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. Diameter of a circle?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2r
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.
360 degrees

2. What is the factored version of x² -2xy + y² ?
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/x^n For example - 6-² = 1/6² = 1/36
A 90-degree angle.
(x-y)²

3. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
x² -2xy + y²
Arrangements - orders - schedules - or lists.
The # falling in the center of an ordered data set

4. Probability Formula
Favorable Outcomes/Total Possible Outcomes
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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

5. How do you multiply fractions?
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.
Multiply numerator times numerator and denominator times denominator.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.

6. Does order matter for a permutation? How about for a combination?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
180 degrees.
Order does matter for a permutation - but does not matter for a combination.
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.

7. HIGH: How do you calculate the circumference of a circle?
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.
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2pr -or- pd

8. HIGH: Rough est. of v3 =
The # falling in the center of an ordered data set
1.7
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.
1.4

9. What number goes on the bottom of a probability fraction?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A radius
An integer is divisible by 2 if its units digit is divisible by 2.
The total # of possible outcomes.

10. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

11. How do you divide fractions?
1/x^n For example - 6-² = 1/6² = 1/36
360 degrees
Invert the second fraction (reciprocal) and multiply
180 degrees

12. HIGH: What is the equation of a line?

13. An integer is divisible by 9 if...
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
A triangle in which one of the three interior angles is 90 degrees.

14. What are the side ratios for a 30:60:90 triangle?
90 degrees each.
60%
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Bh

15. HIGH: What is the mode?
Multiply numerator times numerator and denominator times denominator.
A radius
The value that appears most often in a data set.
Not reading the problems carefully enough!

16. Explain the difference between a digit and a number.

17. How do you solve a combination?

18. On the GRE - should you ever assume that diagrams are truthful?
80%
(x+y)²
Multiply numerator times numerator and denominator times denominator.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

19. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
Percentage Change = Difference/Original * 100
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

20. Convert to a percentage: 3/5
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1. Given event A: A + notA = 1.
60%

21. HIGH: what is the side ratio for a Right Isosceles triangle?
60%
Probability A * Probability B
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S*v2

22. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Probability A + Probability B

23. If x² = 144 - does v144 = x?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

24. Explain how to use an 'Average Pie'
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

25. What'S one way to avoid mistakes on algebra questions in the GRE?

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

27. What causes 80% of errors on the math section of the GRE?
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
Not reading the problems carefully enough!
S*v2
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

28. If something is certain to happen - how is the probability of this event expressed mathematically?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1/1
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

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

30. Convert to a percentage: 1/4
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
25%
(a+b)(a-b)
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.

31. How is a range expressed with inequalities?
Example: 1 < x < 10
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
The average - mean - median - or mode.
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.

32. The three exterior angles of a triangle add up to...
S²
360 degrees
Find a common denominator and make equivalent fractions. Then add or subtract.
80%

33. What is the 'Third side' rule for triangles?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
(x+y)²
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. List two odd behaviors of exponents
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

35. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
First - translate into clear math: 56 = x/100(80) ('56 is x one-hundredths of 80') = 56 = 80x/100 = 56 = 4x/5 Divide both sides by 4/5 (multiply by 5/4) 70 = x - so 70%.

36. HIGH: Describe how to deal with 2 sets of parentheses.
Not reading the problems carefully enough!
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
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)+

37. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Percentage Change = Difference/Original * 100
A radius

38. HIGH: Volume of a cylinder?
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
V=pr²h (This is just the area multiplied by the height)
Probability A * Probability B
The value that appears most often in a data set.

39. HIGH: What is a 'Right isosceles' triangle?
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.
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.
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
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

40. HIGH: What is the Pythagorean theorem?

41. Define a factorial of a number - and how it is written.
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.
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.
1/1
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.

42. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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.
90 degrees each.
The total # of possible outcomes.
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.

43. HIGH: Area of a triangle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
'Big' angles and 'Small' angles.

44. What is the sum of any 'big' angle and any 'Small' angle?
Multiply each numerator by the other fraction'S denominator. Example: 3/7 and 7/12. Multiply 312 = 36 - and 77 = 49. If you completed the full calculation - you'd also cross-multiply the denominators - but you don'T have to in order to compare values
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
180 degrees.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

45. How do you calculate the probability of two events in a row? (Probability of A and B)
(x-y)²
A radius
Probability A * Probability B
6

46. For a bell curve - what three terms might be used to describe the number in the middle?
3:4:5 5:12:13
x² + 2xy + y²
The average - mean - median - or mode.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

47. HIGH: What is the unfactored version of x²-y² ?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(x+y)(x-y)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

48. HIGH: What is the side ratio for a 30:60:90 triangle?
Multiply numerator times numerator and denominator times denominator.
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
180 degrees
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

49. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
A 90-degree angle.
An integer is divisible by 2 if its units digit is divisible by 2.
Find a common denominator and make equivalent fractions. Then add or subtract.

50. What should you do BEFORE you start to solve a GRE math problem?