MathClubforKids

Olympiad Course for Junior School

Number system-1

  • Knowing about numbers
    Example 1: Write the largest 4-digit number.
    Solution: The largest 4-digit number is 9999.
    Example 2: What is the place value of 5 in 4572?
    Solution: The place value of 5 is 500.
  • Basic combinatorics
    Example 1: How many ways can you arrange the letters A and B?
    Solution: 2 ways: AB or BA.
    Example 2: How many ways can you choose 2 balls from 4 differently colored balls?
    Solution: 6 ways.

Arithmetic Operations-1

  1. Operation on numbers -Addition and subtraction
    Example 1: What is 234 + 567?
    Solution: 801.
    Example 2: Subtract 456 from 890.
    Solution: 434.
  2. Operation on numbers -Multiplication and Division
    Example 1: Multiply 23 by 5.
    Solution: 115.
    Example 2: Divide 125 by 5.
    Solution: 25.
  3. Mental mathematics mixed problems
    Example 1: What is 1000 - 357?
    Solution: 643.
    Example 2: Add 68 to 329 mentally.
    Solution: 397.
  4. Factors and multiples
    Example 1: What are the factors of 12?
    Solution: 1, 2, 3, 4, 6, 12.
    Example 2: Find the first five multiples of 7.
    Solution: 7, 14, 21, 28, 35.

Number system-2

  1. Fractions -1
    Example 1: What is 1/2 + 1/4?
    Solution: 3/4.
    Example 2: Subtract 1/3 from 5/6.
    Solution: 1/2.

Arithmetic Operations-2

  1. Fractions -2
    Example 1: Multiply 2/3 by 4/5.
    Solution: 8/15.
    Example 2: Divide 7/8 by 1/2.
    Solution: 7/4.

Number system-3

  1. Decimals-1
    Example 1: Convert 0.75 into a fraction.
    Solution: 3/4.
    Example 2: Write 3.25 as a mixed number.
    Solution: 3 1/4.

Arithmetic Operations-3

  • Decimals-2
    Example 1: Add 4.56 and 3.789.
    Solution: 8.349.
    Example 2: Subtract 2.35 from 7.1.
    Solution: 4.75.
  • Metric Conversion -length ,mass
    Example 1: Convert 5 kilometers into meters.
    Solution: 5000 meters.
    Example 2: Convert 1500 grams to kilograms.
    Solution: 1.5 kilograms.
  • Metric Conversion-time,money,volume
    Example 1: Convert 3 hours into minutes.
    Solution: 180 minutes.
    Example 2: Convert 5 liters into milliliters.
    Solution: 5000 milliliters.
  • Forming 3,4,5,6,-digit smallest and largest number
    Example 1: Form the largest 4-digit number using the digits 3, 7, 1, 8.
    Solution: 8731.
    Example 2: Form the smallest 5-digit number using the digits 9, 0, 1, 5, 3.
    Solution: 10359.
  • profit and loss
    Example 1: A toy was bought for $15 and sold for $20. What is the profit?
    Solution: Profit = $5.
    Example 2: A book was bought for $25 and sold for $18. What is the loss?
    Solution: Loss = $7.

Set Theory

  • Sets and its operations
    Example 1: If Set A = {1, 2, 3, 4} and Set B = {3, 4, 5, 6}, find A union B.
    Solution: {1, 2, 3, 4, 5, 6}.
    Example 2: Find A intersection B for the same sets.
    Solution: {3, 4}.
  • venn diagram basics
    Example 1: In a group of 30 students, 15 like ice cream, 10 like chocolate, and 5 like both. How many students like only ice cream?
    Solution: 10.
    Example 2: In a class, 12 students play football, 8 play basketball, and 4 play both. How many play only basketball?
    Solution: 4.

Mensuration -1

  • Perimeter of square aand triangle
    Example 1: Find the perimeter of a square with a side length of 5 cm.
    Solution: 20 cm.
    Example 2: Find the perimeter of a triangle with sides 3 cm, 4 cm, and 5 cm.
    Solution: 12 cm.
  • Perimeter related advanced question
    Example 1: Find the perimeter of a rectangle with length 8 cm and width 6 cm.
    Solution: 28 cm.
  • Area of squarea and rectangle
    Example 1: Find the area of a square with side length 7 cm.
    Solution: 49 square cm.
    Example 2: Find the area of a rectangle with length 9 cm and width 4 cm.
    Solution: 36 square cm.

Plane Geometry

  • Introduction and questions
    Example 1: Name a shape with 4 equal sides.
    Solution: Square.
    Example 2: How many sides does a pentagon have?
    Solution: 5.
  • Advanced questions
    Example 1: What is the measure of each interior angle of an equilateral triangle?
    Solution: 60 degrees.
    Example 2: What is the sum of the interior angles of a hexagon?
    Solution: 720 degrees.

Verbal and non verbal

  1. patterns of numbers
    Example 1: Find the next number in the series: 5, 10, 20, 40, ___.
    Solution: The pattern is doubling the previous number, so the next number is 80.
    Example 2: Identify the missing number in the sequence: 2, 6, 12, 20, ___.
    Solution: The pattern involves adding consecutive even numbers (4, 6, 8, etc.). The next even number is 10, so the missing number is 30.
  2. clocks
    Example 1: What is the time 4 hours after 9:00 AM?
    Solution: The time will be 1:00 PM.
    Example 2: If the current time is 6:30 PM, what will be the time 5 hours and 45 minutes later?
    Solution: The time will be 12:15 AM the next day.
  3. Folding
    Example 1: A square sheet of paper is folded in half vertically and then in half horizontally. How many sections will there be when unfolded?
    Solution: 4 sections.
    Example 2: If a piece of paper is folded 3 times, how many creases will be visible when it is fully unfolded?
    Solution: After unfolding, there will be 3 creases.
  4. days,months,dates
    Example 1: If today is March 3, what will be the date 10 days from now?
    Solution: The date will be March 13.
    Example 2: If today is Wednesday, what day will it be 9 days from now?
    Solution: It will be Friday.
  5. Time
    Example 1: Convert 135 minutes into hours and minutes.
    Solution: 135 minutes is 2 hours and 15 minutes.
    Example 2: How many seconds are there in 3 hours?
    Solution: 3×60×60=108003 \times 60 \times 60 = 108003×60×60=10800 seconds.
  6. Money
    Example 1: If you have 2 quarters, 3 dimes, and 4 nickels, how much money do you have?
    Solution: 2×0.25+3×0.10+4×0.05=0.50+0.30+0.20=1.002 \times 0.25 + 3 \times 0.10 + 4 \times 0.05 = 0.50 + 0.30 + 0.20 = 1.002×0.25+3×0.10+4×0.05=0.50+0.30+0.20=1.00 dollar.
    Example 2: A toy costs $7.50, and you pay with a $10 bill. How much change will you receive?
    Solution: You will receive $2.50 in change.
  7. Statement type questions
    Example 1: Statement: "All birds have wings. A sparrow is a bird." What can we conclude?
    Solution: A sparrow has wings.
    Example 2: Statement: "Some students are athletes. All athletes train daily." Can we conclude that some students train daily?
    Solution: Yes, we can conclude that some students train daily.
  8. Blood Relation
    Example 1: If Mary is the sister of John, and John is the son of Tom, what is Tom's relationship to Mary?
    Solution: Tom is Mary’s father.
    Example 2: Sarah says, "My mother's brother is John." What is John’s relation to Sarah?
    Solution: John is Sarah’s uncle.
  9. symmetry
    Example 1: How many lines of symmetry does a circle have?
    Solution: A circle has infinite lines of symmetry.
    Example 2: How many lines of symmetry does a regular hexagon have?
    Solution: A regular hexagon has 6 lines of symmetry.
  10. magic square-1
    Example 1: Complete the magic square where the sum of every row, column, and diagonal is 15:
    [8, 1, 6]
    [_, 5, 7]
    [4, 9, 2]Solution: The missing number is 3 (second row, first column).
  11. magic square-2
    Example 1: Complete the magic square where the sum of every row, column, and diagonal is 34:
    [16, 3, 2, 13]
    [_, 10, 11, _]
    [9, _, 7, _]
    [6, 15, 14, _]Solution: The missing numbers are 5, 12, 8, and 1.
  12. pattern of shapes
    Example 1: Identify the next shape in the sequence: Triangle, Circle, Square, Triangle, Circle, ___.
    Solution: The next shape is Square.
    Example 2: Identify the next shape in the sequence: Pentagon, Hexagon, Octagon, ___.
    Solution: The next shape is Decagon (10-sided).

Combinatorics

  • Basics with problems-1
    Example 1: How many ways can you arrange the letters A, B, and C?
    Solution: 3!=3×2×1=63! = 3 \times 2 \times 1 = 63!=3×2×1=6 ways.
    Example 2: How many ways can you choose 2 balls from a set of 5 different colored balls?
    Solution: C(5,2)=5!2!(5−2)!=10C(5, 2) = \frac{5!}{2!(5-2)!} = 10C(5,2)=2!(5−2)!5!​=10 ways.
  • Basics with problems-2
    Example 1: How many ways can 4 people be seated in a row?
    Solution: 4!=244! = 244!=24 ways.
    Example 2: How many ways can you arrange the letters of the word "MATH"?
    Solution: 4!=244! = 244!=24 ways.

Data Handling

  • bar graph

    Example 1: If a bar graph shows 10 students who like apples and 15 students who like bananas, how many more students like bananas than apples?
    Solution: 15 - 10 = 5 more students like bananas.

    Example 2: In a bar graph, if one bar represents 20 books and another bar represents 30 books, what is the ratio of books in the second bar to books in the first?
    Solution: The ratio is 30:20 or 3:2.

  • dot sheet

    Example 1: A dot sheet has 4 rows and 5 columns of dots. How many dots are there in total?
    Solution: 4×5=204 \times 5 = 204×5=20 dots.

    Example 2: On a grid of dots, how many squares can be formed by connecting four dots?
    Solution: You can form 6 squares.

  • pie graph and pictograph

    Example 1: In a pie chart, if 25% of the chart represents the number of students who like pizza, what fraction of students like pizza?
    Solution: 14\frac{1}{4}41​ of the students like pizza.

    Example 2: In a pictograph, each symbol represents 3 apples. If there are 5 symbols for apples, how many apples are there?
    Solution: 5×3=155 \times 3 = 155×3=15 apples.

Visualising 3D shapes and maps

  • Nets of cube

    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 cube is folded from a net of 6 connected squares, how many edges will the resulting cube have?
    Solution: The cube will have 12 edges.

  • Nets of cuboids ,boxes

    Example 1: A net of a cuboid has 2 connected rectangles. How many more rectangles are needed to complete the cuboid?
    Solution: You need 4 more rectangles to complete the net.

    Example 2: How many faces does a cuboid have when unfolded into a net?
    Solution: A cuboid has 6 faces when unfolded.

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