Do You Know These Basic Mathematical Equations and Formulas?

By: Jacqueline Samaroo
Image: Shutterstock

About This Quiz

Mathematical skill has always been seen as a reasonable measure of critical thinking ability. If you've always been the Math Whiz in class, do you think you can complete all the equations and formulae in our quiz? Have a go, but - No Calculators Allowed!

The terms “exponent,” “index” (plural: indices) and “power” all apply to the number to which the base is raised. In typing, the symbol ^ is often used to show one number is raised to the other. For example, 2^5 means 2 raised to the 5th power.

In adding fractions with different denominators, it is necessary to find a number which both denominators can divide into without leaving a remainder. Typically, the lowest common multiple is used but an easy step is to just use the number you get by multiplying one denominator by the other.

Logarithms may be thought of as the opposite or the reverse of exponents. In fact, in logarithms, we are trying to find the power to which we would have to raise the base to get a particular answer. For example, “the logarithm of 9 with base 3 is 2” which is like the reverse of saying “3 raised to the 2nd power is 9."

Many persons use the mnemonic SOH-CAH-TOA to remember the formulae for the sine, cosine and tangent of angles in a right-angled triangle. In this case, SOH gives Sin ɵ = Opposite ÷ Hypotenuse.

In factorials, the symbol ! tells you that you start with the given number and multiply by descending numbers right down to 1. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

In fractions, the denominator is sometimes referred to as the fraction family. When adding or subtracting fractions of different denominators or fraction families, the rule is to change them to the same denominator using a common multiple.

Around 300 BC, Euclid, a Greek mathematician, used the term “power” in reference to squaring a line. Another famous Greek mathematician, Archimedes, is credited with being the first to prove one of the laws of exponents.

Regardless of the base being used, the logarithm of 1 is always zero. That can be restated as saying any number raised to the power of zero is 1.

The definition of a rectangle means that squares are also rectangles (with all sides equal). To differentiate between them, the term “oblong” is sometimes used for rectangles which are not squares.

In fractions, the number above the line is the numerator and the lower number is the denominator. The line between them is called the fraction bar. When adding two numbers with the same denominator, we simply add the numerators and keep the denominator.

The use of brackets in mathematics is rarely seen before the 1700s. Before this, mathematicians used a vinculum or overline to show grouping of terms.

Since we generally use numbers to base 10, logarithm to base ten is often called common logarithm. It is quite usual to omit writing the 10 as a subscript when calculating in the common logarithm.

The powers of 2 and 3 are given special names. In the case of a power of 2, we say “square,” whereas for a power of 3, we say “cube,” For example, 7^2 is read a 7 squared and 4^3 is read as 4 cubed.

The term “hypotenuse” always refers to the longest side of a right-angled triangle which is always across from the right angle. The terms “adjacent side” and “opposite side” can refer to either of the other two sides depending on which of the angles we are working with.

The letter U between the two sets means they are to be joined (without repeats). The U stands for “union” and is always written as capital but not with a stem.

The height used in this formula for the area of a triangle is sometimes more clearly called the “perpendicular height” or the “altitude.” This is because the line used must meet the base at right angles.

The logarithm of any number to its own base is always 1. It is just another way of saying that any number raised to the power of 1 results in the same number. For example, 5^1 = 5.

Exponents may be whole numbers, fractions, positive or negative. Apart from being real numbers, exponents may also be complex numbers with a real and an imaginary part.

The basic explanation of fractions is the separation of a whole into equal parts. The bottom number, or denominator, shows how many equal parts the whole has been divided into. The top number, or numerator, shows how many of those parts we are considering.

The SOHCAHTOA mnemonic for recalling how to calculate the trigonometrical ratios is often read just as it sounds. Other ways to remember it is by saying “Some Old Hippie Caught Another Hippie Tripping On Acid” or “Studying Our Homework Can Always Help To Obtain Achievement.”

The Greek letter π (pi) is used to represent the ratio of a circle’s circumference to its diameter. The number (3.14 to 2 decimal places) is the same for all circles, no matter how large or small they are.

Multiplication of fractions with different denominators is done by simply multiplying numerator by numerator and denominator by denominator. Many persons find it to be one of the easiest fraction operations to perform correctly.

Pascal’s triangle can be used to easily find the coefficients when expanding binomials (two terms added or subtracted in a pair of brackets and raised to a power). 17th century French mathematician Blaise Pascal did not invent it, however, as it was in use well before his time in several regions around the world.

When calculating with exponents, the root of a number becomes a fractional power. For example, √2 is the same as 2^½.

Logarithms have several practical applications. One example is the popularly used Richter scale for measuring earthquake strength which is based on a logarithmic calculation.

By definition, a square is a rectangle with all sides being the same length. It can also be defined as a rhombus with all the angles being the same size.

In general, the term “quadratics” is used when the greatest power of any term being considered is 2. Common examples are quadratic functions and quadratic equations.

Addition of fractions of the same denominator calls for simply adding the numerators. Some people make the common mistake of adding the denominators, as well.

The Greek letter theta (ɵ) is perhaps the most commonly used for denoting an unknown (or generalized) angle. However, any letter or symbol can be used.

Brackets in the case of multiplication and division, mean the exponent applies to both numbers inside the brackets. So, both the a and b are raised to the power of m. Without the brackets, only b would be raised to m and then multiplied by a.

The perimeter of any shape is the distance measured around it. If a square and another quadrilateral (four-sided shape) have the same perimeter, the square will always have the bigger area.

Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down). The first fraction remains unchanged.

This formula is known as either the Pythagorean theorem or Pythagoras’s theorem. It applies to the sides of a right-angled triangle and may be stated as “the square of the hypotenuse is equal to the sum of the squares of the other two sides.”

Fractions come in many forms. There are simple fractions, proper fractions and mixed fractions (a.k.a. mixed numerals).

It is a common mistake to assume that the power can be ignored (or cancelled out) if it is the same in the numerator and the denominator. This is not so and will result in an incorrect answer.

Every whole number can be written as a fraction with a denominator of 1. This is so since division by 1 leaves the number unchanged.

The logarithmic spiral or growth spiral is an example of logarithms which is often seen in nature. It can be found in the pattern made by the shell of the nautilus, a type of marine mollusk.

While the perimeter of any shape is the distance measured around it, the perimeter of a circle gets a special name – its circumference. π (pi) is the relationship which exists between every circle’s circumference and its diameter (or radius).

Two types of fractions are proper fractions and improper fractions. The distinction between them lies in the fact that proper fractions always have a numerator which is less than the denominator (ignoring any negative signs). In improper fractions the numerator is greater.

Volume is a measure of the capacity of a three-dimensional shape or the amount of space it occupies. As it is the multiplication of three lengths, the answer is always given as cubed.

The difference of two squares, as shown in this item, results in a pattern many students of mathematics can easily identify. It can be recalled as “sum times difference.”

A complex fraction has a numerator, denominator or both which is also a fraction or a mixed numeral. Brackets or a longer than usual fraction bar can be used to differentiate the numerator from the denominator.

Quite often, it is easiest to calculate logarithms that are not in base 10 if you first perform what is called “change of base,” as shown in this item. This makes it much easier to do logarithmic calculations on a typical scientific calculator.

A cube is a type of cuboid with all its sides being the same length. Thus, the formula length x width x height for the volume of a cuboid becomes length x length x length (or length ^3) when working with a cube.

Mixed fractions (or mixed numerals) are written with a whole number part and a proper fraction part. The two are added to obtain the value of the entire number. The plus sign, however, is never written.

Just as with exponents, the root sign is applied to each term inside the bracket, but only in cases where the terms are being multiplied or one is dividing the other. The rule does not apply in addition or subtraction.

The term “logarithm” is traced back to 17th century Europe. Its name is derived from the modern Latin word “logarithmus” which itself comes from the Greek words “logos” meaning “reckoning” or “ratio” and “arithmos” meaning “number."

Although a cylinder is not a prism, its volume is found in the same way. That is by multiplying the area of one end face by the distance between the end faces.

Since every whole number is essentially a fraction with 1 in the denominator, 1 is often called the invisible denominator. It allows you to write the reciprocal of a whole number as a fraction with 1 in the numerator. Zero, however, has no reciprocal.

The square root of negative one is called the imaginary unit, i. An imaginary number has a real part multiplied by i.

About Zoo

Our goal at is to keep you entertained in this crazy life we all live.

We want you to look inward and explore new and interesting things about yourself. We want you to look outward and marvel at the world around you. We want you to laugh at past memories that helped shape the person you’ve become. We want to dream with you about all your future holds. Our hope is our quizzes and articles inspire you to do just that.

Life is a zoo! Embrace it on

Explore More Quizzes