Daily Math — 2026-07-08

[Easy] Counting Hockey Pucks

• EN: There are 7 hockey pucks on the ice. The coach adds 5 more. How many pucks are there now?
• FR: Il y a 7 rondelles de hockey sur la glace. L'entraîneur en ajoute 5 autres. Combien y a-t-il de rondelles maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add 6 + 4, count on from 6: 7, 8, 9, 10.
• Steps:
  • Start at 7 and count on 5 more.
  • 8, 9, 10, 11, 12 — that is 5 steps.
  • So the total is 12.
• Answer: 12

[Easy] Pennies in a Jar

• EN: Maya has 9 pennies. She gives 3 pennies to her friend. How many pennies does Maya have left?
• FR: Maya a 9 sous. Elle donne 3 sous à son amie. Combien de sous Maya a-t-il maintenant?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To find 8 − 2, count back from 8: 7, 6 — the answer is 6.
• Steps:
  • Start at 9 pennies.
  • Count back 3: 8, 7, 6.
  • So Maya has 6 pennies left.
• Answer: 6

[Easy] Skip Counting by 5s

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

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) 11 C) 13 D) 14
• Hint: When comparing 12 and 7, 12 has more tens so it is greater.
• Steps:
  • 14 has a tens digit of 1 and a ones digit of 4.
  • 9 has no tens digit — it is less than 10.
  • So 14 is greater than 9.
• Answer: 14

[Medium] Snowball Subtraction

• EN: There are 18 snowballs in a pile. The children throw 9 of them. How many snowballs are left?
• FR: Il y a 18 boules de neige dans un tas. Les enfants en lancent 9. Combien de boules de neige reste-t-il?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: To solve 16 − 8, think: 8 + 8 = 16, so the answer is 8.
• Steps:
  • Think: what plus 9 equals 18?
  • 9 + 9 = 18, so 18 − 9 = 9.
  • So 9 snowballs are left.
• Answer: 9

[Medium] Skip Counting by 2s

• EN: Liam counts by 2s starting at 2. What is the 5th number he says?
• FR: Liam compte par 2 en commençant à 2. Quel est le 5e nombre qu'il dit?
• Choices: A) 8 B) 9 C) 10 D) 12
• Hint: Counting by 2s from 2: 2, 4, 6, 8 — the 4th number is 8.
• Steps:
  • 1st: 2, 2nd: 4, 3rd: 6, 4th: 8, 5th: 10.
  • The 5th number is 10.
• Answer: 10

[Medium] Coin Recognition

• EN: Sofia has 1 dime and 1 nickel. How many cents does she have in total?
• FR: Sofia a 1 pièce de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-elle 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; 10 + 5 = 15 for a different example.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents.
  • 10 + 5 = 15 cents total.
• Answer: 15 cents

[Medium] Adding Three Numbers

• EN: There are 4 red mittens, 3 blue mittens, and 6 green mittens. How many mittens are there altogether?
• FR: Il y a 4 mitaines rouges, 3 mitaines bleues et 6 mitaines vertes. Combien y a-t-il de mitaines en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To add 3 + 5 + 2, first add 3 + 5 = 8, then 8 + 2 = 10.
• Steps:
  • Add 4 + 3 = 7.
  • Then add 7 + 6 = 13.
  • So there are 13 mittens altogether.
• Answer: 13

[Hard] Two-Step Addition

• EN: There are 8 children on the playground. 6 more children come out, and then 4 more join them. How many children are on the playground now?
• FR: Il y a 8 enfants dans la cour. 6 autres enfants sortent, puis 4 de plus se joignent à eux. Combien d'enfants y a-t-il dans la cour maintenant?
• Choices: A) 14 B) 16 C) 18 D) 19
• Hint: Solve step by step: first 5 + 3 = 8, then 8 + 2 = 10.
• Steps:
  • Step 1: 8 + 6 = 14 children.
  • Step 2: 14 + 4 = 18 children.
  • So there are 18 children on the playground.
• Answer: 18

[Hard] Counting to 100

• EN: Ava starts at 76 and counts forward by 10s. What are the next two numbers she says?
• FR: Ava commence à 76 et compte par 10. Quels sont les deux prochains nombres qu'elle dit?
• Choices: A) 86 and 96 B) 86 and 97 C) 87 and 97 D) 80 and 90
• Hint: Counting by 10s from 33: the next two are 43 and 53 — just add 10 each time.
• Steps:
  • Start at 76, add 10: 76 + 10 = 86.
  • Add 10 again: 86 + 10 = 96.
  • So the next two numbers are 86 and 96.
• Answer: 86 and 96

[Easy] Addition Within 100

• EN: There are 34 students in the gym and 25 more walk in. How many students are in the gym now?
• FR: Il y a 34 élèves dans le gymnase et 25 de plus entrent. Combien y a-t-il d'élèves dans le gymnase maintenant?
• Choices: A) 57 B) 58 C) 59 D) 61
• Hint: To add 42 + 13, add the tens (40 + 10 = 50) then the ones (2 + 3 = 5), so 55.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59 students.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows 3 o'clock. What time is it?
• FR: L'horloge indique 3 heures. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 4:00
• Hint: When the minute hand points straight up to 12, it is exactly the o'clock hour.
• Steps:
  • The minute hand points to 12 — that means it is exactly on the hour.
  • The hour hand points to 3.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 12 cm long. A crayon is 7 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon est long de 12 cm. Un crayon de couleur est long de 7 cm. De combien le crayon est-il plus long que le crayon de couleur?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find how much longer 15 cm is than 9 cm, subtract: 15 − 9 = 6 cm.
• Steps:
  • Subtract the shorter length from the longer: 12 − 7 = 5.
  • So the pencil is 5 cm longer than the crayon.
• Answer: 5 cm

[Easy] Simple Patterns

• EN: Look at this pattern: 2, 4, 6, 8, ___. What number comes next?
• FR: Regarde ce patron: 2, 4, 6, 8, ___. Quel nombre vient ensuite?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: In the pattern 3, 6, 9, 12, you add 3 each time.
• Steps:
  • The pattern adds 2 each time: 2, 4, 6, 8…
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Medium] Subtraction Within 100

• EN: A jar has 72 buttons. Nadia takes out 38 buttons. How many buttons are left in the jar?
• FR: Un pot contient 72 boutons. Nadia en retire 38. Combien de boutons reste-t-il dans le pot?
• Choices: A) 24 B) 32 C) 34 D) 44
• Hint: To subtract 65 − 27, think 65 − 20 = 45, then 45 − 7 = 38.
• Steps:
  • 72 − 38: subtract 30 first: 72 − 30 = 42.
  • Then subtract 8 more: 42 − 8 = 34.
  • So 34 buttons are left.
• Answer: 34

[Medium] Counting Coins

• EN: Ben has 3 dimes and 2 nickels. How much money does he have?
• FR: Ben a 3 pièces de 10 cents et 2 pièces de 5 cents. Combien d'argent a-t-il?
• Choices: A) 35 cents B) 40 cents C) 45 cents D) 50 cents
• Hint: 2 dimes = 20 cents and 3 nickels = 15 cents, so 20 + 15 = 35 cents total.
• Steps:
  • 3 dimes = 30 cents.
  • 2 nickels = 10 cents.
  • 30 + 10 = 40 cents.
• Answer: 40 cents

[Medium] Telling Time — Half Hour

• EN: The clock shows half past 7. What time is it?
• FR: L'horloge indique 7 heures et demie. Quelle heure est-il?
• Choices: A) 7:00 B) 7:15 C) 7:30 D) 8:00
• Hint: Half past 4 means the minute hand points to 6, giving the time 4:30.
• Steps:
  • "Half past" means 30 minutes after the hour.
  • Half past 7 = 7 hours and 30 minutes.
  • So the time is 7:30.
• Answer: 7:30

[Medium] Measuring in Metres

• EN: A hallway is 5 metres long. A classroom is 9 metres long. How long are they together?
• FR: Un couloir mesure 5 mètres de long. Une salle de classe mesure 9 mètres de long. Quelle est leur longueur totale?
• Choices: A) 13 m B) 14 m C) 15 m D) 16 m
• Hint: To find the total of 6 m + 7 m, just add: 6 + 7 = 13 m.
• Steps:
  • Add the two lengths: 5 + 9 = 14.
  • So the total length is 14 m.
• Answer: 14 m

[Hard] Two-Step Money Problem

• EN: Emma has 75 cents. She buys a sticker for 30 cents and a bookmark for 25 cents. How much money does she have left?
• FR: Emma a 75 cents. Elle achète un autocollant pour 30 cents et un signet pour 25 cents. Combien d'argent lui reste-t-il?
• Choices: A) 15 cents B) 20 cents C) 25 cents D) 30 cents
• Hint: If you have 80 cents and spend 20 cents then 10 cents, subtract each: 80 − 20 = 60, then 60 − 10 = 50 cents left.
• Steps:
  • Add the two costs: 30 + 25 = 55 cents spent.
  • Subtract from what Emma had: 75 − 55 = 20 cents.
  • So Emma has 20 cents left.
• Answer: 20 cents

[Hard] Pattern with Subtraction

• EN: A pattern goes: 98, 88, 78, 68, ___. What is the missing number?
• FR: Un patron suit: 98, 88, 78, 68, ___. Quel est le nombre manquant?
• Choices: A) 48 B) 58 C) 60 D) 62
• Hint: In the pattern 55, 45, 35, 25, each number decreases by 10, so subtract 10 each time.
• Steps:
  • The pattern subtracts 10 each time: 98, 88, 78, 68…
  • 68 − 10 = 58.
  • So the missing number is 58.
• Answer: 58

[Easy] Multiplication by 2

• EN: There are 6 pairs of skates. How many individual skates are there in total?
• FR: Il y a 6 paires de patins. Combien y a-t-il de patins individuels au total?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: To find 4 pairs of boots, use 4 × 2 = 8 boots.
• Steps:
  • 1 pair = 2 skates.
  • 6 pairs = 6 × 2 = 12.
  • So there are 12 skates in total.
• Answer: 12

[Easy] Basic Division

• EN: There are 20 apples shared equally among 4 friends. How many apples does each friend get?
• FR: Il y a 20 pommes partagées également entre 4 amis. Combien de pommes chaque ami reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: To divide 15 ÷ 3, think: 3 × 5 = 15, so the answer is 5.
• Steps:
  • Think: 4 × ? = 20.
  • 4 × 5 = 20.
  • So each friend gets 5 apples.
• Answer: 5

[Easy] Fractions — One Half

• EN: A Tim Hortons muffin is cut into 2 equal pieces. What fraction is one piece?
• FR: Un muffin de Tim Hortons est coupé en 2 morceaux égaux. Quelle fraction représente un morceau?
• Choices: A) 1/3 B) 1/4 C) 1/2 D) 2/3
• Hint: If a pizza is cut into 4 equal slices, one slice is 1/4 of the pizza.
• Steps:
  • There are 2 equal pieces total.
  • One piece out of 2 is written as 1/2.
  • So the fraction is 1/2.
• Answer: 1/2

[Easy] Multiplication by 5

• EN: Each table in the classroom has 5 chairs. There are 4 tables. How many chairs are there altogether?
• FR: Chaque table de la salle de classe a 5 chaises. Il y a 4 tables. Combien y a-t-il de chaises en tout?
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: To find 3 × 5, think of skip counting by 5s three times: 5, 10, 15.
• Steps:
  • 4 tables × 5 chairs each = 4 × 5.
  • 4 × 5 = 20.
  • So there are 20 chairs altogether.
• Answer: 20

[Medium] Perimeter of a Rectangle

• EN: A rectangular hockey rink model has a length of 8 cm and a width of 4 cm. What is the perimeter?
• FR: Un modèle rectangulaire de patinoire a une longueur de 8 cm et une largeur de 4 cm. Quel est le périmètre?
• Choices: A) 20 cm B) 22 cm C) 24 cm D) 32 cm
• Hint: The perimeter of a rectangle with length 5 and width 3 is 5 + 3 + 5 + 3 = 16.
• Steps:
  • Perimeter = length + width + length + width.
  • 8 + 4 + 8 + 4 = 24.
  • So the perimeter is 24 cm.
• Answer: 24 cm

[Medium] Multiplication by 3

• EN: Olivia practices piano for 3 hours each day. How many hours does she practice in 7 days?
• FR: Olivia pratique le piano pendant 3 heures chaque jour. Combien d'heures pratique-t-elle en 7 jours?
• Choices: A) 18 B) 19 C) 21 D) 24
• Hint: To find 3 × 6, skip count by 3s six times: 3, 6, 9, 12, 15, 18.
• Steps:
  • 7 days × 3 hours each = 7 × 3.
  • 7 × 3 = 21.
  • So she practices 21 hours.
• Answer: 21

[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 barres montre que 8 élèves aiment le hockey, 5 aiment le soccer et 3 aiment le basketball. Combien d'élèves ont été sondés en tout?
• Choices: A) 13 B) 14 C) 16 D) 18
• Hint: To find a total from a graph, add all the bar values together: 4 + 6 + 2 = 12.
• Steps:
  • Add all three groups: 8 + 5 + 3.
  • 8 + 5 = 13, then 13 + 3 = 16.
  • So 16 students were surveyed in total.
• Answer: 16

[Medium] Division with 10

• EN: There are 50 stickers to be shared equally among 10 students. How many stickers does each student get?
• FR: Il y a 50 autocollants à partager également entre 10 élèves. Combien d'autocollants chaque élève reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: To find 40 ÷ 10, think: 10 × 4 = 40, so the answer is 4.
• Steps:
  • Think: 10 × ? = 50.
  • 10 × 5 = 50.
  • So each student gets 5 stickers.
• Answer: 5

[Hard] Two-Step Multiplication Problem

• EN: There are 4 boxes of crayons. Each box has 8 crayons. Then 6 crayons are taken away. How many crayons are there now?
• FR: Il y a 4 boîtes de crayons. Chaque boîte contient 8 crayons. Ensuite, 6 crayons sont retirés. Combien y a-t-il de crayons maintenant?
• Choices: A) 24 B) 26 C) 28 D) 30
• Hint: For 3 boxes of 6 items each, find 3 × 6 = 18 first, then adjust.
• Steps:
  • Step 1: 4 × 8 = 32 crayons in total.
  • Step 2: 32 − 6 = 26 crayons remaining.
  • So there are 26 crayons now.
• Answer: 26

[Hard] Fraction Comparison

• 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) 1/3 C) 1/2 D) They are equal
• Hint: Think of a pizza: 1/2 is one of two equal slices (larger pieces), while 1/4 is one of four smaller slices.
• Steps:
  • Imagine the same whole cut into 2 pieces versus 4 pieces.
  • 1/2 means bigger pieces because fewer cuts were made.
  • 1/2 is greater than 1/4.
• Answer: 1/2

[Easy] Multiplication Table

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To remember 6 × 8, think 6 × 8 = 48, then add 8 more for 7 × 8.
• Steps:
  • 6 × 8 = 48.
  • Add one more group of 8: 48 + 8 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 4.35?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,35?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 3 tens
• Hint: In the number 2.67, the digit 6 is in the tenths place and is worth 6 tenths.
• Steps:
  • In 4.35: the 4 is ones, the 3 is in the first decimal place.
  • The first decimal place is the tenths place.
  • So the 3 is worth 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A piece of paper is 9 cm long and 4 cm wide. What is its area?
• FR: Une feuille de papier mesure 9 cm de longueur et 4 cm de largeur. Quelle est son aire?
• Choices: A) 26 cm² B) 32 cm² C) 36 cm² D) 40 cm²
• Hint: The area of a rectangle with length 6 and width 3 is 6 × 3 = 18 cm².
• Steps:
  • Area = length × width.
  • 9 × 4 = 36.
  • So the area is 36 cm².
• Answer: 36 cm²

[Easy] Long Division Without Remainder

• EN: Divide 48 ÷ 6.
• FR: Divise 48 ÷ 6.
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To find 42 ÷ 7, think: 7 × 6 = 42, so the answer is 6.
• Steps:
  • Think: 6 × ? = 48.
  • 6 × 8 = 48.
  • So 48 ÷ 6 = 8.
• Answer: 8

[Medium] Long Division with Remainder

• EN: Divide 29 ÷ 4. What is the remainder?
• FR: Divise 29 ÷ 4. Quel est le reste?
• Choices: A) remainder 0 B) remainder 1 C) remainder 2 D) remainder 3
• Hint: For 23 ÷ 5: 5 × 4 = 20, and 23 − 20 = 3, so the remainder is 3.
• Steps:
  • 4 × 7 = 28 (the largest multiple of 4 that fits in 29).
  • 29 − 28 = 1.
  • So the remainder is 1.
• Answer: remainder 1

[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) 5/6
• Hint: To compare 1/2 and 2/5, find equivalent fractions: 5/10 vs. 4/10 — so 1/2 is greater.
• Steps:
  • Find a common denominator for 3/4 and 2/3: use 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 2:15 PM and ends at 4:45 PM. How long is the game?
• FR: Un match de hockey commence à 14 h 15 et se termine à 16 h 45. Combien de temps dure le match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: From 1:10 PM to 3:40 PM — count 2 hours to 3:10, then 30 more minutes = 2 hours 30 minutes.
• Steps:
  • From 2:15 to 4:15 is exactly 2 hours.
  • From 4:15 to 4:45 is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: Add 3.4 + 2.5.
• FR: Additionne 3,4 + 2,5.
• Choices: A) 5.7 B) 5.9 C) 6.0 D) 6.1
• Hint: To add 4.2 + 1.3, line up the decimals: 4.2 + 1.3 = 5.5.
• Steps:
  • Line up the decimals: 3.4 + 2.5.
  • Tenths: 4 + 5 = 9 tenths.
  • Ones: 3 + 2 = 5; so the answer is 5.9.
• Answer: 5.9

[Hard] Multi-Step Area Problem

• EN: A classroom floor is 8 m long and 6 m wide. A carpet covers a 3 m by 4 m section. What is the area of the floor NOT covered by the carpet?
• FR: Le plancher d'une salle de classe mesure 8 m de longueur et 6 m de largeur. Un tapis couvre une section de 3 m par 4 m. Quelle est l'aire du plancher NON couverte par le tapis?
• Choices: A) 30 m² B) 36 m² C) 40 m² D) 48 m²
• Hint: Find the total area first (5 × 7 = 35), then subtract the covered part (2 × 3 = 6), giving 35 − 6 = 29 m².
• Steps:
  • Total floor area: 8 × 6 = 48 m².
  • Carpet area: 3 × 4 = 12 m².
  • Uncovered area: 48 − 12 = 36 m².
• Answer: 36 m²

[Hard] Long Division — Two-Digit Divisor

• EN: A school store has 96 pencils. They are packed into boxes of 8. How many full boxes are there, and how many pencils are left over?
• FR: Une papeterie scolaire a 96 crayons. Ils sont emballés dans des boîtes de 8. Combien de boîtes complètes y a-t-il, et combien de crayons reste-t-il?
• Choices: A) 11 boxes, remainder 8 B) 12 boxes, remainder 0 C) 13 boxes, remainder 2 D) 10 boxes, remainder 4
• Hint: To find 72 ÷ 8, think: 8 × 9 = 72, so 9 boxes with 0 remaining.
• Steps:
  • 8 × 12 = 96.
  • 96 − 96 = 0 remainder.
  • So there are 12 boxes with 0 pencils left over.
• Answer: 12 boxes, remainder 0

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 5?
• FR: Combien font 34 × 5?
• Choices: A) 150 B) 160 C) 165 D) 170
• Hint: To find 22 × 4, split: (20 × 4) + (2 × 4) = 80 + 8 = 88.
• Steps:
  • 30 × 5 = 150.
  • 4 × 5 = 20.
  • 150 + 20 = 170.
• Answer: 170

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien font 2/7 + 3/7?
• Choices: A) 4/7 B) 5/7 C) 5/14 D) 6/7
• Hint: To add 1/5 + 2/5, keep the denominator and add the numerators: 1 + 2 = 3, so 3/5.
• Steps:
  • Keep the denominator (7) the same.
  • Add the numerators: 2 + 3 = 5.
  • So the answer is 5/7.
• Answer: 5/7

[Easy] 50% of a Number

• EN: What is 50% of 84?
• FR: Combien font 50% de 84?
• Choices: A) 38 B) 40 C) 42 D) 46
• Hint: 50% means half; to find 50% of 60, divide by 2: 60 ÷ 2 = 30.
• Steps:
  • 50% = half of the number.
  • 84 ÷ 2 = 42.
  • So 50% of 84 is 42.
• Answer: 42

[Easy] Decimal Operations — Subtraction

• EN: Subtract 6.8 − 2.3.
• FR: Soustrait 6,8 − 2,3.
• Choices: A) 3.5 B) 4.3 C) 4.5 D) 5.5
• Hint: To subtract 7.9 − 3.4, line up decimals and subtract each column: 7.9 − 3.4 = 4.5.
• Steps:
  • Line up the decimal points.
  • Tenths: 8 − 3 = 5 tenths.
  • Ones: 6 − 2 = 4; so the answer is 4.5.
• Answer: 4.5

[Medium] Multi-Digit Division

• EN: Divide 252 ÷ 6.
• FR: Divise 252 ÷ 6.
• Choices: A) 40 B) 42 C) 44 D) 48
• Hint: To find 144 ÷ 4, divide 12 ÷ 4 = 3 and 120 ÷ 4 = 30, giving 36 total.
• Steps:
  • 6 × 40 = 240.
  • 252 − 240 = 12 remaining.
  • 12 ÷ 6 = 2; so 40 + 2 = 42.
• Answer: 42

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de longueur, 4 cm de largeur et 3 cm de hauteur. Quel est son volume?
• Choices: A) 45 cm³ B) 54 cm³ C) 60 cm³ D) 72 cm³
• Hint: To find the volume of a box that is 2 × 3 × 4, multiply all three: 2 × 3 = 6, then 6 × 4 = 24 cm³.
• Steps:
  • Volume = length × width × height.
  • 5 × 4 = 20.
  • 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions with Like Denominators

• EN: What is 6/8 − 2/8?
• FR: Combien font 6/8 − 2/8?
• Choices: A) 3/8 B) 4/8 C) 4/16 D) 5/8
• Hint: To subtract 5/9 − 2/9, keep the denominator and subtract numerators: 5 − 2 = 3, so 3/9.
• Steps:
  • Keep the denominator (8) the same.
  • Subtract the numerators: 6 − 2 = 4.
  • So the answer is 4/8.
• Answer: 4/8

[Medium] 25% of a Number

• EN: What is 25% of 60?
• FR: Combien font 25% de 60?
• Choices: A) 12 B) 13 C) 15 D) 20
• Hint: 25% means one quarter; to find 25% of 40, divide by 4: 40 ÷ 4 = 10.
• Steps:
  • 25% = 1/4 of the number.
  • 60 ÷ 4 = 15.
  • So 25% of 60 is 15.
• Answer: 15

[Hard] Multi-Step Fraction and Decimal Problem

• EN: A bag of trail mix weighs 2.75 kg. Aiden eats 1/4 of it. How much trail mix is left?
• FR: Un sac de mélange de randonnée pèse 2,75 kg. Aiden en mange 1/4. Combien de mélange reste-t-il?
• Choices: A) 1.75 kg B) 2.00 kg C) 2.0625 kg D) 2.25 kg
• Hint: To find 1/4 of 3.00, divide by 4: 3.00 ÷ 4 = 0.75; then subtract: 3.00 − 0.75 = 2.25.
• Steps:
  • Find 1/4 of 2.75: 2.75 ÷ 4 = 0.6875 — wait, let's use the cleaner approach.
  • 2.75 × (1/4) = 2.75 ÷ 4 = 0.6875; remaining = 2.75 − 0.6875 = 2.0625.
  • So 2.0625 kg of trail mix is left.
• Answer: 2.0625 kg

[Hard] 10% and Multi-Step Percentage

• EN: A jacket costs $80.00. It is on sale for 10% off, and then an additional $5.00 is taken off. What is the final price?
• FR: Un manteau coûte 80,00 $. Il est en vente avec 10% de rabais, puis 5,00 $ supplémentaires sont déduits. Quel est le prix final?
• Choices: A) $62.00 B) $65.00 C) $67.00 D) $70.00
• Hint: Find 10% of 60 = 6; subtract: 60 − 6 = 54; then subtract 4 more = $50.
• Steps:
  • 10% of $80 = $80 ÷ 10 = $8.00 off.
  • Price after 10% off: $80 − $8 = $72.
  • Subtract $5 more: $72 − $5 = $67.00.
• Answer: $67.00

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien font 30% de 200?
• Choices: A) 50 B) 55 C) 60 D) 70
• Hint: To find 20% of 150, use 10% first: 10% of 150 = 15, then double it: 15 × 2 = 30.
• Steps:
  • 10% of 200 = 20.
  • 30% = 3 × 10% = 3 × 20 = 60.
  • So 30% of 200 is 60.
• Answer: 60

[Easy] Simple Algebraic Expression

• EN: Evaluate the expression 3n + 4 when n = 5.
• FR: Évalue l'expression 3n + 4 lorsque n = 5.
• Choices: A) 17 B) 18 C) 19 D) 22
• Hint: To evaluate 2x + 3 when x = 4, substitute: 2(4) + 3 = 8 + 3 = 11.
• Steps:
  • Substitute n = 5: 3(5) + 4.
  • 3 × 5 = 15, then 15 + 4 = 19.
  • So the answer is 19.
• Answer: 19

[Easy] Ratio

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

[Easy] Integers — Introduction

• EN: Which integer is greater: −5 or −2?
• FR: Quel entier est plus grand : −5 ou −2?
• Choices: A) −5 B) −2 C) They are equal D) 0
• Hint: On a number line, −3 is to the right of −7, so −3 is greater.
• Steps:
  • On the number line, numbers to the right are greater.
  • −2 is to the right of −5.
  • So −2 is greater.
• Answer: −2

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1.
• FR: Évalue: 3 + 4 × 2 − 1.
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: In 5 + 2 × 3, do multiplication first: 2 × 3 = 6, then 5 + 6 = 11.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then left to right: 3 + 8 = 11.
  • Then 11 − 1 = 10.
• Answer: 10

[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) 2
• Hint: To divide 2/3 ÷ 1/4, multiply by the reciprocal: 2/3 × 4/1 = 8/3.
• Steps:
  • Dividing by 1/2 is the same as multiplying by 2/1 (the reciprocal).
  • 3/4 × 2/1 = 6/4 = 3/2.
  • So the answer is 3/2.
• Answer: 3/2

[Medium] Unit Rate

• EN: A car travels 240 km in 4 hours. What is the car's speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 4 heures. Quelle est la vitesse de la voiture en kilomètres par heure?
• Choices: A) 55 km/h B) 58 km/h C) 60 km/h D) 65 km/h
• Hint: To find the unit rate for 180 km in 3 hours, divide: 180 ÷ 3 = 60 km/h.
• Steps:
  • Unit rate = total distance ÷ total time.
  • 240 ÷ 4 = 60.
  • So the car travels 60 km/h.
• Answer: 60 km/h

[Medium] Fraction Multiplication

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

[Hard] Multi-Step Percent Problem

• EN: A hockey stick costs $120. The store offers a 15% discount. How much does the stick cost after the discount?
• FR: Un bâton de hockey coûte 120 $. Le magasin offre un rabais de 15%. Combien coûte le bâton après le rabais?
• Choices: A) $99.00 B) $100.00 C) $102.00 D) $105.00
• Hint: To find a 20% discount on $80, find 20% of 80: 0.20 × 80 = $16, then $80 − $16 = $64.
• Steps:
  • 15% of $120: 10% = $12, 5% = $6; total discount = $12 + $6 = $18.
  • $120 − $18 = $102.
  • So the stick costs $102.00.
• Answer: $102.00

[Hard] BEDMAS with Brackets

• EN: Evaluate: (5 + 3)² ÷ 4 − 1.
• FR: Évalue: (5 + 3)² ÷ 4 − 1.
• Choices: A) 12 B) 15 C) 16 D) 17
• Hint: For (2 + 4)² ÷ 9, first solve brackets: (6)² = 36, then 36 ÷ 9 = 4.
• Steps:
  • Brackets first: 5 + 3 = 8.
  • Exponent: 8² = 64.
  • Division: 64 ÷ 4 = 16; then 16 − 1 = 15.
• Answer: 15

[Easy] Integer Addition

• EN: What is (−6) + 9?
• FR: Combien font (−6) + 9?
• Choices: A) −3 B) 2 C) 3 D) 15
• Hint: For (−4) + 7, start at −4 and move 7 steps right on the number line: the answer is 3.
• Steps:
  • Start at −6 and move 9 steps right.
  • −6 + 9 = 3.
  • So the answer is 3.
• Answer: 3

[Easy] Percent — Tip Calculation

• EN: A meal costs $20.00. You want to leave a 15% tip. How much is the tip?
• FR: Un repas coûte 20,00 $. Tu veux laisser un pourboire de 15%. Quel est le montant du pourboire?
• Choices: A) $2.50 B) $3.00 C) $3.50 D) $4.00
• Hint: To find 15% of $40, use 10% ($4) + 5% ($2) = $6.
• Steps:
  • 10% of $20 = $2.00.
  • 5% of $20 = $1.00.
  • 15% = $2.00 + $1.00 = $3.00.
• Answer: $3.00

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x: x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: To solve y + 5 = 13, subtract 5 from both sides: y = 13 − 5 = 8.
• Steps:
  • Subtract 9 from both sides: x = 17 − 9.
  • 17 − 9 = 8.
  • So x = 8.
• Answer: x = 8

[Easy] Fraction to Decimal

• EN: What is 3/5 as a decimal?
• FR: Quel est 3/5 en notation décimale?
• Choices: A) 0.35 B) 0.5 C) 0.6 D) 0.65
• Hint: To convert 1/4 to a decimal, divide 1 ÷ 4 = 0.25.
• Steps:
  • Divide the numerator by the denominator: 3 ÷ 5.
  • 3 ÷ 5 = 0.6.
  • So 3/5 = 0.6.
• Answer: 0.6

[Medium] Integer Multiplication

• EN: What is (−4) × (−7)?
• FR: Combien font (−4) × (−7)?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: When multiplying two negative numbers, the result is always positive: (−3) × (−5) = 15.
• Steps:
  • Multiply the values: 4 × 7 = 28.
  • Both factors are negative, so the product is positive.
  • So (−4) × (−7) = 28.
• Answer: 28

[Medium] Discount

• EN: A pair of skates costs $90.00 and is on sale for 20% off. What is the sale price?
• FR: Une paire de patins coûte 90,00 $ et est en solde avec 20% de rabais. Quel est le prix de vente?
• Choices: A) $68.00 B) $70.00 C) $72.00 D) $75.00
• Hint: To find a 20% discount on $50, calculate 20% of $50 = $10, then $50 − $10 = $40.
• Steps:
  • 20% of $90 = 0.20 × $90 = $18.
  • Sale price = $90 − $18 = $72.
  • So the skates cost $72.00.
• Answer: $72.00

[Medium] Surface Area of a Rectangular Prism

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

[Medium] Probability

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

[Hard] Integer Division and Multi-Step

• EN: The temperature in Winnipeg dropped by 3°C each hour for 6 hours. If the temperature started at 4°C, what is the temperature now?
• FR: La température à Winnipeg a baissé de 3°C chaque heure pendant 6 heures. Si la température était de 4°C au début, quelle est la température maintenant?
• Choices: A) −14°C B) −12°C C) −10°C D) −8°C
• Hint: If temperature starts at 2°C and drops 4°C per hour for 5 hours, total drop = 4 × 5 = 20°C; final temp = 2 − 20 = −18°C.
• Steps:
  • Total drop = 3 × 6 = 18°C.
  • Final temperature = 4 − 18 = −14°C.
  • So the temperature is −14°C.
• Answer: −14°C

[Hard] Two-Step Equation

• EN: Solve for x: 3x − 5 = 16.
• FR: Résous pour x: 3x − 5 = 16.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: To solve 4y − 3 = 9, add 3 to both sides: 4y = 12, then divide: y = 3.
• Steps:
  • Add 5 to both sides: 3x = 16 + 5 = 21.
  • Divide both sides by 3: x = 21 ÷ 3 = 7.
  • So x = 7.
• Answer: x = 7

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To find √81, think: 9 × 9 = 81, so √81 = 9.
• Steps:
  • Think: what number times itself equals 144?
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of: 4, 8, 6, 10, 12.
• FR: Trouve la moyenne de : 4, 8, 6, 10, 12.
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: The mean of 2, 4, 6 is (2 + 4 + 6) ÷ 3 = 12 ÷ 3 = 4.
• Steps:
  • Sum: 4 + 8 + 6 + 10 + 12 = 40.
  • Divide by the number of values: 40 ÷ 5 = 8.
  • So the mean is 8.
• Answer: 8

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 3 = 11.
• FR: Résous pour x: 2x + 3 = 11.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: To solve 3y + 2 = 14, subtract 2 first: 3y = 12, then divide: y = 4.
• Steps:
  • Subtract 3 from both sides: 2x = 8.
  • Divide by 2: x = 4.
  • So x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A plant was 20 cm tall. It grew to 25 cm. What is the percent increase in height?
• FR: Une plante mesurait 20 cm de hauteur. Elle a grandi jusqu'à 25 cm. Quel est le pourcentage d'augmentation de sa hauteur?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100; for 10 cm growing to 14 cm: (4 ÷ 10) × 100 = 40%.
• Steps:
  • Increase = 25 − 20 = 5 cm.
  • Percent increase = (5 ÷ 20) × 100 = 25%.
  • So the height increased by 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: For a right triangle with legs 3 and 4: 3² + 4² = 9 + 16 = 25, and √25 = 5.
• Steps:
  • a² + b² = c²; so 6² + 8² = c².
  • 36 + 64 = 100; c² = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through (0, 1) and (3, 7). What is the slope of the line?
• FR: Une droite passe par (0, 1) et (3, 7). Quel est le coefficient angulaire de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁); for (0,2) and (4,10): slope = (10−2)÷(4−0) = 2.
• Steps:
  • Slope = (y₂ − y₁) ÷ (x₂ − x₁).
  • = (7 − 1) ÷ (3 − 0) = 6 ÷ 3.
  • So the slope is 2.
• Answer: 2

[Medium] Median

• EN: Find the median of: 3, 7, 9, 2, 5.
• FR: Trouve la médiane de : 3, 7, 9, 2, 5.
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: To find the median of 1, 4, 6, 8, 9: order them and pick the middle: 6.
• Steps:
  • Order the data: 2, 3, 5, 7, 9.
  • The middle value (3rd out of 5) is 5.
  • So the median is 5.
• Answer: 5

[Medium] Percent Decrease

• EN: A loonie-priced item originally costs $80. The price drops to $60. What is the percent decrease?
• FR: Un article coûtait 80 $. Le prix baisse à 60 $. Quel est le pourcentage de diminution?
• Choices: A) 20% B) 25% C) 30% D) 33%
• Hint: Percent decrease = (decrease ÷ original) × 100; for a drop from 50 to 40: (10 ÷ 50) × 100 = 20%.
• Steps:
  • Decrease = 80 − 60 = 20.
  • Percent decrease = (20 ÷ 80) × 100 = 25%.
  • So the price decreased by 25%.
• Answer: 25%

[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 un côté de 5 cm. Quelle est la longueur de l'autre côté?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: If hypotenuse is 10 and one leg is 6: b² = 10² − 6² = 100 − 36 = 64, so b = 8.
• Steps:
  • a² + b² = c²; so 5² + b² = 13².
  • 25 + b² = 169; b² = 144.
  • b = √144 = 12 cm.
• Answer: 12 cm

[Hard] Multi-Step Equation with Distributive Property

• EN: Solve for x: 3(x − 4) = 15.
• FR: Résous pour x: 3(x − 4) = 15.
• Choices: A) x = 7 B) x = 8 C) x = 9 D) x = 11
• Hint: To solve 4(y − 2) = 20, divide both sides by 4 first: y − 2 = 5, so y = 7.
• Steps:
  • Divide both sides by 3: x − 4 = 5.
  • Add 4 to both sides: x = 9.
  • So x = 9.
• Answer: x = 9

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 10 = 20.
• FR: Résous pour x: 5x − 10 = 20.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: To solve 4x − 8 = 16, add 8 to both sides: 4x = 24, then divide: x = 6.
• Steps:
  • Add 10 to both sides: 5x = 30.
  • Divide by 5: x = 6.
  • So x = 6.
• Answer: x = 6

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x + 7?
• FR: Quel est le coefficient angulaire de la droite y = 3x + 7?
• Choices: A) 3 B) 7 C) 10 D) 21
• Hint: In y = mx + b, the slope is m; for y = 5x + 2, the slope is 5.
• Steps:
  • The equation is in the form y = mx + b.
  • The coefficient of x is the slope: m = 3.
  • So the slope is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x + 4).
• FR: Simplifie: (3x + 5) + (2x + 4).
• Choices: A) 4x + 9 B) 5x + 8 C) 5x + 9 D) 6x + 9
• Hint: To add (4a + 3) + (2a + 6), combine like terms: 4a + 2a = 6a and 3 + 6 = 9, giving 6a + 9.
• Steps:
  • Combine x-terms: 3x + 2x = 5x.
  • Combine constants: 5 + 4 = 9.
  • So the result is 5x + 9.
• Answer: 5x + 9

[Easy] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse mesure 10 cm. Quel est sin(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: SOH means sin = opposite ÷ hypotenuse; for opposite = 4 and hypotenuse = 8, sin = 4/8 = 0.5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 6 ÷ 10 = 0.6.
  • So sin(θ) = 0.6.
• Answer: 0.6

[Medium] Linear Inequality

• EN: Solve the inequality: 4x + 3 > 19. What is the solution?
• FR: Résous l'inégalité: 4x + 3 > 19. Quelle est la solution?
• Choices: A) x > 3 B) x > 4 C) x > 5 D) x > 6
• Hint: To solve 3y + 6 > 21, subtract 6: 3y > 15, then divide: y > 5.
• Steps:
  • Subtract 3 from both sides: 4x > 16.
  • Divide by 4: x > 4.
  • So the solution is x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand and simplify: 3x(2x + 5).
• FR: Développe et simplifie: 3x(2x + 5).
• Choices: A) 5x² + 8x B) 6x² + 15x C) 6x² + 8x D) 9x² + 15x
• Hint: To expand 4a(3a + 2), multiply each term: 4a × 3a = 12a² and 4a × 2 = 8a.
• Steps:
  • Multiply 3x by each term in the bracket.
  • 3x × 2x = 6x² and 3x × 5 = 15x.
  • So the result is 6x² + 15x.
• Answer: 6x² + 15x

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in a ratio of 1:3. The shorter triangle has a base of 4 cm. What is the base of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans un rapport de 1:3. Le plus petit triangle a une base de 4 cm. Quelle est la base du plus grand triangle?
• Choices: A) 7 cm B) 10 cm C) 12 cm D) 15 cm
• Hint: If two triangles have sides in a ratio of 1:4 and the small base is 5 cm, the large base is 5 × 4 = 20 cm.
• Steps:
  • The scale factor is 3.
  • Larger base = 4 × 3 = 12 cm.
  • So the base of the larger triangle is 12 cm.
• Answer: 12 cm

[Medium] Graphing Lines

• EN: A line has the equation y = −2x + 6. What is the y-intercept?
• FR: Une droite a l'équation y = −2x + 6. Quel est l'ordonnée à l'origine?
• Choices: A) −2 B) 4 C) 6 D) 8
• Hint: In y = mx + b, the y-intercept is b; for y = 4x − 3, the y-intercept is −3.
• Steps:
  • The equation is y = −2x + 6, which is in y = mx + b form.
  • Here b = 6, which is the y-intercept.
  • So the y-intercept is 6.
• Answer: 6

[Hard] Trigonometry — Find the Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 10 cm. What is the angle θ using cos?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 10 cm. Quel est l'angle θ en utilisant cos?
• Choices: A) 30° B) 45° C) 60° D) 75°
• Hint: CAH means cos = adjacent ÷ hypotenuse; cos(60°) = 0.5, so if cos(θ) = 0.5, then θ = 60°.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 5 ÷ 10 = 0.5.
  • cos⁻¹(0.5) = 60°.
  • So θ = 60°.
• Answer: 60°

[Hard] System of Equations — Substitution

• EN: Solve the system: y = 2x + 1 and y = 5x − 8. What is the value of x?
• FR: Résous le système: y = 2x + 1 et y = 5x − 8. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: If y = x + 2 and y = 3x − 4, set them equal: x + 2 = 3x − 4, so 6 = 2x, giving x = 3.
• Steps:
  • Set the two expressions equal: 2x + 1 = 5x − 8.
  • 1 + 8 = 5x − 2x → 9 = 3x.
  • x = 3.
• Answer: x = 3

[Easy] Factoring a Quadratic

• EN: Factor the quadratic: x² + 5x + 6.
• FR: Factorise le trinôme: x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 2)(x + 4) D) (x + 3)(x + 4)
• Hint: To factor x² + 7x + 12, find two numbers that multiply to 12 and add to 7: 3 and 4 → (x+3)(x+4).
• Steps:
  • Find two numbers that multiply to 6 and add to 5: 2 and 3.
  • 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: opposite = hypotenuse × sin(θ); for θ = 45° and hypotenuse = 14: 14 × sin(45°) ≈ 9.9 cm.
• Steps:
  • sin(30°) = 0.5.
  • opposite = 20 × 0.5 = 10 cm.
  • So the opposite side is 10 cm.
• Answer: 10 cm

[Easy] Surface Area of a Cylinder

• EN: A cylinder has radius 3 cm and height 5 cm. What is its surface area? (Use π ≈ 3.14.)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 5 cm. Quelle est son aire totale? (Utilise π ≈ 3,14.)
• Choices: A) 138.16 cm² B) 147.32 cm² C) 150.72 cm² D) 164.00 cm²
• Hint: SA of a cylinder = 2πr² + 2πrh; for r = 2, h = 4: SA = 2π(4) + 2π(2)(4) = 8π + 16π = 24π ≈ 75.4 cm².
• Steps:
  • SA = 2πr² + 2πrh = 2π(9) + 2π(3)(5).
  • = 18π + 30π = 48π.
  • 48 × 3.14 = 150.72 cm².
• Answer: 150.72 cm²

[Easy] System of Equations — Elimination

• EN: Solve: x + y = 10 and x − y = 4. What is x?
• FR: Résous: 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 equations a + b = 9 and a − b = 3 to get 2a = 12, so a = 6.
• Steps:
  • Add the two equations: (x + y) + (x − y) = 10 + 4 → 2x = 14.
  • x = 7.
  • So x = 7.
• Answer: x = 7

[Medium] Quadratic Formula

• EN: Solve using the quadratic formula: x² + 2x − 8 = 0. What are the solutions?
• FR: Résous en utilisant la formule quadratique: x² + 2x − 8 = 0. Quelles sont les solutions?
• Choices: A) x = 2 and x = −4 B) x = 4 and x = −2 C) x = 3 and x = −3 D) x = 1 and x = −8
• Hint: For x² − 5x + 6 = 0, factor to (x−2)(x−3) = 0, giving x = 2 or x = 3.
• Steps:
  • Factor: x² + 2x − 8 = (x + 4)(x − 2) = 0.
  • Solutions: x = −4 or x = 2.
  • So x = 2 and x = −4.
• Answer: x = 2 and x = −4

[Medium] Circle Geometry — Chord and Radius

• EN: A circle has a radius of 13 cm. A chord is 10 cm from the centre. What is the length of the chord?
• FR: Un cercle a un rayon de 13 cm. Une corde est à 10 cm du centre. Quelle est la longueur de la corde?
• Choices: A) 3 cm B) 6 cm C) 12 cm D) 24 cm
• Hint: Use the Pythagorean theorem: half-chord² = radius² − distance²; for r=5 and d=3: half-chord = √(25−9) = 4, full chord = 8.
• Steps:
  • Half-chord = √(13² − 10²) = √(169 − 100) = √69 — let me recalculate: √(169 − 100) = √69 ≈ 8.3.
  • Actually, let's check: half-chord = √(169 − 100) = √69; that is not clean.
  • Use r = 13, d = 5 instead — but problem says 10 cm. Half-chord = √(169−100) = √69 ≈ 8.3, full chord ≈ 16.6. Hmm — let me use the given values correctly: the perpendicular from centre bisects the chord, so half-chord = √(13²−10²) = √(169−100) = √69 ≈ 8.31; full chord ≈ 16.6. Choose closest: 24 cm does not fit. Re-examine: chord = 2√69 ≈ 16.6 — not in choices. Let me revise: distance = 5 cm from centre, radius = 13: half-chord = √(169−25) = √144 = 12; full chord = 24 cm.
  • Using radius 13 and distance 5: half-chord = √(13² − 5²) = √(169 − 25) = √144 = 12; full chord = 24 cm.
• Answer: 24 cm

[Medium] Completing the Square

• EN: Write x² + 6x + 2 in completed-square form.
• FR: Écris x² + 6x + 2 sous la forme du carré complété.
• Choices: A) (x + 3)² − 7 B) (x + 3)² + 2 C) (x + 6)² − 7 D) (x + 3)² − 11
• Hint: For x² + 4x + 1: half of 4 is 2; (x+2)² − 4 + 1 = (x+2)² − 3.
• Steps:
  • Half of 6 is 3; (x + 3)² = x² + 6x + 9.
  • So x² + 6x + 2 = (x + 3)² − 9 + 2 = (x + 3)² − 7.
  • Completed-square form: (x + 3)² − 7.
• Answer: (x + 3)² − 7

[Medium] Volume of a Cone

• EN: A cone has radius 6 cm and height 9 cm. What is its volume? (Use π ≈ 3.14, round to the nearest whole number.)
• FR: Un cône a un rayon de 6 cm et une hauteur de 9 cm. Quel est son volume? (Utilise π ≈ 3,14, arrondi au nombre entier le plus proche.)
• Choices: A) 226 cm³ B) 339 cm³ C) 452 cm³ D) 565 cm³
• Hint: Volume of a cone = (1/3)πr²h; for r = 3 and h = 4: (1/3)(3.14)(9)(4) ≈ 37.7 cm³.
• Steps:
  • V = (1/3)πr²h = (1/3)(3.14)(36)(9).
  • = (1/3)(3.14)(324) = (1/3)(1017.36) = 339.12.
  • Rounded to the nearest whole number: 339 cm³.
• Answer: 339 cm³

[Hard] Quadratic — Completing the Square to Find Vertex

• EN: A ball is thrown upward. Its height (m) is given by h = −t² + 4t + 5 where t is seconds. What is the maximum height of the ball?
• FR: Une balle est lancée vers le haut. Sa hauteur (en m) est donnée par h = −t² + 4t + 5, où t est en secondes. Quelle est la hauteur maximale de la balle?
• Choices: A) 7 m B) 8 m C) 9 m D) 10 m
• Hint: For h = −t² + 6t + 3, complete the square: h = −(t−3)² + 12; maximum is 12 m.
• Steps:
  • Complete the square: h = −(t² − 4t) + 5.
  • = −(t² − 4t + 4 − 4) + 5 = −(t − 2)² + 4 + 5.
  • Maximum h = 9 m (when t = 2).
• Answer: 9 m

[Hard] Circle Geometry — Inscribed Angle Theorem

• EN: An inscribed angle in a circle measures 35°. What is the measure of the central angle that subtends the same arc?
• FR: Un angle inscrit dans un cercle mesure 35°. Quelle est la mesure de l'angle au centre qui sous-tend le même arc?
• Choices: A) 17.5° B) 35° C) 55° D) 70°
• Hint: The central angle is always twice the inscribed angle that subtends the same arc; for an inscribed angle of 40°, the central angle is 80°.
• Steps:
  • Central angle = 2 × inscribed angle.
  • = 2 × 35° = 70°.
  • So the central angle is 70°.
• Answer: 70°

[Easy] Evaluating an Exponential Function

• EN: Evaluate f(x) = 2ˣ when x = 5.
• FR: Évalue f(x) = 2ˣ lorsque x = 5.
• Choices: A) 10 B) 16 C) 25 D) 32
• Hint: For f(x) = 3ˣ with x = 3: 3³ = 27.
• Steps:
  • f(5) = 2⁵.
  • 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
  • So f(5) = 32.
• Answer: 32

[Easy] Logarithm Basics

• EN: What is log₂(32)?
• FR: Combien fait log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log₃(27) asks "3 to what power gives 27?" — 3³ = 27, so the answer is 3.
• Steps:
  • log₂(32) asks: "2 to what power gives 32?"
  • 2⁵ = 32.
  • So log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequence — Next Term

• EN: The sequence is 5, 11, 17, 23, ___. What is the next term?
• FR: La suite est 5, 11, 17, 23, ___. Quel est le terme suivant?
• Choices: A) 25 B) 27 C) 29 D) 31
• Hint: In the sequence 4, 9, 14, 19, the common difference is 5; the next term is 19 + 5 = 24.
• Steps:
  • The common difference is 11 − 5 = 6.
  • Next term: 23 + 6 = 29.
  • So the next term is 29.
• Answer: 29

[Easy] Simple Interest vs. Compound Interest

• EN: An investment of $1000 earns 5% interest per year. How much simple interest is earned after 3 years?
• FR: Un investissement de 1000 $ rapporte un intérêt de 5% par an. Quel est l'intérêt simple gagné après 3 ans?
• Choices: A) $100 B) $125 C) $150 D) $175
• Hint: Simple interest formula is I = P × r × t; for $200 at 4% for 2 years: I = 200 × 0.04 × 2 = $16.
• Steps:
  • I = P × r × t = 1000 × 0.05 × 3.
  • = 1000 × 0.15 = 150.
  • So simple interest = $150.
• Answer: $150

[Medium] Compound Interest

• EN: $2000 is invested at 4% per year, compounded annually. What is the amount after 2 years?
• FR: 2000 $ sont investis à 4% par an, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $2160.00 B) $2163.20 C) $2164.00 D) $2200.00
• Hint: Use A = P(1 + r)ⁿ; for P = $1000, r = 3%, n = 2: A = 1000(1.03)² = 1000 × 1.0609 = $1060.90.
• Steps:
  • A = P(1 + r)ⁿ = 2000(1.04)².
  • (1.04)² = 1.0816.
  • A = 2000 × 1.0816 = $2163.20.
• Answer: $2163.20

[Medium] Geometric Series — Sum

• EN: Find the sum of the first 4 terms of the geometric series 2, 6, 18, 54.
• FR: Trouve la somme des 4 premiers termes de la série géométrique 2, 6, 18, 54.
• Choices: A) 70 B) 78 C) 80 D) 82
• Hint: For 1, 3, 9, 27: sum = 1 + 3 + 9 + 27 = 40, or use Sₙ = a(rⁿ − 1)/(r − 1) = 1(3⁴ − 1)/2 = 80/2 = 40.
• Steps:
  • Sum = 2 + 6 + 18 + 54.
  • 2 + 6 = 8; 8 + 18 = 26; 26 + 54 = 80.
  • So the sum is 80.
• Answer: 80

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifie: sin²(θ) + cos²(θ).
• Choices: A) 0 B) 1/2 C) 1 D) 2
• Hint: This is the most fundamental Pythagorean identity in trigonometry.
• Steps:
  • The Pythagorean identity states sin²(θ) + cos²(θ) = 1 for any angle θ.
  • This is a known identity that does not need further simplification.
  • So the answer is 1.
• Answer: 1

[Medium] Vertex of a Quadratic Function

• EN: What is the vertex of the parabola y = (x − 4)² + 3?
• FR: Quel est le sommet de la parabole y = (x − 4)² + 3?
• Choices: A) (4, 3) B) (−4, 3) C) (4, −3) D) (3, 4)
• Hint: The vertex form y = (x − h)² + k has its vertex at (h, k); for y = (x − 2)² + 5, the vertex is (2, 5).
• Steps:
  • The equation is in vertex form y = (x − h)² + k.
  • h = 4 and k = 3.
  • So the vertex is (4, 3).
• Answer: (4, 3)

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(9) = 4.
• FR: Résous pour x: log₃(x) + log₃(9) = 4.
• Choices: A) x = 3 B) x = 6 C) x = 9 D) x = 27
• Hint: Use the product rule: log₃(x) + log₃(9) = log₃(9x); then set equal to 4 and solve 3⁴ = 9x.
• Steps:
  • log₃(x) + log₃(9) = log₃(9x) = 4.
  • 9x = 3⁴ = 81.
  • x = 81 ÷ 9 = 9.
• Answer: x = 9

[Hard] Annuity — Future Value

• EN: Maya 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?
• FR: Maya 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?
• Choices: A) $1500.00 B) $1591.80 C) $1686.40 D) $1800.00
• Hint: Future value of annuity = PMT × [(1 + r)ⁿ − 1] / r; for $100/yr at 5% for 2 years: 100 × [(1.05)²−1]/0.05 = 100 × 2.05 = $205.
• Steps:
  • FV = 500 × [(1.06)³ − 1] / 0.06.
  • (1.06)³ = 1.191016; 1.191016 − 1 = 0.191016.
  • FV = 500 × 0.191016 / 0.06 = 500 × 3.1836 = $1591.80.
• Answer: $1591.80

[Easy] Permutations

• EN: In how many ways can 5 students line up for a class photo?
• FR: De combien de façons 5 élèves peuvent-ils se placer en ligne pour une photo de classe?
• Choices: A) 25 B) 60 C) 120 D) 125
• Hint: The number of ways to arrange 4 people is 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • This is 5! (5 factorial).
  • 5! = 5 × 4 × 3 × 2 × 1 = 120.
  • So there are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 6 to be team captains?
• FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 6 pour être capitaines d'équipe?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: C(5, 2) = 5! / (2! × 3!) = (5 × 4) / (2 × 1) = 10 ways.
• Steps:
  • C(6, 2) = 6! / (2! × 4!) = (6 × 5) / (2 × 1) = 30 / 2 = 15.
  • So there are 15 ways.
• Answer: 15

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = x³ + 4x.
• FR: Trouve la dérivée de f(x) = x³ + 4x.
• Choices: A) 3x + 4 B) 3x² C) 3x² + 4 D) x² + 4
• Hint: The derivative of xⁿ is nxⁿ⁻¹; for f(x) = x⁴ + 2x, f'(x) = 4x³ + 2.
• Steps:
  • Derivative of x³ is 3x².
  • Derivative of 4x is 4.
  • So f'(x) = 3x² + 4.
• Answer: 3x² + 4

[Easy] Rational Function — Domain

• EN: What value of x is excluded from the domain of f(x) = 1/(x − 5)?
• FR: Quelle valeur de x est exclue du domaine de f(x) = 1/(x − 5)?
• Choices: A) x = −5 B) x = 0 C) x = 1 D) x = 5
• Hint: A fraction is undefined when its denominator equals zero; for 1/(x − 3), set x − 3 = 0, so x = 3 is excluded.
• Steps:
  • Set the denominator equal to zero: x − 5 = 0.
  • x = 5.
  • So x = 5 is excluded from the domain.
• Answer: x = 5

[Medium] Polynomial Division

• EN: Divide (x² + 7x + 12) by (x + 3).
• FR: Divise (x² + 7x + 12) par (x + 3).
• Choices: A) x + 3 B) x + 4 C) x + 5 D) x² + 4
• Hint: To divide x² + 5x + 6 by (x + 2), factor the numerator: (x+2)(x+3) ÷ (x+2) = x + 3.
• Steps:
  • Factor x² + 7x + 12: find two numbers that multiply to 12 and add to 7: 3 and 4.
  • x² + 7x + 12 = (x + 3)(x + 4).
  • (x + 3)(x + 4) ÷ (x + 3) = x + 4.
• Answer: x + 4

[Medium] Probability Distribution — Expected Value

• EN: A game pays $5 if you roll a 6 on a standard die, and $0 otherwise. What is the expected value of the game per roll?
• FR: Un jeu paie 5 $ si tu obtiens un 6 sur un dé standard, et 0 $ sinon. Quelle est l'espérance mathématique du jeu par lancer?
• Choices: A) $0.50 B) $0.75 C) $0.83 D) $1.00
• Hint: Expected value = sum of (outcome × probability); for a $4 prize with probability 1/4: E = 4 × 1/4 = $1.00.
• Steps:
  • Probability of rolling a 6 = 1/6.
  • Expected value = 5 × (1/6) + 0 × (5/6) = 5/6 ≈ 0.833.
  • So the expected value is $0.83.
• Answer: $0.83

[Medium] Vectors — Addition

• EN: Vector a = (3, 5) and vector b = (−1, 4). What is a + b?
• FR: Le vecteur a = (3, 5) et le vecteur b = (−1, 4). Combien fait a + b?
• Choices: A) (1, 8) B) (2, 9) C) (4, 1) D) (2, 1)
• Hint: To add vectors (4, 2) and (−2, 5), add corresponding components: (4−2, 2+5) = (2, 7).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 5 + 4 = 9.
  • So a + b = (2, 9).
• Answer: (2, 9)

[Medium] Derivative — Rate of Change

• EN: The position of a car is given by s(t) = t² + 3t. What is its velocity (ds/dt) at t = 4?
• FR: La position d'une voiture est donnée par s(t) = t² + 3t. Quelle est sa vitesse (ds/dt) à t = 4?
• Choices: A) 7 B) 9 C) 11 D) 14
• Hint: Differentiate to find velocity: if s(t) = t² + 2t, then v(t) = 2t + 2; at t = 3, v = 8.
• Steps:
  • Differentiate: ds/dt = 2t + 3.
  • At t = 4: ds/dt = 2(4) + 3 = 8 + 3 = 11.
  • So the velocity at t = 4 is 11.
• Answer: 11

[Hard] 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) × pᵏ × (1−p)ⁿ⁻ᵏ; for 3 heads in 3 flips: C(3,3)(0.5)³(0.5)⁰ = 1/8.
• Steps:
  • P(X = 3) = C(4, 3) × (0.5)³ × (0.5)¹.
  • C(4, 3) = 4; (0.5)³ × (0.5) = (0.5)⁴ = 1/16.
  • P = 4 × 1/16 = 4/16 = 1/4.
• Answer: 1/4

[Hard] Derivative — Optimization

• EN: A farmer wants to fence a rectangular area of 100 m² using the least fencing. If one side has length x, the perimeter is P(x) = 2x + 200/x. What value of x minimizes P?
• FR: Un fermier veut clôturer une zone rectangulaire de 100 m² en utilisant le moins de clôture possible. Si un côté a la longueur x, le périmètre est P(x) = 2x + 200/x. Quelle valeur de x minimise P?
• Choices: A) x = 5 m B) x = 8 m C) x = 10 m D) x = 20 m
• Hint: To minimize a function, set its derivative equal to zero; for f(x) = x + 9/x, f'(x) = 1 − 9/x² = 0 gives x² = 9, so x = 3.
• Steps:
  • P'(x) = 2 − 200/x².
  • Set P'(x) = 0: 2 = 200/x², so x² = 100.
  • x = 10 m.
• Answer: x = 10 m