Daily Math — 2026-05-05
Grade 1 Problems
- [Easy] Counting Apples
- EN: How many apples are there: 3 red apples + 2 green apples?
- FR: Combien de pommes y a-t-il : 3 pommes rouges + 2 pommes vertes ?
- Choices: A) 5 B) 6 C) 4 D) 7
- Hint: Add the apples together.
- Steps:
- Count the red apples.
- Count the green apples.
- Answer: 5
- [Easy] Subtracting Fish
- EN: You have 10 fish and give away 3. How many fish left?
- FR: Vous avez 10 poissons et en donnez 3. Combien de poissons restent-ils ?
- Choices: A) 6 B) 7 C) 8 D) 5
- Hint: Take away the fish you gave away.
- Steps:
- Start with 10 fish.
- Subtract 3 fish.
- Answer: 7
- [Easy] Counting Coins
- EN: You have 1 loonie and 2 toonies. How many dollars do you have?
- FR: Vous avez 1 dollar et 2 dollars. Combien d'argent avez-vous ?
- Choices: A) 2 B) 3 C) 4 D) 5
- Hint: Remember 1 loonie = 1 dollar.
- Steps:
- Count the toonies.
- Add the loonie.
- Answer: 3
- [Easy] Skipping by 5s
- EN: What is 10 + what equals 20?
- FR: Qu'est-ce que 10 + quoi égale 20 ?
- Choices: A) 5 B) 10 C) 20 D) 15
- Hint: Think of what number added to 10 makes 20.
- Steps:
- Start with 10.
- Count up to 20.
- Answer: 10
- [Medium] Add the Sweets
- EN: You have 5 candies, and your friend gives you 7 more. How many candies now?
- FR: Vous avez 5 bonbons, et votre ami vous en donne 7 de plus. Combien de bonbons avez-vous maintenant ?
- Choices: A) 11 B) 12 C) 10 D) 9
- Hint: Add the candies together.
- Steps:
- Count your candies.
- Add your friend's candies.
- Answer: 12
- [Medium] Subtracting Cookies
- EN: If you start with 15 cookies and eat 4, how many left?
- FR: Si vous commencez avec 15 biscuits et en mangez 4, combien en reste-t-il ?
- Choices: A) 11 B) 12 C) 10 D) 9
- Hint: Figure out how many cookies you ate.
- Steps:
- Start with 15 cookies.
- Subtract the eaten cookies.
- Answer: 11
- [Medium] Counting Students
- EN: There are 8 students in the class, and 5 more join. How many students now?
- FR: Il y a 8 élèves dans la classe, et 5 autres rejoignent. Combien d'élèves y a-t-il maintenant ?
- Choices: A) 12 B) 13 C) 10 D) 11
- Hint: Add the new students to the existing ones.
- Steps:
- Count the original students.
- Add the new ones.
- Answer: 13
- [Medium] Comparing Taller Trees
- EN: If tree A is 5 cm tall and tree B is 3 cm tall, which is taller?
- FR: Si l'arbre A mesure 5 cm de hauteur et l'arbre B mesure 3 cm de hauteur, lequel est le plus grand ?
- Choices: A) Tree A B) Tree B C) They are equal D) Cannot tell
- Hint: Look at the heights.
- Steps:
- Measure both trees.
- Compare their heights.
- Answer: 5
- [Hard] How Many Wheels?
- EN: If 3 bicycles each have 2 wheels, how many wheels in total?
- FR: Si 3 bicyclettes ont chacune 2 roues, combien de roues au total ?
- Choices: A) 5 B) 6 C) 7 D) 8
- Hint: Multiply the number of bicycles by wheels per bicycle.
- Steps:
- Calculate wheels on one bicycle.
- Multiply by the number of bicycles.
- Answer: 6
- [Hard] Total Stars Over Days
- EN: If you see 4 stars on day 1 and 2 more each day for 3 days. How many total stars?
- FR: Si vous voyez 4 étoiles le premier jour et 2 étoiles de plus chaque jour pendant 3 jours. Combien d'étoiles au total ?
- Choices: A) 10 B) 12 C) 9 D) 8
- Hint: Add stars each day.
- Steps:
- Count stars for day 1.
- Add stars for the next 3 days.
- Answer: 10
Grade 2 Problems
- [Easy] Adding Hours
- EN: What is 2 hours + 1 hour?
- FR: Qu'est-ce que 2 heures + 1 heure ?
- Choices: A) 3 B) 2 C) 4 D) 5
- Hint: Imagine adding time on a clock.
- Steps:
- Start with 2 hours.
- Add 1 hour.
- Answer: 3
- [Easy] Count the Dimes
- EN: You have 4 dimes. How much money do you have?
- FR: Vous avez 4 dimes. Combien d'argent avez-vous ?
- Choices: A) 40 cents B) 50 cents C) 35 cents D) 60 cents
- Hint: A dime is worth 10 cents.
- Steps:
- Multiply the number of dimes by 10.
- Answer: 40
- [Easy] Subtracting Days
- EN: If today is Friday, what day was it 2 days ago?
- FR: Si aujourd'hui c'est vendredi, quel jour était-il il y a 2 jours ?
- Choices: A) Wednesday B) Thursday C) Tuesday D) Sunday
- Hint: Think back on the week.
- Steps:
- Count backwards from Friday.
- Answer: Wednesday
- [Easy] Counting Markers
- EN: You have 6 blue markers and 4 green markers. How many markers total?
- FR: Vous avez 6 marqueurs bleus et 4 marqueurs verts. Combien de marqueurs au total ?
- Choices: A) 9 B) 10 C) 11 D) 8
- Hint: Add the two colors.
- Steps:
- Count blue markers.
- Count green markers.
- Answer: 10
- [Medium] Comparing Lengths
- EN: If a pencil is 15 cm and an eraser is 8 cm, which is longer?
- FR: Si un crayon mesure 15 cm et une gomme mesure 8 cm, lequel est plus long ?
- Choices: A) Pencil B) Eraser C) They are equal D) Cannot tell
- Hint: Look at the measurements.
- Steps:
- Compare the lengths of both.
- Answer: Pencil
- [Medium] Adding Coins
- EN: If you have 5 nickels, how much money is that?
- FR: Si vous avez 5 nickels, combien d'argent est-ce ?
- Choices: A) 25 cents B) 30 cents C) 20 cents D) 10 cents
- Hint: Each nickel is 5 cents.
- Steps:
- Multiply the number of nickels by 5.
- Answer: 25
- [Medium] Subtracting Time
- EN: You start homework at 4 PM and finish at 5 PM. How long did you work?
- FR: Vous commencez les devoirs à 16h et finissez à 17h. Combien de temps avez-vous travaillé ?
- Choices: A) 1 hour B) 30 minutes C) 2 hours D) 15 minutes
- Hint: Count the time difference.
- Steps:
- Calculate time from start to finish.
- Answer: 1
- [Medium] Simple Patterns
- EN: If the pattern is red, blue, red, blue, what comes next?
- FR: Si le motif est rouge, bleu, rouge, bleu, que vient-il ensuite ?
- Choices: A) Red B) Blue C) Green D) Yellow
- Hint: Look at the colors.
- Steps:
- Identify the repeating pattern.
- Answer: Red
- [Hard] Adding Measurements
- EN: A ribbon is 30 cm long. If you cut 5 cm, how long is it now?
- FR: Un ruban mesure 30 cm de long. Si vous coupez 5 cm, quelle est sa longueur maintenant ?
- Choices: A) 25 B) 20 C) 30 D) 35
- Hint: Subtract the cut length.
- Steps:
- Start with 30 cm.
- Subtract 5 cm.
- Answer: 25
- [Hard] Money for Treats
- EN: If an ice cream costs $2 and you buy 3, how much total is spent?
- FR: Si une crème glacée coûte 2 $ et que vous en achetez 3, combien dépensez-vous ?
- Choices: A) 5 B) 6 C) 7 D) 8
- Hint: Multiply the cost by the quantity.
- Steps:
- Find the cost of one.
- Multiply by 3.
- Answer: 6
Grade 3 Problems
- [Easy] Adding Apples and Oranges
- EN: You have 3 apples and 2 oranges. How many fruits do you have?
- FR: Vous avez 3 pommes et 2 oranges. Combien de fruits avez-vous ?
- Choices: A) 4 B) 5 C) 6 D) 7
- Hint: Add the apples and oranges together.
- Steps:
- Count the apples.
- Count the oranges.
- Answer: 5
- [Easy] Counting Multiples
- EN: What is 2 × 3?
- FR: Qu'est-ce que 2 × 3 ?
- Choices: A) 5 B) 6 C) 7 D) 8
- Hint: Think of doubling and adding.
- Steps:
- Multiply 2 by 3.
- Answer: 6
- [Easy] Simple Fractions
- EN: What is half of 8?
- FR: Quelle est la moitié de 8 ?
- Choices: A) 2 B) 4 C) 6 D) 8
- Hint: Divide the number by 2.
- Steps:
- Divide 8 by 2.
- Answer: 4
- [Easy] Counting Fingers
- EN: If you have 5 fingers on each hand, how many fingers on 2 hands?
- FR: Si vous avez 5 doigts sur chaque main, combien de doigts avez-vous sur 2 mains ?
- Choices: A) 8 B) 10 C) 12 D) 14
- Hint: Multiply the number of fingers by 2.
- Steps:
- Count the fingers on one hand.
- Multiply by 2 for both hands.
- Answer: 10
- [Medium] Adding Petos
- EN: If you have 6 pets and find 4 more, how many do you have?
- FR: Si vous avez 6 animaux de compagnie et en trouvez 4 de plus, combien avez-vous ?
- Choices: A) 8 B) 10 C) 9 D) 6
- Hint: Add 4 to your 6 pets.
- Steps:
- Count your pets.
- Add the new pets.
- Answer: 10
- [Medium] Subtracting Books
- EN: If you have 9 books and lend 6 to a friend, how many left?
- FR: Si vous avez 9 livres et en prêtez 6 à un ami, combien vous reste-t-il ?
- Choices: A) 2 B) 3 C) 4 D) 5
- Hint: Think about how many you lent.
- Steps:
- Start with 9 books.
- Subtract the ones lent.
- Answer: 3
- [Medium] Comparing Heights
- EN: If your friend is 120 cm tall and you are 110 cm tall, who is taller?
- FR: Si votre ami mesure 120 cm et que vous mesurez 110 cm, qui est le plus grand ?
- Choices: A) You B) Friend C) They are equal D) Cannot tell
- Hint: Compare the heights.
- Steps:
- Measure both heights.
- Compare the numbers.
- Answer: Friend
- [Medium] Finding Area
- EN: A garden is 4 m long and 3 m wide. What is the area?
- FR: Un jardin mesure 4 m de long et 3 m de large. Quelle est la superficie ?
- Choices: A) 12 B) 16 C) 8 D) 15
- Hint: Length times width.
- Steps:
- Multiply the length by the width.
- Answer: 12
- [Hard] Total Distance Hiked
- EN: You hike 5 km on Saturday and 8 km on Sunday. How far did you hike in total?
- FR: Vous marchez 5 km samedi et 8 km dimanche. Quelle est la distance totale parcourue ?
- Choices: A) 10 B) 12 C) 13 D) 14
- Hint: Add the two distances together.
- Steps:
- Count Saturday's hike.
- Count Sunday’s hike.
- Answer: 13
- [Hard] Splitting Candy
- EN: You have 15 candies and want to share with 3 friends equally. How many candies each?
- FR: Vous avez 15 bonbons et souhaitez partager avec 3 amis également. Combien de bonbons chacun ?
- Choices: A) 3 B) 4 C) 5 D) 6
- Hint: Divide the total by 4 (you + friends).
- Steps:
- Include yourself in the total count.
- Divide 15 by 4.
- Answer: 3
Grade 4 Problems
- [Easy] Adding with Remainders
- EN: What is 7 + 9?
- FR: Qu'est-ce que 7 + 9 ?
- Choices: A) 15 B) 16 C) 14 D) 17
- Hint: Think of the total after adding.
- Steps:
- Start with 7.
- Add 9.
- Answer: 16
- [Easy] Length Comparison
- EN: A pencil is 18 cm and a pen is 12 cm. Which is longer?
- FR: Un crayon mesure 18 cm et un stylo mesure 12 cm. Lequel est plus long ?
- Choices: A) Pencil B) Pen C) They are equal D) Cannot tell
- Hint: Look at the measurements.
- Steps:
- Compare both lengths.
- Answer: Pencil
- [Easy] Dividing Treats
- EN: If you have 20 cookies and share with 4 friends, how many cookies each?
- FR: Si vous avez 20 biscuits et que vous les partagez avec 4 amis, combien de biscuits chacun ?
- Choices: A) 4 B) 5 C) 6 D) 7
- Hint: Divide the total cookies.
- Steps:
- Divide 20 by 5 (you + friends).
- Answer: 4
- [Easy] Subtracting Marbles
- EN: You have 10 marbles and lose 3. How many marbles left?
- FR: Vous avez 10 billes et en perdez 3. Combien de billes vous restent-elles ?
- Choices: A) 7 B) 6 C) 8 D) 5
- Hint: Subtract the lost marbles.
- Steps:
- Start with 10 marbles.
- Subtract 3.
- Answer: 7
- [Medium] Comparing Fractions
- EN: Which is greater: 1/2 or 1/4?
- FR: Lequel est plus grand : 1/2 ou 1/4 ?
- Choices: A) 1/2 B) 1/4 C) They are equal D) Cannot tell
- Hint: Think about the sizes of the parts.
- Steps:
- Compare the two fractions.
- Answer: 1/2
- [Medium] Multiplying Dimensions
- EN: A rectangle is 6 cm long and 4 cm wide. What is its area?
- FR: Un rectangle mesure 6 cm de long et 4 cm de large. Quelle est sa superficie ?
- Choices: A) 20 B) 24 C) 25 D) 28
- Hint: Multiply length and width.
- Steps:
- Calculate 6 × 4.
- Answer: 24
- [Medium] Finding Remainders
- EN: What is 29 divided by 5?
- FR: Quel est 29 divisé par 5 ?
- Choices: A) 4 B) 5 C) 3 D) 6
- Hint: Think about how many times 5 fits into 29.
- Steps:
- Divide and find the remainder.
- Answer: 4
- [Medium] Total Time Elapsed
- EN: If you start your homework at 3 PM and finish at 4:30 PM, how long did you work?
- FR: Si vous commencez vos devoirs à 15h et que vous terminez à 16h30, combien de temps avez-vous travaillé ?
- Choices: A) 1 hour B) 1.5 hours C) 2 hours D) 1 hour 30 minutes
- Hint: Calculate the time.
- Steps:
- Find the difference in time.
- Answer: 1.5
[Hard] Adding Fractions
- EN: What is 1/4 + 1/4?
- FR: Qu'est-ce que 1/4 + 1/4 ?
- Choices: A) 1/2 B) 1/4 C) 1 D) 3/4
- Hint: Add the fractions together.
- Steps:
- Find a common denominator.
- Add the numerators.
- Answer: 1/2
- [Hard] Total Guests
- EN: If there are 24 students in a class and 9 aren’t present, how many are there?
- FR: S'il y a 24 élèves dans une classe et que 9 ne sont pas présents, combien y a-t-il ?
- Choices: A) 15 B) 14 C) 16 D) 12
- Hint: Subtract the absent students from the total.
- Steps:
- Start with 24 students.
- Subtract 9.
- Answer: 15
Grade 5 Problems
- [Easy] Simple Multiplication
- EN: What is 4 × 3?
- FR: Qu'est-ce que 4 × 3 ?
- Choices: A) 10 B) 11 C) 12 D) 13
- Hint: Think of adding 4 several times.
- Steps:
- Multiply 4 by 3.
- Answer: 12
- [Easy] Add with Like Denominators
- EN: What is 1/5 + 1/5?
- FR: Qu'est-ce que 1/5 + 1/5 ?
- Choices: A) 1/5 B) 2/5 C) 3/5 D) 4/5
- Hint: Add the numerators together.
- Steps:
- Combine the fractions.
- Answer: 2/5
- [Easy] Counting Volumes
- EN: What is the volume of a box with length 2 cm, width 3 cm, and height 4 cm?
- FR: Quelle est la volume d'une boîte de 2 cm de long, 3 cm de large et 4 cm de haut ?
- Choices: A) 18 B) 24 C) 20 D) 12
- Hint: Use length × width × height.
- Steps:
- Multiply the dimensions.
- Answer: 24
- [Easy] Counting Percentages
- EN: What is 50% of 50?
- FR: Quel est 50 % de 50 ?
- Choices: A) 20 B) 25 C) 30 D) 35
- Hint: Think of half of 50.
- Steps:
- Divide 50 by 2.
- Answer: 25
- [Medium] Subtracting Percentages
- EN: If you have $40 and spend 25%, how much do you have left?
- FR: Si vous avez 40 $ et dépensez 25 %, combien vous reste-t-il ?
- Choices: A) 30 B) 35 C) 38 D) 20
- Hint: Calculate 25% of 40.
- Steps:
- Find 25% of 40.
- Subtract from the total.
- Answer: 30
- [Medium] Adding Mixed Numbers
- EN: What is 2/3 + 1/3?
- FR: Qu'est-ce que 2/3 + 1/3 ?
- Choices: A) 1 B) 2/3 C) 3/3 D) 4/3
- Hint: Use the same denominator to add.
- Steps:
- Add the numerators.
- Answer: 1
- [Medium] Area Calculation
- EN: What is the area of a rectangle that is 7 m long and 5 m wide?
- FR: Quelle est la superficie d'un rectangle de 7 m de long et 5 m de large ?
- Choices: A) 12 B) 35 C) 27 D) 40
- Hint: Multiply length by width.
- Steps:
- Calculate area.
- Answer: 35
- [Medium] Simple Division
- EN: What is 96 divided by 8?
- FR: Quel est 96 divisé par 8 ?
- Choices: A) 10 B) 12 C) 11 D) 14
- Hint: Consider how many times 8 fits into 96.
- Steps:
- Divide 96 by 8.
- Answer: 12
- [Hard] Building Volume
- EN: A box has dimensions 2 m × 3 m × 4 m. What is the volume?
- FR: Une boîte a des dimensions de 2 m × 3 m × 4 m. Quel est le volume ?
- Choices: A) 24 B) 12 C) 20 D) 15
- Hint: Multiply length, width, and height together.
- Steps:
- Calculate the volume.
- Answer: 24
- [Hard] Subtracting Fractions
- EN: What is 3/4 - 1/4?
- FR: Qu'est-ce que 3/4 - 1/4 ?
- Choices: A) 1/2 B) 2/4 C) 3/4 D) 1/4
- Hint: Subtract the numerators.
- Steps:
- Keep the same denominator.
- Subtract.
- Answer: 1/2
Grade 6 Problems
- [Easy] Simple Fractions
- EN: What is 3/4 + 1/4?
- FR: Qu'est-ce que 3/4 + 1/4 ?
- Choices: A) 1 B) 2 C) 4/4 D) 3/4
- Hint: Add the numerators.
- Steps:
- Combine numerators.
- Answer: 1
- [Easy] Ratio Comparison
- EN: If you have 2 apples and 4 oranges, what is the ratio of apples to oranges?
- FR: Si vous avez 2 pommes et 4 oranges, quel est le rapport entre les pommes et les oranges ?
- Choices: A) 1:2 B) 2:1 C) 4:2 D) 1:4
- Hint: Simplify the numbers.
- Steps:
- Write as a fraction and simplify.
- Answer: 1:2
- [Easy] Dividing Evenly
- EN: How much is 12 divided by 3?
- FR: Combien fait 12 divisé par 3 ?
- Choices: A) 2 B) 3 C) 4 D) 5
- Hint: Think of how many groups of 3 in 12.
- Steps:
- Divide 12 by 3.
- Answer: 4
- [Easy] Combining Integers
- EN: What is 5 + (-3)?
- FR: Qu'est-ce que 5 + (-3) ?
- Choices: A) 2 B) 5 C) 3 D) 1
- Hint: Add the negative number.
- Steps:
- Combine the numbers.
- Answer: 2
- [Medium] Distance Calculation
- EN: If you walk 150 meters and then 250 meters, how far do you walk in total?
- FR: Si vous marchez 150 mètres et ensuite 250 mètres, quelle est la distance totale parcourue ?
- Choices: A) 400 B) 350 C) 300 D) 450
- Hint: Add the two distances.
- Steps:
- Combine both distances.
- Answer: 400
- [Medium] Percent Discounts
- EN: A shirt costs $50. What is the price after a 20% discount?
- FR: Une chemise coûte 50 $. Quel est le prix après une remise de 20 % ?
- Choices: A) 40 B) 45 C) 35 D) 30
- Hint: Calculate 20% of 50.
- Steps:
- Find 20% and subtract.
- Answer: 40
- [Medium] Total Cost Calculation
- EN: You buy 3 notebooks at $2 each and 2 pencils at $1 each. What is the total?
- FR: Vous achetez 3 cahiers à 2 $ chacun et 2 crayons à 1 $ chacun. Quel est le total ?
- Choices: A) 8 B) 9 C) 6 D) 7
- Hint: Add the costs together.
- Steps:
- Calculate each item.
- Answer: 8
- [Medium] Average Calculation
- EN: What is the average of 4, 6, and 8?
- FR: Quelle est la moyenne de 4, 6 et 8 ?
- Choices: A) 6 B) 7 C) 5 D) 8
- Hint: Add and divide by 3.
- Steps:
- Find the sum.
- Divide by 3.
- Answer: 6
- [Hard] Fraction Operations
- EN: What is 2/3 × 3/4?
- FR: Qu'est-ce que 2/3 × 3/4 ?
- Choices: A) 1/2 B) 1/4 C) 1 D) 1/3
- Hint: Multiply the numerators and denominators.
- Steps:
- Calculate.
- Answer: 1/2
- [Hard] Solving for x
- EN: If x + 3 = 7, what is x?
- FR: Si x + 3 = 7, quelle est la valeur de x ?
- Choices: A) 2 B) 3 C) 5 D) 7
- Hint: Subtract 3 from both sides.
- Steps:
- Isolate x.
- Answer: 4
- [Hard] Finding Average Speeds
- EN: If you drive 120 km in 2 hours, what's your speed in km/h?
- FR: Si vous conduisez 120 km en 2 heures, quelle est votre vitesse en km/h ?
- Choices: A) 50 B) 60 C) 55 D) 65
- Hint: Divide distance by time.
- Steps:
- Calculate speed.
- Answer: 60
- [Hard] Area of Triangle
- EN: What is the area of a triangle with a base of 10 cm and a height of 5 cm?
- FR: Quelle est la superficie d'un triangle avec une base de 10 cm et une hauteur de 5 cm ?
- Choices: A) 20 B) 25 C) 30 D) 15
- Hint: Use the formula base × height ÷ 2.
- Steps:
- Calculate the area.
- Answer: 25
Grade 7 Problems
- [Easy] Simple Equation Solving
- EN: If x + 5 = 10, what is x?
- FR: Si x + 5 = 10, quelle est la valeur de x ?
- Choices: A) 3 B) 4 C) 5 D) 6
- Hint: Subtract 5 from both sides.
- Steps:
- Isolate x.
- Answer: 5
- [Easy] Integer Operations
- EN: What is 7 - 2?
- FR: Qu'est-ce que 7 - 2 ?
- Choices: A) 5 B) 6 C) 7 D) 4
- Hint: Think of removing from the total.
- Steps:
- Calculate.
- Answer: 5
- [Easy] Adding Decimal Numbers
- EN: What is 3.5 + 2.5?
- FR: Qu'est-ce que 3.5 + 2.5 ?
- Choices: A) 5 B) 6 C) 7 D) 8
- Hint: Add the decimal parts.
- Steps:
- Combine the numbers.
- Answer: 6
- [Easy] Counting in Fractions
- EN: What is 1/2 + 1/2?
- FR: Qu'est-ce que 1/2 + 1/2 ?
- Choices: A) 1 B) 1/2 C) 0 D) 2
- Hint: Simple addition of fractions.
- Steps:
- Combine the fractions.
- Answer: 1
- [Medium] Basic Ratio Problems
- EN: The ratio of cats to dogs is 2:3. If there are 4 cats, how many dogs are there?
- FR: Le rapport entre les chats et les chiens est de 2:3. S'il y a 4 chats, combien de chiens y a-t-il ?
- Choices: A) 5 B) 6 C) 8 D) 10
- Hint: Set up a proportion to find the answer.
- Steps:
- Use the ratio.
- Answer: 6
- [Medium] Finding Percentages
- EN: What is 25% of 200?
- FR: Quel est 25 % de 200 ?
- Choices: A) 50 B) 40 C) 30 D) 60
- Hint: Think of a quarter of the total.
- Steps:
- Calculate 25% of 200.
- Answer: 50
- [Medium] Total Distances
- EN: If you run 2 km on Monday, 3 km on Tuesday, how many did you run in total?
- FR: Si vous courez 2 km lundi, 3 km mardi, combien avez-vous couru au total ?
- Choices: A) 5 B) 4 C) 6 D) 7
- Hint: Add the distances.
- Steps:
- Combine both runs.
- Answer: 5
- [Medium] Area of Rectangle Problem
- EN: What is the area of a rectangle that is 10 m long and 4 m wide?
- FR: Quelle est la superficie d'un rectangle de 10 m de long et 4 m de large ?
- Choices: A) 30 B) 40 C) 50 D) 60
- Hint: Multiply length and width.
- Steps:
- Calculate area.
- Answer: 40
- [Hard] Multiple Operations
- EN: If x = 2, what is the value of 3x + 4?
- FR: Si x = 2, quelle est la valeur de 3x + 4 ?
- Choices: A) 10 B) 12 C) 11 D) 9
- Hint: Substitute and calculate.
- Steps:
- Replace x with 2.
- Answer: 10
- [Hard] Solving Inequalities
- EN: If 2x - 5 > 3, what is x?
- FR: Si 2x - 5 > 3, quelle est la valeur de x ?
- Choices: A) 2 B) 4 C) 3 D) 5
- Hint: Start by adding 5 to both sides.
- Steps:
- Isolate x.
- Answer: 4
- [Hard] Percentage of a Quantity
- EN: What is 15% of 300?
- FR: Quel est 15 % de 300 ?
- Choices: A) 45 B) 50 C) 55 D) 60
- Hint: Use multiplication to find the answer.
- Steps:
- Calculate 15% of 300.
- Answer: 45
- [Hard] Finding Averages
- EN: If your scores are 80, 90, and 70, what is the average?
- FR: Si vos notes sont de 80, 90 et 70, quelle est la moyenne ?
- Choices: A) 75 B) 80 C) 85 D) 90
- Hint: Sum and divide by the number of scores.
- Steps:
- Add the scores together.
- Answer: 80
- [Hard] Surface Area Calculation
- EN: If a cube has a side length of 4 cm, what is its surface area?
- FR: Si un cube a une longueur de côté de 4 cm, quelle est sa superficie ?
- Choices: A) 24 B) 32 C) 48 D) 64
- Hint: Use the formula 6a².
- Steps:
- Calculate surface area.
- Answer: 96
- [Hard] Volume Challenges
- EN: A cylinder has a radius of 3 cm and a height of 5 cm. What is its volume?
- FR: Un cylindre a un rayon de 3 cm et une hauteur de 5 cm. Quel est son volume ?
- Choices: A) 25.12 B) 28.26 C) 30 D) 33.51
- Hint: Use the formula πr²h.
- Steps:
- Calculate volume.
- Answer: 28.26
Grade 8 Problems
- [Easy] Solving Simple Two-Step Equations
- EN: If 2x + 3 = 11, what is x?
- FR: Si 2x + 3 = 11, quelle est la valeur de x ?
- Choices: A) 3 B) 4 C) 5 D) 6
- Hint: Subtract 3 from both sides.
- Steps:
- Isolate x.
- Answer: 4
- [Easy] Finding Simple Average
- EN: What is the average of 5, 10, and 15?
- FR: Quelle est la moyenne de 5, 10 et 15 ?
- Choices: A) 10 B) 12 C) 15 D) 20
- Hint: Add and divide by 3.
- Steps:
- Calculate the sum and divide.
- Answer: 10
- [Easy] Simple Geometry
- EN: What is the perimeter of a rectangle with length 6 cm and width 3 cm?
- FR: Quelle est la circonférence d'un rectangle de 6 cm de long et de 3 cm de large ?
- Choices: A) 12 B) 18 C) 20 D) 16
- Hint: Use the formula 2(l + w).
- Steps:
- Multiply and add.
- Answer: 18
- [Easy] Evaluating Expressions
- EN: What is the value of 3a if a = 5?
- FR: Quelle est la valeur de 3a si a = 5 ?
- Choices: A) 10 B) 15 C) 20 D) 25
- Hint: Multiply 3 by a.
- Steps:
- Calculate.
- Answer: 15
- [Medium] Solving for x
- EN: If 3x - 2 = 10, what is x?
- FR: Si 3x - 2 = 10, quelle est la valeur de x ?
- Choices: A) 3 B) 4 C) 5 D) 2
- Hint: Add 2 to both sides first.
- Steps:
- Solve for x.
- Answer: 4
- [Medium] Calculating Slope
- EN: What is the slope of the line through points (1,2) and (3,4)?
- FR: Quelle est la pente de la droite passant par les points (1,2) et (3,4) ?
- Choices: A) 2 B) 1 C) 3 D) 0
- Hint: Use (y2 - y1) / (x2 - x1).
- Steps:
- Calculate the differences.
- Answer: 1
- [Medium] Solving Inequalities
- EN: If 3x + 1 < 10, what is x?
- FR: Si 3x + 1 < 10, quelle est la valeur de x ?
- Choices: A) 4 B) 3 C) 2 D) 1
- Hint: Isolate x by subtracting 1 and dividing by 3.
- Steps:
- Calculate.
- Answer: 3
- [Medium] Percentages Calculation
- EN: What is 60% of 80?
- FR: Quel est 60 % de 80 ?
- Choices: A) 40 B) 45 C) 48 D) 50
- Hint: Find a portion of 80.
- Steps:
- Calculate.
- Answer: 48
- [Hard] Quadratic Equation
- EN: What are the roots of x² - 5x + 6 = 0?
- FR: Quelles sont les racines de x² - 5x + 6 = 0 ?
- Choices: A) 2,3 B) -2,-3 C) 1,6 D) 3,6
- Hint: Factor the equation if possible.
- Steps:
- Solve for x using factoring.
- Answer: 2,3
- [Hard] Finding Average Speed
- EN: If you travel 150 km in 2.5 hours, what is your average speed?
- FR: Si vous parcourez 150 km en 2,5 heures, quelle est votre vitesse moyenne ?
- Choices: A) 60 km/h B) 30 km/h C) 20 km/h D) 100 km/h
- Hint: Divide distance by time.
- Steps:
- Calculate speed.
- Answer: 60
- [Hard] Surface Area Calculation
- EN: What is the surface area of a rectangular prism with dimensions 3 m, 4 m, and 5 m?
- FR: Quelle est la superficie d'un prisme rectangulaire ayant des dimensions de 3 m, 4 m et 5 m ?
- Choices: A) 58 m² B) 60 m² C) 62 m² D) 64 m²
- Hint: Use the formula SA = 2lw + 2lh + 2wh.
- Steps:
- Calculate the areas.
- Answer: 58
- [Hard] Simplifying Expressions
- EN: Simplify: 2(x + 3) + 3(x - 4).
- FR: Simplifiez : 2(x + 3) + 3(x - 4).
- Choices: A) 5x-6 B) 5x-10 C) 5x-12 D) 5x-8
- Hint: Distribute and combine like terms.
- Steps:
- Calculate step by step.
- Answer: 5x-6
- [Hard] Finding Roots
- EN: What are the roots of 2x² + 4x - 6 = 0?
- FR: Quelles sont les racines de 2x² + 4x - 6 = 0 ?
- Choices: A) -1, 3 B) -3, 1 C) -1, 2 D) 2, 3
- Hint: Use the quadratic formula.
- Steps:
- Calculate roots.
- Answer: -1, 3
- [Hard] Volume of a Cylinder
- EN: What is the volume of a cylinder with a radius of 3 cm and height of 10 cm?
- FR: Quel est le volume d'un cylindre ayant un rayon de 3 cm et une hauteur de 10 cm ?
- Choices: A) 90π cm³ B) 80π cm³ C) 70π cm³ D) 60π cm³
- Hint: Use the formula V = πr²h.
- Steps:
- Calculate volume.
- Answer: 90π
Grade 9 Problems
- [Easy] Evaluate Expressions
- EN: If y = 4, calculate 3y + 2.
- FR: Si y = 4, calculez 3y + 2.
- Choices: A) 10 B) 14 C) 12 D) 16
- Hint: Substitute and calculate.
- Steps:
- Replace y with 4.
- Answer: 14
- [Easy] Solving Linear Equations
- EN: What is x if x + 2 = 5?
- FR: Quelle est la valeur de x si x + 2 = 5 ?
- Choices: A) 2 B) 3 C) 4 D) 5
- Hint: Subtract 2 from both sides.
- Steps:
- Isolate x.
- Answer: 3
- [Easy] Working with Integers
- EN: What is -2 + 5?
- FR: Qu'est-ce que -2 + 5 ?
- Choices: A) 3 B) 4 C) 2 D) 1
- Hint: Think about positive and negative numbers.
- Steps:
- Add the integers.
- Answer: 3
- [Easy] Area of a Rectangle
- EN: If a rectangle has a length of 8 m and a width of 3 m, what is its area?
- FR: Si un rectangle a une longueur de 8 m et une largeur de 3 m, quelle est sa superficie ?
- Choices: A) 18 B) 24 C) 30 D) 36
- Hint: Use length × width.
- Steps:
- Calculate the area.
- Answer: 24
- [Medium] Solving Inequalities
- EN: Solve the inequality 2x - 3 < 5.
- FR: Résolvez l'inégalité 2x - 3 < 5.
- Choices: A) x < 4 B) x > 4 C) x ≤ 6 D) x ≥ 6
- Hint: First, add 3 to both sides.
- Steps:
- Isolate x.
- Answer: x < 4
- [Medium] Graphing Linear Equations
- EN: What is the slope of the line 2y = 4x + 6?
- FR: Quelle est la pente de la ligne 2y = 4x + 6 ?
- Choices: A) 3 B) 2 C) 1 D) 4
- Hint: Convert to slope-intercept form.
- Steps:
- Rearrange the equation.
- Answer: 2
- [Medium] Volume of Cylinder
- EN: What is the volume of a cylinder with a radius of 2 cm and height of 5 cm?
- FR: Quel est le volume d'un cylindre ayant un rayon de 2 cm et une hauteur de 5 cm ?
- Choices: A) 8π cm³ B) 10π cm³ C) 6π cm³ D) 12π cm³
- Hint: Use the formula V = πr²h.
- Steps:
- Calculate the volume.
- Answer: 8π
- [Medium] Solving Quadratics
- EN: Find the roots of the equation x² - 5x + 6 = 0.
- FR: Trouvez les racines de l'équation x² - 5x + 6 = 0.
- Choices: A) 2, 3 B) -2, -3 C) 1, 6 D) 0, 5
- Hint: Factor the quadratic.
- Steps:
- Solve for x.
- Answer: 2, 3
- [Hard] Finding Roots
- EN: What are the roots of x² + 4x + 3 = 0?
- FR: Quelles sont les racines de x² + 4x + 3 = 0 ?
- Choices: A) -1, -3 B) 1, 3 C) -4,-3 D) -2,-1
- Hint: Factor the quadratic.
- Steps:
- Solve for x.
- Answer: -1, -3
- [Hard] Calculating Perimeter
- EN: What is the perimeter of a triangle with sides of lengths 3 cm, 4 cm, and 5 cm?
- FR: Quelle est la circonférence d'un triangle avec des côtés de 3 cm, 4 cm et 5 cm ?
- Choices: A) 10 cm B) 12 cm C) 14 cm D) 15 cm
- Hint: Add all the sides.
- Steps:
- Calculate the perimeter.
- Answer: 12 cm
- [Hard] Coordinate Geometry
- EN: What is the distance between points (3,4) and (7,1)?
- FR: Quelle est la distance entre les points (3,4) et (7,1) ?
- Choices: A) 4 B) 5 C) 6 D) 7
- Hint: Use the distance formula.
- Steps:
- Calculate distance.
- Answer: 5
- [Hard] Equation of Line
- EN: What is the equation of the line with slope 2 and y-intercept 3?
- FR: Quelle est l'équation de la droite avec une pente de 2 et un intercept y de 3 ?
- Choices: A) y = 2x + 3 B) y = 3x + 2 C) y = 2x - 3 D) y = -2x + 3
- Hint: Use the slope-intercept form.
- Steps:
- Write the equation.
- Answer: y = 2x + 3
- [Hard] Surface Area of Sphere
- EN: What is the surface area of a sphere with radius 5 cm?
- FR: Quelle est la surface d'une sphère avec un rayon de 5 cm ?
- Choices: A) 75π cm² B) 100π cm² C) 50π cm² D) 25π cm²
- Hint: Use the formula A = 4πr².
- Steps:
- Calculate the area.
- Answer: 100π
- [Hard] Two-Variable Equations
- EN: If 2x + 3y = 12 and x = 3, what is y?
- FR: Si 2x + 3y = 12 et x = 3, quelle est la valeur de y ?
- Choices: A) 4 B) 6 C) 2 D) 3
- Hint: Substitute x and solve for y.
- Steps:
- Calculate.
- Answer: 2
- [Hard] Solving Exponential Equations
- EN: Solve for x: 3^x = 81.
- FR: Résolvez pour x : 3^x = 81.
- Choices: A) 3 B) 4 C) 5 D) 2
- Hint: Rewrite 81 as a power of 3.
- Steps:
- Solve the exponential.
- Answer: 4
Grade 10 Problems
- [Easy] Evaluating Function Values
- EN: If f(x) = 2x + 3, what is f(2)?
- FR: Si f(x) = 2x + 3, quelle est la valeur de f(2) ?
- Choices: A) 5 B) 6 C) 7 D) 8
- Hint: Replace x with 2 and calculate.
- Steps:
- Substitute and calculate.
- Answer: 7
- [Easy] Solving for x
- EN: If 4x = 20, what is x?
- FR: Si 4x = 20, quelle est la valeur de x ?
- Choices: A) 3 B) 4 C) 5 D) 6
- Hint: Divide both sides by 4.
- Steps:
- Isolate x.
- Answer: 5
- [Easy] Finding Roots of Linear Functions
- EN: What is the root of the equation 2x + 6 = 0?
- FR: Quelle est la racine de l'équation 2x + 6 = 0 ?
- Choices: A) -3 B) 3 C) 0 D) -2
- Hint: Isolate x.
- Steps:
- Calculate.
- Answer: -3
- [Easy] Area of Parallelogram
- EN: What is the area of a parallelogram with base 10 cm and height 5 cm?
- FR: Quelle est la superficie d'un parallélogramme ayant une base de 10 cm et une hauteur de 5 cm ?
- Choices: A) 30 B) 40 C) 50 D) 60
- Hint: Use the formula base × height.
- Steps:
- Calculate.
- Answer: 50
- [Medium] Finding Slope of a Line
- EN: What is the slope of the line passing through (2,5) and (6,9)?
- FR: Quelle est la pente de la ligne passant par (2,5) et (6,9) ?
- Choices: A) 1 B) 1.5 C) 2 D) 4
- Hint: Use (y2 - y1) / (x2 - x1).
- Steps:
- Find the slope.
- Answer: 1
- [Medium] Solving Quadratic Equations
- EN: What are the roots of x² - 6x + 9 = 0?
- FR: Quelles sont les racines de x² - 6x + 9 = 0 ?
- Choices: A) 3 B) 2 C) 1 D) 4
- Hint: Factor the equation.
- Steps:
- Solve for x.
- Answer: 3
- [Medium] Finding the Vertex
- EN: What is the vertex of the parabola y = x² - 4x + 6?
- FR: Quelle est le sommet de la parabole y = x² - 4x + 6 ?
- Choices: A) (2, 2) B) (2, 0) C) (0, 6) D) (4, 6)
- Hint: Use the vertex formula -b/(2a).
- Steps:
- Find the vertex.
- Answer: (2, 2)
- [Medium] Permutations Calculation
- EN: How many ways can you arrange 3 books?
- FR: Combien de façons pouvez-vous arranger 3 livres ?
- Choices: A) 3 B) 6 C) 9 D) 12
- Hint: Use the factorial.
- Steps:
- Calculate 3!.
- Answer: 6
- [Hard] Solving Systems of Equations
- [Hard] Finding Surface Area of aCylinder
- [Hard] Calculating the Average of a Data Set
- [Hard] Probability of an Event
- [Hard] Transformations of Functions
- [Hard] Area of a trapezoid
Grade 11 Problems
- [Easy] Finding Function Value
- EN: What is f(2) if f(x) = x² + 3x?
- FR: Quelle est f(2) si f(x) = x² + 3x ?
- Choices: A) 10 B) 12 C) 14 D) 16
- Hint: Substitute and calculate.
- Steps:
- Replace x with 2.
- Answer: 10
- [Easy] Evaluating Expressions
- EN: What is the value of 3a + 4 if a = 5?
- FR: Quelle est la valeur de 3a + 4 si a = 5 ?
- Choices: A) 19 B) 18 C) 20 D) 17
- Hint: Substitute a with 5.
- Steps:
- Calculate.
- Answer: 19
- [Easy] Finding Limits
- EN: Find lim (x → 2) (x² - 4)/(x - 2).
- FR: Trouvez lim (x → 2) (x² - 4)/(x - 2).
- Choices: A) 3 B) 4 C) 0 D) 2
- Hint: Factor the numerator.
- Steps:
- Substitute and simplify.
- Answer: 4
- [Easy] Evaluating Logarithms
- EN: What is log₁₀(100)?
- FR: Quelle est log₁₀(100) ?
- Choices: A) 1 B) 2 C) 3 D) 4
- Hint: Remember that 10² = 100.
- Steps:
- Evaluate the logarithm.
- Answer: 2
- [Medium] Solving Quadratic Equations
- EN: Solve for x: x² - 5x + 6 = 0.
- FR: Résolvez pour x : x² - 5x + 6 = 0.
- Choices: A) 2,3 B) -1, -6 C) 1,6 D) 0,5
- Hint: Factor if possible.
- Steps:
- Find the roots.
- Answer: 2,3
- [Medium] Finding Maximum Value
- EN: What is the maximum of the function f(x) = -x² + 4x?
- FR: Quelle est le maximum de la fonction f(x) = -x² + 4x ?
- Choices: A) 4 B) 6 C) 8 D) 5
- Hint: Vertex formula.
- Steps:
- Find the vertex.
- Answer: 5
- [Medium] Solving Exponential Equations
- EN: If 2^x = 16, what is x?
- FR: Si 2^x = 16, quelle est la valeur de x ?
- Choices: A) 2 B) 4 C) 3 D) 5
- Hint: Rewrite 16 as a power of 2.
- Steps:
- Solve the exponential.
- Answer: 4
- [Medium] Finding Logarithms
- EN: If log₂(8) = x, what is x?
- FR: Si log₂(8) = x, quelle est la valeur de x ?
- Choices: A) 2 B) 3 C) 4 D) 5
- Hint: Rewrite 8 in terms of powers of 2.
- Steps:
- Evaluate the logarithm.
- Answer: 3
- [Hard] Generating Functions
- EN: If f(x) = x² - 3x + 2, what is f(3)?
- FR: Si f(x) = x² - 3x + 2, quelle est la valeur de f(3) ?
- Choices: A) 0 B) 6 C) 4 D) 2
- Hint: Substitute.
- Steps:
- Calculate.
- Answer: 0
- [Hard] Composing Functions
- EN: If f(x) = 2x and g(x) = x + 3, what is f(g(2))?
- FR: Si f(x) = 2x et g(x) = x + 3, quelle est la valeur de f(g(2)) ?
- Choices: A) 10 B) 14 C) 12 D) 8
- Hint: Substitute step by step.
- Steps:
- First find g(2), then find f(g(2)).
- Answer: 10
- [Hard] Analyzing Compound Interest
- EN: If $1000 is invested at 5% interest compounded annually, how much will it be after 2 years?
- FR: Si 1000 $ sont investis à un taux de 5 % d'intérêt composé annuellement, combien cela fera-t-il après 2 ans ?
- Choices: A) 1050 B) 1100 C) 1105 D) 1150
- Hint: Use the formula A = P(1 + r)^t.
- Steps:
- Substitute values in.
- Answer: 1105
- [Hard] Finding Complex Numbers
- EN: What is the modulus of the complex number 3 + 4i?
- FR: Quelle est le module du nombre complexe 3 + 4i ?
- Choices: A) 7 B) 5 C) 6 D) 8
- Hint: Use √(a² + b²).
- Steps:
- Calculate.
- Answer: 5
- [Hard] Rational Functions
- EN: What is the domain of f(x) = 1/(x-3)?
- FR: Quel est le domaine de f(x) = 1/(x-3) ?
- Choices: A) x ≠ 3 B) x = 3 C) All real numbers D) x > 3
- Hint: Identify restrictions on x.
- Steps:
- Declare values that make the denominator zero.
- Answer: x ≠ 3
- [Hard] Analyzing Sequences
- EN: What is the 10th term of the sequence defined by an = 3n + 1?
- FR: Quelle est la 10ème terme de la séquence définie par an = 3n + 1 ?
- Choices: A) 30 B) 31 C) 28 D) 29
- Hint: Substitute n = 10.
- Steps:
- Calculate.
- Answer: 31
- [Hard] Derivatives of Polynomial Functions
- EN: What is the derivative of f(x) = 3x² + 2x?
- FR: Quelle est la dérivée de f(x) = 3x² + 2x ?
- Choices: A) 6x + 2 B) 3x + 2 C) 2x + 3 D) 3x² + 2
- Hint: Apply power rule.
- Steps:
- Differentiate the function.
- Answer: 6x + 2
Grade 12 Problems
- [Easy] Evaluate the Function
- EN: If f(x) = x² + 2x, what is f(4)?
- FR: Si f(x) = x² + 2x, quelle est la valeur de f(4) ?
- Choices: A) 20 B) 18 C) 15 D) 22
- Hint: Substitute x with 4.
- Steps:
- Calculate.
- Answer: 24
- [Easy] Finding Limits
- EN: What is the limit as x approaches 2 in f(x) = x² + 3?
- FR: Quelle est la limite quand x approche 2 dans f(x) = x² + 3 ?
- Choices: A) 4 B) 5 C) 6 D) 7
- Hint: Substitute 2 into the function.
- Steps:
- Calculate the function value.
- Answer: 7
- [Easy] Finding the Derivative
- EN: What is the derivative of f(x) = 5x²?
- FR: Quelle est la dérivée de f(x) = 5x² ?
- Choices: A) 10x B) 5x C) 15x² D) 2x
- Hint: Use the power rule.
- Steps:
- Differentiate the term.
- Answer: 10x
- [Easy] Evaluating Logarithmic Functions
- EN: If log₁₀(100) = x, what is x?
- FR: Si log₁₀(100) = x, quelle est la valeur de x ?
- Choices: A) 100 B) 2 C) 10 D) 20
- Hint: Find the power of 10.
- Steps:
- Evaluate the logarithm.
- Answer: 2
- [Medium] Solving System of Equations
- EN: Solve for x and y: x + y = 10 and y = x + 2.
- FR: Résolvez pour x et y : x + y = 10 et y = x + 2.
- Choices: A) (2,8) B) (6,4) C) (5,5) D) (3,7)
- Hint: Substitute one equation into the other.
- Steps:
- Solve the system.
- Answer: (4,6)
- [Medium] Evaluating Definite Integrals
- EN: What is ∫(2x)dx from 1 to 3?
- FR: Quelle est ∫(2x)dx de 1 à 3 ?
- Choices: A) 8 B) 9 C) 7 D) 6
- Hint: Find the area under the curve.
- Steps:
- Calculate the integral.
- Answer: 8
- [Medium] Finding Eigenvalues
- EN: What are the eigenvalues of the matrix [[2, 1], [1, 2]]?
- FR: Quelles sont les valeurs propres de la matrice [[2, 1], [1, 2]] ?
- Choices: A) 1, 3 B) 2, 4 C) 3, 5 D) 0, 5
- Hint: Use the characteristic polynomial.
- Steps:
- Calculate eigenvalues.
- Answer: 1, 3
- [Medium] Solving Complex Numbers
- EN: What is the modulus of z = 3 + 4i?
- FR: Quelle est le module de z = 3 + 4i ?
- Choices: A) 5 B) 6 C) 4 D) 3
- Hint: Use √(a² + b²).
- Steps:
- Calculate modulus.
- Answer: 5
- [Hard] Finding Roots of a Polynomial
- EN: What are the roots of the polynomial p(x) = x³ - 6x² + 11x - 6?
- FR: Quelles sont les racines du polynôme p(x) = x³ - 6x² + 11x - 6 ?
- Choices: A) 1, 2, 3 B) 3, 2, 1 C) 6, -6 D) 0, 6, 3
- Hint: Factor the polynomial.
- Steps:
- Solve for roots.
- Answer: 1, 2, 3
- [Hard] Solving Complex Derivatives
- EN: What is the derivative of f(x) = sin(2x)?
- FR: Quelle est la dérivée de f(x) = sin(2x) ?
- Choices: A) 2cos(2x) B) cos(2x) C) 2sin(2x) D) -2sin(2x)
- Hint: Use chain rule.
- Steps:
- Differentiate carefully.
- Answer: 2cos(2x)
- [Hard] Solving Linear Differential Equations
- EN: Solve dy/dx + 2y = 0.
- FR: Résolvez dy/dx + 2y = 0.
- Choices: A) 0 B) Ce^(-2x) C) xy D) 2x^2
- Hint: Use separation of variables.
- Steps:
- Isolate y and integrate.
- Answer: Ce^(-2x)
- [Hard] Probability of Events
- EN: If a die is rolled, what is the probability of rolling an even number?
- FR: Si un dé est lancé, quelle est la probabilité d'obtenir un nombre pair ?
- Choices: A) 1/6 B) 1/3 C) 1/2 D) 2/3
- Hint: Count favorable outcomes.
- Steps:
- Divide favorable by total outcomes.
- Answer: 1/2
- [Hard] Finding Area of Regions
- EN: What is the area between the curves y = x² and y = x + 2?
- FR: Quelle est la surface entre les courbes y = x² et y = x + 2 ?
- Choices: A) 1 B) 2 C) 3 D) 4
- Hint: Set up integral for area.
- Steps:
- Calculate definite integral.
- Answer: 1
- [Hard] Analyzing Sequences
- EN: What is the sum of the first 100 positive integers?
- FR: Quelle est la somme des 100 premiers entiers positifs ?
- Choices: A) 5000 B) 5050 C) 5100 D) 5150
- Hint: Use the formula n(n+1)/2.
- Steps:
- Calculate sum.
- Answer: 5050
- [Hard] Finding Transformations on Functions
- EN: What is the transformation of the function g(x) = f(x-2) + 3?
- FR: Quelle est la transformation de la fonction g(x) = f(x-2) + 3 ?
- Choices: A) Shift left 2, up 3 B) Shift right 2, down
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