Daily Math — 2026-07-02

[Easy] Counting Candles

• EN: Mia has 7 birthday candles. She gets 5 more. How many candles does she have now?
• FR: Mia a 7 bougies d'anniversaire. Elle en reçoit 5 de plus. Combien de bougies a-t-elle maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add, count on from the bigger number — 6 + 3 means start at 6 and count up 3 more.
• Steps:
  • Start at 7.
  • Count up 5 more: 8, 9, 10, 11, 12.
• Answer: 12

[Easy] Hockey Pucks

• EN: There are 9 hockey pucks on the ice. 4 are taken away. How many pucks are left?
• FR: Il y a 9 rondelles de hockey sur la glace. On en enlève 4. Combien de rondelles reste-t-il?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: To subtract, count back — 8 − 2 means start at 8 and count back 2.
• Steps:
  • Start at 9.
  • Count back 4: 8, 7, 6, 5.
• Answer: 5

[Easy] Skip Counting by 2s

• EN: Count by 2s: 2, 4, 6, __, 10. What is the missing number?
• FR: Compte par 2: 2, 4, 6, __, 10. Quel est le nombre manquant?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Skip counting by 2s means adding 2 each time — 10, 12, 14, …
• Steps:
  • The pattern adds 2 each time.
  • 6 + 2 = 8.
• Answer: 8

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents?
• FR: Quelle pièce vaut 10 cents?
• Choices: A) Penny B) Nickel C) Dime D) Quarter
• Hint: A penny = 1¢, a nickel = 5¢, a dime = 10¢.
• Steps:
  • A penny is worth 1 cent.
  • A dime is worth 10 cents.
• Answer: Dime

[Medium] Snowflake Counting

• EN: Liam drew 14 snowflakes. He drew 6 more. How many snowflakes did he draw in all?
• FR: Liam a dessiné 14 flocons de neige. Il en dessine 6 de plus. Combien de flocons a-t-il dessinés en tout?
• Choices: A) 18 B) 19 C) 20 D) 21
• Hint: For 13 + 5, start at 13 and count up 5 to get 18.
• Steps:
  • Start at 14.
  • Count up 6: 15, 16, 17, 18, 19, 20.
• Answer: 20

[Medium] Compare Numbers

• EN: Which number is greater: 17 or 13?
• FR: Quel nombre est plus grand: 17 ou 13?
• Choices: A) 13 B) 17 C) They are equal D) 15
• Hint: Numbers with more tens are bigger — 20 is bigger than 12.
• Steps:
  • Both numbers have a 1 in the tens place.
  • Look at the ones: 7 is more than 3, so 17 is greater.
• Answer: 17

[Medium] Skip Counting by 5s

• EN: Count by 5s: 5, 10, 15, __, 25. What is the missing number?
• FR: Compte par 5: 5, 10, 15, __, 25. Quel est le nombre manquant?
• Choices: A) 18 B) 19 C) 20 D) 22
• Hint: Counting by 5s: 20, 25, 30, 35 — you add 5 each time.
• Steps:
  • The pattern adds 5 each time.
  • 15 + 5 = 20.
• Answer: 20

[Medium] Apples and Oranges

• EN: There are 8 apples and 9 oranges in a basket. How many pieces of fruit are there in total?
• FR: Il y a 8 pommes et 9 oranges dans un panier. Combien y a-t-il de fruits en tout?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: For 6 + 7, start at 7 and count up 6 to get 13.
• Steps:
  • Start at 9 (the bigger number).
  • Count up 8: 10, 11, 12, 13, 14, 15, 16, 17.
• Answer: 17

[Hard] Pennies in a Jar

• EN: Sofia has 10 pennies. She spends 3 pennies and then finds 5 more. How many pennies does she have now?
• FR: Sofia a 10 sous. Elle dépense 3 sous, puis en trouve 5 autres. Combien de sous a-t-elle maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: Do one step at a time — first subtract, then add with the result.
• Steps:
  • 10 − 3 = 7.
  • 7 + 5 = 12.
• Answer: 12

[Hard] Mystery Number

• EN: I am a number between 15 and 20. I am even. If you add 1 to me, you get 17. What number am I?
• FR: Je suis un nombre entre 15 et 20. Je suis pair. Si tu m'ajoutes 1, tu obtiens 17. Quel nombre suis-je?
• Choices: A) 14 B) 15 C) 16 D) 18
• Hint: If adding 1 gives you 13, then the mystery number is 12.
• Steps:
  • Adding 1 gives 17, so the number is 17 − 1 = 16.
  • 16 is between 15 and 20 and is even. ✓
• Answer: 16

[Easy] Telling Time

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: L'horloge montre la petite aiguille sur le 3 et la grande aiguille sur le 12. Quelle heure est-il?
• Choices: A) 12:00 B) 3:00 C) 3:30 D) 6:00
• Hint: When the long hand is on 12, it is exactly on the hour — 5 o'clock looks like this.
• Steps:
  • Short hand on 3 → the hour is 3.
  • Long hand on 12 → exactly on the hour.
• Answer: 3:00

[Easy] Adding to 100

• EN: 35 + 20 = ?
• FR: 35 + 20 = ?
• Choices: A) 45 B) 50 C) 55 D) 60
• Hint: For 42 + 30, add the tens: 4 + 3 = 7, so the answer is 72.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Keep the ones: 5.
  • 50 + 5 = 55.
• Answer: 55

[Easy] Measuring Length

• EN: A pencil is 15 cm long. A crayon is 9 cm long. How much longer is the pencil?
• FR: Un crayon est long de 15 cm. Un crayon de couleur est long de 9 cm. Combien le crayon est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: For 12 − 7, count up from 7 to 12: 8, 9, 10, 11, 12 — that's 5 steps.
• Steps:
  • Subtract: 15 − 9.
  • Count up from 9 to 15: 10, 11, 12, 13, 14, 15 — that is 6.
• Answer: 6 cm

[Easy] Counting Coins

• EN: You have 2 dimes and 1 nickel. How much money do you have?
• FR: Tu as 2 pièces de 10 cents et 1 pièce de 5 cents. Combien d'argent as-tu?
• Choices: A) 20 cents B) 22 cents C) 25 cents D) 30 cents
• Hint: 1 dime = 10¢, so 3 dimes = 30¢; add any nickels after.
• Steps:
  • 2 dimes = 20 cents.
  • 1 nickel = 5 cents.
  • 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtraction Within 100

• EN: 82 − 37 = ?
• FR: 82 − 37 = ?
• Choices: A) 44 B) 45 C) 46 D) 55
• Hint: For 74 − 28, subtract ones first (borrow if needed), then tens: 74 − 28 = 46.
• Steps:
  • Ones: 2 − 7 needs borrowing → 12 − 7 = 5.
  • Tens: (8 − 1) − 3 = 7 − 3 = 4.
  • Answer: 45
• Answer: 45

[Medium] Telling Time — Half Hour

• EN: The long hand is on 6 and the short hand is between 7 and 8. What time is it?
• FR: La grande aiguille est sur le 6 et la petite aiguille est entre 7 et 8. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:00
• Hint: Long hand on 6 always means 30 minutes past the hour — so 4:30 has the short hand between 4 and 5.
• Steps:
  • Long hand on 6 → 30 minutes past.
  • Short hand between 7 and 8 → the hour is 7.
  • Time is 7:30.
• Answer: 7:30

[Medium] Simple Pattern

• EN: What comes next in the pattern? 10, 20, 30, 40, __
• FR: Qu'est-ce qui vient ensuite dans ce modèle? 10, 20, 30, 40, __
• Choices: A) 45 B) 48 C) 50 D) 60
• Hint: In the pattern 3, 6, 9, 12, you add 3 each time — find what is added in each step.
• Steps:
  • Each number increases by 10.
  • 40 + 10 = 50.
• Answer: 50

[Medium] Counting Coins to $1

• EN: You have 3 quarters. How much money do you have?
• FR: Tu as 3 pièces de 25 cents. Combien d'argent as-tu?
• Choices: A) 60 cents B) 70 cents C) 75 cents D) 80 cents
• Hint: 2 quarters = 50¢, so add another 25¢ for a third quarter.
• Steps:
  • 1 quarter = 25 cents.
  • 25 + 25 + 25 = 75 cents.
• Answer: 75 cents

[Hard] Two-Step Word Problem

• EN: There are 48 students at recess. 13 go inside. Then 7 more come outside. How many students are outside now?
• FR: Il y a 48 élèves à la récréation. 13 rentrent à l'intérieur. Ensuite, 7 autres sortent dehors. Combien d'élèves sont dehors maintenant?
• Choices: A) 40 B) 41 C) 42 D) 43
• Hint: Do it in two steps — 30 − 8 = 22, then 22 + 5 = 27.
• Steps:
  • 48 − 13 = 35.
  • 35 + 7 = 42.
• Answer: 42

[Hard] Measuring and Comparing

• EN: A ribbon is 1 metre long. Emma cuts off 45 cm. How many centimetres of ribbon are left?
• FR: Un ruban mesure 1 mètre. Emma coupe 45 cm. Combien de centimètres de ruban reste-t-il?
• Choices: A) 45 cm B) 55 cm C) 60 cm D) 65 cm
• Hint: 1 metre = 100 cm; for 100 − 30, the answer is 70 cm.
• Steps:
  • Convert: 1 metre = 100 cm.
  • 100 − 45 = 55.
• Answer: 55 cm

[Easy] Multiplication by 2

• EN: 6 × 2 = ?
• FR: 6 × 2 = ?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiplying by 2 is the same as doubling — 7 × 2 = 14.
• Steps:
  • 6 groups of 2: 2, 4, 6, 8, 10, 12.
  • 6 × 2 = 12.
• Answer: 12

[Easy] Multiplication by 5

• EN: 4 × 5 = ?
• FR: 4 × 5 = ?
• Choices: A) 15 B) 20 C) 25 D) 30
• Hint: Multiples of 5 always end in 0 or 5 — 3 × 5 = 15.
• Steps:
  • Count by 5s four times: 5, 10, 15, 20.
  • 4 × 5 = 20.
• Answer: 20

[Easy] Basic Division

• EN: 15 ÷ 3 = ?
• FR: 15 ÷ 3 = ?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Division asks how many groups — 12 ÷ 3 = 4 because 4 × 3 = 12.
• Steps:
  • Think: what times 3 equals 15?
  • 5 × 3 = 15, so 15 ÷ 3 = 5.
• Answer: 5

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal slices. Omar eats 1 slice. What fraction of the pizza did he eat?
• FR: Une pizza est coupée en 2 tranches égales. Omar mange 1 tranche. Quelle fraction de la pizza a-t-il mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: A fraction is parts eaten over total equal parts — 1 out of 4 equal parts is 1/4.
• Steps:
  • Total slices = 2; slices eaten = 1.
  • Fraction = 1/2.
• Answer: 1/2

[Medium] Multiplication by 4

• EN: 7 × 4 = ?
• FR: 7 × 4 = ?
• Choices: A) 24 B) 26 C) 28 D) 32
• Hint: Double, then double again — 6 × 4: double 6 = 12, double 12 = 24.
• Steps:
  • Double 7 = 14.
  • Double 14 = 28.
  • 7 × 4 = 28.
• Answer: 28

[Medium] Perimeter

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

[Medium] Reading a Graph

• EN: A bar graph shows: hockey — 8 students, soccer — 5 students, swimming — 3 students. How many more students like hockey than swimming?
• FR: Un diagramme à barres montre: hockey — 8 élèves, soccer — 5 élèves, natation — 3 élèves. Combien d'élèves aiment le hockey de plus que la natation?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: To find "how many more," subtract — if hockey has 10 and swimming has 4, then 10 − 4 = 6 more.
• Steps:
  • Hockey = 8, swimming = 3.
  • 8 − 3 = 5.
• Answer: 5

[Medium] Fractions — Quarters

• EN: A chocolate bar is cut into 4 equal pieces. Leo eats 3 pieces. What fraction is left?
• FR: Une tablette de chocolat est coupée en 4 morceaux égaux. Léo mange 3 morceaux. Quelle fraction reste-t-il?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) 1/3
• Hint: If 2 out of 8 pieces are eaten, 6/8 remain — total minus eaten over total.
• Steps:
  • Total pieces = 4; eaten = 3.
  • Left = 4 − 3 = 1 piece.
  • Fraction left = 1/4.
• Answer: 1/4

[Hard] Division with Grouping

• EN: 36 students are put into groups of 4. How many groups are there?
• FR: 36 élèves sont répartis en groupes de 4. Combien y a-t-il de groupes?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: For 24 ÷ 4, ask: 4 × ? = 24 → 4 × 6 = 24, so the answer is 6.
• Steps:
  • 36 ÷ 4 = ?
  • 4 × 9 = 36, so 36 ÷ 4 = 9.
• Answer: 9

[Hard] Multi-Step Problem

• EN: A box holds 10 crayons. Ms. Chen has 3 full boxes and 5 extra crayons. How many crayons does she have?
• FR: Une boîte contient 10 crayons. Mme Chen a 3 boîtes pleines et 5 crayons de plus. Combien de crayons a-t-elle?
• Choices: A) 30 B) 33 C) 35 D) 38
• Hint: For 4 boxes of 6 plus 2 extra: 4 × 6 = 24, then 24 + 2 = 26.
• Steps:
  • 3 × 10 = 30 crayons in boxes.
  • 30 + 5 = 35 total crayons.
• Answer: 35

[Easy] Multiplication Tables

• EN: 8 × 7 = ?
• FR: 8 × 7 = ?
• Choices: A) 54 B) 56 C) 58 D) 63
• Hint: Think 8 × 7 as 8 × 5 + 8 × 2 = 40 + 16; try a similar split for other facts.
• Steps:
  • 8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 40
• Hint: In 5.62, the 6 is in the tenths place and the 2 is in the hundredths place.
• Steps:
  • 3.47: 3 is ones, 4 is tenths, 7 is hundredths.
  • The digit 4 is in the tenths place.
• Answer: 4 tenths

[Easy] Area of Rectangle

• EN: A garden is 6 m long and 4 m wide. What is its area?
• FR: Un jardin mesure 6 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 10 m² B) 20 m² C) 24 m² D) 28 m²
• Hint: Area = length × width; for a 5 m × 3 m room, area = 15 m².
• Steps:
  • Area = 6 × 4.
  • 6 × 4 = 24 m².
• Answer: 24 m²

[Easy] Long Division

• EN: 56 ÷ 8 = ?
• FR: 56 ÷ 8 = ?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Ask yourself: 8 × ? = 56 — think of your 8 times table.
• Steps:
  • 8 × 7 = 56.
  • So 56 ÷ 8 = 7.
• Answer: 7

[Medium] Long Division with Remainder

• EN: 47 ÷ 5 = ?
• FR: 47 ÷ 5 = ?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 9 remainder 3 D) 10 remainder 2
• Hint: For 23 ÷ 4: 4 × 5 = 20, remainder 23 − 20 = 3, so answer is 5 remainder 3.
• Steps:
  • 5 × 9 = 45; 47 − 45 = 2.
  • 47 ÷ 5 = 9 remainder 2.
• Answer: 9 remainder 2

[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 compare
• Hint: To compare 1/2 and 1/3, convert to the same denominator: 3/6 vs 2/6 — so 1/2 > 1/3.
• 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: Hockey practice starts at 2:15 and ends at 3:45. How long is the practice?
• FR: L'entraînement de hockey commence à 14h15 et se termine à 15h45. Combien de temps dure l'entraînement?
• Choices: A) 1 hour 15 minutes B) 1 hour 30 minutes C) 1 hour 45 minutes D) 2 hours
• Hint: For start 1:10 to end 2:50, count 50 minutes to 2:10 then 40 more = 1 hour 40 minutes.
• Steps:
  • From 2:15 to 3:15 = 1 hour.
  • From 3:15 to 3:45 = 30 minutes.
  • Total = 1 hour 30 minutes.
• Answer: 1 hour 30 minutes

[Medium] Decimal Operations

• EN: 4.5 + 2.3 = ?
• FR: 4,5 + 2,3 = ?
• Choices: A) 6.5 B) 6.7 C) 6.8 D) 7.8
• Hint: Line up the decimals — for 3.2 + 1.5, add tenths: 2 + 5 = 7, add ones: 3 + 1 = 4, answer is 4.7.
• Steps:
  • Add tenths: 5 + 3 = 8 tenths.
  • Add ones: 4 + 2 = 6.
  • Answer: 6.8
• Answer: 6.8

[Hard] Multi-Step Division

• EN: A store has 98 Tim Hortons cups to pack into boxes of 9. How many full boxes can be made, and how many cups are left over?
• FR: Un magasin a 98 tasses Tim Hortons à emballer dans des boîtes de 9. Combien de boîtes pleines peut-on faire, et combien de tasses reste-t-il?
• Choices: A) 10 boxes, 7 left over B) 10 boxes, 8 left over C) 11 boxes, 0 left over D) 9 boxes, 8 left over
• Hint: For 50 ÷ 6: 6 × 8 = 48, remainder 2 → 8 boxes, 2 left over.
• Steps:
  • 9 × 10 = 90; 98 − 90 = 8.
  • 10 full boxes with 8 cups left over.
• Answer: 10 boxes, 8 left over

[Hard] Perimeter and Area

• EN: A square has a perimeter of 36 cm. What is its area?
• FR: Un carré a un périmètre de 36 cm. Quelle est son aire?
• Choices: A) 64 cm² B) 72 cm² C) 81 cm² D) 144 cm²
• Hint: For a square with perimeter 20 cm, each side = 20 ÷ 4 = 5 cm; area = 5 × 5 = 25 cm².
• Steps:
  • Side = 36 ÷ 4 = 9 cm.
  • Area = 9 × 9 = 81 cm².
• Answer: 81 cm²

[Easy] Multi-Digit Multiplication

• EN: 34 × 6 = ?
• FR: 34 × 6 = ?
• Choices: A) 184 B) 200 C) 204 D) 214
• Hint: For 23 × 4: (20 × 4) + (3 × 4) = 80 + 12 = 92.
• Steps:
  • 30 × 6 = 180.
  • 4 × 6 = 24.
  • 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions — Like Denominators

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

[Easy] Percentage — 50%

• EN: What is 50% of 80?
• FR: Quel est 50% de 80?
• Choices: A) 20 B) 30 C) 40 D) 50
• Hint: 50% means half — 50% of 60 = 60 ÷ 2 = 30.
• Steps:
  • 50% = one half.
  • 80 ÷ 2 = 40.
• Answer: 40

[Easy] Decimal Operations

• EN: 7.85 − 3.40 = ?
• FR: 7,85 − 3,40 = ?
• Choices: A) 3.45 B) 4.35 C) 4.45 D) 5.45
• Hint: For 9.76 − 4.30, subtract each column: ones 5, tenths 4, hundredths 6 → 5.46.
• Steps:
  • Ones: 7 − 3 = 4.
  • Tenths: 8 − 4 = 4.
  • Hundredths: 5 − 0 = 5.
  • Answer: 4.45
• Answer: 4.45

[Medium] Multi-Digit Division

• EN: 432 ÷ 9 = ?
• FR: 432 ÷ 9 = ?
• Choices: A) 46 B) 47 C) 48 D) 54
• Hint: For 270 ÷ 9: 9 × 30 = 270, so the answer is 30.
• Steps:
  • 9 × 40 = 360; 432 − 360 = 72.
  • 9 × 8 = 72.
  • 40 + 8 = 48.
• Answer: 48

[Medium] Subtracting Fractions

• EN: 6/8 − 2/8 = ?
• FR: 6/8 − 2/8 = ?
• Choices: A) 3/8 B) 4/8 C) 5/8 D) 4/0
• Hint: For 5/9 − 2/9, keep the denominator and subtract tops: 5 − 2 = 3, so 3/9.
• Steps:
  • Denominators match (8).
  • 6 − 2 = 4.
  • Answer: 4/8
• Answer: 4/8

[Medium] Percentage — 25% and 10%

• EN: A sweater costs $60.00. It is on sale for 25% off. How much is the discount?
• FR: Un chandail coûte 60,00 $. Il est en solde à 25% de réduction. Quel est le rabais?
• Choices: A) $10.00 B) $12.00 C) $15.00 D) $20.00
• Hint: 25% of 80 = 80 ÷ 4 = 20 (since 25% = one quarter).
• Steps:
  • 25% = one quarter.
  • 60 ÷ 4 = 15.
  • The discount is $15.00.
• Answer: $15.00

[Medium] Volume of Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 47 cm³ B) 55 cm³ C) 60 cm³ D) 75 cm³
• Hint: Volume = length × width × height; for a box 2 × 3 × 4, volume = 24 cm³.
• Steps:
  • V = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60.
• Answer: 60 cm³

[Hard] Multi-Step Fraction Problem

• EN: A recipe needs 3/5 cup of flour. Ava wants to make 3 batches. How many cups of flour does she need in total?
• FR: Une recette nécessite 3/5 tasse de farine. Ava veut faire 3 recettes. Combien de tasses de farine lui faut-il en tout?
• Choices: A) 1 cup B) 1 and 2/5 cups C) 1 and 4/5 cups D) 2 cups
• Hint: For 2 batches of 2/5 cup: 2 × 2/5 = 4/5 cup; then convert if needed.
• Steps:
  • 3 × 3/5 = 9/5.
  • 9/5 = 1 and 4/5.
• Answer: 1 and 4/5 cups

[Hard] Percentage Problem

• EN: A hockey team won 18 out of 24 games. What percentage of games did they win?
• FR: Une équipe de hockey a remporté 18 parties sur 24. Quel pourcentage de parties ont-ils gagné?
• Choices: A) 65% B) 70% C) 75% D) 80%
• Hint: For 12 wins out of 16 games: 12/16 = 3/4 = 75%.
• Steps:
  • Fraction won = 18/24.
  • Simplify: 18/24 = 3/4.
  • 3/4 = 75%.
• Answer: 75%

[Easy] Order of Operations — BEDMAS

• EN: 3 + 4 × 2 = ?
• FR: 3 + 4 × 2 = ?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: Multiplication comes before addition — for 5 + 2 × 3, do 2 × 3 = 6 first, then 5 + 6 = 11.
• Steps:
  • Multiply first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
• Answer: 11

[Easy] Percent of a Number

• EN: What is 10% of 350?
• FR: Quel est 10% de 350?
• Choices: A) 3.5 B) 35 C) 350 D) 70
• Hint: 10% of any number means divide by 10 — 10% of 80 = 8.
• Steps:
  • 10% = divide by 10.
  • 350 ÷ 10 = 35.
• Answer: 35

[Easy] Integers — Comparing

• EN: Which is greater: −5 or −2?
• FR: Lequel 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 — −1 is greater than −4.
• Steps:
  • On a number line, −2 is to the right of −5.
  • −2 is greater.
• Answer: −2

[Easy] Ratio

• EN: For every 2 red marbles there are 5 blue marbles. What is the ratio of red to blue?
• FR: Pour chaque 2 billes rouges, il y a 5 billes bleues. Quel est le rapport des rouges aux bleues?
• Choices: A) 5:2 B) 2:5 C) 2:7 D) 5:7
• Hint: A ratio compares two quantities in order — red to blue means red first, then blue.
• Steps:
  • Red = 2, Blue = 5.
  • Ratio red to blue = 2:5.
• Answer: 2:5

[Medium] Fraction Multiplication

• EN: 2/3 × 3/4 = ?
• FR: 2/3 × 3/4 = ?
• Choices: A) 5/12 B) 6/12 C) 5/7 D) 8/12
• Hint: For 1/2 × 2/3, multiply tops: 1 × 2 = 2, multiply bottoms: 2 × 3 = 6, answer = 2/6 = 1/3.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 = 1/2, but as written: 6/12.
• Answer: 6/12

[Medium] BEDMAS with Brackets

• EN: (10 − 4) × 3 + 2 = ?
• FR: (10 − 4) × 3 + 2 = ?
• Choices: A) 18 B) 20 C) 22 D) 24
• Hint: Do brackets first — (8 − 3) × 2 + 1 = 5 × 2 + 1 = 10 + 1 = 11.
• Steps:
  • Brackets: 10 − 4 = 6.
  • Multiply: 6 × 3 = 18.
  • Add: 18 + 2 = 20.
• Answer: 20

[Medium] Unit Rate

• EN: A car travels 240 km in 4 hours. What is the speed in km per hour?
• FR: Une voiture parcourt 240 km en 4 heures. Quelle est la vitesse en km par heure?
• Choices: A) 50 km/h B) 55 km/h C) 60 km/h D) 65 km/h
• Hint: For 180 km in 3 hours, rate = 180 ÷ 3 = 60 km/h.
• Steps:
  • Rate = total distance ÷ time.
  • 240 ÷ 4 = 60 km/h.
• Answer: 60 km/h

[Medium] Simple Algebraic Expression

• EN: If n = 5, what is the value of 4n − 3?
• FR: Si n = 5, quelle est la valeur de 4n − 3?
• Choices: A) 15 B) 17 C) 19 D) 23
• Hint: For 3x − 2 when x = 4: substitute → 3(4) − 2 = 12 − 2 = 10.
• Steps:
  • 4n − 3 = 4(5) − 3.
  • = 20 − 3 = 17.
• Answer: 17

[Hard] Fraction Division

• EN: 3/4 ÷ 1/2 = ?
• FR: 3/4 ÷ 1/2 = ?
• Choices: A) 3/8 B) 1 C) 1 and 1/2 D) 2
• Hint: To divide fractions, multiply by the reciprocal — 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
• Steps:
  • Flip the second fraction: 1/2 → 2/1.
  • Multiply: 3/4 × 2/1 = 6/4 = 3/2.
  • 3/2 = 1 and 1/2.
• Answer: 1 and 1/2

[Hard] Percent Problem — Multi-Step

• EN: A jacket costs $120. It is discounted by 30%, then taxed 13% (HST) on the sale price. What is the final price?
• FR: Un manteau coûte 120 $. Il est réduit de 30%, puis la TVH de 13% est appliquée sur le prix de vente. Quel est le prix final?
• Choices: A) $94.92 B) $95.76 C) $96.72 D) $100.80
• Hint: For a $50 item discounted 20% then taxed 10%: sale price = $40; tax = $4; final = $44.
• Steps:
  • Discount: 30% of $120 = $36; sale price = $120 − $36 = $84.
  • HST: 13% of $84 = $10.92.
  • Final = $84 + $10.92 = $94.92.
• Answer: $94.92

[Easy] Integer Addition

• EN: −8 + 5 = ?
• FR: −8 + 5 = ?
• Choices: A) −13 B) −3 C) 3 D) 13
• Hint: For −6 + 4, the result is negative because the negative is bigger: |−6| > |4|, so −2.
• Steps:
  • |−8| = 8; |5| = 5; 8 > 5, so the answer is negative.
  • 8 − 5 = 3; answer is −3.
• Answer: −3

[Easy] Integer Subtraction

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

[Easy] Discount

• EN: A backpack costs $40. There is a 20% discount. What is the sale price?
• FR: Un sac à dos coûte 40 $. Il y a un rabais de 20%. Quel est le prix de vente?
• Choices: A) $28 B) $30 C) $32 D) $35
• Hint: Find the discount first, then subtract — 10% of $60 = $6; 20% = $12; $60 − $12 = $48.
• Steps:
  • 20% of $40 = $8.
  • $40 − $8 = $32.
• Answer: $32

[Easy] One-Step Equation

• EN: Solve: x + 9 = 15
• FR: Résous: x + 9 = 15
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 24
• Hint: To solve x + 7 = 12, subtract 7 from both sides: x = 12 − 7 = 5.
• Steps:
  • x + 9 = 15.
  • x = 15 − 9 = 6.
• Answer: x = 6

[Medium] Integer Multiplication

• EN: (−4) × (−7) = ?
• FR: (−4) × (−7) = ?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: Negative × negative = positive — (−3) × (−5) = +15.
• Steps:
  • Negative × negative = positive.
  • 4 × 7 = 28.
  • Answer: 28
• Answer: 28

[Medium] Percent — Tip

• EN: A meal at a restaurant costs $48. You want to leave a 15% tip. How much is the tip?
• FR: Un repas au restaurant coûte 48 $. Tu veux laisser un pourboire de 15%. Quel est le montant du pourboire?
• Choices: A) $5.20 B) $6.40 C) $7.20 D) $8.40
• Hint: 15% = 10% + 5%; for $60: 10% = $6, 5% = $3, total tip = $9.
• Steps:
  • 10% of $48 = $4.80.
  • 5% of $48 = $2.40.
  • Total tip = $4.80 + $2.40 = $7.20.
• Answer: $7.20

[Medium] Surface Area — Rectangular Prism

• EN: A cereal box is 20 cm tall, 10 cm wide, and 5 cm deep. What is its surface area?
• FR: Une boîte de céréales mesure 20 cm de haut, 10 cm de large et 5 cm de profond. Quelle est son aire totale?
• Choices: A) 650 cm² B) 700 cm² C) 750 cm² D) 800 cm²
• Hint: Surface area = 2(lw + lh + wh); for a 3 × 2 × 4 box: 2(6 + 12 + 8) = 2(26) = 52 cm².
• Steps:
  • 2(lw + lh + wh) = 2(10×5 + 20×5 + 20×10).
  • = 2(50 + 100 + 200) = 2(350) = 700 cm².
• Answer: 700 cm²

[Medium] Probability

• EN: A bag has 3 red and 7 blue marbles. If you pick one without looking, what is the probability of picking red?
• FR: Un sac contient 3 billes rouges et 7 bleues. Si tu en piges une sans regarder, quelle est la probabilité de piger rouge?
• Choices: A) 3/7 B) 3/10 C) 7/10 D) 1/3
• Hint: Probability = favourable outcomes ÷ total outcomes; for 2 red out of 8 total: P = 2/8 = 1/4.
• Steps:
  • Total marbles = 3 + 7 = 10.
  • P(red) = 3/10.
• Answer: 3/10

[Hard] Multi-Step Percent

• EN: A store raises the price of a game from $45 to $54. What is the percent increase?
• FR: Un magasin augmente le prix d'un jeu de 45 $ à 54 $. Quel est le pourcentage d'augmentation?
• Choices: A) 15% B) 17% C) 20% D) 25%
• Hint: % increase = (change ÷ original) × 100; for $20 rising to $25: change = $5, 5/20 × 100 = 25%.
• Steps:
  • Change = 54 − 45 = 9.
  • % increase = (9 ÷ 45) × 100 = 20%.
• Answer: 20%

[Hard] Integer Division and Order of Operations

• EN: −36 ÷ (−4) + (−2) × 3 = ?
• FR: −36 ÷ (−4) + (−2) × 3 = ?
• Choices: A) −3 B) 3 C) 6 D) −6
• Hint: For −20 ÷ (−5) + (−3) × 2: division first = 4, then multiplication = −6, then 4 + (−6) = −2.
• Steps:
  • −36 ÷ (−4) = 9.
  • (−2) × 3 = −6.
  • 9 + (−6) = 3.
• Answer: 3

[Easy] Perfect Squares

• EN: What is √81?
• FR: Quelle est √81?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: Think: what number times itself equals 81? — for √64, the answer is 8 because 8 × 8 = 64.
• Steps:
  • 9 × 9 = 81.
  • √81 = 9.
• Answer: 9

[Easy] Mean

• EN: Find the mean of: 4, 8, 6, 10, 12
• FR: Trouve la moyenne de: 4, 8, 6, 10, 12
• Choices: A) 6 B) 7 C) 8 D) 10
• Hint: Mean = sum of all values ÷ count; for 2, 4, 6: sum = 12, count = 3, mean = 4.
• Steps:
  • Sum = 4 + 8 + 6 + 10 + 12 = 40.
  • Mean = 40 ÷ 5 = 8.
• Answer: 8

[Easy] Two-Step Equation

• EN: Solve: 2x + 3 = 11
• FR: Résous: 2x + 3 = 11
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: For 3x + 2 = 14, subtract 2 first to get 3x = 12, then divide by 3: x = 4.
• Steps:
  • 2x + 3 = 11 → 2x = 11 − 3 = 8.
  • x = 8 ÷ 2 = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A price increases from $50 to $60. What is the percent increase?
• FR: Un prix passe de 50 $ à 60 $. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: % increase = (change ÷ original) × 100; for $30 to $36, change = $6, 6/30 × 100 = 20%.
• Steps:
  • Change = 60 − 50 = 10.
  • 10 ÷ 50 × 100 = 20%.
• Answer: 20%

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et 8 cm. Quelle est l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: For legs 3 and 4: 3² + 4² = 9 + 16 = 25, √25 = 5; this is a Pythagorean triple.
• Steps:
  • c² = 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope

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

[Medium] Median and Mode

• EN: Find the median: 3, 7, 7, 9, 11
• FR: Trouve la médiane: 3, 7, 7, 9, 11
• Choices: A) 3 B) 7 C) 8 D) 9
• Hint: The median is the middle value when sorted — for 2, 5, 8, 9, 12 the median is 8.
• Steps:
  • Already sorted: 3, 7, 7, 9, 11.
  • Middle value (3rd of 5) = 7.
• Answer: 7

[Medium] Two-Step Equation — Fractions

• EN: Solve: x/3 + 4 = 9
• FR: Résous: x/3 + 4 = 9
• Choices: A) x = 10 B) x = 12 C) x = 15 D) x = 18
• Hint: For x/4 + 2 = 7: subtract 2 → x/4 = 5, then multiply by 4 → x = 20.
• Steps:
  • x/3 + 4 = 9 → x/3 = 5.
  • x = 5 × 3 = 15.
• Answer: x = 15

[Hard] Pythagorean Theorem — Unknown Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the other leg.
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Trouve l'autre cathète.
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: For hypotenuse 10 and one leg 6: b² = 100 − 36 = 64, b = √64 = 8.
• Steps:
  • b² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12 cm.
• Answer: 12 cm

[Hard] Percent Decrease — Multi-Step

• EN: A snowboard originally costs $280. It is reduced by 15%, then reduced by a further 10% on the new price. What is the final price?
• FR: Une planche à neige coûte 280 $ à l'origine. Elle est réduite de 15%, puis de 10% supplémentaire sur le nouveau prix. Quel est le prix final?
• Choices: A) $210.00 B) $213.12 C) $214.20 D) $220.00
• Hint: For $200 reduced 20% then 10%: $200 × 0.80 = $160; $160 × 0.90 = $144.
• Steps:
  • After 15%: $280 × 0.85 = $238.00.
  • After 10%: $238 × 0.90 = $214.20.
• Answer: $214.20

[Easy] Solving a Linear Equation

• EN: Solve: 3x − 7 = 14
• FR: Résous: 3x − 7 = 14
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: For 4x − 5 = 15, add 5 to both sides → 4x = 20, divide by 4 → x = 5.
• Steps:
  • 3x − 7 = 14 → 3x = 21.
  • x = 21 ÷ 3 = 7.
• Answer: x = 7

[Easy] Slope-Intercept Form

• EN: What is the y-intercept of y = 4x − 3?
• FR: Quel est l'ordonnée à l'origine de y = 4x − 3?
• Choices: A) −4 B) −3 C) 3 D) 4
• Hint: In y = mx + b, b is always the y-intercept — for y = 2x + 5, the y-intercept is 5.
• Steps:
  • y = 4x − 3 is in y = mx + b form.
  • b = −3.
• Answer: −3

[Easy] Adding Polynomials

• EN: (3x + 5) + (2x − 1) = ?
• FR: (3x + 5) + (2x − 1) = ?
• Choices: A) 5x + 4 B) 5x − 4 C) 6x + 4 D) 5x + 6
• Hint: Combine like terms — for (4x + 3) + (x − 2), add x terms and constant terms separately: 5x + 1.
• Steps:
  • x terms: 3x + 2x = 5x.
  • Constants: 5 + (−1) = 4.
  • Answer: 5x + 4
• Answer: 5x + 4

[Easy] Similar Triangles

• EN: Two triangles are similar. The smaller has a base of 4 cm. The ratio of sides is 1:3. What is the base of the larger triangle?
• FR: Deux triangles sont semblables. Le petit a une base de 4 cm. Le rapport des côtés est 1:3. Quelle est la base du grand triangle?
• Choices: A) 7 cm B) 10 cm C) 12 cm D) 16 cm
• Hint: For ratio 1:2 and smaller base of 5, the larger base = 5 × 2 = 10 cm.
• Steps:
  • Scale factor = 3.
  • Larger base = 4 × 3 = 12 cm.
• Answer: 12 cm

[Medium] Linear Inequality

• EN: Solve: 2x + 1 > 9. Which is correct?
• FR: Résous: 2x + 1 > 9. Quelle réponse est correcte?
• Choices: A) x > 3 B) x > 4 C) x < 4 D) x ≥ 5
• Hint: For 3x − 2 > 7, add 2 then divide by 3: x > 3.
• Steps:
  • 2x + 1 > 9 → 2x > 8.
  • x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x − 5)
• FR: Développe: 3x(2x − 5)
• Choices: A) 6x − 15 B) 6x² − 15 C) 6x² − 15x D) 5x² − 15x
• Hint: Distribute — for 4x(x + 2): 4x × x = 4x², 4x × 2 = 8x; answer = 4x² + 8x.
• Steps:
  • 3x × 2x = 6x².
  • 3x × (−5) = −15x.
  • Answer: 6x² − 15x
• Answer: 6x² − 15x

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse mesure 10 cm. Quel est sin(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: SOH means sin = opposite ÷ hypotenuse — for opposite = 4, 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 2 and y-intercept −1. Which equation represents it?
• FR: Une droite a une pente de 2 et une ordonnée à l'origine de −1. Quelle équation la représente?
• Choices: A) y = −x + 2 B) y = 2x + 1 C) y = 2x − 1 D) y = −2x − 1
• Hint: y = mx + b; for slope 3 and y-intercept 4, the equation is y = 3x + 4.
• Steps:
  • m = 2, b = −1.
  • y = 2x − 1.
• Answer: y = 2x − 1

[Hard] Solving Systems of Equations

• EN: Solve: y = 2x + 1 and y = −x + 7. What is the solution?
• FR: Résous: y = 2x + 1 et y = −x + 7. Quelle est la solution?
• Choices: A) (1, 3) B) (2, 5) C) (3, 4) D) (4, 9)
• Hint: Set the two expressions equal and solve for x — for y = x + 3 and y = 2x + 1: x + 3 = 2x + 1, so x = 2.
• Steps:
  • Set equal: 2x + 1 = −x + 7 → 3x = 6 → x = 2.
  • y = 2(2) + 1 = 5.
  • Solution: (2, 5).
• Answer: (2, 5)

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What is the angle θ, to the nearest degree?
• FR: Dans un triangle rectangle, le côté adjacent mesure 8 cm et l'hypoténuse mesure 10 cm. Quel est l'angle θ, au degré près?
• Choices: A) 37° B) 40° C) 53° D) 60°
• Hint: CAH means cos = adjacent ÷ hypotenuse; use cos⁻¹ to find the angle — for cos(θ) = 0.5, θ = 60°.
• Steps:
  • cos(θ) = 8 ÷ 10 = 0.8.
  • θ = cos⁻¹(0.8) ≈ 37°.
• Answer: 37°

[Easy] Factoring Quadratics

• EN: Factor: x² + 5x + 6
• FR: Factorise: x² + 5x + 6
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x − 2)(x − 3) D) (x + 3)(x + 2)
• Hint: Find two numbers that multiply to +6 and add to +5 — for x² + 7x + 12, look for 3 and 4.
• Steps:
  • Need two numbers: multiply to 6, add to 5 → 2 and 3.
  • (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — TOA

• EN: In a right triangle, the opposite side is 5 and the adjacent side is 5. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 5 et le côté adjacent est 5. Quel est tan(θ)?
• Choices: A) 0 B) 0.5 C) 1 D) 2
• Hint: TOA means tan = opposite ÷ adjacent; for opposite = 3, adjacent = 6: tan = 0.5.
• Steps:
  • tan(θ) = opposite ÷ adjacent = 5 ÷ 5 = 1.
• Answer: 1

[Easy] System of Equations

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

[Easy] Volume of a Cylinder

• EN: A cylinder has radius 3 cm and height 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 188.4 cm³ B) 235.5 cm³ C) 282.6 cm³ D) 314.0 cm³
• Hint: V = π × r² × h; for r = 2 and h = 5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = 3.14 × 3² × 10 = 3.14 × 9 × 10.
  • = 3.14 × 90 = 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x − 7 = 0
• FR: Résous en complétant le carré: x² + 6x − 7 = 0
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 7 or x = 1 D) x = 2 or x = −4
• Hint: For x² + 4x − 12 = 0: (x + 2)² = 16, x + 2 = ±4, x = 2 or x = −6.
• Steps:
  • x² + 6x = 7 → (x + 3)² − 9 = 7 → (x + 3)² = 16.
  • x + 3 = ±4 → x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry

• EN: A central angle in a circle is 80°. What is the measure of the inscribed angle that subtends the same arc?
• FR: Un angle au centre d'un cercle est de 80°. Quelle est la mesure de l'angle inscrit qui intercepte le même arc?
• Choices: A) 20° B) 40° C) 80° D) 160°
• Hint: The inscribed angle theorem says the inscribed angle is always half the central angle — for a 60° central angle, the inscribed angle is 30°.
• Steps:
  • Inscribed angle = central angle ÷ 2.
  • 80° ÷ 2 = 40°.
• Answer: 40°

[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 or x = 6 B) x = 2 or x = 3 C) x = −2 or x = −3 D) x = 3 or x = −2
• Hint: For x² − 7x + 12 = 0, the discriminant = 49 − 48 = 1, so x = (7 ± 1)/2 = 4 or 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 a Side

• EN: In a right triangle, angle θ = 30°, and the hypotenuse is 20 cm. Find the opposite side.
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse est de 20 cm. Trouve le côté opposé.
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 14 cm
• Hint: For sin(45°) = 0.707 and hypotenuse = 10: opposite = 10 × 0.707 ≈ 7.07 cm.
• Steps:
  • sin(30°) = 0.5.
  • opposite = 20 × 0.5 = 10 cm.
• Answer: 10 cm

[Hard] Surface Area of a Cone

• EN: A cone has radius 6 cm and slant height 10 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 6 cm et une apothème de 10 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 282.6 cm² B) 301.4 cm² C) 452.2 cm² D) 489.8 cm²
• Hint: Total surface area of cone = πrl + πr²; for r = 4 and l = 5: 3.14(4)(5) + 3.14(16) = 62.8 + 50.24 = 113.04 cm².
• Steps:
  • Lateral area = π × 6 × 10 = 3.14 × 60 = 188.4 cm².
  • Base area = π × 6² = 3.14 × 36 = 113.04 cm².
  • Total = 188.4 + 113.04 = 301.44 ≈ 301.4 cm².
• Answer: 301.4 cm²

[Hard] System of Equations — Non-Linear

• EN: A rectangle has a perimeter of 28 cm and an area of 48 cm². What are its dimensions?
• FR: Un rectangle a un périmètre de 28 cm et une aire de 48 cm². Quelles sont ses dimensions?
• Choices: A) 4 cm × 12 cm B) 6 cm × 8 cm C) 5 cm × 9 cm D) 3 cm × 10 cm
• Hint: For perimeter 20 and area 24: 2(l+w) = 20 so l+w = 10; lw = 24; try factor pairs of 24 that sum to 10 → 4 and 6.
• Steps:
  • 2(l + w) = 28 → l + w = 14.
  • lw = 48; pairs that sum to 14: 6 × 8 = 48 ✓.
  • Dimensions: 6 cm × 8 cm.
• Answer: 6 cm × 8 cm

[Easy] Exponential Function

• EN: For f(x) = 3^x, what is f(4)?
• FR: Pour f(x) = 3^x, quelle est f(4)?
• Choices: A) 12 B) 27 C) 64 D) 81
• Hint: For f(x) = 2^x: f(5) = 2⁵ = 32 — multiply the base by itself the exponent number of times.
• Steps:
  • f(4) = 3⁴ = 3 × 3 × 3 × 3.
  • = 81.
• Answer: 81

[Easy] Logarithm Intro

• EN: What is log₂(16)?
• FR: Quel est log₂(16)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log_b(x) = n means b^n = x — for log₃(27): 3³ = 27, so the answer is 3.
• Steps:
  • Ask: 2 to what power equals 16?
  • 2⁴ = 16, so log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequence

• EN: The sequence is 5, 9, 13, 17, ... What is the 6th term?
• FR: La suite est 5, 9, 13, 17, ... Quel est le 6e terme?
• Choices: A) 21 B) 23 C) 25 D) 27
• Hint: For sequence 3, 7, 11, 15, ... the common difference is 4; use a_n = a₁ + (n−1)d.
• Steps:
  • Common difference d = 4; a₁ = 5.
  • a₆ = 5 + (6−1)×4 = 5 + 20 = 25.
• Answer: 25

[Easy] Compound Interest

• EN: $1,000 is invested at 5% per year, compounded annually, for 2 years. How much interest is earned?
• FR: 1 000 $ est investi à 5% par an, composé annuellement, pendant 2 ans. Combien d'intérêts sont gagnés?
• Choices: A) $100.00 B) $102.50 C) $105.00 D) $110.00
• Hint: For $500 at 4% for 2 years: A = 500(1.04)² = 500(1.0816) = $540.80; interest = $40.80.
• Steps:
  • A = 1000(1.05)² = 1000 × 1.1025 = $1,102.50.
  • Interest = $1,102.50 − $1,000 = $102.50.
• Answer: $102.50

[Medium] Quadratic Function — Vertex

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

[Medium] Geometric Sequence

• EN: The sequence is 3, 6, 12, 24, ... What is the 7th term?
• FR: La suite est 3, 6, 12, 24, ... Quel est le 7e terme?
• Choices: A) 96 B) 144 C) 192 D) 384
• Hint: For sequence 2, 6, 18, 54, ... with ratio 3: a₅ = 2 × 3⁴ = 2 × 81 = 162.
• Steps:
  • Common ratio r = 2; a₁ = 3.
  • a₇ = 3 × 2⁶ = 3 × 64 = 192.
• Answer: 192

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ)
• FR: Simplifie: sin²(θ) + cos²(θ)
• Choices: A) 0 B) sin(2θ) C) 1 D) 2
• Hint: The Pythagorean identity always holds for any angle — it is one of the most important trig facts.
• Steps:
  • This is the Pythagorean identity.
  • sin²(θ) + cos²(θ) = 1 for all θ.
• Answer: 1

[Medium] Annuity

• EN: You deposit $200 per month for 6 months at 0% interest. How much do you have at the end?
• FR: Tu déposes 200 $ par mois pendant 6 mois à 0% d'intérêt. Combien as-tu à la fin?
• Choices: A) $1,000 B) $1,100 C) $1,200 D) $1,400
• Hint: For $50 per month for 5 months at 0%: total = 50 × 5 = $250.
• Steps:
  • Total = 200 × 6 = $1,200 (no interest earned).
• Answer: $1,200

[Hard] Logarithm — Solving an Equation

• EN: Solve: 2^(x + 1) = 32
• FR: Résous: 2^(x + 1) = 32
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: For 3^(x − 1) = 27: rewrite as 3^(x−1) = 3³, so x − 1 = 3, x = 4.
• Steps:
  • Rewrite 32 as a power of 2: 32 = 2⁵.
  • 2^(x + 1) = 2⁵ → x + 1 = 5 → x = 4.
• Answer: x = 4

[Hard] Compound Interest — Solve for Time

• EN: You invest $2,000 at 6% compounded annually. About how many years will it take to double? (Use the Rule of 72)
• FR: Tu investis 2 000 $ à 6% composé annuellement. En combien d'années environ doublera-t-il? (Utilise la règle de 72)
• Choices: A) 10 years B) 12 years C) 14 years D) 16 years
• Hint: The Rule of 72 says divide 72 by the interest rate — for 8%, 72 ÷ 8 = 9 years to double.
• Steps:
  • Rule of 72: 72 ÷ 6 = 12.
  • It takes approximately 12 years.
• Answer: 12 years

[Easy] Permutations

• EN: How many ways can 5 students line up for a class photo?
• FR: De combien de façons 5 élèves peuvent-ils se placer en ligne pour une photo de classe?
• Choices: A) 25 B) 60 C) 120 D) 240
• Hint: For 4 students in a line: 4 × 3 × 2 × 1 = 24 ways.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
• Answer: 120

[Easy] Combinations

• EN: How many ways can you choose 2 toppings from 5 options?
• FR: De combien de façons peut-on choisir 2 garnitures parmi 5 options?
• Choices: A) 5 B) 10 C) 20 D) 25
• Hint: C(n, r) = n! ÷ (r! × (n−r)!); for C(4, 2) = 4!/(2! × 2!) = 24/4 = 6.
• Steps:
  • C(5,2) = 5! ÷ (2! × 3!) = 120 ÷ (2 × 6) = 120 ÷ 12 = 10.
• Answer: 10

[Easy] Derivative — Power Rule

• EN: If f(x) = x³, what is f'(x)?
• FR: Si f(x) = x³, quelle est f'(x)?
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: Power rule: bring the exponent to the front and reduce it by 1 — for x⁵, the derivative is 5x⁴.
• Steps:
  • f(x) = x³; bring exponent down: 3.
  • Reduce power by 1: x².
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Polynomial End Behaviour

• EN: As x → +∞, what happens to f(x) = −2x³ + 5x − 1?
• FR: Quand x → +∞, que se passe-t-il avec f(x) = −2x³ + 5x − 1?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 5
• Hint: The leading term dominates as x grows — for −3x⁴, as x → +∞, the function → −∞.
• Steps:
  • Leading term is −2x³ (negative, odd degree).
  • As x → +∞, −2x³ → −∞.
• Answer: f(x) → −∞

[Medium] Derivative — Finding Rate of Change

• EN: f(x) = 4x² − 3x + 2. What is f'(x)?
• FR: f(x) = 4x² − 3x + 2. Quelle est f'(x)?
• Choices: A) 4x − 3 B) 8x + 3 C) 8x − 3 D) 8x − 3x
• Hint: Differentiate each term — for 5x³ − 2x + 7: f'(x) = 15x² − 2.
• Steps:
  • Derivative of 4x² = 8x.
  • Derivative of −3x = −3.
  • Derivative of 2 = 0.
  • f'(x) = 8x − 3.
• Answer: 8x − 3

[Medium] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: Une pièce équitable est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces?
• Choices: A) 1/8 B) 1/4 C) 3/8 D) 1/2
• Hint: P(exactly k successes) = C(n, k) × p^k × (1−p)^(n−k); for n=3, k=2, p=0.5: C(3,2)(0.5²)(0.5) = 3/8.
• Steps:
  • P(3 heads) = C(4,3) × (1/2)³ × (1/2)¹.
  • = 4 × 1/8 × 1/2 = 4/16 = 1/4.
• Answer: 1/4

[Medium] Vector Addition

• EN: Vector u = (3, 5) and vector v = (−1, 4). What is u + v?
• FR: Le vecteur u = (3, 5) et le vecteur v = (−1, 4). Quel est u + v?
• Choices: A) (2, 1) B) (2, 9) C) (4, 9) D) (−3, 20)
• Hint: Add corresponding components — for (2, 7) + (3, −2) = (5, 5).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: 5 + 4 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Medium] Rational Function — Vertical Asymptote

• EN: For f(x) = 1/(x − 4), what is the vertical asymptote?
• FR: Pour f(x) = 1/(x − 4), quelle est l'asymptote verticale?
• Choices: A) x = −4 B) x = 1 C) x = 4 D) y = 4
• Hint: The vertical asymptote is where the denominator equals zero — for 1/(x + 3), set x + 3 = 0, so x = −3.
• Steps:
  • Set denominator to zero: x − 4 = 0 → x = 4.
  • Vertical asymptote at x = 4.
• Answer: x = 4

[Hard] Derivative — Tangent Line

• EN: f(x) = x² + 2x. What is the equation of the tangent line at x = 3?
• FR: f(x) = x² + 2x. Quelle est l'équation de la tangente en x = 3?
• Choices: A) y = 6x − 3 B) y = 8x − 9 C) y = 8x − 9 D) y = 5x + 3
• Hint: For f(x) = x², f'(x) = 2x; at x = 1: slope = 2, f(1) = 1; tangent: y − 1 = 2(x − 1) → y = 2x − 1.
• Steps:
  • f'(x) = 2x + 2; at x = 3: slope = 2(3) + 2 = 8.
  • f(3) = 9 + 6 = 15.
  • y − 15 = 8(x − 3) → y = 8x − 24 + 15 = 8x − 9.
• Answer: y = 8x − 9

[Hard] Probability Distribution — Expected Value

• EN: A game pays $10 if you roll a 6 on a standard die, $0 otherwise. You pay $2 to play. What is the expected value of the game (net)?
• FR: Un jeu paie 10 $ si tu lances un 6 avec un dé standard, 0 $ sinon. Tu paies 2 $ pour jouer. Quelle est la valeur espérée nette?
• Choices: A) −$0.33 B) $0.33 C) −$1.33 D) $1.67
• Hint: E(X) = Σ[x × P(x)]; for winning $8 with prob 1/6 and losing $2 with prob 5/6: E = 8/6 − 10/6 = −2/6 ≈ −$0.33.
• Steps:
  • Net win if 6: $10 − $2 = $8; Net loss otherwise: −$2.
  • E = (1/6)(8) + (5/6)(−2) = 8/6 − 10/6 = −2/6 ≈ −$0.33.
• Answer: −$0.33