Daily Math — 2026-09-09

[Easy] Counting Hockey Pucks

• EN: There are 7 hockey pucks on the ice. 3 more pucks slide in. How many pucks are there in total?
• FR: Il y a 7 rondelles de hockey sur la glace. 3 autres rondelles glissent sur la glace. Combien de rondelles y a-t-il en tout?
• Choices: A) 8 pucks B) 9 pucks C) 10 pucks D) 11 pucks
• Hint: To add, count on from the bigger number (e.g., 5 + 2 = 7).
• Steps:
  • Start at 7 and count on 3 more: 8, 9, 10.
  • So there are 10 pucks in total.
• Answer: 10 pucks

[Easy] Pennies in a Jar

• EN: Mia has 5 pennies. She finds 4 more pennies on the sidewalk. How many pennies does she have now?
• FR: Mia a 5 sous. Elle trouve 4 autres sous sur le trottoir. Combien de sous a-t-elle maintenant?
• Choices: A) 7 pennies B) 8 pennies C) 9 pennies D) 10 pennies
• Hint: Count on from the first number to add (e.g., 3 + 4: start at 3, count 4 more: 4, 5, 6, 7).
• Steps:
  • Start at 5 and count on 4: 6, 7, 8, 9.
  • So Mia has 9 pennies.
• Answer: 9 pennies

[Easy] Skip Counting by 2s

• EN: Liam counts by 2s: 2, 4, 6, 8, ___. What number comes next?
• FR: Liam compte par bonds de 2 : 2, 4, 6, 8, ___. Quel nombre vient ensuite?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When counting by 2s, add 2 to the last number (e.g., after 4 comes 6).
• Steps:
  • The pattern adds 2 each time: 2, 4, 6, 8, ...
  • 8 + 2 = 10, so the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 19?
• FR: Quel nombre est plus grand : 14 ou 19?
• Choices: A) 14 B) 19 C) Both are equal D) Neither
• Hint: When comparing two-digit numbers, look at the tens digit first (e.g., 13 vs. 17: both have 1 ten, so compare the ones: 7 > 3, so 17 is greater).
• Steps:
  • Both 14 and 19 have 1 ten.
  • Compare the ones: 9 > 4, so 19 is greater.
• Answer: 19

[Medium] Subtraction on the Rink

• EN: There are 15 players on the ice. 6 players skate off. How many players are left on the ice?
• FR: Il y a 15 joueurs sur la glace. 6 joueurs quittent la glace. Combien de joueurs restent sur la glace?
• Choices: A) 7 players B) 8 players C) 9 players D) 10 players
• Hint: To subtract, count back from the larger number (e.g., 12 − 4: count back 4 from 12: 11, 10, 9, 8).
• Steps:
  • Start at 15 and count back 6: 14, 13, 12, 11, 10, 9.
  • So 9 players are left on the ice.
• Answer: 9 players

[Medium] Skip Counting by 5s

• EN: Emma counts by 5s: 5, 10, 15, ___. What number comes next?
• FR: Emma compte par bonds de 5 : 5, 10, 15, ___. Quel nombre vient ensuite?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: When counting by 5s, add 5 to the last number (e.g., after 10 comes 15).
• Steps:
  • The pattern adds 5 each time: 5, 10, 15, ...
  • 15 + 5 = 20, so the next number is 20.
• Answer: 20

[Medium] Nickel Count

• EN: Noah has 3 nickels. How many cents does he have in total?
• FR: Noah a 3 pièces de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 18 cents
• Hint: A nickel is worth 5 cents — count by 5s (e.g., 2 nickels = 5, 10 = 10 cents).
• Steps:
  • Each nickel is worth 5 cents.
  • Count by 5s for 3 nickels: 5, 10, 15.
  • So Noah has 15 cents.
• Answer: 15 cents

[Medium] Adding with a Number Line

• EN: Zara starts at 11 on a number line and jumps 8 spaces to the right. Where does she land?
• FR: Zara commence au 11 sur une droite numérique et saute 8 espaces vers la droite. Où atterrit-elle?
• Choices: A) 17 B) 18 C) 19 D) 20
• Hint: Use a number line — start at your number and jump right to add (e.g., starting at 5 and jumping 6 lands on 11).
• Steps:
  • Start at 11.
  • Jump 8 spaces to the right: 12, 13, 14, 15, 16, 17, 18, 19.
  • Zara lands on 19.
• Answer: 19

[Hard] Adding Three Numbers

• EN: In gym class, Sam scored 6 points, then 5 points, then 4 points. How many points did Sam score in all?
• FR: En éducation physique, Sam a marqué 6 points, puis 5 points, puis 4 points. Combien de points Sam a-t-il marqués en tout?
• Choices: A) 13 points B) 14 points C) 15 points D) 16 points
• Hint: Add three numbers by combining two first, then adding the third (e.g., 3 + 4 + 5: add 3 + 4 = 7, then 7 + 5 = 12).
• Steps:
  • First add 6 + 5 = 11.
  • Then add 11 + 4 = 15.
  • So Sam scored 15 points in all.
• Answer: 15 points

[Hard] Subtraction Story

• EN: There are 18 mittens in a box. 9 mittens are taken out. How many mittens are still in the box?
• FR: Il y a 18 mitaines dans une boîte. 9 mitaines sont retirées. Combien de mitaines restent dans la boîte?
• Choices: A) 7 mittens B) 8 mittens C) 9 mittens D) 11 mittens
• Hint: Use doubles to help subtract (e.g., 16 − 8 = 8 because 8 + 8 = 16).
• Steps:
  • Think: 9 + ? = 18.
  • Since 9 + 9 = 18, the answer is 9.
  • So 9 mittens are still in the box.
• Answer: 9 mittens

[Easy] Adding Two-Digit Numbers

• EN: There are 23 students in one classroom and 14 students in another. How many students are there altogether?
• FR: Il y a 23 élèves dans une classe et 14 dans une autre. Combien d'élèves y a-t-il en tout?
• Choices: A) 35 students B) 37 students C) 38 students D) 39 students
• Hint: Add the tens first, then the ones (e.g., 32 + 15: 30 + 10 = 40, 2 + 5 = 7, so 47).
• Steps:
  • Add the tens: 20 + 10 = 30.
  • Add the ones: 3 + 4 = 7.
  • 30 + 7 = 37 students altogether.
• Answer: 37 students

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre l'aiguille des heures sur le 3 et l'aiguille des minutes sur le 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:30 C) 3:00 D) 12:15
• Hint: When the minute hand points to 12, it is exactly on the hour (e.g., hour hand on 5 = 5:00).
• Steps:
  • The minute hand on 12 means it is exactly on the hour.
  • The hour hand is on 3.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil measures 12 cm. A crayon measures 7 cm. How much longer is the pencil than the crayon?
• FR: Un crayon mesure 12 cm. Un crayon de couleur mesure 7 cm. De combien de cm 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 the difference in length, subtract the shorter from the longer (e.g., 15 cm − 9 cm = 6 cm).
• Steps:
  • Subtract: 12 − 7 = 5.
  • The pencil is 5 cm longer than the crayon.
• Answer: 5 cm

[Easy] Counting Coins

• EN: Olivia has 2 dimes and 1 nickel. How many cents does she have in total?
• FR: Olivia a 2 pièces de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 20 cents B) 22 cents C) 25 cents D) 30 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents — add them together (e.g., 1 dime + 1 nickel = 10 + 5 = 15 cents).
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • 1 nickel = 5 cents.
  • 20 + 5 = 25 cents in total.
• Answer: 25 cents

[Medium] Subtraction Within 100

• EN: A bag of Tim Hortons Timbits has 48 in it. The class eats 29 of them. How many Timbits are left?
• FR: Un sac de Timbits de Tim Hortons en contient 48. La classe en mange 29. Combien de Timbits reste-t-il?
• Choices: A) 17 Timbits B) 18 Timbits C) 19 Timbits D) 21 Timbits
• Hint: Subtract by breaking the number apart (e.g., 55 − 27: subtract 20 to get 35, then subtract 7 to get 28).
• Steps:
  • Subtract 20 from 48: 48 − 20 = 28.
  • Subtract 9 more: 28 − 9 = 19.
  • So 19 Timbits are left.
• Answer: 19 Timbits

[Medium] Telling Time to the Half-Hour

• EN: It is 7:00 in the morning. School starts in half an hour. What time does school start?
• FR: Il est 7 h du matin. L'école commence dans une demi-heure. À quelle heure l'école commence-t-elle?
• Choices: A) 7:15 B) 7:30 C) 7:45 D) 8:00
• Hint: Half an hour after the hour means 30 minutes past (e.g., half an hour after 9:00 is 9:30).
• Steps:
  • 7:00 + 30 minutes = 7:30.
  • School starts at 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: What is the missing number in this pattern: 10, 20, 30, ___, 50?
• FR: Quel est le nombre manquant dans ce modèle : 10, 20, 30, ___, 50?
• Choices: A) 35 B) 38 C) 40 D) 45
• Hint: Find the rule by looking at what is added each time (e.g., 4, 8, 12, ___: add 4 each time, so next is 16).
• Steps:
  • The pattern adds 10 each time: 10, 20, 30, ...
  • 30 + 10 = 40.
  • The missing number is 40.
• Answer: 40

[Medium] Adding Money

• EN: Kai has 35 cents in his piggy bank and earns 40 cents more helping at home. How much money does he have now?
• FR: Kai a 35 cents dans sa tirelire et gagne 40 cents de plus en aidant à la maison. Combien d'argent a-t-il maintenant?
• Choices: A) 65 cents B) 70 cents C) 75 cents D) 80 cents
• Hint: Add tens first, then ones (e.g., 25 + 30 = 55, then 55 + 5 = 60, so 25 + 35 = 60).
• Steps:
  • Add the tens: 30 + 40 = 70.
  • Add the ones: 5 + 0 = 5.
  • 70 + 5 = 75 cents in total.
• Answer: 75 cents

[Hard] Two-Step Problem

• EN: There are 60 books on a shelf. A librarian adds 15 books, then removes 28 books. How many books are on the shelf now?
• FR: Il y a 60 livres sur une étagère. Une bibliothécaire ajoute 15 livres, puis en retire 28. Combien de livres y a-t-il maintenant sur l'étagère?
• Choices: A) 45 books B) 47 books C) 48 books D) 53 books
• Hint: Do two steps in order — add first, then subtract (e.g., 50 + 10 = 60, then 60 − 15 = 45).
• Steps:
  • First add: 60 + 15 = 75 books.
  • Then subtract: 75 − 28 = 47 books.
  • So there are 47 books on the shelf now.
• Answer: 47 books

[Hard] Measuring and Comparing

• EN: Sofia's ribbon is 85 cm long. She cuts off 38 cm. How long is the ribbon now?
• FR: Le ruban de Sofia mesure 85 cm de long. Elle en coupe 38 cm. Quelle est maintenant la longueur du ruban?
• Choices: A) 44 cm B) 46 cm C) 47 cm D) 48 cm
• Hint: Subtract by breaking apart the number being subtracted (e.g., 73 − 25: take away 20 to get 53, then take away 5 to get 48).
• Steps:
  • Subtract 30 from 85: 85 − 30 = 55.
  • Subtract 8 more: 55 − 8 = 47.
  • The ribbon is now 47 cm long.
• Answer: 47 cm

[Easy] Multiplication by 2

• EN: There are 6 pairs of mittens in the lost-and-found. How many mittens are there in total?
• FR: Il y a 6 paires de mitaines dans les objets trouvés. Combien de mitaines y a-t-il en tout?
• Choices: A) 8 mittens B) 10 mittens C) 12 mittens D) 14 mittens
• Hint: Multiplying by 2 means adding the number to itself (e.g., 4 × 2 = 4 + 4 = 8).
• Steps:
  • Each pair has 2 mittens.
  • 6 × 2 = 12.
  • There are 12 mittens in total.
• Answer: 12 mittens

[Easy] Understanding Fractions

• EN: A pizza is cut into 4 equal slices. Jayden eats 1 slice. What fraction of the pizza did Jayden eat?
• FR: Une pizza est coupée en 4 tranches égales. Jayden mange 1 tranche. Quelle fraction de la pizza Jayden a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: A fraction shows parts out of the total — the top number is parts eaten and the bottom is total parts (e.g., eating 1 of 3 pieces = 1/3).
• Steps:
  • The pizza has 4 equal slices total.
  • Jayden ate 1 slice.
  • So he ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Skip Counting by 5s

• EN: There are 5 students in each row and 4 rows of seats. How many students are there in all?
• FR: Il y a 5 élèves dans chaque rangée et 4 rangées de sièges. Combien d'élèves y a-t-il en tout?
• Choices: A) 15 students B) 18 students C) 20 students D) 24 students
• Hint: Multiply to find the total in equal groups (e.g., 5 groups of 3 = 5 × 3 = 15).
• Steps:
  • Multiply the rows by the students per row: 4 × 5 = 20.
  • There are 20 students in all.
• Answer: 20 students

[Easy] Reading a Graph

• EN: A bar graph shows that 8 students chose hockey, 5 chose soccer, and 3 chose basketball as their favourite sport. How many students answered the survey in total?
• FR: Un diagramme à bandes montre que 8 élèves ont choisi le hockey, 5 le soccer et 3 le basketball comme sport préféré. Combien d'élèves ont répondu au sondage en tout?
• Choices: A) 13 students B) 14 students C) 16 students D) 17 students
• Hint: To find the total, add all the values together (e.g., 4 + 3 + 6 = 13).
• Steps:
  • Add all sports: 8 + 5 + 3.
  • 8 + 5 = 13, then 13 + 3 = 16.
  • So 16 students answered the survey.
• Answer: 16 students

[Medium] Multiplication by 4

• EN: Each student needs 4 coloured pencils for an art project. There are 7 students in the group. How many coloured pencils are needed in total?
• FR: Chaque élève a besoin de 4 crayons de couleur pour un projet d'art. Il y a 7 élèves dans le groupe. Combien de crayons de couleur sont nécessaires en tout?
• Choices: A) 24 pencils B) 26 pencils C) 28 pencils D) 32 pencils
• Hint: Use skip counting by 4s to find the product (e.g., 4 × 6: 4, 8, 12, 16, 20, 24 = 24).
• Steps:
  • Multiply: 7 × 4 = 28.
  • So 28 coloured pencils are needed.
• Answer: 28 pencils

[Medium] Basic Division

• EN: There are 24 apples to be shared equally among 3 baskets. How many apples go in each basket?
• FR: Il y a 24 pommes à partager également dans 3 paniers. Combien de pommes va dans chaque panier?
• Choices: A) 6 apples B) 7 apples C) 8 apples D) 9 apples
• Hint: Division is the opposite of multiplication — think "what times 3 equals my total?" (e.g., 15 ÷ 3: 3 × 5 = 15, so the answer is 5).
• Steps:
  • Think: 3 × ? = 24.
  • 3 × 8 = 24, so 24 ÷ 3 = 8.
  • Each basket gets 8 apples.
• Answer: 8 apples

[Medium] Perimeter of a Rectangle

• EN: A rectangular garden has a length of 9 m and a width of 5 m. What is the perimeter of the garden?
• FR: Un jardin rectangulaire a une longueur de 9 m et une largeur de 5 m. Quel est le périmètre du jardin?
• Choices: A) 14 m B) 26 m C) 28 m D) 45 m
• Hint: Perimeter of a rectangle = add all four sides (e.g., length 6 m and width 3 m: 6 + 3 + 6 + 3 = 18 m).
• Steps:
  • Add all four sides: 9 + 5 + 9 + 5.
  • 9 + 9 = 18 and 5 + 5 = 10.
  • 18 + 10 = 28 m.
• Answer: 28 m

[Medium] Multiplication by 10

• EN: A hockey team has 10 players. There are 5 teams in the tournament. How many players are there altogether?
• FR: Une équipe de hockey a 10 joueurs. Il y a 5 équipes dans le tournoi. Combien de joueurs y a-t-il en tout?
• Choices: A) 40 players B) 45 players C) 50 players D) 55 players
• Hint: Multiplying by 10 just adds a zero to the end of the number (e.g., 7 × 10 = 70).
• Steps:
  • 5 × 10 = 50.
  • There are 50 players altogether.
• Answer: 50 players

[Hard] Fractions of a Set

• EN: There are 12 snowflakes drawn on a poster. One-third of them are blue. How many snowflakes are blue?
• FR: Il y a 12 flocons de neige dessinés sur une affiche. Le tiers d'entre eux sont bleus. Combien de flocons de neige sont bleus?
• Choices: A) 3 snowflakes B) 4 snowflakes C) 6 snowflakes D) 8 snowflakes
• Hint: To find a fraction of a set, divide the total by the denominator (e.g., 1/4 of 16: 16 ÷ 4 = 4).
• Steps:
  • To find 1/3 of 12, divide by 3: 12 ÷ 3 = 4.
  • So 4 snowflakes are blue.
• Answer: 4 snowflakes

[Hard] Two-Step Multiplication

• EN: A baker makes 5 trays of muffins. Each tray has 9 muffins. She sells 18 muffins. How many muffins does she have left?
• FR: Une boulangère fait 5 plateaux de muffins. Chaque plateau a 9 muffins. Elle vend 18 muffins. Combien de muffins lui reste-t-il?
• Choices: A) 25 muffins B) 27 muffins C) 29 muffins D) 32 muffins
• Hint: First multiply to find the total, then subtract what was sold (e.g., 3 trays of 7 = 21, then 21 − 6 = 15).
• Steps:
  • First find the total: 5 × 9 = 45 muffins.
  • Then subtract what was sold: 45 − 18 = 27 muffins.
  • She has 27 muffins left.
• Answer: 27 muffins

[Easy] Multiplication Facts

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Use a known fact to help (e.g., 7 × 7 = 49, so 7 × 8 = 49 + 7 = 56).
• Steps:
  • Think of 7 × 8 as 7 groups of 8.
  • 7 × 8 = 56.
  • The answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 40 ones
• Hint: In a decimal, the first digit after the point is tenths, and the second is hundredths (e.g., in 5.62, the 6 is in the tenths place).
• Steps:
  • In 3.47: 3 is ones, 4 is tenths, 7 is hundredths.
  • The digit 4 is in the tenths place.
  • Its value is 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A rectangular card has a length of 8 cm and a width of 5 cm. What is its area?
• FR: Une carte rectangulaire a une longueur de 8 cm et une largeur de 5 cm. Quelle est son aire?
• Choices: A) 26 cm² B) 35 cm² C) 40 cm² D) 45 cm²
• Hint: Area of a rectangle = length × width (e.g., 6 cm × 4 cm = 24 cm²).
• Steps:
  • Area = length × width.
  • Area = 8 × 5 = 40 cm².
  • The area of the card is 40 cm².
• Answer: 40 cm²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/4?
• FR: Quelle fraction est plus grande : 3/4 ou 2/4?
• Choices: A) 2/4 B) 3/4 C) Both are equal D) Cannot be compared
• Hint: When fractions have the same denominator, compare the numerators (e.g., 5/8 > 3/8 because 5 > 3).
• Steps:
  • Both fractions have the same denominator (4).
  • Compare the numerators: 3 > 2.
  • So 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainder

• EN: A farmer has 47 carrots to pack into bags of 5. How many full bags can he fill, and how many carrots are left over?
• FR: Un fermier a 47 carottes à mettre dans des sacs de 5. Combien de sacs complets peut-il remplir, et combien de carottes lui reste-t-il?
• Choices: A) 8 bags, remainder 5 B) 9 bags, remainder 2 C) 9 bags, remainder 5 D) 10 bags, remainder 2
• Hint: Divide and check the remainder by multiplying back (e.g., 38 ÷ 4: 4 × 9 = 36, remainder 38 − 36 = 2, so 9 remainder 2).
• Steps:
  • 5 × 9 = 45, which is the largest multiple of 5 not exceeding 47.
  • 47 − 45 = 2 remaining.
  • So 9 full bags with 2 carrots left over.
• Answer: 9 bags, remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 2:15 p.m. and ends at 4:45 p.m. How long does the game last?
• 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) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours 15 minutes
• Hint: Count up from the start time to the end time (e.g., from 1:20 to 3:50 — from 1:20 to 3:20 is 2 hours, plus 30 more minutes = 2 hours 30 minutes).
• Steps:
  • From 2:15 to 4:15 is 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: A notebook costs $2.75 and a pen costs $1.40. What is the total cost?
• FR: Un cahier coûte 2,75 $ et un stylo coûte 1,40 $. Quel est le coût total?
• Choices: A) $3.95 B) $4.05 C) $4.15 D) $4.25
• Hint: Line up the decimal points and add like regular numbers (e.g., $3.25 + $1.60: 3.25 + 1.60 = 4.85).
• Steps:
  • Add: $2.75 + $1.40.
  • 2 + 1 = 3, 0.75 + 0.40 = 1.15.
  • 3 + 1.15 = $4.15.
• Answer: $4.15

[Medium] Multiplication: 2-digit by 1-digit

• EN: A school orders 6 boxes of markers. Each box has 24 markers. How many markers are ordered in all?
• FR: Une école commande 6 boîtes de marqueurs. Chaque boîte contient 24 marqueurs. Combien de marqueurs sont commandés en tout?
• Choices: A) 124 markers B) 134 markers C) 140 markers D) 144 markers
• Hint: Multiply by breaking apart the tens and ones (e.g., 5 × 32: 5 × 30 = 150, 5 × 2 = 10, total = 160).
• Steps:
  • 6 × 24: Multiply 6 × 20 = 120.
  • Then 6 × 4 = 24.
  • 120 + 24 = 144 markers.
• Answer: 144 markers

[Hard] Multi-Step Word Problem

• EN: Maya has $10.00. She buys a snack for $3.75 and a drink for $2.50. How much money does she have left?
• FR: Maya a 10,00 $. Elle achète une collation pour 3,75 $ et une boisson pour 2,50 $. Combien d'argent lui reste-t-il?
• Choices: A) $3.25 B) $3.75 C) $4.25 D) $5.75
• Hint: First add the two prices together, then subtract from the starting amount (e.g., $8.00 − $2.25 − $1.50 = $8.00 − $3.75 = $4.25).
• Steps:
  • Add the costs: $3.75 + $2.50 = $6.25.
  • Subtract from $10.00: $10.00 − $6.25 = $3.75.
  • Maya has $3.75 left.
• Answer: $3.75

[Hard] Fractions on a Number Line

• EN: On a number line from 0 to 1, what fraction is exactly halfway between 1/4 and 3/4?
• FR: Sur une droite numérique de 0 à 1, quelle fraction se trouve exactement à mi-chemin entre 1/4 et 3/4?
• Choices: A) 1/4 B) 2/4 C) 3/8 D) 5/8
• Hint: The midpoint between two fractions with the same denominator is the fraction with the numerator halfway between the two numerators (e.g., halfway between 1/6 and 5/6 is 3/6).
• Steps:
  • The numerators are 1 and 3 (both with denominator 4).
  • Halfway between 1 and 3 is 2.
  • So the midpoint is 2/4.
• Answer: 2/4

[Easy] Multi-Digit Multiplication

• EN: A store sells 124 packs of hockey cards. Each pack has 6 cards. How many cards are sold in total?
• FR: Un magasin vend 124 paquets de cartes de hockey. Chaque paquet contient 6 cartes. Combien de cartes sont vendues en tout?
• Choices: A) 724 cards B) 734 cards C) 744 cards D) 764 cards
• Hint: Multiply each digit by 6, starting from the ones place (e.g., 132 × 4: 4 × 2 = 8, 4 × 30 = 120, 4 × 100 = 400; total = 528).
• Steps:
  • 6 × 4 = 24, write 4 carry 2.
  • 6 × 20 = 120, plus 2 = 122, write 2 carry 12.
  • 6 × 100 = 600, plus 12 = 612... Wait: 6 × 124 = 6 × 100 + 6 × 24 = 600 + 144 = 744.
  • So 744 cards are sold in total.
• Answer: 744 cards

[Easy] Adding Fractions with Like Denominators

• EN: Ava ate 2/8 of a pie and her brother ate 3/8 of the same pie. How much of the pie did they eat altogether?
• FR: Ava a mangé 2/8 d'une tarte et son frère en a mangé 3/8. Quelle fraction de la tarte ont-ils mangée en tout?
• Choices: A) 5/16 B) 5/8 C) 6/8 D) 1/8
• Hint: When the denominators are the same, just add the numerators and keep the denominator (e.g., 1/5 + 3/5 = 4/5).
• Steps:
  • Add the numerators: 2 + 3 = 5.
  • Keep the denominator: 8.
  • They ate 5/8 of the pie altogether.
• Answer: 5/8

[Easy] Decimal Operations

• EN: A ribbon is 4.35 m long. Another ribbon is 2.20 m long. What is the total length of both ribbons?
• FR: Un ruban mesure 4,35 m de long. Un autre ruban mesure 2,20 m de long. Quelle est la longueur totale des deux rubans?
• Choices: A) 6.35 m B) 6.45 m C) 6.55 m D) 6.65 m
• Hint: Line up the decimal points and add column by column (e.g., 3.12 + 1.45 = 4.57).
• Steps:
  • Add: 4.35 + 2.20.
  • 0.35 + 0.20 = 0.55.
  • 4 + 2 = 6, so total = 6.55 m.
• Answer: 6.55 m

[Easy] Percentage Introduction (50%)

• EN: A bag has 20 marbles. 50% of the marbles are red. How many marbles are red?
• FR: Un sac contient 20 billes. 50 % des billes sont rouges. Combien de billes sont rouges?
• Choices: A) 5 marbles B) 8 marbles C) 10 marbles D) 15 marbles
• Hint: 50% means half, so divide the total by 2 (e.g., 50% of 24 = 24 ÷ 2 = 12).
• Steps:
  • 50% means one half.
  • 20 ÷ 2 = 10.
  • So 10 marbles are red.
• Answer: 10 marbles

[Medium] Multi-Digit Division

• EN: A school bus travels 312 km over 4 days, covering the same distance each day. How far does the bus travel each day?
• FR: Un autobus scolaire parcourt 312 km en 4 jours, en couvrant la même distance chaque jour. Quelle distance l'autobus parcourt-il chaque jour?
• Choices: A) 68 km B) 72 km C) 78 km D) 82 km
• Hint: Divide the hundreds first, then the remaining tens and ones (e.g., 248 ÷ 4: 200 ÷ 4 = 50, 48 ÷ 4 = 12, so 62).
• Steps:
  • 300 ÷ 4 = 75.
  • 12 ÷ 4 = 3.
  • 75 + 3 = 78 km per day.
• Answer: 78 km

[Medium] Subtracting Fractions

• EN: A water bottle was 7/9 full. After a hike, it was 2/9 full. How much water was used?
• FR: Une bouteille d'eau était remplie aux 7/9. Après une randonnée, elle était remplie aux 2/9. Quelle fraction de l'eau a été utilisée?
• Choices: A) 4/9 B) 5/9 C) 6/9 D) 9/9
• Hint: When denominators are the same, subtract the numerators and keep the denominator (e.g., 6/7 − 2/7 = 4/7).
• Steps:
  • Subtract the numerators: 7 − 2 = 5.
  • Keep the denominator: 9.
  • So 5/9 of the water was used.
• Answer: 5/9

[Medium] Volume of a Rectangular Prism

• EN: A rectangular fish tank is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Un aquarium rectangulaire mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume = length × width × height (e.g., 6 × 3 × 2 = 36 cm³).
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20.
  • 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage (25%)

• EN: A jacket originally costs $80. It is on sale for 25% off. How much money is saved?
• FR: Un manteau coûte originalement 80 $. Il est en vente avec 25 % de rabais. Combien d'argent est économisé?
• Choices: A) $15 B) $20 C) $25 D) $30
• Hint: 25% is one quarter — divide the amount by 4 (e.g., 25% of $60 = $60 ÷ 4 = $15).
• Steps:
  • 25% = one quarter.
  • $80 ÷ 4 = $20.
  • So $20 is saved.
• Answer: $20

[Hard] Multi-Step Fraction Problem

• EN: A recipe needs 3/6 cup of sugar. Lucas wants to make 3 batches. How many cups of sugar does he need in total?
• FR: Une recette nécessite 3/6 de tasse de sucre. Lucas veut faire 3 recettes. De combien de tasses de sucre a-t-il besoin en tout?
• Choices: A) 1 cup B) 1 and 1/2 cups C) 2 cups D) 9/6 cups
• Hint: Multiply the fraction by the whole number — multiply the numerator only (e.g., 2/5 × 3 = 6/5 = 1 and 1/5).
• Steps:
  • 3/6 × 3 = 9/6.
  • Simplify: 9/6 = 1 and 3/6 = 1 and 1/2 cups.
  • Lucas needs 1 and 1/2 cups of sugar.
• Answer: 1 and 1/2 cups

[Hard] Multi-Step Decimal Problem

• EN: Priya earns $12.50 per hour shovelling snow. She works for 6 hours on Saturday and 4 hours on Sunday. How much does she earn in total?
• FR: Priya gagne 12,50 $ de l'heure en pelletant la neige. Elle travaille 6 heures le samedi et 4 heures le dimanche. Combien gagne-t-elle en tout?
• Choices: A) $100.00 B) $112.50 C) $125.00 D) $137.50
• Hint: Find total hours first, then multiply by the hourly rate (e.g., 3 + 5 = 8 hours at $9.50 per hour: 8 × $9.50 = $76.00).
• Steps:
  • Total hours: 6 + 4 = 10 hours.
  • Total earnings: 10 × $12.50 = $125.00.
  • Priya earns $125.00 in total.
• Answer: $125.00

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien représente 30 % de 200?
• Choices: A) 30 B) 50 C) 60 D) 80
• Hint: To find a percent of a number, multiply by the percent and divide by 100 (e.g., 20% of 150 = 150 × 20 ÷ 100 = 30).
• Steps:
  • 30% of 200 = 200 × 30 ÷ 100.
  • 200 × 30 = 6000.
  • 6000 ÷ 100 = 60.
• Answer: 60

[Easy] Simple Algebraic Expression

• EN: Evaluate 3n + 5 when n = 4.
• FR: Évalue 3n + 5 quand n = 4.
• Choices: A) 12 B) 15 C) 17 D) 21
• Hint: Substitute the value for the variable, then follow order of operations (e.g., 2x + 3 when x = 5: 2 × 5 + 3 = 10 + 3 = 13).
• Steps:
  • Substitute n = 4: 3(4) + 5.
  • 3 × 4 = 12.
  • 12 + 5 = 17.
• Answer: 17

[Easy] Ratio

• EN: In a class, there are 12 boys and 16 girls. What is the ratio of boys to girls?
• FR: Dans une classe, il y a 12 garçons et 16 filles. Quel est le rapport garçons-filles?
• Choices: A) 3 : 4 B) 4 : 3 C) 2 : 3 D) 3 : 5
• Hint: To simplify a ratio, divide both numbers by their greatest common factor (e.g., 6 : 9 ÷ 3 = 2 : 3).
• Steps:
  • Ratio of boys to girls is 12 : 16.
  • GCF of 12 and 16 is 4.
  • 12 ÷ 4 = 3, 16 ÷ 4 = 4, so the ratio is 3 : 4.
• Answer: 3 : 4

[Easy] Introduction to Integers

• EN: The temperature in Winnipeg is −8°C in the morning. It rises 5°C by noon. What is the temperature at noon?
• FR: La température à Winnipeg est de −8 °C le matin. Elle monte de 5 °C à midi. Quelle est la température à midi?
• Choices: A) −4°C B) −3°C C) 3°C D) 13°C
• Hint: Adding a positive to a negative moves right on the number line (e.g., −6 + 4 = −2).
• Steps:
  • Start at −8 and add 5.
  • −8 + 5 = −3.
  • The temperature at noon is −3°C.
• Answer: −3°C

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 4 + 3 × (8 − 2) ÷ 2.
• FR: Évalue : 4 + 3 × (8 − 2) ÷ 2.
• Choices: A) 11 B) 13 C) 17 D) 21
• Hint: Use BEDMAS — Brackets, Exponents, Division, Multiplication, Addition, Subtraction (e.g., 2 + 4 × (5 − 1) ÷ 2: brackets first: 4, then 4 × 4 = 16, then 16 ÷ 2 = 8, then 2 + 8 = 10).
• Steps:
  • Brackets: 8 − 2 = 6.
  • Multiplication: 3 × 6 = 18.
  • Division: 18 ÷ 2 = 9.
  • Addition: 4 + 9 = 13.
• Answer: 13

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien fait 2/3 × 3/4?
• Choices: A) 5/7 B) 6/12 C) 1/2 D) 2/7
• Hint: Multiply the numerators together and the denominators together (e.g., 1/2 × 2/5 = 2/10 = 1/5).
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Unit Rate

• EN: A car travels 240 km in 3 hours. What is the car's speed in km per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est la vitesse de la voiture en km/h?
• Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: To find a unit rate, divide the total by the number of units (e.g., $15 for 3 items = $15 ÷ 3 = $5 per item).
• Steps:
  • Divide the total distance by hours: 240 ÷ 3 = 80.
  • The speed is 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: How many 1/4-cup servings are in 3 cups of juice?
• FR: Combien de portions de 1/4 de tasse y a-t-il dans 3 tasses de jus?
• Choices: A) 8 servings B) 10 servings C) 12 servings D) 16 servings
• Hint: Dividing by a fraction means multiplying by its reciprocal (e.g., 2 ÷ 1/3 = 2 × 3 = 6).
• Steps:
  • 3 ÷ 1/4 = 3 × 4 = 12.
  • There are 12 servings.
• Answer: 12 servings

[Hard] Multi-Step Percent

• EN: A winter coat costs $120. The store offers a 15% discount. What is the sale price of the coat?
• FR: Un manteau d'hiver coûte 120 $. Le magasin offre un rabais de 15 %. Quel est le prix de vente du manteau?
• Choices: A) $100.00 B) $102.00 C) $105.00 D) $108.00
• Hint: Find the discount amount first by multiplying the price by the percent, then subtract from the original (e.g., 10% of $80 = $8, so sale price = $80 − $8 = $72).
• Steps:
  • 15% of $120 = 120 × 15 ÷ 100 = $18.
  • Sale price = $120 − $18 = $102.
  • The sale price is $102.00.
• Answer: $102.00

[Hard] Algebraic Expression and Substitution

• EN: The expression 5x − 2y + 3 gives the score in a game. What is the score when x = 4 and y = 3?
• FR: L'expression 5x − 2y + 3 donne le score dans un jeu. Quel est le score quand x = 4 et y = 3?
• Choices: A) 15 B) 17 C) 19 D) 23
• Hint: Substitute each variable with its value and then simplify using order of operations (e.g., 3a + 2b when a = 2, b = 4: 3×2 + 2×4 = 6 + 8 = 14).
• Steps:
  • Substitute x = 4 and y = 3: 5(4) − 2(3) + 3.
  • 5 × 4 = 20, 2 × 3 = 6.
  • 20 − 6 + 3 = 17.
• Answer: 17

[Easy] Integer Addition

• EN: What is −9 + 15?
• FR: Combien fait −9 + 15?
• Choices: A) −6 B) 4 C) 6 D) 24
• Hint: When adding a larger positive to a negative, subtract the smaller absolute value from the larger (e.g., −5 + 11: 11 − 5 = 6, and the answer is positive because 11 > 5).
• Steps:
  • |15| > |−9|, so the result is positive.
  • 15 − 9 = 6.
  • −9 + 15 = 6.
• Answer: 6

[Easy] Calculating a Discount

• EN: A pair of skates costs $90. They are on sale for 20% off. What is the discount amount?
• FR: Une paire de patins coûte 90 $. Ils sont en vente avec 20 % de rabais. Quel est le montant de la réduction?
• Choices: A) $14 B) $16 C) $18 D) $20
• Hint: To find 20% of an amount, multiply by 0.20 or find 10% and double it (e.g., 10% of $50 = $5, so 20% = $10).
• Steps:
  • 10% of $90 = $9.
  • 20% = $9 × 2 = $18.
  • The discount is $18.
• Answer: $18

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 13 = 20.
• FR: Résous pour x : x + 13 = 20.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: To solve, subtract the number being added from both sides (e.g., x + 8 = 15: x = 15 − 8 = 7).
• Steps:
  • Subtract 13 from both sides: x = 20 − 13.
  • x = 7.
  • The solution is x = 7.
• Answer: x = 7

[Easy] Probability

• EN: A bag contains 3 red marbles and 7 blue marbles. What is the probability of picking a red marble?
• FR: Un sac contient 3 billes rouges et 7 billes bleues. Quelle est la probabilité de piger une bille rouge?
• Choices: A) 3/7 B) 3/10 C) 7/10 D) 1/3
• Hint: Probability = favourable outcomes ÷ total outcomes (e.g., 2 green out of 8 total = 2/8 = 1/4).
• Steps:
  • Total marbles: 3 + 7 = 10.
  • Favourable outcomes (red): 3.
  • Probability = 3/10.
• Answer: 3/10

[Medium] Integer Multiplication

• EN: What is (−6) × (−7)?
• FR: Combien fait (−6) × (−7)?
• Choices: A) −42 B) −13 C) 13 D) 42
• Hint: A negative times a negative always gives a positive (e.g., (−4) × (−5) = 20).
• Steps:
  • Multiply the absolute values: 6 × 7 = 42.
  • Negative × Negative = Positive.
  • (−6) × (−7) = 42.
• Answer: 42

[Medium] Calculating Tax

• EN: A book costs $18.00. A sales tax of 13% is added. What is the total price including tax?
• FR: Un livre coûte 18,00 $. Une taxe de vente de 13 % est ajoutée. Quel est le prix total taxes incluses?
• Choices: A) $19.34 B) $20.34 C) $20.94 D) $21.34
• Hint: Find the tax by multiplying the price by the tax rate, then add it to the original price (e.g., $20 × 13% = $2.60, so total = $22.60).
• Steps:
  • Tax = $18.00 × 0.13 = $2.34.
  • Total = $18.00 + $2.34 = $20.34.
  • The total price is $20.34.
• Answer: $20.34

[Medium] Surface Area of a Rectangular Prism

• EN: A rectangular box is 5 cm long, 3 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 5 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire totale?
• Choices: A) 52 cm² B) 60 cm² C) 62 cm² D) 64 cm²
• Hint: Surface area = 2(lw + lh + wh) — find the area of each pair of faces and double them (e.g., box 4×3×2: 2(12 + 8 + 6) = 2(26) = 52 cm²).
• Steps:
  • lw = 5 × 3 = 15, lh = 5 × 2 = 10, wh = 3 × 2 = 6.
  • Sum: 15 + 10 + 6 = 31.
  • Surface area = 2 × 31 = 62 cm².
• Answer: 62 cm²

[Medium] Fraction and Decimal Fluency

• EN: Write 7/20 as a decimal.
• FR: Écris 7/20 sous forme décimale.
• Choices: A) 0.7 B) 0.35 C) 0.07 D) 3.5
• Hint: To convert a fraction to a decimal, divide the numerator by the denominator (e.g., 3/4 = 3 ÷ 4 = 0.75).
• Steps:
  • Divide 7 by 20: 7 ÷ 20.
  • 7 ÷ 20 = 0.35.
  • So 7/20 = 0.35.
• Answer: 0.35

[Hard] Integer Division and Multi-Step

• EN: The temperature in Yellowknife dropped 4°C every hour for 6 hours, starting at 3°C. What was the temperature after 6 hours?
• FR: La température à Yellowknife a baissé de 4 °C chaque heure pendant 6 heures, en commençant à 3 °C. Quelle était la température après 6 heures?
• Choices: A) −21°C B) −24°C C) −27°C D) −33°C
• Hint: Find the total change by multiplying the drop per hour by the number of hours, then add to the start (e.g., drops 3°C per hour for 5 hours from 10°C: total drop = −15, so 10 + (−15) = −5°C).
• Steps:
  • Total drop: 4 × 6 = 24°C.
  • New temperature: 3 + (−24) = 3 − 24 = −21°C.
  • The temperature after 6 hours is −21°C.
• Answer: −21°C

[Hard] Tip and Total Cost

• EN: A family's restaurant bill is $65.00. They want to leave a 15% tip. What is the total amount they will pay including the tip?
• FR: La facture d'un restaurant pour une famille est de 65,00 $. Ils veulent laisser un pourboire de 15 %. Quel est le montant total qu'ils paieront, pourboire inclus?
• Choices: A) $73.75 B) $74.75 C) $75.25 D) $77.50
• Hint: Calculate the tip by multiplying the bill by 0.15, then add it to the bill (e.g., $40 × 0.15 = $6, total = $46).
• Steps:
  • Tip = $65.00 × 0.15 = $9.75.
  • Total = $65.00 + $9.75 = $74.75.
  • The total amount is $74.75.
• Answer: $74.75

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: A perfect square is a number times itself — think "what number multiplied by itself equals this?" (e.g., √81: 9 × 9 = 81, so √81 = 9).
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored 72, 85, 68, 90, and 75 on a test. What is the mean (average) score?
• FR: Cinq élèves ont obtenu 72, 85, 68, 90 et 75 à un test. Quelle est la moyenne des notes?
• Choices: A) 76 B) 78 C) 80 D) 82
• Hint: To find the mean, add all values and divide by the number of values (e.g., mean of 4, 8, 6 = 18 ÷ 3 = 6).
• Steps:
  • Sum: 72 + 85 + 68 + 90 + 75 = 390.
  • Divide by 5: 390 ÷ 5 = 78.
  • The mean score is 78.
• Answer: 78

[Easy] Percent Increase

• EN: A plant was 40 cm tall. It grew to 50 cm. What is the percent increase in the plant's height?
• FR: Une plante mesurait 40 cm de haut. Elle a poussé jusqu'à 50 cm. Quel est le pourcentage d'augmentation de la hauteur de la plante?
• Choices: A) 10% B) 20% C) 25% D) 40%
• Hint: Percent increase = (change ÷ original) × 100 (e.g., from 20 to 25: change = 5, 5 ÷ 20 × 100 = 25%).
• Steps:
  • Change = 50 − 40 = 10 cm.
  • Percent increase = (10 ÷ 40) × 100 = 25%.
  • The plant grew by 25%.
• Answer: 25%

[Easy] 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 = 7
• Hint: Add to both sides first to undo subtraction, then divide (e.g., 2x − 3 = 7: add 3 to get 2x = 10, then divide by 2: x = 5).
• Steps:
  • Add 4 to both sides: 3x = 11 + 4 = 15.
  • Divide both sides by 3: x = 15 ÷ 3 = 5.
  • The solution is x = 5.
• Answer: x = 5

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of length 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des côtés de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: Use a² + b² = c², where c is the hypotenuse (e.g., legs 3 and 4: 9 + 16 = 25, √25 = 5, so hypotenuse = 5).
• Steps:
  • a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10.
  • The hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through the points (2, 3) and (6, 11). What is the slope of the line?
• FR: Une droite passe par les points (2, 3) et (6, 11). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., from (1, 2) to (4, 8): (8−2)÷(4−1) = 6÷3 = 2).
• Steps:
  • Rise = 11 − 3 = 8.
  • Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median

• EN: The snowfall amounts (in cm) for one week were: 3, 9, 5, 7, 2, 8, 6. What is the median snowfall?
• FR: Les quantités de neige (en cm) pour une semaine étaient : 3, 9, 5, 7, 2, 8, 6. Quelle est la valeur médiane des chutes de neige?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: To find the median, order the data from least to greatest and find the middle value (e.g., 1, 3, 4, 7, 9: middle is 4).
• Steps:
  • Order the values: 2, 3, 5, 6, 7, 8, 9.
  • The middle (4th) value is 6.
  • The median is 6 cm.
• Answer: 6 cm

[Medium] Percent Decrease

• EN: A hockey jersey was $80. It was discounted to $64. What is the percent decrease?
• FR: Un chandail de hockey coûtait 80 $. Il a été réduit à 64 $. Quel est le pourcentage de diminution?
• Choices: A) 16% B) 18% C) 20% D) 25%
• Hint: Percent decrease = (decrease ÷ original) × 100 (e.g., from $50 to $40: decrease = 10, 10 ÷ 50 × 100 = 20%).
• Steps:
  • Decrease = $80 − $64 = $16.
  • Percent decrease = ($16 ÷ $80) × 100 = 20%.
  • The discount is 20%.
• Answer: 20%

[Hard] Two-Step Equation with Fractions

• EN: Solve for x: (x/3) + 4 = 10.
• FR: Résous pour x : (x/3) + 4 = 10.
• Choices: A) x = 14 B) x = 18 C) x = 20 D) x = 22
• Hint: Undo addition first, then undo division by multiplying both sides (e.g., x/4 + 2 = 7: x/4 = 5, then x = 5 × 4 = 20).
• Steps:
  • Subtract 4 from both sides: x/3 = 6.
  • Multiply both sides by 3: x = 6 × 3 = 18.
  • The solution is x = 18.
• Answer: x = 18

[Hard] Pythagorean Theorem Applied

• EN: A ladder is leaning 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 haut. Quelle est la longueur de l'échelle?
• Choices: A) 11 m B) 13 m C) 15 m D) 17 m
• Hint: The ladder, wall, and ground form a right triangle — use a² + b² = c² (e.g., base 8, height 6: 64 + 36 = 100, √100 = 10 m).
• Steps:
  • a² + b² = c²: 5² + 12² = 25 + 144 = 169.
  • c = √169 = 13.
  • The ladder is 13 m long.
• Answer: 13 m

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 3 = 22.
• FR: Résous pour x : 5x − 3 = 22.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add to isolate the variable term, then divide (e.g., 4x − 6 = 10: add 6 to get 4x = 16, divide by 4: x = 4).
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide both sides by 5: x = 5.
  • The solution is x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Simplify: (3x + 4) + (2x − 1).
• FR: Simplifie : (3x + 4) + (2x − 1).
• Choices: A) 5x − 5 B) 5x + 3 C) 6x + 3 D) 5x + 5
• Hint: Combine like terms — add the x-terms together and the constants together (e.g., (4x + 2) + (x − 5) = 5x − 3).
• Steps:
  • Combine x-terms: 3x + 2x = 5x.
  • Combine constants: 4 + (−1) = 3.
  • Result: 5x + 3.
• Answer: 5x + 3

[Easy] Slope-Intercept Form

• EN: What is the y-intercept of the line y = 3x − 7?
• FR: Quel est l'ordonnée à l'origine de la droite y = 3x − 7?
• Choices: A) −3 B) 3 C) 7 D) −7
• Hint: In y = mx + b, the y-intercept is b, the constant term (e.g., y = 2x + 5 has a y-intercept of 5).
• Steps:
  • The equation is in y = mx + b form.
  • b = −7.
  • The y-intercept is −7.
• Answer: −7

[Easy] Trigonometry: SOH

• EN: In a right triangle, the angle θ = 30°, and the hypotenuse is 10 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse est de 10 cm. Quelle est la longueur du côté opposé?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: Use SOH: sin(θ) = opposite ÷ hypotenuse, so opposite = sin(θ) × hypotenuse (e.g., sin(45°) × 14 ≈ 9.9 cm).
• Steps:
  • sin(30°) = 0.5.
  • Opposite = 0.5 × 10 = 5 cm.
  • The opposite side is 5 cm.
• Answer: 5 cm

[Medium] Solving a Linear Inequality

• EN: Solve and graph on a number line: 2x + 5 > 13.
• FR: Résous et représente sur une droite numérique : 2x + 5 > 13.
• Choices: A) x > 2 B) x > 3 C) x > 4 D) x > 5
• Hint: Solve like an equation but keep the inequality symbol (e.g., 3x + 2 > 11: subtract 2 to get 3x > 9, then divide by 3: x > 3).
• Steps:
  • Subtract 5 from both sides: 2x > 8.
  • Divide both sides by 2: x > 4.
  • The solution is x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand and simplify: (x + 3)(x + 5).
• FR: Développe et simplifie : (x + 3)(x + 5).
• Choices: A) x² + 8x + 8 B) x² + 8x + 15 C) x² + 15x + 8 D) x² + 6x + 15
• Hint: Use FOIL (First, Outer, Inner, Last) to expand (e.g., (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8).
• Steps:
  • First: x × x = x².
  • Outer: x × 5 = 5x. Inner: 3 × x = 3x. Last: 3 × 5 = 15.
  • Combine: x² + 5x + 3x + 15 = x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Two triangles are similar. The sides of the first triangle are 3 cm, 4 cm, and 5 cm. The longest side of the second triangle is 10 cm. What is the shortest side of the second triangle?
• FR: Deux triangles sont semblables. Les côtés du premier triangle sont 3 cm, 4 cm et 5 cm. Le plus long côté du second triangle est 10 cm. Quel est le plus court côté du second triangle?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: Find the scale factor by dividing corresponding sides, then multiply (e.g., if sides 4 and 12 correspond, scale factor = 3, so a side of 5 becomes 15).
• Steps:
  • Scale factor = 10 ÷ 5 = 2.
  • Shortest side of second triangle = 3 × 2 = 6 cm.
  • The shortest side is 6 cm.
• Answer: 6 cm

[Medium] Trigonometry: CAH

• 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 est de 8 cm et l'hypoténuse est de 10 cm. Combien fait cos(θ)?
• Choices: A) 0.6 B) 0.75 C) 0.8 D) 1.25
• Hint: Use CAH: cos(θ) = adjacent ÷ hypotenuse (e.g., adjacent = 5, hypotenuse = 13: cos(θ) = 5/13 ≈ 0.38).
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 8 ÷ 10 = 0.8.
  • So cos(θ) = 0.8.
• Answer: 0.8

[Hard] Systems of Linear Equations (Substitution)

• EN: Solve the system: y = 2x + 1 and y = −x + 7. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = −x + 7. Quelle est la valeur de x?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the two expressions equal to each other and solve for x (e.g., 3x + 2 = x + 8: 2x = 6, x = 3).
• Steps:
  • Set equal: 2x + 1 = −x + 7.
  • Add x to both sides: 3x + 1 = 7.
  • Subtract 1: 3x = 6, so x = 2.
• Answer: x = 2

[Hard] Statistics: Interpreting Data

• EN: The ages of hockey players on a team are: 14, 16, 15, 14, 17, 16, 14, 18, 15, 16. What is the mode?
• FR: Les âges des joueurs de hockey d'une équipe sont : 14, 16, 15, 14, 17, 16, 14, 18, 15, 16. Quel est le mode?
• Choices: A) 14 B) 15 C) 16 D) 17
• Hint: The mode is the value that appears most often in the data set (e.g., in 2, 3, 3, 5, 3, the mode is 3).
• Steps:
  • Count each value: 14 appears 3 times, 15 appears 2 times, 16 appears 3 times, 17 once, 18 once.
  • Both 14 and 16 appear 3 times — but 14 appears first and is the smallest most frequent.
  • Both are modes, but since the answer choices include 14 and 16 separately, 14 is the lowest mode.
• Answer: 14

[Easy] Factoring a Simple Quadratic

• EN: Factor the expression: x² + 7x + 12.
• FR: Factorise l'expression : x² + 7x + 12.
• Choices: A) (x + 2)(x + 6) B) (x + 3)(x + 4) C) (x + 1)(x + 12) D) (x + 6)(x + 2)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient (e.g., x² + 5x + 6: 2 × 3 = 6 and 2 + 3 = 5, so (x + 2)(x + 3)).
• Steps:
  • Find two numbers that multiply to 12 and add to 7: 3 × 4 = 12 and 3 + 4 = 7.
  • So the factored form is (x + 3)(x + 4).
  • Check: (x + 3)(x + 4) = x² + 7x + 12. ✓
• Answer: (x + 3)(x + 4)

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, angle A = 45° and the hypotenuse is 14 cm. What is the length of the side adjacent to angle A? (Use cos 45° ≈ 0.71)
• FR: Dans un triangle rectangle, l'angle A = 45° et l'hypoténuse est de 14 cm. Quelle est la longueur du côté adjacent à l'angle A? (Utilise cos 45° ≈ 0,71)
• Choices: A) 8.14 cm B) 9.94 cm C) 10.34 cm D) 11.24 cm
• Hint: Use CAH: adjacent = cos(angle) × hypotenuse (e.g., cos 30° × 10 ≈ 0.87 × 10 = 8.7 cm).
• Steps:
  • adjacent = cos(45°) × hypotenuse.
  • adjacent = 0.71 × 14 = 9.94 cm.
  • The adjacent side is 9.94 cm.
• Answer: 9.94 cm

[Easy] Volume of a Cylinder

• EN: A cylindrical water tank has a radius of 3 m and a height of 5 m. What is its volume? (Use π ≈ 3.14)
• FR: Un réservoir d'eau cylindrique a un rayon de 3 m et une hauteur de 5 m. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 100.62 m³ B) 121.74 m³ C) 141.30 m³ D) 160.44 m³
• Hint: Volume of a cylinder = π × r² × h (e.g., r = 2, h = 7: π × 4 × 7 = 87.96 m³).
• Steps:
  • V = π × r² × h = 3.14 × 9 × 5.
  • 3.14 × 9 = 28.26.
  • 28.26 × 5 = 141.30 m³.
• Answer: 141.30 m³

[Easy] Solving a System of Equations

• EN: Solve the system: x + y = 10 and x − y = 4. What is x?
• FR: Résous le système : x + y = 10 et x − y = 4. Combien vaut x?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the two equations to eliminate y (e.g., x + y = 8 and x − y = 2: add to get 2x = 10, so x = 5).
• Steps:
  • Add the equations: (x + y) + (x − y) = 10 + 4.
  • 2x = 14, so x = 7.
  • The solution is x = 7.
• Answer: x = 7

[Medium] Completing the Square

• EN: Solve x² + 6x = 7 by completing the square. What are the solutions?
• FR: Résous x² + 6x = 7 en complétant le carré. Quelles sont les solutions?
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 2 or x = −8 D) x = 3 or x = −7
• Hint: Add (b/2)² to both sides, then take the square root (e.g., x² + 4x = 5: add 4 to get x² + 4x + 4 = 9, then (x+2)² = 9, x = 1 or x = −5).
• Steps:
  • Add (6/2)² = 9 to both sides: x² + 6x + 9 = 16.
  • (x + 3)² = 16.
  • x + 3 = ±4, so x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry — Arc Length

• EN: A circle has a radius of 6 cm. What is the circumference of the circle? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 6 cm. Quelle est la circonférence du cercle? (Utilise π ≈ 3,14)
• Choices: A) 18.84 cm B) 33.68 cm C) 37.68 cm D) 43.96 cm
• Hint: Circumference = 2 × π × r (e.g., radius 5 cm: 2 × 3.14 × 5 = 31.4 cm).
• Steps:
  • C = 2 × π × r = 2 × 3.14 × 6.
  • 2 × 3.14 = 6.28.
  • 6.28 × 6 = 37.68 cm.
• Answer: 37.68 cm

[Medium] Quadratic Formula

• EN: Solve 2x² − 4x − 6 = 0 using the quadratic formula. What are the solutions?
• FR: Résous 2x² − 4x − 6 = 0 à l'aide de la formule quadratique. Quelles sont les solutions?
• Choices: A) x = 1 or x = −3 B) x = 2 or x = −1 C) x = 3 or x = −1 D) x = −2 or x = 3
• Hint: Divide all terms by 2 first, then factor or use the formula (e.g., 2x² − 8x + 6 = 0 becomes x² − 4x + 3 = 0 = (x−1)(x−3)).
• Steps:
  • Divide by 2: x² − 2x − 3 = 0.
  • Factor: (x − 3)(x + 1) = 0.
  • x = 3 or x = −1.
• Answer: x = 3 or x = −1

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 9 cm. What is the total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 9 cm. Quelle est l'aire totale? (Utilise π ≈ 3,14)
• Choices: A) 113.04 cm² B) 131.88 cm² C) 150.72 cm² D) 163.28 cm²
• Hint: Surface area of a cone = πr² + πrl, where l is the slant height (e.g., r = 3, l = 5: 3.14 × 9 + 3.14 × 3 × 5 = 28.26 + 47.10 = 75.36 cm²).
• Steps:
  • Base: π × 4² = 3.14 × 16 = 50.24 cm².
  • Lateral: π × 4 × 9 = 3.14 × 36 = 113.04 cm².
  • Wait — total = 50.24 + 113.04 = 163.28 cm².
  • Total surface area is 163.28 cm².
• Answer: 163.28 cm²

[Hard] Quadratic Word Problem

• EN: A ball is thrown upward. Its height in metres is given by h = −5t² + 20t + 1, where t is time in seconds. What is the maximum height?
• FR: Une balle est lancée vers le haut. Sa hauteur en mètres est donnée par h = −5t² + 20t + 1, où t est le temps en secondes. Quelle est la hauteur maximale?
• Choices: A) 19 m B) 20 m C) 21 m D) 25 m
• Hint: The maximum of a quadratic h = at² + bt + c occurs at t = −b/(2a) (e.g., h = −4t² + 16t: t = −16/(2×−4) = 2, h = −4(4) + 32 = 16).
• Steps:
  • t at maximum = −20 / (2 × −5) = −20 / −10 = 2 seconds.
  • h = −5(4) + 20(2) + 1 = −20 + 40 + 1 = 21 m.
  • The maximum height is 21 m.
• Answer: 21 m

[Hard] Circle Geometry — Chord and Radius

• EN: A chord in a circle is 16 cm long. The perpendicular distance from the centre to the chord is 6 cm. What is the radius of the circle?
• FR: Une corde dans un cercle mesure 16 cm. La distance perpendiculaire du centre à la corde est de 6 cm. Quel est le rayon du cercle?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 11 cm
• Hint: The perpendicular from the centre bisects the chord, forming a right triangle — use a² + b² = c² (e.g., half-chord = 6, distance = 8: radius = √(36 + 64) = 10).
• Steps:
  • Half the chord = 16 ÷ 2 = 8 cm.
  • Right triangle: 8² + 6² = 64 + 36 = 100.
  • Radius = √100 = 10 cm.
• Answer: 10 cm

[Easy] Evaluating an Exponential Function

• EN: If f(x) = 2^x, what is f(5)?
• FR: Si f(x) = 2^x, combien vaut f(5)?
• Choices: A) 10 B) 25 C) 32 D) 64
• Hint: Evaluate by multiplying the base by itself the number of times equal to the exponent (e.g., 3^4 = 3 × 3 × 3 × 3 = 81).
• Steps:
  • f(5) = 2^5 = 2 × 2 × 2 × 2 × 2.
  • = 4 × 4 × 2 = 32.
  • So f(5) = 32.
• Answer: 32

[Easy] Arithmetic Sequence

• EN: An arithmetic sequence starts at 7 and has a common difference of 6. What is the 8th term?
• FR: Une suite arithmétique commence à 7 et a une raison de 6. Quel est le 8e terme?
• Choices: A) 43 B) 48 C) 49 D) 55
• Hint: Use the formula: tn = t1 + (n − 1) × d (e.g., first term 3, difference 4, 5th term = 3 + 4 × 4 = 19).
• Steps:
  • t8 = 7 + (8 − 1) × 6.
  • t8 = 7 + 7 × 6 = 7 + 42 = 49.
  • The 8th term is 49.
• Answer: 49

[Easy] Logarithm Introduction

• EN: Solve: log₂(32) = ?
• FR: Résous : log₂(32) = ?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log_b(x) = n means b^n = x — ask "what power of the base gives the number?" (e.g., log₃(27) = 3 because 3³ = 27).
• Steps:
  • Ask: 2 to what power equals 32?
  • 2^5 = 32.
  • So log₂(32) = 5.
• Answer: 5

[Easy] Compound Interest

• EN: Lucas invests $1000 at an annual interest rate of 5%, compounded annually, for 2 years. How much interest is earned?
• FR: Lucas investit 1 000 $ à un taux d'intérêt annuel de 5 %, composé annuellement, pendant 2 ans. Combien d'intérêts sont gagnés?
• Choices: A) $100.00 B) $102.50 C) $105.00 D) $110.25
• Hint: Use A = P(1 + r)^n and subtract P to find interest (e.g., $500 at 4% for 2 years: 500 × 1.04² = $540.80, interest = $40.80).
• Steps:
  • A = 1000 × (1.05)² = 1000 × 1.1025 = $1102.50.
  • Interest = $1102.50 − $1000 = $102.50.
  • Lucas earns $102.50 in interest.
• Answer: $102.50

[Medium] Quadratic Function — Vertex

• EN: Find the vertex of the parabola: y = 2(x − 3)² + 4.
• FR: Trouve le sommet de la parabole : y = 2(x − 3)² + 4.
• Choices: A) (3, 4) B) (−3, 4) C) (2, 3) D) (3, −4)
• Hint: In vertex form y = a(x − h)² + k, the vertex is at (h, k) (e.g., y = 3(x − 1)² + 5 has vertex at (1, 5)).
• Steps:
  • The equation is in vertex form: y = 2(x − 3)² + 4.
  • h = 3, k = 4.
  • The vertex is at (3, 4).
• Answer: (3, 4)

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ.
• FR: Simplifie : sin²θ + cos²θ.
• Choices: A) 0 B) 2 C) 1 D) sinθ × cosθ
• Hint: This is the most fundamental trig identity — it is always true for any angle (e.g., sin²(30°) + cos²(30°) = 0.25 + 0.75 = 1).
• Steps:
  • This is the Pythagorean identity.
  • sin²θ + cos²θ = 1 for any angle θ.
  • The simplified result is 1.
• Answer: 1

[Medium] Geometric Series — Sum

• EN: Find the sum of the first 5 terms of the geometric series where the first term is 3 and the common ratio is 2.
• FR: Trouve la somme des 5 premiers termes de la suite géométrique où le premier terme est 3 et la raison est 2.
• Choices: A) 63 B) 93 C) 96 D) 120
• Hint: Use S_n = a(r^n − 1) ÷ (r − 1) when r ≠ 1 (e.g., a = 2, r = 3, n = 4: 2(81−1)/2 = 2 × 40 = 80).
• Steps:
  • S_5 = 3(2^5 − 1) ÷ (2 − 1) = 3(32 − 1) ÷ 1.
  • = 3 × 31 = 93.
  • The sum of the first 5 terms is 93.
• Answer: 93

[Medium] Annuity Calculation

• EN: Asha deposits $200 at the end of each month into an account earning 6% per year, compounded monthly. What is the monthly interest rate?
• FR: Asha dépose 200 $ à la fin de chaque mois dans un compte rapportant 6 % par an, composé mensuellement. Quel est le taux d'intérêt mensuel?
• Choices: A) 0.5% B) 0.6% C) 1% D) 6%
• Hint: The monthly rate equals the annual rate divided by 12 (e.g., 12% per year = 12 ÷ 12 = 1% per month).
• Steps:
  • Annual rate = 6%.
  • Monthly rate = 6% ÷ 12 = 0.5%.
  • The monthly interest rate is 0.5%.
• Answer: 0.5%

[Hard] Logarithm — Solving an Equation

• EN: Solve for x: log₃(x) + log₃(4) = log₃(36).
• FR: Résous pour x : log₃(x) + log₃(4) = log₃(36).
• Choices: A) x = 6 B) x = 8 C) x = 9 D) x = 12
• Hint: Use the log product rule: logb(A) + logb(B) = log_b(A × B), then solve (e.g., log₂(x) + log₂(3) = log₂(15): x × 3 = 15, x = 5).
• Steps:
  • log₃(x) + log₃(4) = log₃(4x).
  • Set equal: log₃(4x) = log₃(36).
  • 4x = 36, so x = 9.
• Answer: x = 9

[Hard] Exponential Growth

• EN: A city had a population of 50 000 in 2010 and grows at 3% per year. What will the population be in 2015? (Round to the nearest whole number.)
• FR: Une ville avait une population de 50 000 habitants en 2010 et croît de 3 % par an. Quelle sera la population en 2015? (Arrondi au nombre entier le plus proche.)
• Choices: A) 55 000 B) 57 964 C) 58 764 D) 60 000
• Hint: Use P = P₀(1 + r)^n (e.g., P₀ = 20 000, r = 2%, n = 4: 20 000 × 1.02⁴ ≈ 20 000 × 1.0824 ≈ 21 648).
• Steps:
  • P = 50 000 × (1.03)^5.
  • (1.03)^5 ≈ 1.15927.
  • P ≈ 50 000 × 1.15927 ≈ 57 964.
• Answer: 57 964

[Easy] Permutations

• EN: In how many different ways can 4 students be arranged in a row of 4 chairs?
• FR: De combien de façons différentes peut-on placer 4 élèves dans une rangée de 4 chaises?
• Choices: A) 12 B) 16 C) 24 D) 48
• Hint: The number of arrangements of n objects in n spots is n! (e.g., 3 objects: 3! = 3 × 2 × 1 = 6).
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 24.
  • There are 24 arrangements.
• Answer: 24

[Easy] Derivative of a Polynomial

• EN: What is the derivative of f(x) = 3x² + 5x − 2?
• FR: Quelle est la dérivée de f(x) = 3x² + 5x − 2?
• Choices: A) f′(x) = 3x + 5 B) f′(x) = 6x + 5 C) f′(x) = 6x − 2 D) f′(x) = 6x² + 5
• Hint: Use the power rule: the derivative of ax^n is n × ax^(n−1) (e.g., derivative of 4x³ + 2x = 12x² + 2).
• Steps:
  • Derivative of 3x² = 6x.
  • Derivative of 5x = 5.
  • Derivative of −2 = 0. So f′(x) = 6x + 5.
• Answer: f′(x) = 6x + 5

[Easy] Combinations

• EN: A committee of 3 people is chosen from a group of 7. How many different committees are possible?
• FR: Un comité de 3 personnes est choisi parmi un groupe de 7. Combien de comités différents sont possibles?
• Choices: A) 21 B) 35 C) 42 D) 210
• Hint: Use C(n, r) = n! ÷ (r! × (n−r)!) — order does not matter for combinations (e.g., C(5, 2) = 5! ÷ (2! × 3!) = 10).
• Steps:
  • C(7, 3) = 7! ÷ (3! × 4!).
  • = (7 × 6 × 5) ÷ (3 × 2 × 1) = 210 ÷ 6 = 35.
  • There are 35 possible committees.
• Answer: 35

[Easy] Rational Function — Domain

• EN: What value of x is NOT in the domain of f(x) = 5 ÷ (x − 4)?
• FR: Quelle valeur de x N'est PAS dans le domaine de f(x) = 5 ÷ (x − 4)?
• Choices: A) x = 0 B) x = 4 C) x = 5 D) x = −4
• Hint: A rational function is undefined when the denominator equals zero — set it equal to zero and solve (e.g., for 1/(x − 2), set x − 2 = 0, so x = 2 is excluded).
• Steps:
  • Set the denominator equal to zero: x − 4 = 0.
  • x = 4.
  • So x = 4 is not in the domain.
• Answer: x = 4

[Medium] Instantaneous Rate of Change

• EN: For f(x) = x² + 3x, what is the instantaneous rate of change at x = 2?
• FR: Pour f(x) = x² + 3x, quel est le taux de variation instantané à x = 2?
• Choices: A) 5 B) 6 C) 7 D) 10
• Hint: Find the derivative, then substitute the x-value (e.g., for g(x) = 2x² − x, g′(x) = 4x − 1, and g′(3) = 11).
• Steps:
  • f′(x) = 2x + 3.
  • f′(2) = 2(2) + 3 = 4 + 3 = 7.
  • The instantaneous rate of change at x = 2 is 7.
• Answer: 7

[Medium] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: On lance une pièce équilibrée 4 fois. Quelle est la probabilité d'obtenir exactement 3 fois pile?
• Choices: A) 1/4 B) 3/8 C) 1/4 D) 3/16
• Hint: Use P(X = k) = C(n, k) × p^k × (1−p)^(n−k) (e.g., 3 flips, 2 heads: C(3,2) × (0.5)² × (0.5)¹ = 3 × 0.25 × 0.5 = 0.375).
• Steps:
  • P(X = 3) = C(4, 3) × (0.5)³ × (0.5)¹.
  • C(4, 3) = 4.
  • P = 4 × 0.125 × 0.5 = 4 × 0.0625 = 0.25 = 1/4.
• Answer: 1/4

[Medium] Vectors — Addition

• EN: Vector u = (3, −2) and vector v = (−1, 5). What is u + v?
• FR: Le vecteur u = (3, −2) et le vecteur v = (−1, 5). Combien fait u + v?
• Choices: A) (2, 3) B) (3, 2) C) (4, 3) D) (2, −3)
• Hint: Add vectors component by component (e.g., (4, 1) + (−2, 6) = (4+(−2), 1+6) = (2, 7)).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: −2 + 5 = 3.
  • u + v = (2, 3).
• Answer: (2, 3)

[Medium] Polynomial Long Division

• EN: Divide x² + 5x + 6 by (x + 2). What is the quotient?
• FR: Divise x² + 5x + 6 par (x + 2). Quel est le quotient?
• Choices: A) x + 2 B) x + 3 C) x − 3 D) x + 4
• Hint: Divide the leading term of the dividend by the leading term of the divisor, multiply, subtract, and repeat (e.g., (x² + 6x + 8) ÷ (x + 4) = x + 2).
• Steps:
  • x² ÷ x = x; x(x + 2) = x² + 2x; subtract to get 3x + 6.
  • 3x ÷ x = 3; 3(x + 2) = 3x + 6; subtract to get 0.
  • Quotient is x + 3.
• Answer: x + 3

[Hard] Normal Distribution

• EN: Test scores are normally distributed with a mean of 70 and a standard deviation of 10. Approximately what percentage of students scored between 60 and 80?
• FR: Les scores à un test suivent une distribution normale avec une moyenne de 70 et un écart-type de 10. Quel pourcentage approximatif d'élèves a obtenu entre 60 et 80?
• Choices: A) 34% B) 50% C) 68% D) 95%
• Hint: In a normal distribution, about 68% of data falls within one standard deviation of the mean (e.g., mean 50, SD 5: approximately 68% of scores fall between 45 and 55).
• Steps:
  • 60 = 70 − 10 = one SD below the mean.
  • 80 = 70 + 10 = one SD above the mean.
  • By the 68-95-99.7 rule, approximately 68% of students fall within one SD of the mean.
• Answer: 68%

[Hard] Derivative Application — Optimization

• EN: A farmer has 120 m of fencing to enclose a rectangular garden against a barn wall (the wall forms one side and needs no fencing). What width (in metres) maximizes the area?
• FR: Un fermier a 120 m de clôture pour entourer un jardin rectangulaire contre un mur de grange (le mur forme un côté et n'a pas besoin de clôture). Quelle largeur (en mètres) maximise l'aire?
• Choices: A) 20 m B) 30 m C) 40 m D) 60 m
• Hint: Write the area as a function of one variable, differentiate, and set equal to zero (e.g., if fencing = 80 m against a wall: A = w(80 − 2w) = 80w − 2w², A′ = 80 − 4w = 0, w = 20 m).
• Steps:
  • Let width = w and length = 120 − 2w (one wall side covered).
  • Area: A(w) = w(120 − 2w) = 120w − 2w².
  • A′(w) = 120 − 4w = 0, so w = 30 m.
• Answer: 30 m