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Hey
students I am teacher of math and physics I hope you understand my opinion in this subjects
I am a very friendly teacher you ever met I am also same age of your I believe in study and
friendly environment with students I don't believe in strictness I hope you understand my point of view
Sure! Here are ten tricky maths problems along with their solutions:

### 1. **Algebra: Solve for x**
\\
3x + 5 = 20
\\
**Solution:**
\\
3x = 20 - 5 \\
3x = 15 \\
x = 5
\\
End
x^2 - 4x - 5 = 0
]
Solution:
Applying the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):
[
a = 1, b = -4, c = -5 \\
x = \frac{4 \pm \sqrt{(-4)^2 - 4 \cdot 1 \cdot (-5)}}{2 \cdot 1} \\
x = \\frac{4 \pm \sqrt{16 + 20}}{2} \\\\
x = \\frac{4 \pm \sqrt{36}}{2} \\\\
x = \\frac{4 \pm 6}{2} \\\\
x = 5 \\text{ or } -1
]

### 3. **Calculus: Derivative**
Calculate the derivative of f(x) = 3x^3 - 5x^2 + 2x - 4.
Solution:
[
f'(x) = 9x^2 - 10x + 2
]

### 4. **Geometry: Area of a Circle**
Find the area of a circle with a radius of 7 cm.
Solution:
[
A = πr^2 = π(7^2) = 49π cm^2
]

### 5. **Probability: Coin Toss
What is the probability of getting exactly 3 heads in 5 tosses of a fair coin?
**Solution:**
\[
P(X = 3) = \\\\binom{5}{3} \\\\left(\\\\frac{1}{2}\\\\right)^5 = 10 \\\\cdot \\\\frac{1}{32} = \\frac{10}{32} = \\frac{5}{16}\
\\\\]

### 6. **Statistics: Mean**
Find the mean of the following numbers: 2, 4, 6, 8, 10.
**Solution:**
\\\\[:]
Mean = (2 + 4 + 6 + 8 + 10)/5 = (30)/5 = 6
]

### 7. Trigonometry: Sin and Cos
If sin(x) = 3/5, find cos(x).
Solution:
From the Pythagorean identity sin2(x)+cos2(x) = 1:
[cos2(x) = 1 - (3/5)2 = 1 - 9/25 = 16/25
\\\\cos(x) = \\\\pm \\\\frac{4}{5}
]

### 8. **Exponents: Simplify**
Simplify \\\\(x^3 \\\\cdot x^{-5}\\\\).
Solution:
\\\\\
x^{3 - 5} = x^{-2} = \frac{1}{x^2}
\\\\\

### 9. **Inequalities: Solve**
Solve the inequality \\\\(2x - 3 < 5\\\\).
Solution:
\\\\\
2x < 5 + 3 \|
2x < 8 \\
x < 4
]

### 10. **Logarithms: Solve for x**
Solve for \(x\) in the equation \(2^x = 16\).
**Solution:**
[
16 = 2^4 \\
x = 4
]

Subjects

  • Math Grade 6-Grade 9

  • Physics (10th Class)

Experience

No experience mentioned.

Education

  • Secondary (May, 2022–now) from white house english school karachi

Fee details

    Rs1,500–2,000/week (US$5.38–7.18/week)

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