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The SAT Math Test: Passport to Advanced Math

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

SAT Math questions fall into different categories called "domains." One of these domains is Passport to Advanced Math: questions that ask you to analyze advanced mathematical expressions.

You will not need to know domain names for the test!
The SAT is designed to assess how ready you might be to tackle more advanced mathematics in college or later on in your career, so it includes some more advanced topics.
Passport to Advanced Math problems will test your understanding of the structure of expressions, and you will be asked to analyze, manipulate, and rewrite these expressions. This includes an understanding of the key parts of expressions, such as terms, factors, and coefficients.
This category also includes other skills crucial for success in later mathematics and scientific fields, such as:
  • Solving quadratic and other nonlinear equations
Example
If a, squared, plus, 14, a, equals, 51 and a, is greater than, 0, what is the value of a, plus, 7 ?
  • 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

  • Understanding the graphs of quadratic and higher-order functions
  • Interpreting a solution, constant variable, or term based on the context of a nonlinear equation in one variable
  • Creating and using quadratic or exponential functions
  • Using a graph to identify other equations in a system with a non-linear equation
Example
The function f, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, minus, 2, point, 4, x, squared is graphed in the x, y-plane as shown above. If k is a constant such that the equation f, left parenthesis, x, right parenthesis, equals, k has 4 solutions, which of the following could be the value of k ?
Choose 1 answer:
Choose 1 answer:

Are you ready to start practicing? 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?

  • blobby green style avatar for user wsha0900
    About how many questions are there on the real SAT under the "passport to Advanced math" category? How many are considered "Heart of Algebra"?
    (18 votes)
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  • leafers tree style avatar for user Anne Shirley
    HI! I need help with this:
    An electronic store offers its employees two different compensation plans. Employees on Plan A earn $500 per week plus a 25% commission on their weekly sales of the products. Employees on Plan B earn $750 per week plus a 15% commisson on their weekly sales of the products. Which inequality describes the amount in sales each week, x dollars, for which employees on Plan A earn more than employees on Plan B?
    The answer is x>2500.
    Can anyone please show me how to do this one? I don't understand this question
    (5 votes)
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    • duskpin sapling style avatar for user Lin Gh.
      Alright, first of all, let's write down the info the problem has given us:

      Plan A earn 500 per week, plus a 25% commission on their weekly sales of the products. If x dollars is the amount in sales each week, the equation for the earning of the week for Plan A would be:

      A = 500 + 0.25x

      Plan B earn 750 per week, plus a 15% commission on their weekly sales of the products. The equation for the earning of the week for Plan B would be:

      B = 750 + 0.15x

      Now the questions wants to know at what value of x, A becomes greater than B.

      We can substitute the equations above in A > B

      500 + 0.25x > 750 + 0.15x

      0.25x - 0.15x > 750 - 500

      0.10x > 250

      0.1x/0.1 > 250/0.1

      x > 250/0.1 --> x > 2500

      Hope this helped.

      Please understand that I'm just a fellow student who happens to be studying for the SAT, so my answer might not be 100% accurate.
      (25 votes)
  • mr pants green style avatar for user Lorij2199
    I'm practicing for the sat right now but I am stuck on one practice question. The question is if x + y = 13 and x - y = 2, what is the value of x^2 - y^2. Can someone explain this question please?
    (0 votes)
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  • female robot ada style avatar for user Tanishqa
    In one question in practice questions of this section 1^1/2=1 but shouldn't the answer be 1 or -1 ??
    (6 votes)
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    • blobby green style avatar for user connorgleason1
      Not sure what question you're talking about, but normally yes 1^(1/2) could be 1 or -1 because 1^2 is 1 and -1^2 is also 1. I assume that the question asked for the positive answer or it just made sense in context of the problem, such as a distance or something (since distance can't be negative)
      (3 votes)
  • duskpin ultimate style avatar for user Hiba Nasir
    Does permutation and combination come in SAT maths?
    (4 votes)
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    • duskpin seedling style avatar for user BrotherCuber
      Not that I am aware of. What does come up is analysis of data sets. For those you should know the concepts of mean, median, mode, and standard deviation (for standard deviation you should not have to calculate it precisely, you just need to know how it increases and decreases.
      (1 vote)
  • male robot johnny style avatar for user death7360
    How to deal with the questions in passport to advanced maths if we forget the basics of 10th grade? Need some advice and guidelines to improve in this section.
    (4 votes)
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  • blobby green style avatar for user Zeineb Benfredj
    are polynomials included in the sat test and can you please give me the list of the exact math lessons that i need to learn for the test i couldn't find them anywhere
    thank you
    (3 votes)
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  • blobby green style avatar for user FletcherAbrianna0
    Can someone tell me the answers and also give an explanation on how to solve them?
    (1 vote)
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  • blobby green style avatar for user annie.wang2366
    If n > 4, which of the following expressions is equivalent to n - 4 square root n + 4/ square root n - 2?

    a. square root n
    b. 2 square root n
    c. square root n + 2
    d. square root n - 2


    please explain thoroughly.
    (2 votes)
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  • female robot amelia style avatar for user Sandra Mathew
    Is pre-calculus and calculus included in "Passport to advanced maths"?
    (2 votes)
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