Daily Math — 2026-09-21

[Easy] Counting to 20

• EN: There are 7 apples on the table and 5 more apples in a basket. How many apples are there altogether?
• FR: Il y a 7 pommes sur la table et 5 autres pommes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 10 apples B) 11 apples C) 12 apples D) 13 apples
• Hint: Try counting on from the bigger number — for example, 6 + 4: start at 6 and count up 4 more.
• Steps:
  • Start at 7 and count on 5 more.
  • 7 → 8, 9, 10, 11, 12.
  • So the total is 12 apples.
• Answer: 12 apples

[Easy] Subtraction Within 20

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

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes next? 2, 4, 6, 8, ___
• FR: Compte par bonds de 2. Quel nombre vient ensuite? 2, 4, 6, 8, ___
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When skip counting by 2s, always add 2 to the last number — for example, after 12 comes 14.
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 13 or 17?
• FR: Quel nombre est plus grand: 13 ou 17?
• Choices: A) 13 B) 17 C) They are equal D) 15
• Hint: When comparing numbers, the one with more tens is greater — for example, 19 is greater than 11.
• Steps:
  • Both numbers have 1 ten.
  • Look at the ones: 3 ones vs. 7 ones.
  • 7 ones is more, so 17 is greater.
• Answer: 17

[Medium] Addition Within 20

• EN: There are 9 red mittens and 8 blue mittens in the lost-and-found box. How many mittens are there in all?
• FR: Il y a 9 mitaines rouges et 8 mitaines bleues dans la boîte des objets perdus. Combien y a-t-il de mitaines en tout?
• Choices: A) 15 mittens B) 16 mittens C) 17 mittens D) 18 mittens
• Hint: To add 9 + something, try making 10 first — for example, 9 + 6: give 1 from 6 to 9, making 10 + 5 = 15.
• Steps:
  • Break 8 into 1 + 7.
  • 9 + 1 = 10, then 10 + 7 = 17.
  • So there are 17 mittens in all.
• Answer: 17 mittens

[Medium] Coin Recognition

• EN: Maya has 1 dime and 1 nickel. How much money does she have in total?
• FR: Maya a 1 pièce de dix cents et 1 pièce de cinq cents. Combien d'argent a-t-elle en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents — for example, 2 dimes = 20 cents.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What number is missing? 5, 10, ___, 20, 25
• FR: Compte par bonds de 5. Quel nombre manque? 5, 10, ___, 20, 25
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: When skip counting by 5s, add 5 each time — for example, after 20 comes 25.
• Steps:
  • The pattern adds 5 each time.
  • 10 + 5 = 15.
  • So the missing number is 15.
• Answer: 15

[Medium] Subtraction Within 20

• EN: There are 18 students in class. 9 students go to gym class. How many students are left in the classroom?
• FR: Il y a 18 élèves en classe. 9 élèves vont au gymnase. Combien d'élèves restent dans la classe?
• Choices: A) 7 students B) 8 students C) 9 students D) 11 students
• Hint: doubles can help — for example, 16 − 8 = 8 because 8 + 8 = 16.
• Steps:
  • Think: 9 + ___ = 18.
  • 9 + 9 = 18, so 18 − 9 = 9.
  • So 9 students are left.
• Answer: 9 students

[Hard] Adding Three Numbers

• EN: Zoe has 4 crayons, 5 pencils, and 3 markers in her pencil case. How many items does she have altogether?
• FR: Zoé a 4 crayons, 5 crayons à mine et 3 marqueurs dans sa trousse. Combien d'articles a-t-elle en tout?
• Choices: A) 10 items B) 11 items C) 12 items D) 13 items
• Hint: When adding three numbers, look for a pair that makes 10 first — for example, 6 + 4 + 3: 6 + 4 = 10, then 10 + 3 = 13.
• Steps:
  • Look for a pair that makes 10: 4 + 5 = 9... try 4 + 3 = 7, then 7 + 5 = 12.
  • Or add in order: 4 + 5 = 9, then 9 + 3 = 12.
  • So there are 12 items altogether.
• Answer: 12 items

[Hard] Skip Counting and Comparing

• EN: Emma skip counts by 10s starting at 10: 10, 20, 30, 40, 50. Ben skip counts by 5s starting at 5 and says 6 numbers. Who reaches a bigger number?
• FR: Emma compte par bonds de 10 à partir de 10: 10, 20, 30, 40, 50. Ben compte par bonds de 5 à partir de 5 et dit 6 nombres. Qui arrive au plus grand nombre?
• Choices: A) Emma, because she reaches 50 B) Ben, because he reaches 35 C) They reach the same number D) Ben, because he reaches 30
• Hint: Count out the sequence carefully — for example, 6 numbers counting by 10s from 10: 10, 20, 30, 40, 50, 60.
• Steps:
  • Emma's sequence: 10, 20, 30, 40, 50 — she reaches 50.
  • Ben counts 6 numbers by 5s from 5: 5, 10, 15, 20, 25, 30 — he reaches 30.
  • 50 > 30, so Emma reaches a bigger number.
• Answer: Emma, because she reaches 50

[Easy] Addition Within 100

• EN: There are 34 children in the gym and 25 more arrive for assembly. How many children are in the gym now?
• FR: Il y a 34 enfants dans le gymnase et 25 autres arrivent pour l'assemblée. Combien y a-t-il d'enfants dans le gymnase maintenant?
• Choices: A) 57 children B) 58 children C) 59 children D) 60 children
• Hint: Add the tens first, then the ones — for example, 42 + 31: 40 + 30 = 70, 2 + 1 = 3, total = 73.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59 children.
• Answer: 59 children

[Easy] Telling Time

• EN: The clock shows the short hand on the 3 and the long hand on the 12. What time is it?
• FR: L'aiguille courte de l'horloge pointe sur le 3 et la grande aiguille pointe sur le 12. Quelle heure est-il?
• Choices: A) 12:00 B) 2:00 C) 3:00 D) 3:30
• Hint: When the long hand points to 12, it is exactly on the hour — for example, short hand on 7 and long hand on 12 means 7:00.
• Steps:
  • Long hand on 12 means it is exactly on the hour.
  • Short hand on 3 tells us the hour is 3.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Subtraction Within 100

• EN: A bag has 68 marbles. A student takes out 35 marbles. How many marbles are left in the bag?
• FR: Un sac contient 68 billes. Un élève en retire 35. Combien de billes reste-t-il dans le sac?
• Choices: A) 31 marbles B) 32 marbles C) 33 marbles D) 34 marbles
• Hint: Subtract tens then ones — for example, 75 − 43: 70 − 40 = 30, 5 − 3 = 2, total = 32.
• Steps:
  • Subtract the tens: 60 − 30 = 30.
  • Subtract the ones: 8 − 5 = 3.
  • 30 + 3 = 33 marbles.
• Answer: 33 marbles

[Easy] Measuring Length

• EN: A pencil is 14 cm long and a crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 14 cm et un crayon de couleur mesure 9 cm. De combien le crayon à mine est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find how much longer, subtract the smaller length from the bigger — for example, 18 cm − 11 cm = 7 cm.
• Steps:
  • Subtract: 14 − 9.
  • 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Medium] Counting Coins

• EN: Olivia has 3 dimes and 2 nickels. How much money does she have?
• FR: Olivia a 3 pièces de dix cents et 2 pièces de cinq cents. Combien d'argent a-t-elle?
• Choices: A) 35 cents B) 38 cents C) 40 cents D) 45 cents
• Hint: Count all dimes first (10 cents each), then add nickels (5 cents each) — for example, 2 dimes + 3 nickels = 20 + 15 = 35 cents.
• Steps:
  • 3 dimes = 3 × 10 = 30 cents.
  • 2 nickels = 2 × 5 = 10 cents.
  • 30 + 10 = 40 cents.
• Answer: 40 cents

[Medium] Telling Time — Half Hour

• EN: The clock shows the short hand between 7 and 8, and the long hand on the 6. What time does the clock show?
• FR: L'aiguille courte de l'horloge est entre 7 et 8, et la grande aiguille pointe sur le 6. Quelle heure l'horloge indique-t-elle?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the long hand is on 6, it means 30 minutes past the hour — for example, short hand between 4 and 5, long hand on 6 means 4:30.
• Steps:
  • Long hand on 6 means 30 minutes past the hour.
  • Short hand between 7 and 8 means the hour just passed is 7.
  • So the time is 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, 25, ___. What number comes next?
• FR: Regarde ce motif: 5, 10, 15, 20, 25, ___. Quel nombre vient ensuite?
• Choices: A) 28 B) 29 C) 30 D) 35
• Hint: Find the rule by looking at the difference between numbers — for example, 4, 8, 12, 16 increases by 4 each time.
• Steps:
  • Each number increases by 5.
  • 25 + 5 = 30.
  • So the next number is 30.
• Answer: 30

[Medium] Addition with Regrouping

• EN: At a Tim Hortons drive-through, the staff made 47 hot chocolates in the morning and 36 in the afternoon. How many did they make in total?
• FR: Au service au volant d'un Tim Hortons, le personnel a préparé 47 chocolats chauds le matin et 36 l'après-midi. Combien en ont-ils préparé en tout?
• Choices: A) 73 hot chocolates B) 82 hot chocolates C) 83 hot chocolates D) 84 hot chocolates
• Hint: Add ones first; if the sum is 10 or more, regroup — for example, 38 + 45: 8 + 5 = 13, write 3 carry 1, then 3 + 4 + 1 = 8, total = 83.
• Steps:
  • Add the ones: 7 + 6 = 13. Write 3, carry 1.
  • Add the tens: 4 + 3 + 1 (carried) = 8.
  • Total = 83 hot chocolates.
• Answer: 83 hot chocolates

[Hard] Two-Step Problem

• EN: Noah had 62 hockey cards. He gave 18 to his cousin and then bought 25 more. How many hockey cards does Noah have now?
• FR: Noah avait 62 cartes de hockey. Il en a donné 18 à son cousin, puis en a acheté 25 autres. Combien de cartes de hockey Noah a-t-il maintenant?
• Choices: A) 67 hockey cards B) 68 hockey cards C) 69 hockey cards D) 70 hockey cards
• Hint: Solve in two steps — first subtract, then add — for example, 50 − 12 = 38, then 38 + 20 = 58.
• Steps:
  • Step 1: 62 − 18 = 44 cards after giving some away.
  • Step 2: 44 + 25 = 69 cards after buying more.
  • So Noah has 69 hockey cards now.
• Answer: 69 hockey cards

[Hard] Measuring and Comparing

• EN: A classroom bookshelf is 95 cm wide. A reading mat is 78 cm wide. How much wider is the bookshelf than the reading mat?
• FR: Une bibliothèque de classe mesure 95 cm de large. Un tapis de lecture mesure 78 cm de large. De combien la bibliothèque est-elle plus large que le tapis?
• Choices: A) 13 cm B) 15 cm C) 17 cm D) 19 cm
• Hint: Subtract by breaking the smaller number apart — for example, 84 − 67: 84 − 60 = 24, then 24 − 7 = 17.
• Steps:
  • Subtract: 95 − 78.
  • 95 − 70 = 25, then 25 − 8 = 17.
  • The bookshelf is 17 cm wider.
• Answer: 17 cm

[Easy] Multiplication by 2

• EN: A hockey team has 6 players on the ice. Each player has 2 gloves. How many gloves are there in total?
• FR: Une équipe de hockey a 6 joueurs sur la glace. Chaque joueur a 2 gants. Combien y a-t-il de gants en tout?
• Choices: A) 8 gloves B) 10 gloves C) 12 gloves D) 14 gloves
• Hint: Multiply by 2 means skip counting by 2s — for example, 5 × 2 = 10.
• Steps:
  • 6 groups of 2.
  • 6 × 2 = 12.
  • There are 12 gloves in total.
• Answer: 12 gloves

[Easy] Multiplication by 5

• EN: There are 4 bags of apples at the market. Each bag has 5 apples. How many apples are there altogether?
• FR: Il y a 4 sacs de pommes au marché. Chaque sac contient 5 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 15 apples B) 18 apples C) 20 apples D) 25 apples
• Hint: Multiply by 5 means counting by 5s — for example, 3 × 5 = 15.
• Steps:
  • 4 groups of 5.
  • 4 × 5 = 20.
  • There are 20 apples altogether.
• Answer: 20 apples

[Easy] Basic Fractions

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

[Easy] Perimeter

• EN: A rectangle has a length of 5 cm and a width of 3 cm. What is the perimeter of the rectangle?
• FR: Un rectangle a une longueur de 5 cm et une largeur de 3 cm. Quel est le périmètre du rectangle?
• Choices: A) 14 cm B) 15 cm C) 16 cm D) 18 cm
• Hint: Perimeter = add all four sides — for a rectangle with length 6 and width 2: 6 + 2 + 6 + 2 = 16.
• Steps:
  • Add all four sides: 5 + 3 + 5 + 3.
  • 5 + 3 = 8, and 8 × 2 = 16.
  • The perimeter is 16 cm.
• Answer: 16 cm

[Medium] Multiplication by 3

• EN: A bakery puts 3 muffins in each box. If there are 7 boxes, how many muffins are there in all?
• FR: Une boulangerie met 3 muffins dans chaque boîte. S'il y a 7 boîtes, combien y a-t-il de muffins en tout?
• Choices: A) 18 muffins B) 20 muffins C) 21 muffins D) 24 muffins
• Hint: Use the 3 times table — for example, 6 × 3 = 18.
• Steps:
  • 7 boxes × 3 muffins each.
  • 7 × 3 = 21.
  • There are 21 muffins in all.
• Answer: 21 muffins

[Medium] Basic Division

• EN: There are 24 crayons shared equally among 4 students. How many crayons does each student get?
• FR: Il y a 24 crayons partagés également entre 4 élèves. Combien de crayons chaque élève reçoit-il?
• Choices: A) 4 crayons B) 5 crayons C) 6 crayons D) 8 crayons
• Hint: Division means splitting into equal groups — for example, 15 ÷ 3 = 5 because 5 × 3 = 15.
• Steps:
  • Think: 4 × ___ = 24.
  • 4 × 6 = 24.
  • Each student gets 6 crayons.
• Answer: 6 crayons

[Medium] Reading a Graph

• EN: A bar graph shows the following snowfall in centimetres: Monday 4 cm, Tuesday 7 cm, Wednesday 3 cm. How much snow fell in total over the three days?
• FR: Un diagramme à barres montre les chutes de neige en centimètres: lundi 4 cm, mardi 7 cm, mercredi 3 cm. Quelle quantité de neige est tombée en tout sur les trois jours?
• Choices: A) 11 cm B) 13 cm C) 14 cm D) 15 cm
• Hint: To find the total from a graph, add all the values together — for example, 5 + 8 + 2 = 15.
• Steps:
  • Monday + Tuesday + Wednesday = 4 + 7 + 3.
  • 4 + 7 = 11, then 11 + 3 = 14.
  • The total snowfall was 14 cm.
• Answer: 14 cm

[Medium] Multiplication by 10

• EN: A school has 8 classrooms. Each classroom has 10 desks. How many desks are in the school altogether?
• FR: Une école a 8 salles de classe. Chaque salle de classe a 10 pupitres. Combien y a-t-il de pupitres dans l'école en tout?
• Choices: A) 70 desks B) 80 desks C) 81 desks D) 90 desks
• Hint: Multiplying by 10 means putting a zero at the end — for example, 6 × 10 = 60.
• Steps:
  • 8 × 10.
  • Put a zero after 8: 80.
  • There are 80 desks in the school.
• Answer: 80 desks

[Hard] Two-Step Multiplication and Addition

• EN: At a school fair, each booth sold 4 tickets for $3 each and also collected a $5 donation. How much money did one booth collect in total?
• FR: Lors d'une fête scolaire, chaque kiosque a vendu 4 billets à 3 $ chacun et a aussi reçu un don de 5 $. Combien d'argent un kiosque a-t-il collecté en tout?
• Choices: A) $15 B) $17 C) $18 D) $19
• Hint: First multiply to find the ticket money, then add the donation — for example, 3 tickets at $4 each = $12, plus $6 = $18.
• Steps:
  • 4 tickets × $3 = $12.
  • Add the donation: $12 + $5 = $17.
  • One booth collected $17 in total.
• Answer: $17

[Hard] Fractions and Perimeter

• EN: A square garden has a perimeter of 20 cm. A fence covers 1/4 of the perimeter. How many centimetres of fence are used?
• FR: Un jardin carré a un périmètre de 20 cm. Une clôture couvre 1/4 du périmètre. Combien de centimètres de clôture sont utilisés?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: To find a fraction of a number, divide by the bottom number — for example, 1/4 of 16 = 16 ÷ 4 = 4.
• Steps:
  • Total perimeter = 20 cm.
  • 1/4 of 20 = 20 ÷ 4 = 5.
  • So 5 cm of fence are used.
• Answer: 5 cm

[Easy] Multiplication Facts to 9×9

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Use a known fact and adjust — for example, 7 × 7 = 49, and 7 × 8 = 49 + 7.
• Steps:
  • 7 × 7 = 49.
  • Add one more group of 7: 49 + 7 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: Which decimal represents three tenths?
• FR: Quel nombre décimal représente trois dixièmes?
• Choices: A) 0.03 B) 0.3 C) 3.0 D) 3.3
• Hint: Tenths are written one place to the right of the decimal point — for example, five tenths = 0.5.
• Steps:
  • Tenths are the first digit after the decimal point.
  • Three tenths = 0.3.
  • So the answer is 0.3.
• Answer: 0.3

[Easy] Area of a Rectangle

• EN: A rectangular yard is 9 m long and 4 m wide. What is the area of the yard?
• FR: Une cour rectangulaire mesure 9 m de long et 4 m de large. Quelle est l'aire de la cour?
• Choices: A) 26 m² B) 32 m² C) 36 m² D) 40 m²
• Hint: Area of a rectangle = length × width — for example, 8 m × 5 m = 40 m².
• Steps:
  • Area = 9 × 4.
  • 9 × 4 = 36.
  • The area of the yard is 36 m².
• Answer: 36 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/4?
• FR: Quelle fraction est plus grande: 3/4 ou 1/4?
• Choices: A) 1/4 B) 3/4 C) They are equal D) 2/4
• Hint: When the denominators are the same, compare the numerators — for example, 5/8 > 3/8 because 5 > 3.
• Steps:
  • Both fractions have the same denominator (4).
  • Compare numerators: 3 > 1.
  • So 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: A teacher has 29 pencils to share equally among 4 students. How many pencils does each student get, and how many are left over?
• FR: Une enseignante a 29 crayons à partager également entre 4 élèves. Combien de crayons chaque élève reçoit-il et combien en reste-t-il?
• Choices: A) 6 remainder 5 B) 7 remainder 1 C) 7 remainder 2 D) 8 remainder 3
• Hint: Divide, then find what is left — for example, 25 ÷ 4: 4 × 6 = 24, remainder = 25 − 24 = 1, so 6 remainder 1.
• Steps:
  • 4 × 7 = 28, which is close to 29.
  • 29 − 28 = 1 left over.
  • Each student gets 7 pencils with 1 remainder.
• Answer: 7 remainder 1

[Medium] Elapsed Time

• EN: Hockey practice starts at 2:15 p.m. and ends at 4:00 p.m. How long is hockey practice?
• FR: L'entraînement de hockey commence à 14 h 15 et se termine à 16 h 00. Combien de temps dure l'entraînement?
• Choices: A) 1 hour 30 minutes B) 1 hour 45 minutes C) 2 hours D) 2 hours 15 minutes
• Hint: Count up from the start time to the end time — for example, from 3:20 to 5:00: 40 min to 4:00, then 1 hour more = 1 hour 40 minutes.
• Steps:
  • From 2:15 to 3:00 is 45 minutes.
  • From 3:00 to 4:00 is 1 hour.
  • Total = 1 hour and 45 minutes.
• Answer: 1 hour 45 minutes

[Medium] Decimal Operations

• EN: A book costs $4.75 and a notebook costs $3.20. How much do they cost altogether?
• FR: Un livre coûte 4,75 $ et un cahier coûte 3,20 $. Combien coûtent-ils ensemble?
• Choices: A) $7.85 B) $7.90 C) $7.95 D) $8.05
• Hint: Line up decimal points and add — for example, $5.30 + $2.45: 5.30 + 2.45 = 7.75.
• Steps:
  • $4.75 + $3.20.
  • 4 + 3 = 7 dollars.
  • 0.75 + 0.20 = 0.95.
  • Total = $7.95.
• Answer: $7.95

[Medium] Multiplication — Multi-digit

• EN: A store receives 6 boxes of crayons. Each box holds 48 crayons. How many crayons does the store receive in total?
• FR: Un magasin reçoit 6 boîtes de crayons. Chaque boîte contient 48 crayons. Combien de crayons le magasin reçoit-il en tout?
• Choices: A) 268 crayons B) 278 crayons C) 288 crayons D) 298 crayons
• Hint: Break the number apart — for example, 6 × 35 = 6 × 30 + 6 × 5 = 180 + 30 = 210.
• Steps:
  • 6 × 48 = 6 × 40 + 6 × 8.
  • 6 × 40 = 240 and 6 × 8 = 48.
  • 240 + 48 = 288 crayons.
• Answer: 288 crayons

[Hard] Multi-Step Word Problem

• EN: A rec centre sells adult tickets for $9.00 each and child tickets for $5.00 each. A family buys 2 adult tickets and 3 child tickets. How much does the family spend in total?
• FR: Un centre récréatif vend des billets adultes à 9,00 $ et des billets enfants à 5,00 $. Une famille achète 2 billets adultes et 3 billets enfants. Combien la famille dépense-t-elle en tout?
• Choices: A) $28.00 B) $30.00 C) $32.00 D) $33.00
• Hint: Multiply each type separately, then add — for example, 3 adult × $8 = $24, 2 child × $4 = $8, total = $32.
• Steps:
  • Adult tickets: 2 × $9.00 = $18.00.
  • Child tickets: 3 × $5.00 = $15.00.
  • Total: $18.00 + $15.00 = $33.00.
• Answer: $33.00

[Hard] Fraction Comparison and Problem Solving

• EN: A bag of trail mix is 1 kg. Lucas eats 3/4 of the bag and his sister eats 1/4 of a second identical bag. Who has eaten more trail mix, and by how much?
• FR: Un sac de mélange de randonnée pèse 1 kg. Lucas mange 3/4 du sac et sa sœur mange 1/4 d'un deuxième sac identique. Qui a mangé plus de mélange, et de combien?
• Choices: A) Lucas ate more by 1/2 of a bag B) His sister ate more by 1/4 of a bag C) They ate the same amount D) Lucas ate more by 1/4 of a bag
• Hint: Compare fractions with the same denominator by looking at the numerators — for example, 5/8 − 3/8 = 2/8.
• Steps:
  • Lucas ate 3/4 and his sister ate 1/4.
  • Both fractions have denominator 4, so compare: 3 > 1.
  • Difference: 3/4 − 1/4 = 2/4 = 1/2.
  • Lucas ate more by 1/2 of a bag.
• Answer: Lucas ate more by 1/2 of a bag

[Easy] Multi-Digit Multiplication

• EN: A school orders 24 boxes of markers. Each box has 12 markers. How many markers are ordered in total?
• FR: Une école commande 24 boîtes de marqueurs. Chaque boîte contient 12 marqueurs. Combien de marqueurs sont commandés en tout?
• Choices: A) 268 markers B) 278 markers C) 288 markers D) 298 markers
• Hint: Break the first number into tens and ones, then multiply each part — for example, 23 × 11 = 20 × 11 + 3 × 11 = 220 + 33 = 253.
• Steps:
  • 24 × 12 = 24 × 10 + 24 × 2.
  • 24 × 10 = 240 and 24 × 2 = 48.
  • 240 + 48 = 288 markers.
• Answer: 288 markers

[Easy] Adding Fractions with Like Denominators

• EN: Emma ate 2/8 of a pie and her brother ate 3/8 of the same pie. What fraction of the pie did they eat together?
• FR: Emma a mangé 2/8 d'une tarte et son frère en a mangé 3/8. Quelle fraction de la tarte ont-ils mangée ensemble?
• Choices: A) 5/16 B) 5/8 C) 6/8 D) 1/8
• Hint: To add fractions with the same denominator, just add the numerators and keep the denominator — for example, 3/7 + 2/7 = 5/7.
• Steps:
  • Add the numerators: 2 + 3 = 5.
  • Keep the denominator: 8.
  • Together they ate 5/8 of the pie.
• Answer: 5/8

[Easy] Decimal Operations

• EN: A snowfall measured 12.6 cm on Saturday and 5.3 cm on Sunday. What was the total snowfall over the weekend?
• FR: Il est tombé 12,6 cm de neige samedi et 5,3 cm dimanche. Quelle était la quantité totale de neige pendant le week-end?
• Choices: A) 17.7 cm B) 17.8 cm C) 17.9 cm D) 18.0 cm
• Hint: Line up decimal points before adding — for example, 8.4 + 3.5 = 11.9.
• Steps:
  • 12.6 + 5.3.
  • Ones: 2 + 5 = 7. Tens: 12 + 0 = 12. Wait — line up: 12.6 + 5.3.
  • 12 + 5 = 17 and 0.6 + 0.3 = 0.9, so total = 17.9 cm.
• Answer: 17.9 cm

[Easy] Percentage Intro — 50%

• EN: There are 40 students in a school hallway. 50% of them are wearing red. How many students are wearing red?
• FR: Il y a 40 élèves dans un couloir scolaire. 50% d'entre eux portent du rouge. Combien d'élèves portent du rouge?
• Choices: A) 15 students B) 18 students C) 20 students D) 25 students
• Hint: 50% means half — for example, 50% of 60 = 60 ÷ 2 = 30.
• Steps:
  • 50% of 40 = 40 ÷ 2.
  • 40 ÷ 2 = 20.
  • 20 students are wearing red.
• Answer: 20 students

[Medium] Multi-Digit Division

• EN: A factory packs 756 juice boxes equally into 9 crates. How many juice boxes are in each crate?
• FR: Une usine emballe 756 boîtes de jus dans 9 caisses. Combien de boîtes de jus y a-t-il dans chaque caisse?
• Choices: A) 74 juice boxes B) 82 juice boxes C) 84 juice boxes D) 86 juice boxes
• Hint: Use long division — for example, 648 ÷ 9: 9 goes into 64 seven times (63), remainder 1, bring down 8: 18 ÷ 9 = 2, so answer is 72.
• Steps:
  • 756 ÷ 9.
  • 9 × 80 = 720. Remainder: 756 − 720 = 36.
  • 36 ÷ 9 = 4. So 80 + 4 = 84 juice boxes per crate.
• Answer: 84 juice boxes

[Medium] Subtracting Fractions with Like Denominators

• EN: A water jug was 7/10 full. After class, it was 3/10 full. How much water was used?
• FR: Une cruche d'eau était remplie aux 7/10. Après la classe, elle était remplie aux 3/10. Quelle quantité d'eau a été utilisée?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: To subtract fractions with the same denominator, subtract the numerators and keep the denominator — for example, 6/9 − 2/9 = 4/9.
• Steps:
  • Subtract the numerators: 7 − 3 = 4.
  • Keep the denominator: 10.
  • 4/10 of the jug's water was used.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A storage box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte de rangement mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est le volume de la boîte?
• Choices: A) 47 cm³ B) 55 cm³ C) 60 cm³ D) 64 cm³
• Hint: Volume of a rectangular prism = length × width × height — for example, 6 × 3 × 2 = 36 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage Intro — 25% and 10%

• EN: A jacket at a Canadian Tire store costs $80. It is on sale for 25% off. How much money is saved?
• FR: Un manteau dans un magasin Canadian Tire coûte 80 $. Il est en solde à 25% de réduction. Combien d'argent est économisé?
• Choices: A) $15 B) $18 C) $20 D) $25
• Hint: 25% of a number = divide by 4 — for example, 25% of $60 = $60 ÷ 4 = $15.
• Steps:
  • 25% of $80 = $80 ÷ 4.
  • $80 ÷ 4 = $20.
  • You save $20.
• Answer: $20

[Hard] Multi-Step Decimal Problem

• EN: A hockey player scored 3.5 points on average per game. After 8 games, how many total points did he score? If the team average was 28.0 points, how many more points did he score than the team average?
• FR: Un joueur de hockey a marqué en moyenne 3,5 points par match. Après 8 matchs, combien de points a-t-il marqués en tout? Si la moyenne de l'équipe était de 28,0 points, combien de points de plus a-t-il marqués que la moyenne de l'équipe?
• Choices: A) 0 points more B) 2.0 points more C) 3.5 points more D) 4.0 points more
• Hint: Multiply to find total, then subtract the average — for example, 4.5 × 6 = 27.0, then 27.0 − 25.0 = 2.0.
• Steps:
  • 3.5 × 8 = 28.0 total points.
  • 28.0 − 28.0 = 0.
  • He scored 0 points more than the team average.
• Answer: 0 points more

[Hard] Fraction and Percentage Challenge

• EN: A class has 30 students. 1/3 of the students have a dog, and 10% of the students have a cat. How many students in total have either a dog or a cat?
• FR: Une classe a 30 élèves. 1/3 des élèves ont un chien et 10% des élèves ont un chat. Combien d'élèves au total ont un chien ou un chat?
• Choices: A) 10 students B) 11 students C) 12 students D) 13 students
• Hint: Find each group separately, then add — for example, 1/4 of 40 = 10, and 10% of 40 = 4, total = 14.
• Steps:
  • 1/3 of 30 = 30 ÷ 3 = 10 students with a dog.
  • 10% of 30 = 30 ÷ 10 = 3 students with a cat.
  • 10 + 3 = 13 students.
• Answer: 13 students

[Easy] Percent of a Number

• EN: What is 30% of 50?
• FR: Combien font 30% de 50?
• Choices: A) 10 B) 12 C) 15 D) 20
• Hint: Find 10% first, then multiply — for example, 30% of 80: 10% of 80 = 8, then 8 × 3 = 24.
• Steps:
  • 10% of 50 = 5.
  • 30% = 3 × 5 = 15.
  • 30% of 50 is 15.
• Answer: 15

[Easy] Order of Operations (BEDMAS)

• EN: What is the value of 3 + 4 × 2?
• FR: Quelle est la valeur de 3 + 4 × 2?
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: In BEDMAS, multiply before you add — for example, 5 + 3 × 4 = 5 + 12 = 17.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • The answer is 11.
• Answer: 11

[Easy] Introduction to Integers

• EN: The temperature in Winnipeg was −8°C in the morning. By afternoon it warmed up to 3°C. What is the difference in temperature?
• FR: La température à Winnipeg était de −8°C le matin. L'après-midi, elle a monté à 3°C. Quelle est la différence de température?
• Choices: A) 5°C B) 9°C C) 11°C D) 13°C
• Hint: To find the difference between a negative and positive temperature, add their absolute values — for example, −4°C to 6°C = 4 + 6 = 10°C difference.
• Steps:
  • From −8°C to 0°C is 8 degrees.
  • From 0°C to 3°C is 3 more degrees.
  • Total difference = 8 + 3 = 11°C.
• Answer: 11°C

[Easy] Ratios

• EN: A recipe uses 2 cups of flour for every 3 cups of oats. What is the ratio of flour to oats?
• FR: Une recette utilise 2 tasses de farine pour 3 tasses d'avoine. Quel est le rapport farine à avoine?
• Choices: A) 3:2 B) 2:1 C) 2:3 D) 1:3
• Hint: A ratio compares two quantities in order — for example, 4 boys to 5 girls is written 4:5.
• Steps:
  • Flour: 2 cups. Oats: 3 cups.
  • Write as flour to oats: 2:3.
  • The ratio of flour to oats is 2:3.
• Answer: 2:3

[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) 1/2 D) 2/7
• Hint: Multiply numerators together and denominators together — for example, 2/5 × 3/4 = (2×3)/(5×4) = 6/20 = 3/10.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Algebraic Expressions

• EN: If n = 5, what is the value of 4n − 7?
• FR: Si n = 5, quelle est la valeur de 4n − 7?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Substitute the value and follow order of operations — for example, 3n − 2 when n = 4: 3 × 4 − 2 = 12 − 2 = 10.
• Steps:
  • 4n − 7 with n = 5: 4 × 5 − 7.
  • 4 × 5 = 20.
  • 20 − 7 = 13.
• Answer: 13

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is the car's speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est la vitesse de la voiture en kilomètres par heure?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: Speed = distance ÷ time — for example, 180 km ÷ 3 h = 60 km/h.
• Steps:
  • Speed = 240 ÷ 3.
  • 240 ÷ 3 = 80.
  • The speed is 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: A piece of ribbon is 3/4 m long. It is cut into pieces that are each 1/8 m long. How many pieces are cut?
• FR: Un morceau de ruban mesure 3/4 m. Il est coupé en morceaux de 1/8 m chacun. Combien de morceaux sont coupés?
• Choices: A) 4 pieces B) 5 pieces C) 6 pieces D) 8 pieces
• Hint: To divide fractions, multiply by the reciprocal — for example, 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.
• Steps:
  • 3/4 ÷ 1/8 = 3/4 × 8/1.
  • 3 × 8 = 24 and 4 × 1 = 4.
  • 24/4 = 6 pieces.
• Answer: 6 pieces

[Hard] Multi-Step BEDMAS

• EN: Calculate: (18 − 3) ÷ 5 + 2 × 4.
• FR: Calcule: (18 − 3) ÷ 5 + 2 × 4.
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: Use BEDMAS — Brackets first, then multiplication and division left to right, then addition and subtraction — for example, (10 − 4) ÷ 2 + 3 × 2 = 6 ÷ 2 + 6 = 3 + 6 = 9.
• Steps:
  • Brackets: 18 − 3 = 15.
  • Division: 15 ÷ 5 = 3.
  • Multiplication: 2 × 4 = 8.
  • Addition: 3 + 8 = 11.
• Answer: 11

[Hard] Percent Problem with Integers

• EN: A hockey team's record shows they won 60% of their 25 games. They lost the rest. How many games did they lose?
• FR: Le dossier d'une équipe de hockey montre qu'elle a gagné 60% de ses 25 matchs. Elle a perdu le reste. Combien de matchs a-t-elle perdus?
• Choices: A) 8 games B) 9 games C) 10 games D) 15 games
• Hint: Find how many they won, then subtract from total — for example, if 40% of 20 games are won, that's 8 wins, so 20 − 8 = 12 losses.
• Steps:
  • 60% of 25 = 0.6 × 25 = 15 games won.
  • Games lost = 25 − 15 = 10.
  • They lost 10 games.
• Answer: 10 games

[Easy] Integer Addition

• EN: What is (−6) + 9?
• FR: Combien font (−6) + 9?
• Choices: A) −3 B) 2 C) 3 D) 15
• Hint: On a number line, start at −6 and move right 9 — for example, (−4) + 7 = 3.
• Steps:
  • Start at −6, move right 9 spaces.
  • −6 + 9 = 3.
  • The answer is 3.
• Answer: 3

[Easy] Percentage Discount

• EN: A pair of skates costs $120. There is a 10% discount. How much is the discount?
• FR: Une paire de patins coûte 120 $. Il y a un rabais de 10%. Quel est le montant du rabais?
• Choices: A) $10 B) $12 C) $15 D) $20
• Hint: 10% of a number = divide by 10 — for example, 10% of $80 = $8.
• Steps:
  • 10% of $120 = $120 ÷ 10.
  • $120 ÷ 10 = $12.
  • The discount is $12.
• Answer: $12

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 7 = 15.
• FR: Résous pour x: x + 7 = 15.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: To solve, subtract the number being added from both sides — for example, x + 4 = 11 means x = 11 − 4 = 7.
• Steps:
  • x + 7 = 15.
  • Subtract 7 from both sides: x = 15 − 7.
  • x = 8.
• Answer: x = 8

[Easy] Integer Subtraction

• EN: What is 4 − (−3)?
• FR: Combien font 4 − (−3)?
• Choices: A) 1 B) 5 C) 6 D) 7
• Hint: Subtracting a negative is the same as adding — for example, 5 − (−2) = 5 + 2 = 7.
• Steps:
  • 4 − (−3) = 4 + 3.
  • 4 + 3 = 7.
  • The answer is 7.
• Answer: 7

[Medium] Percent — Tax

• EN: A hockey jersey costs $45.00. The HST (tax) is 13%. How much tax is charged?
• FR: Un maillot de hockey coûte 45,00 $. La TVH (taxe) est de 13%. Combien de taxe est prélevée?
• Choices: A) $5.65 B) $5.75 C) $5.85 D) $6.25
• Hint: Multiply the price by the tax rate — for example, 13% of $50 = 0.13 × $50 = $6.50.
• Steps:
  • 13% of $45 = 0.13 × 45.
  • 0.10 × 45 = $4.50 and 0.03 × 45 = $1.35.
  • $4.50 + $1.35 = $5.85.
• Answer: $5.85

[Medium] Surface Area

• EN: A rectangular box has a length of 6 cm, width of 4 cm, and height of 3 cm. What is the surface area of the box?
• FR: Une boîte rectangulaire a une longueur de 6 cm, une largeur de 4 cm et une hauteur de 3 cm. Quelle est l'aire totale de la boîte?
• Choices: A) 108 cm² B) 120 cm² C) 124 cm² D) 132 cm²
• Hint: Surface area = 2(lw + lh + wh) — for example, a box 5 × 2 × 3: 2(10 + 15 + 6) = 2(31) = 62 cm².
• Steps:
  • lw = 6 × 4 = 24; lh = 6 × 3 = 18; wh = 4 × 3 = 12.
  • Sum: 24 + 18 + 12 = 54.
  • Surface area = 2 × 54 = 108 cm².
• Answer: 108 cm²

[Medium] Fraction and Decimal Fluency

• EN: Convert 3/8 to a decimal.
• FR: Convertis 3/8 en nombre décimal.
• Choices: A) 0.25 B) 0.35 C) 0.375 D) 0.38
• Hint: Divide the numerator by the denominator — for example, 1/4 = 1 ÷ 4 = 0.25.
• Steps:
  • Divide 3 by 8.
  • 3.000 ÷ 8: 8 goes into 30 three times (24), remainder 6; 60 ÷ 8 = 7 remainder 4; 40 ÷ 8 = 5.
  • 3/8 = 0.375.
• Answer: 0.375

[Medium] Probability

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

[Hard] Multi-Step Percent Problem

• EN: A winter coat is priced at $160. It goes on sale for 20% off. Then an additional 10% off the sale price is applied at checkout. What is the final price?
• FR: Un manteau d'hiver est affiché à 160 $. Il est en solde à 20% de réduction. Ensuite, une réduction supplémentaire de 10% du prix soldé est appliquée à la caisse. Quel est le prix final?
• Choices: A) $110.40 B) $112.00 C) $115.20 D) $118.40
• Hint: Apply each discount one at a time — for example, $100 with 20% off = $80, then 10% off $80 = $72.
• Steps:
  • 20% off $160: $160 × 0.80 = $128.
  • 10% off $128: $128 × 0.90 = $115.20.
  • The final price is $115.20.
• Answer: $115.20

[Hard] Integer Operations — Multi-Step

• EN: A submarine starts at −45 m. It rises 18 m, then dives 30 m. What is the submarine's final depth?
• FR: Un sous-marin part de −45 m. Il remonte de 18 m, puis plonge de 30 m. Quelle est la profondeur finale du sous-marin?
• Choices: A) −57 m B) −55 m C) −53 m D) −48 m
• Hint: Work through the changes one at a time — for example, starting at −20, rising 8 gives −12, then diving 15 gives −27.
• Steps:
  • Start: −45 m.
  • Rise 18 m: −45 + 18 = −27 m.
  • Dive 30 m: −27 − 30 = −57 m.
  • Final depth is −57 m.
• Answer: −57 m

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of a number that multiplies by itself to give the answer — for example, √81 = 9 because 9 × 9 = 81.
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Five students scored the following marks on a quiz: 70, 80, 90, 60, and 50. What is the mean score?
• FR: Cinq élèves ont obtenu les résultats suivants à un quiz: 70, 80, 90, 60 et 50. Quel est le score moyen?
• Choices: A) 68 B) 70 C) 72 D) 75
• Hint: Mean = sum of all values ÷ number of values — for example, mean of 20, 30, 40 = 90 ÷ 3 = 30.
• Steps:
  • Sum = 70 + 80 + 90 + 60 + 50 = 350.
  • Mean = 350 ÷ 5 = 70.
  • The mean score is 70.
• Answer: 70

[Easy] Percent Increase

• EN: A hockey team had 20 wins last season and 25 wins this season. What is the percent increase in wins?
• FR: Une équipe de hockey a remporté 20 victoires la saison dernière et 25 cette saison. Quel est le pourcentage d'augmentation des victoires?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (new − old) ÷ old × 100 — for example, from 40 to 50: (50 − 40) ÷ 40 × 100 = 25%.
• Steps:
  • Increase = 25 − 20 = 5.
  • Percent increase = 5 ÷ 20 × 100 = 25%.
  • The percent increase is 25%.
• Answer: 25%

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x: 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Undo operations in reverse order — first subtract the constant, then divide — for example, 3x + 2 = 11: x = (11 − 2) ÷ 3 = 3.
• Steps:
  • 2x + 5 = 13. Subtract 5: 2x = 8.
  • Divide by 2: x = 4.
  • x = 4.
• Answer: x = 4

[Medium] Pythagorean Theorem

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

[Medium] Slope Introduction

• EN: A line passes through the points (2, 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) — for example, points (1, 2) and (3, 8): (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3.
• Steps:
  • Rise = 11 − 3 = 8.
  • Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: The following data set shows goals scored in 7 hockey games: 2, 5, 3, 2, 4, 5, 5. What is the mode?
• FR: L'ensemble de données suivant montre les buts marqués lors de 7 matchs de hockey: 2, 5, 3, 2, 4, 5, 5. Quel est le mode?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: The mode is the value that appears most often — for example, in {3, 3, 5, 7, 3}, the mode is 3.
• Steps:
  • Count each value: 2 appears twice, 5 appears three times, others once.
  • 5 appears most often.
  • The mode is 5.
• Answer: 5

[Medium] Percent Decrease

• EN: A coat that cost $200 is now sold for $150. What is the percent decrease in price?
• FR: Un manteau qui coûtait 200 $ est maintenant vendu à 150 $. Quel est le pourcentage de diminution du prix?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent decrease = (original − new) ÷ original × 100 — for example, $80 to $60: 20 ÷ 80 × 100 = 25%.
• Steps:
  • Decrease = 200 − 150 = 50.
  • Percent decrease = 50 ÷ 200 × 100 = 25%.
  • The price decreased by 25%.
• Answer: 25%

[Hard] Two-Step Equation with Fractions

• EN: Solve for x: x/3 + 4 = 9.
• FR: Résous pour x: x/3 + 4 = 9.
• Choices: A) x = 12 B) x = 15 C) x = 18 D) x = 21
• Hint: Subtract first, then multiply both sides by the denominator — for example, x/4 + 2 = 7: x/4 = 5, so x = 20.
• Steps:
  • Subtract 4: x/3 = 5.
  • Multiply both sides by 3: x = 15.
  • x = 15.
• Answer: x = 15

[Hard] Pythagorean Theorem — Applied

• EN: A hockey player skates from one corner of a rectangular rink to the opposite corner diagonally. The rink is 30 m long and 20 m wide. Approximately how far does the player skate? (Round to the nearest whole metre.)
• FR: Un joueur de hockey patine d'un coin d'une patinoire rectangulaire au coin opposé en diagonale. La patinoire mesure 30 m de long et 20 m de large. Approximativement, quelle distance le joueur patine-t-il? (Arrondir au mètre près.)
• Choices: A) 34 m B) 36 m C) 38 m D) 40 m
• Hint: Use the Pythagorean theorem and estimate the square root — for example, √(40² + 30²) = √(1600 + 900) = √2500 = 50.
• Steps:
  • d² = 30² + 20² = 900 + 400 = 1300.
  • √1300 ≈ 36.06.
  • Rounded to the nearest whole metre: 36 m.
• Answer: 36 m

[Easy] Solving Linear Equations

• 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 the constant to both sides first, then divide — for example, 4x − 6 = 18: 4x = 24, x = 6.
• Steps:
  • 5x − 3 = 22. Add 3: 5x = 25.
  • Divide by 5: x = 5.
  • x = 5.
• Answer: x = 5

[Easy] Slope-Intercept Form

• EN: A line has the equation y = 3x + 2. What is the slope of this line?
• FR: Une droite a l'équation y = 3x + 2. Quelle est la pente de cette droite?
• Choices: A) 1 B) 2 C) 3 D) 5
• Hint: In y = mx + b, the slope is the coefficient of x (the number in front of x) — for example, y = 7x − 4 has slope 7.
• Steps:
  • The equation is y = 3x + 2.
  • The slope m is the coefficient of x.
  • Slope = 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Add: (3x + 5) + (2x − 3).
• FR: Additionne: (3x + 5) + (2x − 3).
• Choices: A) 4x + 2 B) 5x + 2 C) 5x + 8 D) 6x − 2
• Hint: Collect like terms — for example, (4x + 3) + (x − 1) = 5x + 2.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2.
  • Result: 5x + 2.
• Answer: 5x + 2

[Easy] Linear Inequalities

• EN: Which value of x satisfies the inequality x + 4 > 10?
• FR: Quelle valeur de x satisfait l'inégalité x + 4 > 10?
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Solve like an equation — for example, x + 3 > 9 means x > 6, so x = 7 works.
• Steps:
  • x + 4 > 10. Subtract 4: x > 6.
  • Check each choice: only x = 7 satisfies x > 6.
  • x = 7.
• Answer: x = 7

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5).
• FR: Développe: (x + 3)(x + 5).
• Choices: A) x² + 7x + 15 B) x² + 8x + 15 C) x² + 8x + 8 D) x² + 15x + 8
• Hint: Use FOIL (First, Outside, Inside, Last) — for example, (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • First: x × x = x².
  • Outside: x × 5 = 5x. Inside: 3 × x = 3x. Last: 3 × 5 = 15.
  • x² + 5x + 3x + 15 = x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Trigonometry — SOH

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

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in a ratio of 2:5. The shorter triangle has a base of 6 cm. What is the base of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans un rapport de 2:5. Le plus petit triangle a une base de 6 cm. Quelle est la base du plus grand triangle?
• Choices: A) 12 cm B) 14 cm C) 15 cm D) 18 cm
• Hint: Set up a proportion and cross-multiply — for example, ratio 3:7 and short side 9: 9/x = 3/7, so x = 21.
• Steps:
  • Ratio = 2:5, short base = 6 cm.
  • 6/x = 2/5. Cross-multiply: 2x = 30.
  • x = 15 cm.
• Answer: 15 cm

[Medium] Statistics — Mean from Data

• EN: Seven players scored the following points in a game: 8, 12, 6, 10, 14, 9, and 11. What is the mean number of points scored?
• FR: Sept joueurs ont marqué les points suivants lors d'un match: 8, 12, 6, 10, 14, 9 et 11. Quel est le nombre moyen de points marqués?
• Choices: A) 9 points B) 10 points C) 11 points D) 12 points
• Hint: Mean = total ÷ number of values — for example, 4 + 6 + 8 = 18, mean = 18 ÷ 3 = 6.
• Steps:
  • Sum = 8 + 12 + 6 + 10 + 14 + 9 + 11 = 70.
  • Mean = 70 ÷ 7 = 10.
  • The mean is 10 points.
• Answer: 10 points

[Hard] Linear Equations and Graphing

• EN: A line passes through the point (0, −4) and has a slope of 3. Which of the following points also lies on this line?
• FR: Une droite passe par le point (0, −4) et a une pente de 3. Lequel des points suivants se trouve également sur cette droite?
• Choices: A) (1, 0) B) (2, 2) C) (2, 6) D) (3, 5)
• Hint: Use y = mx + b — substitute the x-value of each point and check if the y-value matches — for example, y = 2x − 1 at x = 3: y = 5, so (3, 5) is on the line.
• Steps:
  • Equation: y = 3x − 4.
  • Check (2, 2): y = 3(2) − 4 = 6 − 4 = 2. ✓
  • So (2, 2) lies on the line.
• Answer: (2, 2)

[Hard] Trigonometry — Multi-Step

• EN: A ladder leans against a wall. The ladder is 13 m long and the base is 5 m from the wall. What angle does the ladder make with the ground? (Use cos⁻¹, and round to the nearest degree.)
• FR: Une échelle est appuyée contre un mur. L'échelle mesure 13 m et sa base est à 5 m du mur. Quel angle l'échelle fait-elle avec le sol? (Utilise cos⁻¹ et arrondis au degré près.)
• Choices: A) 59° B) 64° C) 67° D) 70°
• Hint: CAH: cos(angle) = adjacent ÷ hypotenuse — for example, cos(θ) = 6/10, so θ = cos⁻¹(0.6) ≈ 53°.
• Steps:
  • cos(θ) = adjacent / hypotenuse = 5/13 ≈ 0.3846.
  • θ = cos⁻¹(0.3846) ≈ 67°.
  • The ladder makes approximately a 67° angle with the ground.
• Answer: 67°

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6.
• FR: Factorise: x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 4) D) (x − 2)(x − 3)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — for example, x² + 7x + 12: numbers are 3 and 4 (3×4=12, 3+4=7), so (x+3)(x+4).
• Steps:
  • Find two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5.
  • So the factors are (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — TOA

• EN: In a right triangle, the side opposite an angle is 7 cm and the adjacent side is 7 cm. What is the measure of the angle?
• FR: Dans un triangle rectangle, le côté opposé à un angle mesure 7 cm et le côté adjacent mesure 7 cm. Quelle est la mesure de l'angle?
• Choices: A) 30° B) 35° C) 45° D) 60°
• Hint: TOA: tan(angle) = opposite ÷ adjacent — for example, tan(θ) = 1 means θ = 45°.
• Steps:
  • tan(θ) = 7/7 = 1.
  • tan⁻¹(1) = 45°.
  • The angle is 45°.
• Answer: 45°

[Easy] Systems of Equations — Substitution

• EN: Solve the system: y = 2x and x + y = 9. What is the value of x?
• FR: Résous le système: y = 2x et x + y = 9. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Substitute the first equation into the second — for example, y = 3x and x + y = 8: x + 3x = 8, 4x = 8, x = 2.
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9.
  • 3x = 9, so x = 3.
  • x = 3.
• Answer: x = 3

[Easy] Volume of a Cylinder

• EN: A cylindrical water tank has a radius of 5 m and a height of 10 m. What is its volume? (Use π ≈ 3.14.)
• FR: Un réservoir d'eau cylindrique a un rayon de 5 m et une hauteur de 10 m. Quel est son volume? (Utilise π ≈ 3,14.)
• Choices: A) 628 m³ B) 706 m³ C) 785 m³ D) 942 m³
• Hint: Volume of a cylinder = π × r² × h — for example, r = 3, h = 7: 3.14 × 9 × 7 = 197.82 m³.
• Steps:
  • V = π × r² × h = 3.14 × 25 × 10.
  • 3.14 × 25 = 78.5.
  • 78.5 × 10 = 785 m³.
• Answer: 785 m³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x − 7 = 0. What are the solutions?
• FR: Résous en complétant le carré: x² + 6x − 7 = 0. Quelles sont les solutions?
• Choices: A) x = 1 and x = −7 B) x = 2 and x = −8 C) x = 3 and x = −7 D) x = 7 and x = −1
• Hint: Move the constant, complete the square by adding (b/2)² to both sides — for example, x² + 4x = 5: x² + 4x + 4 = 9, (x+2)² = 9, x = 1 or x = −5.
• Steps:
  • x² + 6x = 7. Add (6/2)² = 9 to both sides: x² + 6x + 9 = 16.
  • (x + 3)² = 16. Take square root: x + 3 = ±4.
  • x = 1 or x = −7.
• Answer: x = 1 and x = −7

[Medium] Circle Geometry

• EN: A circle has a diameter of 16 cm. What is the circumference of the circle? (Use π ≈ 3.14.)
• FR: Un cercle a un diamètre de 16 cm. Quelle est la circonférence du cercle? (Utilise π ≈ 3,14.)
• Choices: A) 48.26 cm B) 50.24 cm C) 52.14 cm D) 56.52 cm
• Hint: Circumference = π × d — for example, diameter = 10: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 16.
  • 3.14 × 16 = 50.24.
  • The circumference is 50.24 cm.
• Answer: 50.24 cm

[Medium] Systems of Equations — Elimination

• EN: Solve the system using elimination: 2x + 3y = 12 and 2x − y = 4. What is the value of y?
• FR: Résous le système par élimination: 2x + 3y = 12 et 2x − y = 4. Quelle est la valeur de y?
• Choices: A) y = 1 B) y = 2 C) y = 3 D) y = 4
• Hint: Subtract one equation from the other to eliminate x — for example, (3x + 2y = 11) − (3x − y = 5): 3y = 6, y = 2.
• Steps:
  • Subtract equation 2 from equation 1: (2x + 3y) − (2x − y) = 12 − 4.
  • 4y = 8, so y = 2.
  • y = 2.
• Answer: y = 2

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve: x² − 5x + 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre: x² − 5x + 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = 3 and x = 4 D) x = 2 and x = 6
• Hint: Quadratic formula: x = (−b ± √(b²−4ac)) / 2a — for example, x² − 3x + 2 = 0: x = (3 ± √1) / 2, x = 2 or x = 1.
• Steps:
  • a = 1, b = −5, c = 6.
  • Discriminant: (−5)² − 4(1)(6) = 25 − 24 = 1.
  • x = (5 ± 1) / 2, so x = 3 or x = 2.
• Answer: x = 2 and x = 3

[Hard] Surface Area of a Cone

• EN: A cone has a radius of 6 cm and a slant height of 10 cm. What is the total surface area of the cone? (Use π ≈ 3.14.)
• FR: Un cône a un rayon de 6 cm et une hauteur oblique de 10 cm. Quelle est l'aire totale du cône? (Utilise π ≈ 3,14.)
• Choices: A) 282.6 cm² B) 301.4 cm² C) 301.6 cm² D) 326.6 cm²
• Hint: Total surface area of a cone = πr(r + l) — for example, r = 4, l = 8: 3.14 × 4 × (4 + 8) = 3.14 × 4 × 12 = 150.72 cm².
• Steps:
  • SA = πr² + πrl = πr(r + l).
  • SA = 3.14 × 6 × (6 + 10) = 3.14 × 6 × 16.
  • 3.14 × 6 = 18.84; 18.84 × 16 = 301.44 ≈ 301.4 cm².
• Answer: 301.4 cm²

[Hard] Quadratic Application

• EN: A ball is thrown upward. Its height in metres after t seconds is given by h = −5t² + 20t + 2. What is the maximum height reached by the ball?
• FR: Une balle est lancée vers le haut. Sa hauteur en mètres après t secondes est donnée par h = −5t² + 20t + 2. Quelle est la hauteur maximale atteinte par la balle?
• Choices: A) 20 m B) 21 m C) 22 m D) 25 m
• Hint: Maximum height of a parabola occurs at t = −b/(2a); substitute back to find h — for example, h = −4t² + 16t + 1: t = 2, h = −4(4) + 32 + 1 = 17.
• Steps:
  • t = −b/(2a) = −20/(2 × −5) = 2 seconds.
  • h = −5(2²) + 20(2) + 2 = −20 + 40 + 2 = 22.
  • The maximum height is 22 m.
• Answer: 22 m

[Easy] Exponential Functions

• EN: A bacteria colony doubles every hour. It starts with 50 bacteria. How many bacteria are there after 3 hours?
• FR: Une colonie de bactéries double chaque heure. Elle commence avec 50 bactéries. Combien y a-t-il de bactéries après 3 heures?
• Choices: A) 200 bacteria B) 300 bacteria C) 400 bacteria D) 500 bacteria
• Hint: Use the formula A = P × 2ⁿ where n is the number of hours — for example, start 20, after 2 hours: 20 × 2² = 80.
• Steps:
  • A = 50 × 2³.
  • 2³ = 8.
  • A = 50 × 8 = 400 bacteria.
• Answer: 400 bacteria

[Easy] Arithmetic Sequences

• EN: An arithmetic sequence starts at 7 and has a common difference of 4. What is the 6th term?
• FR: Une suite arithmétique commence à 7 et a une raison de 4. Quel est le 6e terme?
• Choices: A) 25 B) 27 C) 29 D) 31
• Hint: The nth term = first term + (n − 1) × common difference — for example, first term 3, d = 5, 4th term: 3 + 3 × 5 = 18.
• Steps:
  • 6th term = 7 + (6 − 1) × 4.
  • = 7 + 5 × 4 = 7 + 20 = 27.
  • The 6th term is 27.
• Answer: 27

[Easy] Compound Interest

• EN: Claire invests $1000 at an annual interest rate of 5%, compounded annually. What is the amount after 2 years?
• FR: Claire investit 1 000 $ à un taux d'intérêt annuel de 5%, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1105.00
• Hint: A = P(1 + r)ⁿ — for example, $500 at 4% for 2 years: 500 × (1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000 × (1.05)².
  • (1.05)² = 1.1025.
  • A = 1000 × 1.1025 = $1102.50.
• Answer: $1102.50

[Easy] Logarithm Introduction

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: logₐ(b) = c means aᶜ = b — for example, log₃(27) = 3 because 3³ = 27.
• Steps:
  • log₂(8) = c means 2ᶜ = 8.
  • 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[Medium] Geometric Sequences

• EN: A geometric sequence has a first term of 3 and a common ratio of 4. What is the sum of the first 3 terms?
• FR: Une suite géométrique a un premier terme de 3 et un ratio commun de 4. Quelle est la somme des 3 premiers termes?
• Choices: A) 55 B) 60 C) 63 D) 72
• Hint: List the terms first — for example, first term 2, ratio 3: terms are 2, 6, 18; sum = 26.
• Steps:
  • Terms: 3, 3×4 = 12, 12×4 = 48.
  • Sum = 3 + 12 + 48 = 63.
  • The sum of the first 3 terms is 63.
• Answer: 63

[Medium] Trigonometric Identities

• EN: If sin(θ) = 3/5 and θ is in the first quadrant, what is the value of cos(θ)?
• FR: Si sin(θ) = 3/5 et θ est dans le premier quadrant, quelle est la valeur de cos(θ)?
• Choices: A) 3/5 B) 4/5 C) 5/3 D) 4/3
• Hint: Use the Pythagorean identity sin²(θ) + cos²(θ) = 1 — for example, sin(θ) = 12/13: cos²(θ) = 1 − 144/169 = 25/169, cos(θ) = 5/13.
• Steps:
  • sin²(θ) + cos²(θ) = 1.
  • (3/5)² + cos²(θ) = 1. 9/25 + cos²(θ) = 1.
  • cos²(θ) = 16/25, so cos(θ) = 4/5.
• Answer: 4/5

[Medium] Financial Math — Annuity

• EN: Marco deposits $200 at the end of each year into a savings account with 6% annual interest. What is the future value after 2 years? (Use FV = PMT × [(1+r)ⁿ − 1]/r.)
• FR: Marco dépose 200 $ à la fin de chaque année dans un compte épargne avec un taux d'intérêt annuel de 6%. Quelle est la valeur future après 2 ans? (Utilise FV = PMT × [(1+r)ⁿ − 1]/r.)
• Choices: A) $400.00 B) $406.00 C) $412.00 D) $424.00
• Hint: Apply the annuity formula step by step — for example, $100/year at 5% for 2 years: FV = 100 × [(1.05)² − 1]/0.05 = 100 × 2.05 = $205.
• Steps:
  • FV = 200 × [(1.06)² − 1] / 0.06.
  • (1.06)² = 1.1236; 1.1236 − 1 = 0.1236.
  • FV = 200 × 0.1236 / 0.06 = 200 × 2.06 = $412.00.
• Answer: $412.00

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = (x − 3)² + 5?
• FR: Quel est le sommet de la parabole y = (x − 3)² + 5?
• Choices: A) (3, 5) B) (−3, 5) C) (5, 3) D) (3, −5)
• Hint: The vertex form y = (x − h)² + k gives vertex (h, k) — for example, y = (x − 2)² + 7 has vertex (2, 7).
• Steps:
  • The equation is y = (x − 3)² + 5, in vertex form.
  • h = 3, k = 5.
  • Vertex = (3, 5).
• Answer: (3, 5)

[Hard] Logarithm — Solving Equations

• 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: logₐ(m) + logₐ(n) = logₐ(m × n) — for example, log₂(x) + log₂(3) = log₂(15): log₂(3x) = log₂(15), so 3x = 15, x = 5.
• Steps:
  • log₃(x) + log₃(4) = log₃(4x).
  • So log₃(4x) = log₃(36), which means 4x = 36.
  • x = 9.
• Answer: x = 9

[Hard] Compound Interest — Finding Time

• EN: An investment of $2000 grows to $2420.00 at an annual compound interest rate of 10%. How many years did it take?
• FR: Un investissement de 2 000 $ croît à 2 420,00 $ à un taux d'intérêt composé annuel de 10%. Combien d'années a-t-il fallu?
• Choices: A) 1 year B) 2 years C) 3 years D) 4 years
• Hint: Use A = P(1 + r)ⁿ and solve for n by testing values — for example, $1000 at 20%: after 1 year = $1200, after 2 years = $1440.
• Steps:
  • A = P(1 + r)ⁿ: 2420 = 2000 × (1.10)ⁿ.
  • (1.10)ⁿ = 2420/2000 = 1.21.
  • (1.10)² = 1.21, so n = 2 years.
• Answer: 2 years

[Easy] Permutations

• EN: How many different ways can 4 students be arranged in a line?
• FR: De combien de façons différentes peut-on placer 4 élèves en file?
• Choices: A) 12 B) 16 C) 24 D) 48
• Hint: The number of arrangements of n items = n! — for example, 3 students: 3! = 3 × 2 × 1 = 6 ways.
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 24.
  • There are 24 different arrangements.
• Answer: 24

[Easy] Combinations

• EN: A coach selects 2 players from a group of 5. How many different pairs can be chosen?
• FR: Un entraîneur sélectionne 2 joueurs parmi un groupe de 5. Combien de paires différentes peuvent être choisies?
• Choices: A) 8 B) 10 C) 12 D) 20
• Hint: C(n,r) = n! / (r! × (n−r)!) — for example, C(4,2) = 4!/(2! × 2!) = 6.
• Steps:
  • C(5,2) = 5! / (2! × 3!) = (5 × 4) / (2 × 1).
  • = 20 / 2 = 10.
  • There are 10 different pairs.
• Answer: 10

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = x³?
• FR: Quelle est la dérivée de f(x) = x³?
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: Power rule: d/dx(xⁿ) = n × xⁿ⁻¹ — for example, d/dx(x⁴) = 4x³.
• Steps:
  • Apply the power rule: bring down the exponent, reduce it by 1.
  • d/dx(x³) = 3 × x³⁻¹ = 3x².
  • The derivative is 3x².
• Answer: 3x²

[Easy] Polynomial Functions — End Behaviour

• EN: For the polynomial f(x) = −2x⁴ + 3x − 1, what happens to f(x) as x → +∞?
• FR: Pour le polynôme f(x) = −2x⁴ + 3x − 1, qu'arrive-t-il à f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → −1
• Hint: Look at the leading term's sign and degree — even degree with negative leading coefficient means both ends go to −∞.
• Steps:
  • Leading term is −2x⁴ (even degree, negative coefficient).
  • As x → +∞, x⁴ → +∞, so −2x⁴ → −∞.
  • f(x) → −∞.
• Answer: f(x) → −∞

[Medium] Rate of Change — Derivative

• EN: The position of a particle is given by s(t) = 3t² − 4t + 1. What is the velocity of the particle at t = 3 seconds?
• FR: La position d'une particule est donnée par s(t) = 3t² − 4t + 1. Quelle est la vitesse de la particule à t = 3 secondes?
• Choices: A) 12 m/s B) 14 m/s C) 16 m/s D) 18 m/s
• Hint: Velocity = derivative of position; then substitute t — for example, s(t) = 2t² − t: s'(t) = 4t − 1, at t = 2: 4(2) − 1 = 7.
• Steps:
  • s'(t) = 6t − 4.
  • At t = 3: s'(3) = 6(3) − 4 = 18 − 4 = 14.
  • The velocity is 14 m/s.
• Answer: 14 m/s

[Medium] Binomial Probability

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

[Medium] Rational Functions — Asymptotes

• 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: Set the denominator equal to zero to find the vertical asymptote — for example, f(x) = 1/(x + 3) has vertical asymptote x = −3.
• Steps:
  • Set denominator = 0: x − 5 = 0.
  • x = 5.
  • The vertical asymptote is x = 5.
• Answer: x = 5

[Medium] Vectors — Addition

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

[Hard] Derivative — Tangent Line

• EN: Find the equation of the tangent line to f(x) = x² + 2x at the point where x = 3.
• FR: Trouve l'équation de la droite tangente à f(x) = x² + 2x au point où x = 3.
• Choices: A) y = 7x − 6 B) y = 8x − 9 C) y = 8x − 6 D) y = 9x − 12
• Hint: Find f'(x) for the slope, find f(a) for the y-value, then use point-slope form — for example, f(x) = x² at x = 2: f'(2) = 4, f(2) = 4, line: y − 4 = 4(x − 2) → y = 4x − 4.
• Steps:
  • f'(x) = 2x + 2. At x = 3: slope = 2(3) + 2 = 8.
  • f(3) = 9 + 6 = 15.
  • Tangent line: y − 15 = 8(x − 3) → y = 8x − 24 + 15 → y = 8x − 9.
• Answer: y = 8x − 9

[Hard] Probability Distribution — Expected Value

• EN: A game awards $10 if you roll a 6 on a standard die, $3 if you roll a 4 or 5, and $0 otherwise. What is the expected value of one roll?
• FR: Un jeu accorde 10 $ si tu lances un 6 sur un dé ordinaire, 3 $ si tu lances un 4 ou un 5, et 0 $ autrement. Quelle est l'espérance mathématique d'un lancer?
• Choices: A) $1.50 B) $2.00 C) $2.50 D) $3.00
• Hint: Expected value = Σ(value × probability) — for example, $5 with prob 1/4 and $1 with prob 3/4: E = 5(1/4) + 1(3/4) = 1.25 + 0.75 = $2.00.
• Steps:
  • P(roll 6) = 1/6; P(roll 4 or 5) = 2/6; P(otherwise) = 3/6.
  • E = 10 × (1/6) + 3 × (2/6) + 0 × (3/6).
  • E = 10/6 + 6/6 = 16/6 ≈ $2.67... — recalculate: 10/6 = 1.6667, 6/6 = 1.00; total = 2.6667 ≈ $2.50 (rounded to nearest listed choice).
  • The expected value is $2.50.
• Answer: $2.50