Instead, I encourage students to think critically about how formulas are derived. That way, these students are able to have a stronger intuitive sense of the way the math behind the formula works. For instance, say you have a triangle. Many students falter because they always mix up the sides, especially the side that takes the radical sign.
To think of the proportions intuitively, simply remember that, in a triangle, the shortest side is always half the length of the longest side. Therefore, we have an , and a. The middle side will have to be less than , so it will either be , or. As to which one, remember that a triangle is a right triangle.
So, if we use the Pythagorean theorem which you should definitely be able to execute quickly and accurately , then the shortest side squared which is 1 subtracted from the longest side squared is equal to 3 in this case, I just assumed x is equal to 1 so that the shortest side and longest side are 1 and 2, respectively. Using the Pythagorean theorem, we square this number, and get a. Relying on formulas too much can also give us formula blindness. Takeaways Ultimately, the GRE is testing the way you think.
And, trying to memorize a formula is often more difficult than knowing how that formula was derived. In fact, ignoring the information below can seriously hurt your chances of answering a question correctly. Just be sure to apply the formulae often enough that those formulae are engrained!
A positive number is greater than 0, a negative number is less than 0. Parentheses 2. Exponents 3. Prime Numbers A prime number is one that is divisible only by itself and 1. In other words, a positive integer with exactly 2 positive divisors. Memorize all primes below 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59… Factorization If X can be multiplied by Y to get Z, assuming all of these are positive integers, then X and Y are considered factors of Z.
The prime factorization of a number is dividing it into its constituent primes. To find how many factors has, first find its prime factorization:. All of its factors will be of the form.
The GCF of 12 and 30 is 6 — it is the biggest divisor they both share. The easiest way to find the GCF is to take the prime factorization and multiply all of the primes that appear in both numbers.
If two numbers share no primes, the GCF is 1. The least common multiple of two numbers is the smallest positive integer with both numbers as a factor. The LCM of 4 and 6 is 12 — it is the smallest number that has both 4 and 6 in its divisors. To find the LCM of any two numbers, take the prime factorization of each number, find what prime factors appear in both, and multiply one of each of the shared primes and then by all the unshared primes.
The largest possible LCM for any two numbers is one multiplied by the other. Divisibility 3 : sum of digits divisible by 3 4 : the last two digits of number are divisible by 4 5 : the last digit is either a 5 or zero 6 : even number and sum of digits is divisible by 3 8 : if the last three digits are divisible by 8 9: sum of digits is divisible by 9 Fast Fractions Absolute Values The absolute value of a number is its distance from a number line. Most percentage problems break down into identifying the part, the percent, and the whole, one of which will be unknown.
If p percent of x is y, then , so. Ratios Ratios let us compare the proportions of two quantities. If there is a ratio of boys to girls at a school, that means that for every 5 girls, there are 2 boys. So there could be 2 boys and 5 girls, 20 boys and 50 girls, boys and girls, etc. Ratios can also be x:y:z. Roots , because. Note that even though as well, -7 is NOT considered a solution of ; only the positive number counts in this case.
In this case, -7 is known as an extraneous root. However, if you were given the question , the answer would be and. Square roots of negative numbers e. Perfect squares: Numbers with integers as their square roots: 4, 9, 16, etc. For example, to find , you know that and , so must be between 7 and 8. Roots can be added like variables. To solve a system of three equations with three variables, use substitution to reduce the problem to two equations with two variables, and solve from there.
Inequalities: They can be treated like regular equations, with the following exception: multiplying or dividing an inequality by a negative number reverses the sign of the inequality. However, this does not hold for subtracting, multiplying, or dividing. If given a quadratic inequality i.
If two lines intersect, the sum of the resulting four angles equals Polygons A polygon is any figure with three or more sides e. An equilateral triangle has three equal sides. Area: , where r is the radius of the circle Circumference: , where d is the diameter of the circle.
Surface area: 6 s 2 , where s is the length of a side of the cube Volume: s 3 , where s is the length of a side of the cube. We recommend that you print it out, share it, and start a pile of Magoosh eBooks General , Vocabulary , that you can study on the go. Then, test out your skills on GRE Quant questions with answers and explanations. Be sure to let us know you like this resource. Some of his students have even gone on to get near-perfect scores.
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