The use of ( )

What is the use of a bracket?
4 (x + 3)
4 (x + 3) (x + 3)
4 (x + 3)squared

When can you open out a bracket and when is it not allowed?

What is the differences in the following?
log 4
log 4x
log 4x + 3
log (4x + 3)
log (4x + 3)squared

Simple Algebraic Expressions

What will you say to students who do the following in an attempt to help them?


Example 1
1.14 x + 3.42 = 2x - 1
2x - 1.14x - 1 - 3.42 = 0

Example 2
1.338x - 0.699 = 0.778x + 2.334
1.338x + 0.778x = 2.334 - 0.699

Exponents

Below show some exponent approaches. This time the power will be in brackets i.e. ( )

Example 1
5 (2x - 1) = 6 (x + 3)
Multiply left by 6
Multiply right by 5
30 (2x - 1) = 30 (x + 3)
2x -1 = x + 3

Example 2
5 (2x - 1) = 6 (x +3)
log (5) 2x - 1 = log (6) x + 3
log 2x - 1 / log 5 = log x + 3 / log 6
12x - 6 = 5x + 15

Example 3
5 (2x - 1) = 6 (x +3)
log (5) 2x - 1 = log (6) x + 3
2x - 1 log 5 = x + 3 log 6
2x - 1 log 5 - x + 3 log 6 = 0
log [5] (2x - 1) + log [6] (-x + 3) = 0
log 10x - 5 + 9 - x = 0
log 9x + 9 = 0
log 9x = 9

Evaluation of simple logs

Examine the following statements. Remember that the base will be represented in (). Help these students.

Example 1
log (4) x = 12
log x = log 12
log 4
log x = 1.08 * 0.6
log x = 0.65
x = 4.5

Example 2
log (4) x = 12
log 4 = 12
x = 12 / log 4
x = 20

Example 3
log (4) x = 12
log (4) x = log 12

Example 4
log (4) x = 12
log (4)12 = x

Example 5
log (8) 32 = x
x = 8/32
x = = 1/4

The [] is used since subscript and superscript are not allowed.
2 [3] = 8 can also be expressed as log [2] 8 = 3


Is this correct?
0.035 [x] = 2.74 Find x?

1. Re-express as a log which is log [0.035] 2.74 = x
2. Draw line
3. log 2.74__ = x

log 0.035

Or is this correct?

0.035 [x] = 2.74 Find x?

1. Log both sides
   log 0.035 [x] = log 2.74
2. Re-express to remove power

x log 0.035 = log 2.74

1. Make x the subject of the equation

x = log 2.74 / log 0.035

Derivative

What really is first derivative?
Is first derivative any thing to do with differentation? Explain.
What really is the use of firat derivative in maths?
How can I understand first derivative in relation to the world?

Limits

What is Limits

Why is limits needed in maths

What is the purpose of limits with respect to graphs

Why is limits used in the delta process