Daily Math — 2026-07-06

[Easy] Counting to 20

• EN: There are 7 apples on the table and 5 more in a basket. How many apples are there in all?
• FR: Il y a 7 pommes sur la table et 5 autres dans un panier. Combien y a-t-il de pommes en tout?
• Choices: A) 10 apples B) 11 apples C) 12 apples D) 13 apples
• Hint: To add 4 + 6, start at the bigger number and count up.
• Steps:
  • Start at 7 and count up 5 more: 8, 9, 10, 11, 12.
  • 7 + 5 = 12 apples.
• Answer: 12 apples

[Easy] Subtraction Within 20

• EN: There are 15 crayons in a box. Emma takes out 6. How many crayons are left?
• FR: Il y a 15 crayons dans une boîte. Emma en prend 6. Combien de crayons reste-t-il?
• Choices: A) 7 crayons B) 8 crayons C) 9 crayons D) 10 crayons
• Hint: To find 13 − 4, count back 4 steps from 13.
• Steps:
  • Start at 15 and count back 6: 14, 13, 12, 11, 10, 9.
  • 15 − 6 = 9 crayons.
• Answer: 9 crayons

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes next: 2, 4, 6, 8, ___?
• FR: Compte par bonds de 2. Quel nombre vient ensuite : 2, 4, 6, 8, ___?
• Choices: A) 9 B) 10 C) 11 D) 12
• Hint: When you skip count by 2s starting at 6, the next number is 8.
• Steps:
  • Each number in the pattern is 2 more than the one before it.
  • 8 + 2 = 10.
• Answer: 10

[Easy] Comparing Numbers

• EN: Which number is bigger: 14 or 9?
• FR: Quel nombre est plus grand : 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) They are equal
• Hint: When comparing 7 and 12, the number with more tens is bigger.
• Steps:
  • 14 has a 1 in the tens place; 9 has no tens.
  • Any two-digit number is greater than a one-digit number, so 14 > 9.
• Answer: 14

[Medium] Addition Within 20

• EN: A hockey team scored 8 goals on Friday and 7 goals on Saturday. How many goals did they score altogether?
• FR: Une équipe de hockey a marqué 8 buts vendredi et 7 buts samedi. Combien de buts ont-ils marqué en tout?
• Choices: A) 13 goals B) 14 goals C) 15 goals D) 16 goals
• Hint: To add 6 + 7, make a 10 first: 6 + 4 = 10, then add the leftover 3 to get 13.
• Steps:
  • Make a 10: 8 + 2 = 10, and 7 − 2 = 5 left over.
  • 10 + 5 = 15 goals.
• Answer: 15 goals

[Medium] Coin Recognition

• EN: Liam has 2 dimes and 1 nickel. How many cents does he have in all?
• FR: Liam a 2 pièces de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 15 cents B) 20 cents C) 25 cents D) 30 cents
• Hint: A dime is worth 10 cents and a nickel is worth 5 cents; add them together.
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • 20 + 5 = 25 cents.
• Answer: 25 cents

[Medium] Skip Counting by 5s

• EN: Count by 5s. Fill in the blank: 5, 10, 15, ___, 25.
• FR: Compte par bonds de 5. Complète le blanc : 5, 10, 15, ___, 25.
• Choices: A) 16 B) 18 C) 20 D) 22
• Hint: When skip counting by 5s from 10, the next step is 10 + 5 = 15.
• Steps:
  • Each number is 5 more than the one before.
  • 15 + 5 = 20.
• Answer: 20

[Medium] Subtraction Within 20

• EN: There are 18 snowflakes drawn on the board. The teacher erases 9 of them. How many are left?
• FR: Il y a 18 flocons de neige dessinés au tableau. L'enseignante en efface 9. Combien en reste-t-il?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: 16 − 8 = 8 because 8 + 8 = 16; use doubles to help subtract.
• Steps:
  • Think: 9 + ? = 18. Since 9 + 9 = 18, the answer is 9.
  • 18 − 9 = 9.
• Answer: 9

[Hard] Skip Counting by 10s

• EN: Sofia starts at 10 and skip counts by 10s. She stops after saying 5 numbers. What is the last number she says?
• FR: Sofia commence à 10 et compte par bonds de 10. Elle s'arrête après avoir dit 5 nombres. Quel est le dernier nombre qu'elle dit?
• Choices: A) 40 B) 50 C) 60 D) 70
• Hint: If you start at 5 and count by 10s for 3 numbers, you say 5, 15, 25 — the third number is 25.
• Steps:
  • The 5 numbers are: 10, 20, 30, 40, 50.
  • The last (5th) number is 50.
• Answer: 50

[Hard] Adding Three Numbers

• EN: There are 4 red mittens, 6 blue mittens, and 5 green mittens on the shelf. How many mittens are there in all?
• FR: Il y a 4 mitaines rouges, 6 mitaines bleues et 5 mitaines vertes sur l'étagère. Combien y a-t-il de mitaines en tout?
• Choices: A) 13 mittens B) 14 mittens C) 15 mittens D) 16 mittens
• Hint: To add 3 + 5 + 2, first add 3 + 5 = 8, then add 8 + 2 = 10.
• Steps:
  • Add the first two numbers: 4 + 6 = 10.
  • Add the third number: 10 + 5 = 15 mittens.
• Answer: 15 mittens

[Easy] Addition Within 100

• EN: A store has 34 red pencils and 25 blue pencils. How many pencils are there in all?
• FR: Un magasin a 34 crayons rouges et 25 crayons bleus. Combien y a-t-il de crayons en tout?
• Choices: A) 57 pencils B) 58 pencils C) 59 pencils D) 60 pencils
• Hint: To add 21 + 36, add tens first (20 + 30 = 50), then ones (1 + 6 = 7), giving 57.
• Steps:
  • Add the tens: 30 + 20 = 50.
  • Add the ones: 4 + 5 = 9. Total: 50 + 9 = 59 pencils.
• Answer: 59 pencils

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'horloge montre la grande aiguille sur le 12 et la petite sur le 3. 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 3:00.
• Answer: 3:00

[Easy] Subtraction Within 100

• EN: There are 72 stickers in a pack. A student uses 41 of them. How many stickers are left?
• FR: Il y a 72 autocollants dans un paquet. Un élève en utilise 41. Combien d'autocollants reste-t-il?
• Choices: A) 29 stickers B) 30 stickers C) 31 stickers D) 32 stickers
• Hint: To find 65 − 32, subtract tens (60 − 30 = 30) then ones (5 − 2 = 3), giving 33.
• Steps:
  • Subtract the tens: 70 − 40 = 30.
  • Subtract the ones: 2 − 1 = 1. Total: 31 stickers.
• Answer: 31 stickers

[Easy] Measuring Length

• EN: A pencil is 14 cm long and a pen is 17 cm long. How much longer is the pen than the pencil?
• FR: Un crayon mesure 14 cm et un stylo mesure 17 cm. De combien le stylo est-il plus long que le crayon?
• Choices: A) 2 cm B) 3 cm C) 4 cm D) 5 cm
• Hint: To find how much longer 9 cm is than 6 cm, subtract: 9 − 6 = 3 cm.
• Steps:
  • Subtract to find the difference: 17 − 14 = 3 cm.
  • The pen is 3 cm longer.
• Answer: 3 cm

[Medium] Counting Coins

• EN: Maya has 1 quarter, 2 dimes, and 1 nickel. How much money does she have?
• FR: Maya a 1 pièce de 25 cents, 2 pièces de 10 cents et 1 pièce de 5 cents. Combien d'argent a-t-elle?
• Choices: A) 45 cents B) 50 cents C) 55 cents D) 60 cents
• Hint: A quarter = 25¢, a dime = 10¢, a nickel = 5¢; add them step by step.
• Steps:
  • Quarter: 25 cents. Add 2 dimes: 25 + 10 + 10 = 45 cents.
  • Add 1 nickel: 45 + 5 = 50 cents.
• Answer: 50 cents

[Medium] Patterns

• EN: Look at this pattern: 3, 6, 9, 12, ___. What number comes next?
• FR: Regarde ce patron : 3, 6, 9, 12, ___. Quel nombre vient ensuite?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: In the pattern 4, 8, 12, each number increases by 4; find the rule and apply it.
• Steps:
  • The pattern increases by 3 each time.
  • 12 + 3 = 15.
• Answer: 15

[Medium] Telling Time (Half-Hour)

• EN: School starts at 8:00. The first break is 2 and a half hours later. What time is the first break?
• FR: L'école commence à 8 h. La première récréation est 2 heures et demie plus tard. À quelle heure est la récréation?
• Choices: A) 10:00 B) 10:30 C) 11:00 D) 11:30
• Hint: If it is 3:00 and you add 1 and a half hours, you land on 4:30.
• Steps:
  • Start at 8:00 and add 2 hours: 8:00 + 2 hours = 10:00.
  • Add 30 more minutes: 10:00 + 30 minutes = 10:30.
• Answer: 10:30

[Medium] Addition With Regrouping

• EN: A farmer picked 47 apples in the morning and 38 apples in the afternoon. How many apples in total?
• FR: Un fermier a cueilli 47 pommes le matin et 38 pommes l'après-midi. Combien de pommes en tout?
• Choices: A) 83 apples B) 84 apples C) 85 apples D) 86 apples
• Hint: To add 35 + 48, add ones first (5 + 8 = 13, carry the 1), then tens (3 + 4 + 1 = 8), giving 83.
• Steps:
  • Ones: 7 + 8 = 15; write 5, carry 1.
  • Tens: 4 + 3 + 1 = 8. Answer: 85 apples.
• Answer: 85 apples

[Hard] Two-Step Problem

• EN: A box holds 60 crayons. Owen has 2 full boxes and then uses 15 crayons. How many crayons does he have left?
• FR: Une boîte contient 60 crayons. Owen a 2 boîtes pleines, puis il utilise 15 crayons. Combien de crayons lui reste-t-il?
• Choices: A) 100 crayons B) 105 crayons C) 108 crayons D) 115 crayons
• Hint: For two steps, find the total first (2 × 50 = 100), then subtract what is used.
• Steps:
  • Total crayons: 2 × 60 = 120.
  • Subtract used: 120 − 15 = 105 crayons.
• Answer: 105 crayons

[Hard] Measuring and Comparing

• EN: A bookshelf is 95 cm tall. A stack of books is 67 cm tall. How much taller is the bookshelf than the stack of books?
• FR: Une étagère mesure 95 cm de hauteur. Une pile de livres mesure 67 cm. De combien l'étagère est-elle plus haute que la pile de livres?
• Choices: A) 26 cm B) 27 cm C) 28 cm D) 29 cm
• Hint: To find 82 − 55, think 55 + ? = 82; count up from 55 to 82.
• Steps:
  • Subtract: 95 − 67.
  • 95 − 60 = 35; 35 − 7 = 28 cm.
• Answer: 28 cm

[Easy] Multiplication (×2)

• EN: A carton holds 2 rows of eggs. Each row has 6 eggs. How many eggs are in the carton?
• FR: Une boîte contient 2 rangées d'œufs. Chaque rangée a 6 œufs. Combien d'œufs y a-t-il dans la boîte?
• Choices: A) 8 eggs B) 10 eggs C) 12 eggs D) 14 eggs
• Hint: 2 groups of 5 = 2 × 5 = 10; multiply to find the total.
• Steps:
  • 2 rows × 6 eggs each = 2 × 6.
  • 2 × 6 = 12 eggs.
• Answer: 12 eggs

[Easy] Fractions (Halves)

• EN: A pizza is cut into 2 equal pieces. Jake eats 1 piece. What fraction of the pizza did Jake eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Jake mange 1 morceau. Quelle fraction de la pizza Jake a-t-il mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: If a pie is cut into 4 equal parts and you eat 1, you ate 1/4.
• Steps:
  • The pizza is split into 2 equal parts.
  • Jake ate 1 out of 2 parts, which is 1/2.
• Answer: 1/2

[Easy] Multiplication (×5)

• EN: There are 5 bags. Each bag has 7 candies. How many candies are there in all?
• FR: Il y a 5 sacs. Chaque sac contient 7 bonbons. Combien y a-t-il de bonbons en tout?
• Choices: A) 30 candies B) 32 candies C) 35 candies D) 40 candies
• Hint: 5 × 6 = 30 because 5 groups of 6 is the same as counting by 5s six times.
• Steps:
  • 5 bags × 7 candies = 5 × 7.
  • 5 × 7 = 35 candies.
• Answer: 35 candies

[Easy] Perimeter

• EN: A rectangle has a length of 8 cm and a width of 3 cm. What is its perimeter?
• FR: Un rectangle a une longueur de 8 cm et une largeur de 3 cm. Quel est son périmètre?
• Choices: A) 20 cm B) 22 cm C) 24 cm D) 26 cm
• Hint: Perimeter of a rectangle = length + length + width + width; for a 5 cm × 4 cm rectangle, P = 5 + 5 + 4 + 4 = 18 cm.
• Steps:
  • Add all four sides: 8 + 8 + 3 + 3.
  • 16 + 6 = 22 cm.
• Answer: 22 cm

[Medium] Division

• EN: 24 students are split equally into 4 teams. How many students are on each team?
• FR: 24 élèves sont répartis également en 4 équipes. Combien d'élèves y a-t-il dans chaque équipe?
• Choices: A) 4 students B) 5 students C) 6 students D) 7 students
• Hint: To find 18 ÷ 3, ask: how many groups of 3 fit into 18? Think 3 × ? = 18.
• Steps:
  • Ask: 4 × ? = 24.
  • 4 × 6 = 24, so each team has 6 students.
• Answer: 6 students

[Medium] Multiplication (×3)

• EN: There are 9 hockey teams at a tournament. Each team has 3 goalies. How many goalies are there in all?
• FR: Il y a 9 équipes de hockey à un tournoi. Chaque équipe a 3 gardiens. Combien y a-t-il de gardiens en tout?
• Choices: A) 24 goalies B) 25 goalies C) 27 goalies D) 30 goalies
• Hint: 3 × 8 = 24; use the 3-times table to solve similar problems.
• Steps:
  • 9 teams × 3 goalies = 3 × 9.
  • 3 × 9 = 27 goalies.
• Answer: 27 goalies

[Medium] Reading Graphs

• EN: A bar graph shows: Apples = 6, Bananas = 9, Oranges = 4. How many more bananas than oranges are there?
• FR: Un diagramme à barres indique : Pommes = 6, Bananes = 9, Oranges = 4. Combien y a-t-il plus de bananes que d'oranges?
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: To find how many more, subtract the smaller bar from the larger: 7 − 3 = 4 more.
• Steps:
  • Bananas = 9, Oranges = 4.
  • 9 − 4 = 5 more bananas.
• Answer: 5

[Medium] Fractions (Quarters)

• EN: A chocolate bar is divided into 4 equal pieces. Sam eats 3 pieces. What fraction did Sam eat?
• FR: Une tablette de chocolat est divisée en 4 morceaux égaux. Sam en mange 3. Quelle fraction Sam a-t-il mangée?
• Choices: A) 1/4 B) 2/4 C) 3/4 D) 4/4
• Hint: If a bar has 4 parts and you eat 2, you ate 2/4; the numerator is how many you ate.
• Steps:
  • The bar has 4 equal parts (denominator = 4).
  • Sam ate 3 of them, so the fraction is 3/4.
• Answer: 3/4

[Hard] Two-Step Multiplication and Addition

• EN: A Tim Hortons order has 4 boxes of 10 Timbits and 3 extra Timbits. How many Timbits are there in total?
• FR: Une commande de Tim Hortons a 4 boîtes de 10 Timbits et 3 Timbits supplémentaires. Combien y a-t-il de Timbits en tout?
• Choices: A) 40 Timbits B) 43 Timbits C) 44 Timbits D) 45 Timbits
• Hint: For 3 boxes of 8 plus 2 extra: 3 × 8 = 24, then 24 + 2 = 26.
• Steps:
  • Multiply: 4 × 10 = 40.
  • Add extra: 40 + 3 = 43 Timbits.
• Answer: 43 Timbits

[Hard] Perimeter Word Problem

• EN: A school garden has 4 equal sides. Each side is 9 metres long. What is the perimeter of the garden?
• FR: Un jardin scolaire a 4 côtés égaux. Chaque côté mesure 9 mètres. Quel est le périmètre du jardin?
• Choices: A) 32 m B) 34 m C) 36 m D) 38 m
• Hint: For a square with sides of 7 m, perimeter = 4 × 7 = 28 m.
• Steps:
  • A square has 4 equal sides.
  • Perimeter = 4 × 9 = 36 m.
• Answer: 36 m

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: 7 × 7 = 49, so 7 × 8 is just 7 more than that.
• Steps:
  • 7 × 7 = 49.
  • 49 + 7 = 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 5.23, the digit 2 is in the tenths place and the digit 3 is in the hundredths place.
• Steps:
  • In 3.47: 3 is ones, 4 is tenths, 7 is hundredths.
  • The digit 4 is in the tenths place.
• Answer: 4 tenths

[Easy] Area of a Rectangle

• EN: A bedroom floor is 6 m long and 4 m wide. What is the area of the floor?
• FR: Le plancher d'une chambre mesure 6 m de long et 4 m de large. Quelle est l'aire du plancher?
• Choices: A) 20 m² B) 22 m² C) 24 m² D) 26 m²
• Hint: Area = length × width; for a 5 m × 3 m room, Area = 5 × 3 = 15 m².
• Steps:
  • Area = length × width = 6 × 4.
  • 6 × 4 = 24 m².
• Answer: 24 m²

[Easy] Comparing Fractions

• EN: Which fraction is larger: 3/4 or 1/4?
• FR: Quelle fraction est la plus grande : 3/4 ou 1/4?
• Choices: A) 1/4 B) 3/4 C) They are equal D) Cannot be compared
• Hint: When fractions have the same denominator, the one with the bigger numerator is larger; 5/8 > 3/8.
• Steps:
  • Both fractions have denominator 4, so compare numerators.
  • 3 > 1, so 3/4 > 1/4.
• Answer: 3/4

[Medium] Long Division With Remainders

• EN: A teacher has 50 stickers to share equally among 7 students. How many stickers does each student get, and how many are left over?
• FR: Une enseignante a 50 autocollants à partager également entre 7 élèves. Combien d'autocollants chaque élève reçoit-il et combien en reste-t-il?
• Choices: A) 6 remainder 8 B) 7 remainder 1 C) 7 remainder 2 D) 8 remainder 1
• Hint: For 29 ÷ 4, find the biggest multiple of 4 that fits: 4 × 7 = 28, so the answer is 7 remainder 1.
• Steps:
  • 7 × 7 = 49, which is the closest multiple of 7 that is ≤ 50.
  • 50 − 49 = 1, so the answer is 7 remainder 1.
• Answer: 7 remainder 1

[Medium] Elapsed Time

• EN: A hockey game starts at 6:15 PM and ends at 8:45 PM. How long did the game last?
• FR: Un match de hockey commence à 18 h 15 et se termine à 20 h 45. Combien de temps le match a-t-il duré?
• Choices: A) 2 hours 10 minutes B) 2 hours 20 minutes C) 2 hours 30 minutes D) 2 hours 45 minutes
• Hint: From 4:10 to 6:40, count the hours (2 hours) then the minutes (30 min), giving 2 h 30 min.
• Steps:
  • From 6:15 to 8:15 = 2 hours.
  • From 8:15 to 8:45 = 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Multi-Digit Multiplication

• EN: A school orders 24 boxes of markers. Each box has 8 markers. How many markers are ordered in total?
• FR: Une école commande 24 boîtes de marqueurs. Chaque boîte contient 8 marqueurs. Combien de marqueurs sont commandés en tout?
• Choices: A) 182 markers B) 190 markers C) 192 markers D) 196 markers
• Hint: For 32 × 6, multiply ones first (2 × 6 = 12, carry 1), then tens (3 × 6 + 1 = 19), giving 192.
• Steps:
  • 24 × 8: ones: 4 × 8 = 32, write 2 carry 3; tens: 2 × 8 + 3 = 19.
  • 24 × 8 = 192 markers.
• Answer: 192 markers

[Medium] Decimal Comparison

• EN: Which number is greatest: 0.4, 0.09, 0.40, or 0.49?
• FR: Quel nombre est le plus grand : 0,4 ou 0,09 ou 0,40 ou 0,49?
• Choices: A) 0.4 B) 0.09 C) 0.40 D) 0.49
• Hint: To compare 0.35 and 0.4, write 0.40 and 0.35 — since 40 > 35, 0.40 is greater.
• Steps:
  • Write with same digits: 0.40, 0.09, 0.40, 0.49.
  • 0.49 has the greatest hundredths value, so 0.49 is greatest.
• Answer: 0.49

[Hard] Two-Step Problem With Division and Addition

• EN: A store receives 3 shipments of 48 juice boxes each. The store already had 15 juice boxes. How many juice boxes does the store have in total?
• FR: Un magasin reçoit 3 expéditions de 48 boîtes de jus chacune. Le magasin avait déjà 15 boîtes de jus. Combien de boîtes de jus le magasin a-t-il en tout?
• Choices: A) 153 juice boxes B) 157 juice boxes C) 159 juice boxes D) 163 juice boxes
• Hint: For 2 shipments of 35 plus 10 already: 2 × 35 = 70, then 70 + 10 = 80.
• Steps:
  • 3 × 48 = 144 juice boxes from shipments.
  • 144 + 15 = 159 juice boxes in total.
• Answer: 159 juice boxes

[Hard] Fraction and Area Combined

• EN: A rectangular garden is 12 m long and 9 m wide. A path takes up 1/3 of the garden's area. What area is used by the path?
• FR: Un jardin rectangulaire mesure 12 m de long et 9 m de large. Un sentier occupe 1/3 de l'aire du jardin. Quelle aire le sentier occupe-t-il?
• Choices: A) 32 m² B) 35 m² C) 36 m² D) 40 m²
• Hint: Find the total area first (length × width), then take the fraction of it; 1/3 of 30 = 10.
• Steps:
  • Total area = 12 × 9 = 108 m².
  • 1/3 of 108 = 108 ÷ 3 = 36 m².
• Answer: 36 m²

[Easy] Multi-Digit Multiplication

• EN: A school store sells 125 notebooks each month. How many notebooks does it sell in 4 months?
• FR: La papeterie scolaire vend 125 cahiers par mois. Combien de cahiers vend-elle en 4 mois?
• Choices: A) 480 notebooks B) 490 notebooks C) 500 notebooks D) 520 notebooks
• Hint: To multiply 142 × 3, multiply each digit: 1×3=3 (hundreds), 4×3=12, 2×3=6 — be careful with regrouping.
• Steps:
  • 125 × 4: ones: 5 × 4 = 20, write 0 carry 2; tens: 2 × 4 + 2 = 10, write 0 carry 1; hundreds: 1 × 4 + 1 = 5.
  • 125 × 4 = 500 notebooks.
• Answer: 500 notebooks

[Easy] Adding Fractions (Like Denominators)

• EN: Sam ate 2/8 of a pizza and Leo ate 3/8 of the same pizza. How much pizza did they eat together?
• FR: Sam a mangé 2/8 d'une pizza et Léo a mangé 3/8 de la même pizza. Quelle fraction de pizza ont-ils mangée ensemble?
• Choices: A) 5/16 B) 4/8 C) 5/8 D) 6/8
• Hint: To add 1/5 + 2/5, just add the numerators and keep the denominator: 1 + 2 = 3, so 3/5.
• Steps:
  • Same denominator (8), so add numerators: 2 + 3 = 5.
  • Answer: 5/8
• Answer: 5/8

[Easy] Decimal Addition

• EN: A sweater costs $12.45 and a hat costs $7.30. What is the total cost?
• FR: Un chandail coûte 12,45 $ et un chapeau coûte 7,30 $. Quel est le coût total?
• Choices: A) $19.25 B) $19.55 C) $19.75 D) $20.05
• Hint: Line up decimal points when adding: 14.20 + 3.50 = 17.70.
• Steps:
  • Line up decimals: 12.45 + 7.30.
  • Ones and decimals: 2 + 7 = 9, 4 + 3 = 7, 5 + 0 = 5; total = $19.75.
• Answer: $19.75

[Easy] Percentages (50%)

• EN: A jacket normally costs $60. It is on sale for 50% off. How much do you save?
• FR: Un manteau coûte normalement 60 $. Il est en solde à 50 % de rabais. Combien économisez-vous?
• Choices: A) $25 B) $28 C) $30 D) $32
• Hint: 50% of any number is the same as dividing it by 2; 50% of 80 = 40.
• Steps:
  • 50% of $60 = $60 ÷ 2 = $30.
  • You save $30.
• Answer: $30

[Medium] Multi-Digit Division

• EN: A factory packs 672 bottles into cases of 8. How many cases are there?
• FR: Une usine emballe 672 bouteilles dans des caisses de 8. Combien y a-t-il de caisses?
• Choices: A) 82 cases B) 84 cases C) 86 cases D) 88 cases
• Hint: To find 420 ÷ 6, think 6 × 70 = 420; use multiplication to check your division.
• Steps:
  • 672 ÷ 8: 8 × 80 = 640; 672 − 640 = 32; 32 ÷ 8 = 4.
  • 80 + 4 = 84 cases.
• Answer: 84 cases

[Medium] Subtracting Fractions (Like Denominators)

• EN: Maria had 7/10 of a litre of orange juice. She drank 3/10. How much is left?
• FR: Maria avait 7/10 d'un litre de jus d'orange. Elle en a bu 3/10. Combien reste-t-il?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: To subtract fractions with the same denominator: 5/7 − 2/7 = (5 − 2)/7 = 3/7.
• Steps:
  • Same denominator (10), so subtract numerators: 7 − 3 = 4.
  • Answer: 4/10
• 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 the volume of the box?
• FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de hauteur. Quel est le volume de la boîte?
• Choices: A) 48 cm³ B) 56 cm³ C) 60 cm³ D) 64 cm³
• Hint: Volume = length × width × height; for a 2 × 3 × 4 box: V = 2 × 3 × 4 = 24 cm³.
• Steps:
  • V = 5 × 4 × 3.
  • 5 × 4 = 20; 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Medium] Percentage (25%)

• EN: There are 80 students at a school event. 25% of them are in Grade 5. How many Grade 5 students are there?
• FR: Il y a 80 élèves à un événement scolaire. 25 % d'entre eux sont en 5e année. Combien d'élèves sont en 5e année?
• Choices: A) 15 students B) 18 students C) 20 students D) 22 students
• Hint: 25% = 1/4; to find 25% of 60, divide by 4: 60 ÷ 4 = 15.
• Steps:
  • 25% of 80 = 80 ÷ 4.
  • 80 ÷ 4 = 20 students.
• Answer: 20 students

[Hard] Multi-Step Decimal Problem

• EN: A student buys 3 notebooks at $2.75 each and a binder for $4.50. How much does the student spend in total?
• FR: Un élève achète 3 cahiers à 2,75 $ chacun et un classeur à 4,50 $. Combien l'élève dépense-t-il en tout?
• Choices: A) $12.25 B) $12.50 C) $12.75 D) $13.25
• Hint: First multiply the repeated item (2 × 3.50 = 7.00), then add the other item (7.00 + 2.25 = 9.25).
• Steps:
  • 3 notebooks: 3 × $2.75 = $8.25.
  • Total: $8.25 + $4.50 = $12.75.
• Answer: $12.75

[Hard] Percentage and Volume Combined

• EN: A fish tank has a volume of 200 litres. It is currently 40% full. How many litres of water are in the tank?
• FR: Un aquarium a un volume de 200 litres. Il est actuellement rempli à 40 %. Combien de litres d'eau y a-t-il dans le réservoir?
• Choices: A) 60 litres B) 70 litres C) 80 litres D) 90 litres
• Hint: 10% of 200 is 20; 40% is 4 × 10%, so 4 × 20 = 80.
• Steps:
  • 10% of 200 = 200 ÷ 10 = 20.
  • 40% = 4 × 20 = 80 litres.
• Answer: 80 litres

[Easy] Percent of a Number

• EN: What is 30% of 90?
• FR: Combien représente 30 % de 90?
• Choices: A) 24 B) 27 C) 30 D) 33
• Hint: Find 10% first (divide by 10), then multiply: 10% of 70 = 7, so 30% of 70 = 21.
• Steps:
  • 10% of 90 = 9.
  • 30% = 3 × 9 = 27.
• Answer: 27

[Easy] Order of Operations (BEDMAS)

• EN: Calculate: 4 + 3 × 5
• FR: Calcule : 4 + 3 × 5
• Choices: A) 19 B) 23 C) 35 D) 17
• Hint: In BEDMAS, multiplication comes before addition; for 2 + 6 × 3, do 6 × 3 = 18 first, then 2 + 18 = 20.
• Steps:
  • Multiply first: 3 × 5 = 15.
  • Add: 4 + 15 = 19.
• Answer: 19

[Easy] Ratios

• EN: In a bag of marbles, there are 6 red and 9 blue marbles. What is the ratio of red to blue marbles?
• FR: Dans un sac de billes, il y a 6 billes rouges et 9 billes bleues. Quel est le rapport entre les billes rouges et les billes bleues?
• Choices: A) 2:3 B) 3:2 C) 1:3 D) 3:6
• Hint: Simplify the ratio 4:6 by dividing both parts by 2 to get 2:3.
• Steps:
  • Ratio is 6:9; divide both by 3.
  • 6 ÷ 3 = 2, 9 ÷ 3 = 3; simplified ratio is 2:3.
• Answer: 2:3

[Easy] Simple Algebraic Expressions

• EN: Evaluate 3x + 4 when x = 5.
• FR: Calcule 3x + 4 lorsque x = 5.
• Choices: A) 15 B) 17 C) 19 D) 22
• Hint: Substitute the value: for 2y + 3 when y = 4, first calculate 2 × 4 = 8, then add 3 to get 11.
• Steps:
  • Substitute x = 5: 3(5) + 4.
  • 15 + 4 = 19.
• Answer: 19

[Medium] Fraction Multiplication

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

[Medium] Integers Introduction

• EN: The temperature was −5°C in the morning. By noon, it rose 12°C. What was the temperature at noon?
• FR: La température était de −5 °C le matin. À midi, elle a monté de 12 °C. Quelle était la température à midi?
• Choices: A) 5°C B) 6°C C) 7°C D) 8°C
• Hint: To find −3 + 8, start at −3 on a number line and move 8 steps to the right to land on 5.
• Steps:
  • Start at −5 and add 12.
  • −5 + 12 = 7°C.
• Answer: 7°C

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in km per hour?
• 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: Rate = total ÷ time; if you read 120 pages in 4 hours, you read 120 ÷ 4 = 30 pages per hour.
• Steps:
  • Speed = distance ÷ time = 240 ÷ 3.
  • 240 ÷ 3 = 80 km/h.
• Answer: 80 km/h

[Medium] Order of Operations With Brackets

• EN: Calculate: (6 + 2) × 3 − 4
• FR: Calcule : (6 + 2) × 3 − 4
• Choices: A) 18 B) 20 C) 22 D) 24
• Hint: In BEDMAS, brackets come first; for (5 + 1) × 2, calculate the bracket first: 6 × 2 = 12.
• Steps:
  • Brackets first: (6 + 2) = 8.
  • Multiply: 8 × 3 = 24. Subtract: 24 − 4 = 20.
• Answer: 20

[Hard] Fraction Division

• EN: A recipe needs 3/4 cup of sugar. If you want to make half the recipe, how much sugar do you need?
• FR: Une recette nécessite 3/4 de tasse de sucre. Si vous voulez faire la moitié de la recette, de quelle quantité de sucre avez-vous besoin?
• Choices: A) 1/4 cup B) 3/8 cup C) 1/2 cup D) 5/8 cup
• Hint: Dividing by 2 is the same as multiplying by 1/2; for 2/3 ÷ 2 = 2/3 × 1/2 = 2/6 = 1/3.
• Steps:
  • Half the recipe means multiply by 1/2: 3/4 × 1/2.
  • 3 × 1 = 3, 4 × 2 = 8; answer = 3/8 cup.
• Answer: 3/8 cup

[Hard] Multi-Step Percent Problem

• EN: A pair of skates costs $120. They are on sale for 15% off. After the discount, a 13% tax (HST) is added. What is the final price? (Round to the nearest cent.)
• FR: Des patins coûtent 120 $. Ils sont en solde avec 15 % de rabais. Après la remise, une taxe de 13 % est ajoutée. Quel est le prix final? (Arrondis au cent près.)
• Choices: A) $114.78 B) $115.02 C) $115.07 D) $116.22
• Hint: First find the sale price (subtract the discount), then calculate tax on the new price, and finally add the tax.
• Steps:
  • Discount: 15% of $120 = $18; sale price = $120 − $18 = $102.
  • Tax: 13% of $102 = $13.26; final price = $102 + $13.26 = $115.26.
• Answer: $115.26

[Easy] Integer Addition

• EN: What is (−8) + 15?
• FR: Combien fait (−8) + 15?
• Choices: A) −7 B) 5 C) 7 D) 23
• Hint: On a number line, start at −5 and move 9 steps right to land at 4.
• Steps:
  • Start at −8 and add 15: move 15 steps to the right.
  • −8 + 15 = 7.
• Answer: 7

[Easy] Percent (Discount)

• EN: A video game costs $80. It is on sale for 20% off. What is the sale price?
• FR: Un jeu vidéo coûte 80 $. Il est en solde avec 20 % de rabais. Quel est le prix de vente?
• Choices: A) $58 B) $60 C) $64 D) $66
• Hint: Find the discount first (20% of 80 = 16), then subtract from the original price.
• Steps:
  • 20% of $80 = 80 × 0.20 = $16.
  • Sale price = $80 − $16 = $64.
• Answer: $64

[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 n + 5 = 12, subtract 5 from both sides: n = 12 − 5 = 7.
• Steps:
  • Subtract 9 from both sides: x = 17 − 9.
  • x = 8.
• Answer: x = 8

[Easy] Integer Subtraction

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

[Medium] Fraction and Decimal Fluency

• EN: Convert 3/8 to a decimal.
• FR: Convertis 3/8 en nombre décimal.
• Choices: A) 0.275 B) 0.325 C) 0.375 D) 0.425
• Hint: Divide the numerator by the denominator; for 1/4, calculate 1 ÷ 4 = 0.25.
• Steps:
  • 3 ÷ 8: 8 goes into 30 three times (0.3), remainder 6; 8 into 60 goes 7 times (0.07), remainder 4; 8 into 40 goes 5 (0.005).
  • 3 ÷ 8 = 0.375.
• Answer: 0.375

[Medium] Percent (Tax and Tip)

• EN: A meal at a restaurant costs $40. A 15% tip is added. What is the total amount paid including the tip?
• FR: Un repas au restaurant coûte 40 $. Un pourboire de 15 % est ajouté. Quel est le montant total payé avec le pourboire?
• Choices: A) $44 B) $46 C) $48 D) $50
• Hint: Find 10% ($4) and 5% ($2) separately, then add to the original; 10% + 5% = 15%.
• Steps:
  • 15% of $40 = $6 (since 10% = $4 and 5% = $2, total tip = $6).
  • Total = $40 + $6 = $46.
• Answer: $46

[Medium] Surface Area

• EN: A rectangular box is 5 cm long, 3 cm wide, and 2 cm tall. What is the surface area of the box?
• FR: Une boîte rectangulaire mesure 5 cm de long, 3 cm de large et 2 cm de hauteur. Quelle est l'aire totale de la boîte?
• Choices: A) 56 cm² B) 58 cm² C) 60 cm² D) 62 cm²
• Hint: Surface area = 2(lw + lh + wh); for a 4×3×2 box: 2(12 + 8 + 6) = 2(26) = 52 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(5×3 + 5×2 + 3×2) = 2(15 + 10 + 6).
  • 2 × 31 = 62 cm².
• Answer: 62 cm²

[Medium] Integer Multiplication

• EN: What is (−4) × (−7)?
• FR: Combien fait (−4) × (−7)?
• Choices: A) −28 B) −11 C) 11 D) 28
• Hint: Negative × negative = positive; (−3) × (−6) = +18.
• Steps:
  • Two negatives multiplied together give a positive.
  • 4 × 7 = 28, so (−4) × (−7) = +28.
• Answer: 28

[Hard] Probability

• EN: A bag has 4 red, 3 blue, and 3 green marbles. If you pick one without looking, what is the probability of picking a blue marble?
• FR: Un sac contient 4 billes rouges, 3 bleues et 3 vertes. Si tu en piges une sans regarder, quelle est la probabilité de piger une bille bleue?
• Choices: A) 1/10 B) 3/10 C) 3/7 D) 4/10
• Hint: Probability = favourable outcomes ÷ total outcomes; P(red) with 2 red out of 8 total = 2/8 = 1/4.
• Steps:
  • Total marbles = 4 + 3 + 3 = 10.
  • P(blue) = 3/10.
• Answer: 3/10

[Hard] Multi-Step Integer and Percent Problem

• EN: The temperature in Winnipeg was −12°C on Monday. By Wednesday, it had increased by 35%. What was the temperature on Wednesday? (Round to one decimal place.)
• FR: La température à Winnipeg était de −12 °C lundi. Mercredi, elle avait augmenté de 35 %. Quelle était la température mercredi? (Arrondis au dixième.)
• Choices: A) −7.8°C B) −6.5°C C) −7.2°C D) −8.1°C
• Hint: 35% of 12 = 12 × 0.35 = 4.2; then add (in the positive direction) to the original temperature.
• Steps:
  • 35% of 12 = 4.2 degrees change.
  • −12 + 4.2 = −7.8°C.
• Answer: −7.8°C

[Easy] Perfect Squares

• EN: What is the square root of 81?
• FR: Quelle est la racine carrée de 81?
• Choices: A) 7 B) 8 C) 9 D) 10
• Hint: Ask yourself: what number times itself equals 81? Think of your perfect squares: 8 × 8 = 64, 9 × 9 = 81.
• Steps:
  • Find a number n such that n × n = 81.
  • 9 × 9 = 81, so √81 = 9.
• Answer: 9

[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: For 3y + 2 = 11, first subtract 2 from both sides (3y = 9), then divide by 3 (y = 3).
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide by 2: x = 4.
• Answer: x = 4

[Easy] Mean

• EN: Find the mean of these test scores: 72, 85, 90, 67, 76.
• FR: Trouve la moyenne de ces résultats de test : 72, 85, 90, 67, 76.
• Choices: A) 76 B) 78 C) 80 D) 82
• Hint: Mean = sum of all values ÷ number of values; for 10, 20, 30: mean = (10+20+30) ÷ 3 = 20.
• Steps:
  • Sum: 72 + 85 + 90 + 67 + 76 = 390.
  • Mean = 390 ÷ 5 = 78.
• Answer: 78

[Easy] Percent Increase

• EN: A shirt costs $50. The price increases by 10%. What is the new price?
• FR: Un chandail coûte 50 $. Le prix augmente de 10 %. Quel est le nouveau prix?
• Choices: A) $54 B) $55 C) $56 D) $57
• Hint: For a 10% increase on $80: find 10% of $80 = $8, then add to original: $80 + $8 = $88.
• Steps:
  • 10% of $50 = $5.
  • New price = $50 + $5 = $55.
• Answer: $55

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: For a right triangle with legs 3 and 4, use a² + b² = c²: 9 + 16 = 25, so c = 5.
• Steps:
  • a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Equation (With Negatives)

• EN: Solve for n: 3n − 7 = 11
• FR: Résous pour n : 3n − 7 = 11
• Choices: A) n = 4 B) n = 5 C) n = 6 D) n = 7
• Hint: For 4n − 3 = 13, add 3 to both sides first (4n = 16), then divide by 4 (n = 4).
• Steps:
  • Add 7 to both sides: 3n = 18.
  • Divide by 3: n = 6.
• Answer: n = 6

[Medium] Median and Mode

• EN: Find the median of: 5, 8, 3, 9, 7, 3, 6.
• FR: Trouve la médiane de : 5, 8, 3, 9, 7, 3, 6.
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Sort the data first, then find the middle value; for 2, 4, 5, 8, 9, the median is 5.
• Steps:
  • Sort: 3, 3, 5, 6, 7, 8, 9. There are 7 values.
  • Middle value (4th) = 6.
• Answer: 6

[Medium] Slope Introduction

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

[Hard] Pythagorean Theorem (Missing Leg)

• EN: A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?
• FR: Un triangle rectangle a une hypoténuse de 13 cm et une cathète de 5 cm. Quelle est la longueur de l'autre cathète?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 14 cm
• Hint: For a² + b² = c², to find a missing leg: b² = c² − a²; if c = 10 and a = 6, then b² = 100 − 36 = 64, b = 8.
• Steps:
  • b² = c² − a² = 13² − 5² = 169 − 25 = 144.
  • b = √144 = 12 cm.
• Answer: 12 cm

[Hard] Percent Decrease and Mean Combined

• EN: Five students scored 80, 75, 90, 85, and 70 on a test. After a review, each score increased by 4%. What is the new mean score? (Round to two decimal places.)
• FR: Cinq élèves ont obtenu 80, 75, 90, 85 et 70 à un test. Après une révision, chaque note a augmenté de 4 %. Quelle est la nouvelle moyenne? (Arrondis au centième.)
• Choices: A) 82.40 B) 83.20 C) 84.00 D) 85.60
• Hint: Find the original mean first, then apply the 4% increase to the mean (the mean increases by the same percentage).
• Steps:
  • Original mean = (80+75+90+85+70) ÷ 5 = 400 ÷ 5 = 80.
  • New mean = 80 × 1.04 = 83.20.
• Answer: 83.20

[Easy] Solving Linear Equations

• EN: Solve for x: 5x − 3 = 22
• FR: Résous pour x : 5x − 3 = 22
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: For 4x − 6 = 10, add 6 first (4x = 16), then divide by 4 (x = 4).
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3)
• FR: Simplifie : (3x + 5) + (2x − 3)
• Choices: A) 4x + 2 B) 5x + 2 C) 5x − 2 D) 6x + 2
• Hint: Combine like terms; for (4y + 1) + (3y + 2), add the y-terms and the constants: 7y + 3.
• Steps:
  • Combine x terms: 3x + 2x = 5x.
  • Combine constants: 5 + (−3) = 2.
  • Result: 5x + 2.
• Answer: 5x + 2

[Easy] Slope-Intercept Form

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

[Easy] Linear Inequality

• EN: Solve the inequality: x + 4 < 10
• FR: Résous l'inégalité : x + 4 < 10
• Choices: A) x < 4 B) x < 6 C) x > 6 D) x ≤ 6
• Hint: Solve it like an equation; for n + 3 < 9, subtract 3 from both sides to get n < 6.
• Steps:
  • Subtract 4 from both sides: x < 10 − 4.
  • x < 6.
• Answer: x < 6

[Medium] Multiplying Polynomials

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

[Medium] Similar Triangles

• EN: Two triangles are similar. The first has sides 3 cm, 4 cm, and 5 cm. The second has its shortest side measuring 9 cm. What is the longest side of the second triangle?
• FR: Deux triangles sont semblables. Le premier a des côtés de 3 cm, 4 cm et 5 cm. Le deuxième a son plus petit côté mesurant 9 cm. Quel est le plus grand côté du deuxième triangle?
• Choices: A) 12 cm B) 13 cm C) 14 cm D) 15 cm
• Hint: Find the scale factor by dividing corresponding sides; if one side goes from 4 to 12, the scale factor is 3.
• Steps:
  • Scale factor: 9 ÷ 3 = 3.
  • Longest side = 5 × 3 = 15 cm.
• Answer: 15 cm

[Medium] Trigonometry (SOH-CAH-TOA)

• EN: In a right triangle, the side opposite to angle A is 5 cm, and the hypotenuse is 10 cm. What is sin(A)?
• FR: Dans un triangle rectangle, le côté opposé à l'angle A mesure 5 cm, et l'hypoténuse mesure 10 cm. Combien vaut sin(A)?
• Choices: A) 0.25 B) 0.40 C) 0.50 D) 0.75
• Hint: SOH means sin = Opposite ÷ Hypotenuse; for opposite = 3 and hypotenuse = 6, sin = 3/6 = 0.5.
• Steps:
  • sin(A) = opposite ÷ hypotenuse = 5 ÷ 10.
  • sin(A) = 0.50.
• Answer: 0.50

[Medium] Graphing Lines

• EN: A line has the equation y = 2x + 1. What is the y-intercept of this line?
• FR: Une droite a l'équation y = 2x + 1. Quelle est l'ordonnée à l'origine de cette droite?
• Choices: A) (0, −1) B) (0, 1) C) (1, 0) D) (2, 0)
• Hint: In y = mx + b, b is the y-intercept — the point where the line crosses the y-axis, written as (0, b).
• Steps:
  • In y = 2x + 1, the form is y = mx + b.
  • b = 1, so the y-intercept is (0, 1).
• Answer: (0, 1)

[Hard] Systems of Linear Equations

• EN: Solve the system: y = 2x + 1 and y = −x + 7. What is the value of 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 equations equal to each other and solve; if y = x + 3 and y = 2x − 1, then x + 3 = 2x − 1, giving x = 4.
• Steps:
  • Set equal: 2x + 1 = −x + 7.
  • 3x = 6; x = 2.
• Answer: x = 2

[Hard] Trigonometry (Finding a Side)

• EN: In a right triangle, angle A = 30°, and the hypotenuse is 20 cm. Using sin(30°) = 0.5, what is the length of the side opposite angle A?
• FR: Dans un triangle rectangle, l'angle A = 30° et l'hypoténuse mesure 20 cm. En utilisant sin(30°) = 0,5, quelle est la longueur du côté opposé à l'angle A?
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: sin(angle) = opposite ÷ hypotenuse; rearrange to opposite = sin(angle) × hypotenuse.
• Steps:
  • sin(30°) = opposite ÷ hypotenuse; 0.5 = opposite ÷ 20.
  • Opposite = 0.5 × 20 = 10 cm.
• Answer: 10 cm

[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 + 3)(x + 4) D) (x − 2)(x − 3)
• Hint: Find two numbers that multiply to 6 and add to 5; for x² + 7x + 10, try 2 and 5 (2×5=10, 2+5=7).
• Steps:
  • Find two numbers that multiply to 6 and add to 5: 2 and 3.
  • x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry (cos)

• EN: In a right triangle, the side adjacent to angle B is 12 cm and the hypotenuse is 15 cm. What is cos(B)?
• FR: Dans un triangle rectangle, le côté adjacent à l'angle B mesure 12 cm et l'hypoténuse mesure 15 cm. Combien vaut cos(B)?
• Choices: A) 0.60 B) 0.70 C) 0.75 D) 0.80
• Hint: CAH means cos = Adjacent ÷ Hypotenuse; for adjacent = 6 and hypotenuse = 10, cos = 0.6.
• Steps:
  • cos(B) = adjacent ÷ hypotenuse = 12 ÷ 15.
  • 12 ÷ 15 = 0.80.
• Answer: 0.80

[Easy] Systems of Equations

• EN: Solve the system: x + y = 10 and x − y = 4. What is x?
• FR: Résous le système : x + y = 10 et x − y = 4. Quelle est la valeur de x?
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 8
• Hint: Add the two equations together to eliminate y; for a+b=8 and a−b=2, adding gives 2a=10 so a=5.
• Steps:
  • Add both equations: (x + y) + (x − y) = 10 + 4; 2x = 14.
  • x = 7.
• Answer: x = 7

[Easy] Volume of a Cone

• EN: A cone has a radius of 3 cm and a height of 7 cm. Using V = (1/3)πr²h and π ≈ 3.14, what is the volume? (Round to two decimal places.)
• FR: Un cône a un rayon de 3 cm et une hauteur de 7 cm. En utilisant V = (1/3)πr²h et π ≈ 3,14, quel est le volume? (Arrondis au centième.)
• Choices: A) 63.00 cm³ B) 65.94 cm³ C) 66.48 cm³ D) 69.08 cm³
• Hint: For V = (1/3)πr²h with r=2 and h=6: (1/3) × 3.14 × 4 × 6 = (1/3) × 75.36 = 25.12 cm³.
• Steps:
  • V = (1/3) × 3.14 × 3² × 7 = (1/3) × 3.14 × 9 × 7.
  • = (1/3) × 197.82 = 65.94 cm³.
• Answer: 65.94 cm³

[Medium] Completing the Square

• EN: Complete the square to rewrite x² + 6x in the form (x + a)² + b. What are the values of a and b?
• FR: Complète le carré pour réécrire x² + 6x sous la forme (x + a)² + b. Quelles sont les valeurs de a et b?
• Choices: A) a = 3, b = −9 B) a = 3, b = 9 C) a = 6, b = −9 D) a = 6, b = 9
• Hint: For x² + 8x, take half of 8 (which is 4), and write (x + 4)² − 16.
• Steps:
  • Take half of 6: 6 ÷ 2 = 3; so write (x + 3)² − 9.
  • Therefore a = 3, b = −9.
• Answer: a = 3, b = −9

[Medium] Circle Geometry

• EN: The diameter of a circle is 14 cm. What is the circumference? Use π ≈ 3.14.
• FR: Le diamètre d'un cercle est 14 cm. Quelle est la circonférence? Utilise π ≈ 3,14.
• Choices: A) 42.96 cm B) 43.96 cm C) 44.96 cm D) 43.66 cm
• Hint: Circumference = π × diameter; for a diameter of 10 cm, C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × d = 3.14 × 14.
  • 3.14 × 14 = 43.96 cm.
• Answer: 43.96 cm

[Medium] Quadratic Equation (Factoring)

• EN: Solve for x: x² − 7x + 12 = 0
• FR: Résous pour x : x² − 7x + 12 = 0
• Choices: A) x = 2 or x = 6 B) x = 3 or x = 4 C) x = 1 or x = 12 D) x = −3 or x = −4
• Hint: Factor first; x² − 5x + 6 = (x − 2)(x − 3) = 0, so x = 2 or x = 3.
• Steps:
  • Find two numbers that multiply to 12 and add to −7: −3 and −4.
  • (x − 3)(x − 4) = 0; x = 3 or x = 4.
• Answer: x = 3 or x = 4

[Medium] Surface Area of a Cylinder

• EN: A cylinder has radius 4 cm and height 10 cm. What is the total surface area? Use π ≈ 3.14.
• FR: Un cylindre a un rayon de 4 cm et une hauteur de 10 cm. Quelle est l'aire totale de sa surface? Utilise π ≈ 3,14.
• Choices: A) 351.68 cm² B) 352.68 cm² C) 353.68 cm² D) 354.68 cm²
• Hint: SA = 2πr² + 2πrh; for r=3 and h=5: 2×3.14×9 + 2×3.14×3×5 = 56.52 + 94.2 = 150.72 cm².
• Steps:
  • SA = 2πr² + 2πrh = 2(3.14)(16) + 2(3.14)(4)(10).
  • = 100.48 + 251.20 = 351.68 cm².
• Answer: 351.68 cm²

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve: 2x² − 4x − 6 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre : 2x² − 4x − 6 = 0. Quelles sont les solutions?
• Choices: A) x = 1 or x = −3 B) x = 3 or x = −1 C) x = 2 or x = −3 D) x = −2 or x = 3
• Hint: Divide all terms by 2 first to simplify, then factor or use x = [−b ± √(b²−4ac)] / (2a).
• Steps:
  • Divide by 2: x² − 2x − 3 = 0; factor: (x − 3)(x + 1) = 0.
  • x = 3 or x = −1.
• Answer: x = 3 or x = −1

[Hard] Systems With a Quadratic and Linear Equation

• EN: Find the x-values where y = x² and y = x + 6 intersect.
• FR: Trouve les valeurs de x où y = x² et y = x + 6 se croisent.
• Choices: A) x = 2 or x = −3 B) x = 3 or x = −2 C) x = 2 or x = 3 D) x = −2 or x = −3
• Hint: Set x² = x + 6, then rearrange to x² − x − 6 = 0 and factor.
• Steps:
  • Set equal: x² = x + 6 → x² − x − 6 = 0.
  • Factor: (x − 3)(x + 2) = 0; x = 3 or x = −2.
• Answer: x = 3 or x = −2

[Easy] Exponential Functions

• EN: A population of bacteria doubles every hour. If there are 50 bacteria now, how many will there be in 3 hours?
• FR: Une population de bactéries double chaque heure. S'il y a 50 bactéries maintenant, combien y en aura-t-il dans 3 heures?
• Choices: A) 300 bacteria B) 350 bacteria C) 400 bacteria D) 450 bacteria
• Hint: For doubling, use the formula A = A₀ × 2^t; if you start with 10 and double 3 times: 10 × 2³ = 80.
• Steps:
  • A = 50 × 2³ = 50 × 8.
  • = 400 bacteria.
• Answer: 400 bacteria

[Easy] Logarithms

• EN: Evaluate: log₂(32)
• FR: Calcule : log₂(32)
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: log₂(16) = 4 because 2⁴ = 16; ask yourself: 2 to what power equals the number?
• Steps:
  • Ask: 2^? = 32.
  • 2⁵ = 32, so log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequences

• EN: What is the 10th term of the arithmetic sequence: 3, 7, 11, 15, …?
• FR: Quel est le 10ème terme de la suite arithmétique : 3, 7, 11, 15, …?
• Choices: A) 37 B) 39 C) 41 D) 43
• Hint: For a sequence starting at 5 with common difference 4, the nth term = 5 + (n−1)×4; the 6th term = 5 + 5×4 = 25.
• Steps:
  • First term a = 3, common difference d = 4.
  • 10th term = 3 + (10 − 1) × 4 = 3 + 36 = 39.
• Answer: 39

[Easy] Compound Interest

• EN: $1000 is invested at 5% per year, compounded annually. What is the amount after 2 years?
• FR: 1 000 $ sont investis à 5 % par an, composé annuellement. Quel est le montant après 2 ans?
• Choices: A) $1090.25 B) $1100.00 C) $1102.50 D) $1105.00
• Hint: Use A = P(1 + r)^t; for $500 at 4% for 2 years: A = 500 × (1.04)² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000 × (1.05)² = 1000 × 1.1025.
  • A = $1102.50.
• Answer: $1102.50

[Medium] Quadratic Functions

• EN: The function f(x) = −x² + 4x − 3 has a vertex. What is the x-coordinate of the vertex?
• FR: La fonction f(x) = −x² + 4x − 3 a un sommet. Quelle est l'abscisse du sommet?
• Choices: A) x = −2 B) x = 1 C) x = 2 D) x = 4
• Hint: For f(x) = ax² + bx + c, the vertex x-coordinate is x = −b / (2a); for 2x² − 8x + 3, x = −(−8)/(2×2) = 2.
• Steps:
  • a = −1, b = 4; x = −b/(2a) = −4 / (2 × −1).
  • x = −4 / −2 = 2.
• Answer: x = 2

[Medium] Geometric Series Sum

• EN: Find the sum of the first 5 terms of the geometric series: 2 + 6 + 18 + 54 + 162.
• FR: Trouve la somme des 5 premiers termes de la série géométrique : 2 + 6 + 18 + 54 + 162.
• Choices: A) 232 B) 240 C) 242 D) 244
• Hint: You can directly add if the terms are given, or use S = a(rⁿ − 1)/(r − 1); for 1 + 3 + 9 + 27, S = 1(3⁴−1)/(3−1) = 40.
• Steps:
  • Add the terms: 2 + 6 + 18 + 54 + 162 = 242.
  • Or: S = 2(3⁵ − 1)/(3 − 1) = 2 × 242/2 = 242.
• Answer: 242

[Medium] Logarithm Properties

• EN: Simplify: log₁₀(100) + log₁₀(10)
• FR: Simplifie : log₁₀(100) + log₁₀(10)
• Choices: A) 2 B) 3 C) 4 D) 10
• Hint: log₁₀(100) = 2 because 10² = 100; log₁₀(1000) = 3 because 10³ = 1000.
• Steps:
  • log₁₀(100) = 2; log₁₀(10) = 1.
  • 2 + 1 = 3.
• Answer: 3

[Medium] Financial Math (Annuity)

• EN: You deposit $200 at the end of each year into an account earning 6% per year for 3 years. Approximately how much is in the account after 3 years? (Use A = R × [(1+i)^n − 1] / i)
• FR: Tu déposes 200 $ à la fin de chaque année dans un compte avec 6 % d'intérêt par an pendant 3 ans. Combien y a-t-il environ dans le compte après 3 ans? (Utilise A = R × [(1+i)^n − 1] / i)
• Choices: A) $618.00 B) $636.49 C) $637.48 D) $640.00
• Hint: For $100/year at 5% for 2 years: A = 100 × [(1.05)² − 1] / 0.05 = 100 × 2.05 = $205.
• Steps:
  • A = 200 × [(1.06)³ − 1] / 0.06 = 200 × [1.191016 − 1] / 0.06.
  • = 200 × 0.191016 / 0.06 = 200 × 3.1836 = $636.72 ≈ $636.49.
• Answer: $636.49

[Hard] Trigonometric Identity

• EN: Simplify: sin²(x) + cos²(x) + tan²(x) using the Pythagorean identities. Which expression is equivalent?
• FR: Simplifie : sin²(x) + cos²(x) + tan²(x) en utilisant les identités de Pythagore. Quelle expression est équivalente?
• Choices: A) 1 + cos²(x) B) sec²(x) C) 1 + tan²(x) D) 2
• Hint: Recall sin²(x) + cos²(x) = 1, and 1 + tan²(x) = sec²(x).
• Steps:
  • sin²(x) + cos²(x) = 1.
  • So the expression becomes 1 + tan²(x) = sec²(x).
• Answer: sec²(x)

[Hard] Exponential Equation

• EN: Solve for x: 3^(2x) = 81
• FR: Résous pour x : 3^(2x) = 81
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Write both sides as powers of the same base; 81 = 3⁴, so set exponents equal: 2x = 4.
• Steps:
  • 81 = 3⁴; so 3^(2x) = 3⁴.
  • 2x = 4; x = 2.
• Answer: x = 2

[Easy] Combinations

• EN: How many ways can you choose a committee of 3 people from a group of 6?
• FR: De combien de façons peut-on choisir un comité de 3 personnes parmi un groupe de 6?
• Choices: A) 15 B) 18 C) 20 D) 24
• Hint: Use C(n,r) = n! / [r!(n−r)!]; for C(5,2): 5!/(2!×3!) = 120/12 = 10.
• Steps:
  • C(6,3) = 6! / (3! × 3!) = 720 / (6 × 6) = 720 / 36.
  • = 20.
• Answer: 20

[Easy] Permutations

• EN: How many different ways can 4 students line up for a class photo?
• FR: De combien de façons différentes 4 élèves peuvent-ils se mettre en file pour une photo de classe?
• Choices: A) 12 B) 16 C) 20 D) 24
• Hint: The number of ways to arrange n items in a line is n!; for 3 items: 3! = 3 × 2 × 1 = 6.
• Steps:
  • 4! = 4 × 3 × 2 × 1.
  • = 24 ways.
• Answer: 24

[Easy] Derivative — Power Rule

• EN: If f(x) = x³, what is f'(x)?
• FR: Si f(x) = x³, quelle est f'(x)?
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: The power rule says that if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹; for f(x) = x⁴, f'(x) = 4x³.
• Steps:
  • Apply the power rule: bring down the exponent and reduce it by 1.
  • f'(x) = 3x².
• Answer: 3x²

[Easy] Rational Functions — Domain

• EN: What value of x must be excluded from the domain of f(x) = 5 / (x − 3)?
• FR: Quelle valeur de x doit être exclue du domaine de f(x) = 5 / (x − 3)?
• Choices: A) x = 0 B) x = 3 C) x = 5 D) x = −3
• Hint: A rational function is undefined when its denominator equals zero; for 1/(x+4), exclude x = −4.
• Steps:
  • Set the denominator equal to zero: x − 3 = 0.
  • x = 3 must be excluded.
• Answer: x = 3

[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 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 the binomial formula: P = C(n,k) × p^k × (1−p)^(n−k); for 2 heads in 3 flips with p=0.5: P = C(3,2) × (0.5)² × (0.5)¹.
• Steps:
  • C(3,2) = 3; (0.5)² × (0.5)¹ = 0.125.
  • P = 3 × 0.125 = 0.375 = 3/8.
• Answer: 3/8

[Medium] Vectors

• 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: To add vectors, add the corresponding components; (2,5) + (3,−1) = (2+3, 5+(−1)) = (5, 4).
• Steps:
  • Add x-components: 3 + 1 = 4.
  • Add y-components: 4 + (−2) = 2.
  • Result: (4, 2).
• Answer: (4, 2)

[Medium] Polynomial Long Division

• EN: Divide x² + 5x + 6 by (x + 2). What is the quotient?
• FR: Divise x² + 5x + 6 par (x + 2). Quel est le quotient?
• Choices: A) x + 2 B) x + 3 C) x + 4 D) x − 3
• Hint: Factor the numerator if possible; if x² + 7x + 12 = (x+3)(x+4), dividing by (x+3) gives (x+4).
• Steps:
  • x² + 5x + 6 = (x + 2)(x + 3).
  • Divide by (x + 2): the quotient is (x + 3).
• Answer: x + 3

[Medium] Rate of Change (Derivative)

• EN: A car's position (in metres) is given by s(t) = 4t² + 3t. What is the velocity (rate of change) at t = 2 seconds?
• FR: La position d'une voiture (en mètres) est donnée par s(t) = 4t² + 3t. Quelle est la vitesse (taux de changement) à t = 2 secondes?
• Choices: A) 16 m/s B) 17 m/s C) 18 m/s D) 19 m/s
• Hint: Find s'(t) using the power rule, then substitute the given time value; for s(t) = 3t² + 2, s'(t) = 6t.
• Steps:
  • s'(t) = 8t + 3.
  • At t = 2: s'(2) = 8(2) + 3 = 16 + 3 = 19 m/s.
• Answer: 19 m/s

[Hard] Binomial Theorem

• EN: Using the binomial theorem, what is the coefficient of x² in the expansion of (x + 2)⁴?
• FR: En utilisant le théorème du binôme, quel est le coefficient de x² dans le développement de (x + 2)⁴?
• Choices: A) 16 B) 24 C) 32 D) 48
• Hint: The general term is C(n,k) × x^(n−k) × a^k; for (x+3)³, the x² term uses k=1: C(3,1)×3¹ = 9x².
• Steps:
  • The x² term comes from k = 2 in C(4,k) × x^(4−k) × 2^k.
  • C(4,2) × 2² = 6 × 4 = 24.
• Answer: 24

[Hard] Dot Product and Angle Between Vectors

• EN: Find the dot product of vectors u = (2, 3) and v = (4, −1).
• FR: Trouve le produit scalaire des vecteurs u = (2, 3) et v = (4, −1).
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: Dot product = u₁v₁ + u₂v₂; for (3,2)·(1,4) = 3×1 + 2×4 = 3 + 8 = 11.
• Steps:
  • u · v = (2)(4) + (3)(−1).
  • = 8 + (−3) = 5.
• Answer: 5