Friday, May 20, 2022

What Kind Of Math Is On The Sat

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Sat Math Topics You Should Know About

SAT Math: Critical Concepts for an 800 – Heart of Algebra (Part 1 of 4)

If youre getting ready to take the SATchances are, youre a little nervous about the SAT Math topics. And its probably just because youre not really sure whats coming.

Will I have to do calculus? Will I need a protractor? Will I have to use pi???

But like any good warrioror high school studentknows, half the battle for the SAT exam is knowing what to expect. And this is where we get to help you out!

In this article, well go over the general structure of the math portion, the types of math covered on the SAT, and what you can skip studying.

Ready? Lets go!

Its About The Real World

Instead of testing you on every math topic there is, the SAT asks you to use the math that youll rely on most in all sorts of situations. Questions on the Math Test are designed to mirror the problem solving and modeling youll do in:

  • College math, science, and social science courses
  • The jobs that you hold
  • Your personal life

For instance, to answer some questions youll need to use several stepsbecause in the real world a single calculation is rarely enough to get the job done.

Problem Solving And Data Analysis

This knowledge category deals specifically with quantitative math and its various applications. You will rely on this form of math the most frequently once you graduate from high school and move on to either higher education or the workforce, hence its heavier emphasis on the new edition of the SAT exam. Questions under this category will be written to conform to various scenarios you may encounter in life. To prepare for this exam, we recommend brushing up on the various properties of data sets, as well as how to interpret them. Answering these questions may involve assessing data sets, evaluating percentages and similar types of data, interpreting various types of graphic mathematical data, and working with assorted units of measurement, among similar themes.

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Association With College Or University Majors And Rankings

In 2010, physicists Stephen Hsu and James Schombert of the University of Oregon examined five years of student records at their school and discovered that the academic standing of students majoring in mathematics or physics was strongly dependent on SAT mathematics scores. Students with an SAT mathematics scores below 600 were highly unlikely to excel as a mathematics or physics major. Nevertheless, they found no such patterns between the SAT verbal, or combined SAT verbal and mathematics and the other aforementioned subjects.

In 2015, educational psychologist Jonathan Wai of Duke University analyzed average test scores from the Army General Classification Test in 1946 , the Selective Service College Qualification Test in 1952 , Project Talent in the early 1970s , the Graduate Record Examination between 2002 and 2005 , and the SAT Math and Verbal in 2014 . Wai identified one consistent pattern: those with the highest test scores tended to pick the physical sciences and engineering as their majors while those with the lowest were more likely to choose education and agriculture.

Whats On The Sat Math With Calculator Test

What Kind of Math Is on the SAT? : Math Concepts

The SAT Math with Calculator test is the fourth and final section of the SAT. Students have 55 minutes to complete 38 questions. The first 30 of which are multi choice followed by 8 grid-in questions . This section counts for of the total SAT math score. The SAT Math section divides questions into 4 distinct categories: Heart of Algebra, Problem Solving & Data Analysis, Passport to Advanced Math, Additional Topics in Mathematics. But before we get into the different categories and their contents, a quick note about equations on the SAT:


Unlike the ACT, students are given a list of equations at the start of both math sections. Students are sometimes misguided to think these are the only equations needed for the test, but they in fact only cover geometry! Over the next few sections, well touch on a few of the other formulas you need to know.

Heart of Algebra

Heart of Algebra is the first category of SAT Math questions you will encounter. They include but are not limited to, linear equations, Inequalities, absolute value, functions, graphs

Linear Equations are, usually, the most straightforward kind of Heart of Algebra problem. Think of the classic solve for x questions youve done in school. You may also see systems of equations here that require you to use two equations in tandem to solve for both x and y.

Inequality questions require students to balance and simplify a given inequality. Remember that < means less than and means less than or equal to!

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Sat Math Topics: Passport To Advanced Math

  • Use a quadratic or exponential function to model a real-life context.
  • Simplify an expression with exponents.
  • Manipulate and interpret a nonlinear expression in its context.
  • Isolate a variable in a nonlinear equation.
  • Solve a quadratic equation .
  • Perform operations with polynomial expressions.
  • Solve an equation containing variables in the denominator.
  • Solve a system of equations consisting of a quadratic and linear equation.
  • Know how the zeros and factors of a polynomial relate to one another and to the polynomials graph.
  • Know how a nonlinear graph relates to an equation or system of nonlinear equations.
  • Understand function notation and how transformations/compositions are performed in this notation.
  • Vertex Form Of A Parabola/quadratic


    You may be more familiar with a quadratic in its factored form, or in the form \. However, you should be able to recognize vertex form and convert quadratics to this form for the SAT. The values of \ and \ give you the coordinates of the vertex, \\).

    The distance formula is derived from the Pythagorean Theorem and its useful for quickly finding the distance between two points. Take the values of the coordinates and plug them into this formula to find the distance, and be sure to apply the squares and the square root at the right step.

    The quadratic formula helps you find the roots of a quadratic equation if you cant easily factor it. You need the quadratic to be in the form \, and then you simply plug the coefficients and constants into the formula. Note that you will get two answers because there is the plus and minus sign in the numerator.

    Knowing how to manipulate exponents in a variety of ways will help you tremendously on the SAT, especially the no-calculator portion. In this case, if you have the same base number raised to different powers being multiplied together, you can add the exponents together.

    Similar to the multiplication rule above, if you have the same base number raised to different powers being divided, you can subtract the exponents. You can also rewrite the expression on the right to mirror the one on the left.

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    Subjects This Section Covers

    Even though the SAT Reading passages will be on different subjects such as literature, science, and social science, you don’t need to worry about having any prior knowledge on what each passage discusses. You’ll be able to answer all the questions based on information provided in the passage, so you don’t need to worry about memorizing information on biology, U.S. documents, etc. beforehand.

    The SAT Reading section primarily tests critical reading skills such as the ability to read a passage and understand the conclusions the author makes, being able to understand what certain vocabulary means, and the ability to analyze the relationship between graphics and the passages they accompany. The skills you use for this section are similar to the skills you use in your English classes when you’re reading a book, article, or other form of writing. For both your class and the exam, you’ll need to be able to analyze the piece of writing and the author’s intentions.

    Introduction And Abandonment Of The ‘adversity Score’ And Launching Of ‘landscape’

    How to Study for SAT Math – A Detailed Plan of Action

    In May 2019, the College Board announced that it would calculate each SAT taker’s “Adversity Score” using factors such as the proportion of students in a school district receiving free or subsidized lunch or the level of crime in that neighborhood. The higher the score, the more adversity the student faced. However, this triggered a strong backlash from the general public as people were skeptical of how complex information can be conveyed with a single number and were concerned that it might be politically weaponized. The College Board thus abandoned the Adversity Score and instead created a new tool called ‘Landscape’ to provide the same sort of details to admissions officers using government information but without calculating a score.

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    Quick Overview Of The Sat Math Test Syllabus

    Type of QuestionsMultiple Choice and Student-Produced Response
    Total Number of Questions
    Time Allotted to the TestCalculator Portion 55 minutes
    Algebra, Problem Solving, and Data Analysis, Passport to Advanced Math, Additional Topics in Math
    Passage Writing ModesOne nonfiction narrative, one to two informative/explanatory texts, and one to two arguments

    What Kind Of Calculator Should I Bring

    If you have a graphing calculator, great. If you dont, dont sweat it! Graphing calculators are not necessary on the SAT. If you do decide to use a graphing calculator, keep in mind that it cannot have a QWERTY-style keyboard on it . Also, you can’t use the calculator on your phone. On test day, you will have to turn your phone off and put it underneath your seat.

    These SAT math questions and explanations come straight from our book

    Work these practice questions without your calculator.

    1. 1 8 + 1 10 = a b In the equation above, if a and b are positive integers and a b is in its simplest reduced form, what is the value of a?

    2 9 18 40

    Answer: The lowest number that both 8 and 10 are factors of is 40. Convert the fractions to a denominator of 40: 5 40 + 4 40 = 9 40 .There is no factor that 9 and 40 have in common, so the fraction cannot be reduced. The number in place of a in a b is 9, so the answer is . Be careful! The value of b is in .

    2. The length of a certain rectangle is twice the width. If the area of the rectangle is 128, what is the length of the rectangle?

    4 8 16 21

    3. Let the function f be defined such that f = x 2 – c, where c is a constant. If f = 6, what is the value of c ?

    -10 -2 0 2

    Answer: Start by plugging in what you know into the function given. If f = x 2 – c, and f = 6, then plug in 2 for x in the function: f = 2 c. Solve and replace f with 6: 6 = 4 c 2 = c and c = 2. If you picked , you forgot that 2 is positive 4.

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    How Many Times Should Students Take The Sat

    At least half of all students take the SAT twice, and most students do see an improvement in their scores the second time they take the test. However, students should be cautioned against taking the SAT too many times, since there is no evidence that taking the SAT multiple times significantly changes your score. Instead, students should focus their time on other important components of their college application and on doing well at school. Students should also note that some universities might ask to see all your scores.

    Question : Calculator Permitted Grid

    SAT : Getting the lowest score possible

    Answer: 750

    Category: Heart of Algebrasystems of linear inequalities

    Heres how to solve it:

  • In this question, were told coordinates \\) lies in the solution set of these equations, and we want to know a maximum possible value. With inequalities, the graph will be shaded to include the set of values that satisfy the inequality, so \\) lies in this overlapping region. Because its a grid-in response we know that the value of \ must be limited by the point of intersection. Since the inequalities are both less than or equal to, we know that the lines are included in the solution set. If there were only less/greater than symbols, the lines would not be included in the solution set.
  • This means we can find the point of intersection to find a maximum value of \ and solve it just like a system of equations using the substitution method. This gives us the inequality \. In this case, \ is equivalent to \, and the y-value is equivalent to \.
  • Move the variables to the same side by adding \ to both sides. \.
  • Divide both sides by \ to find out what \ is. \. Many students might stop here, but remember we want coordinate \ in \\), or the y-value.
  • We can plug \ into either equation to find the value of \. We picked the second one since its simpler: \. Thats our answer!
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    Sat Math: What To Study & Review

    Here’s a list of math concepts that are tested on the SAT:

  • Algebra I and II
  • Arithmetic/Probability/Data Analysis
  • Plane Geometry/Coordinate Geometry/Trigonometry
  • Thats it! Of these categories, Algebra makes up the largest part of the test, accounting for more than half of the questions. Plane Geometry and Trigonometry make up the smallest partthere will only be a maximum of 6 questions from that category on the SAT.

    Association With General Cognitive Ability

    In a 2000 study, psychometrician Ann M. Gallagher and her colleagues found that only the top students made use of intuitive reasoning in solving problems encountered on the mathematics section of the SAT. Cognitive psychologists Brenda Hannon and Mary McNaughton-Cassill discovered that having a good working memory, the ability of knowledge integration, and low levels of test anxiety predicts high performance on the SAT.

    Psychometrician Linda Gottfredson noted that the SAT is effective at identifying intellectually gifted college-bound students.

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    Exponential Growth And Decay


    This is technically two different equations, one where there is a plus in the equation and one where there is a minus. Knowing the general format of exponential equations will help you on several SAT questions, as you may need to interpret or manipulate these equations. The value \ is the initial value, \ is the rate of growth when its positive and the rate of decay when its negative.

    Binomial Product 2perfect Squares Trinomial

    [SAT Math] Every Type of SAT Math Parabola questions [Part 2] – Tips/Tricks to Always Get Them Right


    Students sometimes forget the perfect squares trinomial once theyve left their algebra class, but this is also a good one to recognize. It saves you time because you can quickly convert from one form to another, but its a little more difficult to catch than the expanded difference of squares. A good way to know if youre dealing with one is to look at the first and last valuesare they perfect squares?

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    What Is The Ssat And Do You Need To Take It

    When it comes to navigating American Test Prep, things are always a bit tricky. However, usually we can break things down into just “take the ACT/SAT, and if your not a native speaker, take the TOEFL.”

    However, when it comes to boarding schools, in particular the more prominent ones, students will need to take the SSAT or ISEE. While the ACT and SAT are rather straight forward, these tests can be a nightmare to navigate for both parents and students alike. In this article I will focus on the SSAT, its various versions, who should take them, and why its important to prepare for each of them.


    How Many Levels are there?

    There are 3 levels of SSAT, Elementary , Middle, and Upper levels. Unlike the past, all three of these levels now share a common direction, with the only difference being the difficulty level of the questions on the tests. Who should take them?This is actually a difficult question to answer. I often tell people that no one should really take any of them unless absolutely required, and the lower level test is almost never required. The official guidance is as follows:

    • Middle – Grade 5-7
    • Upper – Grade 8-11
    • Math – Basic Algebra, Basic Geometry, Word Problems, and Arithmetic
    • Reading – 30 questions in 1 passage-based section.
    • Verbal – 15 Synonym and 15 Analogy questions
    • Essay – On the elementary version of this test the essay involves writing a story about an image they provide. Only 15 minutes to write the essay.

    Upper Level Test


    Association With Types Of Schooling

    While there seems to be evidence that private schools tend to produce students who do better on standardized tests such as the ACT or the SAT, Keven Duncan and Jonathan Sandy showed, using data from the National Longitudinal Surveys of Youth, that when student characteristics, such as age, race, and sex , family background , school quality , and other factors were taken into account, the advantage of private schools diminished by 78%. The researchers concluded that students attending private schools already had the attributes associated with high scores on their own.

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    Area Of An Equilateral Triangle

    The regular area of a triangle formula is provided on the SAT reference sheet, but it requires that you know the height of a triangle. Sometimes you arent given the height and youll need to calculate it, but you can quickly find the area of an equilateral triangle by plugging the length of one of its sides into the formula above. No need to calculate the height!

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