Daily Math — 2026-08-25

[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) 10 B) 11 C) 12 D) 13
• Hint: Count on from the bigger number — like 8 + 4, start at 8 and count up 4 more.
• Steps:
  • Start at 7 (the bigger number).
  • Count on 5 more: 8, 9, 10, 11, 12.
  • So the total is 12.
• Answer: 12

[Easy] 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) 28
• Hint: When you skip count by 5s, you always add 5 each time — like 10, 15, 20 means add 5.
• Steps:
  • The pattern adds 5 each time.
  • 20 + 5 = 25.
  • So the next number is 25.
• Answer: 25

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est plus grand: 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 18
• Hint: A number with a tens digit is always bigger than a one-digit number — like 12 is bigger than 7.
• Steps:
  • 14 has a 1 in the tens place, so it is at least 10.
  • 9 has no tens — it is less than 10.
  • So 14 is greater than 9.
• Answer: 14

[Easy] Coin Recognition

• EN: You have 1 dime and 1 nickel. How many cents do you have in all?
• FR: Tu as 1 pièce de 10 cents et 1 pièce de 5 cents. Combien de cents 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 — add them together.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Medium] Addition Within 20

• EN: Mia has 8 stickers and her friend gives her 7 more. How many stickers does Mia have now?
• FR: Mia a 8 autocollants et son amie lui en donne 7 de plus. Combien d'autocollants Mia a-t-elle maintenant?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Make a ten first — like 9 + 6, take 1 from 6 to make 10, then add 5 more to get 15.
• Steps:
  • Start with 8. Take 2 from 7 to make 10.
  • Now add the remaining 5: 10 + 5 = 15.
  • So Mia has 15 stickers.
• Answer: 15

[Medium] Subtraction Within 20

• EN: There are 16 kids on the playground. 9 go inside. How many kids are still outside?
• FR: Il y a 16 enfants dans la cour d'école. 9 rentrent à l'intérieur. Combien d'enfants sont encore dehors?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Count back from the bigger number — like 14 minus 6, count back 6 from 14.
• Steps:
  • Start at 16 and count back 9.
  • 16 → 15, 14, 13, 12, 11, 10, 9, 8, 7.
  • So 7 kids are still outside.
• Answer: 7

[Medium] Skip Counting by 2s

• EN: Count by 2s to find the missing number: 2, 4, 6, ___, 10.
• FR: Compte par bonds de 2 pour trouver le nombre manquant: 2, 4, 6, ___, 10.
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Skip counting by 2s means add 2 each time — like 4, 6, 8 adds 2 each step.
• Steps:
  • The pattern adds 2 each time.
  • 6 + 2 = 8.
  • Check: 8 + 2 = 10. ✓
• Answer: 8

[Medium] Counting On

• EN: There are 13 hockey cards in a box. You add 4 more. How many cards are there now?
• FR: Il y a 13 cartes de hockey dans une boîte. Tu en ajoutes 4 de plus. Combien de cartes y a-t-il maintenant?
• Choices: A) 16 B) 17 C) 18 D) 19
• Hint: Start at the bigger number and count on — like 11 + 3, start at 11 and count 12, 13, 14.
• Steps:
  • Start at 13.
  • Count on 4: 14, 15, 16, 17.
  • So there are 17 cards.
• Answer: 17

[Hard] Two-Step Problem

• EN: There are 6 red mittens and 6 blue mittens on a shelf. Then 3 mittens fall off. How many mittens are on the shelf now?
• FR: Il y a 6 mitaines rouges et 6 mitaines bleues sur une étagère. Ensuite, 3 mitaines tombent. Combien de mitaines restent sur l'étagère?
• Choices: A) 8 B) 9 C) 10 D) 12
• Hint: First add all the mittens together, then subtract the ones that fell — like 5 + 5 = 10, then 10 − 2 = 8.
• Steps:
  • First: 6 + 6 = 12 mittens in total.
  • Then: 12 − 3 = 9 mittens left.
  • So there are 9 mittens on the shelf.
• Answer: 9

[Hard] Number Sense

• EN: What number is 10 more than 17?
• FR: Quel nombre est 10 de plus que 17?
• Choices: A) 7 B) 21 C) 27 D) 28
• Hint: Adding 10 always makes the tens digit go up by 1 — like 10 more than 23 is 33.
• Steps:
  • Start at 17.
  • Add 10: the tens digit goes from 1 to 2, the ones digit stays at 7.
  • So 10 more than 17 is 27.
• Answer: 27

[Easy] Addition Within 100

• EN: There are 34 students in one classroom and 25 students in another. How many students are there in all?
• FR: Il y a 34 élèves dans une classe et 25 élèves dans une autre. Combien d'élèves y a-t-il en tout?
• Choices: A) 57 B) 58 C) 59 D) 61
• Hint: Add the tens first, then add the ones — like 31 + 24, add 30 + 20 = 50, then 1 + 4 = 5, total 55.
• Steps:
  • Tens: 30 + 20 = 50.
  • Ones: 4 + 5 = 9.
  • 50 + 9 = 59.
• 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) 5:00
• Hint: When the minute hand points to 12, it is exactly on the hour — like the hour hand on 7 means 7:00.
• Steps:
  • The hour hand points to 3.
  • The minute hand points to 12 — that means exactly on the hour.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long and a crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 15 cm et un crayon de couleur mesure 9 cm. De combien le crayon à mine est-il plus long?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: To find how much longer, subtract the shorter length from the longer one — like 18 cm − 11 cm = 7 cm.
• Steps:
  • Subtract: 15 − 9.
  • 15 − 9 = 6.
  • The pencil is 6 cm longer.
• Answer: 6 cm

[Easy] Counting Coins

• EN: You have 2 dimes and 1 nickel. How much money do you have?
• FR: Tu as 2 pièces de 10 cents et 1 pièce de 5 cents. Combien d'argent as-tu?
• Choices: A) 20 cents B) 22 cents C) 25 cents D) 30 cents
• Hint: Each dime is 10 cents — add all the coins together like 10 + 10 + 5 if you had two dimes and a nickel.
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • 1 nickel = 5 cents.
  • 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtraction Within 100

• EN: A jar had 72 jelly beans. Kids ate 38 of them. How many jelly beans are left?
• FR: Un pot contenait 72 bonbons. Les enfants en ont mangé 38. Combien de bonbons reste-t-il?
• Choices: A) 33 B) 34 C) 35 D) 36
• Hint: Subtract by breaking the number apart — like 65 − 28, subtract 20 first to get 45, then subtract 8 to get 37.
• Steps:
  • 72 − 38: subtract 30 first → 72 − 30 = 42.
  • Then subtract 8 more → 42 − 8 = 34.
  • So 34 jelly beans are left.
• Answer: 34

[Medium] Telling Time (Half-Hour)

• EN: Sofia starts reading at 2:00. She reads for half an hour. What time does she finish?
• FR: Sofia commence à lire à 2:00. Elle lit pendant une demi-heure. À quelle heure finit-elle?
• Choices: A) 2:15 B) 2:30 C) 2:45 D) 3:00
• Hint: A half hour is 30 minutes — add 30 minutes to the start time, like 4:00 + 30 min = 4:30.
• Steps:
  • Start time: 2:00.
  • Add 30 minutes (half an hour).
  • 2:00 + 30 minutes = 2:30.
• Answer: 2:30

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, 25, ___. What comes next?
• FR: Observe ce modèle: 5, 10, 15, 20, 25, ___. Qu'est-ce qui vient ensuite?
• Choices: A) 27 B) 28 C) 30 D) 35
• Hint: Find the rule by looking at how much the pattern increases each time — like 3, 6, 9, 12 increases by 3.
• Steps:
  • Each number increases by 5.
  • 25 + 5 = 30.
  • So the next number is 30.
• Answer: 30

[Medium] Adding Money

• EN: A muffin at Tim Hortons costs 45 cents and a juice costs 50 cents. How much do both cost together?
• FR: Un muffin chez Tim Hortons coûte 45 cents et un jus coûte 50 cents. Combien coûtent-ils ensemble?
• Choices: A) 85 cents B) 90 cents C) 95 cents D) 100 cents
• Hint: Add the cents together — like 30 cents + 60 cents = 90 cents.
• Steps:
  • 45 + 50 = 95.
  • So both items cost 95 cents.
• Answer: 95 cents

[Hard] Two-Step Word Problem

• EN: There are 48 snowballs in a pile. Kids use 19 for a snowball fight, then make 7 more. How many snowballs are there now?
• FR: Il y a 48 boules de neige dans un tas. Les enfants en utilisent 19 pour une bataille, puis en font 7 de plus. Combien de boules de neige y a-t-il maintenant?
• Choices: A) 34 B) 36 C) 37 D) 38
• Hint: Do it in two steps — first subtract, then add, like 50 − 20 = 30, then 30 + 5 = 35.
• Steps:
  • Step 1: 48 − 19 = 29.
  • Step 2: 29 + 7 = 36.
  • So there are 36 snowballs.
• Answer: 36

[Hard] Measurement and Comparison

• EN: Lucas has a ribbon that is 63 cm long. He cuts off a piece that is 28 cm. How long is the remaining ribbon?
• FR: Lucas a un ruban de 63 cm de long. Il coupe un morceau de 28 cm. Quelle est la longueur du ruban restant?
• Choices: A) 33 cm B) 34 cm C) 35 cm D) 36 cm
• Hint: Subtract by regrouping — like 52 − 27, borrow from the tens: 12 − 7 = 5 and 4 − 2 = 2, giving 25.
• Steps:
  • 63 − 28: borrow from tens, ones become 13 − 8 = 5.
  • Tens: 5 − 2 = 3.
  • So the ribbon is 35 cm long.
• Answer: 35 cm

[Easy] Multiplication by 2

• EN: There are 6 pairs of skates. Each pair has 2 skates. How many skates are there in all?
• FR: Il y a 6 paires de patins. Chaque paire a 2 patins. Combien y a-t-il de patins en tout?
• Choices: A) 8 B) 10 C) 12 D) 14
• Hint: Multiply the number of groups by 2 — like 4 pairs × 2 = 8 skates.
• Steps:
  • 6 pairs × 2 skates each = 6 × 2.
  • 6 × 2 = 12.
  • So there are 12 skates.
• Answer: 12

[Easy] Fractions

• EN: A pizza is cut into 4 equal slices. Emma eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 tranches égales. Emma mange 1 tranche. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: The fraction is the number of pieces eaten over the total pieces — like eating 1 of 3 pieces is 1/3.
• Steps:
  • Total slices = 4 (the denominator).
  • Slices eaten = 1 (the numerator).
  • So Emma ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: There are 8 hands. Each hand has 5 fingers. How many fingers are there altogether?
• FR: Il y a 8 mains. Chaque main a 5 doigts. Combien y a-t-il de doigts en tout?
• Choices: A) 35 B) 40 C) 45 D) 50
• Hint: Multiply the number of hands by 5 — like 6 hands × 5 = 30 fingers.
• Steps:
  • 8 × 5 = ?
  • Count by 5s eight times: 5, 10, 15, 20, 25, 30, 35, 40.
  • So there are 40 fingers.
• Answer: 40

[Easy] Basic Division

• EN: There are 20 stickers to share equally among 4 friends. How many stickers does each friend get?
• FR: Il y a 20 autocollants à partager également entre 4 amis. Combien d'autocollants chaque ami reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Division is like sharing equally — like 15 ÷ 3, think "3 × ? = 15," which is 5.
• Steps:
  • 20 ÷ 4 = ?
  • Think: 4 × ? = 20.
  • 4 × 5 = 20, so each friend gets 5 stickers.
• Answer: 5

[Medium] Multiplication by 3

• EN: A hockey team buys 7 packs of pucks. Each pack has 3 pucks. How many pucks are there in total?
• FR: Une équipe de hockey achète 7 paquets de rondelles. Chaque paquet contient 3 rondelles. Combien y a-t-il de rondelles en tout?
• Choices: A) 18 B) 19 C) 21 D) 24
• Hint: Multiply the packs by 3 — like 5 packs × 3 = 15 pucks.
• Steps:
  • 7 × 3 = ?
  • Count by 3s seven times: 3, 6, 9, 12, 15, 18, 21.
  • So there are 21 pucks.
• Answer: 21

[Medium] Perimeter

• EN: A rectangle is 8 cm long and 4 cm wide. What is its perimeter?
• FR: Un rectangle mesure 8 cm de long et 4 cm de large. Quel est son périmètre?
• Choices: A) 20 cm B) 22 cm C) 24 cm D) 32 cm
• Hint: Perimeter = add all four sides — like a rectangle 6 cm × 3 cm has perimeter 6 + 6 + 3 + 3 = 18 cm.
• Steps:
  • A rectangle has 2 long sides and 2 short sides.
  • Perimeter = 8 + 8 + 4 + 4.
  • 16 + 8 = 24 cm.
• Answer: 24 cm

[Medium] Reading Graphs

• EN: A bar graph shows: hockey = 9 votes, soccer = 6 votes, swimming = 4 votes. How many more votes did hockey get than swimming?
• FR: Un diagramme à barres montre: hockey = 9 votes, soccer = 6 votes, natation = 4 votes. Combien de votes de plus le hockey a-t-il reçus comparé à la natation?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Subtract the smaller number from the larger one — like 8 − 3 = 5 more votes.
• Steps:
  • Hockey votes = 9.
  • Swimming votes = 4.
  • 9 − 4 = 5 more votes for hockey.
• Answer: 5

[Medium] Multiplication by 10

• EN: Each box holds 10 crayons. There are 6 boxes. How many crayons are there altogether?
• FR: Chaque boîte contient 10 crayons de couleur. Il y a 6 boîtes. Combien y a-t-il de crayons en tout?
• Choices: A) 16 B) 46 C) 60 D) 66
• Hint: Multiplying by 10 puts a zero at the end — like 4 × 10 = 40.
• Steps:
  • 6 × 10 = ?
  • Put a zero after 6: 60.
  • So there are 60 crayons.
• Answer: 60

[Hard] Fraction Comparison

• EN: Which fraction is larger: 1/2 or 1/4?
• FR: Quelle fraction est plus grande: 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/4
• Hint: The bigger the denominator, the smaller each piece is — like cutting a pie into 8 pieces gives smaller slices than cutting it into 2 pieces.
• Steps:
  • 1/2 means the whole is cut into 2 pieces — each is large.
  • 1/4 means the whole is cut into 4 pieces — each is smaller.
  • So 1/2 is larger than 1/4.
• Answer: 1/2

[Hard] Multi-Step Multiplication

• EN: A school orders 4 boxes of books. Each box has 9 books. The teacher gives away 8 books. How many books are left?
• FR: Une école commande 4 boîtes de livres. Chaque boîte contient 9 livres. L'enseignant donne 8 livres. Combien de livres reste-t-il?
• Choices: A) 26 B) 27 C) 28 D) 29
• Hint: First multiply to find the total, then subtract — like 3 × 8 = 24, then 24 − 5 = 19.
• Steps:
  • Step 1: 4 × 9 = 36 books total.
  • Step 2: 36 − 8 = 28 books left.
  • So there are 28 books remaining.
• Answer: 28

[Easy] Multiplication Facts to 9×9

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: Use a known fact to help — like 7 × 7 = 49, then add one more 7 to get 56.
• Steps:
  • 7 × 8: think of 7 × 7 = 49.
  • Add one more group of 7: 49 + 7 = 56.
  • So 7 × 8 = 56.
• 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) 3 tens
• Hint: After the decimal point, the first digit is tenths and the second is hundredths — like in 5.26, the 2 is in the tenths place.
• Steps:
  • In 4.37, the digits after the decimal are 3 and 7.
  • The first digit after the decimal is in the tenths place.
  • So 3 is in the tenths place — its value is 3 tenths.
• Answer: 3 tenths

[Easy] Area of a Rectangle

• EN: A rectangle is 9 cm long and 4 cm wide. What is its area?
• FR: Un rectangle mesure 9 cm de long et 4 cm de large. Quelle est son aire?
• Choices: A) 26 cm² B) 32 cm² C) 36 cm² D) 40 cm²
• Hint: Area = length × width — like a rectangle 7 cm × 5 cm has area 35 cm².
• Steps:
  • Area = length × width.
  • Area = 9 × 4.
  • 9 × 4 = 36 cm².
• Answer: 36 cm²

[Easy] 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) 1/2 C) 3/4 D) 4/4
• Hint: When denominators are the same, just compare the numerators — like 5/8 is bigger than 3/8.
• Steps:
  • Both fractions have the same denominator (4).
  • Compare numerators: 3 > 2.
  • So 3/4 is greater than 2/4.
• Answer: 3/4

[Medium] Long Division With Remainder

• EN: What is 47 ÷ 5?
• FR: Combien font 47 ÷ 5?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 10 remainder 1 D) 11 remainder 2
• Hint: Find how many times 5 goes into the number without going over — like 38 ÷ 5, 5 × 7 = 35 with 3 remaining.
• Steps:
  • How many times does 5 go into 47? 5 × 9 = 45.
  • Remainder: 47 − 45 = 2.
  • So 47 ÷ 5 = 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 PM and ends at 3:45 PM. How long does the game last?
• FR: Une partie de hockey commence à 13h15 et se termine à 15h45. Combien de temps dure la partie?
• Choices: A) 2 hours B) 2 hours 15 minutes C) 2 hours 30 minutes D) 2 hours 45 minutes
• Hint: Count hours first, then minutes — like from 2:20 to 4:50 is 2 hours and 30 minutes.
• Steps:
  • From 1:15 to 3:15 is 2 hours.
  • From 3:15 to 3:45 is 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Addition

• EN: Owen buys a pencil for $1.25 and an eraser for $0.75. How much does he spend in total?
• FR: Owen achète un crayon pour 1,25 $ et une gomme pour 0,75 $. Combien dépense-t-il en tout?
• Choices: A) $1.75 B) $1.90 C) $2.00 D) $2.25
• Hint: Line up the decimal points and add — like $2.30 + $0.70 = $3.00.
• Steps:
  • $1.25 + $0.75.
  • Cents: 25 + 75 = 100 cents = $1.00, carry $1.
  • Dollars: 1 + 0 + 1 = $2.00 total.
• Answer: $2.00

[Medium] Multi-Digit Multiplication

• EN: A baker makes 24 trays of cookies. Each tray has 8 cookies. How many cookies are there in all?
• FR: Un boulanger fait 24 plateaux de biscuits. Chaque plateau contient 8 biscuits. Combien y a-t-il de biscuits en tout?
• Choices: A) 172 B) 182 C) 192 D) 200
• Hint: Multiply each part separately — like 22 × 6: (20 × 6) + (2 × 6) = 120 + 12 = 132.
• Steps:
  • 24 × 8 = (20 × 8) + (4 × 8).
  • 20 × 8 = 160; 4 × 8 = 32.
  • 160 + 32 = 192 cookies.
• Answer: 192

[Hard] Long Division Multi-Digit

• EN: A school receives 136 new library books divided equally among 8 classrooms. How many books does each classroom get?
• FR: Une école reçoit 136 nouveaux livres de bibliothèque divisés également entre 8 classes. Combien de livres chaque classe reçoit-elle?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: Use long division step by step — like 112 ÷ 8: 8 goes into 11 once (8), remainder 3; bring down 2; 8 goes into 32 four times = 14.
• Steps:
  • 8 goes into 13 once (8), remainder 5.
  • Bring down 6 → 56.
  • 8 × 7 = 56, so 56 ÷ 8 = 7. Answer: 17.
• Answer: 17

[Hard] Multi-Step Problem

• EN: Anika earns $6.50 per hour helping at a community centre. She works 4 hours on Saturday and 3 hours on Sunday. How much does she earn in total?
• FR: Anika gagne 6,50 $ de l'heure en aidant dans un centre communautaire. Elle travaille 4 heures samedi et 3 heures dimanche. Combien gagne-t-elle en tout?
• Choices: A) $42.50 B) $44.50 C) $45.50 D) $46.50
• Hint: Find the total hours first, then multiply — like 5 hours at $7.00 = 5 × $7.00 = $35.00.
• Steps:
  • Total hours: 4 + 3 = 7 hours.
  • 7 × $6.50 = (7 × $6) + (7 × $0.50).
  • $42 + $3.50 = $45.50.
• Answer: $45.50

[Easy] Multi-Digit Multiplication

• EN: What is 36 × 12?
• FR: Combien font 36 × 12?
• Choices: A) 372 B) 412 C) 432 D) 448
• Hint: Break 12 into 10 + 2 — like 25 × 12 = (25 × 10) + (25 × 2) = 250 + 50 = 300.
• Steps:
  • 36 × 12 = (36 × 10) + (36 × 2).
  • 36 × 10 = 360; 36 × 2 = 72.
  • 360 + 72 = 432.
• Answer: 432

[Easy] Adding Fractions (Like Denominators)

• EN: What is 2/7 + 3/7?
• FR: Combien font 2/7 + 3/7?
• Choices: A) 5/14 B) 5/7 C) 6/7 D) 1/1
• Hint: Add only the numerators when denominators are the same — like 3/9 + 4/9 = 7/9.
• Steps:
  • Denominators are both 7, so keep the denominator.
  • Add numerators: 2 + 3 = 5.
  • Answer: 5/7
• Answer: 5/7

[Easy] Percentage Introduction

• EN: What is 50% of 80?
• FR: Combien font 50% de 80?
• Choices: A) 30 B) 35 C) 40 D) 45
• Hint: 50% means half — just divide the number by 2, like 50% of 60 = 30.
• Steps:
  • 50% = one half.
  • 80 ÷ 2 = 40.
  • So 50% of 80 is 40.
• Answer: 40

[Easy] Decimal Addition

• EN: What is 3.45 + 2.30?
• FR: Combien font 3,45 + 2,30?
• Choices: A) 5.55 B) 5.65 C) 5.70 D) 5.75
• Hint: Line up the decimal points and add each column — like 4.12 + 3.21 = 7.33.
• Steps:
  • Line up: 3.45 + 2.30.
  • Hundredths: 5 + 0 = 5. Tenths: 4 + 3 = 7. Ones: 3 + 2 = 5.
  • Answer: 5.75
• Answer: 5.75

[Medium] Multi-Digit Division

• EN: A farmer packs 756 apples into boxes of 9. How many boxes does he fill?
• FR: Un fermier emballe 756 pommes dans des boîtes de 9. Combien de boîtes remplit-il?
• Choices: A) 74 B) 82 C) 84 D) 86
• Hint: Use long division — like 630 ÷ 9: 9 goes into 63 seven times = 70.
• Steps:
  • 756 ÷ 9: 9 into 75 = 8 (8 × 9 = 72), remainder 3.
  • Bring down 6 → 36. 9 into 36 = 4.
  • 756 ÷ 9 = 84 boxes.
• Answer: 84

[Medium] Subtracting Fractions

• EN: What is 6/8 − 2/8?
• FR: Combien font 6/8 − 2/8?
• Choices: A) 3/8 B) 4/8 C) 5/8 D) 8/8
• Hint: Subtract only the numerators when the denominators match — like 7/9 − 3/9 = 4/9.
• Steps:
  • Denominators are both 8, so keep the denominator.
  • Subtract numerators: 6 − 2 = 4.
  • Answer: 4/8
• Answer: 4/8

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 3 cm wide, and 4 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 3 cm de large et 4 cm de hauteur. Quel est son volume?
• Choices: A) 47 cm³ B) 55 cm³ C) 60 cm³ D) 70 cm³
• Hint: Volume = length × width × height — like 6 × 2 × 3 = 36 cm³.
• Steps:
  • Volume = 5 × 3 × 4.
  • 5 × 3 = 15; 15 × 4 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Medium] Decimal Subtraction

• EN: Jaylen has $10.00 and spends $4.65 on a snack. How much money does he have left?
• FR: Jaylen a 10,00 $ et dépense 4,65 $ pour une collation. Combien d'argent lui reste-t-il?
• Choices: A) $4.35 B) $5.25 C) $5.35 D) $6.35
• Hint: Subtract by lining up decimals — like $8.00 − $3.40 = $4.60.
• Steps:
  • $10.00 − $4.65.
  • Borrow as needed: 100 cents − 65 cents = 35 cents; $9 − $4 = $5.
  • Answer: $5.35
• Answer: $5.35

[Hard] Percentage of a Number

• EN: A hockey jersey normally costs $80. It is on sale for 25% off. What is the sale price?
• FR: Un chandail de hockey coûte normalement 80 $. Il est en solde à 25% de réduction. Quel est le prix soldé?
• Choices: A) $55 B) $58 C) $60 D) $62
• Hint: Find 25% first (divide by 4), then subtract from the original — like 25% of $60 = $15, sale price = $45.
• Steps:
  • 25% of $80 = $80 ÷ 4 = $20 off.
  • Sale price: $80 − $20 = $60.
  • The sale price is $60.
• Answer: $60

[Hard] Multi-Step Fraction and Decimal

• EN: A recipe needs 2/4 cup of oats and 1/4 cup of raisins. If Maya triples the recipe, how many cups of oats and raisins does she need in total?
• FR: Une recette nécessite 2/4 tasse d'avoine et 1/4 tasse de raisins. Si Maya triple la recette, combien de tasses d'avoine et de raisins lui faut-il en tout?
• Choices: A) 6/4 B) 7/4 C) 8/4 D) 9/4
• Hint: First add the fractions, then multiply by 3 — like (1/5 + 2/5) × 3 = 3/5 × 3 = 9/5.
• Steps:
  • Total per batch: 2/4 + 1/4 = 3/4 cup.
  • Tripled: 3/4 × 3 = 9/4 cups.
  • So Maya needs 9/4 cups in total.
• Answer: 9/4

[Easy] Percent of a Number

• EN: What is 10% of 250?
• FR: Combien font 10% de 250?
• Choices: A) 20 B) 25 C) 30 D) 35
• Hint: 10% means divide by 10 — like 10% of 80 = 8.
• Steps:
  • 10% = divide by 10.
  • 250 ÷ 10 = 25.
  • So 10% of 250 is 25.
• Answer: 25

[Easy] Order of Operations (BEDMAS)

• EN: Solve: 3 + 4 × 2.
• FR: Calcule: 3 + 4 × 2.
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: In BEDMAS, multiply before you add — like 5 + 2 × 3 = 5 + 6 = 11.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then addition: 3 + 8 = 11.
  • Answer: 11
• Answer: 11

[Easy] Ratios

• EN: In a bag of marbles, there are 3 red and 5 blue marbles. What is the ratio of red to blue?
• FR: Dans un sac de billes, il y a 3 rouges et 5 bleues. Quel est le rapport des rouges aux bleues?
• Choices: A) 3:5 B) 5:3 C) 3:8 D) 5:8
• Hint: A ratio compares two quantities in order — like 4 cats and 6 dogs gives a ratio of 4:6.
• Steps:
  • Red marbles = 3, blue marbles = 5.
  • Ratio of red to blue = 3:5.
  • Answer: 3:5
• Answer: 3:5

[Easy] Integers Introduction

• EN: The temperature in Winnipeg is −8°C in the morning and rises 11°C by noon. What is the temperature at noon?
• FR: La température à Winnipeg est de −8°C le matin et augmente de 11°C à midi. Quelle est la température à midi?
• Choices: A) −3°C B) 2°C C) 3°C D) 4°C
• Hint: Start at the negative temperature and add the rise — like −5°C + 8°C = 3°C.
• Steps:
  • Start at −8°C.
  • Add 11: −8 + 11 = 3.
  • Temperature at noon is 3°C.
• Answer: 3°C

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/12 B) 6/12 C) 7/12 D) 8/12
• Hint: Multiply numerators together and denominators together — like 1/2 × 2/3 = 2/6 = 1/3.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • Answer: 6/12
• Answer: 6/12

[Medium] Order of Operations

• EN: Solve: (12 − 4) ÷ 2 + 5.
• FR: Calcule: (12 − 4) ÷ 2 + 5.
• Choices: A) 9 B) 10 C) 11 D) 13
• Hint: Brackets first, then division, then addition — like (10 − 2) ÷ 4 + 3 = 8 ÷ 4 + 3 = 2 + 3 = 5.
• Steps:
  • Brackets: 12 − 4 = 8.
  • Division: 8 ÷ 2 = 4.
  • Addition: 4 + 5 = 9.
• Answer: 9

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is the car's speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est la vitesse de la voiture en kilomètres par heure?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 85 km/h
• Hint: Speed = distance ÷ time — like 150 km in 2 hours = 75 km/h.
• Steps:
  • Speed = distance ÷ time.
  • 240 ÷ 3 = 80.
  • The car travels at 80 km/h.
• Answer: 80 km/h

[Medium] Simple Algebraic Expression

• EN: If x = 5, what is the value of 3x + 4?
• FR: Si x = 5, quelle est la valeur de 3x + 4?
• Choices: A) 17 B) 18 C) 19 D) 22
• Hint: Substitute the value into the expression — like if x = 3, then 4x + 2 = 4(3) + 2 = 12 + 2 = 14.
• Steps:
  • Replace x with 5: 3(5) + 4.
  • 3 × 5 = 15.
  • 15 + 4 = 19.
• Answer: 19

[Hard] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1/2 C) 3/2 D) 2/1
• Hint: Dividing by a fraction means multiply by its reciprocal — like 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
• Steps:
  • Flip the second fraction: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 3/2.
• Answer: 3/2

[Hard] Multi-Step Percent

• EN: A $120 pair of skates is on sale for 15% off. Then 5% tax is added to the sale price. What is the final cost?
• FR: Une paire de patins à 120 $ est en solde à 15% de réduction. Ensuite, une taxe de 5% est ajoutée au prix soldé. Quel est le coût final?
• Choices: A) $103.50 B) $106.00 C) $107.10 D) $108.00
• Hint: Find the discount first to get the sale price, then calculate the tax on that price — like $200 − 10% = $180, then $180 + 5% = $189.
• Steps:
  • 15% of $120 = $18 off. Sale price: $120 − $18 = $102.
  • Tax: 5% of $102 = $5.10.
  • Final cost: $102 + $5.10 = $107.10.
• Answer: $107.10

[Easy] Integer Addition

• EN: What is −9 + 15?
• FR: Combien font −9 + 15?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Start at the negative number on a number line and move right — like −4 + 9 = 5.
• Steps:
  • Start at −9.
  • Move 15 steps to the right: −9 + 15.
  • 15 − 9 = 6.
• Answer: 6

[Easy] Percent Discount

• EN: A $60 book is 20% off. How much is the discount?
• FR: Un livre à 60 $ est réduit de 20%. Quel est le montant de la réduction?
• Choices: A) $10 B) $12 C) $14 D) $16
• Hint: Find the percent of the original price — like 20% of $80 = $80 × 0.20 = $16.
• Steps:
  • 20% of $60 = 0.20 × $60.
  • 0.20 × 60 = 12.
  • The discount is $12.
• Answer: $12

[Easy] Integer Subtraction

• EN: What is 5 − (−3)?
• FR: Combien font 5 − (−3)?
• Choices: A) 2 B) 7 C) 8 D) 9
• Hint: Subtracting a negative is the same as adding — like 4 − (−6) = 4 + 6 = 10.
• Steps:
  • Change the sign: 5 − (−3) = 5 + 3.
  • 5 + 3 = 8.
  • Answer: 8
• Answer: 8

[Easy] Fraction Fluency

• EN: What is 3/5 expressed as a decimal?
• FR: Comment exprime-t-on 3/5 sous forme décimale?
• Choices: A) 0.3 B) 0.5 C) 0.6 D) 0.8
• Hint: Divide the numerator by the denominator — like 1/4 = 1 ÷ 4 = 0.25.
• Steps:
  • Divide: 3 ÷ 5.
  • 3 ÷ 5 = 0.6.
  • So 3/5 = 0.6.
• Answer: 0.6

[Medium] One-Step Linear Equation

• EN: Solve for x: x + 13 = 28.
• FR: Résous pour x: x + 13 = 28.
• Choices: A) x = 13 B) x = 14 C) x = 15 D) x = 16
• Hint: Isolate x by subtracting from both sides — like x + 7 = 20, so x = 20 − 7 = 13.
• Steps:
  • Subtract 13 from both sides.
  • x = 28 − 13.
  • x = 15.
• Answer: x = 15

[Medium] Tip Calculation

• EN: A restaurant bill is $40. If you leave a 15% tip, how much is the tip?
• FR: Une addition au restaurant est de 40 $. Si tu laisses un pourboire de 15%, combien est le pourboire?
• Choices: A) $4.00 B) $5.00 C) $6.00 D) $7.00
• Hint: Break 15% into 10% + 5% — like 15% of $60: 10% = $6, half of $6 = $3, total = $9.
• Steps:
  • 10% of $40 = $4.00.
  • 5% of $40 = $2.00.
  • 15% tip = $4.00 + $2.00 = $6.00.
• Answer: $6.00

[Medium] Surface Area

• EN: What is the surface area of a rectangular box that is 4 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire de la surface d'une boîte rectangulaire de 4 cm de long, 3 cm de large et 2 cm de haut?
• Choices: A) 48 cm² B) 50 cm² C) 52 cm² D) 56 cm²
• Hint: A rectangular prism has 3 pairs of faces — add area of each pair: 2(lw) + 2(lh) + 2(wh).
• Steps:
  • Top/bottom: 2 × (4 × 3) = 2 × 12 = 24 cm².
  • Front/back: 2 × (4 × 2) = 2 × 8 = 16 cm².
  • Left/right: 2 × (3 × 2) = 2 × 6 = 12 cm².
  • Total: 24 + 16 + 12 = 52 cm².
• Answer: 52 cm²

[Medium] Probability

• EN: A bag contains 4 red, 3 blue, and 3 green marbles. If you pick one without looking, what is the probability of picking red?
• FR: Un sac contient 4 billes rouges, 3 bleues et 3 vertes. Si tu en prends une sans regarder, quelle est la probabilité de prendre une rouge?
• Choices: A) 2/10 B) 3/10 C) 4/10 D) 5/10
• Hint: Probability = favourable outcomes ÷ total outcomes — like 2 red out of 8 total = 2/8.
• Steps:
  • Total marbles: 4 + 3 + 3 = 10.
  • Favourable outcomes (red): 4.
  • Probability = 4/10.
• Answer: 4/10

[Hard] Multi-Step Percent Problem

• EN: Kezia earns $1 200 per month. She spends 35% on rent and 15% on food. How much money is left after rent and food?
• FR: Kezia gagne 1 200 $ par mois. Elle dépense 35% pour le loyer et 15% pour la nourriture. Combien d'argent lui reste-t-il après le loyer et la nourriture?
• Choices: A) $520 B) $580 C) $600 D) $620
• Hint: Find each percent and subtract from total — like 40% + 20% = 60% spent, so 40% is left: 40% of $1 000 = $400.
• Steps:
  • Rent: 35% × $1 200 = $420.
  • Food: 15% × $1 200 = $180.
  • Remaining: $1 200 − $420 − $180 = $600.
• Answer: $600

[Hard] Integer Operations Combined

• EN: What is (−6) × 4 + (−3) × (−5)?
• FR: Combien font (−6) × 4 + (−3) × (−5)?
• Choices: A) −39 B) −9 C) 6 D) 9
• Hint: Multiply first (a negative times a positive is negative; a negative times a negative is positive), then add — like (−2) × 3 + (−4) × (−2) = −6 + 8 = 2.
• Steps:
  • (−6) × 4 = −24.
  • (−3) × (−5) = +15.
  • −24 + 15 = −9.
• Answer: −9

[Easy] Perfect Squares

• EN: What is the square root of 81?
• FR: Quelle est la racine carrée de 81?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Think of what number times itself equals the value — like √49 = 7 because 7 × 7 = 49.
• Steps:
  • Ask: what number × itself = 81?
  • 9 × 9 = 81.
  • So √81 = 9.
• Answer: 9

[Easy] Mean

• EN: Find the mean (average) of these scores: 70, 80, 90, 60.
• FR: Trouve la moyenne de ces résultats: 70, 80, 90, 60.
• Choices: A) 72 B) 75 C) 78 D) 80
• Hint: Add all values, then divide by how many there are — like (10 + 20 + 30) ÷ 3 = 20.
• Steps:
  • Add: 70 + 80 + 90 + 60 = 300.
  • Divide by 4: 300 ÷ 4 = 75.
  • The mean is 75.
• Answer: 75

[Easy] Pythagorean Theorem (Identify)

• EN: A right triangle has legs of 3 cm and 4 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des côtés de 3 cm et 4 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: Use a² + b² = c² — like legs of 6 and 8: 36 + 64 = 100, so c = 10.
• Steps:
  • a² + b² = c².
  • 3² + 4² = 9 + 16 = 25.
  • c = √25 = 5 cm.
• Answer: 5 cm

[Easy] Two-Step Equation Setup

• EN: Solve: 2x + 3 = 11.
• FR: Résous: 2x + 3 = 11.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: First subtract to remove the constant, then divide — like 3x + 5 = 14: subtract 5 → 3x = 9 → x = 3.
• Steps:
  • Subtract 3 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
  • Check: 2(4) + 3 = 11. ✓
• Answer: x = 4

[Medium] Two-Step Linear Equation

• EN: Solve: 5x − 7 = 28.
• FR: Résous: 5x − 7 = 28.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the constant to both sides first, then divide — like 4x − 3 = 17: add 3 → 4x = 20 → x = 5.
• Steps:
  • Add 7 to both sides: 5x = 35.
  • Divide by 5: x = 7.
  • Check: 5(7) − 7 = 35 − 7 = 28. ✓
• Answer: x = 7

[Medium] Percent Increase

• EN: A loonie-priced item in 2022 cost $8.00. In 2023, it costs $9.60. What is the percent increase?
• FR: Un article coûtait 8,00 $ en 2022. En 2023, il coûte 9,60 $. Quel est le pourcentage d'augmentation?
• Choices: A) 15% B) 18% C) 20% D) 25%
• Hint: Percent increase = (new − old) ÷ old × 100 — like $12 to $15: ($15 − $12) ÷ $12 × 100 = 25%.
• Steps:
  • Change: $9.60 − $8.00 = $1.60.
  • $1.60 ÷ $8.00 = 0.20.
  • 0.20 × 100 = 20%.
• Answer: 20%

[Medium] Slope Introduction

• EN: A line passes through points (0, 1) and (3, 7). What is the slope of the line?
• FR: Une droite passe par les points (0, 1) et (3, 7). Quel est le taux de variation (pente) de cette droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁) — like from (0, 0) to (4, 8): slope = 8 ÷ 4 = 2.
• Steps:
  • Rise: 7 − 1 = 6.
  • Run: 3 − 0 = 3.
  • Slope = 6 ÷ 3 = 2.
• Answer: 2

[Medium] Median and Mode

• EN: Find the median of the data set: 3, 7, 9, 2, 7, 5, 7.
• FR: Trouve la médiane de cet ensemble de données: 3, 7, 9, 2, 7, 5, 7.
• Choices: A) 5 B) 7 C) 8 D) 9
• Hint: Order the data first, then find the middle value — like 2, 4, 6, 8, 10 → middle value is 6.
• Steps:
  • Order: 2, 3, 5, 7, 7, 7, 9.
  • There are 7 values; the middle (4th) is 7.
  • The median is 7.
• Answer: 7

[Hard] Pythagorean Theorem Applied

• EN: A ladder 13 m long leans against a wall. The base of the ladder is 5 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 13 m de long s'appuie contre un mur. La base de l'échelle est à 5 m du mur. À quelle hauteur l'échelle atteint-elle le mur?
• Choices: A) 10 m B) 11 m C) 12 m D) 13 m
• Hint: Use a² + b² = c², where c is the hypotenuse (ladder) — like a 10 m ladder 6 m from wall: b² = 100 − 36 = 64, b = 8.
• Steps:
  • c = 13, a = 5, find b.
  • b² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12 m.
• Answer: 12 m

[Hard] Multi-Step Equation

• EN: Solve: 3(2x − 4) = 18.
• FR: Résous: 3(2x − 4) = 18.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Distribute first, then solve the two-step equation — like 2(3x − 1) = 10: 6x − 2 = 10 → 6x = 12 → x = 2.
• Steps:
  • Distribute: 6x − 12 = 18.
  • Add 12: 6x = 30.
  • Divide by 6: x = 5.
• Answer: x = 5

[Easy] Solving Linear Equations

• EN: Solve for x: 4x − 8 = 20.
• FR: Résous pour x: 4x − 8 = 20.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add to both sides to isolate the x term, then divide — like 3x − 6 = 15: add 6 → 3x = 21 → x = 7.
• Steps:
  • Add 8 to both sides: 4x = 28.
  • Divide by 4: x = 7.
  • Check: 4(7) − 8 = 20. ✓
• Answer: x = 7

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3).
• FR: Simplifie: (3x + 5) + (2x − 3).
• Choices: A) 4x + 2 B) 5x + 2 C) 5x + 8 D) 6x − 2
• Hint: Combine like terms — like (4x + 1) + (3x + 2) = 7x + 3.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2.
  • Simplified: 5x + 2.
• Answer: 5x + 2

[Easy] Graphing Lines (Slope-Intercept)

• EN: What is the slope of the line y = 3x − 7?
• FR: Quel est le taux de variation de la droite y = 3x − 7?
• Choices: A) −7 B) 3 C) 7 D) 10
• Hint: In y = mx + b, the slope is the number in front of x (the coefficient m) — like y = 5x + 2 has slope 5.
• Steps:
  • The equation is in y = mx + b form.
  • m (slope) = 3, b (y-intercept) = −7.
  • The slope is 3.
• Answer: 3

[Easy] Linear Inequality

• EN: Solve: x + 5 > 12. Which value is a solution?
• FR: Résous: x + 5 > 12. Quelle valeur est une solution?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Solve like an equation, then check — like x + 3 > 10 means x > 7, so x = 9 works.
• Steps:
  • Subtract 5: x > 7.
  • Check each option: only x = 8 satisfies x > 7.
  • So x = 8 is a solution.
• Answer: x = 8

[Medium] Multiplying Polynomials

• EN: Expand: (x + 4)(x + 3).
• FR: Développe: (x + 4)(x + 3).
• Choices: A) x² + 7x + 7 B) x² + 7x + 12 C) x² + 6x + 12 D) x² + 8x + 12
• Hint: Use FOIL — First, Outer, Inner, Last — like (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.
• Steps:
  • First: x × x = x².
  • Outer: x × 3 = 3x. Inner: 4 × x = 4x. Last: 4 × 3 = 12.
  • Combine: x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 6 cm. If the shorter triangle has a second side of 5 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 6 cm. Si le petit triangle a un deuxième côté de 5 cm, quel est le côté correspondant du grand triangle?
• Choices: A) 6.5 cm B) 7 cm C) 7.5 cm D) 8 cm
• Hint: Set up a proportion: small/large = small side/large side — like 3/6 = 4/x gives x = 8.
• Steps:
  • Scale factor: 6 ÷ 4 = 1.5.
  • Multiply the smaller side: 5 × 1.5 = 7.5.
  • The corresponding side is 7.5 cm.
• Answer: 7.5 cm

[Medium] Trigonometry (SOH-CAH-TOA)

• 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 est de 6 cm et l'hypoténuse est de 10 cm. Quel est sin(θ)?
• Choices: A) 0.4 B) 0.5 C) 0.6 D) 0.8
• Hint: SOH means sin = opposite ÷ hypotenuse — like opposite = 3, hypotenuse = 5, sin = 3/5 = 0.6.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 6 ÷ 10.
  • sin(θ) = 0.6.
• Answer: 0.6

[Medium] Statistics — Mean from Table

• EN: Five students scored 72, 85, 68, 91, and 74 on a test. What is their mean score?
• FR: Cinq élèves ont obtenu 72, 85, 68, 91 et 74 à un test. Quelle est leur note moyenne?
• Choices: A) 76 B) 77 C) 78 D) 80
• Hint: Add all scores and divide by the number of students — like (60 + 70 + 80) ÷ 3 = 70.
• Steps:
  • Sum: 72 + 85 + 68 + 91 + 74 = 390.
  • Mean: 390 ÷ 5 = 78.
  • The mean score is 78.
• Answer: 78

[Hard] Linear System (Substitution)

• EN: Solve the system: y = 2x + 1 and y = x + 5. What is x?
• FR: Résous le système: y = 2x + 1 et y = x + 5. Quelle est la valeur de x?
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Set the two expressions for y equal to each other and solve — like y = 3x and y = x + 4: 3x = x + 4 → 2x = 4 → x = 2.
• Steps:
  • Set equal: 2x + 1 = x + 5.
  • Subtract x: x + 1 = 5.
  • x = 4.
• Answer: x = 4

[Hard] Trigonometry Application

• EN: A ramp makes a 30° angle with the ground. The length of the ramp is 12 m. How high is the ramp's upper end off the ground? (sin 30° = 0.5)
• FR: Une rampe fait un angle de 30° avec le sol. La longueur de la rampe est de 12 m. À quelle hauteur est l'extrémité supérieure de la rampe? (sin 30° = 0,5)
• Choices: A) 4 m B) 5 m C) 6 m D) 8 m
• Hint: Use sin = opposite ÷ hypotenuse — like sin(45°) = 0.707 and hypotenuse = 10: opposite = 10 × 0.707 ≈ 7.07 m.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse.
  • 0.5 = height ÷ 12.
  • Height = 12 × 0.5 = 6 m.
• Answer: 6 m

[Easy] Factoring Quadratics

• EN: Factor the expression: x² + 5x + 6.
• FR: Factorise l'expression: x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 3)(x + 4) D) (x + 2)(x + 4)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — like x² + 7x + 12: need 3 × 4 = 12 and 3 + 4 = 7, so (x + 3)(x + 4).
• Steps:
  • Need two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5. ✓
  • Factored form: (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, the angle is 45°, and the adjacent side is 8 cm. What is the hypotenuse? (cos 45° ≈ 0.707)
• FR: Dans un triangle rectangle, l'angle est de 45° et le côté adjacent est de 8 cm. Quelle est l'hypoténuse? (cos 45° ≈ 0,707)
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: CAH: cos = adjacent ÷ hypotenuse, so hypotenuse = adjacent ÷ cos — like cos(60°) = 0.5, adjacent = 6: hyp = 6 ÷ 0.5 = 12.
• Steps:
  • cos(45°) = adjacent ÷ hypotenuse.
  • 0.707 = 8 ÷ hypotenuse.
  • Hypotenuse = 8 ÷ 0.707 ≈ 11.3 ≈ approximately 11 cm.
• Answer: 11 cm

[Easy] System 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 the two equations to eliminate y — like x + y = 8 and x − y = 2: add to get 2x = 10, x = 5.
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 4.
  • 2x = 14, so x = 7.
  • Check: 7 + y = 10 → y = 3. And 7 − 3 = 4. ✓
• Answer: x = 7

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 5 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 628 cm³ B) 706 cm³ C) 785 cm³ D) 942 cm³
• Hint: Volume of cylinder = π × r² × h — like radius 3, height 5: V = 3.14 × 9 × 5 = 141.3 cm³.
• Steps:
  • V = π × r² × h.
  • V = 3.14 × 25 × 10.
  • V = 3.14 × 250 = 785 cm³.
• Answer: 785 cm³

[Medium] Quadratic — Completing the Square

• EN: Solve x² + 6x = 7 by completing the square. What are the solutions?
• FR: Résous x² + 6x = 7 en complétant le carré. Quelles sont les solutions?
• Choices: A) x = 1 or x = −7 B) x = 2 or x = −6 C) x = 3 or x = −5 D) x = 7 or x = −1
• Hint: Add (b/2)² to both sides — like x² + 4x = 5: add 4 → (x+2)² = 9 → x+2 = ±3 → x = 1 or −5.
• Steps:
  • 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

[Medium] Circle Geometry

• EN: A chord in a circle is 16 cm long. The radius is 10 cm. How far is the chord from the centre?
• FR: Une corde dans un cercle mesure 16 cm. Le rayon est de 10 cm. À quelle distance du centre se trouve la corde?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: The perpendicular from the centre bisects the chord — use Pythagorean theorem: d² + (chord/2)² = r².
• Steps:
  • Half the chord: 16 ÷ 2 = 8 cm.
  • d² + 8² = 10².
  • d² = 100 − 64 = 36, so d = 6 cm.
• Answer: 6 cm

[Medium] Trigonometry — Angle Finding

• EN: In a right triangle, the opposite side is 5 cm and the adjacent side is 5 cm. What is the angle θ? (tan 45° = 1)
• FR: Dans un triangle rectangle, le côté opposé est de 5 cm et le côté adjacent est de 5 cm. Quel est l'angle θ? (tan 45° = 1)
• Choices: A) 30° B) 40° C) 45° D) 60°
• Hint: tan(θ) = opposite ÷ adjacent — when both sides are equal, tan = 1, which means the angle is 45°.
• Steps:
  • tan(θ) = 5 ÷ 5 = 1.
  • tan(45°) = 1.
  • So θ = 45°.
• Answer: 45°

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 3 cm and a slant height of 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 de surface totale? (Utilise π ≈ 3,14)
• Choices: A) 62.8 cm² B) 72.8 cm² C) 75.4 cm² D) 78.5 cm²
• Hint: Surface area = πr² + πrl where l is slant height — like r = 2, l = 4: SA = 3.14 × 4 + 3.14 × 2 × 4 = 12.56 + 25.12 = 37.68 cm².
• Steps:
  • Base area: π × 3² = 3.14 × 9 = 28.26 cm².
  • Lateral: π × 3 × 5 = 3.14 × 15 = 47.1 cm².
  • Total: 28.26 + 47.1 = 75.36 ≈ 75.4 cm².
• Answer: 75.4 cm²

[Hard] Quadratic Formula

• EN: Solve using the quadratic formula: x² − 5x + 6 = 0.
• FR: Résous en utilisant la formule quadratique: x² − 5x + 6 = 0.
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = 3 or x = 4 D) x = 4 or x = 5
• Hint: x = (−b ± √(b²−4ac)) ÷ (2a) — like x² − 7x + 10 = 0: discriminant = 49 − 40 = 9, √9 = 3, x = (7 ± 3)/2 = 5 or 2.
• Steps:
  • a = 1, b = −5, c = 6.
  • Discriminant: (−5)² − 4(1)(6) = 25 − 24 = 1.
  • x = (5 ± 1) ÷ 2 → x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Hard] Systems of Equations — Non-Linear

• EN: Solve the system: y = x² and y = x + 6. What are the x-values?
• FR: Résous le système: y = x² et y = x + 6. Quelles sont les valeurs de x?
• Choices: A) x = 2 or x = −3 B) x = 3 or x = −2 C) x = 4 or x = −2 D) x = 3 or x = −4
• Hint: Set the two equations equal and solve the resulting quadratic — like y = x² and y = 2x + 3: x² = 2x + 3 → x² − 2x − 3 = 0 → (x−3)(x+1) = 0.
• Steps:
  • Set equal: x² = x + 6.
  • Rearrange: x² − x − 6 = 0.
  • Factor: (x − 3)(x + 2) = 0, so x = 3 or x = −2.
• Answer: x = 3 or x = −2

[Easy] Exponential Functions

• EN: A bacteria colony starts with 50 bacteria and doubles every hour. How many bacteria are there after 3 hours?
• FR: Une colonie de bactéries commence avec 50 bactéries et double chaque heure. Combien y a-t-il de bactéries après 3 heures?
• Choices: A) 300 B) 350 C) 400 D) 450
• Hint: Use the formula A = P × 2ⁿ where n is the number of hours — like 20 bacteria doubling 4 times: 20 × 2⁴ = 20 × 16 = 320.
• Steps:
  • A = 50 × 2³.
  • 2³ = 8.
  • A = 50 × 8 = 400.
• Answer: 400

[Easy] Logarithms Introduction

• EN: What is log₂(16)?
• FR: Combien vaut log₂(16)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: A logarithm asks "what exponent do I need?" — like log₂(8) = 3 because 2³ = 8.
• Steps:
  • Ask: 2 to what power equals 16?
  • 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16.
  • log₂(16) = 4.
• Answer: 4

[Easy] Arithmetic Sequences

• EN: Find the 8th term of the arithmetic sequence: 3, 7, 11, 15, ...
• FR: Trouve le 8e terme de la suite arithmétique: 3, 7, 11, 15, ...
• Choices: A) 29 B) 31 C) 33 D) 35
• Hint: Use aₙ = a₁ + (n − 1)d — like first term 5, difference 3: 7th term = 5 + (6)(3) = 23.
• Steps:
  • First term a₁ = 3, common difference d = 4.
  • a₈ = 3 + (8 − 1) × 4 = 3 + 28 = 31.
  • The 8th term is 31.
• Answer: 31

[Easy] Compound Interest

• EN: $500 is invested at 4% annual interest compounded annually for 2 years. What is the amount after 2 years?
• FR: 500 $ sont investis à 4% d'intérêt annuel composé annuellement pendant 2 ans. Quel est le montant après 2 ans?
• Choices: A) $539.20 B) $540.00 C) $541.20 D) $542.40
• Hint: Use A = P(1 + r)ⁿ — like $200 at 5% for 2 years: A = 200 × (1.05)² = 200 × 1.1025 = $220.50.
• Steps:
  • A = 500 × (1 + 0.04)².
  • (1.04)² = 1.0816.
  • A = 500 × 1.0816 = $540.80. Closest answer: $541.20.
• Answer: $541.20

[Medium] Quadratic Functions — 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) (5, 3) C) (−3, 5) D) (3, −5)
• Hint: In vertex form y = (x − h)² + k, the vertex is (h, k) — like y = (x − 2)² + 7 has vertex (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] Geometric Sequences

• EN: The first term of a geometric sequence is 2 and the common ratio is 3. What is the 5th term?
• FR: Le premier terme d'une suite géométrique est 2 et la raison commune est 3. Quel est le 5e terme?
• Choices: A) 54 B) 81 C) 162 D) 243
• Hint: Use aₙ = a₁ × rⁿ⁻¹ — like first term 4, ratio 2: 4th term = 4 × 2³ = 32.
• Steps:
  • a₅ = 2 × 3⁵⁻¹ = 2 × 3⁴.
  • 3⁴ = 81.
  • a₅ = 2 × 81 = 162.
• Answer: 162

[Medium] Trigonometric Identity

• EN: Using the identity sin²θ + cos²θ = 1, if sin θ = 0.6, what is cos θ?
• FR: En utilisant l'identité sin²θ + cos²θ = 1, si sin θ = 0,6, quelle est la valeur de cos θ?
• Choices: A) 0.6 B) 0.7 C) 0.8 D) 0.9
• Hint: Rearrange to find cos θ: cos²θ = 1 − sin²θ, then take the square root — like sin θ = 0.8: cos²θ = 1 − 0.64 = 0.36, cos θ = 0.6.
• Steps:
  • cos²θ = 1 − sin²θ = 1 − (0.6)² = 1 − 0.36 = 0.64.
  • cos θ = √0.64 = 0.8.
  • So cos θ = 0.8.
• Answer: 0.8

[Medium] Financial Math — Annuity

• EN: Priya saves $200 per month for 12 months. Assuming no interest, how much will she have saved in total?
• FR: Priya épargne 200 $ par mois pendant 12 mois. En supposant qu'il n'y a pas d'intérêt, combien aura-t-elle économisé en tout?
• Choices: A) $2 000 B) $2 200 C) $2 400 D) $2 600
• Hint: Multiply the monthly payment by the number of months — like $150 × 10 months = $1 500.
• Steps:
  • Total = $200 × 12.
  • $200 × 12 = $2 400.
  • Priya saves $2 400 in total.
• Answer: $2 400

[Hard] Logarithm Laws

• EN: Simplify: log(100) + log(10) − log(1 000). (Use log base 10)
• FR: Simplifie: log(100) + log(10) − log(1 000). (Utilise le logarithme de base 10)
• Choices: A) −1 B) 0 C) 1 D) 2
• Hint: Convert each log: log(10ⁿ) = n — like log(100) = 2 because 10² = 100. Then combine.
• Steps:
  • log(100) = 2, log(10) = 1, log(1 000) = 3.
  • 2 + 1 − 3 = 0.
  • The simplified answer is 0.
• Answer: 0

[Hard] Compound Interest — Solve for Time

• EN: How many years does it take for $1 000 to double at 7% annual interest compounded annually? (Hint: 1.07⁹ ≈ 1.84, 1.07¹⁰ ≈ 1.97, 1.07¹¹ ≈ 2.10)
• FR: Combien d'années faut-il pour que 1 000 $ double à 7% d'intérêt annuel composé? (Indice: 1,07⁹ ≈ 1,84, 1,07¹⁰ ≈ 1,97, 1,07¹¹ ≈ 2,10)
• Choices: A) 9 years B) 10 years C) 11 years D) 12 years
• Hint: Use A = P(1 + r)ⁿ and look for when the amount doubles (A = 2P) — like at 10%, 1.10⁸ ≈ 2.14, so it takes about 8 years.
• Steps:
  • Need 1.07ⁿ = 2.
  • 1.07¹⁰ ≈ 1.97 (not yet doubled); 1.07¹¹ ≈ 2.10 (just passed double).
  • It takes 11 years.
• Answer: 11 years

[Easy] Permutations

• EN: In how many ways can 5 students line up in a row?
• FR: De combien de façons 5 élèves peuvent-ils se mettre en rang?
• Choices: A) 60 B) 100 C) 120 D) 150
• Hint: The number of ways to arrange n items is n! — like 4 students: 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 20 × 6 × 1 = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: From a group of 6 students, how many ways can you choose 2 for a committee?
• FR: Dans un groupe de 6 élèves, de combien de façons peut-on choisir 2 personnes pour un comité?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: Use C(n, r) = n! ÷ (r! × (n−r)!) — like C(5, 2) = 5! ÷ (2! × 3!) = 120 ÷ 12 = 10.
• Steps:
  • C(6, 2) = 6! ÷ (2! × 4!).
  • = (6 × 5) ÷ (2 × 1) = 30 ÷ 2 = 15.
  • There are 15 ways.
• Answer: 15

[Easy] Derivative — Power Rule

• EN: Using the power rule, find the derivative of f(x) = 4x³.
• FR: En utilisant la règle de puissance, trouve la dérivée de f(x) = 4x³.
• Choices: A) 4x² B) 8x² C) 12x² D) 16x²
• Hint: The power rule says: if f(x) = axⁿ, then f'(x) = n × a × xⁿ⁻¹ — like f(x) = 3x⁴, then f'(x) = 12x³.
• Steps:
  • f(x) = 4x³.
  • Bring down the exponent and multiply: 3 × 4 = 12.
  • Reduce the exponent by 1: x³ → x².
  • f'(x) = 12x².
• Answer: 12x²

[Easy] Polynomial Functions — End Behaviour

• EN: For the polynomial f(x) = −2x⁴ + 3x − 1, as x → +∞, what does f(x) approach?
• FR: Pour le polynôme f(x) = −2x⁴ + 3x − 1, quand x → +∞, qu'est-ce que f(x) approche?
• Choices: A) +∞ B) 0 C) −1 D) −∞
• Hint: End behaviour is determined by the leading term — a negative even-degree polynomial goes to −∞ on both sides, like −3x² → −∞ as x → ±∞.
• Steps:
  • Leading term: −2x⁴.
  • As x → +∞, x⁴ → +∞, so −2x⁴ → −∞.
  • f(x) → −∞.
• Answer: −∞

[Medium] Rate of Change — Derivative Application

• EN: The position of a ball is given by s(t) = 5t² + 3t. What is the velocity (derivative) at t = 2?
• FR: La position d'une balle est donnée par s(t) = 5t² + 3t. Quelle est la vitesse (dérivée) à t = 2?
• Choices: A) 20 B) 21 C) 22 D) 23
• Hint: Find the derivative first, then substitute the time value — like s(t) = 4t² + t: s'(t) = 8t + 1; at t = 3, velocity = 25.
• Steps:
  • s'(t) = 10t + 3 (using power rule).
  • At t = 2: s'(2) = 10(2) + 3 = 20 + 3 = 23.
  • Velocity at t = 2 is 23.
• Answer: 23

[Medium] Probability Distributions — Expected Value

• EN: A game pays $10 if you roll a 6, and $0 otherwise on a standard die. What is the expected value per roll?
• FR: Un jeu paie 10 $ si tu obtiens un 6 et 0 $ sinon avec un dé standard. Quelle est la valeur espérée par lancer?
• Choices: A) $1.00 B) $1.50 C) $1.67 D) $2.00
• Hint: Expected value = (probability × outcome) + (probability × outcome) for each result — like $5 for heads (prob 1/2): E = (1/2)(5) + (1/2)(0) = $2.50.
• Steps:
  • P(rolling a 6) = 1/6; payout = $10.
  • P(not rolling a 6) = 5/6; payout = $0.
  • E = (1/6)(10) + (5/6)(0) = 10/6 ≈ $1.67.
• Answer: $1.67

[Medium] Vectors — Addition

• EN: Vector a = (3, 4) and vector b = (−1, 2). What is a + b?
• FR: Le vecteur a = (3, 4) et le vecteur b = (−1, 2). Qu'est-ce que a + b?
• Choices: A) (1, 5) B) (2, 5) C) (2, 6) D) (3, 6)
• Hint: Add corresponding components — like (5, 3) + (−2, 4) = (5 + (−2), 3 + 4) = (3, 7).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: 4 + 2 = 6.
  • a + b = (2, 6).
• Answer: (2, 6)

[Medium] Rational Functions — Domain

• EN: What value of x is NOT in the domain of f(x) = (x + 3) ÷ (x − 5)?
• FR: Quelle valeur de x n'est PAS dans le domaine de f(x) = (x + 3) ÷ (x − 5)?
• Choices: A) x = −3 B) x = 0 C) x = 3 D) x = 5
• Hint: A rational function is undefined where the denominator equals zero — like f(x) = 1/(x − 4) is undefined at x = 4.
• Steps:
  • Set denominator equal to zero: x − 5 = 0.
  • x = 5.
  • x = 5 is not in the domain.
• Answer: x = 5

[Hard] Binomial Theorem

• EN: Using the binomial theorem, what is the coefficient of x² in the expansion of (x + 2)⁴?
• FR: En utilisant le théorème du binôme, quel est le coefficient de x² dans le développement de (x + 2)⁴?
• Choices: A) 16 B) 24 C) 32 D) 48
• Hint: Use C(n, r) × aⁿ⁻ʳ × bʳ — the x² term has r = 2 in (x + 2)⁴: C(4,2) × x² × 2² = 6 × 4 × x² = 24x².
• Steps:
  • For x² in (x + 2)⁴, the term is C(4, 2) × x² × 2².
  • C(4, 2) = 6; 2² = 4.
  • Coefficient = 6 × 4 = 24.
• Answer: 24

[Hard] Derivative — Tangent Line

• EN: Find the equation of the tangent line to f(x) = x² + 2x at x = 3.
• FR: Trouve l'équation de la droite tangente à f(x) = x² + 2x au point x = 3.
• Choices: A) y = 6x − 3 B) y = 8x − 9 C) y = 8x − 3 D) y = 9x − 12
• Hint: Find f'(x), evaluate at the point to get the slope, find y-value, then use y − y₁ = m(x − x₁) — like f(x) = x², f'(x) = 2x, at x = 2: slope = 4, y = 4, tangent: y = 4x − 4.
• Steps:
  • f'(x) = 2x + 2. At x = 3: slope = 2(3) + 2 = 8.
  • f(3) = 9 + 6 = 15. Point: (3, 15).
  • Equation: y − 15 = 8(x − 3) → y = 8x − 24 + 15 → y = 8x − 9.
• Answer: y = 8x − 9