Test your basic knowledge |

GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. HIGH: what is the side ratio for a Right Isosceles triangle?
180 degrees
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

2. HIGH: Explain the process to solve '56 is what percent of 80?'

3. HIGH: Rough est. of v2 =
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
(x+y)(x-y)
2r
1.4

4. Area of a square?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
An integer is divisible by 2 if its units digit is divisible by 2.
90 degrees each.
S²

5. Explain how to calculate an average (arithmetic mean)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given
Length of an Arc = (n/360)(2pr) - where 'n' equals the central angle (the angle formed by the two edge radii of the arc). For example: if n=60 - then n/360 = 1/6 - which means the arc formed by the 60-degree central angle will be 1/6 of the circle'S

6. HIGH: Rough est. of v1 =
1
The # falling in the center of an ordered data set
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Invert the second fraction (reciprocal) and multiply

7. HIGH: Area of a circle
(0 -0)
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A=pr²
An integer is divisible by 3 if the sum of its digits is divisible by 3. For example - adding the digits of the number 2 -145 (2+1+4+5) = 12 - which is divisible by 3.

8. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
By Plugging In an actual value for the variable(s). This will be quicker - more accurate - you'll avoid built-in traps - and you can use the calculator. When Plugging In - use simple numbers but avoid 1 and 0.
Always read the answer choices first. Try to eliminate choices by ballparking or estimating. But watch out for 'Trap' answers that look temptingly correct at first glance.

9. HIGH: What is 'absolute value' - and how is it represented?

10. HIGH: How do you calculate the length of an arc?

11. For a bell curve - what three terms might be used to describe the number in the middle?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
An integer is divisible by 4 if its last two digits form a number that'S divisible by 4. For example - 712 is divisible by 4 because its last two digits (12) is divisible by 4.
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The average - mean - median - or mode.

12. HIGH: What is the unfactored version of (x-y)² ?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
x² -2xy + y²

13. What is the name of a line that extends from the center of a circle to the edge of a circle?
A radius
1
(x+y)²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

14. HIGH: Define the 'Third side' rule for triangles

15. How do you solve a permutation?
'Big' angles and 'Small' angles.
The length of any one side of a triangle must be less than the sum of the other two sides - and greater than the difference between the other two sides.
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.
1. Figure out how many slots you have (i.e. there are 3 winning positions in a race - 1st - 2nd - and 3rd) 2. Write down the number of possible options for each slot (i.e. 5 runners in the race - so 5 options for the 1st slot - 4 options for the 2nd

16. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
The value that appears most often in a data set.
1.7
Percentage Change = Difference/Original * 100
Probability A + Probability B

17. HIGH: What is the factored version of (x+y)(x-y) ?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x²-y²
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

18. HIGH: List the two most common side ratios for right triangles
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
3:4:5 5:12:13
1. Given event A: A + notA = 1.

19. What degree angle is a line?
A line is a 180-degree angle.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

20. The three exterior angles of a triangle add up to...
360 degrees
V75 = v253 = 5v3 - and v27 = v93 = 3v3. So we have 5v3/3v3. The v3 in the top and bottom of the fraction cancel - leaving 5/3.
Find the total - or whole - first - and then set up a Ratio Box.
A median is the middle value of a set of numbers. For an odd number of values - it'S simply the middle number. For an even number of values - take the average of the center two values.

21. HIGH: Area of a triangle?
1/x^n For example - 6-² = 1/6² = 1/36
Length of an Arc = (n/360)(2pr) - where 'n' equals the central angle (the angle formed by the two edge radii of the arc). For example: if n=60 - then n/360 = 1/6 - which means the arc formed by the 60-degree central angle will be 1/6 of the circle'S
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

22. Explain the special properties of zero.
Zero is even. It is an integer. It is neither positive nor negative. Zero multiplied by any other number = zero. You cannot divide by zero.
Example: 1 < x < 10
Find a common denominator and make equivalent fractions. Then add or subtract.
Absolute value is a number'S distance away from zero on the number line. It is always positive - regardless of whether the number is positive or negative. It is represented with | |. For example - |-5| = 5 - and |5| = 5.

23. Explain the difference between handling a permutation versus a combination.
x² -2xy + y²
PEMDAS (Please Excuse My Dear Aunt Sally): P = Parentheses. Solve anything inside of parentheses first. E = Exponents. Solve these second. MD = Multiplication - Division. From left to right - do all multiplication and division during one step through
If order matters - then you have a permutation -- do NOT divide. If order does NOT matter - then you have a combination -- divide by the factorial of the number of available slots.
The factorial of a number is that number times every positive whole number smaller than that number - down to 1. Example: 6! means the factorial of 6 - which = 65432*1 = 720.

24. What is a 'Right' triangle?
Not necessarily. This is a trick question - because x could be either positive or negative.
A triangle in which one of the three interior angles is 90 degrees.
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
This is similar to an Average Pie - and can be used for some story problems. Draw a circle. Top half holds the Distance or other Amount. Bottom left holds Time. Bottom right holds Rate. Rate * Time = Amount

25. An integer is divisible by 9 if...
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(x-y)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
An integer is divisible by 9 if the sum of its digits is divisible by 9.

26. HIGH: How do you calculate the circumference of a circle?
1.7
x² + 2xy + y²
A 90-degree angle.
2pr -or- pd

27. HIGH: Describe how to deal with 2 sets of parentheses.
90 degrees each.
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+
Calculate and add the areas of all of 6 its sides. Example: for a rectangle with dimensions 2 x 3 x 4 - there will be 2 sides each - for each combination of these dimensions. That is - 2 each of 2x3 - 2 each of 3x4 - and 2 each of 4x2.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

28. What are the side ratios for a 30:60:90 triangle?
An integer is divisible by 5 if its units digit is either 0 or 5.
The value that appears most often in a data set.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Between 0 and 1.

29. An integer is divisible by 8 if...

30. Explain how to solve for 7/¼
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The range is the difference between the biggest and smallest numbers in the set. Example: for the set {2 -6 -13 -3 -15 -4 -9} the smallest number is 2 - largest is 15 - so the range is 15-2=13.
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

31. Probability Formula
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Favorable Outcomes/Total Possible Outcomes
Invert the second fraction (reciprocal) and multiply

32. An integer is divisible by 3 if...
Find a common denominator and make equivalent fractions. Then add or subtract.
The range is the difference between the biggest and smallest numbers in the set. Example: for the set {2 -6 -13 -3 -15 -4 -9} the smallest number is 2 - largest is 15 - so the range is 15-2=13.
An integer is divisible by 3 if the sum of its digits is divisible by 3. For example - adding the digits of the number 2 -145 (2+1+4+5) = 12 - which is divisible by 3.
Find the total - or whole - first - and then set up a Ratio Box.

33. What is the 'Third side' rule for triangles?
60%
Not reading the problems carefully enough!
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The length of any one side of a triangle must be less than the sum of the other two sides - and greater than the difference between the other two sides.

34. If something is possible but not certain - what is the numeric range of probability of it happening?
Groups - teams - or committees.
V=pr²h (This is just the area multiplied by the height)
1. Factored: x² - y² Unfactored: (x+y)(x-y) 2. Factored: (x+y)² Unfactored: x² + 2xy + y² 3. Factored: (x-y)² Unfactored: x² - 2xy + y²
Between 0 and 1.

35. What is the equation for a group problem?
360 degrees
1. Factored: x² - y² Unfactored: (x+y)(x-y) 2. Factored: (x+y)² Unfactored: x² + 2xy + y² 3. Factored: (x-y)² Unfactored: x² - 2xy + y²
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group
(x+y)²

36. HIGH: how do you calculate the surface area of a rectangular box?
If order matters - then you have a permutation -- do NOT divide. If order does NOT matter - then you have a combination -- divide by the factorial of the number of available slots.
6
Probability A * Probability B
Calculate and add the areas of all of 6 its sides. Example: for a rectangle with dimensions 2 x 3 x 4 - there will be 2 sides each - for each combination of these dimensions. That is - 2 each of 2x3 - 2 each of 3x4 - and 2 each of 4x2.

37. What do combination problems usually ask for?
Groups - teams - or committees.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

38. The three interior angles of a triangle add up to...
The range is the difference between the biggest and smallest numbers in the set. Example: for the set {2 -6 -13 -3 -15 -4 -9} the smallest number is 2 - largest is 15 - so the range is 15-2=13.
S²
180 degrees
Probability A + Probability B

39. An integer is divisible by 4 if...

40. HIGH: Volume of a cylinder?
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.
V=pr²h (This is just the area multiplied by the height)
The equation must be set equal to zero. If during the test one appears that'S not - before you can solve it you must first manipulate it so it is equal to zero.
A(b+c) = ab + ac a(b-c) = ab - ac - For example - 12(66) + 12(24) is the same as 12(66+24) - or 12(90) = 1 -080.

41. HIGH: What is the factored version of x² + 2xy + y² ?
Always read the answer choices first. Try to eliminate choices by ballparking or estimating. But watch out for 'Trap' answers that look temptingly correct at first glance.
(x+y)²
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
Between 0 and 1.

42. HIGH: Volume of a cube?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
V=s³
Example: 1 < x < 10
180 degrees

43. What is the factored version of x² -2xy + y² ?
6
(0 -0)
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(x-y)²

44. How do you add or subtract fractions?
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1. Figure out how many slots you have (i.e. there are 3 winning positions in a race - 1st - 2nd - and 3rd) 2. Write down the number of possible options for each slot (i.e. 5 runners in the race - so 5 options for the 1st slot - 4 options for the 2nd
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+
Find a common denominator and make equivalent fractions. Then add or subtract.

45. If x² = 144 - does v144 = x?
360 degrees
A(b+c) = ab + ac a(b-c) = ab - ac - For example - 12(66) + 12(24) is the same as 12(66+24) - or 12(90) = 1 -080.
Not necessarily. This is a trick question - because x could be either positive or negative.
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.

46. Convert to a percentage: 3/5
1. Factored: x² - y² Unfactored: (x+y)(x-y) 2. Factored: (x+y)² Unfactored: x² + 2xy + y² 3. Factored: (x-y)² Unfactored: x² - 2xy + y²
Between 0 and 1.
60%
1

47. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Favorable Outcomes/Total Possible Outcomes
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2
1. Given event A: A + notA = 1.

48. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
6
Between 0 and 1.
1.4

49. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
1
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
S*v2

50. HIGH: What is the unfactored version of x²-y² ?
90 degrees each.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1. Factored: x² - y² Unfactored: (x+y)(x-y) 2. Factored: (x+y)² Unfactored: x² + 2xy + y² 3. Factored: (x-y)² Unfactored: x² - 2xy + y²
(x+y)(x-y)