs, 4 × 2 = 8 mittens.
• Steps:
  • Each pair has 2 mittens.
  • 6 × 2 = 12.
  • There are 12 mittens altogether.
• Answer: 12

[Easy] Multiplication by 5

• EN: A Tim Hortons cup holds 5 Timbits. How many Timbits are in 7 cups?
• FR: Un gobelet Tim Hortons contient 5 Timbits. Combien y a-t-il de Timbits dans 7 gobelets?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: For 4 cups with 5 each: 4 × 5 = 20 Timbits.
• Steps:
  • Multiply: 7 × 5 = 35.
  • There are 35 Timbits in 7 cups.
• Answer: 35

[Easy] Basic Fractions

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

[Easy] Basic Division

• EN: A teacher has 20 crayons to share equally among 4 students. How many crayons does each student get?
• FR: Une enseignante a 20 crayons à partager également entre 4 élèves. Combien de crayons chaque élève reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: To divide 15 crayons among 3 students, think: 3 × ? = 15, so each gets 5.
• Steps:
  • Divide 20 by 4: 20 ÷ 4 = 5.
  • Each student gets 5 crayons.
• Answer: 5

[Medium] Multiplication by 3

• EN: A hockey team has 3 players on each line. There are 6 lines. How many players are there in total?
• FR: Une équipe de hockey compte 3 joueurs par ligne. Il y a 6 lignes. Combien y a-t-il de joueurs en tout?
• Choices: A) 15 B) 16 C) 18 D) 21
• Hint: For 4 lines with 3 players each: 4 × 3 = 12 players.
• Steps:
  • Multiply: 6 × 3 = 18.
  • There are 18 players in total.
• Answer: 18

[Medium] Perimeter of a Rectangle

• EN: A rectangular classroom mat is 5 m long and 3 m wide. What is the perimeter of the mat?
• FR: Un tapis rectangulaire de classe mesure 5 m de long et 3 m de large. Quel est le périmètre du tapis?
• Choices: A) 8 m B) 12 m C) 15 m D) 16 m
• Hint: For a rectangle 4 m by 2 m, add all sides: 4 + 2 + 4 + 2 = 12 m.
• Steps:
  • Add all four sides: 5 + 3 + 5 + 3.
  • 5 + 3 + 5 + 3 = 16.
  • The perimeter is 16 m.
• Answer: 16 m

[Medium] Reading a Bar Graph

• EN: A bar graph shows that 8 students like skiing, 5 like skating, and 3 like snowshoeing. How many students were surveyed in total?
• FR: Un graphique à barres montre que 8 élèves aiment le ski, 5 aiment le patinage et 3 aiment la raquette. Combien d'élèves ont été sondés en tout?
• Choices: A) 13 B) 14 C) 16 D) 18
• Hint: To find the total from a bar graph, add all bar values: 6 + 4 + 2 = 12.
• Steps:
  • Add all three values: 8 + 5 + 3.
  • 8 + 5 = 13, then 13 + 3 = 16.
  • A total of 16 students were surveyed.
• Answer: 16

[Medium] Multiplication by 10

• EN: A box holds 10 hockey pucks. There are 9 boxes. How many pucks are there altogether?
• FR: Une boîte contient 10 rondelles de hockey. Il y a 9 boîtes. Combien y a-t-il de rondelles en tout?
• Choices: A) 19 B) 80 C) 90 D) 100
• Hint: Any number times 10 just adds a zero: 7 × 10 = 70.
• Steps:
  • Multiply: 9 × 10 = 90.
  • There are 90 pucks altogether.
• Answer: 90

[Hard] Comparing Fractions

• EN: Which fraction is larger: 1/2 or 1/3?
• FR: Quelle fraction est la plus grande : 1/2 ou 1/3?
• Choices: A) 1/3 B) 1/2 C) They are equal D) Neither is a fraction
• Hint: Think of sharing 1 pizza among 2 friends versus among 4 friends — fewer people means bigger slices.
• Steps:
  • Imagine dividing something into 2 equal parts versus 3 equal parts.
  • When you divide into 2 parts, each part is bigger than when you divide into 3 parts.
  • So 1/2 is larger than 1/3.
• Answer: 1/2

[Hard] Multi-Step Multiplication

• EN: A bakery makes 4 trays of muffins each day. Each tray holds 5 muffins. If they bake for 3 days, how many muffins do they make in total?
• FR: Une boulangerie fait 4 plateaux de muffins par jour. Chaque plateau contient 5 muffins. Si elle cuit pendant 3 jours, combien de muffins fait-elle en tout?
• Choices: A) 45 B) 55 C) 60 D) 65
• Hint: For 2 trays × 3 muffins = 6 muffins per day; over 4 days: 6 × 4 = 24 muffins.
• Steps:
  • Muffins per day: 4 × 5 = 20.
  • Over 3 days: 20 × 3 = 60.
  • They make 60 muffins in total.
• Answer: 60

[Easy] Multiplication Tables

• EN: What is 8 × 7?
• FR: Combien font 8 × 7?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To find 6 × 7, think of 6 × 5 = 30 and then add 6 × 2 = 12: 30 + 12 = 42.
• Steps:
  • Use the multiplication table: 8 × 7.
  • 8 × 7 = 56.
  • The answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the digit in the tenths place in the number 4.73?
• FR: Quel est le chiffre à la position des dixièmes dans le nombre 4,73?
• Choices: A) 3 B) 4 C) 7 D) 73
• Hint: In the number 2.58, the digit 5 is in the tenths place and 8 is in the hundredths place.
• Steps:
  • In 4.73, after the decimal point comes the tenths place, then hundredths.
  • The first digit after the decimal is 7.
  • The digit in the tenths place is 7.
• Answer: 7

[Easy] Area of a Rectangle

• EN: A school garden is 6 m long and 4 m wide. What is the area of the garden?
• FR: Un jardin scolaire mesure 6 m de long et 4 m de large. Quelle est l'aire du jardin?
• Choices: A) 10 m² B) 20 m² C) 24 m² D) 28 m²
• Hint: Area of a rectangle = length × width; for a 5 m by 3 m room, area = 5 × 3 = 15 m².
• Steps:
  • Area = length × width = 6 × 4.
  • 6 × 4 = 24.
  • The area of the garden is 24 m².
• Answer: 24 m²

[Easy] Long Division

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

[Medium] Long Division With Remainder

• EN: A bag holds 50 marbles. If you share them equally among 7 friends, how many marbles does each friend get, and how many are left over?
• FR: Un sac contient 50 billes. Si tu les partages également entre 7 amis, combien chaque ami reçoit-il de billes et combien en reste-t-il?
• Choices: A) 6 remainder 8 B) 7 remainder 1 C) 7 remainder 2 D) 8 remainder 1
• Hint: For 25 ÷ 4: 4 × 6 = 24, which is less than 25, so the answer is 6 remainder 1.
• Steps:
  • 7 × 7 = 49, which is less than 50.
  • 50 − 49 = 1 left over.
  • Each friend gets 7 marbles with 1 remainder.
• Answer: 7 remainder 1

[Medium] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 5/8?
• FR: Quelle fraction est plus grande : 3/4 ou 5/8?
• Choices: A) 3/4 B) 5/8 C) They are equal D) Neither can be compared
• Hint: To compare 2/3 and 3/4, convert to a common denominator (12): 8/12 vs. 9/12 — so 3/4 is bigger.
• Steps:
  • Convert 3/4 to eighths: 3/4 = 6/8.
  • Compare 6/8 and 5/8.
  • 6/8 > 5/8, so 3/4 is greater.
• Answer: 3/4

[Medium] Decimal Operations

• EN: A loaf of bread costs $2.45 and a carton of milk costs $1.30. How much do they cost together?
• FR: Un pain coûte 2,45 $ et un carton de lait coûte 1,30 $. Combien coûtent-ils ensemble?
• Choices: A) $3.55 B) $3.65 C) $3.75 D) $4.75
• Hint: To add $1.25 + $2.40, line up the decimals: 1.25 + 2.40 = 3.65.
• Steps:
  • Line up the decimals: 2.45 + 1.30.
  • Add hundredths: 5 + 0 = 5. Add tenths: 4 + 3 = 7. Add ones: 2 + 1 = 3.
  • The total is $3.75.
• Answer: $3.75

[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: From 2:20 to 4:50 — count 2 hours to get to 4:20, then 30 more minutes to 4:50; total is 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.
  • The movie is 2 hours 30 minutes long.
• Answer: 2 hours 30 minutes

[Hard] Multi-Step Word Problem

• EN: A school orders 9 boxes of markers. Each box has 8 markers. The school uses 36 markers for an art project. How many markers are left?
• FR: Une école commande 9 boîtes de marqueurs. Chaque boîte contient 8 marqueurs. L'école utilise 36 marqueurs pour un projet d'art. Combien de marqueurs reste-t-il?
• Choices: A) 36 B) 54 C) 72 D) 108
• Hint: For 3 boxes × 7 markers = 21 total; if 9 are used, then 21 − 9 = 12 remain.
• Steps:
  • Total markers: 9 × 8 = 72.
  • Subtract markers used: 72 − 36 = 36.
  • There are 36 markers left.
• Answer: 36

[Hard] Decimal Place Value and Comparison

• EN: Order these numbers from least to greatest: 3.6, 3.06, 3.60, 3.16.
• FR: Mets ces nombres en ordre du plus petit au plus grand : 3,6, 3,06, 3,60, 3,16.
• Choices: A) 3.06, 3.16, 3.6, 3.60 B) 3.6, 3.60, 3.16, 3.06 C) 3.06, 3.6, 3.16, 3.60 D) 3.16, 3.06, 3.6, 3.60
• Hint: Note that 3.6 and 3.60 are equal; then compare the tenths digit first: 0 < 1 < 6.
• Steps:
  • Recognize that 3.6 = 3.60 (they are the same value).
  • Compare: 3.06 < 3.16 < 3.6 = 3.60.
  • The correct order is 3.06, 3.16, 3.6, 3.60.
• Answer: 3.06, 3.16, 3.6, 3.60

[Easy] Multi-Digit Multiplication

• EN: A farmer plants 24 rows of corn with 12 plants in each row. How many plants are there in total?
• FR: Un fermier plante 24 rangées de maïs avec 12 plants dans chaque rangée. Combien y a-t-il de plants en tout?
• Choices: A) 248 B) 268 C) 288 D) 308
• Hint: To multiply 23 × 11, use 23 × 10 = 230 and 23 × 1 = 23; add them: 230 + 23 = 253.
• Steps:
  • 24 × 12 = 24 × 10 + 24 × 2.
  • 24 × 10 = 240; 24 × 2 = 48.
  • 240 + 48 = 288 plants in total.
• Answer: 288

[Easy] Adding Fractions With Like Denominators

• EN: A recipe uses 2/8 cup of oats and 3/8 cup of flour. How much dry ingredients is that in total?
• FR: Une recette utilise 2/8 de tasse d'avoine et 3/8 de tasse de farine. Quelle est la quantité totale d'ingrédients secs?
• Choices: A) 4/8 B) 5/8 C) 5/16 D) 6/16
• Hint: To add 1/5 + 2/5, keep the denominator and add numerators: 1 + 2 = 3, so the answer is 3/5.
• Steps:
  • The denominators are the same (8), so just add the numerators: 2 + 3 = 5.
  • The total is 5/8.
• Answer: 5/8

[Easy] Decimal Operations

• EN: A bottle of maple syrup costs $4.75. A student pays with a $10 bill. How much change do they receive?
• FR: Une bouteille de sirop d'érable coûte 4,75 $. Un élève paie avec un billet de 10 $. Combien de monnaie reçoit-il?
• Choices: A) $4.25 B) $5.00 C) $5.25 D) $6.25
• Hint: For $7.40 change from $10.00: 10.00 − 7.40 = 2.60.
• Steps:
  • Subtract: $10.00 − $4.75.
  • 10.00 − 4.75 = 5.25.
  • The change is $5.25.
• Answer: $5.25

[Easy] Percentage Introduction (50%)

• EN: What is 50% of 80 students?
• FR: Combien font 50 % de 80 élèves?
• Choices: A) 30 B) 40 C) 50 D) 60
• Hint: 50% means half; half of 60 is 30.
• Steps:
  • 50% means half of the number.
  • Half of 80 = 80 ÷ 2 = 40.
  • 50% of 80 is 40.
• Answer: 40

[Medium] Multi-Digit Division

• EN: A school library has 312 books to sort equally onto 8 shelves. How many books go on each shelf?
• FR: La bibliothèque de l'école a 312 livres à répartir également sur 8 étagères. Combien de livres y a-t-il sur chaque étagère?
• Choices: A) 37 B) 38 C) 39 D) 41
• Hint: To divide 240 by 6, think 6 × 40 = 240, so the answer is 40.
• Steps:
  • Divide: 312 ÷ 8.
  • 8 × 39 = 312.
  • Each shelf gets 39 books.
• Answer: 39

[Medium] Subtracting Fractions With Like Denominators

• EN: Marcus had 7/10 of a granola bar. He ate 3/10 of it. How much is left?
• FR: Marcus avait 7/10 d'une barre granola. Il en a mangé 3/10. Combien reste-t-il?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 7/10
• Hint: To subtract 5/9 − 2/9, keep the denominator and subtract numerators: 5 − 2 = 3, giving 3/9.
• Steps:
  • Same denominator (10), so subtract numerators: 7 − 3 = 4.
  • The amount left is 4/10.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A storage box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte de rangement 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; for a 2 cm × 3 cm × 4 cm box, V = 2 × 3 × 4 = 24 cm³.
• Steps:
  • Volume = length × width × height = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage Introduction (25%)

• EN: A school store has 60 pencils. They put 25% of them on sale. How many pencils are on sale?
• FR: La boutique de l'école a 60 crayons. Elle en met 25 % en vente. Combien de crayons sont en vente?
• Choices: A) 12 B) 15 C) 20 D) 25
• Hint: 25% means one quarter; one quarter of 40 is 40 ÷ 4 = 10.
• Steps:
  • 25% = 1/4 of the total.
  • 60 ÷ 4 = 15.
  • There are 15 pencils on sale.
• Answer: 15

[Hard] Multi-Step Decimal Problem

• EN: Sofia buys 3 notebooks for $2.45 each and a ruler for $1.30. She pays with a $20 bill. How much change does she receive?
• FR: Sofia achète 3 cahiers à 2,45 $ chacun et une règle à 1,30 $. Elle paie avec un billet de 20 $. Combien de monnaie reçoit-elle?
• Choices: A) $11.05 B) $12.05 C) $13.25 D) $15.55
• Hint: Find total cost (2 items × $3.50 = $7.00 + $2.00 = $9.00), then subtract from $20.00 to get change.
• Steps:
  • Cost of 3 notebooks: 3 × $2.45 = $7.35.
  • Add the ruler: $7.35 + $1.30 = $8.65.
  • Change: $20.00 − $8.65 = $11.35.
• Answer: $11.35

(Correction: recalculate — $20.00 − $8.65 = $11.35. Adjusted choices accordingly.)

• Choices: A) $8.65 B) $11.35 C) $12.65 D) $13.35
• Answer: $11.35

[Hard] Multi-Step Fractions and Percent

• EN: A juice jug holds 20 cups. The class drinks 2/5 of the jug in the morning. How many cups were drunk in the morning?
• FR: Une cruche de jus contient 20 tasses. La classe boit 2/5 de la cruche le matin. Combien de tasses ont été bues le matin?
• Choices: A) 4 cups B) 6 cups C) 8 cups D) 10 cups
• Hint: To find 3/5 of 25, first find 1/5: 25 ÷ 5 = 5; then multiply by 3: 5 × 3 = 15.
• Steps:
  • Find 1/5 of 20: 20 ÷ 5 = 4.
  • Multiply by 2: 4 × 2 = 8.
  • The class drank 8 cups in the morning.
• Answer: 8 cups

[Easy] Percent of a Number

• EN: What is 10% of 90?
• FR: Combien font 10 % de 90?
• Choices: A) 7 B) 9 C) 10 D) 19
• Hint: 10% means dividing by 10; 10% of 50 = 50 ÷ 10 = 5.
• Steps:
  • 10% = divide by 10.
  • 90 ÷ 10 = 9.
  • 10% of 90 is 9.
• Answer: 9

[Easy] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2.
• FR: Calcule : 3 + 4 × 2.
• Choices: A) 10 B) 11 C) 14 D) 24
• Hint: In BEDMAS, multiply before adding; for 2 + 3 × 4, do 3 × 4 = 12 first, then 2 + 12 = 14.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then addition: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Integer Introduction

• EN: The temperature in Winnipeg is −8°C in the morning and rises by 5°C by noon. What is the temperature at noon?
• FR: La température à Winnipeg est de −8 °C le matin et monte de 5 °C à midi. Quelle est la température à midi?
• Choices: A) −13°C B) −3°C C) 3°C D) 13°C
• Hint: Adding a positive to a negative: −10 + 4 = −6 (move right on the number line).
• Steps:
  • Start at −8°C and add 5: −8 + 5 = −3.
  • The temperature at noon is −3°C.
• Answer: −3°C

[Easy] Ratios

• 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 sur garçons?
• Choices: A) 2:3 B) 3:2 C) 4:3 D) 8:12
• Hint: To simplify ratio 6:4, divide both by 2 to get 3:2.
• Steps:
  • Ratio of girls to boys is 12:8.
  • Divide both by 4: 12 ÷ 4 = 3, 8 ÷ 4 = 2.
  • The simplified ratio is 3:2.
• Answer: 3:2

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 1/2 B) 5/12 C) 2/4 D) 6/7
• Hint: To multiply fractions, multiply the tops together and the bottoms together: 1/2 × 2/3 = 2/6 = 1/3.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • Simplify: 6/12 = 1/2.
• Answer: 1/2

[Medium] Fraction Division

• EN: A ribbon 3/4 m long is cut into pieces that are each 1/8 m long. How many pieces are there?
• FR: Un ruban de 3/4 m de long est coupé en morceaux de 1/8 m chacun. Combien y a-t-il de morceaux?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: To divide 1/2 ÷ 1/6, flip the second fraction and multiply: 1/2 × 6/1 = 6/2 = 3.
• Steps:
  • Divide: 3/4 ÷ 1/8 = 3/4 × 8/1.
  • 3 × 8 = 24 and 4 × 1 = 4; so 24/4 = 6.
  • There are 6 pieces.
• Answer: 6

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is the car's speed in km/h?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est la vitesse de la voiture en km/h?
• Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: Rate = total ÷ time; for 150 km in 3 h, speed = 150 ÷ 3 = 50 km/h.
• Steps:
  • Speed = distance ÷ time = 240 ÷ 3.
  • 240 ÷ 3 = 80.
  • The car's speed is 80 km/h.
• Answer: 80 km/h

[Medium] Simple Algebraic Expressions

• 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) 20 C) 23 D) 27
• Hint: Substitute the value: for 3x + 2 when x = 4, do 3 × 4 + 2 = 12 + 2 = 14.
• Steps:
  • Replace n with 5: 4(5) + 3.
  • 4 × 5 = 20; 20 + 3 = 23.
  • The value is 23.
• Answer: 23

[Hard] Multi-Step Percent Problem

• EN: A jacket originally costs $80. It is on sale for 25% off. How much does the jacket cost after the discount?
• FR: Un manteau coûte 80 $ à l'origine. Il est en solde à 25 % de rabais. Combien coûte le manteau après la réduction?
• Choices: A) $20 B) $55 C) $60 D) $65
• Hint: Find the discount: 25% of $60 = $60 ÷ 4 = $15; then subtract: $60 − $15 = $45.
• Steps:
  • Find 25% of $80: $80 ÷ 4 = $20.
  • Subtract discount: $80 − $20 = $60.
  • The jacket costs $60 after the discount.
• Answer: $60

[Hard] Order of Operations With Brackets

• EN: Evaluate: (5 + 3) × 2 − 4 ÷ 2.
• FR: Calcule : (5 + 3) × 2 − 4 ÷ 2.
• Choices: A) 10 B) 14 C) 16 D) 18
• Hint: For (2 + 4) × 3 − 6 ÷ 2, brackets first: 6 × 3 = 18; then 6 ÷ 2 = 3; then 18 − 3 = 15.
• Steps:
  • Brackets first: 5 + 3 = 8.
  • Multiplication: 8 × 2 = 16.
  • Division: 4 ÷ 2 = 2; then subtraction: 16 − 2 = 14.
• Answer: 14

[Easy] Integer Addition

• EN: What is −12 + 7?
• FR: Combien font −12 + 7?
• Choices: A) −19 B) −5 C) 5 D) 19
• Hint: On a number line, −9 + 4 means start at −9 and move 4 steps right; you land on −5.
• Steps:
  • Start at −12 on a number line and move 7 steps right.
  • −12 + 7 = −5.
  • The answer is −5.
• Answer: −5

[Easy] Integer Subtraction

• EN: What is 3 − (−6)?
• FR: Combien font 3 − (−6)?
• Choices: A) −9 B) −3 C) 3 D) 9
• Hint: Subtracting a negative is the same as adding a positive: 5 − (−2) = 5 + 2 = 7.
• Steps:
  • Subtracting −6 is the same as adding 6.
  • 3 + 6 = 9.
  • The answer is 9.
• Answer: 9

[Easy] Percent Discount

• EN: A pair of skates costs $120. They are 10% off. How much is the discount?
• FR: Une paire de patins coûte 120 $. Elle est à 10 % de rabais. Quel est le montant du rabais?
• Choices: A) $10 B) $12 C) $15 D) $20
• Hint: 10% of any number: divide by 10; 10% of $80 = $8.
• Steps:
  • 10% of $120 = $120 ÷ 10 = $12.
  • The discount is $12.
• Answer: $12

[Easy] Fraction Fluency

• EN: What is 3/5 + 1/5?
• FR: Combien font 3/5 + 1/5?
• Choices: A) 3/10 B) 4/5 C) 4/10 D) 5/5
• Hint: When denominators are the same, just add the numerators: 2/7 + 3/7 = 5/7.
• Steps:
  • Same denominator (5), add numerators: 3 + 1 = 4.
  • The answer is 4/5.
• Answer: 4/5

[Medium] Percent Tax

• EN: A book costs $15.00. There is a 13% HST in Ontario. How much tax is added?
• FR: Un livre coûte 15,00 $. La TVH en Ontario est de 13 %. Quel est le montant de la taxe ajoutée?
• Choices: A) $1.30 B) $1.80 C) $1.95 D) $2.15
• Hint: To find 13% of $20: 10% = $2.00 and 3% = $0.60; together that's $2.60.
• Steps:
  • 10% of $15.00 = $1.50.
  • 3% of $15.00 = $0.45.
  • Total tax: $1.50 + $0.45 = $1.95.
• Answer: $1.95

[Medium] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x : x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: To solve n + 5 = 12, subtract 5 from both sides: n = 12 − 5 = 7.
• Steps:
  • Subtract 9 from both sides: x = 17 − 9.
  • x = 8.
  • The solution is x = 8.
• Answer: x = 8

[Medium] Integer Multiplication

• EN: What is (−4) × 6?
• FR: Combien font (−4) × 6?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: A negative times a positive gives a negative result; (−3) × 5 = −15.
• Steps:
  • Multiply the absolute values: 4 × 6 = 24.
  • One factor is negative, so the result is negative: −24.
  • The answer is −24.
• Answer: −24

[Medium] Surface Area of a Rectangular Prism

• EN: A rectangular box is 4 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 4 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire de surface?
• Choices: A) 24 cm² B) 40 cm² C) 52 cm² D) 60 cm²
• Hint: Surface area of a rectangular prism = 2(lw + lh + wh); for a 2×3×1 box: 2(6 + 2 + 3) = 2(11) = 22 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(4×3 + 4×2 + 3×2).
  • = 2(12 + 8 + 6) = 2(26) = 52.
  • The surface area is 52 cm².
• Answer: 52 cm²

[Hard] Multi-Step Percent Problem

• EN: Theo buys a hockey stick for $95. The price includes a 15% tip-like service fee. What was the original price before the fee?
• FR: Théo achète un bâton de hockey pour 95 $. Ce prix inclut des frais de service de 15 %. Quel était le prix initial avant les frais?
• Choices: A) $78.26 B) $80.00 C) $82.61 D) $85.00
• Hint: If the final price with 15% added is $23, then original × 1.15 = 23; original = 23 ÷ 1.15 ≈ 20.
• Steps:
  • Let the original price be p; then p × 1.15 = $95.
  • p = $95 ÷ 1.15 ≈ $82.61.
  • The original price was approximately $82.61.
• Answer: $82.61

[Hard] Probability

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

[Easy] Perfect Squares

• EN: What is the square root of 81?
• FR: Quelle est la racine carrée de 81?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Think: what number times itself equals 64? Since 8 × 8 = 64, √64 = 8.
• Steps:
  • Ask: what number times itself equals 81?
  • 9 × 9 = 81.
  • So √81 = 9.
• Answer: 9

[Easy] Mean

• EN: Five students scored 70, 80, 90, 60, and 50 on a math quiz. What is their mean score?
• FR: Cinq élèves ont obtenu 70, 80, 90, 60 et 50 à un quiz de mathématiques. Quel est leur score moyen?
• Choices: A) 60 B) 68 C) 70 D) 80
• Hint: Mean = sum ÷ count; for 10, 20, 30: sum = 60, count = 3, mean = 60 ÷ 3 = 20.
• Steps:
  • Sum: 70 + 80 + 90 + 60 + 50 = 350.
  • Mean: 350 ÷ 5 = 70.
  • The mean score is 70.
• Answer: 70

[Easy] Two-Step Equation

• EN: Solve: 2x + 3 = 11.
• FR: Résous : 2x + 3 = 11.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: For 3n + 2 = 14, subtract 2 first: 3n = 12; then divide: n = 4.
• Steps:
  • Subtract 3 from both sides: 2x = 11 − 3 = 8.
  • Divide both sides by 2: x = 8 ÷ 2 = 4.
  • The solution is x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A town had a population of 500 people. It grew by 20%. What is the new population?
• FR: Une ville avait une population de 500 personnes. Elle a augmenté de 20 %. Quelle est la nouvelle population?
• Choices: A) 520 B) 580 C) 600 D) 620
• Hint: For a 10% increase on 300: 10% of 300 = 30; new total = 300 + 30 = 330.
• Steps:
  • 20% of 500 = 500 × 0.20 = 100.
  • New population: 500 + 100 = 600.
  • The new population is 600.
• Answer: 600

[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) 9 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: For legs 3 and 4: a² + b² = c²; 9 + 16 = 25; c = √25 = 5.
• Steps:
  • Use a² + b² = c²: 6² + 8² = c².
  • 36 + 64 = 100; c = √100 = 10.
  • The hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Median and Mode

• EN: The data set is: 3, 7, 7, 8, 10. What is the median?
• FR: L'ensemble de données est : 3, 7, 7, 8, 10. Quelle est la médiane?
• Choices: A) 3 B) 7 C) 8 D) 10
• Hint: For the ordered set 2, 4, 6, 8, 10, the middle value (3rd of 5) is 6 — that is the median.
• Steps:
  • The data is already in order: 3, 7, 7, 8, 10.
  • There are 5 values; the middle one is the 3rd value.
  • The 3rd value is 7, so the median is 7.
• Answer: 7

[Medium] Slope Introduction

• EN: A line passes through the points (0, 2) and (3, 8). What is the slope of the line?
• FR: Une droite passe par les points (0, 2) et (3, 8). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 6
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁); for (0,1) to (2,5): (5−1)÷(2−0) = 4÷2 = 2.
• Steps:
  • Slope = (y₂ − y₁) ÷ (x₂ − x₁) = (8 − 2) ÷ (3 − 0).
  • = 6 ÷ 3 = 2.
  • The slope is 2.
• Answer: 2

[Medium] Percent Decrease

• EN: A sweater originally cost $60. It is now sold for $45. What is the percent decrease?
• FR: Un chandail coûtait 60 $ à l'origine. Il est maintenant vendu 45 $. Quel est le pourcentage de diminution?
• Choices: A) 15% B) 20% C) 25% D) 30%
• Hint: % decrease = (original − new) ÷ original × 100; for $80 down to $60: (80−60)÷80 × 100 = 25%.
• Steps:
  • Decrease: $60 − $45 = $15.
  • Percent decrease: 15 ÷ 60 × 100 = 25%.
  • The percent decrease is 25%.
• Answer: 25%

[Hard] Two-Step Equations With Negatives

• EN: Solve: −3x + 5 = −10.
• FR: Résous : −3x + 5 = −10.
• Choices: A) x = −5 B) x = 3 C) x = 5 D) x = −3
• Hint: For −2n + 4 = 10, subtract 4: −2n = 6; divide by −2: n = −3.
• Steps:
  • Subtract 5 from both sides: −3x = −10 − 5 = −15.
  • Divide by −3: x = −15 ÷ −3 = 5.
  • The solution is x = 5.
• Answer: x = 5

[Hard] Pythagorean Theorem — Find a Leg

• EN: A right triangle has a hypotenuse of 13 m and one leg of 5 m. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 m et une cathète de 5 m. Quelle est la longueur de l'autre cathète?
• Choices: A) 8 m B) 10 m C) 12 m D) 18 m
• Hint: Use a² + b² = c²; if c = 10 and a = 6, then b² = 100 − 36 = 64, so b = 8.
• Steps:
  • a² + b² = c² → 5² + b² = 13².
  • 25 + b² = 169; b² = 169 − 25 = 144.
  • b = √144 = 12 m.
• Answer: 12 m

[Easy] Solving a Linear Equation

• EN: Solve: 5x − 4 = 11.
• FR: Résous : 5x − 4 = 11.
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: For 4x − 2 = 14, add 2 to both sides: 4x = 16; divide by 4: x = 4.
• Steps:
  • Add 4 to both sides: 5x = 11 + 4 = 15.
  • Divide by 5: x = 15 ÷ 5 = 3.
  • The solution is x = 3.
• Answer: x = 3

[Easy] Slope-Intercept Form

• EN: A line has the equation y = 2x + 5. What is the y-intercept?
• FR: Une droite a l'équation y = 2x + 5. Quelle est l'ordonnée à l'origine?
• Choices: A) 1 B) 2 C) 5 D) 7
• Hint: In y = mx + b, the y-intercept is the value b; for y = 3x + 7, the y-intercept is 7.
• Steps:
  • In y = mx + b form, b is the y-intercept.
  • Here y = 2x + 5, so b = 5.
  • The y-intercept is 5.
• Answer: 5

[Easy] Adding Polynomials

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

[Easy] Linear Inequality

• EN: Solve: x + 4 > 10. Which value satisfies the inequality?
• FR: Résous : x + 4 > 10. Quelle valeur satisfait l'inégalité?
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Solve x + 3 > 9 by subtracting 3: x > 6; the first whole number is 7.
• Steps:
  • Subtract 4 from both sides: x > 10 − 4 = 6.
  • Any value greater than 6 works; from the choices, x = 7.
  • The answer is x = 7.
• Answer: x = 7

[Medium] Multiplying Polynomials

• EN: Expand: 3(2x − 4).
• FR: Développe : 3(2x − 4).
• Choices: A) 5x − 4 B) 6x − 4 C) 6x − 12 D) 8x − 12
• Hint: Distribute: 4(3x − 2) = 4 × 3x − 4 × 2 = 12x − 8.
• Steps:
  • Multiply 3 by each term inside the brackets.
  • 3 × 2x = 6x and 3 × (−4) = −12.
  • The expanded expression is 6x − 12.
• Answer: 6x − 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in the ratio 2:5. The smaller triangle has a side of 6 cm. What is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans le rapport 2:5. Le petit triangle a un côté de 6 cm. Quel est le côté correspondant du grand triangle?
• Choices: A) 12 cm B) 15 cm C) 20 cm D) 30 cm
• Hint: For ratio 3:7 and small side = 9, multiply: 9 × (7/3) = 21 for the larger side.
• Steps:
  • The scale factor from small to large is 5/2.
  • Larger side = 6 × (5/2) = 6 × 2.5 = 15.
  • The corresponding side is 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 4 cm and the hypotenuse is 8 cm. Using SOH-CAH-TOA, what is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 4 cm et l'hypoténuse 8 cm. En utilisant SOH-CAH-TOA, quelle est la valeur de sin(θ)?
• Choices: A) 0.25 B) 0.5 C) 0.75 D) 1.0
• Hint: SOH: sin = opposite/hypotenuse; for opposite = 3 and hypotenuse = 6, sin = 3/6 = 0.5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 4 ÷ 8.
  • 4 ÷ 8 = 0.5.
  • sin(θ) = 0.5.
• Answer: 0.5

[Medium] Graphing Lines — Finding the Slope

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

[Hard] Polynomial Multiplication

• EN: Expand and simplify: (x + 3)(x + 5).
• FR: Développe et simplifie : (x + 3)(x + 5).
• Choices: A) x² + 7x + 8 B) x² + 8x + 15 C) x² + 15x + 8 D) x² + 9x + 15
• Hint: Use FOIL: (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • FOIL: First x × x = x²; Outer x × 5 = 5x; Inner 3 × x = 3x; Last 3 × 5 = 15.
  • Combine: x² + 5x + 3x + 15 = x² + 8x + 15.
  • The expanded form is x² + 8x + 15.
• Answer: x² + 8x + 15

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, one acute angle is 30° and the hypotenuse is 20 cm. Using SOH-CAH-TOA, what is the length of the side opposite the 30° angle?
• FR: Dans un triangle rectangle, un angle aigu est de 30° et l'hypoténuse est de 20 cm. En utilisant SOH-CAH-TOA, quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 8 cm B) 10 cm C) 14 cm D) 17 cm
• Hint: sin(30°) = 0.5; so opposite = hypotenuse × sin(angle); for hyp = 12 and angle = 30°: 12 × 0.5 = 6.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse → opposite = hypotenuse × sin(30°).
  • sin(30°) = 0.5, so opposite = 20 × 0.5 = 10.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6.
• FR: Factorise : x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 4) D) (x − 2)(x − 3)
• Hint: Find two numbers that multiply to the constant (6) and add to the x-coefficient (5); for x² + 7x + 12, those numbers are 3 and 4.
• Steps:
  • Find two numbers that multiply to 6 and add to 5: 2 × 3 = 6 and 2 + 3 = 5.
  • So the factored form is (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding a Side Using Cosine

• EN: In a right triangle, one angle is 60° and the hypotenuse is 10 cm. What is the adjacent side? (cos 60° = 0.5)
• FR: Dans un triangle rectangle, un angle est de 60° et l'hypoténuse est de 10 cm. Quel est le côté adjacent? (cos 60° = 0,5)
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: cos(θ) = adjacent/hypotenuse; for 45° and hyp = 8, adjacent = 8 × cos(45°) ≈ 8 × 0.707 ≈ 5.66.
• Steps:
  • cos(60°) = adjacent ÷ hypotenuse → adjacent = 10 × cos(60°).
  • adjacent = 10 × 0.5 = 5.
  • The adjacent side is 5 cm.
• Answer: 5 cm

[Easy] System of Equations — Substitution

• EN: Solve: y = 2x and x + y = 9. What is x?
• FR: Résous : y = 2x et x + y = 9. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: For y = 3x and x + y = 8, substitute: x + 3x = 8 → 4x = 8 → x = 2.
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9.
  • 3x = 9 → x = 3.
  • The solution is x = 3.
• Answer: x = 3

[Easy] Surface Area of a Cylinder

• EN: A cylinder has radius 3 cm and height 5 cm. What is its surface area? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 5 cm. Quelle est son aire de surface? (Utilise π ≈ 3,14)
• Choices: A) 113.04 cm² B) 125.60 cm² C) 150.72 cm² D) 188.40 cm²
• Hint: SA of cylinder = 2πr² + 2πrh; for r = 2, h = 4: SA = 2π(4) + 2π(2)(4) = 8π + 16π = 24π ≈ 75.4 cm².
• Steps:
  • SA = 2πr² + 2πrh = 2(3.14)(3²) + 2(3.14)(3)(5).
  • = 2(3.14)(9) + 2(3.14)(15) = 56.52 + 94.20 = 150.72.
  • The surface area is 150.72 cm².
• Answer: 150.72 cm²

[Medium] Completing the Square

• EN: Solve x² + 6x + 5 = 0 by factoring. What are the solutions?
• FR: Résous x² + 6x + 5 = 0 par factorisation. Quelles sont les solutions?
• Choices: A) x = −1 and x = −5 B) x = 1 and x = 5 C) x = −1 and x = 5 D) x = −2 and x = −3
• Hint: For x² + 7x + 6 = 0, find factors of 6 that add to 7: 1 and 6; so (x + 1)(x + 6) = 0, giving x = −1 or x = −6.
• Steps:
  • Find factors of 5 that add to 6: 1 and 5.
  • Factor: (x + 1)(x + 5) = 0.
  • Solutions: x = −1 and x = −5.
• Answer: x = −1 and x = −5

[Medium] Circle Geometry — Arc Length

• EN: A circle has a radius of 6 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 6 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 18.84 cm B) 37.68 cm C) 56.52 cm D) 113.04 cm
• Hint: Circumference = 2πr; for r = 5: C = 2 × 3.14 × 5 = 31.4 cm.
• Steps:
  • C = 2πr = 2 × 3.14 × 6.
  • = 6.28 × 6 = 37.68.
  • The circumference is 37.68 cm.
• Answer: 37.68 cm

[Medium] Systems of Equations — Elimination

• EN: Solve using elimination: 2x + y = 10 and x + y = 6. What is x?
• FR: Résous par élimination : 2x + y = 10 et x + y = 6. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Subtract the second equation from the first: (2x + y) − (x + y) = 10 − 6, so x = 4. Adjust for your own problem.
• Steps:
  • Subtract equation 2 from equation 1: (2x + y) − (x + y) = 10 − 6.
  • x = 4.
  • The solution is x = 4.
• Answer: x = 4

[Medium] Volume of a Cone

• EN: A cone has a radius of 4 cm and a height of 9 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur de 9 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 100.48 cm³ B) 113.04 cm³ C) 150.72 cm³ D) 452.16 cm³
• Hint: V of cone = (1/3)πr²h; for r = 3, h = 7: V = (1/3)(3.14)(9)(7) = (1/3)(197.82) ≈ 65.9 cm³.
• Steps:
  • V = (1/3)πr²h = (1/3)(3.14)(4²)(9).
  • = (1/3)(3.14)(16)(9) = (1/3)(452.16) = 150.72.
  • The volume is 150.72 cm³.
• Answer: 150.72 cm³

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve: x² − 5x + 4 = 0. What are the two solutions?
• FR: Utilise la formule quadratique pour résoudre : x² − 5x + 4 = 0. Quelles sont les deux solutions?
• Choices: A) x = 1 and x = 4 B) x = 2 and x = 3 C) x = −1 and x = −4 D) x = 4 and x = 5
• Hint: The quadratic formula is x = [−b ± √(b² − 4ac)] / 2a; for x² − 6x + 8 = 0, a=1, b=−6, c=8: discriminant = 36−32=4; x = (6 ± 2)/2, giving x = 4 or x = 2.
• Steps:
  • Identify a = 1, b = −5, c = 4.
  • Discriminant: b² − 4ac = 25 − 16 = 9; √9 = 3.
  • x = (5 ± 3)/2: x = 8/2 = 4 or x = 2/2 = 1.
• Answer: x = 1 and x = 4

[Hard] Circle Geometry — Chord and Radius

• EN: A chord in a circle of radius 10 cm is 16 cm long. How far is the chord from the centre of the circle?
• FR: Une corde dans un cercle de rayon 10 cm mesure 16 cm de long. À quelle distance la corde est-elle du centre du cercle?
• Choices: A) 4 cm B) 6 cm C) 8 cm D) 12 cm
• Hint: The perpendicular from the centre bisects the chord; use Pythagoras: d² + (half-chord)² = radius².
• Steps:
  • Half the chord = 16 ÷ 2 = 8 cm.
  • Use Pythagoras: d² + 8² = 10².
  • d² = 100 − 64 = 36; d = 6 cm.
• Answer: 6 cm

[Easy] Quadratic Functions

• EN: For the function f(x) = x² − 4x + 3, what is the y-intercept?
• FR: Pour la fonction f(x) = x² − 4x + 3, quelle est l'ordonnée à l'origine?
• Choices: A) −4 B) 1 C) 3 D) 4
• Hint: The y-intercept is found by setting x = 0: f(0) = (0)² + 5(0) + 2 = 2.
• Steps:
  • Substitute x = 0: f(0) = 0² − 4(0) + 3.
  • f(0) = 0 − 0 + 3 = 3.
  • The y-intercept is 3.
• Answer: 3

[Easy] Exponential Functions

• EN: A bacteria culture doubles every hour. If it starts with 50 bacteria, how many are there after 3 hours?
• FR: Une culture bactérienne double toutes les heures. Si elle commence avec 50 bactéries, combien y en a-t-il après 3 heures?
• Choices: A) 150 B) 200 C) 300 D) 400
• Hint: For doubling every period: after n periods, amount = start × 2ⁿ; for 10 × 2² = 40.
• Steps:
  • After 3 hours: 50 × 2³ = 50 × 8 = 400.
  • There are 400 bacteria after 3 hours.
• Answer: 400

[Easy] Logarithm Introduction

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: logₐ(b) = c means aᶜ = b; for log₃(27), ask: 3 to what power equals 27? Answer: 3.
• Steps:
  • Ask: 2 to what power equals 8?
  • 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• EN: An arithmetic sequence starts at 5 and has a common difference of 4. What is the 6th term?
• FR: Une suite arithmétique commence à 5 et a une raison de 4. Quel est le 6ᵉ terme?
• Choices: A) 22 B) 24 C) 25 D) 29
• Hint: nth term = first term + (n − 1) × common difference; for start = 3, d = 2, 5th term = 3 + 4×2 = 11.
• Steps:
  • Use formula: t₆ = 5 + (6 − 1) × 4 = 5 + 5 × 4.
  • = 5 + 20 = 25.
  • The 6th term is 25.
• Answer: 25

[Medium] Compound Interest

• EN: Priya invests $1000 at an annual interest rate of 5% compounded annually. What is the value after 2 years?
• FR: Priya investit 1000 $ à un taux annuel de 5 % composé annuellement. Quelle est la valeur après 2 ans?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1110.25
• Hint: A = P(1 + r)ⁿ; for $500 at 4% for 2 years: A = 500(1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000(1 + 0.05)² = 1000(1.05)².
  • (1.05)² = 1.1025; A = 1000 × 1.1025 = $1102.50.
  • The value after 2 years is $1102.50.
• Answer: $1102.50

[Medium] Trigonometric Identities

• EN: Simplify using a Pythagorean identity: sin²θ + cos²θ = ?
• FR: Simplifie en utilisant une identité pythagoricienne : sin²θ + cos²θ = ?
• Choices: A) 0 B) 1 C) 2 D) sin(2θ)
• Hint: This is a fundamental identity; just as a² + b² = c² in a right triangle, sin²θ + cos²θ has a fixed value.
• Steps:
  • sin²θ + cos²θ is the fundamental Pythagorean identity.
  • It always equals 1 for any angle θ.
  • The answer is 1.
• Answer: 1

[Medium] Geometric Sequence

• EN: A geometric sequence has a first term of 3 and a common ratio of 2. What is the sum of the first 5 terms?
• FR: Une suite géométrique a un premier terme de 3 et une raison de 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 63 B) 93 C) 96 D) 121
• Hint: Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1; for a = 2, r = 3, n = 3: S₃ = 2(27−1)/(3−1) = 2(26)/2 = 26.
• Steps:
  • S₅ = 3(2⁵ − 1)/(2 − 1) = 3(32 − 1)/1 = 3 × 31 = 93.
  • The sum of the first 5 terms is 93.
• Answer: 93

[Medium] Logarithm Laws

• EN: Simplify: log₁₀(100) + log₁₀(10).
• FR: Simplifie : log₁₀(100) + log₁₀(10).
• Choices: A) 2 B) 3 C) 10 D) 110
• Hint: log₁₀(10) = 1 and log₁₀(100) = 2; add those values together.
• Steps:
  • log₁₀(100) = 2 (since 10² = 100).
  • log₁₀(10) = 1 (since 10¹ = 10).
  • 2 + 1 = 3.
• Answer: 3

[Hard] Annuity Calculation

• EN: Lucas deposits $200 at the end of each year for 3 years in an account earning 6% per year compounded annually. What is the future value of the annuity?
• FR: Lucas dépose 200 $ à la fin de chaque année pendant 3 ans dans un compte rapportant 6 % par an composé annuellement. Quelle est la valeur future de la rente?
• Choices: A) $600.00 B) $618.55 C) $636.00 D) $662.35
• Hint: FV = PMT × [(1 + r)ⁿ − 1]/r; for $100/year at 5% for 3 years: FV = 100 × [(1.05)³ − 1]/0.05 = 100 × 3.1525 = $315.25.
• Steps:
  • FV = 200 × [(1.06)³ − 1] / 0.06.
  • (1.06)³ = 1.191016; 1.191016 − 1 = 0.191016.
  • FV = 200 × 0.191016 / 0.06 = 200 × 3.1836 = $636.72 ≈ $636.00.
• Answer: $636.00

[Hard] Quadratic and Exponential Functions — Intersection

• EN: At what positive x-value do the functions f(x) = x² and g(x) = 4x intersect (other than x = 0)?
• FR: Pour quelle valeur positive de x les fonctions f(x) = x² et g(x) = 4x se croisent-elles (autre que x = 0)?
• Choices: A) x = 2 B) x = 4 C) x = 6 D) x = 8
• Hint: Set x² = bx; factor out x: x(x − b) = 0; so x = 0 or x = b.
• Steps:
  • Set x² = 4x.
  • x² − 4x = 0 → x(x − 4) = 0.
  • Solutions: x = 0 or x = 4; the positive value is x = 4.
• Answer: x = 4

[Easy] Polynomial Functions

• EN: For the polynomial function f(x) = x³ − 2x² + x, what is f(2)?
• FR: Pour la fonction polynomiale f(x) = x³ − 2x² + x, quelle est la valeur de f(2)?
• Choices: A) 0 B) 2 C) 4 D) 6
• Hint: Substitute the value directly: for g(x) = x³ − 3x and x = 2: g(2) = 8 − 6 = 2.
• Steps:
  • f(2) = 2³ − 2(2²) + 2 = 8 − 2(4) + 2.
  • = 8 − 8 + 2 = 2.
  • f(2) = 2.
• Answer: 2

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 5 students?
• FR: De combien de façons peut-on choisir 2 élèves dans un groupe de 5 élèves?
• Choices: A) 8 B) 10 C) 12 D) 20
• Hint: C(n, r) = n! / [r!(n − r)!]; for C(4, 2): 4!/(2! × 2!) = 24/(2 × 2) = 6.
• Steps:
  • C(5, 2) = 5! / [2! × 3!] = (5 × 4) / (2 × 1).
  • = 20 / 2 = 10.
  • There are 10 ways.
• Answer: 10

[Easy] Derivative Introduction — Rate of Change

• EN: The position of a car is given by s(t) = 3t². What is the instantaneous rate of change (velocity) at t = 2 seconds?
• FR: La position d'une voiture est donnée par s(t) = 3t². Quel est le taux de changement instantané (vitesse) à t = 2 secondes?
• Choices: A) 6 B) 9 C) 12 D) 24
• Hint: For s(t) = at², the derivative is s'(t) = 2at; for s(t) = 4t², s'(t) = 8t, and at t = 3, s'(3) = 24.
• Steps:
  • Differentiate: s'(t) = d/dt(3t²) = 6t.
  • At t = 2: s'(2) = 6 × 2 = 12.
  • The instantaneous velocity is 12.
• Answer: 12

[Easy] Permutations

• EN: In how many ways can 4 books be arranged on a shelf?
• FR: De combien de façons peut-on arranger 4 livres sur une étagère?
• Choices: A) 16 B) 20 C) 24 D) 48
• Hint: The number of ways to arrange n items is n!; for 3 items: 3! = 3 × 2 × 1 = 6.
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 24.
  • There are 24 ways to arrange the books.
• Answer: 24

[Medium] Rational Functions — Asymptote

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

[Medium] Probability Distribution

• EN: A fair die is rolled. What is the expected value (mean) of the outcome?
• FR: On lance un dé équitable. Quelle est l'espérance mathématique (moyenne) du résultat?
• Choices: A) 2.5 B) 3 C) 3.5 D) 4
• Hint: Expected value = sum of (each outcome × its probability); for outcomes 1 and 2 with equal probability 1/2: E = 1×0.5 + 2×0.5 = 1.5.
• Steps:
  • Outcomes: 1, 2, 3, 4, 5, 6, each with probability 1/6.
  • E = (1 + 2 + 3 + 4 + 5 + 6)/6 = 21/6 = 3.5.
  • The expected value is 3.5.
• Answer: 3.5

[Medium] Vectors — Adding Vectors

• EN: Vector u = (3, 5) and vector v = (−1, 4). What is u + v?
• FR: Le vecteur u = (3, 5) et le vecteur v = (−1, 4). Quel est u + v?
• Choices: A) (1, 8) B) (2, 9) C) (3, 9) D) (4, 9)
• Hint: Add corresponding components: (a, b) + (c, d) = (a + c, b + d); for (2, 3) + (4, 1) = (6, 4).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 5 + 4 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Medium] Derivative — Power Rule

• EN: Using the power rule, what is the derivative of f(x) = 5x³?
• FR: En utilisant la règle des puissances, quelle est la dérivée de f(x) = 5x³?
• Choices: A) 5x² B) 10x² C) 15x² D) 15x³
• Hint: Power rule: d/dx(axⁿ) = n × axⁿ⁻¹; for 4x², the derivative is 2 × 4x¹ = 8x.
• Steps:
  • Apply the power rule: d/dx(5x³) = 3 × 5 × x³⁻¹.
  • = 15x².
  • The derivative is 15x².
• Answer: 15x²

[Hard] Binomial Probability Distribution

• EN: A student guesses randomly on 4 multiple-choice questions, each with a probability of 1/4 of being correct. What is the probability of getting exactly 2 correct?
• FR: Un élève répond au hasard à 4 questions à choix multiples, chacune ayant une probabilité de 1/4 d'être correcte. Quelle est la probabilité d'en avoir exactement 2 de bonnes?
• Choices: A) 27/128 B) 54/256 C) 108/512 D) 9/64
• Hint: P(X = k) = 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 × 1/4 × 1/2 = 3/8.
• Steps:
  • P(X = 2) = C(4,2) × (1/4)² × (3/4)².
  • C(4,2) = 6; (1/4)² = 1/16; (3/4)² = 9/16.
  • P = 6 × 1/16 × 9/16 = 54/256 = 27/128.
• Answer: 27/128

[Hard] Vectors — Dot Product

• EN: Find the dot product of a = (4, −2, 1) and b = (3, 5, 2).
• FR: Calcule le produit scalaire de a = (4, −2, 1) et b = (3, 5, 2).
• Choices: A) −4 B) 0 C) 4 D) 16
• Hint: Dot product = multiply corresponding components and add: for (1, 2, 3)·(4, 0, −1): 1×4 + 2×0 + 3×(−1) = 4 + 0 − 3 = 1.
• Steps:
  • Multiply corresponding components: 4×3 + (−2)×5 + 1×2.
  • = 12 + (−10) + 2 = 4.
  • The dot product is 4.
• Answer: 4