Daily Math — 2026-10-05
Grade 1 Problems
[Easy] Counting Skates
- EN: There are 7 pairs of skates on the shelf. How many skates are there in total?
- FR: Il y a 7 paires de patins sur l'étagère. Combien y a-t-il de patins en tout?
- Choices: A) 12 skates B) 14 skates C) 16 skates D) 11 skates
- Hint: If there are 3 pairs, that means 3 + 3 = 6 skates total.
- Steps:
- Think of pairs as groups of 2.
- 7 + 7 = 14 skates.
- So the total number of skates is 14.
- Answer: 14 skates
[Easy] Puck Addition
- EN: A hockey player scored 5 goals on Monday and 6 goals on Tuesday. How many goals did she score in total?
- FR: Une joueuse de hockey a marqué 5 buts lundi et 6 buts mardi. Combien de buts a-t-elle marqués en tout?
- Choices: A) 10 goals B) 13 goals C) 11 goals D) 9 goals
- Hint: To add 4 + 5, count up from 4: five, six, seven, eight, nine — that's 9.
- Steps:
- Start at 5 and count up 6 more.
- 5 → 6, 7, 8, 9, 10, 11.
- So the total is 11.
- Answer: 11 goals
[Easy] Skip Counting by 5s
- EN: Count by 5s. What number comes after 15?
- FR: Compte par 5. Quel nombre vient après 15?
- Choices: A) 18 B) 25 C) 20 D) 16
- Hint: When counting by 5s starting at 5, the pattern is 5, 10, 15, 20, 25 …
- Steps:
- The skip-counting-by-5 pattern goes 5, 10, 15, …
- Add 5 to 15: 15 + 5 = 20.
- So the next number is 20.
- Answer: 20
[Easy] Coin Recognition
- EN: Which coin is worth 10 cents in Canada?
- FR: Quelle pièce vaut 10 cents au Canada?
- Choices: A) Penny B) Loonie C) Nickel D) Dime
- Hint: A penny = 1 cent, a nickel = 5 cents, and the coin with the bluenose schooner is worth 10 cents.
- Steps:
- A penny is worth 1 cent.
- A nickel is worth 5 cents.
- A dime is worth 10 cents.
- So the answer is a dime.
- Answer: Dime
[Medium] Snowball Subtraction
- EN: There were 18 snowballs. The kids threw 9 of them. How many snowballs are left?
- FR: Il y avait 18 boules de neige. Les enfants en ont lancé 9. Combien en reste-t-il?
- Choices: A) 8 snowballs B) 11 snowballs C) 7 snowballs D) 9 snowballs
- Hint: For 16 − 8, think: 8 + 8 = 16, so 16 − 8 = 8.
- Steps:
- Start with 18 snowballs.
- Subtract 9: think 9 + 9 = 18, so 18 − 9 = 9.
- So 9 snowballs are left.
- Answer: 9 snowballs
[Medium] Comparing Numbers
- EN: Which number is greater: 43 or 34?
- FR: Quel nombre est le plus grand : 43 ou 34?
- Choices: A) 34 B) 43 C) They are equal D) 30
- Hint: Compare the tens digit first. The number with more tens is greater.
- Steps:
- 43 has 4 tens; 34 has 3 tens.
- 4 tens is more than 3 tens.
- So 43 is greater.
- Answer: 43
[Medium] Skip Counting by 2s
- EN: Skip count by 2s. What is the missing number: 8, 10, __, 14?
- FR: Compte par 2. Quel est le nombre manquant : 8, 10, __, 14?
- Choices: A) 13 B) 11 C) 12 D) 15
- Hint: When counting by 2s, add 2 each time: 4, 6, 8, 10 …
- Steps:
- The pattern adds 2 each time.
- 10 + 2 = 12.
- Check: 12 + 2 = 14. Correct!
- Answer: 12
[Medium] Adding Three Numbers
- EN: Mia has 3 stickers, 4 stickers, and 6 stickers. How many stickers does she have altogether?
- FR: Mia a 3 autocollants, 4 autocollants et 6 autocollants. Combien en a-t-elle en tout?
- Choices: A) 14 stickers B) 12 stickers C) 13 stickers D) 11 stickers
- Hint: To add 2 + 5 + 3, first add 2 + 5 = 7, then 7 + 3 = 10.
- Steps:
- First add 3 + 4 = 7.
- Then add 7 + 6 = 13.
- So Mia has 13 stickers altogether.
- Answer: 13 stickers
[Hard] Counting to 100
- EN: What is the number that is 10 more than 87?
- FR: Quel est le nombre qui est 10 de plus que 87?
- Choices: A) 97 B) 77 C) 98 D) 96
- Hint: To find 10 more than 52, just change the tens digit: 52 + 10 = 62.
- Steps:
- Start at 87.
- Add 10 more: the tens digit goes from 8 to 9.
- 87 + 10 = 97.
- Answer: 97
[Hard] Coin Counting
- EN: Luca has 1 dime and 2 nickels. How many cents does he have in total?
- FR: Luca a 1 pièce de 10 cents et 2 pièces de 5 cents. Combien de cents a-t-il en tout?
- Choices: A) 17 cents B) 25 cents C) 15 cents D) 20 cents
- Hint: If you have 1 dime and 1 nickel, that is 10 + 5 = 15 cents.
- Steps:
- 1 dime = 10 cents.
- 2 nickels = 5 + 5 = 10 cents.
- 10 + 10 = 20 cents total.
- Answer: 20 cents
Grade 2 Problems
[Easy] Adding to 100
- EN: What is 34 + 25?
- FR: Combien font 34 + 25?
- Choices: A) 58 B) 69 C) 59 D) 61
- Hint: Add the ones first, then the tens: for 21 + 14, ones: 1 + 4 = 5, tens: 2 + 1 = 3, answer is 35.
- Steps:
- Ones: 4 + 5 = 9.
- Tens: 3 + 2 = 5.
- So 34 + 25 = 59.
- Answer: 59
[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) 3:30 C) 3:00 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.
- Steps:
- The hour hand points to 3.
- The minute hand points to 12, meaning it is exactly on the hour.
- So the time is 3:00.
- Answer: 3:00
[Easy] Measuring Length
- EN: A pencil is 15 cm long. A crayon is 9 cm long. How much longer is the pencil?
- FR: Un crayon à mine mesure 15 cm de long. Un crayon de couleur mesure 9 cm de long. De combien le crayon à mine est-il plus long?
- Choices: A) 5 cm B) 7 cm C) 6 cm D) 8 cm
- Hint: To find the difference, subtract: 12 − 7 = 5 cm.
- Steps:
- Subtract the shorter length from the longer: 15 − 9.
- 15 − 9 = 6.
- The pencil is 6 cm longer.
- Answer: 6 cm
[Easy] Simple Patterns
- EN: Look at the pattern: 2, 4, 6, 8, __. What number comes next?
- FR: Regarde le motif : 2, 4, 6, 8, __. Quel nombre vient ensuite?
- Choices: A) 9 B) 11 C) 10 D) 12
- Hint: If the pattern is 1, 3, 5, 7, each number increases by 2, so the next is 7 + 2 = 9.
- Steps:
- Each number increases by 2.
- 8 + 2 = 10.
- So the next number is 10.
- Answer: 10
[Medium] Subtraction Within 100
- EN: There are 72 students at the school. 38 students go home for lunch. How many students are still at school?
- FR: Il y a 72 élèves à l'école. 38 élèves rentrent chez eux pour dîner. Combien d'élèves sont encore à l'école?
- Choices: A) 36 students B) 44 students C) 34 students D) 38 students
- Hint: For 65 − 27, borrow from the tens: 15 − 7 = 8, then 5 − 2 = 3, answer is 38.
- Steps:
- 72 − 38: borrow from tens — ones become 12 − 8 = 4.
- Tens: 6 − 3 = 3.
- So 72 − 38 = 34 students.
- Answer: 34 students
[Medium] Telling Time — Half Hour
- EN: The hockey game starts at half past 6. What time does the game start?
- FR: Le match de hockey commence à 6 h 30. À quelle heure commence le match?
- Choices: A) 6:15 B) 7:00 C) 6:00 D) 6:30
- Hint: Half past 4 means the minute hand is on 6 and the hour hand is between 4 and 5, so the time is 4:30.
- Steps:
- "Half past 6" means 30 minutes after 6 o'clock.
- The minute hand is on the 6; the hour hand is between 6 and 7.
- So the time is 6:30.
- Answer: 6:30
[Medium] Counting Coins to $1
- EN: Anaya has 3 quarters. How many cents does she have?
- FR: Anaya a 3 pièces de 25 cents. Combien de cents a-t-elle?
- Choices: A) 65 cents B) 60 cents C) 75 cents D) 80 cents
- Hint: 2 quarters = 25 + 25 = 50 cents, so add one more 25 cents for 3 quarters.
- Steps:
- Each quarter = 25 cents.
- 25 + 25 + 25 = 75 cents.
- So Anaya has 75 cents.
- Answer: 75 cents
[Medium] Measuring with a Ruler
- EN: A worm is 8 cm long. It grows 5 more cm. How long is the worm now?
- FR: Un ver mesure 8 cm de long. Il grandit de 5 cm de plus. Quelle est maintenant la longueur du ver?
- Choices: A) 14 cm B) 12 cm C) 13 cm D) 11 cm
- Hint: If a caterpillar is 6 cm and grows 4 cm, its new length is 6 + 4 = 10 cm.
- Steps:
- Start with 8 cm.
- Add 5 cm: 8 + 5 = 13.
- The worm is now 13 cm long.
- Answer: 13 cm
[Hard] Two-Step Word Problem
- EN: Tim Hortons has 45 timbits in a box. A class eats 18 of them. Then someone adds 10 more. How many timbits are in the box now?
- FR: Tim Hortons a 45 timbits dans une boîte. Une classe en mange 18. Ensuite, quelqu'un en ajoute 10 de plus. Combien de timbits y a-t-il maintenant dans la boîte?
- Choices: A) 38 timbits B) 37 timbits C) 36 timbits D) 33 timbits
- Hint: For 30 − 12 + 5, first do 30 − 12 = 18, then 18 + 5 = 23.
- Steps:
- Start with 45 timbits.
- After eating 18: 45 − 18 = 27.
- After adding 10: 27 + 10 = 37.
- Answer: 37 timbits
[Hard] Number Patterns
- EN: The pattern is: 100, 90, 80, 70, __. What number comes next?
- FR: Le motif est : 100, 90, 80, 70, __. Quel nombre vient ensuite?
- Choices: A) 55 B) 65 C) 60 D) 68
- Hint: If the pattern is 50, 40, 30, 20, each number decreases by 10, so the next is 20 − 10 = 10.
- Steps:
- Each number decreases by 10.
- 70 − 10 = 60.
- So the next number is 60.
- Answer: 60
Grade 3 Problems
[Easy] Multiplication — Times 2
- EN: What is 6 × 2?
- FR: Combien font 6 × 2?
- Choices: A) 14 B) 10 C) 12 D) 8
- Hint: 4 × 2 means 4 groups of 2: 2 + 2 + 2 + 2 = 8.
- Steps:
- 6 × 2 means 6 groups of 2.
- 2 + 2 + 2 + 2 + 2 + 2 = 12.
- So 6 × 2 = 12.
- Answer: 12
[Easy] Basic Division
- EN: There are 20 apples shared equally among 4 friends. How many apples does each friend get?
- FR: Il y a 20 pommes partagées également entre 4 amis. Combien de pommes chaque ami reçoit-il?
- Choices: A) 6 apples B) 4 apples C) 5 apples D) 8 apples
- Hint: If 15 stickers are shared among 5 friends, ask: 5 × ? = 15, so each gets 3.
- Steps:
- 20 ÷ 4 = ?
- Think: 4 × 5 = 20.
- Each friend gets 5 apples.
- Answer: 5 apples
[Easy] Fractions
- EN: A pizza is cut into 4 equal slices. Emma eats 1 slice. What fraction of the pizza did she eat?
- FR: Une pizza est coupée en 4 parts égales. Emma mange 1 part. Quelle fraction de la pizza a-t-elle mangée?
- Choices: A) 1/2 B) 1/3 C) 2/4 D) 1/4
- Hint: If you eat 1 slice out of 3 equal slices, you ate 1/3 of the pizza.
- Steps:
- The pizza is divided into 4 equal parts.
- Emma ate 1 of those 4 parts.
- The fraction is 1/4.
- Answer: 1/4
[Easy] Reading a Graph
- EN: A bar graph shows that 8 students chose hockey as their favourite sport and 5 students chose soccer. How many more students chose hockey?
- FR: Un diagramme à barres montre que 8 élèves ont choisi le hockey comme sport préféré et 5 ont choisi le soccer. Combien d'élèves de plus ont choisi le hockey?
- Choices: A) 4 students B) 2 students C) 3 students D) 5 students
- Hint: To find "how many more," subtract the smaller number from the larger: 9 − 6 = 3.
- Steps:
- Hockey: 8 students; soccer: 5 students.
- 8 − 5 = 3 more students.
- So 3 more students chose hockey.
- Answer: 3 students
[Medium] Multiplication — Times 5
- EN: What is 7 × 5?
- FR: Combien font 7 × 5?
- Choices: A) 30 B) 40 C) 35 D) 45
- Hint: Counting by 5s: 5, 10, 15, 20, 25, 30 — that's 6 fives, so 6 × 5 = 30.
- Steps:
- Count by 5s seven times: 5, 10, 15, 20, 25, 30, 35.
- So 7 × 5 = 35.
- Answer: 35
[Medium] Missing Factor
- EN: __ × 3 = 24. What is the missing number?
- FR: __ × 3 = 24. Quel est le nombre manquant?
- Choices: A) 9 B) 7 C) 6 D) 8
- Hint: For __ × 4 = 20, ask: how many groups of 4 make 20? Count by 4s: 4, 8, 12, 16, 20 — that's 5.
- Steps:
- Ask: what number times 3 equals 24?
- Count by 3s: 3, 6, 9, 12, 15, 18, 21, 24 — that's 8 steps.
- So 8 × 3 = 24; the missing number is 8.
- Answer: 8
[Medium] Perimeter
- EN: A rectangle has a length of 7 cm and a width of 3 cm. What is its perimeter?
- FR: Un rectangle a une longueur de 7 cm et une largeur de 3 cm. Quel est son périmètre?
- Choices: A) 21 cm B) 18 cm C) 20 cm D) 22 cm
- Hint: Perimeter of a rectangle = length + length + width + width: for a 5 cm × 2 cm shape, P = 5 + 5 + 2 + 2 = 14 cm.
- Steps:
- Add all four sides: 7 + 7 + 3 + 3.
- 7 + 7 = 14; 3 + 3 = 6.
- 14 + 6 = 20 cm.
- Answer: 20 cm
[Medium] Multiplication — Times 10
- EN: There are 9 bags. Each bag has 10 marbles. How many marbles are there in total?
- FR: Il y a 9 sacs. Chaque sac contient 10 billes. Combien y a-t-il de billes en tout?
- Choices: A) 80 marbles B) 19 marbles C) 90 marbles D) 100 marbles
- Hint: Any number times 10 just adds a zero: 6 × 10 = 60.
- Steps:
- 9 × 10 = 90.
- So there are 90 marbles in total.
- Answer: 90 marbles
[Hard] Multi-Step Problem
- EN: A box holds 4 rows of cookies. Each row has 5 cookies. If Ben eats 3 cookies, how many cookies are left?
- FR: Une boîte contient 4 rangées de biscuits. Chaque rangée a 5 biscuits. Si Ben mange 3 biscuits, combien en reste-t-il?
- Choices: A) 18 cookies B) 15 cookies C) 17 cookies D) 20 cookies
- Hint: First find the total: 3 rows × 4 cookies = 12, then subtract what was eaten: 12 − 2 = 10.
- Steps:
- Find total cookies: 4 × 5 = 20.
- Subtract the cookies Ben ate: 20 − 3 = 17.
- So 17 cookies are left.
- Answer: 17 cookies
[Hard] Fractions of a Group
- EN: There are 12 hockey players on the ice. One quarter (1/4) of them play defence. How many players play defence?
- FR: Il y a 12 joueurs de hockey sur la glace. Un quart (1/4) d'entre eux jouent en défense. Combien de joueurs jouent en défense?
- Choices: A) 4 players B) 6 players C) 3 players D) 2 players
- Hint: To find 1/4 of 8, divide 8 by 4: 8 ÷ 4 = 2.
- Steps:
- To find 1/4 of a group, divide the total by 4.
- 12 ÷ 4 = 3.
- So 3 players play defence.
- Answer: 3 players
Grade 4 Problems
[Easy] Multiplication Tables
- EN: What is 8 × 7?
- FR: Combien font 8 × 7?
- Choices: A) 54 B) 63 C) 56 D) 48
- Hint: Think of 8 × 6 = 48, then add one more group of 8: 48 + 8 = 56.
- Steps:
- 8 × 7 = 8 × 6 + 8 = 48 + 8 = 56.
- So 8 × 7 = 56.
- Answer: 56
[Easy] Decimal Place Value
- EN: What is the value of the digit 3 in the number 4.37?
- FR: Quelle est la valeur du chiffre 3 dans le nombre 4,37?
- Choices: A) 3 ones B) 3 tenths C) 3 hundredths D) 3 tens
- Hint: In the number 2.58, the 5 is in the tenths place and the 8 is in the hundredths place.
- Steps:
- In 4.37, the digit 4 is in the ones place.
- The digit 3 is in the tenths place.
- The digit 7 is in the hundredths place.
- Answer: 3 tenths
[Easy] Missing Factor
- EN: 36 ÷ __ = 9. What is the missing number?
- FR: 36 ÷ __ = 9. Quel est le nombre manquant?
- Choices: A) 3 B) 6 C) 5 D) 4
- Hint: For 24 ÷ __ = 6, think 6 × ? = 24: 6 × 4 = 24, so the missing number is 4.
- Steps:
- Think: 9 × ? = 36.
- 9 × 4 = 36.
- So the missing number is 4.
- Answer: 4
[Easy] Area of a Rectangle
- EN: A classroom floor is 9 m long and 6 m wide. What is the area of the floor?
- FR: Le plancher d'une salle de classe mesure 9 m de long et 6 m de large. Quelle est l'aire du plancher?
- Choices: A) 30 m² B) 54 m² C) 45 m² D) 60 m²
- Hint: Area of a rectangle = length × width: for a 5 m × 4 m floor, Area = 5 × 4 = 20 m².
- Steps:
- Area = length × width.
- Area = 9 × 6 = 54.
- The area of the floor is 54 m².
- Answer: 54 m²
[Medium] Long Division with Remainder
- EN: What is 47 ÷ 5?
- FR: Combien font 47 ÷ 5?
- Choices: A) 8 remainder 7 B) 9 remainder 2 C) 7 remainder 4 D) 10 remainder 3
- Hint: For 23 ÷ 4, ask how many 4s fit in 23: 4 × 5 = 20, with 3 left over, so the answer is 5 remainder 3.
- Steps:
- How many times does 5 go into 47?
- 5 × 9 = 45; 47 − 45 = 2.
- So 47 ÷ 5 = 9 remainder 2.
- Answer: 9 remainder 2
[Medium] Elapsed Time
- EN: A skating class starts at 10:15 a.m. and ends at 11:45 a.m. How long is the class?
- FR: Un cours de patinage commence à 10 h 15 et se termine à 11 h 45. Quelle est la durée du cours?
- Choices: A) 1 hour 15 minutes B) 2 hours C) 1 hour 30 minutes D) 1 hour 45 minutes
- Hint: From 2:10 to 3:40, count up: 50 minutes to reach 3:00, then 40 more minutes = 1 hour 30 minutes.
- Steps:
- From 10:15 to 11:15 is exactly 1 hour.
- From 11:15 to 11:45 is 30 more minutes.
- Total: 1 hour 30 minutes.
- Answer: 1 hour 30 minutes
[Medium] Comparing Fractions
- EN: Which fraction is greater: 3/4 or 2/3?
- FR: Quelle fraction est plus grande : 3/4 ou 2/3?
- Choices: A) 2/3 B) They are equal C) 1/2 D) 3/4
- Hint: To compare 1/2 and 3/4, find a common denominator of 4: 1/2 = 2/4, and 3/4 > 2/4, so 3/4 is greater.
- Steps:
- Find a common denominator for 3/4 and 2/3. Use 12.
- 3/4 = 9/12; 2/3 = 8/12.
- 9/12 > 8/12, so 3/4 is greater.
- Answer: 3/4
[Medium] Table Word Problem
- EN: The table below shows the price of school supplies. A pen costs $1.25 and a notebook costs $2.50. How much would 2 pens and 1 notebook cost?
- FR: Le tableau ci-dessous indique le prix des fournitures scolaires. Un stylo coûte 1,25 $ et un cahier coûte 2,50 $. Combien coûteraient 2 stylos et 1 cahier?
- Choices: A) $4.75 B) $5.25 C) $5.00 D) $6.25
- Hint: For 2 erasers at $0.75 each and 1 ruler at $1.50, compute 2 × $0.75 + $1.50 = $1.50 + $1.50 = $3.00.
- Steps:
- 2 pens: 2 × $1.25 = $2.50.
- 1 notebook: $2.50.
- Total: $2.50 + $2.50 = $5.00.
- Answer: $5.00
[Hard] Multi-Step Division and Multiplication
- EN: A teacher has 96 pencils. She divides them equally into 8 boxes. Then she removes 5 pencils from each box for an art project. How many pencils are left in each box?
- FR: Une enseignante a 96 crayons. Elle les répartit également dans 8 boîtes. Ensuite, elle retire 5 crayons de chaque boîte pour un projet d'art. Combien reste-t-il de crayons dans chaque boîte?
- Choices: A) 6 pencils B) 8 pencils C) 7 pencils D) 10 pencils
- Hint: For 60 pencils in 6 boxes with 4 removed from each: 60 ÷ 6 = 10 per box, then 10 − 4 = 6 pencils left.
- Steps:
- First divide: 96 ÷ 8 = 12 pencils per box.
- Then subtract: 12 − 5 = 7 pencils left per box.
- So 7 pencils remain in each box.
- Answer: 7 pencils
[Hard] Decimal Operations
- EN: Isabella scored 8.45 points in a skating competition. Her teammate scored 7.90 points. What is the total score for the team?
- FR: Isabella a obtenu 8,45 points dans une compétition de patinage. Sa coéquipière a obtenu 7,90 points. Quel est le score total de l'équipe?
- Choices: A) 16.45 points B) 15.35 points C) 16.35 points D) 15.75 points
- Hint: Add decimals by lining up the decimal points: 3.25 + 4.60 = 7.85.
- Steps:
- Line up the decimal points: 8.45 + 7.90.
- Hundredths: 5 + 0 = 5. Tenths: 4 + 9 = 13, carry 1.
- Ones: 8 + 7 + 1 = 16. Total: 16.35.
- Answer: 16.35 points
Grade 5 Problems
[Easy] Multi-Digit Multiplication
- EN: What is 24 × 6?
- FR: Combien font 24 × 6?
- Choices: A) 148 B) 124 C) 144 D) 136
- Hint: For 13 × 4, multiply ones: 3 × 4 = 12, write 2 carry 1; multiply tens: 1 × 4 + 1 = 5; answer is 52.
- Steps:
- Ones: 4 × 6 = 24, write 4, carry 2.
- Tens: 2 × 6 = 12, plus 2 = 14.
- So 24 × 6 = 144.
- Answer: 144
[Easy] Adding Fractions with Like Denominators
- EN: What is 2/7 + 3/7?
- FR: Combien font 2/7 + 3/7?
- Choices: A) 5/14 B) 6/7 C) 4/7 D) 5/7
- Hint: When adding fractions with the same denominator, add only the numerators: 1/5 + 2/5 = 3/5.
- Steps:
- The denominators are the same (7), so add the numerators.
- 2 + 3 = 5.
- So 2/7 + 3/7 = 5/7.
- Answer: 5/7
[Easy] Percentage Intro — 50%
- EN: What is 50% of 80?
- FR: Combien font 50% de 80?
- Choices: A) 30 B) 45 C) 40 D) 50
- Hint: 50% means half, so 50% of 60 = 60 ÷ 2 = 30.
- Steps:
- 50% means half.
- 80 ÷ 2 = 40.
- So 50% of 80 is 40.
- Answer: 40
[Easy] Decimal Operations
- EN: What is 3.6 + 2.8?
- FR: Combien font 3,6 + 2,8?
- Choices: A) 5.4 B) 6.4 C) 6.2 D) 5.8
- Hint: Line up the decimal points: 2.4 + 1.9: tenths: 4 + 9 = 13, write 3 carry 1; ones: 2 + 1 + 1 = 4; answer is 4.3.
- Steps:
- Tenths: 6 + 8 = 14, write 4, carry 1.
- Ones: 3 + 2 + 1 = 6.
- So 3.6 + 2.8 = 6.4.
- Answer: 6.4
[Medium] Multi-Digit Division
- EN: What is 252 ÷ 7?
- FR: Combien font 252 ÷ 7?
- Choices: A) 34 B) 38 C) 36 D) 42
- Hint: For 120 ÷ 6, ask how many 6s fit in 12: that's 2, so 6 fits into 12 twice, giving 20.
- Steps:
- How many 7s in 25? That's 3 (3 × 7 = 21). Remainder: 25 − 21 = 4. Bring down the 2: 42.
- How many 7s in 42? That's 6 (6 × 7 = 42). Remainder: 0.
- So 252 ÷ 7 = 36.
- Answer: 36
[Medium] Missing Factor
- EN: __ × 18 = 108. What is the missing number?
- FR: __ × 18 = 108. Quel est le nombre manquant?
- Choices: A) 5 B) 7 C) 4 D) 6
- Hint: For __ × 12 = 60, think 12 × 5 = 60, so the missing number is 5.
- Steps:
- Ask: 18 × ? = 108.
- Try 6: 18 × 6 = 108. Yes!
- The missing number is 6.
- Answer: 6
[Medium] Volume of a Rectangular Prism
- EN: A box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
- FR: Une boîte mesure 5 cm de long, 4 cm de large et 3 cm de haut. Quel est le volume de la boîte?
- Choices: A) 48 cm³ B) 64 cm³ C) 60 cm³ D) 56 cm³
- Hint: Volume = length × width × height: for a 2 cm × 3 cm × 4 cm box, V = 2 × 3 × 4 = 24 cm³.
- Steps:
- V = length × width × height.
- V = 5 × 4 × 3 = 20 × 3 = 60.
- The volume is 60 cm³.
- Answer: 60 cm³
[Medium] Table Word Problem
- EN: The table shows items sold at a school bake sale. Muffins cost $1.50 each, cookies cost $0.75 each, and juice boxes cost $1.00 each. Olivier buys 2 muffins, 3 cookies, and 1 juice box. How much does he spend in total?
- FR: Le tableau montre les articles vendus lors d'une vente de pâtisseries scolaires. Les muffins coûtent 1,50 $ chacun, les biscuits 0,75 $ chacun et les boîtes de jus 1,00 $ chacune. Olivier achète 2 muffins, 3 biscuits et 1 boîte de jus. Combien dépense-t-il en tout?
- Choices: A) $5.75 B) $6.25 C) $7.00 D) $5.25
- Hint: Calculate each group separately then add: 2 × $2.00 + 1 × $1.50 = $4.00 + $1.50 = $5.50.
- Steps:
- 2 muffins: 2 × $1.50 = $3.00.
- 3 cookies: 3 × $0.75 = $2.25.
- 1 juice box: $1.00. Total: $3.00 + $2.25 + $1.00 = $6.25.
- Answer: $6.25
[Hard] Percentage — 25% and 10%
- EN: A hockey jersey originally costs $80. It is on sale for 25% off. What is the sale price?
- FR: Un chandail de hockey coûte originalement 80 $. Il est en solde à 25 % de rabais. Quel est le prix de vente?
- Choices: A) $65 B) $55 C) $70 D) $60
- Hint: 25% of 40 = 40 ÷ 4 = 10, so the sale price is 40 − 10 = $30.
- Steps:
- 25% of $80 = $80 ÷ 4 = $20 (the discount).
- Sale price = $80 − $20 = $60.
- The jersey costs $60 on sale.
- Answer: $60
[Hard] Subtracting Fractions and Decimals
- EN: A container holds 5.75 litres of maple syrup. A chef uses 2/4 of a litre. How much maple syrup is left? (Hint: 2/4 = 0.5)
- FR: Un contenant contient 5,75 litres de sirop d'érable. Un chef utilise 2/4 de litre. Quelle quantité de sirop d'érable reste-t-il? (Indice : 2/4 = 0,5)
- Choices: A) 5.50 litres B) 5.00 litres C) 5.25 litres D) 4.75 litres
- Hint: Convert the fraction to a decimal first, then subtract: 3.80 − 0.25 = 3.55 litres.
- Steps:
- Convert 2/4 to a decimal: 2/4 = 0.50.
- Subtract: 5.75 − 0.50 = 5.25.
- So 5.25 litres of maple syrup is left.
- Answer: 5.25 litres
Grade 6 Problems
[Easy] Percent of a Number
- EN: What is 30% of 200?
- FR: Combien font 30% de 200?
- Choices: A) 50 B) 60 C) 70 D) 80
- Hint: 10% of 150 = 15, so 30% = 3 × 15 = 45.
- Steps:
- 10% of 200 = 200 ÷ 10 = 20.
- 30% = 3 × 20 = 60.
- So 30% of 200 is 60.
- Answer: 60
[Easy] Integer Introduction
- EN: It is −8°C in Winnipeg in the morning. By noon, the temperature rises 12°C. What is the temperature at noon?
- FR: Il fait −8°C à Winnipeg le matin. À midi, la température monte de 12°C. Quelle est la température à midi?
- Choices: A) 6°C B) 3°C C) 4°C D) 20°C
- Hint: For −5 + 9, start at −5 on the number line and move 9 steps right: −5, −4, −3, −2, −1, 0, 1, 2, 3, 4.
- Steps:
- Start at −8.
- Add 12: −8 + 12 = 4.
- The temperature at noon is 4°C.
- Answer: 4°C
[Easy] Order of Operations (BEDMAS)
- EN: What is 3 + 4 × 2?
- FR: Combien font 3 + 4 × 2?
- Choices: A) 14 B) 10 C) 11 D) 9
- Hint: BEDMAS says multiply before you add: for 5 + 3 × 2, do 3 × 2 = 6 first, then 5 + 6 = 11.
- Steps:
- Multiplication before addition (BEDMAS).
- 4 × 2 = 8.
- Then 3 + 8 = 11.
- Answer: 11
[Easy] Simple Algebraic Expression
- EN: If n = 5, what is the value of 3n + 4?
- FR: Si n = 5, quelle est la valeur de 3n + 4?
- Choices: A) 22 B) 17 C) 19 D) 24
- Hint: For 2n + 3 when n = 4, substitute: 2 × 4 + 3 = 8 + 3 = 11.
- Steps:
- Substitute n = 5: 3 × 5 + 4.
- 3 × 5 = 15.
- 15 + 4 = 19.
- Answer: 19
[Medium] Fraction Multiplication
- EN: What is 2/3 × 3/4?
- FR: Combien font 2/3 × 3/4?
- Choices: A) 5/12 B) 6/12 C) 1/2 D) 2/7
- Hint: To multiply fractions, multiply numerators together and denominators together: 1/2 × 2/5 = 2/10 = 1/5.
- Steps:
- Multiply numerators: 2 × 3 = 6.
- Multiply denominators: 3 × 4 = 12.
- 6/12 = 1/2.
- Answer: 1/2
[Medium] Ratios and Rates
- EN: A car travels 180 km in 3 hours. What is its speed in km/h?
- FR: Une voiture parcourt 180 km en 3 heures. Quelle est sa vitesse en km/h?
- Choices: A) 70 km/h B) 50 km/h C) 60 km/h D) 65 km/h
- Hint: For 120 km in 4 hours, speed = 120 ÷ 4 = 30 km/h.
- Steps:
- Speed = distance ÷ time.
- 180 ÷ 3 = 60.
- The car's speed is 60 km/h.
- Answer: 60 km/h
[Medium] Fraction Division
- EN: What is 3/4 ÷ 1/2?
- FR: Combien font 3/4 ÷ 1/2?
- Choices: A) 3/2 B) 3/8 C) 2/3 D) 1/2
- Hint: To divide by a fraction, multiply by its reciprocal: 2/5 ÷ 1/3 = 2/5 × 3/1 = 6/5.
- Steps:
- Flip the second fraction (find its reciprocal): 1/2 becomes 2/1.
- Multiply: 3/4 × 2/1 = 6/4.
- Simplify: 6/4 = 3/2.
- Answer: 3/2
[Medium] Multi-Step Table Word Problem
- EN: The table shows hockey game ticket prices: adult tickets cost $12 each, student tickets cost $7 each, and child (under 6) tickets are free. The Tremblay family buys 2 adult tickets, 3 student tickets, and 1 child ticket. How much do they pay in total?
- FR: Le tableau montre le prix des billets de match de hockey : les billets adultes coûtent 12 $ chacun, les billets étudiants coûtent 7 $ chacun et les billets enfants (moins de 6 ans) sont gratuits. La famille Tremblay achète 2 billets adultes, 3 billets étudiants et 1 billet enfant. Combien paient-ils en tout?
- Choices: A) $40 B) $47 C) $45 D) $55
- Hint: Calculate each category separately: 1 adult × $10 + 2 students × $6 + free = $10 + $12 = $22.
- Steps:
- 2 adult tickets: 2 × $12 = $24.
- 3 student tickets: 3 × $7 = $21.
- 1 child ticket: $0. Total: $24 + $21 + $0 = $45.
- Answer: $45
[Hard] BEDMAS with Brackets
- EN: What is (5 + 3) × 4 − 10 ÷ 2?
- FR: Combien font (5 + 3) × 4 − 10 ÷ 2?
- Choices: A) 22 B) 30 C) 27 D) 26
- Hint: BEDMAS: Brackets first, then multiply/divide left to right, then add/subtract: (2 + 1) × 5 − 4 ÷ 2 = 3 × 5 − 2 = 15 − 2 = 13.
- Steps:
- Brackets: 5 + 3 = 8.
- Multiply: 8 × 4 = 32.
- Divide: 10 ÷ 2 = 5.
- Subtract: 32 − 5 = 27.
- Answer: 27
[Hard] Percent Problem with Multiple Steps
- EN: A school store normally sells a binder for $6.00. This week it is 15% off. What is the sale price of the binder?
- FR: La boutique scolaire vend normalement un classeur 6,00 $. Cette semaine, il est à 15 % de rabais. Quel est le prix de vente du classeur?
- Choices: A) $5.10 B) $4.90 C) $5.50 D) $4.80
- Hint: To find 15% of a number, find 10% and then 5% (half of 10%), then add them: 10% of $8 = $0.80; 5% = $0.40; total discount = $1.20; sale price = $8 − $1.20 = $6.80.
- Steps:
- 10% of $6.00 = $0.60.
- 5% of $6.00 = $0.30.
- 15% discount = $0.60 + $0.30 = $0.90. Sale price = $6.00 − $0.90 = $5.10.
- Answer: $5.10
Grade 7 Problems
[Easy] Integer Operations — Addition
- EN: What is (−14) + 9?
- FR: Combien font (−14) + 9?
- Choices: A) −6 B) −4 C) −5 D) 23
- Hint: For (−10) + 6, start at −10 and move 6 steps right on the number line: the answer is −4.
- Steps:
- Start at −14 and move 9 steps toward zero.
- −14 + 9 = −5.
- The answer is −5.
- Answer: −5
[Easy] Fraction Fluency
- EN: What is 5/6 − 1/3? (Hint: convert 1/3 to sixths first.)
- FR: Combien font 5/6 − 1/3? (Indice : convertis d'abord 1/3 en sixièmes.)
- Choices: A) 4/6 B) 3/6 C) 2/6 D) 1/3
- Hint: For 3/4 − 1/4, the denominators are already the same, so just subtract the numerators: 3 − 1 = 2, giving 2/4 = 1/2.
- Steps:
- Convert 1/3 to sixths: 1/3 = 2/6.
- Now subtract: 5/6 − 2/6 = 3/6.
- Simplify: 3/6 = 1/2.
- Answer: 3/6
[Easy] Percentage — Discount
- EN: A loonie-store item originally costs $4.00. There is a 25% discount. How much is the discount in dollars?
- FR: Un article dans un magasin à prix réduit coûte originalement 4,00 $. Il y a un rabais de 25 %. Quel est le montant du rabais en dollars?
- Choices: A) $0.75 B) $1.25 C) $0.50 D) $1.00
- Hint: 25% of a number = divide by 4. For 25% of $8, that's $8 ÷ 4 = $2.
- Steps:
- 25% of $4.00 = $4.00 ÷ 4 = $1.00.
- The discount is $1.00.
- Answer: $1.00
[Easy] One-Step Linear Equation
- EN: Solve for x: x + 13 = 27.
- FR: Résous pour x : x + 13 = 27.
- Choices: A) x = 15 B) x = 40 C) x = 14 D) x = 16
- Hint: For x + 5 = 11, subtract 5 from both sides: x = 11 − 5 = 6.
- Steps:
- Subtract 13 from both sides: x = 27 − 13.
- 27 − 13 = 14.
- So x = 14.
- Answer: x = 14
[Medium] Integer Operations — Multiplication
- EN: What is (−6) × (−7)?
- FR: Combien font (−6) × (−7)?
- Choices: A) −42 B) 36 C) 13 D) 42
- Hint: When two negative numbers are multiplied, the result is positive: (−3) × (−4) = 12.
- Steps:
- Multiply the absolute values: 6 × 7 = 42.
- Negative × negative = positive.
- So (−6) × (−7) = 42.
- Answer: 42
[Medium] Percentage — Tax
- EN: A book costs $18.00. The HST is 13%. What is the total price including tax?
- FR: Un livre coûte 18,00 $. La TVH est de 13 %. Quel est le prix total incluant la taxe?
- Choices: A) $20.34 B) $19.80 C) $21.34 D) $23.40
- Hint: To find 13% of $20, find 10% ($2.00) + 3% ($0.60) = $2.60 tax; total = $20 + $2.60 = $22.60.
- Steps:
- 10% of $18 = $1.80; 3% of $18 = $0.54.
- Tax = $1.80 + $0.54 = $2.34.
- Total = $18.00 + $2.34 = $20.34.
- Answer: $20.34
[Medium] Surface Area
- EN: What is the surface area of a rectangular box that is 5 cm long, 3 cm wide, and 2 cm tall?
- FR: Quelle est l'aire totale d'une boîte rectangulaire de 5 cm de long, 3 cm de large et 2 cm de haut?
- Choices: A) 62 cm² B) 30 cm² C) 48 cm² D) 52 cm²
- Hint: SA = 2(lw + lh + wh). For a 3 × 2 × 1 box: SA = 2(6 + 3 + 2) = 2 × 11 = 22 cm².
- Steps:
- SA = 2(lw + lh + wh) = 2(5×3 + 5×2 + 3×2).
- = 2(15 + 10 + 6) = 2 × 31.
- = 62 cm².
- Answer: 62 cm²
[Medium] Table Word Problem
- EN: The table below shows the number of goals scored by three hockey players this season. Maya scored 18 goals, Priya scored 12 goals, and Sam scored 15 goals. The coach gives a $5 bonus for every goal scored above 14. How many bonus dollars does Maya earn?
- FR: Le tableau ci-dessous montre le nombre de buts marqués par trois joueuses de hockey cette saison. Maya a marqué 18 buts, Priya en a marqué 12 et Sam en a marqué 15. L'entraîneur donne un bonus de 5 $ pour chaque but marqué au-delà de 14. Combien de dollars de bonus Maya gagne-t-elle?
- Choices: A) $15 B) $25 C) $20 D) $30
- Hint: If a player scored 17 goals and the bonus starts above 12, they scored 5 bonus goals at $3 each: 5 × $3 = $15.
- Steps:
- Maya scored 18 goals; bonus applies to goals above 14: 18 − 14 = 4 bonus goals.
- 4 × $5 = $20.
- Maya earns $20 in bonuses.
- Answer: $20
[Hard] Integer Division and Probability
- EN: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If you pick one marble at random, what is the probability (as a fraction) of picking a blue marble?
- FR: Un sac contient 5 billes rouges, 3 billes bleues et 2 billes vertes. Si tu piges une bille au hasard, quelle est la probabilité (en fraction) de piger une bille bleue?
- Choices: A) 1/5 B) 3/8 C) 3/10 D) 1/3
- Hint: Probability = (number of favourable outcomes) ÷ (total outcomes). For 4 red and 2 blue marbles, P(blue) = 2/6 = 1/3.
- Steps:
- Total marbles: 5 + 3 + 2 = 10.
- Blue marbles: 3.
- P(blue) = 3/10.
- Answer: 3/10
[Hard] Multi-Step Percent Problem
- EN: A pair of hockey gloves costs $95.00. They go on sale for 20% off. Then an additional 10% off the sale price is offered at the cashier. What is the final price?
- FR: Une paire de gants de hockey coûte 95,00 $. Elle est en solde à 20 % de rabais. Puis un rabais supplémentaire de 10 % sur le prix de vente est offert à la caisse. Quel est le prix final?
- Choices: A) $68.40 B) $63.00 C) $70.00 D) $57.00
- Hint: Apply each discount one at a time. For $100 with 20% off: sale price = $80; then 10% off $80 = $8 more off; final = $72.
- Steps:
- 20% off $95: discount = $19; sale price = $95 − $19 = $76.
- Additional 10% off $76: discount = $7.60; final = $76 − $7.60 = $68.40.
- The final price is $68.40.
- Answer: $68.40
Grade 8 Problems
[Easy] Perfect Squares
- EN: What is √144?
- FR: Combien vaut √144?
- Choices: A) 14 B) 11 C) 12 D) 13
- Hint: Think: what number times itself equals 144? Try 12: 12 × 12 = 144.
- Steps:
- Ask: what number squared equals 144?
- 12 × 12 = 144. ✓
- So √144 = 12.
- Answer: 12
[Easy] Mean
- EN: Find the mean of these five test scores: 80, 75, 90, 85, 70.
- FR: Trouve la moyenne de ces cinq résultats de test : 80, 75, 90, 85, 70.
- Choices: A) 85 B) 78 C) 80 D) 75
- Hint: Mean = sum of all values ÷ number of values. For scores 60, 70, 80: sum = 210, mean = 210 ÷ 3 = 70.
- Steps:
- Sum: 80 + 75 + 90 + 85 + 70 = 400.
- Divide by 5: 400 ÷ 5 = 80.
- The mean is 80.
- Answer: 80
[Easy] Two-Step Linear Equation
- EN: Solve for x: 2x + 5 = 13.
- FR: Résous pour x : 2x + 5 = 13.
- Choices: A) x = 9 B) x = 3 C) x = 4 D) x = 6
- Hint: For 3x + 2 = 11, subtract 2: 3x = 9, then divide by 3: x = 3.
- Steps:
- Subtract 5 from both sides: 2x = 8.
- Divide both sides by 2: x = 4.
- So x = 4.
- Answer: x = 4
[Easy] Percent Increase
- EN: A hockey player's salary increased from $200,000 to $250,000. What is the percent increase?
- FR: Le salaire d'un joueur de hockey est passé de 200 000 $ à 250 000 $. Quel est le pourcentage d'augmentation?
- Choices: A) 20% B) 30% C) 25% D) 15%
- Hint: Percent increase = (increase ÷ original) × 100. For a rise from $60 to $75: increase = $15; 15/60 × 100 = 25%.
- Steps:
- Increase = $250,000 − $200,000 = $50,000.
- Percent increase = (50,000 ÷ 200,000) × 100 = 0.25 × 100 = 25%.
- So the percent increase is 25%.
- Answer: 25%
[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) 12 cm B) 14 cm C) 11 cm D) 10 cm
- Hint: Use a² + b² = c². For legs 3 and 4: 9 + 16 = 25, so c = √25 = 5.
- Steps:
- a² + b² = c²: 6² + 8² = c².
- 36 + 64 = 100.
- c = √100 = 10 cm.
- Answer: 10 cm
[Medium] Two-Step Equation — Harder
- EN: Solve for x: 3x − 7 = 14.
- FR: Résous pour x : 3x − 7 = 14.
- Choices: A) x = 6 B) x = 8 C) x = 9 D) x = 7
- Hint: For 4x − 3 = 13, add 3: 4x = 16, then divide by 4: x = 4.
- Steps:
- Add 7 to both sides: 3x = 21.
- Divide both sides by 3: x = 7.
- So x = 7.
- Answer: x = 7
[Medium] Slope Introduction
- EN: A line passes through the points (2, 3) and (6, 7). What is the slope of the line?
- FR: Une droite passe par les points (2, 3) et (6, 7). Quel est le taux de variation (pente) de la droite?
- Choices: A) 2 B) 1/2 C) 3 D) 1
- Hint: Slope = (y₂ − y₁) ÷ (x₂ − x₁). For (1, 2) and (3, 6): slope = (6−2)/(3−1) = 4/2 = 2.
- Steps:
- Slope = (7 − 3) ÷ (6 − 2) = 4 ÷ 4.
- 4 ÷ 4 = 1.
- The slope is 1.
- Answer: 1
[Medium] Median and Mode
- EN: Find the median of this data set: 3, 7, 7, 9, 11, 14, 15.
- FR: Trouve la médiane de cet ensemble de données : 3, 7, 7, 9, 11, 14, 15.
- Choices: A) 7 B) 11 C) 9 D) 10
- Hint: The median is the middle value when data is in order. For 2, 5, 8, 10, 12, the median is the 3rd value: 8.
- Steps:
- Data is already in order: 3, 7, 7, 9, 11, 14, 15.
- There are 7 values; the middle (4th) value is 9.
- The median is 9.
- Answer: 9
[Hard] Pythagorean Theorem — Applied
- EN: A ramp goes from the ground to a platform that is 5 m high. The base of the ramp is 12 m from the wall. How long is the ramp?
- FR: Une rampe va du sol à une plateforme haute de 5 m. La base de la rampe est à 12 m du mur. Quelle est la longueur de la rampe?
- Choices: A) 17 m B) 11 m C) 14 m D) 13 m
- Hint: Use a² + b² = c². For height 8 and base 6: 64 + 36 = 100, so the ramp = √100 = 10 m.
- Steps:
- a² + b² = c²: 5² + 12² = c².
- 25 + 144 = 169.
- c = √169 = 13 m.
- Answer: 13 m
[Hard] Percent Decrease and Two-Step Problem
- EN: A store reduces the price of a winter coat by 40%. The original price was $150. After the reduction, a coupon gives an additional $10 off. What is the final price?
- FR: Un magasin réduit le prix d'un manteau d'hiver de 40 %. Le prix original était de 150 $. Après la réduction, un coupon offre 10 $ de plus. Quel est le prix final?
- Choices: A) $80 B) $85 C) $90 D) $95
- Hint: Reduce by 40%: new price = original × 0.60. For $200: $200 × 0.60 = $120, then subtract coupon.
- Steps:
- 40% of $150 = $60 discount; sale price = $150 − $60 = $90.
- Apply coupon: $90 − $10 = $80.
- The final price is $80.
- Answer: $80
Grade 9 Problems
[Easy] Solving a Linear Equation
- EN: Solve for x: 5x − 3 = 22.
- FR: Résous pour x : 5x − 3 = 22.
- Choices: A) x = 6 B) x = 4 C) x = 5 D) x = 3
- Hint: For 4x − 1 = 11, add 1 to get 4x = 12, then divide by 4: x = 3.
- Steps:
- Add 3 to both sides: 5x = 25.
- Divide both sides by 5: x = 5.
- So x = 5.
- Answer: x = 5
[Easy] Adding Polynomials
- EN: Simplify: (3x + 5) + (2x − 3).
- FR: Simplifie : (3x + 5) + (2x − 3).
- Choices: A) 6x + 2 B) 5x − 2 C) 5x + 2 D) 6x − 2
- Hint: Combine like terms: for (4a + 1) + (3a − 2), add the a-terms and the number terms separately: 7a − 1.
- Steps:
- Combine x-terms: 3x + 2x = 5x.
- Combine constants: 5 + (−3) = 2.
- Result: 5x + 2.
- Answer: 5x + 2
[Easy] Slope-Intercept Form
- EN: What is the slope of the line y = 4x − 7?
- FR: Quel est le taux de variation de la droite y = 4x − 7?
- Choices: A) 7 B) −7 C) 4 D) −4
- Hint: In y = mx + b, m is the slope and b is the y-intercept. For y = 3x + 2, the slope is 3.
- Steps:
- The equation is in slope-intercept form: y = mx + b.
- Here m = 4 and b = −7.
- The slope is 4.
- Answer: 4
[Easy] SOH-CAH-TOA Introduction
- EN: In a right triangle, the side opposite to angle A is 3 and the hypotenuse is 5. What is sin(A)?
- FR: Dans un triangle rectangle, le côté opposé à l'angle A est 3 et l'hypoténuse est 5. Quel est sin(A)?
- Choices: A) 5/3 B) 3/4 C) 4/5 D) 3/5
- Hint: SOH means sin = Opposite ÷ Hypotenuse. For opposite = 4 and hypotenuse = 10, sin = 4/10 = 2/5.
- Steps:
- sin(A) = opposite ÷ hypotenuse.
- sin(A) = 3 ÷ 5.
- So sin(A) = 3/5.
- Answer: 3/5
[Medium] Multiplying Polynomials
- EN: Expand: (x + 3)(x + 4).
- FR: Développe : (x + 3)(x + 4).
- Choices: A) x² + 8x + 12 B) x² + 7x + 7 C) x² + 7x + 12 D) x² + 12x + 7
- Hint: Use FOIL: (x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.
- Steps:
- First: x × x = x².
- Outer + Inner: x × 4 + 3 × x = 4x + 3x = 7x.
- Last: 3 × 4 = 12. Result: x² + 7x + 12.
- Answer: x² + 7x + 12
[Medium] Linear Inequality
- EN: Solve for x: 3x + 4 > 19.
- FR: Résous pour x : 3x + 4 > 19.
- Choices: A) x > 6 B) x > 4 C) x > 7 D) x > 5
- Hint: Treat it like an equation: for 2x + 1 > 9, subtract 1: 2x > 8, divide by 2: x > 4.
- Steps:
- Subtract 4 from both sides: 3x > 15.
- Divide both sides by 3: x > 5.
- The solution is x > 5.
- Answer: x > 5
[Medium] Similar Triangles
- EN: Two similar triangles have corresponding sides in the ratio 3:5. If the shorter triangle has a side of 9 cm, what is the corresponding side of the larger triangle?
- FR: Deux triangles semblables ont des côtés correspondants dans le rapport 3:5. Si le plus petit triangle a un côté de 9 cm, quel est le côté correspondant du plus grand triangle?
- Choices: A) 12 cm B) 18 cm C) 20 cm D) 15 cm
- Hint: Set up a proportion: 3/5 = 6/x. Cross multiply: 3x = 30, so x = 10.
- Steps:
- Ratio is 3:5; shorter side is 9.
- Set up proportion: 3/5 = 9/x.
- Cross multiply: 3x = 45; x = 15 cm.
- Answer: 15 cm
[Medium] Graphing Lines
- EN: A line has slope 2 and y-intercept −3. Which equation represents this line?
- FR: Une droite a un taux de variation de 2 et une ordonnée à l'origine de −3. Quelle équation représente cette droite?
- Choices: A) y = 3x − 2 B) y = −3x + 2 C) y = 2x + 3 D) y = 2x − 3
- Hint: Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Slope = 5, y-intercept = 1 gives y = 5x + 1.
- Steps:
- Use y = mx + b.
- m = 2, b = −3.
- The equation is y = 2x − 3.
- Answer: y = 2x − 3
[Hard] Trigonometry — Finding a Side
- EN: In a right triangle, angle A = 30° and the hypotenuse is 20 cm. What is the length of the side opposite to angle A? (Use sin 30° = 0.5)
- FR: Dans un triangle rectangle, l'angle A = 30° et l'hypoténuse est de 20 cm. Quelle est la longueur du côté opposé à l'angle A? (Utilise sin 30° = 0,5)
- Choices: A) 12 cm B) 8 cm C) 11 cm D) 10 cm
- Hint: SOH: sin(angle) = opposite/hypotenuse, so opposite = hypotenuse × sin(angle). For 40° and hypotenuse 15: opposite = 15 × sin(40°).
- Steps:
- sin(30°) = opposite / hypotenuse.
- opposite = 20 × sin(30°) = 20 × 0.5.
- opposite = 10 cm.
- Answer: 10 cm
[Hard] Systems of Equations by Substitution
- EN: Solve the system: y = 2x + 1 and y = x + 5. What is x?
- FR: Résous le système : y = 2x + 1 et y = x + 5. Quelle est la valeur de x?
- Choices: A) x = 3 B) x = 5 C) x = 6 D) x = 4
- Hint: If y = 3x and y = x + 8, set them equal: 3x = x + 8, then 2x = 8, so x = 4.
- Steps:
- Set the two expressions equal: 2x + 1 = x + 5.
- Subtract x from both sides: x + 1 = 5.
- Subtract 1: x = 4.
- Answer: x = 4
Grade 10 Problems
[Easy] Factoring Quadratics
- EN: Factor the quadratic: x² + 5x + 6.
- FR: Factorise le trinôme : x² + 5x + 6.
- Choices: A) (x + 1)(x + 6) B) (x + 3)(x + 2) C) (x + 2)(x + 4) D) (x + 5)(x + 1)
- Hint: Find two numbers that multiply to the constant and add to the middle coefficient. For x² + 7x + 12, the numbers are 3 and 4 (3 × 4 = 12, 3 + 4 = 7), so (x + 3)(x + 4).
- Steps:
- Find two numbers that multiply to 6 and add to 5.
- 2 × 3 = 6 and 2 + 3 = 5. ✓
- So x² + 5x + 6 = (x + 3)(x + 2).
- Answer: (x + 3)(x + 2)
[Easy] Trigonometry — Finding an Angle
- EN: In a right triangle, the opposite side is 4 cm and the adjacent side is 4 cm. What is the measure of the angle? (tan(45°) = 1)
- FR: Dans un triangle rectangle, le côté opposé est de 4 cm et le côté adjacent est de 4 cm. Quelle est la mesure de l'angle? (tan(45°) = 1)
- Choices: A) 30° B) 60° C) 45° D) 90°
- Hint: tan(angle) = opposite/adjacent. If opposite = adjacent, then tan = 1, and the angle whose tangent is 1 is 45°.
- Steps:
- tan(angle) = opposite/adjacent = 4/4 = 1.
- The angle whose tangent is 1 is 45°.
- So the angle is 45°.
- Answer: 45°
[Easy] System of Equations
- EN: Solve the system: x + y = 10 and x − y = 4. What is x?
- FR: Résous le système : x + y = 10 et x − y = 4. Quelle est la valeur de x?
- Choices: A) x = 8 B) x = 5 C) x = 6 D) x = 7
- Hint: To eliminate y, add the two equations together. For x + y = 8 and x − y = 2: 2x = 10, so x = 5.
- Steps:
- Add the equations: (x + y) + (x − y) = 10 + 4.
- 2x = 14; x = 7.
- So x = 7.
- Answer: x = 7
[Easy] Surface Area of a Cylinder
- EN: A cylinder has radius 3 cm and height 10 cm. Using π ≈ 3.14, what is its lateral surface area?
- FR: Un cylindre a un rayon de 3 cm et une hauteur de 10 cm. En utilisant π ≈ 3,14, quelle est son aire latérale?
- Choices: A) 188.4 cm² B) 94.2 cm² C) 282.6 cm² D) 150.0 cm²
- Hint: Lateral SA = 2πrh. For r = 2, h = 5: 2 × 3.14 × 2 × 5 = 62.8 cm².
- Steps:
- Lateral SA = 2πrh = 2 × 3.14 × 3 × 10.
- = 2 × 3.14 × 30 = 2 × 94.2.
- = 188.4 cm².
- Answer: 188.4 cm²
[Medium] Completing the Square
- EN: Solve by completing the square: x² + 6x − 7 = 0. What are the solutions?
- FR: Résous en complétant le carré : x² + 6x − 7 = 0. Quelles sont les solutions?
- Choices: A) x = 2 or x = −7 B) x = 1 or x = −7 C) x = 1 or x = −8 D) x = 3 or x = −7
- Hint: For x² + 4x − 5 = 0, complete the square: (x+2)² = 9, so x + 2 = ±3; x = 1 or x = −5.
- Steps:
- Rearrange: x² + 6x = 7. Complete the square: (x + 3)² − 9 = 7.
- (x + 3)² = 16; x + 3 = ±4.
- x = 1 or x = −7.
- Answer: x = 1 or x = −7
[Medium] Circle Geometry
- EN: A chord in a circle is 16 cm long. The radius is 10 cm. How far is the chord from the centre of the circle?
- FR: Une corde dans un cercle mesure 16 cm de long. Le rayon est de 10 cm. À quelle distance la corde est-elle du centre du cercle?
- Choices: A) 8 cm B) 5 cm C) 7 cm D) 6 cm
- Hint: Draw a perpendicular from the centre to the chord, creating a right triangle. Half the chord and the radius are the two known sides; use the Pythagorean theorem to find the distance.
- Steps:
- Half-chord = 16/2 = 8 cm; radius = 10 cm.
- Use Pythagorean theorem: d² + 8² = 10².
- d² = 100 − 64 = 36; d = 6 cm.
- Answer: 6 cm
[Medium] Quadratic — Using the Quadratic Formula
- EN: Use the quadratic formula to solve 2x² − 4x − 6 = 0. What is the positive root?
- FR: Utilise la formule quadratique pour résoudre 2x² − 4x − 6 = 0. Quelle est la racine positive?
- Choices: A) x = 4 B) x = 2 C) x = 3 D) x = 5
- Hint: For x² − 3x − 4 = 0, the discriminant is 9 + 16 = 25; roots are (3 ± 5)/2, giving x = 4 or x = −1.
- Steps:
- Divide through by 2: x² − 2x − 3 = 0.
- Factor: (x − 3)(x + 1) = 0.
- Roots: x = 3 or x = −1. The positive root is x = 3.
- Answer: x = 3
[Medium] Volume of a Cone
- EN: A cone has radius 6 cm and height 9 cm. Using π ≈ 3.14, what is its volume? (V = 1/3 πr²h)
- FR: Un cône a un rayon de 6 cm et une hauteur de 9 cm. En utilisant π ≈ 3,14, quel est son volume? (V = 1/3 πr²h)
- Choices: A) 339.12 cm³ B) 508.68 cm³ C) 113.04 cm³ D) 282.60 cm³
- Hint: For a cone with r = 3 and h = 4: V = 1/3 × 3.14 × 9 × 4 = 1/3 × 113.04 = 37.68 cm³.
- Steps:
- V = (1/3) × 3.14 × 6² × 9.
- = (1/3) × 3.14 × 36 × 9 = (1/3) × 1017.36.
- = 339.12 cm³.
- Answer: 339.12 cm³
[Hard] Systems of Equations — Non-Linear
- EN: Solve the system: y = x² and y = x + 6. What are the x-values of the intersection points?
- FR: Résous le système : y = x² et y = x + 6. Quelles sont les valeurs de x aux points d'intersection?
- Choices: A) x = 3 and x = −2 B) x = 4 and x = −2 C) x = 2 and x = −3 D) x = 6 and x = −1
- Hint: Set x² = x + k, rearrange to x² − x − k = 0, and factor or use the quadratic formula.
- Steps:
- Set equal: x² = x + 6; rearrange: x² − x − 6 = 0.
- Factor: (x − 3)(x + 2) = 0.
- x = 3 and x = −2.
- Answer: x = 3 and x = −2
[Hard] Trigonometry — Ambiguous Case / Applied
- EN: In triangle ABC, angle A = 60°, side a = 9 cm (opposite A), and side b = 6 cm. Using the Sine Rule (a/sin A = b/sin B), what is sin B?
- FR: Dans le triangle ABC, l'angle A = 60°, le côté a = 9 cm (opposé à A) et le côté b = 6 cm. En utilisant la règle des sinus (a/sin A = b/sin B), quel est sin B?
- Choices: A) sin B = √3/2 B) sin B = 1/2 C) sin B = √3/3 D) sin B = 2/3
- Hint: Rearrange the sine rule: sin B = b × sin A / a. Substitute the known values and simplify.
- Steps:
- sin B = b × sin(A) / a = 6 × sin(60°) / 9.
- sin(60°) = √3/2. So sin B = 6 × (√3/2) / 9 = 3√3 / 9 = √3/3.
- So sin B = √3/3.
- Answer: sin B = √3/3
Grade 11 Problems
[Easy] Exponential Function
- EN: A bacterial culture starts with 50 bacteria and doubles every hour. How many bacteria are there after 3 hours?
- FR: Une culture bactérienne commence avec 50 bactéries et double chaque heure. Combien y a-t-il de bactéries après 3 heures?
- Choices: A) 300 bacteria B) 450 bacteria C) 150 bacteria D) 400 bacteria
- Hint: For a quantity that doubles, use A = start × 2^t. For 20 bacteria after 2 hours: 20 × 2² = 20 × 4 = 80.
- Steps:
- A = 50 × 2³ = 50 × 8 = 400.
- After 3 hours, there are 400 bacteria.
- Answer: 400 bacteria
[Easy] Logarithm Introduction
- EN: What is the value of log₂(32)?
- FR: Quelle est la valeur de log₂(32)?
- Choices: A) 4 B) 6 C) 16 D) 5
- Hint: log₂(8) asks "2 to what power equals 8?" Since 2³ = 8, the answer is 3.
- Steps:
- Ask: 2 to what power equals 32?
- 2⁵ = 32. ✓
- So log₂(32) = 5.
- Answer: 5
[Easy] Arithmetic Sequence
- EN: The first term of an arithmetic sequence is 7 and the common difference is 4. What is the 6th term?
- FR: Le premier terme d'une suite arithmétique est 7 et la raison est 4. Quel est le 6e terme?
- Choices: A) 31 B) 35 C) 27 D) 29
- Hint: The nth term formula is aₙ = a₁ + (n − 1)d. For a₁ = 3, d = 5, the 4th term is 3 + (3)(5) = 18.
- Steps:
- aₙ = a₁ + (n − 1)d = 7 + (6 − 1)(4).
- = 7 + 5 × 4 = 7 + 20.
- = 27.
- Answer: 27
[Easy] Compound Interest
- EN: $1,000 is invested at 6% interest compounded annually for 2 years. What is the amount after 2 years? (Use A = P(1 + r)ⁿ)
- FR: 1 000 $ est investi à 6 % d'intérêt composé annuellement pendant 2 ans. Quel est le montant après 2 ans? (Utilise A = P(1 + r)ⁿ)
- Choices: A) $1,120.00 B) $1,123.60 C) $1,060.00 D) $1,116.00
- Hint: For P = $500, r = 4%, n = 2: A = 500 × (1.04)² = 500 × 1.0816 = $540.80.
- Steps:
- A = 1000 × (1.06)².
- (1.06)² = 1.1236.
- A = 1000 × 1.1236 = $1,123.60.
- Answer: $1,123.60
[Medium] Quadratic Function — Vertex
- EN: Find the vertex of the parabola y = x² − 4x + 7.
- FR: Trouve le sommet de la parabole y = x² − 4x + 7.
- Choices: A) (3, 4) B) (2, 3) C) (4, 7) D) (1, 4)
- Hint: The x-coordinate of the vertex is x = −b/(2a). For y = x² − 6x + 11, x = 6/2 = 3, then y = 9 − 18 + 11 = 2, vertex = (3, 2).
- Steps:
- x-vertex = −(−4)/(2×1) = 4/2 = 2.
- y-vertex = (2)² − 4(2) + 7 = 4 − 8 + 7 = 3.
- Vertex is (2, 3).
- Answer: (2, 3)
[Medium] Trigonometric Identity
- EN: Simplify: sin²(x) + cos²(x).
- FR: Simplifie : sin²(x) + cos²(x).
- Choices: A) 2 B) sin(2x) C) 0 D) 1
- Hint: This is the most fundamental Pythagorean identity — it always holds for any angle x.
- Steps:
- This is the Pythagorean identity.
- sin²(x) + cos²(x) = 1 for all values of x.
- The simplified result is 1.
- Answer: 1
[Medium] Geometric Series Sum
- EN: Find the sum of the first 5 terms of a geometric series where the first term is 3 and the common ratio is 2. (Use Sₙ = a(rⁿ − 1)/(r − 1))
- FR: Trouve la somme des 5 premiers termes d'une suite géométrique dont le premier terme est 3 et la raison est 2. (Utilise Sₙ = a(rⁿ − 1)/(r − 1))
- Choices: A) 93 B) 96 C) 60 D) 48
- Hint: For a = 2, r = 3, n = 4: S₄ = 2(3⁴ − 1)/(3 − 1) = 2(81 − 1)/2 = 80.
- Steps:
- S₅ = 3(2⁵ − 1)/(2 − 1) = 3(32 − 1)/1.
- = 3 × 31 = 93.
- The sum of the first 5 terms is 93.
- Answer: 93
[Medium] Annuity — Financial Math
- EN: Zara deposits $200 at the end of every year into an account that earns 5% annual interest. What is the future value after 3 years? (Use FV = PMT × [(1 + r)ⁿ − 1]/r)
- FR: Zara dépose 200 $ à la fin de chaque année dans un compte qui rapporte 5 % d'intérêt annuel. Quelle est la valeur future après 3 ans? (Utilise FV = PMT × [(1 + r)ⁿ − 1]/r)
- Choices: A) $630.50 B) $600.00 C) $661.00 D) $615.25
- Hint: For PMT = $100, r = 10%, n = 2: FV = 100 × [(1.10)² − 1]/0.10 = 100 × 0.21/0.10 = $210.
- Steps:
- FV = 200 × [(1.05)³ − 1] / 0.05.
- (1.05)³ = 1.157625; subtract 1: 0.157625.
- FV = 200 × 0.157625 / 0.05 = 200 × 3.1525 = $630.50.
- Answer: $630.50
[Hard] Logarithm Equation
- EN: Solve for x: log₃(x) + log₃(x − 2) = log₃(8).
- FR: Résous pour x : log₃(x) + log₃(x − 2) = log₃(8).
- Choices: A) x = 3 B) x = 5 C) x = 6 D) x = 4
- Hint: Use the product rule: log(a) + log(b) = log(a × b). Then set the arguments equal and solve the resulting equation.
- Steps:
- Combine: log₃(x(x − 2)) = log₃(8).
- So x(x − 2) = 8; x² − 2x − 8 = 0.
- Factor: (x − 4)(x + 2) = 0; x = 4 (reject x = −2 since log is undefined for negatives).
- Answer: x = 4
[Hard] Compound Interest with Periodic Compounding
- EN: $5,000 is invested at 8% per year compounded quarterly for 3 years. Using A = P(1 + r/n)^(nt) with n = 4, what is the amount to the nearest dollar?
- FR: 5 000 $ est investi à 8 % par an, composé trimestriellement pendant 3 ans. En utilisant A = P(1 + r/n)^(nt) avec n = 4, quel est le montant arrondi au dollar près?
- Choices: A) $6,341 B) $6,400 C) $6,848 D) $6,200
- Hint: For P = $1000, r = 0.08, n = 4, t = 3: first find r/n = 0.02, then nt = 12, compute (1.02)¹² ≈ 1.2682, then A = 1000 × 1.2682 ≈ $1,268.
- Steps:
- r/n = 0.08/4 = 0.02; nt = 4 × 3 = 12.
- (1.02)¹² ≈ 1.2682.
- A = 5000 × 1.2682 ≈ $6,341.
- Answer: $6,341
Grade 12 Problems
[Easy] Permutations
- EN: In how many ways can 5 different books be arranged on a shelf?
- FR: De combien de façons peut-on ranger 5 livres différents sur une étagère?
- Choices: A) 60 B) 100 C) 25 D) 120
- Hint: The number of ways to arrange n distinct objects is n! For 4 books: 4! = 4 × 3 × 2 × 1 = 24.
- Steps:
- 5! = 5 × 4 × 3 × 2 × 1.
- = 120.
- There are 120 ways to arrange the books.
- Answer: 120
[Easy] Combinations
- EN: A team of 3 students is chosen from 6 candidates. How many different teams are possible? (Use C(n,r) = n!/(r!(n−r)!))
- FR: Une équipe de 3 élèves est choisie parmi 6 candidats. Combien d'équipes différentes sont possibles? (Utilise C(n,r) = n!/(r!(n−r)!))
- Choices: A) 18 B) 15 C) 20 D) 12
- Hint: C(5, 2) = 5!/(2! × 3!) = (5 × 4)/(2 × 1) = 10.
- Steps:
- C(6, 3) = 6!/(3! × 3!) = (6 × 5 × 4)/(3 × 2 × 1).
- = 120/6 = 20.
- There are 20 possible teams.
- Answer: 20
[Easy] Derivative — Power Rule
- EN: Using the power rule, what is the derivative of f(x) = x³ + 2x?
- FR: En utilisant la règle de puissance, quelle est la dérivée de f(x) = x³ + 2x?
- Choices: A) 3x² + 2 B) 3x + 2 C) x² + 2 D) 3x²
- Hint: The power rule says d/dx (xⁿ) = nxⁿ⁻¹. For f(x) = x⁴ + 5x, f'(x) = 4x³ + 5.
- Steps:
- Differentiate x³: 3x².
- Differentiate 2x: 2.
- f'(x) = 3x² + 2.
- Answer: 3x² + 2
[Easy] Vector 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). Quel est u + v?
- Choices: A) (4, 9) B) (2, 9) C) (3, 8) D) (2, 7)
- Hint: Add corresponding components: for (2, 6) + (3, −1) = (2+3, 6+(−1)) = (5, 5).
- Steps:
- Add x-components: 3 + (−1) = 2.
- Add y-components: 5 + 4 = 9.
- u + v = (2, 9).
- Answer: (2, 9)
[Medium] Binomial Distribution
- EN: A fair coin is flipped 4 times. Using P(X = k) = C(n,k)(0.5)ⁿ, what is the probability of getting exactly 3 heads?
- FR: Une pièce équitable est lancée 4 fois. En utilisant P(X = k) = C(n,k)(0,5)ⁿ, quelle est la probabilité d'obtenir exactement 3 faces?
- Choices: A) 1/4 B) 3/16 C) 1/8 D) 1/2
- Hint: For n = 3 flips and k = 2 heads: C(3,2) × (0.5)³ = 3 × 1/8 = 3/8.
- Steps:
- P(X = 3) = C(4, 3) × (0.5)⁴.
- C(4, 3) = 4; (0.5)⁴ = 1/16.
- P = 4 × 1/16 = 4/16 = 1/4.
- Answer: 1/4
[Medium] Rational Function — Domain
- EN: What value(s) of x are NOT in the domain of f(x) = (x + 2) / (x² − 9)?
- FR: Quelle(s) valeur(s) de x ne font PAS partie du domaine de f(x) = (x + 2) / (x² − 9)?
- Choices: A) x = 0 only B) x = 3 and x = −3 C) x = 9 only D) x = 2 and x = −2
- Hint: A rational function is undefined where the denominator equals zero. Set x² − 4 = 0: x = ±2. Those values are excluded from the domain.
- Steps:
- Set the denominator equal to zero: x² − 9 = 0.
- Factor: (x − 3)(x + 3) = 0; x = 3 or x = −3.
- These values are excluded from the domain.
- Answer: x = 3 and x = −3
[Medium] Derivative — Rate of Change Application
- EN: The position of a hockey puck is given by s(t) = 4t² − 3t (in metres, t in seconds). What is the velocity of the puck at t = 2 seconds?
- FR: La position d'une rondelle de hockey est donnée par s(t) = 4t² − 3t (en mètres, t en secondes). Quelle est la vitesse de la rondelle à t = 2 secondes?
- Choices: A) 14 m/s B) 10 m/s C) 16 m/s D) 13 m/s
- Hint: Velocity = s'(t). Differentiate: for s(t) = 3t² − 2t, s'(t) = 6t − 2. At t = 1, velocity = 4.
- Steps:
- Differentiate: s'(t) = 8t − 3.
- Substitute t = 2: s'(2) = 8(2) − 3 = 16 − 3.
- = 13 m/s.
- Answer: 13 m/s
[Medium] Polynomial Long Division
- EN: Divide (x³ + 2x² − 5x − 6) by (x − 2). What is the quotient?
- FR: Divise (x³ + 2x² − 5x − 6) par (x − 2). Quel est le quotient?
- Choices: A) x² + 3x + 1 B) x² + 5x + 5 C) x² − 3x − 1 D) x² + 4x + 3
- Hint: Use synthetic division or long division step by step. For (x³ + 3x² − 4x) ÷ (x − 1): test x = 1 in the polynomial and proceed step by step.
- Steps:
- Synthetic division with root x = 2: bring down 1; 1×2=2, 2+2=4; 4×2=8, −5+8=3; 3×2=6, −6+6=0.
- Coefficients of quotient: 1, 4, 3 → x² + 4x + 3.
- The quotient is x² + 4x + 3.
- Answer: x² + 4x + 3
[Hard] Probability — Conditional Probability
- EN: In a Grade 12 class, 60% of students play a sport and 30% of students play a sport and are on the honour roll. Given that a student plays a sport, what is the probability they are also on the honour roll?
- FR: Dans une classe de 12e année, 60 % des élèves pratiquent un sport et 30 % des élèves pratiquent un sport et sont au tableau d'honneur. Sachant qu'un élève pratique un sport, quelle est la probabilité qu'il soit aussi au tableau d'honneur?
- Choices: A) 50% B) 30% C) 40% D) 60%
- Hint: P(B|A) = P(A and B) / P(A). For P(A) = 0.40 and P(A and B) = 0.10: P(B|A) = 0.10/0.40 = 25%.
- Steps:
- P(sport) = 0.60; P(sport and honour roll) = 0.30.
- P(honour roll | sport) = 0.30 / 0.60.
- = 0.50 = 50%.
- Answer: 50%
[Hard] Vector — Dot Product and Angle
- EN: Find the angle between vectors a = (3, 4) and b = (4, 3). Use cos θ = (a · b) / (|a| |b|). Round to the nearest degree. (cos⁻¹(0.96) ≈ 16°)
- FR: Trouve l'angle entre les vecteurs a = (3, 4) et b = (4, 3). Utilise cos θ = (a · b) / (|a| |b|). Arrondis au degré près. (cos⁻¹(0,96) ≈ 16°)
- Choices: A) 45° B) 30° C) 16° D) 20°
- Hint: Dot product = a₁b₁ + a₂b₂. Both magnitudes = √(a₁² + a₂²). Then divide and find the inverse cosine.
- Steps:
- a · b = 3×4 + 4×3 = 12 + 12 = 24.
- |a| = √(9+16) = 5; |b| = √(16+9) = 5.
- cos θ = 24/25 = 0.96; θ = cos⁻¹(0.96) ≈ 16°.
- Answer: 16°
Today's Encouragement
Trying something difficult and not giving up is the bravest thing a student can do today.
A Story of Kindness
Lena arrived early at the Whitehorse hockey rink for Saturday morning practice. She noticed a younger boy sitting alone near the boards, struggling to lace up his skates. Without being asked, Lena kneeled down and carefully tied them for him, showing him the bunny-ears trick. The boy's face lit up, and he skated onto the ice with a big smile.
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