Explore some advanced algebra lessons. Topics include exponential and logarithmic functions, algebra proofs, and 100 tough algebra word problems.
While research shows that knowledge of math facts is important, Boaler said the best way for students to know math facts is by using them regularly and developing understanding of numerical relations. Memorization, speed and test pressure can be damaging, she added. Number sense is critical. How to Understand Math. Math can be a difficult subject, but it is something that everyone is capable of mastering. Math is based on logic and rules that you can study and apply – there isn't any special skill involved. Great problem solvers know the best results come from groups of open-minded people. Your problem-solving team must be willing to get outside of the box and uncomfortable. Ultimately this approach. Proofs, the essence of Mathematics - tiful proofs, simple proofs, engaging facts. Proofs are to mathematics what spelling (or even calligraphy) is to poetry. They’ll challenge you to look at the “problems” a different way and test your logic and problem-solving skills while you’re solving. And if math isn’t your strong suit, take heart—most of these.
Exponential and logarithmic functions
Exponential and logarithm functions
Define, write, and evaluate exponential functions
Define exponential growth and decay
Modeling and graphing exponential growth and decay
Define, write, and evaluate logarithms
Simplify logarithms
Expanding logarithms
Properties of logarithms
Solve exponential and logarithmic functions
Interesting and challenging algebra topics!
Can you solved these very hard 100 algebra word problems?
Algebra proofs
Learn how to prove things by induction
Learn how to prove the Pythagorean theorem
Learn how to prove the quadratic formula
Prove that there is no rational number whose square is 2
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When we say 'Percent' we are really saying 'per 100'
One percent (1%) means 1 per 100.
1% of this line is shaded green: it is very small isn't it?
| 25% means 25 per 100 (25% of this box is green) |
Examples:
100% means all. Example: 100% of 80 is 100100 × 80 = 80 |
50% means half. |
5% means 5/100ths. Example: 5% of 80 is 5100 × 80 = 4 |
Using Percent
Use the slider and try some different numbers
(What is 40% of 80? What is 10% of 200? What is 90% of 10?)
Because 'Percent' means 'per 100' think:
So 75% really means 75100
And 100% is 100100, or exactly 1 (100% of any number is just the number, unchanged)
And 200% is 200100, or exactly 2 (200% of any number is twice the number)
Math Problem Solving Questions
A Percent can also be expressed as a Decimal or aFraction
|
Read more about this at Decimals, Fractions and Percentages.
Some Worked Examples
Example: Calculate 25% of 80
25% = 25100
And 25100 × 80 = 20
So 25% of 80 is 20
Example: 15% of 200 apples are bad. How many apples are bad?
15% = 15100
| And 15100 × 200 | = 15 × 200100 |
| = 15 × 2 | |
| = 30 apples |
30 apples are bad
Example: if only 10 of the 200 apples are bad, what percent is that?
As a fraction, 10200 = 0.05
As a percentage it is: 10200 x 100 = 5%
5% of those apples are bad
Example: A Skateboard is reduced 25% in price in a sale.
The old price was $120.
Find the new price.
Example Of Problem Solving Skills
First, find 25% of $120:
25% = 25100
And 25100 × $120 = $30
25% of $120 is $30
So the reduction is $30
Take the reduction from the original price
$120 − $30 = $90
The Price of the Skateboard in the sale is $90
Calculation Trick
This little rule can make some calculations easier:
x% of y = y% of x
Example: 8% of 50
8% of 50 is the same as 50% of 8
And 50% of 8 is 4
So 8% of 50 is also 4
The Word
Percent vs Percentage
My Dictionary says 'Percentage' is the 'result obtained by multiplying a quantity by a percent'. So 10 percent of 50 apples is 5 apples: the 5 apples is the percentage.
But in practice people use both words the same way.