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

2. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
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.
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.

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

4. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
(0 -0)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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'.

5. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
Between 0 and 1.
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
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.

6. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
The value that appears most often in a data set.
V=pr²h (This is just the area multiplied by the height)

7. HIGH: What is the Pythagorean theorem?

8. How many degrees does a circle contain?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
360 degrees
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Probability A + Probability B

9. Simplify this: v32
(a+b)(a-b)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

10. What is a 'Right' triangle?
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.
A triangle in which one of the three interior angles is 90 degrees.
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.
A 90-degree angle.

11. What is the formula to determine probability?
Favorable Outcomes/Total Possible Outcomes
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Arrangements - orders - schedules - or lists.

12. Define 'proportionate' values
4 angles are formed. Their sum is 360 degrees
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Probability A + Probability B
x² + 2xy + y²

13. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
(x+y)²
1/1
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.

14. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
(x-y)²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
V=s³

15. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

16. HIGH: What is the formula for the diagonal of any square?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S*v2
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.

17. HIGH: how do you calculate the surface area of a rectangular box?
The # falling in the center of an ordered data set
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.
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.
2pr -or- pd

18. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
Between 0 and 1.
4 angles are formed. Their sum is 360 degrees

19. HIGH: Describe how to deal with 2 sets of parentheses.
The value that appears most often in a data set.
The average - mean - median - or mode.
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
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)+

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

21. Convert to a percentage: 1/4
25%
An integer is divisible by 9 if the sum of its digits is divisible by 9.
x²-y²
Bh

22. Explain how to divide fractions.
An integer is divisible by 5 if its units digit is either 0 or 5.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
(x-y)²
Find a common denominator and make equivalent fractions. Then add or subtract.

23. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
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
V=s³
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

24. What do permutation problems often ask for?
3:4:5 5:12:13
(x+y)²
Arrangements - orders - schedules - or lists.
Not reading the problems carefully enough!

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

26. What is the key to dealing with ratio questions?
S*v2
Find the total - or whole - first - and then set up a Ratio Box.
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
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.

27. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
A radius
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.
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

28. What number goes on the bottom of a probability fraction?
V=s³
x² -2xy + y²
x² + 2xy + y²
The total # of possible outcomes.

29. What is an 'equilateral' triangle?
2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Example: 1 < x < 10
V=s³

30. HIGH: Volume of a cube?
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
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.
V=s³
Between 0 and 1.

31. HIGH: What is the unfactored version of (x-y)² ?
(x-y)²
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
A=pr²
x² -2xy + y²

32. What is the equation for a group problem?
1.7
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
60%

33. Convert to a percentage: 2/5
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
40%
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.
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

34. Define the range of a set of numbers.
Order does matter for a permutation - but does not matter for a combination.
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.
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.
1/1

35. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Not reading the problems carefully enough!
Invert the second fraction (reciprocal) and multiply
V=pr²h (This is just the area multiplied by the height)

36. Define the mode of a set of numbers.
Between 0 and 1.
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.
Invert the second fraction (reciprocal) and multiply
An integer is divisible by 5 if its units digit is either 0 or 5.

37. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
(0 -0)
80%
Find the total - or whole - first - and then set up a Ratio Box.

38. Explain how to use an 'Average Pie'
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

39. In a coordinate system - identify the quadrants and describe their location.
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.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

40. What'S the most important thing to remember about charts you'll see on the GRE?
A line is a 180-degree angle.
(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.
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.

41. Explain the difference between handling a permutation versus a combination.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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 total # of possible outcomes.

42. Convert to a percentage: 4/5
S²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
80%
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

43. An integer is divisible by 9 if...
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

44. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

45. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
Percentage Change = Difference/Original * 100
1/x^n For example - 6-² = 1/6² = 1/36

46. An integer is divisible by 5 if...
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
V=s³
An integer is divisible by 5 if its units digit is either 0 or 5.

47. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Probability A * Probability B
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

48. How do you calculate the probability of two events in a row? (Probability of A and B)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
V=pr²h (This is just the area multiplied by the height)
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.
Probability A * Probability B

49. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

50. Probability Formula
1. Given event A: A + notA = 1.
Favorable Outcomes/Total Possible Outcomes
A=pr²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.