Daily Math — 2026-07-12

[Easy] Counting Carrots

• EN: Mia has 7 carrots. She picks 5 more. How many carrots does she have now?
• FR: Mia a 7 carottes. Elle en cueille 5 de plus. Combien de carottes a-t-elle maintenant?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: To add, count on from the bigger number — 9 + 3, start at 9 and count up 3.
• Steps:
  • Start at 7.
  • Count on 5 more: 8, 9, 10, 11, 12.
  • So Mia has 12 carrots.
• Answer: 12

[Easy] Hockey Pucks

• EN: There are 9 hockey pucks on the ice. 3 are taken away. How many are left?
• FR: Il y a 9 rondelles de hockey sur la glace. On en enlève 3. Combien en reste-t-il?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To subtract, count backwards — 8 take away 2 means count back 2 from 8.
• Steps:
  • Start at 9.
  • Count back 3: 8, 7, 6.
  • So 6 pucks are left.
• Answer: 6

[Easy] Skip Counting by 2s

• EN: Skip count by 2s. What number comes after 12, 14, 16?
• FR: Compte par bonds de 2. Quel nombre vient après 12, 14, 16?
• Choices: A) 17 B) 18 C) 19 D) 20
• Hint: Skip counting by 2s means add 2 each time — 4, 6, 8, the next is 10.
• Steps:
  • The pattern adds 2 each time.
  • 16 + 2 = 18.
  • So the next number is 18.
• Answer: 18

[Easy] Recognizing Coins

• EN: Which coin is worth 10 cents in Canada?
• FR: Quelle pièce vaut 10 cents au Canada?
• Choices: A) Penny B) Nickel C) Dime D) Loonie
• Hint: Think about how many cents each Canadian coin is worth — a nickel is worth 5 cents.
• Steps:
  • A penny = 1 cent.
  • A nickel = 5 cents.
  • A dime = 10 cents.
  • So the answer is a Dime.
• Answer: Dime

[Medium] Snowballs in a Row

• EN: Luc made 15 snowballs. He threw 8 of them. How many does he have left?
• FR: Luc a fait 15 boules de neige. Il en a lancé 8. Combien lui en reste-t-il?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: To subtract, count back from the bigger number — 14 take away 6, count back 6 from 14.
• Steps:
  • Start at 15.
  • Count back 8: 14, 13, 12, 11, 10, 9, 8, 7.
  • So Luc has 7 snowballs left.
• Answer: 7

[Medium] Comparing Numbers

• EN: Which number is greater: 47 or 74?
• FR: Quel nombre est plus grand : 47 ou 74?
• Choices: A) 47 B) 74 C) They are equal D) 57
• Hint: Compare the tens digit first — the number with the bigger tens digit is greater.
• Steps:
  • 47 has 4 tens; 74 has 7 tens.
  • 7 tens is more than 4 tens.
  • So 74 is greater.
• Answer: 74

[Medium] Skip Counting by 5s

• EN: Count by 5s. What is the missing number: 5, 10, 15, ___, 25?
• FR: Compte par bonds de 5. Quel est le nombre manquant : 5, 10, 15, ___, 25?
• Choices: A) 18 B) 19 C) 20 D) 21
• Hint: Skip counting by 5s means each number is 5 more than the one before.
• Steps:
  • 5, 10, 15 — each step adds 5.
  • 15 + 5 = 20.
  • So the missing number is 20.
• Answer: 20

[Medium] Counting to 100

• EN: What number is 10 more than 83?
• FR: Quel nombre est 10 de plus que 83?
• Choices: A) 73 B) 84 C) 92 D) 93
• Hint: Adding 10 to a number changes the tens digit by 1 — 10 more than 62 is 72.
• Steps:
  • 83 has 8 tens and 3 ones.
  • Adding 10 gives 9 tens and 3 ones.
  • So 10 more than 83 is 93.
• Answer: 93

[Hard] Coin Counting

• EN: Aisha has 1 dime, 1 nickel, and 2 pennies. How many cents does she have in total?
• FR: Aisha a 1 pièce de 10 cents, 1 pièce de 5 cents et 2 pennies. Combien de cents a-t-elle en tout?
• Choices: A) 15 cents B) 16 cents C) 17 cents D) 18 cents
• Hint: Add up each coin's value — a dime is 10, a nickel is 5, a penny is 1.
• Steps:
  • Dime = 10 cents.
  • Nickel = 5 cents; 10 + 5 = 15 cents.
  • 2 pennies = 2 cents; 15 + 2 = 17 cents.
  • So Aisha has 17 cents.
• Answer: 17 cents

[Hard] Two-Step Addition

• EN: There are 6 red mittens, 5 blue mittens, and 4 green mittens in a basket. How many mittens are there in all?
• FR: Il y a 6 mitaines rouges, 5 bleues et 4 vertes dans un panier. Combien y a-t-il de mitaines en tout?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Add the first two numbers, then add the third — 3 + 4 + 5, first do 3 + 4 = 7, then 7 + 5 = 12.
• Steps:
  • 6 + 5 = 11.
  • 11 + 4 = 15.
  • So there are 15 mittens in all.
• Answer: 15

[Easy] Adding to 100

• EN: What is 34 + 25?
• FR: Combien font 34 + 25?
• Choices: A) 57 B) 58 C) 59 D) 60
• Hint: Add the ones first, then the tens — 32 + 15: ones are 2 + 5 = 7, tens are 3 + 1 = 4, so 47.
• Steps:
  • Ones: 4 + 5 = 9.
  • Tens: 3 + 2 = 5.
  • So 34 + 25 = 59.
• Answer: 59

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'aiguille des heures est sur le 3 et l'aiguille des minutes est sur le 12. Quelle heure est-il?
• Choices: A) 12:03 B) 3:00 C) 3:30 D) 12:15
• Hint: When the minute hand points to 12, it is exactly on the hour — like 5:00 or 7:00.
• Steps:
  • The hour hand is on 3, so the hour is 3.
  • The minute hand is on 12, so it is exactly on the hour.
  • So the time is 3:00.
• Answer: 3:00

[Easy] Measuring Length

• EN: A pencil is 15 cm long and an eraser is 4 cm long. How much longer is the pencil?
• FR: Un crayon mesure 15 cm et une gomme mesure 4 cm. 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, subtract — 18 cm take away 6 cm is 12 cm longer.
• Steps:
  • 15 − 4 = 11.
  • So the pencil is 11 cm longer.
• Answer: 11 cm

[Easy] Simple Patterns

• EN: What comes next in this pattern: 2, 4, 6, 8, ___?
• FR: Quel nombre vient ensuite dans ce patron : 2, 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: Look at how much is added each time — 3, 6, 9, 12, the next would be 15.
• Steps:
  • Each number increases by 2.
  • 8 + 2 = 10.
  • So the next number is 10.
• Answer: 10

[Medium] Subtracting Within 100

• EN: Omar scored 72 points in a game. He lost 38 points. How many points does he have now?
• FR: Omar a marqué 72 points dans un jeu. Il en a perdu 38. Combien de points a-t-il maintenant?
• Choices: A) 32 B) 33 C) 34 D) 36
• Hint: Subtract the ones first, then the tens — if you can't subtract the ones, regroup from the tens.
• Steps:
  • Ones: 2 − 8, need to regroup; borrow 1 ten, now 12 − 8 = 4.
  • Tens: 6 − 3 = 3 (since we used one ten).
  • So 72 − 38 = 34.
• Answer: 34

[Medium] Counting Coins to $1

• EN: Priya has 3 quarters. How many cents does she have?
• FR: Priya a 3 pièces de 25 cents. Combien de cents a-t-elle?
• Choices: A) 55 cents B) 65 cents C) 75 cents D) 85 cents
• Hint: A quarter is worth 25 cents — count by 25s to find the total.
• Steps:
  • 1 quarter = 25 cents.
  • 25 + 25 = 50 cents.
  • 50 + 25 = 75 cents.
  • So Priya has 75 cents.
• Answer: 75 cents

[Medium] Telling Time (Half Hour)

• EN: The hour hand is between 7 and 8, and the minute hand is on 6. What time is it?
• FR: L'aiguille des heures est entre 7 et 8, et l'aiguille des minutes est sur le 6. Quelle heure est-il?
• Choices: A) 6:30 B) 7:00 C) 7:30 D) 8:30
• Hint: When the minute hand points to 6, it is half past the hour — like 4:30.
• Steps:
  • Minute hand on 6 means 30 minutes past.
  • The hour hand is just past 7, so the hour is 7.
  • So the time is 7:30.
• Answer: 7:30

[Medium] Addition with Carrying

• EN: A Tim Hortons box has 48 Timbits and another box has 37 Timbits. How many Timbits are there in all?
• FR: Une boîte de Tim Hortons contient 48 Timbits et une autre en contient 37. Combien y a-t-il de Timbits en tout?
• Choices: A) 74 B) 75 C) 85 D) 86
• Hint: Add ones first — if the total is 10 or more, carry the ten to the tens column.
• Steps:
  • Ones: 8 + 7 = 15; write 5, carry 1.
  • Tens: 4 + 3 + 1 (carried) = 8.
  • So 48 + 37 = 85.
• Answer: 85

[Hard] Measuring and Adding

• EN: A garden path is 45 m long. Workers add another 38 m of path. What is the total length of the path?
• FR: Un sentier de jardin mesure 45 m de long. Des ouvriers en ajoutent 38 m. Quelle est la longueur totale du sentier?
• Choices: A) 72 m B) 73 m C) 83 m D) 84 m
• Hint: Add ones first, carry if needed, then add the tens including any carried value.
• Steps:
  • Ones: 5 + 8 = 13; write 3, carry 1.
  • Tens: 4 + 3 + 1 = 8.
  • So the total length is 83 m.
• Answer: 83 m

[Hard] Two-Step Word Problem

• EN: Jade has 60 stickers. She gives 15 to her friend and then buys 22 more. How many stickers does Jade have now?
• FR: Jade a 60 autocollants. Elle en donne 15 à son amie, puis en achète 22 de plus. Combien d'autocollants Jade a-t-elle maintenant?
• Choices: A) 65 B) 67 C) 68 D) 69
• Hint: Do one step at a time — first subtract, then add the new amount to what remains.
• Steps:
  • Step 1: 60 − 15 = 45.
  • Step 2: 45 + 22 = 67.
  • So Jade has 67 stickers.
• Answer: 67

[Easy] Multiplication Table of 5

• EN: What is 5 × 6?
• FR: Combien font 5 × 6?
• Choices: A) 25 B) 30 C) 35 D) 40
• Hint: Multiply by 5 by skip counting — 5, 10, 15, 20, 25, 30 (that's 6 fives).
• Steps:
  • Count by 5s six times: 5, 10, 15, 20, 25, 30.
  • So 5 × 6 = 30.
• Answer: 30

[Easy] Basic Division

• EN: 20 apples are shared equally among 4 children. How many apples does each child get?
• FR: 20 pommes sont partagées également entre 4 enfants. Combien de pommes chaque enfant reçoit-il?
• Choices: A) 4 B) 5 C) 6 D) 8
• Hint: Division is sharing equally — if 12 items are shared among 3, each gets 4.
• Steps:
  • 20 ÷ 4 = ?
  • Ask: 4 × ? = 20; 4 × 5 = 20.
  • So each child gets 5 apples.
• Answer: 5

[Easy] Fractions

• EN: A pizza is cut into 4 equal slices. Tomás eats 1 slice. What fraction of the pizza did he eat?
• FR: Une pizza est coupée en 4 parts égales. Tomás mange 1 part. Quelle fraction de la pizza a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: A fraction shows parts out of a whole — 1 piece out of 4 equal pieces is written as 1/4.
• Steps:
  • Total slices = 4 (the denominator).
  • Slices eaten = 1 (the numerator).
  • So Tomás ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Multiplication Table of 2

• EN: There are 7 pairs of hockey skates. How many skates are there in total?
• FR: Il y a 7 paires de patins de hockey. Combien y a-t-il de patins en tout?
• Choices: A) 12 B) 13 C) 14 D) 16
• Hint: Each pair has 2 skates, so multiply the number of pairs by 2.
• Steps:
  • 7 × 2 = 14.
  • So there are 14 skates in total.
• Answer: 14

[Medium] Perimeter

• EN: A rectangle is 8 cm long and 3 cm wide. What is its perimeter?
• FR: Un rectangle mesure 8 cm de long et 3 cm de large. Quel est son périmètre?
• Choices: A) 11 cm B) 22 cm C) 24 cm D) 26 cm
• Hint: Perimeter is the distance around a shape — add all four sides, or use 2 × (length + width).
• Steps:
  • Perimeter = 2 × (length + width).
  • = 2 × (8 + 3) = 2 × 11 = 22.
  • So the perimeter is 22 cm.
• Answer: 22 cm

[Medium] Reading a Graph

• EN: A bar graph shows that 6 students like hockey, 9 like soccer, and 3 like swimming. How many students were surveyed in total?
• FR: Un diagramme à barres montre que 6 élèves aiment le hockey, 9 aiment le soccer et 3 aiment la natation. Combien d'élèves ont été sondés en tout?
• Choices: A) 15 B) 16 C) 18 D) 19
• Hint: To find the total from a graph, add all the values together.
• Steps:
  • 6 + 9 = 15.
  • 15 + 3 = 18.
  • So 18 students were surveyed.
• Answer: 18

[Medium] Multiplication Table of 4

• EN: A school buys 4 boxes of crayons. Each box has 8 crayons. How many crayons are there in all?
• FR: Une école achète 4 boîtes de crayons. Chaque boîte contient 8 crayons. Combien y a-t-il de crayons en tout?
• Choices: A) 28 B) 30 C) 32 D) 36
• Hint: Multiply the number of groups by the number in each group — 3 boxes × 7 crayons = 21.
• Steps:
  • 4 × 8 = 32.
  • So there are 32 crayons in all.
• Answer: 32

[Medium] Division with a Context

• EN: 27 students are put into 3 equal groups for a relay race. How many students are in each group?
• FR: 27 élèves sont divisés en 3 groupes égaux pour une course de relais. Combien d'élèves y a-t-il dans chaque groupe?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: To divide equally, ask yourself what times the number of groups equals the total.
• Steps:
  • 27 ÷ 3 = ?
  • 3 × 9 = 27.
  • So there are 9 students in each group.
• Answer: 9

[Hard] Fractions and Comparing

• EN: Which fraction is larger: 1/2 or 1/3?
• FR: Quelle fraction est plus grande : 1/2 ou 1/3?
• Choices: A) 1/3 B) 1/2 C) They are equal D) 2/3
• Hint: Think of a pizza — if you split it into fewer pieces, each piece is bigger.
• Steps:
  • 1/2 means 1 out of 2 equal parts.
  • 1/3 means 1 out of 3 equal parts.
  • Fewer parts means bigger pieces, so 1/2 is larger.
• Answer: 1/2

[Hard] Multi-Step Multiplication

• EN: A farmer plants 5 rows of corn with 9 plants in each row, and 3 rows of beans with 8 plants in each row. How many plants does the farmer have in total?
• FR: Un fermier plante 5 rangées de maïs avec 9 plants dans chaque rangée et 3 rangées de haricots avec 8 plants dans chaque rangée. Combien de plants le fermier a-t-il en tout?
• Choices: A) 65 B) 68 C) 69 D) 72
• Hint: Multiply each crop separately first, then add the two results together.
• Steps:
  • Corn: 5 × 9 = 45.
  • Beans: 3 × 8 = 24.
  • Total: 45 + 24 = 69.
• Answer: 69

[Easy] Multiplication to 9×9

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 64
• Hint: Remember your 7s table — 7 × 6 = 42, 7 × 7 = 49, 7 × 8 = ?
• Steps:
  • 7 × 8 means 7 groups of 8.
  • 7 × 8 = 56.
  • So 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) 40 ones
• Hint: In a decimal number, the first digit after the decimal point is the tenths place.
• Steps:
  • 3.47: 3 is in the ones place, 4 is in the tenths place, 7 is in the hundredths place.
  • So the digit 4 is worth 4 tenths.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A bedroom floor is 6 m long and 4 m wide. What is its area?
• FR: Le plancher d'une chambre mesure 6 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 10 m² B) 20 m² C) 24 m² D) 26 m²
• Hint: Area of a rectangle = length × width.
• Steps:
  • Area = 6 × 4.
  • 6 × 4 = 24.
  • So the area 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) 2/4 B) 3/4 C) They are equal D) 1/4
• Hint: When the denominators are the same, the fraction with the bigger numerator is greater.
• Steps:
  • Both fractions have the same denominator (4).
  • Compare numerators: 3 > 2.
  • So 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: 53 students need to be put into groups of 6. How many complete groups can be made, and how many students are left over?
• FR: 53 élèves doivent être mis en groupes de 6. Combien de groupes complets peut-on former, et combien d'élèves restent-il?
• Choices: A) 7 remainder 11 B) 8 remainder 5 C) 9 remainder 1 D) 8 remainder 7
• Hint: Divide to find how many times the divisor fits, then multiply back and subtract to find the remainder.
• Steps:
  • 6 × 8 = 48; 6 × 9 = 54 (too big), so 8 groups.
  • 53 − 48 = 5 left over.
  • So there are 8 complete groups with 5 students left over.
• Answer: 8 remainder 5

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 p.m. and ends at 3:45 p.m. How long does the game last?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps dure le match?
• Choices: A) 1 hour 30 minutes B) 2 hours C) 2 hours 30 minutes D) 2 hours 45 minutes
• Hint: Count up from the start time to the end time in steps — first count the hours, then the minutes.
• Steps:
  • From 1:15 to 3:15 is 2 hours.
  • From 3:15 to 3:45 is 30 more minutes.
  • So the game lasts 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A juice bottle holds 1.75 L. A water bottle holds 2.50 L. How much liquid is there in total?
• FR: Une bouteille de jus contient 1,75 L. Une bouteille d'eau contient 2,50 L. Quelle est la quantité totale de liquide?
• Choices: A) 3.25 L B) 4.15 L C) 4.25 L D) 4.50 L
• Hint: Line up the decimal points when adding — add hundredths, then tenths, then ones.
• Steps:
  • 1.75 + 2.50: ones: 1 + 2 = 3.
  • Tenths: 7 + 5 = 12; write 2, carry 1 to ones: 3 + 1 = 4.
  • Hundredths: 5 + 0 = 5.
  • So the total is 4.25 L.
• Answer: 4.25 L

[Medium] Multiplication with Larger Numbers

• EN: A bakery makes 9 trays of muffins. Each tray has 24 muffins. How many muffins are made in all?
• FR: Une boulangerie fait 9 plateaux de muffins. Chaque plateau contient 24 muffins. Combien de muffins sont faits en tout?
• Choices: A) 196 B) 206 C) 216 D) 226
• Hint: Multiply the ones first, then the tens, and add the partial products together.
• Steps:
  • 9 × 4 = 36; write 6, carry 3.
  • 9 × 2 = 18; 18 + 3 = 21.
  • So 9 × 24 = 216.
• Answer: 216

[Hard] Multi-Step Area Problem

• EN: A rectangular park is 15 m long and 12 m wide. A square sandbox inside the park has sides of 4 m. What is the area of the park that is NOT the sandbox?
• FR: Un parc rectangulaire mesure 15 m de long et 12 m de large. Un carré de sable à l'intérieur du parc a des côtés de 4 m. Quelle est l'aire du parc qui n'est PAS la zone de sable?
• Choices: A) 164 m² B) 165 m² C) 164 m² D) 180 m²
• Hint: Find the area of the whole shape, then subtract the area of the smaller shape inside.
• Steps:
  • Area of park: 15 × 12 = 180 m².
  • Area of sandbox: 4 × 4 = 16 m².
  • Remaining area: 180 − 16 = 164 m².
• Answer: 164 m²

[Hard] Long Division and Reasoning

• EN: A school orders 148 books to be shared equally among 4 classrooms. How many books does each classroom get?
• FR: Une école commande 148 livres à partager également entre 4 classes. Combien de livres chaque classe reçoit-elle?
• Choices: A) 35 B) 36 C) 37 D) 38
• Hint: Use long division — divide the hundreds digit first, then bring down each remaining digit.
• Steps:
  • 4 goes into 14 three times (3 × 4 = 12); remainder 2.
  • Bring down 8: 28 ÷ 4 = 7.
  • So 148 ÷ 4 = 37.
• Answer: 37

[Easy] Multi-Digit Multiplication

• EN: What is 36 × 7?
• FR: Combien font 36 × 7?
• Choices: A) 242 B) 252 C) 258 D) 263
• Hint: Multiply the ones digit first, then the tens digit, remembering to carry if needed.
• Steps:
  • 7 × 6 = 42; write 2, carry 4.
  • 7 × 3 = 21; 21 + 4 = 25.
  • So 36 × 7 = 252.
• Answer: 252

[Easy] Adding Fractions with Like Denominators

• EN: What is 2/8 + 3/8?
• FR: Combien font 2/8 + 3/8?
• Choices: A) 5/8 B) 5/16 C) 6/8 D) 1/2
• Hint: When denominators are the same, add just the numerators and keep the denominator.
• Steps:
  • 2/8 + 3/8: add the numerators: 2 + 3 = 5.
  • Keep the denominator: 8.
  • So the answer is 5/8.
• Answer: 5/8

[Easy] Introduction to Percentages

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

[Easy] Decimal Operations

• EN: What is 4.6 + 2.3?
• FR: Combien font 4,6 + 2,3?
• Choices: A) 6.7 B) 6.8 C) 6.9 D) 7.0
• Hint: Line up the decimal points and add each column — tenths with tenths, ones with ones.
• Steps:
  • Tenths: 6 + 3 = 9.
  • Ones: 4 + 2 = 6.
  • So 4.6 + 2.3 = 6.9.
• Answer: 6.9

[Medium] Volume of Rectangular Prism

• EN: A storage box is 5 cm long, 4 cm wide, and 3 cm tall. What is its volume?
• FR: Une boîte de rangement mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est son volume?
• Choices: A) 47 cm³ B) 55 cm³ C) 60 cm³ D) 65 cm³
• Hint: Volume of a rectangular prism = length × width × height.
• Steps:
  • V = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60.
  • So the volume is 60 cm³.
• Answer: 60 cm³

[Medium] Subtracting Fractions with Like Denominators

• EN: What is 7/10 − 3/10?
• FR: Combien font 7/10 − 3/10?
• Choices: A) 3/10 B) 4/10 C) 4/20 D) 5/10
• Hint: When denominators are the same, subtract just the numerators and keep the denominator.
• Steps:
  • 7/10 − 3/10: subtract numerators: 7 − 3 = 4.
  • Keep the denominator: 10.
  • So the answer is 4/10.
• Answer: 4/10

[Medium] Finding 25% and 10%

• EN: A sweater at a Canadian store costs $60. It is on sale for 25% off. How much is the discount?
• FR: Un chandail dans un magasin canadien coûte 60 $. Il est en solde à 25 % de rabais. Quel est le montant du rabais?
• Choices: A) $12 B) $15 C) $20 D) $25
• Hint: 25% = one quarter — divide the price by 4 to find 25% of it.
• Steps:
  • 25% of $60 = $60 ÷ 4.
  • $60 ÷ 4 = $15.
  • So the discount is $15.
• Answer: $15

[Medium] Multi-Digit Division

• EN: 168 students are split equally into 8 teams for a school tournament. How many students are on each team?
• FR: 168 élèves sont répartis également en 8 équipes pour un tournoi scolaire. Combien d'élèves y a-t-il dans chaque équipe?
• Choices: A) 19 B) 20 C) 21 D) 22
• Hint: Use long division — divide step by step, bringing down digits as you go.
• Steps:
  • 8 goes into 16 twice (2 × 8 = 16); remainder 0.
  • Bring down 8: 8 ÷ 8 = 1.
  • So 168 ÷ 8 = 21.
• Answer: 21

[Hard] Multi-Step Decimal Problem

• EN: Maya buys 3 notebooks at $2.75 each and a pen for $1.50. She pays with a $10 bill. How much change does she get?
• FR: Maya achète 3 cahiers à 2,75 $ chacun et un stylo à 1,50 $. Elle paie avec un billet de 10 $. Combien reçoit-elle en monnaie?
• Choices: A) $0.25 B) $0.50 C) $1.00 D) $1.25
• Hint: Find the total cost first by multiplying and adding, then subtract from the amount paid.
• Steps:
  • Cost of notebooks: 3 × $2.75 = $8.25.
  • Total cost: $8.25 + $1.50 = $9.75.
  • Change: $10.00 − $9.75 = $0.25.
• Answer: $0.25

[Hard] Volume and Comparison

• EN: Box A is 6 cm × 5 cm × 4 cm. Box B is 8 cm × 5 cm × 3 cm. How much greater is Box A's volume than Box B's volume?
• FR: La boîte A mesure 6 cm × 5 cm × 4 cm. La boîte B mesure 8 cm × 5 cm × 3 cm. Quel est l'écart de volume entre la boîte A et la boîte B?
• Choices: A) 0 cm³ B) 10 cm³ C) 15 cm³ D) 20 cm³
• Hint: Calculate each volume separately using length × width × height, then subtract.
• Steps:
  • Volume A: 6 × 5 × 4 = 120 cm³.
  • Volume B: 8 × 5 × 3 = 120 cm³.
  • Difference: 120 − 120 = 0 cm³.
• Answer: 0 cm³

[Easy] Percent of a Number

• EN: What is 10% of 250?
• FR: Combien font 10 % de 250?
• Choices: A) 20 B) 25 C) 30 D) 35
• Hint: 10% of a number means divide it by 10 — move the decimal point one place to the left.
• Steps:
  • 10% of 250 = 250 ÷ 10.
  • 250 ÷ 10 = 25.
  • So 10% of 250 is 25.
• Answer: 25

[Easy] Integers Introduction

• EN: The temperature in Winnipeg was −8°C in the morning and rose by 5°C by noon. What is the temperature at noon?
• FR: La température à Winnipeg était de −8 °C le matin et a augmenté de 5 °C à midi. Quelle est la température à midi?
• Choices: A) −4°C B) −3°C C) −2°C D) −1°C
• Hint: Adding a positive number to a negative number moves you to the right on the number line.
• Steps:
  • Start at −8.
  • Add 5: −8 + 5 = −3.
  • So the temperature at noon is −3°C.
• Answer: −3°C

[Easy] Ratios

• EN: For every 2 red beads, there are 5 blue beads on a bracelet. What is the ratio of red to blue beads?
• FR: Pour chaque 2 perles rouges, il y a 5 perles bleues sur un bracelet. Quel est le rapport entre les perles rouges et les perles bleues?
• Choices: A) 2:5 B) 5:2 C) 2:7 D) 5:7
• Hint: A ratio compares two quantities in order — list the first amount, then the second.
• Steps:
  • Red beads = 2; blue beads = 5.
  • Ratio of red to blue = 2:5.
  • So the answer is 2:5.
• Answer: 2:5

[Easy] Order of Operations (BEDMAS)

• EN: What is 3 + 4 × 2?
• FR: Combien font 3 + 4 × 2?
• Choices: A) 10 B) 11 C) 14 D) 16
• Hint: BEDMAS says to multiply before adding — do the multiplication first, then add.
• Steps:
  • Multiplication first: 4 × 2 = 8.
  • Then add: 3 + 8 = 11.
  • So the answer is 11.
• Answer: 11

[Medium] Fraction Multiplication

• EN: What is 2/3 × 3/4?
• FR: Combien font 2/3 × 3/4?
• Choices: A) 5/7 B) 6/12 C) 1/2 D) 2/7
• Hint: To multiply fractions, multiply the numerators together and the denominators together.
• Steps:
  • Multiply numerators: 2 × 3 = 6.
  • Multiply denominators: 3 × 4 = 12.
  • Simplify: 6/12 = 1/2.
• Answer: 1/2

[Medium] 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) 70 km/h B) 75 km/h C) 80 km/h D) 85 km/h
• Hint: Speed = distance ÷ time — divide the total distance by the number of hours.
• Steps:
  • Speed = 240 ÷ 3.
  • 240 ÷ 3 = 80.
  • So the speed is 80 km/h.
• Answer: 80 km/h

[Medium] Algebraic Expressions

• EN: Evaluate 5n − 3 when n = 4.
• FR: Évalue 5n − 3 lorsque n = 4.
• Choices: A) 13 B) 14 C) 17 D) 22
• Hint: Substitute the given value in place of the variable, then follow BEDMAS.
• Steps:
  • Replace n with 4: 5 × 4 − 3.
  • 5 × 4 = 20.
  • 20 − 3 = 17.
• Answer: 17

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 2
• Hint: To divide by a fraction, multiply by its reciprocal — flip the second fraction and multiply.
• Steps:
  • 3/4 ÷ 1/2 = 3/4 × 2/1.
  • 3 × 2 = 6; 4 × 1 = 4.
  • 6/4 = 3/2.
• Answer: 3/2

[Hard] Multi-Step Percent Problem

• EN: A pair of hockey gloves costs $80. The price increases by 15%. What is the new price?
• FR: Une paire de gants de hockey coûte 80 $. Le prix augmente de 15 %. Quel est le nouveau prix?
• Choices: A) $88 B) $90 C) $92 D) $95
• Hint: Find 15% of the original price, then add it to the original — or multiply by 1.15.
• Steps:
  • 10% of $80 = $8; 5% of $80 = $4.
  • 15% = $8 + $4 = $12.
  • New price: $80 + $12 = $92.
• Answer: $92

[Hard] BEDMAS with Integers

• EN: What is (−3 + 7) × 2 − 10 ÷ 5?
• FR: Combien font (−3 + 7) × 2 − 10 ÷ 5?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Work inside brackets first, then multiply and divide from left to right, then add and subtract.
• Steps:
  • Brackets: −3 + 7 = 4.
  • Multiply: 4 × 2 = 8.
  • Divide: 10 ÷ 5 = 2.
  • Subtract: 8 − 2 = 6.
• Answer: 6

[Easy] Integer Addition

• EN: What is −12 + 7?
• FR: Combien font −12 + 7?
• Choices: A) −6 B) −5 C) 5 D) 6
• Hint: When adding a positive to a negative, subtract the smaller absolute value from the larger.
• Steps:
  • |−12| = 12, |7| = 7; 12 − 7 = 5.
  • The larger absolute value (12) is negative, so the answer is −5.
  • So −12 + 7 = −5.
• Answer: −5

[Easy] Percentage — Discount

• EN: A toonie-priced item normally costs $12. It is 25% off. What is the sale price?
• FR: Un article coûte normalement 12 $. Il est à 25 % de rabais. Quel est le prix de vente?
• Choices: A) $7 B) $8 C) $9 D) $10
• Hint: Find 25% of the price (divide by 4), then subtract it from the original price.
• Steps:
  • 25% of $12 = $12 ÷ 4 = $3.
  • Sale price = $12 − $3 = $9.
  • So the sale price is $9.
• Answer: $9

[Easy] Integer Subtraction

• EN: What is 5 − (−3)?
• FR: Combien font 5 − (−3)?
• Choices: A) 2 B) 6 C) 7 D) 8
• Hint: Subtracting a negative number is the same as adding a positive — two negatives make a positive.
• Steps:
  • 5 − (−3) = 5 + 3.
  • 5 + 3 = 8.
  • So the answer is 8.
• Answer: 8

[Easy] Fraction to Decimal

• EN: What is 3/4 as a decimal?
• FR: Quel est 3/4 en décimal?
• Choices: A) 0.25 B) 0.50 C) 0.75 D) 0.80
• Hint: Divide the numerator by the denominator — 1 ÷ 4 = 0.25, so 3 ÷ 4 = ?
• Steps:
  • 3 ÷ 4: 4 goes into 3 zero times; 4 goes into 30 seven times (28); remainder 2.
  • 4 goes into 20 five times.
  • So 3/4 = 0.75.
• Answer: 0.75

[Medium] One-Step Linear Equation

• EN: Solve for x: x + 13 = 29.
• FR: Résous pour x : x + 13 = 29.
• Choices: A) x = 14 B) x = 15 C) x = 16 D) x = 17
• Hint: To isolate x, do the opposite operation — subtract 13 from both sides.
• Steps:
  • x + 13 = 29.
  • Subtract 13 from both sides: x = 29 − 13.
  • x = 16.
• Answer: x = 16

[Medium] Surface Area

• EN: What is the surface area of a rectangular prism that is 5 cm long, 3 cm wide, and 2 cm tall?
• FR: Quelle est l'aire totale d'un prisme rectangulaire de 5 cm de long, 3 cm de large et 2 cm de haut?
• Choices: A) 58 cm² B) 60 cm² C) 62 cm² D) 64 cm²
• Hint: Surface area = 2(lw + lh + wh) — add the areas of all three pairs of faces.
• Steps:
  • lw = 5 × 3 = 15; lh = 5 × 2 = 10; wh = 3 × 2 = 6.
  • Sum = 15 + 10 + 6 = 31.
  • SA = 2 × 31 = 62 cm².
• Answer: 62 cm²

[Medium] Tip Calculation

• EN: A family's restaurant bill is $45.00. They want to leave a 20% tip. How much is the tip?
• FR: La facture de restaurant d'une famille est de 45,00 $. Ils veulent laisser un pourboire de 20 %. Quel est le montant du pourboire?
• Choices: A) $7.00 B) $8.00 C) $9.00 D) $10.00
• Hint: Find 10% first by dividing by 10, then double it to get 20%.
• Steps:
  • 10% of $45 = $4.50.
  • 20% = 2 × $4.50 = $9.00.
  • So the tip is $9.00.
• Answer: $9.00

[Medium] Probability

• EN: A bag has 3 red marbles, 5 blue marbles, and 2 green marbles. If you pick one without looking, what is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 billes bleues et 2 billes vertes. Si tu en piges une sans regarder, quelle est la probabilité de piger une bille bleue?
• Choices: A) 1/2 B) 5/10 C) 3/10 D) 2/5
• Hint: Probability = number of favourable outcomes ÷ total number of outcomes.
• Steps:
  • Total marbles = 3 + 5 + 2 = 10.
  • Blue marbles = 5.
  • Probability = 5/10 = 1/2.
• Answer: 1/2

[Hard] Two-Step Equation with Integers

• EN: Solve for x: 3x − 7 = 14.
• FR: Résous pour x : 3x − 7 = 14.
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: Add 7 to both sides first, then divide both sides by the coefficient of x.
• Steps:
  • 3x − 7 = 14; add 7 to both sides: 3x = 21.
  • Divide both sides by 3: x = 7.
  • So x = 7.
• Answer: x = 7

[Hard] Multi-Step Integer and Percentage Problem

• EN: The temperature in Thunder Bay dropped from 4°C to −11°C over two days. Then it rose by 30% of that total drop. What is the final temperature?
• FR: La température à Thunder Bay a chuté de 4 °C à −11 °C en deux jours. Puis elle a augmenté de 30 % de cette baisse totale. Quelle est la température finale?
• Choices: A) −6.5°C B) −7.5°C C) −8.0°C D) −8.5°C
• Hint: Find the total drop, calculate 30% of that drop, then add it to the lowest temperature.
• Steps:
  • Drop = 4 − (−11) = 15°C.
  • 30% of 15 = 0.30 × 15 = 4.5°C rise.
  • Final temperature = −11 + 4.5 = −6.5°C.
• Answer: −6.5°C

[Easy] Perfect Squares

• EN: What is √144?
• FR: Combien fait √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of a number that multiplied by itself gives 144 — try numbers between 10 and 15.
• Steps:
  • 11 × 11 = 121; 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Find the mean of these scores: 70, 80, 90, 60.
• FR: Trouve la moyenne de ces résultats : 70, 80, 90, 60.
• Choices: A) 70 B) 75 C) 80 D) 85
• Hint: Add all values, then divide by how many values there are.
• Steps:
  • Sum: 70 + 80 + 90 + 60 = 300.
  • Number of values: 4.
  • Mean: 300 ÷ 4 = 75.
• Answer: 75

[Easy] Percent Increase

• EN: A hockey team had 20 wins last season and 25 wins this season. What is the percent increase?
• FR: Une équipe de hockey avait 20 victoires la saison dernière et en a 25 cette saison. Quelle est l'augmentation en pourcentage?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100.
• Steps:
  • Increase = 25 − 20 = 5.
  • Percent increase = (5 ÷ 20) × 100 = 25%.
  • So the percent increase is 25%.
• Answer: 25%

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x : 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: Subtract the constant from both sides first, then divide by the coefficient of x.
• Steps:
  • 2x + 5 = 13; subtract 5: 2x = 8.
  • Divide by 2: x = 4.
  • So x = 4.
• Answer: x = 4

[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 côtés de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: Use a² + b² = c² — square both legs, add them, then take the square root.
• Steps:
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10.
  • So the hypotenuse is 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

• EN: A ramp rises 4 m over a horizontal distance of 8 m. What is the slope of the ramp?
• FR: Une rampe monte de 4 m sur une distance horizontale de 8 m. Quelle est la pente de la rampe?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: Slope = rise ÷ run — divide the vertical change by the horizontal change.
• Steps:
  • Rise = 4; run = 8.
  • Slope = 4/8 = 1/2.
  • So the slope is 1/2.
• Answer: 1/2

[Medium] Percent Decrease

• EN: A jacket that originally cost $90 is now on sale for $63. What is the percent decrease?
• FR: Un manteau qui coûtait 90 $ est maintenant en vente à 63 $. Quelle est la diminution en pourcentage?
• Choices: A) 25% B) 27% C) 30% D) 33%
• Hint: Percent decrease = (decrease ÷ original price) × 100.
• Steps:
  • Decrease = 90 − 63 = 27.
  • Percent decrease = (27 ÷ 90) × 100 = 30%.
  • So the percent decrease is 30%.
• Answer: 30%

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 9, 11, 5.
• FR: Trouve la médiane de : 3, 7, 9, 11, 5.
• Choices: A) 5 B) 7 C) 9 D) 11
• Hint: First put the numbers in order from smallest to largest, then find the middle value.
• Steps:
  • Ordered: 3, 5, 7, 9, 11.
  • Middle value (3rd of 5): 7.
  • So the median is 7.
• Answer: 7

[Hard] Pythagorean Theorem Applied

• EN: A ladder 13 m long leans against a wall. The foot of the ladder is 5 m from the wall. How high up the wall does the ladder reach?
• FR: Une échelle de 13 m de long est appuyée contre un mur. Le pied de l'échelle est à 5 m du mur. À quelle hauteur l'échelle atteint-elle le mur?
• Choices: A) 10 m B) 11 m C) 12 m D) 13 m
• Hint: Use a² + b² = c² — the ladder is the hypotenuse; solve for the unknown leg.
• Steps:
  • a² + 5² = 13².
  • a² + 25 = 169; a² = 144.
  • a = √144 = 12 m.
• Answer: 12 m

[Hard] Two-Step Equation with Fractions

• EN: Solve for x: x/3 + 4 = 9.
• FR: Résous pour x : x/3 + 4 = 9.
• Choices: A) x = 12 B) x = 15 C) x = 18 D) x = 21
• Hint: Subtract the constant from both sides first, then multiply both sides by the denominator.
• Steps:
  • x/3 + 4 = 9; subtract 4: x/3 = 5.
  • Multiply both sides by 3: x = 15.
  • So x = 15.
• Answer: x = 15

[Easy] Solving Linear Equations

• EN: Solve for x: 4x − 6 = 18.
• FR: Résous pour x : 4x − 6 = 18.
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add the constant to both sides first, then divide by the coefficient of x.
• Steps:
  • 4x − 6 = 18; add 6: 4x = 24.
  • Divide by 4: x = 6.
  • So x = 6.
• Answer: x = 6

[Easy] Adding Polynomials

• EN: Add (3x + 5) + (2x − 1).
• FR: Additionne (3x + 5) + (2x − 1).
• Choices: A) 4x + 4 B) 5x + 4 C) 5x + 6 D) 6x + 4
• Hint: Combine like terms — add the x terms together and the constant terms together.
• Steps:
  • x terms: 3x + 2x = 5x.
  • Constants: 5 + (−1) = 4.
  • So the sum is 5x + 4.
• Answer: 5x + 4

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x − 2?
• FR: Quelle est la pente de la droite y = 3x − 2?
• Choices: A) −2 B) 2 C) 3 D) 5
• Hint: In y = mx + b, the slope is m — the coefficient of x.
• Steps:
  • y = 3x − 2 is in the form y = mx + b.
  • m = 3; b = −2.
  • So the slope is 3.
• Answer: 3

[Easy] Linear Inequality

• EN: Solve the inequality: x + 4 > 10.
• FR: Résous l'inégalité : x + 4 > 10.
• Choices: A) x > 4 B) x > 5 C) x > 6 D) x > 7
• Hint: Solve an inequality like an equation — subtract the same value from both sides.
• Steps:
  • x + 4 > 10; subtract 4 from both sides.
  • x > 6.
  • So the solution is x > 6.
• Answer: x > 6

[Medium] Multiplying Polynomials

• EN: Expand 3x(2x + 5).
• FR: Développe 3x(2x + 5).
• Choices: A) 5x² + 8x B) 6x² + 15x C) 6x + 15x D) 6x² + 8x
• Hint: Distribute by multiplying the term outside the bracket by each term inside.
• Steps:
  • 3x × 2x = 6x².
  • 3x × 5 = 15x.
  • So the result is 6x² + 15x.
• Answer: 6x² + 15x

[Medium] Similar Triangles

• EN: Two similar triangles have sides of 4 cm and 6 cm corresponding. If the shorter triangle has a second side of 5 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 6 cm. Si le plus petit triangle a un deuxième côté de 5 cm, quel est le côté correspondant du plus grand triangle?
• Choices: A) 6.5 cm B) 7 cm C) 7.5 cm D) 8 cm
• Hint: Use the scale factor — divide the larger corresponding side by the smaller to find it.
• Steps:
  • Scale factor = 6/4 = 1.5.
  • Larger side = 5 × 1.5 = 7.5 cm.
  • So the corresponding side is 7.5 cm.
• Answer: 7.5 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 mesure 9 cm et l'hypoténuse mesure 15 cm. Combien fait sin(θ)?
• Choices: A) 0.45 B) 0.50 C) 0.60 D) 0.75
• Hint: SOH means sin = Opposite ÷ Hypotenuse.
• Steps:
  • sin(θ) = opposite/hypotenuse = 9/15.
  • 9/15 = 0.60.
  • So sin(θ) = 0.60.
• Answer: 0.60

[Medium] Graphing Lines

• EN: A line has a slope of 2 and passes through the point (0, −3). What is its equation?
• FR: Une droite a une pente de 2 et passe par le point (0, −3). Quelle est son équation?
• Choices: A) y = 2x + 3 B) y = −3x + 2 C) y = 2x − 3 D) y = −2x − 3
• Hint: Use y = mx + b — plug in the slope for m and the y-intercept for b.
• Steps:
  • m = 2; the point (0, −3) gives b = −3.
  • Equation: y = 2x − 3.
  • So the equation is y = 2x − 3.
• Answer: y = 2x − 3

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 5 cm and the hypotenuse is 13 cm. What is the angle θ to the nearest degree? (Use cos⁻¹)
• FR: Dans un triangle rectangle, le côté adjacent mesure 5 cm et l'hypoténuse mesure 13 cm. Quel est l'angle θ au degré près? (Utilise cos⁻¹)
• Choices: A) 57° B) 59° C) 67° D) 69°
• Hint: CAH means cos(θ) = adjacent ÷ hypotenuse; then use inverse cosine to find the angle.
• Steps:
  • cos(θ) = 5/13 ≈ 0.3846.
  • θ = cos⁻¹(0.3846) ≈ 67°.
  • So θ ≈ 67°.
• Answer: 67°

[Hard] Systems of Equations (Substitution Intro)

• EN: A class sold adult tickets for $8 and student tickets for $5. They sold 20 tickets in total and made $130. How many adult tickets were sold?
• FR: Une classe a vendu des billets d'adulte à 8 $ et des billets d'élève à 5 $. Ils ont vendu 20 billets en tout et ont amassé 130 $. Combien de billets d'adulte ont été vendus?
• Choices: A) 8 B) 9 C) 10 D) 12
• Hint: Let a = adult tickets and s = student tickets; write two equations and substitute.
• Steps:
  • a + s = 20 and 8a + 5s = 130.
  • From first: s = 20 − a; substitute: 8a + 5(20 − a) = 130.
  • 8a + 100 − 5a = 130; 3a = 30; a = 10.
• Answer: 10

[Easy] Factoring Quadratics

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

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, the angle is 30° and the hypotenuse is 10 cm. What is the length of the opposite side?
• FR: Dans un triangle rectangle, l'angle est de 30° et l'hypoténuse mesure 10 cm. Quelle est la longueur du côté opposé?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 8 cm
• Hint: Use SOH: sin(30°) = 0.5, so opposite = hypotenuse × sin(30°).
• Steps:
  • sin(30°) = opposite/hypotenuse.
  • opposite = 10 × sin(30°) = 10 × 0.5 = 5.
  • So the opposite side is 5 cm.
• Answer: 5 cm

[Easy] System of Equations

• EN: Solve: x + y = 10 and x − y = 4.
• FR: Résous : x + y = 10 et x − y = 4.
• Choices: A) x = 6, y = 4 B) x = 7, y = 3 C) x = 8, y = 2 D) x = 5, y = 5
• Hint: Add the two equations together to eliminate one variable, then solve for the remaining one.
• Steps:
  • Add: (x + y) + (x − y) = 10 + 4 → 2x = 14 → x = 7.
  • Substitute: 7 + y = 10 → y = 3.
  • So x = 7, y = 3.
• Answer: x = 7, y = 3

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 5 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 628 cm³ B) 750 cm³ C) 785 cm³ D) 800 cm³
• Hint: Volume of a cylinder = π × r² × h — square the radius first, then multiply.
• Steps:
  • V = π × 5² × 10 = 3.14 × 25 × 10.
  • 3.14 × 25 = 78.5; 78.5 × 10 = 785.
  • So the volume is 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Solve x² + 6x − 7 = 0 by factoring.
• FR: Résous x² + 6x − 7 = 0 par factorisation.
• Choices: A) x = 1 and x = −7 B) x = −1 and x = 7 C) x = 2 and x = −7 D) x = 7 and x = −1
• Hint: Find two numbers that multiply to −7 and add to +6, then write the factored form.
• Steps:
  • Need numbers that multiply to −7 and add to 6: 7 and −1. ✓
  • (x + 7)(x − 1) = 0.
  • x = −7 or x = 1; so x = 1 and x = −7.
• Answer: x = 1 and x = −7

[Medium] Circle Geometry

• EN: A circle has a diameter of 18 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 18 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 54.52 cm B) 56.52 cm C) 56.72 cm D) 58.52 cm
• Hint: Circumference = π × diameter — multiply π by the full diameter.
• Steps:
  • C = π × d = 3.14 × 18.
  • 3.14 × 18 = 56.52.
  • So the circumference is 56.52 cm.
• Answer: 56.52 cm

[Medium] Trigonometry — tan Ratio

• EN: In a right triangle, the opposite side is 7 cm and the adjacent side is 7 cm. What is tan(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 7 cm et le côté adjacent mesure 7 cm. Combien fait tan(θ)?
• Choices: A) 0.5 B) 0.75 C) 1 D) 1.5
• Hint: TOA: tan = Opposite ÷ Adjacent.
• Steps:
  • tan(θ) = 7/7 = 1.
  • So tan(θ) = 1.
• Answer: 1

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 3 cm and a slant height of 5 cm. What is the lateral surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 3 cm et une hauteur oblique de 5 cm. Quelle est l'aire latérale? (Utilise π ≈ 3,14)
• Choices: A) 42.10 cm² B) 46.00 cm² C) 47.10 cm² D) 50.24 cm²
• Hint: Lateral surface area of a cone = π × r × slant height.
• Steps:
  • Lateral SA = π × 3 × 5 = 3.14 × 15.
  • 3.14 × 15 = 47.10.
  • So the lateral surface area is 47.10 cm².
• Answer: 47.10 cm²

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve 2x² − 4x − 6 = 0.
• FR: Utilise la formule quadratique pour résoudre 2x² − 4x − 6 = 0.
• Choices: A) x = 3 and x = −1 B) x = −3 and x = 1 C) x = 2 and x = −3 D) x = 3 and x = −2
• Hint: Use x = [−b ± √(b² − 4ac)] / 2a with a = 2, b = −4, c = −6.
• Steps:
  • Discriminant: (−4)² − 4(2)(−6) = 16 + 48 = 64; √64 = 8.
  • x = (4 + 8)/4 = 3 or x = (4 − 8)/4 = −1.
  • So x = 3 and x = −1.
• Answer: x = 3 and x = −1

[Hard] System of Equations with Quadratic

• EN: Find the intersection of y = x² and y = x + 2.
• FR: Trouve l'intersection de y = x² et y = x + 2.
• Choices: A) x = −1 and x = 2 B) x = 1 and x = −2 C) x = 2 and x = 3 D) x = −2 and x = 3
• Hint: Set the two expressions equal, rearrange to form a quadratic, and solve by factoring.
• Steps:
  • x² = x + 2 → x² − x − 2 = 0.
  • Factor: (x − 2)(x + 1) = 0.
  • So x = 2 or x = −1.
• Answer: x = −1 and x = 2

[Easy] Evaluating Exponential Functions

• EN: If f(x) = 2^x, what is f(5)?
• FR: Si f(x) = 2^x, combien fait f(5)?
• Choices: A) 16 B) 25 C) 32 D) 64
• Hint: Raise the base to the power of x — 2⁵ means multiply 2 by itself 5 times.
• Steps:
  • f(5) = 2⁵.
  • 2 × 2 × 2 × 2 × 2 = 32.
  • So f(5) = 32.
• Answer: 32

[Easy] Logarithms Introduction

• EN: What is log₂(8)?
• FR: Combien fait log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log₂(8) asks: "2 to what power gives 8?" — think about powers of 2.
• Steps:
  • 2¹ = 2, 2² = 4, 2³ = 8.
  • So log₂(8) = 3.
• Answer: 3

[Easy] Arithmetic Sequences

• EN: What is the 6th term of the arithmetic sequence 3, 7, 11, 15, ...?
• FR: Quel est le 6e terme de la suite arithmétique 3, 7, 11, 15, ...?
• Choices: A) 19 B) 21 C) 23 D) 27
• Hint: Use the formula aₙ = a₁ + (n − 1)d, where d is the common difference.
• Steps:
  • d = 7 − 3 = 4.
  • a₆ = 3 + (6 − 1) × 4 = 3 + 20 = 23.
  • So the 6th term is 23.
• Answer: 23

[Easy] Compound Interest

• EN: Kenji invests $1000 at 5% per year, compounded annually, for 2 years. What is the amount after 2 years?
• FR: Kenji investit 1 000 $ à 5 % par an, composé annuellement, pour 2 ans. Quel est le montant après 2 ans?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1105.00
• Hint: Use A = P(1 + r)ⁿ — multiply the principal by (1 + rate) once for each year.
• Steps:
  • After year 1: $1000 × 1.05 = $1050.
  • After year 2: $1050 × 1.05 = $1102.50.
  • So the amount is $1102.50.
• Answer: $1102.50

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of f(x) = (x − 3)² + 5?
• FR: Quel est le sommet de f(x) = (x − 3)² + 5?
• Choices: A) (−3, 5) B) (3, −5) C) (3, 5) D) (5, 3)
• Hint: In vertex form f(x) = (x − h)² + k, the vertex is (h, k).
• Steps:
  • The function is in vertex form: (x − 3)² + 5.
  • h = 3, k = 5.
  • So the vertex is (3, 5).
• Answer: (3, 5)

[Medium] Geometric Series Sum

• EN: Find the sum of the first 4 terms of the geometric series 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) 82
• Hint: You can add the terms directly for a short series, or use S = a(rⁿ − 1)/(r − 1).
• Steps:
  • 2 + 6 + 18 + 54 = 80.
  • So the sum is 80.
• Answer: 80

[Medium] Logarithm Properties

• EN: Simplify log₃(27) + log₃(3).
• FR: Simplifie log₃(27) + log₃(3).
• Choices: A) 3 B) 4 C) 5 D) 9
• Hint: Evaluate each logarithm separately — 3 to what power gives 27, and 3 to what power gives 3?
• Steps:
  • log₃(27) = 3 (since 3³ = 27).
  • log₃(3) = 1 (since 3¹ = 3).
  • 3 + 1 = 4.
• Answer: 4

[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 the most fundamental Pythagorean identity in trigonometry — memorize it.
• Steps:
  • The Pythagorean identity states: sin²(θ) + cos²(θ) = 1 for all values of θ.
  • So the answer is 1.
• Answer: 1

[Hard] Annuity Calculation

• EN: Fatima deposits $200 at the end of each year for 3 years at 4% annual interest, compounded annually. What is the future value of her annuity?
• FR: Fatima dépose 200 $ à la fin de chaque année pendant 3 ans à 4 % d'intérêt annuel, composé annuellement. Quelle est la valeur future de sa rente?
• Choices: A) $614.67 B) $618.56 C) $624.32 D) $630.00
• Hint: Each deposit earns interest for the remaining years — add them: 200(1.04)² + 200(1.04)¹ + 200.
• Steps:
  • Year 1 deposit grows: 200 × (1.04)² = 200 × 1.0816 = 216.32.
  • Year 2 deposit grows: 200 × 1.04 = 208.00.
  • Year 3 deposit: 200.00.
  • Total: 216.32 + 208.00 + 200.00 = 624.32.
• Answer: $624.32

[Hard] Exponential Growth Problem

• EN: A bacteria colony starts with 500 cells and doubles every 3 hours. How many cells are there after 9 hours?
• FR: Une colonie de bactéries commence avec 500 cellules et double toutes les 3 heures. Combien y a-t-il de cellules après 9 heures?
• Choices: A) 2000 B) 3000 C) 4000 D) 4500
• Hint: Use the formula A = P × 2^(t/d) where d is the doubling time — find how many doublings occur.
• Steps:
  • Number of doublings in 9 hours: 9/3 = 3.
  • A = 500 × 2³ = 500 × 8 = 4000.
  • So there are 4000 cells after 9 hours.
• Answer: 4000

[Easy] Permutations

• EN: How many ways can 4 different books be arranged on a shelf?
• FR: De combien de façons peut-on arranger 4 livres différents sur une étagère?
• Choices: A) 16 B) 20 C) 24 D) 28
• Hint: The number of arrangements of n objects is n! — multiply all positive integers from 1 to n.
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 24.
  • So there are 24 ways.
• Answer: 24

[Easy] Derivative as Rate of Change

• EN: If f(x) = x², what is f'(x)?
• FR: Si f(x) = x², combien fait f'(x)?
• Choices: A) x B) 2 C) 2x D) x²
• Hint: Use the power rule: if f(x) = xⁿ, then f'(x) = n × x^(n−1).
• Steps:
  • f(x) = x²; apply the power rule: bring down the exponent and reduce it by 1.
  • f'(x) = 2 × x^(2−1) = 2x.
  • So f'(x) = 2x.
• Answer: 2x

[Easy] Combinations

• EN: How many ways can you choose 2 students from a group of 6?
• FR: De combien de façons peut-on choisir 2 élèves parmi un groupe de 6?
• Choices: A) 12 B) 15 C) 18 D) 30
• Hint: Use C(n, r) = n! / (r! × (n−r)!) — order doesn't matter in combinations.
• Steps:
  • C(6, 2) = 6! / (2! × 4!) = (6 × 5) / (2 × 1) = 30/2 = 15.
  • So there are 15 ways.
• Answer: 15

[Easy] Rational Function — Domain

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

[Medium] Normal Distribution

• EN: In a normal distribution, the mean is 70 and the standard deviation is 10. What percent of data falls within one standard deviation of the mean (between 60 and 80)?
• FR: Dans une distribution normale, la moyenne est de 70 et l'écart-type est de 10. Quel pourcentage des données se trouve dans un écart-type de la moyenne (entre 60 et 80)?
• Choices: A) 50% B) 64% C) 68% D) 95%
• Hint: Use the 68-95-99.7 rule — approximately 68% of data falls within one standard deviation of the mean.
• Steps:
  • One standard deviation below: 70 − 10 = 60.
  • One standard deviation above: 70 + 10 = 80.
  • By the 68-95-99.7 rule, approximately 68% of data falls in this range.
• Answer: 68%

[Medium] Vector Addition

• EN: Vector a = (3, 4) and vector b = (1, −2). What is a + b?
• FR: Le vecteur a = (3, 4) et le vecteur b = (1, −2). Combien fait a + b?
• Choices: A) (2, 6) B) (3, 2) C) (4, 2) D) (4, 6)
• Hint: Add the corresponding components — add the x-values together and the y-values together.
• Steps:
  • x-component: 3 + 1 = 4.
  • y-component: 4 + (−2) = 2.
  • So a + b = (4, 2).
• Answer: (4, 2)

[Medium] Polynomial Long Division

• EN: What is the remainder when x² + 3x + 5 is divided by (x − 1)?
• FR: Quel est le reste lorsque x² + 3x + 5 est divisé par (x − 1)?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: Use the Remainder Theorem — substitute x = 1 into the polynomial.
• Steps:
  • f(1) = (1)² + 3(1) + 5.
  • = 1 + 3 + 5 = 9.
  • So the remainder is 9.
• Answer: 9

[Medium] Binomial Probability

• EN: A fair coin is flipped 3 times. What is the probability of getting exactly 2 heads?
• FR: On lance une pièce équitable 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 P = C(n, k) × p^k × (1−p)^(n−k) with p = 0.5.
• Steps:
  • C(3, 2) = 3.
  • P = 3 × (1/2)² × (1/2)¹ = 3 × 1/4 × 1/2 = 3/8.
  • So the probability is 3/8.
• Answer: 3/8

[Hard] Derivative Application — Instantaneous Rate

• EN: The position of a particle is given by s(t) = t³ − 3t² + 2. What is the velocity (s'(t)) at t = 2?
• FR: La position d'une particule est donnée par s(t) = t³ − 3t² + 2. Quelle est la vitesse (s'(t)) à t = 2?
• Choices: A) 0 B) 2 C) 4 D) 6
• Hint: Find the derivative s'(t) using the power rule, then substitute t = 2.
• Steps:
  • s'(t) = 3t² − 6t.
  • s'(2) = 3(2)² − 6(2) = 12 − 12 = 0.
  • So the velocity at t = 2 is 0.
• Answer: 0

[Hard] Counting and Probability Combined

• EN: From a standard deck of 52 cards, two cards are drawn without replacement. What is the probability that both cards are aces?
• FR: On tire deux cartes sans remise d'un jeu ordinaire de 52 cartes. Quelle est la probabilité que les deux cartes soient des as?
• Choices: A) 1/169 B) 1/221 C) 2/221 D) 4/221
• Hint: Find the probability of the first ace, then the probability of the second ace given the first was drawn.
• Steps:
  • P(first ace) = 4/52.
  • P(second ace | first ace) = 3/51.
  • P(both aces) = (4/52) × (3/51) = 12/2652 = 1/221.
• Answer: 1/221