Write 50 junior high school mathematics quizzing competition questions with their respective answers using step by step method

Answer 1

Below is a list of 50 junior high school mathematics competition questions along with their respective step-by-step solutions:

Questions and Answers

1. Question 1: What is the value of \(7 \times (3 + 2)\)?

   Answer:

   • Step 1: Solve inside the parentheses: \(3 + 2 = 5\)
   • Step 2: Multiply: \(7 \times 5 = 35\)

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2. Question 2: If \(x = 4\), what is the value of \(2x^2 + 3x - 5\)?

   Answer:

   • Step 1: Substitute \(x\): \(2(4^2) + 3(4) - 5\)
   • Step 2: Calculate \(4^2 = 16\)
   • Step 3: \(2(16) + 12 - 5 = 32 + 12 - 5 = 39\)

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3. Question 3: Solve for \(y\): \(3y - 7 = 2y + 5\)

   Answer:

   • Step 1: Subtract \(2y\) from both sides: \(3y - 2y - 7 = 5\)
   • Step 2: \(y - 7 = 5\)
   • Step 3: Add 7 to both sides: \(y = 12\)

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4. Question 4: What is the area of a triangle with a base of 10 cm and height of 5 cm?

   Answer:

   • Step 1: Use area formula: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\)
   • Step 2: Calculate: \( \frac{1}{2} \times 10 \times 5 = 25 , \text{cm}^2\)

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5. Question 5: What is \(15% \) of 200?

   Answer:

   • Step 1: Convert percentage to decimal: \(15% = 0.15\)
   • Step 2: Multiply: \(0.15 \times 200 = 30\)

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6. Question 6: What is the least common multiple (LCM) of 4 and 6?

   Answer:

   • Step 1: List multiples of 4: \(4, 8, 12, 16, \ldots\)
   • Step 2: List multiples of 6: \(6, 12, 18, \ldots\)
   • Step 3: The first common multiple is \(12\)

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7. Question 7: What is the equation of a line in slope-intercept form with a slope of 2 and y-intercept of -3?

   Answer:

   • Step 1: Use the formula \(y = mx + b\)
   • Step 2: Substitute \(m = 2\) and \(b = -3\):
   • Step 3: The equation is \(y = 2x - 3\)

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8. Question 8: Simplify: \(3(a + 2) - 5\).

   Answer:

   • Step 1: Distribute: \(3a + 6 - 5\)
   • Step 2: Combine like terms: \(3a + 1\)

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9. Question 9: What is the volume of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm?

   Answer:

   • Step 1: Use the volume formula: \( \text{Volume} = l \times w \times h\)
   • Step 2: Calculate: \(4 \times 3 \times 5 = 60 , \text{cm}^3\)

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10. Question 10: What is \(8^2 - 3^2\)?

    Answer:

    • Step 1: Calculate \(8^2 = 64\) and \(3^2 = 9\)
    • Step 2: Subtract: \(64 - 9 = 55\)

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11. Question 11: How many sides does a polygon have if the sum of its interior angles is 540 degrees?

    Answer:

    • Step 1: Use the formula: \( \text{Sum} = (n-2) \times 180\)
    • Step 2: Set up equation: \( (n-2) \times 180 = 540\)
    • Step 3: Divide by 180: \(n - 2 = 3\)
    • Step 4: Solve: \(n = 5\) (Pentagon)

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12. Question 12: Calculate \( \frac{3}{4} + \frac{1}{2} \).

    Answer:

    • Step 1: Find a common denominator: \( \frac{1}{2} = \frac{2}{4}\)
    • Step 2: Add fractions: \( \frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1.25\)

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13. Question 13: What is the distance between the points (1, 2) and (4, 6)?

    Answer:

    • Step 1: Use distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
    • Step 2: \(d = \sqrt{(4 - 1)^2 + (6 - 2)^2}\)
    • Step 3: \(= \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\)

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14. Question 14: If \(f(x) = 3x + 4\), what is \(f(2)\)?

    Answer:

    • Step 1: Substitute \(x = 2\): \(f(2) = 3(2) + 4\)
    • Step 2: \(6 + 4 = 10\)

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15. Question 15: How many degrees are in the angles of a triangle?

    Answer:

    • Step 1: The sum of interior angles of a triangle is always \(180\) degrees.

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16. Question 16: Solve the inequality \(2x + 3 < 7\).

    Answer:

    • Step 1: Subtract 3 from both sides: \(2x < 4\)
    • Step 2: Divide by 2: \(x < 2\)

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17. Question 17: Find the median of the data set: {3, 7, 2, 9, 5}.

    Answer:

    • Step 1: Arrange in order: {2, 3, 5, 7, 9}
    • Step 2: The median (middle value) is \(5\).

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18. Question 18: If a circle has a radius of 3 cm, what is its circumference?

    Answer:

    • Step 1: Use the formula: \(C = 2\pi r\)
    • Step 2: \(C = 2\pi(3) = 6\pi \approx 18.85 , \text{cm}\)

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19. Question 19: Simplify: \(\frac{4x + 8}{4}\).

    Answer:

    • Step 1: Split fraction: \(\frac{4x}{4} + \frac{8}{4}\)
    • Step 2: Simplify: \(x + 2\)

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20. Question 20: Write the expression \(5 + 4x - x\) in simplest form.

    Answer:

    • Step 1: Combine like terms: \(5 + 3x\)

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21. Question 21: If \(2a + 3 = 15\), what is \(a\)?

    Answer:

    • Step 1: Subtract \(3\): \(2a = 12\)
    • Step 2: Divide by \(2\): \(a = 6\)

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22. Question 22: What is the greatest common divisor (GCD) of 18 and 24?

    Answer:

    • Step 1: List the factors:
      • Factors of 18: \(1, 2, 3, 6, 9, 18\)
      • Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
    • Step 2: The greatest common factor is \(6\).

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23. Question 23: What is the value of \( (-3)^3\)?

    Answer:

    • Step 1: Calculate: \((-3) \times (-3) \times (-3) = -27\)

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24. Question 24: Evaluate \(4(3 + 5) - 2^3\).

    Answer:

    • Step 1: Inside parentheses: \(3 + 5 = 8\)
    • Step 2: Multiply: \(4(8) = 32\)
    • Step 3: \(2^3 = 8\)
    • Step 4: Final calculation: \(32 - 8 = 24\)

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25. Question 25: What is the probability of rolling an even number on a standard six-sided die?

    Answer:

    • Step 1: Possible outcomes: \(1, 2, 3, 4, 5, 6\)
    • Step 2: Even numbers: \(2, 4, 6\) (3 outcomes)
    • Step 3: Probability: \( \frac{3}{6} = \frac{1}{2}\)

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26. Question 26: Find \(12^2 + 5^2\).

    Answer:

    • Step 1: Calculate \(12^2 = 144\) and \(5^2 = 25\)
    • Step 2: Add: \(144 + 25 = 169\)

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27. Question 27: What is the square root of 81?

    Answer:

    • Step 1: \( \sqrt{81} = 9\)

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28. Question 28: If a train travels at 60 km/h, how far will it travel in 2 hours?

    Answer:

    • Step 1: Use the formula: Distance = Speed × Time
    • Step 2: Calculate: \(60 , \text{km/h} \times 2 , \text{h} = 120 , \text{km}\)

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29. Question 29: Solve for \(x\): \(5(x - 2) = 15\)

    Answer:

    • Step 1: Distribute: \(5x - 10 = 15\)
    • Step 2: Add 10: \(5x = 25\)
    • Step 3: Divide by 5: \(x = 5\)

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30. Question 30: Calculate \(\frac{3}{5} - \frac{1}{2}\).

    Answer:

    • Step 1: Find a common denominator: (10)
    • Step 2: Convert: \(\frac{3}{5} = \frac{6}{10}, \frac{1}{2} = \frac{5}{10}\)
    • Step 3: Subtract: \(\frac{6}{10} - \frac{5}{10} = \frac{1}{10}\)

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31. Question 31: How many liters are in 3.5 gallons? (1 gallon = 3.78541 liters)

    Answer:

    • Step 1: Calculate: \(3.5 \times 3.78541 \approx 13.248935 , \text{liters}\)

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32. Question 32: If the ratio of boys to girls in a class is 4:3, what fraction of the class are boys?

    Answer:

    • Step 1: Total parts = \(4 + 3 = 7\)
    • Step 2: Fraction of boys = \(\frac{4}{7}\)

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33. Question 33: Evaluate \(5(2x - 3) + 4\) when \(x = 1\).

    Answer:

    • Step 1: Substitute \(x = 1\): \(5(2(1) - 3) + 4\)
    • Step 2: Calculate: \(5(2 - 3) + 4 = 5(-1) + 4 = -5 + 4 = -1\)

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34. Question 34: Solve for \(n\): \(3n + 4 = 1\)

    Answer:

    • Step 1: Subtract 4: \(3n = -3\)
    • Step 2: Divide by 3: \(n = -1\)

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35. Question 35: What is the sum of the angles in a quadrilateral?

    Answer:

    • Step 1: The sum of angles is \(360\) degrees.

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36. Question 36: What is \(9^2 - 6^2\)?

    Answer:

    • Step 1: Calculate \(9^2 = 81\) and \(6^2 = 36\)
    • Step 2: Subtract: \(81 - 36 = 45\)

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37. Question 37: Find the perimeter of a rectangle with length 8 cm and width 5 cm.

    Answer:

    • Step 1: Use the formula: \(P = 2(l + w)\)
    • Step 2: Calculate: \(P = 2(8 + 5) = 2 \times 13 = 26 , \text{cm}\)

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38. Question 38: If \(3(x - 2) = 12\), what is \(x\)?

    Answer:

    • Step 1: Distribute: \(3x - 6 = 12\)
    • Step 2: Add 6: \(3x = 18\)
    • Step 3: Divide by 3: \(x = 6\)

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39. Question 39: Calculate \(7 + 2 \times 4 - 3\).

    Answer:

    • Step 1: Perform multiplication first: \(7 + 8 - 3\)
    • Step 2: Calculate: \(7 + 8 = 15\)
    • Step 3: \(15 - 3 = 12\)

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40. Question 40: If \(a = 2\) and \(b = 3\), find the value of \(2a^3 + b^2\).

    Answer:

    • Step 1: Calculate \(a^3 = 2^3 = 8\) and \(b^2 = 3^2 = 9\)
    • Step 2: Substitute: \(2(8) + 9 = 16 + 9 = 25\)

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41. Question 41: What is \(10^0\)?

    Answer:

    • Step 1: \(10^0 = 1\)

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42. Question 42: Find the value of \( \frac{5}{2} \div \frac{1}{4} \).

    Answer:

    • Step 1: Multiply by the reciprocal: \( \frac{5}{2} \times 4 = \frac{20}{2} = 10\)

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43. Question 43: How many degrees are in each angle of a regular hexagon?

    Answer:

    • Step 1: Use formula \(\frac{(n-2) \times 180}{n}\) for each angle.
    • Step 2: For hexagon \(n = 6\): \( \frac{(6-2) \times 180}{6} = \frac{720}{6} = 120\) degrees.

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44. Question 44: If the equation of a line is \(y = 3x + 1\), what is the y-value when \(x = 2\)?

    Answer:

    • Step 1: Substitute \(x = 2\): \(y = 3(2) + 1 = 6 + 1 = 7\)

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45. Question 45: Simplify \( \frac{12x}{4} \div 3 \).

    Answer:

    • Step 1: \( \frac{12x}{4} = 3x\)
    • Step 2: \(3x \div 3 = x\)

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46. Question 46: Find \(4! (factorial)\).

    Answer:

    • Step 1: Calculate \(4! = 4 \times 3 \times 2 \times 1 = 24\)

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47. Question 47: A bottle has 2/3 of water. If I pour out 1/6, how much water is left?

    Answer:

    • Step 1: Calculate: \( \frac{2}{3} - \frac{1}{6} = \frac{4}{6} - \frac{1}{6} = \frac{3}{6} = \frac{1}{2}\)

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48. Question 48: Find the sum of the first five prime numbers.

    Answer:

    • Step 1: First five primes are: \(2, 3, 5, 7, 11\)
    • Step 2: Sum: \(2 + 3 + 5 + 7 + 11 = 28\)

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49. Question 49: If the perimeter of a square is 36 cm, what is the length of one side?

    Answer:

    • Step 1: \(P = 4s\), where \(s\) is the side length.
    • Step 2: \(36 = 4s\)
    • Step 3: Divide by 4: \(s = 9\)

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50. Question 50: If \(3/4\) of a number \(x\) is equal to 12, what is \(x\)?

    Answer:

    • Step 1: Set up equation: \(\frac{3}{4}x = 12\)
    • Step 2: Multiply both sides by \(\frac{4}{3}\): \(x = 12 \times \frac{4}{3} = 16\)

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Feel free to adjust the difficulty or topics of these problems based on the needs of the competition!