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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: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
x² + 2xy + y²

2. HIGH: Volume of a cube?
The average - mean - median - or mode.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
V=s³

3. Probability Formula
Favorable Outcomes/Total Possible Outcomes
x² + 2xy + y²
Order does matter for a permutation - but does not matter for a combination.
Probability A * Probability B

4. Define a factorial of a number - and how it is written.
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.
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.
Favorable Outcomes/Total Possible Outcomes
Bh

5. What is the equation for a group problem?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
Percentage Change = Difference/Original * 100
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

6. Explain how to calculate an average (arithmetic mean)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
6
90 degrees each.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

7. What is an 'equilateral' triangle?
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
6
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

8. What causes 80% of errors on the math section of the GRE?
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Not reading the problems carefully enough!
V=pr²h (This is just the area multiplied by the height)

9. Explain how to divide fractions.
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
4 angles are formed. Their sum is 360 degrees
A triangle in which one of the three interior angles is 90 degrees.

10. An integer is divisible by 2 if...
1.4
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
An integer is divisible by 2 if its units digit is divisible by 2.
1. Given event A: A + notA = 1.

11. Explain how to use a 'Rate Pie'
1/1
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

12. HIGH: How do you calculate the circumference of a circle?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1. Figure out how many slots you have (i.e. you'Re supposed to bring home 3 different types of ice cream) 2. Write down the number of possible options for each slot (i.e. 5 flavors of ice cream at the store - 5 options for the 1st slot - 4 options fo
2pr -or- pd
25%

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

14. Explain the difference between handling a permutation versus a combination.
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 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.
360 degrees

15. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Not necessarily. This is a trick question - because x could be either positive or negative.
360 degrees

16. HIGH: Volume of a cylinder?
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
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.
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.
V=pr²h (This is just the area multiplied by the height)

17. How do you solve a combination?

18. HIGH: Describe how to deal with 2 sets of parentheses.
S*v2
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1/x^n For example - 6-² = 1/6² = 1/36
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)+

19. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
3:4:5 5:12:13
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%.
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.
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

20. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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

21. What is the 'distributive law'?
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.
360 degrees
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
(0 -0)

22. HIGH: What is a 'Right isosceles' triangle?
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.
2pr -or- pd
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

23. HIGH: How do you multiply powers with the same base?
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Probability A * Probability B

24. How do you calculate the probability of two events in a row? (Probability of A and B)
Percentage Change = Difference/Original * 100
Probability A * Probability B
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.
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'.

25. In a coordinate system - what is the origin?
(0 -0)
1/x^n For example - 6-² = 1/6² = 1/36
A radius
Find the total - or whole - first - and then set up a Ratio Box.

26. HIGH: What is the side ratio for a 30:60:90 triangle?
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

27. For a bell curve - what three terms might be used to describe the number in the middle?
(0 -0)
The average - mean - median - or mode.
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.
A line is a 180-degree angle.

28. HIGH: What is the formula for the diagonal of any square?
S*v2
An integer is divisible by 2 if its units digit is divisible by 2.
1. Given event A: A + notA = 1.
A=pr²

29. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
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
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

30. An integer is divisible by 6 if...

31. What is a 'Right' triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A triangle in which one of the three interior angles is 90 degrees.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

32. HIGH: What is the median?
The # falling in the center of an ordered data set
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
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.
1. Given event A: A + notA = 1.

33. On the GRE - should you ever assume that diagrams are truthful?
Favorable Outcomes/Total Possible Outcomes
Percentage Change = Difference/Original * 100
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

34. What is the formula to determine probability?
The value that appears most often in a data set.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Probability A + Probability B

35. HIGH: What is the Pythagorean theorem?

36. What is the key to dealing with ratio questions?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.
V=s³

37. HIGH: What is the unfactored version of x²-y² ?
x² + 2xy + y²
(x+y)(x-y)
S*v2
40%

38. What do combination problems usually ask for?
Groups - teams - or committees.
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.
6
1. Given event A: A + notA = 1.

39. v4 =
2
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

40. What number goes on the bottom of a probability fraction?
25%
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
The total # of possible outcomes.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

41. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
A=pr²
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

42. Area of a square?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
S²
360 degrees

43. HIGH: Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

44. HIGH: What is the mode?
Arrangements - orders - schedules - or lists.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The value that appears most often in a data set.
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

45. Convert to a percentage: 2/5
180 degrees
40%
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
Probability A * Probability B

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

47. HIGH: How much of your times table should you know - for the GRE?
1.4
Probability A + Probability B
It will be a great advantage on test day to have your times table memorized from 1 through 15.
25%

48. What do permutation problems often ask for?
The value that appears most often in a data set.
Bh
Arrangements - orders - schedules - or lists.
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.

49. What is the 'Third side' rule for triangles?
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.
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.

50. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
180 degrees
60%
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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