From time to time, we will enhance and supplement the content of the Orange Book, and we'd like owners who purchased their books prior to these updates making it to print to get the benefit of those improvements and additions.

These changes include clarifying language, refinements in explanations, and the periodic addition of new real test problem cross-reference tables in the appendix along with the augmentation of the related problem blocks that accompany each topic section in the body of the text.

Revisions and Additions

Note that if you're looking for updated real test problem cross-reference tables for more recent tests, you can now use SMTEx (the SAT Math Topic Explorer) to instantly look up any problem on any released test and get a citation to the page in the Orange Book where the relevant topic is discussed.

  1. 4/1/2021 (v1.15.1): Added real test problem topic cross-reference table for the March 2021 QAS test to the Appendix (see below) and distributed that test's problems to the related problem boxes in all the relevant sections.
  2. 4/1/2021 (v1.15.1): On page 72, "2/13 in" has been changed to "2/13 inches" for clarity.
  3. 4/1/2021 (v1.15.1): On Page 191, a note was added to reinforce the fact that an absolute value can never be negative.
  4. 6/2/2021 (v1.16.0): Added real test problem topic cross-reference table for the April 2021 QAS test, May 2021 US QAS test, and May 2021 International QAS test to the Appendix (see below) and distributed those tests' problems to the related problem boxes in all the relevant sections.
  5. 6/2/2021 (v1.16.0): Mar 2020-C-36 has been added to the real test problem listing for section 2.3.
  6. 6/2/2021 (v1.16.0): Added word "usually" in Section 20.5 discussion of how density equation is usually given or referenced in problems dealing with density (see April 2021-C-10).
  7. 1/24/2021 (v1.17): Added real test problem topic cross-reference table for the October 2021 QAS test to the Appendix (see below).
  8. 9/15/2022 (v.1.17.3): Replaced real test problem cross-reference tables with QR codes that open SMTEx (the SAT Math Topic Explorer).

March 2021 QAS Problem Cross-Reference Table

The above table appears on page 819 of Volume II of copies of the Orange Book printed after 4/1/2021 (v1.15.1).

April 2021 QAS Problem Cross-Reference Table

The above table appears on page 819 of Volume II of copies of the Orange Book printed after 6/2/2021 (v1.16.0)

May 2021 US QAS Problem Cross-Reference Table

The above table appears on page 820 of Volume II of copies of the Orange Book printed after 6/2/2021 (v1.16.0)

May 2021 Int'l QAS Problem Cross-Reference Table

The above table appears on page 820 of Volume II of copies of the Orange Book printed after 6/2/2021 (v1.16.0)

October 2021 QAS Problem Cross-Reference Table

The above table appears on page 820 of Volume II of copies of the Orange Book printed after 1/26/2021 (v1.17.0)


If that picture looks like you trying to figure out why your answer seems right but it doesn't match the answer key in the Orange Book...the mistake might not be yours.

In order to prove that we are not robots, we might have allowed an error or two to creep into our manuscript for the book. When someone discovers one of these hidden nuggets of confusion, we'll add it to the list below.

Because we update our manuscript when errors are discovered, the chances of your copy of the book having any of these errors is very small, and if you haven't yet ordered your volumes, when you do, the copies you'll receive will be free of these, uh, quirks, because we've already fixed them.

If you find a mistake, please let us know by emailing us at [email protected].

Known Imperfections

Books ordered after the date of each item should not have that error. Corrections with no date/version number are pending. Version numbers refer to print book/digital book.

  1. 3/1/2021: The answer for section practice problem 13.1-1 on pg. 465 was incorrectly given as B in the printed answer key on pg. 488. The correct answer is C. This has been corrected.
  2. 3/4/2021: The answer key for section 8.4 had the answers out of order. The correct answers are 1) D, 2) 6, 3) B, 4) 9. This has been corrected.
  3. 3/4/2021 (v1.10.3): Section practice problem 20.3-2 and a few of the real test problems and end-of-chapter practice problems were miscategorized as belonging to section 20.3 rather than section 20.2. Problem 20.3-2 has been replaced with an appropriate problem, the old problem 20.3-2 has been moved to Additional Problem 30, and all answer keys, problem section tags, real-test problem tags, the online quizzes and videos, and the appendix have been adjusted accordingly.
  4. 3/20/2021 (v1.11.2): There was a typo ("on on top of the other") at the bottom of page 123; this has been corrected to "one on top of the other." In the Appendix, the six problems that are listed as pertaining to Section 0.1 on page 1 instead should be categorized with section 0.2 on page 4; this has been corrected.
  5. 3/23/2021 (v1.12.0): The word "numerator" in the box entitled "The 'Tell'" on page 787 should be "denominator." This has been corrected.
  6. 3/24/2021 (v1.13.0): Step 3 in the example problem solution on page 779 should say, “Now that we have values”; this has been corrected.
  7. 4/1/2021 (v1.15.1): Chapter 2 additional problem 26 had the incorrect answer indicated on the answer key on page 86; the correct answer is A, not C; this has been corrected.
  8. 4/1/2021 (v1.15.1): In the answer key for Chapter 3, the word "Additional" was misspelled; this has been corrected.
  9. 4/1/2021 (v1.15.1): On page 73, "1-lb increase in height" should have read, "1-in increase in height;" this has been corrected.
  10. 4/6/2021 (v1.15.2): On page 260, the fraction (-12/8) should be -(-12/8). The final reduced fraction of 3/2 is correct. This has been corrected.
  11. 4/11/2021 (v1.15.3): On page 362, in the instructions for SkillDrill 10.1-1, "→" should be "↓". This has been corrected.
  12. 4/18/2021 (v1.15.4): On page 576, the word "data" is misspelled as "dat" in the second line of the second paragraph.
  13. 4/18/2021 (v1.15.4): On page 605, the section listing the answers to SkillDrill 17.2-1 is incorrectly titled "17.2-3."
  14. 4/18/2021 (v1.15.4): On page 602, in problem 32, the word "weight" in answer choices B and C should be "weigh."
  15. 4/18/2021 (v1.15.4): The units of the answer to SkillDrill 18.2-1 on page 627 should be days, not hours (the value is correct), and the final step in the dimensional analysis chain should be 1 day / 10 hours to complete the computation.
  16. 5/3/2021 (v1.15.5): On page 290, "quadratic expression in Standard Form" should be "quadratic equation in Standard Form" in both instances.
  17. 5/14/2021 (v1.15.6): Section 10.3 practice problem 1 on page 377 is improperly worded. The text, "from which the coordinates of vertex 𝐴 can be identified as constants" should read, "from which the y-coordinate of vertex 𝐴 can be identified as a constant." This is because the x-coordinate of the vertex is -1, and the constant -1 does not appear in the vertex form of the quadratic equation in the correct answer choice.
  18. 6/2/2021 (v1.16.0): Problem Oct 2019-NC-19 moved from Section 4.2 to 4.4.
  19. 6/4/2021 (v1.16.1): On page 32, the word "means" should be "mean". This has been corrected.
  20. 6/17/2021 (v1.16.2): Problem 4-NC-20 should be categorized in section 2.1 instead of in Section 2.3. The problem mention has been moved.
  21. 6/17/2021 (v1.16.2): The equation in example problem 21.4-4 on page 784 should be "x - 5√x - 6 = 0" instead of "x - 5√x - 3 = 0". This has been corrected.
  22. 6/28/2021 (v1.16.3): On page 433, "twice as long" should be "two and a half times as long;" the sentence has been reworded.
  23. 7/3/3021 (v1.16.4): The correct answer to SkillDrill 4.5-1-4 on page 143 is 2/5 or 0.4; the answer key on page 155 incorrectly gives 5/2 or 2.5.
  24. 7/25/2021 (v1.16.5): Several real test problems which are correctly listed in section 1.3 were also incorrectly listed in section 1.4; real test problems May 2021 (US)-C-37 and May 2021 (Int)-C-34 were correctly categorized in the appendix as belonging with section 7.3 but were incorrectly listed in section 7.2; real test problem Test 3-NC-10 was categorized correctly in the appendix as belonging with section 10.5 but was incorrectly listed in section 8.5. All these errors have been corrected.
  25. 8/18/2021 (v1.16.6): The vertical axis on problem 10-21 on page 402 is incorrectly labeled "core". It should be "score." This has been fixed.
  26. 8/18/2021 (v1.16.6): Chapter 20 problem 3 on page 756 has an error in all four answer choices; the second x should be y. This has been corrected.
  27. 8/18/2021 (v1.16.6): The box at the top of page 207 should have the qualification, "when a positive base a is raised to an exponent that is a fraction...", as the equivalence is invalid for negative bases and even roots. This has been revised as indicated.
  28. 8/18/2021 (v1.16.6): At the top of page 180, the second line in the series of inequalities is malformed; the line should have just the inequality 2y ≤ -x + 2, and there should be a third line with y ≤ (-1/2)x + 1, which reflects the result of dividing the inequality through by 2. This has been corrected.
  29. 8/26/2021 (v.1.16.7); Starting with section 19.4, the page numbers given in the Table of Contents are inaccurate. This has been corrected.
  30. 9/4/2021 (v1.16.8): On page 141, the last sentence in the first box, "Systems of Linear Equations with No Solution," has an error. "6 to 2, which reduces to 3 to 1" should say "10 to 6, which reduces to 5 to 3." This has been corrected.
  31. 9/4/2021 (v1.16.8): The "Problems from Real Tests" box on page 229 contains the erroneous problem specification "Oct 2020-NC-22." The correct specification is "Oct 2020-NC-2." This has been corrected.
  32. 1/26/2022 (v1.17.0): On page 415, the expression 3 - 6i in the numerator of the fraction in the introduction of the example should be 3 - 8i. This does not affect the principle being explained. Lower down on the same page, there are extraneous close parentheses on two of the lines in the solution sequence. These errors have been corrected.
  33. 1/26/2022 (v1.17.0): On page 118, there is a missing minus sign; the equation y = 4 + 4 should be y = -4 + 4. This has been corrected.
  34. 9/15/2022 (v1.17.3/v1.0.3): On page 295, answer choice 4 for SkillDrill 8.4-2 should read "(3x - 3)² or 9(x - 1)²".
  35. 9/15/2022 (v1.17.3/v1.0.3): On page 490, mm = f(3) should be m = f(3).
  36. 9/15/2022 (v1.17.3/v1.0.3): Section problem 14.3-3 on page 506 is faulty. While the answer given as correct, C, generally corresponds with the shape of an exponential function, the form of the equation provided in the problem and the constraints on the constants render choice C a poor answer due to its non-zero y-intercept, and choice A can result from certain values of the constants. The problem can be corrected by changing y = ax to y = abˣ.
  37. 9/15/2022 (v1.17.3/v1.0.3): On page 263, on the second line of step 3, the term "5" on the right side of the equation should be "15/8".
  38. 9/15/2022 (v1.17.3/v1.0.3): On page 449, problem 4 should read "...with height 41 inches," not "...with a height 41 inches."
  39. 9/15/2022 (v1.17.3/v1.0.3): On page 665, the first line of the explanation should start, "Since the cosine of a is equal to the sine of b, ..."
  40. 9/15/2022 (v1.17.3/v1.0.3): On page 145, in Solution 3, Step 3, the fraction 32/2 should be 32/3.
  41. 9/15/2022 (v1.17.3/v1.0.3): On page 281, in Step 6, "wrongly assuming that it is the positive solution that is being sought will cause the student to select choice C" should be "wrongly assuming that it is the positive solution for x that is being sought will cause the student to select choice B".
  42. 9/15/2022 (v1.17.3/v1.0.3): On page 277, in Example 8.4-2, "what of the following" should be "which of the following."
  43. 9/15/2022 (v1.17.3/v1.0.3): On page 314, section problem 9.1-3 has two solutions, only one of which is represented by an answer choice. The solution that's available as an answer choice is found by taking the principal (non-negative) square roots of both sides, and the other solution is found by finding the negative of the principal square root for either side, which gives x = 225. The question has been reworded accordingly.
  44. 9/15/2022 (v1.17.3/v1.0.3): On page 744, the observation that "neither shape has appeared on any known tests so far" is no longer correct; for example, problem 36 on the April 2022 Math - Calculator section involves the volume of spheres. The statement has been deleted.
  45. 9/15/2022 (v1.17.3/v1.0.3): On Page 741, in Example 20.5-3, the units of volume are mixed; all volume units should be the same (either cubic inches or cubic centimeters).
  46. 9/15/2022 (v1.17.3/v1.0.3): On page 479, "increase of decrease" should be "increase or decrease."
  47. 9/15/2022 (v1.17.3/v1.0.3): On pages 589 and 592, "cause-and effect" should be "cause-and-effect."
  48. 9/15/2022 (v1.17.3/v1.0.3): On pages 725 and 752, "its relative length it would be" should be "its relative length would be."
  49. On page 803, in example 21.10-2, x should be t and "maximum" should be "minimum."
  50. On page xx, "EEvery" should be "Every."
  51. On page xxi, "there?s" should be "there's," and on page xxii, "students?" should be "students'" [online book only].
  52. On page 70, "is usually indicate by words" should be "is usually indicated by words"
  53. On page 401, in the written pop-up answer explanation for Problem 20, "one of these sideways parabola " should be "one of these sideways parabolas" [online book only].
  54. On page 436, "250 X 23" should be "450 X 23"
  55. On page 647, "all three sides will be the in the same ratios" should be "all three sides will be in the same ratios"
  56. On page 656, "from top vertex" should be "from the top vertex"
  57. On page 666 in the notes for the example, "the two angle" should be "the two angles" and in problem 2, "the two acute angle" should be "the two acute angles"
  58. On page 288, the last line of the pop-up written solution should read, "-7(3) = -21" [online book only].
  59. On page 803, "maximum" should be "minimum" in example 21.10.2.