Angas Tutoring
STEM Education
Your Javascript is disabled. Some navigation on this site will not work without Javascript. Please enable Javascript in your browser to enjoy all features of this site.
Home About Us Subjects Tutored FAQ Testimonials Ponder This Contact Us
Algebra Challenge Geometry Challenge Calculus Challenge Physics I Challenge
Math is like love -- a simple idea but it can get complicated.
R. Drabek
R. Drabek
Algebra and Trigonometry Challenge
1. Difficulty: Beginner 
Find the solution for this equation:
Find the solution for this equation:
x = 2
2. Difficulty: Beginner
Write an equation of the line going through point A(-1,6), parallel to the line through points B(3,5) and C(7,13).
Write an equation of the line going through point A(-1,6), parallel to the line through points B(3,5) and C(7,13).
y = 2x + 8
3. Difficulty: Beginner
Solve the equation:
Solve the equation:
x = 512 or x = 1
4. Difficulty: Easy 
Write an equation of the line going through point A(-1,6), equidistant from points B(3,5) and C(7,13).
Write an equation of the line going through point A(-1,6), equidistant from points B(3,5) and C(7,13).
y = (1/2)x + 13/2
5. Difficulty: Easy
Solve inequality:
Solve inequality:
(-3, -2] U (2, 4]
6. Difficulty: Easy
The angle of elevation of the top of a cellular telephone tower from point A on the ground is 20 degrees. From point B, 30 meters closer to the tower, the angle of elevation is 25 degrees. What is the height of the tower?
The angle of elevation of the top of a cellular telephone tower from point A on the ground is 20 degrees. From point B, 30 meters closer to the tower, the angle of elevation is 25 degrees. What is the height of the tower?
49.8m
7. Difficulty: Medium 
Find all asymptotes of this function:
Find all asymptotes of this function:
VA: x = 2, x = 3
HA: y = 0
HA: y = 0
8. Difficulty: Medium
Solve the equation:
Solve the equation:
9. Difficulty: Medium
A passenger train which is x times as fast as a freight train takes x times as long to pass when overtaking the freight train as it takes to pass when the two trains are going in opposite directions. What is the value of x?
A passenger train which is x times as fast as a freight train takes x times as long to pass when overtaking the freight train as it takes to pass when the two trains are going in opposite directions. What is the value of x?
10. Difficulty: Hard 
How many positive integers less than 1000 are divisible neither by 5 nor by 7?
How many positive integers less than 1000 are divisible neither by 5 nor by 7?
686
11. Difficulty: Hard
What is the smallest number divisible by 17 which, divided by any of the numbers from 2 to 16 inclusive, leaves a remainder of 1?
What is the smallest number divisible by 17 which, divided by any of the numbers from 2 to 16 inclusive, leaves a remainder of 1?
7207201
12. Difficulty: Hard
Solve the equation:
Solve the equation:
13. Difficulty: Hard
Solve the equation:
Solve the equation:
14. Difficulty: Hard
Solve the equation:
Solve the equation:
15. Difficulty: Hard
Show that the following function f(x) is determined for all real x and that it is an odd function ( i.e. f(-x) = - f(x) ):
Show that the following function f(x) is determined for all real x and that it is an odd function ( i.e. f(-x) = - f(x) ):
16. Difficulty: Expert 
Find all real solutions (x, y) of the equation
Find all real solutions (x, y) of the equation
17. Difficulty: Expert
Simplify:
Simplify:
18. Difficulty: Expert
Simplify for
:
Simplify for
:
2
19. Difficulty: Expert
Find the value of this expression (no calculator!)
Find the value of this expression (no calculator!)
3
20. Difficulty: Expert
Solve the inequality for 0 < a < 1:
Solve the inequality for 0 < a < 1:
21. Difficulty: Expert
Solve the equation:
Solve the equation:
22. Difficulty: Expert
What is larger, log23 or log35? Do not use a calculator.
What is larger, log23 or log35? Do not use a calculator.
log23 > log35
23. Difficulty: Expert
Show that the following inequality is satisfied for all positive real x:
Show that the following inequality is satisfied for all positive real x:
24. Difficulty: Expert
Show that the following inequality is satisfied for all real a, x > 0, y > 0:
Show that the following inequality is satisfied for all real a, x > 0, y > 0:
25. Difficulty: Expert
Given: two acute angles A and B are such that:
Show that
Given: two acute angles A and B are such that:
Show that
26. Difficulty: Expert
The price of the diamond is proportional to the square of its weight (in carats). The diamond of p carats has been broken into two parts. This leads to a decrease in the overall worth of the diamond k times (1 < k < 2). Find the weights of the two parts (in terms of given quantities p and k ).
The price of the diamond is proportional to the square of its weight (in carats). The diamond of p carats has been broken into two parts. This leads to a decrease in the overall worth of the diamond k times (1 < k < 2). Find the weights of the two parts (in terms of given quantities p and k ).
27. Difficulty: Expert
Solve the equation:
Solve the equation:
1
28. Difficulty: Expert
Solve the equation:
Solve the equation:
29. Difficulty: Expert
Find all real solutions:
Find all real solutions:
x = 4, 548
30. Difficulty: Expert
Find all solutions:
Find all solutions:
31. Difficulty: Expert
Find all solutions (x,y) for the system of equations:
Find all solutions (x,y) for the system of equations:
32. Difficulty: Expert
Solve equation, i.e. express x in terms of a ( a > 0):
Solve equation, i.e. express x in terms of a ( a > 0):
© Copyright Angas Tutoring. All Rights Reserved.