Preparing for the GRE Math section can be daunting, especially if you are not a math enthusiast or have not studied math in a long time. However, with the proper preparation and practice, you can master the GRE Math section and achieve your target score. Memorising essential GRE Math formulas are a great way to build your confidence and improve your chances of success. Doing so, you will be able to solve problems more efficiently and accurately, saving you valuable time during the exam. In this blog, we'll discuss the importance of memorising GRE Math formulas, provide you with a comprehensive list of critical formulas, and offer tips on effectively integrating them into your test prep.

## Why Should You Memorize GRE Math Formulas?

Memorising GRE Math formulas is essential to perform well in the GRE Math section. Here are some reasons why:

- Time-saving: The GRE Math section is time-limited, and you need to answer a large number of questions in a short amount of time. Memorising formulas will save you time by allowing you to recall the formulas you need to solve a particular problem quickly.
- Accuracy: Memorizing formulas will ensure that you solve problems accurately. You may make mistakes if you need to learn the formula, costing you valuable points.
- Confidence: Knowing the formulas will give you more confidence during the exam. You will be able to tackle problems more quickly and feel more comfortable taking the exam.
- Focus: If you have to derive formulas during the exam, you must focus on the derivation process, which can be time-consuming and distracting. You can focus on solving the problem if you already know the formulas.
- Recall: By memorising formulas, you can recall them quickly when needed, even if you last studied math a while ago.

## Key Concepts of GRE Math

The GRE Math section tests a test taker's understanding of basic mathematical concepts and their ability to apply them to problem-solving. Here are some of the critical concepts of GRE Math that test-takers should understand:

- Arithmetic: Arithmetic involves the basic mathematical operations of addition, subtraction, multiplication, and division. Test-takers should be comfortable with these operations and understand how to apply them to solve problems.
- Algebra: Algebra involves using variables and symbols to represent numbers and equations. Test-takers should be familiar with algebraic expressions, equations, and functions and understand how to solve for variables.
- Geometry: Geometry involves the study of shapes and their properties. Test-takers should be comfortable calculating the area, perimeter, volume, and surface area of basic geometric shapes like squares, triangles, circles, and cubes.
- Statistics: Statistics involves analysing data and making predictions based on that data. Test-takers should be comfortable with statistical concepts like mean, median, mode, and standard deviation.
- Word problems: Many GRE Math questions are presented as word problems. Test-takers should be comfortable reading and interpreting word problems and understand how to apply mathematical concepts to real-world situations.
- Number properties: Test-takers should be familiar with basic number properties, such as even and odd numbers, prime numbers, and integers.
- Probability: Probability involves calculating the likelihood of an event occurring. Test-takers should be comfortable with basic probability concepts and understand how to calculate probabilities using fractions and percentages.
- Sequences and series: Test-takers should understand how to calculate the sum of a sequence or series of numbers and basic arithmetic and geometric sequences.
- Ratios and proportions: Ratios and proportions involve comparing two or more quantities. Test-takers should understand how to simplify and solve problems involving ratios and proportions.
- Exponents and radicals: Test-takers should understand the rules of exponents and how to simplify expressions involving exponents and radicals.

## Some important Formulas

- Quadratic Formula: This formula helps to solve quadratic equations. For a quadratic equation ax² + bx + c = 0, the quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a.

- Distance Formula: This formula calculates the distance between two points in a coordinate plane.

The formula is √((x2 - x1)² + (y2 - y1)²).

- Slope Formula: This formula is used to calculate the slope of a line.

The formula is (y2 - y1) / (x2 - x1).

- Midpoint Formula: This formula calculates the midpoint of a line segment. The formula is ((x1 + x2) / 2, (y1 + y2) / 2).
- Circle Formula: This formula is used to calculate the area and circumference of a circle. The area formula is πr², and the circumference formula is 2πr.
- Pythagorean Theorem: This theorem calculates the length of the sides of a right triangle.

The formula is a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

- Perimeter Formula: This formula calculates the perimeter of a polygon. The formula is the sum of the lengths of all sides.
- Volume Formula: This formula is used to calculate the volume of a three-dimensional object.

The formula varies depending on the object, but for a cube, it is V = s³, where s is the length of a side.

- Surface Area Formula: This formula is used to calculate the surface area of a three-dimensional object.

The formula varies depending on the object, but for a cube, it is SA = 6s².

- Per cent Change Formula calculates the per cent change between two values. The formula is ((new value - old value) / old value) x 100%.
- Simple Interest Formula: This formula calculates the interest earned on loan. The formula is I = Prt, where P is the principal, r is the interest rate, and t is the period.
- Compound Interest Formula: This formula calculates the interest earned on loan with compound interest. The formula is A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the period.
- Probability Formula: This formula calculates the probability of an event occurring. The formula is P(A) = (number of favourable outcomes) / (total number of outcomes).
- Mean Formula: This formula calculates a set of the mean (average) numbers. The formula is (sum of all values) / (number of values).
- Median Formula: This formula calculates a set of numbers' median (middle value). The median is the middle value if the set has an odd number of values. If the set has an even number of values, the median is the average of the two middle values.
- Mode Formula: This formula calculates the mode (most common value) of a set of numbers.
- Range Formula: This formula calculates the range (difference between the largest and smallest values) of a set of numbers. The formula is the most significant value - the smallest value.
- Standard Deviation Formula: This formula measures the spread of a set of numbers. The formula is √((sum of (each value - mean)²) / (number of values)).
- Geometric Mean Formula: This formula calculates the geometric mean of a set of numbers. The formula is the nth root of (product of all values), where n is the number of values.
- Arithmetic Sequence Formula: This formula calculates the nth term of an arithmetic sequence. The formula is a(n) = a(1) + (n-1)d, where a(1) is the first term, n is the term number, and d is a common difference.
- Geometric Sequence Formula: This formula calculates the nth term of a geometric sequence. The formula is a(n) = a(1) x r^(n-1), where a(1) is the first term, n is the term number, and r is the standard ratio.
- The Sum of Arithmetic Sequence Formula: This formula calculates the sum of the first n terms of an arithmetic sequence. The formula is (n/2)(a(1) + a(n)), where a(1) is the first term, a(n) is the nth term, and n is the number of terms.
- The Sum of Geometric Sequence Formula: This formula calculates the sum of the first n terms of a geometric sequence. The formula is (a(1) x (1 - r^n)) / (1 - r), where a(1) is the first term, r is the standard ratio, and n is the number of terms.
- Factorial Formula: This formula calculates the factorial of a number.

The formula is n! = n x (n-1) x (n-2) x ... x 2 x 1.

- Combination Formula: This formula calculates the number of ways to choose r items from n items.

The formula is nCr = n! / (r! x (n-r)!).

- Permutation Formula: This formula calculates the number of ways to arrange r items from a set of n items.

The formula is nPr = n! / (n-r)!.

- Logarithm Formula: This formula is used to calculate the logarithm of a number.

The formula is log(b)x = y if b^y = x, where b is the base, x is the number, and y is the exponent.

- Exponential Formula: This formula calculates the value of an exponential function. The formula is f(x) = a^x, where a is the base and x is the exponent.
- Law of Sines Formula: This formula calculates the length of a side or the measure of an angle in a non-right triangle.

The formula is (sin(A) / a) = (sin(B) / b) = (sin(C) / c), where A, B, and C are the angles, and a, b, and c are the sides.

- Law of Cosines Formula: This formula calculates the length of a side or the measure of an angle in a non-right triangle.

The formula is c² = a² + b² - 2ab cos(C), where a and b are the sides,

C is the angle opposite side c, and c is the side opposite angle C.

- Quadratic Formula: This formula is used to solve quadratic equations of the form ax² + bx + c = 0.

The formula is x = (-b ± sqrt(b² - 4ac)) / 2a, where a, b, and c are constants.

- Distance Formula: This formula calculates the distance between two points in a plane.

The formula is d = sqrt((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.

- Midpoint Formula: This formula calculates the midpoint of a line segment.

The formula is ((x1 + x2) / 2, (y1 + y2) / 2), where (x1, y1) and (x2, y2) are the endpoints of the line segment.

- Slope Formula: This formula is used to calculate the slope of a line.

The formula is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

- Equation of a Line Formula: This formula is used to find the equation of a line.

The formula is y = mx + b, where m is the slope of the line, and b is the y-intercept.

- Equation of a Circle Formula: This formula is used to find the equation of a circle. The formula is (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle, and r is the radius.
- Equation of an Ellipse Formula: This formula is used to find the equation of an ellipse.

The formula is (x - h)² / a² + (y - k)² / b² = 1, where (h, k) is the centre of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.

- Equation of a Hyperbola Formula: This formula is used to find the equation of a hyperbola.

The formula is (x - h)² / a² - (y - k)² / b² = 1, where (h, k) is the centre of the hyperbola, a is the distance from the centre to a vertex, and b is the distance from the centre to a co-vertex.

- Area of a Triangle Formula: This formula is used to find the area of a triangle.

The formula is A = 1/2bh, where b is the triangle's base, and h is the height.

- Area of a Circle Formula: This formula is used to find the area of a circle.

The formula is A = πr², where r is the circle's radius.

- Area of a Sector Formula: This formula is used to find the area of a sector of a circle. The formula is A = (θ/360)πr², where θ is the central angle of the sector.
- Surface Area of a Sphere Formula: This formula is used to find the surface area of a sphere.

The formula is 4πr², where r is the radius of the sphere.

- The volume of a Sphere Formula: This formula is used to find the volume of a sphere.

The formula is (4/3)πr³, where r is the sphere's radius.