⭐ HIGH SCHOOL MATH – HARD LEVEL (in English)
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I. Algebra – Hard Problems
1. Solve the equation
1. Solve for :
\sqrt{3x + 4} + \sqrt{x - 2} = 10
2. Solve:
2^{x+1} + 2^{x-1} = 20
3. Solve the logarithmic equation:
\log_3 (x+2) + \log_3 (x-1) = 3
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2. Inequalities
4. Solve the inequality:
\frac{x^2 - 9}{x - 2} \ge 3
5. Solve the system:
\begin{cases}
x^2 + y^2 \le 25 \\
y > x + 1
\end{cases}
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II. Calculus (12th grade) – Hard
6. Derivatives
Find :
a)
b)
c)
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7. Find extrema (cực trị)
7. Find the local maximum and minimum of:
y = x^4 - 4x^2 + 3
8. Find all points where the tangent is horizontal for:
y = x^3 - 6x^2 + 9x + 2
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8. Integrals
9. Compute the integral:
\int (3x^2 - 4x + 7)\, dx
10. Compute:
\int \frac{2x + 1}{x^2 + x - 6}\, dx
11. Compute the definite integral:
\int_{0}^{2} x\sqrt{4 - x^2}\, dx
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III. Geometry (Analytic) – Hard
12. Distance & Line Equation
12. Find the equation of the line passing through
A(3, –5) and perpendicular to
.
13. Find the distance from point
P(4, –2) to the line
.
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14. Circle
14. Find the equation of a circle with center
and passing through
.
15. Find intersection points between the line
and the circle
.
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IV. Trigonometry – Hard
16. Solve the equation:
2\sin x \cos x - \sin x = 0
17. Solve:
\cos(2x) = \sin(x)
18. Simplify:
\frac{\sin(3x) - \sin(x)}{\cos(x)}
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V. Word Problems (Ứng dụng) – Hard
19. A car accelerates from rest with acceleration .
How long does it take to reach ?
