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SAT Math Practice Exam

By — McGraw-Hill Professional
Updated on Sep 10, 2011

This practice exam contains 50 questions that review the 50 Skills that can be found at SAT Math Prep.Take the test. Then check your answers and review the skills for any questions that were difficult.

  1. If 8x–1 = 2x–7, what is the value of x?
    1. 1
    2. 2
    3. 3
    4. 4
    5. 5
  2. If 2m = 5n and 5n = 6p, what is m in terms of p ?
    1. 5p
    2. 3p
    3. 2.9p
    4. 2.4p
    5. p
  3. On 10 tests, a student calculated her test average to be 82. However, she discovered that 2 of the grades were recorded incorrectly. The number 85 was entered as 80, and the number 99 was entered as 90. To the nearest whole number, what is the correct average for her 10 grades?
    1. 81
    2. 82
    3. 83
    4. 84
    5. 85
  4. Posttest I

  5. In the figure above, what is the value of x ?
  6. Posttest I

  7. In the figure above, m || n. If x = 53, what is the value of y?
    1. 27
    2. 53
    3. 90
    4. 127
    5. 180
  8. Posttest I

  9. If MN = ON in the figure above, and b = 160, what is the value of c?
    1. 5
    2. 10
    3. 20
    4. 30
    5. 80
  10. Posttest I

  11. In the figure above, what is the value of x?
  12. If 3 consecutive even numbers have a sum of 42, what is the smallest number?
  13. If 12 < x < 36, and 36 is the lowest number that is a multiple of 4, 12, and x, what is the value for x?
  14. In an xy coordinate plane, two lines may intersect at how many ordered pairs (x, y) ?
    1. 0
    2. 1
    3. 2
    1. I only
    2. III only
    3. I and II
    4. II and III
    5. I, II, and III
  15. What is the slope of the line through the points (2, 3) and (–1, 0) ?
    1. –1
    2. 0
    3. 1
    4. 3
    5. Undefined
  16. If the line through the points (–1, 3) and (–2, p) is parallel to the line y = 3x – 3, what is the value of p ?
    1. –2
    2. –1
    3. 0
    4. 1
    5. 2
  17. The table above shows the results of a survey in which 310 high school students voted for their favorite Spice Girl. Each student received one vote. According to the graph, how many more students favored Scary Spice than Posh Spice?
    1. 1.5
    2. 15
    3. 20
    4. 25
    5. 30
  18. If f(x) = –3x2 – 2, what is the value of f(–1)?
    1. –6
    2. –5
    3. 1
    4. 5
    5. 6
  19. Posttest I

  20. The table above shows the values of the quadratic function f for selected values of x. Which of the following defines f?
    1. f(x) = x2 + 1
    2. f(x) = x2 + 2
    3. f(x) = 3x2 – 2
    4. f(x) = 3x2 –1
    5. f(x) = 3x2 + 1
  21. If t is a negative number, which of the following must be a positive number?
    1. t + 1
    2. t + 2
    3. 3 – t
    4. 3t
  22. Posttest I

  23. For the circles above, the diameter of circle A is 16 and the radius of circle B is half the diameter of circle A. What is the area of circle B?
    1. 8
    2. 16π
    3. 24π
    4. 64π
    5. 160π
  24. Posttest I

  25. In the figure above, the perimeter of square BCDF is 24, DE = 4, and AB = 12. What is the perimeter of the shaded region?
    1. 28
    2. 43
    3. 56
    4. 68
    5. 82
  26. The ratio 1.4 to 2 is equal to which of the following?
    1. 1 to 4
    2. 14 to 2
    3. 10 to 7
    4. 7 to 10
    5. 7 to 100
  27. A scale model of a certain airplane is the height of the actual airplane. If the scale is 3.5 inches tall, what is the height of the actual plane?
    1. 38
    2. 40
    3. 40
    4. 42
    5. 57
  28. Posttest I

  29. The rectangular solid above has edges of length 20, 8, and 4. If point M (not shown) is the midpoint of segment AB, what is the length of MD?
    1. 4
    2. 3
    3. 6
    4. 2
    5. 8
  30. ABED is a square with sides of length 6. If point C is the midpoint of ED, what is the perimeter of ABCD?
    1. 18
    2. 15 +
    3. 18 +
    4. 22 +
    5. 36
  31. Posttest I

  32. In the right triangle above, what is the value of p?
    1. 8
    2. 16
    3. 32
    4. 48
    5. 64
  33. In right triangle MNO (not shown), the measure of MN is 6 and the measure of NO is 3. Which of the following could be the measure of OM?
    1. 3
    2. 3
    3. 4
    4. 5
    5. 9
  34. Posttest I

  35. In the isosceles triangle MNO above, a segment is drawn between midpoints A and B of the two congruent sides. All the following are true EXCEPT
    1. M O
    2. B A
    3. ΔMNO ~ ΔBNA
    4. BA = MO
    5. BN = NA
  36. When the product of 3 and a number is increased by 5, the result is 350. What is the number?
  37. If x = p(p – 3), then x + 2 =
    1. p2 – 3p
    2. p2 + 3
    3. p2 – 3p + 2
    4. p2 + 3p + 2
    5. p2 + 3p
  38. What is the product of 3bm4 and 2b4 ?
    1. 5mb8
    2. 6mb8
    3. 6m4b4
    4. 5m4b5
    5. 6m4b5
  39. If a–3 = b–9, what is the value of a when b = 2 ?
    1. –2
    2. 0
    3. 2
    4. 4
    5. 5
  40. Posttest I

  41. The figure above shows the graph of the line y = ax + b. Which of the following best represents the graph of y = 3ax + b?
  42. Posttest I

  43. For a fund-raiser, the yoga club is selling teeshirts with a choice of two slogans, "Ooommmm" or "Bend me!" Each shirt is available in lavender or peach and in small, medium, or large. How many different types of shirts are available?
  44. Kate, Jack, Sawyer, Walt, and Hugo are at the beach. If a team of two people will hike to the caves, how many different such pairs are possible?
      {3, 4, 5, 6, 7, 8}
  45. What is the probability of randomly choosing a prime number from the set above?
  46. If 2m – 2, m + 3, and 3m – 4 are all integers and m + 3 is the median of these integers, which of the following could be a value for m?
    1. 2
    2. 4
    3. 6
    4. 8
    5. 10
  47. If m is a positive constant and n = 0, which of the following could be the graph of y = mx2 + 3x + n ?
  48. Posttest I

  49. If all children in the Lederman family are terrific, which of the following statements must be true?
    1. All terrific children are Ledermans.
    2. All children not in the Lederman family are not terrific.
    3. No children who are not terrific are in the Lederman family.
    4. Everyone in the Lederman family who is terrific is a child.
    5. There are four terrific children in the Lederman family.
  50. Which of the following could be the remainders when four consecutive odd integers are each divided by 3 ?
    1. 1, 3, 5, 0
    2. 1, 2, 3, 4
    3. 0, 1, 2, 3
    4. 0, 2, 1, 0
    5. 0, 1, 2, 0
  51. Which of the following are solutions to |x – 2| = 6 ?
    1. 8
    2. –4
    3. –3
    1. I only
    2. II only
    3. I and II
    4. I and III
    5. I, II, and III
      6, 10, 18, 34, …
  52. In the sequence above, the first term is 6, and every number after the first is found by subtracting 1 and then doubling the result. What is the 7th term in the sequence?
    1. 257
    2. 258
    3. 259
    4. 260
    5. 261
      6, 10, 14, 18, …
  53. In the sequence above, the first term is 6, and every number after the first is found by adding 4 to the preceding term. What is the 57th term in the sequence?
    1. 230
    2. 232
    3. 234
    4. 235
    5. 239
  54. When x= –2, which of the following is equivalent to x(2s2 – 2) ?
    1. –4s2 + 4
    2. –4s2 – 4
    3. 4s2 – 4
    4. 4s2 + 4
    5. s2 – 4
  55. If x = 2, then which of the following is equivalent to (yx)2 ?
    1. y – 2
    2. y2 + 4
    3. y2 + 2y + 4
    4. y2 + 4y + 4
    5. y2 – 4y + 4
  56. Posttest I

  57. If point N on the number line above represents –8, and point M (not shown) is between N and –4, which of the following could be represented by point M?
    1. 8
    2. 4
    3. 0
    4. –5
    5. –8
  58. The graph of g(x) is shown above. Which of the following equations represents all the points of g(x) shifted 1 unit down?
    1. y = g(x) + 1
    2. y = g(x + 1)
    3. y = g(x – 1)
    4. y = g(x) – 1
    5. y = g(x)
  59. Let be defined as = ac + db for all integers a, b, c, and d. What is the value of ?
  60. If y is directly proportional to x, and y = 21 when x = 4, what is x when y = 35 ?
  61. If y is inversely proportional to x2, and y when x = 2, what is x when y =
    1. 4
    2. 2
    3. 1
    4. Posttest I
    5. Posttest I
  62. In a basket of orange and purple crayons, the ratio of orange crayons to purple crayons is 2 to 3. Which of the following could be the total number of crayons in the basket?
    1. 2
    2. 6
    3. 14
    4. 15
    5. 27
      {4, 5, 6, 7, 8, 9}
  63. What is the probability of randomly choosing an odd prime number from the set above?
  64. The morning of the test you should
    1. Drink 4 Jolt colas to be wide awake.
    2. Feed your brain with a tall stack of flapjacks, a side of pork, and six potatoes.
    3. Run a few miles.
    4. Take a full 4-hour timed practice test.
    5. Have a normal healthy breakfast.
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