# Exam Resources

68 notes returned

## Prime numbers

A prime number is defined as any natural number with only two factors that are 1 and itself. The number 2 is an example of a prime number. This is because the only way of denoting 2 as a product is 2 x 1 or 1 x2. Also, 2 is the only even prime number.

## Length of a line

A line segment is a section of the straight line that connects two points. Unlike a line, it does not extend in both directions of infinity.  To calculate the length, use the distance formula between the two points.

## Equation of a line through points

A straight line is an infinite one-dimensional shape and does not contain any amplitude. A straight line can be a combination of endless points connected to each side to some extent. A straight line doesn't have any curve in it.

## 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.

## Gradient of a straight line

The gradient is the measure of the angle of a point of a straight line. A gradient can go upward, which means from left to right, or downward, which means from right to left. The gradient can be positive as well as negative, and it does not need to be a whole number.

## Co-ordinates and scale

The coordinates of two numbers or the Cartesian co-ordinates are located at a specific point on a grid known as the coordinate plane. The co-ordinates can be two numbers, or a number and a letter.

## Inverse functions

Let $$X$$ and $$Y$$ be two sets, and $$f$$ be a one-to-one function defined by $$f:{X} \rightarrow Y$$ with domain $$X$$ and range $$Y$$. Then, $$f^{-1}:{Y} \rightarrow X$$ is called the inverse function. Here, $$f^{-1}\left ( x\right )$$ does not mean $$\frac{1}{f\left (x \right )}$$.

## Graphing inequalities

Graphical representation plays an important role in mathematics as it makes the overall material easy to understand for everyone.  Either they are linear or quadratic, equation or inequalities, they can be shown graphically.

## Linear equations

A linear equation can be written in different ways. An equation containing two variables x and y is said to form a linear equation in two variables. The highest degree of both the variables x and y in the equation is 1.

A quadratic equation is a polynomial equation of degree of order 2. ax^2 + bx + c is the general form of a quadratic polynomial. If we equate this polynomial to zero, we get a quadratic equation. The general form of a quadratic equation is ax^2 + bx + c = 0.

## Simultaneous equations 1

A simultaneous equation is where two algebraic expressions (typically in terms of x and y) intersect with each other. When you solve for a simultaneous equation, you are solving for both x and y. And they are co-ordinates.

In algebra, a polynomial consisting of variables and coefficients having the highest degree value of 2 is termed as a quadratic polynomial. The general form of a quadratic polynomial is ax^2+bx+c, where a, b and c are real numbers.

## Factorising algebraic expressions 1

Factorising means the breaking or the decomposition of any entity into the product of other entities. Factorising is the process of finding the factors. It is like dividing an expression into a multiplication of relevant expressions. It is the reverse of expanding.

## How to expand brackets 1

A bracket is a symbol which helps us maintain the difference between two terms. Whenever we have to differ one mathematical term from another mathematical term, we use a bracket. For easy understanding, consider a bracket as a wall, a wall parting two rooms or houses.

## Rearranging formulae 2

Rearranging complicated formulae can be considered the peak of algebra skills. If you manipulate an equation and make your required variable the subject before adding the numeric values, solving for variables becomes easy.

## Rearranging formulae 1

The ability to rearrange formulae or rewrite them is an important skill. There are four main things in rearranging a formula: Add or subtract the same quantity to both sides, and multiply or divide both sides by the same quantity.

## Algebraic indices

An index is used to show how many times a number is multiplied by itself. The plural word for index is indices. If some number is raised to some power, then the power it is raised to is the index of that number.

## Algebraic substitution 1

Substitution is the procedure of putting one thing like a number, a letter or symbol in place of other. In simple words, whenever we use numbers at the position of letters, it is called the substitution process.

## Sets and subsets

Set and subset are a collection of elements. Set contains elements, and if some of those elements are contained in another set, then the second set is called the subset of the main set.

## Introduction to sets and subsets

A set is a collection of well defined objects. The objects in a set are called the members or elements of the set, and a certain condition defines their membership. The elements of a set can be anything that satisfies the definition of membership.

## Foreign exchange

Currency exchange is the process of exchanging currency from one currency to another. It is also known as foreign exchange. The value of a currency depends on the market forces related to trade, investment, tourism and geopolitical risks.

## 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.

## Exponential equations

The exponential function is that function that is represented in the form x^{m} where x is base and m is the exponent. The exponential curve depends on the exponential function, and it also depends on the value of m in the expression x^{m}.

## 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.

## Indices

The index is the power or exponent that is raised to a number or a variable. For example, in number 2^4, 4 is the index of 2. The plural form of index is indices.

## Introduction to law of indices

Indices are a convenient tool in mathematics to compactly denote taking power or roots of a number. Taking power is simply a case of repeated multiplication of a number. Whereas taking root is equivalent to a fractional power of the number.

## 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.

## Squares and cubes

The square of a number is multiplying the number by itself. An example of this is 2 x 2. The cube of a number is the number multiplied by itself twice. An example of this is 2 x 2 x 2.

## 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.

## Rational and irrational numbers

A rational number is defined as a number that can be completely represented in the form of a fraction. 1, 0.5, -.12 are all examples of rational numbers. An irrational number is defined as a number that cannot be represented in the form of a fraction. An example of this would be pi.

## Order of operations

Order of operations follows the BEDMAS principle. When there are lots of operators in an equation, you need to start with the Brackets, Exponents and Division first. Then move onto Multiplication, Addition and lastly Subtraction. An example of this would be (2+3) x 5 + 3 - 1.

## Rounding decimal places

The procedure of rounding to a decimal place depends upon the decimal places that need to be rounded off in the first place. Typically, this type of rounding is called Swedish rounding. Rounding helps to make estimations in things like temperature, money and mass.

## Upper and lower bounds

Anything that can be measured has a margin of error. The magnitude of error depends on how precisely it is measured and the accuracy of the measuring tool. Upper bound and lower bounds helps to provide measurement a degree of accuracy.

## 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.

## Recurring decimals

A recurring decimal number are digits that do not end with zero but are repeated at the same periodic interval. A non-recurring decimal number are digits that do not end with zero, and they do not get repeated after any periodic interval.

## How to calculate percentages

The word ‘percentage’ is derived from the Latin phrase ‘per centum’, which means ‘by the hundred’.  Percentages are fractions with a denominator of 100. Putting in another way, it is the relationship between the portion and the whole in which the whole is always valued at 100.

## 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.

## How to solve and apply ratios

The ratio of a set of numbers is a tool used in comparing two or more values. Sometimes we need to compare two quantities of the same type. So, the comparison by division method makes calculation easier than comparing by finding out the difference.

## 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.

## Directed Numbers

Numbers are used in performing calculations by using operators like addition, subtraction, multiplication, division, and so on. The sign, added sometimes right before a number, plays a vital role in the number system. It can change the entire situation in our decision-making.

## Co-ordinates and scales

The coordinates of two numbers or the Cartesian co-ordinates are located at a specific point on a grid known as the coordinate plane. The co-ordinates can be two numbers, or a number and a letter.