Studying for an Exam
sometimes students spend a lot of time studying for an examination, yet when they take the exam, they score poorly. Contrarily, other students may spend less time studying the same material, yet they ended up with good or excellent scores. Why?This could due to multiple reasons.
It could possibly be that the students who spent a lot of time studying, did not grasp most of the material because they were distracted by other issues going on in their lives, such as personal or family problems. It could also be as a result of poor studying habits, text anxiety, insufficient sleep the night before the exam and so on. There is no doubt that a student will go blank even though they might have known 90% of the material the day prior to the exam. When you are tired, the brain literally shuts down and you are unable to recall much of what you have studied.
Every student does not grasp information at the same rate, and neither does everyone benefits equally from certain study techniques. Also, some people are able to concentrate better during a certain time of the day. For example, some individuals are able to grasp more whenever they study at nights, while others retain more during the early morning hours etc. A student has to figure this out by him/herself.
It is very important for a student to know the learning technique that works best for him/her. For example, some people are visual learners so they tend to study better using visual aids. The verbal learners prefer to hear or read information, so tape recorded notes may help. The sensory learners prefer concrete, practical information, and the intuitive learners prefers conceptual, innovative, and theoretical information.
Irrespective of which method works best for a student, the bottom line is, the student needs to ensure that he/she grasp most or all of the information that is needed to score well on the examination. Therefore, he/she needs to test him/herself on all areas after going over the material in detail. This will allow that student to confirm whether or not all areas on the study guide have been thoroughly learned.
There are several resources available out there on other sites on how to study effectively. Most of the tips and suggestions might be a little more in depth.
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Critical Thinking
The idea that thinking can be taught only to gifted students is an ancient misconception that has been disproved by modern research. Thinking can be taught to all students whether gifted or not. If teachers were to make thinking skills a direct objective, this would allow all students to get regular practice in producing and evaluating ideas.
As far as critical thinking is concerned, if you can remember the principle of contradiction, this is really a good way to maintain a critical thinking perspective. The principle of contradiction is based on the reasoning that an idea cannot be both true and false at the same time in the same way. This statement or otherwise principle of contradiction keeps us aware that ideas sometimes directly contradict each other. Thus, we cannot avoid contradiction by merely saying both sides are right. A better or more logical approach is to first consider the evidence and then come to a conclusion as to which view is right. The principle of contradiction can motivates us to excellence in critical thinking.
Twice the difference of X and 2 is equal to 8 minus 2.
What is the number?
Word Problems Can Be Quite of A Challenge to Many Students. However, if You First Learn to Translate The English Expression to The Correct Algebraic Expression/Equation Very Soon You Will Become a Pro
English Phrase Algebraic Expression Equation
The sum of Y and Z Y+Z
The difference of Y and Z Y - Z
The product of Y and Z YxZ
The quotient of Y and Z Y/Z
2 more than Y Y+2
Twice the sum of Y and Z 2(Y + Z)
The sum of twice Y and 5 2Y+ 5
5 decreased by y 5 - y
2 less than Y Y- 2
In the Fraction Z/Y, the numerator is >
the denominator by 2 Z+2/Y
Make the denominator 2 < the numerator Z/Y- 2
Write the Reciprocal of Z/Y Y/Z
Word problems can be less difficult,if you follow these steps when solving for the unknown quantity asked for:
Step1. Let (X) represents the quantity asked for in the problem.
step2. Write expressions, using the variable(X), that represents other unknown quantities in the problem.
Step3. Write an equation, in (X), that describes the situation.
Step4. Solve the equation found in step 3.
Step5. Check the solution in the original words of the problem.
Let's look at this Example:
Twice the sum of a number and 3 is 16. Find the number
Step 1: Let X = the number asked for
Step 2: Twice the sum of X and 3 is 2(X+3)
Step 3: Below is an equation describing the situation:
2(X + 3) = 16
Step 4: Solving the equation, see below:
2(X+3) = 16
2X +6 = 16
Subtract 6 from both sides, you are left with >> 2X = 10
Dividing both sides by 2, you now have >> X = 5
We can now prove that the number is 5 by going back to the original problem:
Twice the sum of a number and 3 is 16 > > > > 2(5 + 3) = 2 (8) = 16
Now try solving for X in this problem:
You should get 5 for your answer
Learn The Simplest Way to Multiply by Powers of 10
Examples:
200x10=220 0 simply by adding one extra zero
220 x 100= 220 00 simply by adding two extra zeros
220 x 1000 = 220 000 simply by adding three extra zeros
When Dividing by the power of 10 simply think of the decimal point being behind the last number to your right. Now you are going to remove it and take it one position to the left.
Examples:
220/10 = 22.0 simply by moving that imaginary decimal point from behind the last zero
and move it one position to the left
220/100 = 2.20 simply by moving that imaginary decimal two places to the left
Having Problem With Mathematics in General?
One important approach you may want to take...it's very critical or important to your success!
Rule # 1
Always practice solving maths problem repeatedly until you feel you have gotten a clear understanding of those maths you had problem initially understanding. One rule of thumb>>> for each hour you spend in lecture, you should spend at least 3 - 4 times that amount of time practicing those problems you were taught in lecture. For example ...say you have math lecture on Monday and you spend 1hr. 20 mins in lecture. You should spend at least 4 hrs. practicing those same or similar math problems that same day whenever you get home or wherever you choose to study. Set aside this amount of time every day to practice until you are comfortable enough with those math problems. If you have lecture again on Wednesday, do the same....practice for 4 hrs. on Wednesday.
Table 2.1 Tips on Mastering Mathematics
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Table 4.
Understanding basic algebra is the foundation of mathematics.
Therefore, it's very important that you master the basics. As you advanced to higher levels, you will be using these same basic mathematical principles or approaches to solve much more difficult problems.
Table 4.1
Rules To Follow
This is the order that is to be followed when you are solving a problem that involves: brackets, exponents, divisions, multiplications, additions, and subtractions.
First :- solve the expression that is in the innermost brackets or parentheses ( ) and work your way out.
Second :- Simplify all numbers with exponents from left to right, if you have more than one expression with exponents
Third :- Do all the divisions and multiplications proceeding from left to right
Fourth :- Do all additions and subtractions starting from left to right
Example1 : 4 + 2(2+4) = 2 + 7(2)
Correct >> 4 + 12 = 2 + 14 Left side = Right side
Example2 : 3^2 - 2^2 = 5*4 - 5*3
Correct 9 - 4 = 20 - 1 5 L side = R side
I have to repeatedly stress on the importance of mastering the basic principles of mathematics. If you can master the basic foundamentals, I guarantee you will have no problem understanding and mastering all higher level of math.
I highly recommend this Cliffs Quick Review Basic Math and Pre-Algebra text book to anyone who is looking to review the fundamentals of math and pre-algebra fast. It's also an excellent course supplement to pre-algebra and a concise comprehensive reference for arithematic and pre-algebra. It's very helpful and affordable.
Intermediate Algebra
