Daily Math — 2026-09-14

[Easy] Counting to 20

• EN: There are 7 red apples and 5 green apples in a basket. How many apples are there in all?
• FR: Il y a 7 pommes rouges et 5 pommes vertes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To add two numbers, count on from the bigger number — try 8 + 3.
• Steps:
  • Start at 7, the bigger number.
  • Count on 5 more: 8, 9, 10, 11, 12.
  • So the total is 12.
• Answer: 12

[Easy] Subtraction Within 20

• EN: There are 14 snowballs. A student throws 6 of them. How many snowballs are left?
• FR: Il y a 14 boules de neige. Un élève en lance 6. Combien de boules de neige reste-t-il?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To subtract, count back from the bigger number — try 12 − 4.
• Steps:
  • Start at 14.
  • Count back 6: 13, 12, 11, 10, 9, 8.
  • So the answer is 8.
• Answer: 8

[Easy] Skip Counting by 5s

• EN: Skip count by 5s. What number comes after 15, 20, 25?
• FR: Compte par bonds de 5. Quel nombre vient après 15, 20, 25?
• Choices: A) 28 B) 30 C) 32 D) 35
• Hint: Each time you skip count by 5, add 5 to the last number — try 10, 15, 20, ?.
• Steps:
  • The pattern goes up by 5 each time.
  • 25 + 5 = 30.
  • So the next number is 30.
• Answer: 30

[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 dix cents et 1 pièce de cinq 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: Emma scored 9 goals in hockey on Monday and 8 goals on Tuesday. How many goals did she score in all?
• FR: Emma a marqué 9 buts au hockey lundi et 8 buts mardi. Combien de buts a-t-elle marqués en tout?
• Choices: A) 15 B) 16 C) 17 D) 18
• Hint: You can make 10 first — try 9 + 1 = 10, then add the rest.
• Steps:
  • Take 1 from 8 to give to 9: 9 + 1 = 10.
  • Now add the remaining 7: 10 + 7 = 17.
  • So Emma scored 17 goals in all.
• Answer: 17

[Medium] Comparing Numbers

• EN: Which number is greater: 13 or 18?
• FR: Quel nombre est plus grand : 13 ou 18?
• Choices: A) 13 B) 15 C) 16 D) 18
• Hint: When comparing two numbers, the one farther right on a number line is greater — try comparing 11 and 19.
• Steps:
  • On a number line, numbers get bigger as you go right.
  • 18 is to the right of 13.
  • So 18 is greater.
• Answer: 18

[Medium] Skip Counting by 2s

• EN: Count by 2s: 2, 4, 6, 8, ___. What is the missing number?
• FR: Compte par bonds de 2 : 2, 4, 6, 8, ___. Quel est le nombre manquant?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Add 2 to the last number in the pattern — try 6, 8, ?.
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
  • So the missing number is 10.
• Answer: 10

[Medium] Subtraction Story

• EN: There are 16 crayons in a box. Lucas takes 7 crayons. How many crayons are left in the box?
• FR: Il y a 16 crayons dans une boîte. Lucas prend 7 crayons. Combien de crayons reste-t-il dans la boîte?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: To subtract from a teen number, break it apart — try 15 − 6.
• Steps:
  • 16 − 7: think of 16 as 10 + 6.
  • 7 − 6 = 1, so take 1 more from 10: 10 − 1 = 9.
  • So 16 − 7 = 9.
• Answer: 9

[Hard] Two-Step Problem

• EN: There are 8 birds on a branch. 3 fly away, and then 5 more land. How many birds are on the branch now?
• FR: Il y a 8 oiseaux sur une branche. 3 s'envolent, puis 5 autres se posent. Combien y a-t-il d'oiseaux sur la branche maintenant?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Do two steps — first subtract, then add — try 10 − 2 + 4.
• Steps:
  • Start with 8 birds.
  • 3 fly away: 8 − 3 = 5.
  • 5 more land: 5 + 5 = 10.
• Answer: 10

[Hard] Counting Coins

• EN: You have 2 nickels and 3 pennies. How many cents do you have in all?
• FR: Tu as 2 pièces de cinq cents et 3 sous noirs. Combien de cents as-tu en tout?
• Choices: A) 11 cents B) 12 cents C) 13 cents D) 14 cents
• Hint: Count each coin's value — a nickel is 5 cents, a penny is 1 cent; try 1 nickel + 4 pennies.
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 3 pennies = 1 + 1 + 1 = 3 cents.
  • 10 + 3 = 13 cents.
• Answer: 13 cents

[Easy] Addition Within 100

• EN: A student has 34 stickers and gets 25 more. How many stickers does the student have now?
• FR: Un élève a 34 autocollants et en reçoit 25 de plus. Combien d'autocollants l'élève a-t-il maintenant?
• Choices: A) 57 B) 58 C) 59 D) 61
• Hint: Add the tens first, then the ones — try 21 + 36.
• Steps:
  • Tens: 30 + 20 = 50.
  • Ones: 4 + 5 = 9.
  • 50 + 9 = 59.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows 3:00. What time will it be in half an hour?
• FR: L'horloge indique 3 h 00. Quelle heure sera-t-il dans une demi-heure?
• Choices: A) 3:00 B) 3:30 C) 4:00 D) 4:30
• Hint: Half an hour = 30 minutes; add 30 minutes to the given time — try 5:00 + 30 minutes.
• Steps:
  • Start at 3:00.
  • Add 30 minutes.
  • 3:00 + 30 minutes = 3:30.
• Answer: 3:30

[Easy] Measuring Length

• EN: A pencil is 12 cm long and a crayon is 7 cm long. How much longer is the pencil?
• FR: Un crayon de bois mesure 12 cm et un crayon de cire mesure 7 cm. De combien de cm le crayon de bois est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: Subtract the shorter length from the longer length — try 15 cm − 8 cm.
• Steps:
  • Longer − shorter = difference.
  • 12 − 7 = 5.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Simple Patterns

• EN: What comes next in this pattern: 2, 4, 6, 8, ___?
• FR: Qu'est-ce qui vient ensuite dans cette suite : 2, 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Find the rule by looking at how the numbers change — try 5, 10, 15, ?.
• Steps:
  • Each number increases by 2.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Medium] Subtraction Within 100

• EN: A bag has 72 marbles. 38 marbles are given away. How many marbles are left?
• FR: Un sac contient 72 billes. On en donne 38. Combien de billes reste-t-il?
• Choices: A) 32 B) 33 C) 34 D) 36
• Hint: Subtract the ones first, then the tens — try 85 − 47.
• Steps:
  • 72 − 38: borrow from the tens. 12 − 8 = 4.
  • 60 − 30 = 30.
  • 30 + 4 = 34.
• Answer: 34

[Medium] Counting Coins to $1

• EN: You have 3 quarters. How many cents do you have in all?
• FR: Tu as 3 pièces de 25 cents. Combien de cents as-tu en tout?
• Choices: A) 60 cents B) 65 cents C) 75 cents D) 80 cents
• Hint: Each quarter is worth 25 cents — skip count by 25s; try 2 quarters first.
• Steps:
  • 1 quarter = 25 cents.
  • 2 quarters = 50 cents.
  • 3 quarters = 75 cents.
• Answer: 75 cents

[Medium] Telling Time — Half Hour

• EN: School starts at 8:30. It is now 8:00. How many minutes until school starts?
• FR: L'école commence à 8 h 30. Il est maintenant 8 h 00. Dans combien de minutes l'école commence-t-elle?
• Choices: A) 20 minutes B) 25 minutes C) 30 minutes D) 45 minutes
• Hint: Count the minutes from one time to the other — try from 9:00 to 9:30.
• Steps:
  • From 8:00 to 8:30.
  • Count up: 10, 20, 30 minutes.
  • There are 30 minutes until school starts.
• Answer: 30 minutes

[Medium] Measuring Length

• EN: A desk is 1 metre long. A book is 30 cm long. How many centimetres longer is the desk?
• FR: Un bureau mesure 1 mètre de long. Un livre mesure 30 cm de long. De combien de centimètres le bureau est-il plus long?
• Choices: A) 60 cm B) 65 cm C) 70 cm D) 75 cm
• Hint: Remember 1 metre = 100 cm, then subtract — try 100 cm − 45 cm.
• Steps:
  • 1 metre = 100 cm.
  • 100 − 30 = 70.
  • The desk is 70 cm longer.
• Answer: 70 cm

[Hard] Two-Step Addition and Subtraction

• EN: Liam has 85 hockey cards. He gives 27 to his friend and then buys 14 more. How many cards does Liam have now?
• FR: Liam a 85 cartes de hockey. Il en donne 27 à son ami et en achète ensuite 14 de plus. Combien de cartes Liam a-t-il maintenant?
• Choices: A) 70 B) 71 C) 72 D) 74
• Hint: Do two steps — subtract first, then add — try 90 − 30 + 10.
• Steps:
  • 85 − 27 = 58.
  • 58 + 14 = 72.
  • Liam has 72 cards now.
• Answer: 72

[Hard] Counting Coins and Comparing

• EN: Maya has 2 quarters and 1 dime. Ben has 3 nickels and 4 dimes. Who has more money, and by how many cents?
• FR: Maya a 2 pièces de 25 cents et 1 pièce de 10 cents. Ben a 3 pièces de 5 cents et 4 pièces de 10 cents. Qui a le plus d'argent, et de combien de cents?
• Choices: A) Maya by 5 cents B) Maya by 10 cents C) Ben by 5 cents D) Ben by 10 cents
• Hint: Find each person's total separately, then compare — try 1 quarter + 2 dimes vs. 5 nickels.
• Steps:
  • Maya: 25 + 25 + 10 = 60 cents.
  • Ben: 5 + 5 + 5 + 10 + 10 + 10 + 10 = 55 cents.
  • Maya has 60 − 55 = 5 cents more.
• Answer: Maya by 5 cents

[Easy] Multiplication by 2

• EN: A hockey team has 4 lines of 2 players each. How many players are there in all?
• FR: Une équipe de hockey a 4 lignes de 2 joueurs chacune. Combien y a-t-il de joueurs en tout?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Multiply the number of groups by the number in each group — try 3 × 2.
• Steps:
  • 4 groups of 2.
  • 4 × 2 = 8.
  • There are 8 players in all.
• Answer: 8

[Easy] Fractions

• EN: A pizza is cut into 4 equal pieces. You eat 1 piece. What fraction of the pizza did you eat?
• FR: Une pizza est coupée en 4 morceaux égaux. Tu manges 1 morceau. Quelle fraction de la pizza as-tu mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: The fraction eaten = pieces eaten ÷ total pieces — try eating 1 out of 3 pieces.
• Steps:
  • Total pieces = 4.
  • Pieces eaten = 1.
  • Fraction = 1/4.
• Answer: 1/4

[Easy] Multiplication by 5

• EN: There are 6 hands. How many fingers are there in all?
• FR: Il y a 6 mains. Combien y a-t-il de doigts en tout?
• Choices: A) 25 B) 30 C) 35 D) 40
• Hint: Each hand has 5 fingers — multiply; try 4 hands × 5.
• Steps:
  • Each hand has 5 fingers.
  • 6 × 5 = 30.
  • There are 30 fingers in all.
• Answer: 30

[Easy] Basic Division

• EN: 20 stickers are shared equally among 4 students. How many stickers does each student get?
• FR: 20 autocollants sont partagés également entre 4 élèves. Combien d'autocollants chaque élève reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Division is splitting into equal groups — try 15 ÷ 3.
• Steps:
  • 20 ÷ 4 = ?
  • Think: 4 × ? = 20. That is 4 × 5 = 20.
  • Each student gets 5 stickers.
• Answer: 5

[Medium] Perimeter

• EN: A rectangle is 6 cm long and 3 cm wide. What is its perimeter?
• FR: Un rectangle a 6 cm de long et 3 cm de large. Quel est son périmètre?
• Choices: A) 9 cm B) 15 cm C) 18 cm D) 24 cm
• Hint: Perimeter = add all four sides — try a rectangle 5 cm by 2 cm.
• Steps:
  • Two long sides: 6 + 6 = 12 cm.
  • Two short sides: 3 + 3 = 6 cm.
  • Perimeter = 12 + 6 = 18 cm.
• Answer: 18 cm

[Medium] Multiplication by 3

• EN: There are 7 bags. Each bag has 3 apples. How many apples are there in all?
• FR: Il y a 7 sacs. Chaque sac contient 3 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 18 B) 20 C) 21 D) 24
• Hint: Multiply the number of bags by the apples in each — try 5 bags × 3.
• Steps:
  • 7 × 3 = ?
  • Count by 3s seven times: 3, 6, 9, 12, 15, 18, 21.
  • There are 21 apples in all.
• Answer: 21

[Medium] Reading a Graph

• EN: A bar graph shows 8 students like hockey, 5 like soccer, and 3 like basketball. How many more students like hockey than basketball?
• FR: Un diagramme à barres montre que 8 élèves aiment le hockey, 5 aiment le soccer et 3 aiment le basketball. Combien d'élèves de plus aiment le hockey que le basketball?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: Find the difference between two bars by subtracting — try 9 − 4.
• Steps:
  • Hockey: 8, Basketball: 3.
  • 8 − 3 = 5.
  • 5 more students like hockey than basketball.
• Answer: 5

[Medium] Fractions Comparison

• EN: Which fraction is larger: 1/2 or 1/4?
• FR: Quelle fraction est la plus grande : 1/2 ou 1/4?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) They are equal
• Hint: The smaller the denominator, the larger the piece — think of sharing a sandwich.
• Steps:
  • 1/2 means 1 out of 2 equal parts — each part is large.
  • 1/4 means 1 out of 4 equal parts — each part is smaller.
  • So 1/2 is larger than 1/4.
• Answer: 1/2

[Hard] Two-Step Multiplication and Addition

• EN: There are 4 boxes of crayons. Each box has 10 crayons. A teacher adds 8 more crayons from an extra pack. How many crayons are there in all?
• FR: Il y a 4 boîtes de crayons. Chaque boîte contient 10 crayons. Une enseignante ajoute 8 crayons de plus d'un paquet supplémentaire. Combien y a-t-il de crayons en tout?
• Choices: A) 42 B) 46 C) 48 D) 52
• Hint: Multiply first, then add — try 3 × 10 + 5.
• Steps:
  • 4 × 10 = 40 crayons in the boxes.
  • Add 8 more: 40 + 8 = 48.
  • There are 48 crayons in all.
• Answer: 48

[Hard] Perimeter Problem Solving

• EN: A square has a perimeter of 28 cm. What is the length of one side?
• FR: Un carré a un périmètre de 28 cm. Quelle est la longueur d'un côté?
• Choices: A) 5 cm B) 6 cm C) 7 cm D) 8 cm
• Hint: A square has 4 equal sides; divide the perimeter by 4 — try 20 cm ÷ 4.
• Steps:
  • Perimeter of a square = 4 × side.
  • So side = perimeter ÷ 4.
  • 28 ÷ 4 = 7 cm.
• Answer: 7 cm

[Easy] Multiplication 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 multiplication fact you know — try 7 × 7 = 49, then add one more group of 7.
• Steps:
  • 7 × 7 = 49.
  • Add one more 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) 30 ones
• Hint: After the decimal point, the first digit is tenths, the second is hundredths — try 2.51.
• Steps:
  • The digits after the decimal: 4.37.
  • The 3 is the first digit after the decimal.
  • That digit is in the tenths place, so 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 a 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 of a rectangle = length × width — try 8 cm × 3 cm.
• Steps:
  • Area = length × width.
  • 9 × 4 = 36.
  • The area is 36 cm².
• Answer: 36 cm²

[Easy] Long Division

• EN: What is 48 ÷ 6?
• FR: Combien font 48 ÷ 6?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Think of the matching multiplication fact — try 6 × ? = 42.
• Steps:
  • Ask: 6 × ? = 48.
  • 6 × 8 = 48.
  • So 48 ÷ 6 = 8.
• Answer: 8

[Medium] Long Division With Remainder

• EN: What is 47 ÷ 5?
• FR: Combien font 47 ÷ 5?
• Choices: A) 8 remainder 7 B) 9 remainder 2 C) 9 remainder 3 D) 10 remainder 2
• Hint: Find the largest multiple of the divisor that fits, then find what is left over — try 38 ÷ 4.
• Steps:
  • 5 × 9 = 45, which is the closest multiple of 5 less than 47.
  • 47 − 45 = 2 remainder.
  • So 47 ÷ 5 = 9 remainder 2.
• Answer: 9 remainder 2

[Medium] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 2/3?
• FR: Quelle fraction est la plus grande : 3/4 ou 2/3?
• Choices: A) 2/3 B) 3/4 C) They are equal D) 1/2
• Hint: Find a common denominator to compare — try 1/2 and 2/5.
• Steps:
  • Common denominator of 4 and 3 is 12.
  • 3/4 = 9/12; 2/3 = 8/12.
  • 9/12 > 8/12, so 3/4 is larger.
• Answer: 3/4

[Medium] Elapsed Time

• EN: A hockey practice starts at 4:15 and ends at 5:45. How long is the practice?
• FR: Une pratique de hockey commence à 16 h 15 et se termine à 17 h 45. Combien de temps dure la pratique?
• Choices: A) 1 hour 15 minutes B) 1 hour 30 minutes C) 1 hour 45 minutes D) 2 hours
• Hint: Count up from the start time to the end time — try from 2:10 to 3:40.
• Steps:
  • From 4:15 to 5:15 = 1 hour.
  • From 5:15 to 5:45 = 30 minutes.
  • Total = 1 hour 30 minutes.
• Answer: 1 hour 30 minutes

[Medium] Decimal Operations

• EN: What is 3.6 + 2.7?
• FR: Combien font 3,6 + 2,7?
• Choices: A) 5.9 B) 6.1 C) 6.3 D) 6.5
• Hint: Line up the decimal points and add as usual — try 4.5 + 1.8.
• Steps:
  • Line up decimals: 3.6 + 2.7.
  • Tenths: 6 + 7 = 13; write 3, carry 1.
  • Ones: 3 + 2 + 1 = 6. Answer is 6.3.
• Answer: 6.3

[Hard] Multi-Step Problem

• EN: A school store sells notebooks for $2.50 each. A class orders 8 notebooks and pays with two $10 bills. How much change should the class receive?
• FR: La boutique de l'école vend des cahiers à 2,50 $ chacun. Une classe commande 8 cahiers et paie avec deux billets de 10 $. Combien de monnaie la classe devrait-elle recevoir?
• Choices: A) $0 B) $2.00 C) $3.00 D) $4.00
• Hint: Find the total cost first, then subtract from the amount paid — try 5 items at $3.00 each, paid with $20.
• Steps:
  • Cost: 8 × $2.50 = $20.00.
  • Paid: 2 × $10 = $20.00.
  • Change = $20.00 − $20.00 = $0.
• Answer: $0

[Hard] Area and Perimeter Together

• EN: A rectangle has a perimeter of 30 cm and a width of 5 cm. What is the area of the rectangle?
• FR: Un rectangle a un périmètre de 30 cm et une largeur de 5 cm. Quelle est l'aire du rectangle?
• Choices: A) 50 cm² B) 75 cm² C) 100 cm² D) 150 cm²
• Hint: First find the length using perimeter = 2 × (l + w), then find area — try perimeter 24 cm, width 4 cm.
• Steps:
  • Perimeter = 2 × (length + width): 30 = 2 × (l + 5).
  • l + 5 = 15, so l = 10 cm.
  • Area = 10 × 5 = 50 cm².
• Answer: 50 cm²

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 194 B) 200 C) 204 D) 210
• Hint: Multiply the ones, then the tens, and add — try 23 × 4.
• Steps:
  • 6 × 4 = 24; write 4, carry 2.
  • 6 × 3 = 18; add carry: 18 + 2 = 20.
  • Answer: 204
• Answer: 204

[Easy] Adding Fractions With Like Denominators

• EN: What is 2/7 + 3/7?
• FR: Combien font 2/7 + 3/7?
• Choices: A) 5/7 B) 5/14 C) 6/7 D) 1/7
• Hint: Add the numerators and keep the same denominator — try 3/8 + 2/8.
• Steps:
  • Denominators are the same (7), so add numerators.
  • 2 + 3 = 5.
  • Answer: 5/7
• Answer: 5/7

[Easy] Percentages — 50%

• EN: What is 50% of 80?
• FR: Combien font 50 % de 80?
• Choices: A) 20 B) 30 C) 40 D) 50
• Hint: 50% means half — divide the number by 2; try 50% of 60.
• Steps:
  • 50% = 1/2.
  • 80 ÷ 2 = 40.
  • So 50% of 80 = 40.
• Answer: 40

[Easy] Decimal Operations

• EN: What is 7.8 − 3.4?
• FR: Combien font 7,8 − 3,4?
• Choices: A) 3.4 B) 4.0 C) 4.4 D) 5.4
• Hint: Line up decimals and subtract as usual — try 9.6 − 4.2.
• Steps:
  • 7.8 − 3.4.
  • Tenths: 8 − 4 = 4.
  • Ones: 7 − 3 = 4. Answer: 4.4.
• Answer: 4.4

[Medium] Multi-Digit Division

• EN: What is 336 ÷ 8?
• FR: Combien font 336 ÷ 8?
• Choices: A) 40 B) 41 C) 42 D) 43
• Hint: Divide step by step using long division — try 248 ÷ 4.
• Steps:
  • 8 into 33: 8 × 4 = 32, remainder 1. Bring down 6: 16.
  • 8 into 16 = 2.
  • Answer: 42
• Answer: 42

[Medium] Subtracting Fractions

• EN: What is 6/9 − 2/9?
• FR: Combien font 6/9 − 2/9?
• Choices: A) 3/9 B) 4/9 C) 5/9 D) 8/18
• Hint: Subtract the numerators and keep the denominator — try 7/10 − 3/10.
• Steps:
  • Denominators are the same (9).
  • 6 − 2 = 4.
  • Answer: 4/9
• Answer: 4/9

[Medium] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte a 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 40 cm³ B) 55 cm³ C) 60 cm³ D) 65 cm³
• Hint: Volume = length × width × height — try 6 cm × 2 cm × 4 cm.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60.
  • Volume = 60 cm³.
• Answer: 60 cm³

[Medium] Percentages — 25%

• EN: What is 25% of $48?
• FR: Combien font 25 % de 48 $?
• Choices: A) $10 B) $12 C) $14 D) $16
• Hint: 25% means one quarter — divide by 4; try 25% of $60.
• Steps:
  • 25% = 1/4.
  • $48 ÷ 4 = $12.
  • So 25% of $48 = $12.
• Answer: $12

[Hard] Multi-Step Fraction and Decimal Problem

• EN: A juice bottle holds 1.5 litres. A family drinks 3/4 of the bottle. How many litres did they drink?
• FR: Une bouteille de jus contient 1,5 litre. Une famille boit 3/4 de la bouteille. Combien de litres ont-ils bu?
• Choices: A) 0.75 litres B) 1.0 litres C) 1.125 litres D) 1.25 litres
• Hint: Multiply the total amount by the fraction — try 2.0 litres × 3/4.
• Steps:
  • 3/4 of 1.5: find 1/4 first: 1.5 ÷ 4 = 0.375.
  • Then multiply by 3: 0.375 × 3 = 1.125.
  • They drank 1.125 litres.
• Answer: 1.125 litres

[Hard] Multi-Digit Multiplication — Word Problem

• EN: A school orders 24 boxes of coloured pencils. Each box has 48 pencils. How many pencils are ordered in all?
• FR: Une école commande 24 boîtes de crayons de couleur. Chaque boîte contient 48 crayons. Combien de crayons sont commandés en tout?
• Choices: A) 1 052 B) 1 100 C) 1 152 D) 1 200
• Hint: Use long multiplication — try 12 × 36.
• Steps:
  • 24 × 48.
  • 24 × 8 = 192; 24 × 40 = 960.
  • 192 + 960 = 1 152.
• Answer: 1 152

[Easy] Percent of a Number

• EN: What is 30% of 70?
• FR: Combien font 30 % de 70?
• Choices: A) 18 B) 21 C) 24 D) 27
• Hint: Find 10% first then multiply — 10% of 70 is 7, so 30% is 3 × 7; try 20% of 50.
• Steps:
  • 10% of 70 = 7.
  • 30% = 3 × 7 = 21.
  • 30% of 70 = 21.
• Answer: 21

[Easy] Ratios

• EN: In a bag there are 4 red marbles and 6 blue marbles. What is the ratio of red to blue marbles?
• FR: Dans un sac, il y a 4 billes rouges et 6 billes bleues. Quel est le rapport des billes rouges aux billes bleues?
• Choices: A) 2:3 B) 3:2 C) 4:10 D) 6:4
• Hint: Write the ratio as given, then simplify by dividing both by the GCF — try 6 red to 9 blue.
• Steps:
  • Ratio = 4:6.
  • GCF of 4 and 6 is 2.
  • Simplified: 4÷2 : 6÷2 = 2:3.
• Answer: 2:3

[Easy] Integer Introduction

• EN: The temperature is −3°C. It drops 5 more degrees. What is the new temperature?
• FR: La température est de −3 °C. Elle baisse encore de 5 degrés. Quelle est la nouvelle température?
• Choices: A) −9°C B) −8°C C) 2°C D) 8°C
• Hint: On a number line, subtracting moves left — try starting at −2 and going down 4.
• Steps:
  • Start at −3.
  • Drop 5: −3 − 5 = −8.
  • New temperature is −8°C.
• Answer: −8°C

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: In BEDMAS, multiplication comes before addition — try 5 + 3 × 2.
• Steps:
  • Do multiplication first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • Answer: 11
• Answer: 11

[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) 1/2
• Hint: Multiply numerators together and denominators together, then simplify — try 1/2 × 2/3.
• Steps:
  • Numerators: 2 × 3 = 6.
  • Denominators: 3 × 4 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Rate Problems

• EN: A car travels 120 km in 2 hours. What is its speed in km/h?
• FR: Une voiture parcourt 120 km en 2 heures. Quelle est sa vitesse en km/h?
• Choices: A) 55 km/h B) 60 km/h C) 65 km/h D) 70 km/h
• Hint: Speed = distance ÷ time — try 90 km in 3 hours.
• Steps:
  • Speed = distance ÷ time.
  • 120 ÷ 2 = 60.
  • The car's speed is 60 km/h.
• Answer: 60 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) 17 B) 18 C) 19 D) 20
• Hint: Substitute the value into the expression — try n = 3 in 2n + 5.
• Steps:
  • Replace n with 5: 3(5) + 4.
  • 3 × 5 = 15.
  • 15 + 4 = 19.
• Answer: 19

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 2
• Hint: To divide fractions, multiply by the reciprocal — try 2/5 ÷ 1/3.
• Steps:
  • Flip the divisor: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4.
  • Simplify: 6/4 = 3/2.
• Answer: 3/2

[Hard] BEDMAS With Brackets

• EN: What is (6 + 2) × 3 − 4²?
• FR: Combien font (6 + 2) × 3 − 4²?
• Choices: A) 4 B) 8 C) 16 D) 20
• Hint: Follow BEDMAS — Brackets first, then Exponents, then Multiplication/Division, then Addition/Subtraction; try (3 + 1) × 5 − 2².
• Steps:
  • Brackets: 6 + 2 = 8.
  • Exponents: 4² = 16.
  • Multiply: 8 × 3 = 24. Then 24 − 16 = 8.
• Answer: 8

[Hard] Percent — Multi-Step

• EN: A Tim Hortons coffee costs $2.50. The price increases by 20%. What is the new price?
• FR: Un café Tim Hortons coûte 2,50 $. Le prix augmente de 20 %. Quel est le nouveau prix?
• Choices: A) $2.75 B) $3.00 C) $3.25 D) $3.50
• Hint: Find 20% of the original price and add it — try a $5.00 item with 20% increase.
• Steps:
  • 20% of $2.50 = 0.20 × 2.50 = $0.50.
  • New price = $2.50 + $0.50 = $3.00.
  • The new price is $3.00.
• Answer: $3.00

[Easy] Integer Addition

• EN: What is (−7) + 4?
• FR: Combien font (−7) + 4?
• Choices: A) −4 B) −3 C) 3 D) 11
• Hint: On a number line, start at the negative number and move right by the positive amount — try (−5) + 3.
• Steps:
  • Start at −7.
  • Move 4 units to the right.
  • −7 + 4 = −3.
• Answer: −3

[Easy] Integer Subtraction

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

[Easy] Percent Discount

• EN: A hockey stick costs $60 and is on sale at 10% off. How much is the discount?
• FR: Un bâton de hockey coûte 60 $ et est en solde à 10 % de rabais. Quel est le montant du rabais?
• Choices: A) $5 B) $6 C) $10 D) $12
• Hint: Find 10% by dividing by 10 — try 10% of $80.
• Steps:
  • 10% of $60 = $60 ÷ 10 = $6.
  • The discount is $6.
• Answer: $6

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 15.
• FR: Résous l'équation : x + 9 = 15.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 24
• Hint: To isolate the variable, subtract the same number from both sides — try x + 4 = 11.
• Steps:
  • x + 9 = 15.
  • Subtract 9 from both sides: x = 15 − 9.
  • x = 6.
• Answer: x = 6

[Medium] Integer Multiplication

• EN: What is (−4) × (−6)?
• FR: Combien font (−4) × (−6)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: A negative times a negative equals a positive — try (−3) × (−5).
• Steps:
  • Negative × negative = positive.
  • 4 × 6 = 24.
  • (−4) × (−6) = 24.
• Answer: 24

[Medium] Percentage — Tax

• EN: A pair of skates costs $80 before tax. Tax is 13%. What is the total cost after tax?
• FR: Une paire de patins coûte 80 $ avant taxes. La taxe est de 13 %. Quel est le coût total après taxes?
• Choices: A) $88.40 B) $90.00 C) $90.40 D) $93.00
• Hint: Find the tax amount (price × tax rate) then add to original price — try $50 + 13%.
• Steps:
  • Tax = 13% of $80 = 0.13 × 80 = $10.40.
  • Total = $80 + $10.40 = $90.40.
  • The total cost is $90.40.
• Answer: $90.40

[Medium] Surface Area

• EN: A rectangular box is 5 cm long, 3 cm wide, and 2 cm tall. What is the surface area?
• FR: Une boîte rectangulaire a 5 cm de long, 3 cm de large et 2 cm de haut. Quelle est son aire totale?
• Choices: A) 52 cm² B) 60 cm² C) 62 cm² D) 70 cm²
• Hint: Surface area = 2(lw + lh + wh) — try a box 4 cm × 2 cm × 3 cm.
• Steps:
  • lw = 5 × 3 = 15; lh = 5 × 2 = 10; wh = 3 × 2 = 6.
  • 15 + 10 + 6 = 31.
  • 2 × 31 = 62 cm².
• Answer: 62 cm²

[Medium] Probability

• EN: A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of picking a 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) 1/3 C) 1/2 D) 5/10
• Hint: Probability = favourable outcomes ÷ total outcomes — try 4 blue out of 12 marbles.
• Steps:
  • Total marbles = 3 + 5 + 2 = 10.
  • Favourable = 5 blue.
  • Probability = 5/10 = 1/2.
• Answer: 1/2

[Hard] Multi-Step Percent Problem

• EN: A school store sells a notebook for $4.80. A student gets a 15% student discount. How much does the student pay after the discount?
• FR: La boutique de l'école vend un cahier 4,80 $. Un élève obtient un rabais étudiant de 15 %. Combien l'élève paie-t-il après le rabais?
• Choices: A) $3.96 B) $4.00 C) $4.08 D) $4.20
• Hint: Find the discount amount, then subtract from the original price — try $6.00 with a 15% discount.
• Steps:
  • Discount = 15% of $4.80 = 0.15 × 4.80 = $0.72.
  • Price after discount = $4.80 − $0.72 = $4.08.
  • The student pays $4.08.
• Answer: $4.08

[Hard] Solving One-Step Equations With Integers

• EN: Solve for n: −3n = 27.
• FR: Résous pour n : −3n = 27.
• Choices: A) n = −9 B) n = −8 C) n = 8 D) n = 9
• Hint: Divide both sides by the coefficient — be careful with signs; try −4n = 20.
• Steps:
  • −3n = 27.
  • Divide both sides by −3: n = 27 ÷ (−3).
  • n = −9.
• Answer: n = −9

[Easy] Perfect Squares

• EN: What is √81?
• FR: Combien fait √81?
• Choices: A) 7 B) 8 C) 9 D) 11
• Hint: Think: what number multiplied by itself gives this result? — try √49.
• Steps:
  • Ask: ? × ? = 81.
  • 9 × 9 = 81.
  • √81 = 9.
• Answer: 9

[Easy] Mean of a Data Set

• EN: Find the mean of: 4, 8, 6, 10, 7.
• FR: Trouve la moyenne de : 4, 8, 6, 10, 7.
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Mean = sum of values ÷ number of values — try 3, 5, 7.
• Steps:
  • Sum = 4 + 8 + 6 + 10 + 7 = 35.
  • Count = 5.
  • Mean = 35 ÷ 5 = 7.
• Answer: 7

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 3 = 11.
• FR: Résous pour x : 2x + 3 = 11.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 7
• Hint: First subtract the constant from both sides, then divide by the coefficient — try 3x + 2 = 14.
• Steps:
  • 2x + 3 = 11; subtract 3: 2x = 8.
  • Divide by 2: x = 4.
  • x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A price increases from $50 to $60. What is the percent increase?
• FR: Un prix augmente de 50 $ à 60 $. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: Percent increase = (increase ÷ original) × 100 — try a price going from $40 to $48.
• Steps:
  • Increase = 60 − 50 = $10.
  • Percent = (10 ÷ 50) × 100 = 20%.
  • The percent increase is 20%.
• Answer: 20%

[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: Use a² + b² = c² — try legs of 3 and 4.
• Steps:
  • a² + b² = c²: 6² + 8² = c².
  • 36 + 64 = 100; c² = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equations — Harder

• EN: Solve for y: 5y − 7 = 18.
• FR: Résous pour y : 5y − 7 = 18.
• Choices: A) y = 4 B) y = 5 C) y = 6 D) y = 11
• Hint: Add the constant to both sides first, then divide — try 4y − 3 = 17.
• Steps:
  • 5y − 7 = 18; add 7: 5y = 25.
  • Divide by 5: y = 5.
  • y = 5.
• Answer: y = 5

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 5, 9, 5, 11, 5.
• FR: Trouve la médiane de : 3, 7, 5, 9, 5, 11, 5.
• Choices: A) 5 B) 6 C) 7 D) 9
• Hint: Order the numbers and find the middle value — try 2, 4, 6, 8, 10.
• Steps:
  • Order: 3, 5, 5, 5, 7, 9, 11.
  • There are 7 values; the middle (4th) is 5.
  • Median = 5.
• Answer: 5

[Medium] Slope Introduction

• EN: A ramp rises 4 metres over a horizontal distance of 8 metres. What is the slope?
• FR: Une rampe monte de 4 mètres sur une distance horizontale de 8 mètres. Quelle est la pente?
• Choices: A) 1/4 B) 2/4 C) 1/2 D) 2
• Hint: Slope = rise ÷ run — try rise of 3 over run of 9.
• Steps:
  • Slope = rise ÷ run = 4 ÷ 8.
  • 4 ÷ 8 = 1/2.
  • The slope is 1/2.
• Answer: 1/2

[Hard] Pythagorean Theorem — Find a Leg

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 8 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: Rearrange a² + b² = c² to find b² = c² − a² — try c = 10, a = 6.
• Steps:
  • b² = c² − a² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12.
  • The other leg is 12 cm.
• Answer: 12 cm

[Hard] Percent Decrease — Multi-Step

• EN: A jacket originally costs $120. It is first reduced by 25%, then by an additional 10% off the sale price. What is the final price?
• FR: Un manteau coûte 120 $ à l'origine. Il est d'abord réduit de 25 %, puis de 10 % supplémentaires sur le prix de vente. Quel est le prix final?
• Choices: A) $72.00 B) $78.00 C) $81.00 D) $84.00
• Hint: Apply each percent reduction one at a time to the result of the previous step — try $100 with 20% off then 10% off.
• Steps:
  • 25% off $120: $120 × 0.75 = $90.
  • 10% off $90: $90 × 0.90 = $81.
  • Final price = $81.00.
• Answer: $81.00

[Easy] Solving a Linear Equation

• EN: Solve for x: 3x − 5 = 16.
• FR: Résous pour x : 3x − 5 = 16.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 11
• Hint: Add to both sides first, then divide — try 4x − 3 = 13.
• Steps:
  • 3x − 5 = 16; add 5: 3x = 21.
  • Divide by 3: x = 7.
  • x = 7.
• Answer: x = 7

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3).
• FR: Simplifie : (3x + 5) + (2x − 3).
• Choices: A) 5x − 2 B) 5x + 2 C) 5x + 8 D) 6x + 2
• Hint: Combine like terms — terms with x together, constants together; try (4x + 2) + (x − 5).
• Steps:
  • x-terms: 3x + 2x = 5x.
  • Constants: 5 + (−3) = 2.
  • Answer: 5x + 2
• Answer: 5x + 2

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 4x − 7?
• FR: Quelle est la pente de la droite y = 4x − 7?
• Choices: A) −7 B) 4 C) 7 D) 11
• Hint: In y = mx + b, m is the slope — try y = 3x + 5.
• Steps:
  • y = 4x − 7 is in slope-intercept form y = mx + b.
  • m = 4.
  • The slope is 4.
• Answer: 4

[Easy] Solving a Linear Inequality

• EN: Solve for x: x + 4 > 10.
• FR: Résous pour x : x + 4 > 10.
• Choices: A) x > 4 B) x > 5 C) x > 6 D) x > 14
• Hint: Treat it like an equation — subtract from both sides; try x + 3 > 8.
• Steps:
  • x + 4 > 10.
  • Subtract 4 from both sides: x > 6.
  • Solution: x > 6.
• Answer: x > 6

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x + 5).
• FR: Développe : 3x(2x + 5).
• Choices: A) 5x² + 8x B) 6x² + 8x C) 6x² + 15x D) 6x + 15x
• Hint: Distribute the term outside the brackets to each term inside — try 2x(x + 4).
• Steps:
  • 3x × 2x = 6x².
  • 3x × 5 = 15x.
  • Answer: 6x² + 15x
• Answer: 6x² + 15x

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 10 cm. If the shorter triangle has another side of 6 cm, what is the matching side in the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 10 cm. Si le triangle plus petit a un autre côté de 6 cm, quel est le côté correspondant dans le triangle plus grand?
• Choices: A) 12 cm B) 14 cm C) 15 cm D) 16 cm
• Hint: Set up a proportion using the scale factor — try sides 3 and 9, shorter side 4.
• Steps:
  • Scale factor = 10 ÷ 4 = 2.5.
  • Unknown side = 6 × 2.5 = 15.
  • The matching side is 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the angle is 30°, and the hypotenuse is 20 cm. What is the length of the side opposite the 30° angle?
• FR: Dans un triangle rectangle, l'angle est de 30° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: sin(angle) = opposite ÷ hypotenuse; sin(30°) = 0.5 — try hypotenuse 14, angle 30°.
• Steps:
  • sin(30°) = opposite ÷ 20.
  • opposite = 20 × sin(30°) = 20 × 0.5 = 10.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Medium] Graphing Lines

• EN: A line passes through (0, 3) and has a slope of 2. What is the equation of the line?
• FR: Une droite passe par (0, 3) et a une pente de 2. Quelle est l'équation de la droite?
• Choices: A) y = 2x − 3 B) y = 2x + 3 C) y = 3x + 2 D) y = x + 3
• Hint: Use y = mx + b where m is the slope and b is the y-intercept — try slope 3, passing through (0, −1).
• Steps:
  • m = 2, b = 3 (y-intercept is the starting point on y-axis).
  • Equation: y = 2x + 3.
  • That is the equation of the line.
• Answer: y = 2x + 3

[Hard] Systems of Equations by Substitution

• EN: Solve the system: y = 2x + 1 and y = −x + 7.
• FR: Résous le système : y = 2x + 1 et y = −x + 7.
• Choices: A) x = 1, y = 5 B) x = 2, y = 5 C) x = 2, y = 7 D) x = 3, y = 4
• Hint: Set the two expressions for y equal and solve for x, then substitute back — try y = x + 2 and y = 3x − 4.
• Steps:
  • 2x + 1 = −x + 7; add x: 3x + 1 = 7; subtract 1: 3x = 6; x = 2.
  • y = 2(2) + 1 = 5.
  • Solution: x = 2, y = 5.
• Answer: x = 2, y = 5

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 7 cm and the hypotenuse is 14 cm. What is the angle opposite the 7 cm side? (Use sin⁻¹)
• FR: Dans un triangle rectangle, le côté opposé est de 7 cm et l'hypoténuse est de 14 cm. Quel est l'angle opposé au côté de 7 cm? (Utilise sin⁻¹)
• Choices: A) 20° B) 25° C) 30° D) 45°
• Hint: sin(angle) = opposite ÷ hypotenuse; then take the inverse sine — try opposite 5, hypotenuse 10.
• Steps:
  • sin(angle) = 7 ÷ 14 = 0.5.
  • angle = sin⁻¹(0.5) = 30°.
  • The angle is 30°.
• Answer: 30°

[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 − 3) D) (x + 3)(x + 3)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — try x² + 7x + 12.
• Steps:
  • Need two numbers that multiply to 6 and add to 5.
  • 2 × 3 = 6 and 2 + 3 = 5.
  • Answer: (x + 2)(x + 3)
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — CAH

• EN: In a right triangle, the angle is 60° and the hypotenuse is 10 cm. What is the length of the adjacent side?
• FR: Dans un triangle rectangle, l'angle est de 60° et l'hypoténuse est de 10 cm. Quelle est la longueur du côté adjacent?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: cos(angle) = adjacent ÷ hypotenuse; cos(60°) = 0.5 — try hypotenuse 8, angle 60°.
• Steps:
  • cos(60°) = adjacent ÷ 10.
  • adjacent = 10 × 0.5 = 5.
  • The adjacent side is 5 cm.
• Answer: 5 cm

[Easy] Systems of Equations

• EN: Solve the system: x + y = 10 and x − y = 4.
• FR: Résous le système : x + y = 10 et x − y = 4.
• Choices: A) x = 5, y = 5 B) x = 6, y = 4 C) x = 7, y = 3 D) x = 8, y = 2
• Hint: Add the two equations to eliminate one variable — try x + y = 8 and x − y = 2.
• Steps:
  • Add: 2x = 14, so x = 7.
  • Substitute: 7 + y = 10, so y = 3.
  • Solution: x = 7, y = 3.
• Answer: x = 7, y = 3

[Easy] Volume of a Cylinder

• EN: A cylinder has radius 3 cm and height 7 cm. What is the volume? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 7 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 169.56 cm³ B) 179.56 cm³ C) 188.46 cm³ D) 197.82 cm³
• Hint: Volume = πr²h — try r = 2, h = 5.
• Steps:
  • V = π × 3² × 7 = 3.14 × 9 × 7.
  • 3.14 × 9 = 28.26; 28.26 × 7 = 197.82.
  • Volume ≈ 197.82 cm³.
• Answer: 197.82 cm³

[Medium] Completing the Square

• EN: Solve by completing the square: x² + 6x = 7.
• FR: Résous en complétant le carré : x² + 6x = 7.
• Choices: A) x = 1 or x = −7 B) x = −1 or x = 7 C) x = 2 or x = −7 D) x = 1 or x = 7
• Hint: Add (b/2)² to both sides to complete the square — try x² + 4x = 12.
• Steps:
  • x² + 6x + 9 = 7 + 9 = 16.
  • (x + 3)² = 16; x + 3 = ±4.
  • x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Circle Geometry

• EN: A circle has a diameter of 12 cm. What is its circumference? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 12 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 36.68 cm B) 37.68 cm C) 38.68 cm D) 40.00 cm
• Hint: Circumference = π × diameter — try a diameter of 10 cm.
• Steps:
  • C = π × d = 3.14 × 12.
  • 3.14 × 12 = 37.68.
  • Circumference ≈ 37.68 cm.
• Answer: 37.68 cm

[Medium] Quadratic Formula

• EN: Solve using the quadratic formula: x² − 5x + 6 = 0.
• FR: Résous à l'aide de la formule quadratique : x² − 5x + 6 = 0.
• Choices: A) x = 2 or x = 3 B) x = −2 or x = −3 C) x = 1 or x = 6 D) x = 2 or x = 4
• Hint: x = (−b ± √(b²−4ac)) / 2a — identify a, b, c first; try x² − 7x + 12 = 0.
• Steps:
  • a = 1, b = −5, c = 6. Discriminant = 25 − 24 = 1.
  • x = (5 ± 1) / 2: x = 3 or x = 2.
  • Solutions: x = 2 or x = 3.
• Answer: x = 2 or x = 3

[Medium] Surface Area of a Cone

• EN: A cone has radius 4 cm and slant height 9 cm. What is the surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une apothème de 9 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 150.72 cm² B) 163.28 cm² C) 164.00 cm² D) 175.84 cm²
• Hint: Surface area of a cone = πr² + πrl — try r = 3, l = 5.
• Steps:
  • Base area: π × 4² = 3.14 × 16 = 50.24 cm².
  • Lateral area: π × 4 × 9 = 3.14 × 36 = 113.04 cm².
  • Total = 50.24 + 113.04 = 163.28 cm².
• Answer: 163.28 cm²

[Hard] Circle Geometry — Chord and Radius

• EN: A chord in a circle is 16 cm long. The radius of the circle is 10 cm. What is the distance from the centre of the circle to the chord?
• FR: Une corde dans un cercle a 16 cm de long. Le rayon du cercle est de 10 cm. Quelle est la distance du centre du cercle à la corde?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: The perpendicular from the centre bisects the chord; use the Pythagorean theorem — try chord 12 cm, radius 10 cm.
• Steps:
  • Half-chord = 16 ÷ 2 = 8 cm; radius = 10 cm.
  • distance² = 10² − 8² = 100 − 64 = 36.
  • Distance = √36 = 6 cm.
• Answer: 6 cm

[Hard] Systems and Quadratics

• EN: Find the x-values where the line y = x + 2 intersects the parabola y = x².
• FR: Trouve les valeurs de x où la droite y = x + 2 intersecte la parabole y = x².
• Choices: A) x = −1 or x = 2 B) x = 1 or x = −2 C) x = 2 or x = 3 D) x = −2 or x = −1
• Hint: Set the two expressions equal and solve the resulting quadratic — try y = x + 6 and y = x².
• Steps:
  • Set equal: x² = x + 2; rearrange: x² − x − 2 = 0.
  • Factor: (x − 2)(x + 1) = 0.
  • x = 2 or x = −1.
• Answer: x = −1 or x = 2

[Easy] Evaluating an Exponential Function

• EN: If f(x) = 2^x, what is f(5)?
• FR: Si f(x) = 2^x, combien vaut f(5)?
• Choices: A) 10 B) 16 C) 25 D) 32
• Hint: Raise the base to the given power — try f(4) = 2⁴.
• Steps:
  • f(5) = 2^5.
  • 2^5 = 2 × 2 × 2 × 2 × 2 = 32.
  • f(5) = 32.
• Answer: 32

[Easy] Logarithm Introduction

• EN: What is log₂(32)?
• FR: Combien vaut log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: Ask: 2 to what power equals 32? — try log₂(8).
• Steps:
  • log₂(32) = x means 2^x = 32.
  • 2^5 = 32.
  • So log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequence

• EN: What is the 8th term of the arithmetic sequence 3, 7, 11, 15, …?
• FR: Quel est le 8ᵉ terme de la suite arithmétique 3, 7, 11, 15, …?
• Choices: A) 29 B) 31 C) 33 D) 35
• Hint: Use the formula aₙ = a₁ + (n − 1)d — try finding the 5th term if a₁ = 2, d = 4.
• Steps:
  • a₁ = 3, d = 4, n = 8.
  • a₈ = 3 + (8 − 1) × 4 = 3 + 28 = 31.
  • The 8th term is 31.
• Answer: 31

[Easy] Compound Interest

• EN: Alicia invests $1 000 at 5% per year compounded annually for 2 years. What is the amount after 2 years?
• FR: Alicia investit 1 000 $ à 5 % par an composé annuellement pendant 2 ans. Quel est le montant après 2 ans?
• Choices: A) $1 050.00 B) $1 100.00 C) $1 102.50 D) $1 105.00
• Hint: Use A = P(1 + r)ⁿ — try $500 at 4% for 2 years.
• Steps:
  • A = 1000 × (1.05)².
  • (1.05)² = 1.1025.
  • A = $1 102.50.
• Answer: $1 102.50

[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 (h, k) — try y = (x − 2)² + 7.
• Steps:
  • y = (x − 3)² + 5 is in vertex form.
  • h = 3, k = 5.
  • Vertex is (3, 5).
• Answer: (3, 5)

[Medium] Geometric Series Sum

• EN: Find the sum of the first 5 terms of the geometric sequence 2, 6, 18, 54, …
• FR: Trouve la somme des 5 premiers termes de la suite géométrique 2, 6, 18, 54, …
• Choices: A) 182 B) 240 C) 242 D) 256
• Hint: Use Sₙ = a₁(rⁿ − 1) / (r − 1) — try a₁ = 3, r = 2, n = 4.
• Steps:
  • a₁ = 2, r = 3, n = 5.
  • S₅ = 2(3⁵ − 1)/(3 − 1) = 2(243 − 1)/2 = 242.
  • Sum = 242.
• Answer: 242

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ.
• FR: Simplifie : sin²θ + cos²θ.
• Choices: A) 0 B) 1 C) 2 D) sinθ
• Hint: This is the most fundamental Pythagorean identity — think of the unit circle.
• Steps:
  • The Pythagorean identity states: sin²θ + cos²θ = 1.
  • This is always true for any angle θ.
  • Answer: 1
• Answer: 1

[Medium] Annuity — Future Value

• EN: Mia deposits $200 at the end of each year for 3 years into an account earning 4% per year. What is the future value? (Round to the nearest cent.)
• FR: Mia dépose 200 $ à la fin de chaque année pendant 3 ans dans un compte rapportant 4 % par an. Quelle est la valeur future? (Arrondi au cent près.)
• Choices: A) $620.32 B) $624.32 C) $628.48 D) $632.48
• Hint: FV = PMT × [(1 + r)ⁿ − 1] / r — try $100/year for 3 years at 5%.
• Steps:
  • FV = 200 × [(1.04)³ − 1] / 0.04.
  • (1.04)³ = 1.124864; 1.124864 − 1 = 0.124864.
  • FV = 200 × 0.124864 / 0.04 = 200 × 3.1216 = $624.32.
• Answer: $624.32

[Hard] Logarithm — Solving an Equation

• EN: Solve for x: log₃(x − 1) = 3.
• FR: Résous pour x : log₃(x − 1) = 3.
• Choices: A) x = 27 B) x = 28 C) x = 29 D) x = 30
• Hint: Rewrite the logarithmic equation in exponential form — try log₂(x + 1) = 4.
• Steps:
  • log₃(x − 1) = 3 means 3³ = x − 1.
  • 3³ = 27, so x − 1 = 27.
  • x = 28.
• Answer: x = 28

[Hard] Compound Interest — Solving for Time

• EN: How many years will it take for $1 000 to double at 7% interest compounded annually? (Use log₁.₀₇(2) ≈ 10.24)
• FR: Dans combien d'années 1 000 $ doubleront-ils à un taux d'intérêt de 7 % composé annuellement? (Utilise log₁,₀₇(2) ≈ 10,24)
• Choices: A) About 8 years B) About 9 years C) About 10 years D) About 11 years
• Hint: Set up 2 = (1.07)ⁿ and take logarithms — try doubling at 10%.
• Steps:
  • 2 = (1.07)ⁿ; take log: n = log(2)/log(1.07).
  • log(2) ≈ 0.301; log(1.07) ≈ 0.0294.
  • n ≈ 0.301/0.0294 ≈ 10.24, so about 10 years.
• Answer: About 10 years

[Easy] Permutations

• EN: How many ways can 5 students be arranged in a line?
• FR: De combien de façons 5 élèves peuvent-ils être alignés?
• Choices: A) 60 B) 100 C) 120 D) 150
• Hint: Use n! — try arranging 4 students in a line.
• Steps:
  • 5 students: 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: How many ways can 2 students be chosen from a group of 6?
• FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 6?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: Use C(n, r) = n! / (r!(n−r)!) — try choosing 2 from 5.
• 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: What is the derivative of f(x) = x³?
• FR: Quelle est la dérivée de f(x) = x³?
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: Power rule: d/dx(xⁿ) = nxⁿ⁻¹ — try f(x) = x⁴.
• Steps:
  • f(x) = x³; apply power rule.
  • f'(x) = 3 × x^(3−1) = 3x².
  • The derivative is 3x².
• Answer: 3x²

[Easy] Binomial Distribution

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 2 heads?
• FR: On lance une pièce de monnaie équitable 4 fois. Quelle est la probabilité d'obtenir exactement 2 faces?
• Choices: A) 1/4 B) 3/8 C) 5/8 D) 3/4
• Hint: Use C(n, k) × pᵏ × (1−p)ⁿ⁻ᵏ — try 3 flips with 1 head.
• Steps:
  • C(4,2) × (0.5)² × (0.5)² = 6 × 0.25 × 0.25 = 6 × 0.0625.
  • = 0.375 = 3/8.
  • Probability is 3/8.
• Answer: 3/8

[Medium] Polynomial Long Division

• EN: Divide (x³ − 3x² + 2x − 6) by (x − 3). What is the quotient?
• FR: Divise (x³ − 3x² + 2x − 6) par (x − 3). Quel est le quotient?
• Choices: A) x² + 2 B) x² − 2 C) x² + 3x + 2 D) x² − 3x + 2
• Hint: Use long division or factor by grouping — check by multiplying the answer back.
• Steps:
  • Factor by grouping: x²(x − 3) + 2(x − 3) = (x² + 2)(x − 3).
  • Quotient = x² + 2.
  • Answer: x² + 2
• Answer: x² + 2

[Medium] Derivative — Rate of Change

• EN: A ball's position is given by s(t) = 3t² − 2t + 1. What is the instantaneous velocity at t = 4?
• FR: La position d'une balle est donnée par s(t) = 3t² − 2t + 1. Quelle est la vitesse instantanée à t = 4?
• Choices: A) 18 B) 20 C) 22 D) 24
• Hint: Velocity = s'(t); differentiate and substitute — try s(t) = 2t² + t.
• Steps:
  • s'(t) = 6t − 2.
  • At t = 4: s'(4) = 6(4) − 2 = 24 − 2 = 22.
  • Instantaneous velocity = 22.
• Answer: 22

[Medium] Vectors — Addition

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

[Medium] Rational Function — Vertical Asymptote

• EN: Where is the vertical asymptote of f(x) = (x + 4) / (x − 2)?
• FR: Où se trouve l'asymptote verticale de f(x) = (x + 4) / (x − 2)?
• Choices: A) x = −4 B) x = −2 C) x = 2 D) x = 4
• Hint: Vertical asymptotes occur where the denominator equals zero — try (x + 1)/(x − 5).
• Steps:
  • Set denominator equal to zero: x − 2 = 0.
  • x = 2.
  • Vertical asymptote is at x = 2.
• Answer: x = 2

[Hard] Probability Distribution — Expected Value

• EN: A game pays $10 if you roll a 6 on a standard die, and you lose $2 for any other roll. What is the expected value of one roll?
• FR: Un jeu rapporte 10 $ si tu lances un 6 sur un dé standard, et tu perds 2 $ pour tout autre résultat. Quelle est l'espérance mathématique d'un lancer?
• Choices: A) −$1.00 B) −$0.67 C) $0.33 D) $1.00
• Hint: E = Σ(value × probability) — list outcomes and their probabilities.
• Steps:
  • P(6) = 1/6; P(other) = 5/6.
  • E = 10 × (1/6) + (−2) × (5/6).
  • E = 10/6 − 10/6 = 0/6 = $0.
  • Wait — recalculate: 10/6 = 1.667; 10/6 = 1.667; E = 1.667 − 1.667 = $0. Hmm, let me recheck: E = (10)(1/6) + (−2)(5/6) = 10/6 − 10/6 = 0. The answer is $0.00, but that's not a choice. Let me restate: E = 10/6 − 10/6 = 0. The closest choice is $0.33. Recalculating: 10 × (1/6) = 1.6̄; (−2) × (5/6) = −1.6̄; sum = 0. I need to choose a different payoff. Using $10 for rolling a 6 and losing $2 otherwise: E = 0. Let me use $8 for rolling a 6 and losing $1 otherwise: E = 8/6 − 5/6 = 3/6 = $0.50. I'll revise the problem.
• Answer: $0.33

(Correction — revised problem below)

[Hard] Probability Distribution — Expected Value

• EN: A game pays $5 if you roll a 6 on a standard die, and you lose $1 for any other roll. What is the expected value of one roll?
• FR: Un jeu rapporte 5 $ si tu lances un 6 sur un dé standard, et tu perds 1 $ pour tout autre résultat. Quelle est l'espérance mathématique d'un lancer?
• Choices: A) −$0.17 B) $0.00 C) $0.17 D) $0.50
• Hint: E = Σ(value × probability) — list each outcome and multiply by its probability.
• Steps:
  • P(6) = 1/6; gain = $5. P(other) = 5/6; loss = −$1.
  • E = 5 × (1/6) + (−1) × (5/6) = 5/6 − 5/6 = 0.
  • Expected value = $0.00.
• Answer: $0.00

[Hard] Vectors — Dot Product and Angle

• EN: Find the angle between vectors a = (1, 0) and b = (0, 1).
• FR: Trouve l'angle entre les vecteurs a = (1, 0) et b = (0, 1).
• Choices: A) 0° B) 45° C) 90° D) 180°
• Hint: Use cos θ = (a · b) / (|a| × |b|); the dot product of perpendicular vectors is 0.
• Steps:
  • a · b = (1)(0) + (0)(1) = 0.
  • |a| = 1, |b| = 1.
  • cos θ = 0 / 1 = 0; θ = cos⁻¹(0) = 90°.
• Answer: 90°