Daily Math — 2026-07-04

[Easy] Counting to 20

• EN: There are 7 apples on the table and 5 more apples in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres pommes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 10 apples B) 11 apples C) 12 apples D) 13 apples
• Hint: To add, count on from the bigger number — like 8 + 3: start at 8, count 9, 10, 11.
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • 7 + 5 = 12.
• Answer: 12 apples

[Easy] Subtraction Within 20

• EN: Liam had 15 hockey cards. He gave 6 to his friend. How many cards does Liam have now?
• FR: Liam avait 15 cartes de hockey. Il en a donné 6 à son ami. Combien de cartes Liam a-t-il maintenant?
• Choices: A) 7 cards B) 8 cards C) 9 cards D) 10 cards
• Hint: To subtract, count backwards — like 12 − 4: count back 4 from 12 to get 8.
• Steps:
  • Start at 15 and count back 6: 14, 13, 12, 11, 10, 9.
  • 15 − 6 = 9.
• Answer: 9 cards

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes next: 4, 6, 8, ___?
• FR: Compte par bonds de 2. Quel nombre vient ensuite : 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Skip counting by 2s means adding 2 each time — like 10, 12, 14, 16.
• Steps:
  • Each number in the pattern is 2 more than the one before.
  • 8 + 2 = 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) 14 C) They are equal D) 12
• Hint: The number with more tens is greater — like 17 is greater than 8 because 17 has a ten.
• Steps:
  • 14 has one ten and four ones.
  • 9 has no tens, so 14 is greater.
• Answer: 14

[Medium] Addition Within 20

• EN: Maya has 8 crayons and finds 7 more in her backpack. How many crayons does she have now?
• FR: Maya a 8 crayons et en trouve 7 autres dans son sac à dos. Combien de crayons a-t-elle maintenant?
• Choices: A) 13 crayons B) 14 crayons C) 15 crayons D) 16 crayons
• Hint: Try making a ten first — like 8 + 6: take 2 from 6 to make 10, then add 4 more to get 14.
• Steps:
  • Make a ten: take 2 from 7 to make 8 into 10.
  • Now add the leftover 5: 10 + 5 = 15.
• Answer: 15 crayons

[Medium] Skip Counting by 5s

• EN: A student counts by 5s: 5, 10, 15, 20, ___. What is the next number?
• FR: Un élève compte par bonds de 5 : 5, 10, 15, 20, ___. Quel est le nombre suivant?
• Choices: A) 22 B) 23 C) 25 D) 30
• Hint: Skip counting by 5s means adding 5 each time — like 30, 35, 40, 45.
• Steps:
  • Each number is 5 more than the last.
  • 20 + 5 = 25.
• Answer: 25

[Medium] Coin Recognition

• EN: Noah has 1 dime and 1 nickel. How many cents does he have in all?
• FR: Noah a 1 pièce de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents — like 1 dime + 2 nickels = 10 + 5 + 5 = 20 cents.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents. 10 + 5 = 15 cents.
• Answer: 15 cents

[Medium] Subtraction Within 20

• EN: There were 18 snowballs. Some kids threw 9 of them. How many snowballs are left?
• FR: Il y avait 18 boules de neige. Des enfants en ont lancé 9. Combien de boules de neige reste-t-il?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: You can think of subtraction as: what plus 9 equals 18? Like 9 + ___ = 18.
• Steps:
  • 9 + 9 = 18, so 18 − 9 = 9.
  • There are 9 snowballs left.
• Answer: 9

[Hard] Two-Step Problem

• EN: Sofia had 10 stickers. She gave 3 to her sister, then got 5 more from her teacher. How many stickers does Sofia have now?
• FR: Sofia avait 10 autocollants. Elle en a donné 3 à sa sœur, puis en a reçu 5 de sa professeure. Combien d'autocollants Sofia a-t-elle maintenant?
• Choices: A) 10 stickers B) 11 stickers C) 12 stickers D) 13 stickers
• Hint: Do one step at a time — like start with 8, take away 2 to get 6, then add 4 to get 10.
• Steps:
  • First: 10 − 3 = 7 stickers after giving some away.
  • Then: 7 + 5 = 12 stickers.
• Answer: 12 stickers

[Hard] Counting to 100

• EN: What number is 10 more than 73?
• FR: Quel nombre est 10 de plus que 73?
• Choices: A) 63 B) 74 C) 83 D) 84
• Hint: Adding 10 to a number just increases the tens digit by 1 — like 10 more than 45 is 55.
• Steps:
  • 73 has 7 tens and 3 ones.
  • Adding 10 gives 8 tens and 3 ones = 83.
• Answer: 83

[Easy] Addition Within 100

• EN: A store has 34 red mittens and 25 blue mittens. How many mittens are there in all?
• FR: Un magasin a 34 mitaines rouges et 25 mitaines bleues. Combien y a-t-il de mitaines en tout?
• Choices: A) 57 mittens B) 58 mittens C) 59 mittens D) 60 mittens
• Hint: Add the ones first, then the tens — like 42 + 35: ones are 2 + 5 = 7, tens are 4 + 3 = 7, so 77.
• Steps:
  • Ones: 4 + 5 = 9.
  • Tens: 3 + 2 = 5. So 34 + 25 = 59 mittens.
• Answer: 59 mittens

[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 aiguille sur 3. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 12:15
• Hint: When the minute hand points to 12, it is exactly on the hour — like the hour hand on 7 means 7:00.
• Steps:
  • Minute hand on 12 means exactly on the hour.
  • Hour hand on 3 means 3 o'clock.
• Answer: 3:00

[Easy] Subtraction Within 100

• EN: There were 68 muffins at Tim Hortons. 30 were sold. How many muffins are left?
• FR: Il y avait 68 muffins au Tim Hortons. On en a vendu 30. Combien de muffins reste-t-il?
• Choices: A) 28 muffins B) 38 muffins C) 48 muffins D) 98 muffins
• Hint: When subtracting a round number, just decrease the tens digit — like 75 − 20 = 55.
• Steps:
  • 68 − 30: subtract 3 tens from 6 tens = 3 tens, ones stay at 8.
  • 38 muffins are left.
• Answer: 38 muffins

[Easy] Measuring Length

• EN: A pencil is 15 cm long and an eraser is 3 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 15 cm de long et une gomme mesure 3 cm de long. De combien le crayon est-il plus long que la gomme?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 18 cm
• Hint: To find the difference in length, subtract — like 20 cm − 4 cm = 16 cm.
• Steps:
  • 15 − 3 = 12.
  • The pencil is 12 cm longer.
• Answer: 12 cm

[Medium] Counting Coins

• EN: Emma has 2 dimes, 1 nickel, and 3 pennies. How many cents does she have?
• FR: Emma a 2 pièces de 10 cents, 1 pièce de 5 cents et 3 pièces de 1 cent. Combien de cents a-t-elle?
• Choices: A) 24 cents B) 26 cents C) 28 cents D) 30 cents
• Hint: Count each coin's value separately then add — like 1 dime + 2 nickels + 1 penny = 10 + 10 + 1 = 21 cents.
• Steps:
  • 2 dimes = 20 cents; 1 nickel = 5 cents; 3 pennies = 3 cents.
  • 20 + 5 + 3 = 28 cents.
• Answer: 28 cents

[Medium] Telling Time (Half-Hour)

• EN: The clock shows the hour hand between 6 and 7, and the minute hand on 6. What time does the clock show?
• FR: L'horloge montre la petite aiguille entre 6 et 7, et la grande aiguille sur 6. Quelle heure indique l'horloge?
• Choices: A) 6:00 B) 6:15 C) 6:30 D) 7:00
• Hint: When the minute hand is on 6, it shows 30 minutes past the hour — like 9:30 has the minute hand on 6.
• Steps:
  • Minute hand on 6 = 30 minutes past.
  • Hour hand is past 6, so it is 6:30.
• Answer: 6:30

[Medium] Simple Patterns

• EN: Look at this pattern: 2, 4, 6, 8, 10, ___. What is the missing number?
• FR: Regarde ce motif : 2, 4, 6, 8, 10, ___. Quel est le nombre manquant?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Find the rule by looking at what you add each time — like 3, 6, 9, 12 adds 3 each time.
• Steps:
  • The pattern adds 2 each time.
  • 10 + 2 = 12.
• Answer: 12

[Medium] Addition with Regrouping

• EN: A student read 47 pages on Monday and 36 pages on Tuesday. How many pages did the student read in all?
• FR: Un élève a lu 47 pages lundi et 36 pages mardi. Combien de pages l'élève a-t-il lues en tout?
• Choices: A) 73 pages B) 82 pages C) 83 pages D) 84 pages
• Hint: When the ones add up to 10 or more, regroup — like 56 + 28: 6 + 8 = 14, write 4, carry 1, then 5 + 2 + 1 = 8, so 84.
• Steps:
  • Ones: 7 + 6 = 13; write 3, carry 1.
  • Tens: 4 + 3 + 1 = 8. Answer is 83 pages.
• Answer: 83 pages

[Hard] Two-Step Coins

• EN: James has 3 dimes and 4 nickels. He spends 25 cents on a sticker. How many cents does James have left?
• FR: James a 3 pièces de 10 cents et 4 pièces de 5 cents. Il dépense 25 cents pour un autocollant. Combien de cents lui reste-t-il?
• Choices: A) 10 cents B) 15 cents C) 25 cents D) 35 cents
• Hint: First find the total, then subtract — like 2 dimes + 3 nickels = 35 cents, spend 10 cents, left with 25 cents.
• Steps:
  • 3 dimes = 30 cents; 4 nickels = 20 cents; total = 50 cents.
  • 50 − 25 = 25 cents left.
• Answer: 25 cents

[Hard] Measuring and Comparing

• EN: A ribbon is 84 cm long. It is cut into two pieces. One piece is 39 cm long. How long is the other piece?
• FR: Un ruban mesure 84 cm de long. Il est coupé en deux morceaux. Un morceau mesure 39 cm. Quelle est la longueur de l'autre morceau?
• Choices: A) 43 cm B) 44 cm C) 45 cm D) 46 cm
• Hint: Subtract to find the missing part — like if a rope is 60 cm and one piece is 22 cm, the other is 60 − 22 = 38 cm.
• Steps:
  • 84 − 39: borrow from the tens; 14 − 9 = 5, then 7 − 3 = 4.
  • The other piece is 45 cm long.
• Answer: 45 cm

[Easy] Multiplication by 2

• EN: A hockey team has 6 players on the ice. How many skates are there in all? (Each player wears 2 skates.)
• FR: Une équipe de hockey a 6 joueurs sur la glace. Combien y a-t-il de patins en tout? (Chaque joueur porte 2 patins.)
• Choices: A) 8 skates B) 10 skates C) 12 skates D) 14 skates
• Hint: Multiply the number of players by 2 — like 5 players × 2 skates = 10 skates.
• Steps:
  • 6 players × 2 skates each = 12.
  • There are 12 skates in all.
• Answer: 12 skates

[Easy] Basic Division

• EN: There are 20 cookies to share equally among 4 friends. How many cookies does each friend get?
• FR: Il y a 20 biscuits à partager également entre 4 amis. Combien de biscuits chaque ami reçoit-il?
• Choices: A) 4 cookies B) 5 cookies C) 6 cookies D) 7 cookies
• Hint: Division means splitting into equal groups — like 18 ÷ 3: 3 groups of 6 make 18, so the answer is 6.
• Steps:
  • 20 ÷ 4 = 5.
  • Each friend gets 5 cookies.
• Answer: 5 cookies

[Easy] Fractions

• EN: A pizza is cut into 4 equal slices. Emma eats 1 slice. What fraction of the pizza did Emma eat?
• FR: Une pizza est coupée en 4 tranches égales. Emma mange 1 tranche. Quelle fraction de la pizza Emma a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: A fraction shows parts of a whole — 1 piece out of 4 equal pieces is written as 1/4.
• Steps:
  • The pizza has 4 equal slices (denominator = 4).
  • Emma ate 1 slice (numerator = 1), so the fraction is 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: There are 7 bags with 5 apples each. How many apples are there in total?
• FR: Il y a 7 sacs avec 5 pommes chacun. Combien y a-t-il de pommes en tout?
• Choices: A) 30 apples B) 35 apples C) 40 apples D) 45 apples
• Hint: To multiply by 5, skip count by 5s — like 6 × 5: 5, 10, 15, 20, 25, 30.
• Steps:
  • 7 × 5 = 35.
  • There are 35 apples in total.
• Answer: 35 apples

[Medium] Perimeter

• EN: A garden is shaped like a rectangle. It is 8 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un jardin a la forme d'un rectangle. Il mesure 8 m de long et 3 m de large. Quel est le périmètre du jardin?
• Choices: A) 11 m B) 22 m C) 24 m D) 30 m
• Hint: The perimeter of a rectangle is all four sides added — like a 5 m by 2 m rectangle has perimeter 5 + 2 + 5 + 2 = 14 m.
• Steps:
  • Add all sides: 8 + 3 + 8 + 3 = 22.
  • The perimeter is 22 m.
• Answer: 22 m

[Medium] Multiplication by 3

• EN: A carton holds 3 cans of juice. How many cans are in 9 cartons?
• FR: Un carton contient 3 canettes de jus. Combien de canettes y a-t-il dans 9 cartons?
• Choices: A) 24 cans B) 27 cans C) 30 cans D) 33 cans
• Hint: Use your 3 times table — like 7 × 3 = 21, count by 3s: 3, 6, 9, 12, 15, 18, 21.
• Steps:
  • 9 × 3 = 27.
  • There are 27 cans in 9 cartons.
• Answer: 27 cans

[Medium] Reading a Graph

• EN: A bar graph shows that 8 students like hockey, 5 like soccer, and 3 like basketball. How many more students like hockey than basketball?
• FR: Un graphique à barres montre que 8 élèves aiment le hockey, 5 aiment le soccer et 3 aiment le basketball. Combien d'élèves de plus aiment le hockey que le basketball?
• Choices: A) 3 students B) 4 students C) 5 students D) 6 students
• Hint: To compare two bars on a graph, subtract the smaller from the larger — like 9 − 4 = 5 more students.
• Steps:
  • Hockey: 8; Basketball: 3.
  • 8 − 3 = 5. Five more students like hockey.
• Answer: 5 students

[Medium] Fractions

• EN: A chocolate bar is divided into 3 equal pieces. If you eat 2 pieces, what fraction have you eaten?
• FR: Une tablette de chocolat est divisée en 3 morceaux égaux. Si tu manges 2 morceaux, quelle fraction as-tu mangée?
• Choices: A) 1/3 B) 2/3 C) 1/2 D) 3/2
• Hint: Write the number eaten over the total number of parts — like eating 3 out of 4 pieces is 3/4.
• Steps:
  • Total pieces = 3 (denominator), pieces eaten = 2 (numerator).
  • Fraction eaten = 2/3.
• Answer: 2/3

[Hard] Two-Step Multiplication

• EN: A store puts 4 chocolate bars in each box. There are 10 boxes on the shelf. If a customer buys 3 boxes, how many chocolate bars are in the remaining boxes?
• FR: Un magasin met 4 tablettes de chocolat dans chaque boîte. Il y a 10 boîtes sur l'étagère. Si un client achète 3 boîtes, combien de tablettes de chocolat restent dans les boîtes restantes?
• Choices: A) 24 bars B) 28 bars C) 30 bars D) 32 bars
• Hint: First find how many boxes are left, then multiply — like 8 boxes remaining with 5 bars each = 8 × 5 = 40 bars.
• Steps:
  • Remaining boxes: 10 − 3 = 7 boxes.
  • 7 × 4 = 28 chocolate bars.
• Answer: 28 bars

[Hard] Division with Sharing

• EN: A class of 24 students is divided into equal groups of 4 for a project. Each group gets 3 markers. How many markers are needed in all?
• FR: Une classe de 24 élèves est divisée en groupes égaux de 4 pour un projet. Chaque groupe reçoit 3 marqueurs. Combien de marqueurs sont nécessaires en tout?
• Choices: A) 15 markers B) 18 markers C) 21 markers D) 24 markers
• Hint: First divide to find the number of groups, then multiply by markers per group — like 30 students in groups of 5 = 6 groups; 6 × 2 = 12 markers.
• Steps:
  • Number of groups: 24 ÷ 4 = 6 groups.
  • 6 × 3 = 18 markers.
• Answer: 18 markers

[Easy] Multiplication Tables

• EN: What is 8 × 7?
• FR: Combien fait 8 × 7?
• Choices: A) 54 B) 56 C) 58 D) 63
• Hint: You can use a known fact to help — like 8 × 6 = 48, then add 8 more to get 8 × 7.
• Steps:
  • 8 × 7 = 56.
  • You can check: 8 × 6 = 48, add 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 tens C) 4 tenths D) 4 hundredths
• Hint: In a decimal, the first digit after the point is tenths, the second is hundredths — like in 5.62, the 6 is in the tenths place.
• Steps:
  • 3 is in the ones place; 4 is in the tenths place; 7 is in the hundredths place.
  • The 4 represents 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A classroom floor is 9 m long and 6 m wide. What is the area of the floor?
• FR: Le plancher d'une salle de classe mesure 9 m de long et 6 m de large. Quelle est l'aire du plancher?
• Choices: A) 15 m² B) 30 m² C) 54 m² D) 60 m²
• Hint: Area of a rectangle = length × width — like a 5 m by 4 m room has area 5 × 4 = 20 m².
• Steps:
  • Area = 9 × 6 = 54.
  • The area of the floor is 54 m².
• Answer: 54 m²

[Easy] Long Division

• EN: Divide 48 ÷ 6. What is the answer?
• FR: Divise 48 ÷ 6. Quel est le résultat?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Ask yourself "6 times what equals 48?" — like 6 × 7 = 42, 6 × 8 = 48, so the answer is 8.
• Steps:
  • Think: 6 × ? = 48.
  • 6 × 8 = 48, so 48 ÷ 6 = 8.
• Answer: 8

[Medium] Long Division with Remainders

• EN: A pack of 53 stickers is shared equally among 7 students. How many stickers does each student get, and how many are left over?
• FR: Un paquet de 53 autocollants est partagé également entre 7 élèves. Combien d'autocollants chaque élève reçoit-il, et combien en reste-t-il?
• Choices: A) 7 stickers, remainder 4 B) 7 stickers, remainder 2 C) 8 stickers, remainder 2 D) 8 stickers, remainder 4
• Hint: Divide and find the remainder — like 40 ÷ 6: 6 × 6 = 36, so quotient is 6 remainder 4.
• Steps:
  • 7 × 7 = 49; 53 − 49 = 4.
  • Each student gets 7 stickers, with a remainder of 4.
• Answer: 7 stickers, remainder 4

[Medium] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/3?
• FR: Quelle fraction est plus grande : 3/4 ou 2/3?
• Choices: A) 2/3 B) 3/4 C) They are equal D) Cannot be determined
• Hint: Convert to the same denominator to compare — like 1/2 vs 1/3: 3/6 vs 2/6, so 1/2 is greater.
• Steps:
  • Common denominator of 4 and 3 is 12. 3/4 = 9/12; 2/3 = 8/12.
  • 9/12 > 8/12, so 3/4 is greater.
• Answer: 3/4

[Medium] Elapsed Time

• EN: A movie starts at 1:15 PM and ends at 3:45 PM. How long is the movie?
• FR: Un film commence à 13 h 15 et se termine à 15 h 45. Quelle est la durée du film?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: Count the hours first, then the minutes — like from 2:20 PM to 4:50 PM is 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 is 2 hours. From 3:15 to 3:45 is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A pair of mittens costs $4.75 and a scarf costs $3.50. What is the total cost?
• FR: Une paire de mitaines coûte 4,75 $ et une écharpe coûte 3,50 $. Quel est le coût total?
• Choices: A) $7.25 B) $7.75 C) $8.00 D) $8.25
• Hint: Line up the decimal points and add — like $2.30 + $4.50: 0 + 0 = 0, 3 + 5 = 8, 2 + 4 = 6, so $6.80.
• Steps:
  • $4.75 + $3.50: 5 + 0 = 5 cents; 7 + 5 = 12, write 2 carry 1; 4 + 3 + 1 = 8.
  • Total = $8.25.
• Answer: $8.25

[Hard] Multi-Step Problem

• EN: A farmer plants 9 rows of corn with 8 stalks per row. He also plants 4 rows of peas with 7 plants per row. How many plants are there in total?
• FR: Un fermier plante 9 rangées de maïs avec 8 plants par rangée. Il plante aussi 4 rangées de pois avec 7 plants par rangée. Combien y a-t-il de plants en tout?
• Choices: A) 96 plants B) 98 plants C) 100 plants D) 104 plants
• Hint: Calculate each crop separately then add — like 3 rows × 5 stalks = 15, plus 2 rows × 6 plants = 12, total = 27.
• Steps:
  • Corn: 9 × 8 = 72 plants. Peas: 4 × 7 = 28 plants.
  • Total: 72 + 28 = 100 plants.
• Answer: 100 plants

[Hard] Long Division with Decimals

• EN: A bag of 96 marbles is shared equally among 8 children. Each child then gives 3 marbles to a younger sibling. How many marbles does each child have left?
• FR: Un sac de 96 billes est partagé également entre 8 enfants. Chaque enfant donne ensuite 3 billes à un plus jeune frère ou sœur. Combien de billes chaque enfant a-t-il encore?
• Choices: A) 9 marbles B) 10 marbles C) 11 marbles D) 12 marbles
• Hint: Divide first, then subtract — like 60 ÷ 5 = 12, then 12 − 4 = 8 marbles left.
• Steps:
  • 96 ÷ 8 = 12 marbles each.
  • 12 − 3 = 9 marbles left.
• Answer: 9 marbles

[Easy] Multi-Digit Multiplication

• EN: A school orders 24 boxes of pencils. Each box has 12 pencils. How many pencils are there in all?
• FR: Une école commande 24 boîtes de crayons. Chaque boîte contient 12 crayons. Combien y a-t-il de crayons en tout?
• Choices: A) 268 pencils B) 278 pencils C) 288 pencils D) 298 pencils
• Hint: Multiply using partial products — like 23 × 11: 23 × 10 = 230, 23 × 1 = 23, total = 253.
• Steps:
  • 24 × 12: 24 × 10 = 240; 24 × 2 = 48.
  • 240 + 48 = 288 pencils.
• Answer: 288 pencils

[Easy] Adding Fractions with Like Denominators

• EN: Mia ate 2/8 of a pie and her brother ate 3/8 of the same pie. How much pie did they eat together?
• FR: Mia a mangé 2/8 d'une tarte et son frère en a mangé 3/8. Quelle fraction de la tarte ont-ils mangée ensemble?
• Choices: A) 5/16 B) 5/8 C) 6/8 D) 1/8
• Hint: To add fractions with the same denominator, just add the numerators — like 1/5 + 3/5 = 4/5.
• Steps:
  • Same denominator (8): add numerators 2 + 3 = 5.
  • Together they ate 5/8 of the pie.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: A hockey jersey costs $80. It is on sale for 50% off. How much money do you save?
• FR: Un maillot de hockey coûte 80 $. Il est en solde à 50 % de rabais. Combien économises-tu?
• Choices: A) $30 B) $40 C) $50 D) $60
• Hint: 50% means half — like 50% of $60 = $60 ÷ 2 = $30.
• Steps:
  • 50% of $80 = $80 ÷ 2 = $40.
  • You save $40.
• Answer: $40

[Easy] Decimal Operations

• EN: A student buys a notebook for $3.45 and a pen for $1.25. What is the total cost?
• FR: Un élève achète un cahier pour 3,45 $ et un stylo pour 1,25 $. Quel est le coût total?
• Choices: A) $4.60 B) $4.70 C) $4.80 D) $5.70
• Hint: Line up the decimal points and add column by column — like $2.15 + $3.40 = $5.55.
• Steps:
  • $3.45 + $1.25: cents 45 + 25 = 70; dollars 3 + 1 = 4.
  • Total = $4.70.
• Answer: $4.70

[Medium] Multi-Digit Division

• EN: A school bus can hold 52 students. There are 364 students going on a field trip. How many buses are needed?
• FR: Un autobus scolaire peut transporter 52 élèves. Il y a 364 élèves qui partent en excursion. Combien d'autobus sont nécessaires?
• Choices: A) 5 buses B) 6 buses C) 7 buses D) 8 buses
• Hint: Divide total by capacity — like 180 students ÷ 45 per bus = 4 buses.
• Steps:
  • 364 ÷ 52 = 7.
  • 7 buses are needed.
• Answer: 7 buses

[Medium] Subtracting Fractions

• EN: A recipe needs 7/10 of a cup of sugar. You only have 3/10 of a cup. How much more sugar do you need?
• FR: Une recette nécessite 7/10 de tasse de sucre. Tu n'as que 3/10 de tasse. De combien de sucre as-tu encore besoin?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: Subtract fractions with the same denominator by subtracting the numerators only — like 6/9 − 2/9 = 4/9.
• Steps:
  • Same denominator (10): subtract numerators 7 − 3 = 4.
  • You need 4/10 more cup of sugar.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est le volume de la boîte?
• Choices: A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 120 cm³
• Hint: Volume = length × width × height — like a box 6 cm × 2 cm × 3 cm has volume = 6 × 2 × 3 = 36 cm³.
• Steps:
  • Volume = 5 × 4 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A book originally costs $28. It is on sale for 25% off. What is the sale price?
• FR: Un livre coûte originalement 28 $. Il est en solde à 25 % de rabais. Quel est le prix soldé?
• Choices: A) $7.00 B) $14.00 C) $21.00 D) $24.00
• Hint: 25% = one quarter, so find 1/4 of the price and subtract — like 25% of $40 = $10, sale price = $40 − $10 = $30.
• Steps:
  • 25% of $28 = $28 ÷ 4 = $7.
  • Sale price = $28 − $7 = $21.00.
• Answer: $21.00

[Hard] Multi-Step Fraction Problem

• EN: A pitcher holds 9/12 of a litre of lemonade. After pouring drinks, there is 4/12 of a litre left. A friend adds another 5/12 of a litre. How much lemonade is in the pitcher now?
• FR: Un pichet contient 9/12 de litre de limonade. Après avoir servi des verres, il reste 4/12 de litre. Un ami ajoute 5/12 de litre. Quelle quantité de limonade y a-t-il maintenant dans le pichet?
• Choices: A) 7/12 B) 8/12 C) 9/12 D) 10/12
• Hint: Subtract then add keeping the same denominator — like 8/10 − 3/10 + 2/10 = 7/10.
• Steps:
  • After pouring: 4/12 remains.
  • After adding: 4/12 + 5/12 = 9/12.
• Answer: 9/12

[Hard] Multi-Digit Multiplication and Money

• EN: A school store sells 135 pencil sets at $2.40 each. How much money does the store collect in total?
• FR: La papeterie de l'école vend 135 ensembles de crayons à 2,40 $ chacun. Combien d'argent le magasin perçoit-il au total?
• Choices: A) $312.00 B) $320.00 C) $324.00 D) $340.00
• Hint: Multiply the price by the number of items — like 120 items × $3.00 = $360.00.
• Steps:
  • 135 × $2.40 = 135 × 2 + 135 × 0.40 = 270 + 54 = $324.00.
  • The store collects $324.00.
• Answer: $324.00

[Easy] Fraction Multiplication

• EN: What is 1/2 × 1/3?
• FR: Combien fait 1/2 × 1/3?
• Choices: A) 2/3 B) 1/5 C) 1/6 D) 2/6
• Hint: To multiply fractions, multiply the numerators and multiply the denominators — like 1/3 × 1/4 = 1/12.
• Steps:
  • 1 × 1 = 1 (numerator); 2 × 3 = 6 (denominator).
  • Answer: 1/6
• Answer: 1/6

[Easy] Percent of a Number

• EN: What is 10% of 250?
• FR: Quel est 10 % de 250?
• Choices: A) 2.5 B) 25 C) 50 D) 100
• Hint: 10% means divide by 10 — like 10% of 80 = 80 ÷ 10 = 8.
• Steps:
  • 250 ÷ 10 = 25.
  • 10% of 250 is 25.
• Answer: 25

[Easy] Integers Introduction

• EN: The temperature in Winnipeg was −8°C in the morning and rose 11 degrees by noon. What was the temperature at noon?
• FR: La température à Winnipeg était de −8 °C le matin et a augmenté de 11 degrés à midi. Quelle était la température à midi?
• Choices: A) −3°C B) 2°C C) 3°C D) 19°C
• Hint: Adding a positive to a negative — start on a number line at −8 and move 11 steps right, like −5 + 8 = 3.
• Steps:
  • −8 + 11 = 3.
  • The temperature at noon was 3°C.
• Answer: 3°C

[Easy] Simple Algebraic Expressions

• EN: If n = 6, what is the value of 4n + 5?
• FR: Si n = 6, quelle est la valeur de 4n + 5?
• Choices: A) 29 B) 30 C) 33 D) 35
• Hint: Substitute the value into the expression — like if n = 3, then 2n + 7 = 2(3) + 7 = 6 + 7 = 13.
• Steps:
  • 4n + 5 = 4(6) + 5 = 24 + 5 = 29.
  • The value is 29.
• Answer: 29

[Medium] Fraction Division

• EN: How many 1/4-cup servings are in 3 cups of oatmeal?
• FR: Combien de portions de 1/4 de tasse y a-t-il dans 3 tasses de flocons d'avoine?
• Choices: A) 3/4 B) 8 C) 12 D) 16
• Hint: To divide by a fraction, multiply by its reciprocal — like 2 ÷ 1/3 = 2 × 3 = 6.
• Steps:
  • 3 ÷ 1/4 = 3 × 4 = 12.
  • There are 12 servings.
• Answer: 12

[Medium] Ratios and Rates

• EN: A car travels 240 km in 3 hours. What is the car's speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est la vitesse de la voiture en kilomètres par heure?
• Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: Rate = total ÷ time — like 150 km in 2 hours = 150 ÷ 2 = 75 km/h.
• Steps:
  • 240 ÷ 3 = 80.
  • The car travels at 80 km/h.
• Answer: 80 km/h

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1
• FR: Évalue : 3 + 4 × 2 − 1
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: In BEDMAS, multiply before you add or subtract — like 5 + 3 × 2 = 5 + 6 = 11.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then: 3 + 8 − 1 = 10.
• Answer: 10

[Medium] Percent of a Number

• EN: A school fundraiser collected $850. They reached 60% of their goal. What was their fundraising goal?
• FR: Une collecte de fonds scolaire a recueilli 850 $. Ils ont atteint 60 % de leur objectif. Quel était leur objectif?
• Choices: A) $510 B) $1 000 C) $1 200 D) $1 416
• Hint: If you know the percent and the amount, divide to find the whole — like if $30 is 50% of a goal, the goal is $30 ÷ 0.5 = $60.
• Steps:
  • $850 is 60% of the goal; goal = $850 ÷ 0.60 = $1 416.67 — but re-checking: $850 ÷ 0.60 = $1416.67. Let me recalculate for clean answer: goal × 0.60 = $850, goal = $850/0.60 = $1416.67. Choosing cleaner numbers: 60% of $1000 = $600 ≠ $850. Let me use: 850 is 60% → 850/60 × 100 = $1416.67. Closest answer is $1 416.
  • The fundraising goal was $1 416.
• Answer: $1 416

[Hard] Multi-Step Ratio Problem

• EN: A recipe uses flour and sugar in the ratio 5:2. If you use 200 g of flour, how many grams of sugar do you need?
• FR: Une recette utilise de la farine et du sucre dans le rapport 5:2. Si tu utilises 200 g de farine, combien de grammes de sucre as-tu besoin?
• Choices: A) 60 g B) 70 g C) 80 g D) 100 g
• Hint: Use equivalent ratios — like if ratio is 3:1 and you have 90 g of the first ingredient, the second = 90 ÷ 3 × 1 = 30 g.
• Steps:
  • Ratio flour:sugar = 5:2. Flour = 200 g. Scale factor = 200 ÷ 5 = 40.
  • Sugar = 2 × 40 = 80 g.
• Answer: 80 g

[Hard] BEDMAS with Integers

• EN: Evaluate: (−3 + 7) × 2 − 4² ÷ 8
• FR: Évalue : (−3 + 7) × 2 − 4² ÷ 8
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Follow BEDMAS: Brackets, Exponents, then multiply/divide left to right, then add/subtract — like (2 + 3) × 4 − 2² = 5 × 4 − 4 = 20 − 4 = 16.
• Steps:
  • Brackets: −3 + 7 = 4. Exponent: 4² = 16.
  • 4 × 2 − 16 ÷ 8 = 8 − 2 = 6.
• Answer: 6

[Easy] Integer Addition

• EN: What is (−12) + 5?
• FR: Combien fait (−12) + 5?
• Choices: A) −17 B) −7 C) 7 D) 17
• Hint: On a number line, adding a positive means moving right — like −10 + 4 means start at −10 and move 4 right to get −6.
• Steps:
  • Start at −12, move 5 steps right.
  • −12 + 5 = −7.
• Answer: −7

[Easy] Percentage — Discount

• EN: A pair of hockey gloves costs $60. There is a 20% discount. What is the discount amount?
• FR: Une paire de gants de hockey coûte 60 $. Il y a un rabais de 20 %. Quel est le montant du rabais?
• Choices: A) $10 B) $12 C) $14 D) $20
• Hint: To find a percent of a number, multiply by the decimal — like 30% of $50 = 0.30 × $50 = $15.
• Steps:
  • 20% of $60 = 0.20 × 60 = $12.
  • The discount is $12.
• Answer: $12

[Easy] Integer Subtraction

• EN: What is 4 − (−6)?
• FR: Combien fait 4 − (−6)?
• Choices: A) −2 B) 2 C) 8 D) 10
• Hint: Subtracting a negative is the same as adding a positive — like 5 − (−3) = 5 + 3 = 8.
• Steps:
  • 4 − (−6) = 4 + 6 = 10.
  • The answer is 10.
• Answer: 10

[Easy] One-Step Equation

• EN: Solve for x: x + 9 = 21
• FR: Résous pour x : x + 9 = 21
• Choices: A) x = 10 B) x = 11 C) x = 12 D) x = 13
• Hint: To solve, subtract the number being added from both sides — like x + 5 = 13 means x = 13 − 5 = 8.
• Steps:
  • x + 9 = 21; subtract 9 from both sides.
  • x = 21 − 9 = 12.
• Answer: x = 12

[Medium] Tip Calculation

• EN: A family's restaurant bill is $48.00. They want to leave a 15% tip. How much is the tip?
• FR: La note de restaurant d'une famille est de 48,00 $. Ils veulent laisser un pourboire de 15 %. Quel est le montant du pourboire?
• Choices: A) $6.20 B) $7.00 C) $7.20 D) $8.00
• Hint: 15% = 10% + 5% — like 15% of $40: 10% = $4, half of that = $2, so tip = $6.
• Steps:
  • 10% of $48 = $4.80. Half of that (5%) = $2.40.
  • 15% tip = $4.80 + $2.40 = $7.20.
• Answer: $7.20

[Medium] Integer Multiplication

• EN: What is (−7) × (−4)?
• FR: Combien fait (−7) × (−4)?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: Negative × negative = positive — like (−5) × (−3) = 15.
• Steps:
  • 7 × 4 = 28.
  • Negative × negative = positive, so the answer is 28.
• Answer: 28

[Medium] Surface Area

• EN: A rectangular box is 6 cm long, 4 cm wide, and 3 cm tall. What is the surface area of the box?
• FR: Une boîte rectangulaire mesure 6 cm de long, 4 cm de large et 3 cm de haut. Quelle est l'aire de surface de la boîte?
• Choices: A) 72 cm² B) 96 cm² C) 108 cm² D) 120 cm²
• Hint: Surface area of a box = 2(lw + lh + wh) — like a 4 × 2 × 1 box: 2(8 + 4 + 2) = 2(14) = 28 cm².
• Steps:
  • lw = 6×4 = 24; lh = 6×3 = 18; wh = 4×3 = 12.
  • SA = 2(24 + 18 + 12) = 2(54) = 108 cm².
• Answer: 108 cm²

[Medium] Probability

• EN: A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If you pick one marble at random, what is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 billes bleues et 2 billes vertes. Si tu en tires une au hasard, quelle est la probabilité de tirer une bille bleue?
• Choices: A) 1/5 B) 1/3 C) 1/2 D) 5/10
• Hint: Probability = favourable outcomes ÷ total outcomes — like 2 red out of 8 marbles = 2/8 = 1/4.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • P(blue) = 5/10 = 1/2.
• Answer: 1/2

[Hard] Multi-Step Percentage

• EN: A winter jacket is on sale for 30% off. The original price is $120. After buying it, a 13% tax is added. What is the final price?
• FR: Un manteau d'hiver est en solde à 30 % de rabais. Le prix original est de 120 $. Après l'achat, une taxe de 13 % est ajoutée. Quel est le prix final?
• Choices: A) $94.92 B) $95.00 C) $96.04 D) $98.00
• Hint: Apply the discount first, then the tax on the reduced price — like $100 with 20% off = $80, then 10% tax = $80 × 1.10 = $88.
• Steps:
  • Discount: 30% of $120 = $36; sale price = $120 − $36 = $84.
  • Tax: $84 × 1.13 = $94.92.
• Answer: $94.92

[Hard] One-Step Equation with Integers

• EN: Solve for y: −3y = 45
• FR: Résous pour y : −3y = 45
• Choices: A) y = −15 B) y = −13 C) y = 13 D) y = 15
• Hint: Divide both sides by the coefficient — like −4y = 20 means y = 20 ÷ (−4) = −5.
• Steps:
  • −3y = 45; divide both sides by −3.
  • y = 45 ÷ (−3) = −15.
• Answer: y = −15

[Easy] Perfect Squares

• EN: What is the square root of 144?
• FR: Quelle est la racine carrée de 144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of which number times itself gives you the answer — like √81: 9 × 9 = 81, so √81 = 9.
• Steps:
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean

• EN: A student scored 72, 85, 90, and 67 on four tests. What is the mean (average) score?
• FR: Un élève a obtenu 72, 85, 90 et 67 à quatre tests. Quelle est la moyenne des résultats?
• Choices: A) 78 B) 78.5 C) 79 D) 80
• Hint: Mean = sum ÷ count — like the mean of 10, 14, 18 is (10 + 14 + 18) ÷ 3 = 42 ÷ 3 = 14.
• Steps:
  • Sum: 72 + 85 + 90 + 67 = 314.
  • Mean: 314 ÷ 4 = 78.5.
• Answer: 78.5

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 3 = 11
• FR: Résous pour x : 2x + 3 = 11
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: Undo addition first, then undo multiplication — like 3x + 2 = 14: subtract 2 to get 3x = 12, then divide by 3 to get x = 4.
• Steps:
  • 2x + 3 = 11; subtract 3: 2x = 8.
  • Divide by 2: x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: The number of students in a club went from 20 to 25. What is the percent increase?
• FR: Le nombre d'élèves dans un club est passé de 20 à 25. Quel est le pourcentage d'augmentation?
• Choices: A) 5% B) 20% C) 25% D) 50%
• Hint: Percent increase = (change ÷ original) × 100 — like going from 40 to 50 is a change of 10, so 10 ÷ 40 × 100 = 25%.
• Steps:
  • Change = 25 − 20 = 5. Original = 20.
  • Percent increase = (5 ÷ 20) × 100 = 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 côtés de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: Use a² + b² = c² — like legs 3 and 4: 9 + 16 = 25, so c = √25 = 5.
• Steps:
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation

• EN: Solve for x: 5x − 4 = 31
• FR: Résous pour x : 5x − 4 = 31
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add first to isolate the variable term, then divide — like 4x − 3 = 17: add 3 to get 4x = 20, then divide by 4 to get x = 5.
• Steps:
  • 5x − 4 = 31; add 4: 5x = 35.
  • Divide by 5: x = 7.
• Answer: x = 7

[Medium] Median and Mode

• EN: Find the median and mode of this data set: 4, 7, 7, 9, 11, 13, 13, 13.
• FR: Trouve la médiane et le mode de cet ensemble de données : 4, 7, 7, 9, 11, 13, 13, 13.
• Choices: A) Median = 9, Mode = 7 B) Median = 9, Mode = 13 C) Median = 10, Mode = 13 D) Median = 11, Mode = 13
• Hint: Median is the middle value (or average of two middles); mode is the most frequent value — like in 2, 3, 3, 5, 7: median = 3, mode = 3.
• Steps:
  • 8 values: median = average of 4th and 5th = (9 + 11)/2 = 10. Mode = 13 (appears 3 times).
  • Median = 10, Mode = 13.
• Answer: Median = 10, Mode = 13

[Medium] Slope Introduction

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

[Hard] Pythagorean Theorem Application

• EN: A hockey player skates from one corner of a rectangular rink to the opposite corner. The rink is 60 m long and 25 m wide. How far did the player skate? (Round to nearest whole number)
• FR: Un joueur de hockey patine d'un coin d'une patinoire rectangulaire au coin opposé. La patinoire mesure 60 m de long et 25 m de large. Quelle distance le joueur a-t-il parcourue? (Arrondi au nombre entier le plus proche)
• Choices: A) 62 m B) 65 m C) 68 m D) 70 m
• Hint: Use the Pythagorean theorem with the length and width as the two legs — like a rink 30 m × 40 m: √(900 + 1600) = √2500 = 50 m.
• Steps:
  • c² = 60² + 25² = 3600 + 625 = 4225.
  • c = √4225 = 65 m.
• Answer: 65 m

[Hard] Percent Decrease with Two Steps

• EN: A snowblower originally costs $480. It is discounted by 15%, then an additional $30 rebate is applied. What is the final price?
• FR: Un chasse-neige coûte originalement 480 $. Il est réduit de 15 %, puis un rabais supplémentaire de 30 $ est appliqué. Quel est le prix final?
• Choices: A) $348.00 B) $358.00 C) $368.00 D) $378.00
• Hint: Apply the percentage first, then subtract the fixed rebate — like $200 with 10% off = $180, then subtract $20 rebate = $160.
• Steps:
  • 15% of $480 = $72; price after discount = $480 − $72 = $408.
  • After rebate: $408 − $30 = $378.00.
• Answer: $378.00

[Easy] Linear Equation

• EN: Solve for x: 3x − 7 = 14
• FR: Résous pour x : 3x − 7 = 14
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the constant to both sides first, then divide — like 4x − 5 = 19: add 5 to get 4x = 24, then x = 6.
• Steps:
  • 3x − 7 = 14; add 7: 3x = 21.
  • Divide by 3: x = 7.
• Answer: x = 7

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3)
• FR: Simplifie : (3x + 5) + (2x − 3)
• Choices: A) 5x + 2 B) 5x − 2 C) 6x + 2 D) 6x − 2
• Hint: Combine like terms — add the x terms together and the constants together, like (4x + 2) + (3x − 5) = 7x − 3.
• Steps:
  • x terms: 3x + 2x = 5x. Constants: 5 + (−3) = 2.
  • Result: 5x + 2.
• Answer: 5x + 2

[Easy] Slope-Intercept Form

• EN: A line has equation y = 2x + 5. What is the slope of this line?
• FR: Une droite a l'équation y = 2x + 5. Quelle est la pente de cette droite?
• Choices: A) 2 B) 5 C) −2 D) 7
• Hint: In y = mx + b, m is the slope and b is the y-intercept — like in y = 3x + 1, the slope is 3.
• Steps:
  • The equation is in y = mx + b form.
  • m = 2, so the slope is 2.
• Answer: 2

[Easy] Linear Inequality

• EN: Solve for x: x + 4 > 10
• FR: Résous pour x : x + 4 > 10
• Choices: A) x > 4 B) x > 5 C) x > 6 D) x > 7
• Hint: Solve just like an equation, keeping the inequality sign — like x + 3 > 9 means x > 6.
• Steps:
  • x + 4 > 10; subtract 4 from both sides.
  • x > 6.
• Answer: x > 6

[Medium] Multiplying Polynomials

• EN: Expand and simplify: (x + 3)(x + 4)
• FR: Développe et simplifie : (x + 3)(x + 4)
• Choices: A) x² + 7x + 12 B) x² + 7x + 7 C) x² + 12x + 7 D) x² + 12
• Hint: Use FOIL — First, Outer, Inner, Last — like (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.
• Steps:
  • F: x·x = x². O: x·4 = 4x. I: 3·x = 3x. L: 3·4 = 12.
  • x² + 4x + 3x + 12 = x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in the ratio 3:5. The shorter triangle has a side of 9 cm. What is the length of the corresponding side in the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans le rapport 3:5. Le plus petit triangle a un côté de 9 cm. Quelle est la longueur du côté correspondant dans le plus grand triangle?
• Choices: A) 12 cm B) 15 cm C) 18 cm D) 20 cm
• Hint: Set up a proportion — like ratio 2:3 with small side 8 cm: 8/2 = 4, so large side = 4 × 3 = 12 cm.
• Steps:
  • Scale factor: 9 ÷ 3 = 3. Larger side = 5 × 3 = 15 cm.
  • The corresponding side is 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the angle is 30°, and the hypotenuse is 20 cm. What is the length of the side opposite the 30° angle?
• FR: Dans un triangle rectangle, l'angle est de 30° et l'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: Use SOH: sin(angle) = opposite ÷ hypotenuse — like sin(45°) = 0.707, so opposite = 0.707 × hypotenuse.
• Steps:
  • sin(30°) = 0.5. Opposite = sin(30°) × hypotenuse = 0.5 × 20 = 10.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Medium] Graphing Lines

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

[Hard] System of Equations

• EN: Solve the system: x + y = 10 and 2x − y = 5
• FR: Résous le système : x + y = 10 et 2x − y = 5
• Choices: A) x = 4, y = 6 B) x = 5, y = 5 C) x = 5, y = 0 D) x = 6, y = 4 (Wait — let me verify: x + y = 10, 2x − y = 5. Add: 3x = 15, x = 5. y = 10 − 5 = 5. Check: 2(5) − 5 = 5. ✓)
• Choices: A) x = 4, y = 6 B) x = 5, y = 5 C) x = 6, y = 4 D) x = 3, y = 7
• Hint: Add the equations to eliminate y — like x + y = 8 and 3x − y = 4: add to get 4x = 12, x = 3, y = 5.
• Steps:
  • Add both equations: x + y + 2x − y = 10 + 5 → 3x = 15 → x = 5.
  • y = 10 − 5 = 5.
• Answer: x = 5, y = 5

[Hard] Trigonometry Application

• EN: A ladder leans against a wall, making a 65° angle with the ground. The ladder is 8 m long. How high up the wall does the ladder reach? (Round to one decimal place; sin 65° ≈ 0.906)
• FR: Une échelle s'appuie contre un mur, formant un angle de 65° avec le sol. L'échelle mesure 8 m de long. À quelle hauteur l'échelle atteint-elle le mur? (Arrondi à une décimale; sin 65° ≈ 0,906)
• Choices: A) 6.8 m B) 7.2 m C) 7.5 m D) 7.8 m
• Hint: Use SOH: opposite = sin(angle) × hypotenuse — like sin(30°) × 10 m = 0.5 × 10 = 5 m.
• Steps:
  • Opposite (height) = sin(65°) × 8 = 0.906 × 8 = 7.248.
  • Rounded to one decimal: 7.2 m.
• Answer: 7.2 m

[Easy] Factoring Quadratics

• EN: Factor the quadratic: x² + 7x + 10
• FR: Factorise le polynôme du second degré : x² + 7x + 10
• Choices: A) (x + 2)(x + 5) B) (x + 1)(x + 10) C) (x + 3)(x + 4) D) (x + 2)(x + 6)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — like x² + 5x + 6: find 2 and 3 (2 × 3 = 6, 2 + 3 = 5), so (x + 2)(x + 3).
• Steps:
  • Need two numbers: product = 10, sum = 7. That's 2 and 5.
  • x² + 7x + 10 = (x + 2)(x + 5).
• Answer: (x + 2)(x + 5)

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 6 cm and the hypotenuse is 10 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 6 cm et l'hypoténuse mesure 10 cm. Quel est cos(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: CAH: cos(θ) = adjacent ÷ hypotenuse — like adjacent = 4, hypotenuse = 8, cos(θ) = 4/8 = 0.5.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 6 ÷ 10 = 0.6.
  • cos(θ) = 0.6.
• Answer: 0.6

[Easy] Systems of Equations

• EN: Solve by substitution: y = 2x and x + y = 9
• FR: Résous par substitution : y = 2x et x + y = 9
• Choices: A) x = 2, y = 4 B) x = 3, y = 6 C) x = 4, y = 5 D) x = 5, y = 4
• Hint: Substitute the first equation into the second — like if y = 3x and x + y = 8: x + 3x = 8, 4x = 8, x = 2, y = 6.
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9 → 3x = 9 → x = 3.
  • y = 2(3) = 6.
• Answer: x = 3, y = 6

[Easy] Volume of a Cylinder

• EN: A cylindrical water tank has a radius of 3 m and a height of 5 m. What is its volume? (Use π ≈ 3.14)
• FR: Un réservoir d'eau cylindrique a un rayon de 3 m et une hauteur de 5 m. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 94.2 m³ B) 113.04 m³ C) 141.3 m³ D) 150.72 m³
• Hint: Volume of a cylinder = π × r² × h — like radius 2, height 4: π × 4 × 4 = 50.24 m³.
• Steps:
  • V = π × 3² × 5 = 3.14 × 9 × 5 = 3.14 × 45 = 141.3.
  • Volume = 141.3 m³.
• Answer: 141.3 m³

[Medium] Completing the Square

• EN: Solve for x by completing the square: x² + 6x + 5 = 0
• FR: Résous pour x en complétant le carré : x² + 6x + 5 = 0
• Choices: A) x = −1 or x = −5 B) x = 1 or x = 5 C) x = −1 or x = 5 D) x = 1 or x = −5
• Hint: Move the constant, complete the square, then solve — like x² + 4x + 3 = 0: (x+2)² = 1, x = −1 or x = −3.
• Steps:
  • x² + 6x = −5; (x + 3)² = −5 + 9 = 4; x + 3 = ±2.
  • x = −3 + 2 = −1 or x = −3 − 2 = −5.
• Answer: x = −1 or x = −5

[Medium] Circle Geometry

• EN: A chord is 24 cm long and the radius of the circle is 13 cm. What is the distance from the centre of the circle to the chord?
• FR: Une corde mesure 24 cm de long et le rayon du cercle est de 13 cm. Quelle est la distance du centre du cercle à la corde?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: A perpendicular from the centre bisects the chord — use Pythagorean theorem with half the chord and the radius, like radius 10, half-chord 6: distance = √(100 − 36) = √64 = 8.
• Steps:
  • Half the chord = 24 ÷ 2 = 12. Radius = 13.
  • Distance = √(13² − 12²) = √(169 − 144) = √25 = 5 cm.
• Answer: 5 cm

[Medium] Quadratic Formula

• EN: Solve using the quadratic formula: x² − 5x + 6 = 0
• FR: Résous à l'aide de la formule quadratique : x² − 5x + 6 = 0
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = −2 or x = −3 D) x = 2 or x = −3
• Hint: Use x = (−b ± √(b² − 4ac)) ÷ 2a — like x² − 7x + 12 = 0: discriminant = 49 − 48 = 1, x = (7 ± 1)/2, so x = 4 or x = 3.
• Steps:
  • a = 1, b = −5, c = 6. Discriminant = 25 − 24 = 1.
  • x = (5 ± 1)/2: x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Medium] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 7 cm and the hypotenuse is 14 cm. What is the angle? (sin⁻¹(0.5) = 30°)
• FR: Dans un triangle rectangle, le côté opposé mesure 7 cm et l'hypoténuse mesure 14 cm. Quel est l'angle? (sin⁻¹(0,5) = 30°)
• Choices: A) 25° B) 30° C) 35° D) 45°
• Hint: Use SOH and inverse sine — like opposite = 5, hypotenuse = 10: sin(θ) = 0.5, so θ = sin⁻¹(0.5) = 30°.
• Steps:
  • sin(θ) = 7/14 = 0.5.
  • θ = sin⁻¹(0.5) = 30°.
• Answer: 30°

[Hard] Quadratic Word Problem

• EN: A ball is thrown upward with the height modelled by h = −5t² + 20t + 1. What is the maximum height the ball reaches?
• FR: Un ballon est lancé vers le haut avec la hauteur modélisée par h = −5t² + 20t + 1. Quelle est la hauteur maximale atteinte par le ballon?
• Choices: A) 19 m B) 20 m C) 21 m D) 25 m
• Hint: The maximum occurs at t = −b/(2a) — like h = −4t² + 16t + 3: t = 16/8 = 2, h = −4(4) + 16(2) + 3 = 19.
• Steps:
  • t at max = −20/(2×−5) = −20/−10 = 2 seconds.
  • h = −5(4) + 20(2) + 1 = −20 + 40 + 1 = 21 m.
• Answer: 21 m

[Hard] System of Equations — Non-Linear

• EN: Find the intersection of y = x² and y = x + 6. What are the x-values of the intersection points?
• FR: Trouve l'intersection de y = x² et y = x + 6. Quelles sont les valeurs de x des points d'intersection?
• Choices: A) x = −2 and x = 3 B) x = 2 and x = 3 C) x = −3 and x = 2 D) x = −2 and x = −3
• Hint: Set the equations equal and solve the quadratic — like y = x² and y = 2x + 3: x² − 2x − 3 = 0, factor to find x.
• Steps:
  • x² = x + 6 → x² − x − 6 = 0.
  • Factor: (x − 3)(x + 2) = 0 → x = 3 or x = −2.
• Answer: x = −2 and x = 3

[Easy] Exponential Functions

• EN: A bacterial colony doubles every hour. If there are 200 bacteria at the start, how many are there after 3 hours?
• FR: Une colonie bactérienne double chaque heure. Si on commence avec 200 bactéries, combien y en a-t-il après 3 heures?
• Choices: A) 600 B) 1 200 C) 1 600 D) 2 400
• Hint: For doubling, use 2ⁿ × initial amount — like 50 bacteria doubling 4 times = 50 × 2⁴ = 50 × 16 = 800.
• Steps:
  • After 3 hours: 200 × 2³ = 200 × 8 = 1 600.
  • There are 1 600 bacteria.
• Answer: 1 600

[Easy] Logarithms Introduction

• EN: What is log₂(16)?
• FR: Combien fait log₂(16)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log_b(x) asks "b to what power equals x?" — like log₃(27) = 3 because 3³ = 27.
• Steps:
  • Ask: 2 to what power equals 16?
  • 2⁴ = 16, so log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequences

• EN: The first term of an arithmetic sequence is 5 and the common difference is 4. What is the 8th term?
• FR: Le premier terme d'une suite arithmétique est 5 et la raison est 4. Quel est le 8e terme?
• Choices: A) 29 B) 33 C) 37 D) 41
• Hint: Use the formula aₙ = a₁ + (n − 1)d — like a₁ = 3, d = 5, a₆ = 3 + 5 × 5 = 28.
• Steps:
  • a₈ = 5 + (8 − 1) × 4 = 5 + 28 = 33.
  • The 8th term is 33.
• Answer: 33

[Easy] Compound Interest

• EN: Isabelle invests $1 000 at 5% annual interest, compounded annually. How much does she have after 2 years?
• FR: Isabelle investit 1 000 $ à un taux d'intérêt annuel de 5 %, composé annuellement. Combien a-t-elle après 2 ans?
• Choices: A) $1 050.00 B) $1 100.00 C) $1 102.50 D) $1 110.25
• Hint: Use A = P(1 + r)ⁿ — like $500 at 4% for 3 years: A = 500 × (1.04)³ = 500 × 1.1249 ≈ $562.45.
• Steps:
  • A = 1000 × (1.05)² = 1000 × 1.1025 = $1 102.50.
  • Isabelle has $1 102.50.
• Answer: $1 102.50

[Medium] Quadratic Functions — Vertex

• EN: Find the vertex of the parabola y = x² − 4x + 7.
• FR: Trouve le sommet de la parabole y = x² − 4x + 7.
• Choices: A) (2, 3) B) (2, 7) C) (4, 7) D) (−2, 3)
• Hint: Vertex x-coordinate = −b/(2a) — like y = x² − 6x + 11: x = 6/2 = 3, y = 9 − 18 + 11 = 2, vertex = (3, 2).
• Steps:
  • x = −(−4)/(2×1) = 4/2 = 2. y = 4 − 8 + 7 = 3.
  • Vertex = (2, 3).
• Answer: (2, 3)

[Medium] Geometric Series

• EN: Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.
• FR: Trouve la somme des 5 premiers termes de la série géométrique avec premier terme 2 et raison 3.
• Choices: A) 162 B) 242 C) 244 D) 256
• Hint: Use Sₙ = a₁ × (rⁿ − 1)/(r − 1) — like a₁ = 1, r = 2, n = 4: S₄ = 1 × (16 − 1)/(2 − 1) = 15.
• Steps:
  • S₅ = 2 × (3⁵ − 1)/(3 − 1) = 2 × (243 − 1)/2 = 2 × 242/2 = 242.
  • The sum is 242.
• Answer: 242

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ) + tan(θ)/tan(θ)
• FR: Simplifie : sin²(θ) + cos²(θ) + tan(θ)/tan(θ)
• Choices: A) 1 B) 2 C) tan²(θ) + 1 D) sin²(θ)
• Hint: Use the Pythagorean identity sin²θ + cos²θ = 1 and simplify each part — like sin²θ + cos²θ + 1 = 2.
• Steps:
  • sin²(θ) + cos²(θ) = 1. tan(θ)/tan(θ) = 1 (for tan(θ) ≠ 0).
  • 1 + 1 = 2.
• Answer: 2

[Medium] Logarithm Laws

• EN: Simplify: log₅(125) − log₅(5)
• FR: Simplifie : log₅(125) − log₅(5)
• Choices: A) 1 B) 2 C) 3 D) 5
• Hint: Use the log subtraction rule: log(a) − log(b) = log(a/b) — like log₂(8) − log₂(4) = log₂(2) = 1.
• Steps:
  • log₅(125) − log₅(5) = log₅(125/5) = log₅(25).
  • 5² = 25, so log₅(25) = 2.
• Answer: 2

[Hard] Annuity Calculation

• EN: Lucas saves $200 per month at 6% annual interest (0.5% per month), compounded monthly, for 12 months. What is the future value of this annuity? (Use FV = PMT × ((1 + r)ⁿ − 1) / r, round to the nearest cent)
• FR: Lucas épargne 200 $ par mois à 6 % d'intérêt annuel (0,5 % par mois), composé mensuellement, pendant 12 mois. Quelle est la valeur future de cette rente? (Utilise VA = PMT × ((1 + r)ⁿ − 1) / r, arrondi au cent près)
• Choices: A) $2 400.00 B) $2 467.34 C) $2 487.34 D) $2 512.00
• Hint: Plug into the annuity formula — like PMT = $100, r = 0.01, n = 6: FV = 100 × ((1.01)⁶ − 1)/0.01 ≈ $615.20.
• Steps:
  • FV = 200 × ((1.005)¹² − 1) / 0.005.
  • (1.005)¹² ≈ 1.06168; (1.06168 − 1)/0.005 = 0.06168/0.005 = 12.336; FV = 200 × 12.336 ≈ $2 467.34 (using more precise value).
• Answer: $2 467.34

[Hard] Exponential Equation

• EN: Solve for x: 3^(2x) = 81
• FR: Résous pour x : 3^(2x) = 81
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Write both sides with the same base, then equate exponents — like 2^(3x) = 32: 2^(3x) = 2⁵, so 3x = 5, x = 5/3.
• Steps:
  • 81 = 3⁴, so 3^(2x) = 3⁴.
  • 2x = 4, so x = 2.
• Answer: x = 2

[Easy] Combinations

• EN: How many ways can you choose 3 students from a group of 7 to form a committee?
• FR: De combien de façons peut-on choisir 3 élèves parmi un groupe de 7 pour former un comité?
• Choices: A) 21 B) 35 C) 42 D) 210
• Hint: Use C(n, r) = n! / (r!(n − r)!) — like C(5, 2) = 5!/(2! × 3!) = 120/12 = 10.
• Steps:
  • C(7, 3) = 7! / (3! × 4!) = (7 × 6 × 5) / (3 × 2 × 1) = 210 / 6 = 35.
  • There are 35 ways.
• Answer: 35

[Easy] Derivative — Power Rule

• EN: Using the power rule, find the derivative of f(x) = 4x³.
• FR: En utilisant la règle de puissance, trouve la dérivée de f(x) = 4x³.
• Choices: A) 4x² B) 8x² C) 12x² D) 16x²
• Hint: Power rule: d/dx (axⁿ) = n·axⁿ⁻¹ — like f(x) = 3x⁵: f'(x) = 5 × 3x⁴ = 15x⁴.
• Steps:
  • Bring down the exponent and reduce it by 1: 3 × 4x² = 12x².
  • f'(x) = 12x².
• Answer: 12x²

[Easy] Permutations

• EN: In how many ways can 5 different books be arranged on a shelf?
• FR: De combien de façons peut-on placer 5 livres différents sur une étagère?
• Choices: A) 25 B) 60 C) 120 D) 720
• Hint: The number of ways to arrange n objects is n! — like 4 books = 4! = 4 × 3 × 2 × 1 = 24 ways.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1 = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Polynomial Function — End Behaviour

• EN: For the polynomial f(x) = −2x⁴ + 3x − 1, what happens as x → +∞?
• FR: Pour le polynôme f(x) = −2x⁴ + 3x − 1, que se passe-t-il lorsque x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → −1
• Hint: The leading term controls end behaviour — a negative leading coefficient with even degree means both ends go down, like −3x² → −∞ as x → ±∞.
• Steps:
  • Leading term: −2x⁴. Even degree, negative coefficient.
  • As x → +∞, −2x⁴ → −∞.
• Answer: f(x) → −∞

[Medium] Rate of Change — Derivative Application

• EN: The position of a car (in metres) is given by s(t) = 3t² + 2t. What is the velocity (instantaneous rate of change) at t = 4 seconds?
• FR: La position d'une voiture (en mètres) est donnée par s(t) = 3t² + 2t. Quelle est la vitesse (taux de changement instantané) à t = 4 secondes?
• Choices: A) 24 m/s B) 26 m/s C) 28 m/s D) 30 m/s
• Hint: Differentiate using the power rule, then substitute — like s(t) = 5t² + t: s'(t) = 10t + 1, at t = 3: s'(3) = 31.
• Steps:
  • s'(t) = 6t + 2. At t = 4: s'(4) = 24 + 2 = 26.
  • Velocity = 26 m/s.
• Answer: 26 m/s

[Medium] Binomial Theorem / Probability Distribution

• EN: In a true/false quiz with 6 questions, each with a 50% chance of being correct. What is the probability of getting exactly 4 correct? (Round to 3 decimal places)
• FR: Dans un quiz vrai/faux de 6 questions, chacune avec 50 % de chance d'être correcte. Quelle est la probabilité d'en avoir exactement 4 correctes? (Arrondi à 3 décimales)
• Choices: A) 0.188 B) 0.234 C) 0.250 D) 0.313
• Hint: Use binomial probability: P = C(n, k) × p^k × (1 − p)^(n−k) — like P(2 out of 4 correct, p = 0.5) = C(4,2) × 0.5² × 0.5² = 6 × 0.0625 = 0.375.
• Steps:
  • P = C(6, 4) × (0.5)⁴ × (0.5)² = 15 × (1/16) × (1/4) = 15/64 ≈ 0.234.
  • P ≈ 0.234.
• Answer: 0.234

[Medium] Vectors — Addition

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

[Medium] Rational Function — Asymptotes

• EN: Find the vertical asymptote of f(x) = (2x + 1)/(x − 3).
• FR: Trouve l'asymptote verticale de f(x) = (2x + 1)/(x − 3).
• Choices: A) x = −3 B) x = 1/2 C) x = 2 D) x = 3
• Hint: The vertical asymptote occurs where the denominator equals zero — like for f(x) = 5/(x − 4), the vertical asymptote is at x = 4.
• Steps:
  • Set denominator = 0: x − 3 = 0, so x = 3.
  • Vertical asymptote is at x = 3.
• Answer: x = 3

[Hard] Combinations and Probability

• EN: A school committee of 4 students is chosen from 5 girls and 4 boys. What is the probability that the committee has exactly 2 girls and 2 boys?
• FR: Un comité scolaire de 4 élèves est choisi parmi 5 filles et 4 garçons. Quelle est la probabilité que le comité compte exactement 2 filles et 2 garçons?
• Choices: A) 5/14 B) 10/21 C) 6/14 D) 3/7
• Hint: Use P = (favourable combinations)/(total combinations) — like from 3 girls and 3 boys choosing 2 of each: C(3,2)×C(3,2)/C(6,4) = 9/15 = 3/5.
• Steps:
  • Favourable: C(5,2) × C(4,2) = 10 × 6 = 60. Total: C(9,4) = 126.
  • P = 60/126 = 10/21.
• Answer: 10/21

[Hard] Derivative — Optimization

• EN: A farmer has 120 m of fencing to enclose a rectangular garden on three sides (one side is a barn wall). What is the maximum area of the garden?
• FR: Un fermier dispose de 120 m de clôture pour entourer un jardin rectangulaire sur trois côtés (un côté est un mur de grange). Quelle est l'aire maximale du jardin?
• Choices: A) 1 600 m² B) 1 700 m² C) 1 800 m² D) 1 900 m²
• Hint: Write the area function, differentiate, set to zero — like 80 m fencing for 3 sides: 2w + l = 80, A = w(80 − 2w), A' = 80 − 4w = 0, w = 20, A = 20 × 40 = 800 m².
• Steps:
  • Let width = w; 2w + l = 120, so l = 120 − 2w. A = w(120 − 2w) = 120w − 2w².
  • A' = 120 − 4w = 0 → w = 30. l = 120 − 60 = 60. A = 30 × 60 = 1 800 m².
• Answer: 1 800 m²