Calculators

We all have scientific calculators and we all know how to use it. It is indeed simple to use. However, when it comes to specific laws in mathematics, like Algebra, the buttons you press may vary different answers to the right one. So in this article I hope everyone will be more aware and careful!

How to Use a Scientific Calculator for Algebra?

Various functions are provided to understand how to use a scientific calculator for Algebra:
Generally scientific calculators are more featured than standard four or five-function calculator, and this difference is clearly seen in the type of manufacturers and models; however, the main features of scientific calculators are:
scientific notation
Arithmetic including floating Point numbers
logarithmic functions
trigonometric functions
exponential functions
roots can be calculated other than Square root
quick access to constants like P and e

Uses of scientific calculators:
Quick access to mathematical functions is possible with scientific calculators, functions like those related to Trigonometry; the situations involving direct calculations of very large numbers (such as in contexts of astronomical calculations). In schools also the use of scientific calculators is a usual thing, having solved the problems of maths and physics.
An Example can be taken to understand the use of scientific calculators:Q.For example, how would you solve 10 = x^2 + 3*(x ^1) using scientific calculator?
Solution: All the above used operations are present in the scientific calculators which directly calculate the value of ‘x’ solving the algebraic equation:
x ^ 2 + 3* (x ^1) – 10= 0
x = 5 or -2

Try It!

As a follow up from my previous post about Quadratic Equations, try out these questions and test your knowledge!

1.	Solve for y:  y2 - 81= 0 2. Solve for m:   m2 = 7m 3. Solve for x:  x2 - 3x - 10 = 0 4. Solve for y:  2y2 + 4 = 9y

Now try these harder questions! 

6.	Solve for x:     7. Solve for x:     8.    During practice, a softball pitcher throws a ball whose height can be modeled by the equation h = -16t 2  + 24t +1, where h = height in feet and t = time in seconds.  How long does it take for the ball to reach a height of 6 feet?

May the right answers be with you!

Quadratic Equations

What is it?

In elementary algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form

where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation islinear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.^[1]

Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation, and in particular it is a second degree polynomial equation since the greatest power is two.

Quadratic equations can be solved by a process known in American English as factoring and in other varieties of English as factorising, by completing the square, by using thequadratic formula, or by graphing. Solutions to problems equivalent to the quadratic equation were known as early as 2000 BC.

Quadratic Factorisation

The term

${\displaystyle x-r}$

is a factor of the polynomial

${\displaystyle ax^{2}+bx+c}$

if and only if r is a root of the quadratic equation

${\displaystyle ax^{2}+bx+c=0.}$

It follows from the quadratic formula that

${\displaystyle {\begin{aligned}ax^{2}+bx+c&=a\left(x-{\frac {-b+{\sqrt {b^{2}-4ac}}}{2a}}\right)\left(x-{\frac {-b-{\sqrt {b^{2}-4ac}}}{2a}}\right)\\&=a\left(x+{\frac {b-{\sqrt {b^{2}-4ac}}}{2a}}\right)\left(x+{\frac {b+{\sqrt {b^{2}-4ac}}}{2a}}\right).\end{aligned}}}$

In the special case b² = 4ac where the quadratic has only one distinct root (i.e. the discriminant is zero), the quadratic polynomial can be factored as

${\displaystyle ax^{2}+bx+c=a\left(x+{\frac {b}{2a}}\right)^{2}.}$

Histogram

In histograms, the frequency of the data is shown by the area of the bars and not just the height.

Histograms are most commonly used for continuous data.

Histograms often have bars of varying width, i.e. unequal class intervals. This is not a problem as we are dealing with area, not just the height.

The vertical axis of a histogram is labelled frequency density and is calculated by the following formula:

Example:

The ages of people sunbathing on a beach somewhere on a Greek island were recorded and organised into the frequency table below. Draw a histogram of this data.

Ages (x): Frequency (f): Class width: Frequency density:

0 ≤ x < 15 15 15 15/15 = 1

15 ≤ x < 25 28 10 28/10 = 2.8

25 ≤ x < 40 30 15 2

40 ≤ x < 60 42 20 2.1

60 ≤ x < 100 20 40 0.5

All we now need to do is draw this onto graph paper and we have our histogram.

The ages will be on the x-axis (from 0 to 100 on a continuous scale).

Frequency density will be on the y-axis (from 0 to 3).

Cumulative frequency

Cumulative frequency is kind oflike a running total. We add each frequency to the ones before to get an 'at least' total.

These cumulative frequencies ('at least' totals) are plotted against theupper class boundaries to give us a cumulative frequency curve.

The cumulative frequency column is the column you will be expected to add for yourself.

To draw the cumulative frequency curve we simply plot the cumulative frequencies against the upper end of each class interval.

Probability

Problem:	A spinner has 4 equal sectors colored yellow, blue, green and red. What are the chances of landing on blue after spinning the spinner? What are the chances of landing on red?
Solution:	The chances of landing on blue are 1 in 4, or one fourth.
	The chances of landing on red are 1 in 4, or one fourth.

This problem asked us to find some probabilities involving a spinner.  The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. Let's take a look at a slight modification of the problem from the top of the page. Experiment 1:   A spinner has 4 equal sectors colored yellow, blue, green and red. After spinning the spinner, what is the probability of landing on each color? Outcomes:   The possible outcomes of this experiment are yellow, blue, green, and red. Probabilities:   P(yellow)  =  # of ways to land on yellow  =  1 total # of colors  4    P(blue)  =  # of ways to land on blue  =  1 total # of colors  4    P(green)  =  # of ways to land on green  =  1 total # of colors  4    P(red)  =  # of ways to land on red  =  1 total # of colors  4

Formulas

This photo could actually help us memorize the formulas better!

algebra

A study of finding unknowns