Daily Math — 2026-06-26

[Easy] Counting Crayons

• EN: Maya has 7 crayons. She finds 5 more. How many crayons does she have now?
• FR: Maya a 7 crayons. Elle en trouve 5 de plus. Combien de crayons a-t-elle maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: Adding means counting on! For example, if you have 3 apples and get 4 more, start at 3 and count up 4: 4, 5, 6, 7. You get 7! Now try the same idea with Maya's crayons.
• Steps:
  • Step 1: Let's try a similar problem: 4 + 3. Start at 4 and count up 3 more: 5, 6, 7.
  • Step 2: The answer is 7. Adding means counting forward from the first number. Now use the same method: start at 7 and count up 5!
• Answer: 12

[Easy] Hockey Sticks

• EN: There are 9 hockey sticks in the equipment room. 3 are taken out. How many are left?
• FR: Il y a 9 bâtons de hockey dans la salle d'équipement. On en prend 3. Combien en reste-t-il?
• Choices: A) 5 B) 7 C) 6 D) 4
• Hint: Subtracting means taking away! For example, if you have 8 mittens and give away 2, count back 2 from 8: 7, 6. You have 6 left! Try the same idea here.
• Steps:
  • Step 1: Try this: 8 − 2. Start at 8 and count back 2: 7, 6.
  • Step 2: The answer is 6. Subtracting means counting backward. Now count back 3 from 9 to solve the problem!
• Answer: 6

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What comes next? 2, 4, 6, 8, ___
• FR: Compte par bonds de 2. Quel nombre vient ensuite? 2, 4, 6, 8, ___
• Choices: A) 9 B) 11 C) 10 D) 12
• Hint: Skip counting by 2s means adding 2 each time! For example: 10, 12, 14, 16 — each number is 2 more than the one before. Look at the pattern and add 2!
• Steps:
  • Step 1: Try this pattern: 14, 16, 18, ___. Each number goes up by 2, so add 2 to 18: 18 + 2 = 20.
  • Step 2: The answer is 20. Now add 2 to 8 to find the missing number in the real problem!
• Answer: 10

[Easy] Counting Pennies

• EN: Liam has 6 pennies. How many cents does he have?
• FR: Liam a 6 sous (pennies). Combien de cents a-t-il?
• Choices: A) 4¢ B) 8¢ C) 5¢ D) 6¢
• Hint: Each penny is worth 1 cent! For example, 4 pennies = 4 cents because 1 + 1 + 1 + 1 = 4. Count your pennies one by one!
• Steps:
  • Step 1: Try this: 3 pennies. Count: 1¢, 2¢, 3¢. So 3 pennies = 3 cents.
  • Step 2: Each penny equals 1 cent. Now count 6 pennies the same way!
• Answer: 6¢

[Medium] Snowflakes on the Window

• EN: There are 14 snowflakes on one window and 6 on another. How many snowflakes are there in all?
• FR: Il y a 14 flocons sur une fenêtre et 6 sur une autre. Combien y a-t-il de flocons en tout?
• Choices: A) 18 B) 21 C) 20 D) 19
• Hint: To add a teen number and a single digit, try making 10! For example, 13 + 7: start at 13, and count up 7 more: 14, 15, 16, 17, 18, 19, 20. That's 20!
• Steps:
  • Step 1: Try 12 + 8. Start at 12 and count up 8: 13, 14, 15, 16, 17, 18, 19, 20.
  • Step 2: The answer is 20. Now start at 14 and count up 6 to solve the real problem!
• Answer: 20

[Medium] Tim Hortons Timbits

• EN: Sofia had 18 Timbits. She ate some and has 9 left. How many did she eat?
• FR: Sofia avait 18 Timbits. Elle en a mangé quelques-uns et il en reste 9. Combien en a-t-elle mangés?
• Choices: A) 8 B) 10 C) 7 D) 9
• Hint: To find how many were taken away, subtract! For example, if you had 15 grapes and have 7 left, count back from 15 to 7 — or think: 7 + ? = 15. Try 7 + 8 = 15!
• Steps:
  • Step 1: Try 16 − 7. Think: 7 + ? = 16. Count up from 7: 8, 9, 10, 11, 12, 13, 14, 15, 16 — that's 9 steps. So 16 − 7 = 9.
  • Step 2: Now think: 9 + ? = 18. Count up from 9 to 18 to find the answer!
• Answer: 9

[Medium] Comparing Numbers

• EN: Which number is greater: 15 or 19?
• FR: Quel nombre est le plus grand: 15 ou 19?
• Choices: A) 15 B) They are equal C) 19 D) 10
• Hint: To compare numbers, look at the tens first, then the ones. For example, 12 vs. 17: both have 1 ten, but 17 has 7 ones and 12 has only 2 ones, so 17 is greater!
• Steps:
  • Step 1: Compare 13 and 16. Both have 1 ten. But 16 has 6 ones and 13 has only 3 ones.
  • Step 2: Since 6 > 3, we know 16 > 13. Now compare the ones digits of 15 and 19 the same way!
• Answer: 19

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What is the missing number? 5, 10, 15, ___, 25
• FR: Compte par bonds de 5. Quel est le nombre manquant? 5, 10, 15, ___, 25
• Choices: A) 18 B) 22 C) 20 D) 16
• Hint: Skip counting by 5s means adding 5 each time! For example: 25, 30, 35, 40 — each jump is +5. Find the number that fits between 15 and 25 the same way!
• Steps:
  • Step 1: Try this: 30, 35, ___, 45. Add 5 to 35: 35 + 5 = 40.
  • Step 2: The answer is 40. Now add 5 to 15 to find the number between 15 and 25!
• Answer: 20

[Hard] Loonie and Nickels

• EN: Emma has 1 dime and 2 nickels. How many cents does she have in total?
• FR: Emma a 1 pièce de 10 cents et 2 pièces de 5 cents. Combien de cents a-t-elle en tout?
• Choices: A) 15¢ B) 25¢ C) 17¢ D) 20¢
• Hint: A dime = 10 cents, a nickel = 5 cents. For example, 1 dime + 1 nickel = 10 + 5 = 15 cents. Add each coin's value together!
• Steps:
  • Step 1: Try 1 dime + 3 nickels. A dime is 10¢. Three nickels: 5 + 5 + 5 = 15¢. Total: 10 + 15 = 25¢.
  • Step 2: Now use the same method: find the value of 2 nickels (5 + 5), then add the dime (10¢)!
• Answer: 20¢

[Hard] Addition Story

• EN: There are 8 red maple leaves and 9 yellow leaves on the ground. Then 3 more yellow leaves fall. How many leaves are there now?
• FR: Il y a 8 feuilles d'érable rouges et 9 feuilles jaunes par terre. Puis 3 autres feuilles jaunes tombent. Combien y a-t-il de feuilles maintenant?
• Choices: A) 18 B) 21 C) 20 D) 19
• Hint: When there are two steps, solve one at a time! For example, 5 red + 6 blue + 2 more blue: first find 6 + 2 = 8, then add 5 + 8 = 13. Try breaking the leaf problem into two steps!
• Steps:
  • Step 1: Try 4 red + 5 yellow + 2 more yellow. First: 5 + 2 = 7 yellow leaves. Then: 4 + 7 = 11 total.
  • Step 2: The answer is 11. Now try the real problem: first add 9 + 3, then add that to 8!
• Answer: 20

[Easy] Adding at the Rink

• EN: There are 23 players at the hockey rink. 14 more arrive. How many players are there now?
• FR: Il y a 23 joueurs à la patinoire. 14 autres arrivent. Combien y a-t-il de joueurs maintenant?
• Choices: A) 35 B) 38 C) 37 D) 36
• Hint: To add two-digit numbers, add the ones first, then the tens! For example, 31 + 15: ones: 1 + 5 = 6, tens: 3 + 1 = 4, so the answer is 46.
• Steps:
  • Step 1: Try 32 + 16. Ones: 2 + 6 = 8. Tens: 3 + 1 = 4. Answer: 48.
  • Step 2: The answer is 48. Now use the same method — add the ones of 23 and 14, then add the tens!
• Answer: 37

[Easy] Telling Time

• EN: The clock shows 7:00. What time is it?
• FR: L'horloge indique 7:00. Quelle heure est-il?
• Choices: A) 6:00 B) 8:00 C) 7:30 D) 7:00
• Hint: When the minute hand points straight up to 12 and the hour hand points to a number, read that number as the hour! For example, if the hour hand is on 3 and the minute hand is on 12, it is 3:00.
• Steps:
  • Step 1: If the hour hand is on 5 and minute hand is on 12, we say 5:00.
  • Step 2: The "00" means zero minutes — it's exactly on the hour. Now apply the same idea to the clock showing 7!
• Answer: 7:00

[Easy] Measuring a Pencil

• 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. De combien le crayon est-il plus long?
• Choices: A) 5 cm B) 7 cm C) 6 cm D) 8 cm
• Hint: "How much longer" means subtract the shorter length from the longer one! For example, a ruler is 30 cm and a eraser is 10 cm: 30 − 10 = 20 cm longer.
• Steps:
  • Step 1: Try: a book is 20 cm and a card is 8 cm. 20 − 8 = 12 cm difference.
  • Step 2: The answer is 12 cm. Now subtract the crayon length from the pencil length the same way!
• Answer: 6 cm

[Easy] Counting Coins

• EN: Noah has 2 dimes and 3 nickels. How many cents does he have?
• FR: Noah a 2 pièces de 10 cents et 3 pièces de 5 cents. Combien de cents a-t-il?
• Choices: A) 30¢ B) 25¢ C) 35¢ D) 40¢
• Hint: Count dimes by 10s, nickels by 5s, then add! For example, 1 dime + 2 nickels = 10 + 5 + 5 = 20¢.
• Steps:
  • Step 1: Try 3 dimes + 1 nickel. Dimes: 10 + 10 + 10 = 30¢. Nickel: 5¢. Total: 30 + 5 = 35¢.
  • Step 2: Now count 2 dimes (10 + 10) and 3 nickels (5 + 5 + 5), then add them together!
• Answer: 35¢

[Medium] Subtracting at the Bakery

• EN: A Tim Hortons had 82 muffins in the morning. By noon, 47 were sold. How many muffins are left?
• FR: Un Tim Hortons avait 82 muffins le matin. À midi, 47 ont été vendus. Combien de muffins reste-t-il?
• Choices: A) 34 B) 36 C) 35 D) 37
• Hint: To subtract with regrouping, if the ones digit on top is smaller, borrow from the tens! For example, 73 − 46: borrow from 7 to make 13 − 6 = 7 ones, then 6 − 4 = 2 tens. Answer: 27.
• Steps:
  • Step 1: Try 91 − 58. Ones: 1 < 8, so borrow: 11 − 8 = 3. Tens: 8 − 5 = 3. Answer: 33.
  • Step 2: The answer is 33. Now try 82 − 47 the same way — borrow if needed!
• Answer: 35

[Medium] Half-Hour Time

• EN: Zoe starts reading at 2:00. She reads for half an hour. What time does she finish?
• FR: Zoe commence à lire à 2h00. Elle lit pendant une demi-heure. À quelle heure finit-elle?
• Choices: A) 2:00 B) 3:00 C) 2:30 D) 1:30
• Hint: Half an hour = 30 minutes. For example, if you start at 4:00 and wait half an hour, you finish at 4:30 — just add 30 to the minutes!
• Steps:
  • Step 1: Start at 6:00, add 30 minutes: 6:00 + 30 minutes = 6:30.
  • Step 2: The answer is 6:30. Now add 30 minutes to 2:00 to find when Zoe finishes!
• Answer: 2:30

[Medium] Simple Pattern

• EN: What comes next in this pattern? 10, 20, 30, 40, ___
• FR: Quel nombre vient ensuite dans ce modèle? 10, 20, 30, 40, ___
• Choices: A) 42 B) 45 C) 50 D) 48
• Hint: Look at the difference between each number in the pattern! For example, 3, 6, 9, 12 — each number goes up by 3. Find the rule and apply it!
• Steps:
  • Step 1: Try 5, 10, 15, 20, ___. The rule is +5 each time. 20 + 5 = 25.
  • Step 2: The answer is 25. Now find the rule for 10, 20, 30, 40 and apply it!
• Answer: 50

[Medium] Snowfall Length

• EN: In January, 35 cm of snow fell. In February, 48 cm fell. How much snow fell in total?
• FR: En janvier, 35 cm de neige sont tombés. En février, 48 cm sont tombés. Quelle quantité de neige est tombée en tout?
• Choices: A) 81 cm B) 83 cm C) 82 cm D) 84 cm
• Hint: Add the ones first, then the tens. If the ones add up to 10 or more, carry the 1 to the tens! For example, 46 + 37: ones 6 + 7 = 13, write 3 carry 1. Tens: 4 + 3 + 1 = 8. Answer: 83.
• Steps:
  • Step 1: Try 54 + 29. Ones: 4 + 9 = 13. Write 3, carry 1. Tens: 5 + 2 + 1 = 8. Answer: 83.
  • Step 2: The answer is 83. Now use the same steps for 35 + 48!
• Answer: 83 cm

[Hard] Two-Step Shopping

• EN: Ava has 75¢. She buys a sticker for 30¢ and a pencil for 25¢. How much money does she have left?
• FR: Ava a 75¢. Elle achète un autocollant pour 30¢ et un crayon pour 25¢. Combien d'argent lui reste-t-il?
• Choices: A) 15¢ B) 25¢ C) 20¢ D) 10¢
• Hint: Two-step problems need two subtractions (or add the costs first, then subtract)! For example, start with 80¢, spend 20¢ and 10¢: 20 + 10 = 30¢ spent. 80 − 30 = 50¢ left.
• Steps:
  • Step 1: Try starting with 90¢, buy items for 40¢ and 15¢. Total spent: 40 + 15 = 55¢. Left: 90 − 55 = 35¢.
  • Step 2: Now add 30¢ + 25¢ to find total spent, then subtract from 75¢!
• Answer: 20¢

[Hard] Measuring and Comparing

• EN: A maple branch is 98 cm long. After trimming, it is 63 cm long. How much was trimmed off?
• FR: Une branche d'érable mesure 98 cm. Après la taille, elle mesure 63 cm. Quelle longueur a-t-on coupée?
• Choices: A) 33 cm B) 37 cm C) 35 cm D) 39 cm
• Hint: To find how much was removed, subtract the new length from the original! For example, a rope was 85 cm, now it's 52 cm: 85 − 52 = 33 cm was cut off.
• Steps:
  • Step 1: Try 76 − 43. Ones: 6 − 3 = 3. Tens: 7 − 4 = 3. Answer: 33 cm.
  • Step 2: The answer is 33. Now subtract 63 from 98 the same way to find the trimmed amount!
• Answer: 35 cm

[Easy] Multiplication with Maple Syrup

• EN: A farmer fills 4 jars with maple syrup. Each jar holds 5 cups. How many cups in total?
• FR: Un fermier remplit 4 bocaux de sirop d'érable. Chaque bocal contient 5 tasses. Combien de tasses y a-t-il en tout?
• Choices: A) 15 B) 25 C) 20 D) 18
• Hint: Multiplication means equal groups! For example, 3 × 5 means 3 groups of 5: 5 + 5 + 5 = 15. Use the same idea with your problem!
• Steps:
  • Step 1: Try 3 × 4. That means 3 groups of 4: 4 + 4 + 4 = 12.
  • Step 2: The answer is 12. Now find 4 groups of 5 using the same method!
• Answer: 20

[Easy] Sharing Equally

• EN: 12 hockey cards are shared equally among 4 friends. How many cards does each friend get?
• FR: 12 cartes de hockey sont partagées également entre 4 amis. Combien de cartes chaque ami reçoit-il?
• Choices: A) 2 B) 4 C) 3 D) 5
• Hint: Division means sharing equally! For example, 15 ÷ 3: put 15 items into 3 equal groups. 15 ÷ 3 = 5 in each group.
• Steps:
  • Step 1: Try 10 ÷ 2. Share 10 equally into 2 groups: 5 in each group.
  • Step 2: The answer is 5. Now divide 12 into 4 equal groups the same way!
• Answer: 3

[Easy] What Fraction is Shaded?

• EN: A pizza is cut into 4 equal slices. Emma eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 tranches égales. Emma mange 1 tranche. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: A fraction shows parts of a whole. The bottom number (denominator) is how many equal parts total; the top (numerator) is how many you have! For example, 1 out of 3 equal parts = 1/3.
• Steps:
  • Step 1: A chocolate bar is cut into 3 equal pieces. You eat 1. That's 1 out of 3 = 1/3.
  • Step 2: Now use the same idea: Emma ate 1 piece out of how many total slices?
• Answer: 1/4

[Easy] Skip Counting by 10s

• EN: What is 5 × 10?
• FR: Combien font 5 × 10?
• Choices: A) 40 B) 60 C) 55 D) 50
• Hint: Multiplying by 10 means skip counting by 10s! For example, 3 × 10 = 10, 20, 30. Count by 10s that many times!
• Steps:
  • Step 1: Try 4 × 10. Count by 10s four times: 10, 20, 30, 40. Answer: 40.
  • Step 2: The answer is 40. Now count by 10s five times to find 5 × 10!
• Answer: 50

[Medium] Perimeter of a Playground

• EN: A rectangular playground is 8 m long and 5 m wide. What is its perimeter?
• FR: Une cour de récréation rectangulaire mesure 8 m de long et 5 m de large. Quel est son périmètre?
• Choices: A) 24 m B) 26 m C) 40 m D) 28 m
• Hint: Perimeter = adding all sides! A rectangle has 2 long sides and 2 short sides. For example, a rectangle 6 m × 3 m: 6 + 6 + 3 + 3 = 18 m.
• Steps:
  • Step 1: Try a rectangle 7 m × 4 m. Add all sides: 7 + 7 + 4 + 4 = 22 m.
  • Step 2: The answer is 22 m. Now add 8 + 8 + 5 + 5 to find the perimeter of the playground!
• Answer: 26 m

[Medium] Reading a Graph

• EN: A bar graph shows: Monday = 6 campers, Tuesday = 9 campers, Wednesday = 3 campers. How many campers came on Monday and Tuesday combined?
• FR: Un diagramme à barres montre: lundi = 6 campeurs, mardi = 9 campeurs, mercredi = 3 campeurs. Combien de campeurs sont venus lundi et mardi au total?
• Choices: A) 12 B) 18 C) 15 D) 14
• Hint: To combine two bars on a graph, just add their values! For example, if Monday = 8 and Tuesday = 7, combined = 8 + 7 = 15.
• Steps:
  • Step 1: Try Monday = 10, Tuesday = 6. Combined: 10 + 6 = 16 campers.
  • Step 2: Now add Monday's 6 campers and Tuesday's 9 campers the same way!
• Answer: 15

[Medium] Multiplication Table of 3

• EN: A hockey team has 3 lines of players. Each line has 3 players. How many players are on the team?
• FR: Une équipe de hockey a 3 trios de joueurs. Chaque trio compte 3 joueurs. Combien de joueurs y a-t-il dans l'équipe?
• Choices: A) 6 B) 12 C) 9 D) 8
• Hint: Multiplication means equal groups! For example, 3 × 2 means 3 groups of 2: 2 + 2 + 2 = 6. Now find 3 groups of 3!
• Steps:
  • Step 1: Try 4 × 3. That's 4 groups of 3: 3 + 3 + 3 + 3 = 12.
  • Step 2: The answer is 12. Now try 3 groups of 3: 3 + 3 + 3 = ?
• Answer: 9

[Medium] Dividing Timbits

• EN: 20 Timbits are divided equally into 5 boxes. How many Timbits are in each box?
• FR: 20 Timbits sont répartis également dans 5 boîtes. Combien y a-t-il de Timbits dans chaque boîte?
• Choices: A) 3 B) 6 C) 5 D) 4
• Hint: Division is sharing equally. Think: 5 × ? = 20. For example, 18 ÷ 3: think 3 × ? = 18. Since 3 × 6 = 18, the answer is 6!
• Steps:
  • Step 1: Try 15 ÷ 5. Think: 5 × ? = 15. Since 5 × 3 = 15, the answer is 3.
  • Step 2: Now think: 5 × ? = 20. Use your 5 times table to find the answer!
• Answer: 4

[Hard] Two-Step Multiplication Problem

• EN: There are 4 shelves in a store. Each shelf has 5 bottles of maple syrup. The store gets 6 more bottles. How many bottles are there now?
• FR: Il y a 4 tablettes dans un magasin. Chaque tablette a 5 bouteilles de sirop d'érable. Le magasin reçoit 6 autres bouteilles. Combien y a-t-il de bouteilles maintenant?
• Choices: A) 24 B) 26 C) 28 D) 30
• Hint: Two steps: multiply first, then add! For example, 3 shelves × 4 bottles = 12, then + 5 more = 17. Break the problem into two steps!
• Steps:
  • Step 1: Try 3 shelves × 6 bottles = 18, then add 4 more = 22 bottles.
  • Step 2: Now do the real problem: multiply 4 × 5, then add 6 to that answer!
• Answer: 26

[Hard] Fractions Greater Than One Half

• EN: Lucas ate 3 out of 4 pieces of pie. Did he eat more than half of the pie?
• FR: Lucas a mangé 3 des 4 morceaux de tarte. A-t-il mangé plus de la moitié de la tarte?
• Choices: A) No, he ate exactly half B) Yes, 3/4 is more than 1/2 C) No, 3/4 is less than 1/2 D) We cannot tell
• Hint: To compare a fraction to 1/2, think about what half of the total pieces is! For example, 2/3: half of 3 is 1.5, so more than half means having more than 1.5 out of 3. Since 2 > 1.5, yes, 2/3 > 1/2!
• Steps:
  • Step 1: Try 3/6: half of 6 is 3. So 3/6 is exactly 1/2.
  • Step 2: Now try 3/4: half of 4 is 2. Since Lucas ate 3 pieces and 3 > 2, he ate more than half!
• Answer: Yes, 3/4 is more than 1/2

[Easy] Multiplication Fact

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 63 C) 56 D) 48
• Hint: Try breaking the multiplication into smaller known facts! For example, 6 × 7 = 6 × 5 + 6 × 2 = 30 + 12 = 42. Use a strategy you know!
• Steps:
  • Step 1: Try 6 × 8. Think: 6 × 8 = 6 × 4 × 2 = 24 × 2 = 48.
  • Step 2: Now use 7 × 8 = 7 × 4 × 2 = 28 × 2 to find the answer!
• 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 hundredths C) 3 tenths D) 3 tens
• Hint: In a decimal number, the first digit after the decimal point is the tenths place, and the second is the hundredths place! For example, in 2.56: 5 is in the tenths place, 6 is in the hundredths place.
• Steps:
  • Step 1: Look at 5.82. The digit 8 is the first after the decimal point — it is in the tenths place (8 tenths).
  • Step 2: Now look at 4.37. The digit 3 is the first digit after the decimal point. What place is that?
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A camping tent floor is 6 m long and 4 m wide. What is the area?
• FR: Le sol d'une tente de camping mesure 6 m de long et 4 m de large. Quelle est l'aire?
• Choices: A) 20 m² B) 28 m² C) 24 m² D) 18 m²
• Hint: Area of a rectangle = length × width! For example, a floor 5 m × 3 m: Area = 5 × 3 = 15 m².
• Steps:
  • Step 1: Try a rug that is 7 m long and 3 m wide. Area = 7 × 3 = 21 m².
  • Step 2: The answer is 21 m². Now multiply 6 × 4 to find the tent floor area!
• Answer: 24 m²

[Easy] Long Division (No Remainder)

• EN: 36 ÷ 4 = ?
• FR: 36 ÷ 4 = ?
• Choices: A) 7 B) 8 C) 9 D) 6
• Hint: Division is the reverse of multiplication. Think: 4 × ? = 36. Use your 4 times table! For example, 24 ÷ 4: think 4 × ? = 24. Since 4 × 6 = 24, the answer is 6.
• Steps:
  • Step 1: Try 28 ÷ 4. Think 4 × ? = 28. Since 4 × 7 = 28, the answer is 7.
  • Step 2: Now think: 4 × ? = 36. Use your times table to find the answer!
• Answer: 9

[Medium] Long Division with Remainder

• EN: 47 school supplies are packed into boxes of 5. How many boxes are fully filled, and how many supplies are left over?
• FR: 47 fournitures scolaires sont emballées dans des boîtes de 5. Combien de boîtes sont complètes et combien de fournitures reste-t-il?
• Choices: A) 8 boxes, remainder 7 B) 9 boxes, remainder 2 C) 8 boxes, remainder 5 D) 9 boxes, remainder 0
• Hint: For division with remainder, divide and find what's left! For example, 23 ÷ 5: 5 × 4 = 20, so 4 full boxes, and 23 − 20 = 3 left over.
• Steps:
  • Step 1: Try 38 ÷ 5. 5 × 7 = 35, so 7 full boxes. Remainder: 38 − 35 = 3.
  • Step 2: Now find how many times 5 goes into 47, then subtract to find the remainder!
• Answer: 9 boxes, remainder 2

[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) They are equal C) 3/4 D) Cannot compare
• Hint: To compare fractions, find a common denominator or convert to decimals! For example, 1/2 vs. 2/5: 1/2 = 5/10, 2/5 = 4/10. Since 5 > 4, 1/2 is larger.
• Steps:
  • Step 1: Compare 2/3 and 3/5. Common denominator 15: 2/3 = 10/15, 3/5 = 9/15. Since 10 > 9, 2/3 is larger.
  • Step 2: Now compare 3/4 and 2/3. Use denominator 12: 3/4 = 9/12, 2/3 = 8/12. Which is larger?
• Answer: 3/4

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 PM and ends at 3:45 PM. How long is the game?
• FR: Un match de hockey commence à 13h15 et se termine à 15h45. Combien de temps dure le match?
• Choices: A) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours
• Hint: Count on from the start time to the end time! For example, from 2:20 PM to 4:50 PM: from 2:20 to 4:20 is 2 hours, then 4:20 to 4:50 is 30 more minutes = 2 hours 30 minutes.
• Steps:
  • Step 1: Try from 10:10 AM to 12:40 PM. From 10:10 to 12:10 = 2 hours. Then 12:10 to 12:40 = 30 minutes. Total: 2 hours 30 minutes.
  • Step 2: Now count from 1:15 PM to 3:45 PM: first count whole hours, then count the extra minutes!
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A student buys a notebook for $3.45 and a pen for $1.25. How much does she spend in total?
• FR: Une élève achète un cahier pour 3,45 $ et un stylo pour 1,25 $. Combien dépense-t-elle en tout?
• Choices: A) $4.50 B) $4.60 C) $4.70 D) $4.80
• Hint: Add decimals by lining up the decimal points! For example, $2.35 + $1.40: ones 2+1=3, tenths 3+4=7, hundredths 5+0=5. Answer: $3.75.
• Steps:
  • Step 1: Try $4.12 + $2.36. Ones: 4+2=6. Tenths: 1+3=4. Hundredths: 2+6=8. Answer: $6.48.
  • Step 2: Now add $3.45 + $1.25 the same way, lining up the decimal point!
• Answer: $4.70

[Hard] Multi-Step Area Problem

• EN: A school garden is 9 m long and 6 m wide. A pond inside the garden is 3 m long and 2 m wide. What is the area of the garden NOT covered by the pond?
• FR: Un jardin scolaire mesure 9 m de long et 6 m de large. Un étang dans le jardin mesure 3 m de long et 2 m de large. Quelle est l'aire du jardin qui n'est PAS couverte par l'étang?
• Choices: A) 48 m² B) 50 m² C) 52 m² D) 54 m²
• Hint: Find the total area first, then subtract the pond area! For example, a yard 10 × 5 = 50 m², a sandbox 2 × 3 = 6 m². Remaining area = 50 − 6 = 44 m².
• Steps:
  • Step 1: Try a garden 8 × 4 = 32 m², pond 2 × 2 = 4 m². Remaining: 32 − 4 = 28 m².
  • Step 2: Now calculate 9 × 6 for the garden, then subtract 3 × 2 for the pond!
• Answer: 48 m²

[Hard] Long Division Challenge

• EN: 96 campers are divided equally into groups of 8. How many groups are there?
• FR: 96 campeurs sont divisés en groupes égaux de 8. Combien y a-t-il de groupes?
• Choices: A) 10 B) 11 C) 13 D) 12
• Hint: Use long division or the multiplication table! For example, 72 ÷ 8: think 8 × ? = 72. Since 8 × 9 = 72, the answer is 9.
• Steps:
  • Step 1: Try 64 ÷ 8. Think 8 × ? = 64. Since 8 × 8 = 64, the answer is 8 groups.
  • Step 2: Now think 8 × ? = 96. Use your 8 times table or count by 8s to find the answer!
• Answer: 12

[Easy] Multi-Digit Multiplication

• EN: A store sells 24 boxes of hockey pucks. Each box holds 12 pucks. How many pucks are there in total?
• FR: Un magasin vend 24 boîtes de rondelles de hockey. Chaque boîte contient 12 rondelles. Combien y a-t-il de rondelles en tout?
• Choices: A) 268 B) 288 C) 248 D) 276
• Hint: Multiply two-digit numbers by breaking them apart! For example, 23 × 11 = 23 × 10 + 23 × 1 = 230 + 23 = 253.
• Steps:
  • Step 1: Try 22 × 13. Think: 22 × 10 = 220, and 22 × 3 = 66. Then 220 + 66 = 286.
  • Step 2: Now break 24 × 12 into 24 × 10 + 24 × 2 and add the results!
• Answer: 288

[Easy] Adding Fractions (Like Denominators)

• EN: Sofia ate 2/8 of a pizza at lunch and 3/8 at dinner. How much pizza did she eat in total?
• FR: Sofia a mangé 2/8 d'une pizza au dîner et 3/8 au souper. Quelle portion a-t-elle mangée en tout?
• Choices: A) 5/16 B) 6/8 C) 5/8 D) 4/8
• Hint: To add fractions with the same denominator, just add the numerators and keep the denominator the same! For example, 3/7 + 2/7 = 5/7.
• Steps:
  • Step 1: Try 1/6 + 4/6. Same denominator, so add the tops: 1 + 4 = 5. Answer: 5/6.
  • Step 2: Now add the numerators of 2/8 + 3/8 and keep the denominator 8!
• Answer: 5/8

[Easy] Percent — 50% of a Number

• EN: A jacket costs $80. It is on sale for 50% off. How much is the discount?
• FR: Un manteau coûte 80 $. Il est en solde avec 50% de réduction. Quel est le rabais?
• Choices: A) $30 B) $45 C) $40 D) $35
• Hint: 50% means half! For example, 50% of $60 = 60 ÷ 2 = $30. Just divide by 2!
• Steps:
  • Step 1: Try 50% of $90. 90 ÷ 2 = 45. So the discount is $45.
  • Step 2: The answer is $45. Now find half of $80 to solve the real problem!
• Answer: $40

[Easy] Decimal Subtraction

• EN: Lucas had $15.75. He spent $8.50 on a school snack. How much does he have left?
• FR: Lucas avait 15,75 $. Il a dépensé 8,50 $ pour une collation à l'école. Combien lui reste-t-il?
• Choices: A) $6.75 B) $7.50 C) $7.25 D) $6.50
• Hint: Line up decimal points when subtracting! For example, $18.95 − $11.70: ones 8−1=7, tenths 9−7=2, hundredths 5−0=5. Answer: $7.25.
• Steps:
  • Step 1: Try $14.80 − $7.60. Ones: 14−7=7, tenths: 8−6=2, hundredths: 0−0=0. Answer: $7.20.
  • Step 2: Now align the decimals of $15.75 − $8.50 and subtract each column!
• Answer: $7.25

[Medium] Volume of a Rectangular Prism

• EN: A storage box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte de rangement mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 56 cm³ D) 64 cm³
• Hint: Volume = length × width × height! For example, a box 6 cm × 2 cm × 4 cm: 6 × 2 = 12, then 12 × 4 = 48 cm³.
• Steps:
  • Step 1: Try length 7, width 3, height 2. 7 × 3 = 21, then 21 × 2 = 42 cm³.
  • Step 2: The answer is 42 cm³. Now multiply 5 × 4 first, then multiply that by 3!
• Answer: 60 cm³

[Medium] Multi-Digit Division

• EN: 252 students are divided equally into 9 classrooms. How many students are in each classroom?
• FR: 252 élèves sont répartis également dans 9 classes. Combien d'élèves y a-t-il dans chaque classe?
• Choices: A) 27 B) 29 C) 28 D) 26
• Hint: For long division, ask how many times the divisor goes into parts of the dividend! For example, 144 ÷ 6: 6 goes into 14 twice (12), remainder 2, bring down 4 to get 24. 6 goes into 24 four times. Answer: 24.
• Steps:
  • Step 1: Try 189 ÷ 9. 9 into 18 = 2, bring down 9. 9 into 9 = 1. Answer: 21.
  • Step 2: Now use long division to find how many times 9 goes into 252!
• Answer: 28

[Medium] Subtracting Fractions (Like Denominators)

• EN: A camp had 7/10 of a tank of water. They used 3/10 of the tank. How much water is left?
• FR: Un camp avait 7/10 d'un réservoir d'eau. Ils ont utilisé 3/10 du réservoir. Quelle quantité d'eau reste-t-il?
• Choices: A) 3/10 B) 5/10 C) 4/10 D) 6/10
• Hint: To subtract fractions with the same denominator, subtract only the numerators and keep the denominator! For example, 6/9 − 2/9 = 4/9.
• Steps:
  • Step 1: Try 8/12 − 5/12. Subtract numerators: 8 − 5 = 3. Keep denominator 12. Answer: 3/12.
  • Step 2: Now subtract the numerators 7 − 3 and keep denominator 10!
• Answer: 4/10

[Medium] Percent — 25% of a Number

• EN: A hockey jersey originally costs $120. It is on sale for 25% off. How much is the discount?
• FR: Un chandail de hockey coûte à l'origine 120 $. Il est en solde à 25% de réduction. Quel est le rabais?
• Choices: A) $25 B) $35 C) $30 D) $40
• Hint: 25% = one quarter = divide by 4! For example, 25% of $80 = 80 ÷ 4 = $20.
• Steps:
  • Step 1: Try 25% of $60. 60 ÷ 4 = 15. So the discount is $15.
  • Step 2: Now divide $120 by 4 to find 25% of the jersey's price!
• Answer: $30

[Hard] Two-Step Decimal and Percent Problem

• EN: A camping store sells sleeping bags for $96. They are on sale for 25% off. Then a 10% tax is added to the sale price. What is the final price?
• FR: Un magasin de camping vend des sacs de couchage à 96 $. Ils sont en solde à 25% de réduction. Ensuite, une taxe de 10% est ajoutée au prix soldé. Quel est le prix final?
• Choices: A) $72.00 B) $79.20 C) $75.20 D) $76.80
• Hint: Two-step: find the discount, subtract it, then add tax! For example, $80 with 25% off: 80 − 20 = $60 sale price. Then 10% tax: 60 × 0.10 = $6. Final: $66.
• Steps:
  • Step 1: Try $80 at 25% off: 80 ÷ 4 = $20 off. Sale price: $60. Then 10% tax: 60 ÷ 10 = $6. Final price: $60 + $6 = $66.
  • Step 2: Now apply the same steps: find 25% of $96, subtract, then find 10% of the result and add it!
• Answer: $79.20

[Hard] Multi-Step Word Problem

• EN: A school store has 8 boxes of pencils. Each box holds 36 pencils. The store sells 144 pencils during the week. How many pencils are left?
• FR: La papeterie de l'école a 8 boîtes de crayons. Chaque boîte contient 36 crayons. Le magasin vend 144 crayons pendant la semaine. Combien de crayons reste-t-il?
• Choices: A) 144 B) 152 C) 140 D) 148
• Hint: Two steps: find total pencils by multiplying, then subtract what was sold! For example, 5 boxes × 24 pencils = 120 total. Sold 60. Left: 120 − 60 = 60 pencils.
• Steps:
  • Step 1: Try 6 boxes × 30 pencils = 180. Sold 90. Left: 180 − 90 = 90 pencils.
  • Step 2: Now multiply 8 × 36 to get total pencils, then subtract 144 from that total!
• Answer: 144

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Quel est 30% de 200?
• Choices: A) 50 B) 60 C) 70 D) 40
• Hint: To find a percent, multiply the number by the percent as a decimal! For example, 20% of 150 = 150 × 0.20 = 30.
• Steps:
  • Step 1: Try 40% of 150. 150 × 0.40 = 60.
  • Step 2: The answer is 60. Now multiply 200 × 0.30 to find 30% of 200!
• Answer: 60

[Easy] Simple Ratio

• EN: In a classroom, there are 12 girls and 8 boys. What is the ratio of girls to boys?
• FR: Dans une classe, il y a 12 filles et 8 garçons. Quel est le rapport filles:garçons?
• Choices: A) 2:3 B) 8:12 C) 3:2 D) 1:2
• Hint: A ratio compares two quantities! For example, 9 cats and 6 dogs: ratio of cats to dogs = 9:6. Simplify by dividing both by the GCF (3): 3:2.
• Steps:
  • Step 1: Try 10 girls, 6 boys. Ratio = 10:6. GCF is 2. Simplified: 5:3.
  • Step 2: Now simplify 12:8 by dividing both numbers by their GCF (4)!
• Answer: 3:2

[Easy] Order of Operations — BEDMAS

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 14 B) 10 C) 11 D) 9
• Hint: BEDMAS says do Multiplication before Addition! For example, 5 + 3 × 4: first 3 × 4 = 12, then 5 + 12 = 17. Don't just go left to right!
• Steps:
  • Step 1: Try 6 + 2 × 5. First multiply: 2 × 5 = 10. Then add: 6 + 10 = 16.
  • Step 2: The answer is 16. Now solve 3 + 4 × 2 using the same method — multiply first!
• Answer: 11

[Easy] Integer Introduction

• EN: The temperature in Winnipeg is −8°C in the morning and rises 5°C by noon. What is the temperature at noon?
• FR: La température à Winnipeg est de −8°C le matin et monte de 5°C à midi. Quelle est la température à midi?
• Choices: A) −2°C B) −4°C C) −3°C D) −1°C
• Hint: Adding a positive number to a negative moves right on the number line! For example, −6 + 4 = −2. Count up from −6: −5, −4, −3, −2.
• Steps:
  • Step 1: Try −9 + 6. Start at −9 and count up 6: −8, −7, −6, −5, −4, −3. Answer: −3.
  • Step 2: Now start at −8 and count up 5 to find the noon temperature!
• Answer: −3°C

[Easy] Simple Algebraic Expression

• EN: If n = 4, what is the value of 3n + 5?
• FR: Si n = 4, quelle est la valeur de 3n + 5?
• Choices: A) 12 B) 17 C) 15 D) 19
• Hint: Substitute the value into the expression! For example, if n = 3, then 2n + 4 = 2(3) + 4 = 6 + 4 = 10.
• Steps:
  • Step 1: Try n = 5 in the expression 4n + 3. Substitute: 4(5) + 3 = 20 + 3 = 23.
  • Step 2: The answer is 23. Now substitute n = 4 into 3n + 5 the same way!
• Answer: 17

[Medium] Fraction Multiplication

• EN: A recipe needs 2/3 of a cup of maple syrup. If you make 3 batches, how many cups do you need?
• FR: Une recette nécessite 2/3 de tasse de sirop d'érable. Si vous faites 3 lots, combien de tasses faut-il?
• Choices: A) 5/3 B) 2 C) 3/2 D) 1
• Hint: To multiply a fraction by a whole number, multiply the numerator by that number and keep the denominator! For example, 3/4 × 2 = 6/4 = 3/2.
• Steps:
  • Step 1: Try 3/5 × 4 = 12/5. Simplify if needed.
  • Step 2: Now multiply 2/3 × 3: multiply the numerator (2 × 3 = 6) and keep the denominator (3). Simplify 6/3!
• Answer: 2

[Medium] Rate Problem

• EN: A car travels 280 km in 4 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 280 km en 4 heures. Quelle est sa vitesse en km par heure?
• Choices: A) 65 km/h B) 75 km/h C) 70 km/h D) 80 km/h
• Hint: Rate = total ÷ time units! For example, 180 km in 3 hours: 180 ÷ 3 = 60 km/h.
• Steps:
  • Step 1: Try 240 km in 4 hours. 240 ÷ 4 = 60 km/h.
  • Step 2: The answer is 60 km/h. Now divide 280 by 4 to find the speed!
• Answer: 70 km/h

[Medium] Percent of a Number — Tax

• EN: A hockey helmet costs $150. A 13% HST is added. How much is the tax?
• FR: Un casque de hockey coûte 150 $. Une TVH de 13% est ajoutée. Quel est le montant de la taxe?
• Choices: A) $18.50 B) $19.50 C) $19.00 D) $20.00
• Hint: Tax = price × tax rate as a decimal! For example, 13% of $100 = 100 × 0.13 = $13.
• Steps:
  • Step 1: Try 13% of $200. 200 × 0.13 = 26. Tax is $26.
  • Step 2: Now multiply $150 × 0.13 to find the tax on the helmet!
• Answer: $19.50

[Medium] Fraction Division

• EN: How many 1/4 cups fit into 3 cups of flour?
• FR: Combien de 1/4 de tasse y a-t-il dans 3 tasses de farine?
• Choices: A) 9 B) 10 C) 12 D) 8
• Hint: Dividing by a fraction means multiplying by its reciprocal! For example, 2 ÷ 1/3 = 2 × 3 = 6.
• Steps:
  • Step 1: Try 4 ÷ 1/3. Multiply by the reciprocal: 4 × 3 = 12.
  • Step 2: Now try 3 ÷ 1/4. Multiply 3 by the reciprocal of 1/4 (which is 4)!
• Answer: 12

[Medium] BEDMAS with Brackets

• EN: What is (6 + 2) × 3 − 4?
• FR: Combien font (6 + 2) × 3 − 4?
• Choices: A) 24 B) 20 C) 22 D) 18
• Hint: BEDMAS: Brackets first, then Multiplication, then Subtraction! For example, (5 + 3) × 2 − 1 = 8 × 2 − 1 = 16 − 1 = 15.
• Steps:
  • Step 1: Try (4 + 3) × 2 − 5. Brackets: 4 + 3 = 7. Multiply: 7 × 2 = 14. Subtract: 14 − 5 = 9.
  • Step 2: Now do (6 + 2) first, then multiply by 3, then subtract 4!
• Answer: 20

[Medium] Ratio and Proportion

• EN: A recipe uses 2 cups of oats for every 3 cups of flour. If you use 9 cups of flour, how many cups of oats do you need?
• FR: Une recette utilise 2 tasses d'avoine pour 3 tasses de farine. Si vous utilisez 9 tasses de farine, combien de tasses d'avoine faut-il?
• Choices: A) 5 B) 7 C) 6 D) 8
• Hint: Set up a proportion! For example, if 3 apples cost $2, then 9 apples cost: 9 ÷ 3 = 3, so 3 × $2 = $6.
• Steps:
  • Step 1: Try ratio 2:5. If you have 15 of the second item: 15 ÷ 5 = 3. Then 3 × 2 = 6 of the first item.
  • Step 2: Now find how many times 3 goes into 9, then multiply that by 2!
• Answer: 6

[Hard] Multi-Step Percent Problem

• EN: A Tim Hortons coffee is marked at $4.00. There is a 20% loyalty discount, and then 13% HST is added on the discounted price. What is the final price?
• FR: Un café Tim Hortons est marqué à 4,00 $. Il y a une réduction de fidélité de 20%, puis une TVH de 13% est ajoutée sur le prix réduit. Quel est le prix final?
• Choices: A) $3.52 B) $3.61 C) $3.74 D) $3.86
• Hint: Apply discount first, then tax! For example, $5.00 with 20% off: 5 × 0.80 = $4.00 sale price. Then 13% tax: 4 × 1.13 = $4.52.
• Steps:
  • Step 1: Try $6.00 with 20% off: 6 × 0.80 = $4.80. Then 13% tax: 4.80 × 1.13 = $5.424 ≈ $5.42.
  • Step 2: Now apply 20% off to $4.00 (multiply by 0.80), then apply 13% tax (multiply by 1.13)!
• Answer: $3.61

[Hard] Algebraic Expression with Two Variables

• EN: If a = 5 and b = 3, what is the value of 4a − 2b + 1?
• FR: Si a = 5 et b = 3, quelle est la valeur de 4a − 2b + 1?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Substitute both values and follow BEDMAS! For example, if a = 2, b = 4: 3a + 2b − 5 = 3(2) + 2(4) − 5 = 6 + 8 − 5 = 9.
• Steps:
  • Step 1: Try a = 3, b = 2 in 5a − 3b + 2. Substitute: 5(3) − 3(2) + 2 = 15 − 6 + 2 = 11.
  • Step 2: Now substitute a = 5 and b = 3 into 4a − 2b + 1 and solve step by step!
• Answer: 15

[Hard] Integer Operations

• EN: What is (−12) + 7 − (−3)?
• FR: Combien font (−12) + 7 − (−3)?
• Choices: A) −4 B) −2 C) −1 D) 2
• Hint: Subtracting a negative is the same as adding! For example, 5 − (−3) = 5 + 3 = 8. Then work left to right with integers!
• Steps:
  • Step 1: Try (−8) + 5 − (−2). Change to addition: −8 + 5 + 2 = −8 + 7 = −1.
  • Step 2: Now change (−12) + 7 − (−3) to (−12) + 7 + 3, then add left to right!
• Answer: −2

[Hard] Fraction Division in Context

• EN: A camp counsellor has 5 litres of juice to fill cups that each hold 2/5 of a litre. How many cups can be filled?
• FR: Un moniteur de camp a 5 litres de jus pour remplir des verres qui contiennent chacun 2/5 de litre. Combien de verres peut-il remplir?
• Choices: A) 10 B) 15 C) 12 D) 8
• Hint: Divide total by the fraction size using the reciprocal! For example, 4 ÷ 2/3 = 4 × 3/2 = 12/2 = 6 cups.
• Steps:
  • Step 1: Try 6 ÷ 2/3. Multiply by reciprocal: 6 × 3/2 = 18/2 = 9 cups.
  • Step 2: Now do 5 ÷ 2/5. Multiply 5 by the reciprocal of 2/5, which is 5/2!
• Answer: 12

[Easy] Integer Addition

• EN: What is (−6) + (−9)?
• FR: Combien font (−6) + (−9)?
• Choices: A) −13 B) −15 C) 3 D) −3
• Hint: Adding two negatives means going further negative! For example, (−4) + (−5) = −9. Think of it as going left on a number line.
• Steps:
  • Step 1: Try (−7) + (−8). Both are negative, so add the absolute values: 7 + 8 = 15. Keep the negative sign: −15.
  • Step 2: Now add the absolute values of 6 and 9, then keep the negative sign!
• Answer: −15

[Easy] Percent — Finding a Discount

• EN: A pair of skates costs $80. They are on sale for 10% off. What is the sale price?
• FR: Une paire de patins coûte 80 $. Elle est en solde à 10% de réduction. Quel est le prix soldé?
• Choices: A) $68 B) $70 C) $72 D) $74
• Hint: 10% off means you pay 90%! For example, 10% of $60 = $6. Sale price = $60 − $6 = $54. Or: 60 × 0.90 = $54.
• Steps:
  • Step 1: Try $90 at 10% off. 10% of 90 = 9. Sale price = 90 − 9 = $81.
  • Step 2: Now find 10% of $80, then subtract from the original price!
• Answer: $72

[Easy] Mean of a Data Set

• EN: Five students scored 70, 80, 90, 60, and 100 on a math test. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 80, 90, 60 et 100 à un test de mathématiques. Quelle est la moyenne?
• Choices: A) 78 B) 82 C) 80 D) 76
• Hint: Mean = sum of all values ÷ number of values! For example, scores 10, 20, 30: sum = 60, number = 3, mean = 60 ÷ 3 = 20.
• Steps:
  • Step 1: Try scores 50, 60, 70, 80. Sum = 260. Number of scores = 4. Mean = 260 ÷ 4 = 65.
  • Step 2: Now add 70 + 80 + 90 + 60 + 100, then divide by 5!
• Answer: 80

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 14 = 30
• FR: Résous pour x: x + 14 = 30
• Choices: A) 14 B) 18 C) 16 D) 20
• Hint: To solve, do the opposite operation on both sides! For example, x + 7 = 15. Subtract 7 from both sides: x = 15 − 7 = 8.
• Steps:
  • Step 1: Try x + 9 = 25. Subtract 9 from both sides: x = 25 − 9 = 16.
  • Step 2: Now subtract 14 from both sides of x + 14 = 30 to find x!
• Answer: 16

[Easy] Fraction Operations

• EN: What is 3/5 + 2/5?
• FR: Combien font 3/5 + 2/5?
• Choices: A) 5/10 B) 6/5 C) 5/5 D) 1
• Hint: Add fractions with the same denominator by adding only the numerators! For example, 4/7 + 2/7 = 6/7. Remember 5/5 = 1!
• Steps:
  • Step 1: Try 2/6 + 3/6 = 5/6. The denominators are the same, so just add the numerators.
  • Step 2: Now add the numerators of 3/5 + 2/5 and simplify if possible!
• Answer: 1

[Medium] Integer Subtraction

• EN: What is 5 − (−8)?
• FR: Combien font 5 − (−8)?
• Choices: A) −3 B) 3 C) 13 D) −13
• Hint: Subtracting a negative is the same as adding the positive! For example, 6 − (−4) = 6 + 4 = 10.
• Steps:
  • Step 1: Try 9 − (−6). Change to addition: 9 + 6 = 15.
  • Step 2: Now change 5 − (−8) to 5 + 8 and solve!
• Answer: 13

[Medium] Tip Calculation

• EN: A family's restaurant bill is $64. They want to leave a 15% tip. How much is the tip?
• FR: La facture de restaurant d'une famille est de 64 $. Ils veulent laisser un pourboire de 15%. Quel est le montant du pourboire?
• Choices: A) $8.40 B) $9.00 C) $9.60 D) $10.00
• Hint: Find 10% then 5%, and add them for 15%! For example, 15% of $80: 10% = $8, 5% = $4, total = $12.
• Steps:
  • Step 1: Try 15% of $60. 10% of 60 = $6. 5% of 60 = $3. Total: $6 + $3 = $9.
  • Step 2: Now find 10% of $64, then 5% of $64, and add them!
• Answer: $9.60

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 5 cm long, 3 cm wide, and 4 cm tall. What is its surface area?
• FR: Une boîte cadeau mesure 5 cm de long, 3 cm de large et 4 cm de haut. Quelle est son aire totale?
• Choices: A) 90 cm² B) 94 cm² C) 84 cm² D) 88 cm²
• Hint: Surface area = 2(lw + lh + wh)! For example, a box 2 × 3 × 4: 2(6 + 8 + 12) = 2(26) = 52 cm².
• Steps:
  • Step 1: Try l=4, w=2, h=3. lw=8, lh=12, wh=6. Sum=26. SA = 2 × 26 = 52 cm².
  • Step 2: Now calculate lw = 5×3, lh = 5×4, wh = 3×4, add them, then multiply by 2!
• Answer: 94 cm²

[Medium] Percent Increase

• EN: A hockey player scored 20 goals last season and 25 goals this season. What is the percent increase?
• FR: Un joueur de hockey a marqué 20 buts la saison dernière et 25 buts cette saison. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 30% C) 25% D) 15%
• Hint: Percent increase = (increase ÷ original) × 100! For example, from 40 to 50: increase = 10, 10 ÷ 40 × 100 = 25%.
• Steps:
  • Step 1: Try from 60 to 75. Increase = 15. 15 ÷ 60 × 100 = 25%.
  • Step 2: Find the increase (25 − 20), divide by the original (20), then multiply by 100!
• Answer: 25%

[Medium] Probability

• EN: A bag has 3 red marbles, 4 blue marbles, and 3 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 4 billes bleues et 3 billes vertes. Quelle est la probabilité de choisir une bille bleue?
• Choices: A) 3/10 B) 1/4 C) 2/5 D) 4/10
• Hint: Probability = favourable outcomes ÷ total outcomes! For example, 2 red out of 5 total marbles: P(red) = 2/5.
• Steps:
  • Step 1: Try 5 blue out of 20 total. P(blue) = 5/20 = 1/4.
  • Step 2: Count the blue marbles (4) and total marbles (3+4+3=10). Write as a fraction!
• Answer: 4/10

[Medium] Multiplying Integers

• EN: What is (−7) × 4?
• FR: Combien font (−7) × 4?
• Choices: A) 28 B) −28 C) −24 D) 24
• Hint: Negative × Positive = Negative! For example, (−5) × 6 = −30. Multiply the absolute values, then make it negative.
• Steps:
  • Step 1: Try (−8) × 3. Multiply 8 × 3 = 24. Since signs are different, the answer is −24.
  • Step 2: Now multiply 7 × 4 = 28, then apply the sign rule!
• Answer: −28

[Hard] Two-Step Equation

• EN: Solve for n: 3n − 7 = 14
• FR: Résous pour n: 3n − 7 = 14
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Undo operations in reverse order: add first, then divide! For example, 4n − 3 = 13. Add 3: 4n = 16. Divide by 4: n = 4.
• Steps:
  • Step 1: Try 5n − 4 = 16. Add 4 to both sides: 5n = 20. Divide by 5: n = 4.
  • Step 2: Now add 7 to both sides of 3n − 7 = 14, then divide both sides by 3!
• Answer: 7

[Hard] Discount and Tax Combined

• EN: A snowboard costs $340. It is on sale for 15% off. Then 13% HST is added. What is the final price?
• FR: Une planche à neige coûte 340 $. Elle est en solde à 15% de réduction. Ensuite, une TVH de 13% est ajoutée. Quel est le prix final?
• Choices: A) $324.97 B) $333.41 C) $325.51 D) $330.00
• Hint: Step 1: find sale price (multiply by 0.85). Step 2: add tax (multiply by 1.13)! For example, $200 at 15% off: 200 × 0.85 = $170. Tax: 170 × 1.13 = $192.10.
• Steps:
  • Step 1: Try $400 at 15% off. 400 × 0.85 = $340. Add 13% tax: 340 × 1.13 = $384.20.
  • Step 2: Now find 340 × 0.85 for the sale price, then multiply that result by 1.13!
• Answer: $325.51

[Hard] Integer Division in Context

• EN: A submarine descends 180 metres below sea level over 9 equal steps. What integer represents the change per step?
• FR: Un sous-marin descend de 180 mètres sous le niveau de la mer en 9 étapes égales. Quel entier représente le changement par étape?
• Choices: A) −15 B) −20 C) 20 D) −25
• Hint: Dividing a negative by a positive gives a negative result! For example, −60 ÷ 5 = −12. The submarine goes down, so the change is negative.
• Steps:
  • Step 1: Try −150 ÷ 6. Divide 150 by 6 = 25. Keep the negative: −25.
  • Step 2: Now divide −180 by 9 the same way — divide the absolute values and keep the negative sign!
• Answer: −20

[Hard] Data and Probability

• EN: A spinner has sections worth 1, 2, 3, 4, and 5 (equal size). What is the probability of spinning a number greater than 3?
• FR: Une roulette a des sections valant 1, 2, 3, 4 et 5 (tailles égales). Quelle est la probabilité d'obtenir un nombre supérieur à 3?
• Choices: A) 1/5 B) 3/5 C) 2/5 D) 1/2
• Hint: Count favourable outcomes (numbers greater than 3) and divide by total sections! For example, out of 8 equal sections numbered 1–8, numbers >5 are 6,7,8: probability = 3/8.
• Steps:
  • Step 1: Try sections 1–6. Numbers greater than 4 are: 5, 6 — that's 2 out of 6 = 2/6 = 1/3.
  • Step 2: Now count how many numbers in 1–5 are greater than 3, then write that over 5!
• Answer: 2/5

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 13 C) 14 D) 12
• Hint: A perfect square root asks: what number times itself gives this? For example, √81 = 9 because 9 × 9 = 81.
• Steps:
  • Step 1: Try √100. Think: what × what = 100? Since 10 × 10 = 100, √100 = 10.
  • Step 2: Now think: what × what = 144? Try multiplying 12 × 12!
• Answer: 12

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 3 = 11
• FR: Résous pour x: 2x + 3 = 11
• Choices: A) 3 B) 5 C) 7 D) 4
• Hint: Undo operations: subtract first, then divide! For example, 3x + 5 = 14. Subtract 5: 3x = 9. Divide by 3: x = 3.
• Steps:
  • Step 1: Try 4x + 2 = 18. Subtract 2: 4x = 16. Divide by 4: x = 4.
  • Step 2: Now subtract 3 from both sides of 2x + 3 = 11, then divide both sides by 2!
• Answer: 4

[Easy] Percent Increase

• EN: A hockey stick was $60. Its price increased to $75. What is the percent increase?
• FR: Un bâton de hockey coûtait 60 $. Son prix a augmenté à 75 $. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 30% C) 15% D) 25%
• Hint: Percent increase = (increase ÷ original) × 100! For example, from 50 to 65: increase = 15, 15 ÷ 50 × 100 = 30%.
• Steps:
  • Step 1: Try from $80 to $96. Increase = 16. 16 ÷ 80 × 100 = 20%.
  • Step 2: Find the increase ($75 − $60), divide by the original ($60), then multiply by 100!
• Answer: 25%

[Easy] Mode and Median

• EN: Find the median of: 3, 7, 5, 9, 5
• FR: Trouve la médiane de: 3, 7, 5, 9, 5
• Choices: A) 5 B) 7 C) 6 D) 3
• Hint: To find the median, sort the numbers from least to greatest, then find the middle value! For example, 2, 4, 6, 8, 10 — middle value is 6.
• Steps:
  • Step 1: Try 8, 3, 6, 1, 5. Sort: 1, 3, 5, 6, 8. Middle value (3rd out of 5) = 5.
  • Step 2: Sort 3, 7, 5, 9, 5 from least to greatest, then find the middle number!
• Answer: 5

[Easy] Slope Introduction

• EN: A ramp rises 6 metres over a horizontal distance of 12 metres. What is the slope?
• FR: Une rampe monte de 6 mètres sur une distance horizontale de 12 mètres. Quelle est la pente?
• Choices: A) 2 B) 1/3 C) 1/2 D) 2/3
• Hint: Slope = rise ÷ run! For example, rise = 4, run = 8: slope = 4/8 = 1/2.
• Steps:
  • Step 1: Try rise = 3, run = 9. Slope = 3/9 = 1/3.
  • Step 2: Now divide the rise (6) by the run (12) and simplify the fraction!
• Answer: 1/2

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 10 cm B) 12 cm C) 14 cm D) 8 cm
• Hint: Use a² + b² = c². For example, legs 3 and 4: 9 + 16 = 25. √25 = 5. So the hypotenuse is 5.
• Steps:
  • Step 1: Try legs 5 and 12. 5² + 12² = 25 + 144 = 169. √169 = 13.
  • Step 2: Now calculate 6² + 8², add them, and take the square root!
• Answer: 10 cm

[Medium] Two-Step Equation with Negatives

• EN: Solve for y: −3y + 9 = −6
• FR: Résous pour y: −3y + 9 = −6
• Choices: A) 3 B) −5 C) 5 D) −3
• Hint: Subtract 9 from both sides first, then divide by −3! For example, −2y + 5 = 11. Subtract 5: −2y = 6. Divide by −2: y = −3.
• Steps:
  • Step 1: Try −4y + 8 = −12. Subtract 8: −4y = −20. Divide by −4: y = 5.
  • Step 2: Subtract 9 from both sides of −3y + 9 = −6, then divide by −3!
• Answer: 5

[Medium] Percent Decrease

• EN: A jacket originally costs $120. After a sale, it costs $90. What is the percent decrease?
• FR: Un manteau coûte à l'origine 120 $. Après la vente, il coûte 90 $. Quel est le pourcentage de diminution?
• Choices: A) 20% B) 30% C) 25% D) 15%
• Hint: Percent decrease = (decrease ÷ original) × 100! For example, from $80 to $60: decrease = 20, 20 ÷ 80 × 100 = 25%.
• Steps:
  • Step 1: Try from $200 to $150. Decrease = 50. 50 ÷ 200 × 100 = 25%.
  • Step 2: Find the decrease ($120 − $90), divide by original ($120), then multiply by 100!
• Answer: 25%

[Medium] Mean, Median, Mode

• EN: The snowfall (cm) over 5 days was: 4, 8, 4, 10, 4. Find the mode.
• FR: Les chutes de neige (cm) pendant 5 jours étaient: 4, 8, 4, 10, 4. Trouve le mode.
• Choices: A) 8 B) 6 C) 4 D) 10
• Hint: The mode is the value that appears most often! For example, in 2, 5, 2, 7, 2 — the number 2 appears 3 times, so mode = 2.
• Steps:
  • Step 1: Try 9, 3, 9, 6, 3, 9. Count: 9 appears 3 times, 3 appears 2 times. Mode = 9.
  • Step 2: Now count how many times each number appears in 4, 8, 4, 10, 4 and find the most frequent!
• Answer: 4

[Medium] Slope from Two Points

• EN: What is the slope of the line through (2, 5) and (6, 13)?
• FR: Quelle est la pente de la droite passant par (2, 5) et (6, 13)?
• Choices: A) 1 B) 3 C) 2 D) 4
• Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁)! For example, points (1, 3) and (4, 9): slope = (9−3)÷(4−1) = 6÷3 = 2.
• Steps:
  • Step 1: Try (2, 4) and (5, 10). Slope = (10−4) ÷ (5−2) = 6 ÷ 3 = 2.
  • Step 2: Now calculate (13−5) ÷ (6−2) to find the slope of the real line!
• Answer: 2

[Medium] Square Roots and Estimation

• EN: Between which two consecutive whole numbers does √50 lie?
• FR: Entre quels deux nombres entiers consécutifs se trouve √50?
• Choices: A) 6 and 7 B) 8 and 9 C) 7 and 8 D) 5 and 6
• Hint: Find perfect squares on either side! For example, √30: 5² = 25, 6² = 36. So √30 is between 5 and 6.
• Steps:
  • Step 1: Try √75. 8² = 64, 9² = 81. Since 64 < 75 < 81, √75 is between 8 and 9.
  • Step 2: Find what perfect squares are on each side of 50. What are 7² and 8²?
• Answer: 7 and 8

[Hard] Pythagorean Theorem Application

• EN: A camper walks 9 km north and 12 km east. How far is she from her starting point (straight-line distance)?
• FR: Un campeur marche 9 km vers le nord et 12 km vers l'est. Quelle est la distance en ligne droite jusqu'au point de départ?
• Choices: A) 13 km B) 16 km C) 15 km D) 21 km
• Hint: Use a² + b² = c². The two paths are the legs of a right triangle! For example, 6 north and 8 east: 36 + 64 = 100. √100 = 10 km.
• Steps:
  • Step 1: Try 5 km north, 12 km east. 5² + 12² = 25 + 144 = 169. √169 = 13 km.
  • Step 2: Now calculate 9² + 12², add them, and take the square root!
• Answer: 15 km

[Hard] Two-Step Equation — Real Life

• EN: Mia earns $12 per hour. After buying a $9 snack, she has $63 left. How many hours did she work?
• FR: Mia gagne 12 $ par heure. Après avoir acheté une collation à 9 $, il lui reste 63 $. Combien d'heures a-t-elle travaillé?
• Choices: A) 5 B) 7 C) 6 D) 8
• Hint: Set up the equation: 12h − 9 = 63. Solve by adding 9 first, then dividing! For example, 10h − 5 = 45. Add 5: 10h = 50. h = 5.
• Steps:
  • Step 1: Try 8h − 4 = 44. Add 4: 8h = 48. Divide by 8: h = 6.
  • Step 2: Write 12h − 9 = 63. Add 9 to both sides, then divide by 12!
• Answer: 6

[Hard] Percent Increase/Decrease Chain

• EN: A loonie's buying power decreased by 10% and then increased by 20%. What is the overall percent change from the original?
• FR: Le pouvoir d'achat d'un huard a diminué de 10%, puis augmenté de 20%. Quel est le pourcentage de changement global par rapport à l'original?
• Choices: A) 8% B) 10% C) 6% D) 12%
• Hint: Apply each change to the running value! For example, start with 100, decrease 10%: 90, then increase 20%: 90 × 1.20 = 108. That's an 8% overall increase.
• Steps:
  • Step 1: Try decrease 20% then increase 10%. Start at 100: 100 × 0.80 = 80. Then 80 × 1.10 = 88. Change: −12%.
  • Step 2: Start at 100, multiply by 0.90 (10% decrease), then multiply by 1.20 (20% increase). Compare to 100!
• Answer: 8%

[Hard] Slope and Linear Relationship

• EN: A line has slope 3 and passes through (0, −2). What is the y-value when x = 5?
• FR: Une droite a une pente de 3 et passe par (0, −2). Quelle est la valeur de y quand x = 5?
• Choices: A) 11 B) 15 C) 13 D) 17
• Hint: Use y = mx + b. m is the slope, b is the y-intercept! For example, slope = 2, passes through (0, 3): y = 2x + 3. At x = 4: y = 2(4) + 3 = 11.
• Steps:
  • Step 1: Try slope 4, passes through (0, 1): y = 4x + 1. At x = 3: y = 4(3) + 1 = 13.
  • Step 2: Write the equation y = 3x − 2, then substitute x = 5!
• Answer: 13

[Easy] Solving a Linear Equation

• EN: Solve for x: 4x − 6 = 18
• FR: Résous pour x: 4x − 6 = 18
• Choices: A) 4 B) 7 C) 5 D) 6
• Hint: Add 6 to both sides first, then divide by 4! For example, 5x − 3 = 12. Add 3: 5x = 15. Divide: x = 3.
• Steps:
  • Step 1: Try 3x − 5 = 16. Add 5: 3x = 21. Divide by 3: x = 7.
  • Step 2: Now add 6 to both sides of 4x − 6 = 18, then divide both sides by 4!
• Answer: 6

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3)
• FR: Simplifie: (3x + 5) + (2x − 3)
• Choices: A) 5x − 2 B) 5x + 8 C) 5x + 2 D) 6x + 2
• Hint: Combine like terms — add the x terms together and the constants together! For example, (4x + 2) + (3x − 1) = 7x + 1.
• Steps:
  • Step 1: Try (5x + 3) + (4x − 7). x terms: 5x + 4x = 9x. Constants: 3 + (−7) = −4. Answer: 9x − 4.
  • Step 2: Now add the x terms (3x + 2x) and the constants (5 + (−3)) separately!
• Answer: 5x + 2

[Easy] Graphing Lines — Slope-Intercept

• EN: What is the y-intercept of the line y = 4x − 7?
• FR: Quel est l'ordonnée à l'origine de la droite y = 4x − 7?
• Choices: A) 4 B) −4 C) 7 D) −7
• Hint: In y = mx + b, the y-intercept is b — the constant at the end! For example, in y = 3x + 5, the y-intercept is 5.
• Steps:
  • Step 1: Look at y = 6x − 9. The y-intercept is the number added at the end: −9.
  • Step 2: Now identify the constant (b) in y = 4x − 7. That's your y-intercept!
• Answer: −7

[Easy] SOH-CAH-TOA — Finding a Ratio

• EN: In a right triangle, the opposite side is 3 and the hypotenuse is 5. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé est 3 et l'hypoténuse est 5. Quel est sin(θ)?
• Choices: A) 5/3 B) 4/5 C) 3/4 D) 3/5
• Hint: SOH: Sin = Opposite ÷ Hypotenuse! For example, opposite = 4, hypotenuse = 10: sin = 4/10 = 2/5.
• Steps:
  • Step 1: Try opposite = 6, hypotenuse = 10. sin = 6/10 = 3/5.
  • Step 2: Now write opposite (3) over hypotenuse (5) to find sin(θ)!
• Answer: 3/5

[Easy] Linear Inequality

• EN: Solve: x + 5 > 11
• FR: Résous: x + 5 > 11
• Choices: A) x > 5 B) x > 7 C) x > 6 D) x > 4
• Hint: Solve inequalities like equations — isolate the variable! For example, x + 3 > 9. Subtract 3: x > 6.
• Steps:
  • Step 1: Try x + 8 > 15. Subtract 8 from both sides: x > 7.
  • Step 2: Now subtract 5 from both sides of x + 5 > 11!
• Answer: x > 6

[Medium] Multiplying Polynomials

• EN: Expand: 3(2x − 5)
• FR: Développe: 3(2x − 5)
• Choices: A) 6x − 15 B) 6x + 15 C) 5x − 15 D) 6x − 8
• Hint: Distribute — multiply 3 by each term inside the brackets! For example, 4(3x − 2) = 12x − 8.
• Steps:
  • Step 1: Try 5(4x − 3). Multiply: 5 × 4x = 20x, 5 × (−3) = −15. Answer: 20x − 15.
  • Step 2: Now multiply 3 × 2x and 3 × (−5) to expand 3(2x − 5)!
• Answer: 6x − 15

[Medium] Similar Triangles

• EN: Two triangles are similar. The smaller triangle has sides 3 and 5. The larger triangle has a side of 15 corresponding to the 5-side. What is the other side of the larger triangle?
• FR: Deux triangles sont semblables. Le plus petit a des côtés de 3 et 5. Le plus grand a un côté de 15 correspondant au côté 5. Quel est l'autre côté du grand triangle?
• Choices: A) 6 B) 12 C) 9 D) 15
• Hint: Similar triangles have proportional sides. Find the scale factor first! For example, small side 4 → large side 12: scale factor = 12 ÷ 4 = 3. Multiply all small sides by 3.
• Steps:
  • Step 1: Try small sides 2 and 6, large triangle has side 18 corresponding to 6. Scale factor = 18 ÷ 6 = 3. Other side = 2 × 3 = 6.
  • Step 2: Find the scale factor (15 ÷ 5), then multiply the other small side (3) by the scale factor!
• Answer: 9

[Medium] Graphing Lines — Finding Points

• EN: For the line y = 2x + 3, what is y when x = 4?
• FR: Pour la droite y = 2x + 3, quelle est la valeur de y quand x = 4?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Substitute the x-value into the equation! For example, y = 3x − 1 at x = 5: y = 3(5) − 1 = 14.
• Steps:
  • Step 1: Try y = 5x + 2 at x = 3. Substitute: y = 5(3) + 2 = 15 + 2 = 17.
  • Step 2: Now substitute x = 4 into y = 2x + 3 and calculate!
• Answer: 11

[Medium] Trigonometry — Finding a Side

• EN: In a right triangle, θ = 30°, hypotenuse = 20 cm. What is the length of the opposite side? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, θ = 30°, hypoténuse = 20 cm. Quelle est la longueur du côté opposé? (sin 30° = 0,5)
• Choices: A) 8 cm B) 12 cm C) 10 cm D) 15 cm
• Hint: SOH: sin(θ) = opposite ÷ hypotenuse. Rearrange: opposite = sin(θ) × hypotenuse! For example, sin 45° ≈ 0.7, hypotenuse = 10: opposite = 0.7 × 10 = 7 cm.
• Steps:
  • Step 1: Try sin 60° = 0.87, hypotenuse = 20. Opposite = 0.87 × 20 = 17.4 cm.
  • Step 2: Now multiply sin(30°) = 0.5 by the hypotenuse (20 cm)!
• Answer: 10 cm

[Medium] Polynomial Subtraction

• EN: Simplify: (6x² + 4x − 3) − (2x² − x + 5)
• FR: Simplifie: (6x² + 4x − 3) − (2x² − x + 5)
• Choices: A) 4x² + 3x − 8 B) 4x² + 5x − 8 C) 4x² + 3x + 8 D) 8x² + 3x − 8
• Hint: Distribute the negative sign before combining like terms! For example, (5x² + 3x − 1) − (2x² − 4x + 3) = 5x² + 3x − 1 − 2x² + 4x − 3 = 3x² + 7x − 4.
• Steps:
  • Step 1: Try (7x² + 2x − 5) − (3x² − 4x + 1). Distribute negative: 7x² + 2x − 5 − 3x² + 4x − 1 = 4x² + 6x − 6.
  • Step 2: Distribute the negative across (2x² − x + 5), then combine like terms with (6x² + 4x − 3)!
• Answer: 4x² + 5x − 8

[Medium] Statistics — Mean vs. Median

• EN: A student's test scores are: 55, 70, 75, 80, 95. Which is greater: the mean or the median?
• FR: Les résultats de tests d'un élève sont: 55, 70, 75, 80, 95. Qu'est-ce qui est plus grand: la moyenne ou la médiane?
• Choices: A) They are equal B) The median C) The mean D) Cannot tell
• Hint: Mean = sum ÷ count; Median = middle value when sorted. Calculate both and compare! For example, 10, 20, 30: mean = 20, median = 20 — equal!
• Steps:
  • Step 1: Try 40, 60, 80, 100, 120. Mean = 400 ÷ 5 = 80. Median = 80. Equal.
  • Step 2: Find the mean (sum ÷ 5) and median (middle value) of the real scores, then compare!
• Answer: The mean

[Hard] Solving a Linear Inequality and Graphing

• EN: Solve: 2x − 5 < 7. Which value of x is NOT a solution: x = 4, x = 6, x = 0, x = −2?
• FR: Résous: 2x − 5 < 7. Quelle valeur de x n'est PAS une solution: x = 4, x = 6, x = 0, x = −2?
• Choices: A) x = 0 B) x = 4 C) x = −2 D) x = 6
• Hint: Solve the inequality first to find the boundary, then test each option! For example, 3x − 4 < 8: 3x < 12, x < 4. So x = 5 is NOT a solution.
• Steps:
  • Step 1: Try 4x − 3 < 13. Add 3: 4x < 16. Divide: x < 4. Test x = 5: 5 is not < 4, so NOT a solution.
  • Step 2: Solve 2x − 5 < 7 (add 5, then divide by 2) to find the boundary. Then check which given x-value does NOT satisfy it!
• Answer: x = 6

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side = 8 cm and the hypotenuse = 10 cm. What is cos(θ)? Then use that to identify θ. (cos 37° ≈ 0.8)
• FR: Dans un triangle rectangle, le côté adjacent = 8 cm et l'hypoténuse = 10 cm. Quel est cos(θ)? Utilisez-le pour identifier θ. (cos 37° ≈ 0,8)
• Choices: A) θ = 30° B) θ = 45° C) θ = 37° D) θ = 53°
• Hint: CAH: cos(θ) = adjacent ÷ hypotenuse. Then match the decimal to a known angle! For example, adjacent = 6, hypotenuse = 10: cos = 0.6 ≈ cos 53°.
• Steps:
  • Step 1: Try adjacent = 5, hypotenuse = 10. cos = 5/10 = 0.5. Since cos 60° = 0.5, θ = 60°.
  • Step 2: Find cos(θ) = 8/10 = 0.8. Then match 0.8 to the given cosine value!
• Answer: θ = 37°

[Hard] Systems of Equations — Substitution

• EN: Solve the system: y = 2x + 1 and y = x + 5. What is x?
• FR: Résous le système: y = 2x + 1 et y = x + 5. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 5 C) x = 4 D) x = 3
• Hint: Set the two expressions equal to each other! For example, y = 3x − 1 and y = x + 5: 3x − 1 = x + 5. Solve: 2x = 6, x = 3.
• Steps:
  • Step 1: Try y = 4x and y = x + 9. Set equal: 4x = x + 9. 3x = 9. x = 3.
  • Step 2: Set 2x + 1 = x + 5, then solve for x by subtracting x from both sides!
• Answer: x = 4

[Hard] Polynomial Multiplication

• EN: Expand and simplify: (x + 4)(x − 3)
• FR: Développe et simplifie: (x + 4)(x − 3)
• Choices: A) x² + x − 12 B) x² − x + 12 C) x² + x + 12 D) x² − x − 12
• Hint: Use FOIL — First, Outside, Inside, Last! For example, (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.
• Steps:
  • Step 1: Try (x + 3)(x − 2). FOIL: x² − 2x + 3x − 6 = x² + x − 6.
  • Step 2: Now apply FOIL to (x + 4)(x − 3): First = x², Outside = −3x, Inside = 4x, Last = −12. Combine!
• Answer: x² + x − 12

[Easy] Factoring a Quadratic

• EN: Factor: x² + 7x + 12
• FR: Factorise: x² + 7x + 12
• Choices: A) (x + 3)(x + 4) B) (x + 2)(x + 6) C) (x + 1)(x + 12) D) (x + 3)(x + 5)
• Hint: Find two numbers that multiply to 12 and add to 7! For example, x² + 5x + 6: numbers are 2 and 3 (2×3=6, 2+3=5), so (x+2)(x+3).
• Steps:
  • Step 1: Try x² + 9x + 20. Numbers that multiply to 20 and add to 9: 4 and 5. Answer: (x+4)(x+5).
  • Step 2: Now find two numbers that multiply to 12 and add to 7, then write them in factor form!
• Answer: (x + 3)(x + 4)

[Easy] Trigonometric Ratios

• EN: In a right triangle, opposite = 5, adjacent = 12, hypotenuse = 13. What is tan(θ)?
• FR: Dans un triangle rectangle, opposé = 5, adjacent = 12, hypoténuse = 13. Quel est tan(θ)?
• Choices: A) 12/13 B) 5/13 C) 12/5 D) 5/12
• Hint: TOA: tan(θ) = Opposite ÷ Adjacent! For example, opposite = 3, adjacent = 4: tan = 3/4.
• Steps:
  • Step 1: Try opposite = 7, adjacent = 24. tan = 7/24.
  • Step 2: Now write opposite (5) over adjacent (12) to find tan(θ)!
• Answer: 5/12

[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) 5 B) 8 C) 6 D) 7
• Hint: Add the two equations to eliminate y! For example, x + y = 8 and x − y = 2: add them: 2x = 10, x = 5.
• Steps:
  • Step 1: Try x + y = 12 and x − y = 6. Add: 2x = 18. x = 9.
  • Step 2: Now add x + y = 10 and x − y = 4 together. The y terms cancel out!
• Answer: 7

[Easy] Volume of a Cylinder

• EN: A cylindrical can has radius 3 cm and height 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilisez π ≈ 3,14)
• Choices: A) 251.2 cm³ B) 282.6 cm³ C) 264.5 cm³ D) 188.4 cm³
• Hint: Volume of cylinder = π × r² × h! For example, r = 2, h = 5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • Step 1: Try r = 4, h = 7. V = 3.14 × 16 × 7 = 3.14 × 112 = 351.68 cm³.
  • Step 2: Calculate r² = 3² = 9, then V = 3.14 × 9 × 10!
• Answer: 282.6 cm³

[Easy] Circle Geometry — Central Angle

• EN: An arc covers a central angle of 90°. What fraction of the full circle does it represent?
• FR: Un arc couvre un angle central de 90°. Quelle fraction du cercle complet représente-t-il?
• Choices: A) 1/3 B) 1/2 C) 1/6 D) 1/4
• Hint: A full circle = 360°. Divide the central angle by 360°! For example, 120° ÷ 360° = 1/3 of the circle.
• Steps:
  • Step 1: Try 60°. 60 ÷ 360 = 1/6. So a 60° arc is 1/6 of the circle.
  • Step 2: Now divide 90° by 360° to find what fraction of the circle the arc represents!
• Answer: 1/4

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x + 5 = 0
• FR: Résous en complétant le carré: x² + 6x + 5 = 0
• Choices: A) x = −1 or x = −5 B) x = 1 or x = 5 C) x = −1 or x = 5 D) x = 2 or x = −4
• Hint: Complete the square: move the constant, add (b/2)²! For example, x² + 4x + 3 = 0 → x² + 4x = −3 → (x+2)² = 1 → x = −1 or x = −3.
• Steps:
  • Step 1: Try x² + 8x + 7 = 0. Move 7: x² + 8x = −7. Add (4)²=16: (x+4)² = 9. x+4 = ±3. x = −1 or x = −7.
  • Step 2: Now move 5, add (3)²=9 to both sides, take square roots, and solve!
• Answer: x = −1 or x = −5

[Medium] Quadratic Formula

• EN: Using the quadratic formula, solve: x² − 5x + 6 = 0
• FR: En utilisant la formule quadratique, résous: x² − 5x + 6 = 0
• Choices: A) x = 2 or x = 3 B) x = −2 or x = −3 C) x = 1 or x = 6 D) x = 2 or x = −3
• Hint: x = (−b ± √(b²−4ac)) / 2a. For x² − 5x + 6: a=1, b=−5, c=6. Discriminant = 25 − 24 = 1!
• Steps:
  • Step 1: Try x² − 7x + 12 = 0. a=1,b=−7,c=12. Disc = 49−48=1. x = (7±1)/2. x=4 or x=3.
  • Step 2: Calculate disc = (−5)² − 4(1)(6) = 25 − 24 = 1. Then x = (5 ± 1) ÷ 2!
• Answer: x = 2 or x = 3

[Medium] Systems of Equations — Elimination

• EN: Solve: 3x + 2y = 16 and x + 2y = 8. What is x?
• FR: Résous: 3x + 2y = 16 et x + 2y = 8. Quelle est la valeur de x?
• Choices: A) 2 B) 5 C) 4 D) 3
• Hint: Subtract one equation from the other to eliminate a variable! For example, 5x + 2y = 20 and 3x + 2y = 16: subtract: 2x = 4, x = 2.
• Steps:
  • Step 1: Try 4x + y = 15 and 2x + y = 9. Subtract: 2x = 6. x = 3.
  • Step 2: Subtract the second equation from the first: (3x + 2y) − (x + 2y) = 16 − 8. Simplify!
• Answer: 4

[Medium] Trigonometry — Finding a Missing Side

• EN: In a right triangle, θ = 45°, the adjacent side = 9 cm. Find the hypotenuse. (cos 45° ≈ 0.707)
• FR: Dans un triangle rectangle, θ = 45°, le côté adjacent = 9 cm. Trouve l'hypoténuse. (cos 45° ≈ 0,707)
• Choices: A) 10.5 cm B) 12.7 cm C) 11.5 cm D) 13.2 cm
• Hint: CAH: cos(θ) = adjacent ÷ hypotenuse. Rearrange: hypotenuse = adjacent ÷ cos(θ)! For example, adj = 6, cos 30° = 0.866: hyp = 6 ÷ 0.866 ≈ 6.93 cm.
• Steps:
  • Step 1: Try adj = 10, cos 60° = 0.5. Hyp = 10 ÷ 0.5 = 20 cm.
  • Step 2: Now divide the adjacent side (9 cm) by cos(45°) ≈ 0.707!
• Answer: 12.7 cm

[Medium] Surface Area of a Cone

• EN: A cone has radius 4 cm and slant height 9 cm. What is its surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur de côté de 9 cm. Quelle est son aire totale? (Utilisez π ≈ 3,14)
• Choices: A) 163.28 cm² B) 150.72 cm² C) 163.28 cm² D) 175.84 cm²
• Hint: SA of cone = πr² + πrl (base + lateral)! For example, r=3, l=7: SA = 3.14×9 + 3.14×3×7 = 28.26 + 65.94 = 94.2 cm².
• Steps:
  • Step 1: Try r=5, l=8. Base = 3.14×25 = 78.5. Lateral = 3.14×5×8 = 125.6. SA = 204.1 cm².
  • Step 2: Calculate 3.14 × 4² for the base, then add 3.14 × 4 × 9 for the lateral surface!
• Answer: 163.28 cm²

[Medium] Circle Geometry — Inscribed Angle

• EN: An inscribed angle is 35°. What is the central angle that subtends the same arc?
• FR: Un angle inscrit est de 35°. Quel est l'angle central qui sous-tend le même arc?
• Choices: A) 17.5° B) 35° C) 70° D) 105°
• Hint: The central angle is twice the inscribed angle that subtends the same arc! For example, inscribed angle = 40°: central angle = 80°.
• Steps:
  • Step 1: Try inscribed angle = 50°. Central angle = 2 × 50° = 100°.
  • Step 2: Multiply the inscribed angle (35°) by 2 to find the central angle!
• Answer: 70°

[Hard] Completing the Square — Vertex Form

• EN: Write y = x² − 8x + 7 in vertex form. What is the vertex?
• FR: Écris y = x² − 8x + 7 sous forme canonique. Quel est le sommet?
• Choices: A) (4, −9) B) (−4, 9) C) (4, 9) D) (−4, −9)
• Hint: Complete the square: y = (x − h)² + k. The vertex is (h, k)! For example, y = x² − 6x + 5 → y = (x−3)² − 4. Vertex: (3, −4).
• Steps:
  • Step 1: Try y = x² − 10x + 16. Half of 10 = 5. y = (x−5)² − 25 + 16 = (x−5)² − 9. Vertex: (5, −9).
  • Step 2: Take half of 8 = 4. Square it = 16. y = (x−4)² − 16 + 7. Find the vertex!
• Answer: (4, −9)

[Hard] Quadratic Word Problem

• EN: A ball is thrown upward. Its height is h = −5t² + 20t + 0 metres, where t is in seconds. At what time does it reach maximum height?
• FR: Une balle est lancée vers le haut. Sa hauteur est h = −5t² + 20t mètres, où t est en secondes. À quel moment atteint-elle la hauteur maximale?
• Choices: A) t = 1 s B) t = 4 s C) t = 3 s D) t = 2 s
• Hint: For a quadratic h = at² + bt + c, maximum occurs at t = −b/(2a)! For example, h = −4t² + 16t: t = −16/(2×−4) = 2 seconds.
• Steps:
  • Step 1: Try h = −3t² + 12t. t = −12/(2×−3) = −12/−6 = 2 seconds.
  • Step 2: Identify a = −5 and b = 20 in −5t² + 20t. Then calculate t = −20/(2×−5)!
• Answer: t = 2 s

[Hard] System of Equations — Quadratic and Linear

• EN: Find the x-values where y = x² and y = x + 6 intersect.
• FR: Trouve les valeurs de x où y = x² et y = x + 6 se croisent.
• Choices: A) x = 3 and x = −2 B) x = 2 and x = −3 C) x = 6 and x = 1 D) x = −6 and x = 1
• Hint: Set the expressions equal: x² = x + 6. Rearrange to x² − x − 6 = 0, then factor! For example, x² = x + 2: x² − x − 2 = 0 → (x−2)(x+1) = 0, x = 2 or x = −1.
• Steps:
  • Step 1: Try x² = 2x + 3. Rearrange: x² − 2x − 3 = 0. Factor: (x−3)(x+1) = 0. x = 3 or x = −1.
  • Step 2: Set x² = x + 6. Move everything to one side: x² − x − 6 = 0. Then factor!
• Answer: x = 3 and x = −2

[Hard] 3D Geometry — Sphere Surface Area and Volume

• EN: A sphere has radius 6 cm. What is its surface area? (Use π ≈ 3.14)
• FR: Une sphère a un rayon de 6 cm. Quelle est son aire totale? (Utilisez π ≈ 3,14)
• Choices: A) 376.8 cm² B) 452.16 cm² C) 408.2 cm² D) 504.0 cm²
• Hint: Surface area of a sphere = 4πr²! For example, r = 3: SA = 4 × 3.14 × 9 = 113.04 cm².
• Steps:
  • Step 1: Try r = 5. SA = 4 × 3.14 × 25 = 314 cm².
  • Step 2: Now calculate 4 × 3.14 × 6² = 4 × 3.14 × 36!
• Answer: 452.16 cm²

[Easy] Identifying a Function Type

• EN: Which equation represents an exponential function?
• FR: Quelle équation représente une fonction exponentielle?
• Choices: A) y = 3x + 2 B) y = x² C) y = 3ˣ D) y = x + 3
• Hint: Exponential functions have the variable in the exponent! For example, y = 5ˣ or y = 2ˣ. Linear functions have x to the first power; quadratic has x².
• Steps:
  • Step 1: Look at y = 4ˣ. The variable x is in the exponent, so it is exponential.
  • Step 2: Check each option — which one has x as the exponent, not as the base?
• Answer: y = 3ˣ

[Easy] Arithmetic Sequence

• EN: Find the next term: 7, 13, 19, 25, ___
• FR: Trouve le prochain terme: 7, 13, 19, 25, ___
• Choices: A) 29 B) 33 C) 31 D) 35
• Hint: Find the common difference and add it! For example, 4, 9, 14, 19 — difference is 5. Next term: 19 + 5 = 24.
• Steps:
  • Step 1: Try 8, 14, 20, 26. Difference = 6. Next: 26 + 6 = 32.
  • Step 2: Find the difference between terms in 7, 13, 19, 25, then add it to 25!
• Answer: 31

[Easy] Introduction to Logarithms

• EN: What is log₂(8)?
• FR: Combien vaut log₂(8)?
• Choices: A) 4 B) 2 C) 3 D) 5
• Hint: log_b(x) = y means b^y = x! For example, log₃(9) = 2 because 3² = 9.
• Steps:
  • Step 1: Try log₅(25). Ask: 5 to what power = 25? Since 5² = 25, log₅(25) = 2.
  • Step 2: Ask: 2 to what power = 8? Try 2¹ = 2, 2² = 4, 2³ = 8. What is the exponent?
• Answer: 3

[Easy] Simple Interest vs. Compound Interest

• EN: $1000 is invested at 5% annual interest. What is the simple interest earned after 3 years?
• FR: 1 000 $ sont investis à un taux d'intérêt annuel de 5%. Quel est l'intérêt simple gagné après 3 ans?
• Choices: A) $100 B) $175 C) $150 D) $200
• Hint: Simple Interest = Principal × Rate × Time! For example, $500 at 4% for 2 years: 500 × 0.04 × 2 = $40.
• Steps:
  • Step 1: Try $800 at 3% for 4 years. I = 800 × 0.03 × 4 = $96.
  • Step 2: Now calculate 1000 × 0.05 × 3 to find the simple interest!
• Answer: $150

[Easy] Evaluating a Quadratic Function

• EN: If f(x) = 2x² − 3x + 1, what is f(3)?
• FR: Si f(x) = 2x² − 3x + 1, quelle est la valeur de f(3)?
• Choices: A) 8 B) 12 C) 10 D) 14
• Hint: Substitute x = 3 into the function and evaluate! For example, f(x) = x² + 2x, f(4) = 16 + 8 = 24.
• Steps:
  • Step 1: Try f(x) = 3x² − 2x + 4, f(2). Substitute: 3(4) − 2(2) + 4 = 12 − 4 + 4 = 12.
  • Step 2: Now substitute x = 3 into 2x² − 3x + 1: 2(9) − 3(3) + 1 = 18 − 9 + 1!
• Answer: 10

[Medium] Geometric Sequence

• EN: Find the 5th term of the geometric sequence: 2, 6, 18, 54, ___
• FR: Trouve le 5e terme de la suite géométrique: 2, 6, 18, 54, ___
• Choices: A) 108 B) 182 C) 162 D) 144
• Hint: Multiply by the common ratio each time! For example, 3, 12, 48 — ratio = 4. Next: 48 × 4 = 192.
• Steps:
  • Step 1: Try 5, 15, 45, 135. Ratio = 3. Next: 135 × 3 = 405.
  • Step 2: Find the ratio (6 ÷ 2 = 3), then multiply the 4th term (54) by the ratio!
• Answer: 162

[Medium] Compound Interest

• EN: $2000 is invested at 6% compounded annually for 2 years. What is the total amount after 2 years?
• FR: 2 000 $ sont investis à 6% composé annuellement pendant 2 ans. Quel est le montant total après 2 ans?
• Choices: A) $2240.00 B) $2247.20 C) $2224.00 D) $2260.00
• Hint: A = P(1 + r)^t! For example, $1000 at 5% for 2 years: A = 1000 × (1.05)² = 1000 × 1.1025 = $1102.50.
• Steps:
  • Step 1: Try $3000 at 4% for 2 years. A = 3000 × (1.04)² = 3000 × 1.0816 = $3244.80.
  • Step 2: Now calculate 2000 × (1.06)². First find 1.06² = 1.1236, then multiply!
• Answer: $2247.20

[Medium] Logarithm Properties

• EN: Evaluate: log₃(27) + log₃(9)
• FR: Évalue: log₃(27) + log₃(9)
• Choices: A) 4 B) 6 C) 5 D) 7
• Hint: Use the product rule: logb(x) + logb(y) = log_b(xy)! For example, log₂(4) + log₂(8) = log₂(32) = 5.
• Steps:
  • Step 1: Try log₂(4) + log₂(8). Product: log₂(32). Since 2⁵ = 32, answer = 5.
  • Step 2: Either find each log separately (3² = 9, so log₃(9)=2; 3³=27, so log₃(27)=3) and add, or use the product rule!
• Answer: 5

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ)
• FR: Simplifie: sin²(θ) + cos²(θ)
• Choices: A) 2 B) 0 C) sin(2θ) D) 1
• Hint: This is one of the most important trig identities! For example, for any angle, if sin(θ) = 0.6 and cos(θ) = 0.8: 0.36 + 0.64 = 1. Always equals 1!
• Steps:
  • Step 1: Try θ = 30°. sin(30°) = 0.5, cos(30°) ≈ 0.866. (0.5)² + (0.866)² = 0.25 + 0.75 = 1.
  • Step 2: This is the Pythagorean identity — it always simplifies to the same constant!
• Answer: 1

[Medium] Exponential Growth

• EN: A town's population doubles every 10 years. If it starts at 5000, what is the population after 20 years?
• FR: La population d'une ville double tous les 10 ans. Si elle commence à 5 000, quelle sera la population après 20 ans?
• Choices: A) 15000 B) 25000 C) 20000 D) 10000
• Hint: Doubling twice = multiply by 2 twice! For example, starts at 3000, doubles every 5 years: after 10 years = 3000 × 2 × 2 = 12000.
• Steps:
  • Step 1: Try 4000 doubles every 6 years. After 12 years: 4000 × 2 × 2 = 16000.
  • Step 2: If the population doubles every 10 years, after 20 years it has doubled twice. Multiply 5000 × 2 × 2!
• Answer: 20000

[Medium] Arithmetic Series

• EN: Find the sum of the first 8 terms of the sequence: 3, 7, 11, 15, ...
• FR: Trouve la somme des 8 premiers termes de la suite: 3, 7, 11, 15, ...
• Choices: A) 112 B) 130 C) 120 D) 136
• Hint: Sum of arithmetic series = n/2 × (first + last)! First find the 8th term, then use the formula. For example, 1, 4, 7, 10... (d=3): 8th term = 1 + 7×3 = 22. Sum = 8/2 × (1+22) = 4 × 23 = 92.
• Steps:
  • Step 1: Try 5, 9, 13... first 6 terms. 6th term = 5 + 5×4 = 25. Sum = 6/2 × (5+25) = 3 × 30 = 90.
  • Step 2: Find the 8th term (a₈ = 3 + 7×4 = 31), then use S = 8/2 × (3+31)!
• Answer: 136

[Hard] Solving Logarithmic Equations

• EN: Solve for x: log₂(x) + log₂(4) = 5
• FR: Résous pour x: log₂(x) + log₂(4) = 5
• Choices: A) x = 4 B) x = 16 C) x = 8 D) x = 12
• Hint: Combine logs using the product rule, then convert! For example, log₃(x) + log₃(3) = 4 → log₃(3x) = 4 → 3x = 3⁴ = 81 → x = 27.
• Steps:
  • Step 1: Try log₂(x) + log₂(8) = 6. Combine: log₂(8x) = 6. So 8x = 2⁶ = 64. x = 8.
  • Step 2: Combine log₂(x) + log₂(4) = log₂(4x) = 5. So 4x = 2⁵ = 32. Solve for x!
• Answer: x = 8

[Hard] Annuity Calculation

• EN: A student deposits $200 at the end of each month into a savings account with 6% annual interest compounded monthly. What is the approximate total after 3 months?
• FR: Un étudiant dépose 200 $ à la fin de chaque mois dans un compte d'épargne avec un taux annuel de 6% composé mensuellement. Quel est le total approximatif après 3 mois?
• Choices: A) $603.01 B) $606.02 C) $612.04 D) $600.00
• Hint: Monthly rate = 6%/12 = 0.5% = 0.005. Each deposit earns interest for remaining months. Month 1: $200×(1.005)², Month 2: $200×(1.005)¹, Month 3: $200!
• Steps:
  • Step 1: Try 3 monthly deposits of $100 at 0.5%/month. Deposit 1: 100×1.005² = $101.00. Deposit 2: 100×1.005 = $100.50. Deposit 3: $100.00. Total ≈ $301.50.
  • Step 2: Calculate each $200 deposit with compound interest: 200×(1.005)², 200×(1.005)¹, and 200. Then add all three!
• Answer: $606.02

[Hard] Trigonometric Equations

• EN: Solve for θ in [0°, 360°]: 2sin(θ) − 1 = 0
• FR: Résous pour θ dans [0°, 360°]: 2sin(θ) − 1 = 0
• Choices: A) θ = 30° and 150° B) θ = 60° and 120° C) θ = 45° and 135° D) θ = 30° and 210°
• Hint: Solve for sin(θ) first, then find all angles in [0°, 360°]! For example, 2sin(θ) = √2 → sin(θ) = √2/2 → θ = 45° and 135°.
• Steps:
  • Step 1: Try 2sin(θ) − √3 = 0. sin(θ) = √3/2. Angles: 60° and 120°.
  • Step 2: Isolate sin(θ) in 2sin(θ) − 1 = 0. sin(θ) = 1/2. Find both angles where sin = 0.5!
• Answer: θ = 30° and 150°

[Hard] Exponential Equation

• EN: Solve for x: 4ˣ = 64
• FR: Résous pour x: 4ˣ = 64
• Choices: A) x = 2 B) x = 4 C) x = 3 D) x = 5
• Hint: Express 64 as a power of 4, then equate exponents! For example, 3ˣ = 81. Since 81 = 3⁴, x = 4.
• Steps:
  • Step 1: Try 2ˣ = 32. Since 32 = 2⁵, x = 5.
  • Step 2: Express 64 as a power of 4. Since 4¹ = 4, 4² = 16, 4³ = 64, what is x?
• Answer: x = 3

[Easy] Permutations

• EN: In how many ways can 5 students line up in a row?
• FR: De combien de façons 5 élèves peuvent-ils se mettre en file?
• Choices: A) 60 B) 100 C) 120 D) 24
• Hint: Permutation of n items = n! For example, 4 students: 4! = 4 × 3 × 2 × 1 = 24 ways.
• Steps:
  • Step 1: Try 6 students. 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 ways.
  • Step 2: Now calculate 5! = 5 × 4 × 3 × 2 × 1!
• Answer: 120

[Easy] Combinations

• EN: A committee of 3 is chosen from 6 students. How many different committees are possible?
• FR: Un comité de 3 personnes est choisi parmi 6 élèves. Combien de comités différents sont possibles?
• Choices: A) 18 B) 30 C) 20 D) 24
• Hint: C(n, r) = n! / (r!(n−r)!)! For example, C(5,2) = 5!/(2!×3!) = 120/12 = 10.
• Steps:
  • Step 1: Try C(7,3) = 7!/(3!×4!) = 5040/(6×24) = 35.
  • Step 2: Calculate C(6,3) = 6!/(3!×3!) = 720/(6×6)!
• Answer: 20

[Easy] Derivative Basics — Rate of Change

• EN: If f(x) = 3x², what is f'(x)?
• FR: Si f(x) = 3x², quelle est f'(x)?
• Choices: A) 3x B) 6x C) 6 D) 3x²
• Hint: Power rule: if f(x) = axⁿ, then f'(x) = n·ax^(n−1)! For example, f(x) = 5x³: f'(x) = 15x².
• Steps:
  • Step 1: Try f(x) = 4x³. Derivative: 3 × 4x² = 12x².
  • Step 2: Apply the power rule to 3x²: bring the 2 down, multiply by 3, reduce the exponent by 1!
• Answer: 6x

[Easy] Rational Function — Finding a Restriction

• EN: What value of x is NOT in the domain of f(x) = 1/(x − 4)?
• FR: Quelle valeur de x n'est PAS dans le domaine de f(x) = 1/(x − 4)?
• Choices: A) x = 1 B) x = −4 C) x = 4 D) x = 0
• Hint: A fraction is undefined when the denominator = 0! For example, f(x) = 1/(x + 3): x + 3 = 0 → x = −3 is excluded.
• Steps:
  • Step 1: Try f(x) = 1/(x − 7). Set denominator to 0: x − 7 = 0 → x = 7. This value is excluded.
  • Step 2: Set (x − 4) = 0 and solve to find the restricted x-value!
• Answer: x = 4

[Easy] Normal Distribution — Basic Concept

• EN: In a normal distribution, what percent of data falls within one standard deviation of the mean?
• FR: Dans une distribution normale, quel pourcentage des données se situe à un écart-type de la moyenne?
• Choices: A) 50% B) 95% C) 99.7% D) 68%
• Hint: The 68-95-99.7 rule: about 68% falls within 1 standard deviation! For example, if the mean is 70 and SD is 10, about 68% of data is between 60 and 80.
• Steps:
  • Step 1: Recall the rule: 1 SD → 68%, 2 SD → 95%, 3 SD → 99.7%.
  • Step 2: The question asks about ONE standard deviation from the mean — which percent matches?
• Answer: 68%

[Medium] Derivative — Instantaneous Rate

• EN: A car's position is s(t) = t³ − 3t² metres. What is the velocity (derivative) at t = 4 seconds?
• FR: La position d'une voiture est s(t) = t³ − 3t² mètres. Quelle est la vitesse (dérivée) à t = 4 secondes?
• Choices: A) 24 m/s B) 30 m/s C) 34 m/s D) 36 m/s
• Hint: Differentiate to get velocity, then substitute t! For example, s(t) = t² + 2t: v(t) = 2t + 2. At t = 3: v = 8 m/s.
• Steps:
  • Step 1: Try s(t) = 2t³ − t². v(t) = 6t² − 2t. At t = 3: v = 6(9) − 2(3) = 54 − 6 = 48 m/s.
  • Step 2: Differentiate t³ − 3t² to get v(t) = 3t² − 6t. Then substitute t = 4!
• Answer: 24 m/s

[Medium] Polynomial Function — End Behaviour

• EN: For f(x) = −2x³ + 5x − 1, what happens to f(x) as x → +∞?
• FR: Pour f(x) = −2x³ + 5x − 1, que se passe-t-il avec f(x) quand x → +∞?
• Choices: A) f(x) → +∞ B) f(x) → 0 C) f(x) → −∞ D) f(x) → 1
• Hint: The leading term determines end behaviour! For example, f(x) = −3x³: negative leading coefficient, odd degree → as x → +∞, f(x) → −∞.
• Steps:
  • Step 1: Try f(x) = −5x³. Leading coefficient negative, degree 3 (odd): as x → +∞, f(x) → −∞.
  • Step 2: Check the leading term of −2x³ + 5x − 1. What's the degree and sign of the leading coefficient?
• Answer: f(x) → −∞

[Medium] Vectors — Addition

• EN: Vector a = (3, 5) and vector b = (−1, 4). What is a + b?
• FR: Le vecteur a = (3, 5) et le vecteur b = (−1, 4). Quel est a + b?
• Choices: A) (4, 1) B) (2, 9) C) (2, 1) D) (4, 9)
• Hint: Add corresponding components! For example, (4, 2) + (3, −1) = (4+3, 2+(−1)) = (7, 1).
• Steps:
  • Step 1: Try (6, −3) + (2, 5). Add x-components: 6+2=8. Add y-components: −3+5=2. Answer: (8, 2).
  • Step 2: Now add x-components (3 + (−1)) and y-components (5 + 4) separately!
• Answer: (2, 9)

[Medium] Permutations with Restrictions

• EN: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4, 5 without repetition?
• FR: Combien de nombres à 3 chiffres peut-on former avec les chiffres 1, 2, 3, 4, 5 sans répétition?
• Choices: A) 60 B) 100 C) 120 D) 30
• Hint: P(n, r) = n!/(n−r)! For example, arranging 2 from 4 digits: 4 × 3 = 12 ways.
• Steps:
  • Step 1: Try arranging 3 from 4 digits (no repeat). 4 × 3 × 2 = 24 ways.
  • Step 2: For 5 digits choosing 3 positions: 5 choices for the first, 4 for second, 3 for third. Multiply!
• Answer: 60

[Medium] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: On lance une pièce équitable 4 fois. Quelle est la probabilité d'obtenir exactement 3 têtes?
• Choices: A) 1/8 B) 3/8 C) 1/4 D) 1/2
• Hint: P(X=k) = C(n,k) × p^k × (1−p)^(n−k)! For example, 3 flips, 2 heads: C(3,2) × (0.5)² × (0.5)¹ = 3 × 0.25 × 0.5 = 3/8.
• Steps:
  • Step 1: Try n=4, k=2. C(4,2) × (0.5)² × (0.5)² = 6 × 0.0625 = 6/16 = 3/8.
  • Step 2: Calculate C(4,3) × (0.5)³ × (0.5)¹ = 4 × (1/8) × (1/2). Simplify!
• Answer: 1/4

[Medium] Trigonometric Function — Period

• EN: What is the period of y = sin(2x)?
• FR: Quelle est la période de y = sin(2x)?
• Choices: A) 4π B) π C) 2π D) π/2
• Hint: Period of y = sin(bx) is 2π/b! For example, y = sin(3x): period = 2π/3.
• Steps:
  • Step 1: Try y = sin(4x). Period = 2π/4 = π/2.
  • Step 2: Identify b = 2 in y = sin(2x), then calculate 2π/2!
• Answer: π

[Hard] Derivative — Instantaneous Rate Applied

• EN: The profit function for a small maple syrup business is P(x) = −x² + 50x − 200, where x is units sold. At what value of x is the profit maximized?
• FR: La fonction de profit d'une petite entreprise de sirop d'érable est P(x) = −x² + 50x − 200, où x est le nombre d'unités vendues. Pour quelle valeur de x le profit est-il maximisé?
• Choices: A) x = 20 B) x = 30 C) x = 25 D) x = 40
• Hint: Set the derivative equal to zero and solve! P'(x) = −2x + 50 = 0. For example, if P(x) = −x² + 40x, P'(x) = −2x + 40 = 0 → x = 20.
• Steps:
  • Step 1: Try P(x) = −x² + 60x. P'(x) = −2x + 60. Set to 0: −2x + 60 = 0 → x = 30.
  • Step 2: Find P'(x) = −2x + 50. Set it to 0 and solve for x!
• Answer: x = 25

[Hard] Probability Distribution — Expected Value

• EN: A game gives: $10 with probability 0.2, $5 with probability 0.5, and $0 with probability 0.3. What is the expected value?
• FR: Un jeu donne: 10 $ avec une probabilité de 0,2; 5 $ avec une probabilité de 0,5; et 0 $ avec une probabilité de 0,3. Quelle est l'espérance mathématique?
• Choices: A) $4.00 B) $5.00 C) $3.50 D) $4.50
• Hint: Expected value = Σ(value × probability)! For example, $8 × 0.25 + $4 × 0.75 = 2 + 3 = $5.
• Steps:
  • Step 1: Try $12 × 0.3 + $6 × 0.4 + $0 × 0.3 = 3.6 + 2.4 + 0 = $6.00.
  • Step 2: Multiply each prize by its probability: (10 × 0.2) + (5 × 0.5) + (0 × 0.3). Add the results!
• Answer: $4.50

[Hard] Vectors — Dot Product

• EN: Find the dot product of u = (4, −2) and v = (3, 5).
• FR: Trouve le produit scalaire de u = (4, −2) et v = (3, 5).
• Choices: A) 22 B) 10 C) 2 D) −2
• Hint: Dot product = (u₁ × v₁) + (u₂ × v₂)! For example, (3, 4) · (2, −1) = 6 + (−4) = 2.
• Steps:
  • Step 1: Try (5, −3) · (2, 4). 5×2 + (−3)×4 = 10 − 12 = −2.
  • Step 2: Multiply corresponding components of (4,−2) and (3,5), then add: (4×3) + ((−2)×5)!
• Answer: 2

[Hard] Combinations and Probability

• EN: A hockey team of 5 is chosen from 7 forwards and 4 defencemen. The team must include exactly 2 defencemen. How many different teams are possible?
• FR: Une équipe de hockey de 5 joueurs est choisie parmi 7 attaquants et 4 défenseurs. L'équipe doit comprendre exactement 2 défenseurs. Combien d'équipes différentes sont possibles?
• Choices: A) 120 B) 126 C) 105 D) 84
• Hint: Choose defencemen and forwards separately, then multiply! For example, 1 from 3 defencemen and 3 from 5 forwards: C(3,1) × C(5,3) = 3 × 10 = 30.
• Steps:
  • Step 1: Try choose 2 from 3 defencemen and 2 from 4 forwards. C(3,2) × C(4,2) = 3 × 6 = 18.
  • Step 2: Choose 2 from 4 defencemen [C(4,2)] and 3 from 7 forwards [C(7,3)]. Multiply the results!
• Answer: 126