Daily Math — 2026-09-17

[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 total?
• FR: Il y a 7 pommes sur la table et 5 autres pommes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 11 apples B) 12 apples C) 13 apples D) 14 apples
• Hint: To add 6 + 4, start at 6 and count up 4 more: 7, 8, 9, 10.
• Steps:
  • Start at 7 and count up 5 more.
  • 8, 9, 10, 11, 12 — that is 12 apples in total.
• Answer: 12 apples

[Easy] Subtraction Within 20

• EN: There are 15 hockey pucks on the ice. A player takes away 6. How many pucks are left?
• FR: Il y a 15 rondelles de hockey sur la glace. Un joueur en enlève 6. Combien de rondelles reste-t-il?
• Choices: A) 7 pucks B) 8 pucks C) 9 pucks D) 10 pucks
• Hint: To find 14 − 5, start at 14 and count back 5: 13, 12, 11, 10, 9.
• Steps:
  • Start at 15 and count back 6.
  • 14, 13, 12, 11, 10, 9 — there are 9 pucks left.
• Answer: 9 pucks

[Easy] Skip Counting by 5s

• EN: Skip count by 5s. What number comes after 20?
• FR: Compte par bonds de 5. Quel nombre vient après 20?
• Choices: A) 22 B) 23 C) 24 D) 25
• Hint: When skip counting by 5s starting at 10, the next number is 15, then 20, then…
• Steps:
  • The pattern when skip counting by 5s is: 5, 10, 15, 20, 25…
  • The number that comes after 20 when counting by 5s is 25.
• Answer: 25

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est le plus grand : 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 18
• Hint: To compare 12 and 7, think about which is farther along when counting from 1.
• Steps:
  • Count from 1: 9 comes before 14.
  • The number farther along the number line is greater, so 14 is greater.
• Answer: 14

[Medium] Coin Recognition

• EN: Maya has 1 dime and 1 nickel. How many cents does she have altogether?
• FR: Maya a 1 pièce de dix cents et 1 pièce de cinq cents. Combien de cents a-t-elle 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 — put those together.
• Steps:
  • A dime is worth 10 cents. A nickel is worth 5 cents.
  • 10 + 5 = 15 cents altogether.
• Answer: 15 cents

[Medium] Addition Within 20

• EN: There are 8 red mittens and 6 blue mittens in the lost-and-found box. How many mittens are there in all?
• FR: Il y a 8 mitaines rouges et 6 mitaines bleues dans la boîte des objets perdus. Combien y a-t-il de mitaines en tout?
• Choices: A) 12 mittens B) 13 mittens C) 14 mittens D) 16 mittens
• Hint: To add 7 + 5, think: 7 + 3 = 10, then add 2 more to get 12.
• Steps:
  • Break apart 6 into 2 + 4. First add 8 + 2 = 10.
  • Then add 10 + 4 = 14 mittens in all.
• Answer: 14 mittens

[Medium] Skip Counting by 2s

• EN: The teacher lines up students in pairs. She counts by 2s: 2, 4, 6, 8, 10. What is the next number she says?
• FR: La professeure aligne les élèves en paires. Elle compte par bonds de 2 : 2, 4, 6, 8, 10. Quel est le prochain nombre qu'elle dit?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: When counting by 2s from 8, the next number is 10, then add 2 more.
• Steps:
  • The pattern adds 2 each time: 2, 4, 6, 8, 10…
  • 10 + 2 = 12, so the next number is 12.
• Answer: 12

[Medium] Subtraction Within 20

• EN: Liam had 18 stickers. He gave 9 to his friend. How many stickers does Liam have now?
• FR: Liam avait 18 autocollants. Il en a donné 9 à son ami. Combien d'autocollants Liam a-t-il maintenant?
• Choices: A) 7 stickers B) 8 stickers C) 9 stickers D) 11 stickers
• Hint: To solve 16 − 8, think: 8 + 8 = 16, so the answer is 8.
• Steps:
  • Think: 9 + ? = 18. Since 9 + 9 = 18, the missing number is 9.
  • Liam has 9 stickers left.
• Answer: 9 stickers

[Hard] Adding Three Numbers

• EN: There are 4 red balls, 5 blue balls, and 6 green balls in a bag. How many balls are in the bag altogether?
• FR: Il y a 4 balles rouges, 5 balles bleues et 6 balles vertes dans un sac. Combien y a-t-il de balles en tout dans le sac?
• Choices: A) 13 balls B) 14 balls C) 15 balls D) 16 balls
• Hint: To add 3 + 4 + 5, first add 3 + 4 = 7, then add 7 + 5 = 12.
• Steps:
  • First add 4 + 5 = 9.
  • Then add 9 + 6 = 15, so there are 15 balls altogether.
• Answer: 15 balls

[Hard] Counting Coins

• EN: Carlos has 2 nickels and 3 pennies. How many cents does he have in total?
• FR: Carlos a 2 pièces de cinq cents et 3 pièces de un cent. Combien de cents a-t-il en tout?
• Choices: A) 8 cents B) 11 cents C) 13 cents D) 16 cents
• Hint: To count 1 nickel and 4 pennies, think: 5 + 1 + 1 + 1 + 1 = 9 cents.
• Steps:
  • Two nickels = 5 + 5 = 10 cents. Three pennies = 1 + 1 + 1 = 3 cents.
  • 10 + 3 = 13 cents in total.
• Answer: 13 cents

[Easy] Addition Within 100

• EN: There are 34 students in the gym and 25 more students join them. How many students are in the gym now?
• FR: Il y a 34 élèves dans le gymnase et 25 autres les rejoignent. Combien y a-t-il d'élèves dans le gymnase maintenant?
• Choices: A) 57 students B) 59 students C) 61 students D) 63 students
• Hint: To add 42 + 31, add tens first: 40 + 30 = 70, then ones: 2 + 1 = 3, giving 73.
• Steps:
  • Add the tens: 30 + 20 = 50. Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59 students in the gym now.
• Answer: 59 students

[Easy] Subtraction Within 100

• EN: A bag had 80 marbles. A child took out 35 marbles. How many marbles are left in the bag?
• FR: Un sac contenait 80 billes. Un enfant en a sorti 35. Combien de billes reste-t-il dans le sac?
• Choices: A) 43 marbles B) 44 marbles C) 45 marbles D) 46 marbles
• Hint: To subtract 70 − 28, think: 70 − 20 = 50, then 50 − 8 = 42.
• Steps:
  • 80 − 35: subtract the tens: 80 − 30 = 50.
  • Then subtract the ones: 50 − 5 = 45 marbles left.
• Answer: 45 marbles

[Easy] Telling Time — Hour

• EN: The clock shows the short hand on 3 and the long hand on 12. What time does the clock show?
• FR: L'aiguille courte de l'horloge est sur le 3 et l'aiguille longue est sur le 12. Quelle heure l'horloge indique-t-elle?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 4:00
• Hint: When the long hand points to 12, it is an exact hour — just read the short hand.
• Steps:
  • The long hand on 12 means it is exactly on the hour.
  • The short hand is on 3, so the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 14 cm long. A crayon is 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon à mine mesure 14 cm de long. Un crayon de cire mesure 9 cm de long. De combien le crayon à mine est-il plus long que le crayon de cire?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 7 cm
• Hint: To find how much longer 16 cm is than 10 cm, subtract: 16 − 10 = 6 cm.
• Steps:
  • Subtract the shorter length from the longer: 14 − 9.
  • 14 − 9 = 5 cm, so the pencil is 5 cm longer.
• Answer: 5 cm

[Medium] Counting Coins to $1

• EN: Sophie has 3 dimes, 2 nickels, and 4 pennies. How much money does she have?
• FR: Sophie a 3 pièces de dix cents, 2 pièces de cinq cents et 4 pièces de un cent. Combien d'argent a-t-elle?
• Choices: A) 42 cents B) 44 cents C) 46 cents D) 48 cents
• Hint: Count 2 dimes and 1 nickel: 10 + 10 + 5 = 25 cents, then add any pennies.
• Steps:
  • 3 dimes = 30 cents. 2 nickels = 10 cents. 4 pennies = 4 cents.
  • 30 + 10 + 4 = 44 cents.
• Answer: 44 cents

[Medium] Telling Time — Half Hour

• EN: Hockey practice starts at 4:30. The clock's long hand is on 6. Where is the short hand?
• FR: La pratique de hockey commence à 4 h 30. L'aiguille longue de l'horloge est sur le 6. Où est l'aiguille courte?
• Choices: A) Exactly on 4 B) Halfway between 4 and 5 C) Exactly on 5 D) Halfway between 5 and 6
• Hint: At half past any hour, the short hand is always halfway between two numbers on the clock face.
• Steps:
  • When the long hand is on 6, it is half past the hour (30 minutes).
  • At 4:30, the short hand is halfway between 4 and 5.
• Answer: Halfway between 4 and 5

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, ___. What is the missing number?
• FR: Regarde ce modèle : 5, 10, 15, 20, ___. Quel est le nombre manquant?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: In the pattern 3, 6, 9, 12, each number increases by 3 — find the rule first.
• Steps:
  • Each number increases by 5: 5, 10, 15, 20…
  • 20 + 5 = 25, so the missing number is 25.
• Answer: 25

[Medium] Addition Within 100 with Regrouping

• EN: At a bake sale, 47 muffins and 36 cookies were sold. How many baked goods were sold in total?
• FR: Lors d'une vente de pâtisseries, on a vendu 47 muffins et 36 biscuits. Combien de produits de boulangerie ont été vendus en tout?
• Choices: A) 81 baked goods B) 82 baked goods C) 83 baked goods D) 84 baked goods
• Hint: To add 38 + 45, add ones first: 8 + 5 = 13, write 3 carry 1; then tens: 3 + 4 + 1 = 8.
• Steps:
  • Ones: 7 + 6 = 13. Write 3, carry 1.
  • Tens: 4 + 3 + 1 (carried) = 8. So 47 + 36 = 83 baked goods.
• Answer: 83 baked goods

[Hard] Subtraction with Regrouping

• EN: A teacher had 62 sheets of paper. She gave 38 sheets to students. How many sheets does she have left?
• FR: Une enseignante avait 62 feuilles de papier. Elle en a donné 38 aux élèves. Combien lui en reste-t-il?
• Choices: A) 22 sheets B) 24 sheets C) 26 sheets D) 28 sheets
• Hint: To subtract 54 − 27, regroup: borrow 1 ten from 5 tens, making it 14 − 7 in the ones.
• Steps:
  • Ones: can't do 2 − 8, so borrow 1 ten. Now it's 12 − 8 = 4 ones. Tens: 5 − 3 = 2 tens.
  • So 62 − 38 = 24 sheets left.
• Answer: 24 sheets

[Hard] Two-Step Problem

• EN: Theo had 50 cents. He spent 22 cents on a sticker and then earned 15 cents doing a chore. How much money does Theo have now?
• FR: Théo avait 50 cents. Il a dépensé 22 cents pour un autocollant, puis a gagné 15 cents en faisant une tâche ménagère. Combien d'argent Théo a-t-il maintenant?
• Choices: A) 40 cents B) 41 cents C) 43 cents D) 45 cents
• Hint: For two-step problems like 60 − 20 + 10, first subtract, then add the new amount.
• Steps:
  • First subtract what was spent: 50 − 22 = 28 cents.
  • Then add what was earned: 28 + 15 = 43 cents.
• Answer: 43 cents

[Easy] Multiplication — 2s Table

• EN: There are 6 pairs of skates in the locker room. Each pair has 2 blades. How many blades are there in all?
• FR: Il y a 6 paires de patins dans le vestiaire. Chaque paire a 2 lames. Combien y a-t-il de lames en tout?
• Choices: A) 8 blades B) 10 blades C) 12 blades D) 14 blades
• Hint: To find 5 × 2, think of 5 groups of 2: 2, 4, 6, 8, 10.
• Steps:
  • There are 6 pairs, each with 2 blades: 6 × 2.
  • 6 × 2 = 12, so there are 12 blades in all.
• Answer: 12 blades

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal slices. Emma eats 1 slice. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 2 parts égales. Emma mange 1 part. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: If a sandwich is cut into 2 equal halves and you eat one part, you ate 1 out of 2 equal pieces.
• Steps:
  • The pizza is divided into 2 equal parts. Emma ate 1 of those parts.
  • 1 part out of 2 equal parts = 1/2.
• Answer: 1/2

[Easy] Multiplication — 5s Table

• EN: There are 7 bags of apples. Each bag has 5 apples. How many apples are there in all?
• FR: Il y a 7 sacs de pommes. Chaque sac contient 5 pommes. Combien y a-t-il de pommes en tout?
• Choices: A) 30 apples B) 32 apples C) 35 apples D) 40 apples
• Hint: To find 6 × 5, skip count by 5s six times: 5, 10, 15, 20, 25, 30.
• Steps:
  • 7 groups of 5: skip count by 5s seven times.
  • 5, 10, 15, 20, 25, 30, 35 — there are 35 apples in all.
• Answer: 35 apples

[Easy] Perimeter of a Rectangle

• EN: A garden is 4 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un jardin a 4 m de long et 3 m de large. Quel est le périmètre du jardin?
• Choices: A) 7 m B) 12 m C) 14 m D) 16 m
• Hint: The perimeter of a rectangle with length 5 m and width 2 m is 5 + 2 + 5 + 2 = 14 m.
• Steps:
  • Add all four sides: 4 + 3 + 4 + 3.
  • 4 + 3 + 4 + 3 = 14, so the perimeter is 14 m.
• Answer: 14 m

[Medium] Basic Division

• EN: A teacher has 24 crayons to share equally among 4 students. How many crayons does each student get?
• FR: Une enseignante a 24 crayons à partager également entre 4 élèves. Combien de crayons chaque élève reçoit-il?
• Choices: A) 4 crayons B) 5 crayons C) 6 crayons D) 8 crayons
• Hint: To divide 20 ÷ 4, ask: how many groups of 4 fit into 20? Think: 4 × 5 = 20.
• Steps:
  • Ask: 4 × ? = 24. Since 4 × 6 = 24, each student gets 6 crayons.
  • Each student gets 6 crayons.
• Answer: 6 crayons

[Medium] Multiplication — 3s Table

• EN: There are 8 triangles drawn on the board. Each triangle has 3 sides. How many sides are there in total?
• FR: Il y a 8 triangles dessinés au tableau. Chaque triangle a 3 côtés. Combien y a-t-il de côtés au total?
• Choices: A) 21 sides B) 22 sides C) 24 sides D) 27 sides
• Hint: To find 7 × 3, skip count by 3s seven times: 3, 6, 9, 12, 15, 18, 21.
• Steps:
  • 8 triangles × 3 sides each = 8 × 3.
  • 8 × 3 = 24, so there are 24 sides in total.
• Answer: 24 sides

[Medium] Reading a Simple Graph

• EN: A bar graph shows that 9 students chose hockey, 6 chose soccer, and 5 chose skiing as their favourite sport. How many students answered the survey in all?
• FR: Un diagramme à bandes montre que 9 élèves ont choisi le hockey, 6 ont choisi le soccer et 5 ont choisi le ski comme sport préféré. Combien d'élèves ont répondu au sondage en tout?
• Choices: A) 18 students B) 19 students C) 20 students D) 21 students
• Hint: To find the total in a graph showing 8, 5, and 4, add all three bars: 8 + 5 + 4 = 17.
• Steps:
  • Add the values from each bar: 9 + 6 + 5.
  • 9 + 6 = 15, then 15 + 5 = 20 students in all.
• Answer: 20 students

[Medium] Fractions — One Quarter

• EN: A chocolate bar is divided into 4 equal pieces. Jake ate 1 piece. What fraction of the chocolate bar did Jake eat?
• FR: Une tablette de chocolat est divisée en 4 morceaux égaux. Jake a mangé 1 morceau. Quelle fraction de la tablette de chocolat Jake a-t-il mangée?
• Choices: A) 1/5 B) 1/4 C) 1/3 D) 1/2
• Hint: If a ribbon is cut into 4 equal parts and you use 1 part, you used 1 out of 4, which is 1/4.
• Steps:
  • The bar has 4 equal pieces. Jake ate 1 of them.
  • 1 out of 4 equal parts = 1/4.
• Answer: 1/4

[Hard] Two-Step Multiplication and Addition

• EN: There are 5 shelves in the library. Each shelf holds 10 books. Then 8 more books are added to the shelves. How many books are in the library now?
• FR: Il y a 5 étagères dans la bibliothèque. Chaque étagère contient 10 livres. Ensuite, 8 livres de plus sont ajoutés aux étagères. Combien de livres y a-t-il maintenant dans la bibliothèque?
• Choices: A) 55 books B) 56 books C) 57 books D) 58 books
• Hint: First multiply to find the total on shelves, then add any extra items: for 3 × 10 + 6, that is 30 + 6 = 36.
• Steps:
  • First find 5 × 10 = 50 books on the shelves.
  • Then add the extra 8 books: 50 + 8 = 58 books in total.
• Answer: 58 books

[Hard] Division and Fractions Combined

• EN: There are 12 muffins at Tim Hortons. One third of the muffins are blueberry. How many blueberry muffins are there?
• FR: Il y a 12 muffins au Tim Hortons. Un tiers des muffins sont aux bleuets. Combien de muffins aux bleuets y a-t-il?
• Choices: A) 2 blueberry muffins B) 3 blueberry muffins C) 4 blueberry muffins D) 6 blueberry muffins
• Hint: To find 1/3 of 9, divide 9 by 3 to get 3.
• Steps:
  • To find 1/3 of 12, divide 12 by 3.
  • 12 ÷ 3 = 4, so there are 4 blueberry muffins.
• Answer: 4 blueberry muffins

[Easy] Multiplication Tables to 9×9

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To find 6 × 8, think: 6 × 8 = 48. One more group of 8 would give 56.
• Steps:
  • 7 groups of 8: use the known fact 7 × 8.
  • 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value — Tenths

• EN: In the number 3.7, what digit is in the tenths place?
• FR: Dans le nombre 3,7, quel chiffre est dans la position des dixièmes?
• Choices: A) 3 B) 7 C) 0 D) 37
• Hint: In the number 5.2, the digit 5 is in the ones place and 2 is in the tenths place (one spot after the decimal).
• Steps:
  • The decimal point separates ones from tenths.
  • In 3.7, the digit immediately after the decimal is 7, which is in the tenths place.
• Answer: 7

[Easy] Area of a Rectangle

• EN: A classroom rug is 5 m long and 4 m wide. What is the area of the rug?
• FR: Un tapis de classe a 5 m de long et 4 m de large. Quelle est l'aire du tapis?
• Choices: A) 16 m² B) 18 m² C) 20 m² D) 22 m²
• Hint: The area of a rectangle with length 6 m and width 3 m is 6 × 3 = 18 m².
• Steps:
  • Area = length × width = 5 × 4.
  • 5 × 4 = 20, so the area of the rug is 20 m².
• Answer: 20 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/4?
• FR: Quelle fraction est la plus grande : 3/4 ou 1/4?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) 4/4
• Hint: When fractions have the same denominator, like 2/5 and 4/5, the one with the bigger numerator is greater.
• Steps:
  • Both fractions have the same denominator (4), so compare numerators: 3 vs. 1.
  • Since 3 > 1, the fraction 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: A teacher wants to put 53 pencils equally into 6 boxes. How many pencils go in each box, and how many are left over?
• FR: Une enseignante veut mettre 53 crayons également dans 6 boîtes. Combien de crayons y a-t-il dans chaque boîte, et combien en reste-t-il?
• Choices: A) 7 pencils, remainder 5 B) 8 pencils, remainder 5 C) 9 pencils, remainder 2 D) 7 pencils, remainder 8
• Hint: For 40 ÷ 6, ask: how many times does 6 fit into 40? 6 × 6 = 36, so 6 remainder 4.
• Steps:
  • 6 × 8 = 48 and 6 × 9 = 54. Since 54 > 53, use 8.
  • 53 − 48 = 5, so each box gets 8 pencils, remainder 5.
• Answer: 8 pencils, remainder 5

[Medium] Elapsed Time

• EN: School starts at 8:15 a.m. and ends at 3:15 p.m. How long is the school day?
• FR: L'école commence à 8 h 15 et se termine à 15 h 15. Quelle est la durée de la journée scolaire?
• Choices: A) 6 hours B) 7 hours C) 8 hours D) 9 hours
• Hint: To find elapsed time from 9:00 a.m. to 2:00 p.m., count forward: 9 to 2 is 5 hours.
• Steps:
  • Count from 8:15 a.m. to 3:15 p.m.: the minutes are the same (15), so just count the hours.
  • 3:15 p.m. is 15:15, and 15 − 8 = 7, so the school day is 7 hours long.
• Answer: 7 hours

[Medium] Decimal Operations — Tenths and Hundredths

• EN: Ava's snowfall gauge showed 2.4 cm on Monday and 1.3 cm on Tuesday. What was the total snowfall over the two days?
• FR: Le pluviomètre d'Ava indiquait 2,4 cm lundi et 1,3 cm mardi. Quelle était la chute de neige totale sur ces deux jours?
• Choices: A) 3.5 cm B) 3.7 cm C) 4.1 cm D) 4.3 cm
• Hint: To add 1.5 + 2.2, line up the decimal points and add: 1.5 + 2.2 = 3.7.
• Steps:
  • Line up the decimal points: 2.4 + 1.3.
  • Add tenths: 4 + 3 = 7. Add ones: 2 + 1 = 3. Total = 3.7 cm.
• Answer: 3.7 cm

[Medium] All Multiplication Tables

• EN: A hockey team has 9 players on the ice for each of 9 shifts in a game. How many player-shifts are there in all?
• FR: Une équipe de hockey a 9 joueurs sur la glace pendant chacune des 9 présences d'un match. Combien y a-t-il de présences-joueurs en tout?
• Choices: A) 72 player-shifts B) 78 player-shifts C) 81 player-shifts D) 84 player-shifts
• Hint: To find 8 × 8, think of the familiar fact: 8 × 8 = 64; adding one more group of 8 gives 72.
• Steps:
  • 9 × 9 = 81.
  • There are 81 player-shifts in all.
• Answer: 81 player-shifts

[Hard] Multi-Step Problem with Decimals

• EN: Remy bought a notebook for $2.75 and a pen for $1.50. He paid with a $5.00 bill. How much change did he receive?
• FR: Remy a acheté un cahier pour 2,75 $ et un stylo pour 1,50 $. Il a payé avec un billet de 5,00 $. Combien a-t-il reçu en monnaie?
• Choices: A) $0.75 B) $1.25 C) $1.50 D) $2.25
• Hint: First add the two costs together, then subtract from the amount paid — for example, $1.20 + $1.30 = $2.50, and $5.00 − $2.50 = $2.50 change.
• Steps:
  • Total cost: $2.75 + $1.50 = $4.25.
  • Change: $5.00 − $4.25 = $0.75.
• Answer: $0.75

[Hard] Fraction Comparison and Ordering

• EN: Order these fractions from least to greatest: 3/4, 1/2, 1/4.
• FR: Classe ces fractions du plus petit au plus grand : 3/4, 1/2, 1/4.
• Choices: A) 1/4, 1/2, 3/4 B) 1/2, 1/4, 3/4 C) 3/4, 1/2, 1/4 D) 1/4, 3/4, 1/2
• Hint: To compare fractions with the same denominator, think of them as pieces of a pizza: 1 piece out of 4 is less than 2 pieces out of 4.
• Steps:
  • Convert to the same denominator (4): 1/2 = 2/4.
  • Now compare 1/4, 2/4, 3/4 — in order from least to greatest: 1/4, 1/2, 3/4.
• Answer: 1/4, 1/2, 3/4

[Easy] Multi-Digit Multiplication

• EN: A hockey arena has 24 rows of seats. Each row has 30 seats. How many seats are in the arena?
• FR: Un aréna de hockey a 24 rangées de sièges. Chaque rangée a 30 sièges. Combien y a-t-il de sièges dans l'aréna?
• Choices: A) 620 seats B) 680 seats C) 720 seats D) 780 seats
• Hint: To multiply 22 × 30, think: 22 × 3 = 66, then add a zero to get 660.
• Steps:
  • 24 × 30: first compute 24 × 3 = 72, then multiply by 10.
  • 72 × 10 = 720, so there are 720 seats.
• Answer: 720 seats

[Easy] Adding Fractions with Like Denominators

• EN: Sophie ate 2/8 of a granola bar in the morning and 3/8 in the afternoon. What fraction of the granola bar did she eat in total?
• FR: Sophie a mangé 2/8 d'une barre granola le matin et 3/8 l'après-midi. Quelle fraction de la barre granola a-t-elle mangée au total?
• Choices: A) 4/8 B) 5/8 C) 5/16 D) 6/8
• Hint: To add 1/6 + 3/6, just add the numerators and keep the denominator: 1 + 3 = 4, so 4/6.
• Steps:
  • The denominators are the same (8), so add the numerators: 2 + 3 = 5.
  • Sophie ate 5/8 of the granola bar.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: There are 40 students going on a field trip. 50% of them are wearing a red shirt. How many students are wearing red?
• FR: 40 élèves participent à une sortie scolaire. 50 % d'entre eux portent un chandail rouge. Combien d'élèves portent du rouge?
• Choices: A) 15 students B) 18 students C) 20 students D) 25 students
• Hint: 50% of any number means half of it — for example, 50% of 60 is 30.
• Steps:
  • 50% means half: divide 40 by 2.
  • 40 ÷ 2 = 20, so 20 students are wearing red.
• Answer: 20 students

[Easy] Volume of a Rectangular Prism

• EN: A small box is 3 cm long, 4 cm wide, and 2 cm tall. What is the volume of the box?
• FR: Une petite boîte a 3 cm de long, 4 cm de large et 2 cm de haut. Quel est le volume de la boîte?
• Choices: A) 18 cm³ B) 20 cm³ C) 24 cm³ D) 28 cm³
• Hint: The volume of a box that is 5 cm × 2 cm × 3 cm is 5 × 2 × 3 = 30 cm³.
• Steps:
  • Volume = length × width × height = 3 × 4 × 2.
  • 3 × 4 = 12, then 12 × 2 = 24, so the volume is 24 cm³.
• Answer: 24 cm³

[Medium] Multi-Digit Division

• EN: A total of 378 books are placed equally on 9 shelves. How many books are on each shelf?
• FR: Un total de 378 livres sont placés également sur 9 étagères. Combien de livres y a-t-il sur chaque étagère?
• Choices: A) 40 books B) 41 books C) 42 books D) 43 books
• Hint: To divide 270 ÷ 9, think: 9 × 30 = 270, so the answer is 30.
• Steps:
  • 378 ÷ 9: think 9 × 40 = 360, leaving 378 − 360 = 18.
  • 18 ÷ 9 = 2, so 40 + 2 = 42 books per shelf.
• Answer: 42 books

[Medium] Subtracting Fractions with Like Denominators

• EN: A container was 7/10 full of juice. After breakfast, 3/10 was used. How full is the container now?
• FR: Un contenant était rempli aux 7/10 de jus. Après le petit-déjeuner, 3/10 a été utilisé. Quelle est maintenant la fraction de jus dans le contenant?
• Choices: A) 2/10 B) 3/10 C) 4/10 D) 5/10
• Hint: To subtract 5/9 − 2/9, keep the denominator and subtract numerators: 5 − 2 = 3, giving 3/9.
• Steps:
  • Subtract the numerators, keeping the denominator: 7 − 3 = 4.
  • The container is now 4/10 full.
• Answer: 4/10

[Medium] Decimal Operations — Addition

• EN: Luca's lunch at Tim Hortons cost $4.85 and his drink cost $1.75. What was the total cost?
• FR: Le déjeuner de Luca au Tim Hortons a coûté 4,85 $ et sa boisson a coûté 1,75 $. Quel était le coût total?
• Choices: A) $5.60 B) $6.50 C) $6.60 D) $7.10
• Hint: To add $3.45 + $2.35, line up decimals: 45 cents + 35 cents = 80 cents, 3 + 2 = 5 dollars, giving $5.80.
• Steps:
  • Line up the decimal points: $4.85 + $1.75.
  • Cents: 85 + 75 = 160, which is $1.60. Dollars: 4 + 1 = 5, plus the extra dollar = $6. Total = $6.60.
• Answer: $6.60

[Medium] Percentage — 25%

• EN: A bookstore is having a sale. A book normally costs $12.00, and it is 25% off. How much is the discount?
• FR: Une librairie fait une vente. Un livre coûte normalement 12,00 $, et il est à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $2.00 B) $3.00 C) $4.00 D) $5.00
• Hint: 25% of any number is one quarter — for example, 25% of $8.00 is $8.00 ÷ 4 = $2.00.
• Steps:
  • 25% = 1/4. Find 1/4 of $12.00: divide by 4.
  • $12.00 ÷ 4 = $3.00. The discount is $3.00.
• Answer: $3.00

[Hard] Multi-Step Fraction and Whole Number Problem

• EN: A recipe makes 48 cookies. Maya's class ate 3/8 of the cookies. How many cookies are left?
• FR: Une recette donne 48 biscuits. La classe de Maya a mangé 3/8 des biscuits. Combien de biscuits reste-t-il?
• Choices: A) 18 cookies B) 28 cookies C) 30 cookies D) 32 cookies
• Hint: To find 3/8 of 32, first find 1/8 by dividing by 8: 32 ÷ 8 = 4, then multiply by 3: 4 × 3 = 12.
• Steps:
  • Find 3/8 of 48: 48 ÷ 8 = 6, then 6 × 3 = 18 cookies eaten.
  • Cookies left: 48 − 18 = 30 cookies.
• Answer: 30 cookies

[Hard] Multi-Digit Multiplication and Volume

• EN: A classroom storage bin is 12 cm long, 15 cm wide, and 20 cm tall. What is the volume of the bin?
• FR: Un bac de rangement de classe a 12 cm de long, 15 cm de large et 20 cm de haut. Quel est le volume du bac?
• Choices: A) 3 200 cm³ B) 3 400 cm³ C) 3 600 cm³ D) 4 000 cm³
• Hint: For a box 10 × 12 × 15, first multiply 10 × 12 = 120, then 120 × 15 = 1 800 cm³.
• Steps:
  • Volume = 12 × 15 × 20. First: 12 × 15 = 180.
  • Then: 180 × 20 = 3 600, so the volume is 3 600 cm³.
• Answer: 3 600 cm³

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien vaut 30 % de 200?
• Choices: A) 40 B) 50 C) 60 D) 70
• Hint: To find 20% of 150, first find 10% (150 ÷ 10 = 15), then double it: 15 × 2 = 30.
• Steps:
  • Find 10% of 200: 200 ÷ 10 = 20.
  • Multiply by 3 to get 30%: 20 × 3 = 60.
• Answer: 60

[Easy] Order of Operations — BEDMAS

• EN: Evaluate: 3 + 4 × 2.
• FR: Calcule : 3 + 4 × 2.
• Choices: A) 9 B) 10 C) 11 D) 14
• Hint: In 5 + 3 × 4, multiply before adding: 3 × 4 = 12, then 5 + 12 = 17.
• Steps:
  • Using BEDMAS, multiply before adding: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
• Answer: 11

[Easy] Integers Introduction

• EN: The temperature in Winnipeg was −8°C in the morning. By noon it rose by 5 degrees. What is the temperature at noon?
• FR: La température à Winnipeg était de −8°C le matin. À midi, elle a monté de 5 degrés. Quelle est la température à midi?
• Choices: A) −4°C B) −3°C C) −2°C D) −1°C
• Hint: To find −6 + 4, start at −6 on the number line and move 4 steps to the right to get −2.
• Steps:
  • Start at −8 and add 5: −8 + 5.
  • Move 5 steps right on the number line: −8, −7, −6, −5, −4, −3. The temperature is −3°C.
• Answer: −3°C

[Easy] Simple Algebraic Expressions

• EN: If n = 6, what is the value of 4n + 3?
• FR: Si n = 6, quelle est la valeur de 4n + 3?
• Choices: A) 25 B) 27 C) 29 D) 31
• Hint: To evaluate 3x + 5 when x = 4, substitute: 3 × 4 + 5 = 12 + 5 = 17.
• Steps:
  • Substitute n = 6 into 4n + 3: 4 × 6 + 3.
  • 4 × 6 = 24, then 24 + 3 = 27.
• Answer: 27

[Medium] Fraction Multiplication

• EN: A recipe calls for 2/3 of a cup of oats. If you want to make half the recipe, how much oats do you need?
• FR: Une recette demande 2/3 de tasse de flocons d'avoine. Si tu veux faire la moitié de la recette, de quelle quantité de flocons as-tu besoin?
• Choices: A) 1/6 cup B) 1/4 cup C) 1/3 cup D) 2/6 cup
• Hint: To multiply 3/4 × 1/2, multiply the numerators and denominators: (3 × 1)/(4 × 2) = 3/8.
• Steps:
  • Multiply: 2/3 × 1/2 = (2 × 1)/(3 × 2) = 2/6.
  • Simplify 2/6 = 1/3, so you need 1/3 cup.
• Answer: 1/3 cup

[Medium] Ratios and 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) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: To find the rate when a cyclist travels 150 km in 3 hours, divide: 150 ÷ 3 = 50 km/h.
• Steps:
  • Speed = distance ÷ time = 240 ÷ 3.
  • 240 ÷ 3 = 80, so the car travels at 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: How many 1/4-cup servings are in 3 cups of trail mix?
• FR: Combien de portions de 1/4 de tasse y a-t-il dans 3 tasses de mélange montagnard?
• Choices: A) 9 servings B) 10 servings C) 12 servings D) 15 servings
• Hint: To divide 2 ÷ 1/3, multiply by the reciprocal: 2 × 3 = 6 servings.
• Steps:
  • Divide 3 ÷ 1/4: multiply by the reciprocal of 1/4, which is 4.
  • 3 × 4 = 12, so there are 12 servings.
• Answer: 12 servings

[Medium] BEDMAS with Brackets

• EN: Evaluate: (5 + 3) × 4 − 6.
• FR: Calcule : (5 + 3) × 4 − 6.
• Choices: A) 24 B) 26 C) 28 D) 32
• Hint: In (2 + 6) × 3 − 4, solve the bracket first: 2 + 6 = 8, then 8 × 3 = 24, then 24 − 4 = 20.
• Steps:
  • Brackets first: 5 + 3 = 8. Then multiply: 8 × 4 = 32.
  • Then subtract: 32 − 6 = 26.
• Answer: 26

[Hard] Percent — Finding the Whole

• EN: A store sold 60 winter jackets, which was 75% of the jackets in stock. How many jackets were in stock before the sale?
• FR: Un magasin a vendu 60 vestes d'hiver, ce qui représentait 75 % des vestes en stock. Combien de vestes y avait-il en stock avant la vente?
• Choices: A) 72 jackets B) 75 jackets C) 80 jackets D) 85 jackets
• Hint: If 50% of a number is 30, find the whole by dividing 30 by 0.50, or thinking: 30 is half, so the total is 60.
• Steps:
  • 75% of the whole = 60. So 1% = 60 ÷ 75, and 100% = (60 ÷ 75) × 100.
  • 60 ÷ 75 = 0.8, and 0.8 × 100 = 80 jackets in stock.
• Answer: 80 jackets

[Hard] Multi-Step BEDMAS

• EN: Evaluate: 48 ÷ (4 + 4) + 3² − 1.
• FR: Calcule : 48 ÷ (4 + 4) + 3² − 1.
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Use BEDMAS: solve brackets, then exponents, then division, then addition/subtraction — for 20 ÷ (2 + 3) + 2², do 5, then 4, then 4, then add.
• Steps:
  • Brackets: 4 + 4 = 8. Exponents: 3² = 9.
  • Division: 48 ÷ 8 = 6. Then: 6 + 9 − 1 = 14.
• Answer: 14

[Easy] Integer Addition

• EN: What is (−12) + 7?
• FR: Combien vaut (−12) + 7?
• Choices: A) −6 B) −5 C) −4 D) 5
• Hint: To find −9 + 4, start at −9 on the number line and move 4 steps right: −8, −7, −6, −5.
• Steps:
  • Start at −12 on the number line. Move 7 steps to the right.
  • −12 + 7 = −5.
• Answer: −5

[Easy] Fraction and Decimal Fluency

• EN: Write 3/4 as a decimal.
• FR: Écris 3/4 sous forme décimale.
• Choices: A) 0.25 B) 0.34 C) 0.70 D) 0.75
• Hint: To convert 1/4 to a decimal, divide 1 ÷ 4 = 0.25.
• Steps:
  • Divide 3 by 4: 3.00 ÷ 4.
  • 4 goes into 30 seven times (28), remainder 2; 4 goes into 20 five times. So 3/4 = 0.75.
• Answer: 0.75

[Easy] Percent — Discount

• EN: A $40 board game is on sale for 20% off. How much is the discount?
• FR: Un jeu de société à 40 $ est en solde à 20 % de rabais. Quel est le montant du rabais?
• Choices: A) $4 B) $6 C) $8 D) $10
• Hint: To find 20% of $30, find 10% first: $30 ÷ 10 = $3, then double it: $3 × 2 = $6.
• Steps:
  • 10% of $40 = $4. Multiply by 2 to get 20%.
  • 20% of $40 = $8. The discount is $8.
• Answer: $8

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 14 = 30.
• FR: Résous pour x : x + 14 = 30.
• Choices: A) x = 14 B) x = 15 C) x = 16 D) x = 44
• Hint: To solve x + 8 = 20, subtract 8 from both sides: x = 20 − 8 = 12.
• Steps:
  • Subtract 14 from both sides: x = 30 − 14.
  • x = 16.
• Answer: x = 16

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Combien vaut (−6) × (−4)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: When multiplying two negative numbers, the result is always positive: for example, (−3) × (−5) = 15.
• Steps:
  • A negative times a negative is positive.
  • 6 × 4 = 24, so (−6) × (−4) = 24.
• Answer: 24

[Medium] Percentage — Tax

• EN: A pair of skates costs $85.00. The tax rate is 13% (HST). What is the total cost including tax?
• FR: Une paire de patins coûte 85,00 $. Le taux de taxe est de 13 % (TVH). Quel est le coût total, taxe comprise?
• Choices: A) $95.05 B) $96.05 C) $97.05 D) $98.05
• Hint: To find 13% of $60, find 10% = $6 and 3% = $1.80; add them: $7.80. Then add to $60 to get the total.
• Steps:
  • 10% of $85 = $8.50. 3% of $85 = $2.55. Total tax = $8.50 + $2.55 = $11.05.
  • Total cost = $85.00 + $11.05 = $96.05.
• Answer: $96.05

[Medium] Surface Area of a Rectangular Prism

• EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the surface area of the box?
• FR: Une boîte a 5 cm de long, 4 cm de large et 3 cm de haut. Quelle est l'aire totale de la boîte?
• Choices: A) 74 cm² B) 94 cm² C) 104 cm² D) 124 cm²
• Hint: Surface area of a rectangular prism = 2(lw + lh + wh). For a 6 × 2 × 3 box: 2(12 + 18 + 6) = 2 × 36 = 72 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12).
  • = 2(47) = 94 cm².
• Answer: 94 cm²

[Medium] Probability

• EN: A bag contains 3 red marbles, 5 blue marbles, 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 tirer une bille bleue?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 5/10
• Hint: Probability = (number of favourable outcomes) ÷ (total outcomes). For 4 red out of 8 total: P = 4/8 = 1/2.
• Steps:
  • Total marbles = 3 + 5 + 2 = 10.
  • P(blue) = 5/10 = 1/2.
• Answer: 1/2

[Hard] Integer Division and Multi-Step

• EN: The temperature in Iqaluit dropped by 4°C each hour for 6 hours. Then it rose by 11°C. If the starting temperature was 3°C, what is the final temperature?
• FR: La température à Iqaluit a baissé de 4°C par heure pendant 6 heures. Ensuite, elle a monté de 11°C. Si la température de départ était de 3°C, quelle est la température finale?
• Choices: A) −10°C B) −8°C C) −6°C D) −4°C
• Hint: For a multi-step integer problem, find the change step by step: first compute the total drop, then apply the rise.
• Steps:
  • Total drop: 4 × 6 = 24°C. Starting temp minus drop: 3 − 24 = −21°C.
  • Then rose by 11°C: −21 + 11 = −10°C.
• Answer: −10°C

[Hard] Percent — Tip Calculation

• EN: A family's restaurant bill is $124.00. They want to leave a 15% tip. What is the total amount they will pay, including the tip?
• FR: La facture de restaurant d'une famille est de 124,00 $. Ils veulent laisser un pourboire de 15 %. Quel est le montant total qu'ils vont payer, pourboire compris?
• Choices: A) $140.60 B) $141.60 C) $142.60 D) $143.60
• Hint: To find 15% of $80, find 10% ($8) and 5% ($4), add them: $12; then $80 + $12 = $92.
• Steps:
  • 10% of $124 = $12.40. 5% of $124 = $6.20. Total tip = $12.40 + $6.20 = $18.60.
  • Total = $124.00 + $18.60 = $142.60.
• Answer: $142.60

[Easy] Perfect Squares

• EN: What is the square root of 144?
• FR: Quelle est la racine carrée de 144?
• Choices: A) 10 B) 11 C) 12 D) 13
• Hint: To find √100, think: what number times itself equals 100? Since 10 × 10 = 100, √100 = 10.
• Steps:
  • Ask: what number times itself equals 144?
  • 12 × 12 = 144, so √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Five students scored the following marks on a quiz: 70, 80, 90, 60, and 50. What is the mean score?
• FR: Cinq élèves ont obtenu les notes suivantes à un quiz : 70, 80, 90, 60 et 50. Quelle est la note moyenne?
• Choices: A) 68 B) 70 C) 72 D) 74
• Hint: To find the mean of 10, 20, and 30, add them: 60, then divide by 3: 60 ÷ 3 = 20.
• Steps:
  • Add the scores: 70 + 80 + 90 + 60 + 50 = 350.
  • Divide by the number of scores: 350 ÷ 5 = 70.
• Answer: 70

[Easy] Percent Increase

• EN: A hockey player scored 20 goals last season and 25 goals this season. What is the percent increase in goals?
• FR: Un joueur de hockey a marqué 20 buts la saison dernière et 25 buts cette saison. Quel est le pourcentage d'augmentation des buts?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100. For an increase from 40 to 50: (10 ÷ 40) × 100 = 25%.
• Steps:
  • Increase = 25 − 20 = 5. Percent increase = (5 ÷ 20) × 100.
  • (5 ÷ 20) × 100 = 0.25 × 100 = 25%.
• Answer: 25%

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 15.
• FR: Résous pour x : 2x + 5 = 15.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 10
• Hint: To solve 3y + 6 = 18, first subtract 6 from both sides (3y = 12), then divide by 3 (y = 4).
• Steps:
  • Subtract 5 from both sides: 2x = 15 − 5 = 10.
  • Divide both sides by 2: x = 10 ÷ 2 = 5.
• Answer: x = 5

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of length 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des jambes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: For a right triangle with legs 3 and 4, use c² = 3² + 4² = 9 + 16 = 25, so c = 5.
• Steps:
  • c² = a² + b² = 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

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

[Medium] Percent Decrease

• EN: A winter jacket originally costs $160. It is now on sale for $120. What is the percent decrease in price?
• FR: Une veste d'hiver coûtait originalement 160 $. Elle est maintenant en solde à 120 $. Quel est le pourcentage de diminution du prix?
• Choices: A) 20% B) 25% C) 30% D) 40%
• Hint: Percent decrease = (decrease ÷ original) × 100. For a price drop from $80 to $60: (20 ÷ 80) × 100 = 25%.
• Steps:
  • Decrease = $160 − $120 = $40. Percent decrease = (40 ÷ 160) × 100.
  • = 0.25 × 100 = 25%.
• Answer: 25%

[Medium] Median

• EN: Find the median of this data set: 12, 7, 15, 3, 9.
• FR: Trouve la médiane de cet ensemble de données : 12, 7, 15, 3, 9.
• Choices: A) 7 B) 9 C) 12 D) 15
• Hint: To find the median of 4, 8, 2, 11, 6 — first order them: 2, 4, 6, 8, 11. The middle value is 6.
• Steps:
  • Order the data: 3, 7, 9, 12, 15.
  • The middle value (3rd out of 5) is 9.
• Answer: 9

[Hard] Two-Step Equation with Fractions

• EN: Solve for x: x/3 + 7 = 13.
• FR: Résous pour x : x/3 + 7 = 13.
• Choices: A) x = 12 B) x = 15 C) x = 18 D) x = 21
• Hint: To solve x/4 + 3 = 8, subtract 3 first (x/4 = 5), then multiply both sides by 4 (x = 20).
• Steps:
  • Subtract 7 from both sides: x/3 = 13 − 7 = 6.
  • Multiply both sides by 3: x = 6 × 3 = 18.
• Answer: x = 18

[Hard] Pythagorean Theorem — Applied

• EN: A ramp is built against a wall. The ramp touches the ground 5 m from the wall, and it reaches a height of 12 m on the wall. How long is the ramp?
• FR: Une rampe est construite contre un mur. La rampe touche le sol à 5 m du mur et atteint une hauteur de 12 m sur le mur. Quelle est la longueur de la rampe?
• Choices: A) 11 m B) 13 m C) 15 m D) 17 m
• Hint: For a right triangle with legs 8 and 15, c² = 64 + 225 = 289, so c = 17.
• Steps:
  • c² = 5² + 12² = 25 + 144 = 169.
  • c = √169 = 13, so the ramp is 13 m long.
• Answer: 13 m

[Easy] Solving Linear Equations

• EN: Solve for x: 3x − 9 = 12.
• FR: Résous pour x : 3x − 9 = 12.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: To solve 4x − 8 = 16, add 8 to both sides (4x = 24), then divide by 4 (x = 6).
• Steps:
  • Add 9 to both sides: 3x = 12 + 9 = 21.
  • Divide by 3: x = 21 ÷ 3 = 7.
• Answer: x = 7

[Easy] Adding Polynomials

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

[Easy] Slope-Intercept Form

• EN: What is the y-intercept of the line y = 3x + 7?
• FR: Quel est l'ordonnée à l'origine de la droite y = 3x + 7?
• Choices: A) 3 B) 5 C) 7 D) 10
• Hint: In the equation y = 2x + 9, the y-intercept is the constant term 9 (where the line crosses the y-axis).
• Steps:
  • In the form y = mx + b, the y-intercept is b.
  • In y = 3x + 7, the y-intercept is 7.
• Answer: 7

[Easy] Linear Inequality

• EN: Solve the inequality: x + 5 > 11. What is the solution?
• FR: Résous l'inégalité : x + 5 > 11. Quelle est la solution?
• Choices: A) x > 4 B) x > 5 C) x > 6 D) x > 16
• Hint: To solve x + 3 > 10, subtract 3 from both sides: x > 7.
• Steps:
  • Subtract 5 from both sides: x > 11 − 5.
  • x > 6.
• Answer: x > 6

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x + 4).
• FR: Développe : 3x(2x + 4).
• Choices: A) 5x² + 7x B) 6x² + 12x C) 6x² + 7x D) 5x² + 12x
• Hint: To expand 2y(3y + 5), multiply each term: 2y × 3y = 6y² and 2y × 5 = 10y, giving 6y² + 10y.
• Steps:
  • Distribute 3x: 3x × 2x = 6x², and 3x × 4 = 12x.
  • Result: 6x² + 12x.
• Answer: 6x² + 12x

[Medium] Similar Triangles

• EN: Two triangles are similar. The smaller triangle has sides of 4 cm and 6 cm. The larger triangle has a side of 12 cm corresponding to the 6 cm side. What is the length of the side corresponding to 4 cm?
• FR: Deux triangles sont semblables. Le plus petit triangle a des côtés de 4 cm et 6 cm. Le plus grand triangle a un côté de 12 cm correspondant au côté de 6 cm. Quelle est la longueur du côté correspondant à 4 cm?
• Choices: A) 6 cm B) 7 cm C) 8 cm D) 9 cm
• Hint: For similar triangles, find the scale factor first: if one side goes from 5 cm to 15 cm, the scale factor is 3; multiply all corresponding sides by 3.
• Steps:
  • Scale factor = 12 ÷ 6 = 2. Apply to the corresponding side: 4 × 2 = 8 cm.
  • The missing side is 8 cm.
• Answer: 8 cm

[Medium] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 9 cm and the hypotenuse is 15 cm. What is sin θ?
• FR: Dans un triangle rectangle, le côté opposé est de 9 cm et l'hypoténuse est de 15 cm. Quelle est la valeur de sin θ?
• Choices: A) 3/4 B) 3/5 C) 4/5 D) 5/9
• Hint: SOH means sin = Opposite ÷ Hypotenuse. For opposite = 6 and hypotenuse = 10: sin θ = 6/10 = 3/5.
• Steps:
  • sin θ = opposite ÷ hypotenuse = 9 ÷ 15.
  • Simplify: 9/15 = 3/5.
• Answer: 3/5

[Medium] Graphing Lines

• EN: A line has the equation y = −2x + 4. What is the slope of this line?
• FR: Une droite a l'équation y = −2x + 4. Quelle est la pente de cette droite?
• Choices: A) −4 B) −2 C) 2 D) 4
• Hint: In y = mx + b, the slope is always the coefficient m in front of x — for y = 5x + 3, slope = 5.
• Steps:
  • In the form y = mx + b, the slope is m.
  • In y = −2x + 4, m = −2.
• Answer: −2

[Hard] Systems of Linear Equations by Substitution

• EN: Solve the system: y = 2x + 1 and y = 5x − 8. What is x?
• FR: Résous le système : y = 2x + 1 et y = 5x − 8. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Set both equations equal to each other: for y = x + 3 and y = 4x − 6, set x + 3 = 4x − 6 and solve.
• Steps:
  • Set equal: 2x + 1 = 5x − 8. Subtract 2x: 1 = 3x − 8.
  • Add 8: 9 = 3x, so x = 3.
• Answer: x = 3

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, angle θ = 30° and the hypotenuse is 20 cm. What is the length of the side opposite to θ? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé à θ? (sin 30° = 0,5)
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: Use SOH: sin θ = opposite/hypotenuse, so opposite = sin θ × hypotenuse. For sin 45° ≈ 0.707 and hypotenuse = 10: opposite ≈ 7.07 cm.
• Steps:
  • sin 30° = opposite ÷ 20. Rearrange: opposite = sin 30° × 20.
  • opposite = 0.5 × 20 = 10 cm.
• Answer: 10 cm

[Easy] Factoring Quadratics

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

[Easy] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 12 cm and the hypotenuse is 20 cm. What is cos θ?
• FR: Dans un triangle rectangle, le côté adjacent est de 12 cm et l'hypoténuse est de 20 cm. Quelle est la valeur de cos θ?
• Choices: A) 2/5 B) 3/5 C) 4/5 D) 5/12
• Hint: CAH: cos θ = Adjacent ÷ Hypotenuse. For adjacent = 8 and hypotenuse = 10: cos θ = 8/10 = 4/5.
• Steps:
  • cos θ = adjacent ÷ hypotenuse = 12 ÷ 20.
  • Simplify: 12/20 = 3/5.
• Answer: 3/5

[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: To eliminate y, add the two equations: (x + y) + (x − y) = sum of right sides; the y terms cancel.
• Steps:
  • Add both equations: 2x = 10 + 4 = 14. So x = 7.
  • Check: x = 7 and y = 10 − 7 = 3. Then 7 − 3 = 4. ✓
• Answer: x = 7

[Easy] Circle Geometry — Area

• EN: A circular pizza has a radius of 15 cm. What is the area of the pizza? (Use π ≈ 3.14)
• FR: Une pizza circulaire a un rayon de 15 cm. Quelle est l'aire de la pizza? (Utilise π ≈ 3,14)
• Choices: A) 565.2 cm² B) 614.7 cm² C) 706.5 cm² D) 754.3 cm²
• Hint: Area of a circle = π × r². For r = 10 cm: A = 3.14 × 100 = 314 cm².
• Steps:
  • A = π × r² = 3.14 × 15² = 3.14 × 225.
  • 3.14 × 225 = 706.5 cm².
• Answer: 706.5 cm²

[Medium] 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 = −8 C) x = 3 or x = −9 D) x = 4 or x = −10
• Hint: To complete the square for x² + 4x = 5, add (4/2)² = 4 to both sides: (x+2)² = 9, so x + 2 = ±3.
• Steps:
  • Add (6/2)² = 9 to both sides: x² + 6x + 9 = 7 + 9 = 16.
  • (x + 3)² = 16, so x + 3 = ±4. Thus x = 1 or x = −7.
• Answer: x = 1 or x = −7

[Medium] Surface Area of a Cylinder

• EN: A can of maple syrup has a radius of 4 cm and a height of 10 cm. What is the total surface area of the can? (Use π ≈ 3.14)
• FR: Une canette de sirop d'érable a un rayon de 4 cm et une hauteur de 10 cm. Quelle est l'aire totale de la surface de la canette? (Utilise π ≈ 3,14)
• Choices: A) 326.56 cm² B) 351.68 cm² C) 376.80 cm² D) 401.92 cm²
• Hint: SA of a cylinder = 2πr² + 2πrh. For r = 3 and h = 8: SA = 2(3.14)(9) + 2(3.14)(3)(8) = 56.52 + 150.72 = 207.24 cm².
• Steps:
  • SA = 2πr² + 2πrh = 2(3.14)(16) + 2(3.14)(4)(10).
  • = 100.48 + 251.20 = 351.68 cm².
• Answer: 351.68 cm²

[Medium] 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 θ? (sin⁻¹(0.5) = 30°)
• FR: Dans un triangle rectangle, le côté opposé est de 7 cm et l'hypoténuse est de 14 cm. Quel est l'angle θ? (sin⁻¹(0,5) = 30°)
• Choices: A) 25° B) 30° C) 45° D) 60°
• Hint: Use sin θ = opposite/hypotenuse to get a decimal, then use inverse sine (sin⁻¹) to find the angle.
• Steps:
  • sin θ = 7/14 = 0.5.
  • θ = sin⁻¹(0.5) = 30°.
• Answer: 30°

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 or x = 6 B) x = 2 or x = 3 C) x = 2 or x = 6 D) x = 3 or x = 4
• Hint: For x² − 4x + 3 = 0, factor or use the formula: discriminant = 16 − 12 = 4, so x = (4 ± 2)/2, giving x = 3 or x = 1.
• Steps:
  • a=1, b=−5, c=6. Discriminant: (−5)² − 4(1)(6) = 25 − 24 = 1.
  • x = (5 ± 1)/2. So x = 3 or x = 2.
• Answer: x = 2 or x = 3

[Hard] Circle Geometry — Chord and Radius

• EN: A chord of a circle is 16 cm long. The perpendicular from the centre to the chord is 6 cm. What is the radius of the circle?
• FR: Une corde d'un cercle a 16 cm de long. La perpendiculaire du centre à la corde est de 6 cm. Quel est le rayon du cercle?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 11 cm
• Hint: The perpendicular bisects the chord, forming a right triangle with legs of half-chord and the perpendicular, and hypotenuse equal to the radius.
• Steps:
  • Half-chord = 16 ÷ 2 = 8 cm. Use Pythagoras: r² = 8² + 6² = 64 + 36 = 100.
  • r = √100 = 10 cm.
• Answer: 10 cm

[Hard] Volume of a Cone

• EN: An ice cream cone has a radius of 3 cm and a height of 12 cm. What is the volume of the cone? (Use π ≈ 3.14)
• FR: Un cornet de crème glacée a un rayon de 3 cm et une hauteur de 12 cm. Quel est le volume du cornet? (Utilise π ≈ 3,14)
• Choices: A) 100.48 cm³ B) 113.04 cm³ C) 125.60 cm³ D) 138.16 cm³
• Hint: Volume of a cone = (1/3)πr²h. For r = 2 and h = 9: V = (1/3)(3.14)(4)(9) = (1/3)(113.04) = 37.68 cm³.
• Steps:
  • V = (1/3)πr²h = (1/3)(3.14)(9)(12) = (1/3)(3.14)(108).
  • = (1/3)(339.12) = 113.04 cm³.
• Answer: 113.04 cm³

[Easy] Exponential Functions

• EN: A bacteria culture doubles every hour. If you start with 50 bacteria, how many will there be after 3 hours?
• FR: Une culture de bactéries double chaque heure. Si tu commences avec 50 bactéries, combien y en aura-t-il après 3 heures?
• Choices: A) 300 bacteria B) 350 bacteria C) 400 bacteria D) 450 bacteria
• Hint: For exponential growth by a factor of 2 starting at 10: after 1 hour = 20, after 2 hours = 40, after 3 hours = 80.
• Steps:
  • After 1 hour: 50 × 2 = 100. After 2 hours: 100 × 2 = 200. After 3 hours: 200 × 2 = 400.
  • There are 400 bacteria after 3 hours.
• Answer: 400 bacteria

[Easy] Arithmetic Sequences

• EN: The first term of an arithmetic sequence is 7 and the common difference is 4. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 7 et la raison est 4. Quel est le 5e terme?
• Choices: A) 19 B) 21 C) 23 D) 27
• Hint: For an arithmetic sequence starting at 3 with common difference 5, the 4th term is 3 + 3×5 = 18.
• Steps:
  • The nth term = a + (n−1)d. For n = 5: 7 + (4)(4) = 7 + 16 = 23.
  • The 5th term is 23.
• Answer: 23

[Easy] Logarithms Introduction

• EN: Evaluate: log₂(32).
• FR: Calcule : log₂(32).
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log₂(16) asks: "2 to what power equals 16?" Since 2⁴ = 16, the answer is 4.
• Steps:
  • log₂(32) asks: "2 to what power equals 32?"
  • 2⁵ = 32, so log₂(32) = 5.
• Answer: 5

[Easy] Compound Interest

• EN: $1 000 is invested at 5% per year, compounded annually. What is the amount after 2 years?
• FR: 1 000 $ sont investis à 5 % par an, composés annuellement. Quel est le montant après 2 ans?
• Choices: A) $1 050.00 B) $1 100.00 C) $1 102.50 D) $1 110.25
• Hint: For compound interest, use A = P(1 + r)^t. For $500 at 10% for 2 years: A = 500(1.10)² = 500(1.21) = $605.
• Steps:
  • A = P(1 + r)^t = 1000(1.05)² = 1000 × 1.1025.
  • A = $1 102.50.
• Answer: $1 102.50

[Medium] Quadratic Function — Vertex

• EN: The quadratic function is f(x) = x² − 4x + 7. What is the vertex of this parabola?
• FR: La fonction quadratique est f(x) = x² − 4x + 7. Quel est le sommet de cette parabole?
• Choices: A) (1, 4) B) (2, 3) C) (3, 2) D) (4, 7)
• Hint: The vertex x-coordinate is found using x = −b/(2a). For f(x) = x² − 6x + 11: x = 6/2 = 3, then f(3) = 9 − 18 + 11 = 2, so vertex is (3, 2).
• Steps:
  • x-coordinate of vertex: x = −(−4)/(2×1) = 4/2 = 2.
  • f(2) = (2)² − 4(2) + 7 = 4 − 8 + 7 = 3. Vertex is (2, 3).
• Answer: (2, 3)

[Medium] Geometric Series — Sum

• EN: Find the sum of the first 5 terms of a geometric series where the first term is 2 and the common ratio is 3.
• FR: Trouve la somme des 5 premiers termes d'une série géométrique où le premier terme est 2 et la raison commune est 3.
• Choices: A) 182 B) 212 C) 242 D) 272
• Hint: The sum of a geometric series is Sₙ = a(rⁿ − 1)/(r − 1). For a = 1, r = 2, n = 4: S₄ = 1(16−1)/(2−1) = 15.
• Steps:
  • S₅ = 2(3⁵ − 1)/(3 − 1) = 2(243 − 1)/2 = 2(242)/2 = 242.
  • The sum is 242.
• Answer: 242

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ.
• FR: Simplifie : sin²θ + cos²θ.
• Choices: A) 0 B) sin θ C) cos θ D) 1
• Hint: The Pythagorean identity is one of the most fundamental identities in trigonometry — it relates sin and cos to a constant.
• Steps:
  • sin²θ + cos²θ is the Pythagorean identity.
  • It always equals 1, for any value of θ.
• Answer: 1

[Medium] Financial Math — Annuity

• EN: Émile saves $200 at the end of every year for 3 years. The account earns 4% per year compounded annually. How much will he have at the end of 3 years (to the nearest cent)?
• FR: Émile épargne 200 $ à la fin de chaque année pendant 3 ans. Le compte rapporte 4 % par an composé annuellement. Combien aura-t-il à la fin de 3 ans (au cent près)?
• Choices: A) $612.16 B) $624.32 C) $636.48 D) $648.64
• Hint: For an ordinary annuity, add each payment with its interest: the first payment earns interest for 2 years, the second for 1 year, and the third earns none.
• Steps:
  • Year 1 payment grows: 200(1.04)² = 200(1.0816) = $216.32.
  • Year 2 payment grows: 200(1.04)¹ = $208.00. Year 3: $200.00. Total = 216.32 + 208.00 + 200.00 = $624.32.
• Answer: $624.32

[Hard] Logarithm Laws

• EN: Simplify using logarithm laws: log₃(81) − log₃(9).
• FR: Simplifie à l'aide des lois des logarithmes : log₃(81) − log₃(9).
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: The subtraction law states logb(A) − logb(B) = log_b(A/B). For example, log₂(16) − log₂(4) = log₂(4) = 2.
• Steps:
  • log₃(81) − log₃(9) = log₃(81/9) = log₃(9).
  • Since 3² = 9, log₃(9) = 2.
• Answer: 2

[Hard] Exponential Equation

• EN: Solve for x: 4^x = 64.
• FR: Résous pour x : 4^x = 64.
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: To solve 2^x = 32, write 32 as a power of 2: 2^5 = 32, so x = 5.
• Steps:
  • Write 64 as a power of 4: 4¹ = 4, 4² = 16, 4³ = 64.
  • Since 4³ = 64, x = 3.
• Answer: x = 3

[Easy] Permutations

• EN: How many different ways can 5 students line up in a row?
• FR: Combien de façons différentes 5 élèves peuvent-ils se mettre en file?
• Choices: A) 60 B) 100 C) 120 D) 240
• Hint: To arrange 4 objects in a row, use 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • Number of arrangements = 5! = 5 × 4 × 3 × 2 × 1.
  • = 120 ways.
• Answer: 120

[Easy] Combinations

• EN: From a group of 6 students, 2 are chosen for a committee. How many ways can this be done?
• FR: Dans un groupe de 6 élèves, 2 sont choisis pour un comité. Combien de façons cela peut-il être fait?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: C(n, r) = n! / [r!(n−r)!]. For C(5, 2): 5!/(2! × 3!) = (5 × 4)/(2 × 1) = 10.
• Steps:
  • C(6, 2) = 6! / (2! × 4!) = (6 × 5)/(2 × 1) = 30/2 = 15.
  • There are 15 ways.
• Answer: 15

[Easy] Derivative — Constant Rule

• EN: What is the derivative of f(x) = 8?
• FR: Quelle est la dérivée de f(x) = 8?
• Choices: A) 0 B) 1 C) 8 D) 8x
• Hint: The derivative of any constant, like f(x) = 12, is always 0 because a horizontal line has no slope.
• Steps:
  • A constant function has a slope of 0 everywhere.
  • f'(x) = 0.
• Answer: 0

[Easy] Polynomial Functions

• EN: What is the degree of the polynomial 5x⁴ − 3x² + 7x − 2?
• FR: Quel est le degré du polynôme 5x⁴ − 3x² + 7x − 2?
• Choices: A) 2 B) 3 C) 4 D) 5
• Hint: The degree of a polynomial is the highest exponent — for 2x³ + 4x² − x + 1, the degree is 3.
• Steps:
  • Identify the term with the highest exponent: 5x⁴ has exponent 4.
  • The degree of the polynomial is 4.
• Answer: 4

[Medium] Derivative — Power Rule

• EN: Find the derivative of f(x) = 3x⁴ − 5x² + 2x.
• FR: Trouve la dérivée de f(x) = 3x⁴ − 5x² + 2x.
• Choices: A) 12x³ − 10x + 2 B) 12x³ − 5x + 2 C) 12x⁴ − 10x + 2 D) 7x³ − 3x + 2
• Hint: The power rule: d/dx[axⁿ] = n·axⁿ⁻¹. For 4x³: derivative = 3 × 4x² = 12x².
• Steps:
  • d/dx[3x⁴] = 12x³. d/dx[−5x²] = −10x. d/dx[2x] = 2.
  • f'(x) = 12x³ − 10x + 2.
• Answer: 12x³ − 10x + 2

[Medium] Probability Distribution

• EN: A fair die is rolled. Let X be the outcome. What is the expected value E(X)?
• FR: On lance un dé équitable. Soit X le résultat. Quelle est l'espérance mathématique E(X)?
• Choices: A) 2.5 B) 3.0 C) 3.5 D) 4.0
• Hint: For a uniform distribution over the values 1 through n, the expected value is (1 + n)/2. For a four-sided die: (1 + 4)/2 = 2.5.
• Steps:
  • E(X) = (1 + 2 + 3 + 4 + 5 + 6)/6 = 21/6.
  • = 3.5.
• Answer: 3.5

[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). Quelle est la valeur de u + v?
• Choices: A) (1, 8) B) (2, 9) C) (3, 9) D) (4, 8)
• Hint: To add vectors (a, b) + (c, d), simply add corresponding components: (a + c, b + d).
• Steps:
  • Add x-components: 3 + (−1) = 2. Add y-components: 5 + 4 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Medium] Rational Function — Vertical Asymptote

• EN: For the rational function f(x) = 1/(x − 5), what is the vertical asymptote?
• FR: Pour la fonction rationnelle f(x) = 1/(x − 5), quelle est l'asymptote verticale?
• Choices: A) x = −5 B) x = 0 C) x = 1 D) x = 5
• Hint: The vertical asymptote of a rational function occurs where the denominator equals zero — for 1/(x + 3), set x + 3 = 0 to get x = −3.
• Steps:
  • Set the denominator equal to zero: x − 5 = 0.
  • x = 5 is the vertical asymptote.
• Answer: x = 5

[Hard] Derivative Application — Instantaneous Rate of Change

• EN: The position of a hockey puck in metres is given by s(t) = 2t³ − 3t² + t, where t is in seconds. What is the instantaneous velocity at t = 2 seconds?
• FR: La position d'une rondelle de hockey en mètres est donnée par s(t) = 2t³ − 3t² + t, où t est en secondes. Quelle est la vitesse instantanée à t = 2 secondes?
• Choices: A) 9 m/s B) 13 m/s C) 15 m/s D) 17 m/s
• Hint: Velocity is the derivative of position: find s'(t) first using the power rule, then substitute the given time value.
• Steps:
  • s'(t) = 6t² − 6t + 1. Substitute t = 2: s'(2) = 6(4) − 6(2) + 1.
  • = 24 − 12 + 1 = 13 m/s.
• Answer: 13 m/s

[Hard] Binomial Theorem

• EN: Using the Binomial Theorem, what is the coefficient of x² in the expansion of (x + 3)⁴?
• FR: En utilisant le théorème binomial, quel est le coefficient de x² dans le développement de (x + 3)⁴?
• Choices: A) 36 B) 54 C) 72 D) 108
• Hint: In (a + b)ⁿ, the term with xᵏ uses C(n, k) × aᵏ × bⁿ⁻ᵏ. For (x + 2)³, the x¹ term is C(3,1) × x¹ × 2² = 3 × 4 × x = 12x.
• Steps:
  • The x² term in (x + 3)⁴: use C(4, 2) × x² × 3².
  • C(4, 2) = 6. 3² = 9. Coefficient = 6 × 9 = 54.
• Answer: 54