Daily Math — 2026-07-22

[Easy] Counting Hockey Pucks

• EN: There are 7 hockey pucks on the ice. The coach adds 5 more. How many pucks are there now?
• FR: Il y a 7 rondelles de hockey sur la glace. L'entraîneur en ajoute 5 autres. Combien de rondelles y a-t-il maintenant?
• Choices: A) 10 pucks B) 11 pucks C) 12 pucks D) 13 pucks
• Hint: To add 6 + 4, count on from 6: 7, 8, 9, 10 — that is 4 steps, so 6 + 4 = 10.
• Steps:
  • Start at 7 on a number line.
  • Count forward 5 steps: 8, 9, 10, 11, 12.
  • So the total is 12 pucks.
• Answer: 12 pucks

[Easy] Pennies in a Jar

• EN: Mia has 9 pennies. She gives 4 pennies to her friend. How many pennies does Mia have left?
• FR: Mia a 9 sous. Elle en donne 4 à son amie. Combien de sous Mia a-t-elle maintenant?
• Choices: A) 3 pennies B) 4 pennies C) 5 pennies D) 6 pennies
• Hint: To solve 8 − 3, start at 8 and count back 3: 7, 6, 5 — the answer is 5.
• Steps:
  • Start at 9.
  • Count back 4 steps: 8, 7, 6, 5.
  • So Mia has 5 pennies left.
• Answer: 5 pennies

[Easy] Skip Counting by 5s

• EN: Start at 5 and skip count by 5s. What is the next number after 15?
• FR: Commence à 5 et compte par bonds de 5. Quel est le nombre suivant après 15?
• Choices: A) 18 B) 19 C) 20 D) 25
• Hint: Skip counting by 2s from 6 goes 6, 8, 10 — each jump adds 2.
• Steps:
  • The pattern is 5, 10, 15, …
  • Add 5 to 15: 15 + 5 = 20.
  • So the next number is 20.
• Answer: 20

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 18?
• FR: Quel nombre est plus grand : 14 ou 18?
• Choices: A) 11 B) 14 C) 16 D) 18
• Hint: To compare 12 and 17, find them on a number line — the number farther right is greater.
• Steps:
  • Place 14 and 18 on a number line.
  • 18 is farther to the right than 14.
  • So 18 is greater.
• Answer: 18

[Medium] Adding Two Numbers

• EN: There are 13 students in one class and 6 students in another. How many students are there in total?
• FR: Il y a 13 élèves dans une classe et 6 dans une autre. Combien y a-t-il d'élèves en tout?
• Choices: A) 17 students B) 18 students C) 19 students D) 21 students
• Hint: To add 11 + 7, start at 11 and count on 7 more: 12, 13, 14, 15, 16, 17, 18.
• Steps:
  • Start at 13.
  • Count on 6: 14, 15, 16, 17, 18, 19.
  • So there are 19 students in total.
• Answer: 19 students

[Medium] Subtracting at the Rink

• EN: There are 20 players at the hockey rink. 8 players go home. How many players are left?
• FR: Il y a 20 joueurs à la patinoire. 8 joueurs rentrent chez eux. Combien de joueurs reste-t-il?
• Choices: A) 10 players B) 11 players C) 12 players D) 14 players
• Hint: To solve 20 − 5, think of a number plus 5 that makes 20: 15 + 5 = 20, so the answer is 15.
• Steps:
  • Start at 20.
  • Count back 8: 19, 18, 17, 16, 15, 14, 13, 12.
  • So 12 players are left.
• Answer: 12 players

[Medium] Skip Counting by 2s

• EN: Luc counts his mittens by 2s: 2, 4, 6, 8, ___. What comes next?
• FR: Luc compte ses mitaines par bonds de 2 : 2, 4, 6, 8, ___. Quel est le prochain nombre?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When counting by 2s from 12, the next number is 12 + 2 = 14.
• Steps:
  • The pattern adds 2 each time.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Medium] Coin Recognition

• EN: Anika has 1 dime and 1 nickel. How many cents does she have altogether?
• FR: Anika a 1 pièce de 10 cents et 1 pièce de 5 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 — add them to get the total.
• Steps:
  • A dime = 10 cents.
  • A nickel = 5 cents.
  • 10 + 5 = 15 cents.
• Answer: 15 cents

[Hard] Two-Step Addition

• EN: There are 6 red apples, 7 green apples, and 4 yellow apples in a basket. How many apples are there in all?
• FR: Il y a 6 pommes rouges, 7 pommes vertes et 4 pommes jaunes dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 15 apples B) 16 apples C) 17 apples D) 18 apples
• Hint: To add 3 + 5 + 4, first add 3 + 5 = 8, then add 4 to get 12.
• Steps:
  • First add 6 + 7 = 13.
  • Then add 13 + 4 = 17.
  • So there are 17 apples in all.
• Answer: 17 apples

[Hard] Number Patterns

• EN: What number is missing? 10, ___, 30, 40, 50.
• FR: Quel nombre manque-t-il? 10, ___, 30, 40, 50.
• Choices: A) 15 B) 18 C) 20 D) 25
• Hint: In the pattern 5, 10, ___, 20, each number increases by 5, so the missing number is 15.
• Steps:
  • Look at the pattern: 10, ___, 30, 40, 50.
  • Each number increases by 10.
  • 10 + 10 = 20, so the missing number is 20.
• Answer: 20

[Easy] Adding Within 100

• EN: Sam has 34 stickers. He gets 25 more stickers. How many stickers does he have now?
• FR: Sam a 34 autocollants. Il en reçoit 25 autres. Combien d'autocollants a-t-il maintenant?
• Choices: A) 57 stickers B) 58 stickers C) 59 stickers D) 61 stickers
• Hint: To add 32 + 21, add the tens first (30 + 20 = 50) then the ones (2 + 1 = 3) to get 53.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9.
  • 50 + 9 = 59 stickers.
• Answer: 59 stickers

[Easy] Telling Time

• EN: The clock shows the short hand on 3 and the long hand on 12. What time is it?
• FR: La petite aiguille de l'horloge est sur le 3 et la grande aiguille est sur le 12. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 4:00
• Hint: When the long hand points to 12, it is exactly on the 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 measures 14 cm and an eraser measures 3 cm. How much longer is the pencil?
• FR: Un crayon mesure 14 cm et une gomme mesure 3 cm. De combien le crayon est-il plus long?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: To find how much longer one object is, subtract: 18 − 5 = 13 cm.
• Steps:
  • Subtract the eraser length from the pencil length.
  • 14 − 3 = 11.
  • The pencil is 11 cm longer.
• Answer: 11 cm

[Easy] Counting Coins

• EN: Bella has 2 dimes and 1 nickel. How much money does she have?
• FR: Bella a 2 pièces de 10 cents et 1 pièce de 5 cents. Combien d'argent a-t-elle?
• Choices: A) 20 cents B) 22 cents C) 25 cents D) 30 cents
• Hint: Two dimes equal 20 cents; add any nickels (5 cents each) to find the total.
• Steps:
  • 2 dimes = 20 cents.
  • 1 nickel = 5 cents.
  • 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Subtraction Within 100

• EN: There were 72 snowballs in a pile. Kids used 48 of them. How many snowballs are left?
• FR: Il y avait 72 boules de neige dans un tas. Les enfants en ont utilisé 48. Combien en reste-t-il?
• Choices: A) 22 snowballs B) 24 snowballs C) 26 snowballs D) 28 snowballs
• Hint: To subtract 75 − 43, subtract the tens (70 − 40 = 30) then the ones (5 − 3 = 2) to get 32.
• Steps:
  • Subtract the tens: 70 − 40 = 30.
  • Subtract the ones: 2 − 8 is tricky, so regroup: 72 − 48.
  • Borrow: 12 − 8 = 4, and 6 − 4 = 2, giving 24 snowballs.
• Answer: 24 snowballs

[Medium] Telling Time (Half-Hour)

• EN: The clock shows the short hand halfway between 7 and 8, and the long hand on 6. What time is it?
• FR: La petite aiguille est à mi-chemin entre le 7 et le 8, et la grande aiguille est sur le 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:00
• Hint: When the long hand is on 6, it is always a half-hour — read the short hand for the hour.
• Steps:
  • Long hand on 6 means 30 minutes past the hour.
  • Short hand is between 7 and 8, so the hour is 7.
  • The time is 7:30.
• Answer: 7:30

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, ___. What is the missing number?
• FR: Observe ce motif : 5, 10, 15, 20, ___. Quel est le nombre manquant?
• Choices: A) 22 B) 23 C) 24 D) 25
• Hint: In the pattern 3, 6, 9, 12, each number increases by 3, so add 3 to find the next one.
• Steps:
  • The pattern increases by 5 each time.
  • 20 + 5 = 25.
  • The missing number is 25.
• Answer: 25

[Medium] Adding Coins to $1

• EN: Jake has 3 quarters. How much money does he have in cents?
• FR: Jake a 3 pièces de 25 cents. Combien d'argent a-t-il en cents?
• Choices: A) 55 cents B) 65 cents C) 70 cents D) 75 cents
• Hint: One quarter is worth 25 cents, so two quarters equal 25 + 25 = 50 cents.
• Steps:
  • Each quarter is worth 25 cents.
  • 25 + 25 = 50, then 50 + 25 = 75.
  • Jake has 75 cents.
• Answer: 75 cents

[Hard] Two-Step Problem

• EN: A shelf has 45 books. A librarian adds 18 books, then removes 23 books. How many books are on the shelf now?
• FR: Une étagère a 45 livres. Une bibliothécaire en ajoute 18, puis en enlève 23. Combien de livres y a-t-il maintenant?
• Choices: A) 38 books B) 40 books C) 42 books D) 44 books
• Hint: For two-step problems, do the first operation (e.g., 30 + 12 = 42) then the second (42 − 11 = 31).
• Steps:
  • First, add: 45 + 18 = 63.
  • Then subtract: 63 − 23 = 40.
  • There are 40 books on the shelf.
• Answer: 40 books

[Hard] Measuring and Comparing

• EN: A piece of ribbon is 85 cm long. Another ribbon is 37 cm long. How long are both ribbons together?
• FR: Un ruban mesure 85 cm de long. Un autre ruban mesure 37 cm. Quelle est la longueur totale des deux rubans?
• Choices: A) 112 cm B) 118 cm C) 120 cm D) 122 cm
• Hint: To add 64 + 39, add tens (60 + 30 = 90) then ones (4 + 9 = 13), then combine: 90 + 13 = 103.
• Steps:
  • Add the tens: 80 + 30 = 110.
  • Add the ones: 5 + 7 = 12.
  • 110 + 12 = 122 cm.
• Answer: 122 cm

[Easy] Multiplication by 2

• EN: There are 6 bicycles in a garage. Each bicycle has 2 wheels. How many wheels are there in total?
• FR: Il y a 6 vélos dans un garage. Chaque vélo a 2 roues. Combien de roues y a-t-il en tout?
• Choices: A) 8 wheels B) 10 wheels C) 12 wheels D) 14 wheels
• Hint: To find 4 × 2, skip count by 2s four times: 2, 4, 6, 8.
• Steps:
  • Use the multiplication fact: 6 × 2.
  • Skip count by 2s, six times: 2, 4, 6, 8, 10, 12.
  • There are 12 wheels in total.
• Answer: 12 wheels

[Easy] Fractions — One Half

• EN: A pizza is cut into 4 equal slices. Emma eats 2 slices. What fraction of the pizza did she eat?
• FR: Une pizza est coupée en 4 parts égales. Emma mange 2 parts. Quelle fraction de la pizza a-t-elle mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 3/4
• Hint: If a cake is cut into 6 equal pieces and you eat 3, you ate 3/6, which equals 1/2.
• Steps:
  • Emma ate 2 out of 4 slices.
  • The fraction is 2/4.
  • 2/4 simplifies to 1/2.
• Answer: 1/2

[Easy] Multiplication by 5

• EN: A bag holds 5 apples. How many apples are in 4 bags?
• FR: Un sac contient 5 pommes. Combien de pommes y a-t-il dans 4 sacs?
• Choices: A) 15 apples B) 18 apples C) 20 apples D) 25 apples
• Hint: To find 3 × 5, skip count by 5s three times: 5, 10, 15.
• Steps:
  • Use the fact: 4 × 5.
  • Skip count by 5s four times: 5, 10, 15, 20.
  • There are 20 apples in 4 bags.
• Answer: 20 apples

[Easy] Basic Division

• EN: 18 hockey cards are shared equally among 3 friends. How many cards does each friend get?
• FR: 18 cartes de hockey sont partagées également entre 3 amis. Combien de cartes chaque ami reçoit-il?
• Choices: A) 4 cards B) 5 cards C) 6 cards D) 7 cards
• Hint: For 15 ÷ 3, think: what number times 3 equals 15? Since 5 × 3 = 15, the answer is 5.
• Steps:
  • Think: what times 3 equals 18?
  • 6 × 3 = 18.
  • Each friend gets 6 cards.
• Answer: 6 cards

[Medium] Perimeter

• EN: A rectangular garden is 8 m long and 5 m wide. What is its perimeter?
• FR: Un jardin rectangulaire mesure 8 m de long et 5 m de large. Quel est son périmètre?
• Choices: A) 24 m B) 26 m C) 28 m D) 30 m
• Hint: The perimeter of a rectangle with length 6 m and width 4 m is 6 + 6 + 4 + 4 = 20 m.
• Steps:
  • Add all four sides: 8 + 8 + 5 + 5.
  • 8 + 8 = 16 and 5 + 5 = 10.
  • 16 + 10 = 26 m.
• Answer: 26 m

[Medium] Multiplication by 4

• EN: There are 7 boxes of crayons. Each box has 4 crayons. How many crayons are there altogether?
• FR: Il y a 7 boîtes de crayons. Chaque boîte contient 4 crayons. Combien y a-t-il de crayons en tout?
• Choices: A) 24 crayons B) 26 crayons C) 28 crayons D) 32 crayons
• Hint: To find 6 × 4, skip count by 4s six times: 4, 8, 12, 16, 20, 24.
• Steps:
  • Use the fact: 7 × 4.
  • 7 × 4 = 28.
  • There are 28 crayons altogether.
• Answer: 28 crayons

[Medium] Reading a Graph

• EN: A bar graph shows: apples — 6, bananas — 9, oranges — 4. How many pieces of fruit are shown altogether?
• FR: Un diagramme à barres montre : pommes — 6, bananes — 9, oranges — 4. Combien y a-t-il de fruits en tout?
• Choices: A) 17 pieces B) 18 pieces C) 19 pieces D) 20 pieces
• Hint: To read a graph, add the values of each bar: for example, 5 + 7 + 3 = 15.
• Steps:
  • Add all three values: 6 + 9 + 4.
  • 6 + 9 = 15.
  • 15 + 4 = 19 pieces of fruit.
• Answer: 19 pieces

[Medium] Fractions — One Quarter

• EN: A chocolate bar has 8 equal pieces. Theo eats 2 pieces. What fraction did Theo eat?
• FR: Une barre de chocolat a 8 morceaux égaux. Théo en mange 2. Quelle fraction Théo a-t-il mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: If you eat 2 out of 10 equal pieces, you ate 2/10, which simplifies to 1/5.
• Steps:
  • Theo ate 2 out of 8 pieces.
  • The fraction is 2/8.
  • 2/8 simplifies to 1/4.
• Answer: 1/4

[Hard] Multiplication and Subtraction

• EN: A teacher buys 5 packs of pencils with 10 pencils each. She gives out 17 pencils. How many pencils does she have left?
• FR: Une enseignante achète 5 paquets de crayons avec 10 crayons chacun. Elle en distribue 17. Combien lui en reste-t-il?
• Choices: A) 30 pencils B) 33 pencils C) 35 pencils D) 37 pencils
• Hint: First multiply to find the total (e.g., 3 × 10 = 30), then subtract what was used (30 − 8 = 22).
• Steps:
  • Find the total: 5 × 10 = 50 pencils.
  • Subtract the ones given out: 50 − 17 = 33.
  • She has 33 pencils left.
• Answer: 33 pencils

[Hard] Perimeter with Multiplication

• EN: A square playground has a side length of 9 m. What is its perimeter?
• FR: Un terrain de jeu carré a un côté de 9 m. Quel est son périmètre?
• Choices: A) 27 m B) 32 m C) 36 m D) 40 m
• Hint: A square has 4 equal sides, so its perimeter is 4 × side length. For a side of 7 m: 4 × 7 = 28 m.
• Steps:
  • A square has 4 equal sides.
  • Multiply: 4 × 9 = 36.
  • The perimeter is 36 m.
• Answer: 36 m

[Easy] Multiplication Tables

• EN: What is 8 × 7?
• FR: Combien font 8 × 7?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To find 6 × 7, break it up: 6 × 7 = 6 × 5 + 6 × 2 = 30 + 12 = 42.
• Steps:
  • Recall or work out 8 × 7.
  • 8 × 7 = 56.
  • The answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 4 tens
• Hint: In the number 5.62, the digit 6 is in the tenths place and the digit 2 is in the hundredths place.
• Steps:
  • In 3.47, the digits after the decimal are tenths and hundredths.
  • The digit 4 is in the first position after the decimal.
  • That is the tenths place, so 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A classroom rug is 6 m long and 4 m wide. What is its area?
• FR: Un tapis de classe mesure 6 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 20 m² B) 22 m² C) 24 m² D) 28 m²
• Hint: The area of a rectangle is length × width. For a 5 m × 3 m rectangle, area = 15 m².
• Steps:
  • Area = length × width.
  • Area = 6 × 4 = 24.
  • The area of the rug is 24 m².
• Answer: 24 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/4?
• FR: Quelle fraction est plus grande : 3/4 ou 2/4?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) 4/4
• Hint: When fractions have the same denominator, simply compare the numerators: 5/8 > 3/8 because 5 > 3.
• Steps:
  • Both fractions have the same denominator (4).
  • Compare the numerators: 3 > 2.
  • So 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: A baker has 47 muffins to pack into boxes of 5. How many full boxes can be made, and how many muffins are left over?
• FR: Un boulanger a 47 muffins à emballer dans des boîtes de 5. Combien de boîtes complètes peut-il faire et combien de muffins restent-il?
• Choices: A) 8 boxes, 5 left over B) 9 boxes, 2 left over C) 9 boxes, 3 left over D) 10 boxes, 2 left over
• Hint: To divide 38 ÷ 4, find how many 4s fit into 38: 4 × 9 = 36, so 9 remainder 2.
• Steps:
  • Divide: 47 ÷ 5.
  • 5 × 9 = 45, which is the closest multiple of 5 to 47.
  • 47 − 45 = 2, so 9 boxes with 2 muffins left over.
• Answer: 9 boxes, 2 left over

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 p.m. and ends at 3:45 p.m. How long is the game?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Quelle est la durée du match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 3 hours
• Hint: To find elapsed time from 2:20 to 4:50, count the hours (2) then the minutes (30) to get 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 is exactly 2 hours.
  • From 3:15 to 3:45 is 30 more minutes.
  • Total elapsed time is 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A water bottle holds 1.75 L. Another holds 0.50 L. How much water do they hold together?
• FR: Une bouteille d'eau contient 1,75 L. Une autre contient 0,50 L. Combien d'eau contiennent-elles ensemble?
• Choices: A) 2.05 L B) 2.15 L C) 2.25 L D) 2.50 L
• Hint: To add 2.30 + 1.40, line up the decimals and add: 2.30 + 1.40 = 3.70.
• Steps:
  • Line up the decimal points: 1.75 + 0.50.
  • Add the hundredths: 5 + 0 = 5.
  • Add tenths and ones: 1.75 + 0.50 = 2.25 L.
• Answer: 2.25 L

[Medium] Multiplication — Large Numbers

• EN: A school orders 9 boxes of markers. Each box has 8 markers. How many markers are ordered in total?
• FR: Une école commande 9 boîtes de marqueurs. Chaque boîte contient 8 marqueurs. Combien de marqueurs sont commandés en tout?
• Choices: A) 63 markers B) 70 markers C) 72 markers D) 81 markers
• Hint: 7 × 8 = 56; for 9 × 8, add two more groups of 8: 56 + 8 + 8 = 72.
• Steps:
  • Use the multiplication fact: 9 × 8.
  • 9 × 8 = 72.
  • 72 markers are ordered in total.
• Answer: 72 markers

[Hard] Multi-Step Word Problem

• EN: Sophie earns $6 per hour raking leaves. She works 8 hours this week and spends $23 on craft supplies. How much money does she have left?
• FR: Sophie gagne 6 $ de l'heure à ratisser les feuilles. Elle travaille 8 heures cette semaine et dépense 23 $ en fournitures d'artisanat. Combien d'argent lui reste-t-il?
• Choices: A) $22 B) $25 C) $27 D) $29
• Hint: First find total earnings (e.g., 5 × $7 = $35), then subtract spending ($35 − $10 = $25).
• Steps:
  • Total earned: 6 × 8 = $48.
  • Subtract spending: $48 − $23 = $25.
  • Sophie has $25 left.
• Answer: $25

[Hard] Area and Perimeter

• EN: A rectangular park is 9 m long and 7 m wide. What is the difference between its perimeter and its area?
• FR: Un parc rectangulaire mesure 9 m de long et 7 m de large. Quelle est la différence entre son périmètre et son aire?
• Choices: A) 0 B) 5 C) 31 D) 95
• Hint: For a rectangle 4 m × 3 m, perimeter = 2 × (4 + 3) = 14 m and area = 4 × 3 = 12 m²; difference = 2.
• Steps:
  • Perimeter = 2 × (9 + 7) = 2 × 16 = 32 m.
  • Area = 9 × 7 = 63 m².
  • Difference = 63 − 32 = 31.
• Answer: 31

[Easy] Multi-Digit Multiplication

• EN: A school trip has 24 students. Each student pays $15. How much do they pay in total?
• FR: Une sortie scolaire a 24 élèves. Chaque élève paie 15 $. Combien paient-ils en tout?
• Choices: A) $320 B) $340 C) $360 D) $380
• Hint: To multiply 22 × 13, break it into 22 × 10 = 220 and 22 × 3 = 66, then add: 220 + 66 = 286.
• Steps:
  • Multiply: 24 × 15.
  • 24 × 10 = 240 and 24 × 5 = 120.
  • 240 + 120 = $360.
• Answer: $360

[Easy] Adding Fractions with Like Denominators

• EN: Max ate 2/8 of a pie and his sister ate 3/8. What fraction of the pie did they eat together?
• FR: Max a mangé 2/8 d'une tarte et sa sœur en a mangé 3/8. Quelle fraction de la tarte ont-ils mangée ensemble?
• Choices: A) 4/8 B) 5/8 C) 6/8 D) 7/8
• Hint: To add 1/6 + 3/6, add only the numerators and keep the denominator: 1 + 3 = 4, so 4/6.
• Steps:
  • Add the numerators: 2 + 3 = 5.
  • Keep the denominator: 5/8.
  • Together they ate 5/8 of the pie.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: A Tim Hortons muffin costs $2.00. What is 50% of its cost?
• FR: Un muffin de Tim Hortons coûte 2,00 $. Quel est 50 % de son prix?
• Choices: A) $0.50 B) $0.75 C) $1.00 D) $1.25
• Hint: 50% means half — to find 50% of 40, divide by 2: 40 ÷ 2 = 20.
• Steps:
  • 50% means divide by 2.
  • $2.00 ÷ 2 = $1.00.
  • 50% of the cost is $1.00.
• Answer: $1.00

[Easy] Decimal Operations

• EN: A book costs $12.45 and a pen costs $3.30. How much do they cost together?
• FR: Un livre coûte 12,45 $ et un stylo coûte 3,30 $. Combien coûtent-ils ensemble?
• Choices: A) $14.75 B) $15.45 C) $15.75 D) $16.45
• Hint: To add $10.20 + $4.50, line up the decimals: $10.20 + $4.50 = $14.70.
• Steps:
  • Line up: $12.45 + $3.30.
  • Add cents: 45 + 30 = 75 cents.
  • Add dollars: $12 + $3 = $15. Total = $15.75.
• Answer: $15.75

[Medium] Multi-Digit Division

• EN: A school has 156 students to put in groups of 4. How many groups are there?
• FR: Une école a 156 élèves à mettre en groupes de 4. Combien de groupes y a-t-il?
• Choices: A) 36 groups B) 38 groups C) 39 groups D) 42 groups
• Hint: To divide 126 ÷ 3, divide the hundreds (1 ÷ 3 goes 0, bring down), then work through: 12 ÷ 3 = 4, 06 ÷ 3 = 2, giving 42.
• Steps:
  • Divide 156 ÷ 4.
  • 4 × 39 = 156.
  • There are 39 groups.
• Answer: 39 groups

[Medium] Subtracting Fractions

• EN: A jug had 7/10 of a litre of juice. Owen drank 3/10 of a litre. How much juice is left?
• FR: Un pichet contenait 7/10 d'un litre de jus. Owen en a bu 3/10 d'un litre. Combien de jus reste-t-il?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 6/10
• Hint: To subtract 5/9 − 2/9, subtract the numerators and keep the denominator: 5 − 2 = 3, so 3/9.
• Steps:
  • Subtract the numerators: 7 − 3 = 4.
  • Keep the denominator: 4/10.
  • There is 4/10 of a litre left.
• Answer: 4/10

[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 mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 48 cm³ B) 54 cm³ C) 60 cm³ D) 65 cm³
• Hint: Volume of a rectangular prism = length × width × height. For 2 × 3 × 4, volume = 24 cm³.
• Steps:
  • Multiply length × width × height.
  • 5 × 4 = 20, then 20 × 3 = 60.
  • The volume is 60 cm³.
• Answer: 60 cm³

[Medium] Percentage — 25% and 10%

• EN: A jacket costs $80. The store offers a 25% discount. How much money does the discount save?
• FR: Un manteau coûte 80 $. Le magasin offre un rabais de 25 %. Combien le rabais économise-t-il?
• Choices: A) $15 B) $18 C) $20 D) $25
• Hint: 25% equals one quarter — to find 25% of 60, divide by 4: 60 ÷ 4 = 15.
• Steps:
  • 25% = one quarter, so divide by 4.
  • $80 ÷ 4 = $20.
  • The discount saves $20.
• Answer: $20

[Hard] Multi-Step Fraction and Decimal

• EN: A recipe needs 1.5 cups of flour. Maya makes 3 batches but only uses 3/4 of the total flour. How many cups of flour does she use?
• FR: Une recette nécessite 1,5 tasse de farine. Maya fait 3 lots mais n'utilise que 3/4 de la farine totale. Combien de tasses de farine utilise-t-elle?
• Choices: A) 3.00 cups B) 3.25 cups C) 3.375 cups D) 3.75 cups
• Hint: First find the total (e.g., 3 × 2.0 = 6.0), then take 3/4 of it (6.0 × 3/4 = 4.5 cups).
• Steps:
  • Total flour needed: 1.5 × 3 = 4.5 cups.
  • Take 3/4 of 4.5: 4.5 × 3/4 = 13.5/4 = 3.375.
  • Maya uses 3.375 cups.
• Answer: 3.375 cups

[Hard] Multi-Step Percentage and Money

• EN: Noah earns $120 shovelling driveways. He spends 10% on bus fare, 25% on snacks, and saves the rest. How much does Noah save?
• FR: Noah gagne 120 $ en pelletant des entrées. Il dépense 10 % en bus, 25 % en collations et économise le reste. Combien économise-t-il?
• Choices: A) $72 B) $75 C) $78 D) $84
• Hint: Find each percent (10% of 100 = 10, 25% of 100 = 25), add them, then subtract from the total.
• Steps:
  • 10% of $120 = $12 (bus fare).
  • 25% of $120 = $30 (snacks).
  • Total spent: $12 + $30 = $42. Saved: $120 − $42 = $78.
• Answer: $78

[Easy] Order of Operations (BEDMAS)

• EN: What is the value of 3 + 4 × 2?
• FR: Quelle est la valeur de 3 + 4 × 2?
• Choices: A) 9 B) 10 C) 11 D) 14
• Hint: In BEDMAS, multiplication happens before addition — for 5 + 2 × 3, do 2 × 3 = 6 first, then 5 + 6 = 11.
• Steps:
  • Apply BEDMAS: multiplication before addition.
  • 4 × 2 = 8 first.
  • 3 + 8 = 11.
• Answer: 11

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Quel est 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: 20 × 3 = 60.
  • 30% of 200 is 60.
• Answer: 60

[Easy] Integers — Comparing

• EN: Which integer is greater: −5 or −2?
• FR: Quel entier est plus grand : −5 ou −2?
• Choices: A) −6 B) −5 C) −3 D) −2
• Hint: On a number line, −1 is to the right of −4, so −1 > −4.
• Steps:
  • Place both numbers on a number line.
  • −2 is to the right of −5.
  • So −2 is greater.
• Answer: −2

[Easy] Simple Algebraic Expression

• EN: If n = 4, what is the value of 3n + 5?
• FR: Si n = 4, quelle est la valeur de 3n + 5?
• Choices: A) 12 B) 14 C) 17 D) 19
• Hint: To evaluate 2n + 3 when n = 5, substitute: 2 × 5 + 3 = 10 + 3 = 13.
• Steps:
  • Substitute n = 4: 3 × 4 + 5.
  • 3 × 4 = 12.
  • 12 + 5 = 17.
• Answer: 17

[Medium] Fraction Multiplication

• EN: What is 3/4 × 2/3?
• FR: Quel est le résultat de 3/4 × 2/3?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 5/12
• Hint: To multiply fractions, multiply the numerators together and the denominators together: 2/5 × 3/4 = 6/20 = 3/10.
• Steps:
  • Multiply numerators: 3 × 2 = 6.
  • Multiply denominators: 4 × 3 = 12.
  • 6/12 = 1/2.
• Answer: 1/2

[Medium] Ratios and Rates

• EN: A car travels 240 km in 3 hours. What is its speed in km/h?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km/h?
• Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: To find the unit rate, divide the total distance by the time: 150 km ÷ 2 h = 75 km/h.
• Steps:
  • Divide total distance by time.
  • 240 ÷ 3 = 80.
  • The speed is 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Quel est le résultat de 3/4 ÷ 1/2?
• Choices: A) 1/2 B) 3/4 C) 3/2 D) 2/3
• Hint: To divide fractions, multiply by the reciprocal: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
• Steps:
  • Flip the second fraction and multiply: 3/4 × 2/1.
  • 3 × 2 = 6 and 4 × 1 = 4.
  • 6/4 = 3/2.
• Answer: 3/2

[Medium] Integer Addition

• EN: What is (−8) + 3?
• FR: Quel est le résultat de (−8) + 3?
• Choices: A) −6 B) −5 C) 5 D) 11
• Hint: To add −6 + 2, start at −6 on a number line and move 2 steps right to land on −4.
• Steps:
  • Start at −8 on a number line.
  • Move 3 steps to the right.
  • Land on −5.
• Answer: −5

[Hard] Order of Operations — Complex

• EN: Evaluate: (12 − 4) ÷ 2 + 3 × 5.
• FR: Calcule : (12 − 4) ÷ 2 + 3 × 5.
• Choices: A) 16 B) 17 C) 19 D) 23
• Hint: Work through BEDMAS step by step: brackets first, then division/multiplication left to right, then addition/subtraction for (10 − 2) ÷ 2 + 2 × 3 = 8 ÷ 2 + 6 = 4 + 6 = 10.
• Steps:
  • Brackets first: 12 − 4 = 8.
  • Division: 8 ÷ 2 = 4.
  • Multiplication: 3 × 5 = 15. Then 4 + 15 = 19.
• Answer: 19

[Hard] Percent Problem

• EN: A pair of hockey skates normally costs $160. They are on sale for 35% off. What is the sale price?
• FR: Une paire de patins de hockey coûte normalement 160 $. Ils sont en solde à 35 % de rabais. Quel est le prix de vente?
• Choices: A) $96 B) $100 C) $104 D) $112
• Hint: To find the sale price, calculate the discount (e.g., 20% of $80 = $16) then subtract from the original ($80 − $16 = $64).
• Steps:
  • Find 35% of $160: 10% = $16, so 35% = $16 × 3.5 = $56.
  • Subtract: $160 − $56 = $104.
  • The sale price is $104.
• Answer: $104

[Easy] Integer Addition and Subtraction

• EN: What is (−6) − (−4)?
• FR: Quel est le résultat de (−6) − (−4)?
• Choices: A) −10 B) −4 C) −2 D) 2
• Hint: Subtracting a negative is the same as adding a positive: −5 − (−3) = −5 + 3 = −2.
• Steps:
  • Rewrite: (−6) − (−4) = (−6) + 4.
  • Start at −6 and move 4 right: −5, −4, −3, −2.
  • The answer is −2.
• Answer: −2

[Easy] Percentage — Discount

• EN: A backpack costs $50. It is on sale for 20% off. How much is saved?
• FR: Un sac à dos coûte 50 $. Il est en solde à 20 % de rabais. Combien économise-t-on?
• Choices: A) $8 B) $10 C) $12 D) $15
• Hint: To find 20% of $60, find 10% first ($6) then double it to get $12.
• Steps:
  • Find 10% of $50 = $5.
  • Double it for 20%: $5 × 2 = $10.
  • You save $10.
• Answer: $10

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17.
• FR: Résous pour x : x + 9 = 17.
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: To solve x + 5 = 12, subtract 5 from both sides: x = 12 − 5 = 7.
• Steps:
  • Subtract 9 from both sides.
  • x = 17 − 9.
  • x = 8.
• Answer: x = 8

[Easy] Fraction and Decimal Fluency

• EN: Write 3/5 as a decimal.
• FR: Écris 3/5 en décimale.
• Choices: A) 0.35 B) 0.53 C) 0.60 D) 0.75
• Hint: To convert 1/4 to a decimal, divide 1 by 4: 1 ÷ 4 = 0.25.
• Steps:
  • Divide the numerator by the denominator.
  • 3 ÷ 5 = 0.6.
  • So 3/5 = 0.60.
• Answer: 0.60

[Medium] Integer Multiplication

• EN: What is (−7) × (−4)?
• FR: Quel est le résultat de (−7) × (−4)?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: Negative × negative = positive; for (−3) × (−5) = +15.
• Steps:
  • Multiply the values: 7 × 4 = 28.
  • Two negatives make a positive.
  • (−7) × (−4) = 28.
• Answer: 28

[Medium] Percentage — Tax

• EN: A book costs $18.00. If 13% HST is added, what is the total cost?
• FR: Un livre coûte 18,00 $. Si une TVH de 13 % est ajoutée, quel est le coût total?
• Choices: A) $19.34 B) $20.34 C) $21.14 D) $22.34
• Hint: To add 10% tax to $40, find 10% ($4.00) and add it: $40 + $4 = $44.00.
• Steps:
  • Find 13% of $18.00: 10% = $1.80, 3% = $0.54. Total tax = $2.34.
  • Add to original: $18.00 + $2.34 = $20.34.
  • The total cost is $20.34.
• Answer: $20.34

[Medium] Surface Area

• EN: A rectangular box is 6 cm long, 4 cm wide, and 2 cm tall. What is its surface area?
• FR: Une boîte rectangulaire mesure 6 cm de long, 4 cm de large et 2 cm de haut. Quelle est son aire totale?
• Choices: A) 68 cm² B) 76 cm² C) 88 cm² D) 96 cm²
• Hint: Surface area of a box = 2(lw + lh + wh). For a 3 × 2 × 1 box: 2(6 + 3 + 2) = 2 × 11 = 22 cm².
• Steps:
  • Calculate each pair of faces: 2(6 × 4) = 48, 2(6 × 2) = 24, 2(4 × 2) = 16.
  • Add: 48 + 24 + 16 = 88.
  • Surface area = 88 cm².
• Answer: 88 cm²

[Medium] Probability

• EN: A bag has 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 piger une bille bleue?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 5/9
• Hint: Probability = number of favourable outcomes ÷ total outcomes. For 4 red out of 12 total: 4/12 = 1/3.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Probability of blue: 5/10.
  • Simplified: 5/10 = 1/2.
• Answer: 1/2

[Hard] Multi-Step Percent Problem

• EN: A store marks up a sweater by 40% from its cost of $35, then offers a 10% sale. What is the final price?
• FR: Un magasin majore un chandail de 40 % par rapport à son coût de 35 $, puis offre une vente à 10 %. Quel est le prix final?
• Choices: A) $42.70 B) $43.20 C) $44.10 D) $45.00
• Hint: First find the marked-up price (cost + 40% of cost), then apply the 10% discount to that new price.
• Steps:
  • Marked-up price: $35 + 40% of $35 = $35 + $14 = $49.
  • Apply 10% discount: $49 − 10% of $49 = $49 − $4.90 = $44.10.
  • The final price is $44.10.
• Answer: $44.10

[Hard] Data — Mean and Probability

• EN: In five hockey games, Nia scored 3, 1, 4, 2, and 5 goals. What is the mean number of goals per game?
• FR: En cinq matchs de hockey, Nia a marqué 3, 1, 4, 2 et 5 buts. Quel est le nombre moyen de buts par match?
• Choices: A) 2 goals B) 2.5 goals C) 3 goals D) 3.5 goals
• Hint: Mean = sum of all values ÷ number of values. For 2, 4, 6, 8: sum = 20, mean = 20 ÷ 4 = 5.
• Steps:
  • Add all scores: 3 + 1 + 4 + 2 + 5 = 15.
  • Divide by number of games: 15 ÷ 5 = 3.
  • The mean is 3 goals per game.
• Answer: 3 goals

[Easy] Perfect Squares

• EN: What is √144?
• FR: Quel est √144?
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: To find √81, think: what number times itself equals 81? Since 9 × 9 = 81, √81 = 9.
• Steps:
  • Think: what number squared equals 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean, Median, Mode

• EN: Find the mode of this data set: 4, 7, 3, 7, 9, 2, 7.
• FR: Trouve le mode de cet ensemble de données : 4, 7, 3, 7, 9, 2, 7.
• Choices: A) 2 B) 4 C) 7 D) 9
• Hint: The mode is the number that appears most often. In 3, 5, 5, 8, 9, the mode is 5.
• Steps:
  • Count how many times each number appears.
  • 7 appears three times — more than any other number.
  • The mode is 7.
• Answer: 7

[Easy] Two-Step Equation

• EN: Solve: 2x + 5 = 13.
• FR: Résous : 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: To solve 3x + 2 = 11, first subtract 2 from both sides (3x = 9), then divide by 3 (x = 3).
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide both sides by 2: x = 4.
  • The solution is x = 4.
• Answer: x = 4

[Easy] Percent Increase

• EN: A town's population was 500 last year. It is now 600. What is the percent increase?
• FR: La population d'une ville était de 500 l'an dernier. Elle est maintenant de 600. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 15% C) 20% D) 25%
• Hint: Percent increase = (new − old) ÷ old × 100. For old = 80, new = 100: (20 ÷ 80) × 100 = 25%.
• Steps:
  • Increase = 600 − 500 = 100.
  • Percent increase = (100 ÷ 500) × 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) 12 cm D) 14 cm
• Hint: Use a² + b² = c². For legs of 3 and 4: 9 + 16 = 25, so c = √25 = 5.
• Steps:
  • Apply the theorem: 6² + 8² = c².
  • 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation (Harder)

• EN: Solve: 5x − 3 = 22.
• FR: Résous : 5x − 3 = 22.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: To solve 4x − 5 = 15, add 5 to both sides (4x = 20), then divide by 4 (x = 5).
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 5.
  • The solution is x = 5.
• Answer: x = 5

[Medium] Slope Introduction

• EN: A line passes through (0, 1) and (3, 7). What is the slope of the line?
• FR: Une droite passe par (0, 1) et (3, 7). Quel est le coefficient angulaire de la droite?
• Choices: A) 1 B) 2 C) 3 D) 4
• Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁). For points (1, 2) and (3, 8): slope = (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3.
• Steps:
  • Slope = (7 − 1) ÷ (3 − 0).
  • = 6 ÷ 3 = 2.
  • The slope is 2.
• Answer: 2

[Medium] Percent Decrease

• EN: A coat was $120 and is now $90. What is the percent decrease?
• FR: Un manteau coûtait 120 $ et coûte maintenant 90 $. Quel est le pourcentage de diminution?
• Choices: A) 20% B) 25% C) 30% D) 33%
• Hint: Percent decrease = (old − new) ÷ old × 100. For $80 down to $60: (20 ÷ 80) × 100 = 25%.
• Steps:
  • Decrease = 120 − 90 = 30.
  • Percent decrease = (30 ÷ 120) × 100 = 25%.
  • The percent decrease is 25%.
• Answer: 25%

[Hard] Pythagorean Theorem — Multi-Step

• EN: A ramp rises 5 m vertically over a horizontal distance of 12 m. What is the length of the ramp?
• FR: Une rampe monte de 5 m verticalement sur une distance horizontale de 12 m. Quelle est la longueur de la rampe?
• Choices: A) 11 m B) 13 m C) 15 m D) 17 m
• Hint: Think of the ramp as the hypotenuse: use a² + b² = c², with legs 5 and 12.
• Steps:
  • a² + b² = c²: 5² + 12² = c².
  • 25 + 144 = 169.
  • c = √169 = 13 m.
• Answer: 13 m

[Hard] Two-Step Equation with Fractions

• EN: Solve: x/3 + 4 = 9.
• FR: Résous : x/3 + 4 = 9.
• Choices: A) x = 10 B) x = 12 C) x = 15 D) x = 18
• Hint: To solve x/4 + 2 = 6, subtract 2 from both sides (x/4 = 4), then multiply by 4 (x = 16).
• Steps:
  • Subtract 4 from both sides: x/3 = 5.
  • Multiply both sides by 3: x = 15.
  • The solution is x = 15.
• Answer: x = 15

[Easy] Linear Equations

• EN: Solve for x: 3x − 6 = 15.
• FR: Résous pour x : 3x − 6 = 15.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: To solve 2x − 4 = 10, add 4 to both sides (2x = 14), then divide by 2 (x = 7).
• Steps:
  • Add 6 to both sides: 3x = 21.
  • Divide by 3: x = 7.
  • The solution is x = 7.
• Answer: x = 7

[Easy] Graphing Lines — Slope-Intercept

• EN: What is the slope of the line y = 4x − 3?
• FR: Quel est le coefficient angulaire de la droite y = 4x − 3?
• Choices: A) −3 B) 1 C) 3 D) 4
• Hint: In y = mx + b, m is the slope and b is the y-intercept. For y = 5x + 2, the slope is 5.
• Steps:
  • Compare y = 4x − 3 to y = mx + b.
  • The coefficient of x is 4.
  • The slope is 4.
• Answer: 4

[Easy] Adding Polynomials

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

[Easy] Trigonometry — SOH

• EN: In a right triangle, the opposite side is 3 cm and the hypotenuse is 5 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 3 cm et l'hypoténuse 5 cm. Quel est sin(θ)?
• Choices: A) 3/4 B) 3/5 C) 4/5 D) 5/3
• Hint: SOH means sin = opposite ÷ hypotenuse. For opposite = 4 and hypotenuse = 10, sin = 4/10 = 2/5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse.
  • sin(θ) = 3 ÷ 5.
  • sin(θ) = 3/5.
• Answer: 3/5

[Medium] Linear Inequalities

• EN: Solve and graph: 2x + 3 < 11. Which value is a solution?
• FR: Résous et représente : 2x + 3 < 11. Quelle valeur est une solution?
• Choices: A) x = 5 B) x = 4 C) x = 3 D) x = 8
• Hint: Solve like an equation: 2x + 3 < 11 → 2x < 8 → x < 4. Any value less than 4 works.
• Steps:
  • Subtract 3: 2x < 8.
  • Divide by 2: x < 4.
  • Among the choices, only x = 3 satisfies x < 4.
• Answer: x = 3

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5).
• FR: Développe : (x + 3)(x + 5).
• Choices: A) x² + 7x + 12 B) x² + 7x + 15 C) x² + 8x + 15 D) x² + 9x + 15
• Hint: Use FOIL: (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • FOIL: x · x = x², x · 5 = 5x, 3 · x = 3x, 3 · 5 = 15.
  • Combine like terms: x² + 8x + 15.
  • Result: x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Two triangles are similar. The first has sides 4 cm and 6 cm. The second has a side corresponding to 4 cm that is now 10 cm. What is the corresponding side to 6 cm?
• FR: Deux triangles sont semblables. Le premier a des côtés de 4 cm et 6 cm. Dans le second, le côté correspondant à 4 cm mesure 10 cm. Quel est le côté correspondant à 6 cm?
• Choices: A) 12 cm B) 13 cm C) 15 cm D) 18 cm
• Hint: In similar triangles, corresponding sides are proportional: if scale factor is 2 and one side is 5 cm, the corresponding side is 10 cm.
• Steps:
  • Find the scale factor: 10 ÷ 4 = 2.5.
  • Multiply the 6 cm side by 2.5: 6 × 2.5 = 15.
  • The corresponding side is 15 cm.
• Answer: 15 cm

[Medium] Trigonometry — CAH

• EN: In a right triangle, the adjacent side is 8 cm and the hypotenuse is 10 cm. What is cos(θ)?
• FR: Dans un triangle rectangle, le côté adjacent mesure 8 cm et l'hypoténuse 10 cm. Quel est cos(θ)?
• Choices: A) 4/5 B) 3/5 C) 5/4 D) 8/6
• Hint: CAH means cos = adjacent ÷ hypotenuse. For adjacent = 6 and hypotenuse = 10, cos = 6/10 = 3/5.
• Steps:
  • cos(θ) = adjacent ÷ hypotenuse.
  • cos(θ) = 8 ÷ 10.
  • cos(θ) = 4/5.
• Answer: 4/5

[Hard] Systems of Linear Equations

• EN: Solve the system: y = 2x + 1 and y = −x + 7. What is x?
• FR: Résous le système : y = 2x + 1 et y = −x + 7. Quelle est la valeur de x?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the two expressions equal and solve: if y = 3x − 2 and y = x + 4, then 3x − 2 = x + 4, giving 2x = 6, x = 3.
• Steps:
  • Set equal: 2x + 1 = −x + 7.
  • Add x to both sides: 3x + 1 = 7.
  • Subtract 1 and divide: 3x = 6, x = 2.
• Answer: x = 2

[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 opposite side? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle θ = 30° et l'hypoténuse est 20 cm. Quelle est la longueur du côté opposé? (sin 30° = 0,5)
• Choices: A) 8 cm B) 10 cm C) 12 cm D) 15 cm
• Hint: Use sin(θ) = opposite ÷ hypotenuse, so opposite = sin(θ) × hypotenuse. For sin 45° ≈ 0.707 and hypotenuse = 10, opposite ≈ 7.07.
• Steps:
  • opposite = sin(30°) × hypotenuse.
  • opposite = 0.5 × 20.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Easy] Factoring Quadratics

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

[Easy] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 5 cm and the hypotenuse is 10 cm. What is sin(θ) as a fraction?
• FR: Dans un triangle rectangle, le côté opposé mesure 5 cm et l'hypoténuse 10 cm. Quel est sin(θ) sous forme de fraction?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: sin(θ) = opposite ÷ hypotenuse. For opposite = 3 and hypotenuse = 9, sin = 3/9 = 1/3.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 5 ÷ 10.
  • Simplify: 5/10 = 1/2.
  • sin(θ) = 1/2.
• Answer: 1/2

[Easy] Systems of Equations — Substitution

• EN: Solve: y = x + 2 and y = 3x − 4. What is x?
• FR: Résous : y = x + 2 et y = 3x − 4. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Set the expressions equal: x + 2 = 3x − 4 → 6 = 2x → x = 3.
• Steps:
  • Set equal: x + 2 = 3x − 4.
  • Subtract x: 2 = 2x − 4.
  • Add 4: 6 = 2x, so x = 3.
• Answer: x = 3

[Easy] Surface Area of a Cylinder

• EN: A cylinder has a radius of 3 cm and a height of 10 cm. Which formula gives the correct surface area? (Use π ≈ 3.14)
• FR: Un cylindre a un rayon de 3 cm et une hauteur de 10 cm. Quelle formule donne l'aire totale correcte? (Utilise π ≈ 3,14)
• Choices: A) 2π(3)(10) only B) 2π(3²) + 2π(3)(10) C) π(3²)(10) D) 2π(3²) only
• Hint: Total surface area of a cylinder = 2πr² (two circles) + 2πrh (curved side). Both parts are needed.
• Steps:
  • The surface area includes the two circular ends and the curved surface.
  • Formula: 2πr² + 2πrh.
  • This matches choice B: 2π(3²) + 2π(3)(10).
• Answer: 2π(3²) + 2π(3)(10)

[Medium] Completing the Square

• EN: Complete the square to rewrite x² + 6x + 5 in vertex form.
• FR: Complète le carré pour réécrire x² + 6x + 5 sous la forme au sommet.
• Choices: A) (x + 2)² − 3 B) (x + 3)² − 4 C) (x + 3)² + 4 D) (x + 6)² − 5
• Hint: To complete the square for x² + 4x + 1, take half of 4 (that is 2), square it (4), rewrite as (x + 2)² − 4 + 1 = (x + 2)² − 3.
• Steps:
  • Take half of 6: that is 3. Square it: 9.
  • Rewrite: x² + 6x + 9 − 9 + 5 = (x + 3)² − 4.
  • Vertex form: (x + 3)² − 4.
• Answer: (x + 3)² − 4

[Medium] Circle Geometry

• EN: A chord of a circle is 16 cm long. The perpendicular distance from the centre to the chord is 6 cm. What is the radius of the circle?
• FR: Une corde d'un cercle mesure 16 cm. La distance 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: A perpendicular from the centre bisects the chord, forming a right triangle. Use a² + b² = c² with half the chord length and the distance.
• Steps:
  • Half the chord = 8 cm. Distance = 6 cm.
  • r² = 8² + 6² = 64 + 36 = 100.
  • r = √100 = 10 cm.
• Answer: 10 cm

[Medium] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = 2 and x = 4 D) x = 3 and x = 5
• Hint: The quadratic formula is x = (−b ± √(b²−4ac)) / 2a. You can also factor if the equation factors nicely.
• Steps:
  • Factor: x² − 5x + 6 = (x − 2)(x − 3).
  • Set each factor to zero: x − 2 = 0 → x = 2; x − 3 = 0 → x = 3.
  • Solutions: x = 2 and x = 3.
• Answer: x = 2 and x = 3

[Medium] Volume of a Cone

• EN: A cone has a radius of 6 cm and a height of 9 cm. What is its volume? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 6 cm et une hauteur de 9 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 226.08 cm³ B) 339.12 cm³ C) 452.16 cm³ D) 508.68 cm³
• Hint: Volume of a cone = (1/3)πr²h. For r = 3 and h = 4: V = (1/3)(3.14)(9)(4) ≈ 37.68 cm³.
• Steps:
  • V = (1/3)πr²h = (1/3)(3.14)(36)(9).
  • (1/3)(3.14)(324) = (1/3)(1017.36).
  • V ≈ 339.12 cm³.
• Answer: 339.12 cm³

[Hard] Quadratic Equation — Real-World

• EN: A ball is launched upward. Its height in metres is h = −5t² + 20t + 1, where t is seconds. At what time does the ball reach a height of 21 m? (first time)
• FR: Un ballon est lancé vers le haut. Sa hauteur en mètres est h = −5t² + 20t + 1, où t est en secondes. À quel moment le ballon atteint-il 21 m? (première fois)
• Choices: A) t = 1 second B) t = 2 seconds C) t = 3 seconds D) t = 4 seconds
• Hint: Substitute h = 21 and solve −5t² + 20t + 1 = 21, which simplifies to −5t² + 20t − 20 = 0, then divide and factor.
• Steps:
  • Set −5t² + 20t + 1 = 21: −5t² + 20t − 20 = 0.
  • Divide by −5: t² − 4t + 4 = 0 → (t − 2)² = 0.
  • t = 2 seconds (first and only time the ball reaches exactly 21 m).
• Answer: t = 2 seconds

[Hard] Systems of Equations — Non-Linear

• EN: Find the positive x-value where y = x² and y = x + 6 intersect.
• FR: Trouve la valeur positive de x où y = x² et y = x + 6 se croisent.
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set the two expressions equal: x² = x + 6, rearrange to x² − x − 6 = 0, then factor.
• Steps:
  • Set equal: x² = x + 6 → x² − x − 6 = 0.
  • Factor: (x − 3)(x + 2) = 0.
  • Positive solution: x = 3.
• Answer: x = 3

[Easy] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = (x − 4)² + 3?
• FR: Quel est le sommet de la parabole y = (x − 4)² + 3?
• Choices: A) (−4, 3) B) (3, 4) C) (4, 3) D) (4, −3)
• Hint: In vertex form y = (x − h)² + k, the vertex is at the point (h, k).
• Steps:
  • Compare to y = (x − h)² + k.
  • h = 4 and k = 3.
  • The vertex is (4, 3).
• Answer: (4, 3)

[Easy] Exponential Function

• EN: A savings account doubles every 5 years. If you start with $200, how much do you have after 10 years?
• FR: Un compte d'épargne double tous les 5 ans. Si tu commences avec 200 $, combien auras-tu après 10 ans?
• Choices: A) $400 B) $600 C) $800 D) $1000
• Hint: If money doubles every period and starts at $100, after 2 periods it is $100 × 2² = $400.
• Steps:
  • After 5 years: $200 × 2 = $400.
  • After 10 years: $400 × 2 = $800.
  • The balance is $800.
• Answer: $800

[Easy] Logarithm Introduction

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

[Easy] Arithmetic Sequence

• EN: Find the 8th term of the arithmetic sequence: 3, 7, 11, 15, …
• FR: Trouve le 8ᵉ terme de la suite arithmétique : 3, 7, 11, 15, …
• Choices: A) 28 B) 29 C) 30 D) 31
• Hint: The nth term of an arithmetic sequence is a + (n − 1)d. For a = 2, d = 4, n = 5: term = 2 + (4)(4) = 18.
• Steps:
  • First term a = 3, common difference d = 4.
  • 8th term = 3 + (8 − 1) × 4 = 3 + 28 = 31.
  • The 8th term is 31.
• Answer: 31

[Medium] Compound Interest

• EN: Priya invests $1 000 at 6% annual interest, compounded annually. What is the balance after 2 years?
• FR: Priya investit 1 000 $ à 6 % d'intérêt annuel, composé annuellement. Quel est le solde après 2 ans?
• Choices: A) $1 110.00 B) $1 120.00 C) $1 123.60 D) $1 130.00
• Hint: Use A = P(1 + r)ⁿ. For $500 at 4% for 2 years: A = 500(1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000(1 + 0.06)².
  • (1.06)² = 1.1236.
  • A = $1 000 × 1.1236 = $1 123.60.
• Answer: $1 123.60

[Medium] Trigonometric Identity

• EN: Simplify: sin²(θ) + cos²(θ).
• FR: Simplifie : sin²(θ) + cos²(θ).
• Choices: A) 0 B) 1 C) 2 D) sin(2θ)
• Hint: This is a fundamental Pythagorean identity in trigonometry — it always equals a specific constant.
• Steps:
  • This is the Pythagorean identity.
  • sin²(θ) + cos²(θ) = 1 for all values of θ.
  • The answer is 1.
• Answer: 1

[Medium] Geometric Sequence

• EN: Find the sum of the first 4 terms of the geometric sequence 2, 6, 18, 54, …
• FR: Trouve la somme des 4 premiers termes de la suite géométrique 2, 6, 18, 54, …
• Choices: A) 70 B) 78 C) 80 D) 86
• Hint: To find the sum of 1, 3, 9, 27 (4 terms), simply add: 1 + 3 + 9 + 27 = 40.
• Steps:
  • Add the four terms: 2 + 6 + 18 + 54.
  • 2 + 6 = 8, 8 + 18 = 26, 26 + 54 = 80.
  • The sum is 80.
• Answer: 80

[Medium] Financial Math — Annuity

• EN: Chloe deposits $100 at the end of each month into an account. After 3 months with no interest, how much is in the account?
• FR: Chloé dépose 100 $ à la fin de chaque mois dans un compte. Après 3 mois sans intérêts, combien y a-t-il dans le compte?
• Choices: A) $200 B) $250 C) $300 D) $350
• Hint: For a simple annuity with no interest, the total is just the payment multiplied by the number of periods.
• Steps:
  • Deposit $100 per month for 3 months.
  • Total = $100 × 3 = $300.
  • The account holds $300.
• Answer: $300

[Hard] Logarithm — Solving an Equation

• EN: Solve for x: 2^x = 32.
• FR: Résous pour x : 2^x = 32.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Express both sides with the same base: 2^x = 2^n means x = n. For 3^x = 27, since 27 = 3³, x = 3.
• Steps:
  • Write 32 as a power of 2: 32 = 2⁵.
  • So 2^x = 2⁵.
  • Therefore x = 5.
• Answer: x = 5

[Hard] Compound Interest — Comparing Investments

• EN: An investment of $2 000 earns 5% compounded annually. After 3 years, how much interest has been earned?
• FR: Un investissement de 2 000 $ rapporte 5 % composé annuellement. Après 3 ans, combien d'intérêts ont été gagnés?
• Choices: A) $300.00 B) $305.00 C) $315.25 D) $330.50
• Hint: Use A = P(1 + r)ⁿ and subtract the principal: interest = A − P. For $1000 at 4% for 2 years, A = $1000(1.04)² = $1081.60, interest = $81.60.
• Steps:
  • A = 2000(1.05)³ = 2000 × 1.157625 = $2 315.25.
  • Interest earned = $2 315.25 − $2 000 = $315.25.
  • The interest earned is $315.25.
• Answer: $315.25

[Easy] Permutations

• EN: How many ways can 5 students line up in a row?
• FR: De combien de façons 5 élèves peuvent-ils se placer en file?
• Choices: A) 60 B) 100 C) 120 D) 150
• Hint: The number of ways to arrange n objects in a row is n!. For 4 students: 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • The number of arrangements = 5!
  • 5! = 5 × 4 × 3 × 2 × 1 = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: How many ways can you choose 2 books from a shelf of 6 books?
• FR: De combien de façons peut-on choisir 2 livres sur une étagère de 6 livres?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: Use C(n, r) = n! ÷ (r!(n−r)!). For C(5, 2) = 5! ÷ (2! × 3!) = 120 ÷ 12 = 10.
• Steps:
  • C(6, 2) = 6! ÷ (2! × 4!) = (6 × 5) ÷ (2 × 1) = 30 ÷ 2 = 15.
  • There are 15 ways.
  • The answer is 15.
• Answer: 15

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = x³.
• FR: Trouve la dérivée de f(x) = x³.
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: The power rule says if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹. For f(x) = x⁴, f'(x) = 4x³.
• Steps:
  • Apply the power rule: bring the exponent down and reduce it by 1.
  • f'(x) = 3 · x^(3−1) = 3x².
  • The derivative is 3x².
• Answer: 3x²

[Easy] Polynomial Function

• EN: What are the zeros of f(x) = (x − 2)(x + 5)?
• FR: Quels sont les zéros de f(x) = (x − 2)(x + 5)?
• Choices: A) x = 2 and x = 5 B) x = −2 and x = 5 C) x = 2 and x = −5 D) x = −2 and x = −5
• Hint: Set each factor equal to zero. For (x − 3)(x + 4) = 0: x − 3 = 0 gives x = 3; x + 4 = 0 gives x = −4.
• Steps:
  • Set each factor to zero: x − 2 = 0 gives x = 2.
  • x + 5 = 0 gives x = −5.
  • The zeros are x = 2 and x = −5.
• Answer: x = 2 and x = −5

[Medium] Rate of Change — Derivative

• EN: The position of a car is given by s(t) = 3t² + 2t. What is the instantaneous velocity at t = 4 seconds?
• FR: La position d'une voiture est donnée par s(t) = 3t² + 2t. Quelle est la vitesse instantanée à t = 4 secondes?
• Choices: A) 24 m/s B) 26 m/s C) 28 m/s D) 30 m/s
• Hint: Find the derivative s'(t) using the power rule, then substitute the given t-value. For s(t) = 2t² + 3t, s'(t) = 4t + 3.
• Steps:
  • Differentiate: s'(t) = 6t + 2.
  • Substitute t = 4: s'(4) = 6(4) + 2 = 24 + 2 = 26.
  • The instantaneous velocity is 26 m/s.
• Answer: 26 m/s

[Medium] Probability Distribution

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

[Medium] Vectors — Addition

• EN: Vector a = (3, 5) and vector b = (−1, 4). What is a + b?
• FR: Le vecteur a = (3, 5) et le vecteur b = (−1, 4). Quel est a + b?
• Choices: A) (1, 8) B) (2, 9) C) (3, 9) D) (4, 9)
• Hint: To add vectors, add the corresponding components: (2, 3) + (4, 1) = (2 + 4, 3 + 1) = (6, 4).
• Steps:
  • Add x-components: 3 + (−1) = 2.
  • Add y-components: 5 + 4 = 9.
  • a + b = (2, 9).
• Answer: (2, 9)

[Medium] Rational Function

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

[Hard] Derivative — Tangent Line

• EN: Find the equation of the tangent line to f(x) = x² + 3x at x = 2.
• FR: Trouve l'équation de la droite tangente à f(x) = x² + 3x en x = 2.
• Choices: A) y = 5x − 4 B) y = 7x − 4 C) y = 7x − 8 D) y = 9x − 4
• Hint: Find f'(x) for the slope, evaluate at x = a, find f(a) for the point, then use y − y₁ = m(x − x₁). For f(x) = x² at x = 3: f'(x) = 2x, slope = 6, point (3, 9), tangent: y − 9 = 6(x − 3) → y = 6x − 9.
• Steps:
  • f'(x) = 2x + 3. At x = 2: slope = 2(2) + 3 = 7.
  • f(2) = 4 + 6 = 10. Point: (2, 10).
  • y − 10 = 7(x − 2) → y = 7x − 14 + 10 = 7x − 4. Wait — recheck: y = 7(2) − 4 = 10. ✓
• Answer: y = 7x − 4

[Hard] Combinations and Probability

• EN: A committee of 3 is chosen from 5 boys and 4 girls. What is the probability that the committee has exactly 2 girls?
• FR: Un comité de 3 personnes est choisi parmi 5 garçons et 4 filles. Quelle est la probabilité que le comité ait exactement 2 filles?
• Choices: A) 5/14 B) 6/14 C) 10/21 D) 12/21
• Hint: P = (ways to choose 2 girls × ways to choose 1 boy) ÷ total ways to choose 3 from 9. Use combinations for each part.
• Steps:
  • Choose 2 girls from 4: C(4, 2) = 6. Choose 1 boy from 5: C(5, 1) = 5. Favourable = 30.
  • Total committees from 9: C(9, 3) = 84.
  • P = 30/84 = 5/14.
• Answer: 5/14