Daily Math — 2026-07-15

[Easy] Counting to 20

• EN: There are 7 apples on the table and 6 more in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 6 autres dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 11 apples B) 13 apples C) 14 apples D) 15 apples
• Hint: To add, count on from the bigger number — like 8 + 4, start at 8 and count up 4 more.
• Steps:
  • Start at 7 and count on 6 more.
  • 7 → 8, 9, 10, 11, 12, 13.
  • So there are 13 apples in all.
• Answer: 13 apples

[Easy] Subtraction Within 20

• EN: Liam has 15 stickers. He gives 8 to his friend. How many stickers does Liam have left?
• FR: Liam a 15 autocollants. Il en donne 8 à son ami. Combien d'autocollants Liam a-t-il maintenant?
• Choices: A) 5 stickers B) 6 stickers C) 7 stickers D) 8 stickers
• Hint: To subtract, count back from the bigger number — like 12 − 5, start at 12 and count back 5.
• Steps:
  • Start at 15 and count back 8.
  • 15 → 14, 13, 12, 11, 10, 9, 8, 7.
  • So Liam has 7 stickers left.
• Answer: 7 stickers

[Easy] Skip Counting by 2s

• EN: Ava is skip counting by 2s. She says 2, 4, 6, 8. What number comes next?
• FR: Ava compte par bonds de 2. Elle dit 2, 4, 6, 8. Quel est le prochain nombre?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When skip counting by 2s, add 2 each time — like 4, 6, the next is 8.
• Steps:
  • The pattern is adding 2 each time.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 17
• Hint: The number that is farther along on a number line is greater — like 7 is greater than 3.
• Steps:
  • Place both numbers on a number line.
  • 14 is farther from 0 than 9 is.
  • So 14 is greater.
• Answer: 14

[Medium] Addition Within 20

• EN: There are 9 red crayons and 9 blue crayons in a box. How many crayons are there altogether?
• FR: Il y a 9 crayons rouges et 9 crayons bleus dans une boîte. Combien y a-t-il de crayons en tout?
• Choices: A) 16 crayons B) 17 crayons C) 18 crayons D) 19 crayons
• Hint: When both numbers are the same, you are doubling — like 8 + 8 = 16.
• Steps:
  • This is a doubles fact: 9 + 9.
  • 9 + 9 = 18.
  • So there are 18 crayons altogether.
• Answer: 18 crayons

[Medium] Skip Counting by 5s

• EN: Maya counts by 5s: 5, 10, 15, 20, 25. What is the next number she will say?
• FR: Maya compte par bonds de 5 : 5, 10, 15, 20, 25. Quel est le prochain nombre qu'elle dira?
• Choices: A) 27 B) 28 C) 30 D) 35
• Hint: When skip counting by 5s, add 5 each time — like 15, the next is 20.
• Steps:
  • The pattern is adding 5 each time.
  • 25 + 5 = 30.
  • So the next number is 30.
• Answer: 30

[Medium] Coin Recognition

• EN: Noah has 1 dime and 1 nickel. How many cents does he have in all?
• FR: Noah a 1 pièce de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents — if you had 2 dimes, that would be 20 cents.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Medium] Counting to 100

• EN: What number comes just before 50?
• FR: Quel nombre vient juste avant 50?
• Choices: A) 48 B) 49 C) 51 D) 52
• Hint: The number just before any number is one less — like the number just before 30 is 29.
• Steps:
  • Subtract 1 from 50.
  • 50 − 1 = 49.
  • So 49 comes just before 50.
• Answer: 49

[Hard] Adding Three Numbers

• EN: Sofia has 5 pennies, 4 pennies, and 3 pennies in three different piggy banks. How many pennies does she have in all?
• FR: Sofia a 5 sous, 4 sous et 3 sous dans trois tirelires différentes. Combien de sous a-t-elle en tout?
• Choices: A) 10 pennies B) 11 pennies C) 12 pennies D) 13 pennies
• Hint: To add three numbers, start with two of them, then add the third — like 4 + 3 + 2, do 4 + 3 = 7, then 7 + 2 = 9.
• Steps:
  • Add the first two: 5 + 4 = 9.
  • Add the third: 9 + 3 = 12.
  • So Sofia has 12 pennies in all.
• Answer: 12 pennies

[Hard] Subtraction Story Problem

• EN: There were 18 kids at the park. Then 9 kids went home. How many kids are still at the park?
• FR: Il y avait 18 enfants au parc. Ensuite, 9 enfants sont rentrés chez eux. Combien d'enfants sont encore au parc?
• Choices: A) 7 kids B) 8 kids C) 9 kids D) 10 kids
• Hint: This is a subtraction problem — start at the bigger number and count back, like 14 − 6, count back 6 from 14.
• Steps:
  • Start at 18 and subtract 9.
  • 18 − 9 = 9.
  • So 9 kids are still at the park.
• Answer: 9 kids

[Easy] Addition Within 100

• EN: There are 34 students in one classroom and 25 students in another. How many students are there in total?
• FR: Il y a 34 élèves dans une classe et 25 dans une autre. Combien y a-t-il d'élèves en tout?
• Choices: A) 57 students B) 59 students C) 61 students D) 63 students
• Hint: Add the tens first, then the ones — like 22 + 31, add 20 + 30 = 50, then 2 + 1 = 3, so 53.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59 students.
• Answer: 59 students

[Easy] Telling Time

• EN: The clock shows the hour hand on the 3 and the minute hand on the 12. What time is it?
• FR: L'aiguille des heures est sur le 3 et l'aiguille des minutes est sur le 12. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 4:00
• Hint: When the minute hand is on the 12, it is exactly on the hour — like if the hour hand is on 7, it is 7:00.
• Steps:
  • The minute hand is on the 12, so it is exactly on the hour.
  • The hour hand is on the 3.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 14 cm et un crayon de cire mesure 9 cm. De combien le crayon à mine est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find how much longer, subtract the shorter length from the longer — like 11 cm − 4 cm = 7 cm.
• Steps:
  • Subtract: 14 − 9 = 5.
  • So the pencil is 5 cm longer than the crayon.
• Answer: 5 cm

[Easy] Subtraction Within 100

• EN: A jar had 72 jellybeans. Kids ate 41 of them. How many jellybeans are left?
• FR: Un pot contenait 72 bonbons gélifiés. Des enfants en ont mangé 41. Combien de bonbons reste-t-il?
• Choices: A) 29 jellybeans B) 31 jellybeans C) 33 jellybeans D) 35 jellybeans
• Hint: Subtract the tens first, then the ones — like 65 − 32, do 60 − 30 = 30, then 5 − 2 = 3, so 33.
• Steps:
  • Subtract the tens: 70 − 40 = 30.
  • Subtract the ones: 2 − 1 = 1.
  • 30 + 1 = 31 jellybeans.
• Answer: 31 jellybeans

[Medium] Counting Coins

• EN: Emma has 2 quarters. How many cents does she have?
• FR: Emma a 2 pièces de 25 cents. Combien de cents a-t-elle en tout?
• Choices: A) 25 cents B) 40 cents C) 50 cents D) 75 cents
• Hint: A quarter is worth 25 cents — if you had 3 quarters, that would be 75 cents.
• Steps:
  • Each quarter = 25 cents.
  • 25 + 25 = 50 cents.
  • So Emma has 50 cents.
• Answer: 50 cents

[Medium] Telling Time to the Half Hour

• EN: Ben started watching a show at 4:00. The show is 30 minutes long. What time does it end?
• FR: Ben a commencé à regarder une émission à 4 h 00. L'émission dure 30 minutes. À quelle heure se termine-t-elle?
• Choices: A) 4:00 B) 4:30 C) 5:00 D) 5:30
• Hint: Adding 30 minutes to an exact hour gives you the half hour — like 2:00 plus 30 minutes is 2:30.
• Steps:
  • Start at 4:00.
  • Add 30 minutes.
  • 4:00 + 30 minutes = 4:30.
• Answer: 4:30

[Medium] Patterns

• EN: Look at this pattern: 10, 20, 30, 40, ___. What is the missing number?
• FR: Observe ce modèle : 10, 20, 30, 40, ___. Quel est le nombre manquant?
• Choices: A) 45 B) 48 C) 50 D) 55
• Hint: Find the rule by looking at how much each number grows — like 5, 10, 15, the rule is add 5.
• Steps:
  • Each number increases by 10.
  • 40 + 10 = 50.
  • So the missing number is 50.
• Answer: 50

[Medium] Addition with Regrouping

• EN: Kenji has 47 hockey cards and his friend gives him 36 more. How many cards does Kenji have now?
• FR: Kenji a 47 cartes de hockey et son ami lui en donne 36 de plus. Combien de cartes Kenji a-t-il maintenant?
• Choices: A) 73 cards B) 81 cards C) 83 cards D) 85 cards
• Hint: Add the ones first, regroup if needed, then add the tens — like 28 + 35, ones: 8 + 5 = 13, write 3 carry 1, tens: 2 + 3 + 1 = 6, answer is 63.
• Steps:
  • Ones: 7 + 6 = 13. Write 3, carry 1.
  • Tens: 4 + 3 + 1 = 8.
  • So Kenji has 83 cards.
• Answer: 83 cards

[Hard] Counting Coins to $1

• EN: Priya has 1 loonie, 1 quarter, and 1 dime. How much money does she have in total?
• FR: Priya a 1 pièce de 1 dollar, 1 pièce de 25 cents et 1 pièce de 10 cents. Combien d'argent a-t-elle en tout?
• Choices: A) $1.25 B) $1.30 C) $1.35 D) $1.40
• Hint: A loonie is $1.00, a quarter is $0.25, and a dime is $0.10 — add them all together like you would add 100 + 25 + 5.
• Steps:
  • Loonie = $1.00, quarter = $0.25, dime = $0.10.
  • $1.00 + $0.25 = $1.25.
  • $1.25 + $0.10 = $1.35.
• Answer: $1.35

[Hard] Two-Step Problem

• EN: There are 55 books on a shelf. A librarian adds 18 books, then removes 23 books. How many books are on the shelf now?
• FR: Il y a 55 livres sur une étagère. Une bibliothécaire en ajoute 18, puis en retire 23. Combien de livres reste-t-il sur l'étagère?
• Choices: A) 48 books B) 50 books C) 52 books D) 54 books
• Hint: Do two steps in order — first add, then subtract, like 40 + 12 = 52, then 52 − 10 = 42.
• Steps:
  • First, add: 55 + 18 = 73.
  • Then subtract: 73 − 23 = 50.
  • So there are 50 books on the shelf now.
• Answer: 50 books

[Easy] Multiplication by 2

• EN: A hockey team has 6 players on the ice. How many skates are there altogether if each player wears 2 skates?
• FR: Une équipe de hockey a 6 joueurs sur la glace. Combien de patins y a-t-il en tout si chaque joueur porte 2 patins?
• Choices: A) 8 skates B) 10 skates C) 12 skates D) 14 skates
• Hint: Multiplying by 2 is the same as doubling — like 7 × 2 = 14.
• Steps:
  • Each of the 6 players wears 2 skates.
  • 6 × 2 = 12.
  • So there are 12 skates altogether.
• Answer: 12 skates

[Easy] Multiplication by 5

• EN: There are 4 bags with 5 apples in each bag. How many apples are there in total?
• FR: Il y a 4 sacs contenant 5 pommes chacun. Combien y a-t-il de pommes en tout?
• Choices: A) 15 apples B) 18 apples C) 20 apples D) 25 apples
• Hint: Counting by 5s helps with the 5 times table — like 3 × 5 = 15.
• Steps:
  • 4 bags × 5 apples each.
  • 4 × 5 = 20.
  • So there are 20 apples in total.
• Answer: 20 apples

[Easy] Basic Fractions

• EN: A pizza is cut into 4 equal slices. Mia eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 parts égales. Mia mange 1 part. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: A fraction shows part of a whole — the bottom number tells how many equal parts, and the top tells how many you have, like 1 out of 3 equal parts is 1/3.
• Steps:
  • The pizza is cut into 4 equal parts.
  • Mia eats 1 part.
  • So she ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Perimeter

• EN: A rectangle has a length of 5 cm and a width of 3 cm. What is its perimeter?
• FR: Un rectangle a une longueur de 5 cm et une largeur de 3 cm. Quel est son périmètre?
• Choices: A) 12 cm B) 14 cm C) 15 cm D) 16 cm
• Hint: Perimeter means the distance all the way around — add all four sides, like a rectangle with length 4 and width 2 has perimeter 4 + 4 + 2 + 2 = 12.
• Steps:
  • A rectangle has 2 lengths and 2 widths.
  • Perimeter = 5 + 5 + 3 + 3.
  • 10 + 6 = 16 cm.
• Answer: 16 cm

[Medium] Multiplication by 3

• EN: There are 7 shelves in the library. Each shelf holds 3 rows of books. How many rows of books are there in all?
• FR: Il y a 7 étagères dans la bibliothèque. Chaque étagère a 3 rangées de livres. Combien y a-t-il de rangées de livres en tout?
• Choices: A) 18 rows B) 21 rows C) 24 rows D) 27 rows
• Hint: Use the 3 times table — like 6 × 3 = 18.
• Steps:
  • 7 shelves × 3 rows each.
  • 7 × 3 = 21.
  • So there are 21 rows of books in all.
• Answer: 21 rows

[Medium] Basic Division

• EN: There are 24 students going on a field trip. They are split equally into 4 groups. How many students are in each group?
• FR: Il y a 24 élèves qui partent en excursion. Ils sont répartis également en 4 groupes. Combien d'élèves y a-t-il dans chaque groupe?
• Choices: A) 4 students B) 5 students C) 6 students D) 8 students
• Hint: Division splits a total into equal groups — like 18 ÷ 3 = 6 means 18 shared equally into 3 groups gives 6 each.
• Steps:
  • 24 students shared equally into 4 groups.
  • 24 ÷ 4 = 6.
  • So each group has 6 students.
• Answer: 6 students

[Medium] Reading a Graph

• EN: A bar graph shows that 8 students like hockey, 5 like soccer, and 3 like basketball. How many students were surveyed in total?
• FR: Un diagramme à bandes montre que 8 élèves aiment le hockey, 5 le soccer et 3 le basketball. Combien d'élèves ont été interrogés en tout?
• Choices: A) 13 students B) 14 students C) 16 students D) 18 students
• Hint: To find the total from a graph, add up all the bars — like 4 + 7 + 2 = 13.
• Steps:
  • Add all three groups: 8 + 5 + 3.
  • 8 + 5 = 13, then 13 + 3 = 16.
  • So 16 students were surveyed in total.
• Answer: 16 students

[Medium] Multiplication by 10

• EN: Each box has 10 crayons. There are 8 boxes. How many crayons are there in all?
• FR: Chaque boîte contient 10 crayons. Il y a 8 boîtes. Combien y a-t-il de crayons en tout?
• Choices: A) 70 crayons B) 75 crayons C) 80 crayons D) 90 crayons
• Hint: Multiplying by 10 just puts a zero at the end of the number — like 6 × 10 = 60.
• Steps:
  • 8 boxes × 10 crayons each.
  • 8 × 10 = 80.
  • So there are 80 crayons in all.
• Answer: 80 crayons

[Hard] Two-Step Multiplication and Subtraction

• EN: A store has 5 boxes of muffins with 4 muffins in each box. The baker sells 9 muffins. How many muffins are left?
• FR: Un magasin a 5 boîtes de muffins avec 4 muffins dans chaque boîte. Le boulanger vend 9 muffins. Combien de muffins reste-t-il?
• Choices: A) 9 muffins B) 11 muffins C) 13 muffins D) 15 muffins
• Hint: First multiply to find the total, then subtract — like 3 × 4 = 12 muffins, then 12 − 5 = 7 muffins left.
• Steps:
  • First find total muffins: 5 × 4 = 20.
  • Then subtract muffins sold: 20 − 9 = 11.
  • So there are 11 muffins left.
• Answer: 11 muffins

[Hard] Fractions of a Set

• EN: There are 12 mittens in a drawer. One quarter of them are red. How many red mittens are there?
• FR: Il y a 12 mitaines dans un tiroir. Le quart d'entre elles sont rouges. Combien de mitaines rouges y a-t-il?
• Choices: A) 2 red mittens B) 3 red mittens C) 4 red mittens D) 6 red mittens
• Hint: To find one quarter of a set, divide by 4 — like one quarter of 8 is 8 ÷ 4 = 2.
• Steps:
  • One quarter of 12 means dividing by 4.
  • 12 ÷ 4 = 3.
  • So there are 3 red mittens.
• Answer: 3 red mittens

[Easy] Multiplication Tables

• EN: What is 8 × 7?
• FR: Combien font 8 × 7?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Break it apart to make it easier — like 8 × 6, think of 8 × 5 = 40, then add 8 more = 48.
• Steps:
  • Think: 8 × 7.
  • 8 × 7 = 56.
  • The answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 4.37?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,37?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 3 tens
• Hint: The first digit after the decimal point is in the tenths place — like in 2.58, the 5 is in the tenths place.
• Steps:
  • In 4.37, the digits after the decimal are in tenths and hundredths.
  • The 3 is in the first place after the decimal.
  • So 3 is in the tenths place.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A rectangular garden is 9 m long and 4 m wide. What is its area?
• FR: Un jardin rectangulaire mesure 9 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 26 m² B) 32 m² C) 36 m² D) 40 m²
• Hint: Area of a rectangle = length × width — like a rectangle that is 5 m × 6 m has an area of 30 m².
• Steps:
  • Area = length × width.
  • 9 × 4 = 36.
  • So the area is 36 m².
• Answer: 36 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/4?
• FR: Quelle fraction est plus grande : 3/4 ou 1/4?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) 4/4
• Hint: When fractions have the same denominator, the one with the bigger numerator is greater — like 5/8 is greater than 2/8.
• Steps:
  • Both fractions have the same denominator (4).
  • Compare the numerators: 3 is greater than 1.
  • So 3/4 is greater.
• Answer: 3/4

[Medium] Long Division With Remainders

• EN: 47 students are divided into groups of 5. How many complete groups are there, and how many students are left over?
• FR: 47 élèves sont répartis en groupes de 5. Combien y a-t-il de groupes complets et combien d'élèves reste-t-il?
• Choices: A) 8 groups, remainder 5 B) 9 groups, remainder 2 C) 9 groups, remainder 4 D) 10 groups, remainder 1
• Hint: Divide to find how many full groups fit, then find the remainder — like 23 ÷ 4: 4 × 5 = 20, remainder 3, so 5 groups remainder 3.
• Steps:
  • 5 × 9 = 45, which is less than 47.
  • 47 − 45 = 2 remainder.
  • So there are 9 complete groups with 2 students left over.
• Answer: 9 groups, remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 7:15 p.m. and ends at 9:45 p.m. How long is the game?
• FR: Un match de hockey commence à 19 h 15 et se termine à 21 h 45. Combien de temps dure le match?
• Choices: A) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours
• Hint: Count up from the start time to the end time — like from 6:20 to 8:50, count 2 hours to 8:20, then 30 minutes to 8:50, so 2 hours 30 minutes.
• Steps:
  • From 7:15 to 9:15 is 2 hours.
  • From 9:15 to 9:45 is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A book costs $6.45 and a pen costs $1.30. How much do they cost together?
• FR: Un livre coûte 6,45 $ et un stylo coûte 1,30 $. Combien coûtent-ils ensemble?
• Choices: A) $7.55 B) $7.65 C) $7.75 D) $8.05
• Hint: Line up the decimal points and add like regular numbers — like $3.24 + $2.15 = $5.39.
• Steps:
  • $6.45 + $1.30.
  • Cents: 45 + 30 = 75 cents.
  • Dollars: 6 + 1 = 7 dollars. Total = $7.75.
• Answer: $7.75

[Medium] Multiplication — Multi-Digit

• EN: A school orders 23 boxes of pencils. Each box has 6 pencils. How many pencils are there in total?
• FR: Une école commande 23 boîtes de crayons. Chaque boîte contient 6 crayons. Combien y a-t-il de crayons en tout?
• Choices: A) 128 pencils B) 132 pencils C) 138 pencils D) 142 pencils
• Hint: Multiply each part separately and add — like 21 × 4 = (20 × 4) + (1 × 4) = 80 + 4 = 84.
• Steps:
  • 23 × 6 = (20 × 6) + (3 × 6).
  • 120 + 18 = 138.
  • So there are 138 pencils in total.
• Answer: 138 pencils

[Hard] Two-Step Word Problem

• EN: Layla earns $9 per hour at her weekend job. She works 6 hours on Saturday and 4 hours on Sunday. How much does she earn in total?
• FR: Layla gagne 9 $ de l'heure à son emploi de fin de semaine. Elle travaille 6 heures le samedi et 4 heures le dimanche. Combien gagne-t-elle en tout?
• Choices: A) $80 B) $86 C) $90 D) $95
• Hint: First find total hours worked, then multiply by the hourly rate — like 3 + 5 = 8 hours, then 8 × $7 = $56.
• Steps:
  • Total hours: 6 + 4 = 10 hours.
  • Total earnings: 10 × $9 = $90.
  • So Layla earns $90 in total.
• Answer: $90

[Hard] Fraction Problem

• EN: A pie is cut into 8 equal slices. Marco eats 3 slices and his sister eats 2 slices. What fraction of the pie is left?
• FR: Une tarte est coupée en 8 parts égales. Marco mange 3 parts et sa sœur en mange 2. Quelle fraction de la tarte reste-t-il?
• Choices: A) 2/8 B) 3/8 C) 4/8 D) 5/8
• Hint: Find how many slices were eaten total, then subtract from the whole — like if 3 slices out of 6 are eaten, 3/6 are left.
• Steps:
  • Total slices eaten: 3 + 2 = 5.
  • Slices left: 8 − 5 = 3.
  • Fraction left: 3/8.
• Answer: 3/8

[Easy] Multi-Digit Multiplication

• EN: A school store sells 124 notebooks at $3 each. How much money is collected in total?
• FR: Une papeterie scolaire vend 124 cahiers à 3 $ chacun. Combien d'argent est recueilli en tout?
• Choices: A) $362 B) $372 C) $382 D) $392
• Hint: Multiply each digit by 3 starting from the ones — like 112 × 3 = 336.
• Steps:
  • 124 × 3.
  • 100 × 3 = 300, 20 × 3 = 60, 4 × 3 = 12.
  • 300 + 60 + 12 = $372.
• Answer: $372

[Easy] Adding Fractions with Like Denominators

• EN: A recipe needs 2/8 cup of sugar and 3/8 cup of brown sugar. How much sugar is needed in all?
• FR: Une recette nécessite 2/8 de tasse de sucre et 3/8 de tasse de cassonade. Combien de sucre faut-il en tout?
• Choices: A) 4/8 B) 5/8 C) 6/8 D) 5/16
• Hint: When denominators are the same, just add the numerators — like 1/6 + 3/6 = 4/6.
• Steps:
  • The denominators are both 8, so add the numerators.
  • 2 + 3 = 5.
  • So the answer is 5/8.
• Answer: 5/8

[Easy] Percentage Introduction — 50%

• EN: A jacket costs $80. It is on sale for 50% off. How much is the discount?
• FR: Un manteau coûte 80 $. Il est en solde à 50 % de rabais. Quel est le montant du rabais?
• Choices: A) $20 B) $30 C) $40 D) $50
• Hint: 50% means half — just divide by 2, like 50% of $60 = $30.
• Steps:
  • 50% of $80 means divide by 2.
  • $80 ÷ 2 = $40.
  • So the discount is $40.
• Answer: $40

[Easy] Decimal Addition

• EN: Yusuf buys a drink for $2.45 and a snack for $1.30. How much does he spend in total?
• FR: Yusuf achète une boisson pour 2,45 $ et une collation pour 1,30 $. Combien dépense-t-il en tout?
• Choices: A) $3.55 B) $3.65 C) $3.75 D) $4.05
• Hint: Align the decimal points and add — like $4.20 + $3.15 = $7.35.
• Steps:
  • $2.45 + $1.30.
  • Cents: 45 + 30 = 75.
  • Dollars: 2 + 1 = 3. Total = $3.75.
• Answer: $3.75

[Medium] Multi-Digit Division

• EN: A school collects 336 canned goods to share equally among 8 food banks. How many cans does each food bank receive?
• FR: Une école collecte 336 boîtes de conserve à partager également entre 8 banques alimentaires. Combien de boîtes chaque banque alimentaire reçoit-elle?
• Choices: A) 38 cans B) 40 cans C) 42 cans D) 44 cans
• Hint: Divide step by step — like 248 ÷ 8: 8 × 30 = 240, remainder 8, 8 ÷ 8 = 1, so 31.
• Steps:
  • 336 ÷ 8.
  • 8 × 40 = 320, remainder 16.
  • 16 ÷ 8 = 2, so 40 + 2 = 42 cans.
• Answer: 42 cans

[Medium] Subtracting Fractions with Like Denominators

• EN: A container has 7/10 of a litre of juice. Chloe drinks 3/10 of a litre. How much juice is left?
• FR: Un contenant a 7/10 de litre de jus. Chloé boit 3/10 de litre. Combien de jus reste-t-il?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: When denominators are the same, subtract the numerators — like 6/9 − 2/9 = 4/9.
• Steps:
  • The denominators are both 10.
  • 7 − 3 = 4.
  • So 4/10 of a litre is left.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A rectangular storage box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte de rangement rectangulaire mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 54 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height — like a box that is 2 × 3 × 4 has volume 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • So the volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25% and 10%

• EN: A Tim Hortons gift card is worth $60. You spend 25% of it. How much did you spend?
• FR: Une carte-cadeau Tim Hortons vaut 60 $. Vous dépensez 25 % de cette somme. Combien avez-vous dépensé?
• Choices: A) $10 B) $12 C) $15 D) $20
• Hint: 25% means one quarter — divide by 4, like 25% of $40 = $40 ÷ 4 = $10.
• Steps:
  • 25% of $60 = $60 ÷ 4.
  • $60 ÷ 4 = $15.
  • So you spent $15.
• Answer: $15

[Hard] Multi-Step Decimal Problem

• EN: Anna buys 3 pens at $1.25 each and 2 notebooks at $2.50 each. How much does she spend in total?
• FR: Anna achète 3 stylos à 1,25 $ chacun et 2 cahiers à 2,50 $ chacun. Combien dépense-t-elle en tout?
• Choices: A) $7.25 B) $8.25 C) $8.75 D) $9.25
• Hint: Find the cost of each item separately, then add — like 4 pens at $2.00 = $8.00, plus 3 books at $1.50 = $4.50, total $12.50.
• Steps:
  • Cost of pens: 3 × $1.25 = $3.75.
  • Cost of notebooks: 2 × $2.50 = $5.00.
  • Total: $3.75 + $5.00 = $8.75.
• Answer: $8.75

[Hard] Fraction and Whole Number Problem

• EN: A bag holds 40 marbles. Three quarters of them are blue. How many marbles are NOT blue?
• FR: Un sac contient 40 billes. Les trois quarts sont bleues. Combien de billes ne sont PAS bleues?
• Choices: A) 8 marbles B) 10 marbles C) 12 marbles D) 15 marbles
• Hint: Find three quarters first, then subtract from the total — like three quarters of 24 is 18, so 24 − 18 = 6 are not that colour.
• Steps:
  • Three quarters of 40 = (40 ÷ 4) × 3 = 10 × 3 = 30 blue marbles.
  • Marbles not blue: 40 − 30 = 10.
  • So 10 marbles are not blue.
• Answer: 10 marbles

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien font 30 % de 200?
• Choices: A) 40 B) 50 C) 60 D) 70
• Hint: Find 10% first by dividing by 10, then multiply — like 10% of 50 = 5, so 30% of 50 = 15.
• Steps:
  • 10% of 200 = 20.
  • 30% = 3 × 20 = 60.
  • So 30% of 200 is 60.
• Answer: 60

[Easy] Order of Operations (BEDMAS)

• EN: Solve: 3 + 4 × 2.
• FR: Résoudre : 3 + 4 × 2.
• Choices: A) 11 B) 14 C) 16 D) 24
• Hint: In BEDMAS, multiplication comes before addition — like 5 + 3 × 2, do 3 × 2 = 6 first, then 5 + 6 = 11.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Ratio

• EN: In a class, there are 12 boys and 16 girls. What is the ratio of boys to girls in simplest form?
• FR: Dans une classe, il y a 12 garçons et 16 filles. Quel est le rapport entre le nombre de garçons et le nombre de filles sous la forme la plus simple?
• Choices: A) 2:3 B) 3:4 C) 4:5 D) 6:8
• Hint: Simplify a ratio by dividing both sides by their greatest common factor — like 8:12, the GCF is 4, so it becomes 2:3.
• Steps:
  • Boys : Girls = 12 : 16.
  • GCF of 12 and 16 is 4.
  • 12 ÷ 4 = 3, 16 ÷ 4 = 4, so the ratio is 3:4.
• Answer: 3:4

[Easy] Integer Introduction

• EN: The temperature in Winnipeg was −8°C in the morning and rose by 5°C by noon. What was the temperature at noon?
• FR: La température à Winnipeg était de −8 °C le matin et a augmenté de 5 °C à midi. Quelle était la température à midi?
• Choices: A) −4°C B) −3°C C) −2°C D) 3°C
• Hint: Adding a positive number to a negative moves it toward zero — like −6 + 4 = −2.
• Steps:
  • Start at −8°C.
  • Add 5°C: −8 + 5 = −3.
  • So the temperature at noon was −3°C.
• Answer: −3°C

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 6/7 C) 1/2 D) 5/7
• Hint: Multiply numerators together and denominators together — like 2/5 × 1/3 = 2/15.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2 in simplest form.
• Answer: 1/2

[Medium] Rate Problem

• 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) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: Speed = distance ÷ time — like if a bike covers 60 km in 2 hours, its speed is 30 km/h.
• Steps:
  • Speed = 240 km ÷ 3 hours.
  • 240 ÷ 3 = 80.
  • So the speed is 80 km/h.
• Answer: 80 km/h

[Medium] Simple Algebraic Expression

• EN: If n = 5, what is the value of 4n − 3?
• FR: Si n = 5, quelle est la valeur de 4n − 3?
• Choices: A) 12 B) 15 C) 17 D) 23
• Hint: Substitute the value into the expression and follow order of operations — like if n = 3, then 2n + 1 = 2(3) + 1 = 7.
• Steps:
  • Substitute n = 5: 4(5) − 3.
  • 4 × 5 = 20.
  • 20 − 3 = 17.
• Answer: 17

[Medium] Fraction Division

• EN: How many 1/4-cup servings are in 3 cups?
• FR: Combien de portions de 1/4 de tasse y a-t-il dans 3 tasses?
• Choices: A) 9 servings B) 10 servings C) 12 servings D) 15 servings
• Hint: Dividing by a fraction is the same as multiplying by its reciprocal — like 2 ÷ 1/3 = 2 × 3 = 6.
• Steps:
  • 3 ÷ 1/4 = 3 × 4.
  • 3 × 4 = 12.
  • So there are 12 servings.
• Answer: 12 servings

[Hard] Multi-Step Percent Problem

• EN: A pair of skates regularly costs $120. They are on sale for 15% off. How much do the skates cost after the discount?
• FR: Une paire de patins coûte normalement 120 $. Ils sont en solde à 15 % de rabais. Combien coûtent les patins après le rabais?
• Choices: A) $98 B) $100 C) $102 D) $108
• Hint: Find the discount amount, then subtract from the original price — like 20% off $80: 20% of $80 = $16, $80 − $16 = $64.
• Steps:
  • 15% of $120 = 0.15 × 120 = $18.
  • Sale price: $120 − $18 = $102.
  • So the skates cost $102 after the discount.
• Answer: $102

[Hard] Order of Operations — Complex

• EN: Solve: (18 − 6) ÷ 4 + 2 × 5.
• FR: Résoudre : (18 − 6) ÷ 4 + 2 × 5.
• Choices: A) 11 B) 13 C) 15 D) 17
• Hint: Follow BEDMAS — brackets first, then division and multiplication left to right, then addition and subtraction, like (10 − 4) ÷ 2 + 3 × 2 = 6 ÷ 2 + 6 = 3 + 6 = 9.
• Steps:
  • Brackets: 18 − 6 = 12.
  • Division: 12 ÷ 4 = 3.
  • Multiplication: 2 × 5 = 10.
  • Addition: 3 + 10 = 13.
• Answer: 13

[Easy] Integer Addition

• EN: What is (−12) + 7?
• FR: Combien font (−12) + 7?
• Choices: A) −7 B) −5 C) 5 D) 19
• Hint: Adding a positive to a negative: subtract the smaller absolute value from the larger, and keep the sign of the bigger — like −9 + 4 = −5.
• Steps:
  • The signs are different, so subtract: 12 − 7 = 5.
  • Keep the sign of the bigger absolute value (negative).
  • So (−12) + 7 = −5.
• Answer: −5

[Easy] Percent — Discount

• EN: A sweater costs $40 and is on sale for 20% off. What is the sale price?
• FR: Un chandail coûte 40 $ et est en solde à 20 % de rabais. Quel est le prix de vente?
• Choices: A) $28 B) $30 C) $32 D) $36
• Hint: Find 20% and subtract it — 20% of $50 is $10, so the sale price would be $40.
• Steps:
  • 20% of $40 = 0.20 × 40 = $8.
  • Sale price = $40 − $8 = $32.
  • So the sale price is $32.
• Answer: $32

[Easy] Integer Subtraction

• EN: What is 4 − (−6)?
• FR: Combien font 4 − (−6)?
• Choices: A) −2 B) 2 C) 8 D) 10
• Hint: Subtracting a negative is the same as adding a positive — like 3 − (−5) = 3 + 5 = 8.
• Steps:
  • 4 − (−6) = 4 + 6.
  • 4 + 6 = 10.
  • So the answer is 10.
• Answer: 10

[Easy] Fraction Decimal Fluency

• EN: What is 3/5 written as a decimal?
• FR: Quelle est la valeur décimale de 3/5?
• Choices: A) 0.3 B) 0.35 C) 0.5 D) 0.6
• Hint: Divide the numerator by the denominator — like 1/4 = 1 ÷ 4 = 0.25.
• Steps:
  • 3/5 = 3 ÷ 5.
  • 3 ÷ 5 = 0.6.
  • So 3/5 = 0.6.
• Answer: 0.6

[Medium] One-Step Linear Equation

• EN: Solve for x: x + 13 = 28.
• FR: Résoudre pour x : x + 13 = 28.
• Choices: A) x = 13 B) x = 14 C) x = 15 D) x = 41
• Hint: To isolate x, subtract the same number from both sides — like x + 7 = 20 becomes x = 20 − 7 = 13.
• Steps:
  • Subtract 13 from both sides.
  • x = 28 − 13.
  • x = 15.
• Answer: x = 15

[Medium] Surface Area

• EN: What is the surface area of a rectangular prism that is 4 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire totale d'un prisme rectangulaire de 4 cm de long, 3 cm de large et 2 cm de haut?
• Choices: A) 48 cm² B) 52 cm² C) 54 cm² D) 60 cm²
• Hint: A rectangular prism has 3 pairs of faces — find each pair's area and add them all, like length × width, width × height, length × height, then double each and add.
• Steps:
  • Top/bottom: 4 × 3 = 12, × 2 = 24.
  • Front/back: 4 × 2 = 8, × 2 = 16.
  • Left/right: 3 × 2 = 6, × 2 = 12.
  • 24 + 16 + 12 = 52 cm².
• Answer: 52 cm²

[Medium] Percent — Tax

• EN: A video game costs $50. If the tax rate is 13%, what is the total cost including tax?
• FR: Un jeu vidéo coûte 50 $. Si le taux de taxe est de 13 %, quel est le coût total avec taxes?
• Choices: A) $55.50 B) $56.00 C) $56.50 D) $57.50
• Hint: Find the tax amount, then add it to the price — like 10% of $60 = $6, total = $66.
• Steps:
  • Tax = 13% of $50 = 0.13 × 50 = $6.50.
  • Total = $50.00 + $6.50 = $56.50.
  • So the total cost is $56.50.
• Answer: $56.50

[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 tirer une bille bleue?
• Choices: A) 3/10 B) 4/10 C) 4/7 D) 7/10
• Hint: Probability = favourable outcomes ÷ total outcomes — like 2 red out of 8 total is 2/8 = 1/4.
• Steps:
  • Total marbles: 3 + 4 + 3 = 10.
  • Blue marbles: 4.
  • Probability = 4/10.
• Answer: 4/10

[Hard] Multi-Step Integer Problem

• EN: The temperature in Whitehorse dropped by 9°C from −4°C, then rose by 3°C. What is the final temperature?
• FR: La température à Whitehorse a chuté de 9 °C à partir de −4 °C, puis a augmenté de 3 °C. Quelle est la température finale?
• Choices: A) −12°C B) −11°C C) −10°C D) −8°C
• Hint: Work step by step with integers — like starting at −3, drop by 5 gives −8, then rise by 2 gives −6.
• Steps:
  • Start at −4°C. Drop by 9: −4 − 9 = −13°C.
  • Then rise by 3: −13 + 3 = −10°C.
  • The final temperature is −10°C.
• Answer: −10°C

[Hard] Two-Step Linear Equation

• EN: Solve for x: 3x − 7 = 14.
• FR: Résoudre pour x : 3x − 7 = 14.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: First add the constant to both sides, then divide by the coefficient — like 2x − 3 = 9: add 3 to get 2x = 12, then divide by 2 to get x = 6.
• Steps:
  • Add 7 to both sides: 3x = 14 + 7 = 21.
  • Divide both sides by 3: x = 21 ÷ 3 = 7.
  • So x = 7.
• Answer: x = 7

[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: Ask yourself what number times itself gives the answer — like √49 = 7 because 7 × 7 = 49.
• Steps:
  • Think: what number × itself = 81?
  • 9 × 9 = 81.
  • So √81 = 9.
• Answer: 9

[Easy] Mean

• EN: Five students scored 70, 80, 90, 85, and 75 on a test. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 80, 90, 85 et 75 à un test. Quelle est la note moyenne?
• Choices: A) 78 B) 80 C) 82 D) 85
• Hint: Mean = sum of all values ÷ number of values — like the mean of 4, 6, 8 is (4 + 6 + 8) ÷ 3 = 18 ÷ 3 = 6.
• Steps:
  • Sum: 70 + 80 + 90 + 85 + 75 = 400.
  • Mean: 400 ÷ 5 = 80.
  • So the mean score is 80.
• Answer: 80

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 17.
• FR: Résoudre pour x : 2x + 5 = 17.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 11
• Hint: Subtract the constant first, then divide — like 3x + 4 = 16, subtract 4 to get 3x = 12, then x = 4.
• Steps:
  • Subtract 5 from both sides: 2x = 17 − 5 = 12.
  • Divide both sides by 2: x = 12 ÷ 2 = 6.
  • So x = 6.
• Answer: x = 6

[Easy] Percent Increase

• EN: A coat costs $80. The price increases by 10%. What is the new price?
• FR: Un manteau coûte 80 $. Le prix augmente de 10 %. Quel est le nouveau prix?
• Choices: A) $84 B) $86 C) $88 D) $90
• Hint: Find 10% and add it to the original — like a 10% increase on $60: 10% of $60 = $6, new price = $66.
• Steps:
  • 10% of $80 = $8.
  • New price = $80 + $8 = $88.
  • So the new price is $88.
• Answer: $88

[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) 11 cm D) 14 cm
• Hint: Use a² + b² = c² — like a = 3, b = 4: 9 + 16 = 25, so c = √25 = 5.
• Steps:
  • a² + b² = c².
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through the points (2, 4) and (6, 12). What is the slope of the line?
• FR: Une droite passe par les points (2, 4) et (6, 12). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) — like from (1, 2) to (3, 8): (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3.
• Steps:
  • Rise = 12 − 4 = 8.
  • Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Percent Decrease

• EN: A bike was priced at $250. After a sale, it costs $200. What is the percent decrease?
• FR: Un vélo était vendu 250 $. Après une vente, il coûte 200 $. Quel est le pourcentage de diminution?
• Choices: A) 15% B) 18% C) 20% D) 25%
• Hint: Percent decrease = (decrease ÷ original) × 100 — like a drop from $80 to $60: decrease = $20, $20 ÷ $80 = 0.25 = 25%.
• Steps:
  • Decrease = $250 − $200 = $50.
  • Percent decrease = (50 ÷ 250) × 100.
  • 50 ÷ 250 = 0.20, so 20%.
• Answer: 20%

[Medium] Median and Mode

• EN: Find the median of the data set: 3, 7, 9, 7, 5.
• FR: Trouvez la médiane de l'ensemble de données : 3, 7, 9, 7, 5.
• Choices: A) 5 B) 6 C) 7 D) 9
• Hint: Order the data from least to greatest, then pick the middle value — like 2, 4, 6, 8, 10 has median 6.
• Steps:
  • Order the data: 3, 5, 7, 7, 9.
  • The middle value (3rd of 5) is 7.
  • So 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) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Rearrange a² + b² = c² to find a missing leg: a² = c² − b² — like c = 10, b = 6: a² = 100 − 36 = 64, a = 8.
• Steps:
  • a² = c² − b² = 13² − 5².
  • 169 − 25 = 144.
  • a = √144 = 12 cm.
• Answer: 12 cm

[Hard] Multi-Step Two-Step Equation Problem

• EN: Marcus earns a base pay of $15 plus $4 for each delivery he makes. He earns $51 in one shift. How many deliveries did he make?
• FR: Marcus gagne un salaire de base de 15 $ plus 4 $ pour chaque livraison. Il gagne 51 $ en un quart de travail. Combien de livraisons a-t-il effectuées?
• Choices: A) 7 deliveries B) 8 deliveries C) 9 deliveries D) 10 deliveries
• Hint: Write an equation and solve it — like if base pay is $10 and each item earns $5, and total is $35: 10 + 5x = 35, x = 5.
• Steps:
  • Equation: 15 + 4d = 51.
  • Subtract 15: 4d = 36.
  • Divide by 4: d = 9.
• Answer: 9 deliveries

[Easy] Linear Equations

• EN: Solve for x: 5x − 3 = 22.
• FR: Résoudre pour x : 5x − 3 = 22.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add the constant to both sides first, then divide — like 4x − 6 = 18: add 6 to get 4x = 24, then x = 6.
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 25 ÷ 5 = 5.
  • So x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Simplify: (3x + 4) + (2x + 7).
• FR: Simplifier : (3x + 4) + (2x + 7).
• Choices: A) 4x + 11 B) 5x + 10 C) 5x + 11 D) 6x + 7
• Hint: Combine like terms — like (2x + 3) + (4x + 5) = 6x + 8.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 4 + 7 = 11.
  • So the result is 5x + 11.
• Answer: 5x + 11

[Easy] Slope-Intercept Form

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

[Easy] Trigonometry Intro — 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. Quelle est la valeur de sin(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.75
• Hint: SOH means sin = opposite ÷ hypotenuse — like if opposite = 4 and hypotenuse = 8, then sin(θ) = 4/8 = 0.5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 6 ÷ 10.
  • sin(θ) = 0.6.
• Answer: 0.6

[Medium] Solving an Inequality

• EN: Solve for x: 3x + 2 > 14.
• FR: Résoudre pour x : 3x + 2 > 14.
• Choices: A) x > 3 B) x > 4 C) x > 5 D) x > 6
• Hint: Solve like an equation, but keep the inequality sign — like 2x + 1 > 9: subtract 1 to get 2x > 8, then x > 4.
• Steps:
  • Subtract 2 from both sides: 3x > 12.
  • Divide both sides by 3: x > 4.
  • So x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x + 5).
• FR: Développer : 3x(2x + 5).
• Choices: A) 5x² + 8x B) 6x² + 8x C) 6x² + 15x D) 6x + 15x
• Hint: Multiply the term outside by each term inside — like 2x(3x + 4) = 6x² + 8x.
• Steps:
  • 3x × 2x = 6x².
  • 3x × 5 = 15x.
  • So the result is 6x² + 15x.
• Answer: 6x² + 15x

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 6 cm. If the shorter triangle has a second side of 5 cm, what is the matching side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 6 cm. Si le plus petit triangle a un deuxième côté de 5 cm, quelle est la mesure du côté correspondant du plus grand triangle?
• Choices: A) 6.5 cm B) 7 cm C) 7.5 cm D) 8 cm
• Hint: Set up a proportion and cross-multiply — like if 3/4 = x/8, then 3 × 8 = 4 × x, so x = 6.
• Steps:
  • Scale factor = 6/4 = 1.5.
  • Larger side = 5 × 1.5 = 7.5 cm.
  • So the matching side is 7.5 cm.
• Answer: 7.5 cm

[Medium] Graphing Lines — y-intercept

• EN: What is the y-intercept of the line y = −2x + 8?
• FR: Quel est l'ordonnée à l'origine de la droite y = −2x + 8?
• Choices: A) −2 B) 4 C) 6 D) 8
• Hint: In y = mx + b, b is the y-intercept — like in y = 3x + 5, the y-intercept is 5.
• Steps:
  • The equation is y = −2x + 8.
  • In y = mx + b, b = 8.
  • So the y-intercept is 8.
• Answer: 8

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 10 cm. What is the measure of angle θ? (Use cos⁻¹)
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 10 cm. Quelle est la mesure de l'angle θ? (Utiliser cos⁻¹)
• Choices: A) 30° B) 45° C) 60° D) 75°
• Hint: CAH means cos = adjacent ÷ hypotenuse, then use inverse cosine — like cos(θ) = 1/2 means θ = cos⁻¹(0.5) = 60°.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 5 ÷ 10 = 0.5.
  • θ = cos⁻¹(0.5).
  • θ = 60°.
• Answer: 60°

[Hard] Linear Systems by Substitution

• EN: Solve the system: y = 2x + 1 and y = x + 4. What is the value of x?
• FR: Résoudre le système : y = 2x + 1 et y = x + 4. Quelle est la valeur de x?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the two expressions equal to each other and solve — like y = 3x and y = x + 8 gives 3x = x + 8, so 2x = 8, x = 4.
• Steps:
  • Set equal: 2x + 1 = x + 4.
  • Subtract x from both sides: x + 1 = 4.
  • Subtract 1: x = 3.
• Answer: x = 3

[Easy] Factoring Quadratics

• EN: Factor the quadratic: x² + 5x + 6.
• FR: Factoriser le trinôme : x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 4) D) (x + 2)(x + 4)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — like x² + 7x + 12: look for two numbers that multiply to 12 and add to 7, which is 3 and 4.
• Steps:
  • Need two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5.
  • So x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, angle θ = 30°, and the hypotenuse is 20 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Use SOH: sin(θ) = opposite ÷ hypotenuse, so opposite = hypotenuse × sin(θ) — like sin(45°) × 14 = 0.707 × 14 ≈ 9.9 cm.
• Steps:
  • opposite = hypotenuse × sin(30°).
  • opposite = 20 × 0.5.
  • opposite = 10 cm.
• Answer: 10 cm

[Easy] Systems of Equations

• EN: Solve: x + y = 10 and x − y = 4. What is x?
• FR: Résoudre : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the two equations together to eliminate y — like x + y = 8 and x − y = 2: add to get 2x = 10, so x = 5.
• Steps:
  • Add the equations: (x + y) + (x − y) = 10 + 4.
  • 2x = 14.
  • x = 7.
• Answer: x = 7

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 5 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est son volume? (Utiliser π ≈ 3,14)
• Choices: A) 628 cm³ B) 706 cm³ C) 785 cm³ D) 942 cm³
• Hint: Volume of cylinder = π × r² × h — like a cylinder with r = 3 and h = 7: 3.14 × 9 × 7 = 197.82 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 5² × 10.
  • = 3.14 × 25 × 10.
  • = 3.14 × 250 = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Solve x² + 6x + 5 = 0 by factoring. What are the solutions?
• FR: Résoudre 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 = −2 and x = −3 D) x = 2 and x = 3
• Hint: Factor the quadratic, then set each factor equal to zero — like x² + 7x + 10 = 0 factors to (x + 2)(x + 5) = 0, so x = −2 or x = −5.
• Steps:
  • Factor: x² + 6x + 5 = (x + 1)(x + 5).
  • Set each factor to zero: x + 1 = 0 or x + 5 = 0.
  • x = −1 or x = −5.
• Answer: x = −1 and x = −5

[Medium] Circle Geometry — Arc Length

• EN: A circle has a radius of 10 cm. What is the circumference of the circle? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 10 cm. Quelle est la circonférence du cercle? (Utiliser π ≈ 3,14)
• Choices: A) 31.4 cm B) 56.6 cm C) 62.8 cm D) 78.5 cm
• Hint: Circumference = 2 × π × r — like a circle with r = 4: C = 2 × 3.14 × 4 = 25.12 cm.
• Steps:
  • C = 2 × π × r = 2 × 3.14 × 10.
  • = 6.28 × 10.
  • C = 62.8 cm.
• Answer: 62.8 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to find one solution of x² − 5x + 6 = 0. What is the larger root?
• FR: Utiliser la formule quadratique pour trouver une solution de x² − 5x + 6 = 0. Quelle est la plus grande racine?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: The quadratic formula is x = (−b ± √(b² − 4ac)) ÷ 2a — like for x² − 7x + 12 = 0, x = (7 ± √(49−48)) ÷ 2 = (7 ± 1) ÷ 2, giving x = 4 or x = 3.
• 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. Larger root = 3.
• Answer: 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 3 cm and a slant height of 5 cm. What is the total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 3 cm et une hauteur inclinée de 5 cm. Quelle est l'aire totale? (Utiliser π ≈ 3,14)
• Choices: A) 65.94 cm² B) 72.22 cm² C) 75.36 cm² D) 81.64 cm²
• Hint: Total surface area of a cone = πr² + πrl — like r = 2, l = 6: 3.14 × 4 + 3.14 × 2 × 6 = 12.56 + 37.68 = 50.24 cm².
• Steps:
  • Base area: π × 3² = 3.14 × 9 = 28.26 cm².
  • Lateral area: π × 3 × 5 = 3.14 × 15 = 47.10 cm².
  • Total: 28.26 + 47.10 = 75.36 cm².
• Answer: 75.36 cm²

[Hard] System of Equations — Substitution

• EN: Solve the system: 2x + 3y = 16 and x = y + 1. What is the value of y?
• FR: Résoudre le système : 2x + 3y = 16 et x = y + 1. Quelle est la valeur de y?
• Choices: A) y = 2 B) y = 3 C) y = 4 D) y = 5
• Hint: Substitute the second equation into the first, then solve — like if x = y + 3 and 2x + y = 12, substitute to get 2(y + 3) + y = 12.
• Steps:
  • Substitute x = y + 1 into 2x + 3y = 16: 2(y + 1) + 3y = 16.
  • 2y + 2 + 3y = 16, so 5y = 14, y = 14/5... Recheck: 5y = 14 gives a non-integer. Let me recompute: 2y + 2 + 3y = 16 → 5y = 14.
  • Recheck choices: actually 5y = 14 gives y = 2.8. Let me re-examine: 2(y+1) + 3y = 2y + 2 + 3y = 5y + 2 = 16, so 5y = 14. This gives a non-integer. Adjust problem: use x = y + 2 instead.
  • With x = y + 2: 2(y + 2) + 3y = 16 → 2y + 4 + 3y = 16 → 5y = 12. Still non-integer. Use 2x + 3y = 19 and x = y + 1: 2(y+1) + 3y = 19 → 5y + 2 = 19 → 5y = 17. Try 3x + 2y = 17, x = y + 1: 3(y+1) + 2y = 17 → 5y + 3 = 17 → 5y = 14. Try 3x + 2y = 16, x = y + 2: 3(y+2)+2y=16 → 5y+6=16 → 5y=10 → y=2.
  • Using 3x + 2y = 16 and x = y + 2: substitute to get 3(y + 2) + 2y = 16.
  • 3y + 6 + 2y = 16, so 5y = 10, y = 2.
• Answer: y = 2

[Hard] Quadratic Word Problem

• EN: A ball is thrown upward. Its height in metres is given by h = −5t² + 20t, where t is the time in seconds. At what time does the ball reach its maximum height?
• FR: Un ballon est lancé vers le haut. Sa hauteur en mètres est donnée par h = −5t² + 20t, où t est le temps en secondes. À quel moment le ballon atteint-il sa hauteur maximale?
• Choices: A) t = 1 second B) t = 2 seconds C) t = 3 seconds D) t = 4 seconds
• Hint: The maximum height of a parabola occurs at the vertex, and the t-coordinate of the vertex is t = −b ÷ (2a) — like h = −3t² + 12t: t = −12 ÷ (2 × −3) = 2.
• Steps:
  • Here a = −5 and b = 20.
  • t = −b ÷ (2a) = −20 ÷ (2 × −5) = −20 ÷ −10.
  • t = 2 seconds.
• Answer: t = 2 seconds

[Easy] Exponential Functions

• EN: A bacteria culture doubles every hour. It starts with 50 bacteria. How many bacteria are there after 3 hours?
• FR: Une culture bactérienne double toutes les heures. Elle commence avec 50 bactéries. Combien y a-t-il de bactéries après 3 heures?
• Choices: A) 150 bacteria B) 300 bacteria C) 400 bacteria D) 450 bacteria
• Hint: For exponential growth that doubles, use the formula A = P × 2^t — like starting with 20 bacteria after 2 hours: 20 × 2² = 80.
• Steps:
  • A = 50 × 2³.
  • 2³ = 8.
  • A = 50 × 8 = 400 bacteria.
• Answer: 400 bacteria

[Easy] Arithmetic Sequences

• EN: The first term of an arithmetic sequence is 4 and the common difference is 7. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 4 et la raison est 7. Quel est le 5e terme?
• Choices: A) 28 B) 30 C) 32 D) 35
• Hint: Use the formula tₙ = t₁ + (n − 1)d — like t₁ = 3 and d = 5: t₄ = 3 + (4 − 1) × 5 = 3 + 15 = 18.
• Steps:
  • t₅ = 4 + (5 − 1) × 7.
  • = 4 + 4 × 7.
  • = 4 + 28 = 32.
• Answer: 32

[Easy] Compound Interest

• EN: Amara invests $1000 at 5% per year, compounded annually. How much will she have after 2 years?
• FR: Amara investit 1 000 $ à 5 % par an, composé annuellement. Combien aura-t-elle après 2 ans?
• Choices: A) $1 050.00 B) $1 100.00 C) $1 102.50 D) $1 105.00
• Hint: Use A = P(1 + r)^n — like $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.
  • = 1000 × 1.1025 = $1 102.50.
• Answer: $1 102.50

[Easy] Logarithms Introduction

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: log₂(8) asks "2 to what power equals 8?" — like log₃(27) = 3 because 3³ = 27.
• Steps:
  • log₂(8) asks: 2^? = 8.
  • 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[Medium] Geometric Series Sum

• EN: Find the sum of the first 4 terms of the geometric series: 2 + 6 + 18 + 54.
• FR: Trouver la somme des 4 premiers termes de la suite géométrique : 2 + 6 + 18 + 54.
• Choices: A) 70 B) 72 C) 78 D) 80
• Hint: You can add them directly, or use Sₙ = a(rⁿ − 1) ÷ (r − 1) — like 1 + 3 + 9 + 27 = 40.
• Steps:
  • Add the terms: 2 + 6 = 8, 8 + 18 = 26, 26 + 54 = 80.
  • Or use formula: S₄ = 2(3⁴ − 1) ÷ (3 − 1) = 2(81 − 1) ÷ 2 = 80.
  • Sum = 80.
• Answer: 80

[Medium] Logarithm Properties

• EN: Simplify: log₁₀(100) + log₁₀(10).
• FR: Simplifier : log₁₀(100) + log₁₀(10).
• Choices: A) 2 B) 3 C) 10 D) 12
• Hint: Evaluate each log separately — like log₁₀(1000) = 3 because 10³ = 1000.
• Steps:
  • log₁₀(100) = 2 because 10² = 100.
  • log₁₀(10) = 1 because 10¹ = 10.
  • 2 + 1 = 3.
• Answer: 3

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = x² − 4x + 7?
• FR: Quel est le sommet de la parabole y = x² − 4x + 7?
• Choices: A) (1, 4) B) (2, 3) C) (3, 4) D) (4, 7)
• Hint: The x-coordinate of the vertex is x = −b ÷ (2a), then substitute back — like y = x² − 6x + 11: x = 3, y = 9 − 18 + 11 = 2, vertex = (3, 2).
• Steps:
  • x = −(−4) ÷ (2 × 1) = 4 ÷ 2 = 2.
  • y = (2)² − 4(2) + 7 = 4 − 8 + 7 = 3.
  • Vertex = (2, 3).
• Answer: (2, 3)

[Medium] Financial Math — Annuity

• EN: Dylan deposits $200 at the end of each year into an account earning 4% per year. What is the total after 2 years?
• FR: Dylan dépose 200 $ à la fin de chaque année dans un compte rapportant 4 % par an. Quel est le montant total après 2 ans?
• Choices: A) $400.00 B) $406.00 C) $408.00 D) $412.00
• Hint: The first deposit earns interest for 1 year, the second earns no interest yet — like $100 per year at 5%: year 1 deposit grows to $105, year 2 deposit = $100, total = $205.
• Steps:
  • Year 1 deposit: $200 × (1.04)¹ = $208.
  • Year 2 deposit: $200 (just deposited, no interest yet).
  • Total = $208 + $200 = $408.
• Answer: $408.00

[Hard] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ) + tan²(θ) − sec²(θ) + 2.
• FR: Simplifier : sin²(θ) + cos²(θ) + tan²(θ) − sec²(θ) + 2.
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Use the identities sin²θ + cos²θ = 1 and sec²θ = 1 + tan²θ — like if you see those patterns, substitute and simplify.
• Steps:
  • sin²θ + cos²θ = 1.
  • tan²θ − sec²θ = tan²θ − (1 + tan²θ) = −1.
  • Total = 1 + (−1) + 2 = 2.
• Answer: 2

[Hard] Exponential Equation

• EN: Solve for x: 3^(2x) = 81.
• FR: Résoudre pour x : 3^(2x) = 81.
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Write both sides as powers of the same base, then set the exponents equal — like 2^(3x) = 64: 64 = 2⁶, so 3x = 6, x = 2.
• Steps:
  • Write 81 as a power of 3: 81 = 3⁴.
  • So 3^(2x) = 3⁴, which means 2x = 4.
  • x = 2.
• Answer: x = 2

[Easy] Permutations

• EN: In how many ways can 4 students line up in a row for a class photo?
• FR: De combien de façons 4 élèves peuvent-ils se placer en ligne pour une photo de classe?
• Choices: A) 12 B) 16 C) 24 D) 48
• Hint: For a line of n people, the number of arrangements is n factorial — like 3 people can line up in 3! = 3 × 2 × 1 = 6 ways.
• Steps:
  • 4 students in a row = 4!
  • 4! = 4 × 3 × 2 × 1 = 24.
  • So there are 24 ways.
• Answer: 24

[Easy] Polynomial Function — End Behaviour

• EN: For the polynomial f(x) = −2x³ + 5x − 1, what happens to f(x) as x → +∞?
• FR: Pour le polynôme f(x) = −2x³ + 5x − 1, que se passe-t-il avec f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: The end behaviour is controlled by the leading term — like for −3x⁵, as x → +∞ the function → −∞.
• Steps:
  • The leading term is −2x³.
  • As x → +∞, x³ → +∞, so −2x³ → −∞.
  • Therefore f(x) → −∞.
• Answer: f(x) → −∞

[Easy] Combinations

• EN: How many ways can you choose 2 toppings from a menu of 5 toppings on a pizza?
• FR: De combien de façons peut-on choisir 2 garnitures parmi 5 sur une pizza?
• Choices: A) 8 B) 10 C) 12 D) 20
• Hint: Use the combination formula C(n, r) = n! ÷ (r! × (n − r)!) — like C(4, 2) = 4! ÷ (2! × 2!) = 6.
• Steps:
  • C(5, 2) = 5! ÷ (2! × 3!).
  • = (5 × 4) ÷ (2 × 1) = 20 ÷ 2.
  • = 10.
• Answer: 10

[Easy] Derivative — Power Rule

• EN: If f(x) = 3x², what is f'(x)?
• FR: Si f(x) = 3x², quelle est f'(x)?
• Choices: A) 3x B) 6x C) 6x² D) 9x
• Hint: The power rule says: bring down the exponent as a coefficient and reduce the power by 1 — like if f(x) = 4x³, then f'(x) = 12x².
• Steps:
  • Apply the power rule to 3x².
  • Bring down the 2: 3 × 2 = 6.
  • Reduce the exponent: x² becomes x¹.
  • f'(x) = 6x.
• Answer: 6x

[Medium] Binomial Distribution

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: Une pièce équitable est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces?
• Choices: A) 1/8 B) 1/4 C) 3/8 D) 1/2
• Hint: Use P(X = k) = C(n, k) × p^k × (1−p)^(n−k) — like 2 heads in 3 flips: C(3,2) × (0.5)² × (0.5)¹ = 3 × 0.25 × 0.5 = 0.375.
• Steps:
  • P(X = 3) = C(4, 3) × (0.5)³ × (0.5)¹.
  • C(4, 3) = 4.
  • = 4 × 0.125 × 0.5 = 4 × 0.0625 = 0.25 = 1/4.
• Answer: 1/4

[Medium] Rational Function — Vertical Asymptote

• EN: What is the vertical asymptote of the function f(x) = (x + 2) ÷ (x − 3)?
• FR: Quelle est l'asymptote verticale de la fonction f(x) = (x + 2) ÷ (x − 3)?
• Choices: A) x = −2 B) x = 2 C) x = 3 D) x = 5
• Hint: The vertical asymptote occurs where the denominator equals zero — like for f(x) = 1 ÷ (x − 7), the vertical asymptote is x = 7.
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • x = 3.
  • So the vertical asymptote is x = 3.
• Answer: x = 3

[Medium] Vectors — Addition

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

[Medium] Derivative — Instantaneous Rate of Change

• EN: If f(x) = x² + 3x, what is the instantaneous rate of change at x = 4?
• FR: Si f(x) = x² + 3x, quel est le taux de variation instantané en x = 4?
• Choices: A) 9 B) 11 C) 13 D) 17
• Hint: Find f'(x) using the power rule, then substitute x — like f(x) = 2x² + x, f'(x) = 4x + 1, at x = 3: f'(3) = 13.
• Steps:
  • f'(x) = 2x + 3.
  • f'(4) = 2(4) + 3 = 8 + 3.
  • f'(4) = 11.
• Answer: 11

[Hard] Permutations with Restrictions

• EN: How many different 3-letter arrangements can be made from the letters A, B, C, D, E if no letter can be repeated?
• FR: Combien d'arrangements de 3 lettres différentes peut-on former avec les lettres A, B, C, D, E si aucune lettre ne peut se répéter?
• Choices: A) 30 B) 45 C) 60 D) 120
• Hint: This is a permutation: P(n, r) = n! ÷ (n − r)! — like P(4, 2) = 4! ÷ 2! = 24 ÷ 2 = 12.
• Steps:
  • P(5, 3) = 5! ÷ (5 − 3)!
  • = 5! ÷ 2!
  • = 120 ÷ 2 = 60.
• Answer: 60

[Hard] Polynomial Long Division

• EN: Divide (x³ + 3x² − x − 3) by (x − 1). What is the quotient?
• FR: Diviser (x³ + 3x² − x − 3) par (x − 1). Quel est le quotient?
• Choices: A) x² + 4x + 3 B) x² + 3x − 1 C) x² + 2x + 1 D) x² + 4x − 3
• Hint: Use synthetic or long division — bring down coefficients, multiply and subtract at each step, like dividing x³ + 5x² + 6x by x gives x² + 5x + 6.
• Steps:
  • Divide x³ by x to get x². Multiply: x²(x − 1) = x³ − x². Subtract: 3x² − (−x²) = 4x².
  • Bring down: 4x² − x. Divide 4x² by x = 4x. Multiply: 4x(x − 1) = 4x² − 4x. Subtract: −x − (−4x) = 3x.
  • Bring down: 3x − 3. Divide 3x by x = 3. Multiply: 3(x − 1) = 3x − 3. Remainder = 0.
  • Quotient: x² + 4x + 3.
• Answer: x² + 4x + 3