- 4500 Stonecrest Dr, Ellicott City, MD 21043, USA
Olympiad Course for Middle School
Basic Fundamentals
- Knowing about numbers
Example 1: Write the largest 5-digit number.
Solution: The largest 5-digit number is 99999.Example 2: What is the place value of 7 in 4782?
Solution: The place value of 7 is 700.Example 3: Identify whether 4582 is an odd or even number.
Solution: 4582 is an even number because it ends in 2. - Basic combinatorics
Number system
- Test of divisibility
Example 1: Is 456 divisible by 3?
Solution: Yes, because the sum of digits (4+5+6=15) is divisible by 3.Example 2: Is 1230 divisible by 5?
Solution: Yes, because it ends in 0.Example 3: Is 2145 divisible by 9?
Solution: No, because the sum of the digits (2+1+4+5=12) is not divisible by 9. - Factors and multiples
Example 1: What are the factors of 36?
Solution: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.Example 2: List the first five multiples of 7.
Solution: 7, 14, 21, 28, 35.Example 3: What is the greatest common factor (GCF) of 24 and 36?
Solution: The GCF of 24 and 36 is 12. - Finding largest/smallest number using digits
Example 1: Using the digits 3, 9, 1, and 8, form the largest number.
Solution: 9831.Example 2: Using the digits 5, 0, 2, and 7, form the smallest number.
Solution: 2057.Example 3: Using the digits 6, 4, 2, and 9, form the largest odd number.
Solution: 9643. - Simplification of numbers and Decimals
Example 1: Simplify 4.56 + 3.789.
Solution: 4.56 + 3.789 = 8.349.Example 2: Simplify 12.45 - 8.62.
Solution: 12.45 - 8.62 = 3.83.Example 3: Simplify 68+48\frac{6}{8} + \frac{4}{8}86+84.
Solution: 68+48=108=1.25\frac{6}{8} + \frac{4}{8} = \frac{10}{8} = 1.2586+84=810=1.25. - Integers and Fractions
Example 1: What is 5−(−3)5 - (-3)5−(−3)?
Solution: 5−(−3)=85 - (-3) = 85−(−3)=8.Example 2: Multiply 35×27\frac{3}{5} \times \frac{2}{7}53×72.
Solution: 35×27=635\frac{3}{5} \times \frac{2}{7} = \frac{6}{35}53×72=356.Example 3: Subtract 34\frac{3}{4}43 from 111.
Solution: 1−34=141 - \frac{3}{4} = \frac{1}{4}1−43=41. - Playing with numbers
Example 1: What is the sum of the first 5 prime numbers?
Solution: 2 + 3 + 5 + 7 + 11 = 28.Example 2: Find the product of all even numbers from 1 to 10.
Solution: 2 × 4 × 6 × 8 × 10 = 3840.Example 3: Find the LCM of 8 and 12.
Solution: LCM of 8 and 12 is 24. - Percentage
Example 1: What is 20% of 200?
Solution: 20100×200=40\frac{20}{100} \times 200 = 4010020×200=40.Example 2: If 15% of a number is 75, what is the number?
Solution: 15100×x=75\frac{15}{100} \times x = 7510015×x=75. Solving, x=500x = 500x=500.Example 3: Increase 250 by 10%.
Solution: 10% of 250 = 25, so 250 + 25 = 275. - Profit and loss
Example 1: A pen was bought for $15 and sold for $20. What is the profit percentage?
Solution: Profit = $5. Profit percentage = 515×100=33.33%\frac{5}{15} \times 100 = 33.33\%155×100=33.33%.Example 2: A toy was bought for $60 and sold for $45. What is the loss percentage?
Solution: Loss = $15. Loss percentage = 1560×100=25%\frac{15}{60} \times 100 = 25\%6015×100=25%.Example 3: A book costs $100, and a discount of 15% is given. What is the sale price?
Solution: Discount = 15100×100=15\frac{15}{100} \times 100 = 1510015×100=15, so the sale price is $85.
Arithmetic Operations
- Addition and Subtraction
Example 1: Add 3456 and 7890.
Solution: 3456+7890=113463456 + 7890 = 113463456+7890=11346.Example 2: Subtract 4231 from 8000.
Solution: 8000−4231=37698000 - 4231 = 37698000−4231=3769.Example 3: What is 12345+6789−234512345 + 6789 - 234512345+6789−2345?
Solution: 12345+6789−2345=1678912345 + 6789 - 2345 = 1678912345+6789−2345=16789. - Multiplication and division
Example 1: Multiply 25 by 36.
Solution: 25×36=90025 \times 36 = 90025×36=900.Example 2: Divide 144 by 12.
Solution: 144÷12=12144 \div 12 = 12144÷12=12.Example 3: Divide 1500 by 25.
Solution: 1500÷25=601500 \div 25 = 601500÷25=60. - LCM & HCF
Example 1: Find the LCM of 12 and 18.
Solution: LCM = 36.Example 2: Find the HCF of 28 and 42.
Solution: HCF = 14.Example 3: Find the LCM of 8, 12, and 16.
Solution: LCM = 48. - Magic Squares ,Money
Example 1: Complete the magic square where each row, column, and diagonal sums to 15:
[8, 1, 6]
[_, 5, 7]
[4, 9, 2]
Solution: The missing number is 3.Example 2: A person has $5, and they spend $3.25. How much do they have left?
Solution: They have $1.75 left.Example 3: If a magic square has a row sum of 18, what is the sum of each diagonal?
Solution: The sum of each diagonal will also be 18. - Speed,Time
Example 1: If a car travels 60 km in 2 hours, what is its speed?
Solution: Speed = 602=30\frac{60}{2} = 30260=30 km/h.Example 2: If a cyclist covers 90 km in 3 hours, what is their speed?
Solution: Speed = 903=30\frac{90}{3} = 30390=30 km/h.Example 3: How long will it take to travel 150 km at a speed of 50 km/h?
Solution: Time = 15050=3\frac{150}{50} = 350150=3 hours. - Word problems on age
Example 1: John is 5 years older than Mary. In 10 years, John will be twice Mary’s age. How old are they now?
Solution: Let Mary’s age be xxx. Then John’s age is x+5x + 5x+5. In 10 years, John’s age will be x+15x + 15x+15 and Mary’s will be x+10x + 10x+10. Equation: x+15=2(x+10)x + 15 = 2(x + 10)x+15=2(x+10). Solving, x=5x = 5x=5, so Mary is 5 years old, and John is 10.Example 2: Sarah is 3 years older than Tom. Five years ago, Sarah was twice as old as Tom. How old are they now?
Solution: Sarah is 8 years old, and Tom is 5.Example 3: Mary is 10 years younger than her brother. In 4 years, her brother will be 20. How old is Mary now?
Solution: Her brother is currently 16, so Mary is 6 years old. - Ratio and proportion
Example 1: The ratio of boys to girls in a class is 3:2. If there are 30 boys, how many girls are there?
Solution: There are 20 girls.Example 2: The ratio of the length to the width of a rectangle is 5:3. If the width is 9 cm, what is the length?
Solution: The length is 15 cm.Example 3: A recipe requires 3 cups of flour for every 2 cups of sugar. If you use 6 cups of flour, how many cups of sugar do you need?
Solution: You need 4 cups of sugar.
Basic geometry
- Rays,angles,Straight lines, parallel lines, Angle properties of triangles
Example 1: What is the sum of the interior angles of a triangle?
Solution: The sum of the interior angles of any triangle is always 180∘180^\circ180∘.Example 2: If two parallel lines are cut by a transversal, what is the relationship between the corresponding angles?
Solution: Corresponding angles are equal.Example 3: In a right-angled triangle, if one angle is 90∘90^\circ90∘ and another angle is 45∘45^\circ45∘, what is the third angle?
Solution: The third angle is 180∘−(90∘+45∘)=45∘180^\circ - (90^\circ + 45^\circ) = 45^\circ180∘−(90∘+45∘)=45∘. - Quadrilaterals and Polygons
Example 1: What is the sum of the interior angles of a quadrilateral?
Solution: The sum of the interior angles of a quadrilateral is 360∘360^\circ360∘.Example 2: How many sides does a polygon have if the sum of its interior angles is 720∘720^\circ720∘?
Solution: Using the formula (n−2)×180∘=720∘(n-2) \times 180^\circ = 720^\circ(n−2)×180∘=720∘, solve for nnn. The polygon has 6 sides (a hexagon).Example 3: What is the sum of the interior angles of a pentagon?
Solution: (5−2)×180∘=540∘(5-2) \times 180^\circ = 540^\circ(5−2)×180∘=540∘. - Problems on square,rectangle and circles
Example 1: Find the area of a square with a side length of 6 cm.
Solution: Area = side2=6×6=36\text{side}^2 = 6 \times 6 = 36side2=6×6=36 square cm.Example 2: What is the perimeter of a rectangle with a length of 10 cm and a width of 4 cm?
Solution: Perimeter = 2×(10+4)=282 \times (10 + 4) = 282×(10+4)=28 cm.Example 3: If the radius of a circle is 7 cm, what is the circumference?
Solution: Circumference = 2×π×7=442 \times \pi \times 7 = 442×π×7=44 cm (using π≈3.14\pi \approx 3.14π≈3.14).
Solid Geometry
- 3D shapes and critical thinking problems
Example 1: How many faces does a cube have?
Solution: A cube has 6 faces.Example 2: How many vertices does a rectangular prism (cuboid) have?
Solution: A rectangular prism has 8 vertices.Example 3: How many edges does a cylinder have?
Solution: A cylinder has 2 edges.
Statistics
- Verage,Piechart
Example 1: The test scores of 5 students are 80, 85, 90, 95, and 100. Find the average score.
Solution: Average = 80+85+90+95+1005=90\frac{80+85+90+95+100}{5} = 90580+85+90+95+100=90.Example 2: In a pie chart, 50% of the chart represents students who like apples, 30% represents those who like bananas, and 20% represents those who like oranges. What fraction of students like oranges?
Solution: 20100=15\frac{20}{100} = \frac{1}{5}10020=51.Example 3: If the average of three numbers is 50, and two of the numbers are 60 and 40, find the third number.
Solution: Let the third number be xxx. Then, 60+40+x3=50\frac{60+40+x}{3} = 50360+40+x=50. Solving, x=50x = 50x=50. - Graphs,data handling
Example 1: A bar graph shows the number of books read by 4 students: 5, 8, 12, and 9. How many books were read in total?
Solution: Total = 5+8+12+9=345 + 8 + 12 + 9 = 345+8+12+9=34 books.Example 2: In a line graph, if the temperature rises from 20°C to 30°C over 5 hours, what is the average increase in temperature per hour?
Solution: Average increase = 30−205=2\frac{30 - 20}{5} = 2530−20=2°C per hour.Example 3: How many students liked vanilla if a pictograph shows 6 symbols of ice creams, where each symbol represents 5 students?
Solution: 6×5=306 \times 5 = 306×5=30 students liked vanilla.
Algebra Basics
- Introduction ,Properties of algebra
Example 1: Solve for xxx: 2x+5=152x + 5 = 152x+5=15.
Solution: 2x=102x = 102x=10, so x=5x = 5x=5.Example 2: Solve for yyy: 3y−8=193y - 8 = 193y−8=19.
Solution: 3y=273y = 273y=27, so y=9y = 9y=9.Example 3: What is the distributive property in algebra?
Solution: The distributive property is a(b+c)=ab+aca(b + c) = ab + aca(b+c)=ab+ac. - problems on variable and constants
Example 1: In the equation 2x+3=92x + 3 = 92x+3=9, identify the variable and the constant.
Solution: The variable is xxx, and the constant is 3.Example 2: Solve for xxx: 5x+4=195x + 4 = 195x+4=19.
Solution: 5x=155x = 155x=15, so x=3x = 3x=3.Example 3: In the expression 3y−73y - 73y−7, what is the coefficient of yyy?
Solution: The coefficient of yyy is 3. - word problems on Algebra
Example 1: If John’s age is 3 years more than twice his sister’s age, and his sister is 8 years old, how old is John?
Solution: John’s age = 2×8+3=192 \times 8 + 3 = 192×8+3=19 years.Example 2: The length of a rectangle is 5 cm more than its width. If the perimeter is 40 cm, what are the dimensions of the rectangle?
Solution: Width = 7.5 cm, Length = 12.5 cm.Example 3: A number is tripled and then decreased by 7. The result is 11. What is the number?
Solution: The number is 6.
Mathematcal Reasoning
- Finding number of plane figures
Example 1: How many triangles can be formed in a hexagon by connecting vertices?
Solution: You can form 6 triangles.Example 2: How many diagonals does a pentagon have?
Solution: A pentagon has 5 diagonals. - Paper cutting and folding
Example 1: A square paper is folded in half and then in half again. How many sections are there when the paper is unfolded?
Solution: 4 sections.Example 2: A circle is folded twice. How many visible creases will there be when the circle is unfolded?
Solution: There will be 2 creases. - Math puzzles
Example 1: A train travels 100 miles in 2 hours. How long will it take to travel 250 miles at the same speed?
Solution: It will take 5 hours.Example 2: If two workers can paint a wall in 4 hours, how long will it take 3 workers to paint the same wall?
Solution: It will take 4×23=83\frac{4 \times 2}{3} = \frac{8}{3}34×2=38 hours (2 hours and 40 minutes). - Mirror images and relationships
Example 1: What is the mirror image of the letter “E”?
Solution: The mirror image of “E” is “Ǝ”.Example 2: If a triangle’s mirror image is shown, which side will appear opposite?
Solution: The right side will appear on the left, and vice versa. - Clock and calendar
Example 1: What time will it be 3 hours after 5:00 PM?
Solution: It will be 8:00 PM.Example 2: If today is Monday, what day will it be 10 days from now?
Solution: It will be Thursday. - Net cube and Dice
Example 1: If a cube is unfolded into a net, how many squares will the net have?
Solution: The net will have 6 squares.Example 2: If a die shows 3 on one face, what will be on the opposite face?
Solution: The opposite face will show 4 (standard die). - Direction and patterns
Example 1: A person walks 10 meters north, then 15 meters west, and finally 5 meters south. What is their final position relative to the starting point?
Solution: The person is 10 meters west and 5 meters north of the starting point.Example 2: Identify the next shape in the pattern: Circle, Triangle, Square, Circle, Triangle, ___.
Solution: The next shape is a Square.
Symmetry
- Axes of symmety,rotational
Example 1: How many lines of symmetry does an equilateral triangle have?
Solution: An equilateral triangle has 3 lines of symmetry.Example 2: What is the order of rotational symmetry of a regular pentagon?
Solution: The order of rotational symmetry is 5.Example 3: Does a rectangle have rotational symmetry?
Solution: Yes, it has rotational symmetry of order 2.
Basic Combinatorics
- Sitting arrangement
Example 1: How many ways can 4 people sit in a row?
Solution: 4!=244! = 244!=24 ways.Example 2: How many ways can 3 people sit in a circle?
Solution: (3−1)!=2(3-1)! = 2(3−1)!=2 ways. - Arrangement of objects
Example 1: How many ways can the letters of the word "MATH" be arranged?
Solution: 4!=244! = 244!=24 ways.Example 2: How many ways can you arrange 5 books on a shelf?
Solution: 5!=1205! = 1205!=120 ways.
Verbal reasoning
- Problems practice-1
Example 1: "All birds have wings. Some animals are birds." Can we conclude that some animals have wings?
Solution: Yes.Example 2: "Some fruits are apples. All apples are fruits." Can we conclude that all fruits are apples?
Solution: No. - Problems practice-2
Example 1: If it rains, the ground gets wet. The ground is wet. Did it rain?
Solution: Not necessarily, something else may have caused the ground to get wet.Example 2: If a person is standing in the rain without an umbrella, they get wet. John is standing in the rain without an umbrella. Is John wet?
Solution: Yes, John is wet.
Mensuration
- Perimeter of plane figure
Example 1: Find the perimeter of a rectangle with length 8 cm and width 5 cm.
Solution: Perimeter = 2×(8+5)=262 \times (8 + 5) = 262×(8+5)=26 cm.Example 2: Find the perimeter of a triangle with sides 3 cm, 4 cm, and 5 cm.
Solution: Perimeter = 3+4+5=123 + 4 + 5 = 123+4+5=12 cm. - Area of plane figures
Example 1: Find the area of a rectangle with length 7 cm and width 3 cm.
Solution: Area = 7×3=217 \times 3 = 217×3=21 square cm.Example 2: Find the area of a triangle with base 6 cm and height 4 cm.
Solution: Area = 12×6×4=12\frac{1}{2} \times 6 \times 4 = 1221×6×4=12 square cm.
Mathematical Logic
- Statement related questions
Example 1: "If it is raining, the grass is wet. The grass is wet." Can we conclude that it is raining?
Solution: No, there could be another reason the grass is wet.Example 2: "All dogs are animals. Some animals are pets." Can we conclude that some dogs are pets?
Solution: Yes.
US / Dubai / Singapore Price
$100 / month
- Course Duration : 12 weeks/ 3 months
INDIA PRICE
(For residents of India Only)
₹2000 / month
Admission fee : ₹2000 (for first time only)
- Course Duration : 12 weeks/ 3 month
Pay using QR Code
