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: Rough est. of v2 =
Arrangements - orders - schedules - or lists.
1.4
2
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.

2. What is the formula to determine probability?
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
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.
60%
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

3. What is the name of a line that extends from the center of a circle to the edge of a circle?
60%
S*v2
A radius
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.

4. HIGH: Volume of a cube?
80%
V=s³
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
40%

5. An integer is divisible by 5 if...
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

6. An integer is divisible by 3 if...
(0 -0)
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.

7. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
90 degrees each.
Probability A + Probability B
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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

8. What is the key to dealing with ratio questions?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
3:4:5 5:12:13
Invert the second fraction (reciprocal) and multiply
Find the total - or whole - first - and then set up a Ratio Box.

9. Solve this: v6 * -v6 = ?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
6
(x-y)²

10. HIGH: What is the unfactored version of (x+y)² ?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

11. HIGH: What is the side ratio for a 30:60:90 triangle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
60%
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

12. HIGH: Rough est. of v3 =
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%.
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.
1.7

13. What is the 'distributive law'?
2pr -or- pd
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 6 if it'S divisible by BOTH 2 and 3.
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.

14. Area of a square?
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
Multiply numerator times numerator and denominator times denominator.
Groups - teams - or committees.
S²

15. What number goes on the bottom of a probability fraction?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
1
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.
The total # of possible outcomes.

16. How do you solve a combination?

17. HIGH: To divide powers with the same base...
The value that appears most often in a data set.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
x² -2xy + y²

18. Convert to a percentage: 4/5
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)+
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.
80%
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

19. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
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.

20. In a coordinate system - what is the origin?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Probability A * Probability 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.
(0 -0)

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

22. HIGH: What is the mode?
2r
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.
The value that appears most often in a data set.
Not necessarily. This is a trick question - because x could be either positive or negative.

23. 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)+
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Multiply numerator times numerator and denominator times denominator.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

24. What are 'vertical angles'?
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2r

25. How do you add or subtract fractions?
40%
Find a common denominator and make equivalent fractions. Then add or subtract.
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.

26. What is the sum of any 'big' angle and any 'Small' angle?
80%
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.
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.
180 degrees.

27. List all the prime numbers that are less than 30:
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 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

28. HIGH: Area of a triangle?
V=s³
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
360 degrees
1.7

29. HIGH: What is the factored version of x² + 2xy + y² ?
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.
Probability A * Probability B
(x+y)²
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.

30. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
25%
Probability A * Probability B
2pr -or- pd

31. How do you solve a permutation?
V=s³
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

32. The probability of an event happening and the probability of an event NOT happening must add up to what number?
A triangle in which one of the three interior angles is 90 degrees.
A radius
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. Given event A: A + notA = 1.

33. An integer is divisible by 2 if...
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
6
An integer is divisible by 2 if its units digit is divisible by 2.
Between 0 and 1.

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

35. What are the side ratios for a 30:60:90 triangle?
x² -2xy + y²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x 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.

36. HIGH: What are the percentages for standard deviation?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Favorable Outcomes/Total Possible Outcomes
Order does matter for a permutation - but does not matter for a combination.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

37. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Between 0 and 1.
V=pr²h (This is just the area multiplied by the height)
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.

38. Area of a parallelogram?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Bh
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
The total # of possible outcomes.

39. a² - b² is equal to
(a+b)(a-b)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

40. HIGH: List the two most common side ratios for right triangles
'Big' angles and 'Small' angles.
1
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
3:4:5 5:12:13

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

42. If something is certain to happen - how is the probability of this event expressed mathematically?
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
1/1
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/x^n For example - 6-² = 1/6² = 1/36

43. HIGH: Area of a circle
A=pr²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
V=s³
Not reading the problems carefully enough!

44. What is the 'Third side' rule for triangles?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
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

45. HIGH: How do you calculate the circumference of a circle?
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. 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
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

46. What is a 'Right' angle?
1/x^n For example - 6-² = 1/6² = 1/36
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.
An integer is divisible by 2 if its units digit is divisible by 2.

47. v4 =
2
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.
1.4
180 degrees.

48. What do combination problems usually ask for?
Groups - teams - or committees.
Arrangements - orders - schedules - or lists.
1.4
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

49. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
(x+y)(x-y)
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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

50. Explain how to use a 'Rate Pie'
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
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.
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.
2r