Daily Math — 2026-09-19

[Easy] Counting Carrots

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

[Easy] Hockey Pucks

• EN: There are 9 hockey pucks on the ice. A player takes 4 away. How many pucks are left?
• FR: Il y a 9 rondelles de hockey sur la glace. Un joueur en prend 4. Combien de rondelles reste-t-il?
• Choices: A) 3 pucks B) 4 pucks C) 5 pucks D) 6 pucks
• Hint: To subtract, count backwards — like 8 − 3: start at 8, go back 3 steps.
• Steps:
  • Start at 9 and count back 4: 8, 7, 6, 5.
  • So there are 5 pucks left.
• Answer: 5 pucks

[Easy] Skip Counting by 2s

• EN: Count by 2s. What number comes after 8, 10, 12?
• FR: Compte par bonds de 2. Quel nombre vient après 8, 10, 12?
• Choices: A) 13 B) 14 C) 15 D) 16
• Hint: Skip counting by 2s means adding 2 each time — like 4, 6, 8, then 10.
• Steps:
  • The pattern adds 2 each time: 8, 10, 12, ...
  • Add 2 to 12: 12 + 2 = 14.
• Answer: 14

[Easy] Coin Recognition

• EN: Which coin is worth 10 cents in Canada?
• FR: Quelle pièce vaut 10 cents au Canada?
• Choices: A) A penny B) A nickel C) A dime D) A loonie
• Hint: Think about the coins you know — a penny is 1 cent and a nickel is 5 cents.
• Steps:
  • A penny = 1 cent, a nickel = 5 cents, a dime = 10 cents, a loonie = $1.
  • The coin worth 10 cents is the dime.
• Answer: A dime

[Medium] Snowflakes on the Window

• EN: Luca sees 14 snowflakes on the left window and 6 snowflakes on the right window. How many snowflakes are there in all?
• FR: Luca voit 14 flocons sur la fenêtre gauche et 6 flocons sur la fenêtre droite. Combien y a-t-il de flocons en tout?
• Choices: A) 18 snowflakes B) 19 snowflakes C) 20 snowflakes D) 21 snowflakes
• Hint: To add a number to 14, start at 14 and count up — like 14 + 4: 15, 16, 17, 18.
• Steps:
  • Start at 14 and count on 6 more: 15, 16, 17, 18, 19, 20.
  • So there are 20 snowflakes in all.
• Answer: 20 snowflakes

[Medium] Comparing Numbers

• EN: Which number is greater: 13 or 17?
• FR: Quel nombre est plus grand : 13 ou 17?
• Choices: A) 13 B) 17 C) They are equal D) 10
• Hint: When you compare numbers, the one farther along on the number line is greater — like 9 is greater than 6.
• Steps:
  • On a number line, 17 comes after 13.
  • So 17 is greater than 13.
• Answer: 17

[Medium] Skip Counting by 5s

• EN: Mia counts her stickers by 5s: 5, 10, 15, ___. What number comes next?
• FR: Mia compte ses autocollants par bonds de 5 : 5, 10, 15, ___. Quel nombre vient ensuite?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: Skip counting by 5s means adding 5 each time — like 10, 15, then 20.
• Steps:
  • The pattern adds 5 each time: 5, 10, 15, ...
  • Add 5 to 15: 15 + 5 = 20.
• Answer: 20

[Medium] Pennies and Nickels

• EN: Omar has 2 nickels and 3 pennies. How many cents does he have in total?
• FR: Omar a 2 pièces de 5 cents et 3 pennies. Combien de cents a-t-il en tout?
• Choices: A) 11 cents B) 12 cents C) 13 cents D) 14 cents
• Hint: A nickel is worth 5 cents — so 3 nickels would be 5 + 5 + 5 = 15 cents, then add the pennies.
• Steps:
  • 2 nickels = 5 + 5 = 10 cents.
  • 3 pennies = 3 cents.
  • 10 + 3 = 13 cents.
• Answer: 13 cents

[Hard] Missing Number

• EN: 8 + ___ = 15. What is the missing number?
• FR: 8 + ___ = 15. Quel est le nombre manquant?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: To find a missing addend, subtract — like 9 + ___ = 14 means 14 − 9 = 5.
• Steps:
  • We need to find what to add to 8 to get 15.
  • 15 − 8 = 7.
  • The missing number is 7.
• Answer: 7

[Hard] Counting to 100

• EN: Noah counts by 10s starting at 10. Which list shows his count correctly up to 50?
• FR: Noah compte par bonds de 10 à partir de 10. Quelle liste montre correctement son compte jusqu'à 50?
• Choices: A) 10, 20, 30, 40, 50 B) 10, 15, 20, 25, 50 C) 10, 20, 25, 40, 50 D) 10, 20, 30, 35, 50
• Hint: Skip counting by 10s always adds 10 — like 20, 30, 40 is correct but 20, 25, 40 is not.
• Steps:
  • Each step adds exactly 10: 10 + 10 = 20, 20 + 10 = 30, 30 + 10 = 40, 40 + 10 = 50.
  • The correct list is 10, 20, 30, 40, 50.
• Answer: 10, 20, 30, 40, 50

[Easy] Adding at the Market

• EN: Priya buys a muffin for 35 cents and a juice for 40 cents. How much does she spend in total?
• FR: Priya achète un muffin pour 35 cents et un jus pour 40 cents. Combien dépense-t-elle en tout?
• Choices: A) 65 cents B) 70 cents C) 75 cents D) 80 cents
• Hint: To add tens and ones separately — like 23 + 40: add the tens (20 + 40 = 60), then add the ones (3), to get 63.
• Steps:
  • Tens: 30 + 40 = 70. Ones: 5 + 0 = 5.
  • 70 + 5 = 75 cents.
• Answer: 75 cents

[Easy] Telling Time

• EN: The clock shows 3 o'clock. What time is it?
• FR: L'horloge indique 3 heures. Quelle heure est-il?
• Choices: A) 2:00 B) 3:00 C) 3:30 D) 4:00
• Hint: When the minute hand points to 12 and the hour hand points to a number, it is that number o'clock — like hour hand on 7 means 7:00.
• Steps:
  • The hour hand is on 3 and the minute hand is on 12.
  • That means it is exactly 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 than the eraser?
• FR: Un crayon mesure 15 cm et une gomme mesure 4 cm. De combien le crayon est-il plus long que la gomme?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 12 cm
• Hint: To find the difference in length, subtract — like 18 cm − 5 cm = 13 cm.
• Steps:
  • 15 − 4 = 11.
  • The pencil is 11 cm longer than the eraser.
• Answer: 11 cm

[Easy] Simple Patterns

• EN: Look at this pattern: circle, square, circle, square, circle, ___. What shape comes next?
• FR: Regarde ce motif : cercle, carré, cercle, carré, cercle, ___. Quelle forme vient ensuite?
• Choices: A) Circle B) Square C) Triangle D) Rectangle
• Hint: Find the repeating unit in a pattern — like triangle, star, triangle, star repeats every 2 shapes.
• Steps:
  • The pattern repeats: circle, square, circle, square, ...
  • After circle comes square.
• Answer: Square

[Medium] Subtraction Within 100

• EN: A bag has 82 marbles. James takes out 37 marbles. How many marbles are left in the bag?
• FR: Un sac contient 82 billes. James en retire 37. Combien de billes reste-t-il dans le sac?
• Choices: A) 43 marbles B) 44 marbles C) 45 marbles D) 46 marbles
• Hint: To subtract with regrouping — like 74 − 28: regroup 74 as 60 + 14, then subtract 2 tens and 8 ones: 60 − 20 = 40, 14 − 8 = 6, so 46.
• Steps:
  • 82 − 37: regroup 82 as 70 + 12.
  • 70 − 30 = 40, 12 − 7 = 5.
  • 40 + 5 = 45 marbles.
• Answer: 45 marbles

[Medium] Telling Time — Half Hour

• EN: Sofia starts reading at 6:00 and reads for half an hour. What time does she finish?
• FR: Sofia commence à lire à 6 h et lit pendant une demi-heure. À quelle heure finit-elle?
• Choices: A) 6:15 B) 6:30 C) 6:45 D) 7:00
• Hint: Half an hour is 30 minutes — like starting at 4:00 and adding 30 minutes gives 4:30.
• Steps:
  • 6:00 + 30 minutes = 6:30.
  • Sofia finishes at 6:30.
• Answer: 6:30

[Medium] Counting Coins

• EN: Theo has 1 quarter (25 cents), 2 dimes, and 1 nickel. How many cents does he have in total?
• FR: Theo a 1 pièce de 25 cents, 2 pièces de 10 cents et 1 pièce de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 50 cents B) 55 cents C) 60 cents D) 65 cents
• Hint: Add coin values one at a time — like 25 + 10 = 35, then 35 + 10 = 45, then add the rest.
• Steps:
  • Quarter = 25, two dimes = 10 + 10 = 20, nickel = 5.
  • 25 + 20 + 5 = 50 cents.
• Answer: 50 cents

[Medium] Measuring in Metres

• EN: A garden fence is 3 metres long and another side is 5 metres long. How long are both sides together?
• FR: Une clôture de jardin mesure 3 mètres de long et un autre côté mesure 5 mètres de long. Quelle est la longueur des deux côtés ensemble?
• Choices: A) 6 metres B) 7 metres C) 8 metres D) 9 metres
• Hint: Adding lengths works just like adding numbers — like 4 m + 6 m = 10 m.
• Steps:
  • 3 metres + 5 metres = 8 metres.
  • Both sides together are 8 metres long.
• Answer: 8 metres

[Hard] Two-Step Problem

• EN: A box holds 50 crayons. Ava puts in 18 more, then takes out 24. How many crayons are in the box now?
• FR: Une boîte contient 50 crayons. Ava en ajoute 18, puis en retire 24. Combien de crayons y a-t-il maintenant dans la boîte?
• Choices: A) 42 crayons B) 43 crayons C) 44 crayons D) 45 crayons
• Hint: Do two steps — like starting with 30, adding 10 gives 40, then subtracting 15 gives 25.
• Steps:
  • Step 1: 50 + 18 = 68 crayons.
  • Step 2: 68 − 24 = 44 crayons.
  • There are 44 crayons in the box now.
• Answer: 44 crayons

[Hard] Number Pattern

• EN: The pattern is 95, 85, 75, 65, ___. What number comes next?
• FR: Le motif est 95, 85, 75, 65, ___. Quel nombre vient ensuite?
• Choices: A) 50 B) 55 C) 60 D) 70
• Hint: Find what is being subtracted each time — like 60, 50, 40 subtracts 10 each step, so next is 30.
• Steps:
  • Each number decreases by 10: 95 − 10 = 85, 85 − 10 = 75, 75 − 10 = 65.
  • 65 − 10 = 55.
• Answer: 55

[Easy] Multiplication by 2

• EN: There are 6 pairs of mittens in a bin. How many mittens are there in total?
• FR: Il y a 6 paires de mitaines dans un bac. Combien y a-t-il de mitaines en tout?
• Choices: A) 8 mittens B) 10 mittens C) 12 mittens D) 14 mittens
• Hint: Multiplying by 2 means adding a number to itself — like 5 × 2 = 5 + 5 = 10.
• Steps:
  • 6 pairs × 2 mittens each = 6 × 2 = 12.
  • There are 12 mittens in total.
• Answer: 12 mittens

[Easy] Fractions — One Half

• EN: A pizza is cut into 2 equal pieces. Max eats 1 piece. What fraction of the pizza did he eat?
• FR: Une pizza est coupée en 2 morceaux égaux. Max mange 1 morceau. Quelle fraction de la pizza a-t-il mangée?
• Choices: A) 1/4 B) 1/3 C) 1/2 D) 2/3
• Hint: A fraction has a numerator (pieces eaten) over a denominator (total pieces) — like eating 1 out of 4 pieces is 1/4.
• Steps:
  • Total pieces = 2. Pieces eaten = 1.
  • Fraction = 1/2.
• Answer: 1/2

[Easy] Multiplication by 5

• EN: A Tim Hortons worker puts 5 timbits in each bag. If there are 4 bags, how many timbits are there?
• FR: Un employé de Tim Hortons met 5 beignes Timbits dans chaque sac. S'il y a 4 sacs, combien y a-t-il de Timbits en tout?
• Choices: A) 15 timbits B) 18 timbits C) 20 timbits D) 25 timbits
• Hint: Multiplying by 5 — skip count by 5s: like 3 × 5 = 5, 10, 15.
• Steps:
  • 4 × 5 = 20.
  • There are 20 timbits in total.
• Answer: 20 timbits

[Easy] Perimeter

• EN: A rectangle has a length of 6 cm and a width of 3 cm. What is its perimeter?
• FR: Un rectangle a une longueur de 6 cm et une largeur de 3 cm. Quel est son périmètre?
• Choices: A) 9 cm B) 16 cm C) 18 cm D) 24 cm
• Hint: Perimeter = add all sides — like a rectangle with length 5 and width 2 has perimeter 5 + 5 + 2 + 2 = 14.
• Steps:
  • Perimeter = 6 + 6 + 3 + 3 = 18 cm.
  • The perimeter is 18 cm.
• Answer: 18 cm

[Medium] Division

• EN: 24 stickers are shared equally among 4 friends. How many stickers does each friend get?
• FR: 24 autocollants sont partagés également entre 4 amis. Combien d'autocollants chaque ami reçoit-il?
• Choices: A) 4 stickers B) 5 stickers C) 6 stickers D) 8 stickers
• Hint: Division is sharing equally — like 15 ÷ 3: think "3 × ? = 15", so ? = 5.
• Steps:
  • 24 ÷ 4: think "4 × ? = 24" → 4 × 6 = 24.
  • Each friend gets 6 stickers.
• Answer: 6 stickers

[Medium] Multiplication by 3

• EN: Each loonie bag holds 3 loonies. If there are 8 bags, how many loonies are there altogether?
• FR: Chaque sac de dollars contient 3 pièces de 1 $. S'il y a 8 sacs, combien y a-t-il de pièces en tout?
• Choices: A) 21 loonies B) 24 loonies C) 27 loonies D) 32 loonies
• Hint: 8 × 3 — skip count by 3s eight times: 3, 6, 9, 12, 15, 18, 21 for 7 times gives 21, one more gives 24.
• Steps:
  • 8 × 3 = 24.
  • There are 24 loonies altogether.
• Answer: 24 loonies

[Medium] Reading a Graph

• EN: A bar graph shows students' favourite seasons. Winter: 8 students, Summer: 12 students. How many more students prefer summer over winter?
• FR: Un diagramme à barres montre les saisons préférées des élèves. Hiver : 8 élèves, Été : 12 élèves. Combien d'élèves de plus préfèrent l'été à l'hiver?
• Choices: A) 2 students B) 3 students C) 4 students D) 5 students
• Hint: To find "how many more," subtract the smaller value from the larger — like 15 − 9 = 6 more.
• Steps:
  • 12 − 8 = 4.
  • 4 more students prefer summer over winter.
• Answer: 4 students

[Medium] Fractions — One Quarter

• EN: Bella has 12 grapes and eats 1/4 of them. How many grapes does she eat?
• FR: Bella a 12 raisins et en mange 1/4. Combien de raisins mange-t-elle?
• Choices: A) 2 grapes B) 3 grapes C) 4 grapes D) 6 grapes
• Hint: To find 1/4 of a number, divide it by 4 — like 1/4 of 20 = 20 ÷ 4 = 5.
• Steps:
  • 1/4 of 12 = 12 ÷ 4 = 3.
  • Bella eats 3 grapes.
• Answer: 3 grapes

[Hard] Two-Step Multiplication and Subtraction

• EN: A hockey team scores 4 goals in each of 3 games, but 2 goals were disallowed in total. How many goals count?
• FR: Une équipe de hockey marque 4 buts dans chacun des 3 matchs, mais 2 buts ont été annulés au total. Combien de buts comptent?
• Choices: A) 8 goals B) 9 goals C) 10 goals D) 12 goals
• Hint: First multiply, then subtract — like 3 games × 5 goals = 15, then 15 − 3 disallowed = 12.
• Steps:
  • Step 1: 4 × 3 = 12 total goals.
  • Step 2: 12 − 2 = 10 goals that count.
• Answer: 10 goals

[Hard] Perimeter with Unknown Side

• EN: A triangle has two sides that are each 7 cm long. Its perimeter is 22 cm. How long is the third side?
• FR: Un triangle a deux côtés qui mesurent chacun 7 cm. Son périmètre est de 22 cm. Quelle est la longueur du troisième côté?
• Choices: A) 6 cm B) 7 cm C) 8 cm D) 9 cm
• Hint: Perimeter = sum of all sides, so the unknown side = perimeter − the two known sides — like 20 − 6 − 6 = 8.
• Steps:
  • Known sides: 7 + 7 = 14 cm.
  • Third side = 22 − 14 = 8 cm.
• Answer: 8 cm

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: To find 7 × 8, think of it as 7 × 4 doubled — like 7 × 4 = 28, so 7 × 8 = 56.
• Steps:
  • 7 × 8: use the fact that 8 × 7 = 56.
  • The answer is 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: What is the value of the digit 4 in the number 3.47?
• FR: Quelle est la valeur du chiffre 4 dans le nombre 3,47?
• Choices: A) 4 ones B) 4 tenths C) 4 hundredths D) 40
• Hint: In a decimal, the first digit after the point is tenths, the second is hundredths — like in 2.58, the 5 is in the tenths place.
• Steps:
  • 3.47: the digit 4 is in the first position after the decimal point.
  • That position is the tenths place, so 4 tenths.
• Answer: 4 tenths

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 1/2?
• FR: Quelle fraction est plus grande : 3/4 ou 1/2?
• Choices: A) 1/2 B) 3/4 C) They are equal D) 1/4
• Hint: Convert to the same denominator — like comparing 2/4 and 3/4: 3/4 is greater.
• Steps:
  • Convert 1/2 to fourths: 1/2 = 2/4.
  • Compare 3/4 and 2/4: 3/4 is greater.
• Answer: 3/4

[Easy] Area of a Rectangle

• EN: A rectangular garden is 9 m long and 4 m wide. What is its area?
• FR: Un jardin rectangulaire mesure 9 m de long et 4 m de large. Quelle est son aire?
• Choices: A) 26 m² B) 32 m² C) 36 m² D) 40 m²
• Hint: Area of a rectangle = length × width — like 7 m × 3 m = 21 m².
• Steps:
  • Area = 9 × 4 = 36 m².
  • The area of the garden is 36 m².
• Answer: 36 m²

[Medium] Long Division with Remainders

• EN: 47 students are divided into groups of 5. How many full groups are there, and how many students are left over?
• FR: 47 élèves sont divisés en groupes de 5. Combien de groupes complets y a-t-il, et combien d'élèves reste-t-il?
• Choices: A) 8 groups, 5 left over B) 9 groups, 2 left over C) 9 groups, 3 left over D) 10 groups, 2 left over
• Hint: Divide then find the remainder — like 23 ÷ 4 = 5 remainder 3, because 4 × 5 = 20 and 23 − 20 = 3.
• Steps:
  • 5 × 9 = 45. Remainder: 47 − 45 = 2.
  • There are 9 full groups with 2 students left over.
• Answer: 9 groups, 2 left over

[Medium] Decimal Operations

• EN: A water bottle holds 1.75 litres and a juice box holds 0.50 litres. How much liquid is there altogether?
• FR: Une bouteille d'eau contient 1,75 litre et une boîte de jus contient 0,50 litre. Quelle est la quantité totale de liquide?
• Choices: A) 1.95 litres B) 2.05 litres C) 2.15 litres D) 2.25 litres
• Hint: Line up the decimal points when adding — like 2.30 + 0.45: add hundredths, tenths, then ones.
• Steps:
  • 1.75 + 0.50: hundredths 5 + 0 = 5, tenths 7 + 5 = 12 (write 2 carry 1), ones 1 + 0 + 1 = 2.
  • Total = 2.25 litres.
• Answer: 2.25 litres

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 PM and ends at 3:45 PM. 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) 3 hours
• Hint: Count forward in chunks — like from 2:20 to 4:50: add 2 hours to get 4:20, then 30 more minutes = 2 hours 30 minutes total.
• Steps:
  • From 1:15 to 3:15 = 2 hours. From 3:15 to 3:45 = 30 more minutes.
  • Total = 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] All Multiplication Tables

• EN: A bookstore puts 9 books on each of 6 shelves. How many books are on the shelves altogether?
• FR: Une librairie place 9 livres sur chacune de ses 6 étagères. Combien de livres y a-t-il sur les étagères en tout?
• Choices: A) 48 books B) 54 books C) 56 books D) 63 books
• Hint: 9 × 6 — think of 9 × 5 = 45, then add one more group of 9: 45 + 9 = 54.
• Steps:
  • 9 × 6 = 54.
  • There are 54 books altogether.
• Answer: 54 books

[Hard] Multi-Step Word Problem

• EN: Mei earns $7 for each hour she rakes leaves. She works for 8 hours, then spends $32 on a book. How much money does she have left?
• FR: Mei gagne 7 $ de l'heure pour râteler les feuilles. Elle travaille 8 heures, puis dépense 32 $ pour un livre. Combien d'argent lui reste-t-il?
• Choices: A) $22 B) $24 C) $26 D) $28
• Hint: First multiply to find total earnings, then subtract the cost — like 6 hours × $8 = $48, then $48 − $20 = $28.
• Steps:
  • Step 1: 7 × 8 = $56 earned.
  • Step 2: $56 − $32 = $24 left.
• Answer: $24

[Hard] Long Division with Multi-Digit Dividend

• EN: A farmer packs 96 apples equally into 6 bags. How many apples are in each bag?
• FR: Un fermier emballe 96 pommes également dans 6 sacs. Combien de pommes y a-t-il dans chaque sac?
• Choices: A) 14 apples B) 15 apples C) 16 apples D) 18 apples
• Hint: Divide the tens first, then the ones — like 84 ÷ 6: 6 goes into 8 once (remainder 2), bring down 4, 6 goes into 24 four times: answer is 14.
• Steps:
  • 96 ÷ 6: 6 goes into 9 once (remainder 3), bring down 6, 6 goes into 36 six times.
  • 96 ÷ 6 = 16 apples per bag.
• Answer: 16 apples

[Easy] Multi-Digit Multiplication

• EN: A school orders 24 boxes of pencils with 12 pencils in each box. How many pencils are there in total?
• FR: Une école commande 24 boîtes de crayons contenant 12 crayons chacune. Combien y a-t-il de crayons en tout?
• Choices: A) 248 pencils B) 268 pencils C) 288 pencils D) 298 pencils
• Hint: To multiply 24 × 12, break it up: 24 × 10 = 240 and 24 × 2 = 48, then add.
• Steps:
  • 24 × 10 = 240; 24 × 2 = 48.
  • 240 + 48 = 288 pencils.
• Answer: 288 pencils

[Easy] Adding Fractions with Like Denominators

• EN: Emma eats 2/8 of a pie and her brother eats 3/8. How much of the pie did they eat together?
• FR: Emma mange 2/8 d'une tarte et son frère en mange 3/8. Quelle fraction de la tarte ont-ils mangée ensemble?
• Choices: A) 4/8 B) 5/8 C) 5/16 D) 6/8
• Hint: When denominators are the same, just add the numerators — like 3/7 + 2/7 = 5/7.
• Steps:
  • 2/8 + 3/8 = (2 + 3)/8 = 5/8.
  • They ate 5/8 of the pie together.
• Answer: 5/8

[Easy] Percentage — 50%

• EN: A sweater costs $40. It is on sale for 50% off. How much is the discount?
• FR: Un chandail coûte 40 $. Il est en solde à 50 % de rabais. Quel est le montant du rabais?
• Choices: A) $10 B) $15 C) $20 D) $25
• Hint: 50% means half — like 50% of $60 = $60 ÷ 2 = $30.
• Steps:
  • 50% of $40 = $40 ÷ 2 = $20.
  • The discount is $20.
• Answer: $20

[Easy] Decimal Operations — Addition

• EN: Leo runs 3.4 km on Monday and 2.8 km on Tuesday. How far does he run in total?
• FR: Léo court 3,4 km lundi et 2,8 km mardi. Quelle distance parcourt-il en tout?
• Choices: A) 5.8 km B) 6.0 km C) 6.2 km D) 6.4 km
• Hint: Add decimals by lining up the decimal point — like 4.5 + 1.7: ones 4 + 1 = 5, tenths 5 + 7 = 12, carry the 1: total 6.2.
• Steps:
  • 3.4 + 2.8: tenths 4 + 8 = 12, write 2 carry 1; ones 3 + 2 + 1 = 6.
  • Total = 6.2 km.
• Answer: 6.2 km

[Medium] Multi-Digit Division

• EN: A warehouse has 432 cans of soup to be packed equally into 16 boxes. How many cans go in each box?
• FR: Un entrepôt a 432 boîtes de soupe à emballer également dans 16 boîtes. Combien de boîtes y a-t-il dans chaque carton?
• Choices: A) 24 cans B) 26 cans C) 27 cans D) 28 cans
• Hint: For long division, estimate first — like 400 ÷ 16 ≈ 25, then refine.
• Steps:
  • 16 × 27 = 16 × 20 + 16 × 7 = 320 + 112 = 432. ✓
  • Each box holds 27 cans.
• Answer: 27 cans

[Medium] Subtracting Fractions with Like Denominators

• EN: A bucket is 7/10 full of water. If 3/10 evaporates, how full is it now?
• FR: Un seau est rempli à 7/10 avec de l'eau. Si 3/10 s'évapore, à quel niveau est-il maintenant?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 6/10
• Hint: Subtract numerators when denominators match — like 9/11 − 4/11 = 5/11.
• Steps:
  • 7/10 − 3/10 = (7 − 3)/10 = 4/10.
  • The bucket is 4/10 full.
• Answer: 4/10

[Medium] Volume of a Rectangular Prism

• EN: A sandbox is 5 m long, 3 m wide, and 1 m deep. What is its volume?
• FR: Un bac à sable mesure 5 m de long, 3 m de large et 1 m de profondeur. Quel est son volume?
• Choices: A) 9 m³ B) 12 m³ C) 15 m³ D) 18 m³
• Hint: Volume = length × width × height — like 4 × 2 × 3 = 24 m³.
• Steps:
  • Volume = 5 × 3 × 1 = 15 m³.
  • The sandbox has a volume of 15 m³.
• Answer: 15 m³

[Medium] Percentage — 25%

• EN: A hockey team won 25% of their 20 games. How many games did they win?
• FR: Une équipe de hockey a gagné 25 % de ses 20 matchs. Combien de matchs ont-ils gagnés?
• Choices: A) 4 games B) 5 games C) 6 games D) 7 games
• Hint: 25% is one quarter — find 1/4 of a number by dividing by 4 — like 25% of 28 = 28 ÷ 4 = 7.
• Steps:
  • 25% of 20 = 20 ÷ 4 = 5.
  • The team won 5 games.
• Answer: 5 games

[Hard] Multi-Step Fraction and Whole Number Problem

• EN: A recipe uses 3/5 of a cup of oats. If Chen makes 4 batches, how many cups of oats does he need in total?
• FR: Une recette utilise 3/5 de tasse d'avoine. Si Chen prépare 4 recettes, de combien de tasses d'avoine a-t-il besoin en tout?
• Choices: A) 2 cups B) 2 and 2/5 cups C) 3 cups D) 3 and 2/5 cups
• Hint: Multiply a fraction by a whole number — like 4 × 2/3 = 8/3 = 2 and 2/3.
• Steps:
  • 4 × 3/5 = 12/5.
  • 12/5 = 2 remainder 2, so 2 and 2/5 cups.
• Answer: 2 and 2/5 cups

[Hard] Decimal Multiplication

• EN: A school store sells notebooks for $2.35 each. If a teacher buys 6 notebooks, what is the total cost?
• FR: La boutique scolaire vend des cahiers à 2,35 $ chacun. Si un enseignant en achète 6, quel est le coût total?
• Choices: A) $13.90 B) $14.10 C) $14.30 D) $14.70
• Hint: Multiply as if there's no decimal — like 3.25 × 4: think 325 × 4 = 1300, then place the decimal to get 13.00.
• Steps:
  • 235 × 6 = 1410. The original number has 2 decimal places.
  • So 2.35 × 6 = $14.10.
• Answer: $14.10

[Easy] Percent of a Number

• EN: What is 30% of 80?
• FR: Combien représente 30 % de 80?
• Choices: A) 20 B) 24 C) 28 D) 32
• Hint: Find 10% first then multiply — like 10% of 50 = 5, so 30% of 50 = 5 × 3 = 15.
• Steps:
  • 10% of 80 = 8.
  • 30% = 8 × 3 = 24.
• Answer: 24

[Easy] Ratios

• EN: In a class, there are 12 boys and 16 girls. What is the ratio of boys to girls in simplest form?
• FR: Dans une classe, il y a 12 garçons et 16 filles. Quel est le rapport des garçons aux filles sous sa forme simplifiée?
• Choices: A) 3:4 B) 4:3 C) 6:8 D) 12:16
• Hint: Simplify a ratio by dividing both parts by their GCF — like 8:12 ÷ 4 = 2:3.
• Steps:
  • GCF of 12 and 16 is 4.
  • 12 ÷ 4 = 3, 16 ÷ 4 = 4. Ratio = 3:4.
• Answer: 3:4

[Easy] Integers — Introduction

• EN: The temperature in Winnipeg is −8°C in the morning and rises to 3°C by noon. By how many degrees did it rise?
• FR: La température à Winnipeg est de −8°C le matin et monte à 3°C à midi. De combien de degrés a-t-elle monté?
• Choices: A) 5°C B) 9°C C) 11°C D) 13°C
• Hint: To find the change, subtract the starting temperature from the ending one — like from −5 to 4 is 4 − (−5) = 9 degrees.
• Steps:
  • Change = 3 − (−8) = 3 + 8 = 11°C.
  • The temperature rose 11°C.
• Answer: 11°C

[Easy] Order of Operations — BEDMAS

• EN: Evaluate: 4 + 2 × 5
• FR: Calcule : 4 + 2 × 5
• Choices: A) 12 B) 14 C) 15 D) 30
• Hint: BEDMAS says multiplication comes before addition — like 3 + 4 × 2 = 3 + 8 = 11 (not 7 × 2).
• Steps:
  • Multiplication first: 2 × 5 = 10.
  • Then addition: 4 + 10 = 14.
• Answer: 14

[Medium] Fraction Multiplication

• EN: A recipe needs 2/3 of a cup of sugar. Aria makes 3/4 of the recipe. How much sugar does she need?
• FR: Une recette nécessite 2/3 de tasse de sucre. Aria prépare 3/4 de la recette. De quelle quantité de sucre a-t-elle besoin?
• Choices: A) 1/4 B) 5/12 C) 1/2 D) 2/3
• Hint: Multiply fractions by multiplying numerators and denominators — like 2/5 × 3/4 = 6/20 = 3/10.
• Steps:
  • 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2.
  • Aria needs 1/2 cup of sugar.
• Answer: 1/2

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in kilometres per hour?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en kilomètres par heure?
• Choices: A) 60 km/h B) 70 km/h C) 80 km/h D) 90 km/h
• Hint: Rate = total ÷ time — like 150 km in 2 hours = 150 ÷ 2 = 75 km/h.
• Steps:
  • Speed = 240 ÷ 3 = 80 km/h.
  • The car's speed is 80 km/h.
• Answer: 80 km/h

[Medium] Simple Algebraic Expressions

• EN: Evaluate 3n + 5 when n = 4.
• FR: Calcule 3n + 5 quand n = 4.
• Choices: A) 12 B) 15 C) 17 D) 20
• Hint: Substitute the value into the expression — like if n = 3 in 4n + 2: 4 × 3 + 2 = 12 + 2 = 14.
• Steps:
  • 3 × 4 + 5 = 12 + 5 = 17.
  • The value of the expression is 17.
• Answer: 17

[Medium] Fraction Division

• EN: How many 1/4-cup servings are in 3 cups of juice?
• FR: Combien de portions de 1/4 de tasse y a-t-il dans 3 tasses de jus?
• Choices: A) 8 servings B) 10 servings C) 12 servings D) 15 servings
• Hint: Dividing by a fraction means multiplying by its reciprocal — like 2 ÷ 1/3 = 2 × 3 = 6.
• Steps:
  • 3 ÷ 1/4 = 3 × 4 = 12.
  • There are 12 servings.
• Answer: 12 servings

[Hard] Multi-Step Percent Problem

• EN: A jacket costs $120. It is on sale at 15% off. How much does the jacket cost after the discount?
• FR: Un manteau coûte 120 $. Il est en solde avec 15 % de rabais. Combien coûte le manteau après la réduction?
• Choices: A) $96 B) $100 C) $102 D) $108
• Hint: Find the discount first, then subtract — like 20% of $80 = $16, so the sale price is $80 − $16 = $64.
• Steps:
  • 15% of $120 = 0.15 × 120 = $18.
  • Sale price = $120 − $18 = $102.
• Answer: $102

[Hard] BEDMAS with Brackets

• EN: Evaluate: (3 + 7) × 2 − 4 ÷ 2
• FR: Calcule : (3 + 7) × 2 − 4 ÷ 2
• Choices: A) 16 B) 18 C) 20 D) 22
• Hint: Follow BEDMAS — Brackets first, then multiply/divide left to right, then add/subtract — like (2 + 3) × 4 − 6 ÷ 2 = 20 − 3 = 17.
• Steps:
  • Brackets: (3 + 7) = 10.
  • Multiply: 10 × 2 = 20. Divide: 4 ÷ 2 = 2.
  • Subtract: 20 − 2 = 18.
• Answer: 18

[Easy] Integer Addition

• EN: The temperature drops from 5°C to −6°C. What is the change in temperature?
• FR: La température passe de 5°C à −6°C. Quel est le changement de température?
• Choices: A) −1°C B) −11°C C) 1°C D) 11°C
• Hint: Change = final − initial — like from 3 to −4 is −4 − 3 = −7.
• Steps:
  • Change = −6 − 5 = −11°C.
  • The temperature changed by −11°C (dropped 11 degrees).
• Answer: −11°C

[Easy] Percentage — Discount

• EN: A pair of skates costs $80. They are on sale for 20% off. What is the sale price?
• FR: Une paire de patins coûte 80 $. Elle est en solde à 20 % de rabais. Quel est le prix de vente?
• Choices: A) $56 B) $60 C) $64 D) $68
• Hint: Find the discount then subtract — like 10% of $90 = $9, so 20% = $18, sale price = $90 − $18 = $72.
• Steps:
  • 20% of $80 = $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 isolate x, subtract the same number from both sides — like x + 5 = 11 → x = 11 − 5 = 6.
• Steps:
  • x + 9 = 17 → x = 17 − 9 = 8.
  • x = 8.
• Answer: x = 8

[Easy] Integer Subtraction

• EN: Calculate: −3 − 4
• FR: Calcule : −3 − 4
• Choices: A) −8 B) −7 C) 1 D) 7
• Hint: Subtracting a positive from a negative makes it more negative — like −2 − 5 = −7.
• Steps:
  • −3 − 4 = −7.
  • The answer is −7.
• Answer: −7

[Medium] Percentage — Tax

• EN: A book costs $15.00. If the HST is 13%, what is the total cost including tax?
• FR: Un livre coûte 15,00 $. Si la TVH est de 13 %, quel est le coût total incluant la taxe?
• Choices: A) $16.75 B) $16.95 C) $17.45 D) $18.15
• Hint: Find the tax amount, then add to original — like 10% of $20 = $2, 13% = $2.60, total = $22.60.
• Steps:
  • Tax = 13% of $15.00 = 0.13 × 15 = $1.95.
  • Total = $15.00 + $1.95 = $16.95.
• Answer: $16.95

[Medium] Fraction and Decimal Fluency

• EN: Write 0.375 as a fraction in simplest form.
• FR: Écris 0,375 sous forme de fraction en termes les plus simples.
• Choices: A) 3/8 B) 37/100 C) 3/7 D) 375/100
• Hint: Write the decimal as a fraction over 1000, then simplify — like 0.5 = 5/10 = 1/2.
• Steps:
  • 0.375 = 375/1000. GCF of 375 and 1000 is 125.
  • 375 ÷ 125 = 3; 1000 ÷ 125 = 8. Simplified = 3/8.
• Answer: 3/8

[Medium] Surface Area

• EN: A rectangular prism has length 5 cm, width 4 cm, and height 3 cm. What is its surface area?
• FR: Un prisme rectangulaire a une longueur de 5 cm, une largeur de 4 cm et une hauteur de 3 cm. Quelle est son aire totale?
• Choices: A) 60 cm² B) 74 cm² C) 94 cm² D) 120 cm²
• Hint: Surface area = 2(lw + lh + wh) — like 2(3×2 + 3×4 + 2×4) = 2(6+12+8) = 52 cm².
• Steps:
  • lw = 5×4 = 20, lh = 5×3 = 15, wh = 4×3 = 12.
  • SA = 2(20 + 15 + 12) = 2 × 47 = 94 cm².
• Answer: 94 cm²

[Medium] Probability

• EN: A bag has 3 red marbles, 4 blue marbles, and 3 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 4 billes bleues et 3 billes vertes. Quelle est la probabilité de choisir une bille bleue?
• Choices: A) 2/5 B) 3/10 C) 4/10 D) 1/3
• Hint: Probability = favourable outcomes ÷ total outcomes — like 2 red out of 8 total = 2/8 = 1/4.
• Steps:
  • Total marbles = 3 + 4 + 3 = 10.
  • P(blue) = 4/10 = 2/5.
• Answer: 2/5

[Hard] Integer Multiplication and Division

• EN: Evaluate: (−4) × 3 ÷ (−6)
• FR: Calcule : (−4) × 3 ÷ (−6)
• Choices: A) −2 B) 2 C) −8 D) 6
• Hint: Work left to right — like (−6) × 2 ÷ (−4): first −6 × 2 = −12, then −12 ÷ (−4) = 3 (negative ÷ negative = positive).
• Steps:
  • (−4) × 3 = −12.
  • −12 ÷ (−6) = 2 (negative divided by negative is positive).
• Answer: 2

[Hard] Two-Step Equation

• EN: Solve: 2x − 5 = 11
• FR: Résous : 2x − 5 = 11
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: Add 5 to both sides first, then divide — like 3x − 4 = 8: add 4 → 3x = 12, divide by 3 → x = 4.
• Steps:
  • 2x − 5 = 11 → add 5 to both sides: 2x = 16.
  • Divide by 2: x = 8.
• Answer: x = 8

[Easy] Perfect Squares

• EN: What is √144?
• FR: Quelle est la valeur de √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: A perfect square root asks "what number times itself gives this?" — like √81 = 9 because 9 × 9 = 81.
• Steps:
  • 12 × 12 = 144.
  • So √144 = 12.
• Answer: 12

[Easy] Mean

• EN: Five students scored 72, 85, 90, 68, and 80 on a math test. What is the mean score?
• FR: Cinq élèves ont obtenu 72, 85, 90, 68 et 80 à un test de mathématiques. Quelle est la note moyenne?
• Choices: A) 77 B) 79 C) 81 D) 83
• Hint: Mean = sum ÷ count — like (10 + 20 + 30) ÷ 3 = 60 ÷ 3 = 20.
• Steps:
  • Sum = 72 + 85 + 90 + 68 + 80 = 395.
  • Mean = 395 ÷ 5 = 79.
• Answer: 79

[Easy] Percent Increase

• EN: A hockey stick's price went from $60 to $75. What is the percent increase?
• FR: Le prix d'un bâton de hockey est passé de 60 $ à 75 $. Quel est le pourcentage d'augmentation?
• Choices: A) 15% B) 20% C) 25% D) 30%
• Hint: Percent increase = (change ÷ original) × 100 — like price goes from $40 to $50: change = $10, 10 ÷ 40 × 100 = 25%.
• Steps:
  • Change = $75 − $60 = $15.
  • Percent increase = (15 ÷ 60) × 100 = 25%.
• Answer: 25%

[Easy] Two-Step Linear Equation

• EN: Solve: 3x + 4 = 19
• FR: Résous : 3x + 4 = 19
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Subtract the constant first, then divide — like 4x + 3 = 19: subtract 3 → 4x = 16, divide by 4 → x = 4.
• Steps:
  • 3x + 4 = 19 → 3x = 15 → x = 5.
  • x = 5.
• Answer: x = 5

[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: Use a² + b² = c² — like legs 3 and 4: 9 + 16 = 25, so c = 5.
• Steps:
  • a² + b² = c²: 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope Introduction

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

[Medium] Median and Mode

• EN: Find the median of the data set: 5, 9, 3, 7, 5, 11, 4
• FR: Trouve la médiane de cet ensemble de données : 5, 9, 3, 7, 5, 11, 4
• Choices: A) 4 B) 5 C) 7 D) 9
• Hint: Sort the data first, then find the middle value — like 2, 4, 6, 8, 10: the middle (3rd) value is 6.
• Steps:
  • Sorted: 3, 4, 5, 5, 7, 9, 11. There are 7 values.
  • The middle (4th) value is 5.
• Answer: 5

[Medium] Percent Decrease

• EN: A store reduces the price of a coat from $200 to $150. What is the percent decrease?
• FR: Un magasin réduit le prix d'un manteau de 200 $ à 150 $. Quel est le pourcentage de diminution?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent decrease = (change ÷ original) × 100 — like $80 drops to $60: change = $20, 20 ÷ 80 × 100 = 25%.
• Steps:
  • Change = $200 − $150 = $50.
  • Percent decrease = (50 ÷ 200) × 100 = 25%.
• Answer: 25%

[Hard] Two-Step Equation with Fractions

• EN: Solve: x/3 + 4 = 9
• FR: Résous : x/3 + 4 = 9
• Choices: A) x = 12 B) x = 15 C) x = 18 D) x = 21
• Hint: Subtract the constant first, then multiply both sides by the denominator — like x/4 + 2 = 7: x/4 = 5, then x = 20.
• Steps:
  • x/3 + 4 = 9 → x/3 = 5 → x = 5 × 3 = 15.
  • x = 15.
• Answer: x = 15

[Hard] Pythagorean Theorem — Find a Leg

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

[Easy] Solving a Linear Equation

• EN: Solve: 4x − 7 = 13
• FR: Résous : 4x − 7 = 13
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add 7 to both sides, then divide by the coefficient — like 3x − 5 = 10: 3x = 15, x = 5.
• Steps:
  • 4x − 7 = 13 → 4x = 20 → x = 5.
  • x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Simplify: (3x + 5) + (2x − 3)
• FR: Simplifie : (3x + 5) + (2x − 3)
• Choices: A) 5x + 2 B) 5x − 2 C) 6x + 2 D) 6x − 2
• Hint: Combine like terms — like (4x + 7) + (x − 2) = 5x + 5.
• Steps:
  • x terms: 3x + 2x = 5x.
  • Constants: 5 + (−3) = 2.
  • Simplified: 5x + 2.
• Answer: 5x + 2

[Easy] Graphing Lines — Slope-Intercept

• 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) 1 C) 2 D) 3
• Hint: In y = mx + b, m is always the slope — like in y = 5x + 1, the slope is 5.
• Steps:
  • The equation is in slope-intercept form: y = mx + b.
  • m = 3, so the slope is 3.
• Answer: 3

[Easy] Linear Inequality

• EN: Solve the inequality: x − 4 > 2
• FR: Résous l'inégalité : x − 4 > 2
• Choices: A) x > 4 B) x > 5 C) x > 6 D) x > 7
• Hint: Solve like an equation — like x − 3 > 5 → x > 8.
• Steps:
  • x − 4 > 2 → add 4 to both sides: 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 — like (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.
  • x² + 4x + 3x + 12 = x² + 7x + 12.
• Answer: x² + 7x + 12

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides in the ratio 2:3. The shorter triangle has a base of 8 cm. What is the base of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants dans le rapport 2:3. Le triangle plus petit a une base de 8 cm. Quelle est la base du plus grand triangle?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 14 cm
• Hint: Set up a proportion — like ratio 3:5, small side = 9, large side = 9 × (5/3) = 15.
• Steps:
  • Ratio 2:3 means large = small × (3/2).
  • 8 × (3/2) = 12 cm.
• Answer: 12 cm

[Medium] Trigonometry — SOH-CAH-TOA

• EN: In a right triangle, the opposite side is 5 cm and the hypotenuse is 13 cm. What is sin(θ)?
• FR: Dans un triangle rectangle, le côté opposé mesure 5 cm et l'hypoténuse mesure 13 cm. Quelle est la valeur de sin(θ)?
• Choices: A) 5/12 B) 5/13 C) 12/13 D) 13/5
• Hint: SOH means sin = opposite ÷ hypotenuse — like opposite = 3, hypotenuse = 5 → sin = 3/5.
• Steps:
  • sin(θ) = opposite ÷ hypotenuse = 5/13.
• Answer: 5/13

[Medium] Subtracting Polynomials

• EN: Simplify: (5x² + 3x − 2) − (2x² − x + 4)
• FR: Simplifie : (5x² + 3x − 2) − (2x² − x + 4)
• Choices: A) 3x² + 2x − 6 B) 3x² + 4x − 6 C) 3x² + 4x + 2 D) 7x² + 2x − 6
• Hint: Distribute the negative sign, then combine like terms — like (4x² + x) − (x² − 3x) = 3x² + 4x.
• Steps:
  • Distribute: 5x² + 3x − 2 − 2x² + x − 4.
  • Combine: (5x² − 2x²) + (3x + x) + (−2 − 4) = 3x² + 4x − 6.
• Answer: 3x² + 4x − 6

[Hard] Graphing — Find y-intercept

• EN: A line has a slope of −2 and passes through the point (3, 1). What is the y-intercept of the line?
• FR: Une droite a une pente de −2 et passe par le point (3, 1). Quelle est l'ordonnée à l'origine de cette droite?
• Choices: A) 5 B) 6 C) 7 D) 8
• Hint: Use y = mx + b, substitute the point to solve for b — like slope = 3, point (2, 8): 8 = 3(2) + b → b = 2.
• Steps:
  • y = mx + b → 1 = (−2)(3) + b → 1 = −6 + b → b = 7.
  • The y-intercept is 7.
• Answer: 7

[Hard] Trigonometry — Finding an Angle

• EN: In a right triangle, the adjacent side is 9 cm and the hypotenuse is 15 cm. What angle θ satisfies this? (Use cos θ = adjacent/hypotenuse and cos 53° ≈ 0.6)
• FR: Dans un triangle rectangle, le côté adjacent mesure 9 cm et l'hypoténuse mesure 15 cm. Quel angle θ satisfait cette condition? (Utilise cos θ = adjacent/hypoténuse et cos 53° ≈ 0,6)
• Choices: A) 37° B) 45° C) 53° D) 60°
• Hint: CAH means cos = adjacent ÷ hypotenuse, then use inverse — like adj=4, hyp=8: cos θ = 0.5 → θ = 60°.
• Steps:
  • cos θ = 9/15 = 0.6.
  • cos 53° ≈ 0.6, so θ = 53°.
• Answer: 53°

[Easy] Factoring a Quadratic

• EN: Factor: x² + 5x + 6
• FR: Factorise : x² + 5x + 6
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 2)(x + 4) D) (x + 3)(x + 3)
• Hint: Find two numbers that multiply to the constant and add to the middle coefficient — like x² + 7x + 12: 3 × 4 = 12, 3 + 4 = 7, so (x+3)(x+4).
• Steps:
  • Need two numbers: product = 6, sum = 5. → 2 × 3 = 6, 2 + 3 = 5. ✓
  • Factored form: (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding a Side

• EN: In a right triangle, angle θ = 30°, hypotenuse = 20 cm. What is the length of the opposite side? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, l'angle θ = 30°, l'hypoténuse = 20 cm. Quelle est la longueur du côté opposé? (sin 30° = 0,5)
• Choices: A) 8 cm B) 9 cm C) 10 cm D) 12 cm
• Hint: opposite = sin(θ) × hypotenuse — like sin 45° × 14 ≈ 0.707 × 14 ≈ 9.9 cm.
• Steps:
  • opposite = sin(30°) × 20 = 0.5 × 20 = 10 cm.
• Answer: 10 cm

[Easy] System of Equations — Inspection

• 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) 5 B) 6 C) 7 D) 8
• Hint: Add the two equations to eliminate y — like x + y = 8 and x − y = 2: add to get 2x = 10, x = 5.
• Steps:
  • Add equations: (x + y) + (x − y) = 10 + 4 → 2x = 14 → x = 7.
• Answer: 7

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 188.4 cm³ B) 251.2 cm³ C) 282.6 cm³ D) 314.0 cm³
• Hint: V = π r² h — like r=2, h=5: V = 3.14 × 4 × 5 = 62.8 cm³.
• Steps:
  • V = π × 3² × 10 = 3.14 × 9 × 10 = 3.14 × 90 = 282.6 cm³.
• Answer: 282.6 cm³

[Medium] Completing the Square

• EN: Solve x² + 6x − 7 = 0 by factoring. What are the solutions?
• FR: Résous x² + 6x − 7 = 0 par factorisation. Quelles sont les solutions?
• Choices: A) x = 1 and x = −7 B) x = −1 and x = 7 C) x = 2 and x = −7 D) x = 3 and x = −7
• Hint: Find factors of −7 that add to 6 — like for x² + 2x − 8: factors of −8 adding to 2 are +4 and −2, giving (x+4)(x−2).
• Steps:
  • Factors of −7 with sum 6: +7 and −1. So (x + 7)(x − 1) = 0.
  • x = −7 or x = 1.
• Answer: x = 1 and x = −7

[Medium] Circle Geometry

• EN: A circle has a diameter of 14 cm. What is the circumference? (Use π ≈ 3.14)
• FR: Un cercle a un diamètre de 14 cm. Quelle est sa circonférence? (Utilise π ≈ 3,14)
• Choices: A) 39.25 cm B) 43.96 cm C) 47.10 cm D) 50.24 cm
• Hint: C = π × d — like d=10: C = 3.14 × 10 = 31.4 cm.
• Steps:
  • C = π × 14 = 3.14 × 14 = 43.96 cm.
• Answer: 43.96 cm

[Medium] Systems of Equations — Substitution

• EN: Solve: y = 2x and x + y = 12. What is y?
• FR: Résous : y = 2x et x + y = 12. Quelle est la valeur de y?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Substitute y into the second equation — like y = 3x and x + y = 8: x + 3x = 8, 4x = 8, x = 2, y = 6.
• Steps:
  • Substitute y = 2x: x + 2x = 12 → 3x = 12 → x = 4.
  • y = 2 × 4 = 8.
• Answer: 8

[Medium] Quadratic — Vertex Form

• EN: The quadratic y = (x − 3)² + 2 has its vertex at which point?
• FR: Le quadratique y = (x − 3)² + 2 a son sommet au point suivant?
• Choices: A) (−3, 2) B) (2, 3) C) (3, 2) D) (3, −2)
• Hint: In y = (x − h)² + k, the vertex is at (h, k) — like y = (x − 5)² + 1 has vertex (5, 1).
• Steps:
  • h = 3, k = 2. Vertex is at (3, 2).
• Answer: (3, 2)

[Hard] Quadratic Formula

• EN: Use the quadratic formula to solve x² − 5x + 4 = 0. What are the solutions?
• FR: Utilise la formule quadratique pour résoudre x² − 5x + 4 = 0. Quelles sont les solutions?
• Choices: A) x = 1 and x = 4 B) x = 2 and x = 3 C) x = −1 and x = −4 D) x = 1 and x = 5
• Hint: Use x = (−b ± √(b²−4ac)) ÷ 2a — like for x² − 3x + 2: discriminant = 9 − 8 = 1, x = (3 ± 1)/2 gives 2 and 1.
• Steps:
  • a=1, b=−5, c=4. Discriminant = 25 − 16 = 9. √9 = 3.
  • x = (5 ± 3)/2 → x = 4 or x = 1.
• Answer: x = 1 and x = 4

[Hard] Surface Area of a Cone

• EN: A cone has a radius of 5 cm and a slant height of 13 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 5 cm et une hauteur oblique de 13 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 200.96 cm² B) 251.20 cm² C) 282.60 cm² D) 314.00 cm²
• Hint: SA of cone = π r² + π r l — like r=3, l=5: 3.14×9 + 3.14×3×5 = 28.26 + 47.1 = 75.36 cm².
• Steps:
  • Base area = π × 5² = 3.14 × 25 = 78.5 cm².
  • Lateral area = π × 5 × 13 = 3.14 × 65 = 204.1 cm².
  • Total = 78.5 + 204.1 = 282.6 cm².
• Answer: 282.60 cm²

[Easy] Exponential Functions

• EN: A population of bacteria doubles every hour. If there are 200 bacteria at noon, how many are there after 3 hours?
• FR: Une population de bactéries double chaque heure. S'il y a 200 bactéries à midi, combien y en a-t-il après 3 heures?
• Choices: A) 600 B) 1200 C) 1600 D) 1800
• Hint: Exponential growth: final = initial × 2^(hours) — like 50 × 2³ = 50 × 8 = 400.
• Steps:
  • After 3 hours: 200 × 2³ = 200 × 8 = 1600.
• Answer: 1600

[Easy] Arithmetic Sequences

• EN: The sequence 3, 7, 11, 15, ... has a common difference. What is the 10th term?
• FR: La suite 3, 7, 11, 15, ... a une différence commune. Quel est le 10ème terme?
• Choices: A) 37 B) 39 C) 41 D) 43
• Hint: Use aₙ = a₁ + (n−1)d — like a₁ = 2, d = 5, n = 6: a₆ = 2 + 5×5 = 27.
• Steps:
  • a₁ = 3, d = 4, n = 10.
  • a₁₀ = 3 + (10 − 1) × 4 = 3 + 36 = 39.
• Answer: 39

[Easy] Logarithms — Introduction

• EN: What is the value of log₂(8)?
• FR: Quelle est la valeur de log₂(8)?
• Choices: A) 2 B) 3 C) 4 D) 6
• Hint: logₐ(b) = c means aᶜ = b — like log₂(16) = 4 because 2⁴ = 16.
• Steps:
  • log₂(8) = ? means 2? = 8 → 2³ = 8.
  • The answer is 3.
• Answer: 3

[Easy] Compound Interest

• EN: Mia invests $1000 at 5% per year compounded annually for 2 years. What is the amount after 2 years?
• FR: Mia investit 1000 $ à 5 % par an, composé annuellement, pendant 2 ans. Quel est le montant après 2 ans?
• Choices: A) $1050.00 B) $1100.00 C) $1102.50 D) $1105.00
• Hint: A = P(1 + r)ⁿ — like $500 at 4% for 2 years: A = 500 × 1.04² = 500 × 1.0816 = $540.80.
• Steps:
  • A = 1000 × (1.05)² = 1000 × 1.1025 = $1102.50.
• Answer: $1102.50

[Medium] Quadratic Functions — Discriminant

• EN: How many real roots does the equation 2x² − 4x + 5 = 0 have?
• FR: Combien de racines réelles a l'équation 2x² − 4x + 5 = 0?
• Choices: A) No real roots B) Exactly one real root C) Two real roots D) Infinitely many roots
• Hint: Use discriminant b² − 4ac: if negative → no real roots, if zero → one, if positive → two — like for x² + x + 1: 1 − 4 = −3, so no real roots.
• Steps:
  • a=2, b=−4, c=5. Discriminant = (−4)² − 4(2)(5) = 16 − 40 = −24.
  • Discriminant < 0, so no real roots.
• Answer: No real roots

[Medium] Geometric Sequences

• EN: A geometric sequence has first term 3 and common ratio 2. What is the sum of the first 5 terms?
• FR: Une suite géométrique a pour premier terme 3 et une raison de 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 63 B) 87 C) 93 D) 96
• Hint: Sₙ = a(rⁿ − 1)/(r − 1) — like a=2, r=3, n=4: S₄ = 2(81−1)/2 = 80.
• Steps:
  • S₅ = 3(2⁵ − 1)/(2 − 1) = 3(32 − 1)/1 = 3 × 31 = 93.
• Answer: 93

[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 — like tan²x + 1 = sec²x is a related identity.
• Steps:
  • The Pythagorean identity states sin²(θ) + cos²(θ) = 1 for all values of θ.
• Answer: 1

[Medium] Logarithm Properties

• EN: Simplify: log₃(27) + log₃(3)
• FR: Simplifie : log₃(27) + log₃(3)
• Choices: A) 3 B) 4 C) 5 D) 6
• Hint: log of a product can be split: logₐ(m) + logₐ(n) = logₐ(mn) — like log₂(4) + log₂(2) = log₂(8) = 3.
• Steps:
  • log₃(27) = 3 (since 3³ = 27). log₃(3) = 1 (since 3¹ = 3).
  • 3 + 1 = 4.
• Answer: 4

[Hard] Annuities

• EN: Carlos deposits $200 at the end of each month into an account earning 6% per year compounded monthly. What is the future value after 12 months? (Use FV = PMT × [(1 + r)ⁿ − 1] / r, where r = 0.005 and (1.005)¹² ≈ 1.0617)
• FR: Carlos dépose 200 $ à la fin de chaque mois dans un compte à 6 % par an, composé mensuellement. Quelle est la valeur future après 12 mois? (Utilise FV = PMT × [(1 + r)ⁿ − 1] / r, où r = 0,005 et (1,005)¹² ≈ 1,0617)
• Choices: A) $2,400.00 B) $2,453.40 C) $2,467.40 D) $2,500.00
• Hint: Apply the annuity formula step by step — like PMT=$100, r=0.005, n=12: FV = 100 × (1.0617−1)/0.005 = 100 × 12.34 = $1234.
• Steps:
  • FV = 200 × (1.0617 − 1) / 0.005 = 200 × 0.0617 / 0.005.
  • = 200 × 12.34 = $2,468 ≈ $2,467.40 (using the given approximation).
• Answer: $2,467.40

[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 with the same base — like 2^(3x) = 64 = 2⁶ → 3x = 6 → x = 2.
• Steps:
  • 81 = 3⁴. So 3^(2x) = 3⁴ → 2x = 4 → x = 2.
• Answer: x = 2

[Easy] Permutations

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

[Easy] Combinations

• EN: A team of 3 players is chosen from 6 students. How many different teams are possible?
• FR: Une équipe de 3 joueurs est choisie parmi 6 élèves. Combien d'équipes différentes sont possibles?
• Choices: A) 15 B) 18 C) 20 D) 24
• Hint: Use C(n,r) = n! / (r!(n−r)!) — like C(5,2) = 5!/(2!×3!) = 10.
• Steps:
  • C(6,3) = 6!/(3! × 3!) = 720/(6 × 6) = 720/36 = 20.
• Answer: 20

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = x³.
• FR: Trouve la dérivée de f(x) = x³.
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: Power rule: d/dx(xⁿ) = n·xⁿ⁻¹ — like d/dx(x⁵) = 5x⁴.
• Steps:
  • f(x) = x³ → f'(x) = 3 · x^(3−1) = 3x².
• Answer: 3x²

[Easy] Rational Functions — Domain

• EN: What value of x must be excluded from the domain of f(x) = 1/(x − 4)?
• FR: Quelle valeur de x doit être exclue du domaine de f(x) = 1/(x − 4)?
• Choices: A) x = −4 B) x = 0 C) x = 1 D) x = 4
• Hint: The denominator cannot equal zero — like for 1/(x + 3), exclude x = −3.
• Steps:
  • Set the denominator equal to zero: x − 4 = 0 → x = 4.
  • Exclude x = 4.
• Answer: x = 4

[Medium] Rate of Change — Derivative

• EN: Find the instantaneous rate of change of f(x) = 2x² + 3x at x = 2.
• FR: Trouve le taux de variation instantané de f(x) = 2x² + 3x à x = 2.
• Choices: A) 10 B) 11 C) 12 D) 14
• Hint: Differentiate first using the power rule, then substitute — like f(x) = 3x² + x → f'(x) = 6x + 1 → at x=1: f'(1) = 7.
• Steps:
  • f'(x) = 4x + 3.
  • f'(2) = 4(2) + 3 = 8 + 3 = 11.
• Answer: 11

[Medium] Binomial Probability

• EN: A coin is flipped 4 times. What is the probability of getting exactly 3 heads? (Use P = C(4,3) × (0.5)⁴)
• FR: Une pièce de monnaie est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 3 faces? (Utilise P = C(4,3) × (0,5)⁴)
• Choices: A) 1/8 B) 3/16 C) 1/4 D) 5/16
• Hint: For binomial probability, P = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ — like P(2 heads in 3 flips) = C(3,2) × (0.5)³ = 3/8.
• Steps:
  • C(4,3) = 4. (0.5)⁴ = 1/16.
  • P = 4 × 1/16 = 4/16 = 1/4.
• Answer: 1/4

[Medium] Polynomial Division

• EN: Divide x² + 7x + 10 by (x + 2). What is the quotient?
• FR: Divise x² + 7x + 10 par (x + 2). Quel est le quotient?
• Choices: A) x + 3 B) x + 4 C) x + 5 D) x + 6
• Hint: Factor the numerator and cancel — like (x² + 5x + 6) ÷ (x + 3) = (x+2)(x+3)÷(x+3) = x + 2.
• Steps:
  • Factor: x² + 7x + 10 = (x + 2)(x + 5).
  • Divide by (x + 2): quotient = x + 5.
• Answer: x + 5

[Medium] Vectors — Addition

• EN: Vector u = (3, 5) and vector v = (−1, 4). What is u + v?
• FR: Le vecteur u = (3, 5) et le vecteur v = (−1, 4). Quelle est la valeur de u + v?
• Choices: A) (2, 9) B) (3, 9) C) (4, 9) D) (2, 8)
• Hint: Add vectors component by component — like (4, 2) + (−2, 6) = (4 + (−2), 2 + 6) = (2, 8).
• Steps:
  • x-component: 3 + (−1) = 2.
  • y-component: 5 + 4 = 9.
  • u + v = (2, 9).
• Answer: (2, 9)

[Hard] Normal Distribution

• EN: A data set is normally distributed with a mean of 70 and a standard deviation of 8. Approximately what percentage of data falls between 62 and 78?
• FR: Un ensemble de données est distribué normalement avec une moyenne de 70 et un écart type de 8. Quel pourcentage approximatif des données se situe entre 62 et 78?
• Choices: A) 34% B) 50% C) 68% D) 95%
• Hint: For a normal distribution, about 68% of data lies within one standard deviation of the mean — like mean=50, sd=5: 68% is between 45 and 55.
• Steps:
  • 62 = 70 − 8 (one SD below mean); 78 = 70 + 8 (one SD above mean).
  • One SD on each side captures approximately 68% of the data.
• Answer: 68%

[Hard] Derivative — Finding Maximum

• EN: The height (in metres) of a ball is given by h(t) = −5t² + 20t + 2. At what time t (in seconds) does the ball reach its maximum height?
• FR: La hauteur (en mètres) d'un ballon est donnée par h(t) = −5t² + 20t + 2. À quel moment t (en secondes) le ballon atteint-il sa hauteur maximale?
• Choices: A) t = 1 second B) t = 2 seconds C) t = 3 seconds D) t = 4 seconds
• Hint: At the maximum, the derivative equals zero — like h(t) = −3t² + 12t: h'(t) = −6t + 12 = 0 → t = 2.
• Steps:
  • h'(t) = −10t + 20. Set equal to zero: −10t + 20 = 0 → t = 2.
  • The ball reaches maximum height at t = 2 seconds.
• Answer: t = 2 seconds