Daily Math — 2026-07-14

[Easy] Counting to 20

• EN: There are 7 apples on the table and 5 more apples in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres pommes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To add 6 + 4, count on from 6: 7, 8, 9, 10 — that's 10.
• Steps:
  • Start at 7 and count on 5 more: 8, 9, 10, 11, 12.
  • So there are 12 apples in all.
• Answer: 12

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes next: 2, 4, 6, 8, ___?
• FR: Compte par bonds de 2. Quel nombre vient ensuite : 2, 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Skip counting by 2s means adding 2 each time: 10, 12, 14 …
• Steps:
  • The pattern adds 2 each time: 2, 4, 6, 8, …
  • 8 + 2 = 10, so the next number is 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) 14 C) They are equal D) 11
• Hint: To compare 6 and 12, think about which is farther along when counting: 12 is greater.
• Steps:
  • Count up from 1: 14 comes after 9 on the number line.
  • So 14 is greater than 9.
• Answer: 14

[Easy] Coin Recognition

• EN: Emma has one dime. How many cents does she have?
• FR: Emma a une pièce de dix cents. Combien de cents a-t-elle?
• Choices: A) 1 cent B) 5 cents C) 10 cents D) 25 cents
• Hint: A nickel is worth 5 cents — a dime is worth twice as much.
• Steps:
  • A penny = 1 cent, a nickel = 5 cents, a dime = 10 cents.
  • So one dime = 10 cents.
• Answer: 10 cents

[Medium] Subtraction within 20

• EN: There are 15 hockey pucks in a bag. A player takes out 6. How many pucks are left?
• FR: Il y a 15 rondelles de hockey dans un sac. Un joueur en prend 6. Combien de rondelles reste-t-il?
• Choices: A) 8 B) 9 C) 10 D) 7
• Hint: For 11 − 4, count back 4 from 11: 10, 9, 8, 7 — the answer is 7.
• Steps:
  • Start at 15 and count back 6: 14, 13, 12, 11, 10, 9.
  • So 9 pucks are left.
• Answer: 9

[Medium] Skip Counting by 5s

• EN: Skip count by 5s. What number comes next: 5, 10, 15, 20, ___?
• FR: Compte par bonds de 5. Quel nombre vient ensuite : 5, 10, 15, 20, ___?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: Skip counting by 5s means adding 5 each time: 30, 35, 40 …
• Steps:
  • Each number is 5 more than the one before: 5, 10, 15, 20, …
  • 20 + 5 = 25, so the next number is 25.
• Answer: 25

[Medium] Addition within 20

• EN: Liam has 8 stickers and his friend gives him 7 more. How many stickers does Liam have now?
• FR: Liam a 8 autocollants et son ami lui en donne 7 de plus. Combien d'autocollants Liam a-t-il maintenant?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: To add 6 + 8, make a ten: 6 + 4 = 10, then 10 + 4 = 14.
• Steps:
  • To add 8 + 7, make a ten: 8 + 2 = 10, and 7 − 2 = 5 is left over.
  • 10 + 5 = 15, so Liam has 15 stickers.
• Answer: 15

[Medium] Counting to 100

• EN: Start at 60 and count by 10s. What is the third number you say?
• FR: Commence à 60 et compte par bonds de 10. Quel est le troisième nombre que tu dis?
• Choices: A) 70 B) 80 C) 90 D) 100
• Hint: Start at 20 and count by 10s: 30 (first), 40 (second), 50 (third).
• Steps:
  • Start at 60. First number: 70. Second number: 80. Third number: 90.
  • So the third number is 90.
• Answer: 90

[Hard] Adding Three Numbers

• EN: A jar has 4 red candies, 6 blue candies, and 3 green candies. How many candies are in the jar altogether?
• FR: Un pot contient 4 bonbons rouges, 6 bonbons bleus et 3 bonbons verts. Combien y a-t-il de bonbons dans le pot en tout?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To add 3 + 5 + 2, add the first two: 3 + 5 = 8, then 8 + 2 = 10.
• Steps:
  • Add 4 + 6 first: 4 + 6 = 10.
  • Then add 3 more: 10 + 3 = 13, so there are 13 candies in all.
• Answer: 13

[Hard] Coins and Counting

• EN: Jake has 2 nickels and 1 dime. How many cents does he have in total?
• FR: Jake a 2 pièces de cinq cents et 1 pièce de dix cents. Combien de cents a-t-il en tout?
• Choices: A) 15 cents B) 17 cents C) 20 cents D) 25 cents
• Hint: For 3 nickels and 1 dime: 3 nickels = 15 cents, plus 10 cents = 25 cents.
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 1 dime = 10 cents. Total: 10 + 10 = 20 cents.
• Answer: 20 cents

[Easy] Addition within 100

• EN: A store has 34 red mittens and 25 blue mittens. How many mittens are there in all?
• FR: Un magasin a 34 mitaines rouges et 25 mitaines bleues. Combien y a-t-il de mitaines en tout?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: To add 42 + 31, add tens: 40 + 30 = 70, then ones: 2 + 1 = 3, giving 73.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9. So 50 + 9 = 59 mittens.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows 3 o'clock. What time is it?
• FR: L'horloge indique 3 heures. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 4:00 D) 3:30
• Hint: When the minute hand points straight up (to the 12), it is o'clock time.
• Steps:
  • The hour hand points to 3 and the minute hand points to 12.
  • That means it is exactly 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long and a crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 14 cm et un crayon de cire mesure 9 cm. De combien le crayon à mine 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 11 cm, subtract: 18 − 11 = 7 cm.
• Steps:
  • Subtract the shorter length from the longer: 14 − 9 = 5.
  • The pencil is 5 cm longer than the crayon.
• Answer: 5 cm

[Easy] Simple Patterns

• EN: Look at the pattern: 10, 20, 30, 40, ___. What comes next?
• FR: Observe le motif : 10, 20, 30, 40, ___. Quel nombre vient ensuite?
• Choices: A) 45 B) 48 C) 50 D) 60
• Hint: In the pattern 3, 6, 9, 12, each number is 3 more than the last, so next is 15.
• Steps:
  • The pattern adds 10 each time: 10, 20, 30, 40, …
  • 40 + 10 = 50, so the next number is 50.
• Answer: 50

[Medium] Subtraction within 100

• EN: A school library had 73 books. Students borrowed 28 books. How many books are still on the shelves?
• FR: La bibliothèque de l'école avait 73 livres. Les élèves en ont emprunté 28. Combien de livres restent sur les étagères?
• Choices: A) 44 B) 45 C) 46 D) 47
• Hint: To subtract 56 − 19, think 56 − 20 = 36, then add 1 back: 37.
• Steps:
  • Subtract: 73 − 28. Think 73 − 30 = 43, then add 2 back: 43 + 2 = 45.
  • So 45 books are still on the shelves.
• Answer: 45

[Medium] Telling Time (Half-Hour)

• EN: The clock shows the hour hand between 7 and 8, and the minute hand pointing to 6. What time is it?
• FR: L'horloge montre l'aiguille des heures entre 7 et 8, et l'aiguille des minutes pointant vers le 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the minute hand points to 6, it is always 30 minutes past the hour.
• Steps:
  • The minute hand at 6 means 30 minutes have passed.
  • The hour hand is between 7 and 8, so it is 7:30.
• Answer: 7:30

[Medium] Counting Coins

• EN: Maya has 3 dimes and 2 nickels. How much money does she have?
• FR: Maya a 3 pièces de dix cents et 2 pièces de cinq cents. Combien d'argent a-t-elle?
• Choices: A) 35 cents B) 40 cents C) 45 cents D) 50 cents
• Hint: For 2 dimes and 3 nickels: 2 × 10 = 20 cents, 3 × 5 = 15 cents, total = 35 cents.
• Steps:
  • 3 dimes = 3 × 10 = 30 cents.
  • 2 nickels = 2 × 5 = 10 cents. Total: 30 + 10 = 40 cents.
• Answer: 40 cents

[Medium] Measuring Length in Metres

• EN: A classroom is 8 metres wide and a hallway is 5 metres wide. How much wider is the classroom than the hallway?
• FR: Une salle de classe a 8 mètres de largeur et un couloir a 5 mètres de largeur. De combien la salle de classe est-elle plus large?
• Choices: A) 2 metres B) 3 metres C) 4 metres D) 13 metres
• Hint: To find the difference between 12 m and 7 m, subtract: 12 − 7 = 5 m.
• Steps:
  • Subtract: 8 − 5 = 3.
  • The classroom is 3 metres wider than the hallway.
• Answer: 3 metres

[Hard] Adding with Regrouping

• EN: On Monday 47 students bought a hot lunch, and on Tuesday 56 students bought a hot lunch. How many students bought a hot lunch over the two days?
• FR: Lundi, 47 élèves ont acheté un repas chaud, et mardi, 56 élèves en ont acheté un. Combien d'élèves ont acheté un repas chaud en deux jours?
• Choices: A) 93 B) 101 C) 103 D) 113
• Hint: For 38 + 45, add ones first: 8 + 5 = 13, write 3 carry 1; tens: 3 + 4 + 1 = 8; answer is 83.
• Steps:
  • Add ones: 7 + 6 = 13; write 3, carry 1.
  • Add tens: 4 + 5 + 1 = 10; write 10. Answer: 103 students.
• Answer: 103

[Hard] Counting Coins to $1

• EN: Theo has 2 quarters, 1 dime, and 1 nickel. How much money does he have in total?
• FR: Theo a 2 pièces de vingt-cinq cents, 1 pièce de dix cents et 1 pièce de cinq cents. Combien d'argent a-t-il en tout?
• Choices: A) 55 cents B) 60 cents C) 65 cents D) 70 cents
• Hint: For 1 quarter, 2 dimes, and 1 nickel: 25 + 20 + 5 = 50 cents.
• Steps:
  • 2 quarters = 2 × 25 = 50 cents.
  • 1 dime = 10 cents; 1 nickel = 5 cents. Total: 50 + 10 + 5 = 65 cents.
• Answer: 65 cents

[Easy] Multiplication by 2

• EN: A hockey team has 6 players on the ice. Each player has 2 gloves. How many gloves are there in total?
• FR: Une équipe de hockey a 6 joueurs sur la glace. Chaque joueur a 2 gants. Combien y a-t-il de gants en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: To find 5 × 2, count by 2s five times: 2, 4, 6, 8, 10.
• Steps:
  • Multiply: 6 × 2 = 12.
  • There are 12 gloves in total.
• Answer: 12

[Easy] Basic Division

• EN: A teacher has 20 crayons and wants to share them equally among 4 students. How many crayons does each student get?
• FR: Une enseignante a 20 crayons de cire et veut les partager également entre 4 élèves. Combien de crayons chaque élève reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: To divide 15 ÷ 3, think: what times 3 equals 15? Answer: 5.
• Steps:
  • 20 ÷ 4 = ? Ask: 4 × ? = 20.
  • 4 × 5 = 20, so each student gets 5 crayons.
• Answer: 5

[Easy] Fractions

• EN: A pizza is cut into 4 equal slices. Mia eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 tranches égales. Mia mange 1 tranche. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: If a pie is cut into 3 equal parts and you eat 1, you ate 1/3 of the pie.
• Steps:
  • The pizza has 4 equal slices, so each slice = 1/4 of the pizza.
  • Mia ate 1 slice, so she ate 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: There are 7 bags of apples. Each bag holds 5 apples. How many apples are there altogether?
• FR: Il y a 7 sacs de pommes. Chaque sac contient 5 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: To find 6 × 5, skip count by 5s six times: 5, 10, 15, 20, 25, 30.
• Steps:
  • Multiply: 7 × 5 = 35.
  • There are 35 apples altogether.
• Answer: 35

[Medium] Perimeter

• EN: A rectangular garden is 8 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un jardin rectangulaire a 8 m de longueur et 3 m de largeur. Quel est le périmètre du jardin?
• Choices: A) 11 m B) 22 m C) 24 m D) 26 m
• Hint: The perimeter of a rectangle with length 5 m and width 2 m is 5 + 2 + 5 + 2 = 14 m.
• Steps:
  • A rectangle has two lengths and two widths: 8 + 3 + 8 + 3.
  • 8 + 3 = 11, and 11 × 2 = 22. The perimeter is 22 m.
• Answer: 22 m

[Medium] Multiplication by 3

• EN: Sophie baked 9 batches of cookies. Each batch had 3 cookies. How many cookies did she bake in all?
• FR: Sophie a fait 9 fournées de biscuits. Chaque fournée comptait 3 biscuits. Combien de biscuits a-t-elle cuits en tout?
• Choices: A) 24 B) 27 C) 30 D) 33
• Hint: To find 7 × 3, skip count by 3s seven times: 3, 6, 9, 12, 15, 18, 21.
• Steps:
  • Multiply: 9 × 3 = 27.
  • Sophie baked 27 cookies in all.
• Answer: 27

[Medium] Reading a Simple Graph

• EN: A bar graph shows that 8 students like hockey, 5 like skating, and 4 like skiing. How many more students like hockey than skiing?
• FR: Un diagramme à bandes montre que 8 élèves aiment le hockey, 5 aiment le patin et 4 aiment le ski. Combien d'élèves de plus aiment le hockey que le ski?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: To find how many more 9 is than 6, subtract: 9 − 6 = 3.
• Steps:
  • Subtract the skiing count from the hockey count: 8 − 4 = 4.
  • So 4 more students like hockey than skiing.
• Answer: 4

[Medium] Multiplication by 10

• EN: A parking lot has 6 rows of cars. Each row has 10 cars. How many cars are in the parking lot?
• FR: Un stationnement a 6 rangées de voitures. Chaque rangée a 10 voitures. Combien y a-t-il de voitures dans le stationnement?
• Choices: A) 16 B) 50 C) 60 D) 70
• Hint: Any number times 10 just gets a zero added: 8 × 10 = 80.
• Steps:
  • Multiply: 6 × 10 = 60.
  • There are 60 cars in the parking lot.
• Answer: 60

[Hard] Fractions of a Group

• EN: There are 12 children on the playground. One-third of them are wearing hats. How many children are wearing hats?
• FR: Il y a 12 enfants sur le terrain de jeu. Un tiers d'entre eux portent des chapeaux. Combien d'enfants portent des chapeaux?
• Choices: A) 3 B) 4 C) 6 D) 8
• Hint: To find 1/2 of 10, divide 10 by 2: 10 ÷ 2 = 5.
• Steps:
  • To find 1/3 of 12, divide by 3: 12 ÷ 3 = 4.
  • So 4 children are wearing hats.
• Answer: 4

[Hard] Multi-Step Problem

• EN: A store had 4 boxes of markers. Each box had 8 markers. The teacher gave away 10 markers to students. How many markers does the store have left?
• FR: Un magasin avait 4 boîtes de marqueurs. Chaque boîte contenait 8 marqueurs. L'enseignant a donné 10 marqueurs aux élèves. Combien de marqueurs reste-t-il au magasin?
• Choices: A) 22 B) 24 C) 26 D) 32
• Hint: For 3 boxes of 6 pens minus 5: first multiply 3 × 6 = 18, then subtract 5 to get 13.
• Steps:
  • First, find the total markers: 4 × 8 = 32.
  • Then subtract the ones given away: 32 − 10 = 22. So 22 markers are left.
• Answer: 22

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: To find 6 × 8, think 5 × 8 = 40, then add one more 8: 40 + 8 = 48.
• Steps:
  • Use the multiplication table: 7 × 8 = 56.
  • Double-check: 7 × 4 = 28, and 28 × 2 = 56. Correct!
• 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 ones
• Hint: In 2.56, the digit 5 is in the tenths place and means 5 tenths (or 0.5).
• Steps:
  • In 4.37, the digits after the decimal are tenths and hundredths.
  • The 3 is in the first decimal place, so it means 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A rug is 5 m long and 4 m wide. What is the area of the rug?
• FR: Un tapis a 5 m de longueur et 4 m de largeur. Quelle est l'aire du tapis?
• Choices: A) 18 m² B) 20 m² C) 22 m² D) 24 m²
• Hint: Area of a rectangle = length × width; for a 6 m × 3 m room, area = 18 m².
• Steps:
  • Area = length × width = 5 × 4 = 20.
  • The area of the rug is 20 m².
• Answer: 20 m²

[Easy] Long Division

• EN: A baker baked 36 muffins and packed them equally into 4 boxes. How many muffins are in each box?
• FR: Un boulanger a cuit 36 muffins et les a mis en quantités égales dans 4 boîtes. Combien y a-t-il de muffins dans chaque boîte?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: To divide 45 ÷ 5, ask: 5 × ? = 45. The answer is 9.
• Steps:
  • Divide: 36 ÷ 4 = ? Ask: 4 × ? = 36.
  • 4 × 9 = 36, so each box has 9 muffins.
• Answer: 9

[Medium] Long Division with Remainders

• EN: A coach has 38 jerseys to hand out equally to 5 teams. How many jerseys does each team get, and how many are left over?
• FR: Un entraîneur a 38 chandails à distribuer également à 5 équipes. Combien de chandails chaque équipe reçoit-elle, et combien en reste-t-il?
• Choices: A) 6 remainder 8 B) 7 remainder 3 C) 8 remainder 2 D) 7 remainder 4
• Hint: To divide 29 ÷ 4: 4 × 7 = 28, so the answer is 7 remainder 1.
• Steps:
  • 5 × 7 = 35, which is less than 38. 5 × 8 = 40, which is too big.
  • 38 − 35 = 3, so each team gets 7 jerseys with 3 left over.
• Answer: 7 remainder 3

[Medium] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/4?
• FR: Quelle fraction est plus grande : 3/4 ou 2/4?
• Choices: A) 2/4 B) 3/4 C) They are equal D) 1/4
• Hint: When two fractions have the same denominator, the one with the larger numerator is greater: 5/8 > 3/8.
• Steps:
  • Both fractions have the same denominator (4), so compare the numerators: 3 vs. 2.
  • Since 3 > 2, we know 3/4 > 2/4.
• 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 did the game last?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps a duré le match?
• Choices: A) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours 15 minutes
• Hint: From 2:10 p.m. to 4:40 p.m., count 2 full hours to 4:10, then 30 more minutes: 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 is exactly 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: Ava paid $3.45 for a snack and $2.30 for a drink at Tim Hortons. How much did she spend in total?
• FR: Ava a payé 3,45 $ pour une collation et 2,30 $ pour une boisson chez Tim Hortons. Combien a-t-elle dépensé en tout?
• Choices: A) $5.65 B) $5.70 C) $5.75 D) $6.75
• Hint: To add $4.20 + $3.15, add dollars: 4 + 3 = 7, and cents: 20 + 15 = 35, giving $7.35.
• Steps:
  • Add the dollars: 3 + 2 = 5.
  • Add the cents: 45 + 30 = 75. Total: $5.75.
• Answer: $5.75

[Hard] Multi-Step Multiplication and Division

• EN: A school ordered 9 packs of pencils. Each pack had 8 pencils. The pencils were shared equally among 6 classrooms. How many pencils did each classroom receive?
• FR: Une école a commandé 9 paquets de crayons. Chaque paquet contenait 8 crayons. Les crayons ont été partagés également entre 6 classes. Combien de crayons chaque classe a-t-elle reçu?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: For 4 boxes of 6 items shared among 8 groups: 4 × 6 = 24, then 24 ÷ 8 = 3.
• Steps:
  • First find total pencils: 9 × 8 = 72.
  • Then divide: 72 ÷ 6 = 12. Each classroom gets 12 pencils.
• Answer: 12

[Hard] Comparing Decimals

• EN: Order these numbers from least to greatest: 2.4, 2.04, 2.40, 2.14.
• FR: Ordonne ces nombres du plus petit au plus grand : 2,4 ; 2,04 ; 2,40 ; 2,14.
• Choices: A) 2.04, 2.14, 2.4, 2.40 B) 2.04, 2.14, 2.40, 2.4 C) 2.14, 2.04, 2.4, 2.40 D) 2.40, 2.4, 2.14, 2.04
• Hint: To compare 3.5 and 3.05, note that 3.50 > 3.05 because 50 hundredths > 5 hundredths.
• Steps:
  • Write each as hundredths: 2.04 = 2.04, 2.14 = 2.14, 2.4 = 2.40, 2.40 = 2.40.
  • Note 2.4 and 2.40 are equal. Order: 2.04, 2.14, 2.4, 2.40 (two equal greatest values).
• Answer: 2.04, 2.14, 2.4, 2.40

[Easy] Multi-Digit Multiplication

• EN: A farmer plants 24 rows of corn with 12 plants in each row. How many corn plants are there in all?
• FR: Un agriculteur plante 24 rangées de maïs avec 12 plants par rangée. Combien y a-t-il de plants de maïs en tout?
• Choices: A) 268 B) 278 C) 288 D) 298
• Hint: To find 32 × 11, think 32 × 10 = 320, then add 32: 320 + 32 = 352.
• Steps:
  • Multiply: 24 × 12. Use 24 × 10 = 240, and 24 × 2 = 48.
  • 240 + 48 = 288. There are 288 corn plants.
• Answer: 288

[Easy] Adding Fractions with Like Denominators

• EN: Emma ate 2/6 of a pie and her brother ate 3/6 of the same pie. How much pie was eaten altogether?
• FR: Emma a mangé 2/6 d'une tarte et son frère en a mangé 3/6. Quelle fraction de la tarte a été mangée en tout?
• Choices: A) 5/12 B) 5/6 C) 6/6 D) 1/6
• Hint: To add 3/8 + 2/8, keep the denominator and add the numerators: 5/8.
• Steps:
  • Add the numerators: 2 + 3 = 5. Keep the denominator: 6.
  • The total eaten is 5/6.
• Answer: 5/6

[Easy] Decimal Operations

• EN: A snowfall of 12.5 cm fell on Saturday and 8.3 cm fell on Sunday. What was the total snowfall over the weekend?
• FR: Il est tombé 12,5 cm de neige samedi et 8,3 cm dimanche. Quelle a été la chute de neige totale durant le week-end?
• Choices: A) 19.8 cm B) 20.8 cm C) 21.8 cm D) 22.8 cm
• Hint: To add 6.4 + 3.2, line up the decimal points: 6.4 + 3.2 = 9.6.
• Steps:
  • Line up decimals: 12.5 + 8.3.
  • Add: 12 + 8 = 20 and 0.5 + 0.3 = 0.8. Total: 20.8 cm.
• Answer: 20.8 cm

[Easy] Percentage — 50%

• EN: A hockey team played 20 games and won 50% of them. How many games did the team win?
• FR: Une équipe de hockey a joué 20 matchs et en a gagné 50 %. Combien de matchs l'équipe a-t-elle gagnés?
• Choices: A) 5 B) 8 C) 10 D) 15
• Hint: 50% of any number means half of it: 50% of 14 = 7.
• Steps:
  • 50% means half. Half of 20 = 20 ÷ 2 = 10.
  • The team won 10 games.
• Answer: 10

[Medium] Multi-Digit Division

• EN: A warehouse has 378 boxes of cereal to ship equally to 9 stores. How many boxes does each store receive?
• FR: Un entrepôt a 378 boîtes de céréales à envoyer également à 9 magasins. Combien de boîtes chaque magasin reçoit-il?
• Choices: A) 41 B) 42 C) 43 D) 44
• Hint: To divide 240 ÷ 8, ask how many times 8 goes into 24 (it's 3), then bring down the 0: answer is 30.
• Steps:
  • Divide: 378 ÷ 9. 9 × 40 = 360, remainder 18. 18 ÷ 9 = 2.
  • 40 + 2 = 42. Each store receives 42 boxes.
• Answer: 42

[Medium] Subtracting Fractions

• EN: A jug held 7/8 of a litre of juice. After lunch, 3/8 of a litre was drunk. How much juice is left in the jug?
• FR: Un pichet contenait 7/8 de litre de jus. Après le dîner, 3/8 de litre a été bu. Combien reste-t-il de jus dans le pichet?
• Choices: A) 3/8 B) 4/8 C) 5/8 D) 10/8
• Hint: To subtract 6/9 − 2/9, keep the denominator and subtract numerators: 4/9.
• Steps:
  • Subtract numerators: 7 − 3 = 4. Keep the denominator: 8.
  • There are 4/8 of a litre of juice left.
• Answer: 4/8

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte a 5 cm de longueur, 4 cm de largeur et 3 cm de hauteur. Quel est le volume de la boîte?
• Choices: A) 47 cm³ B) 60 cm³ C) 72 cm³ D) 80 cm³
• Hint: Volume = length × width × height; for a 2 × 6 × 3 box, V = 36 cm³.
• Steps:
  • V = l × w × h = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60. The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25%

• EN: A store is having a sale. A jacket originally costs $80. It is 25% off. How much money do you save?
• FR: Un magasin fait une vente. Un manteau coûtait 80 $ à l'origine. Il est à 25 % de rabais. Combien d'argent économises-tu?
• Choices: A) $15 B) $20 C) $25 D) $40
• Hint: 25% of 40 = one quarter of 40 = 40 ÷ 4 = 10.
• Steps:
  • 25% means one-quarter. Divide 80 by 4: 80 ÷ 4 = 20.
  • You save $20.
• Answer: $20

[Hard] Multi-Step Fractions and Decimals

• EN: A recipe needs 1.75 L of milk. Isabelle has 1/4 L in a small jug and 1.25 L in a large jug. Does she have enough milk, and if so, by how much?
• FR: Une recette nécessite 1,75 L de lait. Isabelle a 1/4 L dans un petit pichet et 1,25 L dans un grand pichet. A-t-elle assez de lait, et si oui, de combien?
• Choices: A) No, she is 0.25 L short B) Yes, by exactly 0 L C) Yes, by 0.25 L D) Yes, by 0.75 L
• Hint: Convert 1/4 to a decimal (0.25), then add to the other amount, and compare to the total needed.
• Steps:
  • Convert: 1/4 = 0.25 L. Total milk: 0.25 + 1.25 = 1.50 L.
  • She needs 1.75 L but has 1.50 L, so she is 0.25 L short.
• Answer: No, she is 0.25 L short

[Hard] Percentage — 10%

• EN: A school fundraiser raised $340. The school keeps 10% as an admin fee. How much money goes to the charity after the fee is removed?
• FR: Une collecte de fonds scolaire a amassé 340 $. L'école garde 10 % à titre de frais d'administration. Combien d'argent va à l'organisme de bienfaisance après la déduction des frais?
• Choices: A) $296 B) $306 C) $314 D) $340
• Hint: 10% of 250 = 25, so the remaining amount = 250 − 25 = 225.
• Steps:
  • 10% of 340 = 340 ÷ 10 = 34. This is the admin fee.
  • Amount to charity: 340 − 34 = 306.
• Answer: $306

[Easy] Fraction Multiplication

• EN: What is 1/2 × 3/4?
• FR: Combien font 1/2 × 3/4?
• Choices: A) 1/4 B) 3/8 C) 4/6 D) 2/8
• Hint: To multiply 2/3 × 1/4, multiply numerators and denominators: (2×1)/(3×4) = 2/12 = 1/6.
• Steps:
  • Multiply numerators: 1 × 3 = 3. Multiply denominators: 2 × 4 = 8.
  • The answer is 3/8.
• Answer: 3/8

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien représentent 30 % de 200?
• Choices: A) 30 B) 60 C) 66 D) 70
• Hint: To find 20% of 150, find 10% first (15), then double it: 30.
• Steps:
  • 10% of 200 = 20. Multiply by 3 to get 30%: 20 × 3 = 60.
  • 30% of 200 = 60.
• Answer: 60

[Easy] Ratios

• EN: In a class, there are 12 boys and 8 girls. What is the ratio of boys to girls in simplest form?
• FR: Dans une classe, il y a 12 garçons et 8 filles. Quel est le rapport entre le nombre de garçons et le nombre de filles sous la forme la plus simple?
• Choices: A) 12:8 B) 3:2 C) 2:3 D) 4:3
• Hint: To simplify the ratio 6:4, divide both numbers by their GCF (2): 3:2.
• Steps:
  • GCF of 12 and 8 is 4. Divide both: 12 ÷ 4 = 3, 8 ÷ 4 = 2.
  • The ratio in simplest form is 3:2.
• Answer: 3:2

[Easy] Integers Introduction

• EN: The temperature outside was −5°C. It rose by 9 degrees. What is the new temperature?
• FR: La température dehors était de −5 °C. Elle a augmenté de 9 degrés. Quelle est la nouvelle température?
• Choices: A) −4°C B) 3°C C) 4°C D) 14°C
• Hint: For −3 + 7, start at −3 on the number line and move 7 steps right to reach 4.
• Steps:
  • Start at −5 and add 9: −5 + 9 = 4.
  • The new temperature is 4°C.
• Answer: 4°C

[Medium] Fraction Division

• EN: How many 1/4-cup servings are in 3 cups of oatmeal?
• FR: Combien de portions de 1/4 de tasse y a-t-il dans 3 tasses de gruau?
• Choices: A) 8 B) 10 C) 12 D) 16
• Hint: To divide 2 ÷ 1/3, multiply by the reciprocal: 2 × 3 = 6.
• Steps:
  • Divide: 3 ÷ 1/4 = 3 × 4 = 12.
  • There are 12 servings of 1/4 cup in 3 cups.
• Answer: 12

[Medium] Order of Operations (BEDMAS)

• EN: Evaluate: 3 + 4 × 2 − 1.
• FR: Calcule : 3 + 4 × 2 − 1.
• Choices: A) 13 B) 10 C) 14 D) 9
• Hint: In BEDMAS, do multiplication before addition or subtraction; for 5 + 3 × 2 − 1: 5 + 6 − 1 = 10.
• Steps:
  • First multiply: 4 × 2 = 8.
  • Then: 3 + 8 − 1 = 10.
• Answer: 10

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is the car's speed in km per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est la vitesse de la voiture en km par heure?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: Rate = total ÷ time; if a cyclist rides 90 km in 3 hours, the rate is 90 ÷ 3 = 30 km/h.
• Steps:
  • Rate = distance ÷ time = 240 ÷ 3.
  • 240 ÷ 3 = 80. The car travels at 80 km/h.
• Answer: 80 km/h

[Medium] Simple Algebraic Expressions

• EN: Evaluate the expression 5n + 3 when n = 4.
• FR: Évalue l'expression 5n + 3 quand n = 4.
• Choices: A) 22 B) 23 C) 24 D) 27
• Hint: To evaluate 3x + 2 when x = 5, substitute: 3 × 5 + 2 = 15 + 2 = 17.
• Steps:
  • Substitute n = 4: 5(4) + 3 = 20 + 3.
  • 20 + 3 = 23.
• Answer: 23

[Hard] Percent Problems

• EN: A pair of skates costs $160. They are on sale for 35% off. What is the sale price?
• FR: Une paire de patins coûte 160 $. Elle est en solde à 35 % de rabais. Quel est le prix de vente?
• Choices: A) $96 B) $100 C) $104 D) $112
• Hint: For a 20% discount on $90: discount = 0.20 × 90 = $18, so sale price = 90 − 18 = $72.
• Steps:
  • Find the discount: 35% of 160 = 0.35 × 160 = 56.
  • Sale price: 160 − 56 = $104.
• Answer: $104

[Hard] Integers and Order of Operations

• EN: Evaluate: (−3) × 4 + (−2) × (−5).
• FR: Évalue : (−3) × 4 + (−2) × (−5).
• Choices: A) −22 B) −2 C) 2 D) 22
• Hint: For (−2) × 3 + (−1) × (−4): first (−2)(3) = −6 and (−1)(−4) = 4; then −6 + 4 = −2.
• Steps:
  • First multiplication: (−3) × 4 = −12.
  • Second multiplication: (−2) × (−5) = 10. Then: −12 + 10 = −2.
• Answer: −2

[Easy] Integer Addition

• EN: What is (−8) + 13?
• FR: Combien font (−8) + 13?
• Choices: A) −5 B) 4 C) 5 D) 21
• Hint: For (−4) + 9, start at −4 on the number line and move 9 steps right: you land on 5.
• Steps:
  • Start at −8 and add 13: move 13 steps right on the number line.
  • −8 + 13 = 5.
• Answer: 5

[Easy] Fraction Fluency

• EN: What is 3/5 + 1/5?
• FR: Combien font 3/5 + 1/5?
• Choices: A) 2/5 B) 3/10 C) 4/5 D) 4/10
• Hint: When fractions share the same denominator, just add the numerators: 2/7 + 3/7 = 5/7.
• Steps:
  • Same denominator (5), so add numerators: 3 + 1 = 4.
  • The answer is 4/5.
• Answer: 4/5

[Easy] Percentage — Discount

• EN: A $50 backpack is on sale for 20% off. How much is the discount?
• FR: Un sac à dos à 50 $ est en vente à 20 % de rabais. Quel est le montant du rabais?
• Choices: A) $8 B) $10 C) $12 D) $15
• Hint: 20% of 80 = 80 ÷ 5 = 16, because 20% is the same as one-fifth.
• Steps:
  • 20% of 50 = 0.20 × 50 = 10.
  • The discount is $10.
• Answer: $10

[Easy] Integer Subtraction

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

[Medium] Percentage — Tax

• EN: A book costs $24.00 at a store in Ontario. A 13% HST is added. What is the total cost?
• FR: Un livre coûte 24,00 $ dans un magasin en Ontario. Une TVH de 13 % est ajoutée. Quel est le coût total?
• Choices: A) $26.72 B) $27.12 C) $27.50 D) $28.12
• Hint: Tax = price × rate; for $30 at 10% tax: 30 × 0.10 = $3, total = $33.
• Steps:
  • Tax = 13% of 24 = 0.13 × 24 = $3.12.
  • Total = 24.00 + 3.12 = $27.12.
• Answer: $27.12

[Medium] One-Step Linear Equations

• EN: Solve for x: x + 14 = 31.
• FR: Résous pour x : x + 14 = 31.
• Choices: A) x = 15 B) x = 17 C) x = 18 D) x = 45
• Hint: To solve n + 6 = 20, subtract 6 from both sides: n = 20 − 6 = 14.
• Steps:
  • Subtract 14 from both sides: x + 14 − 14 = 31 − 14.
  • x = 17.
• Answer: x = 17

[Medium] Surface Area

• EN: Find the surface area of a rectangular box that is 6 cm long, 4 cm wide, and 2 cm tall.
• FR: Trouve l'aire totale d'une boîte rectangulaire de 6 cm de longueur, 4 cm de largeur et 2 cm de hauteur.
• Choices: A) 80 cm² B) 88 cm² C) 96 cm² D) 48 cm²
• Hint: Surface area of a rectangular prism = 2(lw + lh + wh); for a 3 × 2 × 1 box: 2(6 + 3 + 2) = 22 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(6×4 + 6×2 + 4×2).
  • = 2(24 + 12 + 8) = 2(44) = 88 cm².
• Answer: 88 cm²

[Medium] Probability

• EN: A bag contains 3 red marbles, 4 blue marbles, and 3 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 4 billes bleues et 3 billes vertes. Quelle est la probabilité de piger une bille bleue?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 7/10
• Hint: Probability = favourable outcomes ÷ total outcomes; for 2 red out of 6 total: P = 2/6 = 1/3.
• Steps:
  • Total marbles = 3 + 4 + 3 = 10. Favourable (blue) = 4.
  • P(blue) = 4/10.
• Answer: 4/10

[Hard] Integer Multiplication and Division

• 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 par heure pendant 6 heures. Quel est le changement total de température?
• Choices: A) −20°C B) −24°C C) −26°C D) 24°C
• Hint: A repeated negative change can be written as multiplication: (−3) × 5 = −15.
• Steps:
  • Each hour is −4°C, and there are 6 hours: (−4) × 6 = −24.
  • The total change is −24°C.
• Answer: −24°C

[Hard] Percent Problems — Tip

• EN: A family's restaurant bill is $65.00. They want to leave an 18% tip. What is the total amount they pay including the tip?
• FR: La facture au restaurant d'une famille est de 65,00 $. Ils veulent laisser un pourboire de 18 %. Quel est le montant total qu'ils paient, pourboire inclus?
• Choices: A) $75.70 B) $76.70 C) $77.70 D) $78.70
• Hint: For a 15% tip on $40: 0.15 × 40 = $6, total = $46.
• Steps:
  • Tip = 18% of 65 = 0.18 × 65 = $11.70.
  • Total = 65.00 + 11.70 = $76.70.
• Answer: $76.70

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To find √100, ask: what number times itself equals 100? Answer: 10, because 10 × 10 = 100.
• Steps:
  • Ask: what number squared equals 144?
  • 12 × 12 = 144, so √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Five students scored 72, 85, 90, 68, and 85 on a test. What is the mean score?
• FR: Cinq élèves ont obtenu 72, 85, 90, 68 et 85 à un test. Quelle est la moyenne des notes?
• Choices: A) 78 B) 80 C) 82 D) 85
• Hint: Mean = sum of values ÷ number of values; for 10, 20, 30: mean = 60 ÷ 3 = 20.
• Steps:
  • Sum = 72 + 85 + 90 + 68 + 85 = 400.
  • Mean = 400 ÷ 5 = 80.
• Answer: 80

[Easy] Two-Step Linear Equations

• EN: Solve for x: 2x + 5 = 15.
• FR: Résous pour x : 2x + 5 = 15.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 10
• Hint: To solve 3x + 2 = 11, subtract 2 first: 3x = 9, then divide: x = 3.
• Steps:
  • Subtract 5 from both sides: 2x = 10.
  • Divide by 2: x = 5.
• Answer: x = 5

[Easy] Percent Increase

• EN: A shirt originally costs $40 and its price is increased by 25%. What is the new price?
• FR: Un chandail coûte 40 $ à l'origine et son prix augmente de 25 %. Quel est le nouveau prix?
• Choices: A) $44 B) $48 C) $50 D) $55
• Hint: For a 10% increase on $60: increase = $6, new price = $66.
• Steps:
  • Increase = 25% of 40 = 0.25 × 40 = $10.
  • New price = 40 + 10 = $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) 14 cm
• Hint: For legs 3 and 4: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5.
• Steps:
  • c² = 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10. The hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Percent Decrease

• EN: A video game was selling for $80 and the price dropped by 30%. What is the new price?
• FR: Un jeu vidéo se vendait 80 $ et son prix a baissé de 30 %. Quel est le nouveau prix?
• Choices: A) $50 B) $54 C) $56 D) $60
• Hint: For a 20% decrease on $50: decrease = $10, new price = $40.
• Steps:
  • Decrease = 30% of 80 = 0.30 × 80 = $24.
  • New price = 80 − 24 = $56.
• Answer: $56

[Medium] Median and Mode

• EN: Find the median of the data set: 14, 7, 22, 9, 17, 7, 11.
• FR: Trouve la médiane de l'ensemble de données : 14, 7, 22, 9, 17, 7, 11.
• Choices: A) 7 B) 9 C) 11 D) 14
• Hint: To find the median, first order the values from least to greatest, then pick the middle one.
• Steps:
  • Order the values: 7, 7, 9, 11, 14, 17, 22.
  • There are 7 values; the middle (4th) value is 11.
• Answer: 11

[Medium] Slope Introduction

• EN: A line passes through points (2, 3) and (6, 11). What is the slope of the line?
• FR: Une droite passe par les points (2, 3) et (6, 11). Quel est le taux de variation (pente) de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁); for points (1, 2) and (3, 8): slope = (8−2)÷(3−1) = 3.
• Steps:
  • Slope = (11 − 3) ÷ (6 − 2) = 8 ÷ 4.
  • Slope = 2.
• Answer: 2

[Hard] Two-Step Equations with Negatives

• EN: Solve for x: 3x − 7 = −22.
• FR: Résous pour x : 3x − 7 = −22.
• Choices: A) x = −5 B) x = −3 C) x = 5 D) x = 3
• Hint: To solve 4x − 3 = −11, add 3 first: 4x = −8, then divide: x = −2.
• Steps:
  • Add 7 to both sides: 3x = −22 + 7 = −15.
  • Divide by 3: x = −15 ÷ 3 = −5.
• Answer: x = −5

[Hard] Pythagorean Theorem — Applied

• EN: A hockey player skates from one corner of a rink to the opposite corner. The rink is 30 m long and 40 m wide. How far does the player skate?
• FR: Un joueur de hockey patine d'un coin de la patinoire au coin opposé. La patinoire a 30 m de longueur et 40 m de largeur. Quelle distance le joueur parcourt-il?
• Choices: A) 45 m B) 50 m C) 55 m D) 70 m
• Hint: For a 5 m × 12 m rectangle, the diagonal = √(25 + 144) = √169 = 13 m.
• Steps:
  • c² = 30² + 40² = 900 + 1600 = 2500.
  • c = √2500 = 50. The player skates 50 m.
• Answer: 50 m

[Easy] Solving Linear Equations

• EN: Solve for x: 4x − 6 = 18.
• FR: Résous pour x : 4x − 6 = 18.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: To solve 3x − 2 = 10, add 2 first: 3x = 12, then divide by 3: x = 4.
• Steps:
  • Add 6 to both sides: 4x = 24.
  • Divide by 4: x = 6.
• Answer: x = 6

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x − 5?
• FR: Quel est le taux de variation (pente) de la droite y = 3x − 5?
• Choices: A) −5 B) 3 C) 5 D) −3
• Hint: In the equation y = mx + b, m is the slope; for y = 7x + 2, the slope is 7.
• Steps:
  • The equation is in y = mx + b form where m is the slope.
  • Here m = 3, so the slope is 3.
• Answer: 3

[Easy] Adding Polynomials

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

[Easy] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 6 cm et l'hypoténuse mesure 10 cm. Combien vaut sin(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: SOH means sin = opposite ÷ hypotenuse; for opposite = 4 and hypotenuse = 8: sin = 4/8 = 0.5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 6 ÷ 10.
  • sin(θ) = 0.6.
• Answer: 0.6

[Medium] Linear Inequalities

• EN: Solve and graph the inequality: 2x + 3 > 11. What is the solution?
• FR: Résous l'inégalité : 2x + 3 > 11. Quelle est la solution?
• Choices: A) x > 3 B) x > 4 C) x < 4 D) x ≥ 4
• Hint: To solve 3x + 1 > 10, subtract 1 first: 3x > 9, then divide by 3: x > 3.
• Steps:
  • Subtract 3 from both sides: 2x > 8.
  • Divide by 2: x > 4.
• Answer: x > 4

[Medium] Multiplying Polynomials

• EN: Expand and simplify: (x + 3)(x + 5).
• FR: Développe et simplifie : (x + 3)(x + 5).
• Choices: A) x² + 8x + 15 B) x² + 15x + 8 C) x² + 8x + 8 D) x² + 15
• Hint: To expand (x + 2)(x + 4), use FOIL: x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • FOIL: x·x = x², x·5 = 5x, 3·x = 3x, 3·5 = 15.
  • Combine: x² + 5x + 3x + 15 = x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in a ratio of 3:5. The shorter triangle has a side of 9 cm. What is the corresponding side in the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans un rapport de 3:5. Le plus petit triangle a un côté de 9 cm. Quel est le côté correspondant du plus grand triangle?
• Choices: A) 12 cm B) 15 cm C) 18 cm D) 27 cm
• Hint: If triangles are in ratio 2:3 and the small triangle has a side of 8, the large side = 8 × (3/2) = 12.
• Steps:
  • Scale factor: 9 × (5/3) = 15.
  • The corresponding side is 15 cm.
• Answer: 15 cm

[Medium] Statistics — Scatter Plots

• EN: A set of data shows that as study time increases, test scores also increase. What type of correlation does this represent?
• FR: Un ensemble de données montre qu'à mesure que le temps d'étude augmente, les notes aux tests augmentent aussi. Quel type de corrélation cela représente-t-il?
• Choices: A) Negative correlation B) No correlation C) Positive correlation D) Perfect correlation
• Hint: When both variables increase together, the points on a scatter plot go up from left to right — that's a positive trend.
• Steps:
  • As x (study time) increases, y (test score) also increases.
  • This means both variables move in the same direction: positive correlation.
• Answer: Positive correlation

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, one angle is 37°, and the hypotenuse is 20 cm. What is the length of the side opposite the 37° angle? (sin 37° ≈ 0.60)
• FR: Dans un triangle rectangle, un angle mesure 37° et l'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé à l'angle de 37°? (sin 37° ≈ 0,60)
• Choices: A) 10 cm B) 12 cm C) 14 cm D) 16 cm
• Hint: Use SOH: sin(angle) = opposite ÷ hypotenuse, so opposite = hypotenuse × sin(angle).
• Steps:
  • sin(37°) = opposite ÷ hypotenuse → opposite = 20 × 0.60.
  • opposite = 12 cm.
• Answer: 12 cm

[Hard] Linear Systems — Substitution

• EN: Solve the system: y = 2x + 1 and y = x + 5. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = x + 5. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Set both expressions equal to each other: 2x + 1 = x + 5, then solve for x.
• Steps:
  • Set equal: 2x + 1 = x + 5.
  • Subtract x: x + 1 = 5, so x = 4.
• Answer: x = 4

[Easy] Factoring — Common Factor

• EN: Factor the expression: 6x² + 9x.
• FR: Factorise l'expression : 6x² + 9x.
• Choices: A) 3x(2x + 3) B) 6x(x + 3) C) 3(2x² + 3x) D) 9x(x + 1)
• Hint: To factor 4x² + 8x, find the GCF (4x) and divide each term: 4x(x + 2).
• Steps:
  • GCF of 6x² and 9x is 3x.
  • Divide: 6x² ÷ 3x = 2x, 9x ÷ 3x = 3. Factored: 3x(2x + 3).
• Answer: 3x(2x + 3)

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 13 cm. Combien vaut cos(θ)?
• Choices: A) 5/12 B) 5/13 C) 12/13 D) 13/5
• Hint: CAH means cos = adjacent ÷ hypotenuse; for adjacent = 3 and hypotenuse = 5: cos = 3/5.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse = 5 ÷ 13.
  • cos(θ) = 5/13.
• Answer: 5/13

[Easy] Systems of Equations

• EN: Solve the system: x + y = 10 and x − y = 4. What is x?
• FR: Résous le système : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: To use elimination, add the two equations: (x + y) + (x − y) = 2x; solve for x, then find y.
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 4 → 2x = 14.
  • x = 7.
• Answer: x = 7

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 4 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 4 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 376.8 cm³ B) 480.0 cm³ C) 502.4 cm³ D) 628.0 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 = 3.14 × 16 × 10.
  • V = 3.14 × 160 = 502.4 cm³.
• Answer: 502.4 cm³

[Medium] Factoring Trinomials

• EN: Factor the trinomial: x² + 7x + 12.
• FR: Factorise le trinôme : x² + 7x + 12.
• Choices: A) (x + 3)(x + 4) B) (x + 2)(x + 6) C) (x + 1)(x + 12) D) (x + 4)(x + 3)
• Hint: For x² + 5x + 6, look for two numbers that multiply to 6 and add to 5: those are 2 and 3.
• Steps:
  • Find two numbers that multiply to 12 and add to 7: 3 and 4 (3 × 4 = 12; 3 + 4 = 7).
  • Factored form: (x + 3)(x + 4).
• Answer: (x + 3)(x + 4)

[Medium] Quadratic Equations — Factoring

• EN: Solve: x² − 5x + 6 = 0.
• FR: Résous : 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 = 3 or x = 4
• Hint: To solve x² − 7x + 12 = 0, factor into (x − 3)(x − 4) = 0, giving x = 3 or x = 4.
• Steps:
  • Factor: (x − 2)(x − 3) = 0. (Two numbers that multiply to 6 and add to −5: −2 and −3.)
  • Set each factor = 0: x = 2 or x = 3.
• Answer: x = 2 or x = 3

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is the circumference of the circle? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 14 cm. Quelle est la circonférence du cercle? (Utilise π ≈ 3,14)
• Choices: A) 21.98 cm B) 43.96 cm C) 87.92 cm D) 153.86 cm
• Hint: Circumference = π × d; for a diameter of 10 cm: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14.
  • C = 43.96 cm.
• Answer: 43.96 cm

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 3 cm and a slant height of 5 cm. What is the surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 3 cm et une hauteur oblique de 5 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 45.22 cm² B) 56.52 cm² C) 75.36 cm² D) 94.20 cm²
• Hint: Surface area of a cone = π × r × l + π × r²; for r = 2, l = 4: SA = 3.14(2)(4) + 3.14(4) = 37.68 cm².
• Steps:
  • SA = πrl + πr² = 3.14 × 3 × 5 + 3.14 × 9.
  • = 47.1 + 28.26 = 75.36 cm².
• Answer: 75.36 cm²

[Hard] Completing the Square

• EN: Solve by completing the square: x² + 6x − 7 = 0.
• FR: Résous en complétant le carré : x² + 6x − 7 = 0.
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 7 or x = −1 D) x = 2 or x = −8
• Hint: To complete the square for x² + 4x − 5 = 0: move 5, add (4/2)²=4: (x+2)²=9, x = 1 or x = −5.
• Steps:
  • Move constant: x² + 6x = 7. Add (6/2)² = 9 to both sides: x² + 6x + 9 = 16.
  • (x + 3)² = 16 → x + 3 = ±4. So x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Hard] Systems of Equations — Non-Linear

• EN: Where does the line y = x + 2 intersect the parabola y = x²? What are the x-values of intersection?
• FR: Où la droite y = x + 2 intersecte-t-elle la parabole y = x²? Quelles sont les valeurs de x à l'intersection?
• Choices: A) x = −1 or x = 2 B) x = 1 or x = −2 C) x = 2 or x = 3 D) x = −2 or x = 1
• Hint: Set both equations equal: x² = x + 2, then rearrange and factor to find x.
• Steps:
  • Set equal: x² = x + 2 → x² − x − 2 = 0.
  • Factor: (x − 2)(x + 1) = 0. So x = 2 or x = −1.
• Answer: x = −1 or x = 2

[Easy] Evaluating a Function

• EN: Given f(x) = 2x² − 3, find f(4).
• FR: Étant donné f(x) = 2x² − 3, trouve f(4).
• Choices: A) 26 B) 29 C) 31 D) 35
• Hint: To evaluate g(x) = 3x² − 1 at x = 2, substitute: 3(4) − 1 = 11.
• Steps:
  • Substitute x = 4: f(4) = 2(4²) − 3 = 2(16) − 3.
  • = 32 − 3 = 29.
• Answer: 29

[Easy] Arithmetic Sequences

• EN: An arithmetic sequence starts at 7 and has a common difference of 4. What is the 6th term?
• FR: Une suite arithmétique commence à 7 et a une raison de 4. Quel est le 6e terme?
• Choices: A) 25 B) 27 C) 29 D) 31
• Hint: For a sequence starting at 3 with common difference 5, the nth term = 3 + (n−1)×5; the 4th term = 3 + 15 = 18.
• Steps:
  • Use formula: aₙ = a₁ + (n−1)d = 7 + (6−1)(4) = 7 + 20.
  • The 6th term = 27.
• Answer: 27

[Easy] Logarithms Introduction

• EN: What is log₂(32)?
• FR: Combien vaut log₂(32)?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: log₂(8) = 3 because 2³ = 8; ask yourself "what power gives me the number?"
• Steps:
  • Ask: 2 to what power equals 32? 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32.
  • log₂(32) = 5.
• Answer: 5

[Easy] Compound Interest

• EN: $1000 is invested at an annual compound interest rate of 5% for 1 year. How much interest is earned?
• FR: 1000 $ sont investis à un taux d'intérêt annuel composé de 5 % pendant 1 an. Combien d'intérêts sont gagnés?
• Choices: A) $40 B) $45 C) $50 D) $55
• Hint: Interest for 1 year = Principal × Rate; for $200 at 6%: interest = 200 × 0.06 = $12.
• Steps:
  • Interest = 1000 × 0.05 × 1 = $50.
  • The interest earned is $50.
• Answer: $50

[Medium] Exponential Functions

• EN: A population of bacteria doubles every hour. If there are 500 bacteria at the start, how many will there be after 3 hours?
• FR: Une population de bactéries double chaque heure. Si on commence avec 500 bactéries, combien y en aura-t-il après 3 heures?
• Choices: A) 2000 B) 3000 C) 4000 D) 6000
• Hint: If a quantity doubles, use P × 2ⁿ; for P = 100 after 2 doublings: 100 × 2² = 400.
• Steps:
  • After 1 hour: 500 × 2 = 1000. After 2 hours: 1000 × 2 = 2000. After 3 hours: 2000 × 2 = 4000.
  • There are 4000 bacteria after 3 hours.
• Answer: 4000

[Medium] Geometric Sequences

• EN: A geometric sequence has a first term of 3 and a common ratio of 4. What is the 4th term?
• FR: Une suite géométrique a un premier terme de 3 et une raison de 4. Quel est le 4e terme?
• Choices: A) 48 B) 96 C) 192 D) 256
• Hint: For a geometric sequence with first term 2 and ratio 3, the nth term = 2 × 3^(n−1); 4th term = 2 × 27 = 54.
• Steps:
  • aₙ = a₁ × r^(n−1) = 3 × 4^(4−1) = 3 × 4³.
  • 4³ = 64; 3 × 64 = 192.
• Answer: 192

[Medium] Compound Interest — Multiple Years

• EN: $2000 is invested at 4% compounded annually for 2 years. What is the total amount after 2 years?
• FR: 2000 $ sont investis à 4 % composé annuellement pendant 2 ans. Quel est le montant total après 2 ans?
• Choices: A) $2,160.00 B) $2,163.20 C) $2,166.40 D) $2,200.00
• Hint: Use A = P(1 + r)ⁿ; for $500 at 3% for 2 years: A = 500(1.03)² = 500 × 1.0609 = $530.45.
• Steps:
  • A = 2000(1 + 0.04)² = 2000 × (1.04)².
  • (1.04)² = 1.0816; A = 2000 × 1.0816 = $2163.20.
• Answer: $2,163.20

[Medium] Trigonometric Identity

• EN: If sin²(θ) = 0.36, what is cos²(θ)?
• FR: Si sin²(θ) = 0,36, combien vaut cos²(θ)?
• Choices: A) 0.36 B) 0.60 C) 0.64 D) 1.00
• Hint: The Pythagorean identity states sin²(θ) + cos²(θ) = 1, so cos²(θ) = 1 − sin²(θ).
• Steps:
  • Use identity: sin²(θ) + cos²(θ) = 1.
  • cos²(θ) = 1 − 0.36 = 0.64.
• Answer: 0.64

[Hard] Sum of Arithmetic Series

• EN: Find the sum of the first 20 terms of an arithmetic sequence with first term 5 and common difference 3.
• FR: Trouve la somme des 20 premiers termes d'une suite arithmétique dont le premier terme est 5 et la raison est 3.
• Choices: A) 670 B) 680 C) 690 D) 700
• Hint: Sₙ = n/2 × (2a₁ + (n−1)d); for 10 terms starting at 4 with d = 2: S₁₀ = 5 × (8 + 18) = 130.
• Steps:
  • S₂₀ = 20/2 × (2(5) + (20−1)(3)) = 10 × (10 + 57).
  • = 10 × 67 = 670.
• Answer: 670

[Hard] Logarithmic Equations

• EN: Solve for x: log₃(x) + log₃(9) = 4.
• FR: Résous pour x : log₃(x) + log₃(9) = 4.
• Choices: A) x = 3 B) x = 6 C) x = 9 D) x = 27
• Hint: Use the log product rule: log(a) + log(b) = log(ab), then convert to exponential form to solve.
• Steps:
  • Combine: log₃(9x) = 4 → 3⁴ = 9x → 81 = 9x.
  • x = 81 ÷ 9 = 9.
• Answer: x = 9

[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) 25 B) 60 C) 120 D) 240
• Hint: For 4 items in a row, count down: 4 × 3 × 2 × 1 = 24.
• Steps:
  • This is 5! = 5 × 4 × 3 × 2 × 1.
  • = 120 ways.
• Answer: 120

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = x³.
• FR: Trouve la dérivée de f(x) = x³.
• Choices: A) x² B) 3x² C) 3x D) x⁴/4
• Hint: The power rule: if f(x) = xⁿ, then f'(x) = n × xⁿ⁻¹; for f(x) = x⁵, f'(x) = 5x⁴.
• Steps:
  • Apply power rule: f'(x) = 3 × x^(3−1).
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Combinations

• EN: How many ways can a committee of 3 students be chosen from a group of 6 students?
• FR: De combien de façons peut-on choisir un comité de 3 étudiants parmi un groupe de 6 étudiants?
• Choices: A) 18 B) 20 C) 24 D) 30
• Hint: C(n,r) = n! ÷ (r! × (n−r)!); for C(5,2) = 5!/(2!×3!) = 10.
• Steps:
  • C(6,3) = 6! ÷ (3! × 3!) = 720 ÷ (6 × 6) = 720 ÷ 36.
  • = 20 ways.
• Answer: 20

[Easy] Polynomial Functions

• EN: Evaluate the polynomial P(x) = 2x³ − x + 4 at x = 2.
• FR: Évalue le polynôme P(x) = 2x³ − x + 4 en x = 2.
• Choices: A) 16 B) 18 C) 20 D) 22
• Hint: Substitute the value of x into each term and calculate carefully; for P(x) = x² + 2x at x = 3: P(3) = 9 + 6 = 15.
• Steps:
  • P(2) = 2(2³) − 2 + 4 = 2(8) − 2 + 4.
  • = 16 − 2 + 4 = 18.
• Answer: 18

[Medium] Binomial Probability

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads? (Use P = C(4,3) × (0.5)⁴)
• FR: Une pièce équilibrée est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces? (Utilise P = C(4,3) × (0,5)⁴)
• Choices: A) 1/8 B) 1/4 C) 3/8 D) 1/2
• Hint: P(exactly k successes) = C(n,k) × p^k × (1−p)^(n−k); for 2 heads in 3 flips: C(3,2)×0.5³ = 3/8.
• Steps:
  • P = C(4,3) × (0.5)³ × (0.5)¹ = 4 × 0.125 × 0.5.
  • = 4 × 0.0625 = 0.25 = 1/4.
• Answer: 1/4

[Medium] Rate of Change — Derivative Applied

• EN: A ball's height in metres is given by h(t) = −5t² + 20t. What is the instantaneous rate of change (velocity) at t = 3 seconds?
• FR: La hauteur d'une balle en mètres est donnée par h(t) = −5t² + 20t. Quel est le taux de variation instantané (vitesse) à t = 3 secondes?
• Choices: A) −5 m/s B) −10 m/s C) 5 m/s D) 10 m/s
• Hint: Differentiate h(t) to get h'(t), then substitute the time value; for h(t) = −2t² + 8t, h'(t) = −4t + 8.
• Steps:
  • h'(t) = −10t + 20. Substitute t = 3: h'(3) = −10(3) + 20.
  • = −30 + 20 = −10 m/s.
• Answer: −10 m/s

[Medium] Vectors — Adding

• EN: Vector u = (3, −1) and vector v = (−1, 5). What is u + v?
• FR: Le vecteur u = (3, −1) et le vecteur v = (−1, 5). Combien font u + v?
• Choices: A) (2, 4) B) (4, 4) C) (2, 6) D) (4, 6)
• Hint: Add vectors component by component: (a, b) + (c, d) = (a+c, b+d).
• Steps:
  • Add components: (3 + (−1), −1 + 5).
  • = (2, 4).
• Answer: (2, 4)

[Medium] Rational Functions — Vertical Asymptotes

• EN: What is the vertical asymptote of the function f(x) = 5 ÷ (x − 3)?
• FR: Quelle est l'asymptote verticale de la fonction f(x) = 5 ÷ (x − 3)?
• Choices: A) x = −3 B) x = 0 C) x = 3 D) x = 5
• Hint: A vertical asymptote occurs where the denominator equals zero; for f(x) = 1/(x + 2), the asymptote is at x = −2.
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • x = 3 is the vertical asymptote.
• Answer: x = 3

[Hard] Normal Distribution

• EN: In a normal distribution, 68% of data falls within one standard deviation of the mean. The mean mark in a class is 72 with a standard deviation of 8. Between which two marks does approximately 68% of students fall?
• FR: Dans une distribution normale, 68 % des données se trouvent à un écart type de la moyenne. La note moyenne d'une classe est de 72 avec un écart type de 8. Entre quelles deux notes se trouvent approximativement 68 % des élèves?
• Choices: A) Between 60 and 84 B) Between 62 and 80 C) Between 64 and 80 D) Between 68 and 80
• Hint: For a mean of 50 and standard deviation of 10, 68% of data falls between 50 − 10 = 40 and 50 + 10 = 60.
• Steps:
  • Lower bound: 72 − 8 = 64.
  • Upper bound: 72 + 8 = 80. So 68% falls between 64 and 80.
• Answer: Between 64 and 80

[Hard] Derivative — Instantaneous Rate and Optimization

• EN: A farmer wants to maximize the area of a rectangular field enclosed by 100 m of fencing. If the field has width x, the area is A(x) = x(50 − x). What width x maximizes the area?
• FR: Un fermier veut maximiser l'aire d'un champ rectangulaire entouré de 100 m de clôture. Si la largeur du champ est x, l'aire est A(x) = x(50 − x). Quelle largeur x maximise l'aire?
• Choices: A) x = 20 m B) x = 25 m C) x = 30 m D) x = 40 m
• Hint: Expand A(x), find A'(x) using the power rule, set A'(x) = 0, and solve for x.
• Steps:
  • A(x) = 50x − x². A'(x) = 50 − 2x. Set A'(x) = 0: 50 − 2x = 0.
  • 2x = 50, so x = 25. The optimal width is 25 m.
• Answer: x = 25 m