Daily Math — 2026-09-28

[Easy] Counting to 20

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

[Easy] Skip Counting by 2s

• EN: Maya counts by 2s starting at 2. What is the fourth number she says?
• FR: Maya compte par 2 en commençant à 2. Quel est le quatrième nombre qu'elle dit?
• Choices: A) 6 B) 7 C) 8 D) 9
• Hint: Counting by 2s from 4 gives: 4, 6, 8, 10 — the third number is 8.
• Steps:
  • First number: 2. Second: 4. Third: 6. Fourth: 8.
  • The fourth number in the pattern 2, 4, 6, 8 is 8.
• Answer: 8

[Easy] Comparing Numbers

• EN: Which number is greater: 14 or 9?
• FR: Quel nombre est le plus grand : 14 ou 9?
• Choices: A) 9 B) 11 C) 14 D) 18
• Hint: Think of a number line — numbers further to the right are greater, so 13 is greater than 7.
• Steps:
  • 14 has a tens digit of 1 and 9 has no tens digit.
  • Any two-digit number is greater than a one-digit number, so 14 is greater.
• Answer: 14

[Easy] Coin Recognition

• EN: Liam has 2 nickels. How many cents does he have in all?
• FR: Liam a 2 pièces de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 2 cents B) 5 cents C) 10 cents D) 15 cents
• Hint: Each nickel is worth 5 cents, so 3 nickels = 5 + 5 + 5 = 15 cents.
• Steps:
  • One nickel = 5 cents.
  • Two nickels: 5 + 5 = 10 cents.
• Answer: 10 cents

[Medium] Addition Within 20

• EN: There are 8 red crayons and 6 blue crayons in a box. How many crayons are there altogether?
• FR: Il y a 8 crayons rouges et 6 crayons bleus dans une boîte. Combien y a-t-il de crayons en tout?
• Choices: A) 12 crayons B) 13 crayons C) 14 crayons D) 15 crayons
• Hint: To add 7 + 5, make a ten: 7 + 3 = 10, then add the leftover 2 to get 12.
• Steps:
  • Make a ten from 8: 8 + 2 = 10. That uses 2 from the 6, leaving 4.
  • 10 + 4 = 14, so there are 14 crayons altogether.
• Answer: 14 crayons

[Medium] Subtraction Within 20

• EN: There are 15 stickers on a sheet. Sofia gives away 7 stickers. How many stickers are left?
• FR: Il y a 15 autocollants sur une feuille. Sofia donne 7 autocollants. Combien d'autocollants reste-t-il?
• Choices: A) 6 stickers B) 7 stickers C) 8 stickers D) 9 stickers
• Hint: To solve 13 – 6, think "6 + ? = 13" — count up: 7, 8, 9, 10, 11, 12, 13 (7 jumps), so the answer is 7.
• Steps:
  • Think: 7 + ? = 15. Count up from 7: 8, 9, 10, 11, 12, 13, 14, 15 — that is 8 steps.
  • So 15 – 7 = 8. Sofia has 8 stickers left.
• Answer: 8 stickers

[Medium] Skip Counting by 5s

• EN: Ethan counts by 5s starting at 5. What is the fifth number he says?
• FR: Ethan compte par 5 en commençant à 5. Quel est le cinquième nombre qu'il dit?
• Choices: A) 20 B) 25 C) 30 D) 35
• Hint: Counting by 5s from 5: the third number is 15, the fourth is 20.
• Steps:
  • 5, 10, 15, 20, 25 — counting on by 5 each time.
  • The fifth number is 25.
• Answer: 25

[Medium] Skip Counting by 10s

• EN: Ava starts at 10 and counts by 10s. What is the third number she says?
• FR: Ava commence à 10 et compte par 10. Quel est le troisième nombre qu'elle dit?
• Choices: A) 20 B) 30 C) 40 D) 50
• Hint: Skip counting by 10s from 20: 20, 30, 40 — the third number from 20 is 40.
• Steps:
  • First number: 10. Second: 20. Third: 30.
  • The third number is 30.
• Answer: 30

[Hard] Adding Three Numbers

• EN: Noah has 6 toy cars, 4 toy trucks, and 3 toy buses. How many toy vehicles does he have in all?
• FR: Noah a 6 voitures jouets, 4 camions jouets et 3 autobus jouets. Combien de véhicules jouets a-t-il en tout?
• Choices: A) 11 vehicles B) 12 vehicles C) 13 vehicles D) 14 vehicles
• Hint: To add 5 + 3 + 2, first add 5 + 3 = 8, then add 2 to get 10.
• Steps:
  • Add the first two: 6 + 4 = 10.
  • Then add the third: 10 + 3 = 13. Noah has 13 toy vehicles.
• Answer: 13 vehicles

[Hard] Coins and Counting

• EN: Chloe has 1 dime and 3 pennies. How many cents does she have in all?
• FR: Chloe a 1 pièce de 10 cents et 3 pièces de 1 cent. Combien de cents a-t-elle en tout?
• Choices: A) 11 cents B) 12 cents C) 13 cents D) 14 cents
• Hint: A dime is worth 10 cents, so 1 dime + 2 pennies = 10 + 2 = 12 cents.
• Steps:
  • A dime = 10 cents. Three pennies = 3 cents.
  • 10 + 3 = 13 cents altogether.
• Answer: 13 cents

[Easy] Addition Within 100

• EN: A student has 34 marbles and finds 25 more. How many marbles does the student have now?
• FR: Un élève a 34 billes et en trouve 25 autres. Combien de billes a-t-il maintenant?
• Choices: A) 57 marbles B) 58 marbles C) 59 marbles D) 60 marbles
• Hint: To add 21 + 36, add the tens first (20 + 30 = 50), then the ones (1 + 6 = 7), giving 57.
• Steps:
  • Tens: 30 + 20 = 50. Ones: 4 + 5 = 9.
  • 50 + 9 = 59 marbles.
• Answer: 59 marbles

[Easy] Telling Time to the Hour

• EN: The clock shows the hour hand pointing to 4 and the minute hand pointing to 12. What time is it?
• FR: La grande aiguille pointe sur 12 et la petite aiguille pointe sur 4. Quelle heure est-il?
• Choices: A) 3:00 B) 4:00 C) 5:00 D) 12:00
• Hint: When the minute hand is on the 12, read the hour hand directly — if it points to 7, it is 7:00.
• Steps:
  • The minute hand on 12 means it is exactly on the hour.
  • The hour hand points to 4, so the time is 4:00.
• Answer: 4:00

[Easy] Measuring Length in cm

• EN: A pencil measures 14 cm long. A crayon measures 9 cm long. How much longer is the pencil than the crayon?
• FR: Un crayon mesure 14 cm de long. Un crayon de couleur mesure 9 cm de long. De combien le crayon est-il plus long?
• Choices: A) 3 cm B) 4 cm C) 5 cm D) 6 cm
• Hint: To find how much longer 16 cm is than 11 cm, subtract: 16 – 11 = 5 cm.
• Steps:
  • Subtract the shorter from the longer: 14 – 9 = 5.
  • The pencil is 5 cm longer than the crayon.
• Answer: 5 cm

[Easy] Counting Coins to $1

• EN: Ben has 3 dimes and 2 nickels. How many cents does he have in all?
• FR: Ben a 3 pièces de 10 cents et 2 pièces de 5 cents. Combien de cents a-t-il en tout?
• Choices: A) 35 cents B) 40 cents C) 45 cents D) 50 cents
• Hint: 4 dimes = 40 cents, 3 nickels = 15 cents, so together that is 55 cents.
• Steps:
  • 3 dimes = 10 + 10 + 10 = 30 cents.
  • 2 nickels = 5 + 5 = 10 cents. Total: 30 + 10 = 40 cents.
• Answer: 40 cents

[Medium] Subtraction Within 100

• EN: A school store had 72 erasers. Students bought 38 erasers. How many erasers are left?
• FR: Une papeterie scolaire avait 72 gommes à effacer. Les élèves en ont acheté 38. Combien en reste-t-il?
• Choices: A) 33 erasers B) 34 erasers C) 35 erasers D) 36 erasers
• Hint: To solve 65 – 29, regroup: 65 – 30 = 35, then add back 1 to get 36.
• Steps:
  • Regroup: borrow from the tens in 72 → 60 + 12. Subtract ones: 12 – 8 = 4.
  • Subtract tens: 6 – 3 = 3. So 72 – 38 = 34 erasers.
• Answer: 34 erasers

[Medium] Telling Time to the Half-Hour

• EN: The clock shows the hour hand halfway between 2 and 3, and the minute hand pointing to 6. What time is it?
• FR: La petite aiguille est à mi-chemin entre 2 et 3, et la grande aiguille pointe sur le 6. Quelle heure est-il?
• Choices: A) 2:00 B) 2:30 C) 3:00 D) 3:30
• Hint: When the minute hand points to 6, it is always a half-hour — if the hour hand is between 5 and 6, the time is 5:30.
• Steps:
  • Minute hand on 6 = 30 minutes past the hour.
  • Hour hand is between 2 and 3, so it is 2:30.
• Answer: 2:30

[Medium] Simple Patterns

• EN: Look at this pattern: 5, 10, 15, 20, ___. What is the next number?
• FR: Observe ce motif : 5, 10, 15, 20, ___. Quel est le prochain nombre?
• Choices: A) 22 B) 24 C) 25 D) 30
• Hint: In the pattern 3, 6, 9, 12, each number increases by 3, so the next would be 15.
• Steps:
  • Each number increases by 5: 5, 10, 15, 20, …
  • 20 + 5 = 25. The next number is 25.
• Answer: 25

[Medium] Measuring Length in m

• EN: A hallway is 8 metres long. A classroom is 6 metres long. How long are they together?
• FR: Un couloir mesure 8 mètres de long. Une salle de classe mesure 6 mètres de long. Quelle est leur longueur ensemble?
• Choices: A) 12 m B) 13 m C) 14 m D) 15 m
• Hint: To add 9 m + 4 m, simply add the numbers: 9 + 4 = 13 m.
• Steps:
  • Add the two lengths: 8 + 6 = 14.
  • Together they are 14 m long.
• Answer: 14 m

[Hard] Two-Step Addition and Subtraction

• EN: A jar had 85 candies. Olivia ate 17 candies and then put 6 more candies in. How many candies are in the jar now?
• FR: Un bocal contenait 85 bonbons. Olivia en a mangé 17, puis en a mis 6 autres. Combien y a-t-il de bonbons dans le bocal maintenant?
• Choices: A) 72 candies B) 73 candies C) 74 candies D) 75 candies
• Hint: For 90 – 14 + 5, first do 90 – 14 = 76, then 76 + 5 = 81.
• Steps:
  • First, subtract: 85 – 17 = 68 candies remain.
  • Then add: 68 + 6 = 74 candies in the jar.
• Answer: 74 candies

[Hard] Counting Coins to $1

• EN: Emma has 2 quarters, 1 dime, and 3 pennies. How many cents does she have in all?
• FR: Emma a 2 pièces de 25 cents, 1 pièce de 10 cents et 3 pièces de 1 cent. Combien de cents a-t-elle en tout?
• Choices: A) 60 cents B) 63 cents C) 65 cents D) 68 cents
• Hint: 1 quarter + 2 dimes + 4 pennies = 25 + 20 + 4 = 49 cents.
• Steps:
  • 2 quarters = 25 + 25 = 50 cents. 1 dime = 10 cents. 3 pennies = 3 cents.
  • 50 + 10 + 3 = 63 cents.
• Answer: 63 cents

[Easy] Multiplication by 2

• EN: There are 6 pairs of skates at the hockey rink. How many individual skates are there in all?
• FR: Il y a 6 paires de patins à l'aréna. Combien y a-t-il de patins au total?
• Choices: A) 10 skates B) 12 skates C) 14 skates D) 16 skates
• Hint: 5 pairs = 5 × 2 = 10 skates.
• Steps:
  • Each pair has 2 skates: 6 × 2 = 12.
  • There are 12 skates in all.
• Answer: 12 skates

[Easy] Multiplication by 5

• EN: A Tim Hortons order has 4 boxes of Timbits with 5 in each box. How many Timbits are there altogether?
• FR: Une commande chez Tim Hortons comprend 4 boîtes de Timbits avec 5 dans chaque boîte. Combien y a-t-il de Timbits en tout?
• Choices: A) 15 Timbits B) 18 Timbits C) 20 Timbits D) 25 Timbits
• Hint: 3 boxes × 5 = 15 Timbits.
• Steps:
  • 4 groups of 5: 4 × 5 = 20.
  • There are 20 Timbits altogether.
• Answer: 20 Timbits

[Easy] Basic Fractions

• EN: A pizza is cut into 4 equal slices. Lucas eats 1 slice. What fraction of the pizza did Lucas eat?
• FR: Une pizza est coupée en 4 parts égales. Lucas mange 1 part. Quelle fraction de la pizza Lucas a-t-il mangée?
• Choices: A) 1/2 B) 1/3 C) 1/4 D) 2/4
• Hint: If a pie is cut into 3 equal pieces and you eat 1, you ate 1/3 of the pie.
• Steps:
  • The pizza has 4 equal slices (denominator = 4).
  • Lucas ate 1 slice, so he ate 1/4 of the pizza.
• Answer: 1/4

[Easy] Reading a Simple Graph

• EN: A bar graph shows: Monday = 8 books returned, Tuesday = 5 books returned. How many more books were returned on Monday than Tuesday?
• FR: Un diagramme à barres montre : lundi = 8 livres retournés, mardi = 5 livres retournés. Combien de livres de plus ont été retournés lundi que mardi?
• Choices: A) 2 books B) 3 books C) 4 books D) 5 books
• Hint: To compare 10 and 7 on a bar graph, subtract: 10 – 7 = 3 more.
• Steps:
  • Subtract Tuesday from Monday: 8 – 5 = 3.
  • Three more books were returned on Monday.
• Answer: 3 books

[Medium] Multiplication by 3

• EN: A class planted 7 rows of seeds with 3 seeds in each row. How many seeds were planted in all?
• FR: Une classe a planté 7 rangées de graines avec 3 graines dans chaque rangée. Combien de graines ont été plantées en tout?
• Choices: A) 18 seeds B) 19 seeds C) 21 seeds D) 24 seeds
• Hint: 6 rows × 3 = 18 seeds.
• Steps:
  • 7 groups of 3: 7 × 3 = 21.
  • There are 21 seeds planted in all.
• Answer: 21 seeds

[Medium] Basic Division

• EN: There are 24 stickers to share equally among 4 friends. How many stickers does each friend get?
• FR: Il y a 24 autocollants à partager également entre 4 amis. Combien d'autocollants chaque ami reçoit-il?
• Choices: A) 4 stickers B) 5 stickers C) 6 stickers D) 8 stickers
• Hint: To find 18 ÷ 3, ask "3 × ? = 18" — the answer is 6.
• Steps:
  • Ask: 4 × ? = 24. We know 4 × 6 = 24.
  • Each friend gets 6 stickers.
• Answer: 6 stickers

[Medium] Perimeter of a Rectangle

• EN: A rectangular garden is 5 m long and 3 m wide. What is the perimeter of the garden?
• FR: Un jardin rectangulaire mesure 5 m de long et 3 m de large. Quel est le périmètre du jardin?
• Choices: A) 14 m B) 15 m C) 16 m D) 18 m
• Hint: Perimeter of a rectangle with length 4 and width 2: (4 + 2) × 2 = 12.
• Steps:
  • Add length and width: 5 + 3 = 8.
  • Multiply by 2 (two of each side): 8 × 2 = 16 m.
• Answer: 16 m

[Medium] Multiplication by 10

• EN: There are 9 bags with 10 apples each. How many apples are there in all?
• FR: Il y a 9 sacs avec 10 pommes chacun. Combien y a-t-il de pommes en tout?
• Choices: A) 80 apples B) 85 apples C) 90 apples D) 100 apples
• Hint: 6 × 10 = 60 — just put a zero after the single-digit number.
• Steps:
  • 9 × 10 = 90.
  • There are 90 apples in all.
• Answer: 90 apples

[Hard] Multiplication and Fractions Combined

• EN: A rectangle has 4 rows of tiles with 8 tiles in each row. Then half of the tiles are removed. How many tiles remain?
• FR: Un rectangle a 4 rangées de tuiles avec 8 tuiles dans chaque rangée. Ensuite, la moitié des tuiles sont enlevées. Combien de tuiles reste-t-il?
• Choices: A) 14 tiles B) 15 tiles C) 16 tiles D) 18 tiles
• Hint: Find 3 × 6 = 18 total tiles, then half of 18 = 9 tiles remain.
• Steps:
  • Total tiles: 4 × 8 = 32. Half of 32 = 32 ÷ 2 = 16.
  • There are 16 tiles remaining.
• Answer: 16 tiles

[Hard] Multi-Step Word Problem

• EN: A store has 45 books. It sells 9 books each day for 3 days. How many books does the store have left?
• FR: Un magasin a 45 livres. Il vend 9 livres par jour pendant 3 jours. Combien de livres reste-t-il au magasin?
• Choices: A) 16 books B) 17 books C) 18 books D) 27 books
• Hint: If a store sells 5 books per day for 4 days, that is 20 books sold.
• Steps:
  • Books sold in 3 days: 9 × 3 = 27.
  • Books left: 45 – 27 = 18 books.
• Answer: 18 books

[Easy] Multiplication Tables to 9×9

• EN: What is 7 × 8?
• FR: Combien fait 7 × 8?
• Choices: A) 48 B) 54 C) 56 D) 63
• Hint: 6 × 8 = 48, then add one more group of 8: 48 + 8 = 56.
• Steps:
  • Think of 7 × 8 as 7 groups of 8.
  • 7 × 8 = 56.
• Answer: 56

[Easy] Decimal Place Value

• EN: In the number 3.47, what digit is in the tenths place?
• FR: Dans le nombre 3,47, quel chiffre est à la position des dixièmes?
• Choices: A) 3 B) 4 C) 7 D) 47
• Hint: In 5.62, the tenths digit is 6 (first digit after the decimal point).
• Steps:
  • The tenths place is the first digit after the decimal point.
  • In 3.47, that digit is 4.
• Answer: 4

[Easy] Area of a Rectangle

• EN: A rectangular rug is 6 m long and 4 m wide. What is the area of the rug?
• FR: Un tapis rectangulaire a 6 m de long et 4 m de large. Quelle est l'aire du tapis?
• Choices: A) 20 m² B) 22 m² C) 24 m² D) 28 m²
• Hint: For a rectangle 5 m long and 3 m wide, area = 5 × 3 = 15 m².
• Steps:
  • Area = length × width = 6 × 4 = 24.
  • The area of the rug is 24 m².
• Answer: 24 m²

[Easy] Comparing Fractions

• EN: Which fraction is greater: 3/4 or 2/4?
• FR: Quelle fraction est la plus grande : 3/4 ou 2/4?
• Choices: A) 2/4 B) 3/4 C) 1/4 D) 4/4
• Hint: When the denominators are the same, the fraction with the larger numerator is greater — so 5/8 > 3/8.
• Steps:
  • Both fractions have the same denominator (4).
  • Compare numerators: 3 > 2, so 3/4 is greater.
• Answer: 3/4

[Medium] Long Division with Remainders

• EN: A baker packs 53 muffins into boxes of 6. How many full boxes can be filled, and how many muffins are left over?
• FR: Un boulanger emballe 53 muffins dans des boîtes de 6. Combien de boîtes complètes peut-il remplir, et combien de muffins reste-t-il?
• Choices: A) 8 boxes, remainder 4 B) 8 boxes, remainder 5 C) 9 boxes, remainder 2 D) 9 boxes, remainder 3
• Hint: For 29 ÷ 4, think 4 × 7 = 28, so the quotient is 7 and the remainder is 1.
• Steps:
  • 6 × 8 = 48, and 6 × 9 = 54 (too big). So 8 full boxes.
  • 53 – 48 = 5 muffins left over.
• Answer: 8 boxes, remainder 5

[Medium] Elapsed Time

• EN: A hockey game starts at 1:15 and ends at 3:45. How long did the game last?
• FR: Un match de hockey commence à 13 h 15 et se termine à 15 h 45. Combien de temps le match a-t-il duré?
• Choices: A) 2 hours 15 minutes B) 2 hours 30 minutes C) 2 hours 45 minutes D) 3 hours 15 minutes
• Hint: From 10:20 to 12:50 — count 2 hours to 12:20, then 30 minutes to 12:50, giving 2 hours 30 minutes.
• Steps:
  • From 1:15 to 3:15 is exactly 2 hours.
  • From 3:15 to 3:45 is 30 more minutes. Total: 2 hours 30 minutes.
• Answer: 2 hours 30 minutes

[Medium] Decimal Operations

• EN: A water bottle holds 1.75 L and a juice box holds 0.50 L. How much liquid is there in total?
• FR: Une bouteille d'eau contient 1,75 L et une boîte de jus contient 0,50 L. Quelle est la quantité totale de liquide?
• Choices: A) 2.15 L B) 2.20 L C) 2.25 L D) 2.30 L
• Hint: To add 1.30 + 0.40, line up decimal points: 1.30 + 0.40 = 1.70.
• Steps:
  • Line up the decimal points: 1.75 + 0.50.
  • 1.75 + 0.50 = 2.25 L.
• Answer: 2.25 L

[Medium] Multiplication (Two Digits × One Digit)

• EN: A farmer plants 36 seeds in each of 4 rows. How many seeds are planted in all?
• FR: Un fermier plante 36 graines dans chacune de 4 rangées. Combien de graines sont plantées en tout?
• Choices: A) 124 seeds B) 140 seeds C) 144 seeds D) 148 seeds
• Hint: 23 × 3: 20 × 3 = 60 and 3 × 3 = 9, so 60 + 9 = 69.
• Steps:
  • 36 × 4: 30 × 4 = 120 and 6 × 4 = 24.
  • 120 + 24 = 144 seeds.
• Answer: 144 seeds

[Hard] Multi-Step Problem with Decimals

• EN: Mia buys 3 notebooks for $2.49 each and pays with a $10 bill. How much change does she receive?
• FR: Mia achète 3 cahiers à 2,49 $ chacun et paye avec un billet de 10 $. Combien de monnaie reçoit-elle?
• Choices: A) $2.43 B) $2.53 C) $3.03 D) $7.51
• Hint: For 2 items at $3.25 each: 2 × $3.25 = $6.50, then $10.00 – $6.50 = $3.50 change.
• Steps:
  • Total cost: 3 × $2.49 = $7.47.
  • Change: $10.00 – $7.47 = $2.53.
• Answer: $2.53

[Hard] Long Division and Fractions

• EN: A ribbon 84 cm long is cut into pieces of equal length. If each piece is 7 cm, how many pieces are there? Then, what fraction of the ribbon is one piece?
• FR: Un ruban de 84 cm de long est coupé en morceaux de longueur égale. Si chaque morceau mesure 7 cm, combien y a-t-il de morceaux? Ensuite, quelle fraction du ruban représente un morceau?
• Choices: A) 11 pieces, 1/11 B) 12 pieces, 1/12 C) 13 pieces, 1/13 D) 14 pieces, 1/14
• Hint: If 60 cm is cut into 5 cm pieces, 60 ÷ 5 = 12 pieces, and each piece is 1/12 of the ribbon.
• Steps:
  • Number of pieces: 84 ÷ 7 = 12 pieces.
  • Each piece is 1 out of 12 equal parts, so each piece is 1/12 of the ribbon.
• Answer: 12 pieces, 1/12

[Easy] Multi-Digit Multiplication

• EN: A school orders 24 boxes of pencils with 12 pencils in each box. How many pencils are ordered in all?
• FR: Une école commande 24 boîtes de crayons avec 12 crayons dans chaque boîte. Combien de crayons sont commandés en tout?
• Choices: A) 268 pencils B) 278 pencils C) 288 pencils D) 298 pencils
• Hint: 23 × 11 = 23 × 10 + 23 × 1 = 230 + 23 = 253.
• Steps:
  • 24 × 12 = 24 × 10 + 24 × 2 = 240 + 48 = 288.
  • There are 288 pencils ordered in all.
• Answer: 288 pencils

[Easy] Adding Fractions with Like Denominators

• EN: A recipe uses 2/5 of a cup of sugar and another 1/5 of a cup of sugar. How much sugar is used in all?
• FR: Une recette utilise 2/5 de tasse de sucre et encore 1/5 de tasse de sucre. Quelle quantité de sucre est utilisée en tout?
• Choices: A) 2/10 B) 3/5 C) 3/10 D) 4/5
• Hint: 1/7 + 3/7 = (1 + 3)/7 = 4/7 — add the numerators, keep the denominator.
• Steps:
  • Add the numerators: 2 + 1 = 3. Keep the denominator: 5.
  • The total is 3/5 of a cup.
• Answer: 3/5

[Easy] Percentage Introduction — 50%

• EN: A hockey team won 50% of its 20 games. How many games did the team win?
• FR: Une équipe de hockey a gagné 50 % de ses 20 matchs. Combien de matchs a-t-elle gagnés?
• Choices: A) 5 games B) 8 games C) 10 games D) 15 games
• Hint: 50% of 14 = half of 14 = 7.
• Steps:
  • 50% means half.
  • Half of 20 = 10 games won.
• Answer: 10 games

[Easy] Decimal Operations — Addition

• EN: A student runs 2.35 km on Monday and 1.60 km on Tuesday. How far does the student run in total?
• FR: Un élève court 2,35 km le lundi et 1,60 km le mardi. Quelle distance l'élève a-t-il parcouru en tout?
• Choices: A) 3.85 km B) 3.90 km C) 3.95 km D) 4.00 km
• Hint: 3.14 + 2.21 = 5.35 — line up the decimal points and add each column.
• Steps:
  • Add: 2.35 + 1.60. Hundredths: 5 + 0 = 5. Tenths: 3 + 6 = 9. Ones: 2 + 1 = 3.
  • The total is 3.95 km.
• Answer: 3.95 km

[Medium] Multi-Digit Division

• EN: A total of 756 books are arranged equally on 9 shelves. How many books are on each shelf?
• FR: Un total de 756 livres sont rangés de façon égale sur 9 étagères. Combien de livres y a-t-il sur chaque étagère?
• Choices: A) 82 books B) 83 books C) 84 books D) 86 books
• Hint: For 630 ÷ 9, think 9 × 70 = 630, so the answer is 70.
• Steps:
  • 9 × 84 = 9 × 80 + 9 × 4 = 720 + 36 = 756. ✓
  • There are 84 books on each shelf.
• Answer: 84 books

[Medium] Subtracting Fractions with Like Denominators

• EN: A container holds 7/8 of a litre of juice. After pouring out 3/8 of a litre, how much juice is left?
• FR: Un récipient contient 7/8 de litre de jus. Après en avoir versé 3/8 de litre, combien de jus reste-t-il?
• Choices: A) 3/8 B) 4/8 C) 5/8 D) 10/8
• Hint: 5/6 – 2/6 = (5 – 2)/6 = 3/6 — subtract the numerators, keep the denominator.
• Steps:
  • Subtract the numerators: 7 – 3 = 4. Keep the denominator: 8.
  • There is 4/8 of a litre of juice left.
• Answer: 4/8

[Medium] Percentage — 25% and 10%

• EN: A winter jacket originally costs $80. The store is offering a 25% discount. How much is the discount?
• FR: Un manteau d'hiver coûte à l'origine 80 $. Le magasin offre un rabais de 25 %. Quel est le montant du rabais?
• Choices: A) $16 B) $18 C) $20 D) $25
• Hint: 25% of $60 = half of half of $60 = half of $30 = $15.
• Steps:
  • 25% = one quarter. Find one quarter of $80.
  • $80 ÷ 4 = $20 discount.
• Answer: $20

[Medium] Volume of a Rectangular Prism

• EN: A storage box is 5 cm long, 4 cm wide, and 3 cm tall. What is the volume of the box?
• FR: Une boîte de rangement a 5 cm de long, 4 cm de large et 3 cm de hauteur. Quel est le volume de la boîte?
• Choices: A) 48 cm³ B) 56 cm³ C) 60 cm³ D) 64 cm³
• Hint: Volume = length × width × height. For 4 × 3 × 2 = 24 cm³.
• Steps:
  • Volume = 5 × 4 × 3.
  • 5 × 4 = 20, then 20 × 3 = 60 cm³.
• Answer: 60 cm³

[Hard] Multi-Step Decimal and Percentage Problem

• EN: A store sells 3 pairs of hockey gloves for $24.50 each. A customer uses a 10% discount. What is the total price paid?
• FR: Un magasin vend 3 paires de gants de hockey à 24,50 $ chacune. Un client utilise un rabais de 10 %. Quel est le prix total payé?
• Choices: A) $63.25 B) $66.15 C) $68.25 D) $73.50
• Hint: For 2 items at $30 each with 10% off: total = $60, discount = $6, final = $54.
• Steps:
  • Original total: 3 × $24.50 = $73.50.
  • 10% of $73.50 = $7.35. Final price: $73.50 – $7.35 = $66.15.
• Answer: $66.15

[Hard] Multi-Step Fractions and Volume

• EN: A fish tank is 8 cm long, 5 cm wide, and 6 cm tall. It is currently 1/2 full of water. How many cubic centimetres of water are in the tank?
• FR: Un aquarium a 8 cm de long, 5 cm de large et 6 cm de hauteur. Il est actuellement rempli à moitié d'eau. Combien de centimètres cubes d'eau y a-t-il dans l'aquarium?
• Choices: A) 100 cm³ B) 110 cm³ C) 120 cm³ D) 130 cm³
• Hint: A box 6 × 4 × 5 = 120 cm³. If it is 1/2 full, there are 60 cm³ of water.
• Steps:
  • Total volume: 8 × 5 × 6 = 240 cm³.
  • Half full: 240 ÷ 2 = 120 cm³ of water.
• Answer: 120 cm³

[Easy] Percent of a Number

• EN: What is 30% of 90?
• FR: Combien font 30 % de 90?
• Choices: A) 21 B) 24 C) 27 D) 30
• Hint: 30% of 60 = 10% of 60 × 3 = 6 × 3 = 18.
• Steps:
  • 10% of 90 = 9. Multiply by 3 for 30%.
  • 9 × 3 = 27.
• Answer: 27

[Easy] Order of Operations (BEDMAS)

• EN: Evaluate: 4 + 3 × 2.
• FR: Évalue : 4 + 3 × 2.
• Choices: A) 10 B) 12 C) 14 D) 16
• Hint: In 5 + 2 × 3, multiply first: 5 + 6 = 11 (not 7 × 3 = 21).
• Steps:
  • Multiplication first: 3 × 2 = 6.
  • Then addition: 4 + 6 = 10.
• Answer: 10

[Easy] Integers Introduction

• EN: The temperature on a winter morning in Winnipeg was –8°C. By noon it rose 5 degrees. What was the temperature at noon?
• FR: La température un matin d'hiver à Winnipeg était de –8 °C. À midi, elle a augmenté de 5 degrés. Quelle était la température à midi?
• Choices: A) –4°C B) –3°C C) –2°C D) –1°C
• Hint: –10 + 4 = –6 (start at –10, move 4 steps right on the number line).
• Steps:
  • Start at –8 and add 5: –8 + 5 = –3.
  • The temperature at noon was –3°C.
• Answer: –3°C

[Easy] Ratios and Rates

• EN: A recipe uses 2 cups of flour for every 3 cups of milk. If you use 6 cups of flour, how many cups of milk do you need?
• FR: Une recette utilise 2 tasses de farine pour 3 tasses de lait. Si tu utilises 6 tasses de farine, combien de tasses de lait faut-il?
• Choices: A) 7 cups B) 8 cups C) 9 cups D) 12 cups
• Hint: If the ratio is 1:4 and you use 3 of the first ingredient, you need 3 × 4 = 12 of the second.
• Steps:
  • The ratio of flour to milk is 2:3. Flour increased by a factor of 6 ÷ 2 = 3.
  • Milk needed: 3 × 3 = 9 cups.
• Answer: 9 cups

[Medium] Fraction Multiplication

• EN: A garden is 3/4 of a hectare. A fence covers 2/3 of the garden. What fraction of a hectare does the fence cover?
• FR: Un jardin a une superficie de 3/4 d'hectare. Une clôture couvre 2/3 du jardin. Quelle fraction d'un hectare la clôture couvre-t-elle?
• Choices: A) 5/12 B) 6/12 C) 1/2 D) 5/7
• Hint: 1/2 × 3/5 = (1 × 3)/(2 × 5) = 3/10.
• Steps:
  • Multiply numerators: 3 × 2 = 6. Multiply denominators: 4 × 3 = 12.
  • 6/12 = 1/2. The fence covers 1/2 of a hectare.
• Answer: 1/2

[Medium] Fraction Division

• EN: How many 1/4-cup servings are in 3 cups of trail mix?
• FR: Combien de portions de 1/4 de tasse y a-t-il dans 3 tasses de mélange montagnard?
• Choices: A) 9 servings B) 10 servings C) 11 servings D) 12 servings
• Hint: 2 ÷ (1/3) = 2 × 3 = 6 servings — "keep, change, flip."
• Steps:
  • 3 ÷ (1/4) = 3 × 4 = 12.
  • There are 12 servings.
• Answer: 12 servings

[Medium] Simple Algebraic Expressions

• EN: If n = 6, what is the value of 4n – 5?
• FR: Si n = 6, quelle est la valeur de 4n – 5?
• Choices: A) 18 B) 19 C) 20 D) 21
• Hint: If x = 3, then 2x + 4 = 2(3) + 4 = 6 + 4 = 10.
• Steps:
  • Substitute n = 6: 4(6) – 5 = 24 – 5 = 19.
  • The value is 19.
• Answer: 19

[Medium] Order of Operations with Brackets

• EN: Evaluate: (8 + 2) × 3 – 4.
• FR: Évalue : (8 + 2) × 3 – 4.
• Choices: A) 24 B) 26 C) 28 D) 30
• Hint: For (5 + 1) × 4 – 2, first brackets: 6 × 4 – 2 = 24 – 2 = 22.
• Steps:
  • Brackets first: 8 + 2 = 10.
  • Then: 10 × 3 = 30. Then: 30 – 4 = 26.
• Answer: 26

[Hard] Percent, Ratio, and Multi-Step

• EN: A lacrosse team won 18 of its 30 games. What percentage of games did the team win? Then, what is the ratio of wins to losses in simplest form?
• FR: Une équipe de crosse a gagné 18 de ses 30 matchs. Quel pourcentage de matchs l'équipe a-t-elle gagnés? Puis, quel est le rapport victoires-défaites sous la forme la plus simple?
• Choices: A) 60%, 2:3 B) 60%, 3:2 C) 65%, 3:2 D) 70%, 3:1
• Hint: For 12 wins out of 20 games, win % = (12/20) × 100 = 60%, and wins to losses = 12:8 = 3:2.
• Steps:
  • Win %: (18/30) × 100 = 60%.
  • Losses: 30 – 18 = 12. Ratio wins:losses = 18:12 = 3:2.
• Answer: 60%, 3:2

[Hard] Integers and Order of Operations

• EN: Evaluate: –3 × (4 + 2) + 8 ÷ (–2).
• FR: Évalue : –3 × (4 + 2) + 8 ÷ (–2).
• Choices: A) –24 B) –22 C) –20 D) –18
• Hint: For –2 × (3 + 1) + 6 ÷ (–3): brackets first → –2 × 4 + 6 ÷ (–3) = –8 + (–2) = –10.
• Steps:
  • Brackets: 4 + 2 = 6. So: –3 × 6 + 8 ÷ (–2).
  • Multiply and divide: –18 + (–4) = –22.
• Answer: –22

[Easy] Integer Addition

• EN: In Manitoba, the temperature was –12°C in the morning and rose by 7°C by the afternoon. What was the afternoon temperature?
• FR: Au Manitoba, la température était de –12 °C le matin et a augmenté de 7 °C l'après-midi. Quelle était la température l'après-midi?
• Choices: A) –6°C B) –5°C C) –4°C D) –3°C
• Hint: –9 + 4 = –5 (move 4 steps right from –9 on a number line).
• Steps:
  • –12 + 7: start at –12, add 7.
  • –12 + 7 = –5°C.
• Answer: –5°C

[Easy] Percentage — Discount

• EN: A pair of hockey skates costs $120. The store offers a 15% discount. How much is the discount?
• FR: Une paire de patins de hockey coûte 120 $. Le magasin offre un rabais de 15 %. Quel est le montant du rabais?
• Choices: A) $14 B) $16 C) $18 D) $20
• Hint: 15% of $80 = 10% of $80 + 5% of $80 = $8 + $4 = $12.
• Steps:
  • 10% of $120 = $12. 5% of $120 = $6.
  • 15% = $12 + $6 = $18 discount.
• Answer: $18

[Easy] Integer Subtraction

• EN: What is –4 – 9?
• FR: Combien font –4 – 9?
• Choices: A) –15 B) –13 C) –12 D) –5
• Hint: –3 – 5 = –3 + (–5) = –8 — subtracting a positive is the same as adding a negative.
• Steps:
  • –4 – 9 = –4 + (–9) = –13.
  • The answer is –13.
• Answer: –13

[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: In n + 5 = 11, subtract 5 from both sides: n = 6.
• Steps:
  • Subtract 9 from both sides: x = 17 – 9.
  • x = 8.
• Answer: x = 8

[Medium] Integer Multiplication

• EN: A golfer scored –3 on each of 4 holes. What was the golfer's total score?
• FR: Un golfeur a marqué –3 sur chacun des 4 trous. Quel était le score total du golfeur?
• Choices: A) –16 B) –14 C) –12 D) –10
• Hint: –5 × 3 = –15 (a negative times a positive gives a negative result).
• Steps:
  • –3 × 4 = –12.
  • The golfer's total score was –12.
• Answer: –12

[Medium] Percentage — Tax

• EN: A book costs $25 and the tax rate in Ontario is 13% (HST). What is the total price including tax?
• FR: Un livre coûte 25 $ et le taux de taxe en Ontario est de 13 % (TVH). Quel est le prix total avec la taxe?
• Choices: A) $28.00 B) $28.25 C) $28.75 D) $29.00
• Hint: For a $40 item with 10% tax: tax = $4, total = $44.
• Steps:
  • Tax: 13% of $25 = 0.13 × 25 = $3.25.
  • Total: $25.00 + $3.25 = $28.25.
• Answer: $28.25

[Medium] Surface Area of a Rectangular Prism

• EN: A gift box is 8 cm long, 5 cm wide, and 3 cm tall. What is the surface area of the box?
• FR: Une boîte cadeau a 8 cm de long, 5 cm de large et 3 cm de hauteur. Quelle est l'aire totale de la boîte?
• Choices: A) 148 cm² B) 158 cm² C) 168 cm² D) 178 cm²
• Hint: SA = 2(lw + lh + wh). For l=4, w=3, h=2: 2(12 + 8 + 6) = 2 × 26 = 52 cm².
• Steps:
  • SA = 2(lw + lh + wh) = 2(8×5 + 8×3 + 5×3).
  • = 2(40 + 24 + 15) = 2(79) = 158 cm².
• Answer: 158 cm²

[Medium] Data and Probability

• EN: A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. What is the probability of picking a blue marble at random?
• FR: Un sac contient 4 billes rouges, 3 billes bleues et 5 billes vertes. Quelle est la probabilité de piger une bille bleue au hasard?
• Choices: A) 1/4 B) 3/12 C) 5/12 D) 1/3
• Hint: Probability = (number of favourable outcomes) ÷ (total outcomes). If 2 red out of 10 total, P(red) = 2/10 = 1/5.
• Steps:
  • Total marbles: 4 + 3 + 5 = 12.
  • P(blue) = 3/12 = 1/4.
• Answer: 1/4

[Hard] Multi-Step Integer and Percent Problem

• EN: A store had 200 winter toques in stock. On Monday, 35% were sold. On Tuesday, 20 more were sold. How many toques are left?
• FR: Un magasin avait 200 tuques d'hiver en stock. Lundi, 35 % ont été vendues. Mardi, 20 autres ont été vendues. Combien de tuques reste-t-il?
• Choices: A) 100 toques B) 105 toques C) 110 toques D) 115 toques
• Hint: For 300 items with 40% sold: 0.40 × 300 = 120 sold, 300 – 120 = 180 remain.
• Steps:
  • Monday sales: 35% of 200 = 70 toques. Remaining: 200 – 70 = 130.
  • Tuesday: 130 – 20 = 110 toques left.
• Answer: 110 toques

[Hard] One-Step Equation with Integers

• EN: Solve for y: –5y = 35.
• FR: Résous pour y : –5y = 35.
• Choices: A) y = –8 B) y = –7 C) y = 7 D) y = 8
• Hint: For –4x = 20, divide both sides by –4: x = –5. Dividing by a negative flips the sign.
• Steps:
  • Divide both sides by –5: y = 35 ÷ (–5).
  • y = –7.
• Answer: y = –7

[Easy] Perfect Squares and Square Roots

• EN: What is √144?
• FR: Combien vaut √144?
• Choices: A) 11 B) 12 C) 13 D) 14
• Hint: 11² = 121 and 12² = 144, so √144 = 12.
• Steps:
  • Think: which number multiplied by itself gives 144?
  • 12 × 12 = 144, so √144 = 12.
• Answer: 12

[Easy] Mean of a Data Set

• EN: Five students scored 70, 80, 90, 85, and 75 on a test. What is the mean score?
• FR: Cinq élèves ont obtenu 70, 80, 90, 85 et 75 à un test. Quel est le score moyen?
• Choices: A) 78 B) 80 C) 82 D) 85
• Hint: Mean of 10, 20, 30 = (10 + 20 + 30) ÷ 3 = 60 ÷ 3 = 20.
• Steps:
  • Sum: 70 + 80 + 90 + 85 + 75 = 400.
  • Mean: 400 ÷ 5 = 80.
• Answer: 80

[Easy] Percent Increase

• EN: A student's test score went from 60 to 75. What is the percent increase?
• FR: La note d'un élève est passée de 60 à 75. Quel est le pourcentage d'augmentation?
• Choices: A) 20% B) 25% C) 30% D) 35%
• Hint: Percent increase = (increase ÷ original) × 100. From 40 to 50: increase = 10, so (10/40) × 100 = 25%.
• Steps:
  • Increase: 75 – 60 = 15.
  • Percent increase: (15/60) × 100 = 25%.
• Answer: 25%

[Easy] Two-Step Linear Equation

• EN: Solve for x: 2x + 5 = 13.
• FR: Résous pour x : 2x + 5 = 13.
• Choices: A) x = 3 B) x = 4 C) x = 5 D) x = 6
• Hint: For 3x + 2 = 11: subtract 2 first to get 3x = 9, then divide by 3 to get x = 3.
• Steps:
  • Subtract 5 from both sides: 2x = 8.
  • Divide by 2: x = 4.
• Answer: x = 4

[Medium] Pythagorean Theorem

• EN: A right triangle has legs of length 6 cm and 8 cm. What is the length of the hypotenuse?
• FR: Un triangle rectangle a des cathètes de 6 cm et 8 cm. Quelle est la longueur de l'hypoténuse?
• Choices: A) 9 cm B) 10 cm C) 11 cm D) 14 cm
• Hint: For legs of 3 and 4: 3² + 4² = 9 + 16 = 25, and √25 = 5, so the hypotenuse is 5.
• Steps:
  • c² = 6² + 8² = 36 + 64 = 100.
  • c = √100 = 10 cm.
• Answer: 10 cm

[Medium] Two-Step Linear Equation (Harder)

• 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 = 8
• Hint: For 4x – 3 = 13: add 3 to get 4x = 16, then divide by 4 to get x = 4.
• Steps:
  • Add 7 to both sides: 3x = 21.
  • Divide by 3: x = 7.
• Answer: x = 7

[Medium] Slope Introduction

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

[Medium] Median and Mode

• EN: The snowfall amounts (in cm) for seven days were: 3, 7, 2, 9, 7, 5, 4. What is the median amount of snowfall?
• FR: Les quantités de neige (en cm) sur sept jours étaient : 3, 7, 2, 9, 7, 5, 4. Quelle est la médiane?
• Choices: A) 4 cm B) 5 cm C) 7 cm D) 9 cm
• Hint: For 1, 3, 5, 7, 9 (already sorted), the median (middle value) is 5.
• Steps:
  • Sort the values: 2, 3, 4, 5, 7, 7, 9.
  • The middle (4th) value is 5 cm.
• Answer: 5 cm

[Hard] Pythagorean Theorem — Real Context

• EN: A ladder is leaning against a wall. The bottom of the ladder is 5 m from the wall, and the wall is 12 m tall where the ladder reaches it. How long is the ladder?
• FR: Une échelle est appuyée contre un mur. Le bas de l'échelle est à 5 m du mur, et le mur mesure 12 m là où l'échelle le touche. Quelle est la longueur de l'échelle?
• Choices: A) 11 m B) 12 m C) 13 m D) 14 m
• Hint: For legs 8 and 15: 8² + 15² = 64 + 225 = 289, √289 = 17.
• Steps:
  • c² = 5² + 12² = 25 + 144 = 169.
  • c = √169 = 13 m.
• Answer: 13 m

[Hard] Multi-Step Equations and Percent Decrease

• EN: A store originally sold a snowboard for $350. The price was decreased by 20%. Then the remaining price was decreased by a further 10%. What is the final price?
• FR: Un magasin vendait à l'origine une planche à neige 350 $. Le prix a été réduit de 20 %. Puis le prix restant a été réduit de 10 % supplémentaires. Quel est le prix final?
• Choices: A) $238.00 B) $245.00 C) $252.00 D) $262.50
• Hint: For a $200 item with 20% off and then 10% off: $200 × 0.80 = $160, then $160 × 0.90 = $144.
• Steps:
  • After 20% off: $350 × 0.80 = $280.
  • After 10% off: $280 × 0.90 = $252.00.
• Answer: $252.00

[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: For 4x – 1 = 11: add 1 to get 4x = 12, divide by 4 to get x = 3.
• Steps:
  • Add 3 to both sides: 5x = 25.
  • Divide by 5: x = 5.
• Answer: x = 5

[Easy] Adding Polynomials

• EN: Add the polynomials: (3x + 4) + (2x – 1).
• FR: Additionne les polynômes : (3x + 4) + (2x – 1).
• Choices: A) 4x + 3 B) 5x + 3 C) 5x + 5 D) 6x + 3
• Hint: (2x + 7) + (x – 3) = (2x + x) + (7 – 3) = 3x + 4.
• Steps:
  • Combine like terms: (3x + 2x) + (4 – 1).
  • = 5x + 3.
• Answer: 5x + 3

[Easy] Graphing Lines — Slope-Intercept

• EN: A line has equation y = 2x + 3. What is the y-intercept of this line?
• FR: Une droite a pour équation y = 2x + 3. Quelle est l'ordonnée à l'origine de cette droite?
• Choices: A) 1 B) 2 C) 3 D) 5
• Hint: In y = mx + b, the y-intercept is b. For y = 4x + 7, the y-intercept is 7.
• Steps:
  • The equation is in slope-intercept form y = mx + b.
  • Here b = 3, so the y-intercept is 3.
• Answer: 3

[Easy] Trigonometry — Identifying Sides

• EN: In a right triangle with respect to a given angle θ, the side opposite to θ is 5 cm and the hypotenuse is 13 cm. Which ratio represents sin θ?
• FR: Dans un triangle rectangle par rapport à un angle θ donné, le côté opposé à θ mesure 5 cm et l'hypoténuse mesure 13 cm. Quel rapport représente sin θ?
• Choices: A) 5/13 B) 12/13 C) 5/12 D) 13/5
• Hint: SOH — Sin = Opposite ÷ Hypotenuse. For opposite = 3 and hypotenuse = 5, sin θ = 3/5.
• Steps:
  • SOH: sin θ = opposite ÷ hypotenuse.
  • sin θ = 5/13.
• Answer: 5/13

[Medium] Linear Inequality

• EN: Solve the inequality: 3x + 4 > 13. Which of the following is the solution?
• FR: Résous l'inégalité : 3x + 4 > 13. Quelle est la solution?
• Choices: A) x > 2 B) x > 3 C) x > 4 D) x > 5
• Hint: For 2x + 1 > 7, subtract 1: 2x > 6, then divide by 2: x > 3.
• Steps:
  • Subtract 4 from both sides: 3x > 9.
  • Divide by 3: x > 3.
• Answer: x > 3

[Medium] Multiplying Polynomials

• EN: Expand: (x + 3)(x + 5).
• FR: Développe : (x + 3)(x + 5).
• Choices: A) x² + 7x + 15 B) x² + 8x + 15 C) x² + 8x + 8 D) x² + 15x + 8
• Hint: (x + 2)(x + 4) = x² + 4x + 2x + 8 = x² + 6x + 8.
• Steps:
  • Use FOIL: x·x + x·5 + 3·x + 3·5.
  • = x² + 5x + 3x + 15 = x² + 8x + 15.
• Answer: x² + 8x + 15

[Medium] Similar Triangles

• EN: Two similar triangles have corresponding sides of 4 cm and 12 cm. If a side of the smaller triangle is 6 cm, what is the corresponding side of the larger triangle?
• FR: Deux triangles semblables ont des côtés correspondants de 4 cm et 12 cm. Si un côté du petit triangle mesure 6 cm, quel est le côté correspondant du grand triangle?
• Choices: A) 14 cm B) 16 cm C) 18 cm D) 20 cm
• Hint: The scale factor is 12/4 = 3. Multiply any known side of the small triangle by 3 to find the corresponding side.
• Steps:
  • Scale factor: 12 ÷ 4 = 3.
  • Corresponding side: 6 × 3 = 18 cm.
• Answer: 18 cm

[Medium] Statistics — Interpreting Data

• EN: A class of 30 students took a survey. 12 students prefer hockey, 10 prefer soccer, and 8 prefer basketball. What percentage of students prefer hockey?
• FR: Une classe de 30 élèves a répondu à un sondage. 12 élèves préfèrent le hockey, 10 le soccer et 8 le basketball. Quel pourcentage d'élèves préfèrent le hockey?
• Choices: A) 35% B) 38% C) 40% D) 45%
• Hint: Percentage = (part ÷ total) × 100. For 8 out of 20: (8/20) × 100 = 40%.
• Steps:
  • (12 ÷ 30) × 100 = 0.4 × 100 = 40%.
  • 40% of students prefer hockey.
• Answer: 40%

[Hard] Trigonometry — Finding a Side

• EN: In a right triangle, one angle is 35° and the hypotenuse is 20 cm. What is the length of the side opposite to the 35° angle? (Use sin 35° ≈ 0.574.)
• FR: Dans un triangle rectangle, un angle est de 35° et l'hypoténuse mesure 20 cm. Quelle est la longueur du côté opposé à l'angle de 35°? (Utilise sin 35° ≈ 0,574.)
• Choices: A) 10.48 cm B) 11.48 cm C) 12.48 cm D) 13.48 cm
• Hint: SOH: sin θ = opposite/hypotenuse, so opposite = hypotenuse × sin θ. For sin 40° ≈ 0.643 and hypotenuse 10: opposite ≈ 6.43.
• Steps:
  • opposite = hypotenuse × sin(35°) = 20 × 0.574.
  • opposite = 11.48 cm.
• Answer: 11.48 cm

[Hard] Systems of Linear Equations (Substitution)

• EN: Solve the system: y = 2x + 1 and y = –x + 7. What is the value of x?
• FR: Résous le système : y = 2x + 1 et y = –x + 7. Quelle est la valeur de x?
• Choices: A) x = 1 B) x = 2 C) x = 3 D) x = 4
• Hint: Set equal: 3x + 1 = –x + 9 → 4x = 8 → x = 2 (for equations y = 3x + 1 and y = –x + 9).
• Steps:
  • Set equal: 2x + 1 = –x + 7.
  • 3x = 6, so x = 2.
• Answer: x = 2

[Easy] Factoring a Simple Quadratic

• EN: Factor the expression: x² + 5x + 6.
• FR: Factorise l'expression : x² + 5x + 6.
• Choices: A) (x + 1)(x + 6) B) (x + 2)(x + 3) C) (x + 2)(x + 4) D) (x + 3)(x + 3)
• Hint: For x² + 7x + 12, find two numbers that multiply to 12 and add to 7: that is 3 and 4, giving (x + 3)(x + 4).
• Steps:
  • Find two numbers that multiply to 6 and add to 5: 2 × 3 = 6 and 2 + 3 = 5. ✓
  • x² + 5x + 6 = (x + 2)(x + 3).
• Answer: (x + 2)(x + 3)

[Easy] Trigonometry — Finding an Angle

• EN: In a right triangle, the side opposite an angle is 7 cm and the hypotenuse is 14 cm. What is the size of that angle?
• FR: Dans un triangle rectangle, le côté opposé à un angle mesure 7 cm et l'hypoténuse mesure 14 cm. Quelle est la mesure de cet angle?
• Choices: A) 25° B) 30° C) 45° D) 60°
• Hint: sin θ = opposite/hypotenuse. If sin θ = 1/2, then θ = 30°.
• Steps:
  • sin θ = 7/14 = 0.5.
  • θ = sin⁻¹(0.5) = 30°.
• Answer: 30°

[Easy] Systems of Equations

• EN: Solve the system by substitution: x + y = 10 and x = 4. What is the value of y?
• FR: Résous le système par substitution : x + y = 10 et x = 4. Quelle est la valeur de y?
• Choices: A) y = 4 B) y = 5 C) y = 6 D) y = 7
• Hint: If x = 3 and x + y = 8, substitute: 3 + y = 8, so y = 5.
• Steps:
  • Substitute x = 4 into x + y = 10: 4 + y = 10.
  • y = 6.
• Answer: y = 6

[Easy] Volume of a Cylinder

• EN: A cylindrical can has a radius of 5 cm and a height of 10 cm. What is the volume? (Use π ≈ 3.14.)
• FR: Une boîte de conserve cylindrique a un rayon de 5 cm et une hauteur de 10 cm. Quel est le volume? (Utilise π ≈ 3,14.)
• Choices: A) 628 cm³ B) 678 cm³ C) 753 cm³ D) 785 cm³
• Hint: V = π × r² × h. For r = 3 and h = 4: V = 3.14 × 9 × 4 = 113.04 cm³.
• Steps:
  • V = π × r² × h = 3.14 × 5² × 10 = 3.14 × 25 × 10.
  • = 3.14 × 250 = 785 cm³.
• Answer: 785 cm³

[Medium] Completing the Square

• EN: Rewrite x² + 6x + 2 in the form (x + a)² + b. What is the value of b?
• FR: Réécris x² + 6x + 2 sous la forme (x + a)² + b. Quelle est la valeur de b?
• Choices: A) –8 B) –7 C) –6 D) –5
• Hint: For x² + 4x + 1, complete the square: (x + 2)² – 4 + 1 = (x + 2)² – 3, so b = –3.
• Steps:
  • x² + 6x + 2 = (x + 3)² – 9 + 2.
  • = (x + 3)² – 7, so b = –7.
• Answer: –7

[Medium] Quadratic Equation — Solving by Factoring

• EN: Solve: x² – 7x + 12 = 0. What are the solutions?
• FR: Résous : x² – 7x + 12 = 0. Quelles sont les solutions?
• Choices: A) x = 2 and x = 6 B) x = 3 and x = 4 C) x = 1 and x = 12 D) x = 4 and x = 5
• Hint: For x² – 5x + 6 = 0, factor as (x – 2)(x – 3) = 0, giving x = 2 or x = 3.
• Steps:
  • Factor: (x – 3)(x – 4) = 0.
  • x – 3 = 0 → x = 3; x – 4 = 0 → x = 4.
• Answer: x = 3 and x = 4

[Medium] Circle Geometry

• EN: A circle has a radius of 7 cm. What is the area of the circle? (Use π ≈ 3.14.)
• FR: Un cercle a un rayon de 7 cm. Quelle est l'aire du cercle? (Utilise π ≈ 3,14.)
• Choices: A) 143.74 cm² B) 151.94 cm² C) 153.86 cm² D) 161.54 cm²
• Hint: Area of circle = π × r². For r = 5: Area = 3.14 × 25 = 78.5 cm².
• Steps:
  • Area = π × r² = 3.14 × 7² = 3.14 × 49.
  • = 153.86 cm².
• Answer: 153.86 cm²

[Medium] Surface Area of a Cone

• EN: A cone has a radius of 3 cm and a slant height of 5 cm. What is the total surface area? (Use π ≈ 3.14.)
• FR: Un cône a un rayon de 3 cm et une hauteur oblique de 5 cm. Quelle est l'aire totale? (Utilise π ≈ 3,14.)
• Choices: A) 69.08 cm² B) 72.22 cm² C) 75.36 cm² D) 78.50 cm²
• Hint: SA of cone = π × r × l + π × r². For r = 2 and l = 4: 3.14×2×4 + 3.14×4 = 25.12 + 12.56 = 37.68 cm².
• Steps:
  • SA = πrl + πr² = 3.14 × 3 × 5 + 3.14 × 3².
  • = 47.10 + 28.26 = 75.36 cm².
• Answer: 75.36 cm²

[Hard] Solving a Quadratic Using the Quadratic Formula

• EN: Solve: 2x² – 5x – 3 = 0. Use the quadratic formula. Which of the following are the two solutions?
• FR: Résous : 2x² – 5x – 3 = 0 en utilisant la formule quadratique. Lesquelles des solutions suivantes sont correctes?
• Choices: A) x = 3 and x = –1/2 B) x = –3 and x = 1/2 C) x = 3 and x = 1/2 D) x = –3 and x = –1/2
• Hint: For ax² + bx + c = 0, x = (–b ± √(b² – 4ac)) / (2a). For x² + x – 6 = 0: x = (–1 ± √(1+24))/2 = (–1 ± 5)/2, giving x = 2 or x = –3.
• Steps:
  • a = 2, b = –5, c = –3. Discriminant: (–5)² – 4(2)(–3) = 25 + 24 = 49.
  • x = (5 ± 7)/4. So x = 12/4 = 3 or x = –2/4 = –1/2.
• Answer: x = 3 and x = –1/2

[Hard] Systems of Equations — Non-Linear Context

• EN: Two friends start from the same location. Priya walks at y = 3x + 2 km from the start, and James walks at y = –x + 18 km from the start, where x is the number of hours. After how many hours are they the same distance from the start?
• FR: Deux amis partent du même endroit. Priya marche à y = 3x + 2 km du départ, et James à y = –x + 18 km, où x est le nombre d'heures. Après combien d'heures sont-ils à la même distance?
• Choices: A) 3 hours B) 4 hours C) 5 hours D) 6 hours
• Hint: Set both equations equal: 2x + 1 = –x + 7 → 3x = 6 → x = 2 hours.
• Steps:
  • Set 3x + 2 = –x + 18.
  • 4x = 16, x = 4 hours.
• Answer: 4 hours

[Easy] Evaluating an Exponential Function

• EN: A bacteria culture starts with 100 bacteria and doubles every hour. How many bacteria are there after 3 hours?
• FR: Une culture de bactéries commence avec 100 bactéries et double toutes les heures. Combien y a-t-il de bactéries après 3 heures?
• Choices: A) 600 bacteria B) 700 bacteria C) 800 bacteria D) 900 bacteria
• Hint: If 50 bacteria double for 2 hours: 50 × 2² = 50 × 4 = 200 bacteria.
• Steps:
  • After 3 hours: 100 × 2³ = 100 × 8.
  • = 800 bacteria.
• Answer: 800 bacteria

[Easy] Arithmetic Sequences

• EN: An arithmetic sequence starts at 7 with a common difference of 4. What is the 5th term?
• FR: Une suite arithmétique commence à 7 avec une raison de 4. Quel est le 5e terme?
• Choices: A) 19 B) 21 C) 23 D) 27
• Hint: For a sequence starting at 3 with d = 5, the 4th term is 3 + 3(5) = 18.
• Steps:
  • nth term = a + (n – 1)d = 7 + (5 – 1)(4) = 7 + 16.
  • = 23.
• Answer: 23

[Easy] Compound Interest

• EN: An investment of $1000 earns 5% interest compounded annually. What is the total amount after 2 years?
• FR: Un investissement de 1 000 $ rapporte un intérêt de 5 % composé annuellement. Quel est le montant total après 2 ans?
• Choices: A) $1 100.00 B) $1 102.50 C) $1 105.00 D) $1 110.25
• Hint: For $500 at 10% for 2 years: A = 500 × (1.10)² = 500 × 1.21 = $605.
• Steps:
  • A = P(1 + r)ⁿ = 1000 × (1.05)² = 1000 × 1.1025.
  • = $1102.50.
• Answer: $1 102.50

[Easy] Logarithm Introduction

• EN: Evaluate log₂(16).
• FR: Évalue log₂(16).
• Choices: A) 2 B) 3 C) 4 D) 8
• Hint: log₃(27) = 3 because 3³ = 27. Ask "what power gives the number?"
• Steps:
  • Ask: 2 to what power equals 16? 2⁴ = 16.
  • log₂(16) = 4.
• Answer: 4

[Medium] Geometric Sequences and Series

• EN: A geometric sequence has a first term of 3 and a common ratio of 2. What is the sum of the first 5 terms?
• FR: Une suite géométrique a un premier terme de 3 et une raison de 2. Quelle est la somme des 5 premiers termes?
• Choices: A) 88 B) 90 C) 93 D) 96
• Hint: Sum formula: Sₙ = a(rⁿ – 1)/(r – 1). For a = 2, r = 3, n = 4: S₄ = 2(81 – 1)/2 = 80.
• Steps:
  • S₅ = 3(2⁵ – 1)/(2 – 1) = 3(32 – 1)/1 = 3 × 31.
  • = 93.
• Answer: 93

[Medium] Trigonometric Identity

• EN: Which identity is always true for all values of θ?
• FR: Quelle identité est toujours vraie pour toutes les valeurs de θ?
• Choices: A) sin²θ + cos²θ = 2 B) sin²θ – cos²θ = 1 C) sin²θ + cos²θ = 1 D) sinθ × cosθ = 1
• Hint: The Pythagorean identity uses the unit circle definition of sine and cosine.
• Steps:
  • The fundamental Pythagorean identity states sin²θ + cos²θ = 1.
  • This is true for all values of θ.
• Answer: sin²θ + cos²θ = 1

[Medium] Quadratic Functions — Vertex

• EN: The function f(x) = –2(x – 3)² + 5 is in vertex form. What are the coordinates of the vertex?
• FR: La fonction f(x) = –2(x – 3)² + 5 est sous forme canonique. Quelles sont les coordonnées du sommet?
• Choices: A) (–3, 5) B) (3, –5) C) (3, 5) D) (–3, –5)
• Hint: In f(x) = a(x – h)² + k, the vertex is at (h, k). For f(x) = 2(x – 4)² + 1, the vertex is (4, 1).
• Steps:
  • In f(x) = –2(x – 3)² + 5, h = 3 and k = 5.
  • The vertex is at (3, 5).
• Answer: (3, 5)

[Medium] Annuity — Future Value

• EN: A student deposits $200 at the end of each year into a savings account earning 4% annually. What is the total amount after 3 years? (Use FV = PMT × [(1 + r)ⁿ – 1] / r.)
• FR: Un étudiant dépose 200 $ à la fin de chaque année dans un compte d'épargne rapportant 4 % par an. Quel est le montant total après 3 ans? (Utilise FV = PMT × [(1 + r)ⁿ – 1] / r.)
• Choices: A) $614.08 B) $620.00 C) $624.32 D) $632.16
• Hint: For PMT = $100, r = 5%, n = 3: FV = 100 × [(1.05)³ – 1] / 0.05 = 100 × 3.1525 ≈ $315.25.
• Steps:
  • FV = 200 × [(1.04)³ – 1] / 0.04 = 200 × [1.124864 – 1] / 0.04.
  • = 200 × 0.124864 / 0.04 = 200 × 3.1216 = $624.32.
• Answer: $624.32

[Hard] Logarithm Solving

• EN: Solve for x: log₃(x) + log₃(x – 2) = log₃(8). What is the value of x?
• FR: Résous pour x : log₃(x) + log₃(x – 2) = log₃(8). Quelle est la valeur de x?
• Choices: A) x = 2 B) x = 3 C) x = 4 D) x = 6
• Hint: Use the product rule: logb(A) + logb(B) = log_b(A × B). Then set A × B = the number on the right and solve.
• Steps:
  • Combine: log₃[x(x – 2)] = log₃(8), so x(x – 2) = 8.
  • x² – 2x – 8 = 0 → (x – 4)(x + 2) = 0 → x = 4 (reject x = –2 since log requires x > 0).
• Answer: x = 4

[Hard] Compound Interest — Solving for Time

• EN: An investment of $2000 earns 6% compounded annually. Approximately how many years will it take for the investment to reach $2676? (Use trial: 1.06¹ = 1.06, 1.06² ≈ 1.1236, 1.06³ ≈ 1.191, 1.06⁴ ≈ 1.262, 1.06⁵ ≈ 1.338.)
• FR: Un placement de 2 000 $ rapporte 6 % composé annuellement. Environ combien d'années faudra-t-il pour que le placement atteigne 2 676 $? (Utilise : 1,06⁵ ≈ 1,338.)
• Choices: A) 3 years B) 4 years C) 5 years D) 6 years
• Hint: Try each power: A = 2000 × 1.06ⁿ — check when A first meets or exceeds the target.
• Steps:
  • A = 2000 × (1.06)ⁿ. Try n = 5: 2000 × 1.338 = $2676. ✓
  • It takes 5 years.
• Answer: 5 years

[Easy] Permutations

• EN: How many ways can 5 students line up in a row?
• FR: De combien de façons 5 élèves peuvent-ils se mettre en file?
• Choices: A) 60 B) 100 C) 120 D) 125
• Hint: The number of ways to arrange n items is n! For 4 items: 4! = 4 × 3 × 2 × 1 = 24.
• Steps:
  • 5! = 5 × 4 × 3 × 2 × 1.
  • = 120 ways.
• Answer: 120

[Easy] Combinations

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

[Easy] Evaluating a Polynomial Function

• EN: Given f(x) = x³ – 2x + 4, what is f(–1)?
• FR: Étant donné f(x) = x³ – 2x + 4, quelle est la valeur de f(–1)?
• Choices: A) 3 B) 5 C) 7 D) 9
• Hint: For f(x) = x² + 3x – 1, f(2) = 4 + 6 – 1 = 9.
• Steps:
  • f(–1) = (–1)³ – 2(–1) + 4 = –1 + 2 + 4.
  • = 5.
• Answer: 5

[Easy] Derivative — Power Rule

• EN: Find the derivative of f(x) = 4x³.
• FR: Trouve la dérivée de f(x) = 4x³.
• Choices: A) 4x² B) 8x² C) 12x² D) 16x²
• Hint: Power rule: d/dx (axⁿ) = a × n × x^(n–1). For 3x⁴: derivative = 12x³.
• Steps:
  • Multiply the coefficient by the exponent: 4 × 3 = 12. Reduce the exponent by 1: x².
  • f'(x) = 12x².
• Answer: 12x²

[Medium] Rational Functions — Identifying Asymptotes

• EN: For the function f(x) = (2x + 1) / (x – 3), what is the vertical asymptote?
• FR: Pour la fonction f(x) = (2x + 1) / (x – 3), quelle est l'asymptote verticale?
• Choices: A) x = –1 B) x = 1 C) x = 3 D) x = –3
• Hint: The vertical asymptote occurs where the denominator equals zero. For f(x) = 5/(x – 7), the vertical asymptote is x = 7.
• Steps:
  • Set the denominator equal to zero: x – 3 = 0.
  • x = 3 is the vertical asymptote.
• Answer: x = 3

[Medium] Probability Distributions — Binomial

• EN: A fair coin is flipped 4 times. What is the probability of getting exactly 2 heads? (Hint: Use C(4,2) × (0.5)⁴.)
• FR: Une pièce équilibrée est lancée 4 fois. Quelle est la probabilité d'obtenir exactement 2 faces? (Indice : utilise C(4,2) × (0,5)⁴.)
• Choices: A) 3/8 B) 5/16 C) 6/16 D) 7/16
• Hint: For 3 flips, P(exactly 2 heads) = C(3,2) × (0.5)³ = 3 × 0.125 = 3/8.
• Steps:
  • C(4, 2) = 6. (0.5)⁴ = 1/16.
  • P = 6 × (1/16) = 6/16.
• Answer: 6/16

[Medium] Derivative — Finding a Rate of Change

• EN: The position of a hockey puck is given by s(t) = 3t² + 2t metres, where t is in seconds. What is the velocity (rate of change of position) at t = 2 seconds?
• FR: La position d'une rondelle de hockey est donnée par s(t) = 3t² + 2t mètres, où t est en secondes. Quelle est la vitesse (taux de variation) à t = 2 secondes?
• Choices: A) 12 m/s B) 14 m/s C) 16 m/s D) 18 m/s
• Hint: Differentiate s(t) to get v(t), then substitute t. For s(t) = 2t² + t, s'(t) = 4t + 1, and at t = 3: v = 13.
• Steps:
  • s'(t) = 6t + 2. At t = 2: s'(2) = 6(2) + 2 = 12 + 2.
  • = 14 m/s.
• Answer: 14 m/s

[Medium] Vectors — Magnitude

• EN: A vector is given as v = (3, 4). What is the magnitude of v?
• FR: Un vecteur est donné par v = (3, 4). Quelle est la magnitude de v?
• Choices: A) 4 B) 5 C) 6 D) 7
• Hint: Magnitude = √(x² + y²). For (6, 8): √(36 + 64) = √100 = 10.
• Steps:
  • |v| = √(3² + 4²) = √(9 + 16) = √25.
  • = 5.
• Answer: 5

[Hard] Normal Distribution and Probability

• EN: The scores on a standardized test are normally distributed with a mean of 70 and a standard deviation of 10. Approximately what percentage of students scored between 60 and 80? (Use the empirical rule: 68% of data falls within 1 standard deviation of the mean.)
• FR: Les résultats d'un test standardisé sont normalement distribués avec une moyenne de 70 et un écart-type de 10. Environ quel pourcentage des élèves ont obtenu entre 60 et 80? (Règle empirique : 68 % des données se trouvent à 1 écart-type de la moyenne.)
• Choices: A) 50% B) 68% C) 75% D) 95%
• Hint: The empirical rule says about 68% of data lies within one standard deviation of the mean — between μ – σ and μ + σ.
• Steps:
  • 60 = 70 – 10 (one standard deviation below). 80 = 70 + 10 (one standard deviation above).
  • By the empirical rule, approximately 68% of students scored between 60 and 80.
• Answer: 68%

[Hard] Dot Product of Vectors

• EN: Given vectors u = (2, 5) and v = (4, –1), what is the dot product u · v?
• FR: Étant donné les vecteurs u = (2, 5) et v = (4, –1), quel est le produit scalaire u · v?
• Choices: A) –3 B) 2 C) 3 D) 13
• Hint: For u = (a, b) and v = (c, d), the dot product = a·c + b·d. For (1, 3) · (2, 4) = 2 + 12 = 14.
• Steps:
  • u · v = (2)(4) + (5)(–1) = 8 + (–5).
  • = 3.
• Answer: 3