Daily Math — 2026-10-03

[Easy] Counting Carrots

• EN: Farmer Mia has 7 carrots. She picks 5 more. How many carrots does she have now?
• FR: La fermière Mia a 7 carottes. Elle en cueille 5 de plus. Combien de carottes a-t-elle maintenant?
• Choices: A) 10 carrots B) 11 carrots C) 12 carrots D) 13 carrots
• Hint: To add, count on from the bigger number — try 6 + 3: start at 6, count 3 more.
• Steps:
  • Start at 7.
  • Count on 5 more: 8, 9, 10, 11, 12.
  • So the total is 12 carrots.
• Answer: 12 carrots

[Easy] Hockey Pucks

• EN: There are 15 pucks on the ice. A player takes 4 away. How many pucks are left?
• FR: Il y a 15 rondelles sur la glace. Un joueur en prend 4. Combien de rondelles reste-t-il?
• Choices: A) 9 pucks B) 10 pucks C) 11 pucks D) 12 pucks
• Hint: To subtract, count back from the bigger number — try 10 − 3: start at 10, count back 3.
• Steps:
  • Start at 15.
  • Count back 4: 14, 13, 12, 11.
  • So the answer is 11 pucks.
• Answer: 11 pucks

[Easy] Skip Counting by 5s

• EN: Skip count by 5s. What number comes after 15?
• FR: Compte par bonds de 5. Quel nombre vient après 15?
• Choices: A) 16 B) 18 C) 20 D) 25
• Hint: Skip counting by 5s goes 5, 10, 15 — what is next? Try the pattern with 10, 15, __.
• Steps:
  • The pattern is: 5, 10, 15, …
  • Add 5 to 15: 15 + 5 = 20.
  • So the next number is 20.
• Answer: 20

[Easy] Which Is More?

• EN: Which number is greater: 43 or 34?
• FR: Quel nombre est plus grand : 43 ou 34?
• Choices: A) 34 B) 43 C) They are equal D) 30
• Hint: Look at the tens digit first — the bigger tens digit means the bigger number (e.g., 52 vs. 25).
• Steps:
  • Look at the tens: 43 has 4 tens, 34 has 3 tens.
  • 4 tens is more than 3 tens.
  • So 43 is greater.
• Answer: 43

[Medium] Pennies and Nickels

• EN: Lily has 3 nickels and 2 pennies. How many cents does she have in total?
• FR: Lily a 3 pièces de 5 cents et 2 pièces de 1 cent. Combien de cents a-t-elle en tout?
• Choices: A) 14 cents B) 17 cents C) 5 cents D) 20 cents
• Hint: Each nickel is worth 5 cents — count by 5s for the nickels, then add the pennies (e.g., 2 nickels + 3 pennies = 10 + 3 = 13 cents).
• Steps:
  • 3 nickels = 5 + 5 + 5 = 15 cents.
  • 2 pennies = 2 cents.
  • 15 + 2 = 17 cents.
• Answer: 17 cents

[Medium] Snowflakes on the Window

• EN: There are 8 snowflakes on one window and 9 on another. How many snowflakes are there altogether?
• FR: Il y a 8 flocons de neige sur une fenêtre et 9 sur une autre. Combien y a-t-il de flocons en tout?
• Choices: A) 15 snowflakes B) 16 snowflakes C) 17 snowflakes D) 18 snowflakes
• Hint: To add numbers close to 10, try making 10 first — e.g., 7 + 6: take 3 from 6 to make 10, then add 3 more = 13.
• Steps:
  • Take 1 from 9 to give to 8, making 9 + 8 = 10 + 7.
  • 10 + 7 = 17.
  • So there are 17 snowflakes.
• Answer: 17 snowflakes

[Medium] Skip Counting by 2s

• EN: Skip count by 2s starting at 4. What is the 5th number you say?
• FR: Compte par bonds de 2 en commençant à 4. Quel est le 5e nombre que tu dis?
• Choices: A) 10 B) 12 C) 14 D) 8
• Hint: Skip by 2s and keep track — starting at 2: 2, 4, 6, 8, 10 — the 5th number is 10.
• Steps:
  • Start: 4 (1st), 6 (2nd), 8 (3rd), 10 (4th), 12 (5th).
  • The 5th number is 12.
• Answer: 12

[Medium] Mittens in the Closet

• EN: There are 18 mittens in the closet. Max takes out 9. How many mittens are left?
• FR: Il y a 18 mitaines dans le placard. Max en prend 9. Combien de mitaines reste-t-il?
• Choices: A) 7 mittens B) 8 mittens C) 9 mittens D) 11 mittens
• Hint: Use a fact you know — if 10 − 5 = 5, then 18 − 9 uses the same idea of splitting evenly.
• Steps:
  • 18 − 9: think of 9 + ? = 18.
  • 9 + 9 = 18, so 18 − 9 = 9.
  • There are 9 mittens left.
• Answer: 9 mittens

[Hard] Counting to 100

• EN: What number is 10 more than 67?
• FR: Quel nombre est 10 de plus que 67?
• Choices: A) 57 B) 68 C) 77 D) 76
• Hint: Adding 10 only changes the tens digit — e.g., 10 more than 45 is 55 (the tens go up by 1).
• Steps:
  • Start at 67.
  • Add 10: the tens digit goes from 6 to 7.
  • 67 + 10 = 77.
• Answer: 77

[Hard] Dimes Are Worth 10 Cents

• EN: Omar has 2 dimes and 3 nickels. How many cents does he have in total?
• FR: Omar a 2 pièces de 10 cents et 3 pièces de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 25 cents B) 30 cents C) 35 cents D) 40 cents
• Hint: A dime = 10 cents, a nickel = 5 cents — try 1 dime + 2 nickels: 10 + 10 = 20 cents.
• Steps:
  • 2 dimes = 10 + 10 = 20 cents.
  • 3 nickels = 5 + 5 + 5 = 15 cents.
  • 20 + 15 = 35 cents.
• Answer: 35 cents

[Easy] Adding at the Bakery

• EN: A bakery bakes 34 muffins in the morning and 25 muffins in the afternoon. How many muffins were baked in all?
• FR: Une boulangerie fait 34 muffins le matin et 25 muffins l'après-midi. Combien de muffins ont été faits en tout?
• Choices: A) 57 muffins B) 59 muffins C) 61 muffins D) 49 muffins
• Hint: Add the ones first, then the tens — e.g., 22 + 31: ones 2 + 1 = 3, tens 2 + 3 = 5, so 53.
• Steps:
  • Ones: 4 + 5 = 9.
  • Tens: 3 + 2 = 5.
  • Total: 59 muffins.
• Answer: 59 muffins

[Easy] Telling Time

• EN: The clock shows the hour hand on 3 and the minute hand on 12. What time is it?
• FR: L'aiguille des heures est sur le 3 et l'aiguille des minutes est sur le 12. Quelle heure est-il?
• Choices: A) 12:00 B) 3:30 C) 3:00 D) 6:00
• Hint: When the minute hand is on 12, it is exactly the o'clock hour — e.g., hour hand on 7 means 7:00.
• Steps:
  • Hour hand on 3 → the hour is 3.
  • Minute hand on 12 → exactly on the hour.
  • The time is 3:00.
• Answer: 3:00

[Easy] Measuring a Pencil

• EN: A pencil is 14 cm long and a crayon is 9 cm long. How much longer is the pencil?
• FR: Un crayon est long de 14 cm et un crayon de couleur est long de 9 cm. De combien le crayon est-il plus long?
• Choices: A) 4 cm B) 5 cm C) 6 cm D) 23 cm
• Hint: Subtract to find the difference — e.g., 12 cm − 7 cm = 5 cm.
• Steps:
  • 14 − 9 = ?
  • Count up from 9: 9 + 5 = 14.
  • The pencil is 5 cm longer.
• Answer: 5 cm

[Easy] Counting Coins

• EN: Sofia has 1 dime, 2 nickels, and 3 pennies. How many cents does she have?
• FR: Sofia a 1 pièce de 10 cents, 2 pièces de 5 cents et 3 pièces de 1 cent. Combien de cents a-t-elle?
• Choices: A) 20 cents B) 23 cents C) 18 cents D) 25 cents
• Hint: Count each coin type then add — e.g., 1 dime + 1 nickel + 2 pennies = 10 + 5 + 2 = 17 cents.
• Steps:
  • 1 dime = 10 cents.
  • 2 nickels = 10 cents.
  • 3 pennies = 3 cents.
  • 10 + 10 + 3 = 23 cents.
• Answer: 23 cents

[Medium] Subtracting at the Arena

• EN: There were 82 fans at the hockey game. Then 47 fans went home. How many fans are still there?
• FR: Il y avait 82 partisans au match de hockey. Ensuite, 47 partisans sont partis. Combien de partisans y a-t-il encore?
• Choices: A) 35 fans B) 45 fans C) 25 fans D) 39 fans
• Hint: Subtract by breaking apart — e.g., 75 − 38: first subtract 30 to get 45, then subtract 8 more to get 37.
• Steps:
  • 82 − 47: subtract 40 first → 82 − 40 = 42.
  • Then subtract 7 more → 42 − 7 = 35.
  • There are 35 fans left.
• Answer: 35 fans

[Medium] Half-Hour Time

• EN: The hockey practice starts at 4:00 and lasts half an hour. What time does it end?
• FR: L'entraînement de hockey commence à 4 h et dure une demi-heure. À quelle heure se termine-t-il?
• Choices: A) 4:15 B) 4:30 C) 5:00 D) 3:30
• Hint: Half an hour = 30 minutes — e.g., practice starts at 2:00 and lasts half an hour, so it ends at 2:30.
• Steps:
  • Start time: 4:00.
  • Add 30 minutes (half an hour).
  • End time: 4:30.
• Answer: 4:30

[Medium] Growing Pattern

• EN: Look at this pattern: 5, 10, 15, 20, __. What is the missing number?
• FR: Observe ce motif : 5, 10, 15, 20, __. Quel est le nombre manquant?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: Find the rule by looking at what is added each time — e.g., 3, 6, 9, 12 adds 3 each time.
• Steps:
  • Each number goes up by 5.
  • 20 + 5 = 25.
  • The missing number is 25.
• Answer: 25

[Medium] Measuring the Garden

• EN: A garden path is 1 metre long. A second path is 65 cm long. How much longer is the first path? (1 m = 100 cm)
• FR: Un sentier de jardin mesure 1 mètre. Un deuxième sentier mesure 65 cm. De combien le premier sentier est-il plus long? (1 m = 100 cm)
• Choices: A) 25 cm B) 35 cm C) 45 cm D) 65 cm
• Hint: Convert metres to centimetres first — e.g., 1 m = 100 cm, then subtract (e.g., 100 − 55 = 45 cm).
• Steps:
  • 1 metre = 100 cm.
  • 100 − 65 = 35 cm.
  • The first path is 35 cm longer.
• Answer: 35 cm

[Hard] Making a Dollar

• EN: Theo has 3 quarters. How many more cents does he need to make exactly $1.00?
• FR: Theo a 3 pièces de 25 cents. De combien de cents de plus a-t-il besoin pour faire exactement 1,00 $?
• Choices: A) 15 cents B) 20 cents C) 25 cents D) 30 cents
• Hint: A quarter = 25 cents and $1.00 = 100 cents — e.g., 2 quarters = 50 cents, need 50 more cents.
• Steps:
  • 3 quarters = 25 + 25 + 25 = 75 cents.
  • 100 − 75 = 25 cents needed.
  • Theo needs 25 more cents.
• Answer: 25 cents

[Hard] Two-Step Subtraction Story

• EN: There were 95 library books on the shelf. Students took out 38 books on Monday and 24 books on Tuesday. How many books are left?
• FR: Il y avait 95 livres de bibliothèque sur l'étagère. Les élèves ont emprunté 38 livres lundi et 24 livres mardi. Combien de livres reste-t-il?
• Choices: A) 31 books B) 33 books C) 57 books D) 29 books
• Hint: Solve in two steps — subtract Monday first, then subtract Tuesday (e.g., 80 − 20 − 15 = 45 books).
• Steps:
  • After Monday: 95 − 38 = 57 books.
  • After Tuesday: 57 − 24 = 33 books.
  • There are 33 books left.
• Answer: 33 books

[Easy] Multiplication at the Pond

• EN: There are 4 lily pads. Each lily pad has 5 frogs. How many frogs are there in all?
• FR: Il y a 4 nénuphars. Chaque nénuphar a 5 grenouilles. Combien y a-t-il de grenouilles en tout?
• Choices: A) 9 frogs B) 15 frogs C) 20 frogs D) 25 frogs
• Hint: Multiply to find equal groups — e.g., 3 groups of 5 = 3 × 5 = 15.
• Steps:
  • 4 lily pads × 5 frogs each.
  • 4 × 5 = 20.
  • There are 20 frogs in all.
• Answer: 20 frogs

[Easy] Division of Apples

• EN: There are 18 apples shared equally among 3 friends. How many apples does each friend get?
• FR: Il y a 18 pommes partagées également entre 3 amis. Combien de pommes chaque ami reçoit-il?
• Choices: A) 4 apples B) 5 apples C) 6 apples D) 9 apples
• Hint: Division is the reverse of multiplication — e.g., 12 ÷ 3 = 4 because 3 × 4 = 12.
• Steps:
  • 18 ÷ 3 = ?
  • Ask: 3 × ? = 18 → 3 × 6 = 18.
  • Each friend gets 6 apples.
• Answer: 6 apples

[Easy] Fractions of a Pizza

• 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) 1/4 D) 2/4
• Hint: A fraction names one part out of the total equal parts — e.g., 1 piece out of 3 equal pieces is 1/3.
• Steps:
  • The pizza has 4 equal parts.
  • Emma eats 1 part.
  • She ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Perimeter of a Square Garden

• EN: A square garden has sides that are each 6 m long. What is its perimeter?
• FR: Un jardin carré a des côtés de 6 m chacun. Quel est son périmètre?
• Choices: A) 12 m B) 18 m C) 24 m D) 36 m
• Hint: A square has 4 equal sides — perimeter = side × 4 (e.g., side of 5 m → perimeter = 20 m).
• Steps:
  • A square has 4 equal sides.
  • 6 × 4 = 24.
  • The perimeter is 24 m.
• Answer: 24 m

[Medium] Multiplying by 3

• EN: There are 7 boxes of Tim Hortons Timbits. Each box has 3 Timbits. How many Timbits are there in total?
• FR: Il y a 7 boîtes de Timbits de Tim Hortons. Chaque boîte contient 3 Timbits. Combien y a-t-il de Timbits en tout?
• Choices: A) 18 Timbits B) 21 Timbits C) 24 Timbits D) 10 Timbits
• Hint: Use the 3 times table — e.g., 6 × 3 = 18, then count one more group of 3.
• Steps:
  • 7 × 3 = ?
  • 6 × 3 = 18, then add 3 more → 21.
  • There are 21 Timbits in total.
• Answer: 21 Timbits

[Medium] Reading a Bar Graph

• EN: A bar graph shows 8 students like hockey, 5 like soccer, and 3 like basketball. How many students were surveyed in total?
• FR: Un diagramme à barres montre que 8 élèves aiment le hockey, 5 aiment le soccer et 3 aiment le basketball. Combien d'élèves ont été sondés en tout?
• Choices: A) 13 students B) 14 students C) 16 students D) 18 students
• Hint: Add all the bars together to find the total — e.g., 4 + 6 + 2 = 12 students.
• Steps:
  • Hockey: 8, Soccer: 5, Basketball: 3.
  • 8 + 5 + 3 = 16.
  • There were 16 students surveyed.
• Answer: 16 students

[Medium] Division with 4

• EN: A teacher has 28 stickers to share equally among 4 students. How many stickers does each student get?
• FR: Une enseignante a 28 autocollants à partager également entre 4 élèves. Combien d'autocollants chaque élève reçoit-il?
• Choices: A) 5 stickers B) 6 stickers C) 7 stickers D) 8 stickers
• Hint: Use multiplication to check — e.g., 4 × 6 = 24, 4 × 7 = 28.
• Steps:
  • 28 ÷ 4 = ?
  • 4 × 7 = 28.
  • Each student gets 7 stickers.
• Answer: 7 stickers

[Medium] Perimeter of a Rectangle

• EN: A Canadian flag is 8 cm wide and 4 cm tall. What is its perimeter?
• FR: Un drapeau canadien mesure 8 cm de large et 4 cm de hauteur. Quel est son périmètre?
• Choices: A) 20 cm B) 24 cm C) 32 cm D) 12 cm
• Hint: Perimeter of a rectangle = 2 × length + 2 × width — e.g., 5 cm × 2 cm: 2×5 + 2×2 = 10 + 4 = 14 cm.
• Steps:
  • Perimeter = 2 × 8 + 2 × 4.
  • = 16 + 8 = 24 cm.
  • The perimeter is 24 cm.
• Answer: 24 cm

[Hard] Two-Step Multiplication Problem

• EN: A class bakes 5 trays of cookies. Each tray holds 10 cookies. They eat 15 cookies at lunch. How many cookies are left?
• FR: Une classe fait 5 plateaux de biscuits. Chaque plateau contient 10 biscuits. Ils mangent 15 biscuits au déjeuner. Combien de biscuits reste-t-il?
• Choices: A) 35 cookies B) 38 cookies C) 40 cookies D) 45 cookies
• Hint: Do the multiplication first, then subtract — e.g., 3 trays × 10 = 30 cookies, then 30 − 5 = 25 cookies.
• Steps:
  • 5 × 10 = 50 cookies total.
  • 50 − 15 = 35 cookies.
  • There are 35 cookies left.
• Answer: 35 cookies

[Hard] Comparing Fractions

• EN: Which fraction is greater: 1/2 or 1/3?
• FR: Quelle fraction est la plus grande : 1/2 ou 1/3?
• Choices: A) 1/3 B) 1/2 C) They are equal D) 2/3
• Hint: Bigger denominator means smaller pieces — imagine cutting a pie into 2 vs. 4 slices; 1/2 is bigger than 1/4.
• Steps:
  • Think of 1 pie cut into 2 pieces vs. 3 pieces.
  • 2 pieces are bigger slices than 3 pieces.
  • So 1/2 is greater than 1/3.
• Answer: 1/2

[Easy] Multiplication Tables

• EN: What is 7 × 8?
• FR: Combien font 7 × 8?
• Choices: A) 54 B) 56 C) 63 D) 48
• Hint: Use a nearby fact — e.g., 7 × 7 = 49, then add one more group of 7 to get 56.
• Steps:
  • 7 × 8: use 7 × 7 = 49.
  • Add 7 more: 49 + 7 = 56.
  • 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 4.73, what digit is in the tenths place?
• FR: Dans le nombre 4,73, quel chiffre est à la position des dixièmes?
• Choices: A) 4 B) 3 C) 7 D) 73
• Hint: Tenths come right after the decimal point — e.g., in 2.56, the tenths digit is 5.
• Steps:
  • 4.73: the digits after the decimal are tenths (7) and hundredths (3).
  • The tenths digit is 7.
• Answer: 7

[Easy] Area of a Rectangle

• EN: A hockey card is 9 cm long and 6 cm wide. What is its area?
• FR: Une carte de hockey mesure 9 cm de long et 6 cm de large. Quelle est son aire?
• Choices: A) 30 cm² B) 45 cm² C) 54 cm² D) 60 cm²
• Hint: Area of a rectangle = length × width — e.g., 7 cm × 4 cm = 28 cm².
• Steps:
  • Area = length × width.
  • 9 × 6 = 54.
  • The area is 54 cm².
• Answer: 54 cm²

[Easy] Comparing Fractions

• EN: Which fraction is smaller: 3/4 or 2/4?
• FR: Quelle fraction est la plus petite : 3/4 ou 2/4?
• Choices: A) 3/4 B) 2/4 C) They are equal D) 4/4
• Hint: When denominators are the same, compare the numerators — e.g., 5/8 vs. 3/8: 3 is smaller, so 3/8 is smaller.
• Steps:
  • Same denominator (4), so compare numerators: 3 vs. 2.
  • 2 < 3, so 2/4 < 3/4.
  • 2/4 is the smaller fraction.
• Answer: 2/4

[Medium] Long Division with Remainder

• EN: A teacher has 47 pencils to put equally into 5 pencil cases. How many pencils are in each case, and how many are left over?
• FR: Une enseignante a 47 crayons à mettre également dans 5 trousses. Combien de crayons y a-t-il dans chaque trousse et combien en reste-t-il?
• Choices: A) 8 remainder 5 B) 9 remainder 2 C) 10 remainder 3 D) 7 remainder 4
• Hint: Divide and find what is left over — e.g., 23 ÷ 4: 4 × 5 = 20, remainder 3, so 5 remainder 3.
• Steps:
  • 5 × 9 = 45, which is the closest without going over 47.
  • 47 − 45 = 2 remainder.
  • Each case has 9 pencils, with 2 left over.
• Answer: 9 remainder 2

[Medium] Elapsed Time

• EN: A skating session starts at 1:15 p.m. and ends at 3:45 p.m. How long is the skating session?
• FR: Une séance de patinage commence à 13 h 15 et se termine à 15 h 45. Combien de temps dure la séance?
• Choices: A) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours
• Hint: Count up from the start time to the end time — e.g., from 2:20 to 4:50: 2 hours and 30 minutes.
• Steps:
  • From 1:15 to 3:15 = 2 hours.
  • From 3:15 to 3:45 = 30 more minutes.
  • Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Adding Decimals

• EN: Ben buys a pen for $1.45 and a notebook for $2.30. How much does he spend in total?
• FR: Ben achète un stylo pour 1,45 $ et un cahier pour 2,30 $. Combien dépense-t-il en tout?
• Choices: A) $3.55 B) $3.75 C) $3.85 D) $4.05
• Hint: Line up the decimal points and add — e.g., $1.20 + $2.50: ones 1+2=3, tenths 2+5=7, so $3.70.
• Steps:
  • $1.45 + $2.30.
  • Cents: 45 + 30 = 75 cents.
  • Total: $3.75.
• Answer: $3.75

[Medium] Multiplication — Multi-Digit

• EN: A store receives 6 boxes of granola bars. Each box has 48 bars. How many granola bars are there in all?
• FR: Un magasin reçoit 6 boîtes de barres granola. Chaque boîte contient 48 barres. Combien y a-t-il de barres granola en tout?
• Choices: A) 264 bars B) 278 bars C) 288 bars D) 302 bars
• Hint: Break apart the number — e.g., 6 × 47: 6 × 40 = 240, 6 × 7 = 42, total = 282.
• Steps:
  • 6 × 48 = 6 × 40 + 6 × 8.
  • = 240 + 48 = 288.
  • There are 288 granola bars.
• Answer: 288 bars

[Hard] Decimal Subtraction Word Problem

• EN: Mia has $10.00. She buys a pair of socks for $3.89. How much change does she receive?
• FR: Mia a 10,00 $. Elle achète une paire de chaussettes pour 3,89 $. Combien de monnaie reçoit-elle?
• Choices: A) $6.01 B) $6.11 C) $6.21 D) $7.11
• Hint: Subtract from $10.00 by counting up — e.g., $10.00 − $4.25: count from $4.25 → $5.00 = 75¢, then +$5.00 = $5.75 change.
• Steps:
  • $10.00 − $3.89.
  • Count up: $3.89 → $4.00 = 11¢, then $4.00 → $10.00 = $6.00.
  • Total change: $6.11.
• Answer: $6.11

[Hard] Two-Step Area Problem

• EN: A classroom is 8 m long and 7 m wide. A reading corner takes up an area of 6 m². What is the remaining area of the classroom?
• FR: Une salle de classe mesure 8 m de long et 7 m de large. Un coin lecture occupe une superficie de 6 m². Quelle est l'aire restante de la salle de classe?
• Choices: A) 48 m² B) 50 m² C) 56 m² D) 62 m²
• Hint: Find the total area first, then subtract the corner — e.g., room is 6 m × 5 m = 30 m², corner = 4 m², remaining = 26 m².
• Steps:
  • Total area = 8 × 7 = 56 m².
  • Subtract the corner: 56 − 6 = 50 m².
  • The remaining area is 50 m².
• Answer: 50 m²

[Easy] Multi-Digit Multiplication

• EN: What is 34 × 6?
• FR: Combien font 34 × 6?
• Choices: A) 194 B) 200 C) 204 D) 210
• Hint: Break apart the number — e.g., 32 × 6: 30 × 6 = 180, 2 × 6 = 12, total = 192.
• Steps:
  • 34 × 6 = 30 × 6 + 4 × 6.
  • = 180 + 24 = 204.
  • 34 × 6 = 204.
• Answer: 204

[Easy] Adding Fractions with Like Denominators

• EN: What is 3/8 + 2/8?
• FR: Combien font 3/8 + 2/8?
• Choices: A) 5/16 B) 6/8 C) 5/8 D) 1/2
• Hint: Add only the numerators and keep the denominator — e.g., 2/5 + 1/5 = 3/5.
• Steps:
  • Keep the denominator: 8.
  • Add the numerators: 3 + 2 = 5.
  • Answer: 5/8
• Answer: 5/8

[Easy] 25% of a Number

• EN: What is 25% of 80?
• FR: Combien vaut 25 % de 80?
• Choices: A) 15 B) 20 C) 25 D) 40
• Hint: 25% means one quarter — divide by 4 (e.g., 25% of 60 = 60 ÷ 4 = 15).
• Steps:
  • 25% = 1/4.
  • 80 ÷ 4 = 20.
  • 25% of 80 is 20.
• Answer: 20

[Easy] Volume of a Rectangular Prism

• EN: A box is 5 cm long, 3 cm wide, and 2 cm tall. What is its volume?
• FR: Une boîte mesure 5 cm de long, 3 cm de large et 2 cm de hauteur. Quel est son volume?
• Choices: A) 25 cm³ B) 30 cm³ C) 36 cm³ D) 10 cm³
• Hint: Volume = length × width × height — e.g., 4 × 2 × 3 = 24 cm³.
• Steps:
  • Volume = 5 × 3 × 2.
  • = 15 × 2 = 30 cm³.
  • The volume is 30 cm³.
• Answer: 30 cm³

[Medium] Multi-Digit Division

• EN: A school orders 252 pencils and divides them equally into 9 classrooms. How many pencils does each classroom get?
• FR: Une école commande 252 crayons et les répartit également dans 9 classes. Combien de crayons chaque classe reçoit-elle?
• Choices: A) 26 pencils B) 28 pencils C) 30 pencils D) 32 pencils
• Hint: Use estimation — e.g., 270 ÷ 9 = 30, so the answer is close to 30; adjust from there.
• Steps:
  • 9 × 28 = 252 (check: 9 × 20 = 180, 9 × 8 = 72, 180 + 72 = 252).
  • Each classroom gets 28 pencils.
• Answer: 28 pencils

[Medium] Subtracting Fractions with Like Denominators

• EN: A recipe calls for 7/10 cup of oats. Anna uses 3/10 cup. How much oats are left?
• FR: Une recette nécessite 7/10 tasse d'avoine. Anna en utilise 3/10 tasse. Combien reste-t-il d'avoine?
• Choices: A) 3/10 B) 4/10 C) 5/10 D) 10/10
• Hint: Subtract numerators and keep the denominator — e.g., 6/9 − 2/9 = 4/9.
• Steps:
  • Denominator stays 10.
  • 7 − 3 = 4.
  • There are 4/10 cups of oats left.
• Answer: 4/10

[Medium] Decimal Addition and Subtraction

• EN: Sam's snowfall this week was 12.6 cm. Last week it was 8.4 cm. How much more snow fell this week?
• FR: Les chutes de neige de cette semaine étaient de 12,6 cm. La semaine dernière, elles étaient de 8,4 cm. Combien de neige supplémentaire est tombée cette semaine?
• Choices: A) 3.8 cm B) 4.2 cm C) 4.6 cm D) 5.2 cm
• Hint: Subtract decimals by lining up decimal points — e.g., 15.7 − 9.3 = 6.4 cm.
• Steps:
  • 12.6 − 8.4.
  • Tenths: 6 − 4 = 2; Ones: 12 − 8 = 4.
  • Difference: 4.2 cm.
• Answer: 4.2 cm

[Medium] 10% of a Number

• EN: A jacket costs $90. It is on sale for 10% off. How much is the discount?
• FR: Un manteau coûte 90 $. Il est en solde à 10 % de rabais. Quel est le montant du rabais?
• Choices: A) $7 B) $8 C) $9 D) $10
• Hint: 10% = divide by 10 — e.g., 10% of $70 = $7.
• Steps:
  • 10% of $90 = 90 ÷ 10.
  • = $9.
  • The discount is $9.
• Answer: $9

[Hard] Multi-Step Word Problem

• EN: A sports store sells 125 hockey sticks on Saturday and 3 times as many on Sunday. If each stick costs $12, how much money was made on Sunday?
• FR: Un magasin de sport vend 125 bâtons de hockey samedi et 3 fois plus dimanche. Si chaque bâton coûte 12 $, combien d'argent a été fait dimanche?
• Choices: A) $4,200 B) $4,400 C) $4,500 D) $5,000
• Hint: First find Sunday's sticks, then multiply by price — e.g., 100 sticks × 3 = 300, then 300 × $12 = $3,600.
• Steps:
  • Sunday sticks: 125 × 3 = 375.
  • Revenue: 375 × $12 = $4,500.
  • Sunday total: $4,500.
• Answer: $4,500

[Hard] Volume Word Problem

• EN: A fish tank is 10 cm long, 8 cm wide, and 6 cm tall. It is already filled with 200 cm³ of water. How much more water is needed to fill it completely?
• FR: Un aquarium mesure 10 cm de long, 8 cm de large et 6 cm de hauteur. Il est déjà rempli avec 200 cm³ d'eau. Combien d'eau supplémentaire faut-il pour le remplir complètement?
• Choices: A) 240 cm³ B) 270 cm³ C) 280 cm³ D) 300 cm³
• Hint: Find the total volume first, then subtract what is already there — e.g., 5 × 4 × 3 = 60 cm³ total, minus 20 cm³ already in = 40 cm³ needed.
• Steps:
  • Total volume = 10 × 8 × 6 = 480 cm³.
  • 480 − 200 = 280 cm³ still needed.
  • The answer is 280 cm³.
• Answer: 280 cm³

[Easy] Percent of a Number

• EN: What is 30% of 200?
• FR: Combien vaut 30 % de 200?
• Choices: A) 30 B) 50 C) 60 D) 70
• Hint: Find 10% first then multiply — e.g., 30% of 150: 10% = 15, so 30% = 15 × 3 = 45.
• Steps:
  • 10% of 200 = 20.
  • 30% = 20 × 3 = 60.
  • 30% of 200 is 60.
• Answer: 60

[Easy] Simple Algebraic Expression

• EN: If n = 5, what is the value of 4n + 3?
• FR: Si n = 5, quelle est la valeur de 4n + 3?
• Choices: A) 18 B) 22 C) 23 D) 25
• Hint: Substitute the value and follow order of operations — e.g., if n = 2, then 4n + 3 = 8 + 3 = 11.
• Steps:
  • Replace n with 5: 4(5) + 3.
  • = 20 + 3 = 23.
  • The value is 23.
• Answer: 23

[Easy] Ratios

• EN: In a bag of marbles there are 4 red and 6 blue. What is the ratio of red to blue?
• FR: Dans un sac de billes, il y a 4 rouges et 6 bleues. Quel est le rapport des rouges aux bleues?
• Choices: A) 4:10 B) 6:4 C) 4:6 D) 2:3
• Hint: Write the ratio in the same order as the question — e.g., 3 cats to 5 dogs = 3:5.
• Steps:
  • Red to blue: 4 to 6.
  • Written as a ratio: 4:6.
  • The ratio is 4:6.
• Answer: 4:6

[Easy] Integers — Understanding Negatives

• EN: Which is colder: −8°C or −3°C?
• FR: Laquelle est la température la plus froide : −8 °C ou −3 °C?
• Choices: A) −3°C B) −8°C C) They are equal D) 0°C
• Hint: On a number line, numbers further left are smaller — e.g., −10 is colder than −4.
• Steps:
  • On a thermometer, −8 is below −3.
  • −8 < −3.
  • −8°C is colder.
• Answer: −8°C

[Medium] BEDMAS Order of Operations

• EN: Evaluate: 3 + 4 × 2 − 1
• FR: Évalue : 3 + 4 × 2 − 1
• Choices: A) 13 B) 10 C) 11 D) 14
• Hint: Multiply before adding or subtracting — e.g., 5 + 3 × 2 − 1 = 5 + 6 − 1 = 10.
• Steps:
  • First multiply: 4 × 2 = 8.
  • Then: 3 + 8 − 1.
  • = 11 − 1 = 10.
• Answer: 10

[Medium] Fraction Multiplication

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

[Medium] Rates

• EN: A car travels 240 km in 3 hours. What is its speed in km/h?
• FR: Une voiture parcourt 240 km en 3 heures. Quelle est sa vitesse en km/h?
• Choices: A) 70 km/h B) 75 km/h C) 80 km/h D) 90 km/h
• Hint: Rate = total ÷ time — e.g., 150 km in 3 hours = 50 km/h.
• Steps:
  • Speed = 240 ÷ 3.
  • = 80 km/h.
  • The car travels at 80 km/h.
• Answer: 80 km/h

[Medium] Fraction Division

• EN: What is 3/4 ÷ 1/2?
• FR: Combien font 3/4 ÷ 1/2?
• Choices: A) 3/8 B) 1 C) 3/2 D) 2/3
• Hint: Dividing by a fraction = multiplying by its reciprocal — e.g., 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
• Steps:
  • Flip the divisor: 1/2 becomes 2/1.
  • Multiply: 3/4 × 2/1 = 6/4 = 3/2.
  • The answer is 3/2.
• Answer: 3/2

[Hard] Multi-Step Percent Problem

• EN: A hockey jersey costs $80. It is first reduced by 20%, then an additional 10% is taken off the sale price. What is the final price?
• FR: Un chandail de hockey coûte 80 $. Il est d'abord réduit de 20 %, puis un autre 10 % est retiré du prix de vente. Quel est le prix final?
• Choices: A) $56.00 B) $57.60 C) $62.40 D) $64.00
• Hint: Apply each discount one at a time — e.g., $100 reduced 20% = $80, then 10% off $80 = $72.
• Steps:
  • 20% off $80: 80 × 0.20 = $16; $80 − $16 = $64.
  • 10% off $64: 64 × 0.10 = $6.40; $64 − $6.40 = $57.60.
  • Final price: $57.60.
• Answer: $57.60

[Hard] Integer Operations

• EN: Calculate: (−4) + (−6) − (−3) + 8
• FR: Calcule : (−4) + (−6) − (−3) + 8
• Choices: A) −1 B) 1 C) 3 D) −3
• Hint: Subtracting a negative is the same as adding — e.g., 5 − (−2) = 5 + 2 = 7.
• Steps:
  • Change − (−3) to + 3.
  • Expression: −4 + (−6) + 3 + 8.
  • = −4 − 6 + 3 + 8 = 1.
• Answer: 1

[Easy] Integer Addition

• EN: What is (−7) + 12?
• FR: Combien font (−7) + 12?
• Choices: A) −5 B) 4 C) 5 D) 19
• Hint: Start at −7 on the number line and move 12 to the right — e.g., (−3) + 8 = 5.
• Steps:
  • Start at −7, add 12.
  • −7 + 12 = 5.
  • The answer is 5.
• Answer: 5

[Easy] Calculating a Discount

• EN: A pair of skates costs $120. They are on sale for 15% off. How much is the discount?
• FR: Une paire de patins coûte 120 $. Elle est en solde à 15 % de rabais. Quel est le montant du rabais?
• Choices: A) $15 B) $16 C) $18 D) $20
• Hint: 15% = 10% + 5% — e.g., 15% of $80: 10% = $8, 5% = $4, total = $12.
• Steps:
  • 10% of $120 = $12.
  • 5% of $120 = $6.
  • 15% = $12 + $6 = $18.
• Answer: $18

[Easy] One-Step Linear Equation

• EN: Solve for x: x + 9 = 17
• FR: Résous pour x : x + 9 = 17
• Choices: A) x = 6 B) x = 7 C) x = 8 D) x = 9
• Hint: Subtract the same number from both sides — e.g., x + 5 = 12 → x = 12 − 5 = 7.
• Steps:
  • x + 9 = 17.
  • Subtract 9 from both sides: x = 17 − 9.
  • x = 8.
• Answer: x = 8

[Easy] Integer Subtraction

• EN: What is 3 − (−5)?
• FR: Combien font 3 − (−5)?
• Choices: A) −2 B) 2 C) 7 D) 8
• Hint: Subtracting a negative is the same as adding — e.g., 4 − (−3) = 4 + 3 = 7.
• Steps:
  • 3 − (−5) = 3 + 5.
  • = 8.
  • The answer is 8.
• Answer: 8

[Medium] Calculating Tax

• EN: A book costs $24.00. The HST in Ontario is 13%. What is the total cost including tax?
• FR: Un livre coûte 24,00 $. La TVH en Ontario est de 13 %. Quel est le coût total incluant la taxe?
• Choices: A) $26.72 B) $27.00 C) $27.12 D) $28.24
• Hint: Tax = price × tax rate, then add to the price — e.g., $20 × 13% = $2.60, total = $22.60.
• Steps:
  • Tax = $24.00 × 0.13 = $3.12.
  • Total = $24.00 + $3.12 = $27.12.
  • The total cost is $27.12.
• Answer: $27.12

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 5 cm long, 4 cm wide, and 3 cm tall. What is its surface area?
• FR: Une boîte-cadeau mesure 5 cm de long, 4 cm de large et 3 cm de hauteur. Quelle est son aire totale?
• Choices: A) 60 cm² B) 74 cm² C) 80 cm² D) 94 cm²
• Hint: SA = 2(lw + lh + wh) — e.g., for 2 × 3 × 4: 2(6 + 8 + 12) = 2(26) = 52 cm².
• Steps:
  • SA = 2(5×4 + 5×3 + 4×3).
  • = 2(20 + 15 + 12) = 2(47) = 94 cm².
  • The surface area is 94 cm².
• Answer: 94 cm²

[Medium] Integer Multiplication

• EN: What is (−6) × (−4)?
• FR: Combien font (−6) × (−4)?
• Choices: A) −24 B) −10 C) 10 D) 24
• Hint: Negative × negative = positive — e.g., (−3) × (−5) = +15.
• Steps:
  • Two negatives multiplied give a positive.
  • 6 × 4 = 24.
  • (−6) × (−4) = 24.
• Answer: 24

[Medium] Probability

• EN: A bag has 3 red, 5 blue, and 2 green marbles. What is the probability of picking a blue marble?
• FR: Un sac contient 3 billes rouges, 5 bleues et 2 vertes. Quelle est la probabilité de choisir une bille bleue?
• Choices: A) 1/2 B) 5/10 C) 3/10 D) 2/5
• Hint: Probability = favourable outcomes ÷ total outcomes — e.g., 3 red out of 9 total = 3/9 = 1/3.
• Steps:
  • Total marbles: 3 + 5 + 2 = 10.
  • Blue marbles: 5.
  • Probability = 5/10 = 1/2.
• Answer: 1/2

[Hard] Two-Step Equation

• EN: Solve for x: 3x − 7 = 14
• FR: Résous pour x : 3x − 7 = 14
• Choices: A) x = 5 B) x = 6 C) x = 7 D) x = 9
• Hint: Add 7 to both sides first, then divide — e.g., 2x − 5 = 11 → 2x = 16 → x = 8.
• Steps:
  • Add 7 to both sides: 3x = 21.
  • Divide both sides by 3: x = 7.
  • x = 7.
• Answer: x = 7

[Hard] Percent Increase

• EN: The population of a small Canadian town was 2,400 last year. It grew by 12.5% this year. What is the new population?
• FR: La population d'une petite ville canadienne était de 2 400 l'an dernier. Elle a augmenté de 12,5 % cette année. Quelle est la nouvelle population?
• Choices: A) 2,580 B) 2,600 C) 2,700 D) 2,850
• Hint: Percent increase: new = original × (1 + rate) — e.g., 1,000 × 1.10 = 1,100 after a 10% increase.
• Steps:
  • 12.5% of 2,400 = 2,400 × 0.125 = 300.
  • New population = 2,400 + 300 = 2,700.
  • The new population is 2,700.
• Answer: 2,700

[Easy] Perfect Squares

• EN: What is the square root of 144?
• FR: Quelle est la racine carrée de 144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: Think of what number times itself equals the answer — e.g., √121 = 11 because 11 × 11 = 121.
• Steps:
  • Ask: what number × itself = 144?
  • 12 × 12 = 144.
  • √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored 70, 80, 85, 90, and 75 on a math test. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 80, 85, 90 et 75 à un test de maths. Quelle est la moyenne?
• Choices: A) 78 B) 80 C) 82 D) 85
• Hint: Mean = sum of all values ÷ number of values — e.g., scores of 60, 70, 80: sum = 210, mean = 210 ÷ 3 = 70.
• Steps:
  • Sum: 70 + 80 + 85 + 90 + 75 = 400.
  • Mean: 400 ÷ 5 = 80.
  • The mean is 80.
• Answer: 80

[Easy] Percent Decrease

• EN: A $50 sweater is reduced by 20%. What is the sale price?
• FR: Un chandail à 50 $ est réduit de 20 %. Quel est le prix de vente?
• Choices: A) $30 B) $35 C) $40 D) $45
• Hint: Find the discount and subtract — e.g., 20% of $60 = $12, so sale price = $60 − $12 = $48.
• Steps:
  • 20% of $50 = $10.
  • $50 − $10 = $40.
  • The sale price is $40.
• Answer: $40

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13
• FR: Résous pour x : 2x + 5 = 13
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 9
• Hint: Subtract first, then divide — e.g., 3x + 2 = 11: subtract 2 → 3x = 9, divide → x = 3.
• Steps:
  • Subtract 5: 2x = 8.
  • Divide by 2: x = 4.
  • x = 4.
• Answer: x = 4

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et de 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: Use a² + b² = c² — e.g., legs of 3 and 4: 9 + 16 = 25, so hypotenuse = 5.
• Steps:
  • a² + b² = c².
  • 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Slope of a Line

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

[Medium] Median and Mode

• EN: Find the median of: 3, 7, 9, 4, 7, 5, 1
• FR: Trouve la médiane de : 3, 7, 9, 4, 7, 5, 1
• Choices: A) 4 B) 5 C) 7 D) 9
• Hint: Sort the values then find the middle — e.g., 2, 4, 5, 6, 8 → the median is 5 (3rd of 5 values).
• Steps:
  • Sort: 1, 3, 4, 5, 7, 7, 9.
  • There are 7 values; the middle is the 4th: 5.
  • The median is 5.
• Answer: 5

[Medium] Percent Increase

• EN: A hockey player scored 40 goals last season. This season they scored 50 goals. What is the percent increase?
• FR: Un joueur de hockey a marqué 40 buts la saison dernière. Cette saison, il en a marqué 50. Quel est le pourcentage d'augmentation?
• Choices: A) 10% B) 20% C) 25% D) 30%
• Hint: Percent increase = (new − old) ÷ old × 100 — e.g., from 30 to 36: (6 ÷ 30) × 100 = 20%.
• Steps:
  • Increase = 50 − 40 = 10.
  • Percent increase = 10 ÷ 40 × 100 = 25%.
  • The percent increase is 25%.
• Answer: 25%

[Hard] Pythagorean Theorem — Find a Leg

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

[Hard] Two-Step Equations with Fractions

• EN: Solve for x: x/3 + 4 = 9
• FR: Résous pour x : x/3 + 4 = 9
• Choices: A) x = 12 B) x = 15 C) x = 18 D) x = 21
• Hint: Subtract first, then multiply by the denominator — e.g., x/4 + 1 = 6 → x/4 = 5 → x = 20.
• Steps:
  • Subtract 4: x/3 = 5.
  • Multiply both sides by 3: x = 15.
  • x = 15.
• Answer: x = 15

[Easy] Solving a Linear Equation

• EN: Solve for x: 5x − 3 = 22
• FR: Résous pour x : 5x − 3 = 22
• Choices: A) x = 4 B) x = 5 C) x = 6 D) x = 7
• Hint: Add the constant to both sides first, then divide — e.g., 4x − 2 = 14 → 4x = 16 → x = 4.
• Steps:
  • Add 3: 5x = 25.
  • Divide by 5: x = 5.
  • x = 5.
• Answer: x = 5

[Easy] Slope-Intercept Form

• EN: What is the slope of the line y = 3x + 7?
• FR: Quelle est la pente de la droite y = 3x + 7?
• Choices: A) 7 B) 3 C) −3 D) 10
• Hint: In y = mx + b, m is the slope — e.g., y = 5x + 2 has slope 5.
• Steps:
  • Equation is in y = mx + b form.
  • m = 3.
  • The slope is 3.
• Answer: 3

[Easy] Adding Polynomials

• EN: Add: (3x + 5) + (2x − 1)
• FR: Additionne : (3x + 5) + (2x − 1)
• Choices: A) 5x + 4 B) 5x + 6 C) 6x + 4 D) 5x − 4
• Hint: Combine like terms — e.g., (4x + 3) + (x − 2) = 5x + 1.
• Steps:
  • x-terms: 3x + 2x = 5x.
  • Constants: 5 + (−1) = 4.
  • Result: 5x + 4.
• Answer: 5x + 4

[Easy] SOH-CAH-TOA Basics

• EN: In a right triangle, the side opposite the angle is 3 cm and the hypotenuse is 5 cm. What is sin θ?
• FR: Dans un triangle rectangle, le côté opposé à l'angle mesure 3 cm et l'hypoténuse mesure 5 cm. Quel est sin θ?
• Choices: A) 3/4 B) 4/5 C) 3/5 D) 5/3
• Hint: sin = opposite ÷ hypotenuse (SOH) — e.g., opp = 4, hyp = 5 → sin θ = 4/5.
• Steps:
  • sin θ = opposite / hypotenuse.
  • = 3/5.
  • sin θ = 3/5.
• Answer: 3/5

[Medium] Linear Inequality

• EN: Solve: 2x + 3 > 11. Which value is in the solution set?
• FR: Résous : 2x + 3 > 11. Quelle valeur fait partie de l'ensemble solution?
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 2
• Hint: Solve like an equation, then check — e.g., 3x − 1 > 8 → 3x > 9 → x > 3, so x = 4 works.
• Steps:
  • 2x + 3 > 11 → 2x > 8 → x > 4.
  • x = 5 satisfies x > 4.
  • The answer is x = 5.
• Answer: x = 5

[Medium] Multiplying Polynomials

• EN: Expand: 3x(2x + 4)
• FR: Développe : 3x(2x + 4)
• Choices: A) 5x² + 7x B) 6x² + 12x C) 6x + 12 D) 6x² + 4x
• Hint: Distribute the term outside — e.g., 2x(x + 5) = 2x² + 10x.
• Steps:
  • 3x × 2x = 6x².
  • 3x × 4 = 12x.
  • Result: 6x² + 12x.
• Answer: 6x² + 12x

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 6 cm and 9 cm. If the shorter triangle has another side of 8 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 6 cm et 9 cm. Si le plus petit triangle a un autre côté de 8 cm, quel est le côté correspondant du plus grand triangle?
• Choices: A) 10 cm B) 11 cm C) 12 cm D) 14 cm
• Hint: Set up a proportion — e.g., if sides are 4 and 6 (ratio 3:2), and the small side is 10, the large side = 10 × 3/2 = 15.
• Steps:
  • Scale factor: 9/6 = 3/2.
  • Large side = 8 × 3/2 = 12 cm.
  • The corresponding side is 12 cm.
• Answer: 12 cm

[Medium] Graphing Lines

• EN: A line has the equation y = −2x + 5. What is the y-intercept?
• FR: Une droite a l'équation y = −2x + 5. Quel est l'ordonnée à l'origine?
• Choices: A) −2 B) 2 C) 5 D) −5
• Hint: In y = mx + b, b is the y-intercept — e.g., y = 4x − 3 has y-intercept −3.
• Steps:
  • The equation is y = −2x + 5.
  • b = 5.
  • The y-intercept is 5.
• Answer: 5

[Hard] Using SOH-CAH-TOA to Find a Side

• EN: A right triangle has an angle of 30° and a hypotenuse of 20 cm. What is the length of the side opposite the 30° angle?
• FR: Un triangle rectangle a un angle de 30° et une hypoténuse de 20 cm. Quelle est la longueur du côté opposé à l'angle de 30°?
• Choices: A) 8 cm B) 10 cm C) 14 cm D) 17 cm
• Hint: Use sin — opp = hyp × sin(angle) (e.g., hyp = 10, angle = 45°: opp = 10 × sin 45° ≈ 7.07).
• Steps:
  • sin 30° = 0.5.
  • Opposite = 20 × 0.5 = 10 cm.
  • The opposite side is 10 cm.
• Answer: 10 cm

[Hard] Statistics — Standard Application

• EN: A data set is: 12, 15, 15, 18, 20. A new value of 30 is added. Which measure changes the most: mean or median?
• FR: Un ensemble de données est : 12, 15, 15, 18, 20. Une nouvelle valeur de 30 est ajoutée. Quelle mesure change le plus : la moyenne ou la médiane?
• Choices: A) Median changes more B) Mean changes more C) Both change equally D) Neither changes
• Hint: Outliers affect the mean more than the median — e.g., adding 100 to a small data set pulls the mean far up but barely moves the median.
• Steps:
  • Original mean: (12+15+15+18+20)/5 = 80/5 = 16. New mean: 110/6 ≈ 18.3.
  • Original median: 15. New median (sorted: 12,15,15,18,20,30): (15+18)/2 = 16.5.
  • Mean changed by about 2.3; median changed by 1.5. Mean changes more.
• Answer: Mean changes more

[Easy] Factoring a Quadratic

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

[Easy] Trigonometry — Finding an Angle

• EN: In a right triangle, the opposite side is 5 cm and the hypotenuse is 10 cm. What is the angle? (sin 30° = 0.5)
• FR: Dans un triangle rectangle, le côté opposé mesure 5 cm et l'hypoténuse mesure 10 cm. Quel est l'angle? (sin 30° = 0,5)
• Choices: A) 25° B) 30° C) 45° D) 60°
• Hint: sin θ = opposite/hypotenuse, then use inverse sin — e.g., sin θ = 1/2 → θ = 30°.
• Steps:
  • sin θ = 5/10 = 0.5.
  • sin⁻¹(0.5) = 30°.
  • The angle is 30°.
• Answer: 30°

[Easy] Volume of a Cylinder

• EN: A cylindrical tin can has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)
• FR: Une boîte de conserve cylindrique a un rayon de 3 cm et une hauteur de 10 cm. Quel est son volume? (Utilise π ≈ 3,14)
• Choices: A) 188.4 cm³ B) 251.2 cm³ C) 282.6 cm³ D) 314 cm³
• Hint: Volume = π × r² × h — e.g., r = 2, h = 5: π × 4 × 5 = 20π ≈ 62.8 cm³.
• Steps:
  • V = π × 3² × 10 = 3.14 × 9 × 10.
  • = 3.14 × 90 = 282.6 cm³.
  • The volume is 282.6 cm³.
• Answer: 282.6 cm³

[Easy] Solving a System of Equations

• EN: Solve the system: y = 2x and y = x + 4. What is x?
• FR: Résous le système : y = 2x et y = x + 4. Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 5
• Hint: Set the two expressions equal to each other — e.g., 3x = x + 6 → 2x = 6 → x = 3.
• Steps:
  • Set equal: 2x = x + 4.
  • Subtract x: x = 4.
  • x = 4.
• Answer: x = 4

[Medium] Completing the Square

• EN: Complete the square to rewrite x² + 6x + 2 in the form (x + a)² + b.
• FR: Complète le carré pour réécrire x² + 6x + 2 sous la forme (x + a)² + b.
• Choices: A) (x + 3)² − 7 B) (x + 3)² + 2 C) (x + 6)² − 7 D) (x + 2)² − 3
• Hint: Take half the x-coefficient, square it, then adjust the constant — e.g., x² + 4x + 1 = (x+2)² − 3.
• Steps:
  • Half of 6 is 3; 3² = 9.
  • x² + 6x + 2 = (x + 3)² − 9 + 2 = (x + 3)² − 7.
  • Rewritten: (x + 3)² − 7.
• Answer: (x + 3)² − 7

[Medium] Circle Geometry — Arc Length

• EN: A circle has a radius of 6 cm. What is the length of an arc that subtends a central angle of 60°? (Use π ≈ 3.14)
• FR: Un cercle a un rayon de 6 cm. Quelle est la longueur d'un arc qui sous-tend un angle central de 60°? (Utilise π ≈ 3,14)
• Choices: A) 5.24 cm B) 6.28 cm C) 7.85 cm D) 9.42 cm
• Hint: Arc length = (angle/360) × 2πr — e.g., angle 90°, r = 4: (90/360) × 2π(4) = π×2 ≈ 6.28 cm.
• Steps:
  • Arc = (60/360) × 2 × 3.14 × 6.
  • = (1/6) × 37.68 = 6.28 cm.
  • The arc length is 6.28 cm.
• Answer: 6.28 cm

[Medium] Quadratic Formula

• EN: Solve using the quadratic formula: x² − 5x + 6 = 0. What are the roots?
• FR: Résous à l'aide de la formule quadratique : x² − 5x + 6 = 0. Quelles sont les racines?
• Choices: A) x = 1 and x = 6 B) x = 2 and x = 3 C) x = −2 and x = −3 D) x = 3 and x = 4
• Hint: Use x = [−b ± √(b²−4ac)] / 2a — check by factoring too: what two numbers multiply to 6 and add to −5?
• Steps:
  • a=1, b=−5, c=6. Discriminant: 25 − 24 = 1.
  • x = (5 ± 1) / 2 → x = 3 or x = 2.
  • The roots are x = 2 and x = 3.
• Answer: x = 2 and x = 3

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 4 cm and a slant height of 8 cm. What is its total surface area? (Use π ≈ 3.14)
• FR: Un cône a un rayon de 4 cm et une hauteur oblique de 8 cm. Quelle est son aire totale? (Utilise π ≈ 3,14)
• Choices: A) 100.48 cm² B) 125.60 cm² C) 150.72 cm² D) 175.84 cm²
• Hint: SA of cone = πr² + πrl — e.g., r = 3, l = 5: π(9) + π(15) = 24π ≈ 75.36 cm².
• Steps:
  • Base: π × 4² = 3.14 × 16 = 50.24 cm².
  • Lateral: π × 4 × 8 = 3.14 × 32 = 100.48 cm².
  • Total SA = 50.24 + 100.48 = 150.72 cm².
• Answer: 150.72 cm²

[Hard] Systems of Equations — Elimination

• EN: Solve the system: 3x + 2y = 16 and x − y = 1. What is y?
• FR: Résous le système : 3x + 2y = 16 et x − y = 1. Quelle est la valeur de y?
• Choices: A) y = 2 B) y = 3 C) y = 4 D) y = 5
• Hint: Multiply the second equation to match a coefficient, then add — e.g., multiply x − y = 1 by 2: 2x − 2y = 2, then add to 3x + 2y = 16.
• Steps:
  • From x − y = 1 → x = y + 1.
  • Substitute: 3(y+1) + 2y = 16 → 3y + 3 + 2y = 16 → 5y = 13... wait. Let me recheck.
  • 5y = 13 is not integer — let me use elimination: multiply eq2 by 3: 3x − 3y = 3. Subtract from eq1: (3x+2y) − (3x−3y) = 16−3 → 5y = 13. Hmm.
  • Let me try x − y = 1 multiplied by 2: 2x − 2y = 2. 3x + 2y = 16, add: 5x = 18 → not integer.
  • Adjust: use x − y = 2 instead. 3x + 2y = 16, x − y = 2. Multiply eq2 by 2: 2x − 2y = 4. Add to eq1: 5x = 20 → x = 4, y = 2.
  • (Using corrected equations: 3x + 2y = 16 and x − y = 2.)
• EN: Solve the system: 3x + 2y = 16 and x − y = 2. What is y?
• FR: Résous le système : 3x + 2y = 16 et x − y = 2. Quelle est la valeur de y?
• Choices: A) y = 2 B) y = 3 C) y = 4 D) y = 5
• Hint: Multiply the second equation by 2 and add to the first to eliminate y — e.g., for 2x + y = 8 and x − y = 1: add to get 3x = 9 → x = 3.
• Steps:
  • Multiply x − y = 2 by 2: 2x − 2y = 4.
  • Add to 3x + 2y = 16: 5x = 20 → x = 4.
  • Substitute: 4 − y = 2 → y = 2.
• Answer: y = 2

[Hard] Quadratic — Real-World Application

• EN: A ball is thrown upward. Its height (in metres) after t seconds is given by h = −5t² + 20t + 1. What is the maximum height?
• FR: Une balle est lancée vers le haut. Sa hauteur (en mètres) après t secondes est donnée par h = −5t² + 20t + 1. Quelle est la hauteur maximale?
• Choices: A) 19 m B) 20 m C) 21 m D) 25 m
• Hint: Maximum occurs at t = −b/(2a) — then substitute back (e.g., h = −t² + 6t: max at t=3, h = −9+18 = 9 m).
• Steps:
  • t = −20 / (2 × −5) = −20/−10 = 2 seconds.
  • h = −5(4) + 20(2) + 1 = −20 + 40 + 1 = 21 m.
  • The maximum height is 21 m.
• Answer: 21 m

[Easy] Identifying Function Types

• EN: Which equation represents an exponential function?
• FR: Quelle équation représente une fonction exponentielle?
• Choices: A) y = 3x + 2 B) y = x² + 1 C) y = 3ˣ D) y = 1/x
• Hint: An exponential function has the variable in the exponent — e.g., y = 2ˣ grows by doubling each time.
• Steps:
  • Linear: variable × constant (y = 3x + 2). ✗
  • Quadratic: variable squared (y = x² + 1). ✗
  • Exponential: constant raised to variable power (y = 3ˣ). ✓
  • The answer is y = 3ˣ.
• Answer: y = 3ˣ

[Easy] Logarithm Basics

• EN: What is log₂(32)?
• FR: Combien vaut log₂(32)?
• Choices: A) 4 B) 5 C) 6 D) 16
• Hint: Ask "2 to what power equals the number?" — e.g., log₂(8) = 3 because 2³ = 8.
• Steps:
  • Ask: 2ˣ = 32.
  • 2⁵ = 32.
  • log₂(32) = 5.
• Answer: 5

[Easy] Arithmetic Sequence

• EN: The first term of an arithmetic sequence is 4 and the common difference is 6. What is the 5th term?
• FR: Le premier terme d'une suite arithmétique est 4 et la raison est 6. Quel est le 5e terme?
• Choices: A) 22 B) 26 C) 28 D) 30
• Hint: Use tₙ = t₁ + (n−1)d — e.g., t₁ = 2, d = 5, t₄ = 2 + 3×5 = 17.
• Steps:
  • t₅ = 4 + (5−1) × 6 = 4 + 24 = 28.
  • The 5th term is 28.
• Answer: 28

[Easy] Simple Interest vs. Compound Interest

• EN: $1,000 is invested at 5% per year for 2 years, compounded annually. What is the total amount after 2 years?
• FR: 1 000 $ sont investis à 5 % par an pendant 2 ans, composé annuellement. Quel est le montant total après 2 ans?
• Choices: A) $1,050.00 B) $1,100.00 C) $1,102.50 D) $1,105.00
• Hint: Use A = P(1 + r)ⁿ — e.g., $500 at 10% for 2 years: $500 × 1.1² = $500 × 1.21 = $605.
• Steps:
  • A = 1000 × (1 + 0.05)².
  • = 1000 × 1.1025 = $1,102.50.
  • The total is $1,102.50.
• Answer: $1,102.50

[Medium] Quadratic Function — Vertex

• EN: What is the vertex of the parabola y = (x − 3)² + 4?
• FR: Quel est le sommet de la parabole y = (x − 3)² + 4?
• Choices: A) (−3, 4) B) (3, 4) C) (3, −4) D) (4, 3)
• Hint: In vertex form y = (x − h)² + k, the vertex is (h, k) — e.g., y = (x − 2)² + 5 has vertex (2, 5).
• Steps:
  • y = (x − 3)² + 4 is in vertex form.
  • h = 3, k = 4.
  • Vertex: (3, 4).
• Answer: (3, 4)

[Medium] Compound Interest — Future Value

• EN: Priya invests $2,000 in a GIC at 4% per year, compounded quarterly, for 3 years. Which expression gives the total amount?
• FR: Priya investit 2 000 $ dans un CPG à 4 % par an, composé trimestriellement, pendant 3 ans. Quelle expression donne le montant total?
• Choices: A) 2000 × (1 + 0.04)³ B) 2000 × (1 + 0.01)¹² C) 2000 × (1 + 0.04)¹² D) 2000 × (1 + 0.16)³
• Hint: Quarterly compounding: rate per period = annual rate ÷ 4, periods = years × 4 — e.g., 2 years quarterly → 8 periods.
• Steps:
  • Quarterly rate = 4%/4 = 1% = 0.01.
  • Number of periods = 3 × 4 = 12.
  • Expression: 2000 × (1 + 0.01)¹².
• Answer: 2000 × (1 + 0.01)¹²

[Medium] Trigonometric Identity

• EN: Simplify: sin²θ + cos²θ
• FR: Simplifie : sin²θ + cos²θ
• Choices: A) 0 B) 2 C) 1 D) sin θ
• Hint: This is the most fundamental trigonometric identity — it is always equal to a fixed value for any angle.
• Steps:
  • The Pythagorean identity states: sin²θ + cos²θ = 1.
  • This is true for any angle θ.
  • The simplified value is 1.
• Answer: 1

[Medium] Geometric Series — Sum

• EN: Find the sum of the first 4 terms of the geometric series: 2, 6, 18, 54, …
• FR: Trouve la somme des 4 premiers termes de la suite géométrique : 2, 6, 18, 54, …
• Choices: A) 70 B) 78 C) 80 D) 82
• Hint: Add the first 4 terms directly or use S = a(rⁿ − 1)/(r − 1) — e.g., 1, 3, 9, 27: sum = 40.
• Steps:
  • Terms: 2 + 6 + 18 + 54.
  • = 8 + 72 = 80.
  • The sum is 80.
• Answer: 80

[Hard] Logarithm Equation

• EN: Solve for x: log₃(x) + log₃(9) = 4
• FR: Résous pour x : log₃(x) + log₃(9) = 4
• Choices: A) x = 3 B) x = 6 C) x = 9 D) x = 27
• Hint: Combine logs using the product rule: log(a) + log(b) = log(ab) — then convert to exponential form.
• Steps:
  • log₃(x) + log₃(9) = log₃(9x) = 4.
  • 9x = 3⁴ = 81.
  • x = 81/9 = 9.
• Answer: x = 9

[Hard] Annuity — Future Value

• EN: Mei deposits $200 at the end of each month into an account earning 6% per year, compounded monthly, for 2 years. Using FV = PMT × [(1 + r)ⁿ − 1] / r, what is the future value to the nearest dollar? (r = 0.005, n = 24)
• FR: Mei dépose 200 $ à la fin de chaque mois dans un compte rapportant 6 % par an, composé mensuellement, pendant 2 ans. En utilisant VA = PMT × [(1 + r)ⁿ − 1] / r, quelle est la valeur future au dollar près? (r = 0,005, n = 24)
• Choices: A) $4,800 B) $5,004 C) $5,088 D) $5,200
• Hint: Use the annuity formula — e.g., $100/month at 1% monthly for 3 months ≈ $100 × [(1.01)³ −1]/0.01 ≈ $303.
• Steps:
  • (1.005)²⁴ ≈ 1.1272.
  • FV = 200 × (1.1272 − 1) / 0.005 = 200 × 0.1272 / 0.005 = 200 × 25.44 ≈ $5,088.
  • The future value is approximately $5,088.
• Answer: $5,088

[Easy] Permutations

• EN: In how many ways can 5 students line up in a row?
• FR: De combien de façons 5 élèves peuvent-ils se mettre en rang?
• Choices: A) 24 B) 60 C) 120 D) 240
• Hint: Use n! — e.g., 4 students: 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120.
  • There are 120 ways.
• Answer: 120

[Easy] Combinations

• EN: How many ways can a committee of 3 be chosen from 6 students?
• FR: De combien de façons peut-on choisir un comité de 3 parmi 6 élèves?
• Choices: A) 18 B) 20 C) 24 D) 30
• Hint: Use C(n,r) = n! / [r!(n−r)!] — e.g., C(5,2) = 10.
• Steps:
  • C(6,3) = 6! / (3! × 3!) = 720 / (6 × 6) = 720/36 = 20.
  • There are 20 ways.
• Answer: 20

[Easy] Derivative — Power Rule

• EN: What is the derivative of f(x) = x³?
• FR: Quelle est la dérivée de f(x) = x³?
• Choices: A) x² B) 2x² C) 3x² D) 3x³
• Hint: Power rule: if f(x) = xⁿ, then f'(x) = n·xⁿ⁻¹ — e.g., f(x) = x⁴ → f'(x) = 4x³.
• Steps:
  • f(x) = x³, so n = 3.
  • f'(x) = 3x³⁻¹ = 3x².
  • The derivative is 3x².
• Answer: 3x²

[Easy] Intro to Vectors

• EN: A vector has components (3, 4). What is its magnitude?
• FR: Un vecteur a les composantes (3, 4). Quelle est sa magnitude?
• Choices: A) 4 B) 5 C) 7 D) 12
• Hint: Magnitude = √(x² + y²) — e.g., (6, 8): √(36 + 64) = √100 = 10.
• Steps:
  • |v| = √(3² + 4²) = √(9 + 16) = √25.
  • = 5.
  • The magnitude is 5.
• Answer: 5

[Medium] Rational Function — Domain

• EN: What value(s) of x must be excluded from the domain of f(x) = (x + 3) / (x² − 4)?
• FR: Quelles valeurs de x doivent être exclues du domaine de f(x) = (x + 3) / (x² − 4)?
• Choices: A) x = 4 only B) x = −3 only C) x = 2 and x = −2 D) x = 0 only
• Hint: Set the denominator equal to zero and solve — e.g., for 1/(x−5), exclude x = 5.
• Steps:
  • Denominator: x² − 4 = 0 → x² = 4 → x = ±2.
  • Exclude x = 2 and x = −2.
  • Domain excludes x = 2 and x = −2.
• Answer: x = 2 and x = −2

[Medium] Derivative — Rate of Change

• EN: The position of a ball is given by s(t) = 4t² + 2t. What is its velocity (rate of change) at t = 3 seconds?
• FR: La position d'une balle est donnée par s(t) = 4t² + 2t. Quelle est sa vitesse (taux de variation) à t = 3 secondes?
• Choices: A) 24 m/s B) 26 m/s C) 38 m/s D) 42 m/s
• Hint: Differentiate, then substitute t — e.g., s(t) = 3t² + t → s'(t) = 6t + 1; at t = 2: s'(2) = 13.
• Steps:
  • s'(t) = 8t + 2.
  • s'(3) = 8(3) + 2 = 24 + 2 = 26 m/s.
  • The velocity is 26 m/s.
• Answer: 26 m/s

[Medium] Binomial Probability

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

[Medium] Polynomial Division

• EN: Divide: (x² + 5x + 6) ÷ (x + 2)
• FR: Divise : (x² + 5x + 6) ÷ (x + 2)
• Choices: A) x + 2 B) x + 3 C) x − 3 D) x + 4
• Hint: Factor the numerator then cancel — e.g., (x² + 7x + 12) ÷ (x + 3) = (x+3)(x+4)/(x+3) = x + 4.
• Steps:
  • Factor: x² + 5x + 6 = (x + 2)(x + 3).
  • Divide by (x + 2): = x + 3.
  • The result is x + 3.
• Answer: x + 3

[Hard] Dot Product of Vectors

• EN: Two vectors are u = (2, −1, 3) and v = (4, 5, −2). What is u · v?
• FR: Deux vecteurs sont u = (2, −1, 3) et v = (4, 5, −2). Quel est u · v?
• Choices: A) −3 B) 0 C) 3 D) 9
• Hint: Dot product: multiply corresponding components and add — e.g., (1, 2, 3)·(4, −1, 2) = 4 − 2 + 6 = 8.
• Steps:
  • (2)(4) + (−1)(5) + (3)(−2).
  • = 8 − 5 − 6 = −3.
  • u · v = −3.
• Answer: −3

[Hard] Normal Distribution — Z-Score

• EN: In a Grade 12 exam, the mean score is 72 and the standard deviation is 8. A student scored 88. What is their z-score, and what does it indicate?
• FR: Dans un examen de 12e année, la moyenne est de 72 et l'écart-type est de 8. Un élève a obtenu 88. Quel est son score z et qu'indique-t-il?
• Choices: A) z = 1, slightly above average B) z = 2, two standard deviations above the mean C) z = 4, four standard deviations above the mean D) z = 16, well above average
• Hint: z = (x − μ) / σ — e.g., score 85, mean 70, SD 5: z = (85−70)/5 = 3, meaning 3 SDs above the mean.
• Steps:
  • z = (88 − 72) / 8 = 16 / 8 = 2.
  • A z-score of 2 means the student scored 2 standard deviations above the mean.
  • The answer is z = 2, two standard deviations above the mean.
• Answer: z = 2, two standard deviations above the mean