Score High on the SATs and Master Inequalities
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This email is written by Program Officer Jasmine Ngo
We are thrilled to share that our private coaching team has been making great strides in helping students improve their SAT scores. Recently, one of our students was able to boost her SAT score by an impressive 100 points and has expressed interest in continuing sessions with one of our expert private coaches to aim for a score of 1400.
We would like to extend our congratulations to this student for her hard work and dedication. With the guidance of her assigned coach, we are confident that she will be able to achieve her target score in no time.
At Tigerway, we help our students in achieving success on both the current and new Digital SAT. We strive to keep our students up-to-date with our wide collection of resources from our digital library. In addition, we assist students in developing effective strategies for tackling SAT problems and provide individualized support to help each student reach their goals.
Our Online Private Coaching program supports with SAT/ACT, High School Courses (Regular/Ap), and College Admissions Strategy. If you are interested in our program, please contact me, Program Officer Jasmine Ngo, or Coach Larry Cheung. Please give us a call today for a roadmap session on how academic coaching, SAT/ACTs, and college consulting can help you. We currently have a waitlist for private coaching and it will be first come first serve.
Tigerway Team Members, Parents, and Prospective Families,
Like the student above, let’s advance your skills in this math topic: Inequalities
Inequalities is a fundamental topic on the SAT. They are used to show a relationship between two values that are not necessarily equal. You could be tested on your ability to manipulate algebraic expressions, understand the properties of inequalities, and apply them to expressions, graphs, or word problems.
Here is a basic rundown of some properties of inequalities:
If a < b, then -a > -b
If a and b are both positive or both negative and a < b, then 1/a > 1/b
For 0 < a < 1
If 0 < b < 1, then ba < a
a < sqrt(a)
a < 1 < 1/a
If m & n are integers, such that 1 < n < m, then x < x^n < x^m
For expressions, you can combine like terms as if the inequality sign is an equal sign. However, when you are dividing or multiplying by a negative number, you flip the inequality sign. (IMPORTANT)
For graphs, you can treat it like a y = mx + b expression. Draw the line and shade the area that best fits the inequality
It is very easy to make silly mistakes on simple problems like these. Remember to carefully read the problem, write down any relevant equations or inequalities, and check your work to avoid making simple mistakes.
Let's review a real-life SAT question that tests your ability on inequalities!
Make sure to try this question out first before reading my commentary
Let’s break this question down:
We know that W is a positive number and we know that W < W^2 based on the properties I stated above (x < x^n)
Working with W < W^2, we can break this apart as if it was a regular expression:
W^2 - W > 0, Factor out W: W(1 - W) > 0
We can solve this to find the values of W: W > 0 and 1 - W > 0
( -W > -1 —> W < 1)
This means W is 0 < W < 1, W is a fraction
If 0 < W < 1, then any number multiplied by W produces a number smaller than the original number. Therefore, W^2 > W^3, W^3 > W^4, and so on. Statements I and III are correct
For statement II, we are dividing a fraction by 3. In this case, we would Keep, Change, and Flip (multiplying W by 1/3). This makes W > W/3, Statement II is also correct
All statements are correct, C is the answer
Keep this fundamental concept in mind as we progress toward more advanced math topics in the future!
Further resources:
Jack Delehey’s College Confidence Group is a forum-based community where Jack and I answer general questions for parents with college-bound teens.
Tigerway is a proud Founding Member of the National Test Prep Association (NTPA) where the NTPA consistently communicates with the College Board’s SAT Exam Team and ACT Exam to understand the future of academics and standardized testing.
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