Daily Math — 2026-09-30

[Easy] Counting to 20

• EN: There are 7 apples on the table and 5 more in a basket. How many apples are there in total?
• FR: Il y a 7 pommes sur la table et 5 de plus dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Try counting on from the bigger number, like 8 + 4 — start at 8 and count up 4.
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • So 7 + 5 = 12.
• Answer: 12

[Easy] Skip Counting by 2s

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

[Easy] Comparing Numbers

• EN: Which number is bigger: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 16
• Hint: Think about counting — numbers that come later are bigger, just like 6 is bigger than 3.
• Steps:
  • 14 is a two-digit number; 9 is a one-digit number.
  • Two-digit numbers are always greater than one-digit numbers.
  • So 14 is bigger.
• Answer: 14

[Easy] Coin Recognition

• EN: Emma has 1 dime and 1 nickel. How much money does she have in total?
• FR: Emma 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 — add them together like 10 + 3.
• Steps:
  • A dime = 10 cents, a nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Medium] Subtraction within 20

• EN: There are 16 hockey pucks in a bag. A coach takes out 8. How many pucks are left?
• FR: Il y a 16 rondelles dans un sac. Un entraîneur en retire 8. Combien de rondelles reste-t-il?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To subtract, like 14 − 6, count back from 14 six steps.
• Steps:
  • Start at 16 and count back 8: 15, 14, 13, 12, 11, 10, 9, 8.
  • So 16 − 8 = 8.
• Answer: 8

[Medium] Skip Counting by 5s

• EN: Count by 5s. What number comes next: 5, 10, 15, ___?
• FR: Compte par bonds de 5. Quel nombre vient ensuite : 5, 10, 15, ___?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: Skip counting by 5s means adding 5 each time, like 10 + 5 = 15.
• Steps:
  • Each number is 5 more than the one before: 5, 10, 15.
  • 15 + 5 = 20.
• Answer: 20

[Medium] Addition with Coins

• EN: Liam has 2 nickels. How many cents does he have in total?
• FR: Liam a 2 pièces de cinq cents. Combien de cents a-t-il en tout?
• Choices: A) 5 cents B) 8 cents C) 10 cents D) 12 cents
• Hint: If you have 2 dimes, that is 10 + 10 = 20 cents — use the same idea with nickels.
• Steps:
  • Each nickel = 5 cents.
  • 5 + 5 = 10 cents.
• Answer: 10 cents

[Medium] Counting to 100

• EN: What number comes just before 30?
• FR: Quel nombre vient juste avant 30?
• Choices: A) 27 B) 28 C) 29 D) 31
• Hint: The number just before 10 is 9 — use the same idea for 30.
• Steps:
  • Count: …27, 28, 29, 30.
  • The number just before 30 is 29.
• Answer: 29

[Hard] Adding Three Numbers

• EN: Sofia has 4 red crayons, 5 blue crayons, and 6 yellow crayons. How many crayons does she have altogether?
• FR: Sofia a 4 crayons rouges, 5 crayons bleus et 6 crayons jaunes. Combien de crayons a-t-elle en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: To add three numbers like 2 + 3 + 4, first add two of them: 2 + 3 = 5, then 5 + 4 = 9.
• Steps:
  • First add 4 + 5 = 9.
  • Then add 9 + 6 = 15.
• Answer: 15

[Hard] Subtraction Story Problem

• EN: There are 18 students in a class. 9 students go outside to play. How many students are still inside?
• FR: Il y a 18 élèves dans une classe. 9 élèves sortent jouer. Combien d'élèves sont encore à l'intérieur?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: For 15 − 7, think of what plus 7 equals 15 — that is your answer.
• Steps:
  • Think: 9 + ___ = 18.
  • 9 + 9 = 18, so 18 − 9 = 9.
• Answer: 9

[Easy] Addition within 100

• EN: A store has 34 apples and gets 25 more. How many apples does the store have now?
• FR: Un magasin a 34 pommes et en reçoit 25 de plus. Combien de pommes le magasin a-t-il maintenant?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: For 42 + 31, add the tens first: 40 + 30 = 70, then add the ones: 2 + 1 = 3, giving 73.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59.
• Answer: 59

[Easy] Telling Time to the Hour

• EN: The clock shows the short hand on 7 and the long hand on 12. What time is it?
• FR: L'horloge montre la petite aiguille sur le 7 et la grande aiguille sur le 12. Quelle heure est-il?
• Choices: A) 6:00 B) 7:00 C) 8:00 D) 12:07
• Hint: When the long hand points to 12, it is always on the hour — just read where the short hand points.
• Steps:
  • Long hand on 12 means it is exactly on the hour.
  • Short hand on 7 means it is 7 o'clock.
  • The time is 7:00.
• Answer: 7:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A eraser is 4 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 14 cm de long. Une gomme mesure 4 cm de long. De combien le crayon est-il plus long que la gomme?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 18 cm
• Hint: To find how much longer, subtract the smaller length from the bigger one, like 12 − 3 = 9.
• Steps:
  • Subtract the eraser length from the pencil length.
  • 14 − 4 = 10.
  • The pencil is 10 cm longer.
• Answer: 10 cm

[Easy] Counting Coins

• EN: Remy has 3 dimes. How many cents does he have?
• FR: Remy a 3 pièces de dix cents. Combien de cents a-t-il?
• Choices: A) 13 cents B) 20 cents C) 30 cents D) 33 cents
• Hint: If you have 4 dimes, count by 10s: 10, 20, 30, 40 — that is 40 cents.
• Steps:
  • Each dime = 10 cents.
  • Count by 10s: 10, 20, 30.
  • 3 dimes = 30 cents.
• Answer: 30 cents

[Medium] Subtraction within 100

• EN: A hockey team scored 71 points at the end of the season. They scored 43 points in the first half. How many points did they score in the second half?
• FR: Une équipe de hockey a marqué 71 points à la fin de la saison. Ils ont marqué 43 points dans la première moitié. Combien de points ont-ils marqués dans la deuxième moitié?
• Choices: A) 27 B) 28 C) 29 D) 38
• Hint: For 85 − 52, subtract the tens: 80 − 50 = 30, then the ones: 5 − 2 = 3, giving 33.
• Steps:
  • Subtract: 71 − 43.
  • 71 − 40 = 31, then 31 − 3 = 28.
  • They scored 28 points in the second half.
• Answer: 28

[Medium] Telling Time to the Half-Hour

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

[Medium] Simple Patterns

• EN: Look at this pattern: 2, 4, 6, 8, ___. What number comes next?
• FR: Regarde ce motif : 2, 4, 6, 8, ___. Quel nombre vient ensuite?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Find the rule first — for 5, 10, 15, 20, the rule is +5 each time.
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
• Answer: 10

[Medium] Adding Money

• EN: Aisha has 2 quarters. How many cents does she have?
• FR: Aisha a 2 pièces de vingt-cinq cents. Combien de cents a-t-elle?
• Choices: A) 25 cents B) 40 cents C) 50 cents D) 75 cents
• Hint: One quarter = 25 cents, so 3 quarters would be 25 + 25 + 25 = 75 cents.
• Steps:
  • Each quarter = 25 cents.
  • 25 + 25 = 50 cents.
• Answer: 50 cents

[Hard] Measuring and Comparing

• EN: Maya's desk is 80 cm wide. Her bookshelf is 1 m wide. How much wider is the bookshelf than the desk?
• FR: Le bureau de Maya mesure 80 cm de large. Sa bibliothèque mesure 1 m de large. De combien la bibliothèque est-elle plus large que le bureau?
• Choices: A) 10 cm B) 20 cm C) 30 cm D) 80 cm
• Hint: Remember that 1 m = 100 cm — then subtract to compare, like 100 − 75 = 25.
• Steps:
  • Convert 1 m to centimetres: 1 m = 100 cm.
  • Subtract: 100 − 80 = 20 cm.
  • The bookshelf is 20 cm wider.
• Answer: 20 cm

[Hard] Two-Step Money Problem

• EN: Ben has 45 cents. He earns 30 more cents for helping. He then spends 25 cents on a sticker. How many cents does he have left?
• FR: Ben a 45 cents. Il gagne 30 cents de plus en aidant. Il dépense ensuite 25 cents pour un autocollant. Combien de cents lui reste-t-il?
• Choices: A) 40 cents B) 45 cents C) 50 cents D) 55 cents
• Hint: Work in two steps: first add what you earn, then subtract what you spend.
• Steps:
  • Start: 45 cents. Add 30 cents: 45 + 30 = 75 cents.
  • Spend 25 cents: 75 − 25 = 50 cents.
• Answer: 50 cents

[Easy] Multiplication by 2

• EN: A pair of mittens has 2 mittens. How many mittens are in 6 pairs?
• FR: Une paire de mitaines contient 2 mitaines. Combien de mitaines y a-t-il dans 6 paires?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiplying by 2 is the same as doubling — like 5 × 2 = 10.
• Steps:
  • 6 pairs × 2 mittens each = 6 × 2.
  • 6 × 2 = 12.
• Answer: 12

[Easy] Multiplication by 5

• EN: There are 5 players on each basketball team. How many players are on 4 teams?
• FR: Il y a 5 joueurs dans chaque équipe de basketball. Combien de joueurs y a-t-il dans 4 équipes?
• Choices: A) 15 B) 20 C) 25 D) 30
• Hint: Counting by 5s: 5, 10, 15, 20 — so 4 × 5 = 20.
• Steps:
  • 4 teams × 5 players = 4 × 5.
  • 4 × 5 = 20.
• Answer: 20

[Easy] Basic Fractions

• EN: A pizza is cut into 4 equal pieces. Mia eats 1 piece. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 parts égales. Mia mange 1 part. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: The bottom number is how many total equal pieces, and the top number is how many you have.
• Steps:
  • Total pieces = 4, pieces eaten = 1.
  • Fraction = 1 out of 4 = 1/4.
• Answer: 1/4

[Easy] Perimeter of a Rectangle

• EN: A garden is 5 m long and 3 m wide. What is its perimeter?
• FR: Un jardin mesure 5 m de long et 3 m de large. Quel est son périmètre?
• Choices: A) 8 m B) 13 m C) 15 m D) 16 m
• Hint: Perimeter of a rectangle = add all four sides. For a 4 m by 2 m rectangle: 4 + 2 + 4 + 2 = 12 m.
• Steps:
  • Add all four sides: 5 + 3 + 5 + 3.
  • 5 + 3 = 8, 8 + 5 = 13, 13 + 3 = 16 m.
• Answer: 16 m

[Medium] Division

• EN: There are 24 crayons to share equally among 4 students. How many crayons does each student get?
• FR: Il y a 24 crayons à partager également entre 4 élèves. Combien de crayons chaque élève reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Division is the opposite of multiplication — think: 4 × ___ = 24.
• Steps:
  • Think: 4 × ___ = 24.
  • 4 × 6 = 24.
  • Each student gets 6 crayons.
• Answer: 6

[Medium] Multiplication by 3

• EN: A Tim Hortons box holds 3 muffins. How many muffins are in 7 boxes?
• FR: Une boîte de Tim Hortons contient 3 muffins. Combien de muffins y a-t-il dans 7 boîtes?
• Choices: A) 18 B) 21 C) 24 D) 28
• Hint: Skip count by 3s seven times: 3, 6, 9, 12, 15, 18, 21.
• Steps:
  • 7 × 3: count by 3s — 3, 6, 9, 12, 15, 18, 21.
  • 7 × 3 = 21.
• Answer: 21

[Medium] Reading a Graph

• EN: A bar graph shows snowfall: Monday 4 cm, Tuesday 7 cm, Wednesday 3 cm. How much snow fell altogether over the three days?
• FR: Un graphique à barres montre les chutes de neige : lundi 4 cm, mardi 7 cm, mercredi 3 cm. Combien de neige est tombée en tout sur les trois jours?
• Choices: A) 11 cm B) 12 cm C) 13 cm D) 14 cm
• Hint: To find the total, add all the amounts together, like 5 + 6 + 2 = 13.
• Steps:
  • Monday + Tuesday + Wednesday = 4 + 7 + 3.
  • 4 + 7 = 11, then 11 + 3 = 14 cm.
• Answer: 14 cm

[Medium] Comparing Fractions

• EN: Which fraction is greater: 1/2 or 1/4?
• FR: Quelle fraction est plus grande : 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/2 C) They are equal D) 2/4
• Hint: Imagine cutting a sandwich — 1/2 is one cut making 2 pieces, 1/4 is cutting into 4 pieces. Bigger pieces means a bigger fraction.
• Steps:
  • 1/2 means 1 piece out of 2 equal pieces.
  • 1/4 means 1 piece out of 4 equal pieces.
  • Fewer pieces means each piece is bigger, so 1/2 > 1/4.
• Answer: 1/2

[Hard] Multiplication Table 10

• EN: A school fundraiser sold 10 tickets each day for 9 days. How many tickets were sold in total?
• FR: Une collecte de fonds scolaire a vendu 10 billets par jour pendant 9 jours. Combien de billets ont été vendus en tout?
• Choices: A) 80 B) 85 C) 90 D) 99
• Hint: Multiplying by 10 is easy — just place a zero after the number, like 10 × 7 = 70.
• Steps:
  • 9 × 10 = 90.
  • A zero after 9 gives 90.
• Answer: 90

[Hard] Two-Step Word Problem

• EN: A pet store has 5 cages. Each cage holds 4 rabbits. The store owner sells 8 rabbits. How many rabbits are left?
• FR: Une animalerie a 5 cages. Chaque cage contient 4 lapins. Le propriétaire vend 8 lapins. Combien de lapins reste-t-il?
• Choices: A) 10 B) 12 C) 13 D) 17
• Hint: First multiply to find the total, then subtract what was sold — like 3 × 5 = 15, then 15 − 6 = 9.
• Steps:
  • Total rabbits: 5 × 4 = 20.
  • Rabbits left: 20 − 8 = 12.
• Answer: 12

[Easy] Multiplication Tables to 9×9

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Think of 7 × 7 = 49, then add one more group of 7 to get 7 × 8.
• Steps:
  • 7 × 8 = 56.
  • You can check: 7 × 7 = 49, and 49 + 7 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 4.37?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,37?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 30 ones
• Hint: In the number 5.62, the 6 is in the tenths place and the 2 is in the hundredths place.
• Steps:
  • 4.37 — the 4 is in the ones place, the 3 is in the tenths place, the 7 is in the hundredths place.
  • The digit 3 has a value of 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A classroom rug is 6 m long and 4 m wide. What is the area of the rug?
• FR: Un tapis de salle de classe mesure 6 m de long et 4 m de large. Quelle est l'aire du tapis?
• Choices: A) 10 m² B) 20 m² C) 24 m² D) 28 m²
• Hint: Area of a rectangle = length × width, like a 5 m by 3 m rectangle has area 5 × 3 = 15 m².
• Steps:
  • Area = length × width = 6 × 4.
  • 6 × 4 = 24 m².
• Answer: 24 m²

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 2/4?
• FR: Quelle fraction est plus grande : 3/4 ou 2/4?
• Choices: A) 2/4 B) 3/4 C) They are equal D) 1/4
• Hint: When fractions have the same denominator (bottom number), just compare the numerators (top number).
• Steps:
  • Both fractions have 4 as the denominator.
  • Compare the numerators: 3 > 2.
  • So 3/4 is larger.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: 47 students are going on a field trip. Each bus holds 8 students. How many buses are needed to take all the students?
• FR: 47 élèves partent en excursion. Chaque autobus peut accueillir 8 élèves. Combien d'autobus sont nécessaires pour transporter tous les élèves?
• Choices: A) 5 buses B) 6 buses C) 7 buses D) 8 buses
• Hint: Divide and check the remainder — if there are any students left over, you need one extra bus.
• Steps:
  • 47 ÷ 8 = 5 remainder 7.
  • 5 buses hold 40 students; 7 students still need a bus.
  • You need 5 + 1 = 6 buses.
• Answer: 6 buses

[Medium] Elapsed Time

• EN: School starts at 8:30 a.m. and ends at 3:00 p.m. How long is the school day?
• FR: L'école commence à 8 h 30 et se termine à 15 h 00. Quelle est la durée de la journée scolaire?
• Choices: A) 5 hours 30 minutes B) 6 hours C) 6 hours 30 minutes D) 7 hours
• Hint: Count up from the start time to the end time — from 9:00 to 3:00 is 6 hours, then adjust for the extra 30 minutes.
• Steps:
  • From 8:30 to 9:00 is 30 minutes.
  • From 9:00 to 3:00 is 6 hours.
  • Total: 6 hours + 30 minutes = 6 hours 30 minutes.
• Answer: 6 hours 30 minutes

[Medium] Decimal Operations

• EN: A book costs $4.75 and a pencil case costs $3.50. How much do they cost together?
• FR: Un livre coûte 4,75 $ et un étui à crayons coûte 3,50 $. Combien coûtent-ils ensemble?
• Choices: A) $7.25 B) $8.00 C) $8.25 D) $8.50
• Hint: Line up the decimal points when adding decimals, just like 3.20 + 2.45 = 5.65.
• Steps:
  • $4.75 + $3.50.
  • Cents: 75 + 50 = 125 cents = $1.25 carry over $1.
  • Dollars: $4 + $3 + $1 = $8.25.
• Answer: $8.25

[Medium] Multiplying by Multiples of 10

• EN: A school orders 6 boxes of crayons. Each box has 40 crayons. How many crayons are there in total?
• FR: Une école commande 6 boîtes de crayons. Chaque boîte contient 40 crayons. Combien de crayons y a-t-il en tout?
• Choices: A) 180 B) 200 C) 240 D) 260
• Hint: Multiply 6 × 4 = 24 first, then add a zero because of the 40 — giving 240.
• Steps:
  • 6 × 40 = 6 × 4 × 10.
  • 6 × 4 = 24, then 24 × 10 = 240.
• Answer: 240

[Hard] Long Division

• EN: A farmer harvested 96 apples and wants to pack them equally into bags of 8. How many bags will he need?
• FR: Un fermier a récolté 96 pommes et veut les emballer également dans des sacs de 8. Combien de sacs lui faudra-t-il?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: For 72 ÷ 8, think: 8 × 9 = 72, so the answer is 9.
• Steps:
  • 96 ÷ 8 = ?
  • 8 × 12 = 96 (check: 8 × 10 = 80, 8 × 2 = 16, 80 + 16 = 96).
  • He needs 12 bags.
• Answer: 12

[Hard] Two-Step Problem with Decimals

• EN: Zara buys a loonie (worth $1.00) and a toonie (worth $2.00) from her piggy bank. She spends $1.75 at the school book fair. How much money does she have left?
• FR: Zara prend un dollar et un deux-dollars de sa tirelire. Elle dépense 1,75 $ à la foire du livre scolaire. Combien d'argent lui reste-t-il?
• Choices: A) $0.75 B) $1.00 C) $1.25 D) $2.25
• Hint: First add the coins together, then subtract the amount spent.
• Steps:
  • Total money: $1.00 + $2.00 = $3.00.
  • Spent: $3.00 − $1.75 = $1.25.
• Answer: $1.25

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 184 B) 200 C) 204 D) 208
• Hint: Break apart the number: 30 × 6 = 180 and 4 × 6 = 24, then add them together.
• Steps:
  • 34 × 6 = (30 + 4) × 6.
  • 30 × 6 = 180, 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/8 + 3/8?
• FR: Combien font 2/8 + 3/8?
• Choices: A) 4/8 B) 5/8 C) 5/16 D) 6/8
• Hint: When denominators are the same, just add the numerators and keep the denominator — like 1/5 + 2/5 = 3/5.
• Steps:
  • Same denominator (8), so add numerators: 2 + 3 = 5.
  • Answer: 5/8
• Answer: 5/8

[Easy] Percentage Intro — 50%

• EN: 50% of 80 students went on a field trip. How many students went?
• FR: 50% des 80 élèves sont allés en excursion. Combien d'élèves y sont allés?
• Choices: A) 30 B) 35 C) 40 D) 50
• Hint: 50% means half — so just divide by 2, like 50% of 60 = 30.
• Steps:
  • 50% of 80 = 80 ÷ 2.
  • 80 ÷ 2 = 40.
• Answer: 40

[Easy] Decimal Operations

• EN: 12.6 − 5.3 = ?
• FR: 12,6 − 5,3 = ?
• Choices: A) 6.3 B) 7.2 C) 7.3 D) 8.3
• Hint: Line up the decimal points, then subtract just like whole numbers — 14.8 − 6.5 = 8.3.
• Steps:
  • Line up decimals: 12.6 − 5.3.
  • 12 − 5 = 7 and 0.6 − 0.3 = 0.3.
  • Answer: 7.3
• Answer: 7.3

[Medium] Multi-Digit Division

• EN: 348 ÷ 4 = ?
• FR: 348 ÷ 4 = ?
• Choices: A) 82 B) 85 C) 87 D) 92
• Hint: Use long division — divide 3 hundreds by 4, then bring down the tens digit, and so on.
• Steps:
  • 3 ÷ 4 = 0 remainder 3; bring down 4 to get 34.
  • 34 ÷ 4 = 8 remainder 2; bring down 8 to get 28.
  • 28 ÷ 4 = 7.
  • So 348 ÷ 4 = 87.
• Answer: 87

[Medium] Subtracting Fractions

• EN: What is 7/10 − 4/10?
• FR: Combien font 7/10 − 4/10?
• Choices: A) 2/10 B) 3/10 C) 3/0 D) 4/10
• Hint: With like denominators, subtract the numerators only and keep the denominator — like 6/9 − 2/9 = 4/9.
• Steps:
  • Same denominator (10), subtract numerators: 7 − 4 = 3.
  • Answer: 3/10
• Answer: 3/10

[Medium] 25% of a Number

• EN: A hockey jersey originally costs $60. It is on sale for 25% off. How much is the discount?
• FR: Un chandail de hockey coûte à l'origine 60 $. Il est en solde avec 25% de rabais. Quel est le rabais?
• Choices: A) $12 B) $15 C) $20 D) $25
• Hint: 25% = 1/4, so divide the total by 4 — like 25% of $80 = $80 ÷ 4 = $20.
• Steps:
  • 25% of $60 = $60 ÷ 4.
  • $60 ÷ 4 = $15.
  • The discount is $15.
• Answer: $15

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 80 cm³
• Hint: Volume = length × width × height — like a box 6 cm × 2 cm × 4 cm has volume 48 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Hard] 10% of a Number in Context

• EN: A store gives 10% of all sales to charity. In one week, sales totalled $430. How much goes to charity?
• FR: Un magasin donne 10% de toutes ses ventes à un organisme de bienfaisance. En une semaine, les ventes totales étaient de 430 $. Combien va à la bienfaisance?
• Choices: A) $40 B) $43 C) $44 D) $50
• Hint: 10% of any number means divide by 10 — like 10% of $250 = $25.
• Steps:
  • 10% of $430 = $430 ÷ 10.
  • $430 ÷ 10 = $43.
• Answer: $43

[Hard] Multi-Step Fraction and Decimal Problem

• EN: Olivia had 2.50 m of ribbon. She used 3/5 of it for a project. How many metres of ribbon does she have left?
• FR: Olivia avait 2,50 m de ruban. Elle en a utilisé 3/5 pour un projet. Combien de mètres de ruban lui reste-t-il?
• Choices: A) 0.50 m B) 1.00 m C) 1.50 m D) 2.00 m
• Hint: First find 3/5 of the total by multiplying total × 3 ÷ 5, then subtract from the total.
• Steps:
  • 3/5 of 2.50 m = 2.50 × 3 ÷ 5 = 7.50 ÷ 5 = 1.50 m used.
  • Remaining: 2.50 − 1.50 = 1.00 m.
• Answer: 1.00 m

[Easy] Percent of a Number

• EN: What is 30% of 90?
• FR: Combien font 30% de 90?
• Choices: A) 21 B) 27 C) 30 D) 33
• Hint: Find 10% first (divide by 10), then multiply by 3 — like 10% of 50 = 5, so 30% of 50 = 15.
• Steps:
  • 10% of 90 = 90 ÷ 10 = 9.
  • 30% = 3 × 9 = 27.
• Answer: 27

[Easy] Integers Introduction

• EN: The temperature in Winnipeg was −5°C in the morning and rose 8 degrees by noon. What was the temperature at noon?
• FR: La température à Winnipeg était de −5°C le matin et a augmenté de 8 degrés avant midi. Quelle était la température à midi?
• Choices: A) −3°C B) 2°C C) 3°C D) 13°C
• Hint: Moving right on a number line means adding — start at −8 and add 5 to get −3.
• Steps:
  • Start at −5 and add 8.
  • −5 + 8 = 3.
  • The temperature at noon was 3°C.
• Answer: 3°C

[Easy] Ratios

• EN: In a bag of marbles, there are 4 red and 6 blue marbles. What is the ratio of red to blue marbles?
• FR: Dans un sac de billes, il y a 4 billes rouges et 6 billes bleues. Quel est le rapport entre les billes rouges et les billes bleues?
• Choices: A) 2:3 B) 3:2 C) 4:10 D) 6:4
• Hint: A ratio compares two amounts — 4:6 can be simplified by dividing both numbers by 2.
• Steps:
  • Ratio of red to blue = 4:6.
  • Simplify by dividing both by 2: 4 ÷ 2 = 2, 6 ÷ 2 = 3.
  • Simplified ratio = 2:3.
• Answer: 2:3

[Easy] Order of Operations (BEDMAS)

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

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/7 B) 5/12 C) 6/12 D) 1/2
• Hint: To multiply fractions, multiply the numerators together and the denominators together — like 2/5 × 1/3 = 2/15.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Rate Problems

• EN: A car travels 120 km in 2 hours. At this rate, how far will it travel in 5 hours?
• FR: Une voiture parcourt 120 km en 2 heures. À ce rythme, quelle distance parcourra-t-elle en 5 heures?
• Choices: A) 240 km B) 280 km C) 300 km D) 360 km
• Hint: Find the unit rate first (km per hour), then multiply by the number of hours.
• Steps:
  • Rate = 120 km ÷ 2 h = 60 km/h.
  • Distance in 5 hours = 60 × 5 = 300 km.
• Answer: 300 km

[Medium] Simple Algebraic Expressions

• EN: Evaluate 5n − 3 when n = 4.
• FR: Évalue 5n − 3 quand n = 4.
• Choices: A) 12 B) 17 C) 18 D) 23
• Hint: Substitute the value for the variable — for 3x + 2 when x = 5, calculate 3 × 5 + 2 = 17.
• Steps:
  • Replace n with 4: 5(4) − 3.
  • 5 × 4 = 20.
  • 20 − 3 = 17.
• Answer: 17

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 2
• Hint: To divide by a fraction, multiply by its reciprocal — like 2/5 ÷ 1/3 = 2/5 × 3/1 = 6/5.
• Steps:
  • Flip the divisor: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 3/2.
• Answer: 3/2

[Hard] BEDMAS with Multiple Operations

• EN: Evaluate: (12 − 4) × 3 + 6 ÷ 2
• FR: Évalue : (12 − 4) × 3 + 6 ÷ 2
• Choices: A) 24 B) 27 C) 30 D) 33
• Hint: Use BEDMAS — Brackets first, then Multiply and Divide left to right, then Add and Subtract.
• Steps:
  • Brackets: 12 − 4 = 8.
  • Multiply: 8 × 3 = 24.
  • Divide: 6 ÷ 2 = 3.
  • Add: 24 + 3 = 27.
• Answer: 27

[Hard] Percentage with Tax

• EN: A book costs $14.00. The GST (tax) is 5%. What is the total cost of the book including tax?
• FR: Un livre coûte 14,00 $. La TPS (taxe) est de 5%. Quel est le coût total du livre avec la taxe?
• Choices: A) $14.50 B) $14.70 C) $15.00 D) $16.00
• Hint: Find 5% of the price first (divide by 20), then add it to the original price.
• Steps:
  • 5% of $14.00 = $14.00 ÷ 20 = $0.70.
  • Total = $14.00 + $0.70 = $14.70.
• Answer: $14.70

[Easy] Integer Addition

• EN: What is (−6) + 9?
• FR: Combien font (−6) + 9?
• Choices: A) −15 B) −3 C) 3 D) 15
• Hint: On a number line, start at −6 and move right 9 steps — like starting at −4 and moving right 6 gives +2.
• Steps:
  • Start at −6, add 9.
  • −6 + 9 = 3.
• Answer: 3

[Easy] Fraction and Decimal Fluency

• EN: Write 3/5 as a decimal.
• FR: Écris 3/5 sous forme décimale.
• Choices: A) 0.35 B) 0.5 C) 0.6 D) 0.65
• Hint: Divide the numerator by the denominator — like 1/4 = 1 ÷ 4 = 0.25.
• Steps:
  • 3/5 = 3 ÷ 5.
  • 3 ÷ 5 = 0.6.
• Answer: 0.6

[Easy] Percentage — Discount

• EN: A $40 backpack is 20% off. How much money do you save?
• FR: Un sac à dos de 40 $ est réduit de 20%. Combien économisez-vous?
• Choices: A) $4 B) $6 C) $8 D) $10
• Hint: 20% = 2 × 10%, so find 10% first and then double it — 10% of $50 = $5, so 20% = $10.
• Steps:
  • 10% of $40 = $4.
  • 20% = 2 × $4 = $8.
  • You save $8.
• Answer: $8

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 7 = 15
• FR: Résous pour x : x + 7 = 15
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 22
• Hint: To solve x + 5 = 12, subtract 5 from both sides: x = 12 − 5 = 7.
• Steps:
  • Subtract 7 from both sides: x = 15 − 7.
  • x = 8.
• Answer: x = 8

[Medium] Integer Subtraction

• EN: What is (−3) − (−8)?
• FR: Combien font (−3) − (−8)?
• Choices: A) −11 B) −5 C) 5 D) 11
• Hint: Subtracting a negative is like adding a positive — (−4) − (−6) = −4 + 6 = 2.
• Steps:
  • Change subtraction of a negative to addition: (−3) − (−8) = −3 + 8.
  • −3 + 8 = 5.
• Answer: 5

[Medium] Percentage — Tax and Tip

• EN: A meal at a restaurant costs $24.00. You want to leave a 15% tip. How much is the tip?
• FR: Un repas au restaurant coûte 24,00 $. Vous voulez laisser un pourboire de 15%. Quel est le montant du pourboire?
• Choices: A) $2.40 B) $3.00 C) $3.60 D) $4.80
• Hint: 15% = 10% + 5% — find 10% and half of that, then add together.
• Steps:
  • 10% of $24.00 = $2.40.
  • 5% = $2.40 ÷ 2 = $1.20.
  • 15% tip = $2.40 + $1.20 = $3.60.
• Answer: $3.60

[Medium] Surface Area

• EN: What is the surface area of a rectangular prism that is 4 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire totale d'un prisme rectangulaire de 4 cm de long, 3 cm de large et 2 cm de haut?
• Choices: A) 24 cm² B) 36 cm² C) 48 cm² D) 52 cm²
• Hint: Surface area = 2(lw + lh + wh) — find the area of each pair of faces and add them all together.
• Steps:
  • SA = 2(lw + lh + wh).
  • = 2(4×3 + 4×2 + 3×2).
  • = 2(12 + 8 + 6) = 2(26) = 52 cm².
• Answer: 52 cm²

[Medium] Probability

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

[Hard] Integer Multiplication and Division

• EN: Calculate: (−4) × (−3) ÷ (−2)
• FR: Calcule : (−4) × (−3) ÷ (−2)
• Choices: A) −6 B) 6 C) −12 D) 12
• Hint: Multiply first: negative × negative = positive. Then divide: positive ÷ negative = negative.
• Steps:
  • (−4) × (−3) = 12 (negative × negative = positive).
  • 12 ÷ (−2) = −6 (positive ÷ negative = negative).
• Answer: −6

[Hard] Two-Step Equation from Context

• EN: Kira thinks of a number, doubles it, and then adds 5. The result is 21. What was the number she started with?
• FR: Kira pense à un nombre, le double, puis ajoute 5. Le résultat est 21. Quel était le nombre de départ?
• Choices: A) 7 B) 8 C) 13 D) 16
• Hint: Write an equation — if "a number doubled plus 5 = 21", write 2n + 5 = 21 and solve for n.
• Steps:
  • Let n be the number: 2n + 5 = 21.
  • Subtract 5: 2n = 16.
  • Divide by 2: n = 8.
• Answer: 8

[Easy] Perfect Squares

• EN: What is √144?
• FR: Quelle est la valeur de √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of what number times itself gives you the answer — like √81 = 9 because 9 × 9 = 81.
• Steps:
  • Ask: what number times itself equals 144?
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of: 8, 12, 10, 14, 6
• FR: Trouve la moyenne de : 8, 12, 10, 14, 6
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Mean = sum of all values ÷ number of values — for 4, 6, 8, the mean is (4+6+8) ÷ 3 = 6.
• Steps:
  • Sum: 8 + 12 + 10 + 14 + 6 = 50.
  • Mean = 50 ÷ 5 = 10.
• Answer: 10

[Easy] Two-Step Equation

• EN: Solve: 3x + 4 = 19
• FR: Résous : 3x + 4 = 19
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: First subtract the number on the same side as x, then divide — for 2x + 3 = 11, subtract 3 to get 2x = 8, then divide by 2 to get x = 4.
• Steps:
  • Subtract 4 from both sides: 3x = 15.
  • Divide both sides by 3: x = 5.
• Answer: x = 5

[Easy] Percent Increase

• EN: A hockey card was worth $20 and is now worth $25. What is the percent increase?
• FR: Une carte de hockey valait 20 $ et vaut maintenant 25 $. Quel est le pourcentage d'augmentation?
• Choices: A) 15% B) 20% C) 25% D) 30%
• Hint: Percent increase = (increase ÷ original) × 100 — for a price going from $10 to $12, increase = $2, so 2 ÷ 10 × 100 = 20%.
• Steps:
  • Increase = $25 − $20 = $5.
  • Percent increase = (5 ÷ 20) × 100 = 0.25 × 100 = 25%.
• Answer: 25%

[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 jambes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Use a² + b² = c² — for legs 3 and 4, c² = 9 + 16 = 25, so c = 5.
• Steps:
  • c² = 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation — Harder

• EN: Solve: 4x − 7 = 21
• FR: Résous : 4x − 7 = 21
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the constant to both sides first, then divide — for 5x − 3 = 17, add 3 to get 5x = 20, then divide to get x = 4.
• Steps:
  • Add 7 to both sides: 4x = 28.
  • Divide by 4: x = 7.
• Answer: x = 7

[Medium] Slope Introduction

• EN: A line passes through (0, 1) and (3, 7). What is the slope of the line?
• FR: Une droite passe par les points (0, 1) et (3, 7). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (change in y) ÷ (change in x) — for points (1, 2) and (3, 6), slope = (6−2) ÷ (3−1) = 4 ÷ 2 = 2.
• Steps:
  • Rise (change in y) = 7 − 1 = 6.
  • Run (change in x) = 3 − 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 5, 2, 9, 5, 4
• FR: Trouve la médiane de : 3, 7, 5, 2, 9, 5, 4
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Sort the numbers from least to greatest, then find the middle value — for 2, 4, 6, 8, 10, the median is 6.
• Steps:
  • Sort: 2, 3, 4, 5, 5, 7, 9.
  • Middle value (4th of 7) = 5.
• Answer: 5

[Hard] Pythagorean Theorem in Context

• EN: A ladder leans against a wall. The base of the ladder is 5 m from the wall, and the ladder is 13 m long. How high up the wall does the ladder reach?
• FR: Une échelle est appuyée contre un mur. La base de l'échelle est à 5 m du mur, et l'échelle mesure 13 m. À quelle hauteur l'échelle touche-t-elle le mur?
• Choices: A) 8 m B) 10 m C) 12 m D) 14 m
• Hint: Use a² + b² = c² — the ladder is the hypotenuse. Rearrange to find the leg: a² = c² − b².
• Steps:
  • c = 13 (hypotenuse), b = 5 (base), find a.
  • a² = 13² − 5² = 169 − 25 = 144.
  • a = √144 = 12 m.
• Answer: 12 m

[Hard] Percent Decrease in Context

• EN: A winter coat was originally priced at $120. During a Boxing Day sale, it was reduced to $84. What is the percent decrease?
• FR: Un manteau d'hiver était initialement à 120 $. Lors d'une vente du lendemain de Noël, il a été réduit à 84 $. Quel est le pourcentage de réduction?
• Choices: A) 25% B) 30% C) 36% D) 40%
• Hint: Percent decrease = (decrease ÷ original price) × 100 — for a price from $80 to $60, decrease = $20, so 20 ÷ 80 × 100 = 25%.
• Steps:
  • Decrease = $120 − $84 = $36.
  • Percent decrease = (36 ÷ 120) × 100 = 0.30 × 100 = 30%.
• Answer: 30%

[Easy] Solving a Linear Equation

• EN: Solve: 2x − 5 = 11
• FR: Résous : 2x − 5 = 11
• Choices: A) x = 3 B) x = 6 C) x = 8 D) x = 13
• Hint: Add the constant to both sides first, then divide — for 3x − 2 = 13, add 2 to get 3x = 15, divide to get x = 5.
• Steps:
  • Add 5 to both sides: 2x = 16.
  • Divide both sides by 2: x = 8.
• Answer: x = 8

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x + 7?
• FR: Quelle est la pente de la droite y = 3x + 7?
• Choices: A) 1 B) 3 C) 7 D) 10
• Hint: In y = mx + b, the slope is always m (the coefficient of x) — in y = 5x + 2, the slope is 5.
• Steps:
  • The equation is in y = mx + b form.
  • The coefficient of x is 3, so the slope is 3.
• Answer: 3

[Easy] Adding Polynomials

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

[Easy] Linear Inequality

• EN: Solve: x + 4 > 10
• FR: Résous : x + 4 > 10
• Choices: A) x > 4 B) x > 6 C) x > 10 D) x > 14
• Hint: Solve inequalities just like equations — subtract 4 from both sides, like x + 3 > 9 gives x > 6.
• Steps:
  • Subtract 4 from both sides: x > 10 − 4.
  • x > 6.
• Answer: x > 6

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 4)
• FR: Développe : (x + 3)(x + 4)
• Choices: A) x² + 7x + 12 B) x² + 7x + 7 C) x² + 12x + 7 D) x² + 12x + 12
• Hint: Use FOIL — First, Outer, Inner, Last. For (x + 2)(x + 5): x² + 5x + 2x + 10 = x² + 7x + 10.
• Steps:
  • First: x × x = x².
  • Outer: x × 4 = 4x.
  • Inner: 3 × x = 3x.
  • Last: 3 × 4 = 12.
  • Combined: x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Graphing Lines

• EN: A line has slope 2 and y-intercept −3. Which equation represents this line?
• FR: Une droite a une pente de 2 et une ordonnée à l'origine de −3. Quelle équation représente cette droite?
• Choices: A) y = −3x + 2 B) y = 2x − 3 C) y = 3x − 2 D) y = −2x + 3
• Hint: Use y = mx + b where m is the slope and b is the y-intercept — slope 4 and y-intercept 1 gives y = 4x + 1.
• Steps:
  • m = 2, b = −3.
  • Equation: y = 2x − 3.
• Answer: y = 2x − 3

[Medium] Similar Triangles

• EN: Two similar triangles have sides in ratio 3:5. The shorter triangle has a side of 9 cm. What is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans le rapport 3:5. Le triangle le plus petit a un côté de 9 cm. Quel est le côté correspondant du triangle plus grand?
• Choices: A) 12 cm B) 13 cm C) 15 cm D) 18 cm
• Hint: Set up a proportion — 3/5 = 9/x, then cross-multiply and solve.
• Steps:
  • 3/5 = 9/x.
  • Cross-multiply: 3x = 45.
  • x = 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse 10 cm. Quelle est la valeur de sin(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.75
• Hint: SOH means sin = opposite ÷ hypotenuse — if opposite = 4 and hypotenuse = 8, sin = 4/8 = 0.5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 6 ÷ 10 = 0.6.
• Answer: 0.6

[Hard] Solving an Inequality and Graphing

• EN: Solve: 3x − 7 ≤ 14, and state the solution.
• FR: Résous : 3x − 7 ≤ 14, et énonce la solution.
• Choices: A) x ≤ 5 B) x ≤ 6 C) x ≤ 7 D) x ≤ 9
• Hint: Add 7 to both sides first, then divide both sides by 3 — just like solving an equation, the inequality sign stays the same when dividing by a positive number.
• Steps:
  • Add 7: 3x ≤ 21.
  • Divide by 3: x ≤ 7.
• Answer: x ≤ 7

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 5 cm and the adjacent side is 5 cm. What is the measure of angle θ? (Hint: use tan)
• FR: Dans un triangle rectangle, le côté opposé mesure 5 cm et le côté adjacent mesure 5 cm. Quelle est la mesure de l'angle θ? (Indice : utilise tan)
• Choices: A) 30° B) 45° C) 60° D) 90°
• Hint: tan(θ) = opposite ÷ adjacent — when both are equal, tan(θ) = 1, and tan⁻¹(1) = 45°.
• Steps:
  • tan(θ) = opposite ÷ adjacent = 5 ÷ 5 = 1.
  • θ = tan⁻¹(1) = 45°.
• Answer: 45°

[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 + 3) D) (x + 2)(x + 4)
• Hint: Find two numbers that multiply to 6 and add to 5 — for x² + 7x + 12, find two numbers that multiply to 12 and add to 7: 3 and 4.
• Steps:
  • Find two numbers: multiply to 6, add to 5.
  • Those numbers are 2 and 3 (2 × 3 = 6, 2 + 3 = 5).
  • Factored form: (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] 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 mesure 8 cm et l'hypoténuse 10 cm. Quelle est la valeur de cos(θ)?
• Choices: A) 0.6 B) 0.75 C) 0.8 D) 1.25
• Hint: CAH means cos = adjacent ÷ hypotenuse — if adjacent = 3 and hypotenuse = 5, cos = 3/5 = 0.6.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 8 ÷ 10 = 0.8.
• Answer: 0.8

[Easy] Surface Area of a Cylinder

• EN: What is the total surface area of a cylinder with radius 3 cm and height 5 cm? (Use π ≈ 3.14)
• FR: Quelle est l'aire totale d'un cylindre de rayon 3 cm et de hauteur 5 cm? (Utilise π ≈ 3,14)
• Choices: A) 47.1 cm² B) 94.2 cm² C) 150.72 cm² D) 188.4 cm²
• Hint: SA of cylinder = 2πr² + 2πrh — find the two circular ends plus the curved side.
• Steps:
  • Two circles: 2π(3²) = 2 × 3.14 × 9 = 56.52 cm².
  • Curved side: 2π(3)(5) = 2 × 3.14 × 15 = 94.20 cm².
  • Total: 56.52 + 94.20 = 150.72 cm².
• Answer: 150.72 cm²

[Easy] Systems of Equations — Substitution

• EN: If y = 2x and x + y = 12, what is the value of x?
• FR: Si y = 2x et x + y = 12, quelle est la valeur de x?
• Choices: A) x = 3 B) x = 4 C) x = 6 D) x = 8
• Hint: Substitute the expression for y into the second equation — if y = 3x and x + y = 8, then x + 3x = 8, so 4x = 8 and x = 2.
• Steps:
  • Substitute y = 2x into x + y = 12: x + 2x = 12.
  • 3x = 12, so x = 4.
• Answer: x = 4

[Medium] Solving a Quadratic by Factoring

• EN: Solve: x² − 7x + 12 = 0
• FR: Résous : x² − 7x + 12 = 0
• Choices: A) x = 2 or x = 6 B) x = 3 or x = 4 C) x = 1 or x = 12 D) x = 4 or x = 6
• Hint: Factor first — find two numbers that multiply to 12 and add to −7, then set each factor equal to zero.
• Steps:
  • Factor: two numbers that multiply to 12 and add to −7 are −3 and −4.
  • (x − 3)(x − 4) = 0.
  • x = 3 or x = 4.
• Answer: x = 3 or x = 4

[Medium] Circle Geometry

• EN: A circle has a radius of 7 cm. What is the area of the circle? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 7 cm. Quelle est l'aire du cercle? (Utilise π ≈ 3,14)
• Choices: A) 43.96 cm² B) 98.5 cm² C) 153.86 cm² D) 176.4 cm²
• Hint: Area of a circle = πr² — for a radius of 5, Area = 3.14 × 25 = 78.5 cm².
• Steps:
  • Area = πr² = 3.14 × 7².
  • 7² = 49.
  • Area = 3.14 × 49 = 153.86 cm².
• Answer: 153.86 cm²

[Medium] Volume of a Cone

• EN: What is the volume of a cone with radius 6 cm and height 9 cm? (Use π ≈ 3.14)
• FR: Quel est le volume d'un cône de rayon 6 cm et de hauteur 9 cm? (Utilise π ≈ 3,14)
• Choices: A) 169.56 cm³ B) 339.12 cm³ C) 508.68 cm³ D) 1017.36 cm³
• Hint: Volume of a cone = (1/3)πr²h — it is one third the volume of a cylinder with the same dimensions.
• Steps:
  • V = (1/3)πr²h = (1/3) × 3.14 × 6² × 9.
  • 6² = 36; 36 × 9 = 324.
  • V = (1/3) × 3.14 × 324 = 3.14 × 108 = 339.12 cm³.
• Answer: 339.12 cm³

[Medium] Systems of Equations — Elimination

• EN: Solve the system: 2x + y = 10 and x − y = 2. What is x?
• FR: Résous le système : 2x + y = 10 et x − y = 2. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Add the two equations together to eliminate y — the y terms will cancel if they have opposite signs.
• Steps:
  • Add equations: (2x + y) + (x − y) = 10 + 2.
  • 3x = 12.
  • x = 4.
• Answer: x = 4

[Hard] Completing the Square

• EN: Solve x² + 6x + 5 = 0 by completing the square.
• FR: Résous x² + 6x + 5 = 0 en complétant le carré.
• Choices: A) x = −1 or x = −5 B) x = 1 or x = 5 C) x = −2 or x = −3 D) x = 2 or x = 3
• Hint: Move the constant to the right side, then add (b/2)² to both sides — for x² + 4x = 5, add 4 to both sides to get (x+2)² = 9.
• Steps:
  • x² + 6x = −5.
  • Add (6/2)² = 9 to both sides: x² + 6x + 9 = 4.
  • (x + 3)² = 4 → x + 3 = ±2.
  • x = −1 or x = −5.
• Answer: x = −1 or x = −5

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, angle θ = 35° and the hypotenuse is 20 cm. What is the length of the opposite side (to 2 decimal places)? (sin 35° ≈ 0.574)
• FR: Dans un triangle rectangle, l'angle θ = 35° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé (à 2 décimales)? (sin 35° ≈ 0,574)
• Choices: A) 10.20 cm B) 11.48 cm C) 13.00 cm D) 16.38 cm
• Hint: sin(θ) = opposite ÷ hypotenuse, so opposite = hypotenuse × sin(θ) — like for a 45° angle and hypotenuse 14, opposite = 14 × 0.707 ≈ 9.90 cm.
• Steps:
  • sin(35°) = opposite ÷ 20.
  • Opposite = 20 × sin(35°) = 20 × 0.574 = 11.48 cm.
• Answer: 11.48 cm

[Easy] Evaluating a Function

• EN: For f(x) = 2x² − 3, find f(4).
• FR: Pour f(x) = 2x² − 3, trouve f(4).
• Choices: A) 25 B) 27 C) 29 D) 32
• Hint: Substitute the value into the function — for f(x) = 3x − 1, f(5) = 3(5) − 1 = 14.
• Steps:
  • f(4) = 2(4²) − 3.
  • 4² = 16; 2 × 16 = 32.
  • 32 − 3 = 29.
• Answer: 29

[Easy] Logarithms Introduction

• EN: What is log₂(32)?
• FR: Quelle est la valeur de log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log₂(32) asks: "2 to what power equals 32?" — like log₂(8) asks "2 to what power = 8?" and 2³ = 8, so the answer is 3.
• Steps:
  • Find the power: 2^? = 32.
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32.
  • log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequences

• EN: The first term of an arithmetic sequence is 3 and the common difference is 7. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 3 et la raison est 7. Quel est le 5ème terme?
• Choices: A) 28 B) 31 C) 35 D) 38
• Hint: The nth term formula is aₙ = a₁ + (n − 1)d — for a₁ = 2, d = 4, the 4th term = 2 + (3)(4) = 14.
• Steps:
  • aₙ = a₁ + (n − 1)d.
  • a₅ = 3 + (5 − 1) × 7 = 3 + 28 = 31.
• Answer: 31

[Easy] Compound Interest

• EN: $1000 is invested at 5% per year, compounded annually for 2 years. How much interest is earned?
• FR: 1000 $ est investi à 5% par an, capitalisé annuellement pendant 2 ans. Combien d'intérêts sont gagnés?
• Choices: A) $100.00 B) $102.50 C) $105.00 D) $110.00
• Hint: Use A = P(1 + r)ⁿ — for $500 at 4% for 2 years: A = 500(1.04)² = 500 × 1.0816 = $540.80, so interest = $40.80.
• Steps:
  • A = 1000(1 + 0.05)² = 1000(1.05)² = 1000 × 1.1025 = $1102.50.
  • Interest = $1102.50 − $1000 = $102.50.
• Answer: $102.50

[Medium] Exponential Function

• EN: A bacteria population doubles every hour. Starting with 50 bacteria, how many will there be after 4 hours?
• FR: Une population de bactéries double toutes les heures. En commençant avec 50 bactéries, combien y en aura-t-il après 4 heures?
• Choices: A) 400 B) 600 C) 800 D) 1200
• Hint: Exponential growth: A = P × 2ⁿ — for 20 bacteria doubling for 3 hours: 20 × 2³ = 20 × 8 = 160.
• Steps:
  • A = 50 × 2⁴.
  • 2⁴ = 16.
  • A = 50 × 16 = 800.
• Answer: 800

[Medium] Trigonometric Identity

• EN: If sin(θ) = 0.6, what is cos(θ)? (Use the identity sin²θ + cos²θ = 1, assume θ is in the first quadrant)
• FR: Si sin(θ) = 0,6, quelle est la valeur de cos(θ)? (Utilise l'identité sin²θ + cos²θ = 1, suppose que θ est dans le premier quadrant)
• Choices: A) 0.4 B) 0.6 C) 0.8 D) 1.0
• Hint: Use sin²θ + cos²θ = 1, rearrange to cos²θ = 1 − sin²θ, then take the square root.
• Steps:
  • sin²θ + cos²θ = 1.
  • (0.6)² + cos²θ = 1.
  • 0.36 + cos²θ = 1 → cos²θ = 0.64.
  • cos θ = √0.64 = 0.8.
• Answer: 0.8

[Medium] Geometric Sequence — Sum

• EN: Find the sum of the first 4 terms of the geometric sequence: 2, 6, 18, 54, …
• FR: Trouve la somme des 4 premiers termes de la suite géométrique : 2, 6, 18, 54, …
• Choices: A) 60 B) 70 C) 80 D) 90
• Hint: Add the terms directly, or use Sₙ = a(rⁿ − 1)/(r − 1) where a is the first term and r is the common ratio.
• Steps:
  • Sum = 2 + 6 + 18 + 54.
  • 2 + 6 = 8, 8 + 18 = 26, 26 + 54 = 80.
• Answer: 80

[Medium] Financial Math — Annuity

• EN: You deposit $200 at the end of each year into an account that earns 4% per year. What is the total value after 3 years? (Use the formula Sₙ = PMT × [(1+r)ⁿ − 1] / r)
• FR: Tu déposes 200 $ à la fin de chaque année dans un compte qui rapporte 4% par an. Quelle est la valeur totale après 3 ans? (Utilise la formule Sₙ = PMT × [(1+r)ⁿ − 1] / r)
• Choices: A) $600.00 B) $624.32 C) $648.00 D) $662.43
• Hint: Plug values into the annuity formula — PMT = 200, r = 0.04, n = 3.
• Steps:
  • S = 200 × [(1.04)³ − 1] / 0.04.
  • (1.04)³ = 1.124864; 1.124864 − 1 = 0.124864.
  • 0.124864 / 0.04 = 3.1216.
  • S = 200 × 3.1216 = $624.32.
• Answer: $624.32

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(9) = 4
• FR: Résous pour x : log₃(x) + log₃(9) = 4
• Choices: A) x = 3 B) x = 9 C) x = 27 D) x = 81
• Hint: Use the logarithm rule logₐ(m) + logₐ(n) = logₐ(mn), then convert the log equation to exponential form.
• Steps:
  • log₃(x) + log₃(9) = log₃(9x) = 4.
  • Convert: 9x = 3⁴ = 81.
  • x = 81 ÷ 9 = 9.
• Answer: x = 9

[Hard] Compound Interest — Solving for n

• EN: An investment of $500 grows to $605.00 at 10% per year, compounded annually. How many years did it take?
• FR: Un investissement de 500 $ atteint 605,00 $ à un taux de 10% par an, capitalisé annuellement. 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 check each year — after year 1: 500 × 1.1 = $550; after year 2: 550 × 1.1 = $605.
• Steps:
  • Year 1: 500 × 1.10 = $550.
  • Year 2: 550 × 1.10 = $605.
  • It took 2 years.
• Answer: 2 years

[Easy] Combinations

• EN: How many ways can you choose 3 students from a group of 6 to form a committee?
• FR: De combien de façons peut-on choisir 3 élèves parmi un groupe de 6 pour former un comité?
• Choices: A) 15 B) 18 C) 20 D) 24
• Hint: Use the combination formula C(n, r) = n! / (r!(n−r)!) — for C(5, 2) = 5!/(2!×3!) = 10.
• Steps:
  • C(6, 3) = 6! / (3! × 3!).
  • = (6 × 5 × 4) / (3 × 2 × 1) = 120 / 6 = 20.
• Answer: 20

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = 4x³.
• FR: Trouve la dérivée de f(x) = 4x³.
• Choices: A) 4x² B) 12x C) 12x² D) 16x²
• Hint: The power rule says: if f(x) = axⁿ, then f′(x) = a·n·xⁿ⁻¹ — like if f(x) = 5x², then f′(x) = 10x.
• Steps:
  • f(x) = 4x³.
  • f′(x) = 4 × 3 × x³⁻¹ = 12x².
• Answer: 12x²

[Easy] Permutations

• EN: How many 3-letter arrangements can be made from the letters A, B, C, D, E (no repeats)?
• FR: Combien d'arrangements de 3 lettres peut-on former avec les lettres A, B, C, D, E (sans répétition)?
• Choices: A) 30 B) 45 C) 60 D) 120
• Hint: P(n, r) = n! / (n−r)! — for P(4, 2) = 4!/2! = 12.
• Steps:
  • P(5, 3) = 5! / (5 − 3)! = 5! / 2!.
  • = (5 × 4 × 3 × 2 × 1) / (2 × 1) = 120 / 2 = 60.
• Answer: 60

[Easy] Polynomial Function — Finding a Zero

• EN: One zero of f(x) = x³ − 2x² − 5x + 6 is x = 1. Verify this by substituting.
• FR: Un zéro de f(x) = x³ − 2x² − 5x + 6 est x = 1. Vérifie cela par substitution.
• Choices: A) f(1) = 0 B) f(1) = 2 C) f(1) = 4 D) f(1) = 6
• Hint: Substitute x = 1 into the function — calculate each term and add them together.
• Steps:
  • f(1) = (1)³ − 2(1)² − 5(1) + 6.
  • = 1 − 2 − 5 + 6.
  • = 0.
• Answer: f(1) = 0

[Medium] Probability Distribution

• EN: A fair die is rolled twice. What is the probability of getting a sum of 8?
• FR: Un dé équitable est lancé deux fois. Quelle est la probabilité d'obtenir une somme de 8?
• Choices: A) 3/36 B) 4/36 C) 5/36 D) 6/36
• Hint: List all pairs that sum to 8 — count them and divide by 36 total outcomes.
• Steps:
  • Pairs that sum to 8: (2,6), (3,5), (4,4), (5,3), (6,2) — that is 5 pairs.
  • P(sum = 8) = 5/36.
• Answer: 5/36

[Medium] Rate of Change — Derivative in Context

• EN: A ball's height is given by h(t) = −5t² + 20t. What is the instantaneous velocity at t = 2 seconds?
• FR: La hauteur d'une balle est donnée par h(t) = −5t² + 20t. Quelle est la vitesse instantanée à t = 2 secondes?
• Choices: A) 0 m/s B) 5 m/s C) 10 m/s D) 20 m/s
• Hint: Take the derivative h′(t), then substitute the time value — for h(t) = 3t² − 6t, h′(t) = 6t − 6, and at t = 3 it is 12.
• Steps:
  • h′(t) = −10t + 20.
  • h′(2) = −10(2) + 20 = −20 + 20 = 0 m/s.
• Answer: 0 m/s

[Medium] Vectors — Adding Vectors

• EN: Vector u = (3, −1) and vector v = (−2, 5). What is u + v?
• FR: Le vecteur u = (3, −1) et le vecteur v = (−2, 5). Qu'est-ce que u + v?
• Choices: A) (1, 3) B) (1, 4) C) (5, 4) D) (5, 6)
• Hint: Add the x-components together and the y-components together — like (4, 2) + (−1, 3) = (3, 5).
• Steps:
  • x-component: 3 + (−2) = 1.
  • y-component: (−1) + 5 = 4.
  • u + v = (1, 4).
• Answer: (1, 4)

[Medium] Rational Function — Identifying Asymptotes

• EN: What is the vertical asymptote of f(x) = 5 / (x − 4)?
• FR: Quelle est l'asymptote verticale de f(x) = 5 / (x − 4)?
• Choices: A) x = −5 B) x = −4 C) x = 4 D) x = 5
• Hint: A vertical asymptote occurs where the denominator equals zero — for f(x) = 3/(x + 2), set x + 2 = 0 to get x = −2.
• Steps:
  • Set denominator = 0: x − 4 = 0.
  • x = 4.
  • The vertical asymptote is x = 4.
• Answer: x = 4

[Hard] Combination and Probability

• EN: A committee of 4 is chosen from 5 men and 4 women. What is the probability that exactly 2 women are on the committee?
• FR: Un comité de 4 personnes est choisi parmi 5 hommes et 4 femmes. Quelle est la probabilité qu'exactement 2 femmes soient sur le comité?
• Choices: A) 10/21 B) 4/21 C) 6/21 D) 8/21
• Hint: Use combinations — choose 2 women from 4 and 2 men from 5, divide by the total ways to choose 4 from 9.
• Steps:
  • Ways to choose 2 women from 4: C(4,2) = 6.
  • Ways to choose 2 men from 5: C(5,2) = 10.
  • Favourable outcomes: 6 × 10 = 60.
  • Total ways to choose 4 from 9: C(9,4) = 126.
  • P = 60/126 = 10/21.
• Answer: 10/21

[Hard] Derivative — Tangent Line

• EN: Find the equation of the tangent line to f(x) = x² + 3x at the point where x = 2.
• FR: Trouve l'équation de la tangente à f(x) = x² + 3x au point où x = 2.
• Choices: A) y = 7x − 4 B) y = 7x − 6 C) y = 5x + 4 D) y = 5x − 6
• Hint: Find the slope using f′(x) at x = 2, find the point (x, f(x)), then use y − y₁ = m(x − x₁) — like for f(x) = x², f′(x) = 2x, at x = 3, slope = 6 and point is (3, 9).
• Steps:
  • f′(x) = 2x + 3; at x = 2: slope = 2(2) + 3 = 7.
  • Point: f(2) = (2)² + 3(2) = 4 + 6 = 10. Point is (2, 10).
  • Tangent: y − 10 = 7(x − 2) → y = 7x − 14 + 10 → y = 7x − 4.
• Answer: y = 7x − 4