Daily Math — 2026-08-05

[Easy] Counting Crayons

• EN: Mia has 7 crayons. She finds 5 more. How many crayons does she have in all?
• FR: Mia a 7 crayons. Elle en trouve 5 de plus. Combien de crayons a-t-elle en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add, count on from the bigger number. Start at 8, count on 3 more: 9, 10, 11.
• Steps:
  • Start at 7.
  • Count on 5 more: 8, 9, 10, 11, 12.
  • So the total is 12.
• Answer: 12

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes after 8, 10, 12?
• FR: Compte par bonds de 2. Quel nombre vient après 8, 10, 12?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Skip counting by 2s means adding 2 each time. After 4, 6, 8, the next is 10.
• Steps:
  • The pattern is adding 2 each time.
  • 12 + 2 = 14.
  • So the next number is 14.
• Answer: 14

[Easy] Comparing Numbers

• EN: Which number is bigger: 15 or 9?
• FR: Quel nombre est plus grand : 15 ou 9?
• Choices: A) 9 B) 12 C) 15 D) 18
• Hint: A number with more tens is bigger. 15 has 1 ten, 9 has no tens.
• Steps:
  • 15 has 1 ten and 5 ones.
  • 9 has 0 tens and 9 ones.
  • 1 ten is more than 0 tens, so 15 is bigger.
• Answer: 15

[Easy] Coin Recognition

• EN: Lucas has 1 dime. How many cents is that worth?
• FR: Lucas a 1 pièce de 10 cents. Combien de cents vaut-elle?
• Choices: A) 1 cent B) 5 cents C) 10 cents D) 25 cents
• Hint: A nickel is worth 5 cents. A dime is worth more than a nickel.
• Steps:
  • A penny is worth 1 cent.
  • A nickel is worth 5 cents.
  • A dime is worth 10 cents.
• Answer: 10 cents

[Medium] Subtraction at the Rink

• EN: There are 14 hockey pucks on the ice. Players use 6 of them. How many pucks are left?
• FR: Il y a 14 rondelles sur la glace. Les joueurs en utilisent 6. Combien de rondelles reste-t-il?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To subtract, count back from the bigger number. Start at 12, count back 3: 11, 10, 9.
• Steps:
  • Start at 14.
  • Count back 6: 13, 12, 11, 10, 9, 8.
  • So 8 pucks are left.
• Answer: 8

[Medium] Skip Counting by 5s

• EN: Emma skip counts by 5s: 5, 10, 15, 20. What is the next number?
• FR: Emma compte par bonds de 5 : 5, 10, 15, 20. Quel est le prochain nombre?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: Skip counting by 5s means adding 5 each time. After 10, 15, 20, add 5 more.
• Steps:
  • The pattern adds 5 each time.
  • 20 + 5 = 25.
  • So the next number is 25.
• Answer: 25

[Medium] Addition with Pennies

• EN: Omar has 3 pennies and 4 more pennies. How many pennies does he have altogether?
• FR: Omar a 3 pennies et 4 autres pennies. Combien de pennies a-t-il en tout?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Add two small numbers by counting on. Start at 5, count on 2 more: 6, 7.
• Steps:
  • Start at 3.
  • Count on 4 more: 4, 5, 6, 7.
  • So he has 7 pennies altogether.
• Answer: 7

[Medium] Counting to 100

• EN: What number comes just before 100?
• FR: Quel nombre vient juste avant 100?
• Choices: A) 98 B) 99 C) 101 D) 110
• Hint: The number just before any number is one less. The number just before 10 is 9.
• Steps:
  • Count: 97, 98, 99, 100.
  • The number just before 100 is one less than 100.
  • 100 − 1 = 99.
• Answer: 99

[Hard] Adding Three Numbers

• EN: Lily has 4 apples, 3 oranges, and 6 bananas. How many pieces of fruit does she have in all?
• FR: Lily a 4 pommes, 3 oranges et 6 bananes. Combien de fruits a-t-elle en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Add three numbers by adding two first, then the third. 2 + 3 = 5, then 5 + 4 = 9.
• Steps:
  • First add 4 + 3 = 7.
  • Then add 7 + 6 = 13.
  • So she has 13 pieces of fruit in all.
• Answer: 13

[Hard] Subtraction Story

• EN: There are 18 children at the playground. 9 children go home. How many children are still at the playground?
• FR: Il y a 18 enfants au terrain de jeux. 9 enfants rentrent à la maison. Combien d'enfants sont encore au terrain de jeux?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Use a fact you know. 10 − 5 = 5. Try using your doubles facts: 9 + 9 = 18.
• Steps:
  • We know that 9 + 9 = 18.
  • So 18 − 9 = 9.
  • There are 9 children still at the playground.
• Answer: 9

[Easy] Adding Within 100

• EN: What is 34 + 25?
• FR: Combien font 34 + 25?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: Add the tens first, then the ones. 30 + 20 = 50, then add the ones together.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre la grande aiguille sur 12 et la petite sur 3. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 12:15
• Hint: When the minute hand is on 12, it is exactly on the hour. The hour hand tells which hour.
• Steps:
  • The minute hand on 12 means it is exactly the hour.
  • The hour hand is on 3.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon mesure 15 cm. Un crayon de couleur mesure 9 cm. De combien le crayon est-il plus long?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 24 cm
• Hint: To find how much longer, subtract. 12 − 7 = 5, so the first is 5 more than the second.
• Steps:
  • Subtract the shorter from the longer: 15 − 9 = 6.
  • The pencil is 6 cm longer than the crayon.
• Answer: 6 cm

[Easy] Counting Coins

• EN: Aisha has 2 nickels. How many cents does she have in total?
• FR: Aisha a 2 pièces de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 2 cents B) 5 cents C) 10 cents D) 15 cents
• Hint: Each nickel is worth 5 cents. Count by 5s for each nickel you have.
• Steps:
  • Each nickel = 5 cents.
  • 2 nickels: 5, 10.
  • Aisha has 10 cents in total.
• Answer: 10 cents

[Medium] Subtraction Within 100

• EN: There are 72 Tim Hortons cups on a shelf. 38 are sold. How many are left?
• FR: Il y a 72 tasses de Tim Hortons sur une étagère. 38 sont vendues. Combien en reste-t-il?
• Choices: A) 30 B) 34 C) 36 D) 44
• Hint: Subtract by breaking apart the numbers. 70 − 30 = 40, then adjust for the ones.
• Steps:
  • 72 − 38: subtract 30 from 72 to get 42.
  • Then subtract 8 more: 42 − 8 = 34.
  • So 34 cups are left.
• Answer: 34

[Medium] Telling Time: Half Hour

• EN: The minute hand is on the 6 and the hour hand is between 7 and 8. What time does the clock show?
• FR: La grande aiguille est sur le 6 et la petite est entre 7 et 8. Quelle heure montre l'horloge?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the minute hand points to 6, it means 30 minutes past the hour. Look at which hour just passed.
• Steps:
  • Minute hand on 6 means 30 minutes past.
  • The hour hand has just passed 7.
  • So the time is 7:30.
• Answer: 7:30

[Medium] 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 what is added each time. In 1, 3, 5, 7, the pattern adds 2 each time — so next is 9.
• Steps:
  • Each number is 2 more than the one before.
  • 8 + 2 = 10.
  • The next number in the pattern is 10.
• Answer: 10

[Medium] Counting Coins to $1

• EN: Ben has 3 dimes and 2 nickels. How many cents does he have altogether?
• FR: Ben a 3 pièces de 10 cents et 2 pièces de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 30 cents B) 35 cents C) 40 cents D) 50 cents
• Hint: Count the dimes first by 10s, then add each nickel as 5 cents. 2 dimes + 1 nickel = 25 cents.
• Steps:
  • 3 dimes = 30 cents.
  • 2 nickels = 10 cents.
  • 30 + 10 = 40 cents altogether.
• Answer: 40 cents

[Hard] Adding and Subtracting in a Story

• EN: There are 55 students at recess. 18 go inside. Then 7 more come outside. How many students are outside now?
• FR: Il y a 55 élèves à la récréation. 18 rentrent. Puis 7 autres sortent. Combien d'élèves sont dehors maintenant?
• Choices: A) 40 B) 43 C) 44 D) 46
• Hint: Do two steps: first subtract, then add. 20 − 8 = 12, then 12 + 3 = 15.
• Steps:
  • First, 55 − 18 = 37 students outside.
  • Then 7 more come out: 37 + 7 = 44.
  • So 44 students are outside now.
• Answer: 44

[Hard] Measuring and Comparing

• EN: A blue ribbon is 48 cm long. A red ribbon is 29 cm long. How much longer is the blue ribbon than the red ribbon?
• FR: Un ruban bleu mesure 48 cm. Un ruban rouge mesure 29 cm. De combien le ruban bleu est-il plus long?
• Choices: A) 17 cm B) 18 cm C) 19 cm D) 21 cm
• Hint: Subtract the shorter length from the longer one. 35 − 18 = 17, so the blue is 17 cm longer.
• Steps:
  • Subtract: 48 − 29.
  • 48 − 20 = 28, then 28 − 9 = 19.
  • The blue ribbon is 19 cm longer than the red ribbon.
• Answer: 19 cm

[Easy] Multiplication by 2

• EN: What is 6 × 2?
• FR: Combien font 6 × 2?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiplying by 2 is the same as doubling a number. Double 5 is 10.
• Steps:
  • 6 × 2 means 6 groups of 2.
  • 2, 4, 6, 8, 10, 12.
  • So 6 × 2 = 12.
• Answer: 12

[Easy] Basic Division

• EN: 20 ÷ 4 = ?
• FR: Combien font 20 ÷ 4?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Think about what times the divisor equals the dividend. What × 4 = 16? That is 4.
• Steps:
  • Think: what number times 4 equals 20?
  • 4 × 5 = 20.
  • So 20 ÷ 4 = 5.
• Answer: 5

[Easy] Fractions

• EN: A pizza is cut into 4 equal slices. Theo eats 1 slice. What fraction did Theo eat?
• FR: Une pizza est coupée en 4 parts égales. Théo mange 1 part. Quelle fraction Théo a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: The bottom number (denominator) tells how many equal parts in all. The top number tells how many were taken.
• Steps:
  • The pizza has 4 equal slices (denominator = 4).
  • Theo ate 1 slice (numerator = 1).
  • So Theo 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?
• FR: Un rectangle a une longueur de 5 cm et une largeur de 3 cm. Quel est le périmètre?
• Choices: A) 8 cm B) 15 cm C) 16 cm D) 18 cm
• Hint: Perimeter = add all four sides. A rectangle has two lengths and two widths. 4 + 2 + 4 + 2 = 12 cm.
• Steps:
  • Perimeter = 5 + 5 + 3 + 3.
  • 5 + 5 = 10, and 3 + 3 = 6.
  • 10 + 6 = 16 cm.
• Answer: 16 cm

[Medium] Multiplication by 5

• EN: There are 7 bags of pucks. Each bag has 5 pucks. How many pucks are there in all?
• FR: Il y a 7 sacs de rondelles. Chaque sac contient 5 rondelles. Combien y a-t-il de rondelles en tout?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: Count by 5s for each group. 5, 10, 15, 20, 25 — that is 5 groups of 5.
• Steps:
  • 7 × 5 means 7 groups of 5.
  • Count by 5s: 5, 10, 15, 20, 25, 30, 35.
  • So there are 35 pucks in all.
• Answer: 35

[Medium] Division with a Story

• EN: A teacher has 24 stickers to give equally to 3 students. How many stickers does each student get?
• FR: Une enseignante a 24 autocollants à distribuer également à 3 élèves. Combien d'autocollants chaque élève reçoit-il?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Think of the matching multiplication fact. 3 × ? = 21 means each gets 7. Use the same thinking.
• Steps:
  • Ask: 3 × ? = 24.
  • 3 × 8 = 24.
  • Each student gets 8 stickers.
• Answer: 8

[Medium] Reading a Graph

• EN: A bar graph shows that 10 students like hockey, 6 like soccer, and 4 like swimming. How many students were surveyed in total?
• FR: Un diagramme à barres montre que 10 élèves aiment le hockey, 6 aiment le soccer et 4 aiment la natation. Combien d'élèves ont été sondés en tout?
• Choices: A) 16 B) 18 C) 20 D) 22
• Hint: Add all the bar amounts together. 8 + 5 + 3 = 16 for three groups.
• Steps:
  • Add all three groups: 10 + 6 + 4.
  • 10 + 6 = 16, then 16 + 4 = 20.
  • So 20 students were surveyed in total.
• Answer: 20

[Medium] Multiplication by 10

• EN: There are 8 boxes. Each box has 10 books. How many books are there altogether?
• FR: Il y a 8 boîtes. Chaque boîte contient 10 livres. Combien y a-t-il de livres en tout?
• Choices: A) 18 B) 70 C) 80 D) 90
• Hint: Multiplying by 10 is easy — just put a zero after the number. 6 × 10 = 60.
• Steps:
  • 8 × 10 means 8 groups of 10.
  • Put a zero after 8: 80.
  • There are 80 books altogether.
• Answer: 80

[Hard] Fractions of a Group

• EN: There are 12 apples. One quarter (1/4) of the apples are red. How many apples are red?
• FR: Il y a 12 pommes. Un quart (1/4) des pommes sont rouges. Combien de pommes sont rouges?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: To find 1/4 of a group, divide the total into 4 equal parts. 1/4 of 8 = 8 ÷ 4 = 2.
• Steps:
  • 1/4 of 12 means divide 12 into 4 equal groups.
  • 12 ÷ 4 = 3.
  • So 3 apples are red.
• Answer: 3

[Hard] Perimeter Problem

• EN: A square playground has a perimeter of 36 m. What is the length of one side?
• FR: Un terrain de jeux carré a un périmètre de 36 m. Quelle est la longueur d'un côté?
• Choices: A) 6 m B) 8 m C) 9 m D) 12 m
• Hint: A square has 4 equal sides. To find one side from the perimeter, divide by 4. Perimeter 20 m ÷ 4 = 5 m.
• Steps:
  • A square has 4 equal sides.
  • Perimeter ÷ 4 = length of one side.
  • 36 ÷ 4 = 9 m.
• Answer: 9 m

[Easy] Multiplication Table

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: Try breaking it apart. 7 × 8 = 7 × 4 + 7 × 4. Use a fact you already know.
• Steps:
  • 7 × 8 = 7 × (4 + 4).
  • 7 × 4 = 28, so 28 + 28 = 56.
  • So 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

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

[Easy] Area of a Rectangle

• EN: A rectangle is 6 cm long and 4 cm wide. What is its area?
• FR: Un rectangle mesure 6 cm de long et 4 cm de large. Quelle est son aire?
• Choices: A) 10 cm² B) 20 cm² C) 24 cm² D) 28 cm²
• Hint: Area of a rectangle = length × width. A 5 cm by 3 cm rectangle has area 15 cm².
• Steps:
  • Area = length × width.
  • Area = 6 × 4 = 24.
  • The area is 24 cm².
• Answer: 24 cm²

[Easy] Comparing Fractions

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

[Medium] Long Division with Remainders

• EN: What is 47 ÷ 5?
• FR: Combien font 47 ÷ 5?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 10 remainder 3 D) 7 remainder 4
• Hint: Find how many times the divisor fits in. 5 × 4 = 20, remainder 3. Use the same steps with your numbers.
• Steps:
  • 5 goes into 47 how many times? 5 × 9 = 45.
  • 47 − 45 = 2 left over.
  • So 47 ÷ 5 = 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 PM and ends at 3:45 PM. How long is the game?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Quelle est la durée du match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: Count up from the start time to the end time. From 2:00 to 4:30 is 2 hours and 30 minutes.
• Steps:
  • From 1:15 PM to 3:15 PM is 2 hours.
  • From 3:15 PM to 3:45 PM is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: What is 5.6 + 2.3?
• FR: Combien font 5,6 + 2,3?
• Choices: A) 7.6 B) 7.9 C) 8.1 D) 8.9
• Hint: Line up the decimal points and add each column. 3.4 + 1.2 = 4.6.
• Steps:
  • Add the tenths: 6 + 3 = 9 tenths.
  • Add the ones: 5 + 2 = 7.
  • So 5.6 + 2.3 = 7.9.
• Answer: 7.9

[Medium] Multiplication Story

• EN: A store sells hockey cards in packs of 9. If Maya buys 6 packs, how many cards does she get?
• FR: Un magasin vend des cartes de hockey en paquets de 9. Si Maya achète 6 paquets, combien de cartes reçoit-elle?
• Choices: A) 48 B) 54 C) 63 D) 72
• Hint: Multiply the number of groups by the number in each group. 7 × 8 = 56 for 7 packs of 8.
• Steps:
  • 6 packs × 9 cards each.
  • 6 × 9 = 54.
  • Maya gets 54 cards.
• Answer: 54

[Hard] Multi-Step Problem

• EN: Liam earns $48 raking leaves. He spends $19 on a book and saves the rest. Then he earns $13 more. How much does Liam have now?
• FR: Liam gagne 48 $ en ratissant des feuilles. Il dépense 19 $ pour un livre et économise le reste. Ensuite, il gagne 13 $ de plus. Combien Liam a-t-il maintenant?
• Choices: A) $38 B) $40 C) $42 D) $44
• Hint: Solve step by step. First subtract what was spent, then add the new amount earned.
• Steps:
  • $48 − $19 = $29 saved.
  • Then $29 + $13 = $42.
  • Liam has $42 now.
• Answer: $42

[Hard] Area and Perimeter Together

• EN: A rectangular garden has an area of 45 m² and a width of 5 m. What is the perimeter of the garden?
• FR: Un jardin rectangulaire a une aire de 45 m² et une largeur de 5 m. Quel est le périmètre du jardin?
• Choices: A) 28 m B) 32 m C) 36 m D) 40 m
• Hint: First find the length using Area = length × width. Then use Perimeter = 2 × (length + width).
• Steps:
  • Length = Area ÷ width = 45 ÷ 5 = 9 m.
  • Perimeter = 2 × (9 + 5) = 2 × 14 = 28 m.
  • The perimeter is 28 m.
• Answer: 28 m

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 194 B) 200 C) 204 D) 210
• Hint: Multiply each part separately. 30 × 6 = 180, then 4 × 6 = 24. Add them together.
• Steps:
  • 34 × 6 = (30 + 4) × 6.
  • 30 × 6 = 180 and 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien font 2/7 + 3/7?
• Choices: A) 5/7 B) 5/14 C) 6/7 D) 1/7
• Hint: When denominators are the same, just add the numerators. Keep the denominator the same. 1/5 + 2/5 = 3/5.
• Steps:
  • The denominators are both 7, so keep 7.
  • Add the numerators: 2 + 3 = 5.
  • Answer is 5/7.
• Answer: 5/7

[Easy] Percentage Introduction

• EN: What is 50% of 80?
• FR: Combien font 50% de 80?
• Choices: A) 30 B) 40 C) 45 D) 50
• Hint: 50% means half. To find half of a number, divide by 2. Half of 60 is 30.
• Steps:
  • 50% = one half.
  • 80 ÷ 2 = 40.
  • So 50% of 80 is 40.
• Answer: 40

[Easy] Decimal Operations

• EN: What is 6.4 − 2.1?
• FR: Combien font 6,4 − 2,1?
• Choices: A) 3.3 B) 4.1 C) 4.3 D) 5.3
• Hint: Subtract the tenths, then subtract the ones. Line up the decimal points. 7.5 − 3.2 = 4.3.
• Steps:
  • Subtract the tenths: 4 − 1 = 3 tenths.
  • Subtract the ones: 6 − 2 = 4 ones.
  • So 6.4 − 2.1 = 4.3.
• Answer: 4.3

[Medium] Multi-Digit Division

• EN: What is 312 ÷ 4?
• FR: Combien font 312 ÷ 4?
• Choices: A) 72 B) 76 C) 78 D) 80
• Hint: Divide from left to right. 3 ÷ 4 doesn't work, so try 31 ÷ 4 = 7 remainder 3, then bring down the next digit.
• Steps:
  • 4 goes into 31 seven times (4 × 7 = 28), remainder 3.
  • Bring down 2: 32 ÷ 4 = 8.
  • So 312 ÷ 4 = 78.
• Answer: 78

[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) 48 cm³ B) 60 cm³ C) 70 cm³ D) 80 cm³
• Hint: Volume = length × width × height. A box of 2 × 3 × 4 has a volume of 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] 25% of a Number

• EN: What is 25% of 64?
• FR: Combien font 25% de 64?
• Choices: A) 12 B) 14 C) 16 D) 18
• Hint: 25% = one quarter. Divide the number by 4. One quarter of 40 is 40 ÷ 4 = 10.
• Steps:
  • 25% means one quarter (1/4).
  • 64 ÷ 4 = 16.
  • So 25% of 64 is 16.
• Answer: 16

[Medium] Subtracting Fractions

• EN: What is 5/8 − 2/8?
• FR: Combien font 5/8 − 2/8?
• Choices: A) 3/8 B) 3/16 C) 7/8 D) 2/8
• Hint: When denominators match, subtract the numerators only. Keep the denominator. 6/9 − 2/9 = 4/9.
• Steps:
  • The denominators are both 8.
  • Subtract the numerators: 5 − 2 = 3.
  • So 5/8 − 2/8 = 3/8.
• Answer: 3/8

[Hard] Multi-Step Decimal Problem

• EN: Zoe buys 3 notebooks for $2.45 each and pays with a $10 bill. How much change does she receive?
• FR: Zoé achète 3 cahiers à 2,45 $ chacun et paie avec un billet de 10 $. Combien de monnaie reçoit-elle?
• Choices: A) $2.55 B) $2.65 C) $3.15 D) $7.55
• Hint: First multiply the price by the number of items, then subtract from the amount paid. 3 × $1.50 = $4.50; $10.00 − $4.50 = $5.50.
• Steps:
  • 3 × $2.45 = $7.35.
  • $10.00 − $7.35 = $2.65.
  • Zoe receives $2.65 in change.
• Answer: $2.65

[Hard] Volume and Comparison

• EN: Box A has dimensions 6 cm × 5 cm × 4 cm. Box B has dimensions 8 cm × 5 cm × 3 cm. Which box has the greater volume, and by how much?
• FR: La boîte A mesure 6 cm × 5 cm × 4 cm. La boîte B mesure 8 cm × 5 cm × 3 cm. Quelle boîte a le plus grand volume et de combien?
• Choices: A) Box A by 120 cm³ B) Box A by 12 cm³ C) Box B by 20 cm³ D) They are equal
• Hint: Find each volume separately using l × w × h, then compare them.
• Steps:
  • Volume of Box A = 6 × 5 × 4 = 120 cm³.
  • Volume of Box B = 8 × 5 × 3 = 120 cm³.
  • Both volumes are 120 cm³, so they are equal.
• Answer: They are equal

[Easy] Fraction Multiplication

• EN: What is 1/3 × 3/4?
• FR: Combien font 1/3 × 3/4?
• Choices: A) 1/4 B) 3/7 C) 4/7 D) 3/12
• Hint: To multiply fractions, multiply the numerators together and the denominators together. 1/2 × 2/5 = 2/10 = 1/5.
• Steps:
  • Multiply numerators: 1 × 3 = 3.
  • Multiply denominators: 3 × 4 = 12.
  • 3/12 = 1/4, so the answer is 1/4.
• Answer: 1/4

[Easy] Percent of a Number

• EN: What is 10% of 90?
• FR: Combien font 10% de 90?
• Choices: A) 9 B) 19 C) 45 D) 80
• Hint: 10% means divide by 10. Just move the decimal one place to the left. 10% of 70 = 7.
• Steps:
  • 10% = divide by 10.
  • 90 ÷ 10 = 9.
  • So 10% of 90 is 9.
• Answer: 9

[Easy] Integer Introduction

• EN: The temperature in Winnipeg is −8°C in the morning and rises 12 degrees by noon. What is the temperature at noon?
• FR: La température à Winnipeg est de −8 °C le matin et monte de 12 degrés à midi. Quelle est la température à midi?
• Choices: A) −4°C B) 4°C C) 8°C D) 20°C
• Hint: Rising means adding to the temperature. −5 + 7 = +2 means 2 degrees above zero.
• Steps:
  • Start at −8°C.
  • Add 12 degrees: −8 + 12 = 4.
  • The temperature at noon is 4°C.
• Answer: 4°C

[Easy] Simple Algebraic Expressions

• EN: If n = 5, what is the value of 3n + 2?
• FR: Si n = 5, quelle est la valeur de 3n + 2?
• Choices: A) 10 B) 15 C) 17 D) 20
• Hint: Replace the variable with its value, then calculate. If n = 3, then 2n + 1 = 2(3) + 1 = 7.
• Steps:
  • Replace n with 5: 3(5) + 2.
  • 3 × 5 = 15, then 15 + 2 = 17.
  • The value is 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) 5/4
• Hint: To divide by a fraction, multiply by its reciprocal (flip it). 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
• Steps:
  • Flip the second fraction: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 3/2.
• Answer: 3/2

[Medium] Ratios and Rates

• EN: A car travels 150 km in 3 hours. What is the car's speed in km per hour?
• FR: Une voiture parcourt 150 km en 3 heures. Quelle est la vitesse de la voiture en km par heure?
• Choices: A) 40 km/h B) 45 km/h C) 50 km/h D) 60 km/h
• Hint: Rate = total distance ÷ total time. If you go 80 km in 2 hours, your rate is 40 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 150 ÷ 3 = 50.
  • The car's speed is 50 km/h.
• Answer: 50 km/h

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1
• FR: Calcule : 3 + 4 × 2 − 1
• Choices: A) 9 B) 10 C) 13 D) 14
• Hint: BEDMAS: do Multiplication before Addition and Subtraction. In 5 + 3 × 2, do 3 × 2 = 6 first, then 5 + 6 = 11.
• Steps:
  • Do multiplication first: 4 × 2 = 8.
  • Now: 3 + 8 − 1.
  • 3 + 8 = 11, then 11 − 1 = 10.
• Answer: 10

[Medium] Percent of a Number — Tax

• EN: A jacket costs $80. There is a 15% tax. How much tax must be paid?
• FR: Une veste coûte 80 $. Il y a une taxe de 15 %. Combien de taxe doit-on payer?
• Choices: A) $8.00 B) $10.00 C) $12.00 D) $15.00
• Hint: Find 10% first, then find 5% (half of 10%), and add them. 10% of $60 = $6, 5% of $60 = $3, so 15% = $9.
• Steps:
  • 10% of $80 = $8.
  • 5% of $80 = $4.
  • 15% = $8 + $4 = $12.00.
• Answer: $12.00

[Hard] BEDMAS with Brackets

• EN: Evaluate: (5 + 3) × 4 − 2²
• FR: Calcule : (5 + 3) × 4 − 2²
• Choices: A) 24 B) 28 C) 30 D) 32
• Hint: BEDMAS order: Brackets first, then Exponents, then Multiply/Divide, then Add/Subtract. Try (2 + 3) × 2 − 1² = 10 − 1 = 9.
• Steps:
  • Brackets first: (5 + 3) = 8.
  • Exponents: 2² = 4.
  • Multiply: 8 × 4 = 32; then subtract: 32 − 4 = 28.
• Answer: 28

[Hard] Ratio Problem

• EN: In a class, the ratio of boys to girls is 3:5. If there are 40 students in total, how many are girls?
• FR: Dans une classe, le rapport garçons/filles est de 3:5. S'il y a 40 élèves en tout, combien sont des filles?
• Choices: A) 15 B) 20 C) 24 D) 25
• Hint: Add the ratio parts together to find the total parts. Divide the total by that sum, then multiply by each part. Ratio 2:3, total 10 → each part = 2; girls = 3 × 2 = 6.
• Steps:
  • Total parts = 3 + 5 = 8 parts.
  • Value of one part = 40 ÷ 8 = 5.
  • Girls = 5 × 5 = 25.
• Answer: 25

[Easy] Integer Addition

• EN: What is (−6) + 10?
• FR: Combien font (−6) + 10?
• Choices: A) −4 B) 4 C) 16 D) −16
• Hint: On a number line, adding a positive means moving right. Start at −4, move right 7: you land on 3.
• Steps:
  • Start at −6 on a number line.
  • Move 10 steps to the right.
  • Land on 4, so (−6) + 10 = 4.
• Answer: 4

[Easy] Percent Discount

• EN: A pair of skates costs $120. They are on sale for 10% off. What is the sale price?
• FR: Une paire de patins coûte 120 $. Ils sont en solde à 10 % de rabais. Quel est le prix de vente?
• Choices: A) $12 B) $100 C) $108 D) $110
• Hint: Find 10% of the price, then subtract it. 10% of $80 = $8, so the sale price is $80 − $8 = $72.
• Steps:
  • 10% of $120 = $12.
  • Sale price = $120 − $12 = $108.
  • The sale price is $108.
• Answer: $108

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15
• FR: Résous pour x : x + 9 = 15
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 24
• Hint: To solve, do the opposite operation. Subtract the same number from both sides. If x + 4 = 11, then x = 11 − 4 = 7.
• Steps:
  • x + 9 = 15.
  • Subtract 9 from both sides: x = 15 − 9.
  • x = 6.
• Answer: x = 6

[Easy] Integer Subtraction

• EN: What is 3 − (−5)?
• FR: Combien font 3 − (−5)?
• Choices: A) −8 B) −2 C) 2 D) 8
• Hint: Subtracting a negative is the same as adding a positive. 4 − (−3) = 4 + 3 = 7.
• Steps:
  • 3 − (−5) = 3 + 5.
  • 3 + 5 = 8.
  • So the answer is 8.
• Answer: 8

[Medium] Percentage: Tax and Tip

• EN: A meal costs $24.00. If you add a 15% tip, how much is the tip?
• FR: Un repas coûte 24,00 $. Si tu ajoutes un pourboire de 15 %, combien est le pourboire?
• Choices: A) $3.00 B) $3.60 C) $4.80 D) $6.00
• Hint: Find 10% first, then 5% (half of 10%), and add them for the total tip. 10% of $30 = $3, 5% = $1.50, so 15% = $4.50.
• Steps:
  • 10% of $24.00 = $2.40.
  • 5% of $24.00 = $1.20.
  • 15% tip = $2.40 + $1.20 = $3.60.
• Answer: $3.60

[Medium] Integer Multiplication

• EN: What is (−4) × (−7)?
• FR: Combien font (−4) × (−7)?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: Negative × Negative = Positive. Think of it as the opposite of the opposite. (−3) × (−6) = 18.
• Steps:
  • Two negatives multiplied together give a positive result.
  • 4 × 7 = 28.
  • So (−4) × (−7) = 28.
• Answer: 28

[Medium] Surface Area of a Rectangular Prism

• EN: A box measures 3 cm × 2 cm × 5 cm. What is its surface area?
• FR: Une boîte mesure 3 cm × 2 cm × 5 cm. Quelle est son aire totale?
• Choices: A) 30 cm² B) 46 cm² C) 62 cm² D) 70 cm²
• Hint: Surface area = 2(lw + lh + wh). For a 2 × 3 × 4 box: 2(6 + 8 + 12) = 2(26) = 52 cm².
• Steps:
  • lw = 3 × 2 = 6, lh = 3 × 5 = 15, wh = 2 × 5 = 10.
  • Sum = 6 + 15 + 10 = 31.
  • Surface area = 2 × 31 = 62 cm².
• Answer: 62 cm²

[Medium] Data and Probability

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

[Hard] Multi-Step Percent Problem

• EN: A $200 pair of hockey skates is discounted by 20%, and then an 8% tax is applied to the discounted price. What is the final price?
• FR: Une paire de patins de hockey à 200 $ est réduite de 20 %, puis une taxe de 8 % est appliquée au prix réduit. Quel est le prix final?
• Choices: A) $156.00 B) $168.00 C) $172.80 D) $176.00
• Hint: Find the discount price first, then apply the tax to that new price. 30% off $100 → $70; 10% tax on $70 → $7; total = $77.
• Steps:
  • 20% of $200 = $40; discounted price = $200 − $40 = $160.
  • 8% of $160 = $12.80.
  • Final price = $160 + $12.80 = $172.80.
• Answer: $172.80

[Hard] Solving a Two-Step Equation

• EN: Solve for x: 2x − 3 = 11
• FR: Résous pour x : 2x − 3 = 11
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: First add to both sides to isolate the term with x, then divide. If 3x − 2 = 10, add 2 to get 3x = 12, then divide to get x = 4.
• Steps:
  • Add 3 to both sides: 2x − 3 + 3 = 11 + 3, so 2x = 14.
  • Divide both sides by 2: x = 14 ÷ 2 = 7.
  • So x = 7.
• Answer: x = 7

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Find the number that multiplies by itself to give the answer. 9 × 9 = 81, so √81 = 9.
• Steps:
  • Ask: what number times itself equals 144?
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored: 70, 80, 90, 60, and 50. What is the mean score?
• FR: Cinq élèves ont obtenu : 70, 80, 90, 60 et 50. Quelle est la moyenne?
• Choices: A) 60 B) 65 C) 70 D) 75
• Hint: Mean = sum of all values ÷ number of values. For 10, 20, 30: sum = 60, mean = 60 ÷ 3 = 20.
• Steps:
  • Sum = 70 + 80 + 90 + 60 + 50 = 350.
  • Mean = 350 ÷ 5 = 70.
  • The mean score is 70.
• Answer: 70

[Easy] Two-Step Equation

• EN: Solve for x: 3x + 4 = 19
• FR: Résous pour x : 3x + 4 = 19
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Subtract from both sides first, then divide. If 2x + 3 = 11, subtract 3 to get 2x = 8, then x = 4.
• Steps:
  • Subtract 4 from both sides: 3x = 15.
  • Divide both sides by 3: x = 5.
  • So x = 5.
• Answer: x = 5

[Easy] Percent Increase

• EN: A plant was 40 cm tall. It grew to 50 cm. What is the percent increase?
• FR: Une plante mesurait 40 cm. Elle a grandi jusqu'à 50 cm. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 20% C) 25% D) 40%
• Hint: Percent increase = (increase ÷ original) × 100. If something goes from 20 to 25, increase = 5, and 5 ÷ 20 × 100 = 25%.
• Steps:
  • Increase = 50 − 40 = 10 cm.
  • Percent increase = (10 ÷ 40) × 100 = 25%.
  • The plant grew by 25%.
• Answer: 25%

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des 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 legs 3 and 4: 9 + 16 = 25, so the hypotenuse is √25 = 5 cm.
• Steps:
  • a² + b² = c².
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through 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). From (1, 2) to (4, 8): rise = 6, run = 3, slope = 2.
• Steps:
  • Rise = 11 − 3 = 8.
  • Run = 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: The snowfall amounts (in cm) for 7 days were: 3, 7, 2, 7, 5, 9, 7. What is the mode?
• FR: Les quantités de neige (en cm) pour 7 jours étaient : 3, 7, 2, 7, 5, 9, 7. Quel est le mode?
• Choices: A) 5 B) 7 C) 9 D) 40
• Hint: The mode is the value that appears most often. In 4, 6, 4, 8, 4, the mode is 4.
• Steps:
  • Count how often each value appears: 7 appears 3 times.
  • No other value appears as often.
  • The mode is 7.
• Answer: 7

[Medium] Two-Step Equation with Negatives

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

[Hard] Pythagorean Theorem — Find a Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 8 cm B) 11 cm C) 12 cm D) 14 cm
• Hint: Rearrange a² + b² = c² to find a missing leg: b² = c² − a². For c = 10, a = 6: b² = 100 − 36 = 64, so b = 8.
• Steps:
  • b² = c² − a² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12.
  • The other leg is 12 cm.
• Answer: 12 cm

[Hard] Percent Decrease Problem

• EN: A store bought a jacket for $160 and wants to sell it at a 35% markdown from the original selling price of $200. What is the sale price?
• FR: Un magasin a acheté une veste pour 160 $ et veut la vendre avec une réduction de 35 % par rapport au prix de vente original de 200 $. Quel est le prix de vente?
• Choices: A) $120 B) $130 C) $140 D) $165
• Hint: Find the discount amount: percent × original price. Then subtract from the original price. 20% of $150 = $30; sale price = $150 − $30 = $120.
• Steps:
  • 35% of $200 = 0.35 × 200 = $70.
  • Sale price = $200 − $70 = $130.
  • The sale price is $130.
• Answer: $130

[Easy] Linear Equations

• EN: Solve for x: 5x = 35
• FR: Résous pour x : 5x = 35
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Divide both sides by the coefficient of x. If 6x = 42, then x = 42 ÷ 6 = 7.
• Steps:
  • Divide both sides by 5.
  • x = 35 ÷ 5 = 7.
  • So x = 7.
• Answer: x = 7

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x + 5?
• FR: Quelle est la pente de la droite y = 3x + 5?
• Choices: A) 5 B) 3 C) −3 D) 8
• Hint: In y = mx + b, the slope is m and the y-intercept is b. In y = 4x + 2, the slope is 4.
• 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: (2x + 3) + (4x + 5)
• FR: Simplifie : (2x + 3) + (4x + 5)
• Choices: A) 6x + 7 B) 6x + 8 C) 8x + 5 D) 6x + 15
• Hint: Combine like terms — add the x terms together and add the constant terms together. (3x + 2) + (x + 4) = 4x + 6.
• Steps:
  • Combine x terms: 2x + 4x = 6x.
  • Combine constants: 3 + 5 = 8.
  • Result: 6x + 8.
• Answer: 6x + 8

[Easy] Trigonometry Introduction (SOH)

• EN: In a right triangle, the opposite side is 4 cm and the hypotenuse is 8 cm. What is the sine of the angle?
• FR: Dans un triangle rectangle, le côté opposé mesure 4 cm et l'hypoténuse 8 cm. Quel est le sinus de l'angle?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: SOH means sin = opposite ÷ hypotenuse. If opposite = 3 and hypotenuse = 6, then sin = 3/6 = 1/2.
• Steps:
  • sin(angle) = opposite ÷ hypotenuse.
  • sin = 4 ÷ 8 = 1/2.
  • The sine of the angle is 1/2.
• Answer: 1/2

[Medium] Linear Inequality

• EN: Solve for x: 2x − 3 > 7
• FR: Résous pour x : 2x − 3 > 7
• Choices: A) x > 3 B) x > 4 C) x > 5 D) x > 6
• Hint: Solve like an equation but keep the inequality sign. If 3x − 2 > 10, add 2 to get 3x > 12, then x > 4.
• Steps:
  • Add 3 to both sides: 2x > 10.
  • Divide both sides by 2: x > 5.
  • So x > 5.
• Answer: x > 5

[Medium] Multiplying Polynomials

• EN: Expand and simplify: 3x(2x − 4)
• FR: Développe et simplifie : 3x(2x − 4)
• Choices: A) 6x − 12 B) 5x² − 7x C) 6x² − 12x D) 6x² + 12x
• Hint: Distribute the term outside the brackets to each term inside. 2x(3x + 5) = 6x² + 10x.
• Steps:
  • 3x × 2x = 6x².
  • 3x × (−4) = −12x.
  • Result: 6x² − 12x.
• Answer: 6x² − 12x

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 10 cm. If a side in the smaller triangle is 6 cm, what is the corresponding side in the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 10 cm. Si un côté du petit triangle est de 6 cm, quel est le côté correspondant du grand triangle?
• Choices: A) 12 cm B) 14 cm C) 15 cm D) 18 cm
• Hint: Set up a ratio: small side/large side = small side/large side. 3/6 = 5/?, so ? = 10.
• Steps:
  • Scale factor = 10 ÷ 4 = 2.5.
  • Corresponding side = 6 × 2.5 = 15.
  • The corresponding side in the larger triangle is 15 cm.
• Answer: 15 cm

[Medium] Graphing Lines

• EN: A line has equation y = 2x − 1. What is the y-intercept?
• FR: Une droite a comme équation y = 2x − 1. Quel est l'ordonnée à l'origine?
• Choices: A) −2 B) −1 C) 1 D) 2
• Hint: In y = mx + b, b is the y-intercept (the value of y when x = 0). In y = 5x + 3, the y-intercept is 3.
• Steps:
  • The equation is y = 2x − 1, which is in y = mx + b form.
  • The y-intercept is b = −1.
  • So the y-intercept is −1.
• Answer: −1

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, angle A = 30°, and the hypotenuse is 20 cm. Using SOH-CAH-TOA, what is the length of the opposite side (to the nearest whole number)?
• FR: Dans un triangle rectangle, l'angle A = 30° et l'hypoténuse est de 20 cm. En utilisant SOH-CAH-TOA, quelle est la longueur du côté opposé (au nombre entier près)?
• Choices: A) 8 cm B) 10 cm C) 14 cm D) 17 cm
• Hint: sin(angle) = opposite/hypotenuse, so opposite = hypotenuse × sin(angle). sin(45°) ≈ 0.71; opposite = 10 × 0.71 ≈ 7 cm.
• Steps:
  • sin(30°) = 0.5.
  • opposite = hypotenuse × sin(30°) = 20 × 0.5 = 10.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Hard] Linear System by Substitution

• EN: Solve the system: y = 2x + 1 and y = x + 4. What is x?
• FR: Résous le système : y = 2x + 1 et y = x + 4. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Set the two expressions equal since both equal y. 3x + 1 = x + 5 → 2x = 4 → x = 2.
• Steps:
  • Set them equal: 2x + 1 = x + 4.
  • Subtract x from both sides: x + 1 = 4.
  • x = 3.
• Answer: x = 3

[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 + 4)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient. For x² + 7x + 12, find numbers that multiply to 12 and add to 7: that is 3 and 4.
• Steps:
  • Find two numbers: product = 6, sum = 5 → 2 and 3.
  • Write as (x + 2)(x + 3).
  • Check: (x + 2)(x + 3) = x² + 5x + 6. ✓
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — cos Ratio

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 10 cm. What is cos(angle)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse 10 cm. Quel est cos(angle)?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: CAH: cos = adjacent ÷ hypotenuse. If adjacent = 6 and hypotenuse = 12, then cos = 6/12 = 1/2.
• Steps:
  • cos(angle) = adjacent ÷ hypotenuse.
  • cos = 5 ÷ 10 = 1/2.
  • So cos(angle) = 1/2.
• Answer: 1/2

[Easy] Systems of Equations

• EN: Solve the system: x + y = 10 and x − y = 2. What is x?
• FR: Résous le système : x + y = 10 et x − y = 2. Quelle est la valeur de x?
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 8
• Hint: Add the two equations together to eliminate y. Then solve for x. a + b = 8 and a − b = 2 → 2a = 10, a = 5.
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 2.
  • 2x = 12, so x = 6.
  • So x = 6.
• Answer: x = 6

[Easy] Surface Area of a Cylinder

• EN: A cylinder has radius 3 cm and height 7 cm. Using π ≈ 3.14, what is the approximate lateral (curved) surface area?
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 7 cm. En utilisant π ≈ 3,14, quelle est l'aire latérale approximative?
• Choices: A) 65.94 cm² B) 87.92 cm² C) 131.88 cm² D) 197.82 cm²
• Hint: Lateral surface area = 2πrh. For r = 2, h = 5: 2 × 3.14 × 2 × 5 = 62.8 cm².
• Steps:
  • Lateral SA = 2πrh.
  • 2 × 3.14 × 3 × 7 = 2 × 3.14 × 21 = 2 × 65.94 = 131.88 cm².
  • Wait — 2πrh = 2 × 3.14 × 3 × 7 = 131.88 cm².
• Answer: 131.88 cm²

[Medium] Quadratic Formula

• EN: Solve x² − 5x + 6 = 0 by factoring. What are the two solutions?
• FR: Résous x² − 5x + 6 = 0 par factorisation. Quelles sont les deux 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: Factor the quadratic and set each factor equal to zero. For x² − 7x + 12 = 0, factor as (x − 3)(x − 4) = 0, so x = 3 or x = 4.
• Steps:
  • Factor: x² − 5x + 6 = (x − 2)(x − 3).
  • Set each factor to zero: x − 2 = 0 or x − 3 = 0.
  • x = 2 and x = 3.
• Answer: x = 2 and x = 3

[Medium] Circle Geometry

• EN: A circle has a radius of 7 cm. What is the area? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 7 cm. Quelle est son aire? (Utilise π ≈ 3,14)
• Choices: A) 43.96 cm² B) 153.86 cm² C) 197.92 cm² D) 615.44 cm²
• Hint: Area of a circle = πr². For r = 5: π × 25 = 78.5 cm².
• Steps:
  • Area = πr² = 3.14 × 7² = 3.14 × 49.
  • 3.14 × 49 = 153.86.
  • The area is 153.86 cm².
• Answer: 153.86 cm²

[Medium] Completing the Square

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

[Medium] Volume of a Cone

• EN: A cone has a radius of 4 cm and a height of 9 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur de 9 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 113.04 cm³ B) 150.72 cm³ C) 180.86 cm³ D) 452.16 cm³
• Hint: Volume of a cone = (1/3)πr²h. For r = 3, h = 7: (1/3) × 3.14 × 9 × 7 = 65.94 cm³.
• Steps:
  • V = (1/3) × π × r² × h.
  • V = (1/3) × 3.14 × 16 × 9 = (1/3) × 3.14 × 144.
  • V = (1/3) × 452.16 = 150.72 cm³.
• Answer: 150.72 cm³

[Hard] System of Equations — Two Variables

• EN: Solve the system: 2x + 3y = 12 and x − y = 1. What is y?
• FR: Résous le système : 2x + 3y = 12 et x − y = 1. Quelle est la valeur de y?
• Choices: A) y = 1 B) y = 2 C) y = 3 D) y = 4
• Hint: From the simpler equation, express one variable in terms of the other, then substitute. If x − y = 2 and 3x + y = 14, then x = y + 2 → substitute into the second equation.
• Steps:
  • From x − y = 1: x = y + 1.
  • Substitute: 2(y + 1) + 3y = 12 → 2y + 2 + 3y = 12 → 5y = 10.
  • y = 2.
• Answer: y = 2

[Hard] Trigonometry — Angle of Elevation

• EN: A person stands 30 m from the base of a building. The angle of elevation to the top is 60°. Using tan(60°) ≈ 1.73, what is the approximate height of the building?
• FR: Une personne se tient à 30 m de la base d'un bâtiment. L'angle d'élévation jusqu'au sommet est de 60°. En utilisant tan(60°) ≈ 1,73, quelle est la hauteur approximative du bâtiment?
• Choices: A) 17.3 m B) 36.0 m C) 51.9 m D) 60.0 m
• Hint: TOA: tan = opposite ÷ adjacent, so opposite = adjacent × tan(angle). If distance = 20 m and angle = 45°, tan(45°) = 1, so height = 20 × 1 = 20 m.
• Steps:
  • tan(60°) = height ÷ 30.
  • height = 30 × tan(60°) = 30 × 1.73.
  • height ≈ 51.9 m.
• Answer: 51.9 m

[Easy] Exponential Function

• EN: A bacterial culture starts with 50 cells and doubles every hour. How many cells are there after 3 hours?
• FR: Une culture bactérienne commence avec 50 cellules et double chaque heure. Combien y a-t-il de cellules après 3 heures?
• Choices: A) 150 B) 300 C) 400 D) 450
• Hint: Use the formula A = P × 2ⁿ where n is the number of hours. For 20 cells doubling after 2 hours: 20 × 2² = 80.
• Steps:
  • After 1 hour: 50 × 2 = 100.
  • After 2 hours: 100 × 2 = 200.
  • After 3 hours: 200 × 2 = 400.
• Answer: 400

[Easy] Logarithms Introduction

• EN: What is log₂(8)?
• FR: Combien fait log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log_b(x) asks: to what power must b be raised to get x? log₃(27) = 3 because 3³ = 27.
• Steps:
  • Ask: 2 to what power equals 8?
  • 2¹ = 2, 2² = 4, 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 4, and the common difference is 6. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 4 et la raison est 6. Quel est le 5e terme?
• Choices: A) 24 B) 28 C) 30 D) 34
• Hint: Use tₙ = a + (n−1)d. For a = 2, d = 5, t₄ = 2 + (3)(5) = 17.
• Steps:
  • t₅ = a + (5 − 1)d = 4 + 4 × 6.
  • 4 + 24 = 28.
  • The 5th term is 28.
• Answer: 28

[Easy] Compound Interest

• EN: $1000 is invested at 5% per year, compounded annually. What is the amount after 2 years?
• FR: 1000 $ est investi à 5 % par an, composé annuellement. Quelle est la valeur après 2 ans?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1110.00
• Hint: Use A = P(1 + r)ⁿ. For $500 at 4% for 2 years: A = 500(1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000 × (1.05)².
  • (1.05)² = 1.1025.
  • A = 1000 × 1.1025 = $1102.50.
• Answer: $1102.50

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = x² − 4x + 7?
• FR: Quel est le sommet de la parabole y = x² − 4x + 7?
• Choices: A) (2, 3) B) (−2, 3) C) (2, 7) D) (4, 7)
• Hint: The x-coordinate of the vertex is x = −b/(2a). For y = x² − 6x + 5: x = 6/2 = 3, then y = 9 − 18 + 5 = −4. Vertex is (3, −4).
• Steps:
  • x = −(−4)/(2 × 1) = 4/2 = 2.
  • y = (2)² − 4(2) + 7 = 4 − 8 + 7 = 3.
  • The vertex is (2, 3).
• Answer: (2, 3)

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ
• FR: Simplifie : sin²θ + cos²θ
• Choices: A) 0 B) 1 C) 2 D) sinθ × cosθ
• Hint: This is one of the most important identities in trigonometry. Think of the Pythagorean identity on the unit circle.
• Steps:
  • sin²θ + cos²θ is the Pythagorean Identity.
  • It always equals 1 for any angle θ.
  • So the simplified form is 1.
• Answer: 1

[Medium] Geometric Series Sum

• EN: Find the sum of the first 4 terms of the geometric series: 3, 6, 12, 24, ...
• FR: Trouve la somme des 4 premiers termes de la suite géométrique : 3, 6, 12, 24, ...
• Choices: A) 35 B) 42 C) 45 D) 48
• Hint: Sum = a(rⁿ − 1)/(r − 1). For a = 2, r = 3, n = 3: S = 2(27 − 1)/2 = 26.
• Steps:
  • Simply add: 3 + 6 + 12 + 24.
  • 3 + 6 = 9; 9 + 12 = 21; 21 + 24 = 45.
  • The sum of the first 4 terms is 45.
• Answer: 45

[Medium] Annuity Problem

• EN: You deposit $200 at the end of every year into an account that earns 5% per year. What is the future value after 3 years? (Use FV = PMT × [(1+r)ⁿ − 1]/r)
• FR: Tu déposes 200 $ à la fin de chaque année dans un compte qui rapporte 5 % par an. Quelle est la valeur future après 3 ans?
• Choices: A) $600.00 B) $630.50 C) $662.05 D) $700.00
• Hint: Plug values into FV = PMT × [(1+r)ⁿ − 1]/r. PMT = $100, r = 0.05, n = 2: FV = 100 × (1.1025 − 1)/0.05 = 100 × 2.05 = $205.
• Steps:
  • FV = 200 × [(1.05)³ − 1] / 0.05.
  • (1.05)³ = 1.157625; 1.157625 − 1 = 0.157625.
  • FV = 200 × 0.157625 / 0.05 = 200 × 3.1525 = $630.50.
• Answer: $630.50

[Hard] Exponential Equation with Logarithms

• EN: Solve for x: 2ˣ = 32
• FR: Résous pour x : 2ˣ = 32
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 16
• Hint: Rewrite 32 as a power of 2, then set the exponents equal. 3ˣ = 27 → 3ˣ = 3³ → x = 3.
• Steps:
  • Express 32 as a power of 2: 32 = 2⁵.
  • So 2ˣ = 2⁵, which means x = 5.
  • The solution is x = 5.
• Answer: x = 5

[Hard] Trigonometric Equation

• EN: Solve for θ in [0°, 360°]: 2sin(θ) = √2. What are the two solutions?
• FR: Résous pour θ dans [0°, 360°] : 2sin(θ) = √2. Quelles sont les deux solutions?
• Choices: A) 30° and 150° B) 45° and 135° C) 60° and 120° D) 45° and 315°
• Hint: Isolate sin(θ), find the reference angle, then use the CAST rule to find both solutions. 2sin(θ) = 1 → sin(θ) = 0.5 → θ = 30° and 150°.
• Steps:
  • 2sin(θ) = √2 → sin(θ) = √2/2.
  • The reference angle for sin = √2/2 is 45°.
  • sin is positive in Q1 and Q2: θ = 45° and 135°.
• Answer: 45° and 135°

[Easy] Permutations

• EN: How many ways can 5 students line up in a row for a class photo?
• FR: De combien de façons 5 élèves peuvent-ils se placer en rang pour une photo de classe?
• Choices: A) 25 B) 60 C) 120 D) 720
• Hint: For n objects in a line, the number of arrangements is n! (n factorial). 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • 5 × 4 = 20, 20 × 3 = 60, 60 × 2 = 120, 120 × 1 = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: How many ways can you choose 2 toppings from a menu of 5 toppings for a Tim Hortons bagel?
• FR: De combien de façons peut-on choisir 2 garnitures parmi 5 pour un bagel de Tim Hortons?
• Choices: A) 8 B) 10 C) 20 D) 25
• Hint: Use C(n,r) = n! ÷ [r!(n−r)!]. C(6,2) = 6! ÷ (2! × 4!) = (6 × 5) ÷ (2 × 1) = 15.
• Steps:
  • C(5,2) = 5! ÷ [2! × 3!] = (5 × 4) ÷ (2 × 1).
  • = 20 ÷ 2 = 10.
  • There are 10 ways.
• Answer: 10

[Easy] Derivative — Basic Power Rule

• EN: Using the power rule, what is the derivative of f(x) = x³?
• FR: En utilisant la règle de puissance, quelle est la dérivée de f(x) = x³?
• Choices: A) x² B) 3x C) 3x² D) x⁴
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n × xⁿ⁻¹. The derivative of x⁴ is 4x³.
• Steps:
  • f(x) = x³, so n = 3.
  • f'(x) = 3 × x^(3−1) = 3x².
  • The derivative is 3x².
• Answer: 3x²

[Easy] Polynomial Function End Behaviour

• EN: For the polynomial f(x) = −2x⁴ + 3x − 5, what happens to f(x) as x → +∞?
• FR: Pour le polynôme f(x) = −2x⁴ + 3x − 5, que se passe-t-il avec f(x) lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 5
• Hint: The leading term determines end behaviour. A negative leading coefficient and even degree → both ends go down. For −3x², as x → ±∞, f(x) → −∞.
• Steps:
  • Leading term is −2x⁴ (negative coefficient, even degree).
  • As x → +∞, x⁴ → +∞, so −2x⁴ → −∞.
  • Therefore f(x) → −∞.
• Answer: f(x) → −∞

[Medium] Rate of Change — Derivative

• EN: A ball's height (in metres) is given by h(t) = −5t² + 20t. What is the instantaneous rate of change (velocity) at t = 2 seconds?
• FR: La hauteur d'un ballon (en mètres) est donnée par h(t) = −5t² + 20t. Quel est le taux de variation instantané (vitesse) à t = 2 secondes?
• Choices: A) 0 m/s B) 5 m/s C) 10 m/s D) 20 m/s
• Hint: Find the derivative using the power rule, then substitute the time value. If h(t) = −3t² + 12t, then h'(t) = −6t + 12; at t = 1, h'(1) = 6.
• Steps:
  • h'(t) = −10t + 20.
  • h'(2) = −10(2) + 20 = −20 + 20 = 0.
  • The instantaneous rate of change at t = 2 is 0 m/s.
• Answer: 0 m/s

[Medium] Probability Distribution

• EN: A fair die is rolled. Let X be the outcome. What is the expected value E(X)?
• FR: On lance un dé équitable. Soit X le résultat. Quelle est la valeur espérée E(X)?
• Choices: A) 2.5 B) 3.0 C) 3.5 D) 4.0
• Hint: E(X) = Σ[x × P(x)] for all outcomes. For a coin flip (0 or 1, each with prob 0.5): E(X) = 0(0.5) + 1(0.5) = 0.5.
• Steps:
  • Each outcome (1 through 6) has probability 1/6.
  • E(X) = (1 + 2 + 3 + 4 + 5 + 6)/6 = 21/6.
  • E(X) = 3.5.
• Answer: 3.5

[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). Quel est a + b?
• Choices: A) (2, 6) B) (4, 2) C) (4, 6) D) (2, 8)
• Hint: Add vectors component by component. (5, 3) + (2, −1) = (7, 2).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 4 + 2 = 6.
  • a + b = (2, 6).
• Answer: (2, 6)

[Medium] Rational Function — Vertical Asymptote

• EN: What is the vertical asymptote of f(x) = 3/(x − 5)?
• FR: Quelle est l'asymptote verticale de f(x) = 3/(x − 5)?
• Choices: A) x = −5 B) x = 3 C) x = 5 D) y = 5
• Hint: Vertical asymptotes occur where the denominator equals zero. For f(x) = 1/(x + 2), the denominator is 0 when x = −2, so the asymptote is x = −2.
• Steps:
  • Set the denominator equal to zero: x − 5 = 0.
  • x = 5.
  • The vertical asymptote is x = 5.
• Answer: x = 5

[Hard] Binomial Probability

• EN: A hockey player has a 70% chance of scoring on each penalty shot. If she takes 3 penalty shots, what is the probability she scores exactly 2 goals? (Round to 3 decimal places.)
• FR: Une joueuse de hockey a 70 % de chance de marquer sur chaque tir de pénalité. Si elle tire 3 fois, quelle est la probabilité qu'elle marque exactement 2 buts? (Arrondis à 3 décimales.)
• Choices: A) 0.189 B) 0.294 C) 0.441 D) 0.490
• Hint: Use P(X = k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ. For n = 4, k = 2, p = 0.5: C(4,2) × 0.25 × 0.25 = 6 × 0.0625 = 0.375.
• Steps:
  • P(X = 2) = C(3,2) × (0.7)² × (0.3)¹.
  • C(3,2) = 3; (0.7)² = 0.49; (0.3)¹ = 0.3.
  • P = 3 × 0.49 × 0.3 = 3 × 0.147 = 0.441.
• Answer: 0.441

[Hard] Optimization Using Derivatives

• EN: A rectangular garden is to be fenced along three sides (the fourth side is a wall). You have 60 m of fencing. What width (the side perpendicular to the wall) maximizes the area?
• FR: Un jardin rectangulaire doit être clôturé sur trois côtés (le quatrième côté est un mur). Tu disposes de 60 m de clôture. Quelle largeur (côté perpendiculaire au mur) maximise l'aire?
• Choices: A) 10 m B) 15 m C) 20 m D) 30 m
• Hint: Set up an expression for area in terms of one variable, differentiate, and set the derivative to zero. If fencing = 40 m and setup is 2w + L = 40, then L = 40 − 2w and A = w(40 − 2w).
• Steps:
  • Let w = width (2 sides) and L = length. Then 2w + L = 60, so L = 60 − 2w.
  • Area A = w(60 − 2w) = 60w − 2w².
  • dA/dw = 60 − 4w = 0 → w = 15 m.
• Answer: 15 m