Daily Math — 2026-09-20

[Easy] Counting Apples

• EN: There are 7 apples on the table and 5 more in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres dans un panier. Combien de pommes y a-t-il en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add 6 + 4, count on from 6: seven, eight, nine, ten — that gives 10.
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • So 7 + 5 = 12.
• Answer: 12

[Easy] Snowflakes Falling

• EN: Emma counts 9 snowflakes on her mitten and 3 more fall on it. How many snowflakes are on her mitten now?
• FR: Emma compte 9 flocons de neige sur sa mitaine et 3 autres y tombent. Combien de flocons de neige sont sur sa mitaine maintenant?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add 8 + 2, start at 8 and count on 2 more: nine, ten — that gives 10.
• Steps:
  • Start at 9 and count on 3 more: 10, 11, 12.
  • So 9 + 3 = 12.
• Answer: 12

[Easy] Hockey Sticks

• EN: There are 15 hockey sticks in the arena. 6 are taken away. How many are left?
• FR: Il y a 15 bâtons de hockey dans l'aréna. On en prend 6. Combien en reste-t-il?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: To subtract 14 − 5, count back from 14: thirteen, twelve, eleven, thirteen, twelve, eleven, ten, nine — that gives 9.
• Steps:
  • Start at 15 and count back 6: 14, 13, 12, 11, 10, 9.
  • So 15 − 6 = 9.
• Answer: 9

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes after 12, 14, 16?
• FR: Compte par bonds de 2. Quel nombre vient après 12, 14, 16?
• Choices: A) 17 B) 18 C) 19 D) 20
• Hint: When skip counting by 2s from 6, the next number after 8 is 10.
• Steps:
  • The pattern adds 2 each time: 12, 14, 16, …
  • Add 2 to 16: 16 + 2 = 18.
• Answer: 18

[Medium] Comparing Numbers

• EN: Which number is greater: 43 or 38?
• FR: Quel nombre est plus grand : 43 ou 38?
• Choices: A) 38 B) 40 C) 43 D) 45
• Hint: To compare 52 and 47, look at the tens digit first — 5 tens is more than 4 tens.
• Steps:
  • Look at the tens: 43 has 4 tens, 38 has 3 tens.
  • 4 tens is greater than 3 tens, so 43 is greater.
• Answer: 43

[Medium] Coin Recognition

• EN: Liam has 1 dime and 1 nickel. How many cents does he have in all?
• FR: Liam a 1 pièce de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 10 cents B) 12 cents C) 15 cents D) 20 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents; to find the total for 2 dimes, add 10 + 10 = 20.
• Steps:
  • A dime = 10 cents, a nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[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) 16 B) 18 C) 20 D) 22
• Hint: When skip counting by 5s from 10, add 5 each time: 10, 15, 20, 25.
• Steps:
  • The pattern adds 5 each time: 5, 10, 15, ___, 25.
  • 15 + 5 = 20, so the missing number is 20.
• Answer: 20

[Medium] Adding Three Numbers

• EN: Maya has 4 red blocks, 3 blue blocks, and 6 yellow blocks. How many blocks does she have in all?
• FR: Maya a 4 blocs rouges, 3 blocs bleus et 6 blocs jaunes. Combien de blocs a-t-elle en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To add 3 + 2 + 5, first add 3 + 2 = 5, then add 5 + 5 = 10.
• Steps:
  • First add 4 + 3 = 7.
  • Then add 7 + 6 = 13.
• Answer: 13

[Hard] Subtraction Story

• EN: There are 20 children at a Tim Hortons birthday party. 8 children go home. How many children are still at the party?
• FR: Il y a 20 enfants à une fête d'anniversaire au Tim Hortons. 8 enfants rentrent chez eux. Combien d'enfants sont encore à la fête?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: To solve 20 − 6, start at 20 and count back 6 steps: 19, 18, 17, 16, 15, 14.
• Steps:
  • Start at 20 and count back 8: 19, 18, 17, 16, 15, 14, 13, 12.
  • So 20 − 8 = 12.
• Answer: 12

[Hard] Skip Counting by 10s

• EN: Skip count by 10s. What is the missing number: 10, 20, 30, ___, 50, 60?
• FR: Compte par bonds de 10. Quel est le nombre manquant : 10, 20, 30, ___, 50, 60?
• Choices: A) 35 B) 38 C) 40 D) 45
• Hint: When counting by 10s from 50, the next number is 60 because 50 + 10 = 60.
• Steps:
  • The pattern adds 10 each time: 10, 20, 30, ___, 50, 60.
  • 30 + 10 = 40, so the missing number is 40.
• Answer: 40

[Easy] Adding Two-Digit Numbers

• EN: The school store has 34 pencils and 25 more arrive. How many pencils are there now?
• FR: Le magasin de l'école a 34 crayons et 25 autres arrivent. Combien de crayons y a-t-il maintenant?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: To add 32 + 14, add the tens first: 30 + 10 = 40, then the ones: 2 + 4 = 6, total 46.
• Steps:
  • Add the ones: 4 + 5 = 9.
  • Add the tens: 30 + 20 = 50.
  • 50 + 9 = 59.
• Answer: 59

[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 aiguille 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 and the hour hand points to 3, it is 3:00.
• Steps:
  • The minute hand on 12 means it is exactly on the hour.
  • The hour hand on 7 means the hour is 7.
  • The time is 7:00.
• Answer: 7:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long and a crayon is 9 cm long. How much longer is the pencil?
• FR: Un crayon est long de 14 cm et un crayon de couleur mesure 9 cm. De combien le crayon est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find how much longer 18 cm is than 12 cm, subtract: 18 − 12 = 6.
• Steps:
  • Subtract to find the difference: 14 − 9 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Subtracting Two-Digit Numbers

• EN: A farmer brings 78 carrots to the market. She sells 33. How many are left?
• FR: Une fermière apporte 78 carottes au marché. Elle en vend 33. Combien en reste-t-il?
• Choices: A) 43 B) 44 C) 45 D) 46
• Hint: To subtract 68 − 24, subtract the ones: 8 − 4 = 4, then the tens: 60 − 20 = 40, giving 44.
• Steps:
  • Subtract the ones: 8 − 3 = 5.
  • Subtract the tens: 70 − 30 = 40.
  • 40 + 5 = 45.
• Answer: 45

[Medium] Counting Coins

• EN: Sofia has 2 dimes, 1 nickel, and 2 pennies. How much money does she have?
• FR: Sofia a 2 pièces de 10 cents, 1 pièce de 5 cents et 2 pièces de 1 cent. Combien d'argent a-t-elle?
• Choices: A) 24 cents B) 25 cents C) 26 cents D) 27 cents
• Hint: For 1 dime, 1 nickel, and 1 penny, add 10 + 5 + 1 = 16 cents.
• Steps:
  • 2 dimes = 20 cents; 1 nickel = 5 cents; 2 pennies = 2 cents.
  • 20 + 5 + 2 = 27 cents.
• Answer: 27 cents

[Medium] Telling Time (Half Hour)

• EN: Soccer practice starts at 3:00 and lasts half an hour. What time does it end?
• FR: La pratique de soccer commence à 3h00 et dure une demi-heure. À quelle heure se termine-t-elle?
• Choices: A) 3:15 B) 3:30 C) 3:45 D) 4:00
• Hint: If a movie starts at 5:00 and lasts half an hour, it ends at 5:30.
• Steps:
  • Half an hour = 30 minutes.
  • 3:00 + 30 minutes = 3:30.
• Answer: 3:30

[Medium] Simple Patterns

• EN: What is the next shape in this pattern: circle, square, triangle, circle, square, ___?
• FR: Quelle est la prochaine forme dans ce motif : cercle, carré, triangle, cercle, carré, ___?
• Choices: A) circle B) square C) triangle D) rectangle
• Hint: In the pattern red, blue, green, red, blue, the next colour is green.
• Steps:
  • The pattern repeats every 3: circle, square, triangle.
  • After circle, square comes triangle.
• Answer: triangle

[Medium] Adding Within 100

• EN: Noah scores 46 points in a hockey video game and then scores 37 more. How many points does he have in total?
• FR: Noah marque 46 points dans un jeu vidéo de hockey et en marque 37 autres. Combien de points a-t-il en tout?
• Choices: A) 81 B) 82 C) 83 D) 84
• Hint: To add 54 + 28, add 54 + 20 = 74, then 74 + 8 = 82.
• Steps:
  • Add 46 + 30 = 76.
  • Then add 76 + 7 = 83.
• Answer: 83

[Hard] Money Problem

• EN: A muffin at Tim Hortons costs 75 cents. Aiden pays with a one-dollar coin (100 cents). How much change does he get back?
• FR: Un muffin au Tim Hortons coûte 75 cents. Aiden paye avec une pièce d'un dollar (100 cents). Combien de monnaie reçoit-il?
• Choices: A) 20 cents B) 25 cents C) 30 cents D) 35 cents
• Hint: If a cookie costs 60 cents and you pay with 100 cents, your change is 100 − 60 = 40 cents.
• Steps:
  • Subtract the cost from 100 cents: 100 − 75 = 25.
  • Aiden gets 25 cents back.
• Answer: 25 cents

[Hard] Two-Step Problem

• EN: There are 56 students in the gym. 18 leave to go to class, and then 9 more come in. How many students are in the gym now?
• FR: Il y a 56 élèves dans le gymnase. 18 partent en classe, puis 9 autres arrivent. Combien d'élèves sont dans le gymnase maintenant?
• Choices: A) 45 B) 46 C) 47 D) 48
• Hint: For 60 − 20 + 5, first do 60 − 20 = 40, then 40 + 5 = 45.
• Steps:
  • First subtract: 56 − 18 = 38.
  • Then add: 38 + 9 = 47.
• Answer: 47

[Easy] Multiplication by 2

• EN: There are 6 pairs of mittens on the shelf. How many mittens are there in all?
• FR: Il y a 6 paires de mitaines sur l'étagère. Combien de mitaines y a-t-il en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: 4 pairs of socks means 4 × 2 = 8 socks.
• Steps:
  • Each pair has 2 mittens.
  • 6 × 2 = 12.
• Answer: 12

[Easy] Multiplication by 5

• EN: There are 7 bags of apples at the farmers' market. Each bag has 5 apples. How many apples are there in total?
• FR: Il y a 7 sacs de pommes au marché fermier. Chaque sac contient 5 pommes. Combien de pommes y a-t-il en tout?
• Choices: A) 30 B) 32 C) 35 D) 40
• Hint: 6 bags with 5 apples each: 6 × 5 = 30.
• Steps:
  • Multiply: 7 × 5 = 35.
  • There are 35 apples in total.
• Answer: 35

[Easy] Basic Division

• EN: 18 hockey cards are shared equally among 3 friends. How many cards does each friend get?
• FR: 18 cartes de hockey sont partagées également entre 3 amis. Combien de cartes chaque ami reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: To divide 20 ÷ 4, think: 4 × 5 = 20, so the answer is 5.
• Steps:
  • Think: 3 × ? = 18.
  • 3 × 6 = 18, so each friend gets 6 cards.
• Answer: 6

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal slices. Sam eats 1 slice. What fraction of the pizza did Sam eat?
• FR: Une pizza est coupée en 2 tranches égales. Sam mange 1 tranche. Quelle fraction de la pizza Sam a-t-il mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: If a ribbon is cut into 4 equal parts and you take 1 part, you have 1/4.
• Steps:
  • The pizza is divided into 2 equal parts.
  • Sam ate 1 out of 2 parts, which is 1/2.
• Answer: 1/2

[Medium] Perimeter of a Rectangle

• EN: A rectangular garden has a length of 8 m and a width of 3 m. What is its perimeter?
• FR: Un jardin rectangulaire a une longueur de 8 m et une largeur de 3 m. Quel est son périmètre?
• Choices: A) 20 m B) 22 m C) 24 m D) 26 m
• Hint: For a rectangle with length 5 m and width 2 m, the perimeter is 5 + 2 + 5 + 2 = 14 m.
• Steps:
  • Perimeter = length + width + length + width.
  • 8 + 3 + 8 + 3 = 22 m.
• Answer: 22 m

[Medium] Multiplication by 4

• EN: There are 9 tables in the cafeteria. Each table has 4 chairs. How many chairs are there in all?
• FR: Il y a 9 tables dans la cafétéria. Chaque table a 4 chaises. Combien de chaises y a-t-il en tout?
• Choices: A) 32 B) 34 C) 36 D) 38
• Hint: 8 tables with 4 chairs each: 8 × 4 = 32.
• Steps:
  • Multiply: 9 × 4 = 36.
  • There are 36 chairs in all.
• Answer: 36

[Medium] Reading a Graph

• EN: A bar graph shows 12 students chose hockey, 8 chose soccer, and 5 chose basketball. How many students were surveyed in all?
• FR: Un diagramme à bandes montre que 12 élèves ont choisi le hockey, 8 ont choisi le soccer et 5 ont choisi le basketball. Combien d'élèves ont été sondés en tout?
• Choices: A) 23 B) 24 C) 25 D) 26
• Hint: To find the total for 10 + 7 + 4, add step by step: 10 + 7 = 17, then 17 + 4 = 21.
• Steps:
  • Add all three groups: 12 + 8 = 20.
  • Then 20 + 5 = 25.
• Answer: 25

[Medium] Fractions — One Quarter

• EN: A granola bar is cut into 4 equal pieces. Lily eats 3 pieces. What fraction did she eat?
• FR: Une barre de granola est coupée en 4 morceaux égaux. Lily mange 3 morceaux. Quelle fraction a-t-elle mangée?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) 4/4
• Hint: If a bar is cut into 4 equal parts and you eat 1, you have eaten 1/4.
• Steps:
  • The bar is divided into 4 equal parts.
  • Lily ate 3 out of 4 parts, which is 3/4.
• Answer: 3/4

[Hard] Two-Step Multiplication

• EN: There are 5 boxes of crayons. Each box has 10 crayons. 3 crayons are lost. How many crayons are left?
• FR: Il y a 5 boîtes de crayons de couleur. Chaque boîte contient 10 crayons. 3 crayons sont perdus. Combien de crayons reste-t-il?
• Choices: A) 45 B) 46 C) 47 D) 48
• Hint: If 4 boxes each have 10 items (total 40), and 2 are removed, you have 40 − 2 = 38.
• Steps:
  • Total crayons: 5 × 10 = 50.
  • Subtract lost crayons: 50 − 3 = 47.
• Answer: 47

[Hard] Division with Fractions Context

• EN: A farmer has 24 strawberries to divide equally among 4 baskets. Then he adds 2 more strawberries to each basket. How many strawberries are in each basket?
• FR: Un fermier a 24 fraises à répartir également dans 4 paniers. Il ajoute ensuite 2 fraises dans chaque panier. Combien de fraises y a-t-il dans chaque panier?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: If 20 ÷ 4 = 5 and you add 3 to each group, each group has 5 + 3 = 8.
• Steps:
  • Divide: 24 ÷ 4 = 6 strawberries per basket.
  • Add 2 more: 6 + 2 = 8 strawberries per basket.
• Answer: 8

[Easy] Multiplication Facts

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To find 6 × 8, think of 6 groups of 8: 8, 16, 24, 32, 40, 48.
• Steps:
  • Recall the fact: 7 × 8 = 56.
  • Double-check: 7 × 4 = 28, and 28 × 2 = 56. ✓
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 4 tens
• Hint: In the number 5.28, the digit 2 is in the tenths place, so it is worth 2 tenths.
• Steps:
  • In 3.47, the digits after the decimal are in the tenths and hundredths places.
  • The digit 4 is the first digit after the decimal point, so it is in the tenths place.
• Answer: 4 tenths

[Easy] Long Division

• EN: Divide 36 ÷ 4. What is the answer?
• FR: Divise 36 ÷ 4. Quelle est la réponse?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: To solve 28 ÷ 4, think: 4 × 7 = 28, so the answer is 7.
• Steps:
  • Think: 4 × ? = 36.
  • 4 × 9 = 36, so 36 ÷ 4 = 9.
• Answer: 9

[Easy] Area of a Rectangle

• EN: A rectangular bedroom is 6 m long and 4 m wide. What is its area?
• FR: Une chambre rectangulaire est longue de 6 m et large de 4 m. Quelle est son aire?
• Choices: A) 20 m² B) 22 m² C) 24 m² D) 26 m²
• Hint: The area of a rectangle with length 5 m and width 3 m is 5 × 3 = 15 m².
• Steps:
  • Area = length × width.
  • Area = 6 × 4 = 24 m².
• Answer: 24 m²

[Medium] Long Division with Remainder

• EN: 47 stickers are shared equally among 5 students. How many stickers does each student get, and how many are left over?
• FR: 47 autocollants sont partagés également entre 5 élèves. Combien d'autocollants chaque élève reçoit-il, et combien en reste-t-il?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 9 remainder 3 D) 10 remainder 1
• Hint: To divide 23 ÷ 4, think: 4 × 5 = 20, remainder 23 − 20 = 3, so the answer is 5 remainder 3.
• Steps:
  • 5 × 9 = 45, which is less than 47.
  • 47 − 45 = 2 left over, so the answer is 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/3?
• FR: Quelle fraction est plus grande : 3/4 ou 2/3?
• Choices: A) 2/3 B) 3/4 C) They are equal D) 1/2
• Hint: To compare 1/2 and 1/3, convert to the same denominator: 3/6 vs 2/6, so 1/2 is greater.
• Steps:
  • Find a common denominator for 4 and 3: the LCD is 12.
  • 3/4 = 9/12 and 2/3 = 8/12.
  • Since 9/12 > 8/12, the fraction 3/4 is greater.
• Answer: 3/4

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 p.m. and ends at 3:45 p.m. How long is the game?
• FR: Un match de hockey commence à 13h15 et se termine à 15h45. Quelle est la durée du match?
• Choices: A) 2 hours B) 2 hours 15 minutes C) 2 hours 30 minutes D) 2 hours 45 minutes
• Hint: To find the time from 2:10 to 4:40, count: 2:10 to 4:10 is 2 hours, then add 30 more minutes = 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 is 2 hours.
  • From 3:15 to 3:45 is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A bottle of maple syrup costs $3.75 and a jar of honey costs $2.40. What is the total cost?
• FR: Une bouteille de sirop d'érable coûte 3,75 $ et un pot de miel coûte 2,40 $. Quel est le coût total?
• Choices: A) $5.95 B) $6.05 C) $6.15 D) $6.25
• Hint: To add $4.50 and $3.25, add dollars first: 4 + 3 = 7, then cents: 50 + 25 = 75, total $7.75.
• Steps:
  • Add the dollars: $3 + $2 = $5.
  • Add the cents: $0.75 + $0.40 = $1.15.
  • Total: $5 + $1.15 = $6.15.
• Answer: $6.15

[Hard] Multi-Step Problem

• EN: A classroom has 6 rows of desks with 7 desks in each row. The teacher removes 8 desks for a project. How many desks remain?
• FR: Une salle de classe a 6 rangées de pupitres avec 7 pupitres dans chaque rangée. La professeure enlève 8 pupitres pour un projet. Combien de pupitres reste-t-il?
• Choices: A) 32 B) 34 C) 36 D) 38
• Hint: For 5 rows of 6 desks (5 × 6 = 30), if 4 are removed, 30 − 4 = 26 remain.
• Steps:
  • Total desks: 6 × 7 = 42.
  • Subtract removed desks: 42 − 8 = 34.
• Answer: 34

[Hard] Decimal Comparison and Operations

• EN: Isabelle runs 1.75 km on Monday and 2.48 km on Wednesday. How many kilometres did she run in total?
• FR: Isabelle court 1,75 km le lundi et 2,48 km le mercredi. Combien de kilomètres a-t-elle couru en tout?
• Choices: A) 4.13 km B) 4.23 km C) 4.33 km D) 4.43 km
• Hint: To add 2.36 + 1.57, add hundredths: 6 + 7 = 13 (write 3, carry 1), tenths: 3 + 5 + 1 = 9, ones: 2 + 1 = 3, giving 3.93.
• Steps:
  • Add hundredths: 5 + 8 = 13; write 3, carry 1.
  • Add tenths: 7 + 4 + 1 = 12; write 2, carry 1.
  • Add ones: 1 + 2 + 1 = 4.
  • Total: 4.23 km.
• Answer: 4.23 km

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 194 B) 200 C) 204 D) 210
• Hint: To multiply 21 × 4, do (20 × 4) + (1 × 4) = 80 + 4 = 84.
• Steps:
  • Multiply: 30 × 6 = 180.
  • Then: 4 × 6 = 24.
  • Total: 180 + 24 = 204.
• Answer: 204

[Easy] Adding Fractions (Like Denominators)

• EN: What is 2/7 + 3/7?
• FR: Combien font 2/7 + 3/7?
• Choices: A) 4/7 B) 5/7 C) 5/14 D) 6/7
• Hint: To add 1/5 + 2/5, add only the numerators: 1 + 2 = 3, keeping the denominator: 3/5.
• Steps:
  • The denominators are the same (7), so add the numerators: 2 + 3 = 5.
  • The answer is 5/7.
• Answer: 5/7

[Easy] Percentage — 50%

• EN: There are 80 students in the gym. 50% of them are wearing red. How many students are wearing red?
• FR: Il y a 80 élèves dans le gymnase. 50 % d'entre eux portent du rouge. Combien d'élèves portent du rouge?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: 50% of any number means half: 50% of 60 = 60 ÷ 2 = 30.
• Steps:
  • 50% means one half.
  • 80 ÷ 2 = 40.
• Answer: 40

[Easy] Decimal Subtraction

• EN: A loonie is worth $1.00. If you spend $0.65 on a treat, how much money do you have left?
• FR: Un huard vaut 1,00 $. Si tu dépenses 0,65 $ pour une gâterie, combien d'argent te reste-t-il?
• Choices: A) $0.25 B) $0.30 C) $0.35 D) $0.40
• Hint: To solve $1.00 − $0.55, think of it as 100 cents − 55 cents = 45 cents.
• Steps:
  • $1.00 − $0.65 = $0.35.
  • You have $0.35 left.
• Answer: $0.35

[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 est longue de 5 cm, large de 4 cm et haute de 3 cm. Quel est son volume?
• Choices: A) 48 cm³ B) 56 cm³ C) 60 cm³ D) 64 cm³
• Hint: Volume of a rectangular prism with length 4, width 2, and height 3 is 4 × 2 × 3 = 24 cm³.
• Steps:
  • Volume = length × width × height.
  • Volume = 5 × 4 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions (Like Denominators)

• EN: A recipe needs 7/8 cup of flour. You have already added 3/8 cup. How much more flour is needed?
• FR: Une recette nécessite 7/8 de tasse de farine. Tu en as déjà ajouté 3/8. Combien de farine faut-il ajouter?
• Choices: A) 3/8 B) 4/8 C) 5/8 D) 6/8
• Hint: To subtract 5/9 − 2/9, subtract the numerators: 5 − 2 = 3, keeping the denominator: 3/9.
• Steps:
  • Denominators are the same (8), so subtract numerators: 7 − 3 = 4.
  • The answer is 4/8.
• Answer: 4/8

[Medium] Percentage — 25%

• EN: A store has 120 winter coats. 25% are blue. How many blue coats are there?
• FR: Un magasin a 120 manteaux d'hiver. 25 % sont bleus. Combien de manteaux bleus y a-t-il?
• Choices: A) 25 B) 28 C) 30 D) 32
• Hint: 25% of a number means one quarter: 25% of 80 = 80 ÷ 4 = 20.
• Steps:
  • 25% = 1/4.
  • 120 ÷ 4 = 30.
• Answer: 30

[Medium] Multi-Digit Division

• EN: 336 students are divided equally into 8 classes. How many students are in each class?
• FR: 336 élèves sont répartis également dans 8 classes. Combien d'élèves y a-t-il dans chaque classe?
• Choices: A) 40 B) 41 C) 42 D) 43
• Hint: To divide 240 ÷ 6, think: 6 × 40 = 240, so the answer is 40.
• Steps:
  • 8 × 40 = 320; 336 − 320 = 16.
  • 16 ÷ 8 = 2; so 40 + 2 = 42.
• Answer: 42

[Hard] Multi-Step Fraction and Decimal Problem

• EN: Chloe has $5.00. She spends $1.75 on a juice box and $2.50 on a granola bar at the school cafe. How much money does she have left?
• FR: Chloé a 5,00 $. Elle dépense 1,75 $ pour une boîte de jus et 2,50 $ pour une barre de granola à la cafétéria. Combien d'argent lui reste-t-il?
• Choices: A) $0.55 B) $0.65 C) $0.75 D) $0.85
• Hint: For $6.00 − $1.50 − $2.75, first subtract: $6.00 − $1.50 = $4.50, then $4.50 − $2.75 = $1.75.
• Steps:
  • Total spent: $1.75 + $2.50 = $4.25.
  • Money left: $5.00 − $4.25 = $0.75.
• Answer: $0.75

[Hard] Percentage — 10% and Multiple Steps

• EN: A hockey jersey originally costs $90. The store takes off 10%, and then takes off an additional $5. What is the final price?
• FR: Un chandail de hockey coûte 90 $ à l'origine. Le magasin enlève 10 %, puis enlève encore 5 $. Quel est le prix final?
• Choices: A) $74 B) $76 C) $78 D) $80
• Hint: 10% of $60 = $6.00, so if you also subtract $4 more, the final price is $60 − $6 − $4 = $50.
• Steps:
  • 10% of $90 = $90 ÷ 10 = $9.
  • Subtract 10%: $90 − $9 = $81.
  • Subtract additional $5: $81 − $5 = $76.
• Answer: $76

[Easy] Percent of a Number

• EN: What is 20% of 150?
• FR: Combien font 20 % de 150?
• Choices: A) 20 B) 25 C) 30 D) 35
• Hint: To find 20% of 200, calculate 10% first (200 ÷ 10 = 20), then double it: 20 × 2 = 40.
• Steps:
  • 10% of 150 = 15.
  • 20% = 2 × 15 = 30.
• Answer: 30

[Easy] Order of Operations (BEDMAS)

• EN: Calculate: 3 + 4 × 2.
• FR: Calcule : 3 + 4 × 2.
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: In 5 + 3 × 4, do the multiplication first: 3 × 4 = 12, then add 5: 5 + 12 = 17.
• Steps:
  • Multiplication comes before addition (BEDMAS).
  • 4 × 2 = 8, then 3 + 8 = 11.
• Answer: 11

[Easy] Ratios

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

[Easy] Integers — Introduction

• EN: The temperature in Winnipeg is −5°C. It rises by 8°C. What is the new temperature?
• FR: La température à Winnipeg est de −5°C. Elle monte de 8°C. Quelle est la nouvelle température?
• Choices: A) 1°C B) 2°C C) 3°C D) 4°C
• Hint: For −3 + 6, start at −3 on a number line and move 6 places to the right: you land on 3.
• Steps:
  • Start at −5 and add 8: −5 + 8 = 3.
  • The new temperature is 3°C.
• Answer: 3°C

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 6/12 C) 7/12 D) 8/12
• Hint: To multiply 1/2 × 2/5, multiply numerators (1 × 2 = 2) and denominators (2 × 5 = 10), giving 2/10 = 1/5.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • Result: 6/12, which can also be written as 1/2.
• Answer: 6/12

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in km per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km par heure?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 85 km/h
• Hint: If a bicycle travels 60 km in 2 hours, the rate is 60 ÷ 2 = 30 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 240 ÷ 3 = 80 km/h.
• Answer: 80 km/h

[Medium] Algebraic Expressions

• EN: Evaluate the expression 4n + 7 when n = 5.
• FR: Évalue l'expression 4n + 7 quand n = 5.
• Choices: A) 25 B) 27 C) 29 D) 31
• Hint: To evaluate 3x + 2 when x = 4, substitute: 3 × 4 + 2 = 12 + 2 = 14.
• Steps:
  • Substitute n = 5: 4(5) + 7.
  • 4 × 5 = 20; 20 + 7 = 27.
• Answer: 27

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 5/4
• Hint: To divide 2/3 ÷ 1/4, multiply by the reciprocal: 2/3 × 4/1 = 8/3.
• Steps:
  • Dividing by 1/2 is the same as multiplying by 2/1.
  • 3/4 × 2/1 = 6/4 = 3/2.
• Answer: 3/2

[Hard] Multi-Step BEDMAS

• EN: Calculate: (18 ÷ 3) + 4² − 5.
• FR: Calcule : (18 ÷ 3) + 4² − 5.
• Choices: A) 15 B) 17 C) 19 D) 21
• Hint: For (12 ÷ 4) + 2² − 1, solve brackets first (3), then exponent (4), then add and subtract: 3 + 4 − 1 = 6.
• Steps:
  • Brackets: 18 ÷ 3 = 6.
  • Exponent: 4² = 16.
  • 6 + 16 − 5 = 17.
• Answer: 17

[Hard] Percent and Ratio Combined

• EN: In a class of 30 students, the ratio of boys to girls is 2:3. What percentage of the students are boys?
• FR: Dans une classe de 30 élèves, le rapport garçons/filles est de 2:3. Quel pourcentage des élèves sont des garçons?
• Choices: A) 30% B) 35% C) 40% D) 45%
• Hint: In a group of 20 where the ratio of A to B is 1:3, there are 5 in group A, and 5/20 = 25%.
• Steps:
  • Total ratio parts: 2 + 3 = 5 parts.
  • Boys = (2/5) × 30 = 12 boys.
  • Percentage: 12/30 × 100 = 40%.
• Answer: 40%

[Easy] Integer Addition

• EN: What is (−9) + 4?
• FR: Combien font (−9) + 4?
• Choices: A) −7 B) −6 C) −5 D) −4
• Hint: For (−7) + 3, start at −7 on a number line and move 3 steps right to land on −4.
• Steps:
  • Start at −9 and move 4 steps to the right.
  • −9 + 4 = −5.
• Answer: −5

[Easy] Percentage — Discount

• EN: A book originally costs $20. It is on sale for 15% off. How much is the discount?
• FR: Un livre coûte 20 $ à l'origine. Il est en solde avec 15 % de rabais. Quel est le montant du rabais?
• Choices: A) $2.00 B) $2.50 C) $3.00 D) $3.50
• Hint: To find 10% of $40, divide by 10: $40 ÷ 10 = $4. Then 5% is half of that: $2.
• Steps:
  • 10% of $20 = $2.00.
  • 5% of $20 = $1.00.
  • 15% = $2.00 + $1.00 = $3.00.
• Answer: $3.00

[Easy] Integer Subtraction

• EN: What is 3 − (−7)?
• FR: Combien font 3 − (−7)?
• Choices: A) −4 B) 4 C) 8 D) 10
• Hint: Subtracting a negative is the same as adding: 5 − (−2) = 5 + 2 = 7.
• Steps:
  • Subtracting a negative means adding a positive.
  • 3 − (−7) = 3 + 7 = 10.
• Answer: 10

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x : x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: To solve x + 5 = 12, subtract 5 from both sides: x = 12 − 5 = 7.
• Steps:
  • Subtract 9 from both sides: x = 17 − 9.
  • x = 8.
• Answer: x = 8

[Medium] Integer Multiplication

• EN: What is (−6) × (−7)?
• FR: Combien font (−6) × (−7)?
• Choices: A) −42 B) −13 C) 13 D) 42
• Hint: When multiplying two negative numbers, the result is always positive: (−3) × (−4) = 12.
• Steps:
  • A negative times a negative = positive.
  • 6 × 7 = 42, so (−6) × (−7) = 42.
• Answer: 42

[Medium] Percentage — Tax

• EN: A hockey stick costs $85. Ontario sales tax (HST) is 13%. How much tax is added to the price?
• FR: Un bâton de hockey coûte 85 $. La taxe de vente (TVH) en Ontario est de 13 %. Combien de taxe est ajoutée au prix?
• Choices: A) $10.05 B) $11.05 C) $12.05 D) $13.05
• Hint: To find 13% of $100: 10% = $10, 3% = $3, total = $13.
• Steps:
  • 10% of $85 = $8.50.
  • 3% of $85 = $2.55.
  • Tax = $8.50 + $2.55 = $11.05.
• Answer: $11.05

[Medium] Surface Area

• EN: What is the surface area of a rectangular box that is 5 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire totale d'une boîte rectangulaire qui est longue de 5 cm, large de 3 cm et haute de 2 cm?
• Choices: A) 58 cm² B) 60 cm² C) 62 cm² D) 64 cm²
• Hint: For a box with length 4, width 2, height 1: SA = 2(4×2) + 2(4×1) + 2(2×1) = 16+8+4 = 28 cm².
• Steps:
  • SA = 2(lw) + 2(lh) + 2(wh).
  • SA = 2(5×3) + 2(5×2) + 2(3×2).
  • SA = 2(15) + 2(10) + 2(6) = 30 + 20 + 12 = 62 cm².
• Answer: 62 cm²

[Medium] Probability

• EN: A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of picking a red marble?
• FR: Un sac contient 3 billes rouges, 5 billes bleues et 2 billes vertes. Quelle est la probabilité de piger une bille rouge?
• Choices: A) 1/5 B) 3/10 C) 2/5 D) 1/2
• Hint: If there are 4 red and 6 total, the probability of red is 4/6 = 2/3.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • P(red) = 3/10.
• Answer: 3/10

[Hard] Integer Division — Multi-Step

• EN: The temperature in Iqaluit drops 4°C every hour for 6 hours. If the starting temperature was 5°C, what is the temperature after 6 hours?
• FR: La température à Iqaluit descend de 4°C chaque heure pendant 6 heures. Si la température de départ était de 5°C, quelle est la température après 6 heures?
• Choices: A) −17°C B) −18°C C) −19°C D) −20°C
• Hint: If the temperature starts at 3°C and drops 5°C for each of 3 hours: 3 + (−5 × 3) = 3 − 15 = −12°C.
• Steps:
  • Total temperature drop: 4 × 6 = 24°C.
  • New temperature: 5 − 24 = −19°C.
• Answer: −19°C

[Hard] Two-Step Equation and Discount

• EN: A store applies a 20% discount to a $75 jacket and then adds 5% tax on the sale price. What is the final price?
• FR: Un magasin applique un rabais de 20 % sur un manteau de 75 $ puis ajoute une taxe de 5 % sur le prix de vente. Quel est le prix final?
• Choices: A) $61.20 B) $62.20 C) $63.00 D) $64.20
• Hint: For a $100 item with 10% off and 5% tax: sale price = $90, tax = $4.50, final = $94.50.
• Steps:
  • 20% of $75 = $15; sale price = $75 − $15 = $60.
  • 5% tax on $60 = $3.00.
  • Final price: $60 + $3.00 = $63.00.
• Answer: $63.00

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To find √81, think: what number times itself equals 81? Since 9 × 9 = 81, √81 = 9.
• Steps:
  • Think: what number squared gives 144?
  • 12 × 12 = 144, so √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of these quiz scores: 70, 80, 90, 60.
• FR: Trouve la moyenne de ces résultats de quiz : 70, 80, 90, 60.
• Choices: A) 73 B) 74 C) 75 D) 76
• Hint: To find the mean of 10, 20, 30, add them (60) and divide by the number of values (3): 60 ÷ 3 = 20.
• Steps:
  • Sum: 70 + 80 + 90 + 60 = 300.
  • Divide by 4: 300 ÷ 4 = 75.
• Answer: 75

[Easy] Two-Step Equation

• EN: Solve: 2x + 5 = 13.
• FR: Résous : 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: To solve 3x + 2 = 11, subtract 2 first: 3x = 9, then divide by 3: x = 3.
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A snowfall of 10 cm increased to 15 cm overnight. What is the percent increase?
• FR: Une chute de neige de 10 cm est passée à 15 cm pendant la nuit. Quel est le pourcentage d'augmentation?
• Choices: A) 40% B) 45% C) 50% D) 55%
• Hint: Percent increase = (change ÷ original) × 100. If a price goes from $8 to $10, change = $2, so (2/8) × 100 = 25%.
• Steps:
  • Change = 15 − 10 = 5.
  • Percent increase = (5 ÷ 10) × 100 = 50%.
• Answer: 50%

[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) 9 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: For a right triangle with legs 3 and 4, use a² + b² = c²: 9 + 16 = 25, so c = 5.
• Steps:
  • Use a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through the points (2, 4) and (6, 12). What is the slope of the line?
• FR: Une droite passe par les points (2, 4) et (6, 12). Quelle est la pente de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁). For (1, 2) and (3, 6): slope = (6 − 2) ÷ (3 − 1) = 4 ÷ 2 = 2.
• Steps:
  • Slope = (y₂ − y₁) ÷ (x₂ − x₁).
  • Slope = (12 − 4) ÷ (6 − 2) = 8 ÷ 4 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of this data set: 3, 7, 2, 9, 5.
• FR: Trouve la médiane de cet ensemble de données : 3, 7, 2, 9, 5.
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: To find the median of 4, 8, 1, 6, 2: order them first: 1, 2, 4, 6, 8, and the middle value is 4.
• Steps:
  • Order the data: 2, 3, 5, 7, 9.
  • The middle value (3rd of 5) is 5.
• Answer: 5

[Medium] Two-Step Equation (Harder)

• EN: Solve: 3x − 7 = 14.
• FR: Résous : 3x − 7 = 14.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: To solve 4x − 3 = 13, add 3 to both sides: 4x = 16, then divide by 4: x = 4.
• Steps:
  • Add 7 to both sides: 3x = 21.
  • Divide by 3: x = 7.
• Answer: x = 7

[Hard] Pythagorean Theorem — Application

• EN: A ladder 13 m long leans against a wall. Its base is 5 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 13 m est appuyée contre un mur. Sa base est à 5 m du mur. À quelle hauteur sur le mur l'échelle atteint-elle?
• Choices: A) 10 m B) 11 m C) 12 m D) 14 m
• Hint: For a ladder with hypotenuse 10 and base 6, the height is √(10² − 6²) = √(100 − 36) = √64 = 8.
• Steps:
  • Use a² + b² = c²: a² + 5² = 13².
  • a² = 169 − 25 = 144.
  • a = √144 = 12 m.
• Answer: 12 m

[Hard] Percent Decrease and Multi-Step

• EN: A used car was originally priced at $8,000. The price decreased by 15%, and then the dealer added $200 for delivery. What is the final price?
• FR: Une voiture d'occasion était cotée à 8 000 $. Le prix a diminué de 15 %, puis le concessionnaire a ajouté 200 $ pour la livraison. Quel est le prix final?
• Choices: A) $6,800 B) $7,000 C) $7,200 D) $7,400
• Hint: For $5,000 with 10% off plus $100 delivery: $5,000 − $500 + $100 = $4,600.
• Steps:
  • 15% of $8,000 = $1,200.
  • Sale price: $8,000 − $1,200 = $6,800.
  • Final price: $6,800 + $200 = $7,000.
• Answer: $7,000

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 3 = 22.
• FR: Résous pour x : 5x − 3 = 22.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: To solve 4x − 2 = 18, add 2 to both sides (4x = 20), then divide by 4: x = 5.
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 5.
• Answer: x = 5

[Easy] Graphing Lines — Slope-Intercept

• EN: A line has the equation y = 3x + 2. What is its y-intercept?
• FR: Une droite a l'équation y = 3x + 2. Quel est son ordonnée à l'origine?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: In the equation y = mx + b, the y-intercept is b. For y = 5x + 7, the y-intercept is 7.
• Steps:
  • The equation is in y = mx + b form.
  • Here b = 2, so the y-intercept is 2.
• Answer: 2

[Easy] Adding Polynomials

• EN: Add: (3x + 5) + (2x − 1).
• FR: Additionne : (3x + 5) + (2x − 1).
• Choices: A) 4x + 3 B) 5x + 4 C) 5x + 6 D) 6x + 4
• Hint: To add (4x + 3) + (x − 2), combine like terms: 4x + x = 5x and 3 + (−2) = 1, giving 5x + 1.
• Steps:
  • Combine the x terms: 3x + 2x = 5x.
  • Combine the constants: 5 + (−1) = 4.
  • Result: 5x + 4.
• Answer: 5x + 4

[Easy] Linear Inequality

• EN: Solve the inequality: x + 4 > 10.
• FR: Résous l'inégalité : x + 4 > 10.
• Choices: A) x > 4 B) x > 5 C) x > 6 D) x > 7
• Hint: To solve x + 3 > 8, subtract 3 from both sides: x > 5.
• Steps:
  • Subtract 4 from both sides: x > 10 − 4.
  • x > 6.
• Answer: x > 6

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5).
• FR: Développe : (x + 3)(x + 5).
• Choices: A) x² + 7x + 12 B) x² + 8x + 15 C) x² + 8x + 12 D) x² + 7x + 15
• Hint: To expand (x + 2)(x + 4), use FOIL: x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • FOIL: First: x × x = x².
  • Outer: x × 5 = 5x; Inner: 3 × x = 3x; Last: 3 × 5 = 15.
  • Combine: x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Two similar triangles have sides in ratio 3:5. The smaller triangle has a base of 9 cm. What is the base of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans le rapport 3:5. Le petit triangle a une base de 9 cm. Quelle est la base du grand triangle?
• Choices: A) 13 cm B) 14 cm C) 15 cm D) 16 cm
• Hint: If two triangles have ratio 2:6 and the small side is 8, the large side is 8 × (6 ÷ 2) = 24.
• Steps:
  • Set up proportion: 3/5 = 9/x.
  • Cross multiply: 3x = 45.
  • x = 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the angle is 30°, and the hypotenuse is 10 cm. What is the length of the side opposite the 30° angle?
• FR: Dans un triangle rectangle, l'angle est de 30° et l'hypoténuse est de 10 cm. Quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: SOH means sin(angle) = opposite/hypotenuse. For sin(45°) = opposite/8, opposite = 8 × sin(45°) ≈ 5.66.
• Steps:
  • sin(30°) = opposite/hypotenuse.
  • opposite = 10 × sin(30°) = 10 × 0.5 = 5 cm.
• Answer: 5 cm

[Medium] Statistics — Mean from Grouped Data

• EN: Five students scored 72, 85, 91, 68, and 84 on a math test. What is the mean score?
• FR: Cinq élèves ont obtenu 72, 85, 91, 68 et 84 à un test de maths. Quel est le score moyen?
• Choices: A) 78 B) 80 C) 82 D) 84
• Hint: To find the mean of 60, 70, 80, 90: add them (300) and divide by 4 values: 300 ÷ 4 = 75.
• Steps:
  • Sum: 72 + 85 + 91 + 68 + 84 = 400.
  • Mean = 400 ÷ 5 = 80.
• Answer: 80

[Hard] Linear Equation — Application

• EN: A school rents skates for $3 per pair plus a one-time fee of $15. If the total cost is $57, how many pairs of skates were rented?
• FR: Une école loue des patins à 3 $ la paire plus des frais uniques de 15 $. Si le coût total est de 57 $, combien de paires de patins ont été louées?
• Choices: A) 12 B) 13 C) 14 D) 15
• Hint: For 4x + 10 = 50, subtract 10 first (4x = 40), then divide by 4: x = 10.
• Steps:
  • Set up equation: 3x + 15 = 57.
  • Subtract 15: 3x = 42.
  • Divide by 3: x = 14 pairs.
• Answer: 14

[Hard] Trigonometry — CAH Application

• EN: A ramp rises at an angle of 40°. The horizontal distance (adjacent) is 12 m. What is the length of the ramp (hypotenuse)? (Use cos 40° ≈ 0.766)
• FR: Une rampe monte à un angle de 40°. La distance horizontale (côté adjacent) est de 12 m. Quelle est la longueur de la rampe (hypoténuse)? (Utilise cos 40° ≈ 0,766)
• Choices: A) 15.0 m B) 15.7 m C) 16.2 m D) 16.8 m
• Hint: CAH means cos(angle) = adjacent/hypotenuse, so hypotenuse = adjacent ÷ cos(angle). For cos(30°) ≈ 0.866 and adjacent = 8.66 m, hypotenuse = 8.66 ÷ 0.866 = 10 m.
• Steps:
  • cos(40°) = adjacent/hypotenuse.
  • hypotenuse = 12 ÷ 0.766.
  • hypotenuse ≈ 15.7 m.
• Answer: 15.7 m

[Easy] Factoring a Quadratic

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

[Easy] Trigonometry — Tangent

• EN: In a right triangle, the side opposite a 45° angle is 7 cm and the adjacent side is 7 cm. What is tan(45°)?
• FR: Dans un triangle rectangle, le côté opposé à un angle de 45° est de 7 cm et le côté adjacent est de 7 cm. Combien vaut tan(45°)?
• Choices: A) 0 B) 0.5 C) 1 D) 2
• Hint: tan(angle) = opposite ÷ adjacent. For a triangle where opposite = 3 and adjacent = 3, tan = 3/3 = 1.
• Steps:
  • tan(45°) = opposite/adjacent = 7/7 = 1.
• Answer: 1

[Easy] Systems of Equations — Substitution

• EN: If y = 2x and x + y = 9, what is x?
• FR: Si y = 2x et x + y = 9, combien vaut x?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: If y = 3x and x + y = 8, substitute: x + 3x = 8, so 4x = 8 and x = 2.
• Steps:
  • Substitute y = 2x into x + y = 9: x + 2x = 9.
  • 3x = 9, so x = 3.
• Answer: 3

[Easy] Volume of a Cylinder

• EN: A cylindrical water bottle has a radius of 4 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une bouteille d'eau cylindrique a un rayon de 4 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 452.16 cm³ B) 490.00 cm³ C) 502.40 cm³ D) 520.00 cm³
• Hint: Volume of a cylinder = π × r² × h. For r = 3 and h = 5: V = 3.14 × 9 × 5 = 141.3 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 4² × 10.
  • V = 3.14 × 16 × 10 = 502.40 cm³.
• Answer: 502.40 cm³

[Medium] Solving a Quadratic by Factoring

• EN: Solve for x: x² − 5x + 6 = 0.
• FR: Résous pour x : x² − 5x + 6 = 0.
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = 3 and x = 4 D) x = −2 and x = −3
• Hint: To solve x² − 7x + 12 = 0, factor it: (x − 3)(x − 4) = 0, giving x = 3 or x = 4.
• Steps:
  • Factor: x² − 5x + 6 = (x − 2)(x − 3).
  • Set each factor to zero: x − 2 = 0 → x = 2; x − 3 = 0 → x = 3.
• Answer: x = 2 and x = 3

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 40.82 cm B) 43.96 cm C) 45.22 cm D) 47.00 cm
• Hint: Circumference = π × d. For a circle with diameter 10: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14.
  • C = 43.96 cm.
• Answer: 43.96 cm

[Medium] Systems of Equations — Elimination

• EN: Solve the system: 2x + y = 11 and x − y = 1. What is x?
• FR: Résous le système : 2x + y = 11 et x − y = 1. Combien vaut x?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: To eliminate y from 3x + y = 10 and x − y = 2, add the equations: 4x = 12, so x = 3.
• Steps:
  • Add the equations: (2x + y) + (x − y) = 11 + 1.
  • 3x = 12, so x = 4.
• Answer: 4

[Medium] Completing the Square

• EN: Complete the square to rewrite x² + 6x + 5 in the form (x + a)² + b. What are the values of a and b?
• FR: Complète le carré pour réécrire x² + 6x + 5 sous la forme (x + a)² + b. Quelles sont les valeurs de a et b?
• Choices: A) a = 2, b = 1 B) a = 3, b = −4 C) a = 4, b = −3 D) a = 6, b = 5
• Hint: For x² + 4x + 1, take half of 4 (=2), square it (=4): x² + 4x + 4 − 3 = (x + 2)² − 3.
• Steps:
  • Take half of 6: 3; square it: 9.
  • x² + 6x + 5 = (x² + 6x + 9) − 9 + 5 = (x + 3)² − 4.
  • So a = 3 and b = −4.
• Answer: a = 3, b = −4

[Hard] Quadratic — Word Problem

• EN: A ball is launched upward. Its height (in metres) at time t seconds is given by h = −5t² + 20t + 1. After how many seconds does the ball reach a height of 21 m?
• FR: Un ballon est lancé vers le haut. Sa hauteur (en mètres) au temps t secondes est donnée par h = −5t² + 20t + 1. Au bout de combien de secondes le ballon atteint-il une hauteur de 21 m?
• Choices: A) t = 1 s and t = 3 s B) t = 2 s and t = 4 s C) t = 1 s and t = 4 s D) t = 2 s and t = 3 s
• Hint: To find when h = 16 for h = −4t² + 16t: set −4t² + 16t = 16, rearrange, and factor.
• Steps:
  • Set h = 21: −5t² + 20t + 1 = 21.
  • Rearrange: −5t² + 20t − 20 = 0 → 5t² − 20t + 20 = 0 → t² − 4t + 4 = 0.
  • Factor: (t − 2)² = 0, so t = 2 s (a repeated root, meaning the ball reaches 21 m at exactly t = 2 s).
• Answer: t = 2 s and t = 3 s

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the side opposite an unknown angle is 9 cm and the hypotenuse is 15 cm. What is the angle? (Use sin⁻¹(0.6) = 36.87°)
• FR: Dans un triangle rectangle, le côté opposé à un angle inconnu est de 9 cm et l'hypoténuse est de 15 cm. Quel est cet angle? (Utilise sin⁻¹(0,6) = 36,87°)
• Choices: A) 30.00° B) 33.75° C) 36.87° D) 39.50°
• Hint: sin(angle) = opposite/hypotenuse. Find the angle by taking sin⁻¹ of the ratio. For opposite = 4 and hyp = 8, sin = 0.5, so angle = 30°.
• Steps:
  • sin(angle) = 9/15 = 0.6.
  • angle = sin⁻¹(0.6) = 36.87°.
• Answer: 36.87°

[Easy] Exponential Function

• EN: Evaluate f(x) = 3^x when x = 4.
• FR: Évalue f(x) = 3^x quand x = 4.
• Choices: A) 27 B) 64 C) 81 D) 243
• Hint: To evaluate 2^x when x = 5: 2 × 2 × 2 × 2 × 2 = 32.
• Steps:
  • 3^4 = 3 × 3 × 3 × 3.
  • = 9 × 9 = 81.
• Answer: 81

[Easy] Logarithm — Introduction

• EN: Evaluate log₂(32).
• FR: Évalue log₂(32).
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: log₂(8) asks "2 to what power gives 8?" Since 2³ = 8, log₂(8) = 3.
• Steps:
  • Ask: 2 to what power gives 32?
  • 2^5 = 32, so log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequence

• EN: Find the 8th term of the arithmetic sequence: 4, 9, 14, 19, …
• FR: Trouve le 8e terme de la suite arithmétique : 4, 9, 14, 19, …
• Choices: A) 37 B) 38 C) 39 D) 40
• Hint: The nth term of an arithmetic sequence is a + (n − 1)d. For 3, 6, 9, …, the 5th term is 3 + (5 − 1) × 3 = 3 + 12 = 15.
• Steps:
  • First term a = 4, common difference d = 5.
  • 8th term = 4 + (8 − 1) × 5 = 4 + 35 = 39.
• Answer: 39

[Easy] Compound Interest

• EN: You invest $1,000 at 4% annual compound interest for 2 years. What is the total amount after 2 years?
• FR: Tu investis 1 000 $ à un taux d'intérêt annuel composé de 4 % pendant 2 ans. Quel est le montant total après 2 ans?
• Choices: A) $1,080.00 B) $1,081.00 C) $1,081.60 D) $1,082.00
• Hint: For $500 at 5% for 2 years: A = 500 × (1.05)² = 500 × 1.1025 = $551.25.
• Steps:
  • A = P(1 + r)^n = 1000(1.04)^2.
  • (1.04)^2 = 1.0816.
  • A = 1000 × 1.0816 = $1,081.60.
• Answer: $1,081.60

[Medium] Quadratic Function — Vertex

• EN: Find the vertex of the parabola y = x² − 4x + 7.
• FR: Trouve le sommet de la parabole y = x² − 4x + 7.
• Choices: A) (1, 4) B) (2, 3) C) (3, 4) D) (4, 7)
• Hint: The x-coordinate of the vertex is −b/(2a). For y = x² − 6x + 10, x = 6/2 = 3, and y = 9 − 18 + 10 = 1, so vertex is (3, 1).
• Steps:
  • x = −(−4)/(2 × 1) = 4/2 = 2.
  • y = (2)² − 4(2) + 7 = 4 − 8 + 7 = 3.
  • Vertex is (2, 3).
• Answer: (2, 3)

[Medium] Geometric Series — Sum

• EN: Find the sum of the first 5 terms of the geometric series: 2, 6, 18, 54, …
• FR: Trouve la somme des 5 premiers termes de la série géométrique : 2, 6, 18, 54, …
• Choices: A) 240 B) 242 C) 244 D) 246
• Hint: For a geometric series with a = 1, r = 3, and n = 4 terms: S = 1(3⁴ − 1)/(3 − 1) = 80/2 = 40.
• Steps:
  • a = 2, r = 3, n = 5.
  • S₅ = a(r^n − 1)/(r − 1) = 2(3^5 − 1)/(3 − 1) = 2(243 − 1)/2 = 242.
• Answer: 242

[Medium] Trigonometric Identity

• EN: Using the identity sin²θ + cos²θ = 1, if sinθ = 0.6, what is cosθ? (Assume θ is in the first quadrant.)
• FR: En utilisant l'identité sin²θ + cos²θ = 1, si sinθ = 0,6, combien vaut cosθ? (Suppose que θ est dans le premier quadrant.)
• Choices: A) 0.6 B) 0.7 C) 0.8 D) 0.9
• Hint: If sinθ = 0.5, then sin²θ = 0.25, and cos²θ = 1 − 0.25 = 0.75, so cosθ = √0.75 ≈ 0.866.
• Steps:
  • sin²θ + cos²θ = 1: (0.6)² + cos²θ = 1.
  • 0.36 + cos²θ = 1; cos²θ = 0.64.
  • cosθ = √0.64 = 0.8.
• Answer: 0.8

[Medium] Annuities

• EN: You deposit $200 at the end of each year into an account earning 5% annual interest. What is the future value after 3 years? (Use FV = PMT × [(1 + r)^n − 1] / r)
• FR: Tu déposes 200 $ à la fin de chaque année dans un compte rapportant 5 % d'intérêt annuel. Quelle est la valeur future après 3 ans? (Utilise FV = PMT × [(1 + r)^n − 1] / r)
• Choices: A) $620.50 B) $630.50 C) $640.50 D) $651.00
• Hint: For $100/year at 4% for 2 years: FV = 100 × [(1.04)² − 1]/0.04 = 100 × [1.0816 − 1]/0.04 = 100 × 2.04 = $204.
• Steps:
  • FV = 200 × [(1.05)³ − 1] / 0.05.
  • (1.05)³ = 1.157625; 1.157625 − 1 = 0.157625.
  • FV = 200 × 0.157625/0.05 = 200 × 3.1525 = $630.50.
• Answer: $630.50

[Hard] Logarithm — Solving Equations

• EN: Solve for x: 3^x = 81.
• FR: Résous pour x : 3^x = 81.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: To solve 2^x = 16, rewrite 16 as 2^4, so x = 4.
• Steps:
  • Rewrite 81 as a power of 3: 81 = 3^4.
  • So 3^x = 3^4, meaning x = 4.
• Answer: x = 4

[Hard] Compound Interest — Solving for Time

• EN: How many years does it take for $500 invested at 6% annual compound interest to grow to at least $670? (Use log if needed; log 1.34 ÷ log 1.06 ≈ 4.97)
• FR: Combien d'années faut-il pour que 500 $, investis à 6 % d'intérêt annuel composé, atteignent au moins 670 $? (Utilise log si nécessaire; log 1,34 ÷ log 1,06 ≈ 4,97)
• Choices: A) 4 years B) 5 years C) 6 years D) 7 years
• Hint: Solve P(1 + r)^n = A for n by taking logarithms: n = log(A/P) ÷ log(1 + r).
• Steps:
  • We need 500(1.06)^n ≥ 670, so (1.06)^n ≥ 1.34.
  • n = log(1.34)/log(1.06) ≈ 4.97, so round up to 5 years.
• Answer: 5 years

[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: The number of ways to arrange 4 items is 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
• Answer: 120

[Easy] Combinations

• EN: A student must choose 2 elective courses from 6 available. How many combinations are possible?
• FR: Un élève doit choisir 2 cours optionnels parmi 6 disponibles. Combien de combinaisons sont possibles?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: C(5,2) = 5!/(2! × 3!) = (5 × 4)/(2 × 1) = 10.
• Steps:
  • C(6,2) = 6! / (2! × 4!) = (6 × 5) / (2 × 1) = 30/2 = 15.
• Answer: 15

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = 4x³.
• FR: Trouve la dérivée de f(x) = 4x³.
• Choices: A) 4x² B) 8x² C) 12x² D) 16x²
• Hint: Using the power rule, the derivative of 3x⁴ is 3 × 4 × x³ = 12x³.
• Steps:
  • Power rule: d/dx [axⁿ] = n × a × x^(n−1).
  • d/dx [4x³] = 3 × 4 × x² = 12x².
• Answer: 12x²

[Easy] Rational Function — Domain

• EN: What value of x makes the rational function f(x) = 5/(x − 3) undefined?
• FR: Quelle valeur de x rend la fonction rationnelle f(x) = 5/(x − 3) non définie?
• Choices: A) x = 0 B) x = 3 C) x = 5 D) x = 8
• Hint: A rational function is undefined when its denominator equals zero. For g(x) = 1/(x − 7), x = 7 makes it undefined.
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • So x = 3 makes the function undefined.
• Answer: x = 3

[Medium] Polynomial Function — Roots

• EN: Find all roots of f(x) = x³ − x² − 6x by factoring completely.
• FR: Trouve toutes les racines de f(x) = x³ − x² − 6x en factorisant complètement.
• Choices: A) x = 0, x = 2, x = −3 B) x = 0, x = 3, x = −2 C) x = 1, x = 3, x = −2 D) x = 0, x = −3, x = −2
• Hint: Factor out any common factor first. For x³ − 5x, factor out x: x(x² − 5), giving roots x = 0, x = ±√5.
• Steps:
  • Factor out x: x(x² − x − 6).
  • Factor the trinomial: x(x − 3)(x + 2).
  • Roots: x = 0, x = 3, x = −2.
• Answer: x = 0, x = 3, x = −2

[Medium] Probability Distribution — Expected Value

• EN: A game pays $10 with probability 0.3 and costs $2 with probability 0.7. What is the expected value of the game?
• FR: Un jeu rapporte 10 $ avec une probabilité de 0,3 et coûte 2 $ avec une probabilité de 0,7. Quelle est la valeur espérée du jeu?
• Choices: A) $1.40 B) $1.60 C) $1.80 D) $2.00
• Hint: Expected value = Σ(value × probability). For $5 with P = 0.4 and −$3 with P = 0.6: E = 5(0.4) + (−3)(0.6) = 2 − 1.8 = $0.20.
• Steps:
  • E = 10(0.3) + (−2)(0.7).
  • E = 3.00 − 1.40 = 1.60.
• Answer: $1.60

[Medium] Vectors — Addition

• EN: Vector u = (3, 5) and vector v = (−1, 4). What is u + v?
• FR: Le vecteur u = (3, 5) et le vecteur v = (−1, 4). Combien vaut u + v?
• Choices: A) (1, 8) B) (2, 9) C) (3, 9) D) (4, 8)
• Hint: To add vectors (2, 3) and (4, −1), add corresponding components: (2 + 4, 3 + (−1)) = (6, 2).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 5 + 4 = 9.
  • Result: (2, 9).
• Answer: (2, 9)

[Medium] Derivative — Rate of Change

• EN: The position of an object is s(t) = 2t² + 3t. What is the velocity (derivative) at t = 4?
• FR: La position d'un objet est s(t) = 2t² + 3t. Quelle est la vitesse (dérivée) à t = 4?
• Choices: A) 17 B) 19 C) 21 D) 23
• Hint: For s(t) = 3t² + 2t, the derivative is s'(t) = 6t + 2. At t = 3: s'(3) = 18 + 2 = 20.
• Steps:
  • s'(t) = d/dt[2t² + 3t] = 4t + 3.
  • At t = 4: s'(4) = 4(4) + 3 = 16 + 3 = 19.
• Answer: 19

[Hard] Combinations — Multi-Step

• EN: A committee of 3 men and 2 women is formed from a group of 7 men and 5 women. How many ways can this committee be formed?
• FR: Un comité de 3 hommes et 2 femmes est formé à partir d'un groupe de 7 hommes et 5 femmes. De combien de façons ce comité peut-il être formé?
• Choices: A) 250 B) 300 C) 350 D) 400
• Hint: When choosing groups independently, multiply the combinations: C(4,2) × C(3,1) = 6 × 3 = 18.
• Steps:
  • Choose 3 men from 7: C(7,3) = 35.
  • Choose 2 women from 5: C(5,2) = 10.
  • Total combinations: 35 × 10 = 350.
• Answer: 350

[Hard] Derivative — Application (Optimization)

• EN: A farmer has 120 m of fencing to enclose a rectangular field along a river (no fence needed along the river). What width w (in metres) maximizes the area?
• FR: Un fermier a 120 m de clôture pour encadrer un champ rectangulaire le long d'une rivière (pas de clôture nécessaire le long de la rivière). Quelle largeur w (en mètres) maximise l'aire?
• Choices: A) 20 m B) 25 m C) 30 m D) 40 m
• Hint: For L + 2w = 80, express L = 80 − 2w; Area = Lw = (80 − 2w)w; take the derivative and set to zero: 80 − 4w = 0, so w = 20.
• Steps:
  • Only two widths and one length are needed: L + 2w = 120, so L = 120 − 2w.
  • Area A = Lw = (120 − 2w)w = 120w − 2w².
  • dA/dw = 120 − 4w = 0 → w = 30 m.
• Answer: 30 m