# Exam Resources

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## ax + by + c = 0

A straight line is represented by an equation of the form $$Ax+By+C=0$$.  In this case $$A$$, $$B$$ and $$C$$ are arbitrary constants. $$A$$ and $$B$$ cannot both be $$0$$ and $$x$$ and $$y$$ are variables. Divide the equation by $$B$$ and rearranging the terms yield,$$y=\frac{-A}{B}x+\frac{-C}{B}$$ Substitute $$\frac{-A}{B}=m$$ and $$\frac{-C}{B}=c$$ to get $$y=mx+c$$

## y = mx + c

Linear equations are equations that are of the first order. Linear equations are straight-line equations that have simple variable expressions with terms and without exponents. If we come across an equation with $$x$$ or $$y$$, it means we deal with a straight-line equation. If the slope of a line and $$y$$-intercept are given, we use the slope-intercept formula to find the equation of the line.

## Standard form

The standard form is like the short form of a particular function. There are  different standard forms, like the standard form of an equation, standard form of a polynomial and the standard linear equation. The standard form formula is  used to help in finding the general representation for the different types of notations.

## Application of speed, distance and time

Speed, distance and time problems are interesting because they often describe simple situations which people confuse with the wrong formulas. It is also important that in these types of questions, the objects move at constant or average speeds in speed, distance and time scenarios.

## Angles on points and lines

In geometry, lines are the figures used to make infinite points and can be extended infinitely in both the directions. An angle is formed when the two lines or say ray emerge from each other at any common point.

## How to calculate percentage change

The ratio of the difference in the amount to its starting value multiplied by 100 is the percentage change or the percent change of a quantity. Percentage change is the difference between the old and the new values after subtracting the old from the latest, dividing by the old and multiplying the final result by 100 to show it as a percentage.

## How to order numbers

Ordering numbers is an arrangement of the numbers in a sequence. The sequence of the numbers can be in ascending order or descending order. The ascending order is the arrangement of the numbers or alphabet from smallest values to biggest or greatest. The descending order is the arrangement of the numbers or alphabet from the greatest or biggest values to the smallest.

## How to round according to significant figures

The most significant figure is the left-most digit in a number. For example, the most significant figure in 0.0057 is 5 because 0 in any digit works as a placeholder. If the value of the first non-significant figure is less than 5, the least significant figure remains unchanged. Whereas, if it is greater than 5, then the least significant figure increases by 1.

## How to calculate fractions

A fraction consists of two numbers that are written one above the other and are separated by a horizontal line. The number present above the line, is called the ‘numerator’ whereas the number present below the horizontal line, is the denominator.  A denominator represents the total number of equal parts into which something needs to be divided.

## How to calculate reverse percentages

If the value of percentage increase or decrease is given along with the product's final value, and you need to find the initial value before the percentage increases or decreases at that time, the reverse percentage is used. Or it can be said that the value of some quantity after it has been either increased or decreased by a given percentage. Then, find the value of that quantity before it was increased or decreased, and it will be calculated with the help of reverse percentage.

## Inverse proportions

Inverse proportions describes the relationship where when one thing gets bigger, something else gets smaller. For instance, the alarm of an ambulance becomes louder as it approaches you and calmer as it goes farther away. That means if the distance between you and the ambulance is small, then the sound of the alarm of the ambulance heard will be loud.