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The SAT Math Test: Additional Topics in Math

In this series of articles, we take a closer look at the SAT Math Test.

Math questions on the test fall into different categories called "domains." One of these domains is Additional Topics in Math: questions that ask about geometry and complex numbers.

While the majority of problems on the SAT Math Test fall into the first three domains, the test also includes additional topics in high school math. The additional topics include essential geometric and trigonometric concepts and the Pythagorean theorem.
Just a few examples of problems you will be asked to solve:
  • Problems involving area and volume
  • Right triangle trigonometry
  • Using the complex number system to add, subtract, multiply, and divide with complex numbers
  • Using definitions, properties, and theorems relating to circles
Example
A circle in the x, y-plane has equation left parenthesis, x, minus, 3, right parenthesis, squared, plus, left parenthesis, y, minus, 4, right parenthesis, squared, equals, 36. What is the radius of the circle?
Choose 1 answer:
Choose 1 answer:

  • Concepts relating to lines, angles, and triangles
Example
In the figure above, line segments start overline, A, F, end overline and start overline, B, E, end overline are perpendicular and intersect at point C. Angle B is congruent to angle E, and the measure of angle A is 55, degrees. What is the measure, in degrees, of angle E ? (Disregard the degree sign when entering your answer.)
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Reading these articles will only get you so far! Are you ready for some real practice? Head over to the Math Practice Area and try some problems!

Attributions

This article was adapted from the following source: “Test Specifications for the Redesigned SAT.”

Want to join the conversation?

  • primosaur ultimate style avatar for user Dawn Payton
    Overall, I understand most of the math topics, but the only type that bothers me are the complex numbers like trying to figure out what value is i^26 or i^34 etc. Is there any simple way to solve those types of i values?
    (1 vote)
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    • blobby green style avatar for user Tim MacNeil
      First you need to be familiar with the powers of i up to i^4.
      i^0 = 1
      i^1 = i
      i^2 = -1
      i^3 = -i
      i^4 = 1.

      This allows us to re-examine any i exponent bigger than 4, as any i exponent bigger than 4 can be expressed as a product of i^4 and other i exponents. But, because i^4 is 1, all that is relevant is the remaining exponents. For example:

      i^26 = i^4*i^4*i^4*i^4*i^4*i^4*i^2 = 1*1*1*1*1*1*i^2 = i^2 = -1
      i^9 = i^4*i^4*i^1 = 1*1*i^1 = i^1 = i

      For a short cut in finding the results, you can divide the exponent by four and the remainder of the exponent will be the i power that is relevant. For example:

      i^29 = i^1 = i (29/4 = 7 remainder 1)
      i^43 = i^3 = -i (43/4 = 10 remainder 3)
      (56 votes)
  • mr pants purple style avatar for user Olivia  **INACTIVE**
    Can someone help me with this question? It was a grid-in question on the No Calculator section on a practice test and I had no clue how to solve it. It probably doesn't help that I hardly understood anything in my chemistry course that I painfully limped through last year.

    How many liters of a 25% saline solution must be added to 3 liters of a 10% solution to obtain a 15% saline solution?

    Thanks in advance to anyone who can help!
    (7 votes)
    Default Khan Academy avatar avatar for user
    • blobby green style avatar for user ksnar1966
      This is a problem of weighted average and can be easily done using concept of Alligations

      A ----------- B
      25 ----------- 10
      -------15-------
      5 -------------10

      => The ratio A:B is or 1:2

      If quantity of solution B is 3 Litres, the A should be 3/2 = 1.50 Litres

      :-)
      (3 votes)
  • duskpin ultimate style avatar for user Jordan
    How Did you get 78/5, or 15.6?
    (5 votes)
    Default Khan Academy avatar avatar for user
    • piceratops ultimate style avatar for user Homeskool99
      Oh man - that's a heck of a question! Okay let's see.

      Alright so "Since we're dealing with right triangles, you'll need to use the Pythagorean theorem to figure out the missing side length of the big triangle". That's easy enough.
      5^2 + 12^2 = x^2
      25 + 144 = x^2
      169 = x^2
      Square Root of both sides (to clear the x^2) makes 13 = x (Because sq rt of 169 = 13)
      Also, you could remember that 5-12-13 is a common Pythagorean Triple.
      Anyway, that makes the Hypotenuse of the big triangle AE = 13.

      "Then, you'll need to recognize that the smaller triangle is similar" to the bigger triangle and "△AED is similar to △CEB" Okay, not too bad.

      "Next, we'll set up proportions to solve for the length of EC." That means take two corresponding sides of each triangle and set them equal to each other, and one of those sides will be the one we're trying to find, which is EC.

      So we'll take sides DE corresponding to BE, because we have the measure of both. Then we'll use side AE to find CE.

      DE/BE = AE/CE
      5/1 = 13/x
      Cross multiply to get 13 = 5x
      Divide both sides by 5
      So x = 13/5
      So CE = 13/5

      Since we're trying to find AC, we add 13 + 13/5.
      We need a Common Denominator of 5, so we multiply 13/1 (13 as a fraction) by 5:
      13(5)/1(5) = 65/5.
      Then we add 65/5 + 13/5 = 78/5.
      We can divide 78 by 5 to clear the fraction and get the decimal 15.6

      Whew! What a ton of work! Hope that helps:)
      (12 votes)
  • blobby green style avatar for user Swachsstock8100
    So I currently am not taking Algebra II, and I'm in 11th grade. As of right now, I'm taking the below regents level class, College Algebra and Trig. I do not understand any of the trig based questions. I have an SAT to take this weekend. With little to no knowledge on being able to solve those types of questions, should I really study even though theres 99.99% chance I won't understand them?
    (4 votes)
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    • duskpin ultimate style avatar for user Alex
      If you have time to spare today, then yes you should. Use Khan academy's videos to help you at least get the basics of sin, cos, and tan. But don't waste your time if you aren't going anywhere. If you spend 1 hr trying to understand, and you still haven't made any progress, focus on your other weak spots that you know you can improve upon. If you do understand the trig, then make sure you familiarize yourself with the calculator's trig functions and do practice prbs. On the test, fill in those questions which you don't understand immediately, and just move on, and only come back to them if you have extra time. Hope this helped. Good luck tomorrow, I'll also be taking it.
      (4 votes)
  • duskpin tree style avatar for user Haley
    In the example problem with the volume, how would you get the answer? I'm confused what the portion of the vase that is cut out looks like or how to solve it.
    (2 votes)
    Default Khan Academy avatar avatar for user
    • aqualine seed style avatar for user Dave Travis
      The vase is basically a box with another box cut out of it (The interior cut out is another rectangular prism). SO = take the volume of the big box and subtract the volume of the small box. Big Box: 2x2x5 = 20 Small box cut out = 1.5x1.5x4 = 9 Answer = 20-9 = 11
      (6 votes)
  • blobby green style avatar for user Rubina  Haji
    How many questions will be asked on this part of maths in SAT and on which section ?
    (3 votes)
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  • leaf red style avatar for user Di
    This is one of my hardest subjects in the SAT, partly because I am not familiar with many of the necessary equations for the problems. Are there any really important equations I need to memorize for this?
    Thanks in advance!
    (2 votes)
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  • blobby green style avatar for user brunella polastri
    hey im from peru and I really want to take the sat and I thought that the math here is somehow similar to the math I get teached but once I started with the quizzes its complete different story like those questions are so confusing any tips on how can I improve in maths and what can I do to get a good enough grado to get into an Ivy League university pls?
    (2 votes)
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  • female robot ada style avatar for user Onose Ijewere
    How old do I need to be to write SAT?
    (0 votes)
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  • leaf blue style avatar for user Michael Stone
    Will any law of sines and law of cosine questions be included as possible questions for the SAT?
    (1 vote)
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