Grade 7 DataHandling Chapter Test 2025-26

Grade 7 DataHandling Chapter Test 2025-2026

Max marks: 40 Duration 1hr 30 min

Answer the following

One mark questions (1 x 15 = 15 marks)

1. Choose the correct option. 

(i) The probability of getting a number less than or equal to 6 when a die is rolled is: 

(a) 0 (b) 6 (c) 16 (d) 1 

(ii) If a day is selected at random, what is the probability it is not Monday? 

(a) 17 (b) 27 (c) 67 (d) 76

(iii). Which of the following is a random experiment? 

(a) Tossing a coin (b) Rolling a single 6-sided die

(c) Choosing a marble from a jar (d) All of the above 

(iv) Which of the following is an outcome? 

(a) Rolling a pair of dice (b) Coin landing on heads

(c) Choosing 2 marbles from a jar (d) None of the above 

(v) Which of the following experiments does not have equally likely outcomes? 

(a) Choosing a number at random from 1 to 7 (b) Tossing a coin 

(c) Choosing a letter at random from the word SCHOOL (d) None of the above 

(vi)  The arithmetic mean of the first four natural numbers is: 

(a) 2 (b) 2.5 (c) 3 (d) 3.5 

(vi) The median of the first ten natural numbers is: 

(a) 5 (b) 5.5 (c) 6 (d) 6.5 

(viii) What is the mode of the given data? (10, 8, 11, 11, 7, 8, 10, 11, 7, 7, 11} 

(a) 4 (b) 10 (c) 11 (d) 7 

(ix)  The probability of any event cannot exceed: 

(a) 12 (b) 1 (c) 10 (d) 100 

(x) The probability of getting an even number when a die is rolled is

(a) 12 (b) 14  (c) 34 (d) 1 

(xi) A month is selected at random. What is the probability that it has 31 days?

(xii) Find the mean of the given data. 40, 90, 40, 20, 100 

(xiii) Find the median of the given data. 900, 1300, 1200, 1000, 1100 

(xiv)  Find the mode of the given data.  46, 106, 4, 46, 134, 86, 86.5 

(xv)  If a date is randomly selected from April, what is the probability that it is divisible by 7? 

Two marks questions (5 x 2 =10 marks)

1. Find the mean, median and mode of the following set of data: 16, 40, 44, 16, 40, 40, 80, 17, 64, 60, 100 

2.Suppose that the letter cards for the word MATHEMATICS were put face down and mixed up and a card is picked up at random. What is the probability of picking up a vowel? 

3.Find the most popular pizza topping from the list of orders: cheese, cheese, black olives, mushrooms, onions, cheese, mushrooms, black olives, onions, cheese, mushrooms, cheese. 

4. A number tile is randomly selected. 

(i) How many possible outcomes are there? 

(ii) What are the favourable outcomes of choosing a prime? 

(iii) In how many ways can choosing a composite number occur? 

5. Find the probability of getting a sum of 8 when 2 dice are rolled. 

Three mark questions  (5 x 3 = 15 marks)

1.10. A die is rolled once. Find the probability of getting a number: 

(i) less than 4 

(ii) less than or equal to 4 

(iii) greater than 4 

(iv) greater than or equal to 4 

2. A bag contains 4 blue, 4 red, 6 yellow and 10 white marbles. What is the probability of drawing the following? Which of these is a certain event? 

(i) a blue marble (iii) a red marble 

(ii) a yellow marble (iv) a white marble 

(v) a blue or a yellow marble (vii) A red, yellow or white marble 

(vi) a red or a white marble (viii) A red, blue, yellow or white marble.

3.

4.

5.

DOWNLOAD THE QUESTION PAPER CLICK HERE

SOLUTIONS

Grade 7 DataHandling Chapter Test 2025-26

One-mark questions:

(i) The probability of getting a number ≤ 6 on a die (all outcomes 1 to 6):
Answer: (d) 1

(ii) Probability of not Monday = 6/7 (since there are 7 days)
Answer: (d) 6/7 (likely meant “6⁄7” — option marked as 76 is a typo)

(iii) A random experiment has uncertain outcomes.
Answer: (d) All of the above

(iv) An outcome is a single possible result.
Answer: (b) Coin landing on heads

(v) “SCHOOL” has letters with unequal frequency.
Answer: (c) Choosing a letter at random from the word SCHOOL

(vi) First four natural numbers: 1, 2, 3, 4 → Mean = (1+2+3+4)/4 = 2.5
Answer: (b) 2.5

(vii) First ten natural numbers: 1 to 10 → Median = (5 + 6)/2 = 5.5
Answer: (b) 5.5

(viii) Data: 10, 8, 11, 11, 7, 8, 10, 11, 7, 7, 11 → Mode = 11 (occurs 4 times)
Answer: (c) 11

(ix) Probability cannot exceed 1
Answer: (b) 1

(x) Even numbers on a die: 2, 4, 6 → 3 outcomes out of 6 = 3/6 = 1/2
Answer: (a) 1/2

(xi) Months with 31 days: Jan, Mar, May, Jul, Aug, Oct, Dec = 7/12
Answer: 7/12

(xii) Mean of 40, 90, 40, 20, 100 = (40+90+40+20+100)/5 = 58
Answer: 58

(xiii) Data: 900, 1300, 1200, 1000, 1100 → Sorted: 900, 1000, 1100, 1200, 1300 → Median = 1100
Answer: 1100

(xiv) Mode: 46, 106, 4, 46, 134, 86, 86.5 → 46 appears twice
Answer: 46

(xv) Dates in April = 30. Numbers divisible by 7: 7, 14, 21, 28 → 4 outcomes → 4/30 = 2/15
Answer: 2/15

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Two-mark questions:

1. Data: 16, 40, 44, 16, 40, 40, 80, 17, 64, 60, 100

• Mean = sum/11 = (577)/11 = 52.45

• Median (sorted): 16,16,17,40,40,40,44,60,64,80,100 → middle = 40

• Mode = 40 (appears 3 times)

2. MATHEMATICS → Letters: M, A, T, H, E, M, A, T, I, C, S → vowels: A, E, A, I → 4/11
Answer: 4/11

**3. Pizza toppings: cheese (5), black olives (2), mushrooms (3), onions (2)
Answer: Cheese

4. Assume tiles = numbers 1–10:
(i) 10 possible outcomes
(ii) Primes = 2, 3, 5, 7 → 4 favourable outcomes
(iii) Composites = 4, 6, 8, 9, 10 → 5 outcomes

5. Getting a sum of 8 with two dice:
(2,6), (3,5), (4,4), (5,3), (6,2) → 5 favourable outcomes
Total = 36 → Probability = 5/36

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Three-mark questions:

1. Die rolled once (numbers 1–6):
(i) < 4 → {1,2,3} → 3/6 = 1/2
(ii) ≤ 4 → {1,2,3,4} → 4/6 = 2/3
(iii) > 4 → {5,6} → 2/6 = 1/3
(iv) ≥ 4 → {4,5,6} → 3/6 = 1/2

2. Marbles: 4 blue, 4 red, 6 yellow, 10 white = 24 total

• (i) Blue: 4/24 = 1/6

• (ii) Yellow: 6/24 = 1/4

• (iii) Red: 4/24 = 1/6

• (iv) White: 10/24 = 5/12

• (v) Blue or Yellow = (4+6)/24 = 10/24 = 5/12

• (vi) Red or White = (4+10)/24 = 14/24 = 7/12

• (vii) Red, Yellow or White = (4+6+10)/24 = 20/24 = 5/6

• (viii) All colors = 24/24 = 1 → This is the certain event

 Grade 7 Symmetry Chapter Test 2025-2026

Max marks: 30 Duration 1hr 

Answer the following

One mark questions (1 x 15 = 15 marks)

1. Tick the correct option. 

(i) Which of the following letters does not have reflection symmetry? 

(a) A (b) Y (c) H (d) P 

(ii) An equilateral triangle has rotational symmetry of order: 

(a) 1 (b) 2 (c) 3 (d) 4 

(iii) How many axes of reflection symmetry does a square have? 

(a) 1 (b) 2 (c) 3 (d) 4 

(iv) How many axes of symmetry does a circle have? 

(a) 1 (b) 0 (c) 360 (d) infinite 

(v) Which of these cannot be the angle of rotational symmetry? 

(a) 180° (b) 90° (c) 240° (d) 120° 

(vi) How many axes of symmetry does a scalene triangle have? 

(a) 1 (b) 0 (c) 2 (d) 3 

(vii) The number of axes of reflection symmetry and the order of rotational symmetry of the letter X are resp,: 

(a) 2 and 4 (b) 1 and 2 (c) 4 and 2 (d) 1 and 4 

2. Write against each statement whether it is true or false. 

(i) Only round shapes can have rotational symmetry. 

(ii) Every shape has a rotational symmetry of order 1 at least. 

(iii) A shape with one line of symmetry cannot have a rotational symmetry of order greater than 1. 

(iv) A shape with a larger degree of rotational symmetry has a greater order of symmetry. 

(v) A semicircle has rotational symmetry of order 2. 

3. Answer the following

(i) Name a shape that has the same number of lines of symmetry as a rectangle. 

(ii)  Draw a shape that has the same number of lines of symmetry as a square. 

(iii) Does a spiral have rotational symmetry of order greater than 1? 

(iv) How many lines of symmetry does each of the two set squares in the geometry instruments box have? 

(v). How many lines of symmetry does the Indian national flag have? 

(vi) .Draw any shape that has reflection symmetry but no rotational symmetry greater than 1.

(vii) Among the letters E, X, F, G, H, T, R and U, identify the letters having rotational symmetry and find their order of rotational symmetry. 

(viii) Name an irregular polygon (all sides do not have the same length) (a) having reflection symmetry and (b) not having reflection symmetry.

Two marks questions (2 x 2 =04 marks)

1  Draw stars having five, six and seven arms. Find out whether each has rotational symmetry and if so, of what order. 

2.

Three mark questions  (2 x 3 = 06 marks)

1.

2. Fill in the numbers

DOWNLOAD THE QUESTION PAPER CLICK HERE

SOLUTIONS

Q1.

(i) Which of the following letters does not have reflection symmetry?

• (d) P ✅

Explanation: 'A', 'Y', and 'H' have at least one line of symmetry. 'P' has none.

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(ii) An equilateral triangle has rotational symmetry of order:

• (c) 3 ✅

Explanation: It looks the same after rotating 120°, 240°, and 360°.

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(iii) How many axes of reflection symmetry does a square have?

• (d) 4 ✅

Explanation: A square has 2 diagonals and 2 midlines as symmetry axes.

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(iv) How many axes of symmetry does a circle have?

• (d) infinite ✅

Explanation: A circle can be folded about any diameter, giving infinite lines of symmetry.

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(v) Which of these cannot be the angle of rotational symmetry?

• (c) 240° ✅

Explanation: 240° is not a factor of 360° that evenly divides the circle into identical sections. (Corrected: Actually, 240° can be a rotational symmetry angle—see clarification below.)

⚠️ Correction: All listed angles can be rotational symmetry angles, depending on the shape. A regular hexagon, for instance, has 60°, 120°, 180°, 240°, 300°, and 360° rotational symmetry.
Therefore, a better correct answer does not exist from the given options unless the question specifies regular polygons only. In standard multiple-choice format, the best choice might be none of these or question should be revised.

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(vi) How many axes of symmetry does a scalene triangle have?

• (b) 0 ✅

Explanation: A scalene triangle has all unequal sides and angles—no symmetry.

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(vii) The number of axes of reflection symmetry and the order of rotational symmetry of the letter X are respectively:

• (a) 2 and 4 ✅

Explanation: 'X' has 2 axes of symmetry (vertical and diagonal) and rotational symmetry of order 4 (every 90°).

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2. Write True or False for each statement:

(i) Only round shapes can have rotational symmetry.
→ False

Explanation: Many non-round shapes (like equilateral triangles, squares, etc.) have rotational symmetry.

(ii) Every shape has a rotational symmetry of order 1 at least.
→ True

Explanation: Every shape can be rotated by 360° to look the same — this is order 1 rotational symmetry.

(iii) A shape with one line of symmetry cannot have a rotational symmetry of order greater than 1.
→ True

Explanation: Shapes like an isosceles triangle have one line of symmetry and no rotational symmetry beyond order 1.

(iv) A shape with a larger degree of rotational symmetry has a greater order of symmetry.
→ True

Explanation: The order of rotational symmetry increases as the shape repeats more times during a 360° rotation.

(v) A semicircle has rotational symmetry of order 2.
→ False

Explanation: A semicircle has no rotational symmetry beyond order 1; it looks different when rotated before 360°.

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3. Answer the following:

(i) Name a shape that has the same number of lines of symmetry as a rectangle.
→ Answer: Rhombus

Explanation: A rectangle has 2 lines of symmetry (horizontal and vertical), same as a rhombus (diagonals).

(ii) Draw a shape that has the same number of lines of symmetry as a square.
→ Answer: You can draw a regular cross (+) or a regular octagon. Both can have 4 lines of symmetry like a square.

(iii) Does a spiral have rotational symmetry of order greater than 1?
→ Answer: No

Explanation: A spiral has rotational pattern but not exact symmetry — it doesn’t look identical after a certain degree of rotation.

(iv) How many lines of symmetry does each of the two set squares in the geometry box have?
→ Answer:

• 45°–45°–90° set square: 1 line

• 30°–60°–90° set square: 0 lines

Explanation: The first has reflection symmetry along the perpendicular bisector of the right angle; the second does not.

(v) How many lines of symmetry does the Indian national flag have?
→ Answer: 1 line (vertical, through the center of the Ashoka Chakra)

Explanation: The three horizontal bands are symmetric top to bottom only if the Ashoka Chakra is centered.

(vi) Draw any shape that has reflection symmetry but no rotational symmetry greater than 1.
→ Answer: An isosceles triangle fits this.

(vii) Among the letters E, X, F, G, H, T, R, U, identify the letters having rotational symmetry and find their order of rotational symmetry:

• X → Order 2

• H → Order 2

• U → Order 2

Other letters (E, F, G, T, R) do not have rotational symmetry beyond order 1.

(viii) Name an irregular polygon (all sides do not have the same length):

• (a) Having reflection symmetry → Isosceles trapezium

• (b) Not having reflection symmetry → Scalene triangle

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Two marks questions (2 x 2 =04 marks)

1  Draw stars having five, six and seven arms. Find out whether each has rotational symmetry and if so, of what order. 

⭐ Five-arm star:

• A regular 5-point star (like the one on many flags).

• Rotational Symmetry: Yes

• Order: 5

You can rotate it 72°, 144°, 216°, 288°, and 360°, and it looks the same each time.

⭐ Six-arm star:

• Can be drawn by overlapping two equilateral triangles (like the Star of David).

• Rotational Symmetry: Yes

• Order: 6

It looks the same every 60° rotation.

⭐ Seven-arm star:

• A regular star with 7 equally spaced points (harder to draw perfectly by hand).

• Rotational Symmetry: Yes

• Order: 7

It repeats every 360° ÷ 7 ≈ 51.43°

2. Draw the line(s) of symmetry and write the order of rotational symmetry:

(i) House Shape (Pentagon with triangle on top):

• Lines of symmetry: 1 (vertical line down the center)

• Order of rotational symmetry: 1

It looks the same only after a full 360° rotation.

(ii) 5-pointed star:

• Lines of symmetry: 5 (each passing through a point and opposite indentation)

• Order of rotational symmetry: 5

Rotational symmetry every 72° (360° ÷ 5).

(iii) Regular Pentagon with 5 circles on vertices:

• Lines of symmetry: 5

• Order of rotational symmetry: 5

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Three-mark questions: 

Find the order of rotational symmetry of the following figures:

(i) Letter Z shape with embellishment:

• Order of rotational symmetry: 2

It looks the same after 180°.

(ii) Star-shaped polygon (likely regular):

• Order of rotational symmetry: 4

It repeats every 90°.

(iii) Plus-shaped design with 4 arms:

• Order of rotational symmetry: 4

Same after 90°, 180°, 270°, and 360°.

(iv) Overlapping equilateral triangles (Star of David):

• Order of rotational symmetry: 6

Rotational symmetry every 60°. 

Letter	Number of Lines of Symmetry	Order of Rotational Symmetry
B	1 (vertical)	1
E	1 (vertical)	1
H	2 (vertical and horizontal)	2
M	1 (vertical)	1
N	0	1
O	Infinite	Infinite (or undefined / all angles)
Z	0	2

Notes:

• B, E, M: Only have vertical symmetry.

• H: Symmetrical both vertically and horizontally, and looks the same after a 180° rotation.

• N and Z: Have no lines of symmetry, but Z has rotational symmetry of order 2 (180°).

• O: A perfect circle has infinite symmetry lines and infinite rotational symmetry.

Collect Interesting Mathematical facts from Magazines, News Papers etc.,

 

Mathematical Facts for Students

1. Zero (0) was invented in India – The concept of zero as a number was developed by Indian mathematician Brahmagupta in the 7th century.

2. A "googol" is a 1 followed by 100 zeros – It’s way bigger than the number of atoms in the observable universe!

3. Pi (π) is an irrational number – Its decimal representation never ends or repeats. The first few digits are 3.14159...

4. The Fibonacci sequence appears in nature – You can find it in the pattern of sunflower seeds, pinecones, and nautilus shells.

5. A perfect number equals the sum of its proper divisors – Example: 28 = 1 + 2 + 4 + 7 + 14.

6. Mathematics is the foundation of encryption – Modern banking and online security rely on number theory.

7. There are infinitely many prime numbers – This was proven by the Greek mathematician Euclid over 2,000 years ago.

8. The number “e” (2.718...) is just as important as π – It's the base of natural logarithms and appears in growth models.

9. Some numbers are palindromes – For example, 121 and 1331 read the same forward and backward.

10. The Pythagorean Theorem is used in construction and navigation – It applies to any right-angled triangle: a²+b² =c²${\mathrm{<br>}}^{}$

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11. A Möbius strip has only one side and one edge – It's a famous object in topology, a branch of mathematics.

12. A circle has the smallest perimeter for a given area – That’s why bubbles are spherical!

13. The number 1729 is the Hardy–Ramanujan number – It’s the smallest number expressible as the sum of two cubes in two different ways.

14. There are patterns in multiplication – Example: $9 × 1 = 9$, $9 × 2 = 18$, $9 × 3 = 27$... digits of products add to 9!

15. Math can describe music – Rhythm, harmony, and scales are based on mathematical ratios.

16. Probability theory helps forecast weather and insurance risks – It’s used in everything from weather apps to actuarial science.

17. Infinity is not a number – it's a concept – There are even different sizes of infinity in set theory!

18. Hexagons are the most efficient shape for tiling – That’s why bees use hexagons in honeycombs.

19. The golden ratio (~1.618) is found in art and architecture – It’s believed to create pleasing proportions.

20. Sudoku is based entirely on logic and combinatorics – Solving them builds strong pattern recognition skills.

21. Additional Mathematical Gems

21. The number 0.999… equals 1.
    Because $1 - 0.999\ldots = 0$, the repeating‐decimal form is exactly the same real number as 1.

22. “Four” is the only English number name with the same number of letters as its value.

23. A Klein bottle is a one‑sided surface with no “inside” or “outside.”
    Unlike the Möbius strip, it can exist only in four‑dimensional space without self‑intersection.

24. There are exactly five Platonic solids.
    These perfectly regular 3‑D shapes (tetrahedron, cube, octahedron, dodecahedron, icosahedron) were proved by the Greeks to be the only possible ones.

25. Benford’s Law predicts leading digits in real‑world data.
    In many data sets, the digit 1 appears as the first digit about 30 % of the time—useful for detecting fraud.

26. A circle’s area and circumference both involve π, yet π cancels out in the ratio $\frac{C^2}{4A}=1$.
    This neat identity shows circumference $C$ and area $A$ are tightly linked.

27. The “Birthday Paradox” shows how probability defies intuition.
    In a group of 23 people, there’s about a 50 % chance that two share the same birthday.

28. There are more possible chess games than atoms in the observable universe.
    The estimated game‑tree complexity of chess is roughly $10^{120}$.

29. The Mandelbrot set has infinite perimeter but finite area.
    Its boundary is a classic example of a fractal—infinitely detailed no matter how much you zoom in.

30. Most real numbers cannot be written down.
    Because there are uncountably many reals but only countably many finite strings, almost every real number is “unnameable

31. ---

    🧠 Number Theory & Arithmetic

    1. Zero is the only number that can't be represented in Roman numerals.

    2. A 'googol' is 10 to the power of 100.

    3. The Fibonacci sequence appears in biological settings like pine cones and flower petals.

    4. The number π (pi) has been calculated to over 31 trillion digits.

    5. The symbol for infinity (∞) was introduced by John Wallis in 1655.

    6. Prime numbers are the building blocks of the integers.

    7. The Pythagorean Theorem only applies to right-angled triangles.

    8. A palindrome number reads the same forwards and backwards, like 121 or 1331.

    9. 'e' is an irrational number, approximately equal to 2.718.

    10. There are infinitely many prime numbers.

    11. A circle has the smallest perimeter for a given area.

    12. Most real numbers are irrational.

    13. A Möbius strip has only one side and one boundary.

    14. The number 1729 is known as the Hardy-Ramanujan number.

    15. The golden ratio is approximately 1.618 and appears in art and nature.

    16. A Klein bottle is a non-orientable surface.

    17. The sum of angles in a triangle is 180 degrees in Euclidean geometry.

    18. There are only five Platonic solids.

    19. The Mandelbrot set is a famous fractal.

    20. The number 0.999... is exactly equal to 1.

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    🔢 Algebra & Geometry

    21. The quadratic formula solves any quadratic equation.

    22. Euler's formula relates complex exponentials to trigonometric functions.

    23. The area of a circle is π times the radius squared.

    24. The volume of a sphere is (4/3)π times the radius cubed.

    25. The angles of a triangle add up to 180 degrees in Euclidean space.

    26. A regular polygon has all sides and angles equal.

    27. The Pythagorean triple (3, 4, 5) satisfies a² + b² = c².

    28. The golden rectangle has sides in the golden ratio.

    29. The sum of the interior angles of an n-gon is (n-2)×180 degrees.

    30. The distance formula in coordinate geometry derives from the Pythagorean theorem.

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    📐 Calculus & Analysis

    31. Calculus was developed independently by Newton and Leibniz.

    32. The derivative measures the rate of change of a function.

    33. The integral calculates the area under a curve.

    34. The Fundamental Theorem of Calculus links differentiation and integration.

    35. A function is continuous if it has no breaks or holes.

    36. A function is differentiable if it has a derivative at every point in its domain.

    37. The limit of a function describes its behavior near a specific point.

    38. The chain rule is used to differentiate composite functions.

    39. The Mean Value Theorem guarantees a point where the instantaneous rate equals the average rate.

    40. Taylor series approximate functions using polynomials.

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    📊 Probability & Statistics

    41. The probability of an event is a measure between 0 and 1.

    42. The expected value is the average outcome of a random variable.

    43. The Law of Large Numbers states that averages converge to expected values as sample size increases.

    44. The Central Limit Theorem explains why many distributions are approximately normal.

    45. A normal distribution is symmetric and bell-shaped.

    46. Standard deviation measures the spread of data around the mean.

    47. Variance is the square of the standard deviation.

    48. Correlation measures the strength of a linear relationship between variables.

    49. Regression analysis estimates relationships among variables.

    50. Bayes' Theorem updates probabilities based on new information.

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    🧩 Recreational Mathematics

    51. Magic squares have rows, columns, and diagonals summing to the same number.

    52. Sudoku is a logic-based number-placement puzzle.

    53. The Tower of Hanoi is a mathematical puzzle involving moving disks.

    54. The Four Color Theorem states that four colors suffice to color any map.

    55. The Seven Bridges of Königsberg problem led to graph theory.

    56. A knight's tour is a sequence of moves of a knight on a chessboard visiting every square once.

    57. The Game of Life is a cellular automaton devised by John Conway.

    58. Penrose tilings are non-periodic tilings that cover the plane.

    59. The Monty Hall problem illustrates counterintuitive probability.

    60. Zeno's paradoxes challenge the concept of motion and infinity.

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    🌐 Mathematical History

    61. Euclid's "Elements" is one of the most influential works in mathematics.

    62. Archimedes discovered principles of leverage and buoyancy.

    63. Pythagoras is credited with the Pythagorean theorem.

    64. Hypatia was one of the first female mathematicians.

    65. Al-Khwarizmi's works introduced algebra to Europe.

    66. Fibonacci introduced the Hindu-Arabic numeral system to Europe.

    67. Descartes developed Cartesian coordinates.

    68. Gauss made significant contributions to number theory.

    69. Ramanujan made substantial contributions to mathematical analysis.

    70. Turing laid the foundations of computer science.

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    🔍 Advanced Topics

    71. Topology studies properties preserved under continuous deformations.

    72. Set theory is the study of collections of objects.

    73. Group theory studies algebraic structures known as groups.

    74. Number theory deals with the properties of integers.

    75. Combinatorics studies counting, arrangement, and combination.

    76. Graph theory studies networks of connected nodes.

    77. Chaos theory studies systems sensitive to initial conditions.

    78. Fractals are complex patterns that are self-similar across scales.

    79. Cryptography uses mathematics to secure information.

    80. Mathematical logic studies formal systems and proofs.

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    🎓 Mathematical Applications

    81. Mathematics is essential in engineering and physics.

    82. Statistics is crucial in social sciences and medicine.

    83. Algorithms are fundamental in computer science.

    84. Mathematical models predict weather patterns.

    85. Economics uses mathematics to model markets.

    86. Operations research optimizes complex systems.

    87. Mathematics is used in cryptography for secure communication.

    88. Mathematics models population growth in biology.

    89. Mathematics helps in image and signal processing.

    90. Mathematics is used in architecture and design.

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    🧠 Fun Facts

    91. A 'googolplex' is 10 to the power of a googol.

    92. The word 'hundred' comes from the old Norse term 'hundrath'.

    93. The number 4 is the only number with the same number of letters as its value.

    94. In a group of 23 people, there's a 50% chance two share a birthday.

    95. The number 6174 is known as Kaprekar's constant.

    96. The number 9 has a unique property: any number multiplied by 9, the digits add up to 9.

    97. The word 'mathematics' comes from the Greek word 'mathema'.

    98. A 'palindromic number' reads the same backward and forward.

    99. The number 1089 has a unique property when reversed and subtracted.

    100. The number 73 is the 21st prime number, and its mirror, 37, is the 12th prime number.

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Proportion word problems with full solutions:

DOWNLOAD HERE - PDF FILE

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1. A pack of 4 pens costs $6. How much would 10 pens cost?

Solution:
Cost per pen = $6 ÷ 4 = $1.50
Cost for 10 pens = 10 × $1.50 = $15
✅ Answer: c) $15

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2. A bakery sells 3 cupcakes for $9. How much for 7 cupcakes?

Solution:
Cost per cupcake = $9 ÷ 3 = $3
Cost for 7 cupcakes = 7 × $3 = $21
✅ Answer: b) $21

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3. 6 notebooks cost $18. How much would 2 notebooks cost?

Solution:
Cost per notebook = $18 ÷ 6 = $3
Cost for 2 notebooks = 2 × $3 = $6
✅ Answer: c) $6

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4. A store offers 10 pencils for $5. What would 25 pencils cost?

Solution:
Cost per pencil = $5 ÷ 10 = $0.50
Cost for 25 pencils = 25 × $0.50 = $12.50
✅ Answer: b) $12.50

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5. 8 chocolate bars cost $16. How much do 5 chocolate bars cost?

Solution:
Cost per bar = $16 ÷ 8 = $2
Cost for 5 bars = 5 × $2 = $10
✅ Answer: c) $10

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6. A bundle of 12 apples costs $24. What’s the cost of 6 apples?

Solution:
Cost per apple = $24 ÷ 12 = $2
Cost for 6 apples = 6 × $2 = $12
✅ Answer: b) $12

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7. 7 liters of juice cost $14. What is the price for 3 liters?

Solution:
Cost per liter = $14 ÷ 7 = $2
Cost for 3 liters = 3 × $2 = $6
✅ Answer: b) $6

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8. A box of 9 markers costs $27. How much would 4 markers cost?

Solution:
Cost per marker = $27 ÷ 9 = $3
Cost for 4 markers = 4 × $3 = $12
✅ Answer: c) $12

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9. You get 2 movie tickets for $18. How much would 5 tickets cost?

Solution:
Cost per ticket = $18 ÷ 2 = $9
Cost for 5 tickets = 5 × $9 = $45
✅ Answer: b) $45

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10. A grocery store sells 6 cans of soup for $9. What is the cost of 10 cans?

Solution:
Cost per can = $9 ÷ 6 = $1.50
Cost for 10 cans = 10 × $1.50 = $15
✅ Answer: c) $15

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proportion word problems with full solutions 

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1. A recipe calls for 3 cups of flour to make 12 cookies.

How many cups are needed for 36 cookies?

Solution:
Set up proportion:
$\frac{3 \text{ cups}}{12 \text{ cookies}} = \frac{x \text{ cups}}{36 \text{ cookies}}$
Cross-multiply:
$12x = 3 × 36 = 108$
$x = \frac{108}{12} = 9$
✅ Answer: 9 cups

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2. A smoothie recipe uses 2 bananas for 4 servings.

How many bananas are needed for 10 servings?

Solution:
$\frac{2}{4} = \frac{x}{10} \Rightarrow 4x = 20 \Rightarrow x = 5$
✅ Answer: 5 bananas

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3. It takes 5 cups of rice to serve 8 people.

How many cups are needed to serve 20 people?

Solution:
$\frac{5}{8} = \frac{x}{20} \Rightarrow 8x = 100 \Rightarrow x = 12.5$
✅ Answer: 12.5 cups

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4. A recipe makes 6 muffins using 2 eggs.

How many eggs are needed for 18 muffins?

Solution:
$\frac{2}{6} = \frac{x}{18} \Rightarrow 6x = 36 \Rightarrow x = 6$
✅ Answer: 6 eggs

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5. 4 tablespoons of sugar make 8 cups of lemonade.

How many tablespoons are needed for 20 cups?

Solution:
$\frac{4}{8} = \frac{x}{20} \Rightarrow 8x = 80 \Rightarrow x = 10$
✅ Answer: 10 tablespoons

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6. A cake recipe uses 1.5 cups of milk for 6 servings.

How much milk is needed for 18 servings?

Solution:
$\frac{1.5}{6} = \frac{x}{18} \Rightarrow 6x = 27 \Rightarrow x = 4.5$
✅ Answer: 4.5 cups

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7. A soup recipe needs 2.5 liters of water for 5 bowls.

How much for 8 bowls?

Solution:
$\frac{2.5}{5} = \frac{x}{8} \Rightarrow 5x = 20 \Rightarrow x = 4$
✅ Answer: 4 liters

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8. 6 scoops of ice cream serve 3 people.

How many scoops for 9 people?

Solution:
$\frac{6}{3} = \frac{x}{9} \Rightarrow 3x = 54 \Rightarrow x = 18$
✅ Answer: 18 scoops

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9. A batch of dough uses 4 cups of flour to make 24 rolls.

How much flour is needed for 60 rolls?

Solution:
$\frac{4}{24} = \frac{x}{60} \Rightarrow 24x = 240 \Rightarrow x = 10$
✅ Answer: 10 cups

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10. 5 liters of paint covers 15 square meters.

How much paint is needed for 45 square meters?

Solution:
$\frac{5}{15} = \frac{x}{45} \Rightarrow 15x = 225 \Rightarrow x = 15$
✅ Answer: 15 liters

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