Academic Team Math Study Guide 2

  1. Convert the decimal number 34 into a binary numeral.
  2. What is the name for a regular polygon whose interior angles measure 144 degrees each?
  3. Find the volume of a right circular cylinder with radius 4 centimeters and height 5 centimeters.
  4. Find the Cartesian equation of a circle with center at the origin and passing through the point (6, -2).
  5. Find the length of the hypotenuse of a right triangle with legs measuring 32 centimeters and 60 centimeters.
  6. What is the slope of a line perpendicular to the line connecting the origin and the point (3,4)?
  7. Find the coordinates of the point that lies on both of these lines: x + y = 11 and x – y = 3
  8. If f of x equals x squared + 3, and g of x equals 2x – 5, find f of g of 7.
  9. Calculate the log base 125 of 25
  10. Solve for x: x to the one-third power plus 2 equals 5.
  11. Four fair coins are tossed. What is the probability that all four show heads?
  12. A geometric sequence has first term 8 and common ratio negative one-half. Find the fifth term of the sequence.
  13. A pizza company offers four different sizes, three types of crust, and 9 toppings. How many different one-topping pizzas can be ordered based on these choices?
  14. Calculate the determinant of the matrix with top row 5, 7 and bottom row –9, -10.
  15. Given the graph of the equation y = 4 tangent 3x, what is the period of the function?
  16. Simplify: sine 3 pi minus cosine 4 pi.
  17. A vector beginning at the origin has a magnitude of 10 and forms a 45-degree angle with the positive x-axis. Find the coordinates of the other endpoint of the vector.
  18. Express as a single trigonometric function: cosine 20 degrees cosine 15 degrees plus sine 20 degrees sine 15 degrees.
  19. What is the derivative of cotangent x with respect to x?
  20. Without using negative exponents, express the indefinite integral of 10 over x squared with respect to x.
  21. The vectors (3, -5) and (x,6) are perpendicular. Find the value of x.
  22. If a cylinder has a radius and its lateral area is 30 pi, how high is the cylinder?
  23. The set of all points in a plane such that the sum of the distances from two given points, called foci, is constant, is the definition for which conic section?
  24. Simplify the following expression by using the half-angle formulas from trigonometry. 2 times the quantity (cosine x/2) closed quantity squared plus 2 times the quantity (sine x/2) closed quantity squared.
  25. Using Descartes Rule of Signs, the function f of x = x raised to the fifth power-3x cubed plus 2x squared minus 2x minus 1 has how many possible positive real zeroes?
  26. How many 3-letter code words can be made from the letters a, b, c, d and e, if repetition of a letter is allowed?
  27. State the equation of the line which is a horizontal asymptote to the graph of the function y = the quantity 3x+5 divided by the quantity 4x-8.
  28. The sum of the measures of the angles of a convex polygon is 720 degrees. Find the number of sides of the polygon.
  29. A person walks 3 km due south, then 5 km due east, then 17 km due south. How far is the person from the starting point?
  30. The cube root of what number is equal to sixty less than that number?
  31. Its value is approximately 2.718. In mathematics, what letter is used to represent the natural base?
  32. In what quadrant is the sine of an angle negative and the tangent of the angle positive?
  33. Find the second derivative of the sine of 5x.
  34. Find the 13th term in the arithmetic sequence whose first three terms are 3, 6, and 9.
  35. Find the limit of the function f of x = quantity 2x-3 divided by the quantity x+1 as x approaches zero.
  36. The Binomial Theorem is fairly complicated; however, the formula for raising a complex number to an integral power is considerably simple. What is the name of this theorem?
  37. A post office dictates that the sum of the length, width, and height of a package cannot exceed 60 inches. My box has a square base with area of 225 inches squared. What is the maximum height of the regulation sized box?
  38. A circular cylinder has a height of 14 feet. The radius is half the length of the height. What is the surface area of the cylinder?
  39. A right triangle with legs measuring 15 and 36 yards has a circumcircle with radius measuring r. Find r.
  40. A line passes through points (5,3) and (-2, -11). The area above and including this line is shaded. Give the inequality that corresponds to the unshaded region.
  41. An odd function exhibits symmetry around what on the Cartesian grid?
  42. A hyperbola is defined by equation quantity x-4 close quantity squared + 4 times quantity y+5 close quantity squared equals 4. Find the length of the latus rectum.
  43. A universal set is composed of elements {3,6,2,7,4}. P is a subset formed from the universal set and it is defined as the prime numbers of the universal set. What is the complementary set to P?
  44. Express your answer as an improper fraction. A central angle of 1.5 radians intercepts a circle's arc with length of 2 meters. What is the radius of the circle?

Math Answer Key

  1. 1-0-0-0-1-0
  2. Decagon
  3. 80 Pi Cubic Centimeters
  4. X Squared + Y Squared = 40
  5. 68 Centimeters
  6. –3/4
  7. (7,4)
  8. 84
  9. 2/3
  10. 27
  11. 1/16
  12. ½
  13. 108
  14. 13
  15. Pi over 3
  16. –1
  17. (5 Radical 2, 5 Radical 2)
  18. Cosine 5 Degrees
  19. Negative Cosecant Squared X
  20. –10/X + C
  21. 10
  22. 3 units
  23. Ellipse
  24. 2
  25. Three or One
  26. 125
  27. Y=3/4
  28. 6
  29. 5 Radical 17 km
  30. 64
  31. E or e
  32. Quadrant III
  33. Negative 25 sine of 5x
  34. 39
  35. –3
  36. DeMoivre’s Theorem
  37. 30 INCHES
  38. 294 PI SQUARE FEET
  39. 19.5 YARDS
  40. Y - 2X IS LESS THAN -7 (ACCEPT: Y IS GREATER THAN 2X MINUS 7)
  41. ORIGIN
  42. 1
  43. {4,6}
  44. FOUR-THIRDS METERS