Summer and Job Postings 

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by Staffer 

The summertime is here!! School has ended for most students. However, just because school has ended doesn’t mean that learning ends. All 4 One Tutoring LLC will have summer tutoring. 

For school-aged children, we will align sessions to entering grade Common Core State Standards. We have two research-based curriculums that we will use for sessions. Having learning/tutoring sessions will avoid Summer Slide

All 4 One Tutoring LLC will also have sessions for adults. Whether you want to learn a language, prepare for the accuplacer, or even the GED exam, we have you covered! 

Job Postings 

Company Trainer 

We’re seeking a contractual company trainer or trainers who will be responsible for training incoming employees and contractors and conducting trainings throughout the year. We’re seeking someone who will be able to do trainings in Maryland (mainly Baltimore City and County) and someone who will be able to do remote (online) trainings. If you’re able to do both, please state that in your cover letter. If interested, please send us your cover letter and resume to hr@all4onetutoring.com. 


Marketing Intern 

We’re in need of a marketing intern. This internship can be remote or face-to-face. This internship will start unpaid and will become paid after 30 days. Visit our webpage for more details. 


  

What are Functions?

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Functions are an important concept and are therefore, heavily tested on the new SAT. It is important to become proficient with them. But, what is a function anyway? In mathematics, a function relates to an output that resulted from an input. It is like in computer science when you learn about input and output devices and the relationship between both. For example, you put in an input into the computer in the form of instructions, and it resulted in an output in the form of a printed document. In the real world context, other ways in which the concept of functions occurs it in factories where you have large machinery. The machines work in the same context of input and output.

A function is usually denoted by “f(x) =…” , the f, is not unique and any letter can be used.

A function has three main parts:

  1. The input
  2. The relationship
  3. The output

Example: “Multiply by 4” is a very simple function you can grasp.

Input = 5, Relationship = × 4, Output = 20.

Consider this: For an input at 40 what is the output?

Examples of functions

f(x) = x2 + 3

g(x) = 2x – 7

The above definition of a function is considered as the basic understandable definition. It goes deeper. A function may also be considered as a relation that uniquely maps one member of a domain unto another member of a range which is a subset of a codomain. This means, if you have a function which maps set A to B, it is an object f such that   is mapped onto one or more members of the range such that. The range is part of a codomain. This means that a function can be a many to one or one to one relation. If you have a one to many relation that is not a function. Let us look at range, domain and codomain to get a better understanding of the aforementioned definition. But first let us look at one to one and one to many mapping.

Understanding the difference between the range and the codomain is very critical. It even becomes more critical when doing further math such as pre-calculus where a function is undefined.

Example 1

What is the domain and range of the function: f(x) = 2x2 + 6?

To answer this question, you need to think about all the possible values than can be inputted into the function and get an output. By looking at the function you realize than any real number can be placed into the function to produce an output. Also, you may also realize that the set of integers can also be used. If you use any random integer for example -3, you can check

Thus f(-3) = 2(-3)2 + 6

= 2(9) + 6

= 18 + 6

= 22

You may also notice that all the output for the set of real numbers will be the same for the set of integers because of the x2. Therefore the domain is the set of integers. Since the set of real numbers is a subset of the set of integers, we can exclude it. Note that the domain does not have one set definition, because it could also be the set of counting number, whole numbers, etc. However for the range, you will never get a negative output, so the range could never be the set of integers, but it could possibly be the set of even numbers, however the range is the set {8, 14, 22…}. Though the question didn’t ask, but the codomain could be the set of counting numbers, since the output could be any possible counting number.

Evaluating Functions

Evaluating functions is quite simple, all you need to do, if plug in the value that is given, substitute the value for I, then solve the equation.

Example 2

Function f is defined by
f(x) = – 2x2 + 6x – 3, find f(- 2).

What you do in this instance, you substitute -2 for ‘x’ in the function then solve

= -2(-2)2 + 6(-2) – 3

= -2(4) – 12 – 3

= -4 – 12 – 3

= – 19

Example 3

Two functions f and g is defined by

f(x) = 2x + 7 and g(x) = -5x – 3, find (f + g)(x).

When you look at the question it might seem hard, but it is quite simple. You may note that (f + g)(x) denotes is the product of two numbers ideally. It can be expanded as such

(f + g)(x) = f(x) + g(x). As such, this is in a form that we can understand therefore it is:

f(x) + g(x) = (2x + 7) + (-5x – 3). Note: the brackets are there to show the two distinct functions

2x + 7 – 5x – 3 by grouping like terms”

2x – 5x + 7 – 3

= – 3x + 4

Therefore (f + g)(x) = – 3x + 4

Example 4

Two functions f and g is defined by

f(x) = 2x2 – 3x and g(x) = x + 1, find f (g)(-3).

What you see above is called a function of a function. It is quite easier than it looks. What is means that wherever you see x in function f, you are going to plug put the g function then plug in -3. Therefore:

f (g)(x) = 2(x + 1)2 – 3(x + 1). Thus, we first put the g function in the f function. Now we evaluate for:

f (g)(-3) = 2(-3 + 1)2 – 3(-3 + 1)

= 2(-2)2 – 3(-2)

= 2(4) + 6

= 8 + 6

= 14

Therefore f (g)(-3) = 14

If we were not asked to evaluate f (g)(-3), but just find f (g)(x)

The answer would just be: 2(x + 1)2 – 3(x + 1).

You may also note that a function can be graphed and in that context, the x is the domain and y is the range so sometimes you will see that f(x) = y.

Range, Domain and Codomain

The first diagram represents a one to one mapping, where each element of X maps exactly onto one Element of Y. The second diagram represents aone to many mapping where one element of X maps onto one of more element of Y.

A domain is simply all the possible values that can be inputted into a function to produce an output.

The range is simply all the output of a function.

The codomain is all the possible outcomes or output from a function.

 

For more awesome SAT math concepts review, visit our blog: http://exammasters.ca/category/math/

For a FREE SAT Math Practice Test: http://exammasters.ca/free-sat-math-practice-test/

 

Complete SAT 2016 Math Test Breakdown

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                  SAT

PART I – About The SAT Math Test

I want to break down the whole SAT math test and show you what it’s composed of, what it tests, and how to ace to it. The first thing to realize is that the SAT math test has changed its focus to mainly test students on algebra and problem-solving using real-world scenarios. The majority of it covers Basic Algebra and Advance Algebra. Therefore, most of the concepts in these two divisions of math are fair game. And there are a lot of concepts. But, the good news is that you’ve already learned all or most of these concepts in school. The new SAT has really become aligned to your school curriculum. It basically covers most of Grade 11 Math and a tiny bit of Grade 12 Math. Take a look at this TABLE 1 for the main sections on the SAT math test.

From this table, we can see that the additional topics only make up for 10.34% and the rest of the topics account for 89.66% of the total questions in the math section. This is very key for us to know, as it will guide our strategy for the math section.

Calculator and No-Calculator Portions

The math test will be Section 3 and Section 4 of the whole SAT and will consist of portions where you will be allowed to use a calculator and portions where you will NOT be allowed to use a calculator. Don’t let this scare you, as most of the questions will be solvable without calculators. The calculator will mainly be for questions which give you ugly numbers with decimal places or things like the quadratic formula. In general though, the questions in the no-calculator portion will be solvable more faster than the questions in the calculator portions.

Types of Questions

The majority of the questions in each section will be multiple-choice, accounting for 80% of all the questions. Each multiple-choice question will have four options to choose from, with only one correct or best answer. Remember, that there will be NO penalty for guessing wrong. So, make sure to answer each and every question.

The other type of question is the grid-in response question (20% of the total questions), which is basically a question without answer choices for you to choose from. For this type of question, you have to come up with the answer and write it in appropriately on the answer sheet. Again, NO penalty for getting wrong answers. One major thing to note for this is that you must write your answer in the grid-in boxes provided and also fill-in the appropriate bubbles underneath – otherwise, you won’t get the credit!!

Heart of Algebra

The point of this category is to see if you can demonstrate both procedural skill and a thorough understanding of linear equations, linear functions, and linear equalities. This is accomplished by asking you to solve straightforward questions or challenging questions. Remember that a lot of these concepts can and will be asked in many different ways. So, it’s a good idea to practice with as many questions as you can to get an idea of how to solve the same concepts in different contexts.

Here, we have outlined these concept: TABLE 2

It is important to note that many Heart of Algebra questions will ask to solve for the following:

  • Define one or more variables
  • Determine the algebraic relationship between the variables
  • Solve for the required variable
  • Interpret the results to answer what the question is specifically asking

There will be a total of 19 questions for this category – 11 for the Calculator portion and 8 for the No-Calculator portion.

Problem Solving and Data Analysis

This section tests your ability to understand and represent data. This means that you have to pay attention to things such as units, measurements, ratios, trends, and principles of statistics. Some questions may be as simple as reading a value off of a graph, whereas, other questions may ask you to calculate something, like the probability of occurrence of a particular event. You will definitely have to know how to read data from line graphs, bar graphs, histograms, box-and-whisker plots, scatterplots, and two-way tables (categorical data).

Here is a table of all the concepts covered in this section: TABLE 3

For some concepts, you simply have to understand them, rather, than calculate them. For example, you will not be expected to calculate standard deviation, but, will be expected to know that a large standard deviation means the data is more spread out from the mean. You will NOT be asked to calculate standard deviation, margin of error, or confidence intervals. But, you must understand what these concepts mean. Another important thing to note here is that in statistics, confidence intervals other than 95% can be used, but the SAT questions will always use 95% confidence levels.)

There will be a total of 17 questions for this category – all for the Calculator portion.

Passport to Advanced Math

This category is all about understanding the structure of expressions and being able to manipulate them to solve for different variables. This also means that you have to understand what the variables represent. Basically, this section tests concepts that build on the concepts tested in the Heart of Algebra category. You are further expected to know the basics of equations, functions, and polynomial algebra. Yes, this means that all those things you hate – fractions, radicals, and exponents – are all tested!

Here is a table with all the concepts tested in this section: TABLE 4

The SAT Math test uses the following Cartesian plane assumptions for any graph on the xy-plane:

  • The axes are perpendicular and the scales are linear.
  • The values on the horizontal axis increase as you move to the right.
  • The values on the vertical axis increase as you move up.

Note that this means that you CANNOT assume that the size of the units or measurements on the two axes is the same (unless the question specifically states that they are).

When you begin your prep for the SAT math section, make sure you master Heart of Algebra before moving on to this section.

There will be a total of 16 questions for this category – 7 for the Calculator portion and 9 for the No-Calculator portion.

Additional Topics

This section covers topics in geometry and trigonometry. It also covers complex numbers. The good thing here is that a lot of the geometry formulas are provided for you, so, you don’t have to memorize a lot. Remember, that this section only makes up about 10% of the total Math test (6 questions out of 58). So, don’t go spending more time prepping on this section than the other sections!

Here are the concepts: TABLE 5

One important thing to note in this section is that figures ARE drawn to scale unless explicitly stated otherwise (which is totally opposite from the Old SAT).

There will be a total 6 questions for this category – 3 for the Calculator portion and 3 for the No-Calculator portion.

PART II – Most Commonly Tested Concepts

In this part, I want to delve into what this SAT Math test really focuses on. If we can find which concepts are commonly tested and which aren’t, we can make our studying and prep work that much more efficient and productive.

Here’s what we did:

  • We went through the Math Sections of all 4 released tests from CollegeBoard and wrote down which concept was being tested for each and every question.
  • We came up with a total of 26 concepts that showed up repeatedly across the 4 tests, which totaled to 232 questions.
  • We tallied up all the questions according to the concept they tested.
  • We calculated the frequency by dividing the number of times a concept showed up across the 4 tests by the total number of questions we looked at (232).

Here are the results: TABLE 6

This table gives us some interesting stats to think about.

** Caveat **

But first, I just want to mention that all of this should be taken with a grain of salt for the following reasons:

  • This data is only based off of 4 College Board tests – so the sample isn’t really that large, which makes our results less accurate.
  • Just because I say “68% of the tested concepts will be from the first 11 concepts” doesn’t mean that that is exactly what you will see on the real thing. It is simply an analysis of what we found to be the case with the 4 released tests from College Board.
  • All the percentages are from these 4 released College Board Tests and we are assuming that College Board will test in a similar manner on the real administered tests. So, we are trying to make predictions based off of these stats – nothing stated here is a 100% for sure thing.
  • There were a few questions for which it seemed like they were testing a combination of concepts, rather than just one concept explicitly. For this type of question, we used our judgement to decide which concept it was ‘most importantly’ testing.

 

Analysis

The first 11 concepts: TABLE 7

  • The first 11 concepts make up 68% of the questions – which means that for any given math test of 58 questions, 40 of those questions would test these concepts.
  • The last 15 concepts only make up 31% of the questions – which means that for any given math test of 58 questions, 18 of those questions would test these concepts.
  • Out of the first 11 concepts, 6 of the concepts are Heart of Algebra concepts (blue), accounting for 32% or about 1/3 of all tested concepts.
  • Out of the first 11 concepts, 3 of the concepts are Problem Solving and Data Analysis concepts (green), accounting for 22% of all tested concepts.
  • Out of the first 11 concepts, 2 of the concepts are Passport to Advanced Math concepts (yellow), accounting for 14% of all tested concepts.

The next 7 concepts: TABLE 8

I didn’t want to include Function Notation, however, I felt that this concept is sooooo easy, compared to the last 8 concepts, that I might as well include it with this group. So, this next chunk of concepts comprises 20% of tested concepts.

  • Questions about circles, part of the Additional Topics category, appear to be the most tested of the Additional Topics concepts.
  • 5 of these concepts are from Passport to Advanced Math (yellow), accounting for 14% of all tested concepts.
  • Statistics only makes up 3% of all tested concepts.

The last 8 concepts: TABLE 9

  • 5 of the concepts are from the Additional Topics (red) category.
  • 3 of the concepts are from Problem Solving and Data Analysis (green).

Results

  • Just 6 Heart of Algebra concepts account for 32% of all tested concepts.
  • Combined from above, just 4 Problem Solving and Data Analysis concepts make up 25% of all tested concepts.
  • Combined from above, just 7 Passport to Advanced Math concepts make up 28% of all tested concepts.
  • 18 concepts make up 88% of all tested concepts. This is equal to about 51 questions out of 58. This gives a raw score of about 690 according to the raw score conversion tables made available by College Board.
  • 17 of these concepts make up 85% of all tested concepts. This is equal to about 49 questions out of 58. This gives a raw score of about 710 according to the raw score conversion tables made available by College Board.
  • The 11 most common concepts make up 68% of all tested concepts. This is equal to about 40 questions out of 58. This gives a raw score of about 610 according to the raw score conversion tables made available by College Board.

Discussion

So, what does all of this mean? How can it help you? Well, it really depends on what your specific situation and goals are. If you are in a time crunch, for example, then it might be wise to study the 11 most commonly tested concepts, so, that you can still get a score around 600. And if you have a bit more time, then study the first 18 concepts so that you have a chance at a 700. However, if you do have a lot of time on your hands, then it would be wise to begin with the concepts outlined in this analysis of the 4 released CollegeBoard tests. This would allow you to start doing really well on your practice tests, early in your prep, giving you a huge confidence and motivation boost. Then, you can focus on the rarer concepts, common mistakes, and harder material to go from 700 to 800.

Another thing to point out is that out of all of the Additional Topics concepts, it seems that concepts related to circles are the most important. So, if you really hate geometry and don’t want to bother with triangles and such, at the very least, you should study up circles.

In Heart of Algebra, we were quite surprised to see some topics so heavily tested. For example, systems of linear equations. Each of the 4 tests from CollegeBoard had anywhere between 2 to 6 questions on just this concept. Most of the time they gave you both equations, but rarely they asked you to come up with the equations also. Writing linear algebraic equations from word problems is also a big one. The next few heavily tested concepts were ratios & proportions, polynomials, quadratics, and being able to read graphs and tables for things such as trends, max/min points, and specific values. So, without a doubt, do not go into the test without being comfortable with these things.

In terms of difficulty of questions, it seemed that, generally, the difficulty increased as you got further along in the math section. Section 4 (the calculator portion) had more difficult questions than Section 3. However, a lot of the questions in Section 4 could easily be solved without using a calculator. So, depending on how much you rely on your calculator, you may or may not use it much for section 4.

Overall, I believe that the SAT Math test is fair and maybe even easier than the old SAT math. There are no tricks and strangely worded questions. You’ve learned the majority of these concepts in school – mainly Grade 11 Functions. And the questions are exactly as you’ve seen them in school also. I think this familiarity of these questions will help decrease anxiety for many students. If you have done well in math at school, then you will definitely do well on this SAT Math test. If you haven’t, then you’ll have to work a little harder to review all the concepts that your weak in and show colleges that you have improved in math by doing well on the SAT Math test.

I hope that these tables and analysis have given you a little more insight into the SAT Math test, making it a little more predictable and less scary. If you find that you are lacking in certain skills, then there are great resources like Khan Academy to help with your review. Our main goal is to use these findings to create the best practice tests we can for students. As CollegeBoard releases more tests and we can glean more information from student experiences, our tests will get better and better going into the future. We are going to release our first book of practice tests in early August.

PART III – Strategy

General Strategies For The SAT Math Test

Process of Elimination: This strategy is golden when you’re a bit stuck. If you weren’t able to solve the question and find the right answer right away, then start by eliminating the most wrong choices right away – and there are usually one or two of them for every question. Since, you only have four choices to begin with; this really helps narrow it down. After eliminating two choices, even if you have to totally guess, you’re chances to guess correctly are 50%.

Plug-in Answer Choices: This is another thing to try when you’re stuck. Pick one of the answer choices (usually the middle one is the best one to go with) and plug it in to the question. You can usually get the answer this way within two guesses, because the first guess will give you a good idea of what answer choice to try next.

Substitute Numbers for Variables: Sometimes, when you’re given a formula and asked to manipulate it, you substitute easy numbers into it to make sure you did it right.

Target Easy Questions First: This strategy works for those that are very nervous and need a confidence boost early on. You can quickly flip through the section and find which questions you think are easy and do them first. What constitutes an easy question? Well, it’s whatever topic you think you’re most comfortable with and whether you can get the answer under 30 seconds. That seems like a very short amount of time, but it’s not. 30 seconds is a long time. Try counting to 30 seconds right now and you’ll see. If you can’t get the answer in 30 seconds, then it’s not an easy question. Try to notice this during your practice and while you are doing the practice tests in this book. You will notice that you get the easy questions almost immediately. After you’re certain you’ve got all the easy questions, move on to the harder ones.

Save Data Tables For The End: These questions usually want you to analyze the data and that can take you 30 seconds to a minute at least. Then they want you to do something with that data, which will take you another 30 seconds to a minute at least. So, although not hard, these questions are time consuming. Save them for the end. Time management is key to doing well on this test. Do the same for any complicated graph question. Sometimes, though, the question will be very simple – they may just want you to read a value off the graph, which you can do very quickly.

Remember that you can mark-up and write all over your test booklet – so make sure to actually cross things out that you want to eliminate, put a star besides ones that you think are hard, write down things that you’ve memorized, and whatever else you feel will help you.

Read each and every question carefully and try to come up with the answer before looking at the answers. Then look at every answer before picking the right one.

Memorize common formulas and facts: This will naturally help you do questions quicker. This includes memorizing all the formulas provided to you on the reference sheet. This prevents wasting time by flipping back and forth between your question and the reference sheet.

Try not to depend on your calculator too much: Most questions on the SAT math test can be done without using a calculator. We recommend using the calculator for mainly questions with really ugly numbers that make it hard to do mental math.

How To Get A 500+ Score

Getting a score of 500 should be very easy on this test. You just have to know all the basic concepts.

Number of Correct Questions: 22 – 26

Percentage: 38% – 45%

Study Plan

  • 1 hour a day to review concepts for 2 months
  • 30 minutes a day to do practice questions
  • At least 4 timed math practice tests

Main focus of studying:

  • Heart of Algebra
  • Top 11 concepts from our analysis

How To Get A 600+ Score

Getting a score of 600 will require a little more effort but will also be relatively easy to accomplish.

Number of Correct Questions: 32 – 38

Percentage: 55% – 66%

Study Plan

  • 1 – 2 hours a day to review concepts for 2 months
  • 30 minutes a day to do practice questions
  • At least 6 timed math practice tests

Main focus of studying:

  • Heart of Algebra
  • Passport to Advanced Math
  • Top 18 concepts from our analysis

How To Get A 700+ Score

Getting a score of 700 will be harder to accomplish and will require a good amount of effort. We really recommend you start prep early and leave about 4 months to get to this score and above (unless you’re very good at math already). From our analysis, we recommend that you study and be comfortable with all 26 of the most commonly tested concepts. You should also thoroughly review Basic Algebra and Advanced Algebra, which covers things such as quadratics, polynomials, rational expressions, radicals, exponents, graphs, functions, and more. This will prepare you very well for the math test and you should be able to get almost all the questions. You can get the hardest questions wrong. Even if you miss a handful of questions, you can still end up with a 700+ score.

Number of Correct Questions: 43 – 50

Percentage: 74% – 86%

Study Plan

  • 2 – 3 hours a day to review concepts for 2 – 4 months
  • 30 minutes – 1 hour a day to do practice questions
  • At least 8 timed math practice tests

Main focus of studying:

  • Heart of Algebra
  • Passport to Advanced Math
  • Problem Solving and Data Analysis
  • All 26 commonly tested concepts from our analysis

How To Get A Perfect 800 Score

Getting a perfect 800 score will be a challenge and will require a tremendous effort. BUT, it’s totally doable. You don’t have to be a genius to get a perfect 800; you just have to be a hard and disciplined worker. We really recommend you start prep early and leave about 4 months to get to this score. From our analysis, we recommend that you study and be comfortable with all 26 of the most commonly tested concepts, everything outlined for the ‘How To Get A 700+ Score’ section and also all the Additional Topics concepts tested on the SAT. That means that you should definitely be comfortable with trigonometry, geometry, and complex numbers. Three out of four of the practice tests, released by CollegeBoard, show that you need to get all 58 questions correct in order to get 800 – even missing one can drop you down to a 790. The key to this is going to be time management, targeting your weaknesses with practice tests, eliminating careless mistakes, and doing as many timed SAT math practice tests as possible.

Number of Correct Questions: 57 – 58

Percentage: 98% – 100%

Study Plan

  • 2 – 3 hours a day to review concepts for 2 – 4 months
  • 30 minutes – 1 hour a day to do practice questions
  • At least 10 timed math practice tests

Main focus of studying:

  • Heart of Algebra
  • Passport to Advanced Math
  • Problem Solving and Data Analysis
  • Additional Topics
  • Al 26 commonly tested concepts from our analysis

How To Use Practice Tests

  • Always do the practice test under real conditions. Go to a quiet room, time yourself, and complete the whole test without any breaks. Also, it’s a good idea to do the practice test at the same time as when you will give your SAT – usually that’s around 8 am. This will make sure that you get used to having to think this early on in the day.
  • Practice tests (and any practice questions you do) can let you know what your major and minor weaknesses are. Always analyze your results to find the reason why you got any question wrong (this includes questions you had to guess on). Categorize your weaknesses based on concept or question type. Then review those concepts, starting from the ones you get wrong the most and working your way down. And, of course, make sure to go back and re-do the questions you couldn’t do to make sure that you can do them.
  • Practice tests can let you know whether or not your weakness is time management. The way you do this is to start noticing if you are always rushing near the end of a section. If you feel like you’re rushing the last 5 or so questions, then you have a time management issue. You can also check this by doing a practice test where you time yourself, but don’t stop a section once the time has run out. Keep going and finish the section, but make a note of all the questions that you had to do once the allotted time passed. Then when you score your test, break it up into two scores: one for the questions you finished within the allotted time and one score that includes the questions that you needed extra time for. Then compare the two scores. If you see that there is a difference of 50 or more points, then you definitely have a time management issue. And if there is almost no difference, then your timing is excellent and you should focus more on the concepts.
  • Everyone makes careless mistakes. Practice tests give us a great glimpse at what these mistakes are. Go through each practice test and find the careless mistakes you made. Then write down on a piece of paper what that careless mistake was and make sure to read that piece of paper every day. The whole premise behind careless mistakes is that you simply don’t notice them when you make them. So, being more aware of them should help eliminate them.
  • Take one practice test at the beginning of your prep to see where you stand and what you already know really well. This could tell you where to start your prep. For example, if you got most of the algebra questions right, but a lot of the quadratic questions wrong, then you would start your prep by reviewing quadratics concepts. After this first practice test, you should not take any more practice tests for 2 – 4 weeks, while you are reviewing concepts. Give yourself some time to learn a chunk of concepts and practice them on questions. Then, start doing 1 practice test every weekend. Remember to analyze the results of each practice test you do and target those weaknesses for the following week, before you do the next practice test. That way you will definitely see improvements every week and it will give you a big confidence and motivation boost.

About Us and Our SAT Math Book

I’m a tutor and founder of Exam Masters Tutoring Service. We’ve been helping many students in the GTA ace the SAT, amongst other exams and subjects, for years. I’ve also been pretty active and helpful to students on reddit’s SAT subreddit page. I’ve personally been writing educational content and questions, as well as, tutoring for the SAT for over 10 years. I don’t want to bore you with my autobiography; you can read more about me on my Amazon Author page and my website if you like.

Since the SAT has been redesigned, we have analyzed all tests released by College Board to death and created an awesome math practice test book. Our team of math specialists and SAT experts researched all covered subject matter. This book is primarily created to give students a realistic experience for the SAT Math test. There are 6 full math practice tests, which are organized as section 3 and section 4 for each test.

Each test in this book contains the most commonly tested concepts based on our analysis of the materials released by College Board, as well as, concepts that we feel have the potential to be tested. We really spent a lot of time going over every question to make sure that it would help you [the student] prepare well for this test and made sure that there were many questions on the most commonly tested concepts.

There are a few questions which may seem really difficult, but for the student who aims for an 800, these types of questions should be expected. For example, most students learn analytic geometry, but have never come across the scenario of how to find the shortest distance between a point and a perpendicular line. Concepts like this have the potential to be tested, so we made sure to include them in our tests. We also delved into rarely tested concepts. For example, in statistics, every student has heard of the quartile, but few have heard of the decile! We even have questions on box-and-whisper plots – when was the last time, anyone has seen one of those?! Yet, these are testable concepts and must-know material for the student that aims for the perfect 800.

You can get our book on amazon (available worldwide): Get Book Here!

 

Using PEMDAS 

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by Intern 

Please Excuse My Dear Aunt Sally is/was what some of us were told in math class to remember the order of operations as PEMDAS (Parenthesis, Exponents, Multiplication and Division, and Addition and Subtraction). However, do we always or sometimes follow PEMDAS? 
We’ve noticed that PEMDAS is not always appropriate in the order of operations. There can be PERMDAS (Parenthesis, Exponent/Root, Multiplication and Divide, and Addition and Subtraction) and BEDMAS (Brackets, Exponents, Divide and Multiply, and Addition and Subtraction. These are additional order of operations that can also be used as guides. To learn or know more tips visit us at http://www.all4onetutoring.com or every Tuesday on IG and Periscope (11:00am EST during the summer).

Using Real-Life Situations in Education

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By intern 

In education, real-life or world situations are important. Teaching and applying real-life situation make content easier to understand and enjoyable. Once a learner is able to connect a real-life situation with prior knowledge, the material is more receptive and understood. 

In the content of math, we’ve found a couple of websites that explore math through real-life situations. 

Real World Math

RealWorldMath.org provides lessons that build on traditional classroom instruction by providing students with real-life or world scenarios that engage them in the application of concepts combined with problem-solving. The lessons are technology based. 

TedEd
The YouTube based learning platform has a series titled “Math in Real Life.”  The “Find and Flip” feature of TedED allows users to easily create customized lesson around any YouTube video. In a video titled “Time is money,” German Nande explains the math behind interest rates, revealing the equation that will allow you to calculate the future value of your money. 

Connecting real-life situations with subject area content is a great way to connect learners’ prior knowledge. This would allow learners to be receptive to material and understand material.  

  

Robots Move from Clubs to Classrooms

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Robots playing a bigger role in STEM education
By:
Lauren Williams
District Administration, November 2014
STEMClassroom Integration

Students in all grade levels have been using robotics in the classroom at Fayette County Schools in Kentucky.
Students in all grade levels have been using robotics in the classroom at Fayette County Schools in Kentucky.
Many districts are charging up their K12 STEM courses with the use of robotics.

At the St. Vrain Valley School District in Colorado, robotics has expanded from after-school clubs to their K12 curriculum.

This was due in part to the new STEM academy that opened at Skyline High School in 2009, says Axel Reitzig, St. Vrain’s STEM coordinator.

“Over the last five years or so, our district really developed a goal to be more STEM-orientated,” says Reitzig. “And with many of our elementary and middle schools feeding into Skyline, we felt like robotics would be something to get our students excited about STEM.”

On top of the curriculum, St. Vrain high school students can join robotics clubs and competition teams. They also can now take a course in which they design and build robots.

One activity, for example, involves a medical simulation in which students use their robots to move through an artificial human intestinal tract, says Reitzig.

The middle schools also use an aquatic robotics program. Students build a robot that can float and move through water using basic materials, such as PVC pipes.

Students then test their robots on an obstacle course at a local pool. In elementary schools, students learn the basics of robotics from video game simulations.

The clear benefits of robotics are increased student engagement and collaboration—but there’s more, Reitzig says.

“To us, building STEM skills means really mastering technology,” he says. “When students are designing and building robots, there’s a lot of trial and error and they’re getting that immediate feedback, helping them piece together the whole picture.”

At Fayette County Schools in Kentucky, robotics has grown from an after-school activity into two middle school electives and elementary-level lessons, says Leanna Prater, the district’s technology resource coordinator.

In middle school science, robots are used in the study of motion. In one lesson, students build a robotic leg and foot that kicks a ball. They measure the distances of the kicks when the ball or power level of the robot is changed.

Fourth graders study geometry and angles with robots that rotate by different degrees.

“Overall, we’ve seen an increased engagement and many of our younger students see the robotic activities as playing—but it’s play with a purpose.” says Prater.

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The women who STEM-ed their way to power

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by Leigh Gallagher @leighgallagher

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IBM CEO Ginni Rometty at the 2013 Fortune Most Powerful Women Summit in Washington, D.C.

The women at the top of the 2014 Fortune Most Powerful Women list have a serious thing for engineering. And physics. And math.

One of my favorite days of the year at Fortune is MPW day, the day the list of Fortune‘s Most Powerful Women in business comes out. It’s a great celebration of women in power, of women in business generally, and of course it’s always great fun to see how the world reacts to the MPW team’s picks—who’s on, who’s off, who jumped to the top of the list, who fell, who’s brand-new. But beyond these highlights, one of the things I love is the general trends you can pick up by pulling the camera back and looking at how the list changes and evolves over the years.

One strong trend the entire MPW team has noticed over the years is the shift in industry makeup of those at the very top of the list. When Fortune first started the list, the top ranks were consistently held by women in creative fields, like advertising, media and publishing. In 1999—the second year Fortune published its MPW list — Carly Fiorina, then CEO of Hewlett-Packard HPQ 2.00% , was the lone woman CEO in the male-dominated tech sector.

Cut to this year’s list: The women at the top of the list run the bluest of blue chip firms, the biggest industrial and technology giants, and some of the largest companies in the Fortune 500. Just look at the companies with their chief executives now represented in the top 10: IBM IBM 0.94% . General Motors GM 1.75% . Pepsi PEP 0.99% . Lockheed Martin LMT 1.13% . DuPont DD 0.58% . Hewlett-Packard. Not one of the top 10 is in retail; not one is in media; not one is in marketing or advertising (not, of course, that there’s anything wrong with those industries, but the size of the companies is typically smaller and they are fields that traditionally have more women at the top).

The shift speaks volumes about how women’s roles have evolved in business and the kinds of milestones women are achieving in corporate America. (In addition to these corporate giants, we now have a woman running the Fed, a woman Secretary of Commerce, a woman at the helm of Time magazine. It would be nice if we could also have a woman pope and a female president of the United States, but at least one of those two things may not be that far away.)

Here’s another lesser-known commonality about the women at the very top of the list: almost all of them majored in seriously hard sciences. Let’s just tick down the list: IBM’s Ginni Rometty majored in computer science and electrical engineering. GM’s Mary Barra got a BS in electrical engineering. DuPont’s Ellen Kullman? Mechanical engineering (“mech e” in engineering shorthand). PepsiCo’s Indra Nooyi got her BS in physics, chemistry and math—not engineering per se, but a hat trick in STEM studies. HP’s Meg Whitman studied math and science then went into economics. A bit lower down on the list, Yahoo YHOO 1.31% CEO Marissa Mayer majored in symbolic systems and got her masters in computer science; Xerox’s XRX 0.54% Ursula Burns has a BS and MS in mechanical engineering. (Former Google executive GOOG 0.91% Megan Smith is not on our list, but the newly-named chief technology officer of the United States has a BS and MS in mechanical engineering.)

One in seven engineers may be female, but engineers represent three of the top five spots on the MPW list. And while engineering may be the trend among the top ranks of the MPW list, plain old math and science is good too: Mondelez’s MDLZ 1.21% Irene Rosenfeld holds a Ph.D. in marketing and statistics, Archer Daniels Midland’s ADM 1.15% Pat Woertz studied accounting, Lockheed’s Marillyn Hewson and Facebook FB 0.47% COO Sheryl Sandberg studied economics.

In fact, of the top 10 Most Powerful Women, only one was anything close to a liberal arts major: Fidelity president Abigail Johnson, who majored in art history at William Smith College. For everyone else, it’s STEM City.

What’s remarkable about this is that these women were choosing these fields of study decades ago. Right now, tech is the engine of our economy—coding is cool, and everyone has their eye on the riches that can come from the next hot tech idea. And even still, we have a paucity of young women and girls in STEM fields. But these women, encouraged by their passion, their talents, and in many cases parents who gave them the confidence to know they could achieve anything they wanted to—pursued their STEM passions of study at a time when it was far more rare, and it propelled each to the top of their fields.

I bring this up because it’s statistically exceptional (see, I can say that, even though I’m an English major) and generally remarkable. But also because I hope as the Most Powerful Women list grows even more and more powerful, and the number of women CEOs of Fortune 500 companies grows and grows and grows—25 now, up from 10 in 2006 and 2 in 2002 and one in 1997 (and she was co-CEO with her husband)— I hope young girls will look at these women as models of power and inspiration—and might emulate their path to success. If that’s the case, we’ll be that much closer to the day when the number of women CEOs on the Fortune 500 is too numerous to count—even for a math major.

“From the MPW Co-chairs” is a daily series where the editors who oversee the Fortune Most Powerful Women brand share their insights about women leaders.