Math Problems of the Month

MATH PROBLEMS OF THE MONTH

By Victor Li, 9th grade

For MV students taking a math course not above Alg2/Trig, help (process, not answers) are available at email. To submit a form, go to my homepage, where there is also many useful things. Expect response in 2-3 days.

NEW PROBLEMS for September!!!

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1. 5 points

Find the specified term for the sequence:

4, 9, 14, 19, ....; t₂₁

2. 10 points

If e^{3x + 2} = 5, find x in terms of natural logarithms

3. 10 points

Solve 7^{x - 1} = 49^{4 - x}.

4. 10 points

Solve this system:

x + y + z = 2

x - 2y -z = 2

3x + 2y + z = 2

5. 10 points

Find and simplify the term containing x⁸ in (x - 2y)¹¹

6. 10 points

Find the vertex, focus, directix, and axis of the parabola x² + 10x + 16y - 7 = 0

7. 10 points

Find and equation of the ellipse having foci (5, 2) and (-5, 2) and sum of focal radii 12.

8. 10 points

Solve log_ax + log_a(x - 2) = log_a3.

9. 10 points

Find the sum of the series 1 + 2/3 + 4/9 + 8/27 + .....

10. 15 points

If the absolute value of x is less than 1, find the sum of the series 1 + 2x + 3x² + 4x³ + ....

Challenge: 50 points

Find an equation of a circle that passes through exactly 3 lattice points.