Daily Math — 2026-07-25

[Easy] Counting Carrots

• EN: Maya has 7 carrots. She picks 5 more. How many carrots does she have now?
• FR: Maya a 7 carottes. Elle en cueille 5 de plus. Combien de carottes a-t-elle maintenant?
• Choices: A) 10 carrots B) 11 carrots C) 12 carrots D) 13 carrots
• Hint: To add, count on from the bigger number (e.g., 6 + 3: start at 6, count 3 more).
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • So Maya has 12 carrots.
• Answer: 12 carrots

[Easy] Skip Counting by 2s

• EN: Count by 2s. What comes next: 2, 4, 6, 8, ___?
• FR: Compte par 2. Quel nombre vient après: 2, 4, 6, 8, ___?
• Choices: A) 9 B) 11 C) 10 D) 12
• Hint: When skip counting by 2s, add 2 each time (e.g., 10, 12, 14).
• Steps:
  • The pattern adds 2 each time: 2, 4, 6, 8, ...
  • Add 2 to 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) 14 C) They are equal D) 11
• Hint: Numbers with two digits are always bigger than numbers with one digit.
• Steps:
  • 14 has two digits, and 9 has one digit.
  • Two-digit numbers are always bigger than one-digit numbers, so 14 is bigger.
• Answer: 14

[Easy] Coin Recognition

• EN: Lucas has 1 dime. How many cents does he have?
• FR: Lucas a 1 pièce de 10 cents. Combien de cents a-t-il?
• Choices: A) 1 cent B) 5 cents C) 25 cents D) 10 cents
• Hint: A nickel is worth 5 cents, and a dime is worth 10 cents.
• Steps:
  • A dime is a silver coin worth 10 cents.
  • Lucas has 10 cents.
• Answer: 10 cents

[Medium] Hockey Sticks

• EN: There are 15 hockey sticks in the equipment room. Players take 8. How many are left?
• FR: Il y a 15 bâtons de hockey dans la salle d'équipement. Les joueurs en prennent 8. Combien en reste-t-il?
• Choices: A) 6 sticks B) 8 sticks C) 7 sticks D) 9 sticks
• Hint: To subtract, think of what you add to the smaller number to get the bigger one (e.g., 12 − 5: 5 + ? = 12).
• Steps:
  • Start with 15 sticks and take away 8.
  • 15 − 8 = 7. There are 7 sticks left.
• Answer: 7 sticks

[Medium] Skip Counting by 5s

• EN: Sam counts by 5s: 5, 10, 15, ___. What comes next?
• FR: Sam compte par 5: 5, 10, 15, ___. Quel nombre vient après?
• Choices: A) 16 B) 25 C) 20 D) 18
• Hint: When skip counting by 5s, add 5 each time (e.g., 20, 25, 30).
• Steps:
  • The pattern adds 5 each time: 5, 10, 15, ...
  • 15 + 5 = 20.
• Answer: 20

[Medium] Pennies in a Jar

• EN: Aisha has 6 pennies. Her friend gives her 9 more pennies. How many pennies does she have in all?
• FR: Aisha a 6 sous. Son ami lui en donne 9 de plus. Combien de sous a-t-elle en tout?
• Choices: A) 14 pennies B) 16 pennies C) 13 pennies D) 15 pennies
• Hint: To add two numbers, you can count on from the bigger one (e.g., 8 + 5: start at 8, count 5 more).
• Steps:
  • Start at 9 (the bigger number) and count on 6 more: 10, 11, 12, 13, 14, 15.
  • Aisha has 15 pennies.
• Answer: 15 pennies

[Medium] Count to 100

• EN: What number comes just before 100?
• FR: Quel nombre vient juste avant 100?
• Choices: A) 101 B) 99 C) 98 D) 90
• Hint: The number just before any number is one less (e.g., the number before 50 is 49).
• Steps:
  • One less than 100 means 100 − 1.
  • 100 − 1 = 99.
• Answer: 99

[Hard] Snowflakes and Stars

• EN: Lena draws 9 snowflakes and some stars. She draws 17 shapes in all. How many stars did she draw?
• FR: Lena dessine 9 flocons de neige et quelques étoiles. Elle dessine 17 formes en tout. Combien d'étoiles a-t-elle dessinées?
• Choices: A) 9 stars B) 7 stars C) 8 stars D) 6 stars
• Hint: To find a missing number, subtract what you know from the total (e.g., 14 total − 6 = 8).
• Steps:
  • Total shapes = 17, snowflakes = 9.
  • Stars = 17 − 9 = 8.
• Answer: 8 stars

[Hard] Nickels and Dimes

• EN: Emma has 2 nickels and 1 dime. How many cents does she have in all?
• FR: Emma a 2 pièces de 5 cents et 1 pièce de 10 cents. Combien de cents a-t-elle en tout?
• Choices: A) 15 cents B) 25 cents C) 20 cents D) 17 cents
• Hint: First find the value of each group of coins, then add them together (e.g., 3 nickels = 15 cents, 1 dime = 10 cents, total = 25 cents).
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 1 dime = 10 cents.
  • Total = 10 + 10 = 20 cents.
• Answer: 20 cents

[Easy] Adding at the Rink

• EN: There are 23 skaters on the ice. Then 14 more arrive. How many skaters are there in all?
• FR: Il y a 23 patineurs sur la glace. Puis 14 autres arrivent. Combien y a-t-il de patineurs en tout?
• Choices: A) 36 skaters B) 38 skaters C) 37 skaters D) 39 skaters
• Hint: Add the ones first, then the tens (e.g., 31 + 15: ones 1+5=6, tens 3+1=4, answer 46).
• Steps:
  • Ones: 3 + 4 = 7.
  • Tens: 2 + 1 = 3.
  • Total: 37 skaters.
• Answer: 37 skaters

[Easy] Telling Time

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: La petite aiguille de l'horloge est sur le 3 et la grande aiguille est sur le 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:30 C) 3:00 D) 12:15
• Hint: When the long hand points to 12, it is exactly on the hour (e.g., short hand on 7, long hand on 12 = 7:00).
• Steps:
  • Long hand on 12 means it is exactly on the hour.
  • Short hand on 3 means it is 3 o'clock.
  • The time is 3:00.
• Answer: 3:00

[Easy] Measuring a Pencil

• EN: A pencil is 15 cm long. A crayon is 8 cm long. How much longer is the pencil?
• FR: Un crayon mesure 15 cm de long. Un crayon de couleur mesure 8 cm de long. De combien le crayon est-il plus long?
• Choices: A) 8 cm B) 6 cm C) 7 cm D) 9 cm
• Hint: To find how much longer, subtract the shorter length from the longer one (e.g., 18 cm − 11 cm = 7 cm).
• Steps:
  • Subtract: 15 − 8 = 7.
  • The pencil is 7 cm longer.
• Answer: 7 cm

[Easy] Simple Pattern

• EN: What shape comes next in this pattern: circle, square, circle, square, ___?
• FR: Quelle forme vient après dans ce motif: cercle, carré, cercle, carré, ___?
• Choices: A) triangle B) square C) circle D) rectangle
• Hint: Look at the repeating unit of the pattern and find what comes after the last shape shown.
• Steps:
  • The pattern repeats: circle, square, circle, square, ...
  • After square comes circle.
• Answer: circle

[Medium] Subtracting at Tim Hortons

• EN: Noah had 75 cents. He spent 40 cents on a cookie. How many cents does he have left?
• FR: Noah avait 75 cents. Il a dépensé 40 cents pour un biscuit. Combien de cents lui reste-t-il?
• Choices: A) 45 cents B) 25 cents C) 35 cents D) 30 cents
• Hint: Subtract the tens, then bring down the ones (e.g., 86 − 50 = 36).
• Steps:
  • Tens: 7 − 4 = 3 tens = 30.
  • Ones: 5 − 0 = 5.
  • 75 − 40 = 35 cents.
• Answer: 35 cents

[Medium] Counting Coins

• EN: Sofia has 3 dimes and 2 nickels. How many cents does she have in all?
• FR: Sofia a 3 pièces de 10 cents et 2 pièces de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 45 cents B) 50 cents C) 35 cents D) 40 cents
• Hint: Find the value of each group of coins, then add them (e.g., 2 dimes = 20 cents, 3 nickels = 15 cents, total = 35 cents).
• Steps:
  • 3 dimes = 30 cents.
  • 2 nickels = 10 cents.
  • Total = 30 + 10 = 40 cents.
• Answer: 40 cents

[Medium] Telling Time — Half Hour

• EN: The clock shows the short hand between 6 and 7, and the long hand on 6. What time does it show?
• FR: La petite aiguille est entre 6 et 7, et la grande aiguille est sur le 6. Quelle heure montre l'horloge?
• Choices: A) 6:00 B) 7:30 C) 6:30 D) 7:00
• Hint: When the long hand points to 6, it is half past the hour (e.g., short hand between 4 and 5, long hand on 6 = 4:30).
• Steps:
  • Long hand on 6 = half past the hour.
  • Short hand is between 6 and 7, so it is half past 6.
  • The time is 6:30.
• Answer: 6:30

[Medium] Length in Metres

• EN: A garden fence is 3 m long. Another section is 5 m long. What is the total length of the fence?
• FR: Une clôture de jardin mesure 3 m de long. Une autre section mesure 5 m de long. Quelle est la longueur totale de la clôture?
• Choices: A) 9 m B) 7 m C) 8 m D) 6 m
• Hint: Add the two lengths together (e.g., 4 m + 4 m = 8 m).
• Steps:
  • 3 m + 5 m = 8 m.
  • The total length is 8 m.
• Answer: 8 m

[Hard] Two-Step Money Problem

• EN: Priya has 60 cents. She earns 25 more cents doing chores, then spends 30 cents on a sticker. How many cents does she have left?
• FR: Priya a 60 cents. Elle gagne 25 cents de plus en faisant des corvées, puis dépense 30 cents pour un autocollant. Combien de cents lui reste-t-il?
• Choices: A) 65 cents B) 45 cents C) 55 cents D) 50 cents
• Hint: Do one step at a time — first add, then subtract (e.g., start with 40, add 20 = 60, then subtract 15 = 45).
• Steps:
  • Start with 60 cents, add 25: 60 + 25 = 85 cents.
  • Then subtract 30: 85 − 30 = 55 cents.
  • Priya has 55 cents left.
• Answer: 55 cents

[Hard] Missing Number

• EN: 47 + ___ = 83. What is the missing number?
• FR: 47 + ___ = 83. Quel est le nombre manquant?
• Choices: A) 34 B) 44 C) 36 D) 46
• Hint: To find a missing addend, subtract the number you know from the total (e.g., 30 + ___ = 72 means 72 − 30 = 42).
• Steps:
  • Missing number = 83 − 47.
  • 83 − 47 = 36.
  • The missing number is 36.
• Answer: 36

[Easy] Multiplication by 5

• EN: There are 4 bags with 5 apples each. How many apples are there in all?
• FR: Il y a 4 sacs avec 5 pommes chacun. Combien y a-t-il de pommes en tout?
• Choices: A) 9 apples B) 25 apples C) 20 apples D) 15 apples
• Hint: Multiply the number of groups by the number in each group (e.g., 3 bags × 5 = 15).
• Steps:
  • 4 groups × 5 apples each = 4 × 5.
  • 4 × 5 = 20 apples.
• Answer: 20 apples

[Easy] Basic Division

• EN: 12 cookies are shared equally among 3 friends. How many cookies does each friend get?
• FR: 12 biscuits sont partagés également entre 3 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 5 cookies B) 4 cookies C) 3 cookies D) 6 cookies
• Hint: Division splits a total into equal groups (e.g., 15 ÷ 3 = 5 because 3 × 5 = 15).
• Steps:
  • 12 ÷ 3 = ?
  • Ask: 3 × ? = 12. Answer: 3 × 4 = 12.
  • Each friend gets 4 cookies.
• Answer: 4 cookies

[Easy] Identifying One-Half

• EN: A pizza is cut into 2 equal pieces. Kai eats 1 piece. What fraction did Kai eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Kai mange 1 morceau. Quelle fraction Kai a-t-il mangée?
• Choices: A) 1/3 B) 2/3 C) 1/4 D) 1/2
• Hint: A fraction shows part of a whole — the bottom number is total equal parts, the top is parts taken (e.g., 1 out of 3 = 1/3).
• Steps:
  • The pizza is in 2 equal pieces. Kai ate 1 of them.
  • 1 out of 2 = 1/2.
• Answer: 1/2

[Easy] Reading a Bar Graph

• EN: A bar graph shows that 8 students chose hockey and 5 chose soccer as their favourite sport. How many more students chose hockey?
• FR: Un diagramme à barres montre que 8 élèves ont choisi le hockey et 5 ont choisi le soccer comme sport préféré. Combien d'élèves de plus ont choisi le hockey?
• Choices: A) 2 students B) 4 students C) 13 students D) 3 students
• Hint: To find "how many more," subtract the smaller amount from the larger (e.g., 10 − 6 = 4 more).
• Steps:
  • 8 students chose hockey, 5 chose soccer.
  • 8 − 5 = 3 more students chose hockey.
• Answer: 3 students

[Medium] Perimeter of a Rectangle

• EN: A rectangular garden has a length of 6 m and a width of 4 m. What is the perimeter?
• FR: Un jardin rectangulaire a une longueur de 6 m et une largeur de 4 m. Quel est le périmètre?
• Choices: A) 24 m B) 22 m C) 20 m D) 18 m
• Hint: The perimeter of a rectangle = length + length + width + width (e.g., length 5, width 3: 5+5+3+3 = 16).
• Steps:
  • Perimeter = 6 + 6 + 4 + 4.
  • 6 + 6 = 12, 4 + 4 = 8, 12 + 8 = 20.
  • The perimeter is 20 m.
• Answer: 20 m

[Medium] Multiplication by 3

• EN: There are 7 shelves in the library. Each shelf has 3 books. How many books are there in all?
• FR: Il y a 7 étagères dans la bibliothèque. Chaque étagère a 3 livres. Combien y a-t-il de livres en tout?
• Choices: A) 24 books B) 18 books C) 21 books D) 28 books
• Hint: Multiply the number of groups by the size of each group (e.g., 6 shelves × 3 = 18).
• Steps:
  • 7 × 3 = 21.
  • There are 21 books in all.
• Answer: 21 books

[Medium] Fractions — One Quarter

• EN: A loaf of bread is cut into 4 equal slices. Ben eats 1 slice. What fraction did he eat?
• FR: Un pain est coupé en 4 tranches égales. Ben mange 1 tranche. Quelle fraction a-t-il mangée?
• Choices: A) 1/2 B) 3/4 C) 1/3 D) 1/4
• Hint: Write the number of parts taken on top and the total equal parts on the bottom (e.g., 1 out of 4 = 1/4).
• Steps:
  • 4 equal slices total, Ben ate 1.
  • Fraction = 1/4.
• Answer: 1/4

[Medium] Division with Multiplication Table

• EN: A farmer puts 10 strawberries into each basket. He has 50 strawberries. How many baskets does he fill?
• FR: Un fermier met 10 fraises dans chaque panier. Il a 50 fraises. Combien de paniers remplit-il?
• Choices: A) 6 baskets B) 4 baskets C) 5 baskets D) 8 baskets
• Hint: Divide the total by the number in each group (e.g., 40 ÷ 10 = 4 because 10 × 4 = 40).
• Steps:
  • 50 ÷ 10 = ?
  • 10 × 5 = 50, so 50 ÷ 10 = 5.
  • He fills 5 baskets.
• Answer: 5 baskets

[Hard] Two-Step Multiplication

• EN: A class has 4 tables. Each table has 5 crayons and 3 pencils. How many crayons and pencils are there in all?
• FR: Une classe a 4 tables. Chaque table a 5 crayons de couleur et 3 crayons. Combien y a-t-il de crayons de couleur et de crayons en tout?
• Choices: A) 24 items B) 32 items C) 36 items D) 28 items
• Hint: Find the number of items per table first, then multiply by the number of tables (e.g., 2 tables × (4+3) = 2 × 7 = 14).
• Steps:
  • Items per table: 5 + 3 = 8.
  • Total: 4 × 8 = 32.
  • There are 32 items in all.
• Answer: 32 items

[Hard] Fraction of a Group

• EN: There are 12 students in a group. One-third of them are wearing hats. How many students are wearing hats?
• FR: Il y a 12 élèves dans un groupe. Un tiers d'entre eux portent des chapeaux. Combien d'élèves portent des chapeaux?
• Choices: A) 3 students B) 6 students C) 4 students D) 5 students
• Hint: To find a fraction of a group, divide by the bottom number of the fraction (e.g., 1/3 of 9 = 9 ÷ 3 = 3).
• Steps:
  • 1/3 of 12 means 12 ÷ 3.
  • 12 ÷ 3 = 4.
  • Four students are wearing hats.
• Answer: 4 students

[Easy] Multiplication — 7 × 8

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 48 D) 63
• Hint: Use a multiplication fact you know (e.g., 7 × 7 = 49, then add one more 7 to get 56).
• Steps:
  • 7 × 8 = 7 × 7 + 7 = 49 + 7 = 56.
  • The answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What digit is in the tenths place in the number 3.47?
• FR: Quel chiffre est à la position des dixièmes dans le nombre 3,47?
• Choices: A) 3 B) 7 C) 4 D) 0
• Hint: In a decimal, the first digit after the decimal point is in the tenths place (e.g., in 5.62, the tenths digit is 6).
• Steps:
  • 3.47: the digit to the left of the decimal is 3 (ones).
  • The first digit to the right of the decimal is 4 (tenths).
  • The tenths digit is 4.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A classroom door is 2 m wide and 3 m tall. What is its area?
• FR: La porte d'une salle de classe mesure 2 m de large et 3 m de haut. Quelle est son aire?
• Choices: A) 5 m² B) 10 m² C) 8 m² D) 6 m²
• Hint: Area of a rectangle = length × width (e.g., 4 m × 5 m = 20 m²).
• Steps:
  • Area = 2 × 3 = 6.
  • The area is 6 m².
• Answer: 6 m²

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 1/2?
• FR: Quelle fraction est plus grande: 3/4 ou 1/2?
• Choices: A) They are equal B) 1/4 C) 1/2 D) 3/4
• Hint: Convert fractions to the same denominator to compare (e.g., 1/2 = 2/4, so 3/4 > 2/4).
• Steps:
  • Convert 1/2 to quarters: 1/2 = 2/4.
  • Compare 3/4 and 2/4: 3/4 is larger.
• Answer: 3/4

[Medium] Long Division with Remainder

• EN: 67 students are put into groups of 6. How many full groups are there, and how many students are left over?
• FR: 67 élèves sont répartis en groupes de 6. Combien de groupes complets y a-t-il, et combien d'élèves restent-ils?
• Choices: A) 10 groups, remainder 7 B) 11 groups, remainder 1 C) 12 groups, remainder 5 D) 9 groups, remainder 3
• Hint: Divide, then multiply the quotient by the divisor and subtract to find the remainder (e.g., 25 ÷ 4: 4 × 6 = 24, remainder 1).
• Steps:
  • 6 × 11 = 66, which is less than 67.
  • 67 − 66 = 1 remainder.
  • 11 full groups with 1 student left over.
• Answer: 11 groups, remainder 1

[Medium] Elapsed Time

• EN: Hockey practice starts at 4:15 and ends at 5:45. How long is the practice?
• FR: L'entraînement de hockey commence à 16h15 et se termine à 17h45. Combien de temps dure l'entraînement?
• Choices: A) 1 hour 20 minutes B) 2 hours 30 minutes C) 1 hour 30 minutes D) 1 hour 45 minutes
• Hint: Count up from the start time to the end time in two steps — first to the next hour, then to the end (e.g., 3:20 to 4:50 = 40 min + 50 min = 1 hour 30 min).
• Steps:
  • From 4:15 to 5:15 is 1 hour.
  • From 5:15 to 5:45 is 30 more minutes.
  • Total: 1 hour 30 minutes.
• Answer: 1 hour 30 minutes

[Medium] Decimal Operations

• EN: A book costs $4.50 and a pencil case costs $3.25. What is the total cost?
• FR: Un livre coûte 4,50 $ et un étui à crayons coûte 3,25 $. Quel est le coût total?
• Choices: A) $8.25 B) $7.25 C) $7.75 D) $8.75
• Hint: Line up the decimal points when adding (e.g., $2.30 + $4.60 = $6.90).
• Steps:
  • $4.50 + $3.25: add cents 50 + 25 = 75 cents.
  • Add dollars: 4 + 3 = 7 dollars.
  • Total = $7.75.
• Answer: $7.75

[Medium] All Multiplication Tables

• EN: A baker makes 9 trays with 8 muffins each. How many muffins are there in all?
• FR: Un boulanger fait 9 plateaux avec 8 muffins chacun. Combien de muffins y a-t-il en tout?
• Choices: A) 63 muffins B) 72 muffins C) 81 muffins D) 64 muffins
• Hint: Recall the 9 times table: 9 × 8 can be found by 10 × 8 − 8 (e.g., 9 × 6 = 54).
• Steps:
  • 9 × 8 = 72.
  • There are 72 muffins in all.
• Answer: 72 muffins

[Hard] Multi-Step Word Problem

• EN: Olivia buys 3 notebooks at $2.75 each and pays with a $20 bill. How much change does she receive?
• FR: Olivia achète 3 cahiers à 2,75 $ chacun et paie avec un billet de 20 $. Combien de monnaie reçoit-elle?
• Choices: A) $11.75 B) $12.25 C) $11.25 D) $13.75
• Hint: First find the total cost, then subtract from the amount paid (e.g., 4 items at $1.50 = $6.00, change from $10 = $4.00).
• Steps:
  • Total cost: 3 × $2.75 = $8.25.
  • Change: $20.00 − $8.25 = $11.75.
• Answer: $11.75

[Hard] Comparing and Ordering Fractions

• EN: Order these fractions from least to greatest: 1/2, 3/4, 1/4.
• FR: Mets ces fractions en ordre du plus petit au plus grand: 1/2, 3/4, 1/4.
• Choices: A) 1/2, 1/4, 3/4 B) 3/4, 1/2, 1/4 C) 1/4, 3/4, 1/2 D) 1/4, 1/2, 3/4
• Hint: Convert all fractions to the same denominator to compare them (e.g., 1/3 = 2/6, 1/2 = 3/6, so 2/6 < 3/6).
• Steps:
  • Use a common denominator of 4: 1/2 = 2/4, 3/4 = 3/4, 1/4 = 1/4.
  • Order: 1/4, 2/4, 3/4.
  • In original form: 1/4, 1/2, 3/4.
• Answer: 1/4, 1/2, 3/4

[Easy] Multi-Digit Multiplication

• EN: A school store sells 125 pencils each day. How many pencils are sold in 4 days?
• FR: La boutique de l'école vend 125 crayons par jour. Combien de crayons sont vendus en 4 jours?
• Choices: A) 400 pencils B) 500 pencils C) 450 pencils D) 520 pencils
• Hint: Multiply each digit by 4, starting from the ones (e.g., 113 × 4 = 452).
• Steps:
  • 125 × 4: ones 5 × 4 = 20, write 0, carry 2.
  • Tens: 2 × 4 = 8 + 2 = 10, write 0, carry 1.
  • Hundreds: 1 × 4 = 4 + 1 = 5.
  • Answer: 500 pencils
• Answer: 500 pencils

[Easy] Adding Fractions with Like Denominators

• EN: On a hiking trail, Maya walked 2/8 of the trail before lunch and 3/8 after lunch. What fraction of the trail did she walk in all?
• FR: Sur un sentier de randonnée, Maya a parcouru 2/8 du sentier avant le déjeuner et 3/8 après. Quelle fraction du sentier a-t-elle parcourue en tout?
• Choices: A) 5/16 B) 6/8 C) 5/8 D) 4/8
• Hint: When denominators are the same, just add the numerators (e.g., 3/7 + 2/7 = 5/7).
• Steps:
  • 2/8 + 3/8 = (2+3)/8 = 5/8.
  • Maya walked 5/8 of the trail.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: A hockey team won 50% of their 20 games. How many games did they win?
• FR: Une équipe de hockey a gagné 50 % de ses 20 matchs. Combien de matchs ont-ils gagnés?
• Choices: A) 5 games B) 15 games C) 10 games D) 8 games
• Hint: 50% means half — divide the total by 2 (e.g., 50% of 14 = 14 ÷ 2 = 7).
• Steps:
  • 50% of 20 = 20 ÷ 2 = 10.
  • The team won 10 games.
• Answer: 10 games

[Easy] Decimal Operations

• EN: A loaf of bread costs $3.49 and a carton of milk costs $2.50. What is the total cost?
• FR: Un pain coûte 3,49 $ et un carton de lait coûte 2,50 $. Quel est le coût total?
• Choices: A) $6.99 B) $5.89 C) $5.99 D) $6.09
• Hint: Line up the decimal points and add (e.g., $4.25 + $1.60 = $5.85).
• Steps:
  • $3.49 + $2.50: cents 49 + 50 = 99.
  • Dollars: 3 + 2 = 5.
  • Total = $5.99.
• Answer: $5.99

[Medium] Multi-Digit Division

• EN: A farmer has 336 eggs to pack into cartons of 12. How many full cartons can he pack?
• FR: Un fermier a 336 œufs à mettre dans des boîtes de 12. Combien de boîtes pleines peut-il emballer?
• Choices: A) 24 cartons B) 30 cartons C) 28 cartons D) 32 cartons
• Hint: Divide step by step: how many times does 12 go into each part of the number (e.g., 240 ÷ 12 = 20).
• Steps:
  • 12 × 28 = 336. Check: 12 × 20 = 240, 12 × 8 = 96, 240 + 96 = 336.
  • He can pack 28 cartons.
• Answer: 28 cartons

[Medium] Subtracting Fractions

• EN: Zoe had 7/10 of a pizza. She ate 2/10. What fraction is left?
• FR: Zoé avait 7/10 d'une pizza. Elle en a mangé 2/10. Quelle fraction reste-t-il?
• Choices: A) 9/10 B) 4/10 C) 5/10 D) 6/10
• Hint: Subtract the numerators and keep the denominator the same (e.g., 5/9 − 2/9 = 3/9).
• Steps:
  • 7/10 − 2/10 = (7−2)/10 = 5/10.
  • There is 5/10 of the pizza left.
• Answer: 5/10

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 3 cm wide, and 4 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 3 cm de large et 4 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 36 cm³
• Hint: Volume = length × width × height (e.g., 2 × 3 × 6 = 36 cm³).
• Steps:
  • Volume = 5 × 3 × 4.
  • 5 × 3 = 15, 15 × 4 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A store has 40 items on sale. 25% of the items are jackets. How many jackets are on sale?
• FR: Un magasin a 40 articles en solde. 25 % des articles sont des vestes. Combien de vestes sont en solde?
• Choices: A) 8 jackets B) 10 jackets C) 15 jackets D) 12 jackets
• Hint: 25% means one quarter — divide the total by 4 (e.g., 25% of 20 = 20 ÷ 4 = 5).
• Steps:
  • 25% of 40 = 40 ÷ 4 = 10.
  • There are 10 jackets on sale.
• Answer: 10 jackets

[Hard] Multi-Step Decimal Problem

• EN: Liam earns $12.50 mowing a lawn and $8.75 raking leaves. He spends $6.30 on supplies. How much money does he have left?
• FR: Liam gagne 12,50 $ en tondant une pelouse et 8,75 $ en râtelant les feuilles. Il dépense 6,30 $ en fournitures. Combien d'argent lui reste-t-il?
• Choices: A) $15.95 B) $14.95 C) $13.75 D) $16.45
• Hint: Add the two earnings first, then subtract the expense (e.g., $5.00 + $3.50 = $8.50, minus $2.00 = $6.50).
• Steps:
  • Earnings: $12.50 + $8.75 = $21.25.
  • Subtract supplies: $21.25 − $6.30 = $14.95.
• Answer: $14.95

[Hard] Percentage — 10% and Combined

• EN: A school has 200 students. 10% are in Grade 5, and 25% are in Grade 6. How many students are in Grades 5 and 6 combined?
• FR: Une école a 200 élèves. 10 % sont en 5e année et 25 % sont en 6e année. Combien d'élèves sont en 5e et 6e année combinées?
• Choices: A) 60 students B) 70 students C) 50 students D) 80 students
• Hint: Find each percentage separately, then add them (e.g., 10% of 100 = 10, 25% of 100 = 25, total = 35).
• Steps:
  • 10% of 200 = 200 ÷ 10 = 20 students.
  • 25% of 200 = 200 ÷ 4 = 50 students.
  • Total: 20 + 50 = 70 students.
• Answer: 70 students

[Easy] Percent of a Number

• EN: What is 30% of 90?
• FR: Combien font 30 % de 90?
• Choices: A) 27 B) 30 C) 18 D) 21
• Hint: Find 10% first (divide by 10), then multiply by the number of tens (e.g., 30% of 60 = 6 × 3 = 18).
• Steps:
  • 10% of 90 = 9.
  • 30% = 3 × 9 = 27.
• Answer: 27

[Easy] Order of Operations (BEDMAS)

• EN: Solve: 3 + 4 × 2.
• FR: Calcule: 3 + 4 × 2.
• Choices: A) 14 B) 10 C) 11 D) 16
• Hint: In BEDMAS, multiply before you add (e.g., 5 + 3 × 4 = 5 + 12 = 17).
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
• Answer: 11

[Easy] Ratio

• EN: In a bag there are 4 red marbles and 6 blue marbles. What is the ratio of red to blue?
• FR: Dans un sac, il y a 4 billes rouges et 6 billes bleues. Quel est le rapport des billes rouges aux billes bleues?
• Choices: A) 6:4 B) 2:3 C) 4:10 D) 3:2
• Hint: A ratio compares two quantities; simplify by dividing both by their common factor (e.g., 6:9 simplifies to 2:3).
• Steps:
  • Red to blue: 4:6.
  • Simplify by dividing both by 2: 2:3.
• Answer: 2:3

[Easy] Simple Algebraic Expression

• EN: If n = 5, what is the value of 4n + 3?
• FR: Si n = 5, quelle est la valeur de 4n + 3?
• Choices: A) 12 B) 23 C) 18 D) 28
• Hint: Substitute the value for the variable, then follow BEDMAS (e.g., if x = 3, then 2x + 1 = 2×3+1 = 7).
• Steps:
  • Substitute n = 5: 4(5) + 3 = 20 + 3 = 23.
• Answer: 23

[Medium] Fraction Multiplication

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

[Medium] Integers Introduction

• EN: The temperature in Winnipeg was −8°C in the morning. By afternoon it rose 11°C. What is the afternoon temperature?
• FR: La température à Winnipeg était de −8 °C le matin. L'après-midi, elle a augmenté de 11 °C. Quelle est la température de l'après-midi?
• Choices: A) 2°C B) −3°C C) 3°C D) 4°C
• Hint: Adding a positive number to a negative number moves you right on the number line (e.g., −5 + 8 = 3).
• Steps:
  • −8 + 11 = 3.
  • The afternoon temperature is 3°C.
• Answer: 3°C

[Medium] Rate

• EN: A car travels 240 km in 3 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km par heure?
• Choices: A) 70 km/h B) 60 km/h C) 80 km/h D) 90 km/h
• Hint: Divide the total distance by the number of hours to find the rate (e.g., 150 km ÷ 3 h = 50 km/h).
• Steps:
  • Speed = distance ÷ time = 240 ÷ 3 = 80.
  • The speed is 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: How many 1/4-cup servings are in 3 cups of trail mix?
• FR: Combien de portions de 1/4 de tasse y a-t-il dans 3 tasses de mélange de randonnée?
• Choices: A) 9 servings B) 16 servings C) 12 servings D) 8 servings
• Hint: Dividing by a fraction means multiplying by its reciprocal (e.g., 2 ÷ 1/3 = 2 × 3 = 6).
• Steps:
  • 3 ÷ 1/4 = 3 × 4 = 12.
  • There are 12 servings.
• Answer: 12 servings

[Hard] BEDMAS with Brackets

• EN: Solve: (5 + 3) × 2 − 4 ÷ 2.
• FR: Calcule: (5 + 3) × 2 − 4 ÷ 2.
• Choices: A) 12 B) 18 C) 16 D) 14
• Hint: Always start with brackets, then multiply/divide from left to right, then add/subtract (e.g., (2+4) × 3 − 6 ÷ 2 = 6×3−3 = 15).
• Steps:
  • Brackets: 5 + 3 = 8.
  • Multiply: 8 × 2 = 16.
  • Divide: 4 ÷ 2 = 2.
  • Subtract: 16 − 2 = 14.
• Answer: 14

[Hard] Percent Problem — Finding the Original

• EN: After a 20% discount, a jacket costs $48. What was the original price?
• FR: Après une réduction de 20 %, une veste coûte 48 $. Quel était le prix original?
• Choices: A) $56 B) $64 C) $60 D) $68
• Hint: If 80% of the price = sale price, divide the sale price by 0.80 to find the original (e.g., $40 ÷ 0.80 = $50).
• Steps:
  • The sale price is 80% of the original (100% − 20% = 80%).
  • Original = $48 ÷ 0.80 = $60.
• Answer: $60

[Easy] Integer Addition

• EN: What is (−6) + 9?
• FR: Combien font (−6) + 9?
• Choices: A) −3 B) 4 C) 3 D) −15
• Hint: On a number line, start at the negative number and move right for addition (e.g., (−4) + 7 = 3).
• Steps:
  • Start at −6, move 9 to the right.
  • −6 + 9 = 3.
• Answer: 3

[Easy] Finding a Percentage Discount

• EN: A $40 video game is on sale for 25% off. How much is the discount?
• FR: Un jeu vidéo à 40 $ est en solde à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $10 B) $8 C) $15 D) $12
• Hint: Multiply the original price by the percent (as a decimal) to find the discount (e.g., 20% of $50 = 0.20 × $50 = $10).
• Steps:
  • 25% of $40 = 0.25 × 40 = $10.
  • The discount is $10.
• Answer: $10

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15.
• FR: Résous pour x: x + 9 = 15.
• Choices: A) x = 7 B) x = 5 C) x = 6 D) x = 24
• Hint: To solve, subtract the same number from both sides (e.g., x + 4 = 10 → x = 10 − 4 = 6).
• Steps:
  • x + 9 = 15.
  • Subtract 9 from both sides: x = 15 − 9 = 6.
• Answer: x = 6

[Easy] Integer Subtraction

• EN: What is 5 − (−3)?
• FR: Combien font 5 − (−3)?
• Choices: A) 2 B) −8 C) 8 D) 15
• Hint: Subtracting a negative is the same as adding a positive (e.g., 4 − (−2) = 4 + 2 = 6).
• Steps:
  • 5 − (−3) = 5 + 3 = 8.
• Answer: 8

[Medium] Percent — Tax

• EN: A sweater costs $35.00. If the tax rate is 13%, what is the total price including tax?
• FR: Un chandail coûte 35,00 $. Si le taux de taxe est de 13 %, quel est le prix total avec la taxe?
• Choices: A) $39.55 B) $38.50 C) $40.55 D) $41.00
• Hint: Calculate the tax amount first, then add it to the original price (e.g., 13% of $20 = $2.60, total = $22.60).
• Steps:
  • Tax: 13% of $35 = 0.13 × 35 = $4.55.
  • Total: $35.00 + $4.55 = $39.55.
• Answer: $39.55

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 10 cm long, 5 cm wide, and 4 cm tall. What is the surface area of the box?
• FR: Une boîte cadeau mesure 10 cm de long, 5 cm de large et 4 cm de haut. Quelle est l'aire de la surface de la boîte?
• Choices: A) 220 cm² B) 200 cm² C) 260 cm² D) 180 cm²
• Hint: Surface area = 2(lw + lh + wh) (e.g., l=6, w=3, h=2: 2(18+12+6) = 2×36 = 72 cm²).
• Steps:
  • lw = 10×5 = 50, lh = 10×4 = 40, wh = 5×4 = 20.
  • SA = 2(50+40+20) = 2(110) = 220 cm².
• Answer: 220 cm²

[Medium] Integer Multiplication

• EN: What is (−4) × (−7)?
• FR: Combien font (−4) × (−7)?
• Choices: A) −28 B) 11 C) 28 D) −11
• Hint: A negative times a negative gives a positive result (e.g., (−3) × (−5) = 15).
• Steps:
  • (−4) × (−7) = positive result.
  • 4 × 7 = 28, so (−4) × (−7) = 28.
• Answer: 28

[Medium] Probability

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

[Hard] Two-Step Percent Problem

• EN: A store marks up a coat by 40%, then offers a 10% discount on the marked-up price. If the original cost was $80, what is the final selling price?
• FR: Un magasin majore le prix d'un manteau de 40 %, puis offre une réduction de 10 % sur ce prix majoré. Si le coût original était de 80 $, quel est le prix de vente final?
• Choices: A) $110.40 B) $100.80 C) $104.00 D) $96.00
• Hint: Apply the markup first to find a new price, then apply the discount to that new price (e.g., $50 + 20% = $60, then 10% off $60 = $54).
• Steps:
  • Markup: $80 × 1.40 = $112.
  • Discount: $112 × 0.90 = $100.80.
• Answer: $100.80

[Hard] One-Step Equation with Fractions

• EN: Solve for y: y/3 = 7. What is y?
• FR: Résous pour y: y/3 = 7. Quelle est la valeur de y?
• Choices: A) y = 14 B) y = 21 C) y = 3 D) y = 28
• Hint: Multiply both sides by the denominator to isolate the variable (e.g., x/4 = 5 → x = 5 × 4 = 20).
• Steps:
  • y/3 = 7.
  • Multiply both sides by 3: y = 7 × 3 = 21.
• Answer: y = 21

[Easy] Perfect Squares

• EN: What is the square root of 64?
• FR: Quelle est la racine carrée de 64?
• Choices: A) 6 B) 9 C) 7 D) 8
• Hint: The square root is the number that, when multiplied by itself, gives the value (e.g., √49 = 7 because 7×7=49).
• Steps:
  • Ask: what number × itself = 64?
  • 8 × 8 = 64, so √64 = 8.
• Answer: 8

[Easy] Mean of a Data Set

• EN: Five students scored 70, 80, 60, 90, and 50 on a test. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 80, 60, 90 et 50 à un test. Quel est le score moyen?
• Choices: A) 60 B) 80 C) 75 D) 70
• Hint: Mean = sum of all values ÷ number of values (e.g., scores 10, 20, 30: sum = 60, mean = 60 ÷ 3 = 20).
• Steps:
  • Sum: 70 + 80 + 60 + 90 + 50 = 350.
  • Mean: 350 ÷ 5 = 70.
• Answer: 70

[Easy] Two-Step Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x: 2x + 5 = 13.
• Choices: A) x = 6 B) x = 3 C) x = 4 D) x = 9
• Hint: First subtract the constant from both sides, then divide by the coefficient (e.g., 3x + 2 = 11 → 3x = 9 → x = 3).
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide by 2: x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A backpack was $50 and now costs $60. What is the percent increase?
• FR: Un sac à dos coûtait 50 $ et coûte maintenant 60 $. Quel est le pourcentage d'augmentation?
• Choices: A) 25% B) 15% C) 20% D) 10%
• Hint: Percent increase = (increase ÷ original) × 100 (e.g., increase from $40 to $48: increase = 8, 8÷40×100 = 20%).
• Steps:
  • Increase: $60 − $50 = $10.
  • Percent increase: (10 ÷ 50) × 100 = 20%.
• Answer: 20%

[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 côtés de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 14 cm B) 12 cm C) 11 cm D) 10 cm
• Hint: Use a² + b² = c² and then take the square root (e.g., legs 3 and 4: 9 + 16 = 25, √25 = 5).
• Steps:
  • a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10.
  • The hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through the points (2, 3) and (6, 11). What is the slope of the line?
• FR: Une droite passe par les points (2, 3) et (6, 11). Quelle est la pente de la droite?
• Choices: A) 3 B) 4 C) 2 D) 5
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) (e.g., points (1,2) and (3,8): (8−2)÷(3−1) = 6÷2 = 3).
• Steps:
  • Rise: 11 − 3 = 8. Run: 6 − 2 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median

• EN: Find the median of this data set: 3, 7, 9, 2, 5.
• FR: Trouve la médiane de cet ensemble de données: 3, 7, 9, 2, 5.
• Choices: A) 7 B) 9 C) 4 D) 5
• Hint: Order the numbers from least to greatest and find the middle value (e.g., 1, 4, 6, 9, 12 → median is 6).
• Steps:
  • Ordered: 2, 3, 5, 7, 9.
  • The middle value (3rd out of 5) is 5.
• Answer: 5

[Medium] Percent Decrease

• EN: A store reduces the price of a jacket from $80 to $60. What is the percent decrease?
• FR: Un magasin réduit le prix d'une veste de 80 $ à 60 $. Quel est le pourcentage de diminution?
• Choices: A) 30% B) 20% C) 25% D) 15%
• Hint: Percent decrease = (decrease ÷ original) × 100 (e.g., from $50 to $40: decrease = 10, 10÷50×100 = 20%).
• Steps:
  • Decrease: $80 − $60 = $20.
  • Percent decrease: (20 ÷ 80) × 100 = 25%.
• Answer: 25%

[Hard] Two-Step Equation with Negatives

• EN: Solve for x: −3x + 7 = −8.
• FR: Résous pour x: −3x + 7 = −8.
• Choices: A) x = 5 B) x = −5 C) x = 3 D) x = −3
• Hint: Move the constant to the right first, then divide both sides by the coefficient (e.g., −2x + 4 = 10 → −2x = 6 → x = −3).
• Steps:
  • Subtract 7 from both sides: −3x = −15.
  • Divide by −3: x = 5.
• Answer: x = 5

[Hard] Pythagorean Theorem — Finding 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 un côté de 5 cm. Quelle est la longueur de l'autre côté?
• Choices: A) 11 cm B) 14 cm C) 8 cm D) 12 cm
• Hint: Rearrange a² + b² = c² to find the missing leg: b² = c² − a² (e.g., c=10, a=6: b² = 100−36=64, b=8).
• Steps:
  • b² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12.
  • The other leg is 12 cm.
• Answer: 12 cm

[Easy] Solving a Linear Equation

• EN: Solve for x: 3x − 4 = 11.
• FR: Résous pour x: 3x − 4 = 11.
• Choices: A) x = 4 B) x = 7 C) x = 5 D) x = 3
• Hint: Add the constant to both sides first, then divide by the coefficient (e.g., 4x − 3 = 13 → 4x = 16 → x = 4).
• Steps:
  • Add 4 to both sides: 3x = 15.
  • Divide by 3: x = 5.
• Answer: x = 5

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 4x − 3?
• FR: Quelle est la pente de la droite y = 4x − 3?
• Choices: A) −3 B) 3 C) 1 D) 4
• Hint: In y = mx + b, m is the slope and b is the y-intercept (e.g., in y = 6x + 2, the slope is 6).
• Steps:
  • y = 4x − 3 is in y = mx + b form.
  • The slope m = 4.
• Answer: 4

[Easy] Adding Polynomials

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

[Easy] Similar Triangles

• EN: Two similar triangles have sides in ratio 1:3. If the smaller triangle has a side of 4 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans un rapport de 1:3. Si le petit triangle a un côté de 4 cm, quelle est la longueur du côté correspondant du grand triangle?
• Choices: A) 16 cm B) 7 cm C) 14 cm D) 12 cm
• Hint: Multiply the known side by the scale factor to find the corresponding side (e.g., ratio 1:2, small side = 5 cm → large side = 10 cm).
• Steps:
  • Scale factor: 3.
  • Corresponding side: 4 × 3 = 12 cm.
• Answer: 12 cm

[Medium] Linear Inequality

• EN: Solve: 2x + 3 > 11. Which describes the solution?
• FR: Résous: 2x + 3 > 11. Quelle description représente la solution?
• Choices: A) x < 4 B) x > 8 C) x < 8 D) x > 4
• Hint: Solve like an equation, but keep the inequality sign (flip it only if you multiply/divide by a negative) (e.g., 3x + 1 > 10 → 3x > 9 → x > 3).
• Steps:
  • Subtract 3: 2x > 8.
  • Divide by 2: x > 4.
• Answer: x > 4

[Medium] Trigonometry — SOH (Sine)

• EN: In a right triangle, the opposite side to angle A is 5 cm and the hypotenuse is 10 cm. What is sin A?
• FR: Dans un triangle rectangle, le côté opposé à l'angle A est de 5 cm et l'hypoténuse est de 10 cm. Combien vaut sin A?
• Choices: A) 2 B) 0.25 C) 0.75 D) 0.5
• Hint: SOH means sin = opposite ÷ hypotenuse (e.g., opposite=3, hypotenuse=6: sin=3÷6=0.5).
• Steps:
  • sin A = opposite ÷ hypotenuse = 5 ÷ 10 = 0.5.
• Answer: 0.5

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 4).
• FR: Développe: (x + 3)(x + 4).
• Choices: A) x² + 7x + 12 B) x² + 12x + 7 C) x² + 7x + 7 D) x² + 6x + 12
• Hint: Use FOIL — First, Outer, Inner, Last (e.g., (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.
  • Combine: x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Graphing Lines — Y-Intercept

• EN: The line y = −2x + 6 crosses the y-axis at which point?
• FR: La droite y = −2x + 6 coupe l'axe des y à quel point?
• Choices: A) (0, −2) B) (6, 0) C) (0, 2) D) (0, 6)
• Hint: The y-intercept is the value of y when x = 0; it is the b in y = mx + b (e.g., y = 3x + 5 crosses the y-axis at (0, 5)).
• Steps:
  • In y = mx + b, b = 6.
  • The y-intercept is (0, 6).
• Answer: (0, 6)

[Hard] Systems of Linear Equations

• EN: Solve the system: y = 2x + 1 and y = −x + 7. What is the value of x?
• FR: Résous le système: y = 2x + 1 et y = −x + 7. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 7 C) x = 2 D) x = 1
• Hint: Set the two expressions equal to each other and solve (e.g., 3x+1 = x+5 → 2x=4 → x=2).
• Steps:
  • Set equal: 2x + 1 = −x + 7.
  • Add x to both sides: 3x + 1 = 7.
  • Subtract 1: 3x = 6. Divide by 3: x = 2.
• Answer: x = 2

[Hard] Trigonometry — TOA (Tangent)

• EN: A ramp rises 3 m over a horizontal distance of 4 m. What is the tangent of the angle the ramp makes with the ground?
• FR: Une rampe monte de 3 m sur une distance horizontale de 4 m. Quel est le tangent de l'angle que la rampe fait avec le sol?
• Choices: A) 4/3 B) 3/5 C) 4/5 D) 3/4
• Hint: TOA means tan = opposite ÷ adjacent (e.g., opposite=5, adjacent=12: tan=5/12).
• Steps:
  • opposite = 3 m (rise), adjacent = 4 m (horizontal distance).
  • tan = 3/4.
• Answer: 3/4

[Easy] Factoring a Quadratic

• EN: Factor the quadratic: x² + 5x + 6.
• FR: Factorise le trinôme: x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 4) C) (x + 3)(x + 2) D) (x + 6)(x − 1)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient (e.g., x²+7x+12 → 3×4=12, 3+4=7 → (x+3)(x+4)).
• Steps:
  • Find two numbers that multiply to 6 and add to 5: 2 and 3.
  • Factor: (x + 3)(x + 2).
• Answer: (x + 3)(x + 2)

[Easy] Trigonometry — Finding a Side (CAH)

• EN: In a right triangle, angle A = 60°, and the hypotenuse is 10 cm. What is the length of the adjacent side? (cos 60° = 0.5)
• FR: Dans un triangle rectangle, l'angle A = 60° et l'hypoténuse est de 10 cm. Quelle est la longueur du côté adjacent? (cos 60° = 0,5)
• Choices: A) 8 cm B) 7 cm C) 6 cm D) 5 cm
• Hint: CAH means cos = adjacent ÷ hypotenuse, so adjacent = cos × hypotenuse (e.g., cos 45° × 8 = 0.707 × 8).
• Steps:
  • cos 60° = adjacent ÷ 10.
  • adjacent = 0.5 × 10 = 5 cm.
• Answer: 5 cm

[Easy] System of Equations

• EN: Solve: x + y = 10 and x − y = 4. What is x?
• FR: Résous: x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 8 B) x = 3 C) x = 6 D) x = 7
• Hint: Add the two equations together to eliminate y, then solve for x (e.g., x+y=8 and x−y=2: add → 2x=10 → x=5).
• Steps:
  • Add equations: (x+y)+(x−y) = 10+4 → 2x = 14.
  • x = 7.
• Answer: x = 7

[Easy] Volume of a Cylinder

• EN: A cylindrical soup can has a radius of 4 cm and a height of 10 cm. What is its volume? (Use π = 3.14)
• FR: Une boîte de soupe cylindrique a un rayon de 4 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π = 3,14)
• Choices: A) 401.92 cm³ B) 502.40 cm³ C) 125.60 cm³ D) 301.44 cm³
• Hint: Volume of a cylinder = π × r² × h (e.g., r=3, h=5: 3.14 × 9 × 5 = 141.3 cm³).
• Steps:
  • V = π × r² × h = 3.14 × 16 × 10.
  • 3.14 × 16 = 50.24, × 10 = 502.40.
  • Volume = 502.40 cm³.
• Answer: 502.40 cm³

[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 or x = −7 B) x = 3 or x = −7 C) x = 7 or x = −1 D) x = 2 or x = −8
• Hint: Add (half of the x-coefficient)² to both sides (e.g., x²+4x=5 → x²+4x+4=9 → (x+2)²=9 → x=1 or x=−5).
• Steps:
  • Add 9 to both sides: x² + 6x + 9 = 16.
  • (x + 3)² = 16.
  • x + 3 = ±4, so x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry — Chord and Centre

• EN: A chord in a circle is 16 cm long. The perpendicular distance from the centre to the chord is 6 cm. What is the radius of the circle?
• FR: Une corde dans un cercle mesure 16 cm de long. La distance perpendiculaire du centre à la corde est de 6 cm. Quel est le rayon du cercle?
• Choices: A) 12 cm B) 11 cm C) 9 cm D) 10 cm
• Hint: The perpendicular from the centre bisects the chord, forming a right triangle with the radius as the hypotenuse (e.g., chord=12, distance=4: half chord=6, r=√(36+16)=√52).
• Steps:
  • Half the chord = 8 cm. Perpendicular = 6 cm.
  • r² = 8² + 6² = 64 + 36 = 100.
  • r = 10 cm.
• Answer: 10 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve: x² − 5x + 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre: x² − 5x + 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 or x = 6 B) x = 4 or x = 2 C) x = 2 or x = 3 D) x = 5 or x = 1
• Hint: x = (−b ± √(b²−4ac)) / 2a; identify a, b, c first (e.g., x²−7x+12=0: a=1,b=−7,c=12, solutions are x=3 and x=4).
• Steps:
  • a=1, b=−5, c=6. Discriminant: 25−24=1. √1=1.
  • x = (5±1)/2: x=3 or x=2.
• Answer: x = 2 or x = 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 3 cm and a slant height of 5 cm. What is its total surface area? (Use π = 3.14)
• FR: Un cône a un rayon de 3 cm et une hauteur oblique de 5 cm. Quelle est son aire totale? (Utilise π = 3,14)
• Choices: A) 94.2 cm² B) 75.36 cm² C) 84.78 cm² D) 56.52 cm²
• Hint: Total surface area of a cone = πr² + πrl, where l is slant height (e.g., r=2, l=4: 3.14×4+3.14×2×4 = 12.56+25.12 = 37.68 cm²).
• Steps:
  • Base: π × r² = 3.14 × 9 = 28.26 cm².
  • Lateral: π × r × l = 3.14 × 3 × 5 = 47.1 cm².
  • Total = 28.26 + 47.1 = 75.36 cm².
• Answer: 75.36 cm²

[Hard] Solving Quadratic by Factoring

• EN: Solve: 2x² + 7x − 15 = 0. What are the solutions?
• FR: Résous: 2x² + 7x − 15 = 0. Quelles sont les solutions?
• Choices: A) x = 3/2 or x = −5 B) x = 5/2 or x = −3 C) x = 3 or x = −5/2 D) x = 5 or x = −3/2
• Hint: For ax²+bx+c=0, find two numbers that multiply to a×c and add to b, then factor by grouping (e.g., 2x²+5x−3=0 → (2x−1)(x+3)=0).
• Steps:
  • a×c = 2×(−15) = −30. Find factors of −30 that add to 7: 10 and −3.
  • Rewrite: 2x² + 10x − 3x − 15 = 0.
  • Group: 2x(x+5) − 3(x+5) = 0 → (2x−3)(x+5) = 0.
  • x = 3/2 or x = −5.
• Answer: x = 3/2 or x = −5

[Hard] Systems with Substitution

• EN: Solve the system: y = x² and y = x + 6. What are the x-values of the intersection points?
• FR: Résous le système: y = x² et y = x + 6. Quelles sont les valeurs de x aux points d'intersection?
• Choices: A) x = 4 or x = −2 B) x = 3 or x = −3 C) x = 6 or x = −1 D) x = 3 or x = −2
• Hint: Substitute one expression into the other to get a quadratic, then factor or use the formula (e.g., y=x² and y=2x+3 → x²=2x+3 → x²−2x−3=0).
• Steps:
  • Set equal: x² = x + 6 → x² − x − 6 = 0.
  • Factor: (x−3)(x+2) = 0.
  • x = 3 or x = −2.
• Answer: x = 3 or x = −2

[Easy] Evaluating an Exponential Function

• EN: A bacteria sample starts with 200 cells and doubles every hour. How many cells are there after 3 hours?
• FR: Un échantillon de bactéries commence avec 200 cellules et double chaque heure. Combien de cellules y a-t-il après 3 heures?
• Choices: A) 1200 cells B) 1600 cells C) 600 cells D) 2400 cells
• Hint: Exponential growth: final = initial × 2^t (e.g., 50 × 2³ = 50 × 8 = 400).
• Steps:
  • After 3 hours: 200 × 2³ = 200 × 8 = 1600.
  • There are 1600 cells.
• Answer: 1600 cells

[Easy] Logarithm — Basic Evaluation

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 4 B) 2 C) 3 D) 16
• Hint: log_b(x) = y means b^y = x (e.g., log₃(9) = 2 because 3² = 9).
• Steps:
  • log₂(8) = y means 2^y = 8.
  • 2³ = 8, so y = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• EN: The sequence 4, 9, 14, 19, ... is arithmetic. What is the 6th term?
• FR: La suite 4, 9, 14, 19, ... est arithmétique. Quel est le 6e terme?
• Choices: A) 24 B) 34 C) 30 D) 29
• Hint: Use the formula aₙ = a₁ + (n−1)d, where d is the common difference (e.g., a₁=3, d=5, n=5: 3+4×5=23).
• Steps:
  • a₁ = 4, d = 5.
  • a₆ = 4 + (6−1)×5 = 4 + 25 = 29.
• Answer: 29

[Easy] Compound Interest

• EN: $1000 is invested at 5% interest compounded annually for 2 years. What is the amount after 2 years?
• FR: 1 000 $ est investi à 5 % d'intérêt composé annuellement pendant 2 ans. Quel est le montant après 2 ans?
• Choices: A) $1100.00 B) $1025.00 C) $1102.50 D) $1050.00
• Hint: A = P(1 + r)^t (e.g., $500 at 4% for 2 years: 500 × 1.04² = 500 × 1.0816 = $540.80).
• Steps:
  • A = 1000 × (1.05)² = 1000 × 1.1025 = $1102.50.
• Answer: $1102.50

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the quadratic function y = x² − 4x + 7?
• FR: Quel est le sommet de la fonction quadratique y = x² − 4x + 7?
• Choices: A) (2, 3) B) (4, 7) C) (−2, 19) D) (2, 5)
• Hint: The x-coordinate of the vertex is x = −b/(2a); substitute back to find y (e.g., y=x²−6x+10: x=3, y=9−18+10=1, vertex=(3,1)).
• Steps:
  • x = −(−4)/(2×1) = 4/2 = 2.
  • y = 4 − 8 + 7 = 3.
  • Vertex = (2, 3).
• Answer: (2, 3)

[Medium] Geometric Sequence

• EN: The sequence 3, 6, 12, 24, ... is geometric. What is the sum of the first 5 terms?
• FR: La suite 3, 6, 12, 24, ... est géométrique. Quelle est la somme des 5 premiers termes?
• Choices: A) 63 B) 93 C) 48 D) 99
• Hint: S_n = a(rⁿ−1)/(r−1) for r≠1 (e.g., a=2, r=3, n=4: 2(81−1)/2 = 80).
• Steps:
  • a=3, r=2, n=5: S₅ = 3(2⁵−1)/(2−1) = 3(32−1)/1 = 3×31 = 93.
• Answer: 93

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ.
• FR: Simplifie: sin²θ + cos²θ.
• Choices: A) 2 B) tan θ C) 0 D) 1
• Hint: This is one of the most important Pythagorean identities in trigonometry — try substituting a known angle to check (e.g., θ=30°: sin²30°+cos²30°=0.25+0.75=1).
• Steps:
  • sin²θ + cos²θ is the Pythagorean identity.
  • It always equals 1 for any angle θ.
• Answer: 1

[Medium] Annuity — Future Value

• EN: Emma deposits $200 at the end of each year into an account earning 4% per year. What is the future value after 3 years? (Use FV = PMT × [(1+r)ⁿ − 1] / r)
• FR: Emma dépose 200 $ à la fin de chaque année dans un compte qui rapporte 4 % par an. Quelle est la valeur future après 3 ans? (Utilise FV = PMT × [(1+r)ⁿ − 1] / r)
• Choices: A) $640.48 B) $612.16 C) $624.32 D) $658.24
• Hint: Substitute PMT=200, r=0.04, n=3 into the formula (e.g., PMT=100, r=0.05, n=2: 100×[(1.05²−1)/0.05]=100×2.05=$205).
• Steps:
  • (1.04)³ = 1.124864. 1.124864 − 1 = 0.124864.
  • 0.124864 / 0.04 = 3.1216.
  • FV = 200 × 3.1216 = $624.32.
• Answer: $624.32

[Hard] Logarithm Properties

• EN: Solve for x: log₃(x) + log₃(x − 6) = 3.
• FR: Résous pour x: log₃(x) + log₃(x − 6) = 3.
• Choices: A) x = 9 B) x = 6 C) x = 27 D) x = 12
• Hint: Use the product rule: logb(m) + logb(n) = log_b(mn), then convert to exponential form (e.g., log₂(x)+log₂(x−2)=3 → x(x−2)=8 → x²−2x−8=0).
• Steps:
  • log₃(x(x−6)) = 3 → x(x−6) = 3³ = 27.
  • x² − 6x − 27 = 0 → (x−9)(x+3) = 0.
  • x = 9 (reject x = −3 as it makes log undefined).
• Answer: x = 9

[Hard] Exponential Equation

• EN: Solve for x: 4^x = 32. What is x?
• FR: Résous pour x: 4^x = 32. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 2 C) x = 5/2 D) x = 4
• Hint: Write both sides as powers of the same base (e.g., 8^x = 32 → 2^(3x) = 2^5 → 3x = 5 → x = 5/3).
• Steps:
  • Write as powers of 2: 4^x = (2²)^x = 2^(2x) and 32 = 2⁵.
  • So 2^(2x) = 2⁵ → 2x = 5 → x = 5/2.
• Answer: x = 5/2

[Easy] Permutations

• EN: In how many ways can 4 students line up in a row?
• FR: De combien de façons 4 élèves peuvent-ils se mettre en rang?
• Choices: A) 16 B) 12 C) 24 D) 32
• Hint: The number of ways to arrange n items is n! (e.g., 3 items: 3! = 3×2×1 = 6).
• Steps:
  • 4! = 4 × 3 × 2 × 1 = 24.
  • There are 24 ways.
• Answer: 24

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = x³?
• FR: Quelle est la dérivée de f(x) = x³?
• Choices: A) 3x B) x² C) 3x² D) x⁴/4
• Hint: The power rule states: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹ (e.g., f(x)=x⁵ → f'(x)=5x⁴).
• Steps:
  • Bring the exponent down and reduce it by 1.
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Combinations

• EN: How many ways can you choose 2 toppings from a list of 5?
• FR: De combien de façons peut-on choisir 2 garnitures parmi 5?
• Choices: A) 20 B) 15 C) 25 D) 10
• Hint: Use C(n,r) = n! / (r!(n−r)!) (e.g., C(4,2) = 4!/(2!×2!) = 24/(2×2) = 6).
• Steps:
  • C(5,2) = 5! / (2! × 3!) = (5×4)/(2×1) = 20/2 = 10.
• Answer: 10

[Easy] Polynomial — Evaluating

• EN: If f(x) = 2x³ − x + 5, what is f(2)?
• FR: Si f(x) = 2x³ − x + 5, combien vaut f(2)?
• Choices: A) 23 B) 16 C) 19 D) 13
• Hint: Substitute the value into the function and simplify (e.g., g(x)=x²+3x−2, g(3)=9+9−2=16).
• Steps:
  • f(2) = 2(8) − 2 + 5 = 16 − 2 + 5 = 19.
• Answer: 19

[Medium] Rate of Change — Derivative

• EN: For the function f(x) = 3x² − 2x + 1, what is the instantaneous rate of change at x = 3?
• FR: Pour la fonction f(x) = 3x² − 2x + 1, quel est le taux de variation instantané à x = 3?
• Choices: A) 14 B) 20 C) 16 D) 18
• Hint: Find f'(x) using the power rule, then substitute x = 3 (e.g., f(x)=4x²+x → f'(x)=8x+1 → f'(2)=17).
• Steps:
  • f'(x) = 6x − 2.
  • f'(3) = 6(3) − 2 = 18 − 2 = 16.
• Answer: 16

[Medium] Normal Distribution — Probability

• EN: Scores on an exam are normally distributed with mean 70 and standard deviation 10. What percentage of students scored between 60 and 80?
• FR: Les scores d'un examen suivent une distribution normale de moyenne 70 et d'écart-type 10. Quel pourcentage d'élèves ont obtenu entre 60 et 80?
• Choices: A) 95% B) 99% C) 68% D) 50%
• Hint: The 68-95-99.7 rule states that about 68% of data falls within one standard deviation of the mean (e.g., mean=50, sd=5: 45 to 55 contains about 68%).
• Steps:
  • 60 = 70 − 10 (one standard deviation below), 80 = 70 + 10 (one standard deviation above).
  • By the 68-95-99.7 rule, about 68% of data falls within one standard deviation.
• Answer: 68%

[Medium] Vector Addition

• EN: Vector u = (3, 4) and vector v = (−1, 2). What is u + v?
• FR: Le vecteur u = (3, 4) et le vecteur v = (−1, 2). Combien vaut u + v?
• Choices: A) (4, 6) B) (2, 8) C) (−3, 8) D) (2, 6)
• Hint: Add corresponding components: (a,b) + (c,d) = (a+c, b+d) (e.g., (5,1)+(−2,4)=(3,5)).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: 4 + 2 = 6.
  • u + v = (2, 6).
• Answer: (2, 6)

[Medium] Rational Function — Finding a Vertical Asymptote

• EN: What is the vertical asymptote of f(x) = (x + 2) / (x − 5)?
• FR: Quelle est l'asymptote verticale de f(x) = (x + 2) / (x − 5)?
• Choices: A) x = −2 B) x = 2 C) x = 5 D) x = −5
• Hint: A vertical asymptote occurs where the denominator equals zero (e.g., f(x) = 1/(x−3) has a vertical asymptote at x=3).
• Steps:
  • Set the denominator equal to zero: x − 5 = 0.
  • x = 5.
• Answer: x = 5

[Hard] Binomial Theorem

• EN: What is the coefficient of x² in the expansion of (x + 3)⁴?
• FR: Quel est le coefficient de x² dans le développement de (x + 3)⁴?
• Choices: A) 36 B) 54 C) 81 D) 108
• Hint: Use C(n,k) × a^(n−k) × b^k for each term; the x² term has k=2 (e.g., in (x+2)³ the x¹ term: C(3,2)×1¹×2²=12).
• Steps:
  • The x² term: C(4,2) × x² × 3² = 6 × x² × 9 = 54x².
  • The coefficient is 54.
• Answer: 54

[Hard] Optimization with Derivatives

• EN: A farmer wants to enclose a rectangular area with 40 m of fencing. What width w maximizes the area if the length is L = 20 − w?
• FR: Un fermier veut clôturer un espace rectangulaire avec 40 m de clôture. Quelle largeur w maximise l'aire si la longueur est L = 20 − w?
• Choices: A) w = 5 m B) w = 15 m C) w = 10 m D) w = 8 m
• Hint: Write the area as a function of one variable, find its derivative, set it to zero, and solve (e.g., A=x(30−x)=30x−x², A'=30−2x=0 → x=15).
• Steps:
  • Area A = w × (20 − w) = 20w − w².
  • A'(w) = 20 − 2w. Set to zero: 20 − 2w = 0 → w = 10.
  • Maximum area occurs at w = 10 m.
• Answer: w = 10 m