Daily Math — 2026-07-30

[Easy] Counting Carrots

• EN: Mia has 7 carrots. She picks 5 more. How many carrots does she have in all?
• FR: Mia a 7 carottes. Elle en cueille 5 de plus. Combien de carottes a-t-elle en tout?
• Choices: A) 10 carrots B) 11 carrots C) 12 carrots D) 13 carrots
• Hint: To add, count on from the bigger number — if you have 6 and get 3 more, count 7, 8, 9.
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • So Mia has 12 carrots in all.
• Answer: 12 carrots

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes after 8, 10, 12?
• FR: Compte par bonds de 2. Quel nombre vient après 8, 10, 12?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: When you skip count by 2s, always add 2 to the last number — 4, 6, 8 means the next is 10.
• Steps:
  • The pattern goes 8, 10, 12 — each time we add 2.
  • 12 + 2 = 14.
• Answer: 14

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents?
• FR: Quelle pièce vaut 10 cents?
• Choices: A) Penny B) Nickel C) Dime D) Toonie
• Hint: A penny = 1 cent, a nickel = 5 cents, think about which is worth 10 cents.
• Steps:
  • A penny is worth 1 cent.
  • A nickel is worth 5 cents.
  • A dime is worth 10 cents.
• Answer: Dime

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 18
• Hint: Numbers with more tens are always greater — 20 is greater than 8 because 20 has 2 tens.
• Steps:
  • 14 has 1 ten and 4 ones.
  • 9 has 0 tens and 9 ones.
  • 14 is greater than 9.
• Answer: 14

[Medium] Hockey Cards

• EN: Leo has 13 hockey cards. He gives 4 to his friend. How many cards does Leo have left?
• FR: Leo a 13 cartes de hockey. Il en donne 4 à son ami. Combien de cartes Leo a-t-il?
• Choices: A) 7 cards B) 8 cards C) 9 cards D) 11 cards
• Hint: To subtract, count back from the bigger number — 10 minus 3 means count back 3: 9, 8, 7.
• Steps:
  • Start at 13 and count back 4: 12, 11, 10, 9.
  • Leo has 9 cards left.
• Answer: 9 cards

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What is the missing number: 5, 10, 15, ___, 25?
• FR: Compte par bonds de 5. Quel est le nombre manquant : 5, 10, 15, ___, 25?
• Choices: A) 17 B) 18 C) 20 D) 22
• Hint: When skip counting by 5s, add 5 each time — 10, 15, 20, 25 follows the same rule.
• Steps:
  • 5, 10, 15 — each step adds 5.
  • 15 + 5 = 20, then 20 + 5 = 25.
  • The missing number is 20.
• Answer: 20

[Medium] Snowflakes

• EN: There are 6 snowflakes on one mitten and 8 snowflakes on another mitten. How many snowflakes are there in all?
• FR: Il y a 6 flocons de neige sur une mitaine et 8 flocons sur une autre. Combien y a-t-il de flocons en tout?
• Choices: A) 12 snowflakes B) 13 snowflakes C) 14 snowflakes D) 15 snowflakes
• Hint: Put the bigger number in your head and count on — 9 plus 5: start at 9, count 10, 11, 12, 13, 14.
• Steps:
  • Start at 8 (the bigger number) and count on 6 more.
  • 9, 10, 11, 12, 13, 14.
  • There are 14 snowflakes in all.
• Answer: 14 snowflakes

[Medium] Counting to 100

• EN: What number comes just before 20?
• FR: Quel nombre vient juste avant 20?
• Choices: A) 17 B) 18 C) 19 D) 21
• Hint: The number just before any number is one less — the number just before 10 is 9.
• Steps:
  • One less than 20 is 19.
  • So 19 comes just before 20.
• Answer: 19

[Hard] Tim Hortons Timbits

• EN: There are 15 Timbits in a box. Sam eats 6 and Maya eats 3. How many Timbits are left?
• FR: Il y a 15 Timbits dans une boîte. Sam en mange 6 et Maya en mange 3. Combien de Timbits reste-t-il?
• Choices: A) 4 Timbits B) 5 Timbits C) 6 Timbits D) 7 Timbits
• Hint: Subtract one amount at a time — if you start with 12 and take away 4 then 3, first get 8, then get 5.
• Steps:
  • Start with 15 Timbits.
  • Sam eats 6: 15 − 6 = 9.
  • Maya eats 3: 9 − 3 = 6.
  • 6 Timbits are left.
• Answer: 6 Timbits

[Hard] Nickels and Dimes

• EN: Priya has 2 dimes and 1 nickel. How many cents does she have in all?
• FR: Priya a 2 pièces de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 15 cents B) 20 cents C) 25 cents D) 30 cents
• Hint: Count on from the coin worth the most — two nickels and one penny: 5, 10, 11.
• Steps:
  • Each dime is worth 10 cents: 2 × 10 = 20 cents.
  • Add 1 nickel: 20 + 5 = 25 cents.
  • Priya has 25 cents in all.
• Answer: 25 cents

[Easy] Adding Numbers

• EN: What is 34 + 25?
• FR: Combien font 34 + 25?
• Choices: A) 57 B) 59 C) 61 D) 63
• Hint: Add the ones first, then the tens — 32 + 15: ones are 2 + 5 = 7, tens are 3 + 1 = 4, answer is 47.
• Steps:
  • Ones: 4 + 5 = 9.
  • Tens: 3 + 2 = 5.
  • 34 + 25 = 59.
• 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) 4:00 D) 3:30
• Hint: When the minute hand points straight up at 12 and the hour hand points to a number, it is that number o'clock — for example, hour hand at 7 means 7:00.
• Steps:
  • The hour hand points to 3.
  • The minute hand points to 12, so it is exactly 3 o'clock.
  • The time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A crayon is 9 cm long. How much longer is the pencil?
• FR: Un crayon à mine mesure 15 cm. Un crayon de cire mesure 9 cm. De combien le crayon à mine est-il plus long?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: To find the difference in length, subtract the shorter from the longer — 18 cm minus 11 cm is 7 cm.
• Steps:
  • Subtract: 15 − 9 = 6.
  • The pencil is 6 cm longer.
• Answer: 6 cm

[Easy] Subtracting Numbers

• EN: What is 72 − 41?
• FR: Combien font 72 − 41?
• Choices: A) 29 B) 31 C) 33 D) 37
• Hint: Subtract the ones first, then the tens — 85 − 52: ones are 5 − 2 = 3, tens are 8 − 5 = 3, answer is 33.
• Steps:
  • Ones: 2 − 1 = 1.
  • Tens: 7 − 4 = 3.
  • 72 − 41 = 31.
• Answer: 31

[Medium] Counting Coins

• EN: Aiden has 3 dimes and 2 nickels. How many cents does he have?
• FR: Aiden a 3 pièces de 10 cents et 2 pièces de 5 cents. Combien de cents a-t-il?
• Choices: A) 35 cents B) 40 cents C) 45 cents D) 50 cents
• Hint: Multiply each coin by its value and add — two dimes and three nickels: 20 + 15 = 35 cents.
• Steps:
  • 3 dimes = 3 × 10 = 30 cents.
  • 2 nickels = 2 × 5 = 10 cents.
  • Total: 30 + 10 = 40 cents.
• Answer: 40 cents

[Medium] Simple Patterns

• EN: What is the next shape in the pattern: circle, square, circle, square, ___?
• FR: Quelle est la prochaine forme dans le motif : cercle, carré, cercle, carré, ___?
• Choices: A) Triangle B) Circle C) Rectangle D) Square
• Hint: Look at what repeats — if the pattern is red, blue, red, blue, the next colour is red.
• Steps:
  • The pattern repeats: circle, square, circle, square.
  • After square comes circle.
• Answer: Circle

[Medium] Telling Time to the Half-Hour

• EN: The minute hand points to 6 and the hour hand is between 7 and 8. What time is it?
• FR: La grande aiguille pointe sur le 6 et la petite aiguille est entre le 7 et le 8. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:00
• Hint: When the minute hand is on the 6, it is always 30 minutes past the hour — if the hour hand is between 2 and 3, the time is 2:30.
• Steps:
  • Minute hand on 6 = 30 minutes.
  • Hour hand is between 7 and 8, so the hour is 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Adding to 100

• EN: Sofia scores 47 points in a game. She then scores 38 more. How many points does she have?
• FR: Sofia marque 47 points à un jeu. Elle marque ensuite 38 points de plus. Combien de points a-t-elle?
• Choices: A) 75 points B) 82 points C) 85 points D) 89 points
• Hint: Add ones first, then tens, and regroup if needed — 36 + 47: 6 + 7 = 13, write 3 carry 1, then 3 + 4 + 1 = 8, giving 83.
• Steps:
  • Ones: 7 + 8 = 15, write 5 carry 1.
  • Tens: 4 + 3 + 1 = 8.
  • 47 + 38 = 85.
• Answer: 85 points

[Hard] Measuring with Metres

• EN: A classroom is 8 metres long. The hallway is 5 metres longer than the classroom. How long is the hallway?
• FR: Une salle de classe mesure 8 mètres de long. Le couloir est 5 mètres plus long que la salle de classe. Quelle est la longueur du couloir?
• Choices: A) 11 metres B) 12 metres C) 13 metres D) 14 metres
• Hint: To find the total length, add the extra amount to the original — if a room is 6 m and the hall is 4 m longer, the hall is 6 + 4 = 10 m.
• Steps:
  • The classroom is 8 metres long.
  • The hallway is 5 metres longer: 8 + 5 = 13.
  • The hallway is 13 metres long.
• Answer: 13 metres

[Hard] Subtraction with Regrouping

• EN: There are 63 students at a school. 28 students go home early. How many students are still at school?
• FR: Il y a 63 élèves à l'école. 28 élèves rentrent chez eux tôt. Combien d'élèves sont encore à l'école?
• Choices: A) 31 students B) 33 students C) 35 students D) 37 students
• Hint: When you cannot subtract the ones, regroup a ten — for 52 − 17, change 5 tens 2 ones to 4 tens 12 ones, then 12 − 7 = 5 and 4 − 1 = 3, giving 35.
• Steps:
  • Ones: 3 − 8 does not work, so regroup: 13 − 8 = 5.
  • Tens: 5 − 1 (regrouped) − 2 = 3.
  • 63 − 28 = 35.
• Answer: 35 students

[Easy] Multiplication by 2

• EN: What is 6 × 2?
• FR: Combien font 6 × 2?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiplying by 2 is the same as doubling — 7 × 2 is just 7 + 7 = 14.
• Steps:
  • 6 × 2 means 6 groups of 2.
  • 6 + 6 = 12.
• Answer: 12

[Easy] Fractions

• EN: What fraction of this shape is shaded if 1 out of 4 equal parts is shaded?
• FR: Quelle fraction de cette forme est ombrée si 1 partie sur 4 parties égales est ombrée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 1/5
• Hint: The bottom number of a fraction tells how many equal parts in all — if 1 of 3 parts is shaded, the fraction is 1/3.
• Steps:
  • There are 4 equal parts in all.
  • 1 part is shaded.
  • The fraction is 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: What is 4 × 5?
• FR: Combien font 4 × 5?
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: Multiples of 5 always end in 0 or 5 — 3 × 5 = 15, 6 × 5 = 30.
• Steps:
  • 4 × 5 means 4 groups of 5.
  • 5 + 5 + 5 + 5 = 20.
• Answer: 20

[Easy] Reading a Graph

• EN: A bar graph shows that 8 students chose hockey and 5 students chose soccer. How many students chose hockey and soccer in total?
• FR: Un diagramme à barres montre que 8 élèves ont choisi le hockey et 5 ont choisi le soccer. Combien d'élèves ont choisi ces deux sports en tout?
• Choices: A) 11 students B) 12 students C) 13 students D) 14 students
• Hint: Read each bar's value and add them together — if 6 chose basketball and 7 chose baseball, the total is 13.
• Steps:
  • Hockey: 8 students.
  • Soccer: 5 students.
  • Total: 8 + 5 = 13 students.
• Answer: 13 students

[Medium] Basic Division

• EN: A farmer has 24 apples to put equally into 4 baskets. How many apples go in each basket?
• FR: Un fermier a 24 pommes à répartir également dans 4 paniers. Combien de pommes y a-t-il dans chaque panier?
• Choices: A) 4 apples B) 5 apples C) 6 apples D) 8 apples
• Hint: Division is sharing equally — to divide 15 into 3 groups, think: what times 3 equals 15? Answer: 5.
• Steps:
  • 24 ÷ 4 means split 24 into 4 equal groups.
  • Think: 4 × 6 = 24.
  • Each basket gets 6 apples.
• Answer: 6 apples

[Medium] Perimeter

• EN: A rectangle is 5 cm long and 3 cm wide. What is its perimeter?
• FR: Un rectangle mesure 5 cm de longueur et 3 cm de largeur. Quel est son périmètre?
• Choices: A) 14 cm B) 15 cm C) 16 cm D) 18 cm
• Hint: Perimeter is the total distance around a shape — add all four sides; for a rectangle with length 4 and width 2, it is 4 + 2 + 4 + 2 = 12.
• Steps:
  • Add all four sides: 5 + 3 + 5 + 3.
  • 5 + 3 = 8, and 8 + 8 = 16.
  • The perimeter is 16 cm.
• Answer: 16 cm

[Medium] Multiplication by 3

• EN: There are 7 hockey teams. Each team has 3 goalies in training. How many goalies are there in total?
• FR: Il y a 7 équipes de hockey. Chaque équipe a 3 gardiens en entraînement. Combien y a-t-il de gardiens en tout?
• Choices: A) 18 goalies B) 19 goalies C) 20 goalies D) 21 goalies
• Hint: Multiply the number of groups by the number in each group — 6 teams with 3 players each: 6 × 3 = 18.
• Steps:
  • 7 teams × 3 goalies each = 7 × 3.
  • 7 × 3 = 21.
  • There are 21 goalies in total.
• Answer: 21 goalies

[Medium] Fractions of a Group

• EN: There are 12 muffins. One-half of the muffins are blueberry. How many muffins are blueberry?
• FR: Il y a 12 muffins. La moitié des muffins sont aux bleuets. Combien de muffins sont aux bleuets?
• Choices: A) 4 muffins B) 5 muffins C) 6 muffins D) 7 muffins
• Hint: To find one-half of a group, divide by 2 — one-half of 8 is 8 ÷ 2 = 4.
• Steps:
  • One-half of 12 means 12 ÷ 2.
  • 12 ÷ 2 = 6.
  • 6 muffins are blueberry.
• Answer: 6 muffins

[Hard] Multiplication and Perimeter Combined

• EN: A square playground has sides that are each 9 metres long. What is the perimeter of the playground?
• FR: Une cour de jeux carrée a des côtés de 9 mètres chacun. Quel est le périmètre de la cour de jeux?
• Choices: A) 27 metres B) 32 metres C) 36 metres D) 45 metres
• Hint: A square has 4 equal sides, so multiply the side length by 4 — a square with sides of 7 m has a perimeter of 7 × 4 = 28 m.
• Steps:
  • A square has 4 equal sides.
  • Perimeter = 4 × 9.
  • 4 × 9 = 36 metres.
• Answer: 36 metres

[Hard] Multi-Step Problem

• EN: Luca has 5 bags of marbles. Each bag has 4 marbles. He gives away 8 marbles. How many marbles does Luca have left?
• FR: Luca a 5 sacs de billes. Chaque sac contient 4 billes. Il donne 8 billes. Combien de billes Luca a-t-il?
• Choices: A) 10 marbles B) 11 marbles C) 12 marbles D) 13 marbles
• Hint: Multiply first to find the total, then subtract what was given away — 3 bags of 6 marbles is 18; give away 5 and you have 13.
• Steps:
  • First, find the total: 5 × 4 = 20 marbles.
  • Then subtract: 20 − 8 = 12.
  • Luca has 12 marbles left.
• Answer: 12 marbles

[Easy] Multiplication Facts

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 52 C) 56 D) 63
• Hint: Break it apart to make it easier — 7 × 8 is like 7 × 4 doubled; 7 × 4 = 28, so 28 + 28 = 56.
• Steps:
  • 7 × 8 = 56.
  • This is a multiplication fact to memorize.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, what digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre est à la position des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 0
• Hint: In a decimal, the first digit after the point is tenths — in 5.62, the tenths digit is 6.
• Steps:
  • 3 is in the ones place.
  • 4 is in the tenths place.
  • 7 is in the hundredths place.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A rectangle is 6 cm long and 4 cm wide. What is its area?
• FR: Un rectangle mesure 6 cm de longueur et 4 cm de largeur. Quelle est son aire?
• Choices: A) 20 cm² B) 24 cm² C) 28 cm² D) 32 cm²
• Hint: Area of a rectangle = length × width — a rectangle 5 cm by 3 cm has area 5 × 3 = 15 cm².
• Steps:
  • Area = length × width.
  • Area = 6 × 4 = 24.
  • The area is 24 cm².
• Answer: 24 cm²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/2?
• FR: Quelle fraction est plus grande : 3/4 ou 1/2?
• Choices: A) 1/2 B) 1/4 C) 3/4 D) 2/3
• Hint: Change fractions to the same denominator to compare — 1/2 = 2/4, and 2/4 is less than 3/4.
• Steps:
  • Change 1/2 to have the denominator 4: 1/2 = 2/4.
  • Compare 3/4 and 2/4: 3/4 is greater.
• Answer: 3/4

[Medium] Long Division

• EN: What is 84 ÷ 4?
• FR: Combien font 84 ÷ 4?
• Choices: A) 19 B) 21 C) 22 D) 23
• Hint: Divide one digit at a time — for 96 ÷ 3: 9 ÷ 3 = 3, bring down the 6, 6 ÷ 3 = 2, answer is 32.
• Steps:
  • Divide the tens: 8 ÷ 4 = 2, write 2.
  • Divide the ones: 4 ÷ 4 = 1, write 1.
  • 84 ÷ 4 = 21.
• Answer: 21

[Medium] Elapsed Time

• EN: A hockey practice starts at 3:15 p.m. and ends at 4:45 p.m. How long is the practice?
• FR: Un entraînement de hockey commence à 15 h 15 et se termine à 16 h 45. Combien de temps dure l'entraînement?
• Choices: A) 1 hour 15 minutes B) 1 hour 30 minutes C) 1 hour 45 minutes D) 2 hours
• Hint: Count from the start time to the end time — from 2:10 to 3:40 is 1 hour and 30 minutes.
• Steps:
  • From 3:15 to 4:15 is exactly 1 hour.
  • From 4:15 to 4:45 is 30 more minutes.
  • Total: 1 hour 30 minutes.
• Answer: 1 hour 30 minutes

[Medium] Decimal Operations

• EN: What is 2.5 + 1.3?
• FR: Combien font 2,5 + 1,3?
• Choices: A) 3.6 B) 3.7 C) 3.8 D) 4.2
• Hint: Line up the decimal points and add column by column — 3.2 + 2.5: tenths 2 + 5 = 7, ones 3 + 2 = 5, so 5.7.
• Steps:
  • Tenths: 5 + 3 = 8.
  • Ones: 2 + 1 = 3.
  • 2.5 + 1.3 = 3.8.
• Answer: 3.8

[Medium] Long Division with Remainder

• EN: What is 29 ÷ 4?
• FR: Combien font 29 ÷ 4?
• Choices: A) 6 remainder 3 B) 7 remainder 1 C) 7 remainder 2 D) 8 remainder 1
• Hint: Find how many times the divisor fits without going over, then find the leftover — 22 ÷ 5: 5 fits 4 times (5 × 4 = 20), remainder is 22 − 20 = 2, so 4 remainder 2.
• Steps:
  • 4 × 7 = 28, which is the largest multiple of 4 that fits under 29.
  • Remainder: 29 − 28 = 1.
  • 29 ÷ 4 = 7 remainder 1.
• Answer: 7 remainder 1

[Hard] Multi-Step Area Problem

• EN: A room is 9 m long and 6 m wide. A rug covers an area of 12 m² inside the room. What area of the floor is NOT covered by the rug?
• FR: Une pièce mesure 9 m de longueur et 6 m de largeur. Un tapis couvre 12 m² dans la pièce. Quelle superficie du plancher n'est pas couverte par le tapis?
• Choices: A) 40 m² B) 42 m² C) 44 m² D) 54 m²
• Hint: Find the total area first, then subtract the rug area — a room of 8 × 5 = 40 m² with a 10 m² rug leaves 30 m² uncovered.
• Steps:
  • Room area = 9 × 6 = 54 m².
  • Subtract the rug: 54 − 12 = 42 m².
  • 42 m² of the floor is not covered.
• Answer: 42 m²

[Hard] Multi-Step Multiplication

• EN: A school orders 6 boxes of crayons. Each box has 8 packs. Each pack has 9 crayons. How many crayons are there in total?
• FR: Une école commande 6 boîtes de crayons. Chaque boîte contient 8 paquets. Chaque paquet contient 9 crayons. Combien y a-t-il de crayons en tout?
• Choices: A) 388 crayons B) 392 crayons C) 432 crayons D) 480 crayons
• Hint: Multiply step by step — 3 boxes × 4 packs × 5 crayons: first 3 × 4 = 12, then 12 × 5 = 60 crayons.
• Steps:
  • First: 6 × 8 = 48 packs.
  • Then: 48 × 9 = 432 crayons.
  • There are 432 crayons in total.
• Answer: 432 crayons

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 194 B) 200 C) 204 D) 212
• Hint: Multiply ones first, then tens — 23 × 4: ones 3 × 4 = 12, write 2 carry 1; tens 2 × 4 = 8 + 1 = 9; answer is 92.
• Steps:
  • Ones: 4 × 6 = 24, write 4 carry 2.
  • Tens: 3 × 6 = 18 + 2 = 20.
  • 34 × 6 = 204.
• Answer: 204

[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: When denominators are the same, just add the numerators and keep the denominator — 3/8 + 2/8 = 5/8.
• Steps:
  • Same denominator (7), so add numerators: 2 + 3 = 5.
  • Keep the denominator: 5/7.
• Answer: 5/7

[Easy] Percentage Intro

• EN: What is 50% of 80?
• FR: Combien font 50% de 80?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: 50% means one-half — to find 50% of any number, divide it by 2; 50% of 60 is 30.
• Steps:
  • 50% = one-half.
  • 80 ÷ 2 = 40.
• Answer: 40

[Easy] Decimal Operations

• EN: What is 4.6 + 2.8?
• FR: Combien font 4,6 + 2,8?
• Choices: A) 7.2 B) 7.4 C) 7.6 D) 8.2
• Hint: Add tenths first and regroup if needed — 3.7 + 2.5: tenths 7 + 5 = 12, write 2 carry 1; ones 3 + 2 + 1 = 6; answer is 6.2.
• Steps:
  • Tenths: 6 + 8 = 14, write 4 carry 1.
  • Ones: 4 + 2 + 1 = 7.
  • 4.6 + 2.8 = 7.4.
• Answer: 7.4

[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) 48 cm³ B) 56 cm³ C) 60 cm³ D) 72 cm³
• Hint: Volume = length × width × height — a box of 6 × 2 × 4 has volume 6 × 2 × 4 = 48 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions with Like Denominators

• EN: What is 9/10 − 3/10?
• FR: Combien font 9/10 − 3/10?
• Choices: A) 5/10 B) 6/10 C) 7/10 D) 6/20
• Hint: Keep the denominator the same and subtract the numerators — 7/9 − 4/9 = 3/9.
• Steps:
  • Same denominator (10), so subtract numerators: 9 − 3 = 6.
  • Keep the denominator: 6/10.
• Answer: 6/10

[Medium] Multi-Digit Division

• EN: What is 144 ÷ 6?
• FR: Combien font 144 ÷ 6?
• Choices: A) 22 B) 24 C) 26 D) 28
• Hint: Divide from left to right — for 126 ÷ 3: 1 ÷ 3 won't go, so try 12 ÷ 3 = 4, bring down 6, 6 ÷ 3 = 2; answer is 42.
• Steps:
  • 14 ÷ 6 = 2 remainder 2; bring down 4 to get 24.
  • 24 ÷ 6 = 4.
  • 144 ÷ 6 = 24.
• Answer: 24

[Medium] Percentages

• EN: What is 25% of 60?
• FR: Combien font 25% de 60?
• Choices: A) 12 B) 14 C) 15 D) 18
• Hint: 25% is one-quarter, so divide by 4 — 25% of 40 is 40 ÷ 4 = 10.
• Steps:
  • 25% = one-quarter.
  • 60 ÷ 4 = 15.
• Answer: 15

[Hard] Multi-Step Decimal Problem

• EN: Ethan buys 3 notebooks for $2.75 each and pays with a $10 bill. How much change does he get?
• FR: Ethan achète 3 cahiers à 2,75 $ chacun et paie avec un billet de 10 $. Combien d'argent lui rend-on?
• Choices: A) $1.75 B) $2.25 C) $2.50 D) $3.25
• Hint: Multiply the price by the number of items first, then subtract from the amount paid — 4 items at $1.50 each costs $6.00; change from $10 is $4.00.
• Steps:
  • Total cost: 3 × $2.75 = $8.25.
  • Change: $10.00 − $8.25 = $1.75.
• Answer: $1.75

[Hard] Combined Fractions and Percentages

• EN: A bag has 40 marbles. 10% are red, 25% are blue, and the rest are green. How many marbles are green?
• FR: Un sac contient 40 billes. 10% sont rouges, 25% sont bleues et le reste est vert. Combien de billes sont vertes?
• Choices: A) 24 marbles B) 25 marbles C) 26 marbles D) 28 marbles
• Hint: Find each percentage amount, add them, then subtract from the total — if 10% and 20% are taken, 30% are taken, leaving 70%.
• Steps:
  • Red: 10% of 40 = 4 marbles.
  • Blue: 25% of 40 = 10 marbles.
  • Green: 40 − 4 − 10 = 26 marbles.
• Answer: 26 marbles

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: In BEDMAS, multiplication comes before addition — for 5 + 3 × 4, do 3 × 4 = 12 first, then 5 + 12 = 17.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
• Answer: 11

[Easy] Percent of a Number

• EN: What is 20% of 50?
• FR: Combien font 20% de 50?
• Choices: A) 8 B) 10 C) 12 D) 15
• Hint: 20% means 20 per 100, so multiply by 0.20 or find 10% first and double it — 10% of 60 is 6, so 20% is 12.
• Steps:
  • 10% of 50 = 5.
  • 20% = 2 × 5 = 10.
• Answer: 10

[Easy] Simple Algebraic Expression

• EN: If n = 3, what is the value of 4n + 5?
• FR: Si n = 3, quelle est la valeur de 4n + 5?
• Choices: A) 14 B) 16 C) 17 D) 19
• Hint: Substitute the value in for the variable and calculate — if x = 2, then 3x + 7 = 3(2) + 7 = 6 + 7 = 13.
• Steps:
  • Replace n with 3: 4(3) + 5.
  • 4 × 3 = 12, then 12 + 5 = 17.
• Answer: 17

[Easy] Integers Introduction

• EN: The temperature was −3°C in the morning and rose 8 degrees by noon. What was the temperature at noon?
• FR: La température était de −3 °C le matin et a augmenté de 8 degrés à midi. Quelle était la température à midi?
• Choices: A) 3°C B) 4°C C) 5°C D) 6°C
• Hint: To add a positive number to a negative number, move right on the number line — −5 + 9 = 4.
• Steps:
  • Start at −3 and add 8.
  • −3 + 8 = 5.
  • The temperature at noon was 5°C.
• Answer: 5°C

[Medium] Ratio and Rate

• EN: A recipe uses 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed for 6 cups of sugar?
• FR: Une recette utilise 3 tasses de farine pour 2 tasses de sucre. Combien de tasses de farine faut-il pour 6 tasses de sucre?
• Choices: A) 7 cups B) 8 cups C) 9 cups D) 12 cups
• Hint: Find how many times the sugar was multiplied, then multiply the flour by the same amount — if sugar went from 4 to 8, it tripled... actually doubled, so double the flour too.
• Steps:
  • Sugar goes from 2 to 6: multiplied by 3.
  • Multiply flour by 3: 3 × 3 = 9.
  • 9 cups of flour are needed.
• Answer: 9 cups

[Medium] Fraction Division

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

[Medium] BEDMAS with Brackets

• EN: What is (8 + 4) ÷ 3 − 1?
• FR: Combien font (8 + 4) ÷ 3 − 1?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: Always do what is inside brackets first, then division, then subtraction — (6 + 3) ÷ 3 − 1 = 9 ÷ 3 − 1 = 3 − 1 = 2.
• Steps:
  • Brackets first: 8 + 4 = 12.
  • Division: 12 ÷ 3 = 4.
  • Subtraction: 4 − 1 = 3.
• Answer: 3

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 6/12 C) 7/12 D) 8/12
• Hint: Multiply the numerators together and the denominators together — 3/5 × 2/7 = 6/35.
• Steps:
  • Numerators: 2 × 3 = 6.
  • Denominators: 3 × 4 = 12.
  • Result: 6/12, which simplifies to 1/2; but among the choices, 6/12 is given.
• Answer: 6/12

[Hard] Multi-Step Percent Problem

• EN: A jacket costs $80. It is on sale for 30% off. Then a 13% tax is added. What is the final price?
• FR: Un manteau coûte 80 $. Il est en solde à 30% de rabais. Une taxe de 13% est ensuite ajoutée. Quel est le prix final?
• Choices: A) $62.92 B) $63.04 C) $63.84 D) $64.20
• Hint: First find the sale price by subtracting the discount, then multiply by (1 + tax rate) — a $50 item at 20% off is $40, then adding 10% tax: $40 × 1.10 = $44.
• Steps:
  • Discount: 30% of $80 = $24; sale price = $80 − $24 = $56.
  • Tax: 13% of $56 = $7.28.
  • Final price: $56.00 + $7.28 = $63.28. Check choices — rounding: $63.28 is closest; actually let me recalculate: 56 × 1.13 = 56 + 7.28 = $63.28. Adjusting choice: I'll use $63.28.
  • Choices: A) $62.92 B) $63.28 C) $63.84 D) $64.20
  • The final price is $63.28.
• Answer: $63.28

[Hard] Integer Operations

• EN: The temperature changed from −12°C to 6°C over two days. What was the total change in temperature?
• FR: La température est passée de −12 °C à 6 °C en deux jours. Quel a été le changement total de température?
• Choices: A) 16°C B) 17°C C) 18°C D) 19°C
• Hint: To find the change, subtract the starting temperature from the ending temperature — from −7 to 5 is 5 − (−7) = 5 + 7 = 12.
• Steps:
  • Change = ending − starting = 6 − (−12).
  • Subtracting a negative means adding: 6 + 12 = 18.
  • The total change was 18°C.
• Answer: 18°C

[Easy] Integer Addition

• EN: What is −5 + 9?
• FR: Combien font −5 + 9?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: On the number line, start at the negative number and move right when adding a positive — −3 + 7: start at −3, move 7 right, land on 4.
• Steps:
  • Start at −5, add 9.
  • −5 + 9 = 4.
• Answer: 4

[Easy] Fraction Fluency

• EN: What is 3/5 + 2/5?
• FR: Combien font 3/5 + 2/5?
• Choices: A) 5/10 B) 4/5 C) 1 whole D) 6/5
• Hint: Same denominators — add the top numbers and keep the bottom the same — 4/9 + 5/9 = 9/9 = 1 whole.
• Steps:
  • Add numerators: 3 + 2 = 5.
  • Denominator stays 5: 5/5 = 1 whole.
• Answer: 1 whole

[Easy] Discount

• EN: A hockey stick costs $60. It is 10% off. How much is the discount?
• FR: Un bâton de hockey coûte 60 $. Il est à 10% de rabais. Quel est le montant du rabais?
• Choices: A) $4 B) $5 C) $6 D) $7
• Hint: To find 10%, move the decimal one place left — 10% of $90 = $9.
• Steps:
  • 10% of $60 = $60 ÷ 10 = $6.
  • The discount is $6.
• Answer: $6

[Easy] Integer Subtraction

• EN: What is 3 − 8?
• FR: Combien font 3 − 8?
• Choices: A) −6 B) −5 C) −4 D) −3
• Hint: When you subtract a larger number from a smaller one, the result is negative — 4 − 10 = −6.
• Steps:
  • 3 − 8: we need more than we have, so the answer is negative.
  • 8 − 3 = 5, so 3 − 8 = −5.
• Answer: −5

[Medium] 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 x, do the opposite operation on both sides — if x + 4 = 10, subtract 4 from both sides: x = 6.
• Steps:
  • Subtract 7 from both sides: x + 7 − 7 = 15 − 7.
  • x = 8.
• Answer: x = 8

[Medium] Percentage Problem (Tip)

• EN: A restaurant bill is $40. If you leave a 15% tip, how much is the tip?
• FR: Une facture de restaurant est de 40 $. Si tu laisses un pourboire de 15%, combien est le pourboire?
• Choices: A) $4.50 B) $5.00 C) $6.00 D) $6.50
• Hint: Find 10% first and then add half of that for 15% — 10% of $60 = $6, half of $6 = $3, so 15% = $9.
• Steps:
  • 10% of $40 = $4.
  • 5% of $40 = $2.
  • 15% = $4 + $2 = $6.
• Answer: $6.00

[Medium] Surface Area

• EN: A rectangular box is 4 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 4 cm de longueur, 3 cm de largeur et 2 cm de hauteur. Quelle est son aire de surface?
• Choices: A) 48 cm² B) 52 cm² C) 56 cm² D) 60 cm²
• Hint: A box has 3 pairs of faces — find each face area, double each, and add: SA = 2(lw + lh + wh).
• Steps:
  • Top/bottom: 2 × (4 × 3) = 24.
  • Front/back: 2 × (4 × 2) = 16.
  • Left/right: 2 × (3 × 2) = 12.
  • Total: 24 + 16 + 12 = 52 cm².
• Answer: 52 cm²

[Medium] Data and Probability

• EN: A bag has 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of picking a red marble?
• FR: Un sac contient 3 billes rouges, 2 billes bleues et 5 billes vertes. Quelle est la probabilité de piger une bille rouge?
• Choices: A) 1/5 B) 3/10 C) 2/5 D) 1/2
• Hint: Probability = (number of favourable outcomes) ÷ (total outcomes) — 4 red out of 12 total is 4/12 = 1/3.
• Steps:
  • Total marbles: 3 + 2 + 5 = 10.
  • Red marbles: 3.
  • Probability = 3/10.
• Answer: 3/10

[Hard] Multi-Step Integer Problem

• EN: The temperature in Winnipeg was −14°C. It dropped 5 degrees overnight and then rose 12 degrees the next day. What is the final temperature?
• FR: La température à Winnipeg était de −14 °C. Elle a baissé de 5 degrés pendant la nuit, puis a augmenté de 12 degrés le lendemain. Quelle est la température finale?
• Choices: A) −8°C B) −7°C C) −6°C D) −5°C
• Hint: Apply each change in order — start at −10, drop 4: −14, then rise 8: −6.
• Steps:
  • Start: −14.
  • Drop 5: −14 − 5 = −19.
  • Rise 12: −19 + 12 = −7.
  • The final temperature is −7°C.
• Answer: −7°C

[Hard] One-Step Equation Word Problem

• EN: Amara earns the same amount each week. After 6 weeks, she has saved $210. She also received a $30 birthday gift. Her total savings is $240. Write and solve an equation to find her weekly earnings.
• FR: Amara gagne le même montant chaque semaine. Après 6 semaines, elle a économisé 210 $. Elle a aussi reçu un cadeau de 30 $. Ses économies totales sont de 240 $. Écris et résous une équation pour trouver ses gains hebdomadaires.
• Choices: A) $30 per week B) $35 per week C) $40 per week D) $45 per week
• Hint: Set up an equation with the weekly amount as the variable — if 5w + 20 = 120, subtract 20 first: 5w = 100, then divide: w = 20.
• Steps:
  • Let w = weekly earnings. Equation: 6w + 30 = 240.
  • Subtract 30: 6w = 210.
  • Divide by 6: w = 35.
  • She earns $35 per week.
• Answer: $35 per week

[Easy] Perfect Squares

• EN: What is the square root of 49?
• FR: Quelle est la racine carrée de 49?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: The square root asks "what number times itself gives this?" — the square root of 36 is 6 because 6 × 6 = 36.
• Steps:
  • Ask: what number × itself = 49?
  • 7 × 7 = 49.
  • The square root of 49 is 7.
• Answer: 7

[Easy] Mean

• EN: Find the mean of these numbers: 4, 6, 8, 10, 12.
• FR: Trouve la moyenne de ces nombres : 4, 6, 8, 10, 12.
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: Add all values and divide by how many there are — mean of 2, 4, 6 is (2 + 4 + 6) ÷ 3 = 12 ÷ 3 = 4.
• Steps:
  • Sum: 4 + 6 + 8 + 10 + 12 = 40.
  • Count: 5 numbers.
  • Mean: 40 ÷ 5 = 8.
• Answer: 8

[Easy] Pythagorean Theorem

• EN: A right triangle has legs of 3 cm and 4 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des côtés de 3 cm et 4 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: Use a² + b² = c² — for legs 6 and 8: 36 + 64 = 100, so c = 10.
• Steps:
  • a² + b² = c².
  • 3² + 4² = 9 + 16 = 25.
  • c = √25 = 5 cm.
• Answer: 5 cm

[Easy] Percent Increase

• EN: A price increases from $50 to $60. What is the percent increase?
• FR: Un prix augmente de 50 $ à 60 $. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: Percent increase = (increase ÷ original) × 100 — from $20 to $25, increase is $5; 5 ÷ 20 × 100 = 25%.
• Steps:
  • Increase: $60 − $50 = $10.
  • Percent increase: ($10 ÷ $50) × 100 = 20%.
• Answer: 20%

[Medium] Two-Step Linear Equation

• EN: Solve for x: 3x − 4 = 11.
• FR: Résous pour x : 3x − 4 = 11.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Add or subtract first to get the x term alone, then divide — for 2x − 3 = 7: add 3 to get 2x = 10, then divide by 2: x = 5.
• Steps:
  • Add 4 to both sides: 3x = 15.
  • Divide both sides by 3: x = 5.
• Answer: x = 5

[Medium] Slope Introduction

• EN: A line passes through points (0, 2) and (3, 8). What is the slope of the line?
• FR: Une droite passe par les points (0, 2) et (3, 8). Quel est le taux de variation (pente) de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (change in y) ÷ (change in x) — from (1, 3) to (4, 9): rise = 9 − 3 = 6, run = 4 − 1 = 3, slope = 2.
• Steps:
  • Rise: 8 − 2 = 6.
  • Run: 3 − 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of this data set: 3, 7, 5, 9, 5, 1, 11.
• FR: Trouve la médiane de cet ensemble de données : 3, 7, 5, 9, 5, 1, 11.
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: To find the median, put the numbers in order and find the middle one — for 2, 4, 6, 8, 10, the median is 6.
• Steps:
  • Order the data: 1, 3, 5, 5, 7, 9, 11.
  • There are 7 values; the middle (4th) value is 5.
  • The median is 5.
• Answer: 5

[Medium] Pythagorean Theorem Applied

• EN: A ladder leans against a wall. The base of the ladder is 5 m from the wall, and the ladder reaches 12 m up the wall. How long is the ladder?
• FR: Une échelle est appuyée contre un mur. La base de l'échelle est à 5 m du mur et l'échelle atteint 12 m de hauteur. Quelle est la longueur de l'échelle?
• Choices: A) 11 m B) 12 m C) 13 m D) 14 m
• Hint: Use the Pythagorean theorem — legs 6 and 8 give hypotenuse √(36 + 64) = √100 = 10.
• Steps:
  • a² + b² = c².
  • 5² + 12² = 25 + 144 = 169.
  • c = √169 = 13 m.
• Answer: 13 m

[Hard] Two-Step Equation Word Problem

• EN: Chloe thinks of a number. She multiplies it by 4 and then subtracts 9. The result is 23. What is the number?
• FR: Chloé pense à un nombre. Elle le multiplie par 4 et lui soustrait 9. Le résultat est 23. Quel est le nombre?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Work backwards — write the equation, add the subtracted value first, then divide.
• Steps:
  • Equation: 4n − 9 = 23.
  • Add 9: 4n = 32.
  • Divide by 4: n = 8.
• Answer: 8

[Hard] Percent Decrease Word Problem

• EN: A store reduces its inventory of 240 items by 35%. How many items remain in stock?
• FR: Un magasin réduit son inventaire de 240 articles de 35%. Combien d'articles restent en stock?
• Choices: A) 144 items B) 150 items C) 156 items D) 162 items
• Hint: Find the decrease amount and subtract from the original — 20% of 300 = 60, so 300 − 60 = 240 remain.
• Steps:
  • 35% of 240 = 0.35 × 240 = 84 items removed.
  • Remaining: 240 − 84 = 156 items.
• Answer: 156 items

[Easy] Solving a Linear Equation

• EN: Solve for x: 2x + 3 = 11.
• FR: Résous pour x : 2x + 3 = 11.
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Subtract the constant from both sides first, then divide — 3x + 6 = 18: subtract 6 to get 3x = 12, divide by 3: x = 4.
• Steps:
  • Subtract 3: 2x = 8.
  • Divide by 2: x = 4.
• Answer: x = 4

[Easy] Graphing Lines — y-intercept

• EN: For the equation y = 3x + 2, what is the y-intercept?
• FR: Pour l'équation y = 3x + 2, quelle est l'ordonnée à l'origine?
• Choices: A) 1 B) 2 C) 3 D) 6
• Hint: The y-intercept is the value of b in y = mx + b — for y = 5x + 7, the y-intercept is 7.
• Steps:
  • In y = mx + b, b is the y-intercept.
  • In y = 3x + 2, b = 2.
• Answer: 2

[Easy] Adding Polynomials

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

[Easy] Linear Inequality

• EN: Solve: x − 5 > 3.
• FR: Résous : x − 5 > 3.
• Choices: A) x > 6 B) x > 7 C) x > 8 D) x > 9
• Hint: Solve just like an equation, keeping the inequality sign — x − 4 > 6: add 4 to both sides: x > 10.
• Steps:
  • Add 5 to both sides: x > 3 + 5.
  • x > 8.
• Answer: x > 8

[Medium] Multiplying Polynomials

• EN: Expand and simplify: 3(2x − 4) + 5x.
• FR: Développe et simplifie : 3(2x − 4) + 5x.
• Choices: A) 10x − 12 B) 11x − 12 C) 11x − 4 D) 12x − 12
• Hint: Distribute first, then collect like terms — 2(3x + 1) + 4x = 6x + 2 + 4x = 10x + 2.
• Steps:
  • Distribute 3: 6x − 12.
  • Add 5x: 6x + 5x − 12.
  • Result: 11x − 12.
• Answer: 11x − 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in a ratio of 1:3. If one side of the smaller triangle is 4 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans un rapport de 1:3. Si un côté du petit triangle mesure 4 cm, quel est le côté correspondant du grand triangle?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 16 cm
• Hint: Multiply the known side by the scale factor — if the ratio is 1:4 and the small side is 5 cm, the large side is 5 × 4 = 20 cm.
• Steps:
  • Scale factor is 3.
  • Large side = 4 × 3 = 12 cm.
• Answer: 12 cm

[Medium] Trigonometry (SOH-CAH-TOA)

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

[Medium] Graphing Lines — Slope

• EN: What is the slope of the line y = −2x + 5?
• FR: Quel est le taux de variation (pente) de la droite y = −2x + 5?
• Choices: A) −5 B) −2 C) 2 D) 5
• Hint: In y = mx + b, m is the slope — for y = 4x − 3, the slope is 4.
• Steps:
  • In y = mx + b, the slope is m.
  • In y = −2x + 5, m = −2.
• Answer: −2

[Hard] Multi-Step Linear Equation

• EN: Solve for x: 4(x − 2) = 2x + 6.
• FR: Résous pour x : 4(x − 2) = 2x + 6.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Expand the bracket first, then move x terms to one side — 3(x + 1) = x + 9: expand to 3x + 3 = x + 9, subtract x: 2x + 3 = 9, subtract 3: 2x = 6, x = 3.
• Steps:
  • Expand: 4x − 8 = 2x + 6.
  • Subtract 2x: 2x − 8 = 6.
  • Add 8: 2x = 14.
  • Divide by 2: x = 7.
• Answer: x = 7

[Hard] Trigonometry Applied

• EN: A ramp rises 5 m over a horizontal distance of 12 m. What is the angle of elevation to the nearest degree? (sin 22° ≈ 0.37, sin 23° ≈ 0.39, tan 22° ≈ 0.40, tan 23° ≈ 0.42)
• FR: Une rampe monte de 5 m sur une distance horizontale de 12 m. Quel est l'angle d'élévation au degré près? (sin 22° ≈ 0,37, sin 23° ≈ 0,39, tan 22° ≈ 0,40, tan 23° ≈ 0,42)
• Choices: A) 20° B) 21° C) 22° D) 23°
• Hint: Use tangent when you know opposite and adjacent — tan(θ) = opposite / adjacent; then use the table to match.
• Steps:
  • tan(θ) = opposite / adjacent = 5/12 ≈ 0.417.
  • Look at tan 23° ≈ 0.42, which is closest.
  • The angle of elevation is approximately 23°.
• Answer: 23°

[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 + 2)(x + 4) D) (x + 3)(x + 3)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — for x² + 7x + 10, find numbers with product 10 and sum 7: 2 and 5, giving (x + 2)(x + 5).
• Steps:
  • Find two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5.
  • x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 8 cm et l'hypoténuse mesure 10 cm. Quelle est la valeur de cos(θ)?
• Choices: A) 0.5 B) 0.6 C) 0.8 D) 0.9
• Hint: CAH means cosine = adjacent ÷ hypotenuse — if adjacent = 6 and hypotenuse = 10, cos = 6/10 = 0.6.
• Steps:
  • cos(θ) = adjacent / hypotenuse.
  • cos(θ) = 8/10 = 0.8.
• Answer: 0.8

[Easy] System of Equations

• EN: Solve the system: x + y = 10 and x − y = 2.
• FR: Résous le système : x + y = 10 et x − y = 2.
• Choices: A) x = 5, y = 5 B) x = 6, y = 4 C) x = 7, y = 3 D) x = 8, y = 2
• Hint: Add the two equations together to eliminate one variable — equations x + y = 8 and x − y = 4: adding gives 2x = 12, so x = 6 and y = 2.
• Steps:
  • Add the equations: (x + y) + (x − y) = 10 + 2, giving 2x = 12, so x = 6.
  • Substitute: 6 + y = 10, so y = 4.
  • Solution: x = 6, y = 4.
• Answer: x = 6, y = 4

[Easy] Surface Area of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 5 cm. What is the lateral (curved) surface area? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 5 cm. Quelle est l'aire latérale (surface courbe)? (Utilise π ≈ 3,14)
• Choices: A) 84.78 cm² B) 90.12 cm² C) 94.20 cm² D) 96.80 cm²
• Hint: Lateral surface area = 2πrh — for r = 2 and h = 7: 2 × 3.14 × 2 × 7 = 87.92 cm².
• Steps:
  • Lateral SA = 2πrh = 2 × 3.14 × 3 × 5.
  • = 2 × 3.14 × 15 = 2 × 47.1 = 94.20 cm².
• Answer: 94.20 cm²

[Medium] Solving a Quadratic by Factoring

• EN: Solve: x² − 7x + 12 = 0.
• FR: Résous : x² − 7x + 12 = 0.
• Choices: A) x = 2 or x = 6 B) x = 3 or x = 4 C) x = 4 or x = 5 D) x = 1 or x = 12
• Hint: Factor first, then set each factor to zero — x² − 5x + 6 = 0 factors to (x − 2)(x − 3) = 0, giving x = 2 or x = 3.
• Steps:
  • Factor: find numbers with product 12 and sum 7 → 3 and 4.
  • (x − 3)(x − 4) = 0.
  • x = 3 or x = 4.
• Answer: x = 3 or x = 4

[Medium] Circle Geometry

• EN: A circle has a central angle of 90° and a radius of 6 cm. What is the arc length? (Use π ≈ 3.14)
• FR: Un cercle a un angle central de 90° et un rayon de 6 cm. Quelle est la longueur de l'arc? (Utilise π ≈ 3,14)
• Choices: A) 8.42 cm B) 9.42 cm C) 10.42 cm D) 11.42 cm
• Hint: Arc length = (central angle / 360°) × 2πr — for a 60° angle and r = 5: (60/360) × 2 × 3.14 × 5 = (1/6) × 31.4 ≈ 5.23 cm.
• Steps:
  • Arc length = (90/360) × 2 × 3.14 × 6.
  • = (1/4) × 37.68.
  • = 9.42 cm.
• Answer: 9.42 cm

[Medium] Completing the Square

• EN: Complete the square: what is the vertex of y = x² − 4x + 7?
• FR: Complète le carré : quel est le sommet de y = x² − 4x + 7?
• Choices: A) (1, 4) B) (2, 3) C) (3, 4) D) (4, 7)
• Hint: Complete the square by adding and subtracting (b/2)² inside the equation — y = x² − 6x + 11: (−6/2)² = 9; y = (x − 3)² − 9 + 11 = (x − 3)² + 2, vertex is (3, 2).
• Steps:
  • y = x² − 4x + 7; take half of −4: (−2)² = 4.
  • y = (x − 2)² − 4 + 7 = (x − 2)² + 3.
  • Vertex is (2, 3).
• Answer: (2, 3)

[Medium] Volume of a Cone

• EN: A cone has a radius of 4 cm and a height of 9 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur de 9 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 148.12 cm³ B) 150.72 cm³ C) 152.50 cm³ D) 157.00 cm³
• Hint: Volume of a cone = (1/3)πr²h — for r = 3 and h = 7: (1/3) × 3.14 × 9 × 7 = (1/3) × 197.82 ≈ 65.94 cm³.
• Steps:
  • V = (1/3) × π × r² × h.
  • V = (1/3) × 3.14 × 16 × 9.
  • V = (1/3) × 3.14 × 144 = (1/3) × 452.16 = 150.72 cm³.
• Answer: 150.72 cm³

[Hard] Quadratic Formula

• EN: Solve using the quadratic formula: 2x² − 3x − 2 = 0.
• FR: Résous en utilisant la formule quadratique : 2x² − 3x − 2 = 0.
• Choices: A) x = 2 or x = −1/2 B) x = 3 or x = −1 C) x = 1 or x = −2 D) x = 4 or x = −1/2
• Hint: Use x = (−b ± √(b² − 4ac)) / 2a — identify a, b, c, plug in, and simplify both solutions.
• Steps:
  • a = 2, b = −3, c = −2.
  • Discriminant: (−3)² − 4(2)(−2) = 9 + 16 = 25.
  • x = (3 ± 5) / 4.
  • x = 8/4 = 2 or x = −2/4 = −1/2.
• Answer: x = 2 or x = −1/2

[Hard] System of Equations — Substitution

• EN: Solve the system: y = 2x + 1 and 3x + y = 16.
• FR: Résous le système : y = 2x + 1 et 3x + y = 16.
• Choices: A) x = 2, y = 5 B) x = 3, y = 7 C) x = 4, y = 9 D) x = 5, y = 11
• Hint: Substitute the first equation into the second — if y = x + 3 and 2x + y = 12, substitute: 2x + (x + 3) = 12, so 3x = 9, x = 3, y = 6.
• Steps:
  • Substitute y = 2x + 1 into 3x + y = 16.
  • 3x + (2x + 1) = 16 → 5x + 1 = 16 → 5x = 15 → x = 3.
  • y = 2(3) + 1 = 7.
  • Solution: x = 3, y = 7.
• Answer: x = 3, y = 7

[Easy] Quadratic Function Vertex

• 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) (3, 4) B) (4, 3) C) (−4, 3) D) (4, −3)
• Hint: For y = (x − h)² + k, the vertex is the point (h, k) — for y = (x − 2)² + 5, vertex is (2, 5).
• Steps:
  • y = (x − 4)² + 3 is in vertex form.
  • h = 4, k = 3.
  • Vertex is (4, 3).
• Answer: (4, 3)

[Easy] Logarithm Intro

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: A logarithm asks "to what power must the base be raised to get this number?" — log₃(9) = 2 because 3² = 9.
• Steps:
  • Ask: 2 to what power equals 8?
  • 2³ = 8.
  • log₂(8) = 3.
• Answer: 3

[Easy] Exponential Function

• EN: A population of 500 bacteria doubles every hour. What is the population after 3 hours?
• FR: Une population de 500 bactéries double chaque heure. Quelle est la population après 3 heures?
• Choices: A) 2500 B) 3000 C) 4000 D) 5000
• Hint: For exponential growth, use P = P₀ × 2^t — starting with 100 after 4 doublings: 100 × 2⁴ = 100 × 16 = 1600.
• Steps:
  • P = 500 × 2³.
  • 2³ = 8.
  • P = 500 × 8 = 4000.
• Answer: 4000

[Easy] Arithmetic Sequence

• EN: In the arithmetic sequence 5, 9, 13, 17, …, what is the 6th term?
• FR: Dans la suite arithmétique 5, 9, 13, 17, …, quel est le 6e terme?
• Choices: A) 21 B) 23 C) 25 D) 27
• Hint: Use the formula aₙ = a₁ + (n − 1)d — in a sequence starting at 3 with common difference 4, the 5th term is 3 + (5 − 1) × 4 = 19.
• Steps:
  • a₁ = 5, d = 4, n = 6.
  • a₆ = 5 + (6 − 1) × 4 = 5 + 20 = 25.
• Answer: 25

[Medium] Compound Interest

• EN: Nia invests $2000 at 5% interest compounded annually. What is the amount after 3 years?
• FR: Nia investit 2 000 $ à un taux d'intérêt de 5% composé annuellement. Quel est le montant après 3 ans?
• Choices: A) $2205.00 B) $2310.00 C) $2315.25 D) $2320.00
• Hint: Use A = P(1 + r)^n — for $1000 at 4% for 2 years: A = 1000 × (1.04)² = 1000 × 1.0816 = $1081.60.
• Steps:
  • A = 2000 × (1.05)³.
  • (1.05)³ = 1.157625.
  • A = 2000 × 1.157625 = $2315.25.
• Answer: $2315.25

[Medium] Trigonometric Identity

• EN: Which identity is correct?
• FR: Quelle identité est correcte?
• Choices: A) sin²θ + cos²θ = 2 B) sin²θ − cos²θ = 1 C) sin²θ + cos²θ = 1 D) sin²θ × cos²θ = 1
• Hint: The Pythagorean identity relates sine and cosine in every right triangle — think about what a² + b² = c² means when the hypotenuse is 1.
• Steps:
  • In a unit circle, the coordinates satisfy x² + y² = 1.
  • x = cosθ and y = sinθ, so cos²θ + sin²θ = 1.
  • This is the fundamental Pythagorean identity.
• Answer: sin²θ + cos²θ = 1

[Medium] Geometric Series

• EN: Find the sum of the first 5 terms of the geometric series: 2, 6, 18, 54, 162.
• FR: Trouve la somme des 5 premiers termes de la suite géométrique : 2, 6, 18, 54, 162.
• Choices: A) 222 B) 232 C) 242 D) 252
• Hint: Add all the given terms directly, or use Sₙ = a(rⁿ − 1)/(r − 1) — for 1, 2, 4, 8, 16 the sum is 31.
• Steps:
  • Sum = 2 + 6 + 18 + 54 + 162.
  • = 8 + 18 + 54 + 162.
  • = 26 + 54 + 162.
  • = 80 + 162 = 242.
• Answer: 242

[Medium] Logarithm Properties

• EN: Simplify: log₃(27) + log₃(9).
• FR: Simplifie : log₃(27) + log₃(9).
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Evaluate each logarithm separately then add — log₂(4) + log₂(8) = 2 + 3 = 5.
• Steps:
  • log₃(27) = 3 because 3³ = 27.
  • log₃(9) = 2 because 3² = 9.
  • Sum = 3 + 2 = 5.
• Answer: 5

[Hard] Annuity Calculation

• EN: Omar deposits $500 at the end of each year for 4 years at 6% interest compounded annually. Using the annuity formula, what is the future value? (Round to the nearest dollar.)
• FR: Omar dépose 500 $ à la fin de chaque année pendant 4 ans à 6% d'intérêt composé annuellement. En utilisant la formule d'annuité, quelle est la valeur future? (Arrondis au dollar près.)
• Choices: A) $2125 B) $2187 C) $2247 D) $2300
• Hint: FV of an ordinary annuity = PMT × [(1 + r)^n − 1] / r — for $200 per year at 5% for 3 years: 200 × [(1.05)³ − 1] / 0.05 ≈ $630.
• Steps:
  • FV = 500 × [(1.06)⁴ − 1] / 0.06.
  • (1.06)⁴ = 1.26248.
  • FV = 500 × [0.26248 / 0.06] = 500 × 4.3746 ≈ $2187.
• Answer: $2187

[Hard] Solving Exponential Equations Using Logarithms

• EN: Solve for x: 5^x = 125.
• FR: Résous pour x : 5^x = 125.
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Rewrite both sides with the same base if possible — 2^x = 32: rewrite 32 as 2⁵, so x = 5.
• Steps:
  • Rewrite 125 as a power of 5: 125 = 5³.
  • So 5^x = 5³.
  • Therefore x = 3.
• Answer: x = 3

[Easy] Permutations

• EN: In how many ways can 4 students be arranged in a row?
• FR: De combien de façons peut-on placer 4 élèves en rangée?
• Choices: A) 12 B) 16 C) 24 D) 32
• Hint: For n items in a row, the number of arrangements is n! — 3! = 3 × 2 × 1 = 6.
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 24.
• Answer: 24

[Easy] Derivative Introduction (Rate of Change)

• EN: The function f(x) = 3x² + 2. What is the derivative f'(x)?
• FR: La fonction f(x) = 3x² + 2. Quelle est la dérivée f'(x)?
• Choices: A) 3x B) 6x C) 6x + 2 D) 9x
• Hint: Use the power rule: d/dx[axⁿ] = naxⁿ⁻¹; the derivative of a constant is zero — d/dx[4x³ + 1] = 12x².
• Steps:
  • Derivative of 3x² = 2 × 3x¹ = 6x.
  • Derivative of 2 (constant) = 0.
  • f'(x) = 6x.
• Answer: 6x

[Easy] Combinations

• EN: A committee of 3 is to be chosen from 5 people. How many different committees are possible?
• FR: Un comité de 3 personnes doit être choisi parmi 5 personnes. Combien de comités différents sont possibles?
• Choices: A) 8 B) 10 C) 12 D) 15
• Hint: Use C(n, r) = n! / (r!(n − r)!) — C(4, 2) = 4! / (2! × 2!) = 24 / 4 = 6.
• Steps:
  • C(5, 3) = 5! / (3! × 2!) = 120 / (6 × 2) = 120 / 12 = 10.
• Answer: 10

[Easy] Polynomial Function

• EN: What is the degree of the polynomial 4x⁵ − 3x³ + 7x − 2?
• FR: Quel est le degré du polynôme 4x⁵ − 3x³ + 7x − 2?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: The degree of a polynomial is the highest exponent — in 6x⁴ + 2x² − 1, the degree is 4.
• Steps:
  • Look at each term's exponent: 5, 3, 1, 0.
  • The highest exponent is 5.
  • The degree is 5.
• Answer: 5

[Medium] Derivative Application

• EN: The position of a particle is given by s(t) = t³ − 6t² + 9t. Find the velocity v(t) = s'(t).
• FR: La position d'une particule est donnée par s(t) = t³ − 6t² + 9t. Trouve la vitesse v(t) = s'(t).
• Choices: A) 3t² − 12t + 9 B) 3t² − 6t + 9 C) 3t² + 12t − 9 D) t² − 12t + 9
• Hint: Differentiate each term using the power rule — d/dx[5x³ − 4x² + 2x] = 15x² − 8x + 2.
• Steps:
  • Derivative of t³ = 3t².
  • Derivative of −6t² = −12t.
  • Derivative of 9t = 9.
  • v(t) = 3t² − 12t + 9.
• Answer: 3t² − 12t + 9

[Medium] Normal Distribution

• EN: In a data set that is normally distributed with mean 50 and standard deviation 10, approximately what percent of values fall between 40 and 60?
• FR: Dans un ensemble de données normalement distribué avec une moyenne de 50 et un écart-type de 10, quel pourcentage approximatif des valeurs se situe entre 40 et 60?
• Choices: A) 50% B) 68% C) 75% D) 95%
• Hint: In a normal distribution, about 68% of data falls within one standard deviation of the mean — one SD above and one SD below covers the middle 68%.
• Steps:
  • 40 is one SD below the mean (50 − 10 = 40).
  • 60 is one SD above the mean (50 + 10 = 60).
  • Approximately 68% of values fall within one standard deviation.
• Answer: 68%

[Medium] Vector Addition

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

[Medium] Rational Function

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

[Hard] Binomial Probability

• EN: A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads? (Express as a fraction.)
• FR: Une pièce équilibrée est lancée 5 fois. Quelle est la probabilité d'obtenir exactement 3 faces? (Exprime sous forme de fraction.)
• Choices: A) 3/16 B) 5/16 C) 7/16 D) 9/16
• Hint: Use P = C(n, k) × p^k × (1 − p)^(n − k) — for n = 4, k = 2, p = 0.5: C(4,2) × (0.5)⁴ = 6 × 1/16 = 6/16.
• Steps:
  • C(5, 3) = 10.
  • P = 10 × (1/2)³ × (1/2)² = 10 × (1/32) = 10/32 = 5/16.
• Answer: 5/16

[Hard] Derivative to Find Maximum

• EN: Find the value of x that maximizes f(x) = −2x² + 8x + 3.
• FR: Trouve la valeur de x qui maximise f(x) = −2x² + 8x + 3.
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Take the derivative, set it equal to zero, and solve — for f(x) = −3x² + 12x + 1, f'(x) = −6x + 12 = 0, so x = 2.
• Steps:
  • f'(x) = −4x + 8.
  • Set f'(x) = 0: −4x + 8 = 0.
  • Solve: 4x = 8, x = 2.
• Answer: x = 2