Daily Math — 2026-08-20

[Easy] Counting to Ten

• EN: There are 7 apples on the table. How many apples are there?
• FR: Il y a 7 pommes sur la table. Combien y a-t-il de pommes ?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Count each object one by one, like counting 3 bananas: 1, 2, 3!
• Steps:
  • Count the apples one by one.
  • 1, 2, 3, 4, 5, 6, 7 — there are 7 apples.
• Answer: 7

[Easy] Simple Addition

• EN: Mia has 4 stickers. She gets 3 more. How many stickers does she have now?
• FR: Mia a 4 autocollants. Elle en reçoit 3 de plus. Combien d'autocollants a-t-elle maintenant ?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To add 2 + 3, start at 2 and count up 3 more: 3, 4, 5.
• Steps:
  • Start at 4.
  • Count up 3 more: 5, 6, 7.
  • Mia has 7 stickers.
• Answer: 7

[Easy] Simple Subtraction

• EN: There are 9 birds on a fence. 2 fly away. How many birds are left?
• FR: Il y a 9 oiseaux sur une clôture. 2 s'envolent. Combien d'oiseaux reste-t-il ?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To find 6 − 2, start at 6 and count back 2: 5, 4.
• Steps:
  • Start at 9.
  • Count back 2: 8, 7.
  • There are 7 birds left.
• Answer: 7

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes next? 2, 4, 6, ___
• FR: Compte par 2. Quel nombre vient ensuite ? 2, 4, 6, ___
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: When you skip count by 2s, add 2 each time: 10, 12, 14 — next is 16.
• Steps:
  • The pattern adds 2 each time.
  • 6 + 2 = 8.
  • The next number is 8.
• Answer: 8

[Medium] Adding Within 20

• EN: Lucas has 8 hockey cards. He finds 6 more. How many does he have in all?
• FR: Lucas a 8 cartes de hockey. Il en trouve 6 autres. Combien en a-t-il en tout ?
• Choices: A) 12 B) 13 C) 14 D) 15
• Hint: To add 5 + 7, think: 5 + 5 = 10, then 10 + 2 = 12.
• Steps:
  • Start at 8 and count up 6: 9, 10, 11, 12, 13, 14.
  • Or use the make-ten strategy: 8 + 2 = 10, then 10 + 4 = 14.
  • Lucas has 14 cards.
• Answer: 14

[Medium] Subtracting Within 20

• EN: There are 15 snowballs. Kids throw 7 of them. How many snowballs are left?
• FR: Il y a 15 boules de neige. Les enfants en lancent 7. Combien de boules de neige reste-t-il ?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To find 12 − 5, think: what plus 5 equals 12? 5 + 7 = 12, so the answer is 7.
• Steps:
  • Think: 7 + ? = 15.
  • 7 + 8 = 15.
  • There are 8 snowballs left.
• Answer: 8

[Medium] Comparing Numbers

• EN: Which number is greater: 13 or 17?
• FR: Quel nombre est plus grand : 13 ou 17 ?
• Choices: A) 13 B) 17 C) Both are equal D) Neither
• Hint: Compare 8 and 11 — 11 is farther along when counting, so 11 is greater.
• Steps:
  • Count along: 13 comes before 17.
  • The number that comes later is greater.
  • 17 is greater than 13.
• Answer: 17

[Medium] Skip Counting by 5s

• EN: Count by 5s. What number comes next? 5, 10, 15, ___
• FR: Compte par 5. Quel nombre vient ensuite ? 5, 10, 15, ___
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: Skip counting by 5s: 25, 30, 35 — add 5 each time.
• Steps:
  • Each jump adds 5.
  • 15 + 5 = 20.
  • The next number is 20.
• Answer: 20

[Hard] Coin Recognition

• EN: You have 1 dime and 1 nickel. How much money do you have in total?
• FR: Tu as 1 pièce de 10 cents et 1 pièce de 5 cents. Combien d'argent as-tu 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. If you have 2 dimes, that is 10 + 10 = 20 cents.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Hard] Addition Near 20

• EN: There are 9 children on one team and 9 children on another team. How many children are there in all?
• FR: Il y a 9 enfants dans une équipe et 9 enfants dans une autre équipe. Combien y a-t-il d'enfants en tout ?
• Choices: A) 16 B) 17 C) 18 D) 19
• Hint: For 8 + 8, think: 8 + 2 = 10, then 10 + 6 = 16.
• Steps:
  • 9 + 9 can be solved by doubling.
  • 9 + 1 = 10, so 9 + 9 = 10 + 8 = 18.
  • There are 18 children in all.
• Answer: 18

[Easy] Adding Within 100

• EN: A bookshelf has 23 books. Amara adds 14 more books. How many books are on the shelf now?
• FR: Une étagère a 23 livres. Amara en ajoute 14 autres. Combien de livres y a-t-il sur l'étagère maintenant ?
• Choices: A) 34 B) 36 C) 37 D) 39
• Hint: To add 31 + 12, add the tens first: 30 + 10 = 40, then add the ones: 1 + 2 = 3, total 43.
• Steps:
  • Add the tens: 20 + 10 = 30.
  • Add the ones: 3 + 4 = 7.
  • 30 + 7 = 37 books.
• Answer: 37

[Easy] Subtracting Within 100

• EN: There were 58 crayons in a box. 25 were taken out. How many crayons are left?
• FR: Il y avait 58 crayons dans une boîte. 25 ont été retirés. Combien de crayons reste-t-il ?
• Choices: A) 33 B) 34 C) 83 D) 35
• Hint: To find 76 − 32, subtract tens first: 70 − 30 = 40, then ones: 6 − 2 = 4, total 44.
• Steps:
  • Subtract the tens: 50 − 20 = 30.
  • Subtract the ones: 8 − 5 = 3.
  • 30 + 3 = 33 crayons.
• Answer: 33

[Easy] Telling Time (Hour)

• EN: The clock shows the short hand on 4 and the long hand on 12. What time is it?
• FR: L'aiguille courte de l'horloge est sur le 4 et la grande aiguille est sur le 12. Quelle heure est-il ?
• Choices: A) 3:00 B) 4:00 C) 5:00 D) 12:00
• Hint: When the long hand points to 12, it is exactly on the hour — look at the short hand for the hour number.
• Steps:
  • Long hand on 12 means it is exactly on the hour.
  • Short hand is on 4, so the hour is 4.
  • The time is 4:00.
• Answer: 4:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A pen is 18 cm long. Which is longer?
• FR: Un crayon mesure 14 cm. Un stylo mesure 18 cm. Lequel est le plus long ?
• Choices: A) The pencil B) The pen C) They are the same length D) Neither one
• Hint: Compare 9 cm and 12 cm — 12 is bigger, so 12 cm is longer.
• Steps:
  • Compare 14 cm and 18 cm.
  • 18 is greater than 14.
  • The pen is longer.
• Answer: The pen

[Medium] Counting Coins to $1

• EN: You have 3 quarters. How much money do you have in total?
• FR: Tu as 3 pièces de 25 cents. Combien d'argent as-tu en tout ?
• Choices: A) 55 cents B) 65 cents C) 75 cents D) 85 cents
• Hint: If you have 2 quarters, that is 25 + 25 = 50 cents. Add one more quarter to get 75 cents.
• Steps:
  • Each quarter is worth 25 cents.
  • 25 + 25 = 50, then 50 + 25 = 75.
  • You have 75 cents.
• Answer: 75 cents

[Medium] Telling Time (Half-Hour)

• EN: The short hand is between 2 and 3, and the long hand is on 6. What time is it?
• FR: La petite aiguille est entre le 2 et le 3, et la grande aiguille est sur le 6. Quelle heure est-il ?
• Choices: A) 2:00 B) 2:30 C) 3:00 D) 3:30
• Hint: When the long hand is on 6, it is half past the hour — the short hand shows which hour has just passed.
• Steps:
  • Long hand on 6 means half past.
  • Short hand is just past 2, so the hour is 2.
  • The time is 2:30.
• Answer: 2:30

[Medium] Simple Patterns

• EN: What comes next in the pattern? 10, 20, 30, 40, ___
• FR: Qu'est-ce qui vient ensuite dans cette suite ? 10, 20, 30, 40, ___
• Choices: A) 45 B) 48 C) 50 D) 55
• Hint: In the pattern 5, 10, 15, 20, each number goes up by 5, so next is 25.
• Steps:
  • Each number increases by 10.
  • 40 + 10 = 50.
  • The next number is 50.
• Answer: 50

[Medium] Adding with Regrouping

• EN: A Tim Hortons sells 47 muffins in the morning and 36 muffins in the afternoon. How many muffins are sold in all?
• FR: Un Tim Hortons vend 47 muffins le matin et 36 muffins l'après-midi. Combien de muffins sont vendus en tout ?
• Choices: A) 73 B) 83 C) 84 D) 93
• Hint: To add 38 + 25, add ones: 8 + 5 = 13, write 3 carry 1. Add tens: 3 + 2 + 1 = 6. Answer: 63.
• Steps:
  • Add the ones: 7 + 6 = 13, write 3 and carry 1.
  • Add the tens: 4 + 3 + 1 = 8.
  • Total is 83 muffins.
• Answer: 83

[Hard] Subtracting with Regrouping

• EN: A school has 72 students. 38 go on a field trip. How many students stay at school?
• FR: Une école a 72 élèves. 38 partent en excursion. Combien d'élèves restent à l'école ?
• Choices: A) 26 B) 34 C) 44 D) 46
• Hint: To find 53 − 27, regroup: borrow 1 ten from 5 tens, making 13 ones minus 7 = 6, then 4 tens minus 2 = 2, answer 26.
• Steps:
  • Cannot subtract 8 from 2, so regroup: borrow 1 ten from 7, making 12 ones.
  • 12 − 8 = 4. Then 6 tens − 3 tens = 3 tens.
  • 72 − 38 = 34 students.
• Answer: 34

[Hard] Measuring and Comparing

• EN: Sofia's ribbon is 45 cm long. She cuts off 17 cm. How long is the ribbon now?
• FR: Le ruban de Sofia mesure 45 cm. Elle en coupe 17 cm. Quelle est maintenant la longueur du ruban ?
• Choices: A) 26 cm B) 28 cm C) 30 cm D) 62 cm
• Hint: To find 63 − 28, regroup: 13 − 8 = 5, then 5 − 2 = 3, answer 35.
• Steps:
  • Cannot subtract 7 from 5, so regroup: 15 − 7 = 8.
  • 3 tens − 1 ten = 2 tens.
  • 45 − 17 = 28 cm.
• Answer: 28 cm

[Easy] Multiplication by 2

• EN: There are 6 pairs of mittens. How many mittens are there in all?
• FR: Il y a 6 paires de mitaines. Combien y a-t-il de mitaines en tout ?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: 4 pairs means 4 × 2. Think: 4 + 4 = 8.
• Steps:
  • Each pair has 2 mittens.
  • 6 × 2 = 12.
  • There are 12 mittens in all.
• Answer: 12

[Easy] Multiplication by 5

• EN: A hockey player scores 5 points in each of 4 games. How many points does he score in all?
• FR: Un joueur de hockey marque 5 points dans chacun de 4 matchs. Combien de points marque-t-il en tout ?
• Choices: A) 9 B) 15 C) 20 D) 25
• Hint: 3 × 5 = 15. Think of skip counting by 5s: 5, 10, 15.
• Steps:
  • Skip count by 5s, four times: 5, 10, 15, 20.
  • 4 × 5 = 20.
  • The player scores 20 points.
• Answer: 20

[Easy] Basic Division

• EN: 18 stickers are shared equally among 3 friends. How many stickers does each friend get?
• FR: 18 autocollants sont partagés également entre 3 amis. Combien d'autocollants chaque ami reçoit-il ?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: To find 12 ÷ 3, think: 3 × ? = 12. Since 3 × 4 = 12, the answer is 4.
• Steps:
  • Think: 3 × ? = 18.
  • 3 × 6 = 18.
  • Each friend gets 6 stickers.
• Answer: 6

[Easy] Fractions (Half)

• EN: A pizza is cut into 4 equal slices. Zara eats 2 slices. What fraction of the pizza does she eat?
• FR: Une pizza est coupée en 4 parts égales. Zara mange 2 parts. Quelle fraction de la pizza mange-t-elle ?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 3/4
• Hint: If you eat 1 piece out of 2 equal pieces, that is 1/2.
• Steps:
  • Zara eats 2 slices out of 4 total slices.
  • 2/4 is the same as 1/2.
  • Zara eats 1/2 of the pizza.
• Answer: 1/2

[Medium] Multiplication by 3

• EN: There are 7 shelves and each shelf holds 3 books. How many books are there in all?
• FR: Il y a 7 étagères et chacune contient 3 livres. Combien y a-t-il de livres en tout ?
• Choices: A) 18 B) 21 C) 24 D) 27
• Hint: 5 × 3 = 15. Skip count by 3s: 3, 6, 9, 12, 15.
• Steps:
  • Skip count by 3s, seven times: 3, 6, 9, 12, 15, 18, 21.
  • 7 × 3 = 21.
  • There are 21 books in all.
• Answer: 21

[Medium] Perimeter of a Rectangle

• EN: A garden is 5 m long and 3 m wide. What is its perimeter?
• FR: Un jardin mesure 5 m de long et 3 m de large. Quel est son périmètre ?
• Choices: A) 8 m B) 15 m C) 16 m D) 18 m
• Hint: For a rectangle that is 4 m long and 2 m wide, perimeter = 4 + 2 + 4 + 2 = 12 m.
• Steps:
  • Add all four sides: 5 + 3 + 5 + 3.
  • 5 + 5 = 10 and 3 + 3 = 6.
  • 10 + 6 = 16 m.
• Answer: 16 m

[Medium] Reading a Simple Graph

• EN: A bar graph shows: Monday 6 goals, Tuesday 4 goals, Wednesday 8 goals. How many total goals were scored?
• FR: Un diagramme à barres montre : lundi 6 buts, mardi 4 buts, mercredi 8 buts. Combien de buts ont été marqués en tout ?
• Choices: A) 14 B) 16 C) 17 D) 18
• Hint: To total up 3 + 5 + 7, add the first two: 3 + 5 = 8, then add the last: 8 + 7 = 15.
• Steps:
  • Add the goals: 6 + 4 = 10.
  • Then 10 + 8 = 18.
  • There were 18 total goals.
• Answer: 18

[Medium] Fractions (Quarter)

• EN: Oliver has 12 grapes. He gives away 1/4 of them. How many grapes does he give away?
• FR: Oliver a 12 raisins. Il en donne 1/4. Combien de raisins donne-t-il ?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: To find 1/4 of 8, divide by 4: 8 ÷ 4 = 2.
• Steps:
  • To find 1/4 of 12, divide 12 by 4.
  • 12 ÷ 4 = 3.
  • Oliver gives away 3 grapes.
• Answer: 3

[Hard] Multiplication by 4 and 10

• EN: A class has 4 tables and each table has 10 pencils. The teacher also adds 8 extra pencils. How many pencils are there in all?
• FR: Une classe a 4 tables et chaque table a 10 crayons. L'enseignante ajoute aussi 8 crayons supplémentaires. Combien y a-t-il de crayons en tout ?
• Choices: A) 42 B) 46 C) 48 D) 52
• Hint: First find 3 × 10 = 30, then add 5 extra: 30 + 5 = 35.
• Steps:
  • 4 × 10 = 40 pencils on the tables.
  • Add the 8 extra: 40 + 8 = 48.
  • There are 48 pencils in all.
• Answer: 48

[Hard] Division with Fractions Link

• EN: A baker makes 24 cookies and puts them equally into boxes of 4. She then gives 1/3 of the boxes to a neighbour. How many boxes does the neighbour receive?
• FR: Une boulangère fait 24 biscuits et les met également dans des boîtes de 4. Elle donne ensuite 1/3 des boîtes à un voisin. Combien de boîtes le voisin reçoit-il ?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: First divide to find the number of groups, then find 1/3 of that number: 1/3 of 9 = 3.
• Steps:
  • 24 ÷ 4 = 6 boxes total.
  • Find 1/3 of 6: 6 ÷ 3 = 2.
  • The neighbour receives 2 boxes.
• Answer: 2

[Easy] Multiplication Tables to 9×9

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8 ?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: To find 6 × 7, think of it as 6 × 6 = 36, then add one more 6: 36 + 6 = 42.
• Steps:
  • Recall the multiplication fact: 7 × 8.
  • 7 × 8 = 56.
  • The answer is 56.
• Answer: 56

[Easy] Decimal Place Value (Tenths)

• EN: Which decimal shows three tenths?
• FR: Quel nombre décimal représente trois dixièmes ?
• Choices: A) 0.03 B) 0.3 C) 3.0 D) 30.0
• Hint: One tenth = 0.1, two tenths = 0.2, so three tenths = 0.3.
• Steps:
  • Tenths are the first digit after the decimal point.
  • Three tenths is written as 0.3.
  • The answer is 0.3.
• Answer: 0.3

[Easy] Area of a Rectangle

• EN: A rectangle is 6 cm long and 4 cm wide. What is its area?
• FR: Un rectangle mesure 6 cm de long et 4 cm de large. Quelle est son aire ?
• Choices: A) 10 cm² B) 20 cm² C) 24 cm² D) 28 cm²
• Hint: Area of a rectangle = length × width. For a 5 cm × 3 cm rectangle: 5 × 3 = 15 cm².
• Steps:
  • Use the formula: Area = length × width.
  • Area = 6 × 4 = 24.
  • The area is 24 cm².
• Answer: 24 cm²

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 1/2?
• FR: Quelle fraction est la plus grande : 3/4 ou 1/2 ?
• Choices: A) 1/2 B) 3/4 C) They are equal D) Neither one
• Hint: Convert 1/2 to fourths: 1/2 = 2/4. Then compare 2/4 and 3/4.
• Steps:
  • Rewrite 1/2 with denominator 4: 1/2 = 2/4.
  • Compare: 3/4 vs. 2/4.
  • 3/4 is larger.
• Answer: 3/4

[Medium] Long Division Without Remainder

• EN: 84 chairs are arranged into rows of 4. How many rows are there?
• FR: 84 chaises sont disposées en rangées de 4. Combien de rangées y a-t-il ?
• Choices: A) 18 B) 21 C) 24 D) 28
• Hint: For 60 ÷ 3: 3 goes into 6 twice (20), then 3 goes into 0 zero times. Answer: 20.
• Steps:
  • How many times does 4 go into 8? Twice. 2 × 4 = 8.
  • Bring down the 4. How many times does 4 go into 4? Once.
  • 84 ÷ 4 = 21 rows.
• Answer: 21

[Medium] Long Division with Remainder

• EN: 29 students are put into groups of 6. How many full groups are there, and how many students are left over?
• FR: 29 élèves sont répartis en groupes de 6. Combien de groupes complets y a-t-il, et combien d'élèves reste-t-il ?
• Choices: A) 4 groups, remainder 3 B) 4 groups, remainder 5 C) 5 groups, remainder 1 D) 5 groups, remainder 2
• Hint: For 25 ÷ 4: 4 × 6 = 24, so 6 full groups with 1 left over — remainder 1.
• Steps:
  • 6 × 4 = 24, which is less than 29.
  • 6 × 5 = 30, which is too big.
  • 29 − 24 = 5, so 4 groups with remainder 5.
• Answer: 4 groups, remainder 5

[Medium] Elapsed Time

• EN: Hockey practice starts at 3:15 p.m. and ends at 4:45 p.m. How long is practice?
• FR: La pratique de hockey commence à 15 h 15 et se termine à 16 h 45. Quelle est la durée de la pratique ?
• Choices: A) 1 hour 15 minutes B) 1 hour 30 minutes C) 1 hour 45 minutes D) 2 hours
• Hint: From 2:10 to 3:40 — count 50 minutes to get to 3:00, then 40 more minutes = 1 hour 30 minutes total.
• Steps:
  • From 3:15 to 4:15 is exactly 1 hour.
  • From 4:15 to 4:45 is 30 more minutes.
  • Total: 1 hour 30 minutes.
• Answer: 1 hour 30 minutes

[Medium] Decimal Operations (Tenths/Hundredths)

• EN: Emma spent $3.45 on a notebook and $1.20 on a pen. How much did she spend in total?
• FR: Emma a dépensé 3,45 $ pour un cahier et 1,20 $ pour un stylo. Combien a-t-elle dépensé en tout ?
• Choices: A) $4.55 B) $4.65 C) $4.75 D) $5.65
• Hint: To add $2.30 + $1.15, line up the decimal points: 2.30 + 1.15 = 3.45.
• Steps:
  • Line up the decimal points: 3.45 + 1.20.
  • Add hundredths: 5 + 0 = 5. Add tenths: 4 + 2 = 6.
  • Add dollars: 3 + 1 = 4. Total is $4.65.
• Answer: $4.65

[Hard] Multi-Step Area Problem

• EN: A room is 9 m long and 7 m wide. A rug covers a 4 m × 3 m section. What area of the floor is NOT covered by the rug?
• FR: Une salle mesure 9 m de long et 7 m de large. Un tapis couvre une section de 4 m × 3 m. Quelle est l'aire du plancher qui n'est PAS couverte par le tapis ?
• Choices: A) 51 m² B) 55 m² C) 63 m² D) 75 m²
• Hint: Find the large area first, then subtract the small area. For an 8×6 room with a 2×3 rug: 48 − 6 = 42 m².
• Steps:
  • Total room area: 9 × 7 = 63 m².
  • Rug area: 4 × 3 = 12 m².
  • Uncovered area: 63 − 12 = 51 m².
• Answer: 51 m²

[Hard] Fraction and Decimal Connection

• EN: A marathon route is 42 km long. Runners complete 3/4 of the route on Saturday. How many kilometres do they still need to run?
• FR: Un parcours de marathon est long de 42 km. Les coureurs complètent 3/4 du parcours samedi. Combien de kilomètres leur reste-t-il à courir ?
• Choices: A) 8.5 km B) 9.5 km C) 10.5 km D) 14 km
• Hint: To find 1/4 of 40 km: divide by 4 to get 10 km. Then subtract from 40 to get 30 km remaining.
• Steps:
  • Find 3/4 of 42: 42 ÷ 4 = 10.5, then 10.5 × 3 = 31.5 km completed.
  • Subtract from total: 42 − 31.5 = 10.5 km remaining.
  • They still need to run 10.5 km.
• Answer: 10.5 km

[Easy] Multi-Digit Multiplication

• EN: A store sells 24 boxes of Tim Hortons coffee. Each box holds 12 cups. How many cups are there in all?
• FR: Un magasin vend 24 boîtes de café Tim Hortons. Chaque boîte contient 12 tasses. Combien y a-t-il de tasses en tout ?
• Choices: A) 248 B) 264 C) 288 D) 312
• Hint: To multiply 15 × 11: multiply 15 × 10 = 150, then add 15 × 1 = 15; total 165.
• Steps:
  • 24 × 12 = 24 × 10 + 24 × 2 = 240 + 48 = 288.
  • There are 288 cups in all.
• Answer: 288

[Easy] Adding Fractions with Like Denominators

• EN: Liam eats 2/8 of a pie and his sister eats 3/8 of the same pie. What fraction of the pie did they eat together?
• FR: Liam mange 2/8 d'une tarte et sa sœur mange 3/8 de la même tarte. Quelle fraction de la tarte ont-ils mangée ensemble ?
• Choices: A) 4/8 B) 5/8 C) 6/8 D) 5/16
• Hint: To add 1/5 + 2/5, keep the denominator and add the numerators: 1 + 2 = 3, so 3/5.
• Steps:
  • Same denominator (8), so add the numerators: 2 + 3 = 5.
  • The fraction is 5/8.
• Answer: 5/8

[Easy] Percentage Introduction (50%)

• EN: A bag has 40 marbles. 50% of the marbles are red. How many marbles are red?
• FR: Un sac contient 40 billes. 50 % des billes sont rouges. Combien de billes sont rouges ?
• Choices: A) 10 B) 15 C) 20 D) 25
• Hint: 50% means one half. Half of 60 is 30.
• Steps:
  • 50% means divide by 2.
  • 40 ÷ 2 = 20.
  • 20 marbles are red.
• Answer: 20

[Easy] Decimal Operations (Addition)

• EN: Maya's snowboard is 1.35 m long. Her friend's snowboard is 1.42 m long. What is the total length of both boards?
• FR: La planche à neige de Maya mesure 1,35 m. Celle de son amie mesure 1,42 m. Quelle est la longueur totale des deux planches ?
• Choices: A) 2.67 m B) 2.77 m C) 2.87 m D) 3.67 m
• Hint: To add 2.14 + 1.23, line up the decimals: 2.14 + 1.23 = 3.37.
• Steps:
  • Line up decimal points: 1.35 + 1.42.
  • Add hundredths: 5 + 2 = 7. Add tenths: 3 + 4 = 7. Add ones: 1 + 1 = 2.
  • Total is 2.77 m.
• Answer: 2.77 m

[Medium] Multi-Digit Division

• EN: 312 students need to be divided into classes of 24. How many classes are needed?
• FR: 312 élèves doivent être répartis dans des classes de 24. Combien de classes faut-il ?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To find 150 ÷ 15, think: 15 × 10 = 150, so the answer is 10.
• Steps:
  • Estimate: 24 × 10 = 240, 24 × 13 = 312.
  • Check: 24 × 13 = 24 × 10 + 24 × 3 = 240 + 72 = 312. ✓
  • 13 classes are needed.
• Answer: 13

[Medium] Subtracting Fractions with Like Denominators

• EN: A jug holds 7/10 of a litre of juice. Ethan drinks 3/10 of a litre. How much juice is left in the jug?
• FR: Un pichet contient 7/10 d'un litre de jus. Ethan boit 3/10 d'un litre. Combien de jus reste-t-il dans le pichet ?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: To subtract 5/9 − 2/9, keep the denominator and subtract numerators: 5 − 2 = 3, so 3/9.
• Steps:
  • Same denominator (10), so subtract the numerators: 7 − 3 = 4.
  • There is 4/10 of a litre left.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A storage bin is 5 m long, 3 m wide, and 2 m tall. What is its volume?
• FR: Un bac de rangement mesure 5 m de long, 3 m de large et 2 m de haut. Quel est son volume ?
• Choices: A) 16 m³ B) 24 m³ C) 30 m³ D) 36 m³
• Hint: Volume = length × width × height. For a box that is 4 × 2 × 3: 4 × 2 = 8, then 8 × 3 = 24 m³.
• Steps:
  • Volume = 5 × 3 × 2.
  • 5 × 3 = 15, then 15 × 2 = 30.
  • The volume is 30 m³.
• Answer: 30 m³

[Medium] Percentage (25%)

• EN: A winter jacket costs $80. It is on sale for 25% off. How much money is saved?
• FR: Un manteau d'hiver coûte 80 $. Il est en vente avec 25 % de réduction. Combien d'argent est économisé ?
• Choices: A) $15 B) $20 C) $25 D) $40
• Hint: 25% is the same as 1/4. To find 25% of $60, divide by 4: $60 ÷ 4 = $15.
• Steps:
  • 25% = 1/4.
  • $80 ÷ 4 = $20.
  • $20 is saved.
• Answer: $20

[Hard] Multi-Step Fractions and Decimals

• EN: Isabelle runs 3/5 of a 5 km trail on Monday and 1.8 km on Tuesday. How many kilometres does she run in total?
• FR: Isabelle court 3/5 d'un sentier de 5 km lundi et 1,8 km mardi. Combien de kilomètres court-elle en tout ?
• Choices: A) 3.8 km B) 4.8 km C) 5.2 km D) 6.8 km
• Hint: First convert the fraction to a decimal: 3/5 of 10 km = 6 km. Then add the second distance.
• Steps:
  • Find 3/5 of 5 km: 5 × (3/5) = 3 km on Monday.
  • Add Tuesday's distance: 3 + 1.8 = 4.8 km.
  • Isabelle runs 4.8 km in total.
• Answer: 4.8 km

[Hard] Percentage and Multi-Step Problem

• EN: A hockey team played 40 games. They won 10% of their games, lost 50%, and tied the rest. How many games did they tie?
• FR: Une équipe de hockey a joué 40 matchs. Elle en a gagné 10 %, perdu 50 %, et fait match nul dans le reste. Combien de matchs ont été des matchs nuls ?
• Choices: A) 12 B) 14 C) 16 D) 20
• Hint: Find the percent for each result: wins + losses = 10% + 50% = 60%. The rest is 100% − 60% = 40%.
• Steps:
  • Wins: 10% of 40 = 4 games. Losses: 50% of 40 = 20 games.
  • Ties: 40 − 4 − 20 = 16 games.
  • The team tied 16 games.
• Answer: 16

[Easy] Percent of a Number

• EN: What is 30% of 90?
• FR: Combien font 30 % de 90 ?
• Choices: A) 18 B) 24 C) 27 D) 30
• Hint: To find 20% of 50, find 10% first (50 ÷ 10 = 5), then multiply by 2: 5 × 2 = 10.
• Steps:
  • Find 10% of 90: 90 ÷ 10 = 9.
  • Multiply by 3: 9 × 3 = 27.
  • 30% of 90 is 27.
• Answer: 27

[Easy] Order of Operations (BEDMAS)

• EN: Solve: 4 + 3 × 2
• FR: Calcule : 4 + 3 × 2
• Choices: A) 10 B) 14 C) 12 D) 6
• Hint: In BEDMAS, multiplication comes before addition. For 5 + 2 × 3, multiply first: 2 × 3 = 6, then add 5 = 11.
• Steps:
  • Multiply first: 3 × 2 = 6.
  • Then add: 4 + 6 = 10.
  • The answer is 10.
• Answer: 10

[Easy] Ratios

• EN: In a bag of marbles, there are 4 blue and 6 red marbles. What is the ratio of blue to red marbles?
• FR: Dans un sac de billes, il y a 4 billes bleues et 6 billes rouges. Quel est le rapport entre les billes bleues et les billes rouges ?
• Choices: A) 2:3 B) 3:2 C) 4:10 D) 6:4
• Hint: A ratio of 8 to 12 can be simplified by dividing both by 4: 2 to 3.
• Steps:
  • Write the ratio: 4:6.
  • Simplify by dividing both by 2: 4÷2 = 2, 6÷2 = 3.
  • The ratio is 2:3.
• Answer: 2:3

[Easy] Integers Introduction

• EN: The temperature in Winnipeg is −5°C in the morning and −12°C at night. Which temperature is colder?
• FR: La température à Winnipeg est de −5 °C le matin et de −12 °C la nuit. Quelle température est la plus froide ?
• Choices: A) −5°C B) −12°C C) They are the same D) +5°C
• Hint: On a number line, −8 is to the left of −3, so −8 is colder (smaller).
• Steps:
  • On a number line, more negative means colder.
  • −12 is farther left than −5.
  • −12°C is colder.
• Answer: −12°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) 5/7 D) 8/9
• Hint: To multiply 1/2 × 2/3, multiply the numerators and denominators: (1×2)/(2×3) = 2/6 = 1/3.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • 6/12 simplifies to 1/2, but the matching choice is 6/12.
• Answer: 6/12

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en kilomètres par heure ?
• Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: Speed = distance ÷ time. If you travel 150 km in 3 hours: 150 ÷ 3 = 50 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 240 ÷ 3 = 80.
  • The car's speed is 80 km/h.
• Answer: 80 km/h

[Medium] Simple Algebraic Expressions

• EN: If n = 5, what is the value of 3n + 4?
• FR: Si n = 5, quelle est la valeur de 3n + 4 ?
• Choices: A) 12 B) 17 C) 19 D) 24
• Hint: To evaluate 2x + 6 when x = 3, substitute: 2 × 3 + 6 = 6 + 6 = 12.
• Steps:
  • Substitute n = 5 into 3n + 4.
  • 3 × 5 + 4 = 15 + 4.
  • The value is 19.
• Answer: 19

[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) 14
• Hint: Dividing by 1/4 is the same as multiplying by 4. So 2 ÷ (1/4) = 2 × 4 = 8.
• Steps:
  • 3 ÷ (1/4) = 3 × 4 = 12.
  • There are 12 servings.
• Answer: 12

[Hard] BEDMAS with Integers

• EN: Solve: (−3 + 7)² ÷ 4 − 5
• FR: Calcule : (−3 + 7)² ÷ 4 − 5
• Choices: A) −1 B) 3 C) 4 D) 11
• Hint: For (2 + 3)² ÷ 5 + 1: brackets first (5), then exponent (25), then divide (5), then add (6).
• Steps:
  • Brackets: −3 + 7 = 4.
  • Exponent: 4² = 16.
  • Divide: 16 ÷ 4 = 4. Subtract: 4 − 5 = −1.
• Answer: −1

[Hard] Multi-Step Percent and Ratio

• EN: In a class of 30 students, the ratio of girls to boys is 2:3. What percent of the class are girls?
• FR: Dans une classe de 30 élèves, le rapport filles à garçons est 2 : 3. Quel pourcentage de la classe représentent les filles ?
• Choices: A) 30% B) 33% C) 40% D) 60%
• Hint: If the ratio is 1:4, the total parts are 5. Girls = 1/5, and 1/5 as a percent is 20%.
• Steps:
  • Total parts in ratio 2:3 = 2 + 3 = 5 parts.
  • Girls = 2 parts out of 5: 2/5 of 30 = 12 girls.
  • 12/30 × 100% = 40%.
• Answer: 40%

[Easy] Integer Addition

• EN: What is −8 + 5?
• FR: Combien font −8 + 5 ?
• Choices: A) −13 B) −4 C) −3 D) 3
• Hint: For −6 + 4, start at −6 on a number line and move 4 steps right: you land on −2.
• Steps:
  • Start at −8 on the number line.
  • Move 5 steps to the right.
  • −8 + 5 = −3.
• Answer: −3

[Easy] Integer Subtraction

• EN: What is 4 − (−6)?
• FR: Combien font 4 − (−6) ?
• Choices: A) −2 B) 2 C) 8 D) 10
• Hint: Subtracting a negative is like adding a positive: 3 − (−4) = 3 + 4 = 7.
• Steps:
  • Change subtraction of a negative to addition: 4 − (−6) = 4 + 6.
  • 4 + 6 = 10.
  • The answer is 10.
• Answer: 10

[Easy] Fraction Fluency

• EN: What is 5/6 − 1/6?
• FR: Combien font 5/6 − 1/6 ?
• Choices: A) 2/3 B) 4/12 C) 5/12 D) 6/6
• Hint: To subtract 7/9 − 4/9, keep the denominator and subtract the numerators: 7 − 4 = 3, so 3/9 = 1/3.
• Steps:
  • Same denominator (6), subtract numerators: 5 − 1 = 4.
  • 4/6 simplifies to 2/3.
  • The answer is 2/3.
• Answer: 2/3

[Easy] Percentage (Discount)

• EN: A pair of skates costs $120. They are on sale for 10% off. What is the sale price?
• FR: Une paire de patins coûte 120 $. Elle est en solde à 10 % de réduction. Quel est le prix soldé ?
• Choices: A) $100 B) $108 C) $110 D) $115
• Hint: 10% of $80 = $8. Subtract: $80 − $8 = $72.
• Steps:
  • 10% of $120 = $12.
  • Sale price: $120 − $12 = $108.
  • The sale price is $108.
• Answer: $108

[Medium] One-Step Linear Equation

• EN: Solve for x: x + 9 = 22
• FR: Résous pour x : x + 9 = 22
• Choices: A) x = 11 B) x = 12 C) x = 13 D) x = 14
• Hint: To solve x + 4 = 10, subtract 4 from both sides: x = 10 − 4 = 6.
• Steps:
  • Subtract 9 from both sides: x = 22 − 9.
  • x = 13.
• Answer: x = 13

[Medium] Integer Multiplication

• EN: What is (−4) × (−7)?
• FR: Combien font (−4) × (−7) ?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: Negative × negative = positive. For (−3) × (−5) = 15.
• Steps:
  • Multiply the absolute values: 4 × 7 = 28.
  • Negative × negative = positive.
  • The answer is 28.
• Answer: 28

[Medium] Surface Area

• EN: What is the surface area of a rectangular prism that is 5 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire totale d'un prisme rectangulaire de 5 cm de long, 3 cm de large et 2 cm de haut ?
• Choices: A) 30 cm² B) 52 cm² C) 62 cm² D) 71 cm²
• Hint: Surface area = 2(lw + lh + wh). For a box 4×2×1: 2(8+4+2) = 2(14) = 28 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(5×3 + 5×2 + 3×2).
  • = 2(15 + 10 + 6) = 2(31) = 62.
  • The surface area is 62 cm².
• Answer: 62 cm²

[Medium] Data and Probability

• EN: A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 billes bleues et 2 billes vertes. Quelle est la probabilité de piger une bille bleue ?
• Choices: A) 1/4 B) 1/2 C) 5/10 D) 3/10
• Hint: Probability = favourable outcomes ÷ total outcomes. For 2 red out of 8 total: 2/8 = 1/4.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Blue marbles: 5.
  • Probability = 5/10 = 1/2.
• Answer: 1/2

[Hard] Percentage (Tax and Tip)

• EN: A restaurant meal costs $32.00. HST is 13% and you want to leave a 15% tip on the original price. What is the total amount paid?
• FR: Un repas au restaurant coûte 32,00 $. La TVH est de 13 % et tu veux laisser un pourboire de 15 % sur le prix d'origine. Quel est le montant total payé ?
• Choices: A) $37.76 B) $40.96 C) $44.16 D) $45.76
• Hint: For a $20 meal with 10% tax and 10% tip: tax = $2, tip = $2, total = $20 + $2 + $2 = $24.
• Steps:
  • Tax: 13% of $32 = 0.13 × 32 = $4.16.
  • Tip: 15% of $32 = 0.15 × 32 = $4.80.
  • Total: $32 + $4.16 + $4.80 = $40.96.
• Answer: $40.96

[Hard] Multi-Step Equation and Integers

• EN: The temperature drops by 4°C each hour. Starting at 6°C, after how many hours will it reach −10°C?
• FR: La température baisse de 4 °C par heure. En partant de 6 °C, après combien d'heures atteindra-t-elle −10 °C ?
• Choices: A) 3 hours B) 4 hours C) 5 hours D) 6 hours
• Hint: Set up an equation: start − (rate × hours) = target. For start 8, rate 3, target −4: 8 − 3h = −4, so 3h = 12, h = 4.
• Steps:
  • We need 6 − 4h = −10.
  • Subtract 6 from both sides: −4h = −16.
  • h = 4. After 4 hours.
• Answer: 4 hours

[Easy] Square Roots

• EN: What is √144?
• FR: Combien fait √144 ?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To find √81, think: what number times itself equals 81? 9 × 9 = 81, so √81 = 9.
• Steps:
  • Ask: what number times itself equals 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Perfect Squares

• EN: Which of the following is a perfect square?
• FR: Lequel des nombres suivants est un carré parfait ?
• Choices: A) 18 B) 24 C) 36 D) 48
• Hint: A perfect square has a whole number square root. 4 × 4 = 16, so 16 is a perfect square.
• Steps:
  • Check each: √18 ≈ 4.2 (not whole), √24 ≈ 4.9 (not whole).
  • √36 = 6 (whole number). ✓
  • 36 is a perfect square.
• Answer: 36

[Easy] Mean

• EN: Find the mean of these scores: 8, 12, 10, 14, 6.
• FR: Trouve la moyenne de ces résultats : 8, 12, 10, 14, 6.
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Mean = sum of all values ÷ number of values. For 4, 6, 8: sum = 18, count = 3, mean = 6.
• Steps:
  • Sum: 8 + 12 + 10 + 14 + 6 = 50.
  • Divide by the count: 50 ÷ 5 = 10.
  • The mean is 10.
• Answer: 10

[Easy] Percent Increase

• EN: A loonie buys you 5 candies. After a price change, it now buys only 4 candies. What is the percent decrease in candies you receive?
• FR: Un huard t'achète 5 bonbons. Après un changement de prix, tu n'en reçois plus que 4. Quel est le pourcentage de diminution de bonbons que tu reçois ?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: Percent decrease = (decrease ÷ original) × 100. For dropping from 10 to 8: (2 ÷ 10) × 100 = 20%.
• Steps:
  • Decrease in candies: 5 − 4 = 1.
  • Percent decrease: (1 ÷ 5) × 100 = 20%.
  • The decrease is 20%.
• Answer: 20%

[Medium] Two-Step Linear Equation

• EN: Solve for x: 3x − 7 = 14
• FR: Résous pour x : 3x − 7 = 14
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: For 2x + 3 = 11: subtract 3 from both sides (2x = 8), then divide by 2 (x = 4).
• Steps:
  • Add 7 to both sides: 3x = 21.
  • Divide both sides by 3: x = 7.
• Answer: x = 7

[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 a right triangle with legs 3 and 4: 3² + 4² = 9 + 16 = 25, so the hypotenuse = √25 = 5.
• Steps:
  • a² + b² = c². So 6² + 8² = c².
  • 36 + 64 = 100. c = √100 = 10.
  • The hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A line passes through (0, 2) and (4, 10). What is the slope of the line?
• FR: Une droite passe par (0, 2) et (4, 10). Quelle est la pente de la droite ?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁). From (0,1) to (3,7): slope = (7−1)÷(3−0) = 6÷3 = 2.
• Steps:
  • Rise = 10 − 2 = 8. Run = 4 − 0 = 4.
  • Slope = 8 ÷ 4 = 2.
  • The slope is 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of the data: 3, 7, 5, 9, 5, 11, 4.
• FR: Trouve la médiane des données suivantes : 3, 7, 5, 9, 5, 11, 4.
• Choices: A) 4 B) 5 C) 7 D) 9
• Hint: To find the median, arrange data in order and pick the middle value. For 2, 4, 6, 8, 10 the middle (3rd) value is 6.
• Steps:
  • Arrange in order: 3, 4, 5, 5, 7, 9, 11.
  • Middle value (4th of 7): 5.
  • The median is 5.
• Answer: 5

[Hard] Pythagorean Theorem (Multi-Step)

• EN: A ladder leans against a wall. The base of the ladder is 5 m from the wall, and the ladder reaches 12 m up the wall. How long is the ladder?
• FR: Une échelle est appuyée contre un mur. La base de l'échelle est à 5 m du mur, et l'échelle atteint 12 m de hauteur sur le mur. Quelle est la longueur de l'échelle ?
• Choices: A) 11 m B) 13 m C) 15 m D) 17 m
• Hint: For legs 8 and 15: 8² + 15² = 64 + 225 = 289, and √289 = 17.
• Steps:
  • Use: ladder² = 5² + 12².
  • 25 + 144 = 169. Ladder = √169 = 13 m.
  • The ladder is 13 m long.
• Answer: 13 m

[Hard] Two-Step Equations and Percent

• EN: After a 20% price increase, a hockey stick costs $96. What was the original price?
• FR: Après une augmentation de prix de 20 %, un bâton de hockey coûte 96 $. Quel était le prix d'origine ?
• Choices: A) $72 B) $76 C) $80 D) $84
• Hint: If a price increases by 10% to become $55, the original is: $55 ÷ 1.10 = $50.
• Steps:
  • Let the original price = p. After 20% increase: p × 1.20 = $96.
  • p = $96 ÷ 1.20 = $80.
  • The original price was $80.
• Answer: $80

[Easy] Solving a Linear Equation

• EN: Solve for x: 2x + 6 = 20
• FR: Résous pour x : 2x + 6 = 20
• Choices: A) x = 5 B) x = 7 C) x = 9 D) x = 13
• Hint: For 3x + 2 = 11: subtract 2 (3x = 9), then divide by 3 (x = 3).
• Steps:
  • Subtract 6 from both sides: 2x = 14.
  • Divide by 2: x = 7.
• Answer: x = 7

[Easy] Adding Polynomials

• EN: Add: (3x + 5) + (2x − 3)
• FR: Additionne : (3x + 5) + (2x − 3)
• Choices: A) 4x + 2 B) 5x + 2 C) 5x + 8 D) 6x − 2
• Hint: To add (4a + 1) + (3a + 2), combine like terms: 4a + 3a = 7a and 1 + 2 = 3, giving 7a + 3.
• Steps:
  • Combine x-terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2.
  • Result: 5x + 2.
• Answer: 5x + 2

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 4x − 3?
• FR: Quelle est la pente de la droite y = 4x − 3 ?
• Choices: A) −4 B) −3 C) 3 D) 4
• Hint: In y = mx + b, the slope is m. For y = 5x + 1, the slope is 5.
• Steps:
  • The equation is in y = mx + b form.
  • The coefficient of x is 4, so the slope is 4.
• Answer: 4

[Easy] Linear Inequality

• EN: Solve: x − 4 > 3
• FR: Résous : x − 4 > 3
• Choices: A) x > 5 B) x > 6 C) x > 7 D) x > 8
• Hint: For x − 2 > 5: add 2 to both sides, giving x > 7.
• Steps:
  • Add 4 to both sides: x > 3 + 4.
  • x > 7.
• Answer: x > 7

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 4)
• FR: Développe : (x + 3)(x + 4)
• Choices: A) x² + 6x + 12 B) x² + 7x + 12 C) x² + 7x + 7 D) x² + 12x + 12
• Hint: Use FOIL: (x+1)(x+2) = x² + 2x + x + 2 = x² + 3x + 2.
• Steps:
  • First: x × x = x². Outer: x × 4 = 4x. Inner: 3 × x = 3x. Last: 3 × 4 = 12.
  • Combine: x² + 4x + 3x + 12 = x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have sides in a ratio of 2:5. The smaller triangle has a side of 6 cm. What is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés dans un rapport de 2 : 5. Le plus petit triangle a un côté de 6 cm. Quel est le côté correspondant du plus grand triangle ?
• Choices: A) 12 cm B) 15 cm C) 18 cm D) 24 cm
• Hint: If similar triangles have ratio 3:4 and the small side is 9, multiply: 9 × (4/3) = 12 cm.
• Steps:
  • Ratio is 2:5. Scale factor = 5/2.
  • Large side = 6 × (5/2) = 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 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 ?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: sin(angle) = opposite ÷ hypotenuse. For a 45° angle with hypotenuse 8: sin(45°) ≈ 0.707, so opposite ≈ 5.66 cm.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse.
  • 0.5 = opposite ÷ 10.
  • Opposite = 10 × 0.5 = 5 cm.
• Answer: 5 cm

[Medium] Graphing a Line

• EN: What is the y-intercept of the line y = −2x + 7?
• FR: Quel est l'ordonnée à l'origine de la droite y = −2x + 7 ?
• Choices: A) −7 B) −2 C) 2 D) 7
• Hint: In y = mx + b, the y-intercept is b. For y = 3x + 5, the y-intercept is 5.
• Steps:
  • The equation is y = −2x + 7, which is y = mx + b form.
  • The y-intercept (b) is 7.
• Answer: 7

[Hard] System of Linear Equations

• EN: Solve the system: y = 2x + 1 and y = −x + 7. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = −x + 7. Quelle est la valeur de x ?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the two equations equal: if y = x + 3 and y = −2x + 9, then x + 3 = −2x + 9, so 3x = 6, x = 2.
• Steps:
  • Set equal: 2x + 1 = −x + 7.
  • 3x = 6, so x = 2.
• Answer: x = 2

[Hard] Trigonometry (CAH and Multi-Step)

• EN: A surveyor stands 40 m from a building. The angle of elevation to the top is 35°. Approximately how tall is the building? (Use tan 35° ≈ 0.700)
• FR: Un arpenteur-géomètre se trouve à 40 m d'un bâtiment. L'angle d'élévation vers le sommet est de 35°. Quelle est approximativement la hauteur du bâtiment ? (Utilise tan 35° ≈ 0,700)
• Choices: A) 22 m B) 28 m C) 35 m D) 57 m
• Hint: tan(angle) = opposite ÷ adjacent. Opposite = adjacent × tan(angle). For 30 m away at 40°: height = 30 × tan(40°) ≈ 30 × 0.839 ≈ 25 m.
• Steps:
  • tan(35°) = height ÷ 40.
  • Height = 40 × 0.700 = 28.
  • The building is approximately 28 m tall.
• Answer: 28 m

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6
• FR: Factorise : x² + 5x + 6
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 2)(x + 4) D) (x + 3)(x + 3)
• Hint: Find two numbers that multiply to 10 and add to 7: 2 and 5. So x² + 7x + 10 = (x+2)(x+5).
• Steps:
  • Find two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5. ✓
  • x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry (All Ratios)

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 8 cm et l'hypoténuse mesure 10 cm. Combien fait cos(θ) ?
• Choices: A) 0.6 B) 0.75 C) 0.8 D) 1.25
• Hint: cos(θ) = adjacent ÷ hypotenuse. For adjacent = 3 and hypotenuse = 5: cos(θ) = 3/5 = 0.6.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 8 ÷ 10 = 0.8.
• Answer: 0.8

[Easy] Volume of a Cylinder

• EN: A cylindrical can has radius 3 cm and height 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte de conserve cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume ? (Utilise π ≈ 3,14)
• Choices: A) 188.4 cm³ B) 251.2 cm³ C) 282.6 cm³ D) 314 cm³
• Hint: Volume of a cylinder = π × r² × h. For r = 2 and h = 5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 3² × 10.
  • = 3.14 × 9 × 10 = 3.14 × 90 = 282.6.
  • The volume is 282.6 cm³.
• Answer: 282.6 cm³

[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: Add both equations together to eliminate y. For x + y = 8 and x − y = 2: 2x = 10, so x = 5.
• Steps:
  • Add the equations: (x + y) + (x − y) = 10 + 4.
  • 2x = 14, so x = 7.
• Answer: x = 7

[Medium] Completing the Square

• EN: Solve x² + 6x + 5 = 0 by factoring. What are the solutions?
• FR: Résous x² + 6x + 5 = 0 par factorisation. Quelles sont les solutions ?
• Choices: A) x = −1 and x = −5 B) x = 1 and x = 5 C) x = −2 and x = −3 D) x = 2 and x = 3
• Hint: For x² + 7x + 12 = 0: find factors of 12 that add to 7 (3 and 4), so (x+3)(x+4)=0, giving x = −3 or x = −4.
• Steps:
  • Factor: find numbers that multiply to 5 and add to 6: 1 and 5.
  • (x + 1)(x + 5) = 0.
  • x = −1 or x = −5.
• Answer: x = −1 and x = −5

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is its circumference? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence ? (Utilise π ≈ 3,14)
• Choices: A) 22 cm B) 43.96 cm C) 87.92 cm D) 153.86 cm
• Hint: Circumference = π × diameter. For a circle with diameter 10: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14.
  • 3.14 × 14 = 43.96.
  • The circumference is 43.96 cm.
• Answer: 43.96 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 6 = 0. Quelles sont les solutions ?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = −2 and x = −3 D) x = 3 and x = 4
• Hint: x = [−b ± √(b²−4ac)] ÷ 2a. For x² − 7x + 12 = 0: discriminant = 49 − 48 = 1, so x = (7 ± 1)/2, giving x = 4 or x = 3.
• Steps:
  • a=1, b=−5, c=6. Discriminant: (−5)²−4(1)(6) = 25−24 = 1.
  • x = (5 ± 1)/2, giving x = 3 or x = 2.
• Answer: x = 2 and x = 3

[Medium] Surface Area of a Cone

• EN: A cone has radius 3 cm and slant height 5 cm. What is its total 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) 37.68 cm² B) 47.1 cm² C) 75.36 cm² D) 94.2 cm²
• Hint: Surface area of cone = πr² + πrl. For r=2, l=4: SA = 3.14(4) + 3.14(2)(4) = 12.56 + 25.12 = 37.68 cm².
• Steps:
  • SA = πr² + πrl = 3.14(9) + 3.14(3)(5).
  • = 28.26 + 47.10 = 75.36.
  • Total surface area is 75.36 cm².
• Answer: 75.36 cm²

[Hard] System of Equations with Quadratics

• EN: Solve the system: y = x² and y = x + 6. What are the x-values where the graphs intersect?
• FR: Résous le système : y = x² et y = x + 6. Quelles sont les valeurs de x où les graphiques se croisent ?
• Choices: A) x = −2 and x = 3 B) x = 2 and x = −3 C) x = −1 and x = 6 D) x = 3 and x = 6
• Hint: Set x² = x + 6, rearrange to x² − x − 6 = 0, then factor. For x² − x − 2 = 0: (x−2)(x+1) = 0.
• Steps:
  • Set equal: x² = x + 6, so x² − x − 6 = 0.
  • Factor: (x − 3)(x + 2) = 0.
  • x = 3 or x = −2.
• Answer: x = −2 and x = 3

[Hard] Circle Geometry — Chord and Angles

• EN: An inscribed angle in a circle intercepts an arc of 110°. What is the measure of the inscribed angle?
• FR: Un angle inscrit dans un cercle intercepte un arc de 110°. Quelle est la mesure de l'angle inscrit ?
• Choices: A) 35° B) 45° C) 55° D) 110°
• Hint: The inscribed angle theorem states that an inscribed angle is half the intercepted arc. For an arc of 80°: inscribed angle = 40°.
• Steps:
  • Inscribed angle = intercepted arc ÷ 2.
  • 110° ÷ 2 = 55°.
  • The inscribed angle is 55°.
• Answer: 55°

[Easy] Exponential Functions

• EN: A bacteria colony doubles every hour. If you start with 50 bacteria, how many will there be after 3 hours?
• FR: Une colonie de bactéries double chaque heure. Si tu commences avec 50 bactéries, combien y en aura-t-il après 3 heures ?
• Choices: A) 150 B) 300 C) 400 D) 450
• Hint: If you start with 10 and double 3 times: 10 × 2³ = 10 × 8 = 80.
• Steps:
  • Use the formula: amount = 50 × 2³.
  • 2³ = 8. 50 × 8 = 400.
  • There will be 400 bacteria.
• Answer: 400

[Easy] Logarithm Introduction

• EN: Evaluate: log₂(16)
• FR: Évalue : log₂(16)
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log₂(8) asks "2 to what power equals 8?" Since 2³ = 8, the answer is 3.
• Steps:
  • log₂(16) asks: "2 to what power equals 16?"
  • 2⁴ = 16.
  • log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequence

• EN: Find the 10th term of the arithmetic sequence: 3, 7, 11, 15, …
• FR: Trouve le 10e terme de la suite arithmétique : 3, 7, 11, 15, …
• Choices: A) 35 B) 38 C) 39 D) 43
• Hint: For a sequence starting at 2 with common difference 3, the nth term is 2 + (n−1)×3. The 5th term = 2 + 4×3 = 14.
• Steps:
  • First term (a) = 3, common difference (d) = 4.
  • 10th term = a + (n−1)d = 3 + 9 × 4 = 3 + 36 = 39.
• Answer: 39

[Easy] Compound Interest

• EN: $1000 is invested at 5% interest compounded annually. What is the amount after 2 years?
• FR: 1 000 $ est investi à un taux d'intérêt de 5 % composé annuellement. Quel est le montant après 2 ans ?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1105.00
• Hint: Use A = P(1 + r)ⁿ. For $500 at 4% for 2 years: A = 500 × 1.04² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000 × (1.05)².
  • (1.05)² = 1.1025. 1000 × 1.1025 = $1102.50.
• Answer: $1102.50

[Medium] Geometric Series Sum

• EN: Find the sum of the first 5 terms of the geometric series where a = 2 and common ratio r = 3.
• FR: Trouve la somme des 5 premiers termes de la série géométrique où a = 2 et le rapport commun r = 3.
• Choices: A) 180 B) 210 C) 242 D) 320
• Hint: Sum of n terms of a geometric series: Sₙ = a(rⁿ − 1)/(r − 1). For a=1, r=2, n=4: S = 1(16−1)/(2−1) = 15.
• Steps:
  • S₅ = 2(3⁵ − 1)/(3 − 1) = 2(243 − 1)/2 = 242.
  • The sum is 242.
• Answer: 242

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ
• FR: Simplifie : sin²θ + cos²θ
• Choices: A) 0 B) 1 C) 2sinθcosθ D) tan²θ
• Hint: The Pythagorean identity is one of the most fundamental in trigonometry — it equals a whole number.
• Steps:
  • This is the Pythagorean identity.
  • sin²θ + cos²θ = 1 for all values of θ.
• Answer: 1

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = (x − 3)² + 5?
• FR: Quel est le sommet de la parabole y = (x − 3)² + 5 ?
• Choices: A) (−3, 5) B) (3, −5) C) (3, 5) D) (5, 3)
• Hint: In vertex form y = (x − h)² + k, the vertex is at (h, k). For y = (x − 2)² + 7, vertex is (2, 7).
• Steps:
  • The equation is in vertex form y = (x − h)² + k.
  • h = 3 and k = 5.
  • Vertex is (3, 5).
• Answer: (3, 5)

[Medium] Annuity (Future Value)

• EN: Maya deposits $200 per month into an account at 6% annual interest (0.5% per month) for 12 months. What is the approximate future value? (Use Sₙ = R[(1+i)ⁿ − 1]/i with (1.005)¹² ≈ 1.0617)
• FR: Maya dépose 200 $ par mois dans un compte à 6 % d'intérêt annuel (0,5 % par mois) pendant 12 mois. Quelle est la valeur future approximative ? (Utilise Sₙ = R[(1+i)ⁿ − 1]/i avec (1,005)¹² ≈ 1,0617)
• Choices: A) $2 234 B) $2 400 C) $2 468 D) $2 614
• Hint: For $100/month at 1% per month for 6 months: S = 100[(1.01)⁶ − 1]/0.01 ≈ 100[0.0615]/0.01 = $615.
• Steps:
  • S = 200 × [(1.0617 − 1) / 0.005] = 200 × [0.0617 / 0.005].
  • = 200 × 12.34 = $2468.
  • The approximate future value is $2 468.
• Answer: $2 468

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(x − 2) = log₃(8)
• FR: Résous pour x : log₃(x) + log₃(x − 2) = log₃(8)
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Combine logs: logₐ(m) + logₐ(n) = logₐ(mn). For log₂(x) + log₂(3) = log₂(12): x × 3 = 12, so x = 4.
• Steps:
  • Combine: log₃(x(x−2)) = log₃(8).
  • So x(x−2) = 8, giving x² − 2x − 8 = 0.
  • Factor: (x−4)(x+2) = 0. Since x > 2, x = 4.
• Answer: x = 4

[Hard] Compound Interest — Solving for Time

• EN: How many years will it take for $500 to double at 7% annual compound interest? (Use log 2 ÷ log 1.07 ≈ 10.24)
• FR: Combien d'années faudra-t-il pour que 500 $ doublent à un taux d'intérêt composé annuel de 7 % ? (Utilise log 2 ÷ log 1,07 ≈ 10,24)
• Choices: A) Approximately 7 years B) Approximately 9 years C) Approximately 10 years D) Approximately 12 years
• Hint: Solve 1000 = 500(1.07)ⁿ: divide to get 2 = (1.07)ⁿ, then use logs: n = log(2)/log(1.07).
• Steps:
  • Set up: 2 = (1.07)ⁿ. Take logs of both sides.
  • n = log(2) ÷ log(1.07) ≈ 10.24.
  • It takes approximately 10 years.
• Answer: Approximately 10 years

[Easy] Permutations

• EN: How many ways can 5 students line up in a row?
• FR: De combien de façons 5 élèves peuvent-ils se mettre en file ?
• Choices: A) 25 B) 60 C) 100 D) 120
• Hint: For 3 people in a row: 3 × 2 × 1 = 6 ways.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

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

[Easy] Polynomial Function — End Behaviour

• EN: For the polynomial f(x) = −x³ + 2x + 1, as x → +∞, what happens to f(x)?
• FR: Pour le polynôme f(x) = −x³ + 2x + 1, lorsque x → +∞, que se passe-t-il avec f(x) ?
• Choices: A) f(x) → +∞ B) f(x) → −∞ C) f(x) → 0 D) f(x) → 1
• Hint: For an odd-degree polynomial with a negative leading coefficient, as x→+∞ the function goes to −∞.
• Steps:
  • Leading term is −x³ with negative coefficient.
  • Odd degree, negative leading coefficient: as x→+∞, f(x)→−∞.
• Answer: f(x) → −∞

[Easy] Derivative Introduction (Rate of Change)

• EN: The position of a car is given by s(t) = 4t² (in metres). What is the instantaneous velocity at t = 3 seconds? (Derivative of 4t² is 8t)
• FR: La position d'une voiture est donnée par s(t) = 4t² (en mètres). Quelle est la vitesse instantanée à t = 3 secondes ? (La dérivée de 4t² est 8t)
• Choices: A) 12 m/s B) 18 m/s C) 24 m/s D) 36 m/s
• Hint: To find velocity from s(t) = 3t², the derivative is 6t. At t = 2: v = 6 × 2 = 12 m/s.
• Steps:
  • Velocity = s'(t) = 8t.
  • At t = 3: v = 8 × 3 = 24 m/s.
• Answer: 24 m/s

[Medium] Binomial Distribution

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
• FR: Une pièce équilibrée est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces ?
• Choices: A) 1/16 B) 3/16 C) 4/16 D) 6/16
• Hint: P(X=k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ. For flipping 3 coins and getting exactly 2 heads: C(3,2) × (1/2)² × (1/2)¹ = 3 × 1/8 = 3/8.
• Steps:
  • P(X=3) = C(4,3) × (1/2)³ × (1/2)¹.
  • = 4 × (1/8) × (1/2) = 4/16.
• Answer: 4/16

[Medium] Rational Functions — Asymptote

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

[Medium] Vectors — Addition

• EN: Vector u = (3, 4) and vector v = (−1, 2). What is u + v?
• FR: Le vecteur u = (3, 4) et le vecteur v = (−1, 2). Combien fait u + v ?
• Choices: A) (1, 5) B) (2, 6) C) (2, 5) D) (4, 6)
• Hint: To add (5, 3) + (−2, 4), add the x-components and y-components: (5+(−2), 3+4) = (3, 7).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: 4 + 2 = 6.
  • u + v = (2, 6).
• Answer: (2, 6)

[Medium] Derivative — Power Rule

• EN: Find the derivative of f(x) = 5x³ − 2x + 7.
• FR: Trouve la dérivée de f(x) = 5x³ − 2x + 7.
• Choices: A) 5x² − 2 B) 10x² − 2x C) 15x² − 2 D) 15x³ − 2
• Hint: Power rule: derivative of axⁿ is n·axⁿ⁻¹. For 4x³ − 3x + 1: derivative is 12x² − 3.
• Steps:
  • Derivative of 5x³ is 3 × 5x² = 15x².
  • Derivative of −2x is −2. Derivative of 7 (constant) is 0.
  • f'(x) = 15x² − 2.
• Answer: 15x² − 2

[Hard] Probability Distribution — Expected Value

• EN: A game gives $10 with probability 1/4, $4 with probability 1/2, and $0 with probability 1/4. What is the expected value of one play?
• FR: Un jeu rapporte 10 $ avec une probabilité de 1/4, 4 $ avec une probabilité de 1/2 et 0 $ avec une probabilité de 1/4. Quelle est l'espérance mathématique d'un seul jeu ?
• Choices: A) $3.50 B) $4.00 C) $4.50 D) $5.00
• Hint: Expected value = Σ(value × probability). For $6 with prob 1/3 and $0 with prob 2/3: E = 6 × (1/3) + 0 × (2/3) = $2.
• Steps:
  • E = 10×(1/4) + 4×(1/2) + 0×(1/4).
  • = 2.50 + 2.00 + 0 = $4.50.
  • The expected value is $4.50.
• Answer: $4.50

[Hard] Vector Dot Product and Angle

• EN: Find the dot product of u = (2, 5) and v = (4, −1).
• FR: Trouve le produit scalaire de u = (2, 5) et v = (4, −1).
• Choices: A) −3 B) 3 C) 7 D) 28
• Hint: Dot product = (u₁ × v₁) + (u₂ × v₂). For (3, 4)·(2, −1) = 6 + (−4) = 2.
• Steps:
  • u · v = (2 × 4) + (5 × (−1)).
  • = 8 + (−5) = 3.
  • The dot product is 3.
• Answer: 3