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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. Explain how to use an 'Average Pie'
80%
Probability A + Probability B
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
x² -2xy + y²

2. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Between 0 and 1.
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)+
1. Given event A: A + notA = 1.

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

4. An integer is divisible by 3 if...
'Big' angles and 'Small' angles.
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.
4 angles are formed. Their sum is 360 degrees
A 90-degree angle.

5. Convert to a percentage: 4/5
Multiply numerator times numerator and denominator times denominator.
2r
80%
S²

6. How do you solve a combination?

7. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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 value that appears most often in a data set.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Invert the second fraction (reciprocal) and multiply

8. What is an 'equilateral' triangle?
Favorable Outcomes/Total Possible Outcomes
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.
Arrangements - orders - schedules - or lists.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

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

10. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
2r
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
90 degrees each.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

11. HIGH: Volume of a cube?
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
V=s³
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%.

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

13. Explain how to divide fractions.
1/x^n For example - 6-² = 1/6² = 1/36
Favorable Outcomes/Total Possible Outcomes
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.

14. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
1/1
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

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

16. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 360 degrees
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.
A 90-degree angle.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

17. List two odd behaviors of exponents
x²-y²
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.
(x+y)²
Order does matter for a permutation - but does not matter for a combination.

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

19. HIGH: how do you calculate the surface area of a rectangular box?
(x+y)(x-y)
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.

20. a² - b² is equal to
Bh
(a+b)(a-b)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.

21. How do you solve a permutation?
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.
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
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.
60%

22. HIGH: How do you multiply and divide square roots?
(x+y)²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A 90-degree angle.

23. What number goes on the bottom of a probability fraction?
Order does matter for a permutation - but does not matter for a combination.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Arrangements - orders - schedules - or lists.
The total # of possible outcomes.

24. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
'Big' angles and 'Small' angles.
2pr -or- pd
90 degrees each.

25. HIGH: What is the unfactored version of x²-y² ?
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.
Arrangements - orders - schedules - or lists.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(x+y)(x-y)

26. HIGH: Describe how to deal with 2 sets of parentheses.
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)+
A=pr²
Arrangements - orders - schedules - or lists.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

27. What'S the most important thing to remember about charts you'll see on the GRE?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
2pr -or- pd
1/1

28. v4 =
2
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.
Arrangements - orders - schedules - or lists.
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%.

29. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
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.
3:4:5 5:12:13
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

30. HIGH: How do you multiply powers with the same base?
1. Given event A: A + notA = 1.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Favorable Outcomes/Total Possible Outcomes
Not reading the problems carefully enough!

31. The three interior angles of a triangle add up to...
A=pr²
2
It will be a great advantage on test day to have your times table memorized from 1 through 15.
180 degrees

32. HIGH: What is the factored version of x² + 2xy + y² ?
Invert the second fraction (reciprocal) and multiply
Probability A + Probability B
An integer is divisible by 5 if its units digit is either 0 or 5.
(x+y)²

33. What is the factored version of x² -2xy + y² ?
(x-y)²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

34. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
A 90-degree angle.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
25%

35. If something is possible but not certain - what is the numeric range of probability of it happening?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
360 degrees
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Between 0 and 1.

36. Area of a parallelogram?
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.
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Bh

37. What is the sum of any 'big' angle and any 'Small' angle?
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.
(0 -0)
180 degrees.
1/1

38. HIGH: To divide powers with the same base...
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1. Given event A: A + notA = 1.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
6

39. How many degrees does a circle contain?
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.
360 degrees
The value that appears most often in a data set.
Between 0 and 1.

40. HIGH: What are the percentages for standard deviation?
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.
4 angles are formed. Their sum is 360 degrees
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% |

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

42. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
(x-y)²
Invert the second fraction (reciprocal) and multiply
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

43. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
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
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'.
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.

44. What is the 'Third side' rule for triangles?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
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.
Bh

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

46. On the GRE - should you ever assume that diagrams are truthful?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A * Probability B
Find a common denominator and make equivalent fractions. Then add or subtract.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

47. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
4 angles are formed. Their sum is 360 degrees
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A radius

48. Explain how to solve for 7/¼
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.
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.
V=pr²h (This is just the area multiplied by the height)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

49. 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.
(x-y)²
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.
S*v2

50. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?