2015 Math Challenge (1st Practice)
Score:__________
Name:_______________________________________ School:_______________________ Instructions: Write your answer on the space provided before each item. Give all fractions in lowest terms and all expressions in expanded form. If there is more than one answer, write all of them. Eliminate negative exponents and rationalize denominators. Give equations of lines in general forms.
________________1. Simplify: -2√
+5√
-4√
________________2. Solve: 62 (3 x - 2 )=324. ________________3. Find all values of x for which x2 -8x +12 > 0. ________________4. Find the equation of the line passing through (-2, -3) and perpendicular to 7x -5y=40. ________________5. Find the sum of 11+22+33+…+330. ________________6. Solve for x: 52x =5 x + 20. ________________7. Solve the system: 2x + y =14 and x + y=10. ________________8. A 13m steel ladder is leaning against a vertical wall, with the bottom of the ladder 5m from the wall. How high is the top of ladder from the ground? ________________9. If a coin is tossed three times, how many ways can the outcome be one head and two tails? _______________10. If 3a • 3b = 35, find the average of a and b. _______________11. In how many ways can 4 girls and 3 boys sit in a row if boys and girls alter? _______________12. Find the domain of the function f(x) =√
.
_______________13. Find the product of the roots of 3x2 -5x+7=0. _______________14. The x-and-y intercepts of a line are -9 and 6 respectively. Find the point on the line whose ordinate is 5. _______________15. Find the equation of the line passing through (3, -10) and whose slope is half the slope of the line 4x-2y+1=0. _______________16. Find the roots of 3x3 + x2 - 12x - 4 = 0. _______________17. The average of x and 8x is 18. What is the average of x, 3x, 5x and 7x? _______________18. Find an equation whose roots are twice the roots of 2x2 -7x -10 = 0. _______________19. Factor x4 -16 completely. _______________20. What is the next term in the sequence 8, 10, 14, 22, 38, __? _______________21. ∆ABC is equilateral with an altitude of 15 cm. How long is one side? _______________22. Find a polynomial function with integral coefficients and of lowest degree whose roots are -2, ±√ , 1. _______________23. What is the remainder when 5x4 + 3x3 - 4x2 + 5x - 3 is divided by x + 1? _______________24. What is the y-intercept of 2x – 3y = 6?
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______________25. What is the vertex of the graph y= 2x2+ 4x – 3? ______________26. For what value(s) of x is (x2 +3x -10) / (x2 -2x +1) meaningless? ______________27. Find the length of the line segment joining P(-7, 8) and Q(5, -1). ______________28. Write 7x -3y = 21 in the form y= mx + b . ______________29. Write an equation of the line through (3, -5) and parallel to the line 3x - 5y -12=0. ______________30. What is the domain of y=5-4x? ______________31. What is the domain of g(x)= √
?
______________32. Write the equation y=2x2 + 5x + 2 in the form y=a(x + h)2 +k. ______________33. What is the minimum value of y in the function in #14? ______________34. What is the axis of symmetry of the graph of y=2x2 + 5x +2? ______________35. Find the distance between the two parallel lines x -3y +2=0 and 2x- 6y-3=0. ______________36. Which of the following is/are function(s)? c.) x=y2 -3y +2 ,
a.) y=5x-3,
b.) y=x2 +3x,
d.) y=√
______________37. Given A(3, -1) and B(-2, 6) , find an equation of the perpendicular bisector of AB? ______________38. If x + y =3, what is the value of x2 + 2xy + y2 ? ______________39. If the fourth term of geometric progression is 1 and the first term is 8. What is the second term? ______________40. What is the difference between the roots of x2 -70x + 1200=0? ______________41. What is the remainder x4 + 3x2 + 6x -5 is divided by x-2? ______________42. If the roots of x2 + x -2 =0 are each increased by 1, what is the new equation? ______________43. Find the line of symmetry of the function y=2x2 -8x +8? ______________44. Find the distance from the point (2,1) to the line 3x + 4y + 5=0? ______________45. Solve for x: √
√
-3 = 0.
______________46. What is the the 20th term of the arithmetic progression 2, 7, 12, 17,….? ______________47. The sum of the measures of the interior angles 17,640 . How many sides does this polygon have? ______________48. If 3 geometric means are inserted between 3 and 192. What is the middle mean to be inserted? ______________49. If y varies directly as x and inversely as the square of z, and y=2 when x=5 and z=3. Find y when x=25 and z=5. ______________50. Jormart can do a certain job in 15 hours while Herrmann can do the same job in 10 hours. How long will it take the two to do the job together?
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