Exam Resources

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Prime numbers Topic Icon
Prime numbers

September 14, 2021

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.

ax + by + c = 0 Topic Icon
ax + by + c = 0

September 30, 2021

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 Topic Icon
y = mx + c

September 30, 2021

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.

Inverse functions Topic Icon
Inverse functions

September 30, 2021

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 $$\frac{1}{f\left (x \right )}$$.

Functions Topic Icon

September 30, 2021

A function can be thought of as two sets. Let $$X$$ and $$Y$$ be two sets and $$f$$ be the function from the set $$X$$ to $$Y$ then the function $$f$$ is defined as $$ f:X\rightarrow Y$$. Here, the set $$X$$ is called the domain or the set of inputs and set $$Y$$ is the range or the set of outputs. The function $$f$$ associated with each element is $$x$$ in $$X$$ with one and only element $$y$$ in $$Y$$.

Direct and inverse proportion Topic Icon
Direct and inverse proportion

September 30, 2021

Proportion is a statement that defines two specified ratios are equal to each other. Ratio and proportion are explained using fractions. If a fraction is expressed as $$a: b$$, it is called a  ratio. On the other hand, when two ratios are equal, it is called a proportion.

Geometric sequences Topic Icon
Geometric sequences

September 29, 2021

A sequence in which every term is obtained by multiplying or dividing a particular number with the preceding number is a geometric sequence. For example, the geometric progression, $$5, 10, 15, 20, 25, \cdots$$, has a common ratio of $$5$$.

Harmonic sequences Topic Icon
Harmonic sequences

September 29, 2021

A series of numbers is in harmonic sequence if the reciprocals of all the sequence elements form an arithmetic sequence, which does not contain $$0$$. In a harmonic sequence, any terms in the sequence are considered the harmonic means of its two neighbours.

Linear inequalities Topic Icon
Linear inequalities

September 29, 2021

If in an expression, two expressions or values are written equal, then it is called an equation. For instance, $$3x+4y=12$$. On contrary to this, if an expression shows the relation between the two values with the sign ‘$$<$$’(less than), ‘$$>$$’ (greater than), ‘$$\leq$$’(less than or equal to), ‘$$\geq$$’(greater than or equal to), then it is termed as an inequality.

Standard form Topic Icon
Standard form

September 24, 2021

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. 

How to calculate percentage change Topic Icon
How to calculate percentage change

September 20, 2021

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 Topic Icon
How to order numbers

September 20, 2021

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 Topic Icon
How to round according to significant figures

September 17, 2021

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 Topic Icon
Rational and irrational numbers

September 17, 2021

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 Topic Icon
Order of operations

September 17, 2021

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 Topic Icon
Rounding decimal places

September 17, 2021

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 Topic Icon
Upper and lower bounds

September 17, 2021

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 Topic Icon
How to calculate fractions

September 20, 2021

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 percentages Topic Icon
How to calculate percentages

September 20, 2021

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 Topic Icon
How to calculate reverse percentages

September 20, 2021

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 Topic Icon
Inverse proportions

September 20, 2021

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 Topic Icon
Directed Numbers

September 13, 2021

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.

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