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Write 50 mixed junior high school and senior high school mathematics quizzing competition questions with their respective answer in shoving step by step solving

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Sure! Below are 50 mixed mathematics questions suitable for junior high and senior high school students, along with step-by-step solutions for each.

Questions and Solutions

Question 1

What is \( 7x + 2 = 23 \) for \( x \)?

Solution:

  1. Subtract 2 from both sides: \[ 7x = 21 \]
  2. Divide by 7: \[ x = 3 \]

Question 2

Find the area of a triangle with base 10 cm and height 5 cm.

Solution:

  1. Use the area formula \( A = \frac{1}{2} \times \text{base} \times \text{height} \): \[ A = \frac{1}{2} \times 10 \times 5 = 25 \text{ cm}^2 \]

Question 3

What is the value of \( 5^2 - 3^2 \)?

Solution:

  1. Calculate \( 5^2 = 25 \) and \( 3^2 = 9 \): \[ 5^2 - 3^2 = 25 - 9 = 16 \]

Question 4

Solve for \( y \) in the equation \( 3y - 7 = 11 \).

Solution:

  1. Add 7 to both sides: \[ 3y = 18 \]
  2. Divide by 3: \[ y = 6 \]

Question 5

What is \( 12 \div (3 \times 2) \)?

Solution:

  1. Calculate inside the parentheses first: \[ 3 \times 2 = 6 \]
  2. Now divide: \[ 12 \div 6 = 2 \]

Question 6

If \( f(x) = 2x + 3 \), what is \( f(4) \)?

Solution:

  1. Substitute \( x = 4 \) into the function: \[ f(4) = 2(4) + 3 = 8 + 3 = 11 \]

Question 7

What is the slope of the line that passes through the points (1, 2) and (3, 8)?

Solution:

  1. Use the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \): \[ m = \frac{8 - 2}{3 - 1} = \frac{6}{2} = 3 \]

Question 8

Solve for \( x \) in the equation \( 2(x - 3) = 16 \).

Solution:

  1. Distribute the 2: \[ 2x - 6 = 16 \]
  2. Add 6 to both sides: \[ 2x = 22 \]
  3. Divide by 2: \[ x = 11 \]

Question 9

What is the perimeter of a rectangle with length 8 cm and width 3 cm?

Solution:

  1. Use the perimeter formula \( P = 2(\text{length} + \text{width}) \): \[ P = 2(8 + 3) = 2(11) = 22 \text{ cm} \]

Question 10

Calculate \( (4 + 3)^2 \).

Solution:

  1. Calculate inside the parentheses first: \[ 4 + 3 = 7 \]
  2. Now square the result: \[ 7^2 = 49 \]

Question 11

Find \( x \) such that \( 4x + 2 = 18 \).

Solution:

  1. Subtract 2 from both sides: \[ 4x = 16 \]
  2. Divide by 4: \[ x = 4 \]

Question 12

What is the value of \( 3(2 + 5) - 4 \)?

Solution:

  1. Calculate inside the parentheses: \[ 2 + 5 = 7 \]
  2. Then multiply: \[ 3(7) = 21 \]
  3. Subtract 4: \[ 21 - 4 = 17 \]

Question 13

What is the value of \( x \) if \( 5x - 4 = 21 \)?

Solution:

  1. Add 4 to both sides: \[ 5x = 25 \]
  2. Divide by 5: \[ x = 5 \]

Question 14

Find \( x \) such that \( x^2 = 64 \).

Solution:

  1. Take the square root of both sides: \[ x = \pm 8 \]

Question 15

What is the sum of the angles in a triangle?

Solution:

  1. The sum of the angles in any triangle is: \[ 180^\circ \]

Question 16

A bag contains 4 red, 3 blue, and 5 green marbles. What fraction of the marbles are red?

Solution:

  1. Total marbles = \( 4 + 3 + 5 = 12 \).
  2. Fraction of red marbles: \[ \frac{4}{12} = \frac{1}{3} \]

Question 17

What is the volume of a cube with side length 3 cm?

Solution:

  1. Use the volume formula \( V = s^3 \): \[ V = 3^3 = 27 \text{ cm}^3 \]

Question 18

If the angle of a triangle is 60° and another is 90°, what is the third angle?

Solution:

  1. The sum of angles in a triangle is 180°: \[ 180 - 60 - 90 = 30° \]

Question 19

What is the next number in the sequence: 2, 4, 8, 16, __?

Solution:

  1. The sequence is doubling each time: \[ 16 \times 2 = 32 \]

Question 20

Solve for \( x \) in \( \frac{x}{4} + 5 = 9 \).

Solution:

  1. Subtract 5 from both sides: \[ \frac{x}{4} = 4 \]
  2. Multiply by 4: \[ x = 16 \]

Question 21

What is the value of \( 2^3 + 3^2 \)?

Solution:

  1. Calculate \( 2^3 = 8 \) and \( 3^2 = 9 \): \[ 2^3 + 3^2 = 8 + 9 = 17 \]

Question 22

Find the roots of the equation \( x^2 - 5x + 6 = 0 \).

Solution:

  1. Factor: \[ (x - 2)(x - 3) = 0 \]
  2. Set each factor to zero: \[ x - 2 = 0 \implies x = 2 \] \[ x - 3 = 0 \implies x = 3 \]

Question 23

What is 15% of 200?

Solution:

  1. Calculate: \[ 0.15 \times 200 = 30 \]

Question 24

Find the median of the numbers 1, 3, 3, 6, 7, 8, 9.

Solution:

  1. Arrange numbers (already arranged), count: Total numbers = 7 (odd).
  2. Median is the middle number: \[ \text{Median} = 6 \]

Question 25

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

Solution:

  1. Multiples of 4: 4, 8, 12, 16...
  2. Multiples of 6: 6, 12, 18...
  3. LCM = 12.

Question 26

If \( x + 3 = 17 \), what is \( x \)?

Solution:

  1. Subtract 3: \[ x = 14 \]

Question 27

What is the product of -3 and 7?

Solution:

  1. Multiply: \[ -3 \times 7 = -21 \]

Question 28

How many degrees are in a complete circle?

Solution:

  1. There are: \[ 360^\circ \]

Question 29

Solve for \( a \) in \( 8a = 64 \).

Solution:

  1. Divide by 8: \[ a = 8 \]

Question 30

What is \( 3! \) (3 factorial)?

Solution:

  1. Calculate \( 3! = 3 \times 2 \times 1 = 6 \).

Question 31

If the radius of a circle is 7 cm, what is the area?

Solution:

  1. Use the area formula \( A = \pi r^2 \): \[ A = \pi (7^2) = 49\pi \approx 153.94 \text{ cm}^2 \]

Question 32

What is the derivative of \( f(x) = x^2 \)?

Solution:

  1. Derivative: \[ f'(x) = 2x \]

Question 33

What is the sum of the interior angles of a hexagon?

Solution:

  1. Use the formula \( (n - 2) \times 180 \): \[ (6 - 2) \times 180 = 720^\circ \]

Question 34

Find \( \sqrt{64} \).

Solution:

  1. Calculate the square root: \[ \sqrt{64} = 8 \]

Question 35

What is the length of the hypotenuse in a right triangle with legs measuring 6 cm and 8 cm?

Solution:

  1. Use the Pythagorean theorem: \[ c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ cm} \]

Question 36

What is the equation of a line with slope 2 passing through the point (1, 3)?

Solution:

  1. Use point-slope form: \[ y - 3 = 2(x - 1) \implies y = 2x + 1 \]

Question 37

Calculate the mean of the numbers 2, 3, 5, 7, and 10.

Solution:

  1. Sum: \( 2 + 3 + 5 + 7 + 10 = 27 \)
  2. Mean: \( \frac{27}{5} = 5.4 \)

Question 38

What value of \( x \) satisfies \( 2^x = 16 \)?

Solution:

  1. Recognize \( 16 = 2^4 \): \[ x = 4 \]

Question 39

What is the sum of the first five prime numbers?

Solution:

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

Question 40

If \( 5x + 3 = 23 \), find \( x \).

Solution:

  1. Subtract 3: \[ 5x = 20 \]
  2. Divide by 5: \[ x = 4 \]

Question 41

What is the smallest prime number?

Solution:

  1. The smallest prime is: \[ 2 \]

Question 42

Calculate \( 8 \times (3 + 4) \).

Solution:

  1. Inside the parentheses first: \[ 3 + 4 = 7 \]
  2. Then multiply: \[ 8 \times 7 = 56 \]

Question 43

What is the GCD of 24 and 36?

Solution:

  1. Prime factorization:
    • \( 24 = 2^3 \times 3 \)
    • \( 36 = 2^2 \times 3^2 \)
  2. GCD is the lowest power of common factors: \[ GCD = 2^2 \times 3 = 12 \]

Question 44

If a car travels 60 miles in 1 hour, how far will it travel in 2.5 hours?

Solution:

  1. Distance = speed × time: \[ \text{Distance} = 60 \times 2.5 = 150 \text{ miles} \]

Question 45

What is \( 10^3 \)?

Solution:

  1. Calculate: \[ 10^3 = 1000 \]

Question 46

How many edges does a cube have?

Solution:

  1. A cube has: \[ 12 \text{ edges} \]

Question 47

What is the value of \( 20 - 3(4 + 2) \)?

Solution:

  1. Calculate inside parentheses first: \[ 4 + 2 = 6 \]
  2. Multiply: \[ 3 \times 6 = 18 \]
  3. Subtract: \[ 20 - 18 = 2 \]

Question 48

Find the value of \( \log_{10} 1000 \).

Solution:

  1. Since \( 1000 = 10^3 \): \[ \log_{10} 1000 = 3 \]

Question 49

What is the equation of a quadratic function in vertex form for vertex (2, -5) and passes through (3, -2)?

Solution:

  1. Vertex form is \( f(x) = a(x - h)^2 + k \): Substitute vertex (h=2, k=-5): \[ f(x) = a(x - 2)^2 - 5 \]
  2. Use point (3, -2) to solve for \( a \): \[ -2 = a(1)^2 - 5 \] \[ a = 3 \] \[ \text{Final equation: } f(x) = 3(x - 2)^2 - 5 \]

Question 50

If \( x + y = 10 \) and \( x - y = 2 \), find \( x \) and \( y \).

Solution:

  1. Add the equations: \[ (x + y) + (x - y) = 10 + 2 \implies 2x = 12 \implies x = 6 \]
  2. Substitute \( x \) into \( x + y = 10 \): \[ 6 + y = 10 \implies y = 4 \]

These questions cover a variety of topics appropriate for junior and senior high school levels, ranging from basic arithmetic operations to algebra, geometry, and calculus. Feel free to adjust the difficulty or topics as needed for your competition!