Daily Math — 2026-07-10

[Easy] Counting Mittens

• EN: Mia has 7 mittens in her basket. She finds 5 more under the bed. How many mittens does she have in all?
• FR: Mia a 7 mitaines dans son panier. Elle en trouve 5 autres sous le lit. Combien de mitaines a-t-elle en tout?
• Choices: A) 10 mittens B) 11 mittens C) 12 mittens D) 13 mittens
• Hint: To add two numbers, count on from the bigger one — for 6 + 4, start at 6 and count 4 more.
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • So Mia has 12 mittens in all.
• Answer: 12 mittens

[Easy] Counting Pennies

• EN: Leo has 3 pennies and finds 4 more pennies on the table. How many pennies does he have now?
• FR: Léo a 3 sous et en trouve 4 autres sur la table. Combien de sous a-t-il maintenant?
• Choices: A) 5 pennies B) 6 pennies C) 7 pennies D) 8 pennies
• Hint: To add small numbers, you can use your fingers — for 2 + 3, hold up 2 fingers, then add 3 more.
• Steps:
  • Start at 3 and count on 4 more: 4, 5, 6, 7.
  • So Leo has 7 pennies.
• Answer: 7 pennies

[Easy] Skip Counting by 5s

• EN: Sam counts by 5s starting at 5. What number comes after 20?
• FR: Sam compte par 5 en commençant à 5. Quel nombre vient après 20?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: When you skip count by 5s, you add 5 each time — 10, 15, 20, ...
• Steps:
  • Counting by 5s: 5, 10, 15, 20, then add 5 more.
  • 20 + 5 = 25.
• Answer: 25

[Easy] Subtracting Snowballs

• EN: There are 9 snowballs on the fence. A gust of wind knocks off 4 of them. How many snowballs are left?
• FR: Il y a 9 boules de neige sur la clôture. Une rafale en renverse 4. Combien de boules de neige reste-t-il?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: To subtract, start at the bigger number and count back — for 8 − 3, start at 8 and count back 3.
• Steps:
  • Start at 9 and count back 4: 8, 7, 6, 5.
  • So 5 snowballs are left.
• Answer: 5

[Medium] More Pennies and Nickels

• EN: Ava has 2 nickels and 3 pennies. How many cents does she have in all?
• FR: Ava a 2 pièces de 5 cents et 3 sous. Combien de cents a-t-elle en tout?
• Choices: A) 11 cents B) 13 cents C) 15 cents D) 17 cents
• Hint: A nickel is worth 5 cents — for 1 nickel and 2 pennies, that is 5 + 1 + 1 = 7 cents.
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 3 pennies = 1 + 1 + 1 = 3 cents.
  • 10 + 3 = 13 cents.
• Answer: 13 cents

[Medium] Comparing Numbers

• EN: Which number is bigger: 14 or 41?
• FR: Quel nombre est plus grand : 14 ou 41?
• Choices: A) 14 B) 41 C) They are equal D) 40
• Hint: Look at the tens digit first — 4 tens is more than 1 ten, so 40-something is bigger than 10-something.
• Steps:
  • 14 has 1 ten and 4 ones.
  • 41 has 4 tens and 1 one.
  • 4 tens is greater than 1 ten, so 41 is bigger.
• Answer: 41

[Medium] Skip Counting by 2s

• EN: Olivia counts by 2s starting at 2. What is the 5th number she says?
• FR: Olivia compte par 2 en commençant à 2. Quel est le 5e nombre qu'elle dit?
• Choices: A) 8 B) 9 C) 10 D) 12
• Hint: When you skip count by 2s, write the list — 2, 4, 6, 8, 10 — then find the 5th one.
• Steps:
  • Count by 2s: 2 (1st), 4 (2nd), 6 (3rd), 8 (4th), 10 (5th).
  • The 5th number is 10.
• Answer: 10

[Medium] Taking Away from 20

• EN: There are 20 hockey cards on the table. Ben takes 8 of them. How many are left on the table?
• FR: Il y a 20 cartes de hockey sur la table. Ben en prend 8. Combien en reste-t-il sur la table?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: To subtract from 20, think of 20 − 8 the way you think of 10 − 8 = 2, then add 10 back.
• Steps:
  • 20 − 8: think 10 − 8 = 2, then 2 + 10 = 12.
  • So 12 cards are left.
• Answer: 12

[Hard] Adding Three Numbers

• EN: Zoe has 4 crayons, 6 crayons, and 3 crayons in three boxes. How many crayons does she have in all?
• FR: Zoé a 4 crayons, 6 crayons et 3 crayons dans trois boîtes. Combien de crayons a-t-elle en tout?
• Choices: A) 11 crayons B) 12 crayons C) 13 crayons D) 14 crayons
• Hint: Add three numbers by adding the first two first — for 2 + 5 + 3, do 2 + 5 = 7, then 7 + 3 = 10.
• Steps:
  • Add the first two: 4 + 6 = 10.
  • Add the third: 10 + 3 = 13.
  • Zoe has 13 crayons.
• Answer: 13 crayons

[Hard] Number Patterns

• EN: Look at this pattern: 1, 3, 5, 7, ___. What is the missing number?
• FR: Regarde ce motif : 1, 3, 5, 7, ___. Quel est le nombre manquant?
• Choices: A) 8 B) 9 C) 10 D) 11
• Hint: Find the rule by looking at how much you add each time — for 2, 4, 6, 8, you add 2 each time.
• Steps:
  • 1 to 3: add 2. 3 to 5: add 2. 5 to 7: add 2.
  • The rule is add 2 each time.
  • 7 + 2 = 9.
• Answer: 9

[Easy] Adding to 100

• EN: There are 34 students in one class and 25 students in another. How many students are there in all?
• 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 B) 58 C) 59 D) 61
• Hint: Line up the ones and tens — for 32 + 24, add the ones first (2 + 4 = 6), then the tens (30 + 20 = 50), so 56.
• Steps:
  • Ones: 4 + 5 = 9.
  • Tens: 30 + 20 = 50.
  • 50 + 9 = 59.
• Answer: 59

[Easy] Telling Time to the Hour

• EN: The clock shows the short hand on 8 and the long hand on 12. What time does it show?
• FR: L'horloge montre la petite aiguille sur le 8 et la grande aiguille sur le 12. Quelle heure indique-t-elle?
• Choices: A) 7:00 B) 8:00 C) 9:00 D) 12:00
• Hint: When the long hand is on 12, it is exactly on the hour — the short hand tells you which hour.
• Steps:
  • Long hand on 12 means it is exactly on the hour.
  • Short hand on 8 means it is 8 o'clock.
  • The time is 8:00.
• Answer: 8:00

[Easy] Measuring Length

• EN: A pencil is 12 cm long. An eraser is 4 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 12 cm. Une gomme mesure 4 cm. De combien le crayon est-il plus long que la gomme?
• Choices: A) 6 cm B) 7 cm C) 8 cm D) 9 cm
• Hint: To find how much longer, subtract the smaller length from the bigger one — for 10 cm − 3 cm = 7 cm.
• Steps:
  • 12 cm − 4 cm = 8 cm.
  • The pencil is 8 cm longer than the eraser.
• Answer: 8 cm

[Easy] Counting Coins

• EN: Ethan has 2 dimes and 1 nickel. How many cents does he have in all?
• FR: Éthan a 2 pièces de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 15 cents B) 20 cents C) 25 cents D) 30 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents — for 1 dime and 2 nickels: 10 + 5 + 5 = 20 cents.
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • 1 nickel = 5 cents.
  • 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtracting within 100

• EN: A jar had 72 marbles. Kids took out 38 marbles. How many marbles are still in the jar?
• FR: Un pot contenait 72 billes. Des enfants en ont sorti 38. Combien de billes reste-t-il dans le pot?
• Choices: A) 31 B) 33 C) 34 D) 36
• Hint: For 65 − 27, regroup: 15 − 7 = 8 in the ones, and 5 − 2 = 3 in the tens, giving 38.
• Steps:
  • Ones: 2 − 8 needs regrouping. Borrow 1 ten: 12 − 8 = 4.
  • Tens: 6 − 3 = 3 (after borrowing, 7 became 6).
  • 72 − 38 = 34.
• Answer: 34

[Medium] Telling Time to the Half Hour

• EN: The short hand is between 3 and 4, and the long hand is on 6. What time is it?
• FR: La petite aiguille est entre le 3 et le 4, et la grande aiguille est sur le 6. Quelle heure est-il?
• Choices: A) 3:00 B) 3:30 C) 4:00 D) 4:30
• Hint: When the long hand is on 6, it is half past the hour — the short hand is just past the hour number.
• Steps:
  • Long hand on 6 means it is 30 minutes past the hour.
  • Short hand is just past 3, so it is half past 3.
  • The time is 3:30.
• Answer: 3:30

[Medium] Number Patterns

• EN: What are the next two numbers in this pattern: 10, 20, 30, 40, ___, ___?
• FR: Quels sont les deux prochains nombres dans ce motif : 10, 20, 30, 40, ___, ___?
• Choices: A) 45 and 50 B) 50 and 60 C) 48 and 56 D) 42 and 44
• Hint: Find the rule — for 5, 10, 15, 20, you add 5 each time, so the next numbers are 25 and 30.
• Steps:
  • The rule is add 10 each time.
  • 40 + 10 = 50, and 50 + 10 = 60.
  • The next two numbers are 50 and 60.
• Answer: 50 and 60

[Medium] Adding Coins to $1

• EN: Maya has 3 quarters. How many cents does she have in all?
• FR: Maya a 3 pièces de 25 cents. Combien de cents a-t-elle en tout?
• Choices: A) 50 cents B) 60 cents C) 75 cents D) 80 cents
• Hint: A quarter is worth 25 cents — for 2 quarters: 25 + 25 = 50 cents.
• Steps:
  • Each quarter = 25 cents.
  • 25 + 25 + 25 = 75 cents.
  • Maya has 75 cents.
• Answer: 75 cents

[Hard] Two-Step Money Problem

• EN: Chloe has 60 cents. She spends 25 cents on a sticker and 15 cents on a pencil. How much money does she have left?
• FR: Chloé a 60 cents. Elle dépense 25 cents pour un autocollant et 15 cents pour un crayon. Combien d'argent lui reste-t-il?
• Choices: A) 15 cents B) 18 cents C) 20 cents D) 22 cents
• Hint: For two-step problems, first find the total spent — for 30 cents + 20 cents = 50 cents, then subtract from what you started with.
• Steps:
  • Total spent: 25 + 15 = 40 cents.
  • Money left: 60 − 40 = 20 cents.
  • Chloe has 20 cents left.
• Answer: 20 cents

[Hard] Measuring and Comparing

• EN: A ribbon is 85 cm long. Priya cuts off a piece that is 37 cm long. How long is the piece of ribbon that remains?
• FR: Un ruban mesure 85 cm. Priya en coupe un morceau de 37 cm. Quelle est la longueur du morceau de ruban qui reste?
• Choices: A) 46 cm B) 47 cm C) 48 cm D) 52 cm
• Hint: To subtract with regrouping, try 85 − 37: borrow from the tens so 15 − 7 = 8 in the ones, then 7 − 3 = 4 in the tens.
• Steps:
  • Ones: 5 − 7 needs regrouping. Borrow 1 ten: 15 − 7 = 8.
  • Tens: 7 − 3 = 4 (after borrowing, 8 became 7).
  • 85 − 37 = 48 cm.
• Answer: 48 cm

[Easy] Multiplication by 2

• EN: A hockey team has 2 lines of players, each with 6 players. How many players are there in all?
• FR: Une équipe de hockey a 2 lignes de joueurs, chacune avec 6 joueurs. Combien y a-t-il de joueurs en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiplying by 2 is the same as doubling — for 2 × 7 = 14, just double 7.
• Steps:
  • 2 × 6 = 12.
  • There are 12 players in all.
• Answer: 12

[Easy] Multiplication by 5

• EN: There are 5 bags of apples. Each bag holds 4 apples. How many apples are there in total?
• FR: Il y a 5 sacs de pommes. Chaque sac contient 4 pommes. Combien y a-t-il de pommes au total?
• Choices: A) 16 B) 18 C) 20 D) 24
• Hint: Multiplying by 5 — for 5 × 3, count by 5s three times: 5, 10, 15.
• Steps:
  • 5 × 4: count by 5s four times: 5, 10, 15, 20.
  • There are 20 apples in total.
• Answer: 20

[Easy] Identifying Fractions

• EN: A pizza is cut into 4 equal pieces. Emma eats 1 piece. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 parts égales. Emma 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: The fraction is written as the number eaten over the total number of pieces — 1 piece out of 4 is written as 1/4.
• Steps:
  • Total pieces = 4. Emma ate 1 piece.
  • The fraction eaten = 1/4.
• Answer: 1/4

[Easy] Basic Division

• EN: 15 stickers are shared equally among 3 friends. How many stickers does each friend get?
• FR: 15 autocollants sont partagés également entre 3 amis. Combien d'autocollants chaque ami reçoit-il?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Division is the opposite of multiplication — for 12 ÷ 3, ask: 3 × ? = 12, and the answer is 4.
• Steps:
  • 15 ÷ 3: ask 3 × ? = 15.
  • 3 × 5 = 15, so each friend gets 5 stickers.
• Answer: 5

[Medium] Perimeter of a Rectangle

• EN: A garden is 7 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un jardin mesure 7 m de long et 3 m de large. Quel est le périmètre du jardin?
• Choices: A) 18 m B) 20 m C) 21 m D) 24 m
• Hint: Perimeter of a rectangle = add all four sides — for a 5 m × 2 m rectangle: 5 + 5 + 2 + 2 = 14 m.
• Steps:
  • A rectangle has two lengths and two widths.
  • Perimeter = 7 + 7 + 3 + 3 = 20 m.
• Answer: 20 m

[Medium] Multiplication by 10

• EN: A school orders 10 boxes of crayons. Each box has 8 crayons. How many crayons are there in all?
• FR: Une école commande 10 boîtes de crayons. Chaque boîte contient 8 crayons. Combien y a-t-il de crayons en tout?
• Choices: A) 18 B) 60 C) 80 D) 90
• Hint: To multiply by 10, just put a zero at the end of the number — for 10 × 6 = 60.
• Steps:
  • 10 × 8 = 80.
  • There are 80 crayons in all.
• Answer: 80

[Medium] Reading a Bar Graph

• EN: A bar graph shows that 6 students picked hockey, 4 picked soccer, and 8 picked skiing as their favourite sport. How many more students picked skiing than soccer?
• FR: Un diagramme à barres montre que 6 élèves ont choisi le hockey, 4 le soccer et 8 le ski comme sport préféré. Combien d'élèves de plus ont choisi le ski plutôt que le soccer?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: To find how many more, subtract the smaller bar from the larger bar — if one bar shows 9 and another shows 5, there are 9 − 5 = 4 more.
• Steps:
  • Skiing: 8. Soccer: 4.
  • 8 − 4 = 4 more students chose skiing.
• Answer: 4

[Medium] Multiplication by 3

• EN: A shelf holds 3 rows of books. Each row has 9 books. How many books are on the shelf in all?
• FR: Une étagère a 3 rangées de livres. Chaque rangée contient 9 livres. Combien de livres y a-t-il sur l'étagère en tout?
• Choices: A) 21 B) 24 C) 27 D) 30
• Hint: For 3 × 8, count by 3s eight times or use the fact that 3 × 8 = 24.
• Steps:
  • 3 × 9 = 27.
  • There are 27 books on the shelf.
• Answer: 27

[Hard] Comparing Fractions

• EN: Which fraction is greater: 1/2 or 1/4?
• FR: Quelle fraction est plus grande : 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/2 C) They are equal D) 3/4
• Hint: Imagine the same pizza — 1/2 of a pizza is one big slice, while 1/4 is a smaller slice, so 1/2 is greater.
• Steps:
  • 1/2 means 1 out of 2 equal pieces. 1/4 means 1 out of 4 equal pieces.
  • When the whole is divided into more pieces, each piece is smaller.
  • So 1/2 is greater than 1/4.
• Answer: 1/2

[Hard] Two-Step Multiplication and Subtraction

• EN: There are 4 bags, each holding 5 oranges. If 7 oranges are eaten, how many oranges are left?
• FR: Il y a 4 sacs, chacun contenant 5 oranges. Si 7 oranges sont mangées, combien en reste-t-il?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: For two steps, solve the multiplication first, then the subtraction — for 3 × 4 = 12, then 12 − 5 = 7.
• Steps:
  • Total oranges: 4 × 5 = 20.
  • Oranges eaten: 7.
  • 20 − 7 = 13 oranges left.
• Answer: 13

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: You can break it apart — for 6 × 7, think 6 × 5 = 30 and 6 × 2 = 12, then add: 30 + 12 = 42.
• Steps:
  • 7 × 8: use the fact 7 × 8 = 56.
  • Double-check: 7 × 4 = 28, and 28 × 2 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 4.37?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,37?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 30 ones
• Hint: In a decimal, the first digit after the decimal point is in the tenths place — for 2.56, the 5 is in the tenths place.
• Steps:
  • 4.37: the digit 4 is in the ones place, 3 is in the tenths place, 7 is in the hundredths place.
  • The digit 3 has a value of 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A classroom floor is 9 m long and 6 m wide. What is the area of the floor?
• FR: Le plancher d'une salle de classe mesure 9 m de long et 6 m de large. Quelle est l'aire du plancher?
• Choices: A) 30 m² B) 45 m² C) 54 m² D) 60 m²
• Hint: Area of a rectangle = length × width — for a 5 m × 4 m room, the area is 5 × 4 = 20 m².
• Steps:
  • Area = 9 × 6 = 54.
  • The area of the floor is 54 m².
• Answer: 54 m²

[Easy] Long Division without Remainder

• EN: 48 students are split equally into 6 groups. How many students are in each group?
• FR: 48 élèves sont répartis également en 6 groupes. Combien d'élèves y a-t-il dans chaque groupe?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Division is the opposite of multiplication — for 36 ÷ 4, ask 4 × ? = 36, and the answer is 9.
• Steps:
  • 48 ÷ 6: ask 6 × ? = 48.
  • 6 × 8 = 48, so each group has 8 students.
• Answer: 8

[Medium] Long Division with Remainder

• EN: A teacher has 38 pencils to share equally among 5 students. How many pencils does each student get, and how many are left over?
• FR: Un enseignant a 38 crayons à partager également entre 5 élèves. Combien de crayons chaque élève reçoit-il, et combien en reste-t-il?
• Choices: A) 6 remainder 8 B) 7 remainder 3 C) 8 remainder 2 D) 7 remainder 6
• Hint: For 29 ÷ 4, find the biggest multiple of 4 that fits into 29: 4 × 7 = 28, so the quotient is 7 remainder 1.
• Steps:
  • 5 × 7 = 35, which fits into 38.
  • 38 − 35 = 3 left over.
  • Each student gets 7 pencils with 3 remainder.
• Answer: 7 remainder 3

[Medium] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/3?
• FR: Quelle fraction est plus grande : 3/4 ou 2/3?
• Choices: A) 2/3 B) 3/4 C) They are equal D) 1/2
• Hint: To compare fractions with different denominators, find a common denominator — for 1/2 and 1/3, use 6ths: 3/6 > 2/6, so 1/2 > 1/3.
• Steps:
  • Common denominator for 4 and 3 is 12.
  • 3/4 = 9/12 and 2/3 = 8/12.
  • 9/12 > 8/12, so 3/4 is greater.
• Answer: 3/4

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 p.m. and ends at 3:45 p.m. How long was the game?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Quelle a été la durée du match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: Count up from the start time to the end time — from 2:10 to 4:40, count 2 hours then 30 minutes = 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 = 2 hours.
  • From 3:15 to 3:45 = 30 more minutes.
  • Total = 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A bag of apples costs $3.45 and a bag of grapes costs $2.30. What is the total cost?
• FR: Un sac de pommes coûte 3,45 $ et un sac de raisins coûte 2,30 $. Quel est le coût total?
• Choices: A) $5.65 B) $5.75 C) $6.05 D) $6.75
• Hint: Line up the decimal points and add — for $1.25 + $3.40, add the cents first: 25 + 40 = 65, then dollars: 1 + 3 = 4, giving $4.65.
• Steps:
  • $3.45 + $2.30: cents: 45 + 30 = 75, dollars: 3 + 2 = 5.
  • Total = $5.75.
• Answer: $5.75

[Hard] Multi-Step Area Problem

• EN: A living room is 8 m long and 5 m wide. A carpet in the middle is 4 m long and 3 m wide. What is the area of the floor NOT covered by the carpet?
• FR: Un salon mesure 8 m de long et 5 m de large. Un tapis au milieu mesure 4 m de long et 3 m de large. Quelle est l'aire du plancher NON couverte par le tapis?
• Choices: A) 26 m² B) 28 m² C) 30 m² D) 32 m²
• Hint: Find the big area first, then the carpet area, then subtract — for a 6 × 4 room with a 2 × 2 mat: 24 − 4 = 20 m².
• Steps:
  • Area of living room = 8 × 5 = 40 m².
  • Area of carpet = 4 × 3 = 12 m².
  • Floor not covered = 40 − 12 = 28 m².
• Answer: 28 m²

[Hard] Multi-Step Word Problem

• EN: Noah earns $9 per hour shovelling driveways. He works 7 hours on Saturday and 4 hours on Sunday. How much money does he earn in total?
• FR: Noah gagne 9 $ de l'heure pour pelleter des entrées. Il travaille 7 heures samedi et 4 heures dimanche. Combien d'argent gagne-t-il en tout?
• Choices: A) $90 B) $95 C $99 D) $108
• Hint: First find the total number of hours worked, then multiply by the hourly wage — for 5 + 3 = 8 hours at $7/h: 8 × 7 = $56.
• Steps:
  • Total hours: 7 + 4 = 11 hours.
  • Total earnings: 11 × $9 = $99.
• Answer: $99

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 198 C) 204 D) 214
• Hint: Break apart the number — for 23 × 4, do 20 × 4 = 80 and 3 × 4 = 12, then add: 80 + 12 = 92.
• Steps:
  • 34 × 6: 30 × 6 = 180 and 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: Lily eats 2/8 of a granola bar and her friend eats 3/8 of the same bar. How much did they eat together?
• FR: Lily mange 2/8 d'une barre granola et son amie mange 3/8 de la même barre. Combien ont-elles mangé ensemble?
• Choices: A) 5/8 B) 5/16 C) 6/8 D) 1/2
• Hint: When denominators are the same, just add the numerators and keep the denominator — for 1/5 + 2/5 = 3/5.
• Steps:
  • 2/8 + 3/8 = (2 + 3)/8 = 5/8.
  • They ate 5/8 of the granola bar together.
• Answer: 5/8

[Easy] Percentage Introduction (50%)

• EN: A bag contains 20 tokens. 50% of the tokens are red. How many tokens are red?
• FR: Un sac contient 20 jetons. 50 % des jetons sont rouges. Combien de jetons sont rouges?
• Choices: A) 5 B) 8 C) 10 D) 15
• Hint: 50% means half — for 50% of 16, just divide by 2 to get 8.
• Steps:
  • 50% of 20 = 20 ÷ 2 = 10.
  • 10 tokens are red.
• Answer: 10

[Easy] Decimal Addition

• EN: A bottle holds 1.5 L of juice and another holds 2.3 L. How many litres are there in all?
• FR: Une bouteille contient 1,5 L de jus et une autre 2,3 L. Combien de litres y a-t-il en tout?
• Choices: A) 3.5 L B) 3.7 L C) 3.8 L D) 4.2 L
• Hint: Line up decimal points and add — for 1.2 + 2.5: ones are 1 + 2 = 3, tenths are 2 + 5 = 7, giving 3.7.
• Steps:
  • 1.5 + 2.3: ones: 1 + 2 = 3, tenths: 5 + 3 = 8.
  • Total = 3.8 L.
• Answer: 3.8 L

[Medium] Multi-Digit Division

• EN: 216 students are divided equally into 8 teams. How many students are on each team?
• FR: 216 élèves sont répartis également en 8 équipes. Combien d'élèves y a-t-il dans chaque équipe?
• Choices: A) 24 B) 27 C) 28 D) 32
• Hint: For long division of 182 ÷ 7, see how many times 7 goes into 18 (twice, giving 14, remainder 4), then bring down the 2 to get 42 ÷ 7 = 6, so 26.
• Steps:
  • 8 goes into 21 twice (16), remainder 5. Bring down 6 to get 56.
  • 56 ÷ 8 = 7.
  • So 216 ÷ 8 = 27.
• Answer: 27

[Medium] Subtracting Fractions

• EN: A recipe uses 7/10 cup of flour. You have already added 3/10 cup. How much more flour do you need?
• FR: Une recette utilise 7/10 de tasse de farine. Tu as déjà ajouté 3/10 de tasse. De combien de farine as-tu encore besoin?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 6/10
• Hint: When denominators are the same, subtract the numerators — for 5/6 − 2/6 = 3/6.
• Steps:
  • 7/10 − 3/10 = (7 − 3)/10 = 4/10.
  • You need 4/10 cup more flour.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est le volume de la boîte?
• Choices: A) 48 cm³ B) 56 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height — for a 2 × 3 × 4 box: 2 × 3 = 6, then 6 × 4 = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A Tim Hortons fundraiser collected $80. The school keeps 25% for supplies. How much money does the school keep?
• FR: Une collecte de fonds de Tim Hortons a recueilli 80 $. L'école garde 25 % pour les fournitures. Combien d'argent l'école garde-t-elle?
• Choices: A) $15 B) $18 C) $20 D) $25
• Hint: 25% means one-quarter — for 25% of $60, divide by 4 to get $15.
• Steps:
  • 25% of $80 = $80 ÷ 4 = $20.
  • The school keeps $20.
• Answer: $20

[Hard] Multi-Step Fraction and Decimal Problem

• EN: A running track is 0.4 km long. Jayden runs around the track 3 times. He also walks an extra 0.25 km to cool down. How far does Jayden travel in total?
• FR: Une piste de course mesure 0,4 km. Jayden fait 3 tours de piste. Il marche aussi 0,25 km supplémentaire pour récupérer. Quelle distance totale Jayden parcourt-il?
• Choices: A) 1.35 km B) 1.45 km C) 1.55 km D) 1.65 km
• Hint: First find the distance for the laps, then add the cool-down distance — for 3 laps of 0.3 km: 3 × 0.3 = 0.9 km, then add 0.15 km to get 1.05 km.
• Steps:
  • Distance running: 3 × 0.4 = 1.2 km.
  • Total: 1.2 + 0.25 = 1.45 km.
• Answer: 1.45 km

[Hard] Multi-Step Division and Percentage

• EN: A class of 40 students took a science test. 10% scored above 90, and half of the remaining students passed with between 60 and 90. How many students passed with between 60 and 90?
• FR: Une classe de 40 élèves a passé un examen de sciences. 10 % ont eu plus de 90, et la moitié des élèves restants ont réussi avec un score entre 60 et 90. Combien d'élèves ont réussi avec un score entre 60 et 90?
• Choices: A) 14 B) 16 C) 18 D) 20
• Hint: Find 10% first, subtract from the total, then take half of what's left — for 20 students, 10% = 2, remaining = 18, half = 9.
• Steps:
  • 10% of 40 = 4 students scored above 90.
  • Remaining students: 40 − 4 = 36.
  • Half of 36 = 18 students passed with between 60 and 90.
• Answer: 18

[Easy] Percent of a Number

• EN: What is 25% of 60?
• FR: Combien fait 25 % de 60?
• Choices: A) 12 B) 15 C) 18 D) 20
• Hint: 25% is the same as 1/4 — for 25% of 40, divide 40 by 4 to get 10.
• Steps:
  • 25% of 60 = 60 ÷ 4 = 15.
• Answer: 15

[Easy] Simple Algebraic Expression

• EN: What is the value of 3n + 4 when n = 5?
• FR: Quelle est la valeur de 3n + 4 quand n = 5?
• Choices: A) 17 B) 18 C) 19 D) 22
• Hint: Substitute the value for the variable first — for 2x + 3 when x = 4, do 2 × 4 + 3 = 8 + 3 = 11.
• Steps:
  • Substitute n = 5: 3(5) + 4 = 15 + 4 = 19.
• Answer: 19

[Easy] Integers Introduction

• EN: The temperature in Winnipeg was −8°C in the morning and rose by 11°C by afternoon. What was the afternoon temperature?
• FR: La température à Winnipeg était de −8 °C le matin et a augmenté de 11 °C l'après-midi. Quelle était la température l'après-midi?
• Choices: A) 1°C B) 2°C C) 3°C D) 4°C
• Hint: Adding a positive to a negative — for −5 + 8, start at −5 on the number line and move 8 steps right to reach +3.
• Steps:
  • −8 + 11 = 3.
  • The afternoon temperature was 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/garçons?
• Choices: A) 2:3 B) 3:2 C) 4:3 D) 3:4
• Hint: Write the ratio as the first quantity to the second — for 6 cats and 4 dogs, the ratio is 6:4, which simplifies to 3:2.
• Steps:
  • Ratio of girls to boys = 12:8.
  • Simplify by dividing both by 4: 12 ÷ 4 = 3, 8 ÷ 4 = 2.
  • The ratio is 3:2.
• Answer: 3:2

[Medium] Order of Operations (BEDMAS)

• EN: What is the value of 3 + 4 × 2 − 1?
• FR: Quelle est la valeur de 3 + 4 × 2 − 1?
• Choices: A) 9 B) 10 C) 13 D) 14
• Hint: Use BEDMAS — for 5 + 3 × 2, do the multiplication first: 3 × 2 = 6, then add: 5 + 6 = 11.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then left to right: 3 + 8 − 1 = 10.
• Answer: 10

[Medium] Fraction Multiplication

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

[Medium] Rates

• EN: A car travels 150 km in 3 hours. What is its speed in kilometres per hour?
• FR: Une voiture parcourt 150 km en 3 heures. Quelle est sa vitesse en kilomètres par heure?
• Choices: A) 40 km/h B) 45 km/h C) 50 km/h D) 55 km/h
• Hint: Rate = total amount ÷ number of units — for 200 km in 4 hours: 200 ÷ 4 = 50 km/h.
• Steps:
  • Speed = 150 ÷ 3 = 50.
  • The car travels at 50 km/h.
• Answer: 50 km/h

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 4/3
• Hint: To divide fractions, multiply by the reciprocal — for 2/3 ÷ 1/4, flip the second fraction and multiply: 2/3 × 4/1 = 8/3.
• Steps:
  • Flip 1/2 to get 2/1.
  • 3/4 × 2/1 = 6/4 = 3/2.
• Answer: 3/2

[Hard] Multi-Step Percent Problem

• EN: A jacket at a store costs $120. It is on sale for 30% off. How much does the jacket cost after the discount?
• FR: Un manteau dans un magasin coûte 120 $. Il est en solde à 30 % de rabais. Combien coûte le manteau après le rabais?
• Choices: A) $78 B) $80 C) $84 D) $90
• Hint: Find the discount amount first, then subtract it — for 20% off $50: 20% of $50 = $10, so the sale price is $50 − $10 = $40.
• Steps:
  • 30% of $120 = 0.30 × 120 = $36.
  • Sale price = $120 − $36 = $84.
• Answer: $84

[Hard] Order of Operations with Brackets

• EN: What is the value of (5 + 3) × 4 − 2²?
• FR: Quelle est la valeur de (5 + 3) × 4 − 2²?
• Choices: A) 24 B) 28 C) 30 D) 34
• Hint: Follow BEDMAS — for (2 + 3) × 5 − 1², do brackets first: 5 × 5 = 25, then exponent: 1² = 1, then 25 − 1 = 24.
• Steps:
  • Brackets: 5 + 3 = 8.
  • Exponent: 2² = 4.
  • Multiplication: 8 × 4 = 32.
  • Subtraction: 32 − 4 = 28.
• Answer: 28

[Easy] Integer Addition

• EN: What is −9 + 15?
• FR: Combien font −9 + 15?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: On a number line, start at −9 and move 15 steps to the right — for −6 + 10, you land at +4.
• Steps:
  • −9 + 15: the positive is larger, so the answer is positive.
  • 15 − 9 = 6.
• Answer: 6

[Easy] Finding a Discount

• EN: A pair of skates costs $80. A store offers a 10% discount. How much is the discount?
• FR: Une paire de patins coûte 80 $. Un magasin offre un rabais de 10 %. Quel est le montant du rabais?
• Choices: A) $6 B) $7 C) $8 D) $9
• Hint: 10% of a number = divide by 10 — for 10% of $70, just move the decimal: $7.00.
• Steps:
  • 10% of $80 = $80 ÷ 10 = $8.
  • The discount is $8.
• Answer: $8

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 7 = 15.
• FR: Résous pour x : x + 7 = 15.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: To isolate the variable, do the opposite operation — for x + 4 = 9, subtract 4 from both sides: x = 5.
• Steps:
  • x + 7 = 15.
  • Subtract 7 from both sides: x = 15 − 7 = 8.
• Answer: x = 8

[Easy] Integer Subtraction

• EN: What is 3 − (−5)?
• FR: Combien font 3 − (−5)?
• Choices: A) −2 B) 2 C) 7 D) 8
• Hint: Subtracting a negative is the same as adding a positive — for 4 − (−3), think 4 + 3 = 7.
• Steps:
  • 3 − (−5) = 3 + 5 = 8.
• Answer: 8

[Medium] Percentage — Tax

• EN: A book costs $15.00. If the HST is 13%, how much tax is added?
• FR: Un livre coûte 15,00 $. Si la TVH est de 13 %, combien de taxes sont ajoutées?
• Choices: A) $1.65 B) $1.80 C) $1.95 D) $2.10
• Hint: To find tax, multiply the cost by the tax rate as a decimal — for 10% tax on $20: 20 × 0.10 = $2.00.
• Steps:
  • Tax = $15 × 0.13 = $1.95.
  • $1.95 of tax is added.
• Answer: $1.95

[Medium] Surface Area of a Rectangular Prism

• EN: A box has a length of 4 cm, a width of 3 cm, and a height of 2 cm. What is the surface area of the box?
• FR: Une boîte a une longueur de 4 cm, une largeur de 3 cm et une hauteur de 2 cm. Quelle est l'aire de la surface de la boîte?
• Choices: A) 48 cm² B) 52 cm² C) 56 cm² D) 60 cm²
• Hint: Surface area = 2(lw + lh + wh) — for a 3 × 2 × 1 box: 2(6 + 3 + 2) = 2 × 11 = 22 cm².
• Steps:
  • lw = 4 × 3 = 12, lh = 4 × 2 = 8, wh = 3 × 2 = 6.
  • Surface area = 2(12 + 8 + 6) = 2 × 26 = 52 cm².
• Answer: 52 cm²

[Medium] Integer Multiplication

• EN: What is (−4) × (−6)?
• FR: Combien font (−4) × (−6)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: When you multiply two negatives, the answer is positive — for (−3) × (−5) = +15.
• Steps:
  • Negative × Negative = Positive.
  • 4 × 6 = 24, so (−4) × (−6) = 24.
• Answer: 24

[Medium] Probability

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

[Hard] Multi-Step Tip and Tax

• EN: A family eats at a restaurant in Ottawa. The meal costs $56.00. They add a 15% tip AND pay 13% HST on the original price. What is the total amount they pay?
• FR: Une famille mange dans un restaurant à Ottawa. Le repas coûte 56,00 $. Ils ajoutent un pourboire de 15 % ET paient 13 % de TVH sur le prix original. Quel est le montant total qu'ils paient?
• Choices: A) $71.68 B) $72.96 C) $78.40 D) $79.52
• Hint: Calculate tip and tax separately on the original price, then add all three together — for a $40 meal with 10% tip and 5% tax: tip = $4, tax = $2, total = $46.
• Steps:
  • Tip: 15% of $56 = $56 × 0.15 = $8.40.
  • HST: 13% of $56 = $56 × 0.13 = $7.28.
  • Total: $56 + $8.40 + $7.28 = $71.68.
• Answer: $71.68

[Hard] Integer Division and Equations

• EN: The temperature dropped by the same amount each hour for 6 hours. The total drop was 18°C. Write and solve an equation to find the temperature drop per hour, then find the new temperature if it started at 5°C.
• FR: La température a baissé du même montant chaque heure pendant 6 heures. La baisse totale était de 18 °C. Écris et résous une équation pour trouver la baisse de température par heure, puis trouve la nouvelle température si elle a commencé à 5 °C.
• Choices: A) −8°C B) −10°C C) −13°C D) −15°C
• Hint: For a total change problem, divide the total by the number of steps to find the rate, then apply the total change from the starting value.
• Steps:
  • Equation: 6d = 18, so d = 3°C drop per hour.
  • Starting temp = 5°C. Total drop = 18°C.
  • New temperature: 5 − 18 = −13°C.
• Answer: −13°C

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: A perfect square's root is the number multiplied by itself — 11 × 11 = 121 and 12 × 12 = 144.
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144, so √144 = 12.
• Answer: 12

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 17.
• FR: Résous pour x : 2x + 5 = 17.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: First, subtract the constant from both sides, then divide — for 3x + 2 = 11: subtract 2 to get 3x = 9, then divide by 3 to get x = 3.
• Steps:
  • 2x + 5 = 17. Subtract 5: 2x = 12.
  • Divide by 2: x = 6.
• Answer: x = 6

[Easy] Mean of a Data Set

• EN: Five students scored 72, 85, 91, 68, and 74 on a math test. What is the mean score?
• FR: Cinq élèves ont obtenu 72, 85, 91, 68 et 74 à un examen de maths. Quelle est la note moyenne?
• Choices: A) 76 B) 78 C) 80 D) 82
• Hint: Mean = sum of all values ÷ number of values — for 4, 6, 8, 10: sum = 28, mean = 28 ÷ 4 = 7.
• Steps:
  • Sum = 72 + 85 + 91 + 68 + 74 = 390.
  • Mean = 390 ÷ 5 = 78.
• Answer: 78

[Easy] Percent Increase

• EN: A hockey stick was $60. Its price increased to $75. What is the percent increase?
• FR: Un bâton de hockey coûtait 60 $. Son prix est passé à 75 $. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100 — for a price going from $40 to $50: increase = $10, percent = (10 ÷ 40) × 100 = 25%.
• Steps:
  • Increase = $75 − $60 = $15.
  • Percent increase = (15 ÷ 60) × 100 = 25%.
• Answer: 25%

[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 côtés 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 — for legs of 3 and 4: 9 + 16 = 25, so c = √25 = 5.
• Steps:
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10.
  • The hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation with Negatives

• EN: Solve for x: 3x − 4 = 11.
• FR: Résous pour x : 3x − 4 = 11.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add to both sides first, then divide — for 4x − 3 = 9: add 3 to get 4x = 12, then divide by 4 to get x = 3.
• Steps:
  • 3x − 4 = 11. Add 4: 3x = 15.
  • Divide by 3: x = 5.
• Answer: x = 5

[Medium] Slope Introduction

• EN: A ramp rises 6 m vertically over a horizontal distance of 12 m. What is the slope of the ramp?
• FR: Une rampe monte de 6 m à la verticale sur une distance horizontale de 12 m. Quelle est la pente de la rampe?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: Slope = rise ÷ run — for a rise of 3 and a run of 9, slope = 3/9 = 1/3.
• Steps:
  • Slope = rise ÷ run = 6 ÷ 12 = 1/2.
• Answer: 1/2

[Medium] Median and Mode

• EN: Here are seven quiz scores: 4, 7, 9, 7, 5, 8, 7. What is the mode?
• FR: Voici sept résultats de quiz : 4, 7, 9, 7, 5, 8, 7. Quel est le mode?
• Choices: A) 5 B) 7 C) 8 D) 9
• Hint: The mode is the number that appears most often — for 2, 3, 5, 3, 8, the mode is 3 because it appears twice.
• Steps:
  • Count: 4 appears once, 7 appears three times, 5 once, 8 once, 9 once.
  • 7 appears most often, so the mode is 7.
• Answer: 7

[Hard] Pythagorean Theorem Applied

• EN: A 13 m ladder leans against a wall. Its base is 5 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 13 m est appuyée contre un mur. Sa base est à 5 m du mur. À quelle hauteur sur le mur l'échelle arrive-t-elle?
• Choices: A) 10 m B) 11 m C) 12 m D) 13 m
• Hint: For a right triangle, if you know the hypotenuse and one leg, use a² = c² − b² — for c = 10 and b = 6: a² = 100 − 36 = 64, a = 8.
• Steps:
  • a² + 5² = 13². So a² = 169 − 25 = 144.
  • a = √144 = 12.
  • The ladder reaches 12 m up the wall.
• Answer: 12 m

[Hard] Percent Decrease and Two-Step Equation

• EN: A snowmobile's value decreases by 20% each year. It currently costs $5500. What will it be worth after one year?
• FR: La valeur d'une motoneige diminue de 20 % chaque année. Elle coûte actuellement 5 500 $. Quelle sera sa valeur après un an?
• Choices: A) $3 500 B) $4 000 C) $4 400 D) $4 800
• Hint: Percent decrease: find the decrease amount, then subtract — for 15% decrease on $2000: decrease = $300, new value = $1700.
• Steps:
  • Decrease = 20% of $5500 = 0.20 × 5500 = $1100.
  • New value = $5500 − $1100 = $4400.
• Answer: $4 400

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 3 = 13.
• FR: Résous pour x : 4x − 3 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Isolate x by adding or subtracting first, then dividing — for 5x − 2 = 18: add 2 to get 5x = 20, then divide by 5 to get x = 4.
• Steps:
  • Add 3 to both sides: 4x = 16.
  • Divide by 4: x = 4.
• Answer: x = 4

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x + 5?
• FR: Quelle est la pente de la droite y = 3x + 5?
• Choices: A) 3 B) 5 C) 8 D) 15
• Hint: In y = mx + b, the slope is always m (the coefficient of x) — for y = 7x + 2, the slope is 7.
• Steps:
  • In y = 3x + 5, the coefficient of x is 3.
  • The slope is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: What is (2x + 5) + (3x − 2)?
• FR: Combien font (2x + 5) + (3x − 2)?
• Choices: A) 5x − 3 B) 5x + 3 C) 6x + 3 D) 5x + 7
• Hint: Combine like terms — for (4x + 3) + (2x − 1): x terms: 4x + 2x = 6x, constants: 3 − 1 = 2, giving 6x + 2.
• Steps:
  • x terms: 2x + 3x = 5x.
  • Constants: 5 + (−2) = 3.
  • Result: 5x + 3.
• Answer: 5x + 3

[Easy] Similar Triangles

• EN: Two triangles are similar. The first has sides 3, 4, and 5. The second has its shortest side as 6. What is the longest side of the second triangle?
• FR: Deux triangles sont semblables. Le premier a des côtés de 3, 4 et 5. Le second a son côté le plus court de 6. Quel est le côté le plus long du second triangle?
• Choices: A) 8 B) 9 C) 10 D) 12
• Hint: Find the scale factor by dividing the matching sides, then multiply all sides — for triangles where the short side doubles from 3 to 6, multiply every side by 2.
• Steps:
  • Scale factor = 6 ÷ 3 = 2.
  • Longest side = 5 × 2 = 10.
• Answer: 10

[Medium] Linear Inequality

• EN: Solve the inequality: 2x + 1 > 9.
• FR: Résous l'inégalité : 2x + 1 > 9.
• Choices: A) x > 3 B) x > 4 C) x > 5 D) x > 6
• Hint: Solve inequalities the same way as equations, but keep the inequality sign — for 3x + 2 > 11: subtract 2 to get 3x > 9, then divide to get x > 3.
• Steps:
  • 2x + 1 > 9. Subtract 1: 2x > 8.
  • Divide by 2: x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: What is 3x(2x − 5)?
• FR: Combien font 3x(2x − 5)?
• Choices: A) 6x − 15x B) 5x² − 8x C) 6x² − 15x D) 6x² + 15x
• Hint: Use the distributive property — for 2x(3x + 4), multiply 2x by each term: 2x × 3x = 6x² and 2x × 4 = 8x, giving 6x² + 8x.
• Steps:
  • 3x × 2x = 6x².
  • 3x × (−5) = −15x.
  • Result: 6x² − 15x.
• Answer: 6x² − 15x

[Medium] Trigonometry — SOH-CAH-TOA

• EN: In a right triangle, the angle is 30°, and the hypotenuse is 10 cm. What is the length of the side opposite the angle? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle est de 30° et l'hypoténuse est de 10 cm. Quelle est la longueur du côté opposé à l'angle? (sin 30° = 0,5)
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: SOH means sin(angle) = opposite ÷ hypotenuse — for sin 45° = 0.7 with a hypotenuse of 10, opposite = 10 × 0.7 = 7 cm.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse.
  • 0.5 = opposite ÷ 10.
  • Opposite = 10 × 0.5 = 5 cm.
• Answer: 5 cm

[Medium] Graphing Lines — Finding y-intercept

• EN: A line has the equation 2x + y = 8. What is the y-intercept of this line?
• FR: Une droite a l'équation 2x + y = 8. Quelle est l'ordonnée à l'origine de cette droite?
• Choices: A) y = 4 B) y = 6 C) y = 8 D) y = 10
• Hint: To find the y-intercept, set x = 0 and solve — for 3x + y = 9: set x = 0 to get y = 9.
• Steps:
  • Set x = 0: 2(0) + y = 8.
  • y = 8.
• Answer: y = 8

[Hard] Systems of Equations — Substitution

• EN: Solve the system: y = 2x + 1 and y = 5x − 8.
• FR: Résous le système : y = 2x + 1 et y = 5x − 8.
• Choices: A) x = 2, y = 5 B) x = 3, y = 7 C) x = 4, y = 9 D) x = 5, y = 11
• Hint: Set the two expressions equal to each other, solve for x, then substitute back — for y = x + 2 and y = 3x, set x + 2 = 3x: 2 = 2x, x = 1, then y = 3.
• Steps:
  • Set 2x + 1 = 5x − 8.
  • 1 + 8 = 5x − 2x → 9 = 3x → x = 3.
  • y = 2(3) + 1 = 7.
• Answer: x = 3, y = 7

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 7 cm and the adjacent side is 7 cm. What is the angle? (tan 45° = 1)
• FR: Dans un triangle rectangle, le côté opposé est de 7 cm et le côté adjacent est de 7 cm. Quel est l'angle? (tan 45° = 1)
• Choices: A) 30° B) 35° C) 40° D) 45°
• Hint: Use TOA: tan(angle) = opposite ÷ adjacent — for opposite = 5 and adjacent = 5, tan = 1 so the angle is 45°.
• Steps:
  • tan(angle) = opposite ÷ adjacent = 7 ÷ 7 = 1.
  • tan⁻¹(1) = 45°.
• Answer: 45°

[Easy] Factoring a Quadratic

• EN: Factor the expression: x² + 5x + 6.
• FR: Factorise l'expression : 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 term AND add to the x coefficient — for x² + 7x + 12, find numbers that multiply to 12 and add to 7: 3 and 4, giving (x + 3)(x + 4).
• Steps:
  • Find two numbers that multiply to 6 and add to 5: 2 × 3 = 6, 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, the angle is 45°, and the adjacent side is 8 cm. What is the hypotenuse? (cos 45° ≈ 0.707)
• FR: Dans un triangle rectangle, l'angle est de 45° et le côté adjacent est de 8 cm. Quelle est l'hypoténuse? (cos 45° ≈ 0,707)
• Choices: A) 9.1 cm B) 10.8 cm C) 11.3 cm D) 12.0 cm
• Hint: CAH means cos(angle) = adjacent ÷ hypotenuse, so hypotenuse = adjacent ÷ cos(angle) — for cos 60° = 0.5 and adjacent = 5: hypotenuse = 5 ÷ 0.5 = 10.
• Steps:
  • cos(45°) = adjacent ÷ hypotenuse.
  • 0.707 = 8 ÷ hypotenuse.
  • Hypotenuse = 8 ÷ 0.707 ≈ 11.3 cm.
• Answer: 11.3 cm

[Easy] System of Equations — Elimination

• EN: Solve: x + y = 10 and x − y = 4.
• FR: Résous : x + y = 10 et x − y = 4.
• Choices: A) x = 6, y = 4 B) x = 7, y = 3 C) x = 5, y = 5 D) x = 8, y = 2
• Hint: Add the two equations to eliminate y — for x + y = 8 and x − y = 2, adding gives 2x = 10 so x = 5, then y = 3.
• Steps:
  • Add: (x + y) + (x − y) = 10 + 4 → 2x = 14 → x = 7.
  • Substitute: 7 + y = 10 → y = 3.
• Answer: x = 7, y = 3

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 5 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 628 cm³ B) 706 cm³ C) 785 cm³ D) 850 cm³
• Hint: Volume of a cylinder = π × r² × h — for r = 3 and h = 7: V = 3.14 × 9 × 7 ≈ 197.8 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 25 × 10.
  • 3.14 × 25 = 78.5, then 78.5 × 10 = 785.
  • Volume = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Solve x² + 6x + 5 = 0 by factoring.
• FR: Résous x² + 6x + 5 = 0 par factorisation.
• Choices: A) x = −1 or x = −5 B) x = 1 or x = 5 C) x = −2 or x = −3 D) x = 2 or x = 3
• Hint: Factor the quadratic and set each factor equal to zero — for x² + 7x + 6 = 0, factor to (x + 1)(x + 6) = 0, giving x = −1 or x = −6.
• Steps:
  • Factor: x² + 6x + 5 = (x + 1)(x + 5).
  • Set each factor to zero: x + 1 = 0 → x = −1; x + 5 = 0 → x = −5.
• Answer: x = −1 or x = −5

[Medium] Circle Geometry — Chord and Radius

• EN: A chord of length 16 cm is drawn in a circle with radius 10 cm. What is the perpendicular distance from the centre to the chord?
• FR: Une corde de longueur 16 cm est tracée dans un cercle de rayon 10 cm. Quelle est la distance perpendiculaire du centre à la corde?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: The perpendicular from the centre bisects the chord, forming a right triangle — for a chord of 12 and radius 10, half the chord is 6, then use 10² − 6² = 64, so the distance is 8.
• Steps:
  • Half the chord = 16 ÷ 2 = 8 cm.
  • Use Pythagorean theorem: d² + 8² = 10².
  • d² = 100 − 64 = 36, so d = 6 cm.
• Answer: 6 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 6 = 0.
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 6 = 0.
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = −2 or x = −3 D) x = 3 or x = 4
• Hint: The quadratic formula is x = (−b ± √(b² − 4ac)) ÷ 2a — for x² − 5x + 4 = 0: a=1, b=−5, c=4; discriminant = 25 − 16 = 9; x = (5 ± 3)/2, giving x = 4 or x = 1.
• Steps:
  • a = 1, b = −5, c = 6. Discriminant = 25 − 24 = 1.
  • x = (5 ± 1) ÷ 2 → x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 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 oblique de 5 cm. Quelle est l'aire totale de sa surface? (Utilise π ≈ 3,14)
• Choices: A) 66.0 cm² B) 72.2 cm² C) 75.4 cm² D) 80.1 cm²
• Hint: Surface area of a cone = π r l + π r² — for r = 2 and l = 4: 3.14 × 2 × 4 + 3.14 × 4 = 25.12 + 12.56 = 37.68 cm².
• Steps:
  • Lateral area = π r l = 3.14 × 3 × 5 = 47.1 cm².
  • Base area = π r² = 3.14 × 9 = 28.26 cm².
  • Total = 47.1 + 28.26 = 75.36 ≈ 75.4 cm².
• Answer: 75.4 cm²

[Hard] Completing the Square to Find 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: Complete the square — for y = x² − 6x + 11: take half of 6 = 3, then (x − 3)² = x² − 6x + 9, so y = (x − 3)² + 2, and the vertex is (3, 2).
• Steps:
  • y = x² − 4x + 7. Take half of 4: 2. Square it: 4.
  • y = (x² − 4x + 4) + 7 − 4 = (x − 2)² + 3.
  • Vertex is (2, 3).
• Answer: (2, 3)

[Hard] Trigonometry — Sine Law

• EN: In triangle ABC, angle A = 30°, angle B = 45°, and side a = 10 cm (opposite to angle A). Using the Sine Law, what is the length of side b? (sin 30° = 0.5, sin 45° ≈ 0.707)
• FR: Dans le triangle ABC, l'angle A = 30°, l'angle B = 45° et le côté a = 10 cm (opposé à l'angle A). En utilisant la loi des sinus, quelle est la longueur du côté b? (sin 30° = 0,5, sin 45° ≈ 0,707)
• Choices: A) 12.1 cm B) 13.4 cm C) 14.1 cm D) 15.6 cm
• Hint: Sine Law: a/sin A = b/sin B — for a = 8, sin A = 0.5, sin B = 0.866: b = 8 × 0.866 ÷ 0.5 = 13.86.
• Steps:
  • a / sin A = b / sin B.
  • 10 / 0.5 = b / 0.707 → 20 = b / 0.707.
  • b = 20 × 0.707 = 14.14 ≈ 14.1 cm.
• Answer: 14.1 cm

[Easy] Evaluating an Exponential Function

• EN: A population of bacteria doubles every hour. If you start with 50 bacteria, how many are there after 3 hours?
• FR: Une population de bactéries double chaque heure. Si tu commences avec 50 bactéries, combien y en a-t-il après 3 heures?
• Choices: A) 250 B) 350 C) 400 D) 500
• Hint: For doubling, use f(t) = a × 2^t — for 20 bacteria doubling for 2 hours: 20 × 2² = 20 × 4 = 80.
• Steps:
  • f(3) = 50 × 2³ = 50 × 8 = 400.
  • After 3 hours, there are 400 bacteria.
• Answer: 400

[Easy] Arithmetic Sequence

• EN: An arithmetic sequence starts at 4 and has a common difference of 7. What is the 6th term?
• FR: Une suite arithmétique commence à 4 et a une raison de 7. Quel est le 6e terme?
• Choices: A) 35 B) 38 C) 39 D) 42
• Hint: The nth term of an arithmetic sequence = a + (n − 1)d — for a sequence starting at 3 with difference 5, the 4th term = 3 + (4 − 1) × 5 = 3 + 15 = 18.
• Steps:
  • t₆ = 4 + (6 − 1) × 7 = 4 + 35 = 39.
  • The 6th term is 39.
• Answer: 39

[Easy] Compound Interest

• EN: Priya invests $1 000 at an annual interest rate of 5% compounded annually. What is the amount after 2 years?
• FR: Priya investit 1 000 $ à un taux d'intérêt annuel de 5 % composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $1 025.00 B) $1 050.00 C) $1 100.00 D) $1 102.50
• Hint: Use 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 × (1.05)² = 1000 × 1.1025 = $1102.50.
• Answer: $1 102.50

[Easy] Introduction to Logarithms

• EN: What is log₂(16)?
• FR: Combien fait log₂(16)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log_b(x) = n means b^n = x — for log₃(27), ask 3^? = 27, and 3³ = 27, so log₃(27) = 3.
• Steps:
  • log₂(16) = n means 2^n = 16.
  • 2⁴ = 16, so log₂(16) = 4.
• Answer: 4

[Medium] Geometric Sequence

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

[Medium] Logarithm Laws

• EN: Simplify: log(100) + log(10).
• FR: Simplifie : log(100) + log(10).
• Choices: A) 2 B) 3 C) 4 D) 10
• Hint: Use the log addition law: log(a) + log(b) = log(a × b) — for log(10) + log(100) = log(1000) = 3.
• Steps:
  • log(100) = 2 (since 10² = 100).
  • log(10) = 1 (since 10¹ = 10).
  • 2 + 1 = 3.
• Answer: 3

[Medium] Trigonometric Identity

• EN: If sin θ = 3/5, find cos θ for an acute angle θ. (Hint: sin²θ + cos²θ = 1)
• FR: Si sin θ = 3/5, trouve cos θ pour un angle aigu θ. (Indice : sin²θ + cos²θ = 1)
• Choices: A) 3/5 B) 4/5 C) 5/4 D) 3/4
• Hint: Use the Pythagorean identity sin²θ + cos²θ = 1 — for sin θ = 5/13: cos²θ = 1 − 25/169 = 144/169, so cos θ = 12/13.
• Steps:
  • sin²θ + cos²θ = 1 → (3/5)² + cos²θ = 1.
  • 9/25 + cos²θ = 1 → cos²θ = 16/25.
  • cos θ = 4/5.
• Answer: 4/5

[Medium] Sum of an Arithmetic Series

• EN: Find the sum of the first 10 terms of the arithmetic series: 5, 8, 11, 14, …
• FR: Trouve la somme des 10 premiers termes de la suite arithmétique : 5, 8, 11, 14, …
• Choices: A) 155 B) 170 C) 185 D) 200
• Hint: Sum of arithmetic series = (n/2)(first term + last term) — for 5 terms starting at 2 with d = 3: last term = 2 + 4(3) = 14, sum = (5/2)(2 + 14) = 40.
• Steps:
  • First term = 5, d = 3. Last (10th) term = 5 + 9 × 3 = 32.
  • Sum = (10/2)(5 + 32) = 5 × 37 = 185.
• Answer: 185

[Hard] Compound Interest — Solving for Time

• EN: An investment of $2000 grows to $2662.00 at 10% interest compounded annually. How many years did this take? (Hint: 1.1¹ = 1.1, 1.1² = 1.21, 1.1³ = 1.331)
• FR: Un investissement de 2 000 $ croît à 2 662,00 $ à un taux d'intérêt de 10 % composé annuellement. Combien d'années cela a-t-il pris? (Indice : 1,1¹ = 1,1, 1,1² = 1,21, 1,1³ = 1,331)
• Choices: A) 2 years B) 3 years C) 4 years D) 5 years
• Hint: Use A = P(1 + r)^n and try values of n — for $1000 growing to $1210 at 10%: 1000 × 1.1² = 1210, so n = 2 years.
• Steps:
  • 2000 × (1.1)^n = 2662. Divide: (1.1)^n = 1.331.
  • Check: 1.1³ = 1.331. So n = 3.
  • The investment took 3 years.
• Answer: 3 years

[Hard] Annuity Problem

• EN: Marcus deposits $500 at the end of each year into an account earning 6% per year compounded annually. What is the total value after 3 years? (Use the annuity formula: FV = PMT × [(1+r)^n − 1] ÷ r)
• FR: Marcus dépose 500 $ à la fin de chaque année dans un compte qui rapporte 6 % par an composé annuellement. Quelle est la valeur totale après 3 ans? (Utilise la formule d'annuité : FV = PMT × [(1+r)^n − 1] ÷ r)
• Choices: A) $1 500.00 B) $1 573.08 C) $1 591.80 D) $1 640.40
• Hint: Plug values into FV = PMT × [(1+r)^n − 1] ÷ r — for PMT = $200, r = 0.05, n = 3: FV = 200 × [(1.05)³ − 1] ÷ 0.05 = 200 × 0.1576 ÷ 0.05 ≈ $630.50.
• Steps:
  • FV = 500 × [(1.06)³ − 1] ÷ 0.06.
  • (1.06)³ = 1.191016. Numerator: 1.191016 − 1 = 0.191016.
  • FV = 500 × 0.191016 ÷ 0.06 = 500 × 3.1836 = $1591.80.
• Answer: $1 591.80

[Easy] Permutations

• EN: How many ways can 4 different students line up for a photograph?
• FR: De combien de façons 4 élèves différents peuvent-ils se mettre en file pour une photo?
• Choices: A) 12 B) 16 C) 24 D) 48
• Hint: The number of ways to arrange n items = n! — for 3 items: 3! = 3 × 2 × 1 = 6 ways.
• Steps:
  • 4! = 4 × 3 × 2 × 1 = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Combinations

• EN: A committee of 3 people is chosen from a group of 6. How many different committees are possible?
• FR: Un comité de 3 personnes est choisi parmi un groupe de 6. Combien de comités différents sont possibles?
• Choices: A) 15 B) 18 C) 20 D) 30
• Hint: Use C(n, r) = n! ÷ (r!(n − r)!) — for C(5, 2) = 5! ÷ (2! × 3!) = 120 ÷ 12 = 10.
• Steps:
  • C(6, 3) = 6! ÷ (3! × 3!) = 720 ÷ (6 × 6) = 720 ÷ 36 = 20.
  • There are 20 possible committees.
• Answer: 20

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = 4x³?
• FR: Quelle est la dérivée de f(x) = 4x³?
• Choices: A) 3x² B) 4x² C) 12x² D) 12x³
• Hint: Power rule: d/dx[axⁿ] = n × axⁿ⁻¹ — for f(x) = 5x², the derivative is 2 × 5x¹ = 10x.
• Steps:
  • f(x) = 4x³. Bring down the exponent: 3 × 4 = 12. Reduce the exponent: x².
  • f'(x) = 12x².
• Answer: 12x²

[Easy] Evaluating a Polynomial Function

• EN: What is the value of f(x) = x³ − 2x² + 3x − 5 when x = 2?
• FR: Quelle est la valeur de f(x) = x³ − 2x² + 3x − 5 quand x = 2?
• Choices: A) 1 B) 3 C) 5 D) 7
• Hint: Substitute the x value and evaluate from left to right — for f(x) = x² − 3x + 2 at x = 3: 9 − 9 + 2 = 2.
• Steps:
  • f(2) = 2³ − 2(2²) + 3(2) − 5.
  • = 8 − 8 + 6 − 5 = 1.
• Answer: 1

[Medium] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 2 heads?
• FR: Une pièce de monnaie équilibrée est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 1/4 B) 3/8 C) 5/16 D) 7/16
• Hint: Use P = C(n, k) × p^k × (1−p)^(n−k) — for 3 flips with exactly 1 head: C(3,1) × (0.5)¹ × (0.5)² = 3 × 0.125 = 0.375.
• Steps:
  • P = C(4, 2) × (0.5)² × (0.5)² = 6 × 0.25 × 0.25 = 6 × 0.0625 = 0.375.
  • 0.375 = 6/16 = 3/8.
• Answer: 3/8

[Medium] Vectors — Adding Vectors

• EN: Vector a = (3, −2) and vector b = (−1, 5). What is a + b?
• FR: Le vecteur a = (3, −2) et le vecteur b = (−1, 5). Combien font a + b?
• Choices: A) (2, 3) B) (3, 4) C) (4, 3) D) (2, 7)
• Hint: Add vectors component by component — for (2, 1) + (4, 3), add x-values: 2 + 4 = 6, and y-values: 1 + 3 = 4, giving (6, 4).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: −2 + 5 = 3.
  • a + b = (2, 3).
• Answer: (2, 3)

[Medium] Rational Function — Finding Restrictions

• EN: What are the non-permissible values of x in the expression (x + 4) ÷ (x² − 9)?
• FR: Quelles sont les valeurs non permises de x dans l'expression (x + 4) ÷ (x² − 9)?
• Choices: A) x = 3 only B) x = −3 only C) x = 3 and x = −3 D) x = 9 and x = −9
• Hint: Set the denominator equal to zero and solve — for (x + 2) ÷ (x − 5), set x − 5 = 0, giving x = 5 as the non-permissible value.
• Steps:
  • Set x² − 9 = 0. Factor: (x − 3)(x + 3) = 0.
  • x = 3 or x = −3 are non-permissible values.
• Answer: x = 3 and x = −3

[Medium] Derivative — Rate of Change

• EN: The position of a car (in metres) is given by s(t) = 5t² + 3t. What is the velocity (instantaneous rate of change) of the car at t = 4 seconds?
• FR: La position d'une voiture (en mètres) est donnée par s(t) = 5t² + 3t. Quelle est la vitesse (taux de variation instantané) de la voiture à t = 4 secondes?
• Choices: A) 38 m/s B) 40 m/s C) 43 m/s D) 46 m/s
• Hint: Differentiate to find velocity, then substitute t — for s(t) = 3t² + 2t: v(t) = 6t + 2, and at t = 3: v = 18 + 2 = 20 m/s.
• Steps:
  • s'(t) = 10t + 3.
  • At t = 4: v = 10(4) + 3 = 40 + 3 = 43 m/s.
• Answer: 43 m/s

[Hard] Probability Distribution — Expected Value

• EN: A game at a school fair costs $2 to play. You win $5 with a probability of 1/4 and win nothing otherwise. What is the expected value of one game (net gain or loss)?
• FR: Un jeu à la foire de l'école coûte 2 $ à jouer. Tu gagnes 5 $ avec une probabilité de 1/4 et tu ne gagnes rien sinon. Quelle est la valeur espérée d'une partie (gain ou perte nette)?
• Choices: A) −$0.75 B) −$0.50 C) $0.25 D) $1.25
• Hint: Expected value = Σ(outcome × probability) − cost — for a $3 game winning $8 half the time: E = 8 × 0.5 + 0 × 0.5 − 3 = 4 − 3 = $1.00.
• Steps:
  • Win: net gain = $5 − $2 = $3, probability = 1/4.
  • Lose: net gain = $0 − $2 = −$2, probability = 3/4.
  • E = 3 × (1/4) + (−2) × (3/4) = 0.75 − 1.50 = −$0.75.
• Answer: −$0.75

[Hard] Vectors — Dot Product and Angle

• EN: Find the angle between vectors u = (1, 0) and v = (1, 1) using the dot product formula. (cos 45° ≈ 0.707)
• FR: Trouve l'angle entre les vecteurs u = (1, 0) et v = (1, 1) en utilisant la formule du produit scalaire. (cos 45° ≈ 0,707)
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: cos θ = (u · v) ÷ (|u| × |v|) — for u = (1, 0) and v = (0, 1): dot product = 0, so θ = 90°.
• Steps:
  • u · v = (1)(1) + (0)(1) = 1.
  • |u| = √(1² + 0²) = 1. |v| = √(1² + 1²) = √2.
  • cos θ = 1 ÷ (1 × √2) = 1/√2 ≈ 0.707.
  • θ = 45°.
• Answer: 45°