Just to update on the latest blog posts at http://mathtuition88.blogspot.com. I am trying to bring up the page rank for my Blogspot site, hence blogging there for the time being.

This book Why Before How: Singapore Math Computation Strategies, Grades 1-6 is surprisingly very popular. As an Amazon Affiliate, one of the most popular book I promote on my site is actually this book. It is a Singapore Math book that focuses on the “Why” before the “How”, which is very important as nowadays questions are designed to be solved using thinking, not just mechanical procedures.

## Tips to becoming an Oracle DBA

Here are some tips on becoming an Oracle database administrator. It will be useful for students interested in computer science and IT. 🙂

Tips to becoming an Oracle DBA

The Oracle database is the most sophisticated and complex database today. Knowing enough to become a database administrator is not an easy task. Oracle dataset administration is only recommended for information technology, information systems and computer science professionals who have undergone the relevant Oracle training.

The Oracle DBA’s position and salary attracts many young graduates, but few know exactly what it takes before they can earn this hallowed title in any company. An Oracle DBA is typically a senior-level manager in the smaller companies, mid-level in much bigger corporations, and their annual salaries can go as high as \$ 100,000-250,000.

But the money does come with its load of responsibility – data management for the whole company, with the risk of grounding all operations with just a slight glitch. The first thing any aspiring DBA will have to remember is that database administration is just like any other profession; there’s no shortcut leading to the top.

Preparation, preparation and more preparation!

You can’t wake up one morning and decide to enroll for a DBA course, more so an Oracle DBA course. Majority of the successful DBAs in Oracle began to learn after obtaining their Bachelor’s and even Master’s degree in an IT related field. This is a career move that will require thought and plenty of preparation beforehand, and a lot of dedication after.

Oracle DBA requires 24/7 unfailing commitment, with long hours (since most of your work begins after everyone has checked out for the day) and on-call duty during holidays and other important occasions. That’s not all, as a DBA, you must keep yourself updated with every new change that comes in the Oracle and computer systems technology or you risk obsolescence.

You can now see that the Oracle DBA does earn every one of the dollars he’s paid, right?

Below is a list of qualities you should have in order to succeed in the pursuit of a career in Oracle Database Administration:

• Communication skills

An Oracle DBA will constantly be in communication with end-users and managers to determine their data needs and act accordingly. College-level communication skills will be a must, with outstanding abilities to communicate through any medium and interpret information provided.

It helps a lot if you have a college degree in business administration from a proper graduate training institution. This equips you with the foundational understanding of business systems and processes, which is required in order to best perform your job as an Oracle Applications DBA.

• Foundational DBA skills

Prior to becoming an Oracle DBA, which is more demanding and complex, it’s recommended that you practice database administration at lower levels. Oracle has designed levels of learning for beginners, and practicing as you pursue OCA and OCM certification will be very helpful. This is because an Oracle DBA should understand other related database technologies as well e.g. Oracle Application Server and Java – J2EE, JDeveloper, Apache.

• College classes

In preparation for a career in DBA, Operations Research is a class you want to take in your CS or IT course. This involves the development of complex decision rules and their application to real-life datasets. The back-end data store is usually Oracle, and it provides a great platform to prepare for the job setting.

Author Bio

Tom Foster is an expert in database administration. For more information on WordPress, SQL, Oracle and other database management and administration, contact the database professionals by visiting their website.

## Challenging O Level Trigonometry Question (A Maths)

Given that $\sin x+\sin y=a$ and $\cos x+\cos y=a$, where $a\neq 0$, express $\sin x+\cos x$ in terms of $a$.

This is a rather challenging question, since there are many options to start. Which formula(s) should we use? Factor formula? R-formula? Give it a try first if you want to have a challenge.

Solution:

It turns out we can write:

$\sin y=a-\sin x$

#### $\cos y=a-\cos x$

Then, use $\sin^2 y+\cos ^2 y=1$

$(a-\sin x)^2+(a-\cos x)^2=1$

Expanding,

$a^2-2a\sin x+\sin^2 x+a^2-2a\cos x+\cos^2 x=1$

Rearranging,

$2a^2-2a(\sin x+\cos x)+1=1$

$2a(a-(\sin x+\cos x))=0$

Since $a\neq 0$, we have $a-(\sin x+\cos x)=0$.

Thus, $\boxed{\sin x+\cos x=a}$.

#### Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately, there’s Schaum’s. This all-in-one-package includes more than 600 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 20 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems–it’s just like having your own virtual tutor! You’ll find everything you need to build confidence, skills, and knowledge for the highest score possible.

More than 40 million students have trusted Schaum’s to help them succeed in the classroom and on exams. Schaum’s is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum’s Outline gives you

• 618 fully solved problems to reinforce knowledge
• Concise explanations of all trigonometry concepts
• Updates that reflect the latest course scope and sequences, with coverage of periodic functions and curve graphing.

Fully compatible with your classroom text, Schaum’s highlights all the important facts you need to know. Use Schaum’s to shorten your study time–and get your best test scores!

Schaum’s Outlines–Problem Solved.

## 3D Trigonometry Maths Tuition

Solution:

(a) Draw a line to form a small right-angled triangle next to the angle $18^\circ$

Then, you will see that

$\angle ACD=90^\circ-18^\circ=72^\circ$ (vert opp. angles)

$\angle BAC=180^\circ-72^\circ=108^\circ$ (supplementary angles in trapezium)

By sine rule,

$\displaystyle \frac{\sin\angle ABC}{30}=\frac{\sin 108^\circ}{40.9}$

$\sin\angle ABC=0.697596$

$\angle ABC=44.23^\circ$

$\angle ACB=180^\circ-44.23^\circ-108^\circ=27.77^\circ=27.8^\circ$ (1 d.p.)

(b) By Sine Rule,

$\displaystyle\frac{AB}{\sin\angle ACB}=\frac{30}{\sin 44.23^\circ}$

$AB=\frac{30}{\sin 44.23^\circ}\times\sin 27.77^\circ=20.04=20.0 m$ (shown)

(c)

$\angle BCD=\angle ACD-\angle ACB=72^\circ-27.77^\circ=44.23^\circ$

By Cosine Rule,

$BD^2=40.9^2+50^2-2(40.9)(50)\cos 44.23^\circ=1242.139$

$BD=35.24=35.2 m$

(d)

$\displaystyle\frac{\sin\angle BDC}{40.9}=\frac{\sin 44.23^\circ}{35.24}$

$\sin\angle BDC=0.80957$

$\angle BDC=54.05^\circ$

angle of depression = $90^\circ-54.05^\circ=35.95^\circ=36.0^\circ$ (1 d.p.)

(e)

Let X be the point where the man is at the shortest distance from D. Draw a right-angle triangle XDC.

$\displaystyle\cos 72^\circ=\frac{XC}{50}$

$XC=50\cos 72^\circ=15.5 m$

## Rectangle Maths Tuition

Solution:

(a) $\angle SPC=\angle SRQ=90^\circ$

$\angle PCS=\angle SQR$ (given)

Thus $\triangle PCS$ is similar to $\triangle RQS$ (AAA)

(b)(I)

$\angle KRQ=90^\circ /2=45^\circ$ (KR bisects $\angle QRS$)

Thus $\angle QKR=180^\circ-90^\circ-45^\circ=45^\circ$

Hence $\triangle KQR$ is an isosceles triangle.

So $KQ=QR=PS=\frac{1}{2}PQ$

Hence,

$\begin{array}{rcl}PK&=&PQ-KQ\\ &=&PQ-\frac{1}{2}PQ\\ &=&\frac{1}{2}PQ\\ &=&\frac{1}{2}(2PS)\\ &=&PS \end{array}$

(shown)

(ii) By similar triangles,

$\displaystyle\frac{PC}{PS}=\frac{RQ}{RS}=\frac{PS}{PQ}=\frac{PS}{2PS}=\frac{1}{2}$

Thus $PC=\frac{1}{2}PS=\frac{1}{2} PK$

Hence

$\begin{array}{rcl}CK&=&PK-PC\\ &=&PK-\frac{1}{2}PK\\ &=&\frac{1}{2}PK\\ &=&PC \end{array}$

(shown)

## Tips on attempting Geometrical Proof questions (E Maths Tuition)

Tips on attempting Geometrical Proof questions (O Levels E Maths/A Maths)

1) Draw extended lines and additional lines. (using pencil)

Drawing extended lines, especially parallel lines, will enable you to see alternate angles much easier (look for the “Z” shape). Also, some of the more challenging questions can only be solved if you draw an extra line.

2) Use pencil to draw lines, not pen

Many students draw lines with pen on the diagram. If there is any error, it will be hard to remove it.

3) Rotate the page.

Sometimes, rotating the page around will give you a fresh impression of the question. This may help you “see” the way to answer the question.

4) Do not assume angles are right angles, or lines are straight, or lines are parallel unless the question says so, or you have proved it.

For a rigorous proof, we are not allowed to assume anything unless the question explicitly says so. Often, exam setters may set a trap regarding this, making the angle look like a right angle when it is not.

5) Look at the marks of the question

If it is a 1 mark question, look for a short way to solve the problem. If the method is too long, you may be on the wrong track.

6) Be familiar with the basic theorems

The basic theorems are your tools to solve the question! Being familiar with them will help you a lot in solving the problems.

Hope it helps! And all the best for your journey in learning Geometry! Hope you have fun.

“There is no royal road to Geometry.” – Euclid

## Reason for Maths Tuition

My take is that Maths tuition should not be forced. The child must be willing to go for Maths tuition in the first place, in order for Maths tuition to have any benefit. Also, the tuition must not add any additional stress to the student, as school is stressful enough. Rather Maths tuition should reduce the student’s stress by clearing his/her doubts and improving his/her confidence and interest in the subject. There is a quote “One important key to success is self-confidence. An important key to self-confidence is preparation.“. Tuition is one way to help the child with preparation.

## Parallelogram Maths Tuition: Solution

Solution:

(a) We have $\angle APQ=\angle ARQ$ (opp. angles of parallelogram)

$AP=RQ$ (opp. sides of parallelogram)

$AR=PQ$ (opp. sides of parallelogram)

Thus, $\triangle APQ\equiv\triangle QRA$ (SAS)

Similarly, $\triangle ABC\equiv\triangle CDA$ (SAS)

$\triangle CHQ\equiv\triangle QKC$ (SAS)

Thus, $\begin{array}{rcl}\text{area of BPHC}&=&\triangle APQ-\triangle ABC-\triangle CHQ\\ &=&\triangle QRA-\triangle CDA-\triangle QKC\\ &=& \text{area of DCKR} \end{array}$

(proved)

(b)

$\angle ACD=\angle HCQ$ (vert. opp. angles)

$\angle ADC=\angle CHQ$ (alt. angles)

$\angle DAC=\angle CQH$ (alt. angles)

Thus, $\triangle ADC$ is similar to $\triangle QHC$ (AAA)

Hence, $\displaystyle\frac{AC}{DC}=\frac{QC}{HC}$

Thus, $AC\cdot HC=DC\cdot QC$

(proved)

## Tuition That We May Have To Believe In

This insightful article makes a really good read.

Quotes from the article:

To be honest, the amount to be learnt at each level of education is constantly increasing, and tuition could just help you get that edge over others. After all, it was meant to be supplementary in nature.

The toughest part at the end of the day however, is probably this: getting the right tutor.

This commentary, “Tuition That We May Have To Believe In”, is a reply to a previous article on tuition by Howard Chiu (Mr.), “Tuition We Don’t Have To Believe In” (Read).

I must say Howard’s article had me on his side for a moment. He appealed to me emotively. Nothing like a mental picture of some kid attending hours and hours of tuition immediately after school when he could well be enjoying himself thoroughly with… an iPhone or iPad (I highly doubt kids these days still indulge their time at playgrounds). But the second time I read his article, I silenced the part of my brain which still prays the best for children, so do pardon me if I sound a tad too pragmatic at times.

The overarching assertion that Howard projects his points from is that there is “huge over consumption of this good”. Firstly, private tutoring…

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