Daily Math — 2026-10-04

[Easy] Counting Apples

• EN: There are 7 apples on the table and 5 more in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres 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 6 + 4, start at 6 and count up 4 more: 7, 8, 9, 10.
• Steps:
  • Start at 7.
  • Count up 5 more: 8, 9, 10, 11, 12.
  • So there are 12 apples in all.
• Answer: 12 apples

[Easy] Subtraction at the Rink

• EN: There were 9 hockey pucks on the ice. A player took 4 away. How many pucks are left?
• FR: Il y avait 9 rondelles sur la glace. Un joueur en a pris 4. Combien de rondelles reste-t-il?
• Choices: A) 3 pucks B) 4 pucks C) 5 pucks D) 6 pucks
• Hint: To find 8 − 3, start at 8 and count back 3: 7, 6, 5.
• Steps:
  • Start at 9.
  • Count back 4: 8, 7, 6, 5.
  • So 5 pucks are left.
• Answer: 5 pucks

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes after 14?
• FR: Compte par bonds de 2. Quel nombre vient après 14?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: When skip counting by 2s, add 2 each time: 10, 12, 14, …
• Steps:
  • We are counting by 2s.
  • 14 + 2 = 16.
  • So the next number is 16.
• Answer: 16

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents?
• FR: Quelle pièce vaut 10 cents?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: A penny = 1 cent, a nickel = 5 cents — the next coin up is worth even more.
• Steps:
  • A penny is worth 1 cent.
  • A nickel is worth 5 cents.
  • A dime is worth 10 cents.
  • So the answer is Dime.
• Answer: Dime

[Medium] Adding Three Numbers

• EN: Maya has 4 stickers, 3 stickers, and 6 stickers. How many stickers does she have in all?
• FR: Maya a 4 autocollants, 3 autocollants et 6 autocollants. Combien d'autocollants a-t-elle en tout?
• Choices: A) 11 stickers B) 12 stickers C) 13 stickers D) 14 stickers
• Hint: Add 2 + 3 + 5: first 2 + 3 = 5, then 5 + 5 = 10.
• Steps:
  • First add 4 + 3 = 7.
  • Then add 7 + 6 = 13.
  • So Maya has 13 stickers in all.
• Answer: 13 stickers

[Medium] Comparing Numbers

• EN: Which number is greater: 47 or 74?
• FR: Quel nombre est plus grand: 47 ou 74?
• Choices: A) 47 B) 74 C) They are equal D) 44
• Hint: Look at the tens digit first: 3 tens is less than 5 tens, so 35 < 52.
• Steps:
  • Look at the tens digit of 47: it is 4 tens.
  • Look at the tens digit of 74: it is 7 tens.
  • 7 tens is greater than 4 tens, so 74 is greater.
• Answer: 74

[Medium] Skip Counting by 5s

• EN: Count by 5s starting at 5. What is the 4th number you say?
• FR: Compte par bonds de 5 en commençant à 5. Quel est le 4e nombre que tu dis?
• Choices: A) 15 B) 20 C) 25 D) 30
• Hint: Skip count by 5s: 5, 10, 15 — what comes next at position 4?
• Steps:
  • 1st number: 5.
  • 2nd number: 10.
  • 3rd number: 15.
  • 4th number: 20.
• Answer: 20

[Medium] Subtraction Story

• EN: There are 18 children on the playground. 9 go inside. How many children are still outside?
• FR: Il y a 18 enfants dans la cour de récréation. 9 entrent à l'intérieur. Combien d'enfants sont encore dehors?
• Choices: A) 7 children B) 8 children C) 9 children D) 10 children
• Hint: 16 − 8 = 8 because 8 + 8 = 16.
• Steps:
  • Start with 18 children.
  • Subtract 9: 18 − 9 = 9.
  • So 9 children are still outside.
• Answer: 9 children

[Hard] Missing Number

• EN: What number goes in the box? □ + 6 = 14
• FR: Quel nombre va dans la case? □ + 6 = 14
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: If □ + 4 = 11, think: what plus 4 gives 11? Count back from 11.
• Steps:
  • We need a number that, when added to 6, gives 14.
  • Count back from 14 by 6: 14 − 6 = 8.
  • Check: 8 + 6 = 14. ✓
  • So the missing number is 8.
• Answer: 8

[Hard] Counting to 100

• EN: Liam counts by 10s starting at 10. Which list shows his count?
• FR: Liam compte par bonds de 10 en commençant à 10. Quelle liste montre son compte?
• Choices: A) 10, 20, 30, 40, 50 B) 10, 15, 20, 25, 30 C) 10, 12, 14, 16, 18 D) 10, 21, 32, 43, 54
• Hint: Skip counting by 10s means adding 10 each time: 5, 15, 25, 35 …
• Steps:
  • Counting by 10s means we add 10 each time.
  • 10, 20, 30, 40, 50 — each step is +10.
  • The other lists add 5, 2, or odd amounts.
  • So the correct list is 10, 20, 30, 40, 50.
• Answer: 10, 20, 30, 40, 50

[Easy] Adding Within 100

• EN: A store has 34 red pencils and 25 blue pencils. How many pencils are there in all?
• FR: Un magasin a 34 crayons rouges et 25 crayons bleus. Combien y a-t-il de crayons en tout?
• Choices: A) 57 pencils B) 58 pencils C) 59 pencils D) 60 pencils
• Hint: For 22 + 31, add tens first: 20 + 30 = 50, then ones: 2 + 1 = 3, total 53.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59.
  • So there are 59 pencils in all.
• Answer: 59 pencils

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: La grande aiguille est sur le 12 et la petite aiguille est sur le 3. Quelle heure est-il?
• Choices: A) 12:00 B) 3:00 C) 3:30 D) 12:15
• Hint: When the minute hand points to 12, it is exactly on the hour — like 5:00.
• Steps:
  • The minute hand on 12 means it is exactly on the hour.
  • The hour hand is on 3.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long and an eraser is 5 cm long. How much longer is the pencil than the eraser?
• FR: Un crayon mesure 14 cm et une gomme mesure 5 cm. De combien le crayon est-il plus long que la gomme?
• Choices: A) 7 cm B) 8 cm C) 9 cm D) 10 cm
• Hint: To find the difference in length, subtract: 12 − 4 = 8.
• Steps:
  • Subtract the eraser's length from the pencil's length.
  • 14 − 5 = 9.
  • The pencil is 9 cm longer.
• Answer: 9 cm

[Easy] Counting Coins

• EN: Ella has 2 dimes and 3 nickels. How much money does she have in total?
• FR: Ella a 2 pièces de 10 cents et 3 pièces de 5 cents. Combien d'argent a-t-elle en tout?
• Choices: A) 30 cents B) 35 cents C) 40 cents D) 45 cents
• Hint: 1 dime = 10 cents, 1 nickel = 5 cents. For 3 dimes + 2 nickels: 30 + 10 = 40 cents.
• Steps:
  • 2 dimes = 2 × 10 = 20 cents.
  • 3 nickels = 3 × 5 = 15 cents.
  • 20 + 15 = 35 cents.
• Answer: 35 cents

[Medium] Subtraction Within 100

• EN: A farmer picked 82 strawberries. She sold 47 of them. How many strawberries does she have left?
• FR: Une fermière a cueilli 82 fraises. Elle en a vendu 47. Combien de fraises lui reste-t-il?
• Choices: A) 33 strawberries B) 34 strawberries C) 35 strawberries D) 36 strawberries
• Hint: For 71 − 36, regroup: borrow a ten from 7, making 11 − 6 = 5, and 6 − 3 = 3, giving 35.
• Steps:
  • Subtract the ones: 2 − 7 needs regrouping. Borrow a ten: 12 − 7 = 5.
  • Subtract the tens: 7 − 1 (borrowed) − 4 = 2.
  • So 82 − 47 = 35.
• Answer: 35 strawberries

[Medium] Telling Time — Half Hour

• EN: The clock shows the hour hand between 7 and 8, and the minute hand on 6. What time is it?
• FR: La petite aiguille est entre 7 et 8, et la grande aiguille est sur le 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the minute hand points to 6, it is half past the hour — like 4:30.
• Steps:
  • The minute hand on 6 means 30 minutes past the hour.
  • The hour hand is between 7 and 8, so the hour is 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, ___. What is the missing number?
• FR: Regarde ce patron: 5, 10, 15, 20, ___. Quel est le nombre manquant?
• Choices: A) 22 B) 23 C) 24 D) 25
• Hint: Find the rule first: 2, 4, 6, 8 — each number is 2 more than the one before.
• Steps:
  • Each number increases by 5.
  • 20 + 5 = 25.
  • So the missing number is 25.
• Answer: 25

[Medium] Adding With Carrying

• EN: A class collected 56 cans on Monday and 38 cans on Tuesday. How many cans did they collect altogether?
• FR: Une classe a collecté 56 boîtes de conserve lundi et 38 mardi. Combien de boîtes ont-ils collectées en tout?
• Choices: A) 84 cans B) 93 cans C) 94 cans D) 95 cans
• Hint: For 47 + 35, add ones: 7 + 5 = 12, write 2 carry 1; add tens: 4 + 3 + 1 = 8, giving 82.
• Steps:
  • Add the ones: 6 + 8 = 14. Write 4, carry 1.
  • Add the tens: 5 + 3 + 1 = 9.
  • So 56 + 38 = 94.
• Answer: 94 cans

[Hard] Multi-Step Coin Problem

• EN: Ben has 3 dimes, 4 nickels, and 6 pennies. How much money does he have in total?
• FR: Ben a 3 pièces de 10 cents, 4 pièces de 5 cents et 6 pennies. Combien d'argent a-t-il en tout?
• Choices: A) 52 cents B) 55 cents C) 56 cents D) 60 cents
• Hint: For 2 dimes + 3 nickels + 4 pennies: 20 + 15 + 4 = 39 cents.
• Steps:
  • 3 dimes = 30 cents.
  • 4 nickels = 20 cents.
  • 6 pennies = 6 cents.
  • 30 + 20 + 6 = 56 cents.
• Answer: 56 cents

[Hard] Measuring and Comparing

• EN: A bookshelf is 90 cm tall. A desk is 75 cm tall. If you stack the desk on the bookshelf, what is the total height?
• FR: Une bibliothèque mesure 90 cm de hauteur. Un bureau mesure 75 cm. Si tu empiles le bureau sur la bibliothèque, quelle est la hauteur totale?
• Choices: A) 155 cm B) 160 cm C) 165 cm D) 170 cm
• Hint: To add 80 + 65, add tens: 80 + 60 = 140, then ones: 140 + 5 = 145.
• Steps:
  • Add the heights: 90 + 75.
  • Add the tens: 90 + 70 = 160.
  • Add the ones: 160 + 5 = 165.
  • The total height is 165 cm.
• Answer: 165 cm

[Easy] Multiplication by 2

• EN: A carton holds 2 eggs. How many eggs are in 7 cartons?
• FR: Une boîte contient 2 œufs. Combien d'œufs y a-t-il dans 7 boîtes?
• Choices: A) 9 eggs B) 12 eggs C) 14 eggs D) 16 eggs
• Hint: For 2 × 5, think: 5 groups of 2 = 10.
• Steps:
  • 7 cartons × 2 eggs each = 7 × 2.
  • 7 × 2 = 14.
  • So there are 14 eggs in all.
• Answer: 14 eggs

[Easy] Fractions — Half

• EN: A pizza has 8 slices. Sophie eats half of the pizza. How many slices does she eat?
• FR: Une pizza a 8 morceaux. Sophie mange la moitié de la pizza. Combien de morceaux mange-t-elle?
• Choices: A) 2 slices B) 3 slices C) 4 slices D) 6 slices
• Hint: Half of 10 is 5 because 10 ÷ 2 = 5.
• Steps:
  • Half means dividing by 2.
  • 8 ÷ 2 = 4.
  • So Sophie eats 4 slices.
• Answer: 4 slices

[Easy] Multiplication by 5

• EN: There are 5 fingers on each hand. How many fingers are on 6 hands?
• FR: Il y a 5 doigts sur chaque main. Combien de doigts y a-t-il sur 6 mains?
• Choices: A) 25 fingers B) 30 fingers C) 35 fingers D) 40 fingers
• Hint: 5 × 4 = 20 because skip count by 5s four times: 5, 10, 15, 20.
• Steps:
  • 6 hands × 5 fingers = 6 × 5.
  • 6 × 5 = 30.
  • So there are 30 fingers.
• Answer: 30 fingers

[Easy] Basic Division

• EN: There are 20 cookies to share equally among 4 children. How many cookies does each child get?
• FR: Il y a 20 biscuits à partager également entre 4 enfants. Combien de biscuits chaque enfant reçoit-il?
• Choices: A) 4 cookies B) 5 cookies C) 6 cookies D) 8 cookies
• Hint: 18 ÷ 3 = 6 because 3 × 6 = 18.
• Steps:
  • 20 ÷ 4 = ?
  • Think: 4 × 5 = 20.
  • So each child gets 5 cookies.
• Answer: 5 cookies

[Medium] Missing Factor

• EN: What number goes in the blank? __ × 5 = 35
• FR: Quel nombre va dans le blanc? __ × 5 = 35
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: For __ × 3 = 24, think: what times 3 gives 24? Try 8: 8 × 3 = 24.
• Steps:
  • We need a number multiplied by 5 to get 35.
  • Try 7: 7 × 5 = 35. ✓
  • So the missing number is 7.
• Answer: 7

[Medium] Perimeter of a Rectangle

• EN: A garden is 6 m long and 4 m wide. What is the perimeter of the garden?
• FR: Un jardin mesure 6 m de long et 4 m de large. Quel est le périmètre du jardin?
• Choices: A) 10 m B) 20 m C) 24 m D) 28 m
• Hint: For a rectangle 5 m × 3 m, perimeter = 5 + 3 + 5 + 3 = 16 m.
• Steps:
  • A rectangle has 2 lengths and 2 widths.
  • Perimeter = 6 + 4 + 6 + 4.
  • 6 + 4 = 10; 10 × 2 = 20.
  • The perimeter is 20 m.
• Answer: 20 m

[Medium] Reading a Graph

• EN: A bar graph shows: Monday = 8 goals, Tuesday = 5 goals, Wednesday = 7 goals. How many goals were scored in total over the three days?
• FR: Un diagramme à barres montre: lundi = 8 buts, mardi = 5 buts, mercredi = 7 buts. Combien de buts ont été marqués en tout sur trois jours?
• Choices: A) 18 goals B) 19 goals C) 20 goals D) 21 goals
• Hint: To add three numbers like 6 + 4 + 9, add the first two: 6 + 4 = 10, then 10 + 9 = 19.
• Steps:
  • Add Monday and Tuesday: 8 + 5 = 13.
  • Add Wednesday: 13 + 7 = 20.
  • So 20 goals were scored in total.
• Answer: 20 goals

[Medium] Fractions — Quarter

• EN: A ribbon is 12 cm long. Theo cuts off one quarter of it. How long is the piece he cuts off?
• FR: Un ruban mesure 12 cm. Théo en coupe un quart. Quelle est la longueur du morceau qu'il coupe?
• Choices: A) 2 cm B) 3 cm C) 4 cm D) 6 cm
• Hint: One quarter of 8 is 8 ÷ 4 = 2.
• Steps:
  • One quarter means dividing by 4.
  • 12 ÷ 4 = 3.
  • So Theo cuts off 3 cm.
• Answer: 3 cm

[Hard] Missing Factor — Multiplication Table of 4

• EN: What number completes the equation? 4 × __ = 36
• FR: Quel nombre complète l'équation? 4 × __ = 36
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: For 3 × __ = 27, try 9: 3 × 9 = 27. ✓
• Steps:
  • We need a number such that 4 times it equals 36.
  • Try 9: 4 × 9 = 36. ✓
  • So the missing number is 9.
• Answer: 9

[Hard] Multi-Step Word Problem

• EN: A school store sells pencils for $0.10 each and notebooks for $0.50 each. Carlos buys 3 pencils and 2 notebooks. How much does he spend in total?
• FR: La boutique de l'école vend des crayons à 0,10 $ chacun et des cahiers à 0,50 $ chacun. Carlos achète 3 crayons et 2 cahiers. Combien dépense-t-il en tout?
• Choices: A) $0.80 B) $1.20 C) $1.30 D) $1.50
• Hint: For 4 pencils at $0.10 and 1 notebook at $0.50: 4 × $0.10 = $0.40, + $0.50 = $0.90.
• Steps:
  • Cost of 3 pencils: 3 × $0.10 = $0.30.
  • Cost of 2 notebooks: 2 × $0.50 = $1.00.
  • Total: $0.30 + $1.00 = $1.30.
• Answer: $1.30

[Easy] Multiplication — Times Tables

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: 7 × 6 = 42, so 7 × 7 = 49, and one more group of 7 gives 56.
• Steps:
  • 7 × 8 means 8 groups of 7.
  • 7 × 8 = 56.
  • So the answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 4.37?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,37?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 3 tens
• Hint: In 2.54, the digit 5 is in the tenths place, and 4 is in the hundredths place.
• Steps:
  • 4.37 has digits in: ones, tenths, hundredths.
  • 4 is in the ones place.
  • 3 is in the tenths place.
  • 7 is in the hundredths place.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A hockey rink drawing is 9 cm long and 6 cm wide. What is the area of the rectangle?
• FR: Le dessin d'une patinoire de hockey mesure 9 cm de long et 6 cm de large. Quelle est l'aire du rectangle?
• Choices: A) 30 cm² B) 48 cm² C) 54 cm² D) 60 cm²
• Hint: Area = length × width. For a 5 cm × 7 cm rectangle, area = 35 cm².
• Steps:
  • Area = length × width.
  • Area = 9 × 6 = 54.
  • The area is 54 cm².
• Answer: 54 cm²

[Easy] Long Division

• EN: What is 72 ÷ 8?
• FR: Combien fait 72 ÷ 8?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: For 48 ÷ 6, think: 6 × 8 = 48, so 48 ÷ 6 = 8.
• Steps:
  • Think: 8 × ? = 72.
  • 8 × 9 = 72.
  • So 72 ÷ 8 = 9.
• Answer: 9

[Medium] Missing Factor Equation

• EN: What number goes in the blank? 36 ÷ __ = 9
• FR: Quel nombre va dans le blanc? 36 ÷ __ = 9
• Choices: A) 3 B) 4 C) 6 D) 8
• Hint: For 45 ÷ __ = 9, think: 9 × ? = 45, so ? = 5.
• Steps:
  • We need 36 ÷ ? = 9.
  • Rearrange: 9 × ? = 36.
  • 9 × 4 = 36. ✓
  • So the missing number is 4.
• Answer: 4

[Medium] Elapsed Time

• EN: A movie starts at 1:15 p.m. and ends at 3:45 p.m. 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) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours
• Hint: From 2:10 to 4:40 — count up: 2:10 to 4:10 = 2 hours, plus 30 more minutes = 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] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 2/3?
• FR: Quelle fraction est la plus grande: 3/4 ou 2/3?
• Choices: A) 2/3 B) 3/4 C) They are equal D) 1/2
• Hint: Compare 1/2 and 2/5 by converting to decimals: 0.50 vs 0.40 — so 1/2 is larger.
• Steps:
  • Convert to decimals: 3/4 = 0.75, 2/3 ≈ 0.667.
  • 0.75 > 0.667.
  • So 3/4 is larger.
• Answer: 3/4

[Medium] Table Word Problem

• EN: The table shows the price of school supplies. | Item | Price | | Pencil | $0.50 | | Ruler | $1.25 | | Eraser | $0.75 | How much does it cost to buy 1 pencil, 1 ruler, and 2 erasers?
• FR: Le tableau montre le prix des fournitures scolaires. | Article | Prix | | Crayon | 0,50 $ | | Règle | 1,25 $ | | Gomme | 0,75 $ | Combien coûtent 1 crayon, 1 règle et 2 gommes?
• Choices: A) $2.75 B) $3.00 C) $3.25 D) $3.50
• Hint: For 1 pen at $1.00 + 2 notebooks at $0.80 each: $1.00 + $1.60 = $2.60.
• Steps:
  • 1 pencil: $0.50.
  • 1 ruler: $1.25.
  • 2 erasers: 2 × $0.75 = $1.50.
  • Total: $0.50 + $1.25 + $1.50 = $3.25.
• Answer: $3.25

[Hard] Long Division With Remainder

• EN: A farmer has 97 apples to put equally into boxes of 9. How many full boxes can he fill, and how many apples are left over?
• FR: Un fermier a 97 pommes à mettre également dans des boîtes de 9. Combien de boîtes pleines peut-il remplir, et combien de pommes reste-t-il?
• Choices: A) 9 boxes, remainder 5 B) 10 boxes, remainder 7 C) 10 boxes, remainder 8 D) 11 boxes, remainder 1
• Hint: For 53 ÷ 7: 7 × 7 = 49, remainder = 53 − 49 = 4, so 7 remainder 4.
• Steps:
  • 9 × 10 = 90. That uses 90 apples.
  • Remainder: 97 − 90 = 7.
  • So he fills 10 boxes with 7 apples left over.
• Answer: 10 boxes, remainder 7

[Hard] Multi-Step Decimal Problem

• EN: Ava buys a juice box for $1.35 and a muffin for $2.60. She pays with a $5.00 bill. How much change does she receive?
• FR: Ava achète une boîte de jus pour 1,35 $ et un muffin pour 2,60 $. Elle paye avec un billet de 5,00 $. Quelle monnaie reçoit-elle?
• Choices: A) $0.95 B) $1.05 C) $1.15 D) $1.25
• Hint: For $0.80 + $1.90 = $2.70; change from $5.00 = $5.00 − $2.70 = $2.30.
• Steps:
  • Total spent: $1.35 + $2.60 = $3.95.
  • Change: $5.00 − $3.95 = $1.05.
  • Ava receives $1.05 in change.
• Answer: $1.05

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien fait 34 × 6?
• Choices: A) 184 B) 200 C) 204 D) 214
• Hint: For 23 × 4, break it up: 20 × 4 = 80, 3 × 4 = 12, total = 92.
• Steps:
  • Break apart: 30 × 6 = 180, and 4 × 6 = 24.
  • 180 + 24 = 204.
  • So 34 × 6 = 204.
• Answer: 204

[Easy] Adding Fractions — Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien fait 2/7 + 3/7?
• Choices: A) 5/14 B) 5/7 C) 6/7 D) 1/7
• Hint: For 1/5 + 2/5, keep the denominator and add the tops: 1 + 2 = 3, so 3/5.
• Steps:
  • The denominators are the same (7).
  • Add the numerators: 2 + 3 = 5.
  • The answer is 5/7.
• Answer: 5/7

[Easy] Decimal Operations

• EN: What is 3.6 + 2.8?
• FR: Combien fait 3,6 + 2,8?
• Choices: A) 5.4 B) 6.0 C) 6.4 D) 6.8
• Hint: For 4.3 + 1.9, add the tenths: 3 + 9 = 12, write 2 carry 1; add ones: 4 + 1 + 1 = 6; total 6.2.
• Steps:
  • Add tenths: 6 + 8 = 14, write 4 carry 1.
  • Add ones: 3 + 2 + 1 = 6.
  • So 3.6 + 2.8 = 6.4.
• Answer: 6.4

[Easy] Percentage — 50%

• EN: What is 50% of 80?
• FR: Combien fait 50% de 80?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: 50% means half, so 50% of 60 = 60 ÷ 2 = 30.
• Steps:
  • 50% means dividing by 2.
  • 80 ÷ 2 = 40.
  • So 50% of 80 is 40.
• Answer: 40

[Medium] Missing Factor — Larger Numbers

• EN: What number goes in the blank? __ × 18 = 108
• FR: Quel nombre va dans le blanc? __ × 18 = 108
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: For __ × 15 = 75, try 5: 5 × 15 = 75. ✓
• Steps:
  • We need ? × 18 = 108.
  • Try 6: 6 × 18 = 108. ✓
  • So the missing number is 6.
• Answer: 6

[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) 48 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume = length × width × height. For a 2 × 3 × 4 box: 2 × 3 = 6, then 6 × 4 = 24 cm³.
• Steps:
  • Volume = length × width × height.
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions

• EN: What is 6/9 − 2/9?
• FR: Combien fait 6/9 − 2/9?
• Choices: A) 3/9 B) 4/9 C) 5/9 D) 8/9
• Hint: For 5/8 − 2/8, keep the denominator and subtract the tops: 5 − 2 = 3, so 3/8.
• Steps:
  • The denominators are the same (9).
  • Subtract the numerators: 6 − 2 = 4.
  • The answer is 4/9.
• Answer: 4/9

[Medium] Table Word Problem

• EN: The table below shows items at Tim Hortons. | Item | Price | | Coffee | $2.00 | | Muffin | $1.75 | | Bagel | $2.50 | Nadia buys 2 coffees and 1 bagel. How much does she spend?
• FR: Le tableau ci-dessous montre des articles chez Tim Hortons. | Article | Prix | | Café | 2,00 $ | | Muffin | 1,75 $ | | Bagel | 2,50 $ | Nadia achète 2 cafés et 1 bagel. Combien dépense-t-elle?
• Choices: A) $5.50 B) $6.00 C) $6.25 D) $6.50
• Hint: For 2 items at $3.00 and 1 item at $1.50: 2 × $3.00 + $1.50 = $7.50.
• Steps:
  • 2 coffees: 2 × $2.00 = $4.00.
  • 1 bagel: $2.50.
  • Total: $4.00 + $2.50 = $6.50.
• Answer: $6.50

[Hard] Multi-Digit Division

• EN: A box factory made 2 184 boxes and packed them equally into 8 crates. How many boxes went in each crate?
• FR: Une fabrique de boîtes a fabriqué 2 184 boîtes et les a placées également dans 8 caisses. Combien de boîtes y a-t-il dans chaque caisse?
• Choices: A) 263 B) 270 C) 273 D) 280
• Hint: For 1 806 ÷ 6, divide step by step: 18 ÷ 6 = 3, bring down 0: 0 ÷ 6 = 0, bring down 6: 6 ÷ 6 = 1, giving 301.
• Steps:
  • Divide 2 184 ÷ 8.
  • 8 × 200 = 1 600; remainder 2 184 − 1 600 = 584.
  • 8 × 70 = 560; remainder 584 − 560 = 24.
  • 8 × 3 = 24; remainder 0.
  • 200 + 70 + 3 = 273.
• Answer: 273

[Hard] Percentage — 25% and 10%

• EN: A winter jacket costs $120. It is on sale for 25% off. What is the sale price of the jacket?
• FR: Un manteau d'hiver coûte 120 $. Il est en solde à 25 % de rabais. Quel est le prix de solde du manteau?
• Choices: A) $85 B) $88 C) $90 D) $95
• Hint: 25% of $80 = $80 ÷ 4 = $20; sale price = $80 − $20 = $60.
• Steps:
  • Find 25% of $120: $120 ÷ 4 = $30.
  • Subtract the discount: $120 − $30 = $90.
  • The sale price is $90.
• Answer: $90

[Easy] Fraction Multiplication

• EN: What is 1/3 × 12?
• FR: Combien fait 1/3 × 12?
• Choices: A) 3 B) 4 C) 6 D) 9
• Hint: 1/4 × 20 means 20 ÷ 4 = 5.
• Steps:
  • 1/3 × 12 means divide 12 by 3.
  • 12 ÷ 3 = 4.
  • So the answer is 4.
• Answer: 4

[Easy] Ratio

• EN: In a bag of marbles, there are 6 red and 9 blue marbles. What is the ratio of red to blue marbles?
• FR: Dans un sac de billes, il y a 6 billes rouges et 9 billes bleues. Quel est le rapport des billes rouges aux billes bleues?
• Choices: A) 2:3 B) 3:2 C) 1:3 D) 3:1
• Hint: Simplify 4:6 by dividing both by 2: 4 ÷ 2 = 2, 6 ÷ 2 = 3, so 2:3.
• Steps:
  • Red : Blue = 6 : 9.
  • Divide both by 3: 6 ÷ 3 = 2, 9 ÷ 3 = 3.
  • Simplified ratio is 2:3.
• Answer: 2:3

[Easy] Percent of a Number

• EN: What is 30% of 50?
• FR: Combien fait 30% de 50?
• Choices: A) 10 B) 15 C) 20 D) 25
• Hint: 20% of 60 = 0.20 × 60 = 12.
• Steps:
  • 30% = 0.30.
  • 0.30 × 50 = 15.
  • So 30% of 50 is 15.
• Answer: 15

[Easy] Integers — Introduction

• EN: Which integer is greater: −5 or −2?
• FR: Quel entier est plus grand: −5 ou −2?
• Choices: A) −5 B) −2 C) They are equal D) 0
• Hint: On a number line, numbers to the right are greater: −8 is to the left of −3, so −3 > −8.
• Steps:
  • On a number line, −2 is to the right of −5.
  • Numbers to the right are greater.
  • So −2 > −5.
• Answer: −2

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1
• FR: Calcule: 3 + 4 × 2 − 1
• Choices: A) 10 B) 12 C) 13 D) 14
• Hint: For 5 + 3 × 2, do multiplication first: 3 × 2 = 6, then 5 + 6 = 11.
• Steps:
  • Follow BEDMAS: multiplication first.
  • 4 × 2 = 8.
  • Now: 3 + 8 − 1 = 10.
  • The answer is 10.
• Answer: 10

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien fait 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 2
• Hint: For 2/3 ÷ 1/4, flip the second fraction and multiply: 2/3 × 4/1 = 8/3.
• Steps:
  • Dividing by 1/2 means multiplying by 2/1.
  • 3/4 × 2/1 = 6/4 = 3/2.
  • So the answer is 3/2.
• Answer: 3/2

[Medium] Simple Algebraic Expression

• EN: If n = 5, what is the value of 3n + 7?
• FR: Si n = 5, quelle est la valeur de 3n + 7?
• Choices: A) 20 B) 22 C) 24 D) 25
• Hint: For 2n + 4 when n = 3: 2 × 3 + 4 = 6 + 4 = 10.
• Steps:
  • Replace n with 5: 3(5) + 7.
  • 3 × 5 = 15.
  • 15 + 7 = 22.
• Answer: 22

[Medium] Table Word Problem — Multi-Step

• EN: The table shows snowfall data. | Day | Snowfall | | Monday | 8 cm | | Tuesday | 12 cm | | Wednesday | 5 cm | A snow plow can clear 30 cm in one trip. How many centimetres of snowfall remain to clear after one trip?
• FR: Le tableau montre les données de chutes de neige. | Jour | Chute de neige | | Lundi | 8 cm | | Mardi | 12 cm | | Mercredi | 5 cm | Une charrue peut déblayer 30 cm en un passage. Combien de centimètres de neige restent à déblayer après un passage?
• Choices: A) 0 cm B) 3 cm C) 5 cm D) 7 cm
• Hint: Find the total first, then subtract what was cleared: if 18 cm fell and 15 cm was cleared, 3 cm remains.
• Steps:
  • Total snowfall: 8 + 12 + 5 = 25 cm.
  • The plow clears 30 cm but only 25 cm fell.
  • 25 − 25 = 0 cm remain.
  • So 0 cm of snowfall remains to clear.
• Answer: 0 cm

[Hard] Rate Problem

• EN: A car travels 270 km in 3 hours. At the same speed, how far will it travel in 5 hours?
• FR: Une voiture parcourt 270 km en 3 heures. À la même vitesse, quelle distance parcourra-t-elle en 5 heures?
• Choices: A) 400 km B) 430 km C) 450 km D) 470 km
• Hint: For 180 km in 4 hours, speed = 45 km/h; in 7 hours: 45 × 7 = 315 km.
• Steps:
  • Speed = 270 ÷ 3 = 90 km/h.
  • Distance in 5 hours = 90 × 5 = 450 km.
  • The car will travel 450 km.
• Answer: 450 km

[Hard] BEDMAS — Complex Expression

• EN: Evaluate: (5 + 3)² ÷ 4 − 6
• FR: Calcule: (5 + 3)² ÷ 4 − 6
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: For (2 + 4)² ÷ 3 − 1: brackets first (6² = 36), then ÷ 3 = 12, then − 1 = 11.
• Steps:
  • Brackets first: 5 + 3 = 8.
  • Exponent: 8² = 64.
  • Division: 64 ÷ 4 = 16.
  • Subtraction: 16 − 6 = 10.
• Answer: 10

[Easy] Integer Addition

• EN: What is −8 + 5?
• FR: Combien fait −8 + 5?
• Choices: A) −13 B) −3 C) 3 D) 13
• Hint: For −6 + 4, start at −6 and move 4 steps right on the number line: −5, −4, −3, −2.
• Steps:
  • Start at −8 and add 5.
  • Move 5 steps right: −8, −7, −6, −5, −4, −3.
  • The answer is −3.
• Answer: −3

[Easy] Fraction Fluency

• EN: What is 3/5 of 25?
• FR: Combien fait 3/5 de 25?
• Choices: A) 10 B) 12 C) 15 D) 20
• Hint: 2/3 of 12 = (12 ÷ 3) × 2 = 4 × 2 = 8.
• Steps:
  • Divide by the denominator: 25 ÷ 5 = 5.
  • Multiply by the numerator: 5 × 3 = 15.
  • So 3/5 of 25 is 15.
• Answer: 15

[Easy] Percent — Discount

• EN: A pair of skates costs $80. They are on sale for 20% off. How much is the discount?
• FR: Une paire de patins coûte 80 $. Ils sont soldés à 20 % de rabais. Quel est le montant du rabais?
• Choices: A) $12 B) $14 C) $16 D) $18
• Hint: 10% of $60 = $6; 20% = 2 × $6 = $12.
• Steps:
  • Find 20% of $80.
  • 10% of $80 = $8.
  • 20% = 2 × $8 = $16.
  • The discount is $16.
• Answer: $16

[Easy] Integer Subtraction

• EN: What is 4 − (−3)?
• FR: Combien fait 4 − (−3)?
• Choices: A) 1 B) 6 C) 7 D) 9
• Hint: Subtracting a negative is the same as adding a positive: 5 − (−2) = 5 + 2 = 7.
• Steps:
  • Subtracting −3 is the same as adding 3.
  • 4 + 3 = 7.
  • So the answer is 7.
• Answer: 7

[Medium] One-Step Linear Equation

• EN: Solve for x: 3x = 21
• FR: Résous pour x: 3x = 21
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: For 5x = 35, divide both sides by 5: x = 35 ÷ 5 = 7.
• Steps:
  • Divide both sides by 3.
  • x = 21 ÷ 3 = 7.
  • Check: 3 × 7 = 21. ✓
• Answer: x = 7

[Medium] Percent — Tip

• EN: A restaurant bill is $45.00. If you leave a 15% tip, how much is the tip?
• FR: Une facture de restaurant est de 45,00 $. Si tu laisses un pourboire de 15 %, combien est le pourboire?
• Choices: A) $5.25 B) $6.00 C) $6.75 D) $7.50
• Hint: 15% of $60 = 10% of $60 + 5% of $60 = $6 + $3 = $9.
• Steps:
  • 10% of $45 = $4.50.
  • 5% of $45 = $2.25.
  • 15% = $4.50 + $2.25 = $6.75.
• Answer: $6.75

[Medium] Surface Area of a Rectangular Prism

• EN: A box is 3 cm long, 4 cm wide, and 5 cm tall. What is its surface area?
• FR: Une boîte mesure 3 cm de long, 4 cm de large et 5 cm de haut. Quelle est son aire de surface?
• Choices: A) 74 cm² B) 82 cm² C) 94 cm² D) 100 cm²
• Hint: Surface area = 2(lw + lh + wh). For 2 × 3 × 4: 2(6 + 8 + 12) = 2 × 26 = 52 cm².
• Steps:
  • 2(lw + lh + wh) = 2(3×4 + 3×5 + 4×5).
  • = 2(12 + 15 + 20).
  • = 2 × 47 = 94 cm².
• Answer: 94 cm²

[Medium] Table Word Problem

• EN: The table shows prices for a school fundraiser. | Item | Price | | Bracelet | $3.50 | | Bookmark | $1.25 | | Keychain | $2.75 | Sofia bought 2 bracelets and 3 bookmarks. She paid with a $20 bill. How much change did she receive?
• FR: Le tableau montre les prix d'une collecte de fonds scolaire. | Article | Prix | | Bracelet | 3,50 $ | | Signet | 1,25 $ | | Porte-clés | 2,75 $ | Sofia a acheté 2 bracelets et 3 signets. Elle a payé avec un billet de 20 $. Quelle monnaie a-t-elle reçue?
• Choices: A) $8.25 B) $9.25 C) $10.50 D) $11.25
• Hint: For 1 item at $4 and 2 at $2.50: total = $4 + $5 = $9; change from $20 = $11.
• Steps:
  • 2 bracelets: 2 × $3.50 = $7.00.
  • 3 bookmarks: 3 × $1.25 = $3.75.
  • Total: $7.00 + $3.75 = $10.75.
  • Change: $20.00 − $10.75 = $9.25.
• Answer: $9.25

[Hard] Integer Operations — Multi-Step

• EN: What is (−6) × (−3) + (−4) × 2?
• FR: Combien fait (−6) × (−3) + (−4) × 2?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: For (−5) × (−2) + (−3) × 3: 10 + (−9) = 1.
• Steps:
  • (−6) × (−3) = 18 (negative × negative = positive).
  • (−4) × 2 = −8.
  • 18 + (−8) = 18 − 8 = 10.
• Answer: 10

[Hard] Probability

• EN: A bag contains 3 red, 5 blue, 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 piges une bille au hasard, quelle est la probabilité de piger une bille bleue?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 3/10
• Hint: Probability = favourable outcomes ÷ total outcomes. For 4 red out of 12 total: 4/12 = 1/3.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Blue marbles: 5.
  • Probability = 5/10 = 1/2.
• Answer: 1/2

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: √100 = 10 because 10 × 10 = 100.
• Steps:
  • Ask: what number times itself gives 144?
  • 12 × 12 = 144. ✓
  • So √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Find the mean of: 8, 12, 10, 14, 6.
• FR: Trouve la moyenne de: 8, 12, 10, 14, 6.
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: For 4, 6, 8: add them (18), then divide by how many there are (3): 18 ÷ 3 = 6.
• Steps:
  • Add all values: 8 + 12 + 10 + 14 + 6 = 50.
  • Divide by the count of values: 50 ÷ 5 = 10.
  • The mean is 10.
• Answer: 10

[Easy] Two-Step Equation — Setup

• EN: Solve: 2x + 3 = 11
• FR: Résous: 2x + 3 = 11
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: For 3x + 2 = 14: subtract 2 first (3x = 12), then divide by 3 (x = 4).
• Steps:
  • Subtract 3 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
  • Check: 2(4) + 3 = 11. ✓
• Answer: x = 4

[Easy] Percent Increase

• EN: A hockey team won 20 games last year and 25 games this year. What is the percent increase?
• FR: Une équipe de hockey a gagné 20 matchs l'année dernière et 25 cette année. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: % increase = (change ÷ original) × 100. For going from 40 to 50: (10 ÷ 40) × 100 = 25%.
• Steps:
  • Change = 25 − 20 = 5.
  • % increase = (5 ÷ 20) × 100 = 25%.
  • The percent increase is 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: For legs 3 and 4: c² = 3² + 4² = 9 + 16 = 25, so c = 5.
• Steps:
  • c² = a² + b² = 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10.
  • The hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Two-Step Linear Equation

• EN: Solve: 5x − 7 = 18
• FR: Résous: 5x − 7 = 18
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: For 4x − 3 = 13: add 3 to both sides (4x = 16), then divide by 4 (x = 4).
• Steps:
  • Add 7 to both sides: 5x = 25.
  • Divide both sides by 5: x = 5.
  • Check: 5(5) − 7 = 25 − 7 = 18. ✓
• Answer: x = 5

[Medium] Slope Introduction

• EN: A line passes through (0, 2) and (4, 10). What is the slope of the line?
• FR: Une droite passe par (0, 2) et (4, 10). Quel est la pente de cette droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). For (0, 1) and (3, 7): (7−1)÷(3−0) = 6÷3 = 2.
• Steps:
  • Rise = 10 − 2 = 8.
  • Run = 4 − 0 = 4.
  • Slope = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of: 3, 9, 5, 7, 5, 11, 5.
• FR: Trouve la médiane de: 3, 9, 5, 7, 5, 11, 5.
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: For 2, 4, 6, 8, 10: order them (already ordered), middle value is the 3rd out of 5 = 6.
• Steps:
  • Order the values: 3, 5, 5, 5, 7, 9, 11.
  • There are 7 values; the middle (4th) value is 5.
  • The median is 5.
• Answer: 5

[Hard] Pythagorean Theorem — Find a Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et un côté de 5 cm. Quelle est la longueur de l'autre côté?
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: For hypotenuse 10 and leg 6: b² = 10² − 6² = 100 − 36 = 64, so b = 8.
• Steps:
  • a² + b² = c²: 5² + b² = 13².
  • 25 + b² = 169.
  • b² = 144.
  • b = √144 = 12.
• Answer: 12 cm

[Hard] Percent Decrease — Multi-Step

• EN: A winter coat was priced at $180. Its price was decreased by 15%, then decreased again by 10% of the new price. What is the final price?
• FR: Un manteau d'hiver était au prix de 180 $. Son prix a été réduit de 15 %, puis réduit à nouveau de 10 % du nouveau prix. Quel est le prix final?
• Choices: A) $132.30 B) $137.70 C) $140.40 D) $143.00
• Hint: For 20% off $200 = $160; then 10% off $160 = $16 off; final = $144.
• Steps:
  • First discount: 15% of $180 = $27; new price = $180 − $27 = $153.
  • Second discount: 10% of $153 = $15.30; final price = $153 − $15.30 = $137.70.
• Answer: $137.70

[Easy] Solving a Linear Equation

• EN: Solve for x: 2x + 4 = 14
• FR: Résous pour x: 2x + 4 = 14
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: For 3x + 5 = 20, subtract 5 (3x = 15), divide by 3: x = 5.
• Steps:
  • Subtract 4 from both sides: 2x = 10.
  • Divide by 2: x = 5.
  • Check: 2(5) + 4 = 14. ✓
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3)
• FR: Simplifie: (3x + 5) + (2x − 3)
• Choices: A) 4x + 2 B) 5x + 2 C) 5x + 8 D) 6x − 2
• Hint: For (4x + 3) + (x − 1): combine like terms: 4x + x = 5x, and 3 − 1 = 2, giving 5x + 2.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2.
  • Simplified: 5x + 2.
• Answer: 5x + 2

[Easy] Slope-Intercept Form

• EN: What is the y-intercept of the line y = 4x − 7?
• FR: Quelle est l'ordonnée à l'origine de la droite y = 4x − 7?
• Choices: A) −7 B) 4 C) 7 D) −4
• Hint: In y = mx + b, the y-intercept is b. For y = 3x + 5, b = 5.
• Steps:
  • The equation is y = 4x − 7, which is in the form y = mx + b.
  • Here m = 4 and b = −7.
  • The y-intercept is −7.
• Answer: −7

[Easy] Linear Inequality

• EN: Which value of x satisfies the inequality x − 3 > 4?
• FR: Quelle valeur de x satisfait l'inégalité x − 3 > 4?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Solve x − 2 > 5 by adding 2: x > 7, so any value greater than 7 works.
• Steps:
  • Add 3 to both sides: x > 7.
  • Check which choice is greater than 7.
  • x = 8 satisfies x > 7. ✓
• Answer: x = 8

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 4)
• FR: Développe: (x + 3)(x + 4)
• Choices: A) x² + 6x + 12 B) x² + 7x + 12 C) x² + 7x + 7 D) x² + 12x + 7
• Hint: For (x + 2)(x + 5), use FOIL: x² + 5x + 2x + 10 = x² + 7x + 10.
• Steps:
  • FOIL: First: x · x = x².
  • Outer: x · 4 = 4x.
  • Inner: 3 · x = 3x.
  • Last: 3 · 4 = 12.
  • Sum: x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in the ratio 2:5. The shorter triangle has a side of 8 cm. What is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans le rapport 2:5. Le petit triangle a un côté de 8 cm. Quel est le côté correspondant du grand triangle?
• Choices: A) 15 cm B) 18 cm C) 20 cm D) 25 cm
• Hint: For ratio 3:7 and shorter side 6: 6 ÷ 3 = 2 (scale factor), so longer = 2 × 7 = 14 cm.
• Steps:
  • Scale factor = 8 ÷ 2 = 4.
  • Larger side = 4 × 5 = 20 cm.
• Answer: 20 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin θ?
• FR: Dans un triangle rectangle, le côté opposé est 6 cm et l'hypoténuse est 10 cm. Combien fait sin θ?
• Choices: A) 0.5 B) 0.6 C) 0.75 D) 0.8
• Hint: SOH: sin = opposite ÷ hypotenuse. For opposite = 4 and hypotenuse = 8: sin = 4/8 = 0.5.
• Steps:
  • sin θ = opposite ÷ hypotenuse.
  • sin θ = 6 ÷ 10 = 0.6.
• Answer: 0.6

[Medium] Graphing Lines

• EN: A line has slope 3 and passes through (0, −2). Which equation represents this line?
• FR: Une droite a une pente de 3 et passe par (0, −2). Quelle équation représente cette droite?
• Choices: A) y = 3x + 2 B) y = −2x + 3 C) y = 3x − 2 D) y = 2x − 3
• Hint: For slope 5 and y-intercept 1: y = 5x + 1.
• Steps:
  • Use y = mx + b form.
  • m = 3 (slope), b = −2 (y-intercept).
  • Equation: y = 3x − 2.
• Answer: y = 3x − 2

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is the value of cos θ?
• FR: Dans un triangle rectangle, le côté adjacent est 5 cm et l'hypoténuse est 13 cm. Quelle est la valeur de cos θ?
• Choices: A) 5/12 B) 5/13 C) 12/13 D) 13/5
• Hint: CAH: cos = adjacent ÷ hypotenuse. For adjacent = 3 and hypotenuse = 5: cos = 3/5.
• Steps:
  • cos θ = adjacent ÷ hypotenuse.
  • cos θ = 5 ÷ 13 = 5/13.
• Answer: 5/13

[Hard] Solving a System by Substitution

• EN: Solve the system: y = 2x + 1 and y = x + 4. What is the value of x?
• FR: Résous le système: y = 2x + 1 et y = x + 4. Quelle est la valeur de x?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: For y = x + 2 and y = 3x − 4, set equal: x + 2 = 3x − 4 → 6 = 2x → x = 3.
• Steps:
  • Set the equations equal: 2x + 1 = x + 4.
  • Subtract x from both sides: x + 1 = 4.
  • Subtract 1: x = 3.
  • Check: y = 2(3) + 1 = 7; y = 3 + 4 = 7. ✓
• Answer: x = 3

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6
• FR: Factorise: x² + 5x + 6
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 3) D) (x + 2)(x + 4)
• Hint: For x² + 7x + 12, find two numbers that multiply to 12 and add to 7: 3 and 4, giving (x + 3)(x + 4).
• Steps:
  • Find two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5. ✓
  • So x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, the angle θ = 30°. The hypotenuse is 10 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, l'angle θ = 30°. L'hypoténuse mesure 10 cm. Quelle est la longueur du côté opposé?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: sin 30° = 0.5. For hypotenuse = 8: opposite = 0.5 × 8 = 4 cm.
• Steps:
  • sin 30° = opposite ÷ hypotenuse.
  • 0.5 = opposite ÷ 10.
  • Opposite = 0.5 × 10 = 5 cm.
• Answer: 5 cm

[Easy] Volume of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 7 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 7 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 169.56 cm³ B) 179.56 cm³ C) 189.56 cm³ D) 197.82 cm³
• Hint: V = πr²h. For r = 2 and h = 5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × r² × h.
  • V = 3.14 × 9 × 7.
  • V = 3.14 × 63 = 197.82 cm³.
• Answer: 197.82 cm³

[Easy] Systems of Equations — Simple

• EN: Solve the system: x + y = 10 and x − y = 4. What is x?
• FR: Résous le système: x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the equations: (x + y) + (x − y) = total; the y's cancel and you solve for x.
• Steps:
  • Add the equations: (x + y) + (x − y) = 10 + 4.
  • 2x = 14.
  • x = 7.
• Answer: x = 7

[Medium] Completing the Square

• EN: Rewrite x² + 6x + 5 in completed square form. What is the vertex of the parabola?
• FR: Réécris x² + 6x + 5 sous forme de carré complété. Quel est le sommet de la parabole?
• Choices: A) (−3, −4) B) (3, −4) C) (−3, 4) D) (3, 4)
• Hint: For x² + 4x + 1: complete the square → (x + 2)² − 3, vertex at (−2, −3).
• Steps:
  • x² + 6x + 5 = (x² + 6x + 9) − 9 + 5.
  • = (x + 3)² − 4.
  • Vertex form is (x + 3)² − 4, so vertex is (−3, −4).
• Answer: (−3, −4)

[Medium] Circle Geometry

• EN: A chord is 8 cm long and its perpendicular bisector passes through the centre of a circle with radius 5 cm. What is the distance from the centre to the chord?
• FR: Une corde mesure 8 cm et sa médiatrice passe par le centre d'un cercle de rayon 5 cm. Quelle est la distance du centre à la corde?
• Choices: A) 2 cm B) 3 cm C) 4 cm D) 5 cm
• Hint: For chord = 6 cm in a circle of radius 5: half chord = 3; d = √(5² − 3²) = √16 = 4.
• Steps:
  • Half the chord = 8 ÷ 2 = 4 cm.
  • Use Pythagorean theorem: d² + 4² = 5².
  • d² = 25 − 16 = 9.
  • d = 3 cm.
• Answer: 3 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 6 = 0. What are the roots?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 6 = 0. Quelles sont les racines?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = −2 and x = −3 D) x = 1 and x = 5
• Hint: For x² − 7x + 12 = 0, factor to (x − 3)(x − 4) = 0, so x = 3 or x = 4.
• Steps:
  • Factor or use the formula: a = 1, b = −5, c = 6.
  • Discriminant: (−5)² − 4(1)(6) = 25 − 24 = 1.
  • x = (5 ± 1) ÷ 2: x = 3 or x = 2.
• Answer: x = 2 and x = 3

[Medium] Trigonometry — Cosine Rule

• EN: In triangle ABC, side a = 7 cm, side b = 5 cm, and angle C = 60°. What is side c? (Use c² = a² + b² − 2ab cos C)
• FR: Dans le triangle ABC, le côté a = 7 cm, le côté b = 5 cm, et l'angle C = 60°. Combien mesure le côté c? (Utilise c² = a² + b² − 2ab cos C)
• Choices: A) √29 cm B) √39 cm C) √49 cm D) √59 cm
• Hint: For a = 3, b = 4, C = 60°: c² = 9 + 16 − 24(0.5) = 25 − 12 = 13; c = √13.
• Steps:
  • c² = 7² + 5² − 2(7)(5) cos 60°.
  • c² = 49 + 25 − 70(0.5).
  • c² = 74 − 35 = 39.
  • c = √39 cm.
• Answer: √39 cm

[Hard] Systems of Equations — Elimination

• EN: Solve the system: 3x + 2y = 16 and 5x − 2y = 8. What is x?
• FR: Résous le système: 3x + 2y = 16 et 5x − 2y = 8. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Add equations with opposite-sign terms: (2x + 3y) + (4x − 3y) eliminates y, then solve for x.
• Steps:
  • Add the equations: (3x + 2y) + (5x − 2y) = 16 + 8.
  • 8x = 24.
  • x = 3.
  • Check: 3(3) + 2y = 16 → 2y = 7 → y = 3.5; 5(3) − 2(3.5) = 15 − 7 = 8. ✓
• Answer: x = 3

[Hard] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 9 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 9 cm. Quelle est son aire de surface totale? (Utilise π ≈ 3,14)
• Choices: A) 150.72 cm² B) 163.28 cm² C) 175.84 cm² D) 188.40 cm²
• Hint: Total surface area of a cone = πr² + πrl. For r = 3, l = 5: 3.14 × 9 + 3.14 × 3 × 5 = 28.26 + 47.1 = 75.36.
• Steps:
  • Base area = π × 4² = 3.14 × 16 = 50.24 cm².
  • Lateral area = π × 4 × 9 = 3.14 × 36 = 113.04 cm².
  • Total = 50.24 + 113.04 = 163.28 cm².
• Answer: 163.28 cm²

[Easy] Quadratic Function — Vertex

• EN: The function f(x) = (x − 3)² + 5 is a parabola. What is its vertex?
• FR: La fonction f(x) = (x − 3)² + 5 est une parabole. Quel est son sommet?
• Choices: A) (3, 5) B) (−3, 5) C) (5, 3) D) (3, −5)
• Hint: In f(x) = (x − h)² + k, the vertex is at (h, k). For f(x) = (x − 2)² + 7, vertex is (2, 7).
• Steps:
  • The function is in vertex form: f(x) = (x − h)² + k.
  • Here h = 3 and k = 5.
  • The vertex is (3, 5).
• Answer: (3, 5)

[Easy] Exponential Function

• EN: If f(x) = 2ˣ, what is f(4)?
• FR: Si f(x) = 2ˣ, combien fait f(4)?
• Choices: A) 8 B) 10 C) 16 D) 32
• Hint: For f(x) = 3ˣ: f(3) = 3³ = 3 × 3 × 3 = 27.
• Steps:
  • f(4) = 2⁴ = 2 × 2 × 2 × 2 = 16.
• Answer: 16

[Easy] Logarithm — Basic

• EN: What is log₂(8)?
• FR: Combien fait log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: log₃(27) = 3 because 3³ = 27.
• Steps:
  • Ask: 2 to what power equals 8?
  • 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 4 and the common difference is 7. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 4 et la raison est 7. Quel est le 5e terme?
• Choices: A) 28 B) 30 C) 32 D) 35
• Hint: For a₁ = 2 and d = 5: a₅ = 2 + (5−1) × 5 = 2 + 20 = 22.
• Steps:
  • aₙ = a₁ + (n − 1)d.
  • a₅ = 4 + (5 − 1) × 7 = 4 + 28 = 32.
• Answer: 32

[Medium] Compound Interest

• EN: Sara invests $1 000 at an annual interest rate of 5%, compounded annually. How much will she have after 3 years?
• FR: Sara investit 1 000 $ à un taux d'intérêt annuel de 5 %, composé annuellement. Combien aura-t-elle après 3 ans?
• Choices: A) $1 150.00 B) $1 157.63 C) $1 160.00 D) $1 166.40
• Hint: For $500 at 4% for 2 years: A = 500 × (1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • A = P(1 + r)ⁿ = 1000 × (1.05)³.
  • (1.05)³ = 1.157625.
  • A = 1000 × 1.157625 = $1 157.63.
• Answer: $1 157.63

[Medium] Trigonometric Identity

• EN: Which identity is always true?
• FR: Quelle identité est toujours vraie?
• Choices: A) sin²θ + cos²θ = 2 B) sin²θ + cos²θ = 1 C) sin²θ − cos²θ = 1 D) sinθ × cosθ = 1
• Hint: The most fundamental trig identity relates sin and cos squared, and their sum equals a whole number.
• Steps:
  • The Pythagorean identity states: sin²θ + cos²θ = 1.
  • This holds for all values of θ.
• Answer: sin²θ + cos²θ = 1

[Medium] Geometric Series Sum

• EN: Find the sum of the first 4 terms of the geometric series: 3, 6, 12, 24, …
• FR: Trouve la somme des 4 premiers termes de la série géométrique: 3, 6, 12, 24, …
• Choices: A) 40 B) 42 C) 45 D) 48
• Hint: For 2, 4, 8, 16: sum = 2 + 4 + 8 + 16 = 30. Or use Sₙ = a(rⁿ − 1)/(r − 1) = 2(16 − 1)/1 = 30.
• Steps:
  • S₄ = 3 + 6 + 12 + 24.
  • = 9 + 36 = 45.
• Answer: 45

[Medium] Logarithm — Solving

• EN: Solve: log₃(x) = 4
• FR: Résous: log₃(x) = 4
• Choices: A) x = 12 B) x = 64 C) x = 81 D) x = 100
• Hint: For log₄(x) = 3, rewrite as 4³ = x, so x = 64.
• Steps:
  • Rewrite in exponential form: 3⁴ = x.
  • 3⁴ = 81.
  • So x = 81.
• Answer: x = 81

[Hard] Annuity — Future Value

• EN: Mia deposits $500 at the end of each year for 4 years at 6% per year compounded annually. What is the future value of this annuity? (Use FV = PMT × [(1+r)ⁿ − 1]/r)
• FR: Mia dépose 500 $ à la fin de chaque année pendant 4 ans à 6 % par an composé annuellement. Quelle est la valeur future de cette rente? (Utilise FV = PMT × [(1+r)ⁿ − 1]/r)
• Choices: A) $2 000.00 B) $2 187.31 C) $2 247.30 D) $2 300.00
• Hint: For $200/year, 3 years, 5%: FV = 200 × [(1.05)³ − 1]/0.05 = 200 × 3.1525 = $630.50.
• Steps:
  • FV = 500 × [(1.06)⁴ − 1] / 0.06.
  • (1.06)⁴ = 1.26247696.
  • (1.26247696 − 1) = 0.26247696.
  • 0.26247696 ÷ 0.06 = 4.374616.
  • FV = 500 × 4.374616 = $2 187.31.
• Answer: $2 187.31

[Hard] Function Transformations

• EN: The function f(x) = x² is transformed to g(x) = −2(x + 3)² + 1. Which statement correctly describes the transformation?
• FR: La fonction f(x) = x² est transformée en g(x) = −2(x + 3)² + 1. Quelle affirmation décrit correctement la transformation?
• Choices: A) Reflected over x-axis, stretched by 2, shifted right 3 and up 1 B) Reflected over x-axis, stretched by 2, shifted left 3 and up 1 C) Reflected over y-axis, stretched by 2, shifted left 3 and down 1 D) Stretched by 2, shifted right 3 and up 1
• Hint: In a(x − h)² + k: a < 0 means reflection over x-axis, |a| > 1 means vertical stretch, h is horizontal shift (opposite sign), k is vertical shift.
• Steps:
  • a = −2: negative means reflected over x-axis; |−2| = 2 means vertical stretch by 2.
  • (x + 3) means h = −3: shifted left 3.
  • k = 1: shifted up 1.
  • So: reflected, stretched by 2, left 3, up 1.
• Answer: Reflected over x-axis, stretched by 2, shifted left 3 and up 1

[Easy] Permutations

• EN: How many ways can 4 different books be arranged on a shelf?
• FR: De combien de façons peut-on arranger 4 livres différents sur une étagère?
• Choices: A) 16 B) 20 C) 24 D) 32
• Hint: For 3 books, arrangements = 3! = 3 × 2 × 1 = 6.
• Steps:
  • 4 books can be arranged in 4! ways.
  • 4! = 4 × 3 × 2 × 1 = 24.
• Answer: 24

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 6?
• FR: De combien de façons peut-on choisir 2 étudiants dans un groupe de 6?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: C(5, 2) = 5! / (2! × 3!) = (5 × 4) / (2 × 1) = 10.
• Steps:
  • C(6, 2) = 6! / (2! × 4!) = (6 × 5) / (2 × 1) = 30 / 2 = 15.
• Answer: 15

[Easy] Derivative — Power Rule

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

[Easy] Polynomial Function — End Behaviour

• EN: For the polynomial f(x) = −2x⁴ + 3x − 1, what happens to f(x) as x → +∞?
• FR: Pour le polynôme f(x) = −2x⁴ + 3x − 1, que se passe-t-il avec f(x) quand x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: The leading term dominates. For −3x⁶, as x → ∞, the result is −∞ because of the negative leading coefficient and even degree.
• Steps:
  • The leading term is −2x⁴.
  • As x → +∞, x⁴ → +∞.
  • Multiplied by −2, the result → −∞.
• Answer: f(x) → −∞

[Medium] Derivative — Rate of Change

• EN: A ball's position is given by s(t) = 4t² − 3t + 2. What is the velocity (rate of change) at t = 3?
• FR: La position d'une balle est donnée par s(t) = 4t² − 3t + 2. Quelle est la vitesse (taux de variation) à t = 3?
• Choices: A) 18 B) 21 C) 24 D) 33
• Hint: First differentiate: s'(t) = 8t − 3, then substitute the given t value.
• Steps:
  • s'(t) = 8t − 3.
  • s'(3) = 8(3) − 3 = 24 − 3 = 21.
  • The velocity at t = 3 is 21.
• Answer: 21

[Medium] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: Une pièce équilibrée est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces?
• Choices: A) 1/8 B) 3/16 C) 1/4 D) 5/16
• Hint: P(k successes) = C(n, k) × pᵏ × (1−p)ⁿ⁻ᵏ. For n = 3, k = 2, p = 0.5: C(3,2)(0.5)²(0.5)¹ = 3/8.
• Steps:
  • P(X = 3) = C(4, 3) × (0.5)³ × (0.5)¹.
  • C(4, 3) = 4.
  • P = 4 × (1/8) × (1/2) = 4/16 = 1/4.
• Answer: 1/4

[Medium] Vectors — Addition

• EN: Vector a = (3, −1) and vector b = (−2, 5). What is a + b?
• FR: Le vecteur a = (3, −1) et le vecteur b = (−2, 5). Combien fait a + b?
• Choices: A) (1, 4) B) (5, 4) C) (1, 6) D) (5, −6)
• Hint: Add component by component: (a₁ + b₁, a₂ + b₂). For (4, 2) + (−1, 3) = (3, 5).
• Steps:
  • Add x-components: 3 + (−2) = 1.
  • Add y-components: −1 + 5 = 4.
  • So a + b = (1, 4).
• Answer: (1, 4)

[Medium] Rational Function — Vertical Asymptote

• EN: For the rational function f(x) = (x + 2) / (x − 3), what is the vertical asymptote?
• FR: Pour la fonction rationnelle f(x) = (x + 2) / (x − 3), quelle est l'asymptote verticale?
• Choices: A) x = −2 B) x = 2 C) x = 3 D) x = −3
• Hint: Set the denominator equal to zero: for (x − 5), x = 5 is the vertical asymptote.
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • x = 3.
  • The vertical asymptote is x = 3.
• Answer: x = 3

[Hard] Permutations With Restrictions

• EN: How many 4-letter arrangements can be made from the letters A, B, C, D, E if the letter A must always be first?
• FR: Combien d'arrangements de 4 lettres peut-on former avec les lettres A, B, C, D, E si la lettre A doit toujours être en premier?
• Choices: A) 20 B) 24 C) 30 D) 60
• Hint: Fix one item in position 1, then count arrangements of remaining items in remaining spots: for 5 letters with first fixed, arrange 4 from 4 remaining = 4! = 24.
• Steps:
  • A is fixed in position 1.
  • Choose and arrange 3 letters from the remaining 4 (B, C, D, E) for the remaining 3 spots.
  • P(4, 3) = 4 × 3 × 2 = 24.
• Answer: 24

[Hard] Derivative — Optimization

• EN: A farmer has 60 m of fencing to enclose a rectangular pen against a barn wall (one side needs no fencing). What length of the side perpendicular to the barn wall maximizes the area?
• FR: Un fermier dispose de 60 m de clôture pour enclore un enclos rectangulaire contre un mur de grange (un côté n'a pas besoin de clôture). Quelle longueur du côté perpendiculaire au mur maximise l'aire?
• Choices: A) 12 m B) 15 m C) 18 m D) 20 m
• Hint: For L m of fencing, one side open: 2x + y = L, A = xy = x(L − 2x); dA/dx = L − 4x = 0 gives x = L/4.
• Steps:
  • Let x = the length of each side perpendicular to the barn; y = side parallel to barn.
  • Constraint: 2x + y = 60, so y = 60 − 2x.
  • Area A = xy = x(60 − 2x) = 60x − 2x².
  • dA/dx = 60 − 4x = 0 → x = 15.
  • The optimal length is 15 m.
• Answer: 15 m