Daily Math — 2026-06-27

[Easy] Counting Crayons

• EN: Mia has 7 crayons. She finds 5 more. How many crayons does she have in all?
• FR: Mia a 7 crayons. Elle en trouve 5 de plus. Combien de crayons a-t-elle en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: When we add two numbers, we count on from the bigger one. For example, 6 + 3: start at 6 and count 3 more — 7, 8, 9. Try the same idea with your numbers!
• Steps:
  • Step 1: Let's try a similar problem: 8 + 4. Start at 8 and count 4 more: 9, 10, 11, 12. So 8 + 4 = 12.
  • Step 2: Use the same "count on" method starting from the bigger number in your problem!
• Answer: 12

[Easy] Hockey Goals

• EN: A hockey team scored 9 goals on Monday and 4 goals on Tuesday. How many goals in total?
• FR: Une équipe de hockey a marqué 9 buts lundi et 4 buts mardi. Combien de buts en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Count on from the bigger number. For example, 8 + 3: start at 8 and count 3 more — 9, 10, 11. So 8 + 3 = 11. Now try your numbers the same way!
• Steps:
  • Step 1: Try 6 + 5. Start at 6, count 5 more: 7, 8, 9, 10, 11. So 6 + 5 = 11.
  • Step 2: Use the same strategy — start at the bigger number and count on the smaller one!
• Answer: 13

[Easy] Skip Counting Skates

• EN: Count by 2s. What number comes after 12?
• FR: Compte par 2. Quel nombre vient après 12?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Skip counting by 2s means adding 2 each time. For example: 4, 6, 8 — each number is 2 more than the one before. Try adding 2 to your number!
• Steps:
  • Step 1: Let's skip count by 2s starting at 6: 6, 8, 10. Each step adds 2.
  • Step 2: Use that same idea — add 2 to 12 to find the next number!
• Answer: 14

[Easy] Snowball Subtraction

• EN: There are 15 snowballs. Kids throw 6 of them. How many snowballs are left?
• FR: Il y a 15 balles de neige. Des enfants en lancent 6. Combien de balles de neige reste-t-il?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: Subtraction means taking away. For example, 11 − 4: start at 11 and count back 4 — 10, 9, 8, 7. So 11 − 4 = 7. Try counting back on your problem!
• Steps:
  • Step 1: Try 13 − 5. Start at 13, count back 5: 12, 11, 10, 9, 8. So 13 − 5 = 8.
  • Step 2: Count back from 15 the same way to find what's left!
• Answer: 9

[Medium] Penny Count

• EN: You have 3 pennies and 2 nickels. How many cents do you have in all?
• FR: Tu as 3 sous et 2 pièces de 5 cents. Combien de cents as-tu en tout?
• Choices: A) 11 cents B) 13 cents C) 15 cents D) 17 cents
• Hint: A penny is worth 1 cent and a nickel is worth 5 cents. For example, 2 pennies + 1 nickel = 2 + 5 = 7 cents. Add up each coin type separately, then combine!
• Steps:
  • Step 1: Try: 4 pennies + 1 nickel = 4 × 1 + 1 × 5 = 4 + 5 = 9 cents.
  • Step 2: Use the same method — find the value of your pennies, find the value of your nickels, then add them together!
• Answer: 13 cents

[Medium] Comparing Numbers

• EN: Which number is greater: 47 or 74?
• FR: Quel nombre est plus grand : 47 ou 74?
• Choices: A) 47 B) 74 C) They are equal D) Can't tell
• Hint: To compare two-digit numbers, look at the tens digit first. For example, 52 vs. 25: 52 has 5 tens and 25 has 2 tens, so 52 is greater. Try looking at the tens digits in your problem!
• Steps:
  • Step 1: Compare 36 and 63. 36 has 3 tens; 63 has 6 tens. Since 6 tens > 3 tens, 63 is greater.
  • Step 2: Use the same idea — look at the tens digit of each number to decide which is greater!
• Answer: 74

[Medium] Dime Count

• EN: You have 4 dimes. How many cents is that in all?
• FR: Tu as 4 pièces de 10 cents. Combien de cents cela fait-il en tout?
• Choices: A) 20 cents B) 30 cents C) 40 cents D) 50 cents
• Hint: A dime is worth 10 cents. Skip count by 10s to find the total. For example, 3 dimes: 10, 20, 30 — so 3 dimes = 30 cents. Try counting by 10s for your dimes!
• Steps:
  • Step 1: For 5 dimes, count by 10s: 10, 20, 30, 40, 50. So 5 dimes = 50 cents.
  • Step 2: Use the same skip-counting-by-10s method with 4 dimes!
• Answer: 40 cents

[Medium] Skip Counting Maple Leaves

• EN: Count by 5s. What number comes after 25?
• FR: Compte par 5. Quel nombre vient après 25?
• Choices: A) 27 B) 28 C) 30 D) 35
• Hint: Skip counting by 5s means adding 5 each time. For example: 10, 15, 20 — each number is 5 more than the one before. Just add 5 to your number!
• Steps:
  • Step 1: Let's skip count by 5s starting at 10: 10, 15, 20. Each step adds 5.
  • Step 2: Add 5 to 25 using the same idea to find the next number in the pattern!
• Answer: 30

[Hard] Tim Hortons Timbits

• EN: There are 18 Timbits in a box. Some kids eat 9 of them. Then 3 more are added. How many Timbits are there now?
• FR: Il y a 18 Timbits dans une boîte. Des enfants en mangent 9. Puis on en ajoute 3. Combien y a-t-il de Timbits maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: Solve step by step — do one operation at a time. For example, 14 − 6 + 2: first 14 − 6 = 8, then 8 + 2 = 10. Try the same two-step method!
• Steps:
  • Step 1: Try 16 − 7 + 4. First, 16 − 7 = 9. Then, 9 + 4 = 13.
  • Step 2: Use the same two-step method — subtract first, then add — with the numbers in your problem!
• Answer: 12

[Hard] Counting to 100

• EN: What number is 10 more than 83?
• FR: Quel nombre est 10 de plus que 83?
• Choices: A) 73 B) 84 C) 93 D) 103
• Hint: Adding 10 to a number just changes the tens digit by 1. For example, 10 more than 45 is 55 — the tens go from 4 to 5. Try applying that idea to your number!
• Steps:
  • Step 1: 10 more than 62: the tens digit goes from 6 to 7, so the answer is 72.
  • Step 2: Use the same rule — increase the tens digit by 1 — to find 10 more than 83!
• Answer: 93

[Easy] Adding at the Campsite

• EN: There are 34 campers in the morning. 15 more arrive in the afternoon. How many campers are there now?
• FR: Il y a 34 campeurs le matin. 15 autres arrivent l'après-midi. Combien y a-t-il de campeurs maintenant?
• Choices: A) 47 B) 49 C) 49 D) 49
• Hint: To add two-digit numbers, add the ones first, then the tens. For example, 23 + 14: ones: 3 + 4 = 7; tens: 2 + 1 = 3. Answer: 37. Try the same steps!
• Steps:
  • Step 1: Let's try 42 + 13. Ones: 2 + 3 = 5. Tens: 4 + 1 = 5. Answer: 55.
  • Step 2: Add the ones column first, then the tens column — use the same method for your problem!
• Answer: 49

[Easy] Telling Time

• EN: The clock shows the hour hand on 7 and the minute hand on 12. What time is it?
• FR: L'horloge montre la grande aiguille sur le 12 et la petite sur le 7. Quelle heure est-il?
• Choices: A) 6:00 B) 7:00 C) 7:30 D) 8:00
• Hint: When the minute hand points to 12, it is exactly on the hour. For example, if the hour hand is on 3 and the minute hand is on 12, the time is 3:00. What hour hand do you see?
• Steps:
  • Step 1: If the hour hand is on 5 and the minute hand is on 12, the time is 5:00.
  • Step 2: Use the same rule — minute hand on 12 means the time is exactly the hour number o'clock!
• Answer: 7:00

[Easy] Measuring a Pencil

• EN: A pencil is 15 cm long. A crayon is 8 cm long. How much longer is the pencil?
• FR: Un crayon mesure 15 cm de long. Un crayon de couleur mesure 8 cm. De combien le crayon est-il plus long?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: To find the difference in length, subtract the shorter from the longer. For example, 18 cm − 11 cm = 7 cm. Try subtracting in your problem!
• Steps:
  • Step 1: A ruler is 20 cm; an eraser is 6 cm. Difference: 20 − 6 = 14 cm.
  • Step 2: Subtract the smaller measurement from the bigger one the same way!
• Answer: 7 cm

[Easy] Coin Total

• EN: You have 2 dimes and 3 nickels. How many cents do you have?
• FR: Tu as 2 pièces de 10 cents et 3 pièces de 5 cents. Combien de cents as-tu?
• Choices: A) 25 cents B) 30 cents C) 35 cents D) 40 cents
• Hint: Count each coin type separately. A dime = 10 cents; a nickel = 5 cents. For example, 1 dime + 2 nickels = 10 + 5 + 5 = 20 cents. Then add your totals!
• Steps:
  • Step 1: 3 dimes + 1 nickel: 3 × 10 = 30 cents for dimes; 1 × 5 = 5 cents for nickel. Total: 30 + 5 = 35 cents.
  • Step 2: Find the total for each coin type, then add them — use the same method!
• Answer: 35 cents

[Medium] Subtraction at the Store

• EN: Lena had 72 stickers. She gave 38 to her friend. How many stickers does she have left?
• FR: Lena avait 72 autocollants. Elle en a donné 38 à son amie. Combien d'autocollants lui reste-t-il?
• Choices: A) 32 B) 34 C) 36 D) 38
• Hint: For subtraction with borrowing, regroup the tens. For example, 51 − 27: borrow from the tens (11 − 7 = 4 ones, then 4 − 2 = 2 tens). Answer: 24. Try the same idea!
• Steps:
  • Step 1: Try 65 − 29. Ones: 5 − 9 needs borrowing. Borrow 1 ten: 15 − 9 = 6. Tens: 5 − 2 = 3. Answer: 36.
  • Step 2: Use the same borrowing method for the ones and tens in your problem!
• Answer: 34

[Medium] Half-Hour Time

• EN: It is 2:30. Hockey practice starts at 3:00. How many minutes until practice?
• FR: Il est 2h30. La pratique de hockey commence à 3h00. Combien de minutes avant la pratique?
• Choices: A) 20 minutes B) 25 minutes C) 30 minutes D) 35 minutes
• Hint: Count the minutes between two times on the clock. For example, from 4:30 to 5:00 is 30 minutes — that's half an hour. Use the same idea!
• Steps:
  • Step 1: From 1:30 to 2:00: the minute hand moves from 6 to 12, which is 30 minutes.
  • Step 2: Count how many minutes from the half-hour to the next full hour — it's always 30 minutes!
• Answer: 30 minutes

[Medium] Pattern at the Bakery

• EN: A baker puts muffins in this pattern: 2, 4, 6, 8, ___. What number comes next?
• FR: Un boulanger place des muffins selon ce modèle : 2, 4, 6, 8, ___. Quel nombre vient ensuite?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Find the rule by checking how much each number increases. For example, 5, 10, 15, 20 — each number goes up by 5. Find the rule in your pattern and apply it!
• Steps:
  • Step 1: Pattern: 3, 6, 9, 12. Each number increases by 3. So after 12 comes 12 + 3 = 15.
  • Step 2: Find how much each number in your pattern increases, then add that amount to 8!
• Answer: 10

[Medium] Measuring the Hallway

• EN: One hallway at school is 9 metres long. Another is 6 metres long. How long are they together?
• FR: Un couloir à l'école fait 9 mètres de long. Un autre fait 6 mètres. Quelle est leur longueur totale?
• Choices: A) 13 m B) 14 m C) 15 m D) 16 m
• Hint: Adding lengths is just like adding regular numbers — just keep the unit the same. For example, 7 m + 8 m = 15 m. Try adding your two lengths!
• Steps:
  • Step 1: A path is 11 m; another path is 4 m. Total: 11 + 4 = 15 m.
  • Step 2: Add the two hallway lengths together the same way and include the unit "m"!
• Answer: 15 m

[Hard] Making Change

• EN: A school supply costs 63 cents. You pay with 3 quarters (75 cents). How much change do you get?
• FR: Une fourniture scolaire coûte 63 cents. Tu paies avec 3 pièces de 25 cents (75 cents). Combien reçois-tu de monnaie?
• Choices: A) 10 cents B) 11 cents C) 12 cents D) 13 cents
• Hint: Change = amount paid − cost. For example, if something costs 44 cents and you pay 50 cents: 50 − 44 = 6 cents change. Use the same subtraction method!
• Steps:
  • Step 1: A snack costs 57 cents; you pay 70 cents. Change: 70 − 57 = 13 cents.
  • Step 2: Subtract the price from the amount paid the same way to find your change!
• Answer: 12 cents

[Hard] Two-Step Problem

• EN: There are 45 students going on a trip. 18 students take the bus first. Then 14 more students board. How many students are on the bus now?
• FR: Il y a 45 élèves qui partent en excursion. 18 élèves prennent le bus en premier. Ensuite, 14 autres montent. Combien d'élèves sont dans le bus maintenant?
• Choices: A) 28 B) 30 C) 32 D) 34
• Hint: Solve in two steps — do each operation one at a time. For example, 20 + 10 + 5 = 30 + 5 = 35. Work left to right, one step at a time!
• Steps:
  • Step 1: Try 22 + 8 + 6. First: 22 + 8 = 30. Then: 30 + 6 = 36.
  • Step 2: Add the first group and second group together the same way — two steps!
• Answer: 32

[Easy] Maple Syrup Multiplication

• EN: A farmer fills 4 jars with maple syrup. Each jar holds 5 litres. How many litres in all?
• FR: Un fermier remplit 4 pots de sirop d'érable. Chaque pot contient 5 litres. Combien de litres en tout?
• Choices: A) 9 B) 15 C) 20 D) 25
• Hint: Multiplication means equal groups. For example, 3 × 5 = 5 + 5 + 5 = 15. Try adding your group size the right number of times!
• Steps:
  • Step 1: 3 × 4 = 4 + 4 + 4 = 12. There are 3 groups of 4.
  • Step 2: Use the same "equal groups" idea — add 5 four times to find your answer!
• Answer: 20

[Easy] Division at the Campfire

• EN: 12 marshmallows are shared equally among 3 friends. How many does each friend get?
• FR: 12 guimauves sont partagées également entre 3 amis. Combien chaque ami en reçoit-il?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: Division means sharing equally. For example, 15 ÷ 3 = 5 because 3 × 5 = 15. Think: what times your divisor equals the total?
• Steps:
  • Step 1: 10 ÷ 2: what times 2 equals 10? 2 × 5 = 10. So 10 ÷ 2 = 5.
  • Step 2: Ask yourself: what times 3 equals 12? That's your answer!
• Answer: 4

[Easy] Fraction of a Pizza

• EN: A pizza is cut into 4 equal pieces. Luca eats 1 piece. What fraction did he eat?
• FR: Une pizza est coupée en 4 morceaux égaux. Luca en mange 1. Quelle fraction a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 1/5
• Hint: A fraction shows part of a whole. The bottom number is how many equal parts total; the top is how many you have. For example, 1 out of 3 equal parts = 1/3.
• Steps:
  • Step 1: A chocolate bar is split into 2 equal parts. One part = 1 out of 2 = 1/2.
  • Step 2: Use the same idea — 1 part out of 4 total equal parts = your answer!
• Answer: 1/4

[Easy] Perimeter of a Classroom

• EN: A rectangular desk is 4 cm long and 3 cm wide. What is its perimeter?
• FR: Un bureau rectangulaire mesure 4 cm de long et 3 cm de large. Quel est son périmètre?
• Choices: A) 12 cm B) 14 cm C) 16 cm D) 7 cm
• Hint: Perimeter means adding all sides. A rectangle has 2 long sides and 2 short sides. For example, length 5, width 2: perimeter = 5 + 5 + 2 + 2 = 14. Try adding all four sides!
• Steps:
  • Step 1: Rectangle with length 6 and width 2: 6 + 6 + 2 + 2 = 16 cm.
  • Step 2: Add all four sides of your rectangle the same way!
• Answer: 14 cm

[Medium] Hockey Cards

• EN: Jake has 5 packs of hockey cards. Each pack has 9 cards. How many cards in total?
• FR: Jake a 5 paquets de cartes de hockey. Chaque paquet contient 9 cartes. Combien de cartes au total?
• Choices: A) 40 B) 45 C) 50 D) 54
• Hint: Multiply the number of groups by the size of each group. For example, 4 × 7 = 28. Try using your times tables to find the answer!
• Steps:
  • Step 1: 4 × 6 = 24. We have 4 groups of 6.
  • Step 2: Use the same idea — multiply 5 × 9 using your multiplication facts!
• Answer: 45

[Medium] Reading a Graph

• EN: A bar graph shows: apples = 6, oranges = 4, bananas = 8. How many more bananas are there than apples?
• FR: Un graphique à barres montre : pommes = 6, oranges = 4, bananes = 8. Combien y a-t-il de bananes de plus que de pommes?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: To find "how many more," subtract the smaller bar from the bigger bar. For example, if cats = 7 and dogs = 5, then 7 − 5 = 2 more cats. Try subtracting!
• Steps:
  • Step 1: Red = 10, Blue = 6. How many more red? 10 − 6 = 4 more red.
  • Step 2: Subtract the apples total from the bananas total the same way!
• Answer: 2

[Medium] Division with Tables

• EN: 30 students are put into groups of 5. How many groups are there?
• FR: 30 élèves sont répartis en groupes de 5. Combien y a-t-il de groupes?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Division is the opposite of multiplication. For example, 20 ÷ 4 = 5 because 4 × 5 = 20. Think: what times 5 equals 30?
• Steps:
  • Step 1: 24 ÷ 4 = ? Ask: 4 × ? = 24. Since 4 × 6 = 24, the answer is 6.
  • Step 2: Use the same multiplication fact strategy — what times 5 equals 30?
• Answer: 6

[Medium] Fraction Comparison

• EN: Which fraction is larger: 1/2 or 1/4?
• FR: Quelle fraction est plus grande : 1/2 ou 1/4?
• Choices: A) 1/4 B) They are equal C) 1/2 D) Can't tell
• Hint: When the top number (numerator) is the same, the bigger the bottom number, the smaller the piece. For example, 1/3 is bigger than 1/6 because thirds are larger pieces than sixths.
• Steps:
  • Step 1: Compare 1/2 and 1/8. Imagine dividing a chocolate bar: halves are bigger pieces than eighths. So 1/2 > 1/8.
  • Step 2: Use the same thinking — which gives a bigger piece, cutting into 2 parts or 4 parts?
• Answer: 1/2

[Hard] Two-Step Multiplication

• EN: A class collects cans for a food drive. Each of the 4 rows has 3 boxes, and each box has 10 cans. How many cans are there in all?
• FR: Une classe collecte des conserves pour une collecte alimentaire. Chacune des 4 rangées a 3 boîtes, et chaque boîte contient 10 conserves. Combien y a-t-il de conserves en tout?
• Choices: A) 100 B) 110 C) 120 D) 130
• Hint: Work step by step. First find the total number of boxes, then multiply by the cans per box. For example, 2 rows × 4 boxes = 8 boxes; 8 × 5 cans = 40 cans.
• Steps:
  • Step 1: 3 rows × 2 boxes = 6 boxes. Then 6 boxes × 4 cans = 24 cans.
  • Step 2: First find total boxes (4 × 3), then multiply that by 10 cans per box!
• Answer: 120

[Hard] Perimeter Challenge

• EN: A square garden has a perimeter of 28 m. What is the length of one side?
• FR: Un jardin carré a un périmètre de 28 m. Quelle est la longueur d'un côté?
• Choices: A) 5 m B) 6 m C) 7 m D) 8 m
• Hint: A square has 4 equal sides. Perimeter = 4 × side length. To find one side, divide the perimeter by 4. For example, perimeter = 20 m: 20 ÷ 4 = 5 m per side.
• Steps:
  • Step 1: A square has perimeter 36 m. One side = 36 ÷ 4 = 9 m.
  • Step 2: Divide your perimeter by 4 the same way to find the side length!
• Answer: 7 m

[Easy] Multiplication Table Hockey

• EN: A hockey arena has 7 rows of seats. Each row has 8 seats. How many seats are there in all?
• FR: Un aréna de hockey a 7 rangées de sièges. Chaque rangée a 8 sièges. Combien y a-t-il de sièges en tout?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Multiply rows by seats per row. For example, 6 rows × 7 seats = 42. Use your multiplication table to find 7 × 8!
• Steps:
  • Step 1: 5 rows × 9 seats = 45 seats. Use the times table: 5 × 9 = 45.
  • Step 2: Apply the same multiplication fact — look up or recall 7 × 8 in your table!
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 3 in the number 4.37?
• FR: Quelle est la valeur du chiffre 3 dans le nombre 4,37?
• Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 30
• Hint: In a decimal number, the first digit after the decimal point is tenths, and the second is hundredths. For example, in 2.56: 5 is in the tenths place, 6 is in the hundredths place.
• Steps:
  • Step 1: In 7.29: the 2 is in the tenths place, the 9 is in the hundredths place.
  • Step 2: Use the same place-value chart — where is the 3 relative to the decimal point in 4.37?
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A Canadian flag is 6 cm long and 3 cm wide. What is its area?
• FR: Un drapeau canadien mesure 6 cm de long et 3 cm de large. Quelle est son aire?
• Choices: A) 12 cm² B) 15 cm² C) 18 cm² D) 21 cm²
• Hint: Area of a rectangle = length × width. For example, a rectangle that is 4 cm × 5 cm has an area of 4 × 5 = 20 cm². Don't forget the squared unit!
• Steps:
  • Step 1: Rectangle: length = 7 cm, width = 2 cm. Area = 7 × 2 = 14 cm².
  • Step 2: Multiply your length by your width the same way and label your answer cm²!
• Answer: 18 cm²

[Easy] Long Division

• EN: 48 pencils are packed equally into 6 boxes. How many pencils are in each box?
• FR: 48 crayons sont rangés également dans 6 boîtes. Combien y a-t-il de crayons dans chaque boîte?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Division = sharing equally. Ask: what times the divisor equals the dividend? For example, 35 ÷ 5: 5 × 7 = 35, so the answer is 7.
• Steps:
  • Step 1: 42 ÷ 6. Ask: 6 × ? = 42. Since 6 × 7 = 42, the answer is 7.
  • Step 2: Ask the same question — 6 × ? = 48 — to find how many pencils are in each box!
• Answer: 8

[Medium] Long Division with Remainder

• EN: 50 stickers are shared among 7 students. How many does each student get, and how many are left over?
• FR: 50 autocollants sont partagés entre 7 élèves. Combien chaque élève en reçoit-il et combien en reste-t-il?
• Choices: A) 6 remainder 8 B) 7 remainder 1 C) 7 remainder 2 D) 8 remainder 2
• Hint: For division with remainders, find the biggest multiple of the divisor that fits. For example, 23 ÷ 4: 4 × 5 = 20 (fits), so quotient = 5, remainder = 23 − 20 = 3.
• Steps:
  • Step 1: 29 ÷ 6. 6 × 4 = 24 (fits in 29). Remainder: 29 − 24 = 5. Answer: 4 remainder 5.
  • Step 2: Find the biggest multiple of 7 that fits in 50, then subtract to find the remainder!
• Answer: 7 remainder 1

[Medium] Elapsed Time

• EN: School starts at 8:45 a.m. and ends at 3:15 p.m. How long is the school day?
• FR: L'école commence à 8h45 et se termine à 15h15. Combien de temps dure la journée scolaire?
• Choices: A) 5 hours 30 minutes B) 6 hours C) 6 hours 30 minutes D) 7 hours
• Hint: Count up from the start time to the end time. For example, from 9:30 a.m. to 2:00 p.m.: count to 10:00 = 30 min, then 10:00 to 2:00 = 4 hours. Total: 4 hours 30 min.
• Steps:
  • Step 1: From 7:15 a.m. to 12:45 p.m.: 7:15 to 12:15 = 5 hours; 12:15 to 12:45 = 30 min. Total: 5 hours 30 min.
  • Step 2: Use the same count-up method starting from 8:45 a.m. to reach 3:15 p.m.!
• Answer: 6 hours 30 minutes

[Medium] Comparing Fractions

• EN: Which fraction is larger: 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) Can't tell
• Hint: To compare fractions with different denominators, find a common denominator. For example, 1/2 vs. 2/5: convert to tenths — 5/10 vs. 4/10. So 1/2 is larger.
• Steps:
  • Step 1: Compare 2/3 and 3/5. Common denominator = 15. 2/3 = 10/15; 3/5 = 9/15. So 2/3 > 3/5.
  • Step 2: Convert 3/4 and 2/3 to a common denominator (12) and compare them the same way!
• Answer: 3/4

[Medium] Decimal Operations

• EN: A bottle of maple syrup costs $3.45. A jar of honey costs $2.30. What is the total cost?
• FR: Une bouteille de sirop d'érable coûte 3,45 $. Un pot de miel coûte 2,30 $. Quel est le coût total?
• Choices: A) $5.55 B) $5.65 C) $5.75 D) $5.85
• Hint: Line up the decimal points when adding decimals. For example, $4.25 + $1.50: line up the dots, add hundredths (5 + 0 = 5), tenths (2 + 5 = 7), ones (4 + 1 = 5). Answer: $5.75.
• Steps:
  • Step 1: $2.60 + $1.15. Hundredths: 0 + 5 = 5. Tenths: 6 + 1 = 7. Ones: 2 + 1 = 3. Answer: $3.75.
  • Step 2: Line up decimal points for your problem the same way and add column by column!
• Answer: $5.75

[Hard] Multi-Step Area Problem

• EN: A school gym floor is 25 m long and 18 m wide. A storage room inside measures 5 m by 4 m. What is the area of the gym floor NOT including the storage room?
• FR: Le plancher d'un gymnase scolaire fait 25 m de long et 18 m de large. Une salle de rangement à l'intérieur mesure 5 m sur 4 m. Quelle est l'aire du plancher du gymnase sans la salle de rangement?
• Choices: A) 420 m² B) 430 m² C) 440 m² D) 450 m²
• Hint: Find the total area first, then subtract the smaller area. For example, big room = 10 × 8 = 80 m²; small closet = 2 × 3 = 6 m². Remaining = 80 − 6 = 74 m².
• Steps:
  • Step 1: Big rectangle = 20 × 12 = 240 m². Small rectangle = 4 × 3 = 12 m². Remaining = 240 − 12 = 228 m².
  • Step 2: Multiply length × width for each rectangle, then subtract the storage room area from the gym area!
• Answer: 430 m²

[Hard] Division and Multiplication Challenge

• EN: A school store sells 9 boxes of markers. Each box has 8 markers. The markers are divided equally among 6 classrooms. How many markers does each classroom get?
• FR: Une boutique d'école vend 9 boîtes de marqueurs. Chaque boîte contient 8 marqueurs. Les marqueurs sont partagés également entre 6 classes. Combien de marqueurs chaque classe reçoit-elle?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: Solve in two steps — multiply first, then divide. For example: 4 boxes × 6 items = 24 items; shared among 8 groups: 24 ÷ 8 = 3 items per group.
• Steps:
  • Step 1: 5 boxes × 6 items = 30 items. Divided among 5 groups: 30 ÷ 5 = 6 per group.
  • Step 2: First find total markers (9 × 8), then divide by 6 to find each classroom's share!
• Answer: 12

[Easy] Multi-Digit Multiplication

• EN: A camping store orders 24 boxes of granola bars. Each box has 12 bars. How many bars are there in total?
• FR: Un magasin de camping commande 24 boîtes de barres granola. Chaque boîte contient 12 barres. Combien y a-t-il de barres en tout?
• Choices: A) 248 B) 268 C) 288 D) 308
• Hint: Multiply using the standard algorithm. For example, 23 × 11: (23 × 1) + (23 × 10) = 23 + 230 = 253. Break the second number into parts and add the products!
• Steps:
  • Step 1: 21 × 13. (21 × 3) = 63; (21 × 10) = 210. Total: 63 + 210 = 273.
  • Step 2: Use the same partial products method — multiply 24 × 2 and 24 × 10, then add!
• Answer: 288

[Easy] Adding Fractions

• EN: During gym class, Maya ran 2/6 of a lap and then 3/6 of a lap. How far did she run in total?
• FR: Pendant le cours d'éducation physique, Maya a couru 2/6 d'un tour, puis 3/6 d'un tour. Quelle distance a-t-elle parcourue au total?
• Choices: A) 5/12 B) 5/6 C) 6/6 D) 1/6
• Hint: When fractions have the same denominator, just add the numerators and keep the denominator. For example, 1/5 + 2/5 = 3/5. Try the same thing!
• Steps:
  • Step 1: 2/7 + 3/7. Same denominator (7). Add tops: 2 + 3 = 5. Answer: 5/7.
  • Step 2: Add the numerators in your problem the same way, keeping the denominator as 6!
• Answer: 5/6

[Easy] 25% Discount

• EN: A hockey stick costs $40. It is on sale for 25% off. How much is the discount?
• FR: Un bâton de hockey coûte 40 $. Il est en solde à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $5 B) $8 C) $10 D) $12
• Hint: 25% = one quarter. To find 25% of a number, divide by 4. For example, 25% of $60 = $60 ÷ 4 = $15. Try dividing your price by 4!
• Steps:
  • Step 1: 25% of $80 = $80 ÷ 4 = $20 discount.
  • Step 2: Divide the price by 4 the same way to find 25% of $40!
• Answer: $10

[Easy] Volume of a Box

• EN: A storage box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte de rangement fait 5 cm de long, 4 cm de large et 3 cm de hauteur. Quel est son volume?
• Choices: A) 48 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume of a rectangular prism = length × width × height. For example, 6 × 2 × 4 = 48 cm³. Multiply all three dimensions!
• Steps:
  • Step 1: A box: 3 cm × 4 cm × 5 cm = 12 × 5 = 60 cm³. Wait — that's the same. Let's try 7 × 2 × 3 = 14 × 3 = 42 cm³.
  • Step 2: Multiply all three measurements together the same way: 5 × 4 × 3 = ?
• Answer: 60 cm³

[Medium] Multi-Digit Division

• EN: 336 students are divided equally into 14 classrooms. How many students are in each classroom?
• FR: 336 élèves sont répartis également dans 14 classes. Combien d'élèves y a-t-il dans chaque classe?
• Choices: A) 20 B) 22 C) 24 D) 26
• Hint: For long division, estimate first. 14 × 20 = 280; 14 × 24 = 336. Try multiples of 14 to find which one equals 336!
• Steps:
  • Step 1: 180 ÷ 12. 12 × 15 = 180. So 180 ÷ 12 = 15.
  • Step 2: Try multiplying 14 by different numbers until you get 336 — that's your answer!
• Answer: 24

[Medium] Subtracting Fractions

• EN: A Tim Hortons cup was 7/8 full. After drinking, it was 3/8 full. How much was drunk?
• FR: Une tasse de Tim Hortons était remplie aux 7/8. Après avoir bu, elle était remplie aux 3/8. Combien a-t-on bu?
• Choices: A) 3/8 B) 4/8 C) 5/8 D) 10/8
• Hint: Subtract fractions with like denominators by subtracting the numerators and keeping the denominator. For example, 6/9 − 2/9 = 4/9.
• Steps:
  • Step 1: 5/7 − 2/7. Same denominator. Subtract tops: 5 − 2 = 3. Answer: 3/7.
  • Step 2: Subtract the numerators in your problem the same way, keeping 8 as the denominator!
• Answer: 4/8

[Medium] Decimal Operations

• EN: A bag of trail mix weighs 1.75 kg. Another bag weighs 2.40 kg. What is the total weight?
• FR: Un sac de mélange randonnée pèse 1,75 kg. Un autre sac pèse 2,40 kg. Quel est le poids total?
• Choices: A) 3.95 kg B) 4.05 kg C) 4.15 kg D) 4.25 kg
• Hint: Line up the decimal points when adding. Then add column by column from right to left. For example, 2.35 + 1.42: hundredths 5+2=7, tenths 3+4=7, ones 2+1=3. Answer: 3.77.
• Steps:
  • Step 1: 3.25 + 1.60. Hundredths: 5+0=5. Tenths: 2+6=8. Ones: 3+1=4. Answer: 4.85.
  • Step 2: Line up your decimals and add each column from right to left the same way!
• Answer: 4.15 kg

[Medium] Percentage — 10%

• EN: A school fundraiser raised $560. The school keeps 10% for supplies. How much money is kept?
• FR: Une collecte de fonds scolaire a recueilli 560 $. L'école garde 10 % pour les fournitures. Combien d'argent est gardé?
• Choices: A) $46 B) $56 C) $66 D) $76
• Hint: To find 10% of a number, divide by 10 (move the decimal one place left). For example, 10% of $430 = $43.00. Try dividing your amount by 10!
• Steps:
  • Step 1: 10% of $820 = $820 ÷ 10 = $82.
  • Step 2: Divide $560 by 10 the same way to find 10%!
• Answer: $56

[Hard] Multi-Step Fraction and Decimal Problem

• EN: A recipe uses 1/4 kg of butter and 0.50 kg of flour. A baker makes 3 batches. How many kilograms of ingredients are used in total?
• FR: Une recette utilise 1/4 kg de beurre et 0,50 kg de farine. Un boulanger fait 3 lots. Combien de kilogrammes d'ingrédients sont utilisés au total?
• Choices: A) 2.00 kg B) 2.25 kg C) 2.50 kg D) 2.75 kg
• Hint: Find the total per batch first (convert 1/4 to a decimal), then multiply by number of batches. For example, if one batch uses 0.30 + 0.50 = 0.80 kg, then 3 batches = 0.80 × 3 = 2.40 kg.
• Steps:
  • Step 1: 1 batch uses 0.20 kg + 0.60 kg = 0.80 kg. For 4 batches: 0.80 × 4 = 3.20 kg.
  • Step 2: Convert 1/4 to 0.25, add to 0.50 for one batch total, then multiply by 3!
• Answer: 2.25 kg

[Hard] Volume and Percentage

• EN: A fish tank has a volume of 200 cm³. It is filled to 50% capacity. How many cm³ of water are in the tank?
• FR: Un aquarium a un volume de 200 cm³. Il est rempli à 50 % de sa capacité. Combien de cm³ d'eau y a-t-il dans l'aquarium?
• Choices: A) 50 cm³ B) 75 cm³ C) 100 cm³ D) 150 cm³
• Hint: 50% means half. To find 50% of a number, divide by 2. For example, 50% of 340 = 340 ÷ 2 = 170.
• Steps:
  • Step 1: A tank of 160 cm³ at 50%: 160 ÷ 2 = 80 cm³ of water.
  • Step 2: Divide your volume by 2 the same way to find 50% of 200 cm³!
• Answer: 100 cm³

[Easy] Ratio at the Bake Sale

• EN: For every 2 muffins sold, there are 5 cookies sold. If 6 muffins are sold, how many cookies are sold?
• FR: Pour chaque 2 muffins vendus, il y a 5 biscuits vendus. Si 6 muffins sont vendus, combien de biscuits sont vendus?
• Choices: A) 12 B) 13 C) 14 D) 15
• Hint: A ratio is a comparison. If the ratio is 2:5 and you multiply 2 by 3 to get 6, multiply 5 by the same number (3). For example, ratio 3:4; if 3 becomes 9 (×3), then 4 × 3 = 12.
• Steps:
  • Step 1: Ratio 2:7. 2 × 4 = 8. So 7 × 4 = 28.
  • Step 2: Find what you multiply 2 by to get 6, then apply the same multiplier to 5!
• Answer: 15

[Easy] Percent of a Number

• EN: There are 80 students at a school event. 50% of them are wearing red. How many students wear red?
• FR: Il y a 80 élèves à un événement scolaire. 50 % d'entre eux portent du rouge. Combien d'élèves portent du rouge?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: 50% means half. Divide the total by 2. For example, 50% of 60 = 60 ÷ 2 = 30. Apply the same idea to your number!
• Steps:
  • Step 1: 50% of 120 = 120 ÷ 2 = 60.
  • Step 2: Divide 80 by 2 the same way to find 50% of your group!
• Answer: 40

[Easy] Integer Introduction

• EN: The temperature in Winnipeg is −8°C in the morning. By afternoon it rises 5 degrees. What is the afternoon temperature?
• FR: La température à Winnipeg est de −8°C le matin. L'après-midi, elle monte de 5 degrés. Quelle est la température l'après-midi?
• Choices: A) −4°C B) −3°C C) −2°C D) −1°C
• Hint: Adding a positive number to a negative number means moving right on the number line. For example, −6 + 4: start at −6, move right 4 steps → −2.
• Steps:
  • Step 1: −10 + 7. Start at −10 on a number line, move right 7: −10, −9, −8, −7, −6, −5, −4, −3. Answer: −3.
  • Step 2: Start at −8 and count up 5 steps the same way to find the afternoon temperature!
• Answer: −3°C

[Easy] Simple Algebraic Expression

• EN: Write an expression for "3 more than a number n."
• FR: Écris une expression pour «3 de plus qu'un nombre n».
• Choices: A) n − 3 B) 3n C) n + 3 D) n ÷ 3
• Hint: "More than" means addition. For example, "5 more than x" is written as x + 5. Match the words to the operation!
• Steps:
  • Step 1: "7 more than y" → y + 7. The number added goes after the plus sign.
  • Step 2: Use the same word-to-symbol rule — "3 more than n" uses addition!
• Answer: n + 3

[Easy] Rate Problem

• EN: A car travels 90 km in 1 hour. At the same rate, how far does it travel in 3 hours?
• FR: Une voiture parcourt 90 km en 1 heure. Au même rythme, quelle distance parcourt-elle en 3 heures?
• Choices: A) 240 km B) 260 km C) 270 km D) 280 km
• Hint: Rate × time = distance. For example, if a car goes 60 km/h, in 4 hours it travels 60 × 4 = 240 km.
• Steps:
  • Step 1: Speed = 70 km/h. In 5 hours: 70 × 5 = 350 km.
  • Step 2: Multiply the rate (90 km/h) by the number of hours (3) the same way!
• Answer: 270 km

[Medium] Order of Operations (BEDMAS)

• EN: Solve: 3 + 4 × 2 − 1
• FR: Résous : 3 + 4 × 2 − 1
• Choices: A) 13 B) 10 C) 12 D) 9
• Hint: BEDMAS says multiplication comes before addition and subtraction. For example, 5 + 3 × 4 − 2: first 3 × 4 = 12, then 5 + 12 − 2 = 15. Always do multiplication before adding or subtracting!
• Steps:
  • Step 1: Solve 6 + 2 × 5 − 3. First: 2 × 5 = 10. Then: 6 + 10 − 3 = 13.
  • Step 2: Use the same BEDMAS order — do the multiplication in your problem first, then add and subtract left to right!
• Answer: 10

[Medium] Fraction Multiplication

• EN: A recipe calls for 3/4 cup of oats. If you make 2 batches, how many cups do you need?
• FR: Une recette demande 3/4 de tasse d'avoine. Si tu fais 2 lots, de combien de tasses as-tu besoin?
• Choices: A) 5/4 B) 6/4 C) 3/2 D) Both B and C
• Hint: To multiply a fraction by a whole number, multiply the numerator by the whole number and keep the denominator. For example, 2/5 × 3 = 6/5.
• Steps:
  • Step 1: 3/7 × 2 = 6/7. Multiply the top (3 × 2 = 6) and keep the bottom (7).
  • Step 2: Multiply 3/4 × 2 the same way — multiply only the numerator by 2!
• Answer: 6/4

[Medium] Percent Discount

• EN: A pair of skates costs $120. There is a 25% discount. What is the sale price?
• FR: Une paire de patins coûte 120 $. Il y a un rabais de 25 %. Quel est le prix de vente?
• Choices: A) $80 B) $85 C) $90 D) $95
• Hint: Find the discount amount first (25% = ÷4), then subtract from original price. For example, 25% of $80 = $20; sale price = $80 − $20 = $60.
• Steps:
  • Step 1: 25% of $160 = $160 ÷ 4 = $40. Sale price = $160 − $40 = $120.
  • Step 2: Find 25% of $120 (divide by 4), then subtract that from $120!
• Answer: $90

[Medium] Integer Operations

• EN: −15 + (−7) = ?
• FR: −15 + (−7) = ?
• Choices: A) −8 B) −22 C) 22 D) −21
• Hint: Adding two negative numbers gives a larger negative number. Think of moving left on a number line twice. For example, −5 + (−6) = −11.
• Steps:
  • Step 1: −9 + (−4). Both negative: add the values, keep the negative sign. 9 + 4 = 13. Answer: −13.
  • Step 2: Add 15 and 7 together, then put a negative sign on your answer — same rule!
• Answer: −22

[Medium] Fraction Division

• EN: How many 1/3-cup servings are in 4 cups of juice?
• FR: Combien de portions de 1/3 de tasse y a-t-il dans 4 tasses de jus?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Dividing by a fraction means multiplying by its reciprocal. For example, 3 ÷ 1/4 = 3 × 4 = 12. Flip the fraction and multiply!
• Steps:
  • Step 1: 5 ÷ 1/2 = 5 × 2 = 10. Flip 1/2 to get 2, then multiply.
  • Step 2: Apply the same flip-and-multiply rule: 4 ÷ 1/3 = 4 × 3 = ?
• Answer: 12

[Medium] Writing Expressions

• EN: A loonie costs $1. If you have n loonies, write an expression for your total in dollars.
• FR: Un huard vaut 1 $. Si tu as n huards, écris une expression pour ton total en dollars.
• Choices: A) n + 1 B) 1 − n C) n D) n ÷ 1
• Hint: If each item costs $1 and you have n of them, multiply: total = 1 × n = n. For example, 3 loonies = $3; n loonies = $n.
• Steps:
  • Step 1: 5 items at $2 each = 5 × 2 = $10. For n items at $2 each = 2n dollars.
  • Step 2: For n items at $1 each, multiply 1 × n — what does that simplify to?
• Answer: n

[Hard] BEDMAS with Brackets

• EN: Solve: (5 + 3) × 2 − 4 ÷ 2
• FR: Résous : (5 + 3) × 2 − 4 ÷ 2
• Choices: A) 12 B) 14 C) 16 D) 18
• Hint: BEDMAS: Brackets first, then multiplication and division (left to right), then addition and subtraction. For example, (2 + 6) × 3 − 8 ÷ 4 = 8 × 3 − 2 = 24 − 2 = 22.
• Steps:
  • Step 1: Solve (4 + 2) × 3 − 6 ÷ 2. Brackets: 4+2=6. Then: 6×3=18 and 6÷2=3. Finally: 18−3=15.
  • Step 2: Apply the same BEDMAS steps to your expression — brackets, then × and ÷, then − !
• Answer: 14

[Hard] Ratio and Rate Problem

• EN: A car uses 8 litres of gas per 100 km. How many litres are needed for a 375 km trip?
• FR: Une voiture consomme 8 litres d'essence aux 100 km. Combien de litres faut-il pour un trajet de 375 km?
• Choices: A) 28 L B) 30 L C) 32 L D) 34 L
• Hint: Set up a proportion: 8/100 = ?/375. Cross-multiply: 8 × 375 ÷ 100. For example, 6/100 × 200 = 12 litres.
• Steps:
  • Step 1: Rate = 6 L/100 km. For 250 km: (6 × 250) ÷ 100 = 1500 ÷ 100 = 15 L.
  • Step 2: Use the same formula: (8 × 375) ÷ 100 to find the litres needed!
• Answer: 30 L

[Hard] Integer and Expression Challenge

• EN: What is the value of 4n − 3 when n = −2?
• FR: Quelle est la valeur de 4n − 3 lorsque n = −2?
• Choices: A) −11 B) −10 C) −9 D) −8
• Hint: Substitute the value of n into the expression. For example, if n = −3: 4(−3) − 3 = −12 − 3 = −15. Multiply first, then subtract!
• Steps:
  • Step 1: 3n + 5 when n = −4. 3 × (−4) = −12. Then −12 + 5 = −7.
  • Step 2: Substitute n = −2 into 4n − 3: multiply 4 × (−2) first, then subtract 3!
• Answer: −11

[Hard] Percent Increase

• EN: Last year, 200 students joined a school club. This year there are 250 students. What is the percent increase?
• FR: L'année dernière, 200 élèves ont rejoint un club scolaire. Cette année, il y en a 250. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100. For example, if it goes from 40 to 50: increase = 10; 10 ÷ 40 × 100 = 25%.
• Steps:
  • Step 1: From 60 to 90. Increase = 30. (30 ÷ 60) × 100 = 50%.
  • Step 2: Find the increase (250 − 200), divide by 200, multiply by 100 the same way!
• Answer: 25%

[Easy] Integer Addition

• EN: A submarine is at −45 m. It rises 20 m. What is its new depth?
• FR: Un sous-marin est à −45 m. Il monte de 20 m. Quelle est sa nouvelle profondeur?
• Choices: A) −30 m B) −25 m C) −20 m D) −15 m
• Hint: Adding a positive to a negative means moving right (up) on the number line. For example, −30 + 12 = −18. Start at your negative number and add!
• Steps:
  • Step 1: −50 + 15. Start at −50, add 15: −50 + 15 = −35.
  • Step 2: Start at −45 and add 20 the same way to find the new depth!
• Answer: −25 m

[Easy] Percent — Tip Calculation

• EN: A meal at a Canadian restaurant costs $60. You leave a 10% tip. How much is the tip?
• FR: Un repas dans un restaurant canadien coûte 60 $. Tu laisses un pourboire de 10 %. Quel est le montant du pourboire?
• Choices: A) $5 B) $6 C) $7 D) $8
• Hint: 10% of a number = divide by 10. For example, 10% of $90 = $90 ÷ 10 = $9. Try dividing your amount by 10!
• Steps:
  • Step 1: 10% of $150 = $150 ÷ 10 = $15.
  • Step 2: Divide $60 by 10 the same way to find your 10% tip!
• Answer: $6

[Easy] One-Step Equation

• EN: Solve for x: x + 9 = 17
• FR: Résous pour x : x + 9 = 17
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To isolate x, subtract the same number from both sides. For example, x + 5 = 12 → x = 12 − 5 = 7.
• Steps:
  • Step 1: x + 6 = 14. Subtract 6 from both sides: x = 14 − 6 = 8.
  • Step 2: Subtract 9 from both sides of your equation the same way to find x!
• Answer: 8

[Easy] Probability

• EN: A bag has 3 red marbles and 7 blue marbles. What is the probability of picking a red marble?
• FR: Un sac contient 3 billes rouges et 7 billes bleues. Quelle est la probabilité de piger une bille rouge?
• Choices: A) 3/7 B) 3/10 C) 7/10 D) 1/3
• Hint: Probability = favourable outcomes ÷ total outcomes. For example, 4 red out of 9 total = 4/9. Count your total and put red on top!
• Steps:
  • Step 1: 5 green, 5 yellow marbles. P(green) = 5/(5+5) = 5/10.
  • Step 2: Total marbles = 3 + 7 = 10. Put red (3) over total (10) the same way!
• Answer: 3/10

[Easy] Fraction Decimal Conversion

• EN: Convert 3/4 to a decimal.
• FR: Convertis 3/4 en décimale.
• Choices: A) 0.50 B) 0.65 C) 0.75 D) 0.80
• Hint: To convert a fraction to a decimal, divide the numerator by the denominator. For example, 1/4 = 1 ÷ 4 = 0.25.
• Steps:
  • Step 1: 2/5 = 2 ÷ 5 = 0.40.
  • Step 2: Divide 3 by 4 the same way to convert your fraction to a decimal!
• Answer: 0.75

[Medium] Integer Multiplication

• EN: The temperature drops 4°C every hour for 6 hours. What is the total change in temperature?
• FR: La température baisse de 4°C à chaque heure pendant 6 heures. Quel est le changement total de température?
• Choices: A) −20°C B) −24°C C) −28°C D) −32°C
• Hint: A negative times a positive gives a negative. For example, −5 × 3 = −15. Multiply and apply the sign rule!
• Steps:
  • Step 1: −6 × 5 = −30. Negative × positive = negative.
  • Step 2: Multiply −4 × 6 the same way — the answer will be negative!
• Answer: −24°C

[Medium] Discount and Tax

• EN: A backpack costs $80. There is a 15% discount and then 13% tax applied to the sale price. What is the sale price before tax?
• FR: Un sac à dos coûte 80 $. Il y a un rabais de 15 %, puis une taxe de 13 % est appliquée au prix de vente. Quel est le prix de vente avant taxes?
• Choices: A) $64 B) $66 C) $68 D) $70
• Hint: Discount amount = original × (discount% ÷ 100). Sale price = original − discount. For example, 20% off $60: 60 × 0.20 = $12 off; sale price = $60 − $12 = $48.
• Steps:
  • Step 1: 25% off $100. Discount = 100 × 0.25 = $25. Sale price = 100 − 25 = $75.
  • Step 2: Find 15% of $80, then subtract to get the sale price the same way!
• Answer: $68

[Medium] Two-Step Equation

• EN: Solve: 2x + 5 = 19
• FR: Résous : 2x + 5 = 19
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: First subtract the constant from both sides, then divide. For example, 3x + 4 = 13: 3x = 13 − 4 = 9; x = 9 ÷ 3 = 3.
• Steps:
  • Step 1: 4x + 3 = 23. Subtract 3: 4x = 20. Divide by 4: x = 5.
  • Step 2: Subtract 5 from both sides first, then divide by 2 the same way!
• Answer: 7

[Medium] Surface Area

• EN: A rectangular box is 6 cm long, 4 cm wide, and 3 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 6 cm de long, 4 cm de large et 3 cm de hauteur. Quelle est son aire de surface?
• Choices: A) 96 cm² B) 100 cm² C) 108 cm² D) 72 cm²
• Hint: Surface area of a rectangular prism = 2(lw + lh + wh). For example, l=4, w=3, h=2: 2(12 + 8 + 6) = 2(26) = 52 cm².
• Steps:
  • Step 1: l=5, w=2, h=3. lw=10, lh=15, wh=6. Sum=31. SA = 2 × 31 = 62 cm².
  • Step 2: Calculate lw, lh, and wh for your box, add them, then multiply by 2!
• Answer: 108 cm²

[Medium] Mean and Median

• EN: Five students scored: 72, 85, 90, 68, 90. What is the median score?
• FR: Cinq élèves ont obtenu ces résultats : 72, 85, 90, 68, 90. Quel est le résultat médian?
• Choices: A) 80 B) 82 C) 85 D) 90
• Hint: To find the median, arrange the numbers in order and find the middle one. For example, 3, 7, 9, 12, 15 → middle value is 9.
• Steps:
  • Step 1: Scores: 10, 14, 18, 22, 26. Ordered: 10, 14, 18, 22, 26. Middle (3rd) = 18.
  • Step 2: Order your five scores from least to greatest, then pick the middle (3rd) value!
• Answer: 85

[Medium] Percentage Problem

• EN: In a class of 30 students, 40% play hockey. How many students play hockey?
• FR: Dans une classe de 30 élèves, 40 % jouent au hockey. Combien d'élèves jouent au hockey?
• Choices: A) 10 B) 12 C) 14 D) 16
• Hint: Percent of a number = (percent ÷ 100) × total. For example, 30% of 50 = (30/100) × 50 = 0.30 × 50 = 15.
• Steps:
  • Step 1: 20% of 40 = 0.20 × 40 = 8 students.
  • Step 2: Multiply 0.40 × 30 the same way to find your answer!
• Answer: 12

[Hard] Integer All Four Operations

• EN: Evaluate: (−36) ÷ (−4) + (−3) × 5
• FR: Évalue : (−36) ÷ (−4) + (−3) × 5
• Choices: A) −6 B) −3 C) 3 D) 6
• Hint: Negative ÷ negative = positive; negative × positive = negative. Use order of operations: division and multiplication before addition. For example, (−12) ÷ (−3) + (−2) × 4 = 4 + (−8) = −4.
• Steps:
  • Step 1: (−20) ÷ (−5) + (−2) × 6. Division: −20 ÷ −5 = 4. Multiplication: −2 × 6 = −12. Then: 4 + (−12) = −8.
  • Step 2: Do the division and multiplication in your problem first, then add the results!
• Answer: −6

[Hard] Surface Area Challenge

• EN: A triangular prism has a triangular face with base 6 cm and height 4 cm, and a length of 10 cm. The three rectangular faces have widths 5, 5, and 6 cm. What is the total surface area?
• FR: Un prisme triangulaire a une face triangulaire de base 6 cm et de hauteur 4 cm, et une longueur de 10 cm. Les trois faces rectangulaires ont des largeurs de 5, 5 et 6 cm. Quelle est l'aire de surface totale?
• Choices: A) 196 cm² B) 202 cm² C) 208 cm² D) 212 cm²
• Hint: Total SA = 2 × triangle area + sum of rectangular faces. Triangle area = (base × height) ÷ 2. Each rectangle area = width × length of prism.
• Steps:
  • Step 1: Triangle: base=4, height=3. Area = (4×3)÷2 = 6 cm². Two triangles = 12 cm². Three rectangles: widths 3, 3, 4 each × length 8: 24+24+32=80. Total=92 cm².
  • Step 2: Find both triangle areas, then find each rectangle's area (width × 10), and add everything together!
• Answer: 208 cm²

[Hard] Probability

• EN: A spinner has 8 equal sections numbered 1–8. What is the probability of spinning a number greater than 5?
• FR: Une roulette a 8 sections égales numérotées de 1 à 8. Quelle est la probabilité d'obtenir un nombre supérieur à 5?
• Choices: A) 1/4 B) 3/8 C) 1/2 D) 5/8
• Hint: Count the favourable outcomes (numbers greater than 5), then divide by total sections. For example, numbers > 4 on a 6-spinner: 5, 6 = 2 favourables out of 6 → 2/6 = 1/3.
• Steps:
  • Step 1: Numbers > 3 on spinner 1–6: 4, 5, 6 = 3 outcomes. P = 3/6 = 1/2.
  • Step 2: List numbers greater than 5 from 1–8, count them, then divide by 8!
• Answer: 3/8

[Hard] Multi-Step Discount and Tax

• EN: A snowboard originally costs $240. It's on sale for 20% off. Then 13% HST is added. What is the final price?
• FR: Une planche à neige coûte originalement 240 $. Elle est en solde à 20 % de rabais. Ensuite, la TVH de 13 % est ajoutée. Quel est le prix final?
• Choices: A) $210.24 B) $214.24 C) $216.24 D) $220.24
• Hint: Step 1: Find the sale price (original − 20% discount). Step 2: Add 13% tax to the sale price. For example, $100 − 20% = $80; $80 + 13% = $80 × 1.13 = $90.40.
• Steps:
  • Step 1: $200 − 20% = $200 × 0.80 = $160. Then $160 × 1.13 = $180.80.
  • Step 2: Find 80% of $240 first (that's the sale price), then multiply by 1.13 for tax!
• Answer: $216.24

[Easy] Perfect Squares

• EN: What is √144?
• FR: Quel est √144?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: A perfect square root asks: what number times itself equals the value? For example, √81: 9 × 9 = 81, so √81 = 9.
• Steps:
  • Step 1: √100: 10 × 10 = 100. So √100 = 10.
  • Step 2: Ask yourself: what number × itself = 144? That's your square root!
• Answer: 12

[Easy] Two-Step Equation

• EN: Solve: 3x − 4 = 11
• FR: Résous : 3x − 4 = 11
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Add the constant to both sides first, then divide. For example, 5x − 6 = 19: 5x = 25; x = 5.
• Steps:
  • Step 1: 4x − 3 = 13. Add 3: 4x = 16. Divide by 4: x = 4.
  • Step 2: Add 4 to both sides, then divide by 3 the same way!
• Answer: 5

[Easy] Mean

• EN: Five hockey games had scores of: 3, 5, 4, 6, 2. What is the mean score?
• FR: Cinq parties de hockey ont eu les résultats suivants : 3, 5, 4, 6, 2. Quel est le résultat moyen?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Mean = sum of values ÷ number of values. For example, 4, 6, 8, 10: sum = 28; mean = 28 ÷ 4 = 7.
• Steps:
  • Step 1: Values: 2, 4, 6, 8. Sum = 20. Mean = 20 ÷ 4 = 5.
  • Step 2: Add all five scores together, then divide by 5 to find the mean!
• Answer: 4

[Easy] 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) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100. For example, from 40 to 50: increase = 10; (10 ÷ 40) × 100 = 25%.
• Steps:
  • Step 1: From 30 to 36. Increase = 6. (6 ÷ 30) × 100 = 20%.
  • Step 2: Find the increase (25 − 20), divide by original (20), multiply by 100!
• Answer: 25%

[Easy] Pythagorean Theorem — Find Hypotenuse

• EN: A right triangle has legs of 3 cm and 4 cm. What is the hypotenuse?
• FR: Un triangle rectangle a des jambes de 3 cm et 4 cm. Quelle est l'hypoténuse?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: Use a² + b² = c². For example, legs 6 and 8: 36 + 64 = 100; √100 = 10.
• Steps:
  • Step 1: Legs 5 and 12: 25 + 144 = 169. √169 = 13. Hypotenuse = 13 cm.
  • Step 2: Square both legs (3² + 4²), add them, then take the square root!
• Answer: 5 cm

[Medium] Two-Step Equation with Fractions

• EN: Solve: x/3 + 4 = 9
• FR: Résous : x/3 + 4 = 9
• Choices: A) 12 B) 13 C) 14 D) 15
• Hint: Subtract the constant first, then multiply both sides to clear the fraction. For example, x/4 + 2 = 7: x/4 = 5; x = 5 × 4 = 20.
• Steps:
  • Step 1: x/5 + 3 = 8. Subtract 3: x/5 = 5. Multiply by 5: x = 25.
  • Step 2: Subtract 4 from both sides, then multiply by 3 to find x!
• Answer: 15

[Medium] Pythagorean Theorem — Find a 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 un côté de 5 cm. Trouve l'autre côté.
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 13 cm
• Hint: Use a² + b² = c² → b² = c² − a². For example, hypotenuse 10, leg 6: b² = 100 − 36 = 64; b = 8.
• Steps:
  • Step 1: Hypotenuse 17, leg 8: b² = 289 − 64 = 225; b = √225 = 15 cm.
  • Step 2: Square the hypotenuse and the known leg, subtract, then take the square root!
• Answer: 12 cm

[Medium] Slope Introduction

• EN: A ramp rises 6 m over a horizontal distance of 12 m. What is the slope?
• FR: Une rampe monte de 6 m sur une distance horizontale de 12 m. Quel est la pente?
• Choices: A) 1/4 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: Rise = 3, run = 9. Slope = 3/9 = 1/3.
  • Step 2: Divide the rise by the run the same way — simplify your fraction if needed!
• Answer: 1/2

[Medium] Percent Decrease

• EN: A snowblower was $450. After winter it is marked down to $360. What is the percent decrease?
• FR: Un chasse-neige coûtait 450 $. Après l'hiver, son prix est réduit à 360 $. Quel est le pourcentage de diminution?
• Choices: A) 15% B) 18% C) 20% D) 25%
• Hint: Percent decrease = (decrease ÷ original) × 100. For example, $80 to $60: decrease = $20; (20 ÷ 80) × 100 = 25%.
• Steps:
  • Step 1: $200 to $150. Decrease = $50. (50 ÷ 200) × 100 = 25%.
  • Step 2: Find the decrease (450 − 360), divide by original (450), multiply by 100!
• Answer: 20%

[Medium] Mode

• EN: Snowfall amounts (cm) over 7 days: 5, 8, 3, 8, 5, 8, 2. What is the mode?
• FR: Quantités de neige (cm) sur 7 jours : 5, 8, 3, 8, 5, 8, 2. Quel est le mode?
• Choices: A) 2 B) 5 C) 8 D) 3
• Hint: The mode is the value that appears most often. For example, in 4, 7, 4, 9, 4: 4 appears 3 times, so mode = 4.
• Steps:
  • Step 1: Data: 2, 2, 3, 5, 5, 5, 6. 5 appears 3 times — mode = 5.
  • Step 2: Count how many times each number appears in your data set — the most frequent one is the mode!
• Answer: 8

[Medium] Square Roots and Perfect Squares

• EN: Which of the following is NOT a perfect square?
• FR: Lequel des éléments suivants N'est PAS un carré parfait?
• Choices: A) 49 B) 64 C) 72 D) 81
• Hint: A perfect square is the result of multiplying a whole number by itself. For example, 36 = 6 × 6. Check if each number has a whole-number square root!
• Steps:
  • Step 1: Is 50 a perfect square? √50 ≈ 7.07 (not whole). Is 25? √25 = 5 (whole). So 50 is NOT a perfect square.
  • Step 2: Check each choice — can you find a whole number that, squared, gives you that number?
• Answer: 72

[Hard] Two-Step Equation — Negative Coefficients

• EN: Solve: −4x + 7 = 27
• FR: Résous : −4x + 7 = 27
• Choices: A) −7 B) −6 C) −5 D) −4
• Hint: Subtract 7 from both sides, then divide by −4. Remember: dividing by a negative flips the sign. For example, −3x + 5 = 14: −3x = 9; x = 9 ÷ (−3) = −3.
• Steps:
  • Step 1: −5x + 3 = 23. Subtract 3: −5x = 20. Divide: x = 20 ÷ (−5) = −4.
  • Step 2: Subtract 7 from both sides, then divide by −4 — watch the sign!
• Answer: −5

[Hard] Pythagorean Theorem Application

• EN: A 15 m ladder leans against a wall. Its base is 9 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 15 m s'appuie contre un mur. Sa base est à 9 m du mur. À quelle hauteur le long du mur l'échelle atteint-elle?
• Choices: A) 10 m B) 11 m C) 12 m D) 13 m
• Hint: Use a² + b² = c². The ladder is the hypotenuse (c = 15), base = 9, find height. b² = c² − a² = 225 − 81 = 144; b = √144 = 12.
• Steps:
  • Step 1: Hypotenuse = 17, base = 8. Height² = 289 − 64 = 225. Height = √225 = 15 m.
  • Step 2: Square 15 and 9, subtract, then take the square root to find the height!
• Answer: 12 m

[Hard] Slope and Rate of Change

• EN: A swimming pool fills at a constant rate. After 2 hours it has 300 L; after 5 hours it has 750 L. What is the rate of change (slope) in litres per hour?
• FR: Une piscine se remplit à un rythme constant. Après 2 heures, elle contient 300 L; après 5 heures, 750 L. Quel est le taux de variation (pente) en litres par heure?
• Choices: A) 100 L/h B) 130 L/h C) 150 L/h D) 175 L/h
• Hint: Slope = (change in y) ÷ (change in x) = (y₂ − y₁) ÷ (x₂ − x₁). For example, from (1, 50) to (4, 200): (200−50)÷(4−1) = 150÷3 = 50 L/h.
• Steps:
  • Step 1: (3, 180) to (7, 420). Slope = (420−180)÷(7−3) = 240÷4 = 60 L/h.
  • Step 2: Subtract the litres (750 − 300), divide by time difference (5 − 2) the same way!
• Answer: 150 L/h

[Hard] Multi-Step Percent Problem

• EN: A store marks up a $200 item by 30%, then offers a 10% loyalty discount on the marked-up price. What is the final price?
• FR: Un magasin augmente le prix d'un article de 200 $ de 30 %, puis offre un rabais de fidélité de 10 % sur le prix majoré. Quel est le prix final?
• Choices: A) $226 B) $228 C) $230 D) $234
• Hint: Step 1: Find the marked-up price (original × 1.30). Step 2: Apply 10% discount (marked-up × 0.90). For example, $100 × 1.25 = $125; $125 × 0.90 = $112.50.
• Steps:
  • Step 1: $150 × 1.40 = $210. Then $210 × 0.90 = $189.
  • Step 2: Multiply $200 × 1.30 first, then multiply that result × 0.90!
• Answer: $234

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 8 = 17
• FR: Résous pour x : 5x − 8 = 17
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Add the constant to both sides, then divide. For example, 4x − 3 = 21: 4x = 24; x = 6.
• Steps:
  • Step 1: 6x − 5 = 25. Add 5: 6x = 30. Divide: x = 5.
  • Step 2: Add 8 to both sides, then divide by 5 the same way!
• Answer: 5

[Easy] Graphing — Slope-Intercept Form

• EN: What is the slope of the line y = 3x + 2?
• FR: Quel est le pente de la droite y = 3x + 2?
• Choices: A) 1 B) 2 C) 3 D) 5
• Hint: In y = mx + b, m is the slope and b is the y-intercept. For example, in y = 5x − 1, the slope is 5.
• Steps:
  • Step 1: y = 7x + 4. The slope is the coefficient of x, which is 7.
  • Step 2: Look at the coefficient of x in y = 3x + 2 — that number is the slope!
• Answer: 3

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3)
• FR: Simplifie : (3x + 5) + (2x − 3)
• Choices: A) 4x + 2 B) 5x + 2 C) 5x + 8 D) 6x + 2
• Hint: Combine like terms — add the x terms together and the number terms together. For example, (4x + 3) + (x − 1) = 5x + 2.
• Steps:
  • Step 1: (5x + 6) + (3x − 4). x terms: 5x + 3x = 8x. Numbers: 6 − 4 = 2. Answer: 8x + 2.
  • Step 2: Add x terms together and constants together the same way for your problem!
• Answer: 5x + 2

[Easy] SOH-CAH-TOA — Finding a Side

• EN: In a right triangle, the angle is 30° and the hypotenuse is 10 cm. Find the opposite side. (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle est de 30° et l'hypoténuse est de 10 cm. Trouve le côté opposé. (sin 30° = 0,5)
• Choices: A) 3 cm B) 4 cm C) 5 cm D) 6 cm
• Hint: sin(angle) = opposite ÷ hypotenuse. Rearranging: opposite = sin(angle) × hypotenuse. For example, sin 45° × 8 = 0.707 × 8 ≈ 5.66 cm.
• Steps:
  • Step 1: sin 60° = 0.866; hypotenuse = 12. Opposite = 0.866 × 12 ≈ 10.4 cm.
  • Step 2: Multiply sin(30°) = 0.5 by the hypotenuse (10) the same way!
• Answer: 5 cm

[Easy] Linear Inequality

• EN: Solve: x + 6 > 10
• FR: Résous : x + 6 > 10
• Choices: A) x > 2 B) x > 3 C) x > 4 D) x > 5
• Hint: Solve inequalities just like equations — subtract from both sides. For example, x + 3 > 9: x > 6.
• Steps:
  • Step 1: x + 5 > 12. Subtract 5 from both sides: x > 7.
  • Step 2: Subtract 6 from both sides of your inequality the same way!
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5)
• FR: Développe : (x + 3)(x + 5)
• Choices: A) x² + 7x + 15 B) x² + 8x + 15 C) x² + 8x + 12 D) x² + 6x + 15
• Hint: Use FOIL: First, Outer, Inner, Last. For example, (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • Step 1: (x + 1)(x + 6). F: x²; O: 6x; I: x; L: 6. Combine: x² + 7x + 6.
  • Step 2: Apply FOIL to (x + 3)(x + 5) — multiply each term pair and combine like terms!
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Two similar triangles have sides in ratio 2:3. The smaller triangle has a base of 8 cm. What is the base of the larger triangle?
• FR: Deux triangles semblables ont des côtés en rapport 2:3. Le plus petit triangle a une base de 8 cm. Quelle est la base du plus grand triangle?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 14 cm
• Hint: Set up a proportion using the ratio. If smaller = 2 parts and larger = 3 parts: larger base = (3/2) × smaller. For example, smaller = 6 cm: larger = (3/2) × 6 = 9 cm.
• Steps:
  • Step 1: Ratio 2:5, smaller base = 4 cm. Larger = (5/2) × 4 = 10 cm.
  • Step 2: Multiply the smaller base by (3/2) to find the larger base the same way!
• Answer: 12 cm

[Medium] Systems of Equations Introduction

• EN: If x + y = 10 and x − y = 4, what is the value of x?
• FR: Si x + y = 10 et x − y = 4, quelle est la valeur de x?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Add the two equations together to eliminate y. For example, x + y = 8 and x − y = 2: adding gives 2x = 10; x = 5.
• Steps:
  • Step 1: x + y = 12 and x − y = 4. Add: 2x = 16; x = 8.
  • Step 2: Add your two equations together — y cancels out, and you can solve for x!
• Answer: 7

[Medium] Graphing — Y-Intercept

• EN: What is the y-intercept of the line y = −2x + 7?
• FR: Quel est l'ordonnée à l'origine de la droite y = −2x + 7?
• Choices: A) −7 B) −2 C) 2 D) 7
• Hint: In y = mx + b, b is the y-intercept (where the line crosses the y-axis). For example, in y = 4x − 3, the y-intercept is −3.
• Steps:
  • Step 1: y = 5x + 9. The y-intercept is 9 (the b value).
  • Step 2: Identify the b value in y = −2x + 7 — that's the y-intercept!
• Answer: 7

[Medium] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 5 cm and hypotenuse is 10 cm. Find the angle. (sin θ = 0.5 → θ = 30°)
• FR: Dans un triangle rectangle, le côté opposé est de 5 cm et l'hypoténuse de 10 cm. Trouve l'angle. (sin θ = 0,5 → θ = 30°)
• Choices: A) 25° B) 30° C) 45° D) 60°
• Hint: sin θ = opposite ÷ hypotenuse. Find the ratio, then use the inverse sine. For example, opposite = 7, hyp = 14: sin θ = 0.5; θ = 30°.
• Steps:
  • Step 1: Opposite = 6, hypotenuse = 12. sin θ = 6/12 = 0.5. So θ = 30°.
  • Step 2: Divide opposite by hypotenuse (5 ÷ 10 = 0.5), then find the angle with that sine value!
• Answer: 30°

[Medium] Subtracting Polynomials

• EN: Simplify: (5x² + 3x − 2) − (2x² − x + 4)
• FR: Simplifie : (5x² + 3x − 2) − (2x² − x + 4)
• Choices: A) 3x² + 4x − 6 B) 3x² + 2x − 6 C) 3x² + 4x + 6 D) 7x² + 2x − 6
• Hint: Distribute the negative sign to all terms in the second bracket, then combine like terms. For example, (6x² + x − 1) − (2x² − 3x + 5) = 4x² + 4x − 6.
• Steps:
  • Step 1: (4x² + 5x − 3) − (x² − 2x + 1). Distribute negative: 4x² + 5x − 3 − x² + 2x − 1 = 3x² + 7x − 4.
  • Step 2: Flip signs on all terms in the second bracket, then combine like terms the same way!
• Answer: 3x² + 4x − 6

[Hard] Solving a Linear Inequality with Negatives

• EN: Solve: −3x + 5 ≤ 14
• FR: Résous : −3x + 5 ≤ 14
• Choices: A) x ≥ −5 B) x ≥ −4 C) x ≥ −3 D) x ≤ −3
• Hint: When you divide or multiply both sides by a negative number, FLIP the inequality sign. For example, −2x < 8: x > −4 (flip!).
• Steps:
  • Step 1: −4x + 3 ≤ 11. Subtract 3: −4x ≤ 8. Divide by −4 (flip): x ≥ −2.
  • Step 2: Subtract 5 from both sides, then divide by −3 and remember to flip the inequality sign!
• Answer: x ≥ −3

[Hard] Trigonometry — Angle and Side

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What angle does this give? (cos θ = 0.8 → θ ≈ 37°)
• FR: Dans un triangle rectangle, le côté adjacent est de 8 cm et l'hypoténuse de 10 cm. Quel angle cela donne-t-il? (cos θ = 0,8 → θ ≈ 37°)
• Choices: A) 30° B) 37° C) 45° D) 53°
• Hint: cos θ = adjacent ÷ hypotenuse. Find the ratio and then find the angle using inverse cosine. For example, adjacent = 6, hyp = 10: cos θ = 0.6 → θ ≈ 53°.
• Steps:
  • Step 1: Adjacent = 9, hypotenuse = 15. cos θ = 9/15 = 0.6 → θ ≈ 53°.
  • Step 2: Divide 8 by 10 to get the cosine ratio, then match it to the given angle!
• Answer: 37°

[Hard] Polynomial Multiplication

• EN: Expand and simplify: (2x + 3)(3x − 4)
• FR: Développe et simplifie : (2x + 3)(3x − 4)
• Choices: A) 6x² − x − 12 B) 6x² + x − 12 C) 6x² − x + 12 D) 5x² + x − 12
• Hint: Use FOIL on binomials with coefficients. For example, (3x + 2)(2x − 5): F=6x², O=−15x, I=4x, L=−10. Combine: 6x² − 11x − 10.
• Steps:
  • Step 1: (4x + 1)(2x − 3). F: 8x². O: −12x. I: 2x. L: −3. Combine: 8x² − 10x − 3.
  • Step 2: Apply FOIL to (2x + 3)(3x − 4) and combine the like terms!
• Answer: 6x² + x − 12

[Hard] Statistics — Interpreting Data

• EN: A set of test scores has a mean of 78 and a median of 85. What can you conclude?
• FR: Un ensemble de résultats d'examen a une moyenne de 78 et une médiane de 85. Que peut-on conclure?
• Choices: A) Most scores are above the mean B) The data is symmetric C) There are likely some low scores pulling the mean down D) The mode equals the mean
• Hint: When mean < median, the distribution is skewed left — a few low values pull the mean down. For example, if most students scored 85+ but a few scored very low, mean < median.
• Steps:
  • Step 1: Imagine scores: 30, 80, 85, 88, 90. Mean ≈ 74.6; median = 85. The one low score (30) drags the mean below the median.
  • Step 2: Think about what kind of data makes the mean smaller than the median — what pulls a mean down?
• Answer: There are likely some low scores pulling the mean down

[Easy] Factoring Quadratics

• 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 + 4)(x + 4)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient. For example, x² + 5x + 6: 2 × 3 = 6 and 2 + 3 = 5 → (x + 2)(x + 3).
• Steps:
  • Step 1: x² + 9x + 20. Find two numbers: ? × ? = 20 and ? + ? = 9. Try 4 and 5: 4 × 5 = 20, 4 + 5 = 9. → (x + 4)(x + 5).
  • Step 2: Find two numbers that multiply to 12 and add to 7 — those go in your factors!
• Answer: (x + 3)(x + 4)

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, angle A = 45°, adjacent side = 6 cm. Find the opposite side. (tan 45° = 1)
• FR: Dans un triangle rectangle, angle A = 45°, côté adjacent = 6 cm. Trouve le côté opposé. (tan 45° = 1)
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: tan(angle) = opposite ÷ adjacent. Rearrange: opposite = tan(angle) × adjacent. For example, tan 30° ≈ 0.577; adjacent = 10: opposite ≈ 5.77.
• Steps:
  • Step 1: tan 60° ≈ 1.73; adjacent = 4. Opposite = 1.73 × 4 ≈ 6.93 cm.
  • Step 2: Multiply tan(45°) × adjacent (6) the same way — and remember tan 45° = 1!
• Answer: 6 cm

[Easy] Systems of Equations — Substitution

• EN: Solve: y = 2x and x + y = 9. What is x?
• FR: Résous : y = 2x et x + y = 9. Quelle est la valeur de x?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Substitute the first equation into the second. For example, y = 3x; x + y = 8 → x + 3x = 8 → 4x = 8 → x = 2.
• Steps:
  • Step 1: y = 4x; x + y = 10. Substitute: x + 4x = 10 → 5x = 10 → x = 2.
  • Step 2: Replace y with 2x in the second equation, combine like terms, then solve for x!
• Answer: 3

[Easy] Volume of a Cylinder

• EN: A cylindrical water bottle has radius 3 cm and height 12 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une bouteille d'eau cylindrique a un rayon de 3 cm et une hauteur de 12 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 288.00 cm³ B) 301.44 cm³ C) 339.12 cm³ D) 356.00 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: r = 4, h = 7. V = 3.14 × 16 × 7 = 3.14 × 112 = 351.68 cm³.
  • Step 2: Square the radius (3² = 9), multiply by π (3.14) and height (12)!
• Answer: 339.12 cm³

[Easy] Circle Geometry — Circumference

• EN: What is the circumference of a circle with diameter 10 cm? (Use π ≈ 3.14)
• FR: Quelle est la circonférence d'un cercle de diamètre 10 cm? (Utilise π ≈ 3,14)
• Choices: A) 28.26 cm B) 30.14 cm C) 31.40 cm D) 34.54 cm
• Hint: Circumference = π × diameter. For example, diameter = 8: C = 3.14 × 8 = 25.12 cm.
• Steps:
  • Step 1: Diameter = 6 cm. C = 3.14 × 6 = 18.84 cm.
  • Step 2: Multiply π (3.14) × diameter (10) the same way!
• Answer: 31.40 cm

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x = 7
• FR: Résous en complétant le carré : x² + 6x = 7
• Choices: A) x = 1 or x = −7 B) x = 2 or x = −8 C) x = 3 or x = −9 D) x = 1 or x = −8
• Hint: Add (b/2)² to both sides. For example, x² + 4x = 5: add 4 → (x+2)² = 9 → x = 1 or x = −5.
• Steps:
  • Step 1: x² + 8x = 9. Add (4)² = 16: (x+4)² = 25. x+4 = ±5. x = 1 or x = −9.
  • Step 2: Add (6/2)² = 9 to both sides, write as a perfect square, then solve!
• Answer: x = 1 or x = −7

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve: x² − 5x + 6 = 0
• FR: Utilise la formule quadratique pour résoudre : x² − 5x + 6 = 0
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = −2 or x = −3 D) x = 1 or x = 5
• Hint: x = (−b ± √(b²−4ac)) ÷ 2a. For example, x² − 7x + 12: a=1, b=−7, c=12. Discriminant = 49−48=1. x = (7±1)÷2: x=4 or x=3.
• Steps:
  • Step 1: x² − 6x + 8 = 0. a=1, b=−6, c=8. Disc = 36−32=4. x = (6±2)/2. x=4 or x=2.
  • Step 2: Identify a=1, b=−5, c=6; compute discriminant and apply the formula!
• Answer: x = 2 or x = 3

[Medium] Circle Geometry — Arc and Sector

• EN: A circle has radius 6 cm. A sector has a central angle of 90°. What is the area of the sector? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 6 cm. Un secteur a un angle central de 90°. Quelle est l'aire du secteur? (Utilise π ≈ 3,14)
• Choices: A) 25.14 cm² B) 28.26 cm² C) 31.40 cm² D) 34.54 cm²
• Hint: Area of sector = (angle/360) × π × r². For example, 60° sector with r=4: (60/360) × 3.14 × 16 = (1/6) × 50.24 ≈ 8.37 cm².
• Steps:
  • Step 1: 45° sector, r=8. (45/360) × 3.14 × 64 = 0.125 × 200.96 = 25.12 cm².
  • Step 2: Use (90/360) × 3.14 × 36 — simplify 90/360 to 1/4 first!
• Answer: 28.26 cm²

[Medium] Surface Area of a Cone

• EN: A cone has radius 5 cm and slant height 13 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 5 cm et une hauteur oblique de 13 cm. Quelle est son aire de surface totale? (Utilise π ≈ 3,14)
• Choices: A) 270.04 cm² B) 280.14 cm² C) 282.60 cm² D) 294.00 cm²
• Hint: SA of cone = π r² + π r l (base + lateral). For example, r=3, l=5: SA = 3.14×9 + 3.14×3×5 = 28.26 + 47.10 = 75.36 cm².
• Steps:
  • Step 1: r=4, l=10. SA = 3.14×16 + 3.14×4×10 = 50.24 + 125.6 = 175.84 cm².
  • Step 2: Find π×r² for the base and π×r×l for the side, then add them together!
• Answer: 282.60 cm²

[Medium] Systems — Elimination

• EN: Solve using elimination: 2x + 3y = 16 and 2x − y = 4. What is y?
• FR: Résous par élimination : 2x + 3y = 16 et 2x − y = 4. Quelle est la valeur de y?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: Subtract the equations to eliminate x. For example, 3x + 2y = 11 and 3x − y = 5: subtracting gives 3y = 6; y = 2.
• Steps:
  • Step 1: 4x + y = 13 and 4x − 2y = 7. Subtract: 3y = 6; y = 2.
  • Step 2: Subtract the second equation from the first to eliminate 2x, then solve for y!
• Answer: 3

[Medium] Trigonometry — Angle of Elevation

• EN: A tree casts a shadow of 24 m. The angle of elevation to the top is 30°. How tall is the tree? (tan 30° ≈ 0.577)
• FR: Un arbre projette une ombre de 24 m. L'angle d'élévation vers le sommet est de 30°. Quelle est la hauteur de l'arbre? (tan 30° ≈ 0,577)
• Choices: A) 12.4 m B) 13.8 m C) 14.5 m D) 15.2 m
• Hint: tan(angle) = opposite ÷ adjacent. opposite = tan(angle) × adjacent. For example, tan 45° × 18 = 1 × 18 = 18 m tall.
• Steps:
  • Step 1: Shadow = 30 m, angle = 30°. Height = tan 30° × 30 = 0.577 × 30 = 17.31 m.
  • Step 2: Multiply tan(30°) ≈ 0.577 by the shadow length (24) the same way!
• Answer: 13.8 m

[Hard] Quadratic — Word Problem

• EN: A ball is thrown upward. Its height is modelled by h = −5t² + 20t. When does the ball hit the ground? (h = 0)
• FR: Un ballon est lancé vers le haut. Sa hauteur est modélisée par h = −5t² + 20t. Quand le ballon touche-t-il le sol? (h = 0)
• Choices: A) t = 2 s B) t = 3 s C) t = 4 s D) t = 5 s
• Hint: Set h = 0 and factor: −5t² + 20t = 0 → −5t(t − ?) = 0. For example, −4t² + 16t = 0: −4t(t − 4) = 0 → t = 0 or t = 4.
• Steps:
  • Step 1: −3t² + 12t = 0. Factor: −3t(t − 4) = 0. t = 0 or t = 4. Ball hits ground at t = 4.
  • Step 2: Factor out −5t from your equation, set each factor to zero, and choose the non-zero time!
• Answer: t = 4 s

[Hard] Circle Geometry Theorem

• EN: A chord of length 16 cm is 6 cm from the centre of a circle. What is the radius of the circle?
• FR: Une corde de 16 cm de longueur est à 6 cm du centre d'un cercle. Quel est le rayon du cercle?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 11 cm
• Hint: A perpendicular from the centre bisects the chord. Use the Pythagorean theorem: r² = (half chord)² + distance². For example, chord = 12 (half = 6), distance = 8: r² = 36 + 64 = 100; r = 10.
• Steps:
  • Step 1: Chord = 24 (half = 12), distance = 5. r² = 144 + 25 = 169. r = 13 cm.
  • Step 2: Half your chord = 8 cm. Use 8² + 6² = r² to find the radius!
• Answer: 10 cm

[Hard] 3D Surface Area — Composite Shape

• EN: A shape is made of a rectangular prism (4 × 3 × 5 cm) with a cube (side 2 cm) placed on top. What is the exposed surface area of the combined shape? (Subtract the overlapping 2×2 face twice.)
• FR: Une forme est composée d'un prisme rectangulaire (4 × 3 × 5 cm) avec un cube (côté 2 cm) placé sur le dessus. Quelle est l'aire de surface exposée de la forme combinée? (Soustrais la face de chevauchement 2 × 2 deux fois.)
• Choices: A) 118 cm² B) 122 cm² C) 126 cm² D) 130 cm²
• Hint: SA combined = SA of prism + SA of cube − 2 × (area of overlapping face). The two surfaces that touch are hidden.
• Steps:
  • Step 1: SA of prism (4×3×5): 2(12+20+15) = 2(47) = 94 cm². SA of cube (side 2): 6 × 4 = 24 cm². Overlap: 2 × 4 = 8 cm². Combined: 94 + 24 − 8 = 110 cm².
  • Step 2: Use the same method with your dimensions — find each SA, then subtract both overlapping faces!
• Answer: 118 cm²

[Hard] Systems of Equations — Word Problem

• EN: Two canoes rent for different prices. Canoe A costs $15/hour, Canoe B costs $25/hour. For 4 hours, the total cost for both canoes is $140. How many hours did Canoe A rent?
• FR: Deux canots se louent à des prix différents. Le canot A coûte 15 $/heure, le canot B coûte 25 $/heure. Pour 4 heures au total, le coût des deux canots est de 140 $. Combien d'heures le canot A a-t-il été loué?
• Choices: A) 1 hour B) 2 hours C) 3 hours D) 4 hours
• Hint: Let a = hours for A, b = hours for B. Set up: a + b = 4 and 15a + 25b = 140. Solve by substitution or elimination.
• Steps:
  • Step 1: a + b = 3, 10a + 20b = 40. From equation 1: a = 3 − b. Substitute: 10(3−b) + 20b = 40 → 30 − 10b + 20b = 40 → 10b = 10 → b = 1. So a = 2.
  • Step 2: Express a in terms of b from the first equation, substitute into the second, and solve!
• Answer: 2 hours

[Easy] Exponential Function

• EN: A bacteria colony doubles every hour. It starts with 50 bacteria. How many are there after 3 hours?
• FR: Une colonie de bactéries double chaque heure. Elle commence avec 50 bactéries. Combien y en a-t-il après 3 heures?
• Choices: A) 300 B) 350 C) 400 D) 450
• Hint: Exponential growth: amount = initial × (growth factor)^time. For example, starts at 30, doubles: after 3 hours = 30 × 2³ = 30 × 8 = 240.
• Steps:
  • Step 1: Start = 20, doubles every hour. After 4 hours: 20 × 2⁴ = 20 × 16 = 320.
  • Step 2: Multiply 50 × 2³ the same way — calculate 2³ first, then multiply by the initial amount!
• Answer: 400

[Easy] Arithmetic Sequence

• EN: The sequence is 5, 11, 17, 23, ... What is the 6th term?
• FR: La suite est 5, 11, 17, 23, ... Quel est le 6e terme?
• Choices: A) 33 B) 35 C) 37 D) 39
• Hint: In an arithmetic sequence, add the common difference each time. Find d first. For example, 4, 9, 14, 19: d=5. 6th term = 4 + 5×5 = 29.
• Steps:
  • Step 1: Sequence: 3, 8, 13, 18. d = 5. 6th term = 3 + 5×5 = 3 + 25 = 28.
  • Step 2: Find d (11 − 5 = 6), then use: t₆ = first term + 5 × d!
• Answer: 35

[Easy] Compound Interest

• EN: You invest $1,000 at 5% annual compound interest for 2 years. What is the final amount? (Use A = P(1 + r)^t)
• FR: Tu investis 1 000 $ à un taux d'intérêt composé annuel de 5 % pendant 2 ans. Quel est le montant final? (Utilise A = P(1 + r)^t)
• Choices: A) $1,100.25 B) $1,102.50 C) $1,102.75 D) $1,105.00
• Hint: A = P(1 + r)^t. For example, P=$500, r=0.10, t=2: A = 500 × (1.10)² = 500 × 1.21 = $605.
• Steps:
  • Step 1: P=$800, r=0.05, t=2. A = 800 × (1.05)² = 800 × 1.1025 = $882.
  • Step 2: Apply the same formula — 1000 × (1.05)² = 1000 × 1.1025!
• Answer: $1,102.50

[Easy] Quadratic Function — Vertex

• EN: What is the vertex of y = (x − 3)² + 4?
• FR: Quel est le sommet de y = (x − 3)² + 4?
• Choices: A) (−3, 4) B) (3, −4) C) (3, 4) D) (−3, −4)
• Hint: In vertex form y = (x − h)² + k, the vertex is (h, k). For example, y = (x − 2)² + 5: vertex is (2, 5).
• Steps:
  • Step 1: y = (x − 6)² + 1. Vertex is (6, 1). h = 6, k = 1.
  • Step 2: Identify h and k in your equation — remember to flip the sign of h!
• Answer: (3, 4)

[Easy] Logarithm Introduction

• EN: Solve: log₂(8) = ?
• FR: Résous : log₂(8) = ?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: logₐ(b) = c means aᶜ = b. Ask: 2 to what power equals 8? For example, log₂(16): 2⁴ = 16, so log₂(16) = 4.
• Steps:
  • Step 1: log₃(27): 3³ = 27. So log₃(27) = 3.
  • Step 2: Ask: 2 to what power equals 8? That exponent is your answer!
• Answer: 3

[Medium] Geometric Sequence

• EN: A geometric sequence starts at 6 with ratio 3. What is the 4th term?
• FR: Une suite géométrique commence à 6 avec un rapport de 3. Quel est le 4e terme?
• Choices: A) 54 B) 108 C) 162 D) 486
• Hint: tₙ = first term × r^(n−1). For example, first = 4, r = 2, 4th term: 4 × 2³ = 32.
• Steps:
  • Step 1: First = 5, r = 3, 4th term: 5 × 3³ = 5 × 27 = 135.
  • Step 2: Multiply 6 × 3³ the same way — calculate 3³ first, then multiply by 6!
• Answer: 162

[Medium] Logarithm Laws

• EN: Simplify: log(100) + log(10)
• FR: Simplifie : log(100) + log(10)
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: log(a) + log(b) = log(a × b). Also, log₁₀(10ⁿ) = n. For example, log(1000) + log(100) = log(100,000) = 5.
• Steps:
  • Step 1: log(10) + log(100) = log(1000) = log(10³) = 3.
  • Step 2: Add your logs by combining: log(100 × 10) = log(1000) = ?
• Answer: 3

[Medium] Annuity — Future Value

• EN: You deposit $200 per month for 12 months at 0% interest. How much have you saved?
• FR: Tu déposes 200 $ par mois pendant 12 mois à un taux d'intérêt de 0 %. Combien as-tu épargné?
• Choices: A) $2,000 B) $2,200 C) $2,400 D) $2,600
• Hint: At 0% interest, the total is simply the monthly payment × number of months. For example, $150/month × 10 months = $1,500.
• Steps:
  • Step 1: $300/month × 8 months = $2,400.
  • Step 2: Multiply $200 by 12 months the same way!
• Answer: $2,400

[Medium] Trigonometric Identity

• EN: Simplify using an identity: sin²θ + cos²θ
• FR: Simplifie à l'aide d'une identité : sin²θ + cos²θ
• Choices: A) 0 B) 2 C) sin θ D) 1
• Hint: This is the Pythagorean identity — one of the most important in trigonometry! For any angle θ, sin²θ + cos²θ always equals the same value. Think of a unit circle!
• Steps:
  • Step 1: On a unit circle, the point (cos θ, sin θ) is always on a circle of radius 1. By the Pythagorean theorem: cos²θ + sin²θ = 1² = 1.
  • Step 2: The Pythagorean identity tells us that sin²θ + cos²θ always equals which value?
• Answer: 1

[Medium] Exponential Equation

• EN: Solve: 2^x = 32
• FR: Résous : 2^x = 32
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: Rewrite both sides with the same base. For example, 3^x = 81: 81 = 3⁴, so x = 4.
• Steps:
  • Step 1: 2^x = 16. 16 = 2⁴. So x = 4.
  • Step 2: Express 32 as a power of 2 the same way — 32 = 2^? — and that exponent is x!
• Answer: 5

[Medium] Arithmetic Series Sum

• EN: Find the sum of the first 10 terms of the sequence: 3, 7, 11, 15, ...
• FR: Trouve la somme des 10 premiers termes de la suite : 3, 7, 11, 15, ...
• Choices: A) 180 B) 190 C) 200 D) 210
• Hint: Sum = n/2 × (first + last term). First find the 10th term: t₁₀ = 3 + 9 × 4 = 39. Then Sₙ = 10/2 × (3 + 39).
• Steps:
  • Step 1: Sequence 2, 6, 10, 14. d=4, t₈ = 2 + 7×4 = 30. S₈ = 8/2 × (2+30) = 4 × 32 = 128.
  • Step 2: Find the 10th term first, then use S₁₀ = 10/2 × (first + last)!
• Answer: 210

[Hard] Logarithmic Equation

• EN: Solve: log₃(x) + log₃(x − 2) = log₃(8)
• FR: Résous : log₃(x) + log₃(x − 2) = log₃(8)
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Use log(a) + log(b) = log(ab). Then set the arguments equal: x(x−2) = 8. Solve the resulting quadratic and reject negative solutions.
• Steps:
  • Step 1: log₂(x) + log₂(x−1) = log₂(6). → x(x−1) = 6 → x² − x − 6 = 0 → (x−3)(x+2)=0 → x=3 (reject −2).
  • Step 2: Combine the logs on the left, set x(x−2) = 8, solve the quadratic, and reject any negative answer!
• Answer: x = 4

[Hard] Compound Interest — Finding Time

• EN: How many years does it take for $500 to grow to $1,000 at 10% compound interest per year? (Use 2 = 1.10^t; t ≈ 7.27, round to nearest year)
• FR: Combien d'années faut-il pour que 500 $ deviennent 1 000 $ à un taux d'intérêt composé de 10 % par an? (Utilise 2 = 1,10^t; t ≈ 7,27, arrondi à l'année la plus proche)
• Choices: A) 6 years B) 7 years C) 8 years D) 9 years
• Hint: A = P(1+r)^t → 1000 = 500(1.10)^t → 2 = 1.10^t → t = log(2)/log(1.10). Use logarithms to solve for t.
• Steps:
  • Step 1: $300 grows to $600 at 8%. 2 = 1.08^t. t = log(2)/log(1.08) ≈ 0.301/0.0334 ≈ 9.01 years.
  • Step 2: Apply t = log(2)/log(1.10) ≈ 0.301/0.0414 ≈ 7.27, so round to the nearest whole year!
• Answer: 7 years

[Hard] Trigonometric Equation

• EN: Solve for θ in [0°, 360°]: 2sin θ − 1 = 0
• FR: Résous pour θ dans [0°, 360°] : 2sin θ − 1 = 0
• Choices: A) 30° and 150° B) 45° and 135° C) 60° and 120° D) 30° and 330°
• Hint: Isolate sin θ = 1/2. Then find angles where sine equals 1/2 in [0°, 360°]. Sine is positive in Q1 and Q2. For example, sin θ = √3/2 → θ = 60° and 120°.
• Steps:
  • Step 1: sin θ = 1/2. Reference angle: sin⁻¹(0.5) = 30°. Positive in Q1 and Q2: θ = 30° and 150°.
  • Step 2: Isolate sin θ from your equation, find the reference angle, then apply the CAST rule!
• Answer: 30° and 150°

[Hard] Geometric Series Sum

• EN: Find the sum of the first 5 terms of the geometric series: 4, 12, 36, 108, ...
• FR: Trouve la somme des 5 premiers termes de la série géométrique : 4, 12, 36, 108, ...
• Choices: A) 484 B) 484 C) 484 D) 484
• Hint: Sₙ = a(rⁿ − 1)/(r − 1). Here a = 4, r = 3, n = 5: S₅ = 4(3⁵ − 1)/(3−1) = 4(243−1)/2 = 4×242/2 = 4×121 = 484.
• Steps:
  • Step 1: a=2, r=3, n=4. S₄ = 2(3⁴−1)/(3−1) = 2(80)/2 = 80.
  • Step 2: Apply Sₙ = a(rⁿ−1)/(r−1) with a=4, r=3, n=5 — compute 3⁵ = 243 first!
• Answer: 484

[Easy] Permutations

• EN: How many ways can 5 different books be arranged on a shelf?
• FR: De combien de façons peut-on ranger 5 livres différents sur une étagère?
• Choices: A) 60 B) 100 C) 120 D) 150
• Hint: Arrangements of n distinct objects = n! For example, 4 books: 4! = 4 × 3 × 2 × 1 = 24 ways.
• Steps:
  • Step 1: 3 books: 3! = 3 × 2 × 1 = 6 ways.
  • Step 2: Calculate 5! = 5 × 4 × 3 × 2 × 1 the same way!
• Answer: 120

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 6?
• FR: De combien de façons peut-on choisir 2 élèves dans un groupe de 6?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: C(n,r) = n! ÷ (r! × (n−r)!). For example, C(5,2) = 5!/(2!×3!) = 120/(2×6) = 10.
• Steps:
  • Step 1: C(4,2) = 4!/(2!×2!) = 24/(2×2) = 6 ways.
  • Step 2: Apply C(6,2) = 6!/(2!×4!) — calculate and simplify!
• Answer: 15

[Easy] Polynomial — Identifying Degree

• EN: What is the degree of the polynomial: 4x³ − 7x² + 2x − 9?
• FR: Quel est le degré du polynôme : 4x³ − 7x² + 2x − 9?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: The degree is the highest exponent on a variable. For example, 5x⁴ + 3x − 8 has degree 4.
• Steps:
  • Step 1: 6x² + x⁵ − 3. The highest exponent is 5 — degree = 5.
  • Step 2: Find the highest exponent in your polynomial — that's the degree!
• Answer: 3

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = x⁴.
• FR: Trouve la dérivée de f(x) = x⁴.
• Choices: A) x³ B) 4x³ C) 4x D) x⁵
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹. For example, f(x) = x³ → f'(x) = 3x².
• Steps:
  • Step 1: f(x) = x⁵. f'(x) = 5x⁴.
  • Step 2: Bring the exponent (4) down as a coefficient and reduce the power by 1!
• Answer: 4x³

[Easy] Rational Function — Domain

• EN: What value of x is NOT in the domain of f(x) = 1/(x − 5)?
• FR: Quelle valeur de x n'est PAS dans le domaine de f(x) = 1/(x − 5)?
• Choices: A) x = 0 B) x = 1 C) x = 5 D) x = −5
• Hint: A rational function is undefined when its denominator equals zero. For example, f(x) = 1/(x + 3): denominator = 0 when x = −3.
• Steps:
  • Step 1: f(x) = 1/(x − 8). Set denominator = 0: x − 8 = 0 → x = 8. Domain excludes x = 8.
  • Step 2: Set x − 5 = 0 and solve — that value is excluded from the domain!
• Answer: x = 5

[Medium] Derivative — Product Rule

• EN: Find the derivative of f(x) = x² · (3x + 1).
• FR: Trouve la dérivée de f(x) = x² · (3x + 1).
• Choices: A) 9x² + 2x B) 9x² + 4x C) 6x² + 2x D) 6x² + 3x
• Hint: Product rule: (uv)' = u'v + uv'. For example, f(x) = x³·(2x−1): u=x³, v=(2x−1); u'=3x², v'=2. f'(x) = 3x²(2x−1) + x³(2) = 6x³−3x²+2x³ = 8x³−3x².
• Steps:
  • Step 1: f(x) = x²·(4x+3). u=x², u'=2x; v=(4x+3), v'=4. f'(x) = 2x(4x+3)+x²(4) = 8x²+6x+4x² = 12x²+6x.
  • Step 2: Apply product rule to x²·(3x+1) — find u', v', then substitute into u'v + uv'!
• Answer: 9x² + 2x

[Medium] Probability Distribution

• EN: A fair coin is flipped 3 times. What is the probability of getting exactly 2 heads?
• FR: On lance une pièce de monnaie 3 fois. Quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 1/4 B) 3/8 C) 1/2 D) 5/8
• Hint: Use combinations. P(exactly k heads in n flips) = C(n,k) × (1/2)^n. For example, P(1 head in 3 flips) = C(3,1) × (1/2)³ = 3/8.
• Steps:
  • Step 1: P(2 heads in 4 flips) = C(4,2) × (1/2)⁴ = 6 × 1/16 = 6/16 = 3/8.
  • Step 2: Calculate C(3,2) × (1/2)³ the same way — C(3,2)=3 and (1/2)³ = 1/8!
• Answer: 3/8

[Medium] Vector Introduction

• EN: Vector a = (3, −1) and vector b = (−2, 4). What is a + b?
• FR: Le vecteur a = (3, −1) et le vecteur b = (−2, 4). Quel est a + b?
• Choices: A) (1, 3) B) (1, −3) C) (5, 3) D) (5, −5)
• Hint: Add vectors component by component. For example, (4, 2) + (−1, 5) = (4+(−1), 2+5) = (3, 7).
• Steps:
  • Step 1: (6, −3) + (−4, 7) = (6+(−4), −3+7) = (2, 4).
  • Step 2: Add the x-components and y-components of your vectors separately the same way!
• Answer: (1, 3)

[Medium] Rational Function — Asymptotes

• EN: What is the vertical asymptote of f(x) = (x + 2)/(x − 4)?
• FR: Quelle est l'asymptote verticale de f(x) = (x + 2)/(x − 4)?
• Choices: A) x = −2 B) x = 2 C) x = 4 D) x = −4
• Hint: Vertical asymptote occurs where denominator = 0 (and numerator ≠ 0). For example, f(x) = 3/(x+6): vertical asymptote at x = −6.
• Steps:
  • Step 1: f(x) = (x−1)/(x+3). Set denominator = 0: x + 3 = 0 → x = −3. Vertical asymptote at x = −3.
  • Step 2: Set x − 4 = 0 and solve to find the vertical asymptote!
• Answer: x = 4

[Medium] Derivative — Rate of Change

• EN: A car's position is s(t) = t³ − 3t cm after t seconds. What is the velocity at t = 2?
• FR: La position d'une voiture est s(t) = t³ − 3t cm après t secondes. Quelle est la vitesse au temps t = 2?
• Choices: A) 5 cm/s B) 7 cm/s C) 9 cm/s D) 11 cm/s
• Hint: Velocity = derivative of position. Use power rule: s'(t) = 3t² − 3. Then evaluate at t = 2.
• Steps:
  • Step 1: s(t) = t³ − 5t. s'(t) = 3t² − 5. At t=3: 3(9)−5 = 27−5 = 22 cm/s.
  • Step 2: Find s'(t) using the power rule, then substitute t = 2 to get the velocity!
• Answer: 9 cm/s

[Medium] Permutation — With Restriction

• EN: How many 3-letter arrangements can be made from the letters A, B, C, D if no letter repeats?
• FR: Combien d'arrangements de 3 lettres peut-on faire avec les lettres A, B, C, D si aucune lettre ne se répète?
• Choices: A) 12 B) 18 C) 24 D) 36
• Hint: Permutation P(n,r) = n!/(n−r)!. For example, P(5,3) = 5!/(5−3)! = 5×4×3 = 60.
• Steps:
  • Step 1: P(5,2) = 5×4 = 20.
  • Step 2: Calculate P(4,3) = 4 × 3 × 2 the same way!
• Answer: 24

[Hard] Polynomial Division

• EN: Divide (x³ − 3x² + 4) ÷ (x − 2) using long division. What is the quotient?
• FR: Divise (x³ − 3x² + 4) ÷ (x − 2) par division longue. Quel est le quotient?
• Choices: A) x² − x − 2 B) x² − x + 2 C) x² + x − 2 D) x² − 2x − 1
• Hint: In polynomial long division, divide the leading term, multiply back, subtract, and repeat. For example, (x³ + x² − 4x − 4) ÷ (x+2) = x² − x − 2.
• Steps:
  • Step 1: (x³ − 5x² + 6x) ÷ (x−2). x³÷x = x². x²(x−2)=x³−2x². Subtract: −3x²+6x. −3x²÷x=−3x. −3x(x−2)=−3x²+6x. Subtract: 0. Quotient: x²−3x.
  • Step 2: Start by dividing x³ ÷ x = x², multiply x²(x−2), subtract, and continue the process!
• Answer: x² − x − 2

[Hard] Vector 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) 2 B) 4 C) 6 D) 8
• Hint: Dot product = u₁v₁ + u₂v₂. For example, (2, 3)·(4, −1) = 8 + (−3) = 5.
• Steps:
  • Step 1: (5, −3)·(2, 4) = 5×2 + (−3)×4 = 10 − 12 = −2.
  • Step 2: Multiply matching components (4×3 and −2×5), then add them together!
• Answer: 2

[Hard] Normal Distribution

• EN: In a normal distribution, 68% of data falls within 1 standard deviation of the mean. If the mean is 75 and SD is 10, what range contains 68% of the data?
• FR: Dans une distribution normale, 68 % des données se trouvent à 1 écart-type de la moyenne. Si la moyenne est 75 et l'écart-type est 10, quelle plage contient 68 % des données?
• Choices: A) 55 to 95 B) 60 to 90 C) 65 to 85 D) 70 to 80
• Hint: 68% range = (mean − 1 SD) to (mean + 1 SD). For example, mean=50, SD=8: 50−8=42 to 50+8=58.
• Steps:
  • Step 1: Mean = 100, SD = 15. Range = 100−15 to 100+15 = 85 to 115.
  • Step 2: Subtract 1 SD from the mean for the lower bound, add 1 SD for the upper bound!
• Answer: 65 to 85

[Hard] Derivative Application — Maximum

• EN: A farmer has 40 m of fencing to enclose a rectangular garden along a wall (one side is the wall, needing no fence). What width (x) maximizes area? f(x) = x(40 − 2x). Find the x that gives maximum area.
• FR: Un fermier a 40 m de clôture pour enclore un jardin rectangulaire le long d'un mur (un côté est le mur). Quelle largeur (x) maximise l'aire? f(x) = x(40 − 2x). Trouve la valeur de x qui maximise l'aire.
• Choices: A) x = 5 m B) x = 8 m C) x = 10 m D) x = 15 m
• Hint: Expand f(x), then take f'(x) and set it to 0. For example, f(x) = x(30−2x) = 30x−2x². f'(x)=30−4x=0 → x=7.5.
• Steps:
  • Step 1: f(x) = x(20−2x) = 20x−2x². f'(x)=20−4x=0 → 4x=20 → x=5.
  • Step 2: Expand your function to 40x−2x², take the derivative, set it to 0, and solve for x!
• Answer: x = 10 m